source,target
 The orbital solution is eiven in Table 1., The orbital solution is given in Table 1.
 Preliminary solutions included a velocity zero point offset between the, Preliminary solutions included a velocity zero point offset between the
the accretion dise extends up to the tical radius ancl so the asymmetric brightness distribution in the accretion disc we observed can be explained. by the presence of a tically cistorted accretion disc.,the accretion disc extends up to the tidal radius and so the asymmetric brightness distribution in the accretion disc we observed can be explained by the presence of a tidally distorted accretion disc.
 Naravan.AleClintock&Yi(1996).and Naravan.Barret&MeClintock(1997) have proposed an accretion [iow model to explain the observations of quiescent black hole X-rav transients., \citet{Narayan96} and \citet{Narayan97} have proposed an accretion flow model to explain the observations of quiescent black hole X-ray transients.
 Phe accretion disc has two components. an inner hot advection-dominated accretion Dow. CXDAT) that extends from the black hole horizon to a transition radius and a thin acerction disc that extends from the transition disc to the edge of the accretion disc.," The accretion disc has two components, an inner hot advection-dominated accretion flow (ADAF) that extends from the black hole horizon to a transition radius and a thin accretion disc that extends from the transition disc to the edge of the accretion disc."
 Interactions between the hot inner ADAP ancl the cool. outer thin disc. at or near the transition radius could be a source of quasi-periodic variability.," Interactions between the hot inner ADAF and the cool, outer thin disc, at or near the transition radius could be a source of quasi-periodic variability."
 The ADAP flow requires electrons in the gas to cool via svnehrotron. bremsstrahlung. and inverse Compton oocesses which predict the form of the spectrum from racio o hard. X-ravs.," The ADAF flow requires electrons in the gas to cool via synchrotron, bremsstrahlung, and inverse Compton processes which predict the form of the spectrum from radio to hard X-rays."
 lt has been suggested that the [ares observed in aanel other quiescent X-ray transicnts arise. from the ransition radius (Zuritaetal.2003: Shahbazetal. 2003b))., It has been suggested that the flares observed in and other quiescent X-ray transients arise from the transition radius \citealt{Zurita03}; \citealt{Shahbaz03b}) ).
 Indeed. the mmllIz feature detected in CCve has oen used to determine the transition radius. assuming hat the periodicity. represents the Weplerian period. at he transition between the thin and advective disce regions (Shahbazetal.2003b).. and a possible low freequeney. breaks in the power spectrum of mmav have a related origin (Hlvnesctal.2003).," Indeed, the mHz feature detected in Cyg has been used to determine the transition radius, assuming that the periodicity represents the Keplerian period at the transition between the thin and advective disc regions \citep{Shahbaz03b}, and a possible low frequency break in the power spectrum of may have a related origin \citep{Hynes03}."
. In the original. ADA models the optical flux. is produced. by svnchrotron emission., In the original ADAF models the optical flux is produced by synchrotron emission.
 As pointed out in Shahbaz (2003hb).. it is difficult to explain the Dare spectrum in ternis of optically thin synchrotron emission. unless the electrons follow a much steeper power-law electron energy distribution compared to solar [lares: solar and stellar flares have a frequeney spectrum with a power-law index of a=0.5 and an electron energy. distribution with a power-law index of ~ 2.," As pointed out in \citet{Shahbaz03b}, it is difficult to explain the flare spectrum in terms of optically thin synchrotron emission, unless the electrons follow a much steeper power-law electron energy distribution compared to solar flares; solar and stellar flares have a frequency spectrum with a power-law index of $\alpha$ =–0.5 and an electron energy distribution with a power-law index of $\sim$ –2."
 llowever. more recently the ADAE models have »en questioned. and substantial mocifications proposed.," However, more recently the ADAF models have been questioned, and substantial modifications proposed."
 Blandford&Beegclman(1999) emphasised. that the Bernoulli constant of the gas is positive and henee outLlows are possible (as also noted by Naravan&Yi 1994))., \citet{Blandford99} emphasised that the Bernoulli constant of the gas is positive and hence outflows are possible (as also noted by \citealt{Narayan94}) ).
 In he adiabatic inflow outllow solution CXDIOS) mocdel. of DBlandford&Begelman(1999) most of the accretion energy hat is released near the black hole is used to drive a wind rom the surface of the accretion disc., In the adiabatic inflow outflow solution (ADIOS) model of \citet{Blandford99} most of the accretion energy that is released near the black hole is used to drive a wind from the surface of the accretion disc.
 Most of the gas that alls onto the outer edge of the accretion disc is carried. by his wind away from the black hole. with the result that the 1ole’s accretion rate is much smaller than the discs accretion rate.," Most of the gas that falls onto the outer edge of the accretion disc is carried by this wind away from the black hole, with the result that the hole's accretion rate is much smaller than the disc's accretion rate."
 Advective [lows are also expected to be convectively unstable. as also remarked by Naravan&Y1(1994).," Advective flows are also expected to be convectively unstable, as also remarked by \citet{Narayan94}."
. In these models the central accretion rate can also be suppressed., In these models the central accretion rate can also be suppressed.
 For either of these cases. the elfect is to shift the source of cooling outwards. ancl the optical svnchrotron emission is reduced. (Quatacrt&Naravan1000 Ball.Naravan.&Quatacrt 2001)).," For either of these cases, the effect is to shift the source of cooling outwards, and the optical synchrotron emission is reduced \citealt{Quataert99}; \citealt{Ball01}) )."
 In these more realistic cases optical Lares clirecthy from the inner How are less likely., In these more realistic cases $optical$ flares directly from the inner flow are less likely.
 Optical emission might still arise from the inner edge of the outer (thin) disc. or [rom reprocessing of X-ray variability.," Optical emission might still arise from the inner edge of the outer (thin) disc, or from reprocessing of X-ray variability."
 lt was argued by Hvnesetal.(2002). that. since large (~ ew d) flares in. V404CCvg involve enhancements of both Xue and red wings of Hao. they must involve the whole disc.," It was argued by \citet{Hynes02} that since large $\sim$ few d) flares in Cyg involve enhancements of both blue and red wings of $\alpha$, they must involve the whole disc."
 While these observations indicate. participation bv a wide range of azimuths. they leave open the possibility that only he inner disc is involved.," While these observations indicate participation by a wide range of azimuths, they leave open the possibility that only the inner disc is involved."
 Using simultaneous multicolour Xhotometrv Shahbazetal.(2003b). determined the colour of similar larec [lares in V404CCve., Using simultaneous multicolour photometry \citet{Shahbaz03b} determined the colour of similar large flares in Cyg.
 Although the [lare xwameters. determined: are complicated by uncertainties in the interstellar reddening. the Hare temperature was estimated to be ~SOOO KIS. Flares on timescales similar to hose present in (i.c. tens of minutes) were also. observed. but no shysical parameters could. be determined given the large uncertainties in the colour.," Although the flare parameters determined are complicated by uncertainties in the interstellar reddening, the flare temperature was estimated to be $\sim$ K. Flares on timescales similar to those present in (i.e. tens of minutes) were also observed, but no physical parameters could be determined given the large uncertainties in the colour."
 Vhe large (~ few hrs) Hares were observed. to arise from regions that cover at least 3 percent ol the discs surface area., The large $\sim$ few hrs) flares were observed to arise from regions that cover at least 3 percent of the disc's surface area.
 Shahbazetal.(2003b) have suggested that the laree (~ few hes) Uares in V404CCve are produced. in regions further out or further above the disc from a corona than the rapid (~0.5 hhr) and more rapic ( mmin) flares.," \citet{Shahbaz03b}
 have suggested that the large $\sim$ few hrs) flares in Cyg are produced in regions further out or further above the disc from a corona than the rapid $\sim$ hr) and more rapid $\sim$ min) flares."
 Ifthe Dares in C'C'vg and hhave the same origin. then it is interesting to note tha the large Dares (~ few hrs) observed in οvg cover a larger surface area of the disc compared to the rapid. (tens of mins) Hares observed. in.00... which is consisten with the idea that the large Hares arise from regions tha extend. further out. into the disc compared. to the rapic Hares.," If the flares in Cyg and have the same origin, then it is interesting to note that the large flares $\sim$ few hrs) observed in Cyg cover a larger surface area of the disc compared to the rapid (tens of mins) flares observed in, which is consistent with the idea that the large flares arise from regions that extend further out into the disc compared to the rapid flares."
 Although the flare temperatures derived suggest tha large fares are cooler than rapid Lares. the uncertainties are large and so no meaningful conclusion can be drawn a this stage.," Although the flare temperatures derived suggest that large flares are cooler than rapid flares, the uncertainties are large and so no meaningful conclusion can be drawn at this stage."
 Accurate physical parameters for the Lares can only be obtained by resolving the Balmer jump and Paschen continuum., Accurate physical parameters for the flares can only be obtained by resolving the Balmer jump and Paschen continuum.
 For the data presented here on00.. there is evidence that some of the [lare events in the continuum lighteurve are correlated. with the Balmer emission line lightceurves. similar to what is observed in V404C€vg (Ilvnesetal. 2002).," For the data presented here on, there is evidence that some of the flare events in the continuum lightcurve are correlated with the Balmer emission line lightcurves, similar to what is observed in Cyg \citep{Hynes02}."
. The value for the Balmer decrement suggests that the persistent flux is optically thin and the decrease of the Jalmer clecrement during the Lares suggests a significant temperature increase., The value for the Balmer decrement suggests that the persistent flux is optically thin and the decrease of the Balmer decrement during the flares suggests a significant temperature increase.
 We find that the optically thin spectrum of the flare. which lasts tens of minutes. has a temperature of ~12000KI and covers 0.08. percent of the disc's projected surface area (see retE LAIUZ)).," We find that the optically thin spectrum of the flare, which lasts tens of minutes, has a temperature of $\sim$ K and covers 0.08 percent of the disc's projected surface area (see \\ref{FLARE}) )."
 In many high inclination svstems the continuum light from the bright-spot. produces a single hump in the lighteurve. because the bright-spot is obscured by the disc when it is on the side of the disc facing away [rom the observer.," In many high inclination systems the continuum light from the bright-spot produces a single hump in the lightcurve, because the bright-spot is obscured by the disc when it is on the side of the disc facing away from the observer."
 Since lis at an intermediate inclination angle (41°: Shahbazctal. and Gelinoetal. 2001)) where no strong obscuration, Since is at an intermediate inclination angle $^\circ$ ; \citealt{Shahbaz94} and \citealt{Gelino01}) ) where no strong obscuration
scattering processes|52].. In ourmodel. itisassumed. that,made out of valence spin-0 diquark and valence quark.
 incidentbarvons aremainly," Consequently, the magnitude of"
that have already occiured. we can nevertheless conduct meaningful tests and identily the natures of at least some of the lenses.,"that have already occurred, we can nevertheless conduct meaningful tests and identify the natures of at least some of the lenses."
 We should check existing multiwavelength: catalogs and data sets at the position of each event well-sampled enough (hat we are reasonably confident (a) il corresponds (o microlensing and (b) that the short duration is not due to blending., We should check existing multiwavelength catalogs and data sets at the position of each event well-sampled enough that we are reasonably confident (a) it corresponds to microlensing and (b) that the short duration is not due to blending.
 In at least some cases we should find evidence for an object that is not the lensed source. but which could instead be part of the lens svstem.," In at least some cases we should find evidence for an object that is not the lensed source, but which could instead be part of the lens system."
 In cases where (here is a match. the possible contributions of additional observations. including some with LST. should be considered.," In cases where there is a match, the possible contributions of additional observations, including some with HST, should be considered."
 It would be surprising if a comprehensive analvsis of alreacly-cliscoverecl short evenis does not reveal the presence of a set of interesting lenses., It would be surprising if a comprehensive analysis of already-discovered short events does not reveal the presence of a set of interesting lenses.
 The existing data sets are almost certainly minute in comparison with future data sets. which will discover more events per vear.," The existing data sets are almost certainly minute in comparison with future data sets, which will discover more events per year."
 Column 6 of Table 1 shows that we can expect 150 short events among each 1000 events (Column 5) detected by monitoring programs sensitive to short events., Column 6 of Table 1 shows that we can expect $150$ short events among each $1000$ events (Column 5) detected by monitoring programs sensitive to short events.
 The challenge aliead is. therefore. to institute real-time recognition of events to immediately identify those (hat are promising candidates for additional observations. We discuss (his further in 86.," The challenge ahead is, therefore, to institute real-time recognition of short-duration events to immediately identify those that are promising candidates for additional observations, We discuss this further in 6."
 For each type of lens defined bv a given mass range. the selection of short-duration evenis corresponds to a selection of lenses in one of (wo distance regimes.," For each type of lens defined by a given mass range, the selection of short-duration events corresponds to a selection of lenses in one of two distance regimes."
" This is because the equation for Dj, is quadratic. generally admitting (wo solutions. D, and D,. For lenses that are brown clwarls. planets. and neutron stars. D, is shown as a function of vin Figures 1 through 3. respectively."," This is because the equation for $D_L$ is quadratic, generally admitting two solutions, $D_L^+$ and $D_L^-.$ For lenses that are brown dwarfs, planets, and neutron stars, $D_L$ is shown as a function of $v$ in Figures $1$ through $3$, respectively."
" D, can be in the range of tens or hundreds of pe.", $D_L^-$ can be in the range of tens or hundreds of pc.
 When the lens svstem is this close to us. the probability of being able to detect it is large.," When the lens system is this close to us, the probability of being able to detect it is large."
 As discussed in the companion paper. the degeneracy inherent in lensing can therefore olten be broken.," As discussed in the companion paper, the degeneracy inherent in lensing can therefore often be broken."
 In fact. for a given lens. there may be several different wavs of measuring the some Κον qualities. such as the mass of the planet-lens (see. e.g.. 83.2).," In fact, for a given lens, there may be several different ways of measuring the some key quantities, such as the mass of the planet-lens (see, e.g., 3.2)."
" Because nearby lenses can be so well studied. we can use them to make predictions for the population of distant lenses. with D,=D,. Nearby lenses producing short-duration evenis can be identified as planets. brown cdwarfs. or stellar remnants."," Because nearby lenses can be so well studied, we can use them to make predictions for the population of distant lenses, with $D_L=D_L^+.$ Nearby lenses producing short-duration events can be identified as planets, brown dwarfs, or stellar remnants."
" If we assume that stellar populations in the dense source systems contain similar populations. we can predict the distributions of values of 7j; ancl also of values of 85. (85 is more likely to be measured for D,= )."," If we assume that stellar populations in the dense source systems contain similar populations, we can predict the distributions of values of $\tau_E$ and also of values of $\theta_E.$ $\theta_E$ is more likely to be measured for $D_L=D_L^+$ )."
 Comparisons between the predicted and observed distributions will allow us to test models., Comparisons between the predicted and observed distributions will allow us to test models.
" Note. in addition. (hat for a given lens mass and speed. (the requirement that D, be real. places an upper limit on the Einstein diameter crossing time."," Note, in addition, that for a given lens mass and speed, the requirement that $D_L$ be real, places an upper limit on the Einstein diameter crossing time."
"As a starting point, we consider the evolution equation for CDM and baryon density perturbations óc)=δρειυ/βοι in the Newtonian limit and in the presence of a DE-CDM interaction as derived by ?,, in Fourier space and in cosmic time: The additional contribution appearing in the first term on the right hand side of Eq. (10))","As a starting point, we consider the evolution equation for CDM and baryon density perturbations $\delta _{c,b}\equiv \delta \rho _{c,b}/\rho _{c,b}$ in the Newtonian limit and in the presence of a DE-CDM interaction as derived by \citet{Amendola_2004}, in Fourier space and in cosmic time: The additional contribution appearing in the first term on the right hand side of Eq. \ref{gf_c}) )"
" is the extra friction associated with momentum conservation in cDE models (seee.g.?,foradiscus-sionontheeffectsoffrictionterm) and the factor I. defined as includes the effect of the fifth-force mediated by the DE scalar field for CDM density perturbations.", is the extra friction associated with momentum conservation in cDE models \citep[see \eg ][for a discussion on the effects of the friction term]{Baldi_2011b} and the factor $\Gamma _{c}$ defined as includes the effect of the fifth-force mediated by the DE scalar field for CDM density perturbations.
" A few assumptions have to be made in order to derive Eqs. (10,,11)),"," A few assumptions have to be made in order to derive Eqs. \ref{gf_c}, \ref{gf_b}) ),"
" besides the already mentioned Newtonian limit of small scales for the Fourier modes under consideration, A—aH/k< 1."," besides the already mentioned Newtonian limit of small scales for the Fourier modes under consideration, $\lambda \equiv aH/k \ll 1$ ."
" In particular, one has to assume the dimensionless mass of the scalar field $, defined as to be small compared to the Fourier modes at the scales of interest, such that If this condition is not fulfilled, the clustering of the DE scalar field ¢ might grow beyond the linear level at scales below 1/TR, and the fifth force of Eq. (12))"," In particular, one has to assume the dimensionless mass of the scalar field $\phi $, defined as to be small compared to the Fourier modes at the scales of interest, such that If this condition is not fulfilled, the clustering of the DE scalar field $\phi $ might grow beyond the linear level at scales below $1/\hat{m}^{2}_{\phi }$ and the fifth force of Eq. \ref{Gamma_c_massless}) )"
" would then acquire a Yukawa suppression factor given by: Since both the linear treatment of density perturbations discussed in the present Section and the non-linear N-body algorithm used for the analysis presented in the next Section are based on the assumption of a small scalar mass, and therefore on a term like (12)) for the fifth-force implementation, it is important to clarify to which extent this assumption can be considered to hold."," would then acquire a Yukawa suppression factor given by: Since both the linear treatment of density perturbations discussed in the present Section and the non-linear N-body algorithm used for the analysis presented in the next Section are based on the assumption of a small scalar mass, and therefore on a term like \ref{Gamma_c_massless}) ) for the fifth-force implementation, it is important to clarify to which extent this assumption can be considered to hold."
 In Fig., In Fig.
" 4 we plot the quantity Tig? for several comoving wavenumbers k~1,0.1,0.01,0.001h/Mpce as a function of redshift."," \ref{fig:scalar_mass} we plot the quantity $\hat{m}^{2}_{\phi }\lambda ^{2}$ for several comoving wavenumbers $k\sim 1\,,0.1\,,0.01\,,0.001\, h/$ Mpc as a function of redshift."
" As one can see from the plot, the scalar mass can start playing a significant role at z<10 only for scales close to the cosmic horizon, while for all scales below ~700 comoving Mpc/h (k~ 0.01h/Mpc) the influence of a non-zero scalar mass is negligible and Eqs. (10,,11,,12))"," As one can see from the plot, the scalar mass can start playing a significant role at $z<10$ only for scales close to the cosmic horizon, while for all scales below $\sim 700$ comoving $/h$ $k\sim 0.01\, h/$ Mpc) the influence of a non-zero scalar mass is negligible and Eqs. \ref{gf_c}, \ref{gf_b}, \ref{Gamma_c_massless}) )"
 can be safely used., can be safely used.
 For the N- results discussed in Sec., For the N-body results discussed in Sec.
" 4 we will consider simulations with a box of 1 comoving Gpc/h aside, for which only the largest scales sampled by the initial power spectrum might be marginally affected by our massless field approximation, while we will concentrate on nonlinear structure formation processes occurring at much smaller scales."," \ref{sec:sims} we will consider simulations with a box of $1$ comoving $/h$ aside, for which only the largest scales sampled by the initial power spectrum might be marginally affected by our massless field approximation, while we will concentrate on nonlinear structure formation processes occurring at much smaller scales."
" Having clarified the range of validity of the assumptions made in deriving Eqs. (10,,11,,12))"," Having clarified the range of validity of the assumptions made in deriving Eqs. \ref{gf_c}, \ref{gf_b}, \ref{Gamma_c_massless}) )"
 we can now discuss one of the central results of the present work., we can now discuss one of the central results of the present work.
" By numerically solving the system of Eqs. (1--5,,10,,11))"," By numerically solving the system of Eqs. \ref{klein_gordon}- \ref{friedmann}, \ref{gf_c}, \ref{gf_b}) )"
 at subhorizon scales (k~0.1 /Mpc) we can compute the linear growth of density perturbations for all the different cosmological models under investigation and compare it to the standard ACDM growth factor.," at subhorizon scales $k\sim 0.1\, h$ /Mpc) we can compute the linear growth of density perturbations for all the different cosmological models under investigation and compare it to the standard $\Lambda $ CDM growth factor."
 As boundary conditions for our integration we impose that the ratio of baryonic to CDM perturbations at zcwp takes the value 6/5.~3.0x1075 as computed by running the Boltzmann code CAMB (?) fora ACDM cosmology and for the WMAP7 parameters adopted in the present study as listed in Table 1.., As boundary conditions for our integration we impose that the ratio of baryonic to CDM perturbations at $z_{\rm CMB}$ takes the value $\delta _{b}/\delta _{c} \sim 3.0\times 10^{-3}$ as computed by running the Boltzmann code CAMB \citep{camb} for a $\Lambda {\rm CDM}$ cosmology and for the WMAP7 parameters adopted in the present study as listed in Table \ref{tab:parameters}. .
our data well.,our data well.
" We therefore provide a new and more accurate fitting formula for the relation between 65, and ój.", We therefore provide a new and more accurate fitting formula for the relation between $\delta_{\mathrm{m}}^{\mathrm{s}}$ and $\delta_{\mathrm{1}}^{\mathrm{s}}$.
" The redshift range we can study is 0<z10 in 30 bins, logarithmically spaced in (1+z)!."," The redshift range we can study is $0 \leq z \leq 10$ in 30 bins, logarithmically spaced in $(1+z)^{-1}$."
" For each redshift bin, we find that the parameterisation gives a very good fit for all values of 6}: the ratio of the fit residuals to the true value is less than 5 per cent for redshift 0 and lessthan 1 per cent for z>6."," For each redshift bin, we find that the parameterisation gives a very good fit for all values of $\delta_1^{\mathrm{s}}$: the ratio of the fit residuals to the true value is less than 5 per cent for redshift 0 and lessthan 1 per cent for $z>6$."
" The functions A, B and C depend on z in the following way: In the limiting case z—oo, some of the fit coefficients do not show the right asymptotic behaviour (A—0, B—1, C— 0) as one would expect because 65,—67, so this fit should be used for redshifts outside the fitted range."," The functions $A$, $B$ and $C$ depend on $z$ in the following way: In the limiting case $z \rightarrow \infty$, some of the fit coefficients do not show the right asymptotic behaviour $A \rightarrow 0$, $B \rightarrow 1$, $C \rightarrow 0$ ) as one would expect because $\delta_{\mathrm{m}}^{\mathrm{s}} \rightarrow \delta_{\mathrm{1}}^{\mathrm{s}}$, so this fit should be used for redshifts outside the fitted range."
 Both density fields were smoothed with R=12Mpc/h., Both density fields were smoothed with $R=12\ \mathrm{Mpc}/h$.
" The choice of R does not significantly influence the fitting parameters, but the agreement is worse when large values of 6; and ὃν, are allowed (i.e. R is small at low redshifts)."," The choice of $R$ does not significantly influence the fitting parameters, but the agreement is worse when large values of $\delta_1^{\mathrm{s}}$ and $\delta_{\mathrm{m}}^{\mathrm{s}}$ are allowed (i.e. $R$ is small at low redshifts)."
" Another relation between the linear and non-linear density fields that is sometimes used is the lognormal transformation (e.g. ?,, ?))."," Another relation between the linear and non-linear density fields that is sometimes used is the lognormal transformation (e.g. \citealt*{1991MNRAS.248....1C}, \citealt*{1995ApJ...443..479B}) )."
 This has proven to yield a PDF which agrees well with simulations., This has proven to yield a PDF which agrees well with simulations.
" However, this does not imply that it can be used as a point-by-point relation between the linear and non-linear density fields, as pointed out by ?.."," However, this does not imply that it can be used as a point-by-point relation between the linear and non-linear density fields, as pointed out by \citet*{2001ApJ...561...22K}."
" We follow their parameterisation, which can be rewritten as with Here, o? (02) is the variance of the smoothed linear (non-linear) density field."," We follow their parameterisation, which can be rewritten as with Here, $\sigma^2$ $\sigma^2_{\mathrm{m}}$ ) is the variance of the smoothed linear (non-linear) density field."
" We calculate c? and leave ""y as the fit parameter.", We calculate $\sigma^2$ and leave $\gamma$ as the fit parameter.
 This fit yields values for dm which are systematically lower by zz30 per cent at redshift 0 and still 20 per cent at z>6., This fit yields values for $\delta_{\mathrm{m}}$ which are systematically lower by $\approx 30$ per cent at redshift 0 and still 20 per cent at $z>6$.
 So indeed the lognormal transformation can not be used to accurately predict the evolution of an initial Gaussian field into a non-linear field., So indeed the lognormal transformation can not be used to accurately predict the evolution of an initial Gaussian field into a non-linear field.
" Again, this does not mean that the statistics of a non-linear density field can not be described by a lognormal field, just that one can not expect that, for a point-by-point comparison, the linear field used in the transformation corresponds to the initial conditions of that non-linear field."," Again, this does not mean that the statistics of a non-linear density field can not be described by a lognormal field, just that one can not expect that, for a point-by-point comparison, the linear field used in the transformation corresponds to the initial conditions of that non-linear field."
" After calculating the higher order density contrast, we now calculate the matter power spectra up to the 1-loop order."," After calculating the higher order density contrast, we now calculate the matter power spectra up to the 1-loop order."
 We can do this in two ways: calculating the volume average of the SPT density contrast (Eq. 8)), We can do this in two ways: calculating the volume average of the SPT density contrast (Eq. \ref{pgen}) )
" or integrating a given linear power spectrum Pii(k) (Eq. 10)),"," or integrating a given linear power spectrum $P_{11}(k)$ (Eq. \ref{analyt}) ),"
 where Pii(k) is the same power spectrum that was used to set up the initial conditions of the simulation., where $P_{11}(k)$ is the same power spectrum that was used to set up the initial conditions of the simulation.
 This also serves as a consistency check for our grid-based calculation., This also serves as a consistency check for our grid-based calculation.
 The results for the large box are shown in Fig. 5.., The results for the large box are shown in Fig. \ref{fig:p11theo}.
 The small box is not shown because it is very similar., The small box is not shown because it is very similar.
 The lines show the results from Eq. (10)), The lines show the results from Eq. \ref{analyt}) )
" and the points show the numerical result, without smoothing, ie. R= 0."," and the points show the numerical result, without smoothing, i.e. $R=0$ ."
 The errors of the power spectra are calculated assuming that our fields are Gaussian: where ng is the number of modes in each k-bin., The errors of the power spectra are calculated assuming that our fields are Gaussian: where $n_{\mathrm{B}}$ is the number of modes in each $k$ -bin.
 'The linear power spectrum from the simulation agrees, The linear power spectrum from the simulation agrees
subcluster has lost its gas on approaching the cluster from the south and is currently located north to the main cluster.,subcluster has lost its gas on approaching the cluster from the south and is currently located north to the main cluster.
 The image shows an East-West elongated core on the small scale. while on the large scale it appears to be symmetric.," The image shows an East-West elongated core on the small scale, while on the large scale it appears to be symmetric."
 The pressure map has two maxima and two elongations towards the south-west and south-east., The pressure map has two maxima and two elongations towards the south-west and south-east.
 There are some ring-like structures in the temperature map., There are some ring-like structures in the temperature map.
 The entropy state of the cluster ICM appears to correspond to the late stage of a core disruption with filaments of the low-entropy gas spread over a large volume., The entropy state of the cluster ICM appears to correspond to the late stage of a core disruption with filaments of the low-entropy gas spread over a large volume.
 The position of the entropy minimum ts offset from the peak in the pressure., The position of the entropy minimum is offset from the peak in the pressure.
 The cluster has a clover leaf structure in the entropy map like the 0532.9-3701., The cluster has a clover leaf structure in the entropy map like the 0532.9–3701.
 Two pressure maxima could indicate the core rebounce., Two pressure maxima could indicate the core rebounce.
 The symmetry in the pressure map ts regained at 1.5 areminute radius., The symmetry in the pressure map is regained at 1.5 arcminute radius.
 The spectroscopic analysis is reported in Table 12. and Fig.12.., The spectroscopic analysis is reported in Table \ref{t:cl13:t} and \ref{f:cl13}.
 The scenario of the disrupted core (region 4) is supported by the spectral analysis (see also Fig.14))., The scenario of the disrupted core (region 4) is supported by the spectral analysis (see also \ref{f:maps}) ).
 The pressure enhancement (region 5) is marginal., The pressure enhancement (region 5) is marginal.
 Famous for its Chandra image (Markevitch et al., Famous for its Chandra image (Markevitch et al.
 2002). the bullet cluster has some distinct features. which also allow us to understand the observation of other clusters.," 2002), the bullet cluster has some distinct features, which also allow us to understand the observation of other clusters."
 With à Mach number of 3. deduced from the shape of the bullet itself (angle of the Mach cone). the subcluster makes an entropy enhancement in front of it.," With a Mach number of 3, deduced from the shape of the bullet itself (angle of the Mach cone), the subcluster makes an entropy enhancement in front of it."
 There are two other large entropy peaks behind and to the south from the bullet., There are two other large entropy peaks behind and to the south from the bullet.
 Apart from the small-scale structure in the center. there appears to be a lack of features on the pressure map. which we attribute to the propagation of the shock out to large radii. thus strongly reducing the contrast.," Apart from the small-scale structure in the center, there appears to be a lack of features on the pressure map, which we attribute to the propagation of the shock out to large radii, thus strongly reducing the contrast."
 Therefore. the bullet indicates a situation of a strong merger that is just completed in the center and now moves to outskirts.," Therefore, the bullet indicates a situation of a strong merger that is just completed in the center and now moves to outskirts."
 The entropy structure of the core of the main cluster appears disrupted. yet the minimum ts retained. while becoming shallow.," The entropy structure of the core of the main cluster appears disrupted, yet the minimum is retained, while becoming shallow."
 In the temperature map we see clear signatures of turbulence. as indicated by the stochastic fluctuations. which in other clusters correspond to a late stage of merging.," In the temperature map we see clear signatures of turbulence, as indicated by the stochastic fluctuations, which in other clusters correspond to a late stage of merging."
 This once again demonstrates that the time scales for the relaxation are very different for the cluster center and, This once again demonstrates that the time scales for the relaxation are very different for the cluster center and
greater in these regions.,greater in these regions.
 Finally. galaxies with redshifts below 0.01 were excluded. because at these low redshifts the galaxies are very extended and their optical positions are consequently uncertain.," Finally, galaxies with redshifts below 0.01 were excluded, because at these low redshifts the galaxies are very extended and their optical positions are consequently uncertain."
 2., 2.
 The remaining sample was cross—correlated with the NVSS catalogue., The remaining sample was cross–correlated with the NVSS catalogue.
 À list of candidate galaxies that might be associated with multi-NVSS-component radio sources was derived., A list of candidate galaxies that might be associated with multi-NVSS-component radio sources was derived.
 3., 3.
 yoThese multi-NVSS-component candidates were investigated: by necessity. a small proportion of this analysis had to be done visually rather than through automated procedures.," These multi–NVSS–component candidates were investigated; by necessity, a small proportion of this analysis had to be done visually rather than through automated procedures."
 Tf a galaxy was confirmed to be associated with a multi-NVSS-component source. the integrated flux densities of the NVSS components were summed to provide the radio source flux density.," If a galaxy was confirmed to be associated with a multi–NVSS–component source, the integrated flux densities of the NVSS components were summed to provide the radio source flux density."
" 4,", 4.
 All galaxies matched with a single NVSS source were then cross—correlated with the FIRST catalogue., All galaxies matched with a single NVSS source were then cross–correlated with the FIRST catalogue.
 Note. however. that the presence of a FIRST counterpart was not for a source to be accepted.," Note, however, that the presence of a FIRST counterpart was not for a source to be accepted."
 If there was no FIRST counterpart. then the source was accepted or rejected solely upon its NVSS properties.," If there was no FIRST counterpart, then the source was accepted or rejected solely upon its NVSS properties."
 5., 5.
 If a single FIRST counterpart was associated with the NVSS source. then the source was accepted or rejected on the basis of the properties of the FIRST counterpart.," If a single FIRST counterpart was associated with the NVSS source, then the source was accepted or rejected on the basis of the properties of the FIRST counterpart."
 For accepted. matches. however. the adopted radio flux density was taken from the NVSS data.," For accepted matches, however, the adopted radio flux density was taken from the NVSS data."
 6., 6.
 If multiple FIRST components were associated with the NVSS source. then the source was accepted if it satisfied. criteria for a single-component source (with unrelated additional FIRST sources) or for a radio source with multiple FIRST components.," If multiple FIRST components were associated with the NVSS source, then the source was accepted if it satisfied criteria for a single-component source (with unrelated additional FIRST sources) or for a radio source with multiple FIRST components."
 Again. the NVSS catalogue was used to provide the most accurate measure of the radio flux density.," Again, the NVSS catalogue was used to provide the most accurate measure of the radio flux density."
 The exact criteria for accepting and rejecting matches in the procedures outlined above were tested and retined using Monte—Carlo simulations., The exact criteria for accepting and rejecting matches in the procedures outlined above were tested and refined using Monte--Carlo simulations.
 Ten catalogues of random sky locations were constructed. over the same sky area as the SDSS survey.," Ten catalogues of random sky locations were constructed, over the same sky area as the SDSS survey."
 Each catalogue contained the same number as positions as the list of SDSS galaxies. and these random catalogues were taken through exactly the same steps of cross-comparison with the radio data as the SDSS galaxy catalogue.," Each catalogue contained the same number as positions as the list of SDSS galaxies, and these random catalogues were taken through exactly the same steps of cross–comparison with the radio data as the SDSS galaxy catalogue."
 In the subsections that follow. the resulting optimal selection criteria are described. together with the completeness and reliability estimates provided by the Carlo simulations.," In the subsections that follow, the resulting optimal selection criteria are described, together with the completeness and reliability estimates provided by the Monte--Carlo simulations."
 Note that the flux densities adopted for the NVSS sources are true integrated flux densities. rather than the peak flux densities quoted in the NVSS catalogues.," Note that the flux densities adopted for the NVSS sources are true integrated flux densities, rather than the peak flux densities quoted in the NVSS catalogues."
 The formulae for conversion of peak flux densities to integrated flux densities are provided by Condon shorteitecon98.., The formulae for conversion of peak flux densities to integrated flux densities are provided by Condon \\shortcite{con98}.
 Only those radio sources with total flux densities (after summing NVSS components if necessary) above mmJy are retained., Only those radio sources with total flux densities (after summing NVSS components if necessary) above mJy are retained.
 This flux density limit corresponds to approximately 10 times the noise level of the NVSS maps. and is adopted because: (1) at this significance level. all sources should be real and have well—determined positions: (ii) at this flux density limit. the sample is as sensitive to extended single-component NVSS sources (which will have a lower peak flux density) as it is to point sources. and the sensitivity to multi-component NVSS sources will not be significantly worse (for example. a mmJy source composed of two individual components of mmJy would be found).," This flux density limit corresponds to approximately 10 times the noise level of the NVSS maps, and is adopted because: (i) at this significance level, all sources should be real and have well--determined positions; (ii) at this flux density limit, the sample is as sensitive to extended single–component NVSS sources (which will have a lower peak flux density) as it is to point sources, and the sensitivity to multi–component NVSS sources will not be significantly worse (for example, a mJy source composed of two individual components of mJy would be found)."
 The 5mmly limit corresponds to about 107 + at redshift0.1. which is approximately where the radio luminosity function switches from being dominated by star forming galaxies (low luminosities) to being dominated by AGN thigh luminosities).," The mJy limit corresponds to about $10^{23}$ $^{-1}$ at redshift, which is approximately where the radio luminosity function switches from being dominated by star forming galaxies (low luminosities) to being dominated by AGN (high luminosities)."
 In order to search for possible multi-component NVSS sources. a search was made for multiple sources within a radius of 3 aremins from each optical galaxy.," In order to search for possible multi-component NVSS sources, a search was made for multiple sources within a radius of 3 arcmins from each optical galaxy."
 This distance was selected to be large enough that any genuine multi-component radio source should have at least two matches. but still much smaller than the typical separation of NVSS sources (8-10 aremins).," This distance was selected to be large enough that any genuine multi-component radio source should have at least two matches, but still much smaller than the typical separation of NVSS sources (8-10 arcmins)."
 For galaxies with two NVSS matches within 3 aremins. the top panels of Fig |. compare the offsets of the two NVSS matches from the optical position for SDSS galaxies (eft) and for an equivalent number of random positions (right).," For galaxies with two NVSS matches within 3 arcmins, the top panels of Fig \ref{nvssdbls} compare the offsets of the two NVSS matches from the optical position for SDSS galaxies (left) and for an equivalent number of random positions (right)."
 There are a large number of SDSS galaxies for which the nearer NVSS component lies within 15 aresec of the optical galaxy: these are predominantly galaxies containing a single-component NVSS source and the other NVSS source is physically unrelated., There are a large number of SDSS galaxies for which the nearer NVSS component lies within 15 arcsec of the optical galaxy; these are predominantly galaxies containing a single–component NVSS source and the other NVSS source is physically unrelated.
 Such sources were classified as single-component matches (see below)., Such sources were classified as single–component matches (see below).
 In addition to these. there is a clear excess of SDSS galaxies (compared to random) that have the two NVSS components each offset by 20-50 aresec from the optical position.," In addition to these, there is a clear excess of SDSS galaxies (compared to random) that have the two NVSS components each offset by 20-50 arcsec from the optical position."
 For these systems. the flux-weighted mean position of the two NVSS sources is often within 15 aresee of the optical galaxy (indicated. by the diamonds in the upper panel of Fig L1).," For these systems, the flux-weighted mean position of the two NVSS sources is often within 15 arcsec of the optical galaxy (indicated by the diamonds in the upper panel of Fig \ref{nvssdbls}) )."
 Candidate NVSS doubles are therefore selected to be sources with both NVSS components closer than 90 arcsec. a flux-weighted mean position closer than 15 üresec. and the nearer component offset by more than whichever is smaller out of 15 arcsec and the offset of the second source minus 20 arcsec.," Candidate NVSS doubles are therefore selected to be sources with both NVSS components closer than 90 arcsec, a flux-weighted mean position closer than 15 arcsec, and the nearer component offset by more than whichever is smaller out of 15 arcsec and the offset of the second source minus 20 arcsec."
 These selection criteria are indicated by the lines on Fig l|.., These selection criteria are indicated by the lines on Fig \ref{nvssdbls}.
 The 90 aresee limit is chosen since larger offsets are relatively unlikely and the contamination by random galaxies gets increasingly large beyond this., The 90 arcsec limit is chosen since larger offsets are relatively unlikely and the contamination by random galaxies gets increasingly large beyond this.
 Even with this limit. there is still significant contamination. but the next step of comparison with FIRST helps to alleviate much of this.," Even with this limit, there is still significant contamination, but the next step of comparison with FIRST helps to alleviate much of this."
 All of these candidate doubles were cross-correlated with the FIRST catalogue., All of these candidate doubles were cross-correlated with the FIRST catalogue.
 If these are true extended doubles then they may have a central FIRST component associated with a radio source core. and in addition they are likely to be missing flux in the FIRST data due to their extended nature: indeed they may well be undetected by FIRST.," If these are true extended doubles then they may have a central FIRST component associated with a radio source core, and in addition they are likely to be missing flux in the FIRST data due to their extended nature; indeed they may well be undetected by FIRST."
 If they are not true doubles. but two individual NVSS sources. then it is likely that a single or double FIRST counterpart is present at each NVSS location. with little missing flux.," If they are not true doubles, but two individual NVSS sources, then it is likely that a single or double FIRST counterpart is present at each NVSS location, with little missing flux."
 The candidate doubles were thus classified into three categories: (a) accepted doubles: sources were accepted as NVSS doubles if jey either have a FIRST source within 3 arcsee of the optical yosition. or they satisfy the following three conditions (i) no detected FIRST component (ie.," The candidate doubles were thus classified into three categories: (a) accepted doubles: sources were accepted as NVSS doubles if they either have a FIRST source within 3 arcsec of the optical position, or they satisfy the following three conditions (i) no detected FIRST component (ie."
 all of the flux is resolved out by FIRST): ai) both NVSS components lie within 60 aresee of ye SDSS position (larger sources may have additional NVSS Components outside of the 3 aremin limit. and so need to be checked visually: and (it) the angle NVSSI-SDSS-NVSS?2 greater jan. 135 degrees (Ge.," all of the flux is resolved out by FIRST); (ii) both NVSS components lie within 60 arcsec of the SDSS position (larger sources may have additional NVSS components outside of the 3 arcmin limit, and so need to be checked visually); and (iii) the angle NVSS1-SDSS-NVSS2 greater than 135 degrees (ie."
 consistent with a double radio source with a bend of «45 degrees)., consistent with a double radio source with a bend of $<45$ degrees).
Edge-on local starburst ealaxies show unambiguous evidence for ~10 kiloparsec-scale. weaklIy-collimated. ijpolar outflows (Ileckiiun.Lehuert&Armus1993).,"Edge-on local starburst galaxies show unambiguous evidence for $\sim 10$ kiloparsec-scale, weakly-collimated, bipolar outflows \citep{heck93}."
 Cirrent theory holds that these galactic superwinds are owvered by the collective mechanical power of large nuubers of Type II superuovae (SNe) aud stellay siuds. hat result from the laree population of massive stars ornmed in the starburst Chevalier&Cleese(L985). renceforth CC).," Current theory holds that these galactic superwinds are powered by the collective mechanical power of large numbers of Type II supernovae (SNe) and stellar winds, that result from the large population of massive stars formed in the starburst \citet{cc}, henceforth CC)."
 Tf this mechanical euergv is cfiicicutly hermalized m the starburst region converted back into the thermal οποίον of a hot eas Bbv shocks. as SNe and stellar winds collideV then a pressure-driven outflow roni the galaxy results.," If this mechanical energy is efficiently thermalized in the starburst region converted back into the thermal energy of a hot gas by shocks, as SNe and stellar winds collide), then a pressure-driven outflow from the galaxy results."
 The hot gas blows out of the host ealaxv ISM along the minor axis. forming the outflows seen in snon-thenual. radio cussion. optical enission lines. ax μαoft thermal XN-rav enüssonu in the halos of local starbursts.," The hot gas blows out of the host galaxy's ISM along the minor axis, forming the outflows seen in non-thermal radio emission, optical emission lines, and soft thermal X-ray emission in the halos of local starbursts."
 Superwiuds are of cosmological interest απ they transport large amounts of eas. in particular ucwly svuthesized heavy elemieuts aud energy. mto the media (OAD.," Superwinds are of cosmological interest as they transport large amounts of gas, in particular newly synthesized heavy elements, and energy, into the medium (IGM)."
 Quautifving this mass. metal aud energv transport in local starburst galaxies is essential for understanding the significance of outflows from star-fornuue ealaxics integrated. over the history of the Universe.," Quantifying this mass, metal and energy transport in local starburst galaxies is essential for understanding the significance of outflows from star-forming galaxies integrated over the history of the Universe."
 Uowever. even the basic physical propertics of local superwiuds such as mass outflow rates. energv content. abundances ancl kinematics are uncertain.," However, even the basic physical properties of local superwinds such as mass outflow rates, energy content, abundances and kinematics are uncertain."
" Measuring the pliysical properties of the hot eas driving hese outflows is of crucial ο or several simple reasons,", Measuring the physical properties of the hot gas driving these outflows is of crucial importance for several simple reasons.
 Firstly. the hot eas efiicicutly transports the uajoritv of the euergv of the outtlow Strickland&Stevens (2000))).," Firstly, the hot gas efficiently transports the majority of the energy of the outflow \citet{ss2000}) )."
 Secondly. the SN-heated eas is thought o contain the majority of the newly svuthesized metals.," Secondly, the SN-heated gas is thought to contain the majority of the newly synthesized metals."
 Finally. this energetic gas ultimately controls the ejection of mass from the galaxy. (although the majority of the uass of the outflow may be in ambient ISAL swept-up by he wind. this eas is accelerated to high velocity by the vot. fast. wind fluid. CC).," Finally, this energetic gas ultimately controls the ejection of mass from the galaxy (although the majority of the mass of the outflow may be in ambient ISM swept-up by the wind, this gas is accelerated to high velocity by the hot, fast, wind fluid, CC)."
 Iu principle. X-ray observations of the thermal emission roni hot gas in superwinds can be used to measure he properties of the hot eas.," In principle, X-ray observations of the thermal emission from hot gas in superwinds can be used to measure the properties of the hot gas."
 Large amounts ofROSAT and N-rav data on starbursts already: exists (see, Large amounts of and X-ray data on starbursts already exists (see
time ἀσίαν effects (Rubilar&Eckut2001:Wein-bereetal.,"time delay effects \citep{rubilar,weinberg}."
 2005).. For example. a torus of matter of mass m orbiting the black hole at a distance Rowill induce fractional changes in the appareut angular momentum and quadrupole moment of order 6.7/7~GnΑΠΑΟ1v) ," For example, a torus of matter of mass $m$ orbiting the black hole at a distance $R$ will induce fractional changes in the apparent angular momentum and quadrupole moment of order $\delta J/J \sim
(m/M)(R/M)^{1/2}(1/\chi)$ "
We will construct models for the mass distributions of the bulge. disc. bar and dark matter halo using paranieters [from previous studies. anc map light ravs [rom the measured image positions to the source plane.,"We will construct models for the mass distributions of the bulge, disc, bar and dark matter halo using parameters from previous studies, and map light rays from the measured image positions to the source plane."
 Varving the contribution of cach component will vary the convergence and shear within the images and. shift their. back-mapped positions in the source plane., Varying the contribution of each component will vary the convergence and shear within the images and shift their back-mapped positions in the source plane.
 A potential solution is obtained when a particular addition of the four components produces a common source position., A potential solution is obtained when a particular addition of the four components produces a common source position.
 Clearly. the four images originate from the same point in the source plane.," Clearly, the four images originate from the same point in the source plane."
 The actual position of the source quasar cannot be constrained., The actual position of the source quasar cannot be constrained.
 The centre of the galaxy will be considered. fixed. given the relatively few degrees of freedom., The centre of the galaxy will be considered fixed given the relatively few degrees of freedom.
 Rotation curves for potential solutions will be produced and compared with neutral hydrogen rotation measurements and the measured mass lving within the images., Rotation curves for potential solutions will be produced and compared with neutral hydrogen rotation measurements and the measured mass lying within the images.
 The combination of both lensing and dynamical constraints increases the number of constrained parameters. and consequently reduces the number of unknowns., The combination of both lensing and dynamical constraints increases the number of constrained parameters and consequently reduces the number of unknowns.
 The mocels used for the mass clistributions of the four principal galactic components are standard profiles from the literature. tailored to suit this galaxy.," The models used for the mass distributions of the four principal galactic components are standard profiles from the literature, tailored to suit this galaxy."
 The bulece is modelled as both à. modified ce Vaucouleurs surface mass cistribution (cde Vaucouleurs 1948. 1959). where it is assumed the mass follows the light (constant mass-to-light ratio) and an exponential surface mass profile. as in the models of Schmidt (1996).," The bulge is modelled as both a modified de Vaucouleurs surface mass distribution (de Vaucouleurs 1948, 1959), where it is assumed the mass follows the light (constant mass-to-light ratio) and an exponential surface mass profile, as in the models of Schmidt (1996)."
 The modification to both allows the introduction of an ellipticity.- c. such that for the de Vaucouleurs profile. where M is the value of the surface mass density at that position. ry is the characteristic scale length of the bulge. and e is defined. by. where e and b are the semi-major and minor axes respectivelv.," The modification to both allows the introduction of an ellipticity, $e$, such that for the de Vaucouleurs profile, where $\Sigma$ is the value of the surface mass density at that position, $r_b$ is the characteristic scale length of the bulge, and $e$ is defined by, where $a$ and $b$ are the semi-major and minor axes respectively."
 Phe central. surface. density (Xo 1057). is denoted “he., The central surface density $\Sigma_0\times$ $^{3.33}$ ) is denoted `bg'.
" The exponential profile is mocellec simply by introducing the ellipticitv (assumed to be a projection elfect). and again ""bg is the central surface mass clonsity."," The exponential profile is modelled simply by introducing the ellipticity (assumed to be a projection effect), and again `bg' is the central surface mass density."
 The dise is mocelled as an exponential surface density., The disc is modelled as an exponential surface density.
 Unlike the bulge which is treated: with the ellipticity as measured. the disc is rotated to its measured inclination of i607.," Unlike the bulge which is treated with the ellipticity as measured, the disc is rotated to its measured inclination of $i$ $^{\circ}$."
 This involves projecting the volume to a surface mass density by rotating the z-axis and redefining co-ordinates., This involves projecting the volume to a surface mass density by rotating the $z$ -axis and redefining co-ordinates.
 lU we assume the disc is uniformly clistributecd in. the direction. then we can simply. write. where the proportionality. includes a factor reflecting the thickness of the cise. assumed to be constant. ancl ry is the characteristic disc scale length.," If we assume the disc is uniformly distributed in the $z$ direction, then we can simply write, where the proportionality includes a factor reflecting the thickness of the disc, assumed to be constant, and $r_d$ is the characteristic disc scale length."
 Upon rotation about the a-axis (such that it becomes the major axis of the ellipse) by the inclination angle. 760. the surface mass density is the integral through the rotated axis. 2’ where the limits of integration bound. the origina constant disc thickness at the inclination angle. (taken as Az=h00pe). the primec co-ordinates represent the new. observed. Cartesian system and ‘de’ denotes the centra surface mass clonsity.," Upon rotation about the $x$ -axis (such that it becomes the major axis of the ellipse) by the inclination angle, $i$ $^{\circ}$, the surface mass density is the integral through the rotated axis, $z^\prime$, where the limits of integration bound the original constant disc thickness at the inclination angle (taken as $\Delta{z}$ =500pc), the primed co-ordinates represent the new, observed Cartesian system and `dc' denotes the central surface mass density."
 The bar has been extensively modelled: by Schmid (1996) and we will use his surface mass clistribution au position angle., The bar has been extensively modelled by Schmidt (1996) and we will use his surface mass distribution and position angle.
 Schmidt uses a Ferrers model with an ellipticity. €. where ‘br’ is the central surface density. A is the Ferrers exponent. and the Gr.y) co-ordinates lic in the rotated (rame of the bar.," Schmidt uses a Ferrers model with an ellipticity, $e$, where `br' is the central surface density, $\lambda$ is the Ferrers exponent, and the $(x,y)$ co-ordinates lie in the rotated frame of the bar."
 Sehimidt. finds different exponents.. ellipticities ancl scale lengths depending on the profiles used to fit to the light distribution.," Schmidt finds different exponents, ellipticities and scale lengths depending on the profiles used to fit to the light distribution."
 For an exponential bulge and disc. he finds A=2 e=0.64 and b—1.02:0.3 arcsec fit the observations best.," For an exponential bulge and disc, he finds $\lambda$ =2, $e$ =0.64 and $\pm$ 0.3 arcsec fit the observations best."
 For a de Vaucouleurs bulge ancl exponential disc. he finds A=O0.5. e—0.89 and b=3.10.9 arcsec.," For a de Vaucouleurs bulge and exponential disc, he finds $\lambda$ =0.5, $e$ =0.89 and $\pm$ 0.9 arcsec."
 In our analysis. the central surface density (essentially the ML) will remain," In our analysis, the central surface density (essentially the M/L) will remain"
In (his section. we compare the Modified Polvivopic Cardassian Model of Eq. (2)),"In this section, we compare the Modified Polytropic Cardassian Model of Eq. \ref{eq:FRW}) )"
 with current supernovae and cosmüc microwave background (CMD) data., with current supernovae and cosmic microwave background (CMB) data.
 We will see that the existing data can be well fit for several choices of the parameters » aud q., We will see that the existing data can be well fit for several choices of the parameters $n$ and $q$.
 In a smooth Friedmann-BRobertson-Walker (FRW) universe. the metric is given by ds?=a(Ly(dr?/(A=kr?)+(dé?sin?0dc? )]. where a(1) is the cosmic scale factor. and / is the global curvature parameter.," In a smooth Friedmann-Robertson-Walker (FRW) universe, the metric is given by $ds^2=dt^2-a^2(t)[dr^2/(1-kr^2)+r^2 (d\theta^2
+\sin^2\theta \,d\phi^2)]$ , where $a(t)$ is the cosmic scale factor, and $k$ is the global curvature parameter."
" The comoving distance r is given by (Weinberg1972) Lem IQ,|E2. οι... pagο... Ete)TÉu-— CLες)MEAN+ TES7. where 0,—1—QuisOx. and S(x)esinh((r). 2emt,xo =x. Όση KG,og —sn(Cre). 2em&2,«04"," The comoving distance $r$ is given by \citep{Weinberg72}
 1cm | _k, _X, _0^zdz' E(z') (1+z')^3+ _k(1+z')^2, where $\Omega_k = 1-\Omega_m^{obs}- \Omega_X$, and (x), 2cm _k>0 = x, 3cm _k=0 (x), 2cm _k<0."
6 The angular diameter distance is given by d4(z)=r(z)/(1+2). and the luminosity clistance is given by dp(2)=(1+z)r(z).," The angular diameter distance is given by $d_A(z)=r(z)/(1+z)$, and the luminosity distance is given by $d_L(z)=(1+z) r(z)$."
 The distance modulus for a standard candle at recshilt z is slmmAb=Sslogle FH )+25.," The distance modulus for a standard candle at redshift $z$ is _p m-M= ( )+25,"
 The distance modulus for a standard candle at recshilt z is slmmAb=Sslogle FH )+25.(," The distance modulus for a standard candle at redshift $z$ is _p m-M= ( )+25,"
 The distance modulus for a standard candle at recshilt z is slmmAb=Sslogle FH )+25.(1," The distance modulus for a standard candle at redshift $z$ is _p m-M= ( )+25,"
 The distance modulus for a standard candle at recshilt z is slmmAb=Sslogle FH )+25.(17," The distance modulus for a standard candle at redshift $z$ is _p m-M= ( )+25,"
 The distance modulus for a standard candle at recshilt z is slmmAb=Sslogle FH )+25.(17)," The distance modulus for a standard candle at redshift $z$ is _p m-M= ( )+25,"
planetary migration scenario assumes the planetesimals to be initially closer to the planet.,planetary migration scenario assumes the planetesimals to be initially closer to the planet.
" If we started with planetesimals at a larger distance, we would have expected to see, as in the P-R drag scenario, more differences in the resonant structures for planets of different masses."," If we started with planetesimals at a larger distance, we would have expected to see, as in the P-R drag scenario, more differences in the resonant structures for planets of different masses."
" Our results show that, with the forced planetary migration scenario, it is easy to distinguish a planet on a circular orbit from another on a low-eccentricity orbit, except for very low mass planets or very massive planets, because the resonant structures are drastically different."," Our results show that, with the forced planetary migration scenario, it is easy to distinguish a planet on a circular orbit from another on a low-eccentricity orbit, except for very low mass planets or very massive planets, because the resonant structures are drastically different."
 Constraining the planetary mass is more difficult than in the P-R drag scenario and only an order of magnitude can be expected., Constraining the planetary mass is more difficult than in the P-R drag scenario and only an order of magnitude can be expected.
 ? used this scenario to reproduce Vega disk observations at submillimetric wavelengths (?).., \citet{2003ApJ...598.1321W} used this scenario to reproduce Vega disk observations at submillimetric wavelengths \citep{1998Natur.392..788H}.
" We must take into account that, with the large SCUBA PSF, only the two major clumps can be observed."," We must take into account that, with the large SCUBA PSF, only the two major clumps can be observed."
" However, this is enough to distinguish between our three planet mass examples, at least for a migration rate of 0.5 AU Myr!: It is thus possible to obtain an estimate of the planetary mass."," However, this is enough to distinguish between our three planet mass examples, at least for a migration rate of $0.5$ AU $^{-1}$: It is thus possible to obtain an estimate of the planetary mass."
 The situation is well summarized by Figure 11 of ?.., The situation is well summarized by Figure 11 of \citet{2003ApJ...598.1321W}.
" It defines several regions in the (planetary mass, migration rate) parameter space that can be observationally distinguished from each other, but inside each region a wide range of planetary masses is possible."," It defines several regions in the (planetary mass, migration rate) parameter space that can be observationally distinguished from each other, but inside each region a wide range of planetary masses is possible."
 Contradictions however appear between our simulation results and this previous study., Contradictions however appear between our simulation results and this previous study.
 The asymmetry in the emission of the two observed clumps was interpreted as the migration of a Neptune mass planet by ?.., The asymmetry in the emission of the two observed clumps was interpreted as the migration of a Neptune mass planet by \citet{2003ApJ...598.1321W}.
" In his model, a Neptune can trap planetesimals in the 3:2 and 2:1 resonances and generate two asymmetric clumps, like a Saturn mass planet in our simulations."," In his model, a Neptune can trap planetesimals in the $3$ $2$ and $2$ $1$ resonances and generate two asymmetric clumps, like a Saturn mass planet in our simulations."
" With our numerical model, we have found that a Neptune mass planet cannot trap planetesimals in the 2:1 resonance, but only in the 3:2 resonance: the two clumps are thus symmetric and cannot reproduce the Vega disk."," With our numerical model, we have found that a Neptune mass planet cannot trap planetesimals in the $2$ $1$ resonance, but only in the $3$ $2$ resonance: the two clumps are thus symmetric and cannot reproduce the Vega disk."
" A Neptune mass planet at a migration rate of about 0.5 AU Myr7! lies at the sharp transition between a 0 and a 100% trapping probability (?,Fig.4a)..", A Neptune mass planet at a migration rate of about $0.5$ AU $^{-1}$ lies at the sharp transition between a $0$ and a $100\% $ trapping probability \citep[][Fig. 4a]{2003ApJ...598.1321W}.
 A small change in the planetary mass or the migration rate in this configuration produces a large modification in the population of this resonance., A small change in the planetary mass or the migration rate in this configuration produces a large modification in the population of this resonance.
" As ? uses a scaling law to predict the trapping probability, differences between our results may be explained by the approximation of this scaling law."," As \citet{2003ApJ...598.1321W} uses a scaling law to predict the trapping probability, differences between our results may be explained by the approximation of this scaling law."
" Nevertheless, the 2:1 resonance has an interesting behavior in the Neptune mass planet case: it perturbs all the"," Nevertheless, the $2$ $1$ resonance has an interesting behavior in the Neptune mass planet case: it perturbs all the"
focusing on narrow regions where the spectral feature appears to be hiehlv suppressed. indicating a reduced concentration of micron-sized particles.,"focusing on narrow regions where the spectral feature appears to be highly suppressed, indicating a reduced concentration of micron-sized particles."
 These features are likely a subset of (he compact optical depth enhancements identified in both Cassini images (Murray.e£af.2008;Beurleefa£.2010) and UVIS stellar occultations (Espositoefaf.2008:Meinkeefaf 2010).," These features are likely a subset of the compact optical depth enhancements identified in both Cassini images \citep{Murray08, Beurle10} and UVIS stellar occultations \citep{Esposito08, Meinke10}."
. Finally. we discuss possible interpretations of the observed spectral variations in terms of spatially-varving particle densities aud velocity dispersions within these dusty rings.," Finally, we discuss possible interpretations of the observed spectral variations in terms of spatially-varying particle densities and velocity dispersions within these dusty rings."
 VIMS is most often. used to produce spatially-resolved reflectance spectra. οἱ planetary (targets., VIMS is most often used to produce spatially-resolved reflectance spectra of planetary targets.
 ILowever. VIMS is a flexible instrument that can also operate in an occultation mode (Browne£al.2004).," However, VIMS is a flexible instrument that can also operate in an occultation mode \citep{Brown04}."
. In (his mode. the imaging capabilities are disabled. the short-wavelength VIS channel of the instrument is turned off and the Ih channel obtains a series of spectra from a sinele pixel targeted. al a star.," In this mode, the imaging capabilities are disabled, the short-wavelength VIS channel of the instrument is turned off and the IR channel obtains a series of spectra from a single pixel targeted at a star."
 The raw spectra are composed of 248 measurements of the stellar brightness between 0.85 and 5.0 jan with a typical resolution of 0.016 yan Gn occultation mode. eight channels are used to encode timing data).," The raw spectra are composed of 248 measurements of the stellar brightness between 0.85 and 5.0 $\mu$ m with a typical resolution of 0.016 $\mu$ m (in occultation mode, eight channels are used to encode timing data)."
" However. to save on data volume. these dala are usually co-acdded prior to transmission to earth. producing ""summed"" spectra consisting of 31 spectral measurements with a (vpical resolution of 0.1350n. The raw data used in this analvsis are the uncalibrated Data Numbers (DN) returned by the instrument."," However, to save on data volume, these data are usually co-added prior to transmission to earth, producing “summed” spectra consisting of 31 spectral measurements with a typical resolution of $\mu$ m. The raw data used in this analysis are the uncalibrated Data Numbers (DN) returned by the instrument."
 While these DN are linear measures of the photon flux 2004).. no attempt is made to convert these data to absolute fInxes here. although a nean insirumental thermal background spectrum has been subtracted Irom all the spectra for each occultation.," While these DN are linear measures of the photon flux \citep{Brown04}, no attempt is made to convert these data to absolute fluxes here, although a mean instrumental thermal background spectrum has been subtracted from all the spectra for each occultation."
 A precise time stamp is appended to every spectrum to acilitate reconstruction of the occultation geometry., A precise time stamp is appended to every spectrum to facilitate reconstruction of the occultation geometry.
 Each occultation is geometrically navigated based on the positions of the star (obtained from the Hipparcos catalog. and adjusted (ο account for proper motion aud parallax al Saturn) and the position of the spacecralt derived from the appropriate SPICE kernels.," Each occultation is geometrically navigated based on the positions of the star (obtained from the Hipparcos catalog, and adjusted to account for proper motion and parallax at Saturn) and the position of the spacecraft derived from the appropriate SPICE kernels."
 This information was used to predict the apparent position (radius and inerGal longitude) of the star in Saturn's ring plane as a function of time in a planetocentric reference frame. taking into account stellar aberration.," This information was used to predict the apparent position (radius and inertial longitude) of the star in Saturn's ring plane as a function of time in a planetocentric reference frame, taking into account stellar aberration."
 In. nearly all cases. this estimate of the occultation geometry was confirmed to be accurate to within a few kilometers using (he known radii of nearly circular gap edges in the outer A Ring from (Frenchefal.1993).," In nearly all cases, this estimate of the occultation geometry was confirmed to be accurate to within a few kilometers using the known radii of nearly circular gap edges in the outer A Ring from \citep{French93}."
. The exceptions were the low-inclination stars ο Ceti and ὁ Virginis. for which features could be tens of kilometers away [rom their nominal positions.," The exceptions were the low-inclination stars $o$ Ceti and $\delta$ Virginis, for which features could be tens of kilometers away from their nominal positions."
 In these cases. the fiducial position of Saturn's pole was adjusted slightly (bv al most 0.0157) to bring these cuts into alignment. with the other occultations. (," In these cases, the fiducial position of Saturn's pole was adjusted slightly (by at most $^\circ$ ) to bring these cuts into alignment with the other occultations. ("
Note that such corrections were not possible [or the Rev 12 ο Ceti occultation. which,"Note that such corrections were not possible for the Rev 12 $o$ Ceti occultation, which"
electrons with energiesoO of 8 and 25 GeV traversinge thin egold and carbon targetse have been presented in Anthonyetal.(1995).,electrons with energies of $8$ and $25$ GeV traversing thin gold and carbon targets have been presented in \citet{An95}.
. The suppression of bremsstralilung predicted by the LPAI theory is correct to within 5%., The suppression of bremsstrahlung predicted by the LPM theory is correct to within $5\%$.
 The main parameters defining radiation processes in a medium are (he coherence length fo (he mean [ree path of a fast particle in matter /.. the radiation length Ny and the thickness of the target L (AkhiezerandShul'ga(1996) and references therein).," The main parameters defining radiation processes in a medium are the coherence length $l_c$, the mean free path of a fast particle in matter $l_{e}$, the radiation length $X_{0}$ and the thickness of the target $L$ \citet{AkSh96} and references therein)."
 The coherence length is the distance along the particle momentum where interference effects during the radiation process are significant., The coherence length is the distance along the particle momentum where interference effects during the radiation process are significant.
 /. rapidlv grows wilh an increase of the particle enerev and al hieh energies it can be macroscopic., $l_c$ rapidly grows with an increase of the particle energy and at high energies it can be macroscopic.
" Η the energy w of the bremsstrahlung photon produced by an ultra-relativistic particle of energv. E satisfies the condition w<<e. then the average angle ϐ between the incident particle and the photon is small. &,2me?/e."," If the energy $\omega $ of the bremsstrahlung photon produced by an ultra-relativistic particle of energy $E$ satisfies the condition $\omega <<\epsilon
$, then the average angle $\theta $ between the incident particle and the photon is small, $\theta _c\approx mc^2/\epsilon $."
 The average angle between (he scattered. particles is smaller still., The average angle between the scattered particles is smaller still.
 Neglecüng (hese angles. the longitudinal momentiun transfer between the interacting particles is pj~w/25?e. where 5=e/mc?.," Neglecting these angles, the longitudinal momentum transfer between the interacting particles is $p_{\left| {}\right| }\simeq
\omega /2\gamma ^{2}c$, where $\gamma =\epsilon /mc^{2}$."
 The uncertainty principle then requires (hat (he spatial position of the bremsstrahlung process has a longitudinal uncertainty of /.—h/pyzzολο.," The uncertainty principle then requires that the spatial position of the bremsstrahlung process has a longitudinal uncertainty of $l_{c}=\hbar /p_{\left| {}\right| }\approx 2\hbar c\gamma
^{2}/\omega $."
 The coherence length rapidly grows wilh an increase of the particle energy. and al high energies can be macroscopic.," The coherence length rapidly grows with an increase of the particle energy, and at high energies can be macroscopic."
 In alternate language. (he particle aud. photon slowly split apart over the distance /..," In alternate language, the particle and photon slowly split apart over the distance $l_{c} $."
 In a sufficiently dense medium the mean [ree path of the incident particle is much smaller than /.. so a parücle will interact while (raversine the region /..," In a sufficiently dense medium the mean free path of the incident particle is much smaller than $l_{c}$, so a particle will interact while traversing the region $l_{c}$ ."
 Dremsstirahlung is suppressed when the mean square multiple scattering angle over the distance /.. is greater than or equal to 67 (AkhiezerandShul'ga(1996):lein(1999) and references (herein).," Bremsstrahlung is suppressed when the mean square multiple scattering angle over the distance $l_c$, is greater than or equal to $\theta _{k}^{2}$ \citet{AkSh96,Kl99}
 and references therein)."
 [ere is the radiation length and In Eq. (12)), Here is the radiation length and In Eq. \ref{x0}) )
" r,=ες> is the classical radius of the particle (the electron).", $r_{e}=e^{2}/mc^{2}$ is the classical radius of the particle (the electron).
 The effect of multiple suppression on the total radiation emission of the charged particle. d1/duw. can be obtained. for iw<<ee/e?Xy. in the form (Ixlein(1999). and references therein) Thus. multiple scattering results in a decrease of the coherence length. leading. in (urn. to radiation suppression.," The effect of multiple suppression on the total radiation emission of the charged particle, $dI/d\omega
$, can be obtained, for $\omega <<\epsilon _{s}^{2}c/\epsilon
^{2}X_{0}$, in the form \citet{Kl99} and references therein) Thus, multiple scattering results in a decrease of the coherence length, leading, in turn, to radiation suppression."
 The effect appears in (lie case when (he mean-square angle ofthe, The effect appears in the case when the mean-square angle ofthe
favours rates significantly smaller. particularly at the beginning of the AGB phase. with cillerences up to ~1.5 dex compared to the others.,"favours rates significantly smaller, particularly at the beginning of the AGB phase, with differences up to $\sim~1.5$ dex compared to the others."
 A smaller. dillerence exists between the Blocker(1995) and the Weiss&Fergu-son(2009) recipes. the latter being higher by ~0.20.3 dex during most of the evolution.," A smaller difference exists between the \citet{blo} and the \citet{achim} recipes, the latter being higher by $\sim~0.2-0.3$ dex during most of the evolution."
" In the early AGB the Weiss&Ferguson(2009) treatment predicts rates of the order of 10""10.9AL. fve. which are. however. not sullicient to diminish the tota number of LPs so as to recover their original result. (6)."," In the early AGB the \citet{achim} treatment predicts rates of the order of $10^{-7}-10^{-6}~M_{\odot}$ /yr, which are, however, not sufficient to diminish the total number of TPs so as to recover their original result $6$ )."
 Dhis suggests that the main reasons for the smaller number of TPs in the Weiss&Ferguson(2009) investigation compare to our models is an earlier transition to the C-star stage., This suggests that the main reasons for the smaller number of TPs in the \citet{achim} investigation compared to our models is an earlier transition to the C-star stage.
 ‘This dillerence is due to two reasons: a) The mocdelling of convective overshoot [rom the bottom of the envelope (see their equation. 2). based on an exponential decay of the dilfusive coefficient. with the same e-folding clistance usec for main-sequences width fitting.," This difference is due to two reasons: a) The modelling of convective overshoot from the bottom of the envelope (see their equation 2), based on an exponential decay of the diffusive coefficient, with the same e-folding distance used for main-sequences width fitting."
 This approach determines a much deeper extension of EDU when compared with our models (where no overshoot is assumed). and with those by Cristalloetal.(2009).. who adopt an exponential decay. of the convective velocity [rom the inner border of the external mantle. with an e-folding distance tuned in order to allow the synthesis of a given amount of £C available for neutron-captures.," This approach determines a much deeper extension of TDU when compared with our models (where no overshoot is assumed), and with those by \citet{sergio2}, who adopt an exponential decay of the convective velocity from the inner border of the external mantle, with an e-folding distance tuned in order to allow the synthesis of a given amount of $^{13}$ C available for neutron-captures."
 This amount of extra-mixing is also the plausible reason for the smaller number of TIs experienced. by. the Cristalloetal.(2009). model compared to our 806€. and to the different final core-masses (0.67AL... to be compared to τοAM. b) the convective overshoot from the He-burning shell. adopted by. Weiss&Ferguson(2009).. and. neglected here and in Cristalloetal.(2009)... which. as described bv Llerwig&Austin(2004).. renders the pulses stronger.," This amount of extra-mixing is also the plausible reason for the smaller number of TPs experienced by the \citet{sergio2}
 model compared to our S06C, and to the different final core-masses $0.67~M_{\odot}$, to be compared to $0.70~M_{\odot}$ ); b) the convective overshoot from the He-burning shell, adopted by \citet{achim}, and neglected here and in \citet{sergio2}, which, as described by \citet{falk3}, renders the pulses stronger."
 The models presented here. though including no overshoot. are much more similar to those by Cristalloetal.(2009) in terms of duration of the whole AGB phase and of the chemistry of the ejecta.," The models presented here, though including no overshoot, are much more similar to those by \citet{sergio2} in terms of duration of the whole AGB phase and of the chemistry of the ejecta."
 A ctailecl investigation of the ΕΙ phenomenology. and the possible effects. of assuming some convective overshoot from the bottom of the convective envelope. is bevond the scope ofthe present paper: the interested reader may find in Llerwig(2000).. Llerwig (2005).. Mowlavi(1999) and Stranieroctal.(1997) a Cull discussion on the kev issues relevant to address this problem.," A detailed investigation of the TDU phenomenology, and the possible effects of assuming some convective overshoot from the bottom of the convective envelope, is beyond the scope of the present paper; the interested reader may find in \citet{falk}, \citet{falk2}, \citet{mowlavi} and \citet{oscar} a full discussion on the key issues relevant to address this problem."
 Anvhow. the present study. clearly illustrates that the AGB evolution is the product. of a complex. interplay between various processes: the treatment of the extra-mixing. for instance. has a remarkable impact not only on the chemical but also on the physical. properties of these stars.," Anyhow, the present study clearly illustrates that the AGB evolution is the product of a complex interplay between various processes: the treatment of the extra-mixing, for instance, has a remarkable impact not only on the chemical but also on the physical properties of these stars."
 In view of improving the robustness of the results provided by AGB modelling (or at least to quantify the uncertainty range). we have investigated the sensitivity of the main physical ancl chemical properties to the choices inherent the input macro- and micro-physies.," In view of improving the robustness of the results provided by AGB modelling (or at least to quantify the uncertainty range), we have investigated the sensitivity of the main physical and chemical properties to the choices inherent the input macro- and micro-physics."
 We [ind a threshold. mass. that is AJ~3.5M. for Z-—0.001 in the present analysis. (note that it also depends on the assumed overshooting from the central regions during the core L- and Le-burnine). above which the results are little sensitive to the opacity treatment. because LBB prevents the surface C/O ratio to exceed unity.," We find a threshold mass, that is $M\simeq 3.5~M_{\odot}$ for $Z=0.001$ in the present analysis, (note that it also depends on the assumed overshooting from the central regions during the core H- and He-burning), above which the results are little sensitive to the opacity treatment, because HBB prevents the surface C/O ratio to exceed unity."
 In this range of masses mass loss modelling plavs a crucial role., In this range of masses mass loss modelling plays a crucial role.
 Models calculated with a treatment of the mass loss only mildly. dependent on the luminosity. such as the classic Vassiliacis&Wood(1993). or the Stranieroetal.(2006) recipe used here. precict smaller rates during mos of the AGB phase. thus more “PPs are experienced.," Models calculated with a treatment of the mass loss only mildly dependent on the luminosity, such as the classic \citet{VW93}
 or the \citet{oscar2} recipe used here, predict smaller rates during most of the AGB phase, thus more TPs are experienced."
 This also favours the growth of the luminosity ancl temperature at the bottom of the convective zone. and a more acvancec LBB nucleosynthesis: the vields will contain the signature of proton-capture nucleosvnthesis. c.g. lower carbon ane oxvecn abuncanees. and higher nitrogen content.," This also favours the growth of the luminosity and temperature at the bottom of the convective zone, and a more advanced HBB nucleosynthesis: the yields will contain the signature of proton-capture nucleosynthesis, e.g. lower carbon and oxygen abundances, and higher nitrogen content."
 However. rw general patterns of the C-N and O-Na relations. anc vw very small increase in the overall CNO abundance. are almost independent of the opacity anc mass-loss treatment: we expect convection modelling plavs a relevant role here. in agreement with the analysis by Ventura&D'Anton," However, the general patterns of the C-N and O-Na relations, and the very small increase in the overall CNO abundance, are almost independent of the opacity and mass-loss treatment: we expect convection modelling plays a relevant role here, in agreement with the analysis by \citet{paolo4}. ."
a For masses smaller than 3.5A. the interplay between opacity ancl mass-loss treatment is more tricky. because 1e lack of UBB favours the increase in surface carbon.," For masses smaller than $3.5~M_{\odot}$ the interplay between opacity and mass-loss treatment is more tricky, because the lack of HBB favours the increase in surface carbon."
 Generally speaking. we confirm the results by 2007).. Cristalloetal.(2008.2009). and Weiss&Ferguson(2009):: the use of the correct opacities in the Iow-T regime specds-up the loss of the stellar envelope. via the strong winds associated to the general expansion of the structure when the surface C/O ratio exceeds unity.," Generally speaking, we confirm the results by \citet{paola02, paola07}, \citet{sergio, sergio2} and \citet{achim}: the use of the correct opacities in the low-T regime speeds-up the loss of the stellar envelope, via the strong winds associated to the general expansion of the structure when the surface C/O ratio exceeds unity."
 We expect in this case a smaller. number of PPPs. and a less advanced nucleosvnthesis (i£ any) at the bottom of the convective envelope.," We expect in this case a smaller number of TPs, and a less advanced nucleosynthesis (if any) at the bottom of the convective envelope."
 Alocdels caleulated with a miass-loss rate steeply dependent on the luminosity show a more homogeneous behaviour. whereas when a milder dependeney of AL with luminosity. c.g. a relationship that relates A. to the stellar period. is adopted. many physical properties. c.g. core-mass. temperature at the bottom of the convective zone. total number of thermal pulses experienced. follow a completely different behaviour.," Models calculated with a mass-loss rate steeply dependent on the luminosity show a more homogeneous behaviour, whereas when a milder dependency of $\dot M$ with luminosity, e.g. a relationship that relates $\dot M$ to the stellar period, is adopted, many physical properties, e.g. core-mass, temperature at the bottom of the convective zone, total number of thermal pulses experienced, follow a completely different behaviour."
 In this case the quenching of HB determined. by the use of the C-rich opacities. predicted. by Alavigo(2007).. is confirmed. being a common feature of all he models with LS3.0M...," In this case the quenching of HBB determined by the use of the C-rich opacities, predicted by \citet{paola07}, is confirmed, being a common feature of all the models with $1.8-3.0~M_{\odot}$."
 A narrower range of masses (around ~3 AL.) is otherwise allected by this uncertainty when an ellicient. mass-loss prescription. like the Dlócker(1995) formula. is adopted.," A narrower range of masses (around $\sim~3~M_{\odot}$ ) is otherwise affected by this uncertainty when an efficient mass-loss prescription, like the \citet{blo}
 formula, is adopted."
 Contrary to the models experiencing LBB. the vields rom lower mass stars are highly uncertain and moclel-dependent: the average C/Fe] in the ejecta shows up an overall uncertainty of 0.7 dex. though this dillerence reduces Oo 0.3.0.4 dex if mocels calculated with the same opacities are compared.," Contrary to the models experiencing HBB, the yields from lower mass stars are highly uncertain and model-dependent: the average [C/Fe] in the ejecta shows up an overall uncertainty of $0.7$ dex, though this difference reduces to $\sim 0.3-0.4$ dex if models calculated with the same opacities are compared."
 The situation for nitrogen. and sodium is more extreme. as they are particularly sensitive to he ignition of LIBB.," The situation for nitrogen and sodium is more extreme, as they are particularly sensitive to the ignition of HBB."
 Ehe dilferences in ΑΟ and. NaEc] can reach ~2 dex. and even when comparing mocoels with the same assumptions for the opacity treatment. discrepancies of one order of magnitude still persist.," The differences in [N/Fe] and [Na/Fe] can reach $\sim 2$ dex, and even when comparing models with the same assumptions for the opacity treatment, discrepancies of one order of magnitude still persist."
 The oxygen vields appear. instead. more stable.," The oxygen yields appear, instead, more stable."
 These trends should. be considered: representative of AGB models with a low metal content (Z 0.001) while they need to be further exploredat larger mictallicities i.c. including those characteristic of the LAIC (Ventura et al..," These trends should be considered representative of AGB models with a low metal content $Z \sim 0.001$ ) while they need to be further exploredat larger metallicities i.e. including those characteristic of the LMC (Ventura et al.,"
 in preparation)., in preparation).
 Moreover. in the present. unresolved. scenario," Moreover, in the present unresolved scenario"
the quark core appears. the star only spins-up with angular momentum loss. for the rest of its lifetime.,"the quark core appears, the star only spins-up with angular momentum loss, for the rest of its lifetime."
" To summarize. for the particular EOS that we have studied in this paper. normal pulsars do not feature a spin-up era during phase transition, while supramassive pulsars only spin up after the phase transition."," To summarize, for the particular EOS that we have studied in this paper, normal pulsars do not feature a spin-up era during phase transition, while supramassive pulsars only spin up after the phase transition."
 The limiting sequence that divides normal from supramassive pulsars shows a very small era of spin-up and appears to be the dividing line between stars that can spin up and stars that only spin down., The limiting sequence that divides normal from supramassive pulsars shows a very small era of spin-up and appears to be the dividing line between stars that can spin up and stars that only spin down.
 In the previous sections we demonstrated that the refined tabulated/analytic EOS produces a constant baryonic mass sequence with equilibrium properties that are in sharp contrast to the equilibrium properties computed on the basis of the original tabulated EOS., In the previous sections we demonstrated that the refined tabulated/analytic EOS produces a constant baryonic mass sequence with equilibrium properties that are in sharp contrast to the equilibrium properties computed on the basis of the original tabulated EOS.
 In this section. we will use an independent check to verify that the equilibrium properties obtained with the refined EOS are indeed the physically acceptable ones. while the equilibrium sequence obtained with the tabulated EOS suffers from numerical errors.," In this section we will use an independent check to verify that the equilibrium properties obtained with the refined EOS are indeed the physically acceptable ones, while the equilibrium sequence obtained with the tabulated EOS suffers from numerical errors."
 The independent check of the accuracy of the computed equilibrium properties is provided by the use of a relation that was first proved by Ostriker and Gunn (1969) in Newtonian theory and then derived in general relativity by Bardeen (1970)., The independent check of the accuracy of the computed equilibrium properties is provided by the use of a relation that was first proved by Ostriker and Gunn (1969) in Newtonian theory and then derived in general relativity by Bardeen (1970).
 Along a sequence of uniformly rotating models of constant baryonic mass. changes in M and J are related by which can be regarded as an expression of the first law of thermodynamies for such sequences.," Along a sequence of uniformly rotating models of constant baryonic mass, changes in $M$ and $J$ are related by which can be regarded as an expression of the first law of thermodynamics for such sequences."
 We have evaluated the above relation numerically along the obtained sequences of equilibrium models (using sufficiently many individual models to ensure an accurate evaluation of the numerical derivative)., We have evaluated the above relation numerically along the obtained sequences of equilibrium models (using sufficiently many individual models to ensure an accurate evaluation of the numerical derivative).
 We define an error indicator. A. as The evaluation of X along the evolutionary sequence of My=1.551M. (Fig. 7).," We define an error indicator, $\lambda$, as The evaluation of $\lambda$ along the evolutionary sequence of $M_0=1.551
M_\odot$ (Fig. \ref{lambda}) ),"
 shows that the above relation is satisfied with an accuracy of ~1% for models with central energy densities smaller than the energy density at which the pure quark-core appears., shows that the above relation is satisfied with an accuracy of $\sim 1$ for models with central energy densities smaller than the energy density at which the pure quark-core appears.
 After the appearance of the pure quark core. numerical errors result in huge values of A. when using the original tabulated EOS.," After the appearance of the pure quark core, numerical errors result in huge values of $\lambda$, when using the original tabulated EOS."
 With the use of the refined tabulated/analytic EOS. these errors are reduced significantly to an acceptable level and diminish as the resolution ts increased.," With the use of the refined tabulated/analytic EOS, these errors are reduced significantly to an acceptable level and diminish as the resolution is increased."
" The above check confirms that the refined EOS indeed produces physically acceptable results. while the original tabulated EOS produces results that are dominated by numerical error in the region in question,"," The above check confirms that the refined EOS indeed produces physically acceptable results, while the original tabulated EOS produces results that are dominated by numerical error in the region in question."
 If a compact star 1s detected as a pulsar and one can measure the first two time-derivatives €). © of its angular velocity. then one can define an observational braking index In the Newtonian. slow-rotation limit. the spin-down of a pulsar is usually modeled in the form of a power law (see Shapiro Teukolsky.," If a compact star is detected as a pulsar and one can measure the first two time-derivatives $\dot \Omega$, $ \ddot \Omega$ of its angular velocity, then one can define an observational braking index In the Newtonian, slow-rotation limit, the spin-down of a pulsar is usually modeled in the form of a power law (see Shapiro Teukolsky."
 1983). namely assuming that only kinetic energy is lost and that the rate of loss is proportional to some power of the angular velocity of the star. 1.8. where K«0 and &>O are usually assumed to be real constants.," 1983), namely assuming that only kinetic energy is lost and that the rate of loss is proportional to some power of the angular velocity of the star, i.e. where $\kappa<0$ and $\alpha>0$ are usually assumed to be real constants."
 With these assumptions. the braking index is equal to=a|.," With these assumptions, the braking index is equal to $n=\alpha-1$."
 For example. it is assumed that. for magnetic braking. T—ΩΙ. which yields an expected braking index η=3. while. for gravitational wave emission. T~Q°. which yields n—3.," For example, it is assumed that, for magnetic braking, $\dot T \sim \Omega^4$, which yields an expected braking index $n=3$, while, for gravitational wave emission, $\dot T \sim \Omega^6$, which yields $n=5$."
 For slowly rotating pulsars. the above considerations are. in most cases. appropriate.," For slowly rotating pulsars, the above considerations are, in most cases, appropriate."
 However. for rapidly rotating pulsars one has to take into account the rotational flattening of the star.," However, for rapidly rotating pulsars one has to take into account the rotational flattening of the star."
 To a first approximation. this can be done considering rotational effects up to order O(Q7).," To a first approximation, this can be done considering rotational effects up to order $O(\Omega^2)$."
 Glendenning (1997) gives the rotationally corrected Q and braking index 2(Q) for a sequence of uniformly rotating stars. assuming the spin-down law of Equation (7)).," Glendenning (1997) gives the rotationally corrected $\dot \Omega$ and braking index $n(\Omega)$ for a sequence of uniformly rotating stars, assuming the spin-down law of Equation \ref{dT1}) )."
 As we will show here. the expressions given in Glendenning (1997) are incomplete. in the sense that the derivation is not fully consistent to O(Q7). but misses additional contributions of the same order.," As we will show here, the expressions given in Glendenning (1997) are incomplete, in the sense that the derivation is not fully consistent to $O(\Omega^2)$, but misses additional contributions of the same order."
 The energy lost in the form of electromagnetic. or gravitation radiation is not only to the expense of the star's kinetic energy (which would be the case only in the O(Q) slow- approximation) but to the expense of the star's total, The energy lost in the form of electromagnetic or gravitation radiation is not only to the expense of the star's kinetic energy (which would be the case only in the $O(\Omega)$ slow-rotation approximation) but to the expense of the star's total
As shortly described iu Sect.,As shortly described in Sect.
 1. both Zola (1996) aud Dacins (1998) lave analyzed the πο curves of W Cru with a disk model.," 1, both a (1996) and Daems (1998) have analyzed the light curves of W Cru with a disk model."
 Zola used mean light curves coustructed from Marino et ((1988). and Pazzi (1993) photoclectzic photometry. respectively.," a used mean light curves constructed from Marino et (1988), and Pazzi (1993) photoelectric photometry, respectively."
 Dacius study was based on then unpublished Ceneva photometry., Daems study was based on then unpublished Geneva photometry.
 Both studies have arrived to a quite consistent set of the paralcters., Both studies have arrived to a quite consistent set of the parameters.
 While im our initial caleulations we lave started with the parameters which have cover very broad range in the parameter space. it was munediatelv clear hat solutions will be in the narrow range arotnd t values specified by Zola. aud Daeuis. respectively.," While in our initial calculations we have started with the parameters which have cover very broad range in the parameter space, it was immediately clear that solutions will be in the narrow range around the values specified by a, and Daems, respectively."
 Since we are looking for the optimal set of t xumnueters in a imultidinensional parameter sace is recommended to fix as mauy paraneters as possib, Since we are looking for the optimal set of the parameters in a multi-dimensional parameter space it is recommended to fix as many parameters as possible.
 Therefore. we assigned theoretical values to eyavifv xiehtening. hb darkening. and albedo cocfiicicu," Therefore, we assigned theoretical values to gravity brightening, limb darkening, and albedo coefficients."
 ST1e effective temperature of the G supergiaut. only visible stellar componcut. has been derived by Dacus (1998) fro111 he spectral cnerey distribution iu the broad wavelenghi span. froii IUE UV to optical aud IR photometry obtained at ESO.," The effective temperature of the G supergiant, only visible stellar component, has been derived by Daems (1998) from the spectral energy distribution in the broad wavelength span, from IUE UV to optical and IR photometry obtained at ESO."
 Ie has arrived to Τομ=5500 Is.," He has arrived to $T_{2,\rm eff} =
5500$ K."
Cartesian frame (v4.x3).,"Cartesian frame $(x_1,x_2)$."
" Following again Refregier(2003)... we define the polar shapelet basis functions às where 5 and s, are the left-handed and right-handed modes. respectively. and Bernstein&Jarvis(2002) showed that. for, «n,. one can relate to the associated Laguerre polynomial Note the similarities between the Cartesian basis and the polar basis(??=: Both share a Gaussian weighting function and are intrinsically circular."," Following again \citet{Refregier03.1}, we define the polar shapelet basis functions as where $n_l$ and $n_r$ are the left-handed and right-handed modes, respectively, and \citet{Bernstein02.1} showed that, for $n_l<n_r$, one can relate to the associated Laguerre polynomial Note the similarities between the Cartesian basis and the polar basis: Both share a Gaussian weighting function and are intrinsically circular."
" As Baan, is a complex function. if an,τσa. it is computationally more efficient to decompose the galactic shape into Cartesian shapelets according to and then to perform a coordinate transformation T*7 from Cartesian to polar shapelet space (cf.Eq.(69)inRefregier2003).. We will do that for the tests in the following sections."," As $B_{n_r,n_l}$ is a complex function if $n_r\neq n_l$, it is computationally more efficient to decompose the galactic shape into Cartesian shapelets according to and then to perform a coordinate transformation $\mathbf{T}^{c\rightarrow p}$ from Cartesian to polar shapelet space \citep[cf. Eq. (69) in][]{Refregier03.1}, We will do that for the tests in the following sections."
 Performing this transformation enables us to form a conceptionally different family of shear estimators., Performing this transformation enables us to form a conceptionally different family of shear estimators.
" By defining nSΠΕΠ and 1=Πρ1. we can see from(10).. that 5,,, behaves like a field with spin 7."," By defining $n\equiv n_r + n_l$ and $m\equiv n_r - n_l$, we can see from, that $B_{n,m}$ behaves like a field with spin $m$."
 Since the shear behaves like à spin-2 field. its action on a circular source can be described by the v7=2 modes of a polar shapelet model.," Since the shear behaves like a spin-2 field, its action on a circular source can be described by the $m=2$ modes of a polar shapelet model."
 Thus. the most basic one of these estimators. uses only the #7=2 mode of any even polar order of C' (Masseyetal.2007)05i," Thus, the most basic one of these estimators, uses only the $m=2$ mode of any even polar order $n$ of $\tilde{G}^\prime$ \citep{Massey07.2}."
 This estimator must be normalized by radial modes gn.oP? obtained from unlensed sources.," This estimator must be normalized by radial modes $g^p_{n,0}$ obtained from unlensed sources."
 For the tests discussed here. we provide the ulensed image G such that those coefficients can be measured from images having the correct unlensed shape.," For the tests discussed here, we provide the unlensed image $G$ such that those coefficients can be measured from images having the correct unlensed shape."
 This approach is drastically different from measuring the quadrupole moment — in the sense that it depends only on a single lensed and two radial unlensed coefficients — and thus expected to behave in a differentmanner. even though the decomposition is done with Cartesian shapelets in both cases.," This approach is drastically different from measuring the quadrupole moment – in the sense that it depends only on a single lensed and two radial unlensed coefficients – and thus expected to behave in a differentmanner, even though the decomposition is done with Cartesian shapelets in both cases."
 G' is decomposed into Cartesian shapelets of maximum order Hoy€18.12}. which is typical given the significance of images (cf.Kuijken 2006," $G^\prime$ is decomposed into Cartesian shapelets of maximum order $n_{max}\in\lbrace8,12\rbrace$, which is typical given the significance of weak-lensing images \citep[cf.][]{Kuijken06.1}."
).At first. we investigate the modeling fidelity visually.," .At first, we investigate the modeling fidelity visually."
 In Fig. l..," In Fig. \ref{fig:models}, ,"
 we give four examples of Sérrsic-type galaxy shapes, we give four examples of Sérrsic-type galaxy shapes
1.17+0.08&107 erg em sc.,"$1.17\pm 0.08\times
10^{-8}$ erg $^{-2}$ $^{-1}$."
 The best-fit Gaussian indicates a broad line. shifted from the neutral Fe Ka line energy of 6.40 keV: ΕΞ5.3/5! keV. FWHM=3.27558 keV. and W=250£50 eV. The edge is measured to be at ΕΞ6.84:0.3 keV. with a depth of 720.5+0.1.," The best-fit Gaussian indicates a broad line, shifted from the neutral Fe $\alpha$ line energy of 6.40 keV: $=5.3^{+0.1}_{-0.3}$ keV, $=3.2_{-0.6}^{+0.8}$ keV, and $=250\pm 50$ eV. The edge is measured to be at $=6.8\pm 0.3$ keV, with a depth of $\tau=0.5\pm
0.1$."
 However. significant residuals remain in the Fe Ko. line region with this fit. due in part to the non-Gaussian nature of the line profile (see Figure 1).," However, significant residuals remain in the Fe $\alpha$ line region with this fit, due in part to the non-Gaussian nature of the line profile (see Figure 1)."
" Moreover. on a broader energy range (one that includes the 20-30 keV ""Compton hump"" seen in many sources). a reflection model is often required to fit the spectra of stellar-mass black holes (see. e.g.. Gierlinski et al."," Moreover, on a broader energy range (one that includes the 20–30 keV “Compton hump” seen in many sources), a reflection model is often required to fit the spectra of stellar-mass black holes (see, e.g., Gierlinski et al."
 1999)., 1999).
 Broad Gaussian and smeared edge components are merely an approximation to a full reflection model in the 10.0 keV band., Broad Gaussian and smeared edge components are merely an approximation to a full reflection model in the 0.5--10.0 keV band.
 Therefore. we now focus on the results of fitting more sophisticated. physically-motivated reflection models.," Therefore, we now focus on the results of fitting more sophisticated, physically-motivated reflection models."
 These replace the hard power-law. Gaussian. and smeared edge components discussed above.," These replace the hard power-law, Gaussian, and smeared edge components discussed above."
" Anticipating a highly-ionized accretion disk. we made fits with the ""constant density ionized disk"" reflection model (hereafter. CDID: Ross. Fabian. Young 1999)."," Anticipating a highly-ionized accretion disk, we made fits with the “constant density ionized disk” reflection model (hereafter, CDID; Ross, Fabian, Young 1999)."
 This model measures the relative strengths of the directly-observed and reflected flux. the accretion disk ionization parameter Ly /nR?. where Ly is the X-ray luminosity. 1 is the hydrogen number density. and R is radius). and the photon index of the illuminating power-law flux.," This model measures the relative strengths of the directly-observed and reflected flux, the accretion disk ionization parameter $\xi = L_{X}/nR^{2}$ , where $L_{X}$ is the X-ray luminosity, $n$ is the hydrogen number density, and $R$ is radius), and the photon index of the illuminating power-law flux."
 Fe Ko line emission and line broadening due to Comptonization in an ionized disk surface layer are included m this model., Fe $\alpha$ line emission and line broadening due to Comptonization in an ionized disk surface layer are included in this model.
 The fit obtained with this model is shown in the top panel of Figure 2., The fit obtained with this model is shown in the top panel of Figure 2.
 The photon index of the irradiating power law is measured to be ΓΞ 2.08407.The ionization parameter is high: C=1.3%)«IO ergem s! and the relative strength of reflected flux is measured to be f£=UR (where ρω Εκ).," The photon index of the irradiating power law is measured to be $\Gamma=2.08^{+0.02}_{-0.04}$ .The ionization parameter is high: $\xi=1.3^{+0.7}_{-0.1}\times 10^{4}$ erg cm $^{-1}$, and the relative strength of reflected flux is measured to be $f=0.5_{-0.1}^{+0.7}$ (where $F_{total} = F_{direct} + f\times
F_{refl.}$ )."
 While the shape of the Fe K edge is reproduced by this model. the width and shape of the Fe Ka line ts not. and a statistically-poor fit is obtained (4=399.7 for 231 d.o.f.).," While the shape of the Fe K edge is reproduced by this model, the width and shape of the Fe $\alpha$ line is not, and a statistically-poor fit is obtained $\chi^{2}=399.7$ for 231 d.o.f.)."
 The ionization parameter obtained with this model corresponds to a mixture of helium-like and hydrogenie ion species of Fe (Kallman and MeCray 1982)., The ionization parameter obtained with this model corresponds to a mixture of helium-like and hydrogenic ion species of Fe (Kallman and McCray 1982).
 As Doppler shifts and general relativistic smearing may be expected for lines produced in an aecretion. disk close to the black hole. we next made fits after convolving (or. ~blurring”) the CDID model with the line element expected near à Kerr black hole.," As Doppler shifts and general relativistic smearing may be expected for lines produced in an accretion disk close to the black hole, we next made fits after convolving (or, “blurring”) the CDID model with the line element expected near a Kerr black hole."
" We assumed an inner disk radius of 1.24 R,. an outer line production radius of 400 R,. and an inclination of /2457 (in fits with this and other models. intermediate inclinations were marginally preferred in terms of \7)."," We assumed an inner disk radius of 1.24 $R_{g}$ , an outer line production radius of 400 $R_{g}$, and an inclination of $i=45^{\circ}$ (in fits with this and other models, intermediate inclinations were marginally preferred in terms of $\chi^{2}$ )."
 With this blurred model. we obtained parameter constraints which differed marginally from the previous fit: ¢10 erg em s!. f=0.625. and P2," With this blurred model, we obtained parameter constraints which differed marginally from the previous fit: $\xi=2.5^{+5.5}_{-0.1}\times 10^{4}$ erg cm $^{-1}$, $f=0.6^{+0.6}_{-0.1}$, and $\Gamma=1.96^{+0.04}_{-0.06}$."
 The shape and strength. of the Fe Καὶ line are not fit 1.96550.adequately: the fit is slightly worse than the un-blurred model (4=407.8. 231 d.o.f.).," The shape and strength of the Fe $\alpha$ line are not fit adequately; the fit is slightly worse than the un-blurred model $\chi^{2}=407.8$, 231 d.o.f.)."
 Finally. we constructed a model which allows the Fe Ka line and reflection components to be treated separately.," Finally, we constructed a model which allows the Fe $\alpha$ line and reflection components to be treated separately."
" We fit the line with the ""Laor"" line model (Laor 1991). and the power-law and reflection continuum (minus the line) with the “pexriv™ model (Magdziarz Zdziarski 1995)."," We fit the line with the “Laor” line model (Laor 1991), and the power-law and reflection continuum (minus the line) with the “pexriv” model (Magdziarz Zdziarski 1995)."
 With pexriv. f=| corresponds to a disk which intercepts half of the incident power-law flux.," With pexriv, $f=1$ corresponds to a disk which intercepts half of the incident power-law flux."
 It should be noted that this model was also used by Wilms et al. (, It should be noted that this model was also used by Wilms et al. (
2001) in fits to the XMM-Newton//EPIC spectrum of the Seyfert galaxy MC6G-6-30-15. allowing for a direct comparison.,"2001) in fits to the /EPIC spectrum of the Seyfert galaxy MCG–6-30-15, allowing for a direct comparison."
 For the Laor line. we initially fixed the inner disk edge at 1.24 Ας. the outer line production region at 400 ΑΟ. and the inclination at /2457.," For the Laor line, we initially fixed the inner disk edge at 1.24 $R_{g}$, the outer line production region at 400 $R_{g}$, and the inclination at $i=45^{\circ}$."
 The line energy. emissivity profile (e—7: we fit for J). and intensity were allowed to vary.," The line energy, emissivity profile $\epsilon \sim r^{-\beta}$; we fit for $\beta$ ), and intensity were allowed to vary."
 The MCD and pexriv reflection components were blurred as before., The MCD and pexriv reflection components were blurred as before.
 We found that the data could not simultaneously constrain f. &. and the disk surface temperature with pexriv (an additional parameter for this model).," We found that the data could not simultaneously constrain $f$, $\xi$, and the disk surface temperature with pexriv (an additional parameter for this model)."
 We therefore fixed the tonization parameter at £=2.0«107 erg em s7!. and the disksurface temperature at AT=1.3 keV (as per Ross. Fabian. Young 1999 in fits to Cygnus X-1. wherein a similarly low MCD disk temperature but similarly high values of¢ are reported).," We therefore fixed the ionization parameter at $\xi=2.0\times 10^{4}$ erg cm $^{-1}$, and the disksurface temperature at $kT=1.3~$ keV (as per Ross, Fabian, Young 1999 in fits to Cygnus X-1, wherein a similarly low MCD disk temperature but similarly high values of $\xi$ are reported)."
 The fit obtained with this model is shown in the bottom panel of Figure 2., The fit obtained with this model is shown in the bottom panel of Figure 2.
 Statistically. this model represents a significant improvement (4=319.9 for 229 d.o.f.).," Statistically, this model represents a significant improvement $\chi^{2}=319.9$ for 229 d.o.f.)."
 A power-law index of P22.047548 is obtained., A power-law index of $\Gamma=2.04^{+0.03}_{-0.02}$ is obtained.
 We measure the Fe Ka line to be centered at ΕΞ0.811 keV. likely due to a blend of Fe XXV and Fe XXVI (helium-like and hydrogenie Fe) and consistent with the high 10nization parameters previously measured.," We measure the Fe $\alpha$ line to be centered at $=6.8^{+0.2}_{-0.1}$ keV, likely due to a blend of Fe XXV and Fe XXVI (helium-like and hydrogenic Fe) and consistent with the high ionization parameters previously measured."
" The line is strong. with an equivalent width of W=350"") eV and a flux of 2.2+0.3«1079 erg em? sc! (3.2044107 ph em s)"," The line is strong, with an equivalent width of $=350^{+60}_{-40}$ eV and a flux of $2.2\pm 0.3\times
10^{-10}$ erg $^{-2}$ $^{-1}$ $3.2\pm 0.4\times
10^{-2}$ ph $^{-2}$ $^{-1}$ )."
" When the inner disk edge is allowed to vary. an inner radius of 1.24 Αι (the limit of the Laor model. corresponding to «= 0.998) is preferred over an inner radius of 6.0 R, (the marginally stablecircular orbit around a Schwarzschild blackhole) at the 60 level of confidence."," When the inner disk edge is allowed to vary, an inner radius of 1.24 $R_{g}$ (the limit of the Laor model, corresponding to $a=0.998$ ) is preferred over an inner radius of 6.0 $R_{g}$ (the marginally stablecircular orbit around a Schwarzschild blackhole) at the $\sigma$ level of confidence."
" A steep emissivity is suggested via the Laor line model: }=5.4+0.5, "," A steep emissivity is suggested via the Laor line model: $\beta=5.4\pm
0.5$ ."
This emissivity 15 preferred over that for a standard accretion disk (3= 3.0) at the 5.60 level of confidence., This emissivity is preferred over that for a standard accretion disk $\beta=3.0$ ) at the $\sigma$ level of confidence.
" The pexriv reflection ""fraction"" is f= 0.6*5:1. This is consistent with the", The pexriv reflection “fraction” is $f=0.6_{-0.1}^{+0.3}$ This is consistent with the
where f. D. S. 7 denote the time. the rest-mass deusity. the moment density. aud the energy density in a fixed fine where the £uid moves at speed v. respectively.,"where $t$ , $D$ , $\mathbf{S}$, $\tau$ denote the time, the rest-mass density, the momentum density, and the energy density in a fixed frame where the fluid moves at speed $\mathbf{v}$, respectively."
 These variables are related to quantities in the local rest frame of the fluid through where p. p. Wand / denote the proper rest-iiass deusity. the pressure. the fluid Lorentz factor. aud the specific euthalpy. respectively.," These variables are related to quantities in the local rest frame of the fluid through where $\rho$, $p$, $W$ and $h$ denote the proper rest-mass density, the pressure, the fluid Lorentz factor, and the specific enthalpy, respectively."
 The specific euthalpy is giveu by where ¢ is the specific internal enerex., The specific enthalpy is given by where $\varepsilon$ is the specific internal energy.
 We can describe these equations with a Lagraugian coordinate i., 	We can describe these equations with a Lagrangian coordinate $m$.
 Since we are concerned with spherically απλο] explosions. we will rewrite them iun the dimensional spherical coordinate svsten.," Since we are concerned with spherically symmetric explosions, we will rewrite them in the 1-dimensional spherical coordinate system."
" where edenotes the radial velocity. G the eravitational constant. M, the mass meluded within the radius kc. 1/D.s5-—VS-.r/r (v: the racial vector) aud The Lagrangian coordinate i) is rolated to r through The gravity is included in the weak limit where uo eeneral relativistic effect is prominent."," where $v$denotes the radial velocity, $G$ the gravitational constant, $M_r$ the mass included within the radius $r$, $V=1/D$ , $s=V\mathbf{S}\cdot\mathbf{r}/r$ $\mathbf{r}$: the radial vector) and The Lagrangian coordinate $m$ is related to $r$ through The gravity is included in the weak limit where no general relativistic effect is prominent."
" The pressure is described as the sui of the radiation pressure and the eas pressure: where «@ denotes the radiation constant. TZ the temperature. & the Boltzmann constaut. jp the mean molectlar weight. aud i0, the mass of proton."," The pressure is described as the sum of the radiation pressure and the gas pressure: where $a$ denotes the radiation constant, $T$ the temperature, $k$ the Boltzmann constant, $\mu$ the mean molecular weight, and $m_p$ the mass of proton."
 The specific internal cuerey 5 is given by Tere we will iutroduce two kinds of adiabatic iudices. 54 aud 5» defined by The difference scheme of equations (8)) (10)) cau be written in the following form: We use the Codunov method to αποήσαν solve equations (17)) distinguishing these two adiabatic mdices in our Rien solver.," The specific internal energy $\varepsilon$ is given by Here we will introduce two kinds of adiabatic indices, $\gamma_1$ and $\gamma_2$ defined by The difference scheme of equations \ref{massl}) \ref{energyl}) ) can be written in the following form; We use the Godunov method to numerically solve equations \ref{deff2}) ) distinguishing these two adiabatic indices in our Riemann solver."
" The νο of zones are listed in Table ὃν,", The number of zones are listed in Table \ref{tbl-model}.
 To obtain accurate enerev cdistributious of SN ejecta above the threshold euergies for cosmic-ray spallation reactions. our models have zones i the outermost lavers with iiasses well below 107AL...," To obtain accurate energy distributions of SN ejecta above the threshold energies for cosmic-ray spallation reactions, our models have zones in the outermost layers with masses well below $10^{-9}\ \Msun$."
 When we calculate the explosion of a star. we necd to set the boundary conditious at the outer edge of the star as follows: where nes is the zone number corresponding to the outermost laver.," 	When we calculate the explosion of a star, we need to set the boundary conditions at the outer edge of the star as follows; where $imax$ is the zone number corresponding to the outermost layer."
 At the center. which corresponds to the zone interface (=1/2. we consider an mias zone /=0. where the physical quautities are eiven by to keep the svuuuetry with respecto to the ceuter.," At the center, which corresponds to the zone interface $i=1/2$, we consider an imaginary zone $i=0$, where the physical quantities are given by to keep the symmetry with respect to the center."
 We consider four stellar models manediatelv before the core collapse as the initial conditions., 	We consider four stellar models immediately before the core collapse as the initial conditions.
 These stars are originated from 12.~LOAL. main-sequence stars., These stars are originated from $12 - \sim 40\Msun$ main-sequence stars.
 Three of thei are thought to have undergone intense stellar winds aud lost their T-rich aud Πο cuvelopes., Three of them are thought to have undergone intense stellar winds and lost their H-rich and He envelopes.
 As a result. the stellar surfaces αλα] consist of carbou aud oxvecu at explosion.," As a result, the stellar surfaces mainly consist of carbon and oxygen at explosion."
 These three models have corresponding real type Ic supernovae as shown in Table 3.., 	These three models have corresponding real type Ic supernovae as shown in Table \ref{tbl-model}.
 These stars have become fairly compact with radii less than the solar radius., These stars have become fairly compact with radii less than the solar radius.
 This compactucss results iu higher pressures at the shock breakout compared with explosion of a star with an extended envelope if the explosion euergies per unit ejecta mass are the same., This compactness results in higher pressures at the shock breakout compared with explosion of a star with an extended envelope if the explosion energies per unit ejecta mass are the same.
 The other star is thought to e the progenitor of SN 1987À. one of the best. studied supernovac.," The other star is thought to be the progenitor of SN 1987A, one of the best studied supernovae."
 We have calculated the explosion for this supernova aud compare the result with the previous work o check our numerical code., We have calculated the explosion for this supernova and compare the result with the previous work to check our numerical code.
 To initiate explosions. we first replace the central Fe core with the poiut mass located at the center. release he cnerev in theimucrimost severalzones in the foxiu of hermal cuerey (or pressure). aud trace the evolution of physical quantities.," 	To initiate explosions, we first replace the central Fe core with the point mass located at the center, release the energy in theinnermost severalzones in the form of thermal energy (or pressure), and trace the evolution of physical quantities."
 The calculations are stopped when the ejecta keep expanding homologously., The calculations are stopped when the ejecta keep expanding homologously.
 The parameters of each model axe tabulated in Table 3.., The parameters of each model are tabulated in Table \ref{tbl-model}. .
 , 	 
the contour plots presented in Figs.,the contour plots presented in Figs.
 3 - 5 have been calculated first without the imposition of the physical constraints discussed in Section 2., \ref{fig3} - \ref{fig5} have been calculated first without the imposition of the physical constraints discussed in Section 2.
" A typical example of the application of these conditions, and their impact on the credible regions, is shown in Fig."," A typical example of the application of these conditions, and their impact on the credible regions, is shown in Fig."
" 7 for the acoustic scale, la."," \ref{fig7} for the acoustic scale, $l_a$."
 One can see in Fig. 7((, One can see in Fig. \ref{fig7}( (
"b) how the contours are abruptly cut off, in this case by the inclusion of the condition that the universe currently be accelerating.","b) how the contours are abruptly cut off, in this case by the inclusion of the condition that the universe currently be accelerating."
" In other words, in the region enclosed by the contours in the right hand part of Fig. 7(("," In other words, in the region enclosed by the contours in the right hand part of Fig. \ref{fig7}( ("
"a), e.g. for yo«0.6 and n» 1.5, our SFS model predicts a value of J, which is in satisfactory agreement with observations, but for a universe which is not currently accelerating.","a), e.g. for $y_0 < 0.6$ and $n > 1.5$ , our SFS model predicts a value of $l_a$ which is in satisfactory agreement with observations, but for a universe which is not currently accelerating."
" The other cosmological probes such as the age of the universe and the BAO distance parameter are similarly affected, although much less severely, for certain values of 6."," The other cosmological probes such as the age of the universe and the BAO distance parameter are similarly affected, although much less severely, for certain values of $\delta$."
" However, since it is already the case that we find no significant overlap between the credible regions over the entire parameter space applying these additional physical constraints, we will not present any further plots that do include them."," However, since it is already the case that we find no significant overlap between the credible regions over the entire parameter space applying these additional physical constraints, we will not present any further plots that do include them."
" In this paper we have investigated one class of Sudden Future Singularity models proposed by Barrow, by confronting it with the currently available observational data."," In this paper we have investigated one class of Sudden Future Singularity models proposed by Barrow, by confronting it with the currently available observational data."
 After introducingthe theory behind the model and, After introducingthe theory behind the model and
2010).,.
" The radial Coriolis force may drive the meridional circulation in low and perhaps midlatitudes, but it can not do so in high latitudes, because, since there the rotation axis and the local vertical are nearly parallel, the radial Coriolis force is very weak (see Figure 2)."," The radial Coriolis force may drive the meridional circulation in low and perhaps midlatitudes, but it can not do so in high latitudes, because, since there the rotation axis and the local vertical are nearly parallel, the radial Coriolis force is very weak (see Figure 2)."
" Moreover, retaining it in the equations of motion complicates the problem mathematically."," Moreover, retaining it in the equations of motion complicates the problem mathematically."
" In particular, retaining the radial component of Coriolis force precludes using separation of variables to solve even the axisymmetric problem for a spherical polar cap."," In particular, retaining the radial component of Coriolis force precludes using separation of variables to solve even the axisymmetric problem for a spherical polar cap."
 Therefore we will begin from the spherical shell equations but then approximate the spherical polar cap (see Figure 3) by a cylinder with the same polar axis; this eliminates the relatively mild, Therefore we will begin from the spherical shell equations but then approximate the spherical polar cap (see Figure 3) by a cylinder with the same polar axis; this eliminates the relatively mild
The transit probability will be as per Equation (11)).,The transit probability will be as per Equation \ref{eq:630}) ).
" The angle @ is determined by the orbital separation of planet e and the host star at the time of their conjunction. (.2aresin(R./r,)."," The angle $\theta_\mathrm{c}$ is determined by the orbital separation of planet `c' and the host star at the time of their conjunction, $\theta_\mathrm{c} = \arcsin(R_*/r_\mathrm{c})$."
 As an example. consider the HAT-P-13 system (Bakoset 2009).," As an example, consider the HAT-P-13 system \citep{bakos2009}."
 As of this only the inner planet. HAT- has been observed to transit.," As of this only the inner planet, HAT-P-13b, has been observed to transit."
 What is the probability that the outer planet., What is the probability that the outer planet.
 HAT-P-13c. also transits?," HAT-P-13c, also transits?"
 Bakosetal.(2009) measure the orbital inclination of the inner planet to be iy283470.67.," \cite{bakos2009} measure the orbital inclination of the inner planet to be $i_{\mathrm{b,m}} = 83.4^\circ \pm 0.6^\circ$."
 At the time of its conjunction with HAT-P-13. the outer planet is at a distance of r/R.=82.146.1 stellar radii from the star.," At the time of its conjunction with HAT-P-13, the outer planet is at a distance of $r_\mathrm{c}/R_* = 82.1 \pm 6.1$ stellar radii from the star."
 This allows us to determine fjpA) and 0 for the HAT-P-13 system.," This allows us to determine $f_{I_\mathrm{b}}(i_\mathrm{b}|i_{\mathrm{b,m}})$ and $\theta_\mathrm{c}$ for the HAT-P-13 system."
" For the mutual inclination of the two planets. we assumed that the orbital inclination of planet ""ο was evenly distributed within Apemay degrees of the orbital inclination 4, of planet ""b."," For the mutual inclination of the two planets, we assumed that the orbital inclination of planet `c' was evenly distributed within $\pm \lambda_{\mathrm{bc,max}}$ degrees of the orbital inclination $i_\mathrm{b}$ of planet `b'."
" Figure 4 shows the transit probability of HAT-P-13e às a function of Ap,as."," Figure 4 shows the transit probability of HAT-P-13c as a function of $\lambda_{\mathrm{bc,max}}$."
 The probability that planet c? transits is very dependent upon what we assume is a reasonable range of mutual inclination in the HAT-P-13 system., The probability that planet `c' transits is very dependent upon what we assume is a reasonable range of mutual inclination in the HAT-P-13 system.
 For reference. all of the Solar System planets are within 3.4° of the Earth’s orbit except for Mercury (at 7).," For reference, all of the Solar System planets are within $3.4^\circ$ of the Earth's orbit --- except for Mercury (at $7^\circ$ )."
 If the mutual inclination of the two planets orbiting HAT-P-13 is within 3.47. then the outer planet will not transit.," If the mutual inclination of the two planets orbiting HAT-P-13 is within $3.4^\circ$, then the outer planet will not transit."
 If the two planets are misaligned by up to 7. then the transit probability for planet c is7%.," If the two planets are misaligned by up to $7^\circ$, then the transit probability for planet `c' is."
. The maximum transit probability of occurs if we assume that the two planets may be inclined within 87 of each other., The maximum transit probability of occurs if we assume that the two planets may be inclined within $8^\circ$ of each other.
 As the assumed spread in mutual inclination increases. the transit probability will fall back to the a priori value of1.," As the assumed spread in mutual inclination increases, the transit probability will fall back to the a priori value of."
2%.. The transit probability for HAT-P-13e is therefore at most8., The transit probability for HAT-P-13c is therefore at most.
5%. We now demonstrate how using stellar. inclination measurements and the enhanced transit probabilities (Section 2) can aid in the target selection of transit surveys., We now demonstrate how using stellar inclination measurements and the enhanced transit probabilities (Section 2) can aid in the target selection of transit surveys.
 As illustrative cases. we will calculate how many stars need to be observed in a survey looking for hot Jupiters. and for a separate survey searching for planets within the habitable-zone.," As illustrative cases, we will calculate how many stars need to be observed in a survey looking for hot Jupiters, and for a separate survey searching for planets within the habitable-zone."
 In these examples. we will make the simplifying assumption that every star has either a hot Jupiter or habitable-zone planet in orbit. at distances of R..fa=1/10 or 1/215. respectively.," In these examples, we will make the simplifying assumption that every star has either a hot Jupiter or habitable-zone planet in orbit, at distances of $R_*/a=1/10$ or $R_*/a=1/215$ , respectively."
 We assume that the inclinations of the planetary systems are distributed in two ways., We assume that the inclinations of the planetary systems are distributed in two ways.
 For the hot Jupiters. we use the planetary inclination distribution determined by Fabrycky&Winn(2009) from an ensemble of 11 Rossiter—MecLaughlin measurements of spin—orbit alignment.," For the hot Jupiters, we use the planetary inclination distribution determined by \cite{fabrycky2009} from an ensemble of 11 Rossiter—McLaughlin measurements of spin—orbit alignment."
 The authors found that aside from the XO-3 the hot Jupiters they considered had planetary inclinations distributed according to a Rayleigh distribution with a width parameter of 6.67., The authors found that aside from the XO-3 the hot Jupiters they considered had planetary inclinations distributed according to a Rayleigh distribution with a width parameter of $6.6^\circ$.
 Exoplanets within the habitable-zone may not follow this same planetary inclination distribution., Exoplanets within the habitable-zone may not follow this same planetary inclination distribution.
" We use a uniform distribution of planetary inclination within 7.5° of the stellar equator, Earth has an planetary inclination of 7.155"" to the Sun's equator,", We use a uniform distribution of planetary inclination within $7.5^\circ$ of the stellar equator; Earth has an planetary inclination of $7.155^\circ$ to the Sun's equator.
 Including either spread of planetary inclinations into the calculations of transit probabilities acts to spread out the probability of transit. and make stars with stellar inclinations far from 90° more likely to show transits.," Including either spread of planetary inclinations into the calculations of transit probabilities acts to spread out the probability of transit, and make stars with stellar inclinations far from $90^\circ$ more likely to show transits."
 At the same time. the spread of planetary inclinations makes stars with measured stellar inclinations near 907 less likely to show transits.," At the same time, the spread of planetary inclinations makes stars with measured stellar inclinations near $90^\circ$ less likely to show transits."
" Assuming a measurement of (+,=907+5°. and that planetary inclinations are uniformly. distributed within 7.5"" of the stellar equator. then the transit probability for a habitable-zone planet at a distance of R../a=1/215 star drops from to as compared to assuming the orbit is coplanar with the stellar equator."," Assuming a measurement of $\psi_m=90^\circ \pm 5^\circ$, and that planetary inclinations are uniformly distributed within $7.5^\circ$ of the stellar equator, then the transit probability for a habitable-zone planet at a distance of $R_*/a = 1/215$ star drops from to as compared to assuming the orbit is coplanar with the stellar equator."
" Conversely. a star with measured stellar inclination of (0,=807+5” has its transit probability increased from to As our first example. take a survey for hot Jupiters around solar-type stars."," Conversely, a star with measured stellar inclination of $\psi_m=80^\circ \pm 5^\circ$ has its transit probability increased from to As our first example, take a survey for hot Jupiters around solar-type stars."
 We will require a probability that the survey detects at least a single transiting planet., We will require a probability that the survey detects at least a single transiting planet.
 From Equation (17)) this means that P44=0.95., From Equation \ref{eq:2540}) ) this means that $P_\mathrm{det}=0.95$.
" Although we may arbitrarily set Pop, and 7. as shown in the appendix the time required to complete a hot Jupiter survey is minimized if we set Pa,=0.9814."," Although we may arbitrarily set $P_\mathrm{obs}$ and $n_\mathrm{i}$, as shown in the appendix the time required to complete a hot Jupiter survey is minimized if we set $P_\mathrm{obs}=0.9814$."
 To find the number of stars needed in the initial sample we must then solve We must therefore have jj=29 stars in our initial sample., To find the number of stars needed in the initial sample we must then solve We must therefore have $n_\mathrm{i}=29$ stars in our initial sample.
 We next want to know how many stars out of these 29 will actually have to be observed photometrically., We next want to know how many stars out of these 29 will actually have to be observed photometrically.
 That is. how many of the mitial targets with measured inclinations near 90° will we need to look at for transits?," That is, how many of the initial targets with measured inclinations near $90^\circ$ will we need to look at for transits?"
 We will assume that all of the stellar inclination measurementshave Gaussian uncertainties of 5°., We will assume that all of the stellar inclination measurementshave Gaussian uncertainties of $5^\circ$.
" The transit probability for a hot Jupiter can be calculated for various orientation measurements of the form c,d:5"" by using Equation (10)) to account for the inclination of the planetary system: hot Jupiters at a distance ofR.fa=1/10 will show transits up to à maximum angle of 025.737.", The transit probability for a hot Jupiter can be calculated for various orientation measurements of the form $\psi_m \pm 5^\circ$ by using Equation \ref{eq:620}) ) to account for the inclination of the planetary system: hot Jupiters at a distance of $R_*/a = 1/10$ will show transits up to a maximum angle of $\theta = 5.73^\circ$.
" The angle o that defines our observed subsample solves and is o=24.017 To detect at least one hot Jupiter. we must therefore photometrically observe stars that will have measured stellar inclinations within 24.01"" of 907."," The angle $\phi$ that defines our observed subsample solves and is $\phi=24.01^\circ$ To detect at least one hot Jupiter, we must therefore photometrically observe stars that will have measured stellar inclinations within $24.01^\circ$ of $90^\circ$."
 This will give us a probability of Py=95% of detecting at least one hot Jupiter., This will give us a probability of $P_\mathrm{det}=95$ of detecting at least one hot Jupiter.
 The top panel of Figure 5 shows how the number of stars that need to be observed varies as a function of the stellar inclination measurement precision for various confidence levels., The top panel of Figure 5 shows how the number of stars that need to be observed varies as a function of the stellar inclination measurement precision for various confidence levels.
 The top panel also shows how the fraction of the mitial target list that will need to be observed varies with measurement precision., The top panel also shows how the fraction of the initial target list that will need to be observed varies with measurement precision.
 The lower limits in both cases set by the spread in the distribution of f(A) as determined by Fabrycky&Winn (2009). , The lower limits in both cases set by the spread in the distribution of $f_\Lambda(\lambda)$ as determined by \cite{fabrycky2009}. .
In a notional survey for habitable-zone planets. we will also require a chance of detecting at least. one transit.," In a notional survey for habitable-zone planets, we will also require a chance of detecting at least one transit."
 The calculations are similar to those for the survey, The calculations are similar to those for the survey
the ACT results from and SPT results from (2011).,the ACT results from and SPT results from .
 ACT find a, ACT find a
"have a radial distribution proportional to radius. aud should be found in Che vicinity of ry. nol concentrated within 0.27, as is predicted under the black hole conjecture.","have a radial distribution proportional to radius, and should be found in the vicinity of $r_h$, not concentrated within $0.2r_h$ as is predicted under the black hole conjecture."
 Fast-movine stars can have origins other than a black hole. of course.," Fast-moving stars can have origins other than a black hole, of course."
 Ejection from the core curing is one plausible mechanism for producing such stars (Drukieretal.1999).. but their velocity vectors will be radial unlike a star in orbit around a black hole.," Ejection from the core during core-collapse is one plausible mechanism for producing such stars \citep{dcly}, but their velocity vectors will be radial unlike a star in orbit around a black hole."
 We caution that the numbers presented. here are only estimates and depend on the scalines found by Cohu&IKulsrud (1978)., We caution that the numbers presented here are only estimates and depend on the scalings found by \citet{ck}. .
. Those models are sinele-mass anisotropic Planck simulations for the steady-state stellar distribution in the vicinity of the black hole., Those models are single-mass anisotropic Fokker-Planck simulations for the steady-state stellar distribution in the vicinity of the black hole.
 More modern models. which should include. at the very least. a range of stellar masses and a sell-consistent potential. will be needed to fully assess the significance of anv [ast-moving stars which are observed in these clusters.," More modern models, which should include, at the very least, a range of stellar masses and a self-consistent potential, will be needed to fully assess the significance of any fast-moving stars which are observed in these clusters."
 The estimates made here also depend on the current central velocity clispersions in the elobular clusters., The estimates made here also depend on the current central velocity dispersions in the globular clusters.
 Since globular clusters can lose a large fraction of their mass due to stellar evolution and stellar-dvnanmical evolution. the numbers provided in Table 1 may well be underestimated if the proper velocity dispersion lo use in determining black hole masses is the original value. not the current one.," Since globular clusters can lose a large fraction of their mass due to stellar evolution and stellar-dynamical evolution, the numbers provided in Table \ref{T:top
choices} may well be underestimated if the proper velocity dispersion to use in determining black hole masses is the original value, not the current one."
 Further. the mass of any central black hole will have increased to some extent due to the capture of cluster stars.," Further, the mass of any central black hole will have increased to some extent due to the capture of cluster stars."
 Using double the current velocity dispersion. for example. would increase NA. by a factor of 16 and VY. by a factor of 39. in which case the higher slope also predicts significant numbers of observable stars in the top few clusters.," Using double the current velocity dispersion, for example, would increase $N_{\rm M15}^L$ by a factor of 16 and $N_{\rm M15}^H $ by a factor of 39, in which case the higher slope also predicts significant numbers of observable stars in the top few clusters."
 Given (he sensitivity (o these effects. obtaining reliable estimates lor the numbers of high-velocity stars will require fully evolving models.," Given the sensitivity to these effects, obtaining reliable estimates for the numbers of high-velocity stars will require fully evolving models."
 Even in the event (hat proper-motion studies uncover no [ast moving stars. such models will allow for firm upper limits on the mass of anv black hole.," Even in the event that proper-motion studies uncover no fast moving stars, such models will allow for firm upper limits on the mass of any black hole."
 C'ónstructing such models. and carrving out the necessary proper motion observations. is no small task. but given the strong interest and controversy currently surrounding (his topic. we believe that efforts along these lines should be vigorously pursued.," Constructing such models, and carrying out the necessary proper motion observations, is no small task, but given the strong interest and controversy currently surrounding this topic, we believe that efforts along these lines should be vigorously pursued."
 This study was supported by a NASA LTSA grant NAG5-641404., This study was supported by a NASA LTSA grant NAG5-6404.
"of the jitter RAIS o, among all stars in the sample. where we term σῃ (hemagnitude of the Πίου. (","of the jitter RMS $\sigma_*$ among all stars in the sample, where we term $\sigma_0$ the of the jitter. ("
In Section 5. we also trv an exponential distribution.),In Section \ref{sec.tests} we also try an exponential distribution.)
 The RMS jitter in an of stars with a Ravleigh distribution is v/2oy., The RMS jitter in an of stars with a Rayleigh distribution is $\sqrt{2}\sigma_0$.
 Our 6 hr systematic noise level of 3 can be explained if ση=1.8!., Our 6 hr systematic noise level of 3 can be explained if $\sigma_0 = 1.8$.
. The predicted jitter distribution is best described by oy=1.72:0.1 (Figure 3)). consistent with our observations of 3. total RMS.," The predicted jitter distribution is best described by $\sigma_0 = 1.7\pm0.1$ (Figure \ref{fig.activity}) ), consistent with our observations of 3 total RMS."
 Additional noise due to stellar rotation and starspots may occur on longer timescales (Barnesetal.2011).. ancl we perform caleulations with cy over the range 1.5-4.5!.," Additional noise due to stellar rotation and starspots may occur on longer timescales \citep{Barnes2011}, and we perform calculations with $\sigma_0$ over the range 1.5-4.5."
. However. we consider values near the upper limit. corresponding to an average svstematic noise of 6.5|. highly implausible because of the absence ofactive stus in in our sample (inset of Figure 3)).," However, we consider values near the upper limit, corresponding to an average systematic noise of 6.5, highly implausible because of the absence ofactive stars in in our sample (inset of Figure \ref{fig.activity}) )."
 This is discussed further in Section 6.., This is discussed further in Section \ref{sec.discussion}.
 We predict the distribution of RV. RAIS for each set of parameter values bv generating 10.000 Monte Carlo svstems. wilh host stars selected with replacement [rom the M2Ix survey. and orbital inclinations drawn from an isotropic distribution.," We predict the distribution of RV RMS for each set of parameter values by generating 10,000 Monte Carlo systems, with host stars selected with replacement from the M2K survey, and orbital inclinations drawn from an isotropic distribution."
 EachKepler candidate planet has à probabilitv 1/5; of being added to each star., Each candidate planet has a probability $1/s_i$ of being added to each star.
 This ignores any autocorrelation between the presence of planets., This ignores any autocorrelation between the presence of planets.
 Masses are assigned to each planet using theAepler radius and (he MURR., Masses are assigned to each planet using the radius and the MRR.
 We ignore all planet candidates with radii larger than (he largest confirmed transiting planet (~2 Jupiter radii) as main sequence companions or false positives., We ignore all planet candidates with radii larger than the largest confirmed transiting planet $\sim$ 2 Jupiter radii) as main sequence companions or false positives.
 The RV variation induced by each planet is calculated from the planet mass. host star mass. and svstem inclination.," The RV variation induced by each planet is calculated from the planet mass, host star mass, and system inclination."
 Orbits are assumed to be approximately coplanar (Lissaueretal.2011).., Orbits are assumed to be approximately coplanar \citep{Lissauer2011b}.
 Radial velocities are calculated using the actual epochs of observations and random mean anomalies al the first epoch., Radial velocities are calculated using the actual epochs of observations and random mean anomalies at the first epoch.
 We draw longitudes of perihelion from a uniform distribution ancl orbital eccentricities from a Ravleigh distribution with mean of 0.225 (Moorheadοἱal. 2011).., We draw longitudes of perihelion from a uniform distribution and orbital eccentricities from a Rayleigh distribution with mean of 0.225 \citep{Moorhead2011}. .
 We add formal and, We add formal and
To eusure that the lurge-scale diffuse cussion is nof due to the bendius of discrete sources. we present the total intensity radio contours at 1100 MIIz with the VLA in D configuration in the top panel of Fie. 3..,"To ensure that the large-scale diffuse emission is not due to the blending of discrete sources, we present the total intensity radio contours at 1400 MHz with the VLA in D configuration in the top panel of Fig. \ref{radio_sub},"
 after subtraction of disete sources., after subtraction of discrete sources.
 To obtain it. we produced an inaege ofthe discrete sources by using only the lougest yvasclines of the D configuration data-set. and uuiforni weiehtins.," To obtain it, we produced an image of the discrete sources by using only the longest baselines of the D configuration data-set, and uniform weighting."
 T1ο clean componcuts of this nuage were hen subtracted in the wv-plaue by using the AIPS task UVSUD., The clean components of this image were then subtracted in the uv-plane by using the AIPS task UVSUB.
 The image with the discrete sources subtracted confirms the xesence of a low-surface briehtuess radio alo at the chster center connected to a brighter pach of xxiplieral enission to the south-east., The image with the discrete sources subtracted confirms the presence of a low-surface brightness radio halo at the cluster center connected to a brighter patch of peripheral emission to the south-east.
 Iu the botOl xuel of Fig., In the bottom panel of Fig.
" 3 we show a zoo «f the ""Mad custer iu wluch the total inteusitv radio couQUIS. after subraction of discrete sources, are overlaid on the red tage of he Skxu Digital Sky Survey (left) aud ou the NAIA N-rav image (vielit)."," \ref{radio_sub} we show a zoom of the “Main” cluster in which the total intensity radio contours, after subtraction of discrete sources, are overlaid on the red image of the Sloan Digital Sky Survey (left) and on the XMM X-ray image (right)."
 In this figure it is ftither clear that the cloneation of the radio cussion versus west Is located iu οςjucideuce with the ~Subchister”., In this figure it is further clear that the elongation of the radio emission versus west is located in coincidence with the “Subcluster”.
 We note that this feature is visible at 1100 MIIZ in the D configuration data-set only. whie iu the higher resolution nuages presented hero. and in f16 FIRST image (Becker. White IIelfaud. 1f395). any discrete source seenis to be present.," We note that this feature is visible at 1400 MHz in the D configuration data-set only, while in the higher resolution images presented here, and in the FIRST image (Becker, White Helfand 1995), any discrete source seems to be present."
 Ou the otrer haud. di this location a source. classified as ao discrete soleo. Is detected iun CAIRT nuages at 610 MITz (Venturi ct al.," On the other hand, in this location a source, classified as a discrete source, is detected in GMRT images at 610 MHz (Venturi et al."
 2008) and at 327 \ITIz (Cüaciutucci et al., 2008) and at 327 MHz (Giacintucci et al.
 2nO)., 2010).
" We uote that. hints of possible diffuse emission (indicated by arrow"" in the top panel of Fig. 3))."," We note that, hints of possible diffuse emission (indicated by arrows in the top panel of Fig. \ref{radio_sub}) ),"
 left after the subtractio1 process. are preseut on east of the πλain” cluster.," left after the subtraction process, are present on east of the “Main” cluster."
 The: diffuse radio enuüssionus nüeht trace the process of a large-scale structure formation. where cosmic shocks origirated by complex merger eveuts are able to amplity mag1Cic fields aud accelerate svuchrotron clectrous along a €Tister filament. although a deeper observation is required to coufirm the. presence. of these faiut eiisslous.," These diffuse radio emissions might trace the process of a large-scale structure formation, where cosmic shocks originated by complex merger events are able to amplify magnetic fields and accelerate synchrotron electrons along a cluster filament, although a deeper observation is required to confirm the presence of these faint emissions."
 Iu Fig., In Fig.
 Lo we show the radio iso-coutours of ATSL at 325 Mz., \ref{radio2} we show the radio iso-contours of A781 at 325 MHz.
 This nuage has been obtained by combining the VLA data in D. C. and D configuration.," This image has been obtained by combining the VLA data in B, C, and D configuration."
 The resulting iuage hasa EWIIA beau of «995.00., The resulting image hasa FWHM beam of $\times$.
 The VLA nuage has an aneuleuw resolution similar to the tapered GAIRT image at 327 AMIIz presented by Cüaciutucci et al. (, The VLA image has an angular resolution similar to the tapered GMRT image at 327 MHz presented by Giacintucci et al. (
"2010). and displays he same structures,","2010), and displays the same structures."
 Most of the features Visible at 1100 MIIz are also preseut at 325 ALII., Most of the features visible at 1400 MHz are also present at 325 MHz.
 In particular. the soutli-east peripheral patch aie all the discrete sources. with the ouly exception of the source IT. are clearly detected.," In particular, the south-east peripheral patch and all the discrete sources, with the only exception of the source H, are clearly detected."
 There is a lint of «iffuse cuuission on the right of source D. although most of tlhe* radio halo eiissiou visible at 1100 AIIIz is nüssius at 325 MIIEz. likely )ecause of the lower sensitivity of he low-frequency image.," There is a hint of diffuse emission on the right of source D, although most of the radio halo emission visible at 1400 MHz is missing at 325 MHz, likely because of the lower sensitivity of the low-frequency image."
" The only feature which appears to be comparatively brighter at 325 MIIz is the emission iu coincidence with the ""Subceluste.", The only feature which appears to be comparatively brighter at 325 MHz is the emission in coincidence with the “Subcluster”.
 As we will «ee iu the next Section. this feature is characterized NX oa very steep radio spectra.," As we will see in the next Section, this feature is characterized by a very steep radio spectrum."
" By excluding the peripheral patch. the radio halo has a flux deusitv at LlO0 MITzZ of Syjoo,20.5. iid."," By excluding the peripheral patch, the radio halo has a flux density at 1400 MHz of $_{\rm 1400 MHz}\simeq$ 20.5 mJy."
 In lie sune area of about 1Mjpe?. the upper limit to the flux cleusity at 325 AIIIZ is Ssosagyeπλ iuJw.," In the same area of about $^2$, the upper limit to the flux density at 325 MHz is $_{325 MHz}<$ 137 mJy."
 This nut has been calcuated by considering that the surface xiehtuess of the halo. in the primary beam corrected nuage. is evervwwelherc| Jower than the 36 noise level (i.c. 6.6 wJy +).," This limit has been calculated by considering that the surface brightness of the halo, in the primary beam corrected image, is everywhere lower than the $\sigma$ noise level (i.e. 6.6 mJy $^{-1}$ )."
 Thus. we derive an upper Πιτ to the elobal halo spectral index of oj; «1.3.," Thus, we derive an upper limit to the global halo spectral index of $\alpha_{tot}<$ 1.3."
 Iu this section we prescut he spectral iudex nuage of ATSL between 325 IIIz iux 1100 MIIz., In this section we present the spectral index image of A781 between 325 MHz and 1400 MHz.
 Iu order to be xoperlv compared. the two nuages have been corrected or the primary beam atteation of the VLA anuteuuas. reeridded to the sanue οσοuetry. and convolved to a common resohtion of «5:," In order to be properly compared, the two images have been corrected for the primary beam attenuation of the VLA antennas, regridded to the same geometry, and convolved to a common resolution of $\times$."
 We stress. however. that he original resoluticmus of the two images were already very close not just due to he tapering of the uv-data mut because o| the very siluilar intrinsic coverage of he relevant spatial freueucies.," We stress, however, that the original resolutions of the two images were already very close not just due to the tapering of the uv-data but because of the very similar intrinsic coverage of the relevant spatial frequencies."
 We do not preseit thesλοςral nmCX nuage ater subtractio1 of discrete sources because of he low seuxitiviY of the 325 MITz nage., We do not present the spectral index image after subtraction of discrete sources because of the low sensitivity of the 325 MHz image.
 Iu the top panel of Fie. 5..," In the top panel of Fig. \ref{spix},"
 WO presen the s)ectral lucex (left) and t1ο spectral index 1necrtainty (right) nuages between 32M5 zud 1100 ΑΠ with the 110) MIIZ radio lso-contours (primary bean correced) overlaid., we present the spectral index (left) and the spectral index uncertainty (right) images between 325 and 1400 MHz with the 1400 MHz radio iso-contours (primary beam corrected) overlaid.
 They are calcilated. «ulv on those pixels whose brightucss is above the 36 level at both frequencies., They are calculated only on those pixels whose brightness is above the $3\sigma$ level at both frequencies.
 The s)ectral index values ranges |)etwveeen a 20.5 aud à 2. while the COYTCSDOlLliug οτον are in the range 20.02 0.25.," The spectral index values ranges between $\alpha \simeq$ 0.5 and $\alpha \simeq$ 2, while the corresponding errors are in the range $\simeq$ $-$ 0.25."
 The discrete sources have a typical spectral index value of ac06 0.7. oulv the source F has a steep spectrin with a 1.00.2.," The discrete sources have a typical spectral index value of $\alpha\simeq 0.6-0.7$ , only the source F has a steep spectrum with $\alpha$ $\pm$ 0.2."
 Iu the bottom panel of Fig., In the bottom panel of Fig.
 5 we show, \ref{spix} we show
~5.QUM.,"$\sim 5 \times 10^8
\msun$."
" On the other hand a groupof ~LO""AL. can only be the result of a pair of subhalos of 5«.10""AL. in our simulation.", On the other hand a groupof $\sim 10^7 \msun$ can only be the result of a pair of subhalos of $5 \times 10^6 \msun$ in our simulation.
 Our limited resolution also prevents us from quantifying the mass function inside the groups., Our limited resolution also prevents us from quantifying the mass function inside the groups.
 Nevertheless. and for our largest groups we find that these are dominated by a few massive subhalos and many small ones.," Nevertheless, and for our largest groups we find that these are dominated by a few massive subhalos and many small ones."
 The group infall that we have been detecting in our simulation may well be related to the ghostly streams reported by Lynden-Bell&Lynden-Bell (1995)., The group infall that we have been detecting in our simulation may well be related to the ghostly streams reported by \citet{lyndenbell95}.
 The presence of satellites (dwarf galaxies and globular clusters) sharing a common orbital plane seems rather plausible in the context discussed here., The presence of satellites (dwarf galaxies and globular clusters) sharing a common orbital plane seems rather plausible in the context discussed here.
" Instead of the disruption of a large progenitor (Lynden-Bell&Lynden-Bell1995). or the tidal formation of satellites within gas-rich major mergers (Kroupa 1997).. we would be witnessing the disruption by the tidal tield of the Milky Way of a ""sub-group-size object composed by dwarf galaxies."," Instead of the disruption of a large progenitor \citep{lyndenbell95} or the tidal formation of satellites within gas-rich major mergers \citep{kroupa97}, we would be witnessing the disruption by the tidal field of the Milky Way of a “sub-group”-size object composed by dwarf galaxies."
 The possible implications of this finding are discussed in the Conclusions., The possible implications of this finding are discussed in the Conclusions.
 The present-time distribution of angular momentum orientations of subhalos reflects both the anisotropy of the accretion pattern and the dynamical processes that affect subhalos while orbiting he MW-like halo., The present-time distribution of angular momentum orientations of subhalos reflects both the anisotropy of the accretion pattern and the dynamical processes that affect subhalos while orbiting the MW-like halo.
 Fig., Fig.
 6 shows the orientation of the angular momentum of subhalos accreted in the last 13 snapshots. from he present-day (top left) τος~1.08 (bottom left).," \ref{dist_of_angularmoment_orientation_accminus1} shows the orientation of the angular momentum of subhalos accreted in the last 13 snapshots, from the present-day (top left) to $z \sim 1.08$ (bottom left)."
 Here the angular momentum is calculated using the position and velocity of a subhalo in the simulation box frame right before it was accreted., Here the angular momentum is calculated using the position and velocity of a subhalo in the simulation box frame right before it was accreted.
 ote that only a fraction of these subhalos will have survived until he present-time., Note that only a fraction of these subhalos will have survived until the present-time.
 The small scale clustering visible in this figure once again highlights the group infall., The small scale clustering visible in this figure once again highlights the group infall.
 Note the presence of larger-scale patterns lasting over several snapshots (in particular in the op row. which corresponds to the last 2.4 Gyr).," Note the presence of larger-scale patterns lasting over several snapshots (in particular in the top row, which corresponds to the last 2.4 Gyr)."
 This presumably implies that the infall patterns are related with persistent larger scale structures (filaments) in the tidal field., This presumably implies that the infall patterns are related with persistent larger scale structures (filaments) in the tidal field.
 To understand this in more detail. we proceed to trace the evolution of the tidal field around the main halo in our simulation.," To understand this in more detail, we proceed to trace the evolution of the tidal field around the main halo in our simulation."
" To this end we select ""field"" particles. i.e. those that do not belong to the FOF group of the Milky Way-like halo."," To this end we select “field” particles, i.e. those that do not belong to the FOF group of the Milky Way-like halo."
 The projected spatial distribution of these particles within a 25. Mpe on a side box is shown in grey in Fig. 7.., The projected spatial distribution of these particles within a $2h^{-1}$ Mpc on a side box is shown in grey in Fig. \ref{tidal_fields}. .
 Like in Fig. 6..," Like in Fig. \ref{dist_of_angularmoment_orientation_accminus1},"
 each panel corresponds to a different redshift. starting from ο~1.08 in the bottom left panel © the present day in the top left.," each panel corresponds to a different redshift, starting from $z \sim 1.08$ in the bottom left panel to the present day in the top left."
 The distributions of surviving subhalos accreted at the corresponding epoch are overplotted in black., The distributions of surviving subhalos accreted at the corresponding epoch are overplotted in black.
 Fig., Fig.
 7 shows that the Milky Way like halo is embedded in a arger-scale tilamentary pattern., \ref{tidal_fields} shows that the Milky Way like halo is embedded in a larger-scale filamentary pattern.
 These filaments are comparable in extent to the halo itself (as e.g. traced by the accreted subhalos)., These filaments are comparable in extent to the halo itself (as e.g. traced by the accreted subhalos).
 The lumpy nature of the filaments is also clearly visible. showing hat the infall is not a continuous flow. but is in groups as discussed above.," The lumpy nature of the filaments is also clearly visible, showing that the infall is not a continuous flow, but is in groups as discussed above."
 Note that the global orientation of the tidal fields near the main halo has not changed much over the last four snapshots. in agreement with what is observed in the top row of Fig. 6..," Note that the global orientation of the tidal fields near the main halo has not changed much over the last four snapshots, in agreement with what is observed in the top row of Fig. \ref{dist_of_angularmoment_orientation_accminus1}."
 Furthermore. this large scale pattern is more or less aligned with the major axis of the main halo. shown by the dashed line in each panel (asinBailin&Steinmetz2005).," Furthermore, this large scale pattern is more or less aligned with the major axis of the main halo, shown by the dashed line in each panel \citep[as
in][]{bs05}."
. Kroupa.Theis&Boily(2005) and have recently argued that the highly anisotropic distribution of TW satellites could not have been drawn from a nearly spherically distributed subhalo population., \citet{kroupa05} and have recently argued that the highly anisotropic distribution of MW satellites could not have been drawn from a nearly spherically distributed subhalo population.
 Motivated by their claim and the results presented above. we wish to test here under what conditions such a configuration is likely in à ACDM simulation like ours.," Motivated by their claim and the results presented above, we wish to test here under what conditions such a configuration is likely in a $\Lambda$ CDM simulation like ours."
 There are many possible ways to define the degree of fattening of a distribution., There are many possible ways to define the degree of flattening of a distribution.
 We shall here concentrate on the ollowing two measures: In what follows the positions are defined with respect to the centroid of the satellites tor subhalos). rather than with respect to the centre of the MW(-like) halo.," We shall here concentrate on the following two measures: In what follows the positions are defined with respect to the centroid of the satellites (or subhalos), rather than with respect to the centre of the MW(-like) halo."
 For the first measure (1). we use the inertia tensor defined as Note this inertia tensor differs from that previously used in Eq. €1))," For the first measure (i), we use the inertia tensor defined as Note this inertia tensor differs from that previously used in Eq. \ref{inertia_tensor_ell_eq}) )"
 in which the positions were normalized by their ellipsoidal distance., in which the positions were normalized by their ellipsoidal distance.
 Our preference for this new definition is based on the fact that the determination of the ellipsoidal distance is simultaneous to the determination of the eigenvalues of the inertia tensor Z;;., Our preference for this new definition is based on the fact that the determination of the ellipsoidal distance is simultaneous to the determination of the eigenvalues of the inertia tensor $I_{ij}$ .
 This means that aniterative algorithm is used. in which outliers are successively discarded. until the desired level of convergence is," This means that aniterative algorithm is used, in which outliers are successively discarded, until the desired level of convergence is"
 (e.g..Hamannetal.2004).. (e.g..Reynolds1997;Giustinietal.2010).," \citep[e.g.,][]{ham04}. \citep[e.g.,][]{rey97,giustini10}."
. 5000kms! (Gangulyetal.2001) (Mathur.Elvis&Wilkes1995:Brandt.," $5000\mbox{\ km\ s}^{-1}$ \citep{gan01} \citep{mat95,bra00}."
LaorWills2000).. X500 (seeHamann&Sabra2004)., $\lesssim 500$ \citep[see][]{hamsab04}. \\citep{tru06}.
. studies of BALs. since they probe different regions in the quasar surroundings.," studies of BALs, since they probe different regions in the quasar surroundings."
 Although the intrinsic NALs are more difficult to identify. several practical considerations make the derivation of their physical conditions more straightforward than for BALs. (Hamann&Ferland1999).," Although the intrinsic NALs are more difficult to identify, several practical considerations make the derivation of their physical conditions more straightforward than for BALs. \citep{ham99}."
. Because NALs are often unsaturated and resolved. we can measure directly the NAL coverage fractions and column densities of various ions.," Because NALs are often unsaturated and resolved, we can measure directly the NAL coverage fractions and column densities of various ions."
 In BAL systems. doublet transitions are often blended. makingsuch measurement more difficult.," In BAL systems, doublet transitions are often self--blended, makingsuch measurement more difficult."
 Approximately of all quasars show evidence of outflows (Misawaetal.2007;Ganguly&Brotherton2008).," Approximately of all quasars show evidence of outflows \citep{mis07,gan08}."
. Although statistical methods can be used to determine this. partial coverage of doublets and multiplets and time variability analysis are the two most commonly used ways to determine decisively if a particular NAL system ts intrinsic.," Although statistical methods can be used to determine this, partial coverage of doublets and multiplets and time variability analysis are the two most commonly used ways to determine decisively if a particular NAL system is intrinsic."
 These signatures are only seen in low ionization transitions of intervening absorbers. and only rarely in the case of small molecular clouds that could be smaller than the projected size of the background quasar broad emission line region. (," These signatures are only seen in low ionization transitions of intervening absorbers, and only rarely in the case of small molecular clouds that could be smaller than the projected size of the background quasar broad emission line region. ("
e.g.. Jones et al. 2010..,"e.g., Jones et al. \nocite{jon10},"
 Ivanchik et al. 2010))., Ivanchik et al. \nocite{iva10}) ).
 Partial coverage is described by the coverage fraction Cy. which is the fraction of photons from the background source that pass through the absorber (Barlow.Hamann.&Sargent 1997).," Partial coverage is described by the coverage fraction $C_{\rm f}$ , which is the fraction of photons from the background source that pass through the absorber \citep{bhs97}."
. It can be estimated using the residual flux ratio. of resonance doublets (e.g..Barlow&Sargent1997;Gangulyetal. 1999).," It can be estimated using the residual flux ratio of resonance doublets \citep[e.g.,][]{barsar97,gan99}."
. Variability of the absorption lines could be caused by transverse motion of the absorbing material or by changes in its ionization state (Hamann1997;Misawaetal. 2005).," Variability of the absorption lines could be caused by transverse motion of the absorbing material or by changes in its ionization state \citep{ham97,mis05}."
. Using UV spectra of z€1.5 quasars observed at two different epochs separated by 4-10 years with theTelescope. Wiseetal.(2004) concluded that a minimum of 21% of the AALs are variable.," Using UV spectra of $z\leqslant1.5$ quasars observed at two different epochs separated by 4–10 years with the, \citet{wis04} concluded that a minimum of $21\%$ of the AALs are variable."
 A’ similar conclusion was reached for z—2 quasars by Narayananet (2004). , A similar conclusion was reached for $z\sim 2$ quasars by \citet{nar04}. .
Early work investigating metal abundances using narrow associatedabsorption lines indicated supersolar metallicities. Le.. Z=Z. ," Early work investigating metal abundances using narrow associatedabsorption lines indicated supersolar metallicities, i.e., $Z\geqslant
Z_\odot$ "
he combined elfect ofCoulomb and hadronic losses as well as the higher compressibility of composite CR. plus thermal eas leads to a less ellicient CR. bubble feedback. as will e discussed. in more detail in Section. ??..,"the combined effect of Coulomb and hadronic losses as well as the higher compressibility of composite CR plus thermal gas leads to a less efficient CR bubble feedback, as will be discussed in more detail in Section \ref{Importance}."
 However. even hough this allows the gas to cool somewhat more elficiently owards the centre the amount of stars formed is roughly. he same in the thermal and relativistic cases.," However, even though this allows the gas to cool somewhat more efficiently towards the centre the amount of stars formed is roughly the same in the thermal and relativistic cases."
 For ¢>Olfie. the star formation rate begins to »v more suppressed in the run with CR bubbles. because at this stage Lop starts to be comparable to the local Dy.," For $t > 0.1\,t_{\rm Hubble}$, the star formation rate begins to be more suppressed in the run with CR bubbles, because at this stage $P_{\rm
CR}$ starts to be comparable to the local $P_{\rm th}$."
 In fact. for the run with a=2.1. this transition occurs somewhat earlier. than in the simulation with a a. given steeperthat for a=2.1 the cosmic ray pressure reaches values significantsooner.," In fact, for the run with $\alpha = 2.1$, this transition occurs somewhat earlier than in the simulation with a steeper $\alpha$, given that for $\alpha = 2.1$ the cosmic ray pressure reaches significant values sooner."
 Lt can be seen that [or [omOdmaaae the BILAL starts to oscillate dramatically as à consequence of the presence of a dominant relativistic particle component., It can be seen that for $t > 0.1t_{\rm Hubble}$ the BHAR starts to oscillate dramatically as a consequence of the presence of a dominant relativistic particle component.
 A similar behaviour has been observed in the case of star formation in small dwarl galaxies in the work by 7)., A similar behaviour has been observed in the case of star formation in small dwarf galaxies in the work by \cite{Jubelgas2007}.
. When a bubbleis injected into the ICM and its Poy is comparable or higher than the local iy it, When a bubble is injected into the ICM and its $P_{\rm CR}$ is comparable or higher than the local $P_{\rm th}$ it
is consistent with an origin of the broad components well above the stellar surface.,is consistent with an origin of the broad components well above the stellar surface.
" Table 3 summarises measurements of RVs in different groups lines, which are arranged in order of increasing RV amplitude."," Table \ref{mean_rv} summarises measurements of RVs in different groups of lines, which are arranged in order of increasing RV amplitude."
of The mean stellar velocity is +23 kmss~!., The mean stellar velocity is +23 $^{-1}$.
" Note that the mean RV is more positive for the ""high-temperature"" lines, up to +36 kmss~! for the narrow component."," Note that the mean RV is more positive for the ''high-temperature'' lines, up to +36 $^{-1}$ for the narrow component."
 Our search for radial velocity changes was then extended to the other cTTS included in the present study., Our search for radial velocity changes was then extended to the other cTTS included in the present study.
" As shown in Fig. 11,"," As shown in Fig. \ref{anti-ph0},"
 all programme stars show the same type of anti-phase variations as observed for DR, all programme stars show the same type of anti-phase variations as observed for DR
 transitious. providing it with its nune “line-driven wind.," transitions, providing it with its name “line-driven wind”."
 Ou the one hand. mass loss is thought to be a key agent in revealing cliemically processed material at the stellar surface. making it responsible for evolutionary scenarios such as the O > Lunminous Blue Variable (LBV) » WolfRavet (WR) star. » SN sequence (e.g. Conti 1976. Cliosi Maeder 1986. Langer et al.," On the one hand, mass loss is thought to be a key agent in revealing chemically processed material at the stellar surface, making it responsible for evolutionary scenarios such as the O $\rightarrow$ Luminous Blue Variable (LBV) $\rightarrow$ Wolf-Rayet (WR) star $\rightarrow$ SN sequence (e.g. Conti 1976, Chiosi Maeder 1986, Langer et al."
 1991)., 1994).
 Furthermore. it determines the stellar mass before collapse and is thus relevant for the type of compact relmnaut that is left behind G.e. neutron star or black hole).," Furthermore, it determines the stellar mass before collapse and is thus relevant for the type of compact remnant that is left behind (i.e. neutron star or black hole)."
 Ou the other haud. the role of mass loss may be equally relevant for the loss of angular 1iomienutuum (e.g. Mevuet Maeder 2003).," On the other hand, the role of mass loss may be equally relevant for the loss of angular momentum (e.g. Meynet Maeder 2003)."
" With respect to the latter. it has been suggested that low metallicity (actually low ""àirou couteuts: Vink cde Ixoter 2005) leads to less mass aud angular moment loss iu low metallicity euvironmneuts. perliaps resulting in a preference of lone gamma-ray bursts (CORB) in the carly Universe. but however interesting the metallicity dependence aud the long CRB puzzle may be. the temperature dependence of stellar winds and its role in the augular momentum evolution of massive stars has been highlighted more receutly with respect to the possibility of (Wink ct al."," With respect to the latter, it has been suggested that low metallicity (actually low “iron” contents; Vink de Koter 2005) leads to less mass and angular momentum loss in low metallicity environments, perhaps resulting in a preference of long gamma-ray bursts (GRB) in the early Universe, but however interesting the metallicity dependence and the long GRB puzzle may be, the temperature dependence of stellar winds and its role in the angular momentum evolution of massive stars has been highlighted more recently with respect to the possibility of (Vink et al."
 2010)., 2010).
 Caven the crucial role that mass loss plays for luassive star evolution. we discuss the theory of massive star nass loss aud its duplications. with a focus on the imetallicitv (Z) aud effective temperature (Tig) dependence.," Given the crucial role that mass loss plays for massive star evolution, we discuss the theory of massive star mass loss and its implications, with a focus on the metallicity $Z$ ) and effective temperature $T_{\rm eff}$ ) dependence."
 We will see that theopacity plays a domimaut role iu both cases., We will see that the plays a dominant role in both cases.
 The theorv goes back to the early 1970s when Lucy Solomon ((1970) sugeested.OO that selective. radiation pressure on spectral lues is capable of driving stellar, The theory goes back to the early 1970s when Lucy Solomon (1970) suggested that selective radiation pressure on spectral lines is capable of driving stellar
the Antennae galaxies have comparable escape velocities (?).. but ? and ? find that the star clusters in the Autennac show the same “infant mortality” pheuomenon asx those in the Milkv Wav: roughlv of all star clusters dissolve within ~10 Myr of formation. almost certainly because the formation process operates with a low cficiency and removal of a majority of gas leaves the remaining stars unbound.,"the Antennae galaxies have comparable escape velocities \citep{whitmore99a}, but \citet{fall05a} and \citet{whitmore07a} find that the star clusters in the Antennae show the same “infant mortality"" phenomenon as those in the Milky Way: roughly of all star clusters dissolve within $\sim 10$ Myr of formation, almost certainly because the formation process operates with a low efficiency and removal of a majority of gas leaves the remaining stars unbound."
 Clearly some mechanism must remove eas from these clusters as they form. and we argue below that radiation-driven regious are the most natural explanation.," Clearly some mechanism must remove gas from these clusters as they form, and we argue below that radiation-driven regions are the most natural explanation."
 Our approach to the problem is as follows., Our approach to the problem is as follows.
 In 2 we derive a condition for when radiation pressure is nmuportaut. aud we then give a solution to the idealized problemi of an region expaudius iuto au züubient iiedium iucludiug radiation pressure effects.," In \ref{derivation} we derive a condition for when radiation pressure is important, and we then give a solution to the idealized problem of an region expanding into an ambient medium including radiation pressure effects."
 Iu 3 woe discuss the contribution of trapped radiation to region dynamics., In \ref{trapping} we discuss the contribution of trapped radiation to region dynamics.
 In 4. we discuss the relative importance of radiation-driven regions aud supernovac., In \ref{supernovae} we discuss the relative importance of radiation-driven regions and supernovae.
 Finally. we suumuauizein& 5.," Finally, we summarize in \ref{summary}."
 Consider a source of bolometric huuinositv £ that produces ionizing photous at a rate 5. located at 7—0.," Consider a source of bolometric luminosity $L$ that produces ionizing photons at a rate $S$, located at $r=0$."
 Following ?.. we investigate two cases. which cau be treated in parallel.," Following \citet{matzner02}, we investigate two cases, which can be treated in parallel."
 The first is a region of neutral gas of deusity p=polefry)Me., The first is a region of neutral gas of density $\rho=\rho_0 (r/r_0)^{-\krho}$.
" The second is a reeion in which the density is p=py(r/ro)""v for «>O aud 0 for e«0.", The second is a region in which the density is $\rho=\rho_0 (r/r_0)^{-\krho}$ for $x>0$ and 0 for $x<0$.
" The former corresponds to the case of an “embedded” region that is completely surrounded by deuse gas. and the latter to a “blister” region iu which the diiviug source is at the edge of a dense cloud. aud the ionized eas can escape frecly,"," The former corresponds to the case of an “embedded"" region that is completely surrounded by dense gas, and the latter to a “blister"" region in which the driving source is at the edge of a dense cloud, and the ionized gas can escape freely."
 We illustrate these two xossible configurations iu Figure 1.., We illustrate these two possible configurations in Figure \ref{diagram_hiireg}.
 We define ej=13.6 eV as the threshold photon euergyv required to ionize a jeutral hyvdroec4 atom. and for convenience we define CHdk(Sey) o be the ratio of the stars bolometric oower to its jionizing power. counting onlv an cucrey ἐμ CL ioniziue plicXtou.," We define $\epsth = 13.6$ eV as the threshold photon energy required to ionize a neutral hydrogen atom, and for convenience we define $\psi=L/(S\epsth)$ to be the ratio of the star's bolometric power to its ionizing power, counting only an energy $\epsth$ per ionizing photon."
" For massive stars and clusters whose ""nnumositv comes mostly frou massive stars. 0671."," For massive stars and clusters whose luminosity comes mostly from massive stars, $\psi\sim 1$."
 We wish to «etermine how the gas moves in response o the radiation flux. aud to understand uuder what cieunistances radiation plavs an important role iu determining gas motions.," We wish to determine how the gas moves in response to the radiation flux, and to understand under what circumstances radiation plays an important role in determining gas motions."
 Following the usual procedure. we approximate that the ionized gas is isothermal at temperature yy. aud has a sound speed ey which is much leger than the sound speed in the neutral eas.," Following the usual procedure, we approximate that the ionized gas is isothermal at temperature $\tii$, and has a sound speed $\cii$ which is much larger than the sound speed in the neutral gas."
 If radiation pressure is negligible. we have the usual 7— solution: the ionized material expands duc to its thermal pressure.," If radiation pressure is negligible, we have the usual \citet{spitzer78} solution: the ionized material expands due to its thermal pressure."
 This expansion sweeps the neutral eas iuto a thin shell. which coutaius most of the mass that was originally inside the radius my of the reeion.," This expansion sweeps the neutral gas into a thin shell, which contains most of the mass that was originally inside the radius $\rii$ of the region."
" If radiation pressure is the dominant force acting ou the eas then a fluid clement at a distance r from the source undergoes a radiative acceleration dyad[fst)Le7(Acre)dp, whore jo(r) is the opacity of the fiui at radius r to photous of frequency pr. and T(r)=iGpcrdre! is the optical depth frou the source ton that point."," If radiation pressure is the dominant force acting on the gas then a fluid element at a distance $r$ from the source undergoes a radiative acceleration $a_{\rm rad} = \int\, \kappa_\nu(r) L e^{-\tau_\nu(r)}/(4 \pi r^2 c)\, d\nu$ , where $\kappa_\nu(r)$ is the opacity of the fluid at radius $r$ to photons of frequency $\nu$ , and $\tau_\nu(r) = \int_{0}^r \kappa_\nu(r') \rho(r') \, dr'$ is the optical depth from the source to that point."
 Photous below the Lyman luit carry roughly half the radiative ποιοτα. aud suce these are absorbed primarily by dust erains. weeTa? aud thus the radiative acceleration is a decreasing function of ;r.," Photons below the Lyman limit carry roughly half the radiative momentum, and since these are absorbed primarily by dust grains, $\kappa_\nu(r) e^{-\tau_\nu(r)}/r^2$ and thus the radiative acceleration is a decreasing function of $r$."
" The other half of the momenta is carried by photons above the Lyman Πατ, which can be absorbed by either ID or dust erains see Appendix A.."," The other half of the momentum is carried by photons above the Lyman limit, which can be absorbed by either H or dust grains -- see Appendix \ref{dustabsorption}."
 If dust absorption dominates. thle radiative acceleration falls with radius as for lower-energv photons.," If dust absorption dominates, then radiative acceleration falls with radius as for lower-energy photons."
 If II absorption domunates. the acceleration is proportional to the recombination rate. which is cither flat (if the eas density is uniformi) or again declines witli radius (if radiative acceleration causes eas to pile up near the shell edge).," If H absorption dominates, the acceleration is proportional to the recombination rate, which is either flat (if the gas density is uniform) or again declines with radius (if radiative acceleration causes gas to pile up near the shell edge)."
 Thus. the total radiative acceleration is alwavs largest closest to the source. and again material will be swept iuto a thin shell of racius ry.," Thus, the total radiative acceleration is always largest closest to the source, and again material will be swept into a thin shell of radius $\rii$ ."
 The interior of this shell will be optically thin., The interior of this shell will be optically thin.
 Thus. after a rapid initial expansion- phase. the dynamics of the eas reduce to the problem of computing the dynamics of the thin shell that bounds the reeion.," Thus, after a rapid initial expansion phase, the dynamics of the gas reduce to the problem of computing the dynamics of the thin shell that bounds the region."
" Following ?.. we can solve this problem by writing down the momentum equation for the shell: where Afj, aud Ag, are the shelbs mass aud area. and py and wy are the deusity and velocity of the eas iuuuediately iuterior to it."," Following \citet{matzner02}, we can solve this problem by writing down the momentum equation for the shell: where $\msh$ and $\ash$ are the shell's mass and area, and $\rhoii$ and $\uii$ are the density and velocity of the gas immediately interior to it."
" The shell area aud mass are duy=(L2) aud AL,=(L2)rip3. where PU)=[BABbepule/ru)Ke is the mean density inside the spherical or hemusplerical region of radius r in the initial cloud. and the values in pareutheses refer to the cases for a (spherical. hemispherical) region."," The shell area and mass are $\ash = (4,2)\pi \rii^2$ and $\msh = (4,2)\pi \rii^3 \overline{\rho}/3$, where $\overline{\rho}(r)=[3/(3-\krho)]\rho_0 (r/r_0)^{-\krho}$ is the mean density inside the spherical or hemispherical region of radius $r$ in the initial cloud, and the values in parentheses refer to the cases for a (spherical, hemispherical) region."
 The first teiii on the right-hand side represeuts eas pressure. while the second represcuts radiation pressure.," The first term on the right-hand side represents gas pressure, while the second represents radiation pressure."
 Note that in writing this equation we have implicitly assumed that all the radiatiou force is applied at the thin shell. rather han in the region interior.," Note that in writing this equation we have implicitly assumed that all the radiation force is applied at the thin shell, rather than in the region interior."
 This is certainly a good approximation when radiation pressure is dominant. since. as discetsed above. the interior of the shell will ο cleared. by radiation pressure. aud thus all photous will be absorbde in or near the shell.," This is certainly a good approximation when radiation pressure is dominant, since, as discussed above, the interior of the shell will be cleared by radiation pressure, and thus all photons will be absorbed in or near the shell."
 When gas pressure doniiuates au the shell interior is of uuiforii deusitv. he rate of ux1ueutuinmi deposition bv ionizing photous natches the xxconibinatiou rate.," When gas pressure dominates and the shell interior is of uniform density, the rate of momentum deposition by ionizing photons matches the recombination rate."
 Since this is wuiform. so the mean radius at which momentum is deposited is 3/L of the shell radius.," Since this is uniform, so the mean radius at which momentum is deposited is $3/4$ of the shell radius."
 Moreover. uou-ionizius plotous. which carry half the total momentum. still deposit alltheir iiomientun iu the shell," Moreover, non-ionizing photons, which carry half the total momentum, still deposit alltheir momentum in the shell."
 Thus our approximation that all the moment is deposited in the shell is a good one., Thus our approximation that all the momentum is deposited in the shell is a good one.
 The quautity frayin equation (1)) represents the, The quantity $f_{\rm trap}$in equation \ref{momeqn}) ) represents the
the other haud. projection effects could mask the actual orientation of both structures. for instance Tsvetauov&Walsh(1992) proposed that the ionization cone is very inclined (35°) with respect to the plane of the slaw.,"the other hand, projection effects could mask the actual orientation of both structures, for instance \citet{Tsvetanov92} proposed that the ionization cone is very inclined $35^\circ$ ) with respect to the plane of the sky."
 In addition. there is also a tougue extending (075 towards the NNW which euds in two πα. blobs that resembles a structure observed in the excitation maps (sce Figure 2)).," In addition, there is also a tongue extending $0\farcs5$ towards the N–NW which ends in two small blobs that resembles a structure observed in the excitation maps (see Figure \ref{fig:X_OIII}) )."
 The presence of dust within the ionization cone has Όσσα reported before oulv in NGC 1068 (Bocketal.2000)., The presence of dust within the ionization cone has been reported before only in NGC 1068 \citep{Bock00}.
. Towards the uucleus of the galaxy there is an excess of reddening which can be attributed to a natural increase in the extinction due to higher dust concentration., Towards the nucleus of the galaxy there is an excess of reddening which can be attributed to a natural increase in the extinction due to higher dust concentration.
 Assunmiug an intrinsic colour similar to that observed iu the disk of galaxies (IIT 2: 1998). we have estimated a value of Ay-=6.5 mae. which results in Ny=1.2«I?7.," Assuming an intrinsic colour similar to that observed in the disk of galaxies \citep[$\mathrm{I-H} 2; , we have estimated a value of ${A_V = 6.5}$ mag, which results in ${N_H = 1.2\times 10^{22}} \mathrm{cm}^{-2}$."
 N-rav spectral analysis of the observed soft N-rav extended. emission is crucial to determine the excitation nmiechanisni of the plasma. aud its relationship to the optical bicone-like structure (see previous section).," X-ray spectral analysis of the observed soft X-ray extended emission is crucial to determine the excitation mechanism of the plasma, and its relationship to the optical bicone-like structure (see previous section)."
 The combination of high spectral resolution aud high spatial resolution data is key to achieve this purpose., The combination of high spectral resolution and high spatial resolution data is key to achieve this purpose.
 Iun this section we describe iu detail the methodology and main results obtained., In this section we describe in detail the methodology and main results obtained.
 Iu Section ?? we discuss the origiu of this extended ciission based on the results presented iu this section., In Section \ref{sec:origin} we discuss the origin of this extended emission based on the results presented in this section.
 The analysis of the spectral counts was performed using the software package XSPEC 12.1019:1996). ," The analysis of the spectral counts was performed using the software package XSPEC \citep[version 12.4.0\footnote{http://cxc.heasarc.gsfc.nasa.gov/docs/xanadu/xspec/, }; ."
Soft N-rav cussion in Sevfert ealaxies has been proven o consist of a plethora of enüssion nes plus a sinall raction of continui enmiüsson that can be described with a single flat power-law (Cauüinazzictal.2008) with a fixed spectral iudex of P=1., Soft X-ray emission in Seyfert galaxies has been proven to consist of a plethora of emission lines plus a small fraction of continuum emission that can be described with a single flat power-law \citep{Guainazzi08} with a fixed spectral index of $\rm{\Gamma = 1}$.
 We obtained the emission ine fluxes of the central 30 aresec region (note that lis iucludes the uucleus and. circumuuclear emission) using the data., We obtained the emission line fluxes of the central 30 arcsec region (note that this includes the nucleus and circumnuclear emission) using the data.
 We searched for the oeseunce of 37 emission lines of €. O. N. Si. Mg and Fe species bv fitting the spectra of the two RCS cameras ο Gaussian profiles together with a continuum.," We searched for the presence of 37 emission lines of C, O, N, Si, Mg and Fe species by fitting the spectra of the two RGS cameras to Gaussian profiles together with a continuum."
 We usec Cash statistic for this purposes., We used Cash statistic for this purposes.
 The triplet fits were performed keeping the relative distance between centroids im energv aud the ceutrok energv was left as a free pazameter., The triplet fits were performed keeping the relative distance between centroids in energy and the centroid energy was left as a free parameter.
 A line was considere detected when the flux was higher than 0 at the lo level., A line was considered detected when the flux was higher than 0 at the ${\sf \sigma}$ level.
 The resulting RCS spectra aud detected euission mes are presented im Figure D and Table 2.. respectively.," The resulting RGS spectrum and detected emission lines are presented in Figure \ref{fig:RGSspec} and Table \ref{tab:RGS}, respectively."
 Al enerev centroids are consistent with the laboratory value eiven the error bars., All energy centroids are consistent with the laboratory value given the error bars.
 Cominazzietal.(2008). previously studied the spectra of 5573., \citet{Guainazzi08} previously studied the spectra of 573.
 Unfortunately. they ouly reported some of the dues. all of them agreeiug with our cussion liue fluxes.," Unfortunately, they only reported some of the lines, all of them agreeing with our emission line fluxes."
 The ost intense emission lines comprisue the spectrum are: ο VI Ly. O VII G). O VII (f). O VIII Lvo. O VIL. O VITRRC. Fe NVIT 3d-2p. and Ne IN (1).," The most intense emission lines comprising the spectrum are: C VI $\rm{\beta}$, O VII (r), O VII (f), O VIII $\rm{\alpha}$, O VII $\rm{\gamma}$, O VII RRC, Fe XVII 3d-2p, and Ne IX (r)."
 The fit of data with a thermal nodel produces poor results below 2 keV (4? ~16)., The fit of data with a thermal model produces poor results below 2 keV $\sf{\chi^{2}}$ $\sim$ 16).
 lustead. a model composed of multiple emission lines was tried.," Instead, a model composed of multiple emission lines was tried."
" Taking advautage of the fit. we πρόοδος, that the intensity of the lines iu the ow vesolition spectra fit do not exceed the RCS ueasurenieuts."," Taking advantage of the fit, we imposed that the intensity of the lines in the low resolution spectra fit do not exceed the RGS measurements."
 This is acceptable because the crosscalibrations betweeu EPIC aud RCS3ustriuenuts shows a πολλαο constant im the range of 0.9 to 1.0 (seePlu-cluskyetσαal. 2008)., This is acceptable because the cross-calibrations between EPIC and RGS instruments shows a normalization constant in the range of 0.9 to 1.0 \citep[see][]{Plucinsky08}.
. The assumed Caussian width is 100 eV. Note that for EPIC (aud also Chandra)) data we do not question the existence of the emission lines detected ou the but we use them as a template., The assumed Gaussian width is 100 eV. Note that for EPIC (and also ) data we do not question the existence of the emission lines detected on the but we use them as a template.
 Triplets were fitted using the total flux of all components of the He-like lines O VIL. N VI. and Ne IX.," Triplets were fitted using the total flux of all components of the He-like lines O VII, N VI, and Ne IX."
 The coutinmun emission was fitted to a power-law to be consistent with the high spectral resolution analysis., The continuum emission was fitted to a power-law to be consistent with the high spectral resolution analysis.
 However. this fit has poor statistics (\?> 2).," However, this fit has poor statistics $\rm{\chi^{2}_{r} > 2}$ )."
" Five lines were added at energies above 0.95 keV in order to achieve an acceptable fit ο.= 0).8): FoNNN at 0.97 keV (τισ, NoXN Lyo at 1.02 keV. (4225.62). TIX Πο 6 at 1.10 keV (4223.72). XXI. triplet at ~1.33 keV (\2=0.82). and Si XIII triplet at 1.81 keV(\2=0.80)."," Five lines were added at energies above 0.95 keV in order to achieve an acceptable fit $\rm{\chi^{2}_{r} = 0.8}$ ): XX at 0.97 keV $\rm{\chi_{r}^{2}}$ =5.64), X $\rm{\alpha}$ at 1.02 keV $\rm{\chi_{r}^{2}}$ =5.62), IX He $\rm{\delta}$ at 1.16 keV $\rm{\chi_{r}^{2}}$ =3.72), XI triplet at $\rm{\sim}$ 1.33 keV $\rm{\chi_{r}^{2}}$ =0.82), and Si XIII triplet at 1.84 $\rm{\chi_{r}^{2}}$ =0.80)."
 The final ft is shown in Figure 5.., The final fit is shown in Figure \ref{fig:xspecXMM}.
 The low spectral resolution spectrum shows the following intense emission lines: VV Tes. VWI Ly. NVVII Lvo. OVVII triplet. OVVIII Lvo. O VILIITes. OVVIT RRC. NXNVII. 3d-2p. aud triplet. XX Lya. HIN Te 8. and Mg NI triplet.," The low spectral resolution spectrum shows the following intense emission lines: V $\rm{\gamma}$, VI $\rm{\beta}$, VII $\rm{\alpha}$, VII triplet, VIII $\rm{\alpha}$, O $\rm{\gamma}$, VII RRC, XVII 3d-2p, and IX triplet, X $\rm{\alpha}$, IX He $\rm{\delta}$, and Mg XI triplet."
 In HIN.the best- modelthe flux of the OVIII RRC feature appears uceelieible aud the adjaceut line NNVIT 3d2p is preseut., In the best-fit modelthe flux of the OVIII RRC feature appears negligible and the adjacent line XVII 3d2p is present.
 This is in contrast to what happens iu the uuclear spectrum (see Section ?? and Table 3))., This is in contrast to what happens in the nuclear spectrum (see Section \ref{sec:chandraspec} and Table \ref{tab:low}) ).
 Iu order to check the compatibility of the results of both, In order to check the compatibility of the results of both
is - 0.09 dex kpc!. to be compared with - 0.044 and -0.04 dex Κροτ. for M33 and the Milky Way respectively.,"is - 0.09 dex $^{-1}$, to be compared with - 0.044 and -0.04 dex $^{-1}$ for M33 and the Milky Way respectively."
 Indication of steeper gradients. and sizable chemical evolution. are thus the defining characteristics of M81 compared with other spirals.," Indication of steeper gradients, and sizable chemical evolution, are thus the defining characteristics of M81 compared with other spirals."
 The oxygen enrichment indicates that this galaxy has suffered outflow to a lesser extent than the comparison galaxies. and steeper oxygen gradients are compatible with this explanation.," The oxygen enrichment indicates that this galaxy has suffered outflow to a lesser extent than the comparison galaxies, and steeper oxygen gradients are compatible with this explanation."
 It is evident from the above analysis that the metallicity gradient slopes in the galaxies examined do not depend on the average galactic metallicity: M33 is metal poor (its metallicity is similar to that of the LMC. Leisy Dennefeld 2006) and Μδ| is closer in metal contents to the Galaxy.," It is evident from the above analysis that the metallicity gradient slopes in the galaxies examined do not depend on the average galactic metallicity: M33 is metal poor (its metallicity is similar to that of the LMC, Leisy Dennefeld 2006) and M81 is closer in metal contents to the Galaxy."
 Since M81 is also closer to the Galaxy in stellar mass content (see Table 7 for a direet comparison of the main properties of these two galaxies). it makes sense to compare these two galaxies directly. to explore the relations of the metallicity gradients to the characteristics of the galaxy disks and to their evolution.," Since M81 is also closer to the Galaxy in stellar mass content (see Table 7 for a direct comparison of the main properties of these two galaxies), it makes sense to compare these two galaxies directly, to explore the relations of the metallicity gradients to the characteristics of the galaxy disks and to their evolution."
 The observations of PNe tell us that the gradient of M8I is steeper than that of our Galaxy in old stellar populations: the trend seems to persist in the young stellar population. but this needs further confirmation.," The observations of PNe tell us that the gradient of M81 is steeper than that of our Galaxy in old stellar populations; the trend seems to persist in the young stellar population, but this needs further confirmation."
 From a theoretical point of view. there are two main reasons that could influence the gradient slopes. (1) the rotational velocity of the galaxy and (2) the different situation of these two galaxies within their environment.," From a theoretical point of view, there are two main reasons that could influence the gradient slopes, (1) the rotational velocity of the galaxy and (2) the different situation of these two galaxies within their environment."
 Molla Diaz (2005) noted that metallicity gradients depend on the rotational velocity of the galaxy (thus presumably on its total mass) and on its morphological type: more massive galaxies tend to evolve faster and have flatter gradients than lower mass galaxies: for a given rotation velocity. gradients are steeper for late type than for early type galaxies.," Mollá Diaz (2005) noted that metallicity gradients depend on the rotational velocity of the galaxy (thus presumably on its total mass), and on its morphological type: more massive galaxies tend to evolve faster and have flatter gradients than lower mass galaxies; for a given rotation velocity, gradients are steeper for late type than for early type galaxies."
 Both effects would imply a steeper gradient for the Galaxy than for M81. contrary to the observations.," Both effects would imply a steeper gradient for the Galaxy than for M81, contrary to the observations."
 Some other factor must be at play., Some other factor must be at play.
 It is likely that the situation of M81 within its group of galaxies influences its metallicity gradient., It is likely that the situation of M81 within its group of galaxies influences its metallicity gradient.
 The tidal ffeatures near M81 are consistent with a large-scale redistribution of gas in this galaxy., The tidal features near M81 are consistent with a large-scale redistribution of gas in this galaxy.
 MSI is the only massive galaxy of its group. surrounded by several small galaxies.," M81 is the only massive galaxy of its group, surrounded by several small galaxies."
 The interaction of M8] with the dwarf galaxies of its group probably steepens the gradient of the major member due to the effect of stripping gas from the external regions of the major companion. while interaction of galaxies with more or less the same mass would redistribute the gas in both galaxies. and thus flatten the gradient.," The interaction of M81 with the dwarf galaxies of its group probably steepens the gradient of the major member due to the effect of stripping gas from the external regions of the major companion, while interaction of galaxies with more or less the same mass would redistribute the gas in both galaxies, and thus flatten the gradient."
 The chemical evolution models of Valle et al. (, The chemical evolution models of Valle et al. (
2005) consider the effects of gas stripping due to galaxy encounters on the star formation rate and the evolution of the metallicity.,2005) consider the effects of gas stripping due to galaxy encounters on the star formation rate and the evolution of the metallicity.
 They found that. for a stripping occurring. 1-3 Gyr after the formation of the galaxy and removing 97% of the gas. the region affected by the gas removal has a SFR almost a factor of 10 lower than in the model without stripping and the relative metallicity is then reduced by about 40%.," They found that, for a stripping occurring 1-3 Gyr after the formation of the galaxy and removing $\%$ of the gas, the region affected by the gas removal has a SFR almost a factor of 10 lower than in the model without stripping and the relative metallicity is then reduced by about $\%$."
 The metallicity reduction is not strongly dependent on the time and duration of the stripping episode. but is quite sensitive to the relative amount of gas removed from the region.," The metallicity reduction is not strongly dependent on the time and duration of the stripping episode, but is quite sensitive to the relative amount of gas removed from the region."
 This effect should be more pronounced in the outer than the inner galactic regions. due to the proximity of the interacting galaxies. and it might explain why M81 has steeper metallicity gradients than the Galaxy.," This effect should be more pronounced in the outer than the inner galactic regions, due to the proximity of the interacting galaxies, and it might explain why M81 has steeper metallicity gradients than the Galaxy."
 Unfortunately. the models by Valle et al. (," Unfortunately, the models by Valle et al. ("
2005) are limited to a single radial region. thus this conclusion ts of qualitative nature.,"2005) are limited to a single radial region, thus this conclusion is of qualitative nature."
 A radially-resolved chemical evolution modeling taking into account the effects of stripping would be necessary to determine the effect of tidal interaction on the gradient. and also to compare with other results.," A radially-resolved chemical evolution modeling taking into account the effects of stripping would be necessary to determine the effect of tidal interaction on the gradient, and also to compare with other results."
 Hectospec/MMT spectroscopy of a sizable sample of PN and rregions in the nearby M81 galaxy has proven very efficient to find chemistry of the young and old stellar populations. and to pin point the radial metallicity gradients.," Hectospec/MMT spectroscopy of a sizable sample of PN and regions in the nearby M81 galaxy has proven very efficient to find chemistry of the young and old stellar populations, and to pin point the radial metallicity gradients."
 We were able to detect the diagnostic lines for plasma and abundance analysis in 19 PNe and I4 rregions., We were able to detect the diagnostic lines for plasma and abundance analysis in 19 PNe and 14 regions.
 Their analysis indicates that the galaxy is clearly chemically enriched. with <O/HSyiiws./€Ῥννς 5. from MMT spectra where PNe and rregions were simultaneously acquired.," Their analysis indicates that the galaxy is clearly chemically enriched, with $\rm{<O/H>_{\hii\ reg.}/<O/H>_{PN}}$ =1.8, from MMT spectra where PNe and regions were simultaneously acquired."
" We also found that there is a noticeable PN metallicity gradient in oxygen. with Alog(O/H)/ARGz-0.055 dex Κροτ, and that neon and sulfur gradient slopes are within 15% of the oxygen one."," We also found that there is a noticeable PN metallicity gradient in oxygen, with $\Delta{\rm log(O/H)}/\Delta{\rm R_G}$ =-0.055 dex $^{-1}$, and that neon and sulfur gradient slopes are within $\%$ of the oxygen one."
 The MMT sample of rregions have limited galactocentric distribution. thus they are insufficient probes of the metallicity gradient.," The MMT sample of regions have limited galactocentric distribution, thus they are insufficient probes of the metallicity gradient."
 The gradient slope from the combined MMT and GS87 rregion samples is steeper (-0.093 dex kpe7!) than that of the PNe. possibly indicating an evolution of the radial metallicity gradients with time: older stellar population show shallower gradients. thus gradients are steepening with the time since galaxy formation.," The gradient slope from the combined MMT and GS87 region samples is steeper (-0.093 dex $^{-1}$ ) than that of the PNe, possibly indicating an evolution of the radial metallicity gradients with time: older stellar population show shallower gradients, thus gradients are steepening with the time since galaxy formation."
 These results have been compared to their homologous for the Milky Way and M33. where similar (yet less marked) gradient steepening ts inferred.," These results have been compared to their homologous for the Milky Way and M33, where similar (yet less marked) gradient steepening is inferred."
 We plan to, We plan to
seelent of the electron spectrun taking iuto account the anisotropic radiation pattern of the IC compoucut.,"segment of the electron spectrum, taking into account the anisotropic radiation pattern of the IC component."
 Secoud. we compute the expected value of R from the ratio of the cucrey densitics of the CMD to that in the magnetic field (both in the jet frame) (eq. A22)).," Second, we compute the expected value of R from the ratio of the energy densities of the CMB to that in the magnetic field (both in the jet frame) (eq. \ref{eq:rexp}) )."
 Equating these two expressions. we are able to solve for the beaming parameters which satisfy the equality (eq. À23)).," Equating these two expressions, we are able to solve for the beaming parameters which satisfy the equality (eq. \ref{eq:result}) )."
 Since the jet parameters cuter the R equations in Leher complex wavs because of the anisotropic nature of the IC enussion. a nunerieald method is used.," Since the jet parameters enter the R equations in rather complex ways because of the anisotropic nature of the IC emission, a numerical method is used."
 This is demonstrated in fig., This is demonstrated in fig.
 3. aud we obtain a result consistent with that of Celotti et al. (, \ref{fig:method} and we obtain a result consistent with that of Celotti et al. (
2001) for PKSO0637.,2001) for PKS0637.
" We use the ollowius notation: woe prime all quautities iu the jet frame and. im cases where subieuities could arise. we characterize jet paraincters bv the subscript ""j| aud electron paranieters by the subscript ""e."," We use the following notation: we prime all quantities in the jet frame and, in cases where ambiguities could arise, we characterize jet parameters by the subscript “j” and electron parameters by the subscript “e”."
 Tn this section. we provide some of the kev svuchrotron parameters aud beaming descriptors for a few knots in radio jets.," In this section, we provide some of the key synchrotron parameters and beaming descriptors for a few knots in radio jets."
 For the svuchrotron parameters. we usc the standard expressions (6.8. DPacholczyk. 1970) with observables transformed. back to the jet frame.," For the synchrotron parameters, we use the standard expressions (e.g. Pacholczyk, 1970) with observables transformed back to the jet frame."
 For the beaming parameters. our solution to eq.," For the beaming parameters, our solution to eq."
 A23. requires ouly 1 auunubers: Table 1 eives the results and it can be seen that the beaming paraueters range from quite modest values (e.g. PISSLL27) to rather unbelievable extremes (3€ 120)., \ref{eq:result} requires only 4 numbers: Table \ref{tab:results} gives the results and it can be seen that the beaming parameters range from quite modest values (e.g. PKS1127) to rather unbelievable extremes (3C 120).
 We have plotted the key results iu fig., We have plotted the key results in fig.
 Lo which is a represcutation of the beaming paraueters as a fiction of the observalles (eq. À21))., \ref{fig:results} which is a representation of the beaming parameters as a function of the observables (eq. \ref{eq:resulta}) ).
 Iu this section. we deal with the conflicting evidence for seneral beaming nodels aud for svachrotron models.," In this section, we deal with the conflicting evidence for general beaming models and for synchrotron models."
 Ou the oue hid. some sort of beanung appears to be required by the observation that all of the known jet sources (excluding of course the SSC terminal hotspots) produce X-ray Cluission ou only one side. ane that is the side which has the only or dominaut radio jet and for which relativistic effects have been demonstrated (usually on VLBI scales).," On the one hand, some sort of beaming appears to be required by the observation that all of the known jet sources (excluding of course the SSC terminal hotspots) produce X-ray emission on only one side, and that is the side which has the only or dominant radio jet and for which relativistic effects have been demonstrated (usually on VLBI scales)."
" Ou the other haud. for knots such as AL/3C273 or B/3C390.3. the observed X-ray iutensitv is accommodated by an extension of the power law connecting the radio and optical νο, the svuchrotrou spectrin)."," On the other hand, for knots such as A1/3C273 or B/3C390.3, the observed X-ray intensity is accommodated by an extension of the power law connecting the radio and optical (i.e. the synchrotron spectrum)."
 If, If
"Siuce. both. (b,1&) aud the density Nfp. are monotonically ≼∐∖↸⊳↥⋅↸∖⋜↧↴∖↴↕∐∶↴∙⊾↕⋟∏∐↸⊳↑↕∪∐↴∖↴↕⋟∪↥⋅≼↧⋜↧∏↘↽⋯⋜↧↑↑↸∖↥⋅∐⋜↧↕∪↴∖↴∙↑∐↸∖↸∖⊼↻∪∐↸∖∐↑ must be positive.","Since, both, $(\Phi_{\rm{out}} - \Phi)$ and the density $\rho$, are monotonically decreasing functions for dark matter halos, the exponent must be positive."
 Therefore. the factor ¢ has to be in the range O<a« l.," Therefore, the factor $a$ has to be in the range $0<a<1$ ."
 We can coustrain « further by msertiug Eq. (5)), We can constrain $a$ further by inserting Eq. \ref{eq-rho-phi-isotrop}) )
 iuto the Poisson equation., into the Poisson equation.
This results in the Lane-Emden equation (?) (22b Dux Qi) | πό ü,"This results in the Lane-Emden equation \citep{binney:87}
 			r^2 ) 	+ 	4 G c 	 = 	0 	."
 Oue solution of the Laue-Emden equation is a power-law for the relative poteutial and with Eq.| (5))," One solution of the Lane-Emden equation is a power-law for the relative potential ) , 	m = -1) and with Eq. \ref{eq-rho-phi-isotrop}) )"
 also for the densitvthe," also for the density. ,"
" ""Oo πα, y=ὦBal f(a).", 	n = -1) = (2-2a)/(1-2a) 	.
 Tn order to obtain a solution for a finite mass halo the ↴∖↴↕∪↻↸∖∪↕⋟≼∐∖∐↴∖↴↕↑⋅↖↽↻↥⋅∪∐↕↸∖∐⋯↴∖↴↑↴⋝↸∖↴∖↴↿∏−⊔↸⊳↕↸∖↕↕↑↕⋅↖↽↴∖↴↑↸∖↸∖↻∙∐⋜⋯∐∖↕⋅↖↽ nc3.," In order to obtain a solution for a finite mass halo the slope of density profile must be sufficiently steep, namely $n>3$."
 Therefore. the factor à must be in the range L/liljajl/=/2," Therefore, the factor $a$ must be in the range 	1/4<a<1/2 	."
 Note the asvimptotic slope of the NEW-profile. ο>x)= 3. results from. a=4l/l.," Note the asymptotic slope of the NFW-profile, $n(r\to \infty)= 3$ , results from $a=1/4$."
 The simulations.: show that the auisotropy of the velocity dispersion iucreases with radius and amounts to 20.3 at the virial radius., The simulations show that the anisotropy of the velocity dispersion increases with radius and amounts to $\beta \approx 0.3$ at the virial radius.
 This anisotropy affects the allowed parameter range for a: luteeratiug the Jeans equation uuder the condition of a constant anisotropy paraiueter ο) leads to ↕," This anisotropy affects the allowed parameter range for $a$: Integrating the Jeans equation under the condition of a constant anisotropy parameter $\beta$ leads to. ,"
∐↴∖↴↸∖↥⋅↑,r) 	 = 	.
"↕∐∶↴⋁↑↕∐↴∖↴↥⋅↸∖↕⋜↧↑↕∪∐⋜↧∶↴∙⊾⋜↧↕∐↕∐↑∪↑↕∐∖↕⋟∪↕↴∖∷∖↴∪∐↸∖≺∣∏⋜↧↑↕∪∐ ⋜↧∐∪↖↖⇁↴∖↴∏↴∖↴↑∪∐∐≼↧↻∪↖↖⇁↸∖↥⋅≓↕⋜∏↖⇁↴∖↴∪↕∏↑↕∪∐↴∖↴↕⋟∪↥⋅↑∐↸∖↻∪↑↸∖∐↑↕⋜↕↕⋜⋯≼↧ density (D., (Dayne ni = 1) ο."," 	 Inserting this relation again into the Poisson equation allows us to find power-law solutions for the potential andthe density ) 	m = -1) . ,"
since (he inverse (ransform does not involve an integral. issues of quadrature accuracy do nol arise.,"Since the inverse transform does not involve an integral, issues of quadrature accuracy do not arise."
 We can again use the Wigner function relation to write this as The m and m' sums can be computed using FFTs. and are sub-dominant to the scaling. using OL?logL) operations.," We can again use the Wigner function relation to write this as The $m$ and $m'$ sums can be computed using FFTs, and are sub-dominant to the scaling, using ${\cal O}(L^2\log L)$ operations."
 The FFTs will produce (0.6) as a regularly sampled [function on a 2-torus.," The FFTs will produce $f(\theta,\phi)$ as a regularly sampled function on a 2-torus."
 Onlv half of this torus is of interest ancl the 0>7 portion can be ignored., Only half of this torus is of interest and the $\theta > \pi$ portion can be ignored.
 An appendix to? also noted this algorithm for the inverse transform (but does not address the forward transform)., An appendix to also noted this algorithm for the inverse transform (but does not address the forward transform).
 Computation of ο... (—1)TE-. sls again scales as Q(L)., Computation of = (-1)^s _s again scales as ${\cal O}(L^3)$.
 Mirror svmmetries of the Wigner matrices again allow the expression to be rewritten using only (he non-negative quadrant., Mirror symmetries of the Wigner matrices again allow the expression to be rewritten using only the non-negative quadrant.
" The mirror svuunetry on the first azimuthal index of A leads to —""C""IPIE which cuts the computation time in hall.", The mirror symmetry on the first azimuthal index of $\Delta$ leads to = which cuts the computation time in half.
 For a transform {ο a real-valued function. the additional symmetry C44a=65mm can again cul the computation timeby (wo.," For a transform to a real-valued function, the additional symmetry $G_{(-m')(-m)} = G_{m'm}^* $ can again cut the computation timeby two."
difference iu both metallicity aud age within cach galaxy. and therefore a recent eas-ricl luecrger (z«1) et al. 19985)).,"difference in both metallicity and age within each galaxy, and therefore a recent gas-rich merger $<$ 1) (Kissler-Patig et al. \cite{kissfor}) )."
 The availability of the D-I colors for he GCs of NGC τΙΟΤ allows us o £o further iu the aualvsis., The availability of the B-I colors for the GCs of NGC 7457 allows us to go further in the analysis.
 Tudeed the D-I color is roughly twice as sensitive to metallicity han the V-I color (Couture et al. 1990))., Indeed the B-I color is roughly twice as sensitive to metallicity than the V-I color (Couture et al. \cite{couture}) ).
" But an intrinsic difficulty with low-Iunünositv ooOalaxies is) their sunall nunuber of GCs,", But an intrinsic difficulty with low-luminosity galaxies is their small number of GCs.
 Diuuodalitv was shown to be undetectable in a dataset containing less than 50 objects (see section 5.3)., Bimodality was shown to be undetectable in a dataset containing less than 50 objects (see section 5.3).
 Nevertheless. as we will see below. we can expect to observe some differeuces between the widths of a πλοία and a bimodal cistributious.," Nevertheless, as we will see below, we can expect to observe some differences between the widths of a unimodal and a bimodal distributions."
" The dispersion in color of a ""suele population of GCs can be estimated from the halo GCs of the AIW.", The dispersion in color of a “single” population of GCs can be estimated from the halo GCs of the MW.
 On the one haud. we cau conver the imetallicity dispersion iuto a color dispersion.," On the one hand, we can convert the metallicity dispersion into a color dispersion."
 With c([Fe/TI])=0.3 dex (Armandroff Zinn 1988)) we expec aayI)0.05 mag andoa(BI)=0.1 mae from the calibration relations of section 5.," With $\rm \sigma ([Fe/H])=0.3$ dex (Armandroff Zinn \cite{armandroff}) ) we expect a $\rm \sigma (V-I) \sim 
0.05$ mag and $\rm \sigma (B-I)=0.1$ mag from the calibration relations of section 5."
 Ou the other haud. we can measure the dispersion from the V-I aud. 0-1 data of the ~8O halo GCs in the MeMaster catalog (Iris 1996). and obtain a(V¥I)=0.05x0.01 mae aud (BoD=0.09-E0.01 mag in excellent agreement with the first values.," On the other hand, we can measure the dispersion from the V-I and B-I data of the $\sim 80$ halo GCs in the McMaster catalog (Harris 1996), and obtain $\rm \sigma (V-I)=0.05\pm 0.01$ mag and $\rm \sigma (B-I)=0.09\pm 0.01$ mag in excellent agreement with the first values."
 Iu V-L the genuime dispersion iu metallicity is extremely difficult to derive from the V-I colors. the expected dispersion being lower han the typical photometric errors of 0.1 mae.," In V-I, the genuine dispersion in metallicity is extremely difficult to derive from the V-I colors, the expected dispersion being lower than the typical photometric errors of 0.1 mag."
 Iu D-I. however. typical photometric errors aud intrinsic dispersion of a sinele population are comparable. so that several populations would broaden the color distribution to a detectable level.," In B-I, however, typical photometric errors and intrinsic dispersion of a single population are comparable, so that several populations would broaden the color distribution to a detectable level."
 Tn NGC 7157 the dispersion in V-I is oulv slightly avecr than the internal error (0.15 mag agaist L10 mag) and we estima| that the true. dispersion is ~Oll+011 mag according to the relation ," In NGC 7457 the dispersion in V-I is only slightly larger than the internal error (0.15 mag against 0.10 mag) and we estimate that the true dispersion is $\rm \sim 0.11\pm 0.11$ mag according to the relation $\rm \sigma^2_{obs} = 
\sigma^2_{err}+\sigma^2_{true}$."
This standard deviation in V-I rauslates ο~0.120.1 dex when using the calibration relation given in the precedent section., This standard deviation in V-I translates to a $\rm \sigma([Fe/H])\sim 0.4\pm 0.4$ dex when using the calibration relation given in the precedent section.
 The error is estimated bv accounting for he unucertaiuties ou he determination of the standard deviatious aud on the calibration formmla given iu section 5., The error is estimated by accounting for the uncertainties on the determination of the standard deviations and on the calibration formula given in section 5.
 The estimate is very insecure due to the large error on a(VI). For the D-I color we fux a dispersion (0.25 mag) clearly broader than the combination of a single population aud photometric errors., The estimate is very insecure due to the large error on $\rm \sigma(V-I)$ For the B-I color we find a dispersion (0.25 mag) clearly broader than the combination of a single population and photometric errors.
 The above relation leads to Oru.=0.2340.07 nag or o([Fe/T])=0.6£0.2 dex.," The above relation leads to $\rm \sigma_{true}=0.23 \pm 0.07$ mag or $\rm \sigma([Fe/H])=0.6\pm 
0.2$ dex."
 This value is conipatible with the value tentatively deduced from the V-I distribution., This value is compatible with the value tentatively deduced from the V-I distribution.
 Such a dispersion 1- netallicity seenis intermediate between the oue of a suele population aud the tota dispersion of the GC populations im bright cllipticals., Such a dispersion in metallicity seems intermediate between the one of a single population and the total dispersion of the GC populations in bright ellipticals.
 Iudeed single populations such as the Galactic halo GCs (Armanudroff Zinn 1988)). or the GCs around M 81 or À 31 (Pereliuuter Racine 1995)) have ot[FeT)~0.3 dex: the individual components of the biumodal distribution iu NGC L172 have similar dispersions of ~0.38 dex in [Fe/TT (Geisler et al. 19963).," Indeed single populations such as the Galactic halo GCs (Armandroff Zinn \cite{armandroff}) ), or the GCs around M 81 or M 31 (Perelmuter Racine \cite{perelmuter}) ) have $\rm \sigma ([Fe/H])\sim 0.3$ dex; the individual components of the bimodal distribution in NGC 4472 have similar dispersions of $\sim 0.38$ dex in $\rm [Fe/H]$ (Geisler et al. \cite{geisler}) )."
 In coutrast. the total dispersion of the system in M 87 is o(|Fo/II|)=0.65 dex (Lee Coisler 1993)). in NGC 1172 et(|Fe/II|)=0.7 dex (Geisler et al. 1996).," In contrast, the total dispersion of the system in M 87 is $\rm \sigma([Fe/H])=0.65$ dex (Lee Geisler \cite{lee}) ), in NGC 4472 $\rm \sigma([Fe/H])=0.7$ dex (Geisler et al. \cite{geisler}) )."
 Therefore. while the distribution iu metallicity of the GCs around NCC 7157 is found to be mnimodal. the width of the CC metallicity distribution is compatible with the presence of different populations probably less separated in inetallicity than in the eiut clusters ellipticals.," Therefore, while the distribution in metallicity of the GCs around NGC 7457 is found to be unimodal, the width of the GC metallicity distribution is compatible with the presence of different populations probably less separated in metallicity than in the giant clusters ellipticals."
 This sugeests a siguificautly cliffcrent chemical euricliieut. of the GCs in NGC 7157 than. c.go.. the halo population of the Calaxy.," This suggests a significantly different chemical enrichment of the GCs in NGC 7457 than, e.g., the halo population of the Galaxy."
 With Ms=19.55 anda meau metallicity of -.1 dex for its GCs. NGC 7157 follows the general treud found between the absolute maguitude of he galaxies (spirals | ellipticals) and the |Fe/II]| value of their GCs (e.g. Drodie Huchra 1991.. Ashinan Zepf 1998)).," With $\rm M_V=-19.55$ and a mean metallicity of $\ \simeq -1$ dex for its GCs, NGC 7457 follows the general trend found between the absolute magnitude of the galaxies (spirals $+$ ellipticals) and the [Fe/H] value of their GCs (e.g. Brodie Huchra \cite{brodie}, Ashman Zepf \cite{ashzepf}) )."
 Nevertheless. the spirals ποσα to have a lower GC metallicity as compared to elliptieals of similar luminosity aud the memi metallicity of ~1 dex for the GCs around NGC 7157 is cousistent with the mean values found for he metallicitics of the GCs around the bright elliptical galaxies Ww ) oe. Ashman Zepf 1998)).," Nevertheless, the spirals seem to have a lower GC metallicity as compared to ellipticals of similar luminosity and the mean metallicity of $\ \simeq 
-1$ dex for the GCs around NGC 7457 is consistent with the mean values found for the metallicities of the GCs around the bright elliptical galaxies $\rm 
M_V\le -20$ , e.g. Ashman Zepf \cite{ashzepf}) )."
 We can also compare more quantitatively the color distribution of he GCs around NCC 7157 with that of the Galactic GCs., We can also compare more quantitatively the color distribution of the GCs around NGC 7457 with that of the Galactic GCs.
 Iu addition to its broad dispersion. the mean D-I color found for the GCs of NGC 7157 =1.9 mae. see section 5.2) is comparable to the mean of the Galactic disc/bulee GCs z1.9 inag. as derived frou the MeMaster Moreover. Aloute Carlo slinulations οἳ B-I color distributions simular to ours show hat auv metal-poor (B-T=1.55 mag. the mean color of he metal-poor clusters in the Galaxy) population as large as o of the metalaich (B-I=1.92 mae) oue would be detected.," In addition to its broad dispersion, the mean B-I color found for the GCs of NGC 7457 $\ \simeq1.9$ mag, see section 5.2) is comparable to the mean of the Galactic disc/bulge GCs $\ \simeq 1.9$ mag, as derived from the McMaster Moreover, Monte Carlo simulations of B-I color distributions similar to ours show that any metal-poor (B-I=1.55 mag, the mean color of the metal-poor clusters in the Galaxy) population as large as to of the metal-rich $=1.92$ mag) one would be detected."
 Therefore we can couclude to the absence of auy siguificaut population of metal-poor clusters similar to that of the AAW 1alo., Therefore we can conclude to the absence of any significant population of metal-poor clusters similar to that of the MW halo.
 It is likely that such blue elobular clusters were never presenut in NGC 7157 since NGC TLST ds an isolated ealaxy (p=0.13. galaxies/Mpc?) aud shows no sigus of any interaction., It is likely that such blue globular clusters were never present in NGC 7457 since NGC 7457 is an isolated galaxy $\rm \rho=0.13~~ galaxies/Mpc^{3}$ ) and shows no signs of any interaction.
 Thus the loss of blue GCs loss through stripping seenis. The ormnation i a spiral merger would imply the presence of blue GCs from the progenitor spirals unless the latter did not host blue CC's like the MW., Thus the loss of blue GCs loss through stripping seems The formation in a spiral–spiral merger would imply the presence of blue GCs from the progenitor spirals unless the latter did not host blue GCs like the MW.
 Iu situ ornmation models usually explain blue CCS as formed in the carly stage of the galaxy., In situ formation models usually explain blue GCs as formed in the early stage of the galaxy.
 To fit the absence of blue clusters in such scenarios an early epoch of star formation (to curich the eas) without any formation of, To fit the absence of blue clusters in such scenarios an early epoch of star formation (to enrich the gas) without any formation of
"where στ is the Thomson cross-section. and poli) = niktitre) is the electron. pressure of the ICAL where Πο = OATSpeasftiy) is the clectrom umber density. Ay, is the Boltzmann constant. and Zi) is the electron teiperature.","where $\sigma_{\rm T}$ is the Thomson cross-section, and $p_{\rm e}(r)$ = $n_{\rm e}(r)k_{\rm b}T_{\rm e}(r)$ is the electron pressure of the ICM, where $n_{\rm e}(r)$ = $0.875 (\rho_{\rm gas}/m_{\rm p})$ is the electron number density, $k_{\rm b}$ is the Boltzmann constant, and $T_{\rm e}(r)$ is the electron temperature."
 The iutegral is performed along the of sight (/) through the cluster aud the upper lait of the imteeral R) is the extent of the cluster along uv particular of sight., The integral is performed along the $\hbox{--}$ of $\hbox{--}$ sight $l$ ) through the cluster and the upper limit of the integral $+R$ ) is the extent of the cluster along any particular $\hbox{--}$ $\hbox{--}$ sight.
 We do not include the effects of beam size iu caleulatiug the y parameter., We do not include the effects of beam size in calculating the $y$ parameter.
 This approxination is justified by the fact that the pressure profiles are relatively flat iu the iuner region., This approximation is justified by the fact that the pressure profiles are relatively flat in the inner region.
 The variation of pressure integrated along the lineofsight as a function the projected radius is even flatter thus providing more stification for the above approximation., The variation of pressure integrated along the line–of–sight as a function of the projected radius is even flatter thus providing more justification for the above approximation.
 The augular temperature profile projected on the sky due to SZ effect. AT(A)/Toary is given in terms of the Compton parameter in equation (19)) where g(r)= occothGe/2)-]1. oe—hvfkpgTesn. Tex=2.728 (Fixsen ct al.," The angular temperature profile projected on the sky due to SZ effect, $\Delta T(\theta)/T_{\rm CMB}$ is given in terms of the Compton parameter in equation \ref{eq:y_sph_sym}) ) where $g(x)\equiv x$ $x/2$ $4$, $x\equiv h\nu/k_{\rm B}T_{\rm CMB}$, $T_{\rm CMB}=2.728$ (Fixsen et al."
 1996)., 1996).
 In the Ravleigh-Jeaus approximation. g(r)z—2.," In the Rayleigh-Jeans approximation, $g(x)\approx -2$."
 We only evaluate “ceutral” SZ decrement from the pressure profiles of our models., We only evaluate “central” SZ decrement from the pressure profiles of our models.
 In this case. the inteeral in equation (19)) reduces to Tn the Ravleigh-Jeaus part of the ΝΤΟ spectrum. the deviation from the black-body spectrum results iu a decrement of the CMD temperature. We use the pressure profiles resulting from our model to calculate the ceutral SZ decremoeut in the temperature of the CAB.," In this case, the integral in equation \ref{eq:y_sph_sym}) ) reduces to In the Rayleigh-Jeans part of the CMB spectrum, the deviation from the black-body spectrum results in a decrement of the CMB temperature, We use the pressure profiles resulting from our model to calculate the central SZ decrement in the temperature of the CMB."
" The angular two-point correlation functiou of the SZ temperature distribution iu the sky ds convoeutionallv expanded into the Legeudre polvuouials: Since we consider diserete sources. we cam write €;=on|CO where on is the contribution from the Poisson. noise. aud C,AUCI) is. the correlation. among clusters (Peebles 1980. 11)."," The angular two-point correlation function of the SZ temperature distribution in the sky is conventionally expanded into the Legendre polynomials: Since we consider discrete sources, we can write $C_{l}= 
C_{l}^{(P)} + C_{l}^{(C)}$ , where $C_{l}^{(P)}$ is the contribution from the Poisson noise and $C_{l}^{(C)}$ is the correlation among clusters (Peebles 1980, 41)."
 We— define the frequency independent pat in the power spectrmu as C(BP)=2 ο).," We define the frequency independent part in the power spectrum as $C_{l}^{*(P)}\,\equiv\,C_{l}/g^{2}(x)$ ."
" The: integral. expression. of SCIENC, can be derived. following+. Cole Waiser (1988) as where V(:) is the co-moving volume and gj ds the aueular Fourier trausforiu of g(0) oeven bv where Jy is the Bessel function of the first kind of the integral order 0.", The integral expression of $C_{l}^{*(P)}$ can be derived following Cole Kaiser (1988) as where $V(z)$ is the co-moving volume and $y_{l}$ is the angular Fourier transform of $y(\theta)$ given by where $J_{0}$ is the Bessel function of the first kind of the integral order $0$.
 Iu equation (21)). tace is the redshift of photon decoupling and diafdAl is the mass function of clusters which is computed in the Press-Schechter formis (Press Schechter 1971).," In equation \ref{eq:Cl}) ), $z_{\rm dec}$ is the redshift of photon decoupling and $dn/dM$ is the mass function of clusters which is computed in the Press-Schechter formalism (Press Schechter 1974)."
 The mass function has been computed using the power spectrum for a ACDM model with normalization of σς=0.9., The mass function has been computed using the power spectrum for a $\Lambda$ CDM model with normalization of $\sigma_{8}=0.9$.
" We choose Mg,=5SLOPAL. aud Aus=2«107 aud inteexate till redshift of +=5 instead of το."," We choose $M_{\rm min}=5\times 10^{13}M_{\odot}$ and $M_{\rm max}
=2\times 10^{15}M_{\odot}$ and integrate till redshift of $z=5$ instead of $z_{\rm dec}$."
 This is done because tle integral in equation (21)) is found to be insensitive to the upper limit in redshift bevoud +—I the reason being that the mass function is expoucutially suppressed bevoud that redshift in this mass ranee.," This is done because the integral in equation \ref{eq:Cl}) ) is found to be insensitive to the upper limit in redshift beyond $z=4$, the reason being that the mass function is exponentially suppressed beyond that redshift in this mass range."
 Tn this section. we discuss our results for cluster evolution due to heating. cooling aud conduction.," In this section, we discuss our results for cluster evolution due to heating, cooling and conduction."
 We also disctiss our results for the central SZ decrement for clusters with masses ranging from Ma=5«Lote2101?AJ.," We also discuss our results for the central SZ decrement for clusters with masses ranging from $M_{\rm cl}=5\,\times 
10^{13}\hbox{--}2\times 10^{15}M_{\rm \odot}$."
" The eas is heated for a time f,,, and cooled simultaneously.", The gas is heated for a time $t_{\rm\scriptscriptstyle heat}$ and cooled simultaneously.
 After this time. the heating source is switched off.," After this time, the heating source is switched off."
" The gas is then allowed to cool raciatively until a total sinmilation time of £,,21.35 «1019. years has elapsed."," The gas is then allowed to cool radiatively until a total simulation time of $t_{\rm \scriptscriptstyle
H}$ $\times$ $^{10}$ years has elapsed."
 The final eutropy. values at Ο.Ε and roy are compared with the observed oues., The final entropy values at $0.1r_{\rm \scriptscriptstyle 200}$ and $r_{\rm \scriptscriptstyle 500}$ are compared with the observed ones.
" In Figure (1). the evolution of the density aud temperature profiles of the ICM. are shown for a cluster of mass 6s1014 AF, and for a luninosity of =5.25«1077 +."," In Figure \ref{fig:den_temp_cond}) ), the evolution of the density and temperature profiles of the ICM are shown for a cluster of mass $6\times10^{14}$ $M_{\rm \scriptscriptstyle\odot}$ and for a luminosity of $ = 5.25\times 
10^{45}$ $^{-1}$."
 The eas deusity decreases with tine during the heating epoch. aud increases due to radiative cooling aud conduction after the heating source is switched off.," The gas density decreases with time during the heating epoch, and increases due to radiative cooling and conduction after the heating source is switched off."
" It is interesting to note that the chanecs iu density are minimal bevoud 0.5r54,,. as compared to (.2regy in Figure (3) iu RRBNOL and that couduction plavs a very important role in regulating the density profiles after the heating source is switched off."," It is interesting to note that the changes in density are minimal beyond $0.5r_{\rm\scriptscriptstyle 200}$, as compared to $0.2r_{\rss 200}$ in Figure (3) in RRBN04, and that conduction plays a very important role in regulating the density profiles after the heating source is switched off."
 It is secu that couduction actually decreases he deusitv of the gas at larger radii (bevoud 0.57599) by conducting heat out from the ceutral regions., It is seen that conduction actually decreases the density of the gas at larger radii (beyond $0.5r_{\rss 200}$ ) by conducting heat out from the central regions.
 This is secu nore clearly if one studies the evolution of the temperature xofiles., This is seen more clearly if one studies the evolution of the temperature profiles.
 After the heating source is switched off. it is seen hat the temperature of the central regious fall very rapidly since conduction pumps out heat from the ceutral regions and redistiibutes it iu the outer regious of the cluster.," After the heating source is switched off, it is seen that the temperature of the central regions fall very rapidly since conduction pumps out heat from the central regions and redistributes it in the outer regions of the cluster."
 Thus he temperature profiles do not rise towards the centre as compared to what is seen in Figure (3) in RRBNOL., Thus the temperature profiles do not rise towards the centre as compared to what is seen in Figure (3) in RRBN04.
 On the other haud. their evolution shows a rise iu the outer regions (hevond 0.565599) due to thermal conduction even after the reat source has been switched off.," On the other hand, their evolution shows a rise in the outer regions (beyond $0.5r_{\rss 200}$ ) due to thermal conduction even after the heat source has been switched off."
 Thus couductiou acts ike a heating source for larger radii., Thus conduction acts like a heating source for larger radii.
" Figure (2)) shows the time evolution of scaled cutropy xofiles of a cluster of mass A,ον1011, for = 5.25.10 eres 1;"," Figure \ref{fig:ent_cond}) ) shows the time evolution of scaled entropy profiles of a cluster of mass $M_{\rm \scriptscriptstyle cl} = 6\times10^{14}
M_{\rm \scriptscriptstyle \odot}$ for = $\times 10^{45}$ erg $^{-1}$."
 We use the same method of cuissivity weighting as in Rovchowdluwy Nath (2003) to calculate he average quantities., We use the same method of emissivity weighting as in Roychowdhury Nath (2003) to calculate the average quantities.
 The entropy profiles are plotted iu inic-steps of 5«105 veurs., The entropy profiles are plotted in time-steps of $5\times10^{8}$ years.
 They are ποσα to rise withtime as the ICAL is heated., They are seen to rise withtime as the ICM is heated.
" Then. after the heating is switched off (after fí,,=5<109 vears). tle eas loses eutropy due o cooling auc the profiles are seeu to fall progressively."," Then, after the heating is switched off (after $t_{\rm \scriptscriptstyle heat} = 5\times 10^9$ years), the gas loses entropy due to cooling and the profiles are seen to fall progressively."
 The inclusion of conduction removes the negative eradieut, The inclusion of conduction removes the negative gradient
edees of even FR I radio sources (c.g.. MeNaimara O'Connell 1993).,"edges of even FR I radio sources (e.g., McNamara O'Connell 1993)."
 Maintaining our couservative approach. we shall ignore this additional contribution.," Maintaining our conservative approach, we shall ignore this additional contribution."
 Now. dividing Poo(L|D) bythe (fia) gives the actual proper deusity at 2=2.5 of powerful radio sources born in an interval 7. (Willott et 22001).," Now, dividing $\rho_{\rm obs}(1+z)^3$ bythe ${\langle f_d \rangle}$ gives the actual proper density at $z = 2.5$ of powerful radio sources born in an interval $T$, (Willott et 2001)."
 To obtain the inteerated density of radio sources we consider the width of the relevant logP54 biu. which is about [1.25. 1.5| dex.," To obtain the integrated density of radio sources we consider the width of the relevant $ {\log} P_{151}$ bin, which is about [1.25, 1.5] dex."
 Thus the total proper density of galaxies with bean powers sufficient to produce FR II sources (whether or not they are detected iu the survey) is o(P)=[5.1.3.1]«10PTS|iMpe5," Thus the total proper density of galaxies with beam powers sufficient to produce FR II sources (whether or not they are detected in the survey) is $\phi(T) = [5.1,3.1] \times 10^{-5}
T_5 (1+z)^3 {\rm Mpc}^{-3}$."
 We μας finally account for the fact that the epoch during which the nuuber deusitv of sources is roughly constant at the above value exteuds from :zc1.5 to Dom3. with characteristic 2oz2.5 (Jarvis Rawlines 2000: Rawlings 2001).," We must finally account for the fact that the epoch during which the number density of sources is roughly constant at the above value extends from $z \simeq 1.5$ to $z \simeq 3$, with characteristic $z \simeq 2.5$ (Jarvis Rawlings 2000; Rawlings 2001)."
 This corresponds to a quasar cra of lougth for~2 Cyr which cucompasses several generations of radio sources., This corresponds to a quasar era of length $t_{\rm QE} \sim 2$ Gyr which encompasses several generations of radio sources.
 The values of fog vary with Qa; so as to compensate for the difference due to cosmology iu the definition of ρω. so we finally find that the total proper density. 9. of intrinsically powerful radio sources is essentially independent of T.(as long as it exceeds ~107 vr) aud ij: P=o(T)ftog/T)-—17.4«107!Mpe," The values of $t_{\rm QE}$ vary with $\Omega_M$ so as to compensate for the difference due to cosmology in the definition of $\rho_{\rm obs}$, so we finally find that the total proper density, $\Phi$, of intrinsically powerful radio sources is essentially independent of $T$ (as long as it exceeds $\sim 10^8$ yr) and $\Omega_M$: $\Phi = \phi(T) (t_{\rm QE}/ T) = 7.7 \times 10^{-3} ~{\rm Mpc}^{-3}$."
 Recent high-resolution hywdrodyuanuüc simulations of ACDM models sugeest that at the present epoch roughly of the barvous exist in a web of fibuuents as wari eas and cimibedded galaxies and clusters. altogether occupying about of the volume of the universe (Con Ostriker 1999: Davé et 22001).," Recent high-resolution hydrodynamic simulations of $\Lambda$ CDM models suggest that at the present epoch roughly of the baryons exist in a web of filaments as warm-hot gas and embedded galaxies and clusters, altogether occupying about of the volume of the universe (Cen Ostriker 1999; Davé et 2001)."
 However. at the network of flamecents occupied only around colmoving volune. and their mass content has steadily grown since that epoch from about20%.. at the expeuse of the surrounding wari immediun (the eas cooler than ~ QUK. responsible for the Lyauau-a. absorption).," However, at $z \simeq
2.5$, the network of filaments occupied only around of the comoving volume, and their mass content has steadily grown since that epoch from about, at the expense of the surrounding warm medium (the gas cooler than $\sim~10^5$ K, responsible for the ${\alpha}$ absorption)."
" Since massive galaxies. the progenitors of powerful radio sources, lie near theexpectsjunctions of the filaments. their radio jets aud lobes are to directly interact with the cool circtmealactic material as well as the warin-hot aud iof eas contained iu the filaments."," Since massive galaxies, the progenitors of powerful radio sources, lie near the junctions of the filaments, their radio jets and lobes are expected to directly interact with the cool circumgalactic material as well as the warm-hot and hot gas contained in the filaments."
 Significant amounts of star formation are trigecred by the shocks aud high xessure associated with the radio ciuitting features (83)., Significant amounts of star formation are triggered by the shocks and high pressure associated with the radio emitting features 3).
 Thus. if a good fraction of this volue of the universe was permeated by radio lobes iu the quasar era. he lobes could play a substautial role iu trigecrine the intense star formation activity seen iu the universe at D—]l]2," Thus, if a good fraction of this volume of the universe was permeated by radio lobes in the quasar era, the lobes could play a substantial role in triggering the intense star formation activity seen in the universe at $z \sim 1-2$."
 We can now examinethe viability of this proposal., We can now examinethe viability of this proposal.
 The effective. volume of relevance here ds just that of the filaments contaimiug the galaxies aud overdcusc protogalactic gas at 22.5. whichis only the fraction ij of the total volume.," The effective volume of relevance here is just that of the filaments containing the galaxies and overdense protogalactic gas at $z \sim 2.5$, which is only the fraction $\eta$ of the total volume."
 The volume occupied by the svuchrotrou cluitting lobes of a powerful radio source (actually a lower Iuuit to the volume encompassed by the outer bow shock) at au age f ds where Rr. the ratio of the source’s leusth. D. to its width. 28. is typically ~5 LLeaby Williams 1981).," The volume occupied by the synchrotron emitting lobes of a powerful radio source (actually a lower limit to the volume encompassed by the outer bow shock) at an age $t$ is where $R_T$, the ratio of the source's length, $D$, to its width, $2R$, is typically $\sim 5$ Leahy Williams 1984)."
" By iutegratiug equation (3). weighted by the distribution function p(Qu) (sce 82.2). aud usine cquation (1) for D(f.Qu). we compute the average volume filled by these sources at their maxinnun ages to be (ΓΗ=5244Tz""'Mpe""Is?73"," By integrating equation (3), weighted by the distribution function $p(Q_0)$ (see 2.2), and using equation (1) for $D(t, Q_0)$, we compute the average volume filled by these sources at their maximum ages to be $\langle V(T) \rangle = 2.1~ T_5^{18/7} {\rm Mpc}^3$ ."
 Putting together the results from 82. the fractional relevant volume which radio lobes born during the quasar era eumulativelv cover is. for our canonical choice of T (DEW99).," Putting together the results from 2, the fractional relevant volume which radio lobes born during the quasar era cumulatively cover is, for our canonical choice of $T$ (BRW99)."
 We emphasize that this Πιο factor is the stu of the lobe volumes created during the eutire quasar era: this is relevant for estimatiue the domain of star formation triggered bv the lobes., We emphasize that this filling factor is the sum of the lobe volumes created during the entire quasar era; this is relevant for estimating the domain of star formation triggered by the lobes.
 In contrast. only one generation of sources is considered in estimating the contribution to the euergv density. «4. of svuchrotron plana injected iuto the cosmic web bv their lobes. suce the left-over contribution frou. previous generations of lobes should be mareinal. due to severe expansion losses.," In contrast, only one generation of sources is considered in estimating the contribution to the energy density, $u$, of synchrotron plasma injected into the cosmic web by their lobes, since the left-over contribution from previous generations of lobes should be marginal, due to severe expansion losses."
" This leads to «z2.7TQ,00D)x24.10Jin7 within the filamcuts.", This leads to $u \simeq 2.7~ T Q_m \phi(T) \approx 2 \times 10^{-16} {\rm J~m}^{-3}$ within the filaments.
 See Table 1 for specific values., See Table 1 for specific values.
 Thus. the main result is that. quite plausible a very sjeuificaut fraction of the relevant volume of the universe was hapiuged upon by the erowius radio lobes durius the redshift interval when radio source production was at its peak (2z2.5).," Thus, the main result is that, quite plausibly, a very significant fraction of the relevant volume of the universe was impinged upon by the growing radio lobes during the redshift interval when radio source production was at its peak $z \simeq 2.5$ )."
 Radio lobes propagating through this protogalactic medium mainly euncouuter the hot (f> LOTS). vohuue filling. lower deusity eus. but when they M the embedded cooler chuups (P.~10! FK: Fall mRees 1985). the initial bow shock compression will rlarge-scale star formation. which is sustained by the persistent overpressure from the engul&ug radio cocoon.," Radio lobes propagating through this protogalactic medium mainly encounter the hot $T > 10^6$ K), volume filling, lower density gas, but when they envelop the embedded cooler clumps $T \sim 10^4\,$ K; Fall Rees 1985), the initial bow shock compression will trigger large-scale star formation, which is sustained by the persistent overpressure from the engulfing radio cocoon."
 Note that the cocoon pressure is likely to be well above the equipartition estimate (Blundell Rawhnes 2000)., Note that the cocoon pressure is likely to be well above the equipartition estimate (Blundell Rawlings 2000).
 This scenario is supported by many models. both analytical BBeechuan Ciofi 1989: Rees 1989: Daly 1990). aud lydrodvuamiuical DDe Young 1989: Cioffi Dlondin 1992). aud provides an explanation for the remarkable radiooptical aligumeut effect. exhibited by hieh-: radio galaxies υπ(c.e..MeC'arthy et 11987: Chambers. Milev van LOSS).," This scenario is supported by many models, both analytical Begelman Cioffi 1989; Rees 1989; Daly 1990), and hydrodynamical De Young 1989; Cioffi Blondin 1992), and provides an explanation for the remarkable radio–optical alignment effect exhibited by $z$ radio galaxies (e.g., McCarthy et 1987; Chambers, Miley van Breugel 1988)."
 Additional support for jet or lobe-induced star formation comes from the TST images of 2~1 radio galaxies (Best. Lousair Rotttecring 1996). and of some radio sources at üeher 2 iaportantMMiley. et 11992: Bickuell et 22000).," Additional support for jet or lobe-induced star formation comes from the HST images of $z\sim 1$ radio galaxies (Best, Longair Rötttgering 1996), and of some radio sources at higher $z$ Miley et 1992; Bicknell et 2000)."
 It is to check if the overpressure of the expanding lobes over the ambient mecdinu persists hroughout the active lifetime. of the radio source., It is important to check if the overpressure of the expanding lobes over the ambient medium persists throughout the active lifetime of the radio source.
" From BRW99 FFale 19901): piiX££L17000. but Dx£O 7, so oyexDEte)"," From BRW99 Falle 1991): $p_{\rm lobe} \propto 
t^{(-4-\beta)/(5-\beta)}$, but $D \propto t^{3/(5-\beta)}$ , so $p_{\rm lobe} \propto D^{(-4-\beta)/3}$."
" The external xessure declines less rapidly. pasXD. 80 posPeeDi 1127/3, "," The external pressure declines less rapidly, $p_{\rm ext} \propto D^{-\beta}$, so $p_{\rm lobe}/p_{\rm ext} \propto D^{(-4+2\beta)/3}$ ."
For 3=3/2. monetpoeXDYO. while for >=Ll. which might be more reasonable at laree radial distances. Plobe/porXD7%.," For $\beta = 3/2$, $p_{\rm lobe}/p_{\rm ext} \propto D^{-1/3}$, while for $\beta = 1$, which might be more reasonable at large radial distances, $p_{\rm lobe}/p_{\rm ext} \propto
D^{-2/3}$."
" For the ranges of Qu. po and eg cousidered here. appropriate for FR II sources. overpressures at D=50 kpe will amount to factors of LO? 101, corresponding to Mach unmmbers of 10.100 (BRW99) for the |)owshock."," For the ranges of $Q_0$ , $\rho_0$ and $a_0$ considered here, appropriate for FR II sources, overpressures at $D = 50$ kpc will amount to factors of $10^2$ $10^4$ , corresponding to Mach numbers of 10–100 (BRW99) for the bowshock."
" Thus. overpressure should persist even for activityD<>1 AIpc. sustaining lobe expansion even after the jet COnses,"," Thus, overpressure should persist even for $D \gg 1$ Mpc, sustaining lobe expansion even after the jet activity ceases."
 Supersonic CXpausioniuto a two-phase circunigalactie medina will compress many of the cooler, Supersonic expansioninto a two-phase circumgalactic medium will compress many of the cooler
"The Israel Space Agency (ISA) issued a call for xe-xoposals im 1988 for ""scientific experiments to be flow1 on an Israch satellite”.",The Israel Space Agency (ISA) issued a call for pre-proposals in 1988 for “scientific experiments to be flown on an Israeli satellite”.
" The call was answered »* ipproxiniatelv 50 pre-proposals ranging from space astrononiv experinents, to characterizing f1ο behavior ofeectronic devices in the space environment, to the vchavior of fishes in zero-g. All the pre-proposals were evaluated by an internal ISA panel ann two were selected and funded to subit Phase A proposals."," The call was answered by approximately 50 pre-proposals ranging from space astronomy experiments, to characterizing the behavior of electronic devices in the space environment, to the behavior of fishes in zero-g. All the pre-proposals were evaluated by an internal ISA panel and two were selected and funded to submit Phase A proposals."
" Among these, the oue from Tel Aviv University proposed to orbit wo small telescopes to provide relativelv wide-fiek inaegine in the space-ultraviole (UW) domain."," Among these, the one from Tel Aviv University proposed to orbit two small telescopes to provide relatively wide-field imaging in the space-ultraviolet (UV) domain."
" The susequent stibinission stage at the comction ic Pase A. porfmined together with a coinercial ractor (ELOp Electro-Optical 1idustiies low part 16 ELBIT Systems company), prodiced a detailed study of the iiussioji."," The subsequent submission stage at the completion of the Phase A, performed together with a commercial contractor (El-Op Electro-Optical Industries now part of the ELBIT Systems company), produced a detailed study of the mission."
" ELOp was selec‘ted as Prime Contracor since it had a strong heritage «of sopjisticatedli clectro-opical pavloads for eround, naval. and airOTE inaeime while develooue substantial infrasticture for space iuaegiug pavloads."," El-Op was selected as Prime Contractor since it had a strong heritage of sophisticated electro-optical payloads for ground, naval, and airborne imaging while developing substantial infrastructure for space imaging payloads."
" Iu. particular, it operated a thermnal-vacumn clauber equipped wit1 à collimator that allowed a paxoad to be eacd-to-eud ested in vacuum and at extrene temperatures."," In particular, it operated a thermal-vacuum chamber equipped with a collimator that allowed a payload to be end-to-end tested in vacuum and at extreme temperatures."
 The TAUVEN Ph:ie A result was a doesign ΓΙΝΕ in Table 1. with tree 20«πα co-aliered. telescopes mounted within a cvΠιο lia ColId fit he inucr space of an OFEQ-class satellite," The TAUVEX Phase A result was a design summarized in Table 1, with three 20-cm co-aligned telescopes mounted within a cylinder that could fit the inner space of an OFEQ-class satellite."
 T1C field «X view (FOV) of cach telescope was choscu o be approximately one degree., The field of view (FOV) of each telescope was chosen to be approximately one degree.
" Erving on the cojscrvative sice. we decided to use onlv space-proven echuiqes and components, and to require the Prime Contractor to include fully-reduudant svstenis in this first natioial astronomy experiment."," Erring on the conservative side, we decided to use only space-proven techniques and components, and to require the Prime Contractor to include fully-redundant systems in this first national astronomy experiment."
 For UV «letectors we selectec sealed photoclectric§f detectors with Cacsin Telluride ποni-transparent, For UV detectors we selected sealed photoelectric detectors with Caesium Telluride semi-transparent
We beein by assunune a spherical source of radius 7 containing a tangled magnetic feld of streneth B.,We begin by assuming a spherical source of radius $R$ containing a tangled magnetic field of strength $B$.
 We also assune that monocnerectic 5— ravs of energv €. (iu units of ο) ave uniformly produced by some uuspecified mechanigi throughout the volume of the source., We also assume that monoenergetic $\gamma-$ rays of energy $\eg$ (in units of $\melec c^2$ ) are uniformly produced by some unspecified mechanism throughout the volume of the source.
 If these are injected with a bhnuninositv LP! one can define the injected > ray conipactness as) where op is ἳthe Thomsou cross section.," If these are injected with a luminosity $L_\gamma^{\rm inj}$ , one can define the injected $\gamma-$ ray compactness as, where $\sigma_T$ is the Thomson cross section."
 Without any substantial soft photon population inside the source. the  ravs will escape without auv attenuation iu one crossing time.," Without any substantial soft photon population inside the source, the $\gamma-$ rays will escape without any attenuation in one crossing time."
 Towever. as SIS showed. the injected 5 rav conrpactuess cannot become arbitrarily hieh because ifa critical value is reached. the following loop starts operating l.," However, as SK showed, the injected $\gamma-$ ray compactness cannot become arbitrarily high because if a critical value is reached, the following loop starts operating 1."
 Gamunaravs pair-produce on soft photons. which can be arbitrarily low iuside the source.," Gamma-rays pair-produce on soft photons, which can be arbitrarily low inside the source."
 2., 2.
 The produced clectrou-positron pairs cool bx cluitting svuchrotron photons. thus acting as a source of soft photons.," The produced electron-positron pairs cool by emitting synchrotron photons, thus acting as a source of soft photons."
 3., 3.
 The soft photous serve as targets for more 35 luteractions., The soft photons serve as targets for more $\ggabs$ interactions.
 There are two conditions that should be satisfied sinultauneouslv for his uetwork to occi: The first. which is afeedback condition. requires that the svuchrotrou yhotous emitted from the pairs have sufficicut energv O pair-produce on the 3 ravs.," There are two conditions that should be satisfied simultaneously for this network to occur: The first, which is a condition, requires that the synchrotron photons emitted from the pairs have sufficient energy to pair-produce on the $\gamma-$ rays."
 By auaking suitable siupliiug assuniptions. one can derive an analytic relation forif — see also SE.," By making suitable simplifying assumptions, one can derive an analytic relation forit – see also SK."
" Thus. combining (1) the ireshold condition for 35-absorption e.ey—2. (2) re fact that there is equipartition of energv a1nong 1ο create electrou-positroun pairs +,=οσο3€-/2 and (3) the assuniptiouthat the required soft yhotous of energv ερ are the svuchrotron photons that je clectrons/positrous radiate. he. ey=bs? where BiBoi aud Dagnz(ο)zLEslobe 6 is the critical value of the maguetie field. one derives ie nmuininmun value of the maguetie feld required for quenching to become relevantBag."," Thus, combining (1) the threshold condition for $\ggabs$ -absorption $\eg\epsilon_0=2$, (2) the fact that there is equipartition of energy among the created electron-positron pairs $\gamma_p=\gamma_e=\gamma=\eg/2$ and (3) the assumptionthat the required soft photons of energy $\epsilon_0$ are the synchrotron photons that the electrons/positrons radiate, i.e., $\epsilon_0=b\gamma^2$ where $b=B/B_{\rm crit}$ and $B_{\rm crit}=(\melec^2 c^3)/(e\hbar)
\simeq 4.4\times 10^{13}$ G is the critical value of the magnetic field, one derives the minimum value of the magnetic field required for quenching to become relevant."
" Thus for B>D, the eedback criterion is satisfied.", Thus for $B\ge B_q$ the feedback criterion is satisfied.
 Note that this is a coudition that only coutaius the eiitted ~ raw eucrev and the magnetic field strength: moreover. it can casily be satisfied. at least if one is to use the values interred from typical modelling of the sources (2?)..," Note that this is a condition that only contains the emitted $\gamma-$ ray energy and the magnetic field strength; moreover, it can easily be satisfied, at least if one is to use the values inferred from typical modelling of the sources \citep{boettcher07, boettcher09}."
 Along with the feedback criterion. a second criterion must be imposed for the quenching to be fully operative.," Along with the feedback criterion, a second criterion must be imposed for the quenching to be fully operative."
 A simple wav to see this is with the following consideration., A simple way to see this is with the following consideration.
 Asstuue that the  raves pair-produce on sole soft photon and that the created electrou-positron pairs cool bx cluitting svuchrotron photous., Assume that the $\gamma-$ rays pair-produce on some soft photon and that the created electron-positron pairs cool by emitting synchrotron photons.
 Because an electrou cuits several such pliotous before cooling the critical condition occurs if the πιάνο deusitv of the + ravs is such that at least one of the svuchrotrou plotous pair-produces ou a 5 ταν instead of escaping from the source., Because an electron emits several such photons before cooling the critical condition occurs if the number density of the $\gamma-$ rays is such that at least one of the synchrotron photons pair-produces on a $\gamma-$ ray instead of escaping from the source.
Thus the condition for criticality can be written as /3)ntes 8. 1. where ne.) ds the nuuuber deusitv of + ravs. σε ds the cross section for 55 interactions aud A45) is the uunuber of svuchrotrou photons enmütted bv an electron with Lorentz factor 5 before it cools.,"Thus the condition for criticality can be written as /2) ) 1, where $n(\eg)$ is the number density of $\gamma-$ rays, $\sigma_\ggabs$ is the cross section for $\ggabs$ interactions and $\cal{N}_{\rm s}(\gamma)$ is the number of synchrotron photons emitted by an electron with Lorentz factor $\gamma$ before it cools."
 Asstuing that the pair-produciug collisions occur close to threshold. approxinatius the cross section there by σ.-2o7/3 and usineSe MG)°mqn: and (62)=v—áÀvUCerLU4.og the critical condition can be written as l|. where the feedback condition (2)) aud eq. (1))," Assuming that the pair-producing collisions occur close to threshold, approximating the cross section there by $\sigma_\ggabs\simeq\sigma_T/3$ and using ${\cal{N}}_{\rm s}(\gamma)\simeq\frac{\gamma}{b\gamma^2}$ and $n(\eg)=\frac{L_{\gamma}^{\rm inj}}{V\eg \melec c^2}\frac{R}{c}$, the critical condition can be written as 4, where the feedback condition \ref{bcrit}) ) and eq. \ref{lgg}) )"
 were also used., were also used.
 Taken as equalities. relatious (2)) and (1)) define the criterion. which csscutially isa condition for the ταν Duuinosity.," Taken as equalities, relations \ref{bcrit}) ) and \ref{lcr0}) ) define the criterion, which essentially is a condition for the $\gamma-$ ray luminosity."
 We beein by writing the kinetic equations that describe the distributions of οταν photons. soft photons. and electrons in the source.," We begin by writing the kinetic equations that describe the distributions of $\gamma$ -ray photons, soft photons, and electrons in the source."
" These are respectively laOrsay Hay = and =τον. where s. ng and. nm, are the differential οταν, soft xioton. and electrou number densities. respectively. aud €.. c, aud 5 are the corresponding energies normalized Hi ο undts."," These are respectively +n= +n_0 = and =, where $n$ , $n_0$ and, $n_e$ are the differential $\gamma$ -ray, soft photon, and electron number densities, respectively, and $\egamma$, $x$, and $\gamma$ are the corresponding energies normalized in $\melec c^2$ units."
 The densities refer to the uunmber of articles contained in a volume element oH., The densities refer to the number of particles contained in a volume element $\sth R$.
 Du other words. If 9; expresses the nuniber of particles of species i per ores per cn. then a;=στπο].," In other words, if $\hat{n}_i$ expresses the number of particles of species $i$ per ergs per $^3$, then $n_i = \hat{n}_i(\sth R)(\melec c^2)$."
" Tie is rorlualized with respect to the photon crossine/escapeine from the source. £4,= Re."," Time is normalized with respect to the photon crossing/escapetime from the source, $t_{\rm cr}=R/c$ ."
" Thus. 7. which appears iu the sinetic equatious. is dimensionless aud equals T= n2 The operators Q and £ denote injection aud osses. respectively,"," Thus, $\tau$ , which appears in the kinetic equations, is dimensionless and equals $\tau=\frac{ct}{R}$ The operators $\cal{Q}$ and $\cal{L}$ denote injection and losses, respectively."
 The only processes that we takeiuto account are 55 annihilation and svuchrotron cooling of the produced pais, The only processes that we takeinto account are $\gamma \gamma$ annihilation and synchrotron cooling of the produced pairs.
 The svuchrotron οκνττν is, The synchrotron emissivity is
ἡ0140.,$\eta \sim 140$.
 The total flix is shown by the thin solid line., The total flux is shown by the thin solid line.
 In this case. we need to assume larger ISAL turbulence.," In this case, we need to assume larger ISM turbulence."
 In this section. we assume (he values of parameters wilh which we have shown the example cases in (le previous section. and estimate the X-ray. ancl radio afterelows.," In this section, we assume the values of parameters with which we have shown the example cases in the previous section, and estimate the X-ray and radio afterglows."
" The exiinclion correction a, is unity lor X-ray and radio afterglows. and hence Finer1.6 mJv (radio ancl X-ray)."," The extinction correction $a_\nu$ is unity for X-ray and radio afterglows, and hence $F_{\nu,max,f} \sim 1.6$ mJy (radio and X-ray)."
 X-ray Afterglow: Since the N-rav. band. ~5keV is well above the tvpical frequency of the reverse shock emission. the contribution from the reverse shock to the N-rav. band is negligible.," X-ray Afterglow: Since the X-ray band $\sim 5$ keV is well above the typical frequency of the reverse shock emission, the contribution from the reverse shock to the X-ray band is negligible."
 The X-ray afterglow should be described only by the forward shock emission., The X-ray afterglow should be described only by the forward shock emission.
" The huninosity in X-ray band should decrease as [2PE4tip=2,4) or) FP(p=2.2).", The luminosity in X-ray band should decrease as $t^{(2-3p)/4} \sim t^{-1.3}(p=2.4)$ or $t^{-1.15}(p=2.2)$.
 The Chandra X-ray. observatory observed (he alterglow for a total exposure of STksec. beginning al Oct 5 8:55 UT (Sako and Harrison 2002).," The Chandra X-ray observatory observed the afterglow for a total exposure of 87ksec, beginning at Oct 5 8:55 UT (Sako and Harrison 2002)."
 The count rate decrease with a power law slope of —1.02:0.2.," The count rate decrease with a power law slope of $-1.0 \pm
0.2$."
 The mean 2-10 keV. X-ray flux is ~4.3x10.P eres 7s 1., The mean 2-10 keV X-ray flux is $\sim 4.3 \times10^{-13}$ ergs $^{-2}$ $^{-1}$.
 We estimate the 5keVT flux at the observational. mean time. 1.36⋅⋅ days ~3.1.x1015 eres »7? ! forB p24 and 6.4x10.P eres ? ! for p=2.2., We estimate the 5keV flux at the observational mean time 1.36 days $\sim 3.1\times10^{-13}$ ergs $^{-2}$ $^{-1}$ for $p=2.4$ and $\sim 6.4\times10^{-13}$ ergs $^{-2}$ $^{-1}$ for $p=2.2$.
 Our estimates are in a good agreement with the observations., Our estimates are in a good agreement with the observations.
 Radio Afterglow: The forward shock emission in radio band ~10 Gllz increases as [7 until the flux reaches to the maximum ~1.6 mJv al ~80 days for p=2.4 (dashed dotted line in fig?) or at ~50 davs lor p=2.2., Radio Afterglow: The forward shock emission in radio band $\sim 10$ GHz increases as $t^{1/2}$ until the flux reaches to the maximum $\sim 1.6$ mJy at $\sim 80$ days for $p=2.4$ (dashed dotted line in fig2) or at $\sim 50$ days for $p=2.2$.
" After the typical [requeney 14, crosses (he radio band. the reverse shock emission decays as ~/7 (dashed line for p= 2.4)."," After the typical frequency $\nu_{m,r}$ crosses the radio band, the reverse shock emission decays as $\sim t^{-2}$ (dashed line for $p=2.4$ )."
 M low frequencies and early limes. self absorption takes an important role ancl significantly reduces ihe flux.," At low frequencies and early times, self absorption takes an important role and significantly reduces the flux."
 A simple estimate of the maximal flux (dotted line for p= 2.4) is the emission from the black body with the reverse shock temperature (IXobavashi Sari 2000)., A simple estimate of the maximal flux (dotted line for $p=2.4$ ) is the emission from the black body with the reverse shock temperature (Kobayashi Sari 2000).
 The thick and (hin solid line depicts the total {lus for p—2.4 and lor p=2.2. respectively.," The thick and thin solid line depicts the total flux for $p=2.4$ and for $p=2.2$, respectively."
 Since the observations (circles) are done in various frequencies. we scaled the observed. value to the expected value at. 106 by using a spectral slope of 1.1.," Since the observations (circles) are done in various frequencies, we scaled the observed value to the expected value at $10$ GHz by using a spectral slope of $1$ ."
 This burst might also cause a bright radio flare 1 mJv around ~0.5 day as observed in GRB 990123., This burst might also cause a bright radio flare $\sim 1$ mJy around $\sim 0.5$ day as observed in GRB 990123.
 When we fit the, When we fit the
We have shown that the thiourea functional eroup. associated with various carbonaceous structures. has one or two strong emission lines in a spectral range of ~ Lynn. within the 21-52 band emitted by a umuber of pre-planetary uebulae.,"We have shown that the thiourea functional group, associated with various carbonaceous structures, has one or two strong emission lines in a spectral range of $\sim$ 4 $\mu$ m, within the $\mu$ m band emitted by a number of pre-planetary nebulae."
 The combination of nitrogen aud sulphur in thiourea is the esseutial source of Cluission iu this model: the baud disappears if these species are replaced by carbon., The combination of nitrogen and sulphur in thiourea is the essential source of emission in this model: the band disappears if these species are replaced by carbon.
 These two clements are part of the ubiquitous CITONS family because of their high chemical activity., These two elements are part of the ubiquitous CHONS family because of their high chemical activity.
 Thiourea may therefore readily forma in space. aud be found as an independent molecule or as a peripheral eroup attached to carbouaceous structures believed to be abundant ii space.," Thiourea may therefore readily form in space, and be found as an independent molecule or as a peripheral group attached to carbonaceous structures believed to be abundant in space."
 Iu all cases. it carries a strong IR Lue near the molecular thiourea line. which is the strougest and thus determines the peak of the baud.," In all cases, it carries a strong IR line near the molecular thiourea line, which is the strongest and thus determines the peak of the band."
 Obvioush. no single structure can exhibit the required spectrum. for cach ouly contributes discrete lines which camunot be broadened enough by usual broadening mcchanisins.," Obviously, no single structure can exhibit the required spectrum, for each only contributes discrete lines which cannot be broadened enough by usual broadening mechanisms."
 Twelve structures have beeu selected here. but their list is far from begC» exhaustive: thev are only iuteuded as exaniples of the generic thiourea class.," Twelve structures have been selected here, but their list is far from being exhaustive; they are only intended as examples of the generic thiourea class."
 The ehienical software used hiere also allows to determine the types of modal vibrations which cary the lines of interest: this helps designing new structures to fill the wide bands observed im the sky., The chemical software used here also allows to determine the types of modal vibrations which cary the lines of interest; this helps designing new structures to fill the wide bands observed in the sky.
- Using interpolation and smoothing between the coucatenated discrete. lines of the selected structures. we produced svuthetic spectra which exhibit a prominent. asvuumnetrie. feature between I8 aud 25 gan. with ανακια points at 19.6 aud 21.9 gan. very near the observed values.," Using interpolation and smoothing between the concatenated discrete lines of the selected structures, we produced synthetic spectra which exhibit a prominent, asymmetric, feature between 18 and 25 $\mu$ m, with half-maximum points at 19.6 and 21.9 $\mu$ m, very near the observed values."
 However. the peak is 0.6 pan vedward of the observed average.," However, the peak is 0.6 $\mu$ m redward of the observed average."
 The astronomical 21-41. feature extends rechward to merge with the other. prominent 30-/24: band.," The astronomical $\mu$ m feature extends redward to merge with the other, prominent $\mu$ m band."
 It is found that the main characters of this band cau be modelled by the combined spectra of: a) aliphatic chains. made of CIT; eroups. oxvgen bridges and ΟΠ eroups. which provide the 30-4221: ciission: b) siiall. mostly lear. aromatic structures. which contribute to raise the red wing of the 21-422. baud and fill the space between the two main features.," It is found that the main characters of this band can be modelled by the combined spectra of: a) aliphatic chains, made of $_{2}$ groups, oxygen bridges and OH groups, which provide the $\mu$ m emission; b) small, mostly linear, aromatic structures, which contribute to raise the red wing of the $\mu$ m band and fill the space between the two main features."
 The concatenated spectral lines of ten of these structures form a stroug band between 23 and 38 qun. The omission of oxvseu in such structures all but extinguishes the 30-4 enusson., The concatenated spectral lines of ten of these structures form a strong band between 23 and 38 $\mu$ m. The omission of oxygen in such structures all but extinguishes the $\mu$ m emission.
 The fact that these carriers do not involve. aud are likely more abundant than. thiourea derivatives eusures that the 30-420. feature can still be preseut in the absence of the 21-4211 feature. as observed.," The fact that these carriers do not involve, and are likely more abundant than, thiourea derivatives ensures that the $\mu$ m feature can still be present in the absence of the $\mu$ m feature, as observed."
 Combining the discrete lines of the 22 selected structures in different proportions. interpolating aud smoothing. we produced 2 svuthetic spectra which purport," Combining the discrete lines of the 22 selected structures in different proportions, interpolating and smoothing, we produced 2 synthetic spectra which purport"
"(fy.bs) with E,=50 keV and E»=300 keV. For an object al redshift z. the observed energy range (f,.£5) originates in the range (I4(12-z).Es(124-:)) in the objects rest frame. whereas the luminosity refers to the range (£4.F5).","$(E_1,E_2)$ with $E_1 = 50$ keV and $E_2 = 300$ keV. For an object at redshift $z$, the observed energy range $(E_1,E_2)$ originates in the range $(E_1(1+z),E_2(1+z))$ in the object's rest frame, whereas the luminosity refers to the range $(E_1,E_2)$."
 The IX-term is the ratio of the rest frame energies raciated in the (wo ranges. The Dand photon spectrum is ususally described in terms of a break energy. £j.," The K-term is the ratio of the rest frame energies radiated in the two ranges, The Band photon spectrum is ususally described in terms of a break energy $E_0$ ."
 Here we use a Band spectrum NCE.Ey...) where Ey(sp)=(2+a)Ly(sp) assuming that 2«—2 (Banelοἱal.1993).," Here we use a Band spectrum $N(E,E_{pk},\alpha,\beta)$ where $E_{pk}(sp)=(2 + \alpha)E_0(sp)$ assuming that $\beta < -2$ \citep{ban93}."
. We adopt constant. values of a=—0.8 and 9=—2.6 for reasons that will be discussed in Section 5., We adopt constant values of $\alpha = -0.8$ and $\beta = -2.6$ for reasons that will be discussed in Section 5.
 The peak flux P(L.z) observed for a GRB of Iuminositv.L at redshift 2 is where (c/H3).1(z) is the bolometric Iuminosity distance.," The peak flux $P(L,z)$ observed for a GRB of luminosity$L$ at redshift $z$ is where $(c/H_0)A(z)$ is the bolometric luminosity distance."
" We use (he cosmological parameters Hyτο kms ! !. Q4,—0.3. and Q4—0.7."," We use the cosmological parameters $H_0 = 70~$ km $^{-1}$ $^{-1}$ , $\Omega_M = 0.3$, and $\Omega_{\Lambda} = 0.7$."
 The integral peak flux distribution for GhRDs of spectral class sp is. where z(L.P.sp) is derived. [romequation (4). V(z) is the comoving volume and the term (1+2)! represents the time dilation.," The integral peak flux distribution for GRBs of spectral class $sp$ is, where $z(L,P,sp)$ is derived fromequation (4), $V(z)$ is the comoving volume and the term $(1+z)^{-1}$ represents the time dilation."
 With this formulation. it is straightforward to derive the differential source counts dN(>P.sp)/dP. as well as the average values of/Vinas-Poss . 03. elc.," With this formulation, it is straightforward to derive the differential source counts $dN(>P,sp)/dP$, as well as the average values of, $\alpha_{23}$ , etc."
 For a given rate funelion the procedure to iterate the huninoxity function is as follows., For a given rate function the procedure to iterate the luminoxity function is as follows.
" Assume starting values for the central huninosity. Z.(sp) and the rest frame Band peak energy E,(sp).", Assume starting values for the central luminosity $L_c(sp)$ and the rest frame Band peak energy $E_{pk}(sp)$.
" The differential source counts together with —(D/Pj,,)*? produce the expected values of »Gp)forlheGUS BADcalalog.", The differential source counts together with $= (P/P_{lim})^{-3/2}$ produce the expected values of $(sp)$ for the GUSBAD catalog.
 Similarly.," Similarly, the expected values of $(sp)$ are obtained by weighting $/(1+z)$ with the differential source counts."
 theexpe lt i, The iteration isrepeated until the expected values of $(sp)$ and $(sp)$ match the observed ones given in Table 2.
s worth noting that given aad (he shape of the five spectral luminosity ΠαπΙου. the procedure leads lor each spto a single value lor L.(sp) and Γρ).," It is worth noting that given and the shape of the five spectral luminosity functions, the procedure leads for each $sp$to a single value for $L_c(sp)$ and $E_{pk}(sp)$ ."
 The primary unknown is the densityfiction )., The primary unknown is the densityfunction .
. We will use cldata to test various forms of R(z).. see Sec.," We will use data to test various forms of , see Sec."
 !5., 5.
"aggregates are very fluffy, open structures.","aggregates are very fluffy, open structures."
 If one would draw a circumscribing sphere around the aggregate the vacuum fraction inside this sphere would be very large., If one would draw a circumscribing sphere around the aggregate the vacuum fraction inside this sphere would be very large.
 in order to do computations for different aggregate sizes one might simply increase the size of the circumscribing sphere and perform Mie computations using the effective refractive index as given by Eq. (I0])., in order to do computations for different aggregate sizes one might simply increase the size of the circumscribing sphere and perform Mie computations using the effective refractive index as given by Eq. \ref{eq:meffective}) ).
 We will refer to this method as the Aggregate Polarizability Mixing Rule (APMR)., We will refer to this method as the Aggregate Polarizability Mixing Rule (APMR).
 Now we have to determine how to get the required [πι and radius of the homogeneous sphere., Now we have to determine how to get the required $f_\mathrm{fill}$ and radius of the homogeneous sphere.
" As is shown by (2006a) the most natural choice, namely using the circumscribing sphere, leads to an overestimate of the result of the fluffyness of the aggregate."," As is shown by \citet{2006A&A...445.1005M} the most natural choice, namely using the circumscribing sphere, leads to an overestimate of the result of the fluffyness of the aggregate."
 This is because the aggregate constituents are not randomly distributed in the volume circumscribed by this sphere., This is because the aggregate constituents are not randomly distributed in the volume circumscribed by this sphere.
" Therefore, we have to choose a somewhat smaller radius which also somehow takes into account the structure of the aggregates."," Therefore, we have to choose a somewhat smaller radius which also somehow takes into account the structure of the aggregates."
" A choice, which leads to excellent results as shown below, is to use the radius of gyration of the aggregate."," A choice, which leads to excellent results as shown below, is to use the radius of gyration of the aggregate."
" In this equation r; is the location of constituent i, and ro is the center of mass of the aggregate."," In this equation $\vec{r}_i$ is the location of constituent $i$, and $\vec{r}_0$ is the center of mass of the aggregate."
 For fractal aggregates with fractal dimension D; the radius of gyration can be expressed as (Filippovetal2000) where y is a constant depending only on the size of the constituents and on the so-called fractal prefactor.," For fractal aggregates with fractal dimension $D_f$ the radius of gyration can be expressed as \citep{Filippov}
 where $\gamma$ is a constant depending only on the size of the constituents and on the so-called fractal prefactor."
 By comparing the gyration radii computed using Eqs. ᾖᾖΤ)), By comparing the gyration radii computed using Eqs. \ref{eq:rg}) )
 and (12)) one finds that the aggregates we use are best represented using Dy=2.82 and y= 2.44., and \ref{eq:rg2})) one finds that the aggregates we use are best represented using $D_f=2.82$ and $\gamma=2.44$ .
 The filling factor is now defined by, The filling factor is now defined by
of the planet is given by qo.,of the planet is given by $\varphi_0$.
 The value of yo is determined by the relative velocity of the planetary and stellar coronal material., The value of $\varphi_0$ is determined by the relative velocity of the planetary and stellar coronal material.
 Figure | of ? illustrates the scenarios leading to the various shock orientations., Figure 1 of \cite{Vidotto:2010p809} illustrates the scenarios leading to the various shock orientations.
" There are two limiting cases: an “ahead-shock” (yy O0) forms when the planet is embedded in the stellar corona and a ""dayside-shock"" (gj.- 90°) forms when the radial wind velocity is very much greater than the relative azimuthal velocity of the planet."," There are two limiting cases: an “ahead-shock"" $\varphi_0\rightarrow0$ ) forms when the planet is embedded in the stellar corona and a “dayside-shock"" $\varphi_0\rightarrow90^\circ$ ) forms when the radial wind velocity is very much greater than the relative azimuthal velocity of the planet."
 Here we use models for the stellar corona and wind (22). to obtain a value for the plasma density at the planet.," Here we use models for the stellar corona and wind \citep{Vidotto:2010p809,Vidotto:2011p803} to obtain a value for the plasma density at the planet."
 These models assume a typical solar base density of np~100m? (2) and either an isothermal hydrostatic corona or an isothermal thermally driven wind., These models assume a typical solar base density of $n_0\sim10^8\textrm{cm}^{-3}$ \citep{Withbroe:1988p829} and either an isothermal hydrostatic corona or an isothermal thermally driven wind.
 We assume an adiabatic shock with a maximum compression ratio of 4., We assume an adiabatic shock with a maximum compression ratio of 4.
" For an isothermal corona of temperature 7. the density of stellar material. Πρι. at a planet of orbital radius Aj, is given by Equation 8 of ?.. For the stellar wind case we use mass conservation and the momentum equation. to obtain values for the radial velocity. i and density. 7,4."," For an isothermal corona of temperature $T$, the density of stellar material, $n_{\rm obs}$, at a planet of orbital radius $R_{\rm orb}$ is given by Equation 8 of \cite{Vidotto:2010p809}, For the stellar wind case we use mass conservation $(nu_rr^2=\textrm{const})$ and the momentum equation, to obtain values for the radial velocity, $u_r$ and density, $n_{\rm obs}$."
 The plasma density can then be converted into a density of fully ionized magnesium using the relation. where. ny.7j is the ratio of Magnesium number density to Hydrogen number density which is derived from the metallicity of the host star (2)..," The plasma density can then be converted into a density of fully ionized magnesium using the relation, where, $n_{\rm Mg}/n_{\rm H}$ is the ratio of Magnesium number density to Hydrogen number density which is derived from the metallicity of the host star \citep{Hebb:2009p806}."
 For WASP-12. ma./ni=6.76x10? (2).," For WASP-12, $n_{\rm Mg}/n_{\rm H}=6.76\times10^{-5}$ \citep{Vidotto:2010p809}."
 From this density we can then find bow shock geometries and orientations that fit the observations of ?.., From this density we can then find bow shock geometries and orientations that fit the observations of \cite{Fossati:2010p838}.
 To investigate whether the model presented by ?. is able to reproduce the data from the near-UV observations. we use Monte Carlo radiative transfer calculations to produce simulated light curves.," To investigate whether the model presented by \cite{Vidotto:2010p809} is able to reproduce the data from the near-UV observations, we use Monte Carlo radiative transfer calculations to produce simulated light curves."
" The parameters we adopt to match the WASP-12 system are: M,=M;. Rk,=1.79R, (where My and Ry are the mass and radius ofL.431 Jupiter). M,=1.35M. and A,=ΤΝ..."," The parameters we adopt to match the WASP-12 system are: $M_p = 1.41 M_J$, $R_p = 1.79 R_J$ (where $M_J$ and $R_J$ are the mass and radius of Jupiter), $M_\star = 1.35 M_\odot$ and $R_\star = 1.57 R_\odot$."
" The host star is a late F type and the planet orbits in the equatorial plane with an impact parameter b=0.36R, (2)."," The host star is a late F type and the planet orbits in the equatorial plane with an impact parameter $b= 0.36\,R_\star$ \citep{Hebb:2009p806}."
" The shocked material is considered to be at a distance ry, from the planet. with a thickness Ary, and an angular extent 2Ay."," The shocked material is considered to be at a distance $r_M$ from the planet, with a thickness $\Delta r_M$ and an angular extent $2\Delta \varphi$."
 The projected lateral extent of the shock is dependent on 73.qo and Ay.," The projected lateral extent of the shock is dependent on $r_M,\varphi_0$ and $\Delta\varphi$."
 The maximum distance between the planet and the projected lateral extent of the shock. X. can take the following forms Our simulated transit light curves are produced using a 3D Monte Carlo radiation transfer code (2)..," The maximum distance between the planet and the projected lateral extent of the shock, $X_M$ , can take the following forms Our simulated transit light curves are produced using a 3D Monte Carlo radiation transfer code \citep{Wood:1999p822}."
 The circumplanetary density structure is prescribed on a 3D spherical polar grid (coordinates r. 8. ) and is externally irradiated with Monte Carlo photon packets with a distribution that reproduces the spatial intensity distribution of a limb-darkened star.," The circumplanetary density structure is prescribed on a 3D spherical polar grid (coordinates $r$, $\theta$, $\varphi$ ) and is externally irradiated with Monte Carlo photon packets with a distribution that reproduces the spatial intensity distribution of a limb-darkened star."
 We assume a spherical planet and a darkening law such that the intensity / is given by where p=cos@2(1-7)7.0rLH is the radial distance into the stellar disk normalized to the stellar radius and /(0) is the emergent intensity at the centre of the star (2)..," We assume a spherical planet and a limb-darkening law such that the intensity $I$ is given by where $\mu = \cos\theta= (1-r^2)^{1/2}, 0\leq r\leq 1$ is the radial distance into the stellar disk normalized to the stellar radius and $I(0)$ is the emergent intensity at the centre of the star \citep{Mandel:2002p814}."
" The coethcients a, are chosen from ? to match the ii-band limb-darkening of the host star.", The coefficients $a_n$ are chosen from \cite{Claret:2004p807} to match the $u$ -band limb-darkening of the host star.
 We assume that the material absorbs or scatters radiation out of the line-of-sight with no scattering into the line-of-sight. which is valid for the optical depths required to produce the early-ingress transits.," We assume that the material absorbs or scatters radiation out of the line-of-sight with no scattering into the line-of-sight, which is valid for the optical depths required to produce the early-ingress transits."
 For this letter we assume the bow shock is of uniform density and that the material is static. however. our models are very general and can incorporate any density structure: analytic. tabulated. or from dynamical simulations.," For this letter we assume the bow shock is of uniform density and that the material is static, however, our models are very general and can incorporate any density structure: analytic, tabulated, or from dynamical simulations."
Our goal is to determine the range of shock geometries that can provide both an early-ingress and suthcient optical depth in MgIT,Our goal is to determine the range of shock geometries that can provide both an early-ingress and sufficient optical depth in MgII
absorption features present in the wavelength range centered on the Meg line triplet. (AA5164.5173.X... see. Tab. 7)),"absorption features present in the wavelength range centered on the Mg line triplet $\lambda\lambda\,5164,5173,5184$, see Tab. \ref{tab:TW_values}) )"
 using the Fourier Correlation Quotient 5184.method (Bender 1990: Bender et al., using the Fourier Correlation Quotient method (Bender 1990; Bender et al.
 1994). as done in Paper I. We adopted LR 6817 (NILE) as the kinematical template to measure the stellar kinematics of NGC 3412. LR 7429 (IX31HE). for the kinematics of ESO 139-C009 and LC S74. and LR 3145 (ΝΕΤ) for the kinematics of NGC 1308 and NGC 1440.," 1994), as done in Paper I. We adopted HR 6817 (K1III) as the kinematical template to measure the stellar kinematics of NGC 3412, HR 7429 (K3III) for the kinematics of ESO 139-G009 and IC 874, and HR 3145 (K2III) for the kinematics of NGC 1308 and NGC 1440."
 The values of line-ol-sieht velocity. e... and. velocity dispersion c measured along the different slits for cach sample galaxyare given in Table 6..," The values of line-of-sight velocity $v$, and velocity dispersion $\sigma$ measured along the different slits for each sample galaxyare given in Table \ref{tab:kinematics}. ."
penetrate so far.,penetrate so far.
 However. N-rays. could. still increase the ionisation fraction. and hence the associated ellective o. in the active laver.," However, X-rays could still increase the ionisation fraction, and hence the associated effective $\alpha$, in the active layer."
 Igea&Classgold(1999). showed that the X-ray ionisation rate near the surface is significantly larger than that of cosmic ravs., \cite{igea99} showed that the X-ray ionisation rate near the surface is significantly larger than that of cosmic rays.
 The accretion rate through the laver may be higher than predieted in equation (29)) if this is taken into account and perhaps could help to explain the Tauri accretion rates for higher critical magnetic Ievnolds number., The accretion rate through the layer may be higher than predicted in equation \ref{mdoteq}) ) if this is taken into account and perhaps could help to explain the T Tauri accretion rates for higher critical magnetic Reynolds number.
 Observed EU Orionis svstems may be one manifestation of the time-dependent aceretion phenomenon., Observed FU Orionis systems may be one manifestation of the time-dependent accretion phenomenon.
 These luminous voung stellar objects are found in star [orming regions (Llartmann&Wenvon1996)., These luminous young stellar objects are found in star forming regions \citep{hartmann96}.
.. Their optical brightness increases by live magnitudes or more on a timescale of vears and decays on a timescale of 50-100 vears (Llerbig1977)., Their optical brightness increases by five magnitudes or more on a timescale of years and decays on a timescale of 50-100 years \citep{herbig77}.
. The timescale and. brightness. of accretion outbursts from the eravo-magneto instability are similar to the observed. EU. Orionis outbursts (Armitage.Livio&Pringle2001:Zhuetal. 2009b).," The timescale and brightness of accretion outbursts from the gravo-magneto instability are similar to the observed FU Orionis outbursts \citep{armitage01,zhu09b}."
. Time-dependent numerical simulations are needed to investigate these effects more fully in a disc with a dead zone determined by the critical magnetic Ievnolds number., Time-dependent numerical simulations are needed to investigate these effects more fully in a disc with a dead zone determined by the critical magnetic Reynolds number.
 By comparing the resulting outbursts with FU Orionis observations the value of the critical magnetic Revnolds number may be further constrained., By comparing the resulting outbursts with FU Orionis observations the value of the critical magnetic Reynolds number may be further constrained.
 A typical assumption used in time-dependent simulations of accretion disces with dead zones is that the surface density in the MIU active laver above the dead zone is constant with radius., A typical assumption used in time-dependent simulations of accretion discs with dead zones is that the surface density in the MRI active layer above the dead zone is constant with radius.
 However. when the dead zone is identified by the value of the eritical magnetic Revnolcls number including the elfects of recombination. the active laver surface density is eencrally found to increase with radius.," However, when the dead zone is identified by the value of the critical magnetic Reynolds number including the effects of recombination, the active layer surface density is generally found to increase with radius."
 The constant laver is best reproduced. with a low critical magnetic Itevnolds number., The constant layer is best reproduced with a low critical magnetic Reynolds number.
 llowever. MIID. simulations suggest the critical magnetic ltevnolds number may be much higher.," However, MHD simulations suggest the critical magnetic Reynolds number may be much higher."
 For higher critical magnetic Revnolds numbers. estosX100 we have found an analytical fit to the active surface density. (equations 27 and 28)) that will be a useful approximation in future time-dependent. calculations.," For higher critical magnetic Reynolds numbers, $Re_{\rm M,crit}\gtrsim 100$ we have found an analytical fit to the active surface density (equations \ref{fit} and \ref{fit2}) ) that will be a useful approximation in future time-dependent calculations."
 The dead: zone structure is very sensitive to the value of the critical magnetic Itevnolds number. as scen in Fig. 4..," The dead zone structure is very sensitive to the value of the critical magnetic Reynolds number, as seen in Fig. \ref{layer},"
 but the value is still uncertain and needs to be clarified in further work., but the value is still uncertain and needs to be clarified in further work.
 However. this is complicated by the fact that the a parameter in the viscosity is also uncertain.," However, this is complicated by the fact that the $\alpha$ parameter in the viscosity is also uncertain."
 The metallicity variation between our galaxy. the LAIC and the SAIC is not significant enough to alfect the expected size of the dead. zone in a disc (ignoring possible dillerences in dust abundances).," The metallicity variation between our galaxy, the LMC and the SMC is not significant enough to affect the expected size of the dead zone in a disc (ignoring possible differences in dust abundances)."
 When comparing accretion disces in our galaxy with those in the LMC and SMC for example. the high metallicity limit will be appropriate.," When comparing accretion discs in our galaxy with those in the LMC and SMC for example, the high metallicity limit will be appropriate."
 In order to explain the observed cilference in disc lifetimes with metallicity (e.g.DeMarchi.Panagia&Itomaniello2010.2011). some other elfect must be taken into account.," In order to explain the observed difference in disc lifetimes with metallicity \citep[e.g.][]{demarchi10,demarchi11} some other effect must be taken into account."
 We acknowledge useful. comments from the anonymous referee., We acknowledge useful comments from the anonymous referee.
 RGM thanks the Space Telescope Science Institute [or a Giaceoni Fellowship., RGM thanks the Space Telescope Science Institute for a Giacconi Fellowship.
 SUL acknowledges support from NASA erant NNXOYTALT2CG. JEP thanks the Collaborative Visitor Program at STScl for its support and hospitality., SHL acknowledges support from NASA grant NNX07AI72G. JEP thanks the Collaborative Visitor Program at STScI for its support and hospitality.
eas. sugeesting another form of heating is required to allow (he removal of eas from clwarls with larger perigalacticons (e.g.(heperigalacticonof250kpeLuxοἱal. 2010).,"gas, suggesting another form of heating is required to allow the removal of gas from dwarfs with larger perigalacticons \citep[e.g. the perigalacticon of Sextans and Draco is expected to be $>50$~kpc][]{Lux2010}."
. A dwarl consisting of cold. dense gas is resistant. to tidal and ram-pressure stripping with only a thin skin. ionized bv the Galactic of extragalactie UV fields being removed.," A dwarf consisting of cold, dense gas is resistant to tidal and ram-pressure stripping with only a thin skin, ionized by the Galactic of extragalactic UV fields being removed."
 Early star formation however. will heat this cold gas. raising it in the potential well aud making it more easily stripped.," Early star formation however, will heat this cold gas, raising it in the potential well and making it more easily stripped."
 This warm ionized gas. at the same pressure as cold gas will occupy ~60 Gines the volume. and being much less dense will become even easier {ο strip than its height in the potential well would indicate.," This warm ionized gas, at the same pressure as cold gas will occupy $\sim60$ times the volume, and being much less dense will become even easier to strip than its height in the potential well would indicate."
 The star formation in dwarfs is considered to consist of periods of low-level star formation. during which short bursts are induced which increase (he star formation by a factor of 3. consistent wilh clwarls observed by Leeetal.(2009).," The star formation in dwarfs is considered to consist of periods of low-level star formation, during which short bursts are induced which increase the star formation by a factor of $3$, consistent with dwarfs observed by \citet{Lee2009}."
.. We assume these bursts are triggered bv perigalacticon passages. induced by shocks created through tidal interactions. elal. 2010).," We assume these bursts are triggered by perigalacticon passages, induced by shocks created through tidal interactions \citep{Pasetto2010}."
. There is also evidence (hat bursts may. he triggered by the re-accretion of heated. and expanded gas (Valekeetal.2008).. however. much of (his gas will be stripped while in the warm phase and [ar from the centre preventing the re-accretion and subsequent starburst [rom occurring.," There is also evidence that bursts may be triggered by the re-accretion of heated and expanded gas \citep{Valcke2008}, however, much of this gas will be stripped while in the warm phase and far from the centre preventing the re-accretion and subsequent starburst from occurring."
" The base star formation rate is taken to be similar to the dwarfs that surround. M31. with a star formation rate (IxXaisin&Narachentsey2006) where / is a constant calculated by assuming that the gas will be completely depleted αἱ a (me /=5/1,~70 Gyr."," The base star formation rate is taken to be similar to the dwarfs that surround M31, with a star formation rate \citep{Kaisin2006}
 where $k$ is a constant calculated by assuming that the gas will be completely depleted at a time $t=5/H_0\sim70~$ Gyr."
 For an initial gas mass of 5x101 ALL. /=—13.62.," For an initial gas mass of $5\times10^7$ $_\odot$, $k=-13.62$."
 The UV.X-ray spectrum produced by the star formation in the dwarls—which is responsible for the majority of heatingwas calculated with (Leithererοἱal.1999): when a burst occured the change in the spectrum was caleulated bx summing many short bursts together to produce an approximately continuous change in the spectrum., The UV–X-ray spectrum produced by the star formation in the dwarfs—which is responsible for the majority of heating—was calculated with \citep{Leitherer1999}; when a burst occured the change in the spectrum was calculated by summing many short bursts together to produce an approximately continuous change in the spectrum.
 Above the Lyman limit.. (his. spectrum Gin. eres sH H > ©loge 1) and its. changes during. a burst. was well fitted by," Above the Lyman limit, this spectrum (in ergs $s^{-1}$ $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ ) and its changes during a burst was well fitted by"
which lines-o[-sight intersect a cluster with a velocity dispersion large enough to plausibly account for the weak lensing peak (Section 4.2)).,which lines-of-sight intersect a cluster with a velocity dispersion large enough to plausibly account for the weak lensing peak (Section \ref{clusters}) ).
 In this section we evaluate candidate svstems along the line-of-sight toward the 6 robust GTO2dee? weak lensing peaks of the revised Subaru weak lensing map (Section 3.1))., In this section we evaluate candidate systems along the line-of-sight toward the 6 robust $^2$ weak lensing peaks of the revised Subaru weak lensing map (Section \ref{newmap}) ).
 Figures 1l and 12 show the redshift z distribution within 3’ of the central position of each of the candidate halos., Figures \ref{fig:velhisto1.ps} and \ref{fig:velhisto2.ps} show the redshift $z$ distribution within $^\prime$ of the central position of each of the candidate halos.
 The dark histogram shows the redshilt distribution in bius of 0.002(14-: )., The dark histogram shows the redshift distribution in bins of $z$ ).
 The thin histogram shows the redshift distribution in a concentric cone with a 6 radius in each of the candidate halo directions., The thin histogram shows the redshift distribution in a concentric cone with a $6^\prime$ radius in each of the candidate halo directions.
 The probes toward peaks 0 and 1 each contain an impressive peak., The probes toward peaks 0 and 1 each contain an impressive peak.
 These peaks correspond to obvious “fingers” in redshift space (Figure 11))., These peaks correspond to obvious “fingers” in redshift space (Figure \ref{fig:velhisto1.ps}) ).
 The rest frame line-ol-sieht velocity dispersions of these svstems within a 6 probe are. respectively 576464 kins | and 598458 kn 1 in agreement with previous measures (Dressler οἱ al 1999 (peak 0): Hamana οἱ al.," The rest frame line-of-sight velocity dispersions of these systems within a $^\prime$ probe are, respectively $\pm$ 64 km $^{-1}$ and $\pm$ 58 km $^{-1}$ in agreement with previous measures (Dressler et al 1999 (peak 0); Hamana et al."
 2008 (peak 1): see Section 2.1))., 2008 (peak 1); see Section \ref{history}) ).
 Table 3. provides the number of galaxies ancl (he rest frame line-of-sight velocity dispersion for both 3' and 6' probes., Table \ref{tbl:VDisp} provides the number of galaxies and the rest frame line-of-sight velocity dispersion for both $^{\prime}$ and $^{\prime}$ probes.
 The rest. frame velocity dispersions lor these (wo clusters places both of (hem very near the v=3.7 detection threshold., The rest frame line-of-sight velocity dispersions for these two clusters places both of them very near the $\nu = 3.7$ detection threshold.
 Counts of faint galaxy. within these probes show a >Poy excess as one might expect (see Table 3))., Counts of faint galaxy within these probes show a $> 2\sigma_S$ excess as one might expect (see Table \ref{tbl:VDisp}) ).
 We note that the weak lensing map detects the clusters corresponding to peaks 0 and 1 at hieh significance ν» 6., We note that the weak lensing map detects the clusters corresponding to peaks 0 and 1 at high significance $\nu \sim 6$ .
 IIowever lor ν~6. our predicted velocity clispersions for these peaks exceed the measured. values by only2," However for $\nu \sim 6$, our predicted velocity dispersions for these peaks exceed the measured values by only."
0-30%.. The lo errors in the velocity dispersions are =10%., The $\sigma$ errors in the velocity dispersions are $\gtrsim 10$.
. Thus we cannot draw any definitive conclusion for this apparent difference between the measured. velocity. dispersion from (he redshift survey and the weak lensing sensitivity analvsis., Thus we cannot draw any definitive conclusion for this apparent difference between the measured velocity dispersion from the redshift survey and the weak lensing sensitivity analysis.
 The probe toward weak lensing peak 3 shows a more complex situation., The probe toward weak lensing peak 3 shows a more complex situation.
 There are two significant peaks in the histogram. one al 2=0.297 and the other at 2=0.673.," There are two significant peaks in the histogram, one at $z = 0.297$ and the other at $z = 0.673$."
 The velocity dispersions are 567 km | and 558 km 1+. respectively within 3! probes: the rest. [rame line-of-sight velocity dispersions ave svstematically smaller in the 6 probes. but (he errors are large.," The line-of-sight velocity dispersions are 567 km $^{-1}$ and 558 km $^{-1}$, respectively within $^{\prime}$ probes; the rest frame line-of-sight velocity dispersions are systematically smaller in the $^{\prime}$ probes, but the errors are large."
 The faint galaxy. counts show an excess (Table 3)). probably resulting from the more distant svstem.," The faint galaxy counts show an excess (Table \ref{tbl:VDisp}) ), probably resulting from the more distant system."
 Both svstems max contribute to the lensing signal., Both systems may contribute to the lensing signal.
 Probes toward weak lensine peaks 7 and 9 reveal no candidate svstems., Probes toward weak lensing peaks 7 and 9 reveal no candidate systems.
 Figure shows (hat neither of these peaks overlaps awell-populated probe through the reclshilt survey., Figure \ref{fig:sigmamap.scaled.ps} shows that neither of these peaks overlaps awell-populated probe through the redshift survey.
 Furthermore. (here is no excess in (he faint galaxy. counts.," Furthermore, there is no excess in the faint galaxy counts."
 One possibility is (hat the, One possibility is that the
Now. in the case of a spatially fat FRW universe with no cosmological coustaut (only). the αναο equations (5)) allow us to replace 8zGp/23 with (6/a).,"Now, in the case of a spatially flat FRW universe with no cosmological constant (only), the dynamic equations \ref{eq:reldyn}) ) allow us to replace $8 \pi G \rho/3 $ with $(\dot{a}/a)^2$."
 This gives us and we recover the formmla for the cosinological redshift., This gives us and we recover the formula for the cosmological redshift.
 Iu this oue case the cosmological redshift can be broken down iuto a factor of velocity aloue aud one of static eravitation alone., In this one case the cosmological redshift can be broken down into a factor of velocity alone and one of static gravitation alone.
 We may in this case attribute its cause to a simple combination of both static mass andmotion’., We may in this case attribute its cause to a simple combination of both static mass and.
.. There are several reasons to be uneasy over this derivation., There are several reasons to be uneasy over this derivation.
 For one. a static pressurcless universe is iupossible: there iust either be pressure (enough to slow up in the cncrev-momentiu tensor. or possibly as a cosmological coustant) or motion.," For one, a static pressureless universe is impossible; there must either be pressure (enough to show up in the energy-momentum tensor, or possibly as a cosmological constant) or motion."
 More worrviughv. we have both assumed a spatially Hat universe (in substituting the dvnamics equatious in Equation (12)). and one that is curved (Gu using the equation for eravitational redshift): thus the r variables in cach part of the derivation are not necessarily tle same (though at large distances they certainly approach cach other).," More worryingly, we have both assumed a spatially flat universe (in substituting the dynamics equations in Equation \ref{eq:twoshift}) ), and one that is curved (in using the equation for gravitational redshift); thus the $r$ variables in each part of the derivation are not necessarily the same (though at large distances they certainly approach each other)."
 The result should be taken as no more than indicative th:t both motion and eravity coutribute to the cosmological redshift., The result should be taken as no more than indicative that both motion and gravity contribute to the cosmological redshift.
 Moreover. other situations are not even this simple: so we still seek a more general wav of thiukiug of the phenomenon.," Moreover, other situations are not even this simple; so we still seek a more general way of thinking of the phenomenon."
 For this. we consider a different derivation.," For this, we consider a different derivation."
 Note that a light rav follows a null geodesic. so that all along it LEvervwhlere aloug this rax. then. If we integrate this equation aloug the path of propagation from the cussion to the observation of the licht ray we ect which is just the comoving distance between the euütter aud the observer.," Note that a light ray follows a null geodesic, so that all along it Everywhere along this ray, then, If we integrate this equation along the path of propagation from the emission to the observation of the light ray we get which is just the comoving distance between the emitter and the observer."
" Now we integrate the expression again. this time starting at a time just one wavelength later (0f) aud eudiug at a time just one wavelcneth later (0£,)."," Now we integrate the expression again, this time starting at a time just one wavelength later $\delta t_e$ ) and ending at a time just one wavelength later $\delta t_o$ )."
 The difference between this integral and the previous one will be the change in comoving distance., The difference between this integral and the previous one will be the change in comoving distance.
 But if the emitter and observer are both stationary with respect to the comoving coordinates. there is no change m comoving distance.," But if the emitter and observer are both stationary with respect to the comoving coordinates, there is no change in comoving distance."
 So Aud if anv change in e is small diving the period of one light wave.," So And if any change in $a$ is small during the period of one light wave,"
Iu our model we know the time at which the QS collapses to a DIE (the time of the steep decay).,In our model we know the time at which the QS collapses to a BH (the time of the steep decay).
 The calculations above assumed that this occurred at =Ts, The calculations above assumed that this occurred at $t_{\rm collapse}=\tau$.
 However. it could also occur at fep<Τ. which teollapseimplies that the magnetic field is weaker thau found above.," However, it could also occur at $t_{\rm collapse}<\tau$, which implies that the magnetic field is weaker than found above."
 Hence. the magnetic field. found. above is the maximum possible magnetic field. and therefore the spin-down liinosity. accretion rate and prompt eamunua rav energy are also miaxiniuna.," Hence, the magnetic field found above is the maximum possible magnetic field, and therefore the spin-down luminosity, accretion rate and prompt gamma ray energy are also maximum."
 The OS magnetic field needed to explain the flattening observed in GRD 070110 is B—Gs«1015 GG (seo Table 23)., The QS magnetic field needed to explain the flattening observed in GRB 070110 is $B=6.8\times10^{14}$ G (see Table \ref{calculatedtable}) ).
 The correspoucding spiu-down bhmuuinositv is fouud to be 1.G«10/5 eye/s. We can compare this to the observed eugime Iuniuositv assuninug an opening auele of 10 deerees for this outflow., The corresponding spin-down luminosity is found to be $1.6\times10^{48}$ erg/s. We can compare this to the observed engine luminosity assuming an opening angle of 10 degrees for this outflow.
 If ve assume an efficiency. of 1054 in converting kinetic enerev to photons we see that we lave an order of magnitude more eucrey than needed., If we assume an efficiency of $10\%$ in converting kinetic energy to photons we see that we have an order of magnitude more energy than needed.
 Comparing the observed prompt eauuna rav enerev to what we find from the jet launched by the QS. we again find that the jet energy is higher (by a factor 1) than the observed gana ray energy.," Comparing the observed prompt gamma ray energy to what we find from the jet launched by the QS, we again find that the jet energy is higher (by a factor 4) than the observed gamma ray energy."
 The QS magnetic field needed to explain the flattening observed in CRB 0606074 ix B21«107 C (see Table 2) , The QS magnetic field needed to explain the flattening observed in GRB 060607A is $1\times10^{15}$ G (see Table \ref{calculatedtable}) ).
"The corresponding spin-down luminosity is found. to be 3.6sLOS ore/s, Assunüng LOY efficiency im producing N-rav photons. we find (as for GRD 070110) that the estimated Iuninositv is lieher than the observed."," The corresponding spin-down luminosity is found to be $3.6\times10^{48}$ erg/s. Assuming $10\%$ efficiency in producing X-ray photons, we find (as for GRB 070110) that the estimated luminosity is higher than the observed."
 The Sauna rav enerev released during the prompt phase is also higher than the observed. gamuna ray enerev., The gamma ray energy released during the prompt phase is also higher than the observed gamma ray energy.
 The higher luminosities can be because the estimate for the magnetic field is too high. 1ieauing that 7 is lareer and that the QS collapsed to a BIT before £27.," The higher luminosities can be because the estimate for the magnetic field is too high, meaning that $\tau$ is larger and that the QS collapsed to a BH before $t=\tau$."
 A lower magnetic field iuplies that the accretion rate is lower., A lower magnetic field implies that the accretion rate is lower.
 Alternatively. we have overestimated the efficiencies. or the opening auele of the outflow is larger.," Alternatively, we have overestimated the efficiencies, or the opening angle of the outflow is larger."
 Iu GRBOGOGTA there are several N-rav flares observed uutil about 300 seconds (about 75 seconds when corrected for redshift)., In GRB06067A there are several X-ray flares observed until about 300 seconds (about 75 seconds when corrected for redshift).
/ If we explain these flares bx accretion outo the QS as well. that means that the accretion process lasts for about 75 secouds.," If we explain these flares by accretion onto the QS as well, that means that the accretion process lasts for about $75$ seconds."
" The derived accretion rates imply the necessity of a debris disk with a duas of the order of ~10ΤΑΗν, which is reasonable since the QN. goes off inside a collapsar. where such a laree fallback disk is iu principle allowed."," The derived accretion rates imply the necessity of a debris disk with a mass of the order of $\sim 10^{-1}M_\odot$, which is reasonable since the QN goes off inside a collapsar, where such a large fall-back disk is in principle allowed."
 We lave presented a model to explain the fattening and occasional sharp drop-off ποσα im X-ray afterglows of some CRBs., We have presented a model to explain the flattening and occasional sharp drop-off seen in X-ray afterglows of some GRBs.
 Our model borrows the framework of the 3 stage model presented in SODOT which makes use of an intermediate QS stage between the NS and the DIL, Our model borrows the framework of the 3 stage model presented in SOB07 which makes use of an intermediate QS stage between the NS and the BH.
" By appealing to a secoudary outflow. from the QS spin-down due to maenetic braking. our model seenis to explain the GRD itself νο, prompt cussion). the observed flat segment G.c. plateau). aud the subsequent sharp or gradual decay following the plateau."," By appealing to a secondary outflow, from the QS spin-down due to magnetic braking, our model seems to explain the GRB itself (i.e. prompt emission), the observed flat segment (i.e. plateau), and the subsequent sharp or gradual decay following the plateau."
 The sharp or gradual decay. depends ou whether the OS collapses to a DII or not durius spin-down., The sharp or gradual decay depends on whether the QS collapses to a BH or not during spin-down.
 During spiu-down. a break will be seen after a characteristic time 7 given by Eq.," During spin-down, a break will be seen after a characteristic time $\tau$ given by Eq."
 3) followed by a power law with power of 5/3 to 3 (Panaitescu2007)., \ref{eq:charac_time} followed by a power law with power of $-5/3$ to $-3$ \citep{panaitescu07}.
.. A very sharp drop-off will be seen if the QS collapses to a BIT during spin-down., A very sharp drop-off will be seen if the QS collapses to a BH during spin-down.
 We uote that. if there was a wav for launching ultrarelativistic jets from accretion onto NSs. then it would be tempting to not include the QS phase in our model aud appeal ouly to NS to DII transition.," We note that, if there was a way for launching ultrarelativistic jets from accretion onto NSs, then it would be tempting to not include the QS phase in our model and appeal only to NS to BH transition."
 Towever. we are not aware of any such mechanism for αςήπιο au ultrarelativistie jet from accretion outo a NS. aud from an chergctics perspective it secius unlikely.," However, we are not aware of any such mechanism for launching an ultrarelativistic jet from accretion onto a NS, and from an energetics perspective it seems unlikely."
 Hence. the additional energv available from converting hadronic to strange quark matter aud during accretion onto the QS seenis crucial in explaiuiug the nature of CRBs.," Hence, the additional energy available from converting hadronic to strange quark matter and during accretion onto the QS seems crucial in explaining the nature of GRBs."
 Tn addition to au cnerectics point of view. the most inportaut benefits of our GRD 120del involving a QS stage are: (i) the QS offers an additional stage that allows for more enerev to be extracted from the conversion from NS to QS as well as from accretion.," In addition to an energetics point of view, the most important benefits of our GRB model involving a QS stage are: (i) the QS offers an additional stage that allows for more energy to be extracted from the conversion from NS to QS as well as from accretion."
 Also. additional energy is released as the QS quickly evolves from a uou-aligned to au aligued rotator following its birth with up to 10/7 eres released iu a few seconds (Ouyed.ct 2006).," Also, additional energy is released as the QS quickly evolves from a non-aligned to an aligned rotator following its birth with up to $10^{47}$ ergs released in a few seconds \citep{ouyed_niebergal06}."
 As such. the QS phase extends the cugine activity and so cau account for both the prompt ciission id inreenlar N-ray afterglow activity: Gi) a natural uplification of the NS maeuetic field to 104-1025. C during the transition to the QS (wazaki2005).," As such, the QS phase extends the engine activity and so can account for both the prompt emission and irregular X-ray afterglow activity; (ii) a natural amplification of the NS magnetic field to $10^{14}$ $10^{15}$ G during the transition to the QS \citep{iwazaki05}."
. Such lieh streneths eives the correct spin down timeto for the plateau: (ii) since QS in the CFL phase might not have a crust. the spin down cnerev will most likely be extracted as an ele fireball with verv little barvon contamination (seediscussioninNicherealetal.," Such high strengths gives the correct spin down timeto for the plateau; (iii) since QS in the CFL phase might not have a crust, the spin down energy will most likely be extracted as an $e^+e^-$ fireball with very little baryon contamination \citep[see discussion in][]{niebergal06}. ."
 2006).. Panaitescu(2007) favors a birvon free secondary outflow to explain the plateau., \citet{panaitescu07} favors a baryon free secondary outflow to explain the plateau.
of the gap formation time scale is obtained in the zero viscosity limit.,of the gap formation time scale is obtained in the zero viscosity limit.
" In this case, an analytic formulation is provided by Brydenetal.(1999) in the form where P is the orbital period, q=M,/M, and A=2Ry as defined above."," In this case, an analytic formulation is provided by \cite{br99} in the form where $P$ is the orbital period, $q=M_p/M_{\star}$ and $\Delta = 2R_H$ as defined above."
" Assuming Keplerian rotation, we can rewrite the time scale for the gap formation as The upper panel of Figure 12 shows the calculated values of rA"" for the stellar mass of DG Tau (0.3 Mo)."," Assuming Keplerian rotation, we can rewrite the time scale for the gap formation as The upper panel of Figure \ref{fig:tau_delta} shows the calculated values of $\tau^{min}_\Delta$ for the stellar mass of DG Tau (0.3 $M_{\sun}$ )."
" In the case of a planet with a mass between 0.3 and 0.5 M; orbiting at a radius larger than 40 AU, the minimum time scale for the gap formation is comparable with the age of the system (0.1 Myr)."," In the case of a planet with a mass between 0.3 and 0.5 $_J$ orbiting at a radius larger than 40 AU, the minimum time scale for the gap formation is comparable with the age of the system (0.1 Myr)."
" For more massive planets, or for closer radii, the minimum gaps time scale is a small fraction of the age of the system."," For more massive planets, or for closer radii, the minimum gaps time scale is a small fraction of the age of the system."
" We conclude that, for DG Tau, the observations lack the sensitivity and angular resolution required to investigate the presence of planets less massive than about 0.5 M, at any orbital radius."," We conclude that, for DG Tau, the observations lack the sensitivity and angular resolution required to investigate the presence of planets less massive than about 0.5 $_J$ at any orbital radius."
" Our analysis indicates that no planets more massive than Jupiter are present between 5 and 50 AU, unless they are younger than 10 years."," Our analysis indicates that no planets more massive than Jupiter are present between 5 and 50 AU, unless they are younger than $10^4$ years."
" The similarity solution for the disk surface density is characterized by y=—0.56+0.18 and R,~26—3 AU.", The similarity solution for the disk surface density is characterized by $\gamma= -0.56\pm0.18$ and $R_t\sim26\pm3$ AU.
" As shown in Figure 9,, the surface density increases roughly as VR from the inner radius at 0.1 AU up to about 26 AU and then decreases exponentially outward."," As shown in Figure \ref{fig:sigma}, the surface density increases roughly as $\sqrt{R}$ from the inner radius at 0.1 AU up to about 26 AU and then decreases exponentially outward."
 This supports the suggestion in Section 3 that the RY Tau inner disk might be partially dust depleted with respect to power law disk models., This supports the suggestion in Section \ref{sec:morp} that the RY Tau inner disk might be partially dust depleted with respect to power law disk models.
 We note that this surface density profile may provide an explanation for both the double peak intensity at 1.3 mm and the disk excess at infrared wavelengths., We note that this surface density profile may provide an explanation for both the double peak intensity at 1.3 mm and the disk excess at infrared wavelengths.
" Indeed, within 10 AU the model disk remains optically thick at optical and infrared wavelengths, exhibiting the infrared excess typical of classical disks."," Indeed, within 10 AU the model disk remains optically thick at optical and infrared wavelengths, exhibiting the infrared excess typical of classical disks."
" At larger radii, the surface density in RY Tau disk decreases smoothly and the residuals calculated by subtracting the best fit models to the 1.3 mm dust emission map do not show any structure at more than 3c."," At larger radii, the surface density in RY Tau disk decreases smoothly and the residuals calculated by subtracting the best fit models to the 1.3 mm dust emission map do not show any structure at more than $\sigma$ ."
 This excludes strong deviations from an unperturbed viscous disk profile., This excludes strong deviations from an unperturbed viscous disk profile.
" The lower panel of Figure 11 shows the signal-to-noise ratio of the detection of a gap generated by planets of 1, 5 and 10 Jupiter masses as a function of the orbital radius."," The lower panel of Figure \ref{fig:planet_deviation} shows the signal-to-noise ratio of the detection of a gap generated by planets of 1, 5 and 10 Jupiter masses as a function of the orbital radius."
 Dueto the higher, Dueto the higher
lt is now well established that all massive galaxies (AL.5ο0L. 1077 AL.) in the local Universe harbour central super-massive black holes (SMDIIS). with masses proportional to hose of their stellar spheroids (hereafter. bulge: citealt kormendy95::: 723).,"It is now well established that all massive galaxies $M_* \approx
10^{10}$ $10^{12} \Msun$ ) in the local Universe harbour central super-massive black holes (SMBHs), with masses proportional to those of their stellar spheroids (hereafter, bulge; \\citealt{kormendy95}; \citealt{magorrian98}) )."
 Comparisons between the SALBIL mass density in the local Universe and the total energy ooduced. by active galactic nuclei: CXGNs) across. cosmic ime have shown that these SMDBlIIS were primarily grown hrough mass-accretion events citealtsoltans2:: ?:: 2))., Comparisons between the SMBH mass density in the local Universe and the total energy produced by active galactic nuclei (AGNs) across cosmic time have shown that these SMBHs were primarily grown through mass-accretion events \\citealt{soltan82}; \citealt{rees84}; \citealt{marconi04}) ).
 The space density of high-Iuminosity AGNs appears to have peaked at higher redshifts than Lower-uminosity ACGNs. suggesting that the most massive SMDIIs (Mig2107 107 AL.) grew first. a result commonly referred to às “AGN cosmic downsizing citealteowie(ü3:: 2: 2: ?:: 72)).," The space density of high-luminosity AGNs appears to have peaked at higher redshifts than lower-luminosity AGNs, suggesting that the most massive SMBHs $\Mbh \approx 10^8$ $10^9
\Msun$ ) grew first, a result commonly referred to as `AGN cosmic downsizing' \\citealt{cowie03}; \citealt{ueda03}; \citealt{mclure04}; \citealt{hasinger05}; \citealt{alonso08}) )."
 Extrapolation of these results imply that the most rapidly erowing SMDBlIS in the nearby Universe should. be of comparatively low mass (Albu107AL. )., Extrapolation of these results imply that the most rapidly growing SMBHs in the nearby Universe should be of comparatively low mass $\Mbh \ll 10^{8} \Msun$ ).
 To determine the characteristic masses of these growing SAIBLIs requires a complete census of ACGIN activity and SMDLLI masses in the local Universe., To determine the characteristic masses of these growing SMBHs requires a complete census of AGN activity and SMBH masses in the local Universe.
 Using data from the Sloan Digital Sky Survey (SDSS: in conjunction with the well established SMLstellar velocity dispersion relation. (hereafter. ay: eg. ?: ?)). 7T (2004: hereafter. 10141) deduced that relatively low mass SALDIIs (Mpg23.107M. ) residing in moderately niassive bulec-dominated galaxies host. the. majority. of. present- accretion onto SMDlIIs.," Using data from the Sloan Digital Sky Survey \citep[SDSS; ][]
{sdss_tech} in conjunction with the well established SMBH–stellar velocity dispersion relation (hereafter, $\sigma_*$; e.g., \citealt{gebhardt00}; \citealt{tremaine02}) ), \citeauthor{heckman04}
 (2004; hereafter, H04) deduced that relatively low mass SMBHs $\Mbh
\approx 3 \times 10^7 \Msun$ ) residing in moderately massive bulge-dominated galaxies host the majority of present-day accretion onto SMBHs."
 However. the space density. of SALBUs derived from the σι relation in the optical survey," However, the space density of SMBHs derived from the $\sigma_*$ relation in the optical survey"
and σι is in radians.,and $\sigma_{A}$ is in radians.
 This approach excludes the uncertainties in the orbital period aux can therefore oulv vield the lower limit for the detection threshold., This approach excludes the uncertainties in the orbital period and can therefore only yield the lower limit for the detection threshold.
 Hence. ifEq. (6))," Hence, ifEq. \ref{amplitude}) )"
 does not hold. it will be impossible to detect the sigual.," does not hold, it will be impossible to detect the signal."
 However. if it holds. the detectability of such a companion needs to be examined more closely * nunercal simulations aud by analysing the simulated ata using methods such as AICALC and Bayesian model selection criterion.," However, if it holds, the detectability of such a companion needs to be examined more closely by numerical simulations and by analysing the simulated data using methods such as MCMC and Bayesian model selection criterion."
 To fully investigate the ability to detect planctary conrpanions. we must define when a positive detection has been made.," To fully investigate the ability to detect planetary companions, we must define when a positive detection has been made."
 This question can be approached through Bayesian probabilities., This question can be approached through Bayesian probabilities.
 Let Ry be the model im Eq. (1)), Let $\vec{R}_{1}$ be the model in Eq. \ref{model}) )
 with oue planctary companion (corresponding 12 paralucters in the RV and astrometrv models). aud Ry a inode without a planetary companion (5 parameters).," with one planetary companion (corresponding 12 parameters in the RV and astrometry models), and $\vec{R}_{0}$ a model without a planetary companion (5 parameters)."
 Iu general. let Ry be a model with & plaucts.," In general, let $\vec{R}_{k}$ be a model with $k$ planets."
" Using the Bayes theorem. it can be seen that the conditional probability of iiodel Ry. represcuting the data (1) best. out of the p|1 alternatives to be tested. can be written as where the Bayes factor D; is defined as (e.g. Wass aud Raftery. 1995) and PUR,.) is the prior probability of the Ath model. here set equal for all A. because it is assuued that there is no prior information available."," Using the Bayes theorem, it can be seen that the conditional probability of model $\vec{R}_{k}$ representing the data $m$ ) best, out of the $p+1$ alternatives to be tested, can be written as where the Bayes factor $B_{k,j}$ is defined as (e.g. Kass and Raftery, 1995) and $P(\vec{R}_{k})$ is the prior probability of the $k$ th model, here set equal for all $k$, because it is assumed that there is no prior information available."
" Here the likelihood Pon Ry). with paraucters ujCUy for the Ath model. is where ponr|e,.Rp) ds the parameter likelihood fuuction and pu;R,) the prior density."," Here the likelihood $P(m | \vec{R}_{k})$ , with parameters $\vec{u}_{k} \in U_{k}$ for the $k$ th model, is where $p(m | \vec{u}_{k}, \vec{R}_{k})$ is the parameter likelihood function and $p(\vec{u}_{k} | \vec{R}_{k})$ the prior density."
 Since the model probability. defined iu this wav. automatically takes the Occamian principle of parsimony iuto account. the model with the smallest number of paramcters out of those having alinost equal probabilities will be selected.," Since the model probability, defined in this way, automatically takes the Occamian principle of parsimony into account, the model with the smallest number of parameters out of those having almost equal probabilities will be selected."
 Hence. it can be said that a detection has been made if (Jeffreys 1961) This criterion is used throughout this article when deciding whether a statistically siguificaut detection has been made or not.," Hence, it can be said that a detection has been made if (Jeffreys 1961) This criterion is used throughout this article when deciding whether a statistically significant detection has been made or not."
" The fitting was performed by requiring that the values of all the least-squares cost-fiuctious 5, (astrometric e). 5, (astrometric gy). Spy (RV). aud their suu be miunized siunltaueouslv."," The fitting was performed by requiring that the values of all the least-squares cost-functions $S_{x}$ (astrometric $x$ ), $S_{y}$ (astrometric $y$ ), $S_{RV}$ (RV), and their sum be minimized simultaneously."
 This method. called iuultidata inversion. has been used successfully with astrometric and RV nieasurements when detecting stellar binaries (e.g. Torres 2007).," This method, called multidata inversion, has been used successfully with astrometric and RV measurements when detecting stellar binaries (e.g. Torres 2007)."
 See the discussion in Iaasalainen aud Loauberg (2006). where the multidata inversion was applied to asteroid observations.," See the discussion in Kaasalainen and Lamberg (2006), where the multidata inversion was applied to asteroid observations."
 The models for astrometric position aud RV of the two-hody system of interest are non-linear. so an iterative method of fitting the model paramcters is needed.," The models for astrometric position and RV of the two-body system of interest are non-linear, so an iterative method of fitting the model parameters is needed."
 The MCALC with Metropolis-IIastiues (AL-ID) aleorithiu was chosen because it is a elobal method (Metropolis ct al., The MCMC with Metropolis-Hastings (M-H) algorithm was chosen because it is a global method (Metropolis et al.
 1953: [astines 1970). it offers a direct estimate of the posterior probability density. aud )ecause It can be used to verify the existence and uniqueness of the solution.," 1953; Hastings 1970), it offers a direct estimate of the posterior probability density, and because it can be used to verify the existence and uniqueness of the solution."
 Since the probability densities eiven the measurements are available. AICAIC can be used to calculate realistical CLror estimates or the model parameters.," Since the probability densities given the measurements are available, MCMC can be used to calculate realistical error estimates for the model parameters."
 These estimates are typically πιο larger than those calculated using traditional methods (c.c. Ford 2006). implying that MCAIC should )o preferred when assessing the parameter errors.," These estimates are typically much larger than those calculated using traditional methods (e.g. Ford 2006), implying that MCMC should be preferred when assessing the parameter errors."
 Asstuuine Gaussian errors with zero mica. the likelihood. function of the paramcters with respect to RV lneasurelments can be written as When applying MCAIC. a parameter value (ay) is selected for the first member of the chain.," Assuming Gaussian errors with zero mean, the likelihood function of the parameters with respect to RV measurements can be written as When applying MCMC, a parameter value $\vec{u}_{0}$ ) is selected for the first member of the chain."
 The next value wy). 38 fouud by randomly selecting a proposal in he vicinity of u;., The next value $\vec{u}_{k+1}$ is found by randomly selecting a proposal in the vicinity of $\vec{u}_{k}$.
 This is then accepted by comparing he likchhoods of the two paraimcter values., This is then accepted by comparing the likelihoods of the two parameter values.
 Proposed xmeuneter values αν Awith a ereater Bkelibood. than hat of aw; are always selected as the next chain member. mt values with a smaller likelihood cau also be selected according to the criterion of Hastings (1970).," Proposed parameter values $\vec{u}_{k+1}$  with a greater likelihood than that of $\vec{u}_{k}$ are always selected as the next chain member, but values with a smaller likelihood can also be selected according to the criterion of Hastings (1970)."
 Samples of at least LO? points were generated when sampling the waralucter space., Samples of at least $10^{5}$ points were generated when sampling the parameter space.
 For practical details ou AICAIC with astronomical data. see c.g. Gregory (2005).," For practical details on MCMC with astronomical data, see e.g. Gregory (2005)."
 The paramcter space C in this Neplerian two-body uodel has a comparatively small dimension (cant= 12). but iu some cases it already makes the sample colmputationally expensive.," The parameter space $U$ in this Keplerian two-body model has a comparatively small dimension $\dim U = 12$ ), but in some cases it already makes the sampling computationally expensive."
 Especially when covariances )etxyeeen the parameters are large and of non-linear nature. he space of reasonable probability C5CU to be sampled can be verv narrow and. as a result. the next proposed value of parameter vector w in the Markov chain is ikelv to be outside this subspace and thus rejected. cousiderably increasing the time needed to generate a statistically representative chain.," Especially when covariances between the parameters are large and of non-linear nature, the space of reasonable probability $U_{R} \subset U$ to be sampled can be very narrow and, as a result, the next proposed value of parameter vector $\vec{u}$ in the Markov chain is likely to be outside this subspace and thus rejected, considerably increasing the time needed to generate a statistically representative chain."
 For this reason. when musing a iuuitivariate Gaussian density as a proposal. the acceptance rates were low. approximately 0.1 iu the AMCALIC sanaplines.," For this reason, when using a multivariate Gaussian density as a proposal, the acceptance rates were low, approximately 0.1 in the MCMC samplings."
 With more than one source of measurements available. it is possible to get more information from the «απο of interest than when relving ou any sinele observation method alone.," With more than one source of measurements available, it is possible to get more information from the system of interest than when relying on any single observation method alone."
 This is aconsequence of Bayesian infercuce., This is aconsequence of Bayesian inference.
" Denoting the astrometric measuremeuts bv O0, and the RV ineasuremenuts by £,. the conditional probability"," Denoting the astrometric measurements by $\vec{\Theta}_{o}$ and the RV measurements by $\dot{\vec{z}}_{o}$ , the conditional probability"
"In their kinetic simulations of DSA, Kang and Jones (hereafter KJ) evolve the standard time-dependent gasdynamic conservation laws with the CR pressure terms in Eulerian form for one-dimensional plane-parallel geometry 2007), where p=p(z,t) is the gas density, u=u(x,t) is the fluid velocity, P=P(z,t) is the gas (P,) or CR (P,) pressure (eq. 22))","In their kinetic simulations of DSA, Kang and Jones (hereafter KJ) evolve the standard time-dependent gasdynamic conservation laws with the CR pressure terms in Eulerian form for one-dimensional plane-parallel geometry \citep{kjg02,kj07}, , where $\rho=\rho(x,t)$ is the gas density, $u=u(x,t)$ is the fluid velocity, $P=P(x,t)$ is the gas $P_{g}$ ) or CR $P_{c}$ ) pressure (eq. \ref{xicr}) )"
 and y=5/3 is the gas adiabatic index., and $\gamma= 5/3$ is the gas adiabatic index.
" L(x,t) is the injection energy loss term, which accounts for the energy carried away by the suprathermal particles injected into the CR component at the subshock and is subtracted from the postshock gas immediately behind the subshock."," $\mathcal{L}(x,t)$ is the injection energy loss term, which accounts for the energy carried away by the suprathermal particles injected into the CR component at the subshock and is subtracted from the postshock gas immediately behind the subshock."
" The gas heating due to the Alfvénn wave dissipation in the upstream region is modeled following McKenzie&Volk(1982) and is given by the term where v4(z,t)=Bo//4np(x, is the local Alfvénn speed and Bo is the magnetic field strength far upstream."," The gas heating due to the Alfvénn wave dissipation in the upstream region is modeled following \cite{mck-v82} and is given by the term where $v_A(x,t)= B_0/\sqrt{4\pi \rho(x,t)}$ is the local Alfvénn speed and $B_0$ is the magnetic field strength far upstream."
" Here and in the following we will label with the subscript 0 quantities at upstream infinity, and with 1 and 2 quantities immediately upstream and downstream of the subshock, respectively."," Here and in the following we will label with the subscript 0 quantities at upstream infinity, and with 1 and 2 quantities immediately upstream and downstream of the subshock, respectively."
" These equations can be used to describe parallel shocks, where the large-scale magnetic field is aligned with the shock normal and the pressure contribution from the turbulent magnetic fields can be neglected."," These equations can be used to describe parallel shocks, where the large-scale magnetic field is aligned with the shock normal and the pressure contribution from the turbulent magnetic fields can be neglected."
" The CR population is evolved by solving the diffusion-convection equation for the angle-averaged (isotropic in momentum space) distribution function, f(z,p,t), in the form: where D(z,p) is thespatial diffusion coefficient (seee.g.|Skilling)|1975, and p is the scalar, momentum magnitude."," The CR population is evolved by solving the diffusion-convection equation for the pitch-angle-averaged (isotropic in momentum space) distribution function, $f(x,p,t)$, in the form: where $D(x,p)$ is thespatial diffusion coefficient \citep[see e.g.][for a derivation]{ski75} and $p$ is the scalar, momentum magnitude."
 This equation is then usefully rewritten and, This equation is then usefully rewritten and
"and Na-rich stars: although we derive the same Li abundance for the two populations, it is interesting to note that Na-rich stars have a larger scatter in Li with respect to Na-poor ones.","and Na-rich stars: although we derive the same Li abundance for the two populations, it is interesting to note that Na-rich stars have a larger scatter in Li with respect to Na-poor ones."
 A one-tailed Fisher test returns a probability such that a difference can be obtained by chance., A one-tailed Fisher test returns a probability such that a difference can be obtained by chance.
" In fact, if a decrease in O of ~50%//60% occurred (as derived e.g. by Marino et al."," In fact, if a decrease in O of $\sim$ occurred (as derived e.g. by Marino et al."
 2008 and Carretta et al., 2008 and Carretta et al.
" 2010), also Li must have been depleted."," 2010), also Li must have been depleted."
" In a recent work, D’Antona Ventura (2010) have presented the expected Li production as a function of the polluter mass (AGB stars) for metallicity Z=0.001."," In a recent work, D'Antona Ventura (2010) have presented the expected Li production as a function of the polluter mass (AGB stars) for metallicity $Z$ =0.001."
" Looking at their Figure 5, one can see that a very low mass AGB polluter #4 Mo) can produce a moderate Li content with (ie.,values very close to the Li plateau (log n(Li)~2.2-2.3)."," Looking at their Figure 5, one can see that a very low mass AGB polluter (i.e., $\approx$ 4 $M_\odot$ ) can produce a moderate Li content with values very close to the Li plateau $\log{n{\rm (Li)}}$$\sim$ 2.2-2.3)."
" After considering a depletion of a factor of ~20 at the 1DUP, this result agrees very well with our values log n(Li)~1.3-1.4)."," After considering a depletion of a factor of $\sim$ 20 at the 1DUP, this result agrees very well with our values (i.e. $\log{n{\rm (Li)}}$$\sim$ 1.3-1.4)."
 As also briefly explained in the (ie.Section ?? widely discussed in Carretta et al., As also briefly explained in the Section \ref{sec:intro} (and widely discussed in Carretta et al.
" 2010), there are (andfurther indications that only low-mass polluters could have contributed to the observed chemical pattern in M4: an almost “vertical” Na-O anticorrelation, with very (1)small oxygen variation (depletion); and (2) the lack of Mg—Altion, which in fact requires high mass polluters for the activation of higher temperature cycles (T ~65 MK; Prantzos Charbonnel 2006)."," 2010), there are further indications that only low-mass polluters could have contributed to the observed chemical pattern in M4: (1) an almost “vertical"" $-$ O anticorrelation, with very small oxygen variation (depletion); and (2) the lack of $-$ Al, which in fact requires high mass polluters for the activation of higher temperature cycles $T\sim$ 65 MK; Prantzos Charbonnel 2006)."
" A similar case could have occurred for NGC 6397, where according to Pasquini et al. "," A similar case could have occurred for NGC 6397, where according to Pasquini et al. ("
"two stars differ by —0.6 dex in O, but have the (2008),same “normal” Li (log n(Li)=2.2).","2008), two stars differ by $\sim$ 0.6 dex in O, but have the same “normal"" Li $\log{n{\rm (Li)}}$ =2.2)."
" Also, in a recent work Lind et al. ("," Also, in a recent work Lind et al. ("
"2009), based on a sample of ~100 MS and early SGB/stars, found no difference in Li abundances between Na-rich and Na-poor stars with only two stars driving a Li—Na anticorrelation.","2009), based on a sample of $\sim$ 100 MS and early SGB/stars, found no difference in Li abundances between Na-rich and Na-poor stars with only two stars driving a $-$ Na anticorrelation."
" They concluded that Li content is independent of intra-cluster pollution; however the Na—O distribution points out to a certain small) degree of oxygen depletion and, as a consequence,(though of Li destruction as well."," They concluded that Li content is independent of intra-cluster pollution; however the $-$ O distribution points out to a certain (though small) degree of oxygen depletion and, as a consequence, of Li destruction as well."
" Hence, if first and second generation stars share the same Li abundances, a Li production should also be required for this cluster."," Hence, if first and second generation stars share the same Li abundances, a Li production should also be required for this cluster."
" Along with a difference in metallicity of ~0.9 dex, the two clusters, NGC 6397 and M 4, have both quite small integrated magnitudes (i.e., mass) with My«——6.63 and My«—— 7.20, respectively (Harris "," Along with a difference in metallicity of $\sim$ 0.9 dex, the two clusters, NGC 6397 and M 4, have both quite small integrated magnitudes (i.e., mass) with $M_{\rm Vt}$ $-$ 6.63 and $M_{\rm Vt}$ $-$ 7.20, respectively (Harris 1996)."
"The similarity in masses between these two GCs also 1996).seems to suggest a similar “typical” polluter for both M4 and NGC 6397, with the requirement to have in both cases neither very high mass polluters (no extended MgAI/NaO anticorrelations, very little Hehancement?, and no Li—Na anticorrelation) nor low mass polluters (<4 Mo), otherwise the C--N--O is not constant and/or s-process variations should be present (see Ivans 1999; Yong et al."," The similarity in masses between these two GCs also seems to suggest a similar “typical"" polluter for both M4 and NGC 6397, with the requirement to have in both cases neither very high mass polluters (no extended MgAl/NaO anticorrelations, very little He, and no $-$ Na anticorrelation) nor low mass polluters $\leq$ 4 $M_\odot$ ), otherwise the C+N+O is not constant and/or $s$ -process variations should be present (see Ivans 1999; Yong et al."
 2008)., 2008).
 The more massive GC NGC 6752 (Myz=—7.73) could present a different behavior., The more massive GC NGC 6752 $M_{\rm Vt}$ $-$ 7.73) could present a different behavior.
" We might speculate that only a very low Li production from higher mass polluters of z:5—6Mo (see Figure 5 of D'Antona Ventura, 2010) does not erase Li—Na anticorrelation for thiscluster?."," We might speculate that only a very low Li production from higher mass polluters of $\approx$ $-$ $M_\odot$ (see Figure 5 of D'Antona Ventura, 2010) does not erase $-$ Na anticorrelation for this."
". Note in fact that NGC 6752 presents an extended Na—O anticorrelation and a large variation in Al (i.e., the MgAI chain was active in the polluter stars)."," Note in fact that NGC 6752 presents an extended $-$ O anticorrelation and a large variation in Al (i.e., the MgAl chain was active in the polluter stars)."
" On the other hand, it seems very difficult to discriminate the nature of polluters and their properties for 47 Tuc: maybe this GC was similar to NGC 6752 but the intrinsic scatter in Li abundance, independent of intracluster pollution, washes out the fossil imprint by the previous generation of polluter stars (D'Orazi et al."," On the other hand, it seems very difficult to discriminate the nature of polluters and their properties for 47 Tuc: maybe this GC was similar to NGC 6752 but the intrinsic scatter in Li abundance, independent of intracluster pollution, washes out the fossil imprint by the previous generation of polluter stars (D'Orazi et al."
 2010)., 2010).
" Given the large uncertainties linked to model predictions (cross sections, mass loss law, overshooting,"," Given the large uncertainties linked to model predictions (cross sections, mass loss law, overshooting,"
Urea process to be satislied αἱ lower densities due to the increased proton Traction (Prakash 1992).. and depending on their exact concentrations could potentially contribute to the fast cooling of the star throughAyperonie direct. Urea processes (Pageelal.2006)..,"Urca process to be satisfied at lower densities due to the increased proton fraction \citep{1992ApJ...390L..77P}, and depending on their exact concentrations could potentially contribute to the fast cooling of the star through direct Urca processes \citep{Page:2005fq}."
 These considerations would alter the balance between the curves in Fig., These considerations would alter the balance between the curves in Fig.
 9 and ultimately the results displaced in Fie., 9 and ultimately the results displaced in Fig.
 8 in favor of the direct. Urea process. ie. smaller masses and hieher frequencies would be necessary (o close the fast cooling channel.," 8 in favor of the direct Urca process, i.e. smaller masses and higher frequencies would be necessary to close the fast cooling channel."
" This is due to the fact that the overall impact. of (rapid) rotation on the neutron star structure is smaller for more centrally condensed models resulting from ""softer"" ος (Friedmanetal.1984)..", This is due to the fact that the overall impact of (rapid) rotation on the neutron star structure is smaller for more centrally condensed models resulting from “softer” EOSs \citep{1984Natur.312..255F}.
 Therefore. for such models (here is smaller deviation from properties and structure of static configurations.," Therefore, for such models there is smaller deviation from properties and structure of static configurations."
 In addition. al even higher densities matter is expected to undergo a transition to quark-gluon plasma (Weber1999:Baldoetal.2000).. which favors a [ast cooling through enhanced nucleonic direct Urea and quark direct Urea processes (seee.g..Pageetal.2006)..," In addition, at even higher densities matter is expected to undergo a transition to quark-gluon plasma \citep{Weber:1999a,2000PhRvC..61e5801B}, which favors a fast cooling through enhanced nucleonic direct Urca and quark direct Urca processes \citep[see e.g.,][]{Page:2005fq}."
 We have studied properties of (rapidly) rotating neutron stars emploving four nucleonic EOSs., We have studied properties of (rapidly) rotating neutron stars employing four nucleonic EOSs.
 Rapid rotation affects the neutron star structure significantly., Rapid rotation affects the neutron star structure significantly.
 It increases the maximum possible mass up to ~1776 and increases/decreases the equatorial/polar radius by several kilometers., It increases the maximum possible mass up to $\sim 17\%$ and increases/decreases the equatorial/polar radius by several kilometers.
 Our findings. (hrough the application of EOSs with constrained svinmnetry energy by recent nuclear terrestrial laboratory data. allowed us to constrain the mass of the neutron star in NTE J1739-235 to be between 1.7 and 9.111...," Our findings, through the application of EOSs with constrained symmetry energy by recent nuclear terrestrial laboratory data, allowed us to constrain the mass of the neutron star in XTE J1739-285 to be between 1.7 and $2.1M_{\sun}$."
 Additionally. rotation reduces central clensityv and proton fraction in the neutron star core. anc depending on the exact stellar mass ancl rotational frequency. could effectively close the fast cooling channel in millisecond pulsars.," Additionally, rotation reduces central density and proton fraction in the neutron star core, and depending on the exact stellar mass and rotational frequency could effectively close the fast cooling channel in millisecond pulsars."
 This circumstance may have important consequences for both the interpretation of cooling data and the thermal evolution modeling., This circumstance may have important consequences for both the interpretation of cooling data and the thermal evolution modeling.
 WWe would like to thank Nikolaos Stergioulas for making the RNS code available., We would like to thank Nikolaos Stergioulas for making the RNS code available.
 We also (hank Wei-Zhou Jiang for helpful discussions., We also thank Wei-Zhou Jiang for helpful discussions.
 This work was supported by the National science Foundation under Grant No., This work was supported by the National Science Foundation under Grant No.
 PILY0652548 and the Research Corporation under Άννα No., PHY0652548 and the Research Corporation under Award No.
 7123., 7123.
We can perhaps begin to understand why by considering the power spectra shown in figure 3.,We can perhaps begin to understand why by considering the power spectra shown in figure 3.
 Here is the energy. contained in the /th spherical harmonic mode. either poloidal or toroidal. and as in (24) the integration over i includes the energy in the exterior vacuum fickle. (," Here is the energy contained in the $l$ -th spherical harmonic mode, either poloidal or toroidal, and as in (24) the integration over $r$ includes the energy in the exterior vacuum field. ("
"Amel of course the cross-ternis {B,,-Di,dV vanish by the orthogonality of the spherical harmonics.","And of course the cross-terms $\int{\bf B}_{l_1}\cdot
{\bf B}_{l_2}\,dV$ vanish by the orthogonality of the spherical harmonics."
 The total enerey is thus indeed just 1e sum Of these individual £7.), The total energy is thus indeed just the sum of these individual $E_l$ .)
 ‘Turning to the poloidal spectra first. we note that the Rey=200 curve follows an / sealing over the cntire range of /. whereas the lower Be curves start out much the same. but then crop olf somewhat more rapidly. exactly as one might expect.," Turning to the poloidal spectra first, we note that the $R_B=200$ curve follows an $l^{-5}$ scaling over the entire range of $l$, whereas the lower $R_B$ curves start out much the same, but then drop off somewhat more rapidly, exactly as one might expect."
" We note though that there is no sign of a definite dissipation scale. either at the /=O(Ry) appropriate to an /> spectrum. or the --OCR"") appropriate to an /"" spectrum."," We note though that there is no sign of a definite dissipation scale, either at the $l=O(R_B)$ appropriate to an $l^{-2}$ spectrum, or the $l=O(R_B^{2/5})$ appropriate to an $l^{-5}$ spectrum."
 As discussed. in section this suggests that the coupling is not. purely local in wavenumber space.," As discussed in section 2.2, this suggests that the coupling is not purely local in wavenumber space."
 We note also that this particular exponent ο is rather cillerent from. the 2 predicted by Goldreich. Reisenceecr (1992). but of course one should hardly expect the (wo to be the same. given that their result applies to 3D turbulence. whereas our calculations here are 2D laminar.," We note also that this particular exponent $-5$ is rather different from the $-2$ predicted by Goldreich Reisenegger (1992), but of course one should hardly expect the two to be the same, given that their result applies to 3D turbulence, whereas our calculations here are 2D laminar."
 ‘Turning to the toroidal spectra next. for small / they too are of the form //. but now the exponent is around 3.5 rather than 5 or 2.," Turning to the toroidal spectra next, for small $l$ they too are of the form $l^p$, but now the exponent is around $-3.5$ rather than $-5$ or $-2$."
 The entire curves also shift upward slightly with increasing Ae. and show no sign of saturating for sulliciently large. values.," The entire curves also shift upward slightly with increasing $R_B$ , and show no sign of saturating for sufficiently large values."
 Probably more worrisome though is the behaviour for large /.. where the Re=200 curve actually rises ever so slightly. between |—60 and 100.," Probably more worrisome though is the behaviour for large $l$, where the $R_B=200$ curve actually rises ever so slightly between $l=60$ and 100."
 LLowever. runs done at truncations varving between SO and 120 all showed this same minimum at /=60. suggesting that it is real. anc not some numerical artifact.," However, runs done at truncations varying between 80 and 120 all showed this same minimum at $l=60$, suggesting that it is real, and not some numerical artifact."
 Furthermore. the 2g=100 and 50 curves also show slight rises but still fall againthereafter. so perhaps the Ay=200 curve would too. if only we could. include enough. moces.," Furthermore, the $R_B=100$ and 50 curves also show slight rises but still fall againthereafter, so perhaps the $R_B=200$ curve would too, if only we could include enough modes."
 ]t is nevertheless not. quite clear what to make of this Ry=200 curve. and whether it really is fully resolved at the truncations we can alford.," It is nevertheless not quite clear what to make of this $R_B=200$ curve, and whether it really is fully resolved at the truncations we can afford."
 Based on these spectra though. we can certainly unclerstanc why attempting to increase /?g further still was not successful.," Based on these spectra though, we can certainly understand why attempting to increase $R_B$ further still was not successful."
 sriclly returning also to the results of Shalybkov Urpin. we have already noted that. they too obtained helicoidal oscillations much like those in. figure 2.," Briefly returning also to the results of Shalybkov Urpin, we have already noted that they too obtained helicoidal oscillations much like those in figure 2."
" Unfortunately. they did not plot power spectra at all. but simply stated that only the /<5 modes “give an appreciable contribution.” without further comment on what that means quantitatively,"," Unfortunately, they did not plot power spectra at all, but simply stated that only the $l\le5$ modes “give an appreciable contribution,” without further comment on what that means quantitatively."
 With 40 [atitudinal finite cillerence points they were actually resolving considerably more than just the {<5 modes though — although of course considerably. less than the LOO modes we have resolved here., With 40 latitudinal finite difference points they were actually resolving considerably more than just the $l\le5$ modes though – although of course considerably less than the 100 modes we have resolved here.
 I is nevertheless surprising that they obtained. such good. results with such a low resolution. (, It is nevertheless surprising that they obtained such good results with such a low resolution. (
In contrast. the fact that they worked in a full sphere rather than a thin shell makes very. little difference: we also did a few runs with r;/r;=0.5 and 0.25. and obtained spectra quite similar to those in figure 3.),"In contrast, the fact that they worked in a full sphere rather than a thin shell makes very little difference; we also did a few runs with $r_i/r_o=0.5$ and 0.25, and obtained spectra quite similar to those in figure 3.)"
 Finally. we would liketo know what the solutions actually look like. ancl in particular see whether we can identify the features corresponding to these ever. Latter spectra.," Finally, we would liketo know what the solutions actually look like, and in particular see whether we can identify the features corresponding to these ever flatter spectra."
 Figure 4 shows the field for Re=200 and / between 4 and 05. that is. covering the last two of these helicoida oscillations in figure 2 (and also precisely the time over which 10 spectra in figure 5 were averaged).," Figure 4 shows the field for $R_B=200$ and $t$ between 0.4 and 0.5, that is, covering the last two of these helicoidal oscillations in figure 2 (and also precisely the time over which the spectra in figure 3 were averaged)."
 We see that these oscillations involve reversals in the sign of D. originating a )0 equator and. propagating to the poles.," We see that these oscillations involve reversals in the sign of $B$, originating at the equator and propagating to the poles."
 What we do no see. however. are any. small scale features corresponding to us part of the spectrum between 60 and. 100.," What we do not see, however, are any small scale features corresponding to this part of the spectrum between 60 and 100."
 In retrospec js is probably not surprising though. since this plateau is after all 6 orders of magnitude down from the large scale eatures. and therefore shouldn't be expected to be visible on a simple contour plot such as this.," In retrospect this is probably not surprising though, since this plateau is after all 6 orders of magnitude down from the large scale features, and therefore shouldn't be expected to be visible on a simple contour plot such as this."
 In some of our solutions xlow though we will see small scale features as well. at which point we will better understand why they break down or sulliciently large Lp.," In some of our solutions below though we will see small scale features as well, at which point we will better understand why they break down for sufficiently large $R_B$."
 The maximum toroidal field in figure 4 is only 0.1. and even in the earlier stages of evolution it never exceeds 0.25.," The maximum toroidal field in figure 4 is only 0.1, and even in the earlier stages of evolution it never exceeds 0.25."
" [t is therefore probably. not surprising that 65 never becomes comparable with 5,. since according to (12) the toroidal field is a crucial ingredient in inducing higher harmonics in the poloidal field."," It is therefore probably not surprising that $b_3$ never becomes comparable with $b_1$, since according to (12) the toroidal field is a crucial ingredient in inducing higher harmonics in the poloidal field."
 Lf sve did have a Iarger toroidal field though. it seems likely we would.also obtain a larger by. perhaps even comparable with οι.," If we did have a larger toroidal field though, it seems likely we wouldalso obtain a larger $b_3$ , perhaps even comparable with $b_1$ ."
 To test this hypothesis. we add," To test this hypothesis, we add"
"scattering, and to reproduce images and polarization maps at various viewing angles.","scattering, and to reproduce images and polarization maps at various viewing angles."
 The benchmark case consists. once again. of a central star surrounded by a disk., The benchmark case consists once again of a central star surrounded by a disk.
" The central star has a radius of 2RRo and a temperature of KK, with a blackbody spectrum."," The central star has a radius of $_\odot$ and a temperature of K, with a blackbody spectrum."
" The disk extends from 0.1 to AAU (with cylindrical edges), and the density is given by Equation (9)), with ro=100 AAU, ho=10 AAU, a=2.625, and B=1.125."," The disk extends from 0.1 to AU (with cylindrical edges), and the density is given by Equation \ref{eq:disk}) ), with $r_0=100$ AU, $h_0=10$ AU, $\alpha=2.625$, and $\beta=1.125$."
 The disk is made up of dust grains with a, The disk is made up of dust grains with a
different from the aligned m=1 case.,different from the aligned $m=1$ case.
" The reason is simply wavenumber parameter £ will also \ m=0, =0.45, n-1 in equation (71)) LIalter", The reason is simply that the additional radial wavenumber parameter $\xi$ will also alter values of coefficients in equation \ref{spiral}) ).
 ervalues : of H again use asymptotic expression (65)) (3 to estimate A and then userecursion relation. (64)) ' . . . analvtical expressionB for Ay (8) _E EE| namely'hto fragmentationthan-- 0.54.[=," In this case, we again use asymptotic expression \ref{asymN}) ) to estimate ${\cal N}_4(\xi)$ and then use recursion relation \ref{recurN}) ) to derive an approximate analytical expression for ${\cal N}_1(\xi)$ , namelywith relative error less than $0.5\%$."
" With 4, = with£7 |relative |s—25TerrorB,=4:37 ibLA1 according to definitions (69)). we immecdiately obtain which increases monotonically with increasing € [orfixed 3 values and attains its nininium"," With ${\cal A}_1
=\xi^2+5/4+2\beta$ and ${\cal B}_1=4\beta^2-1$ according to definitions \ref{ABCHspiral}) ), we immediately obtain which increases monotonically with increasing $\xi$ forfixed $\beta$ values and attains its minimum"
Α natural assumption for describing multi-planet svstems is (hat the n-planet distribution [unction isseparable. (hat is. This assumption can only be approximately validlor example. it is inconsistent with (he observational finding Chat planets tend to be concentrated near nmtual orbital resonances. and with the theoretical finding that planets separated bv less than a few Lill radii are unstable.,"A natural assumption for describing multi-planet systems is that the $n$ -planet distribution function is, that is, This assumption can only be approximately valid—for example, it is inconsistent with the observational finding that planets tend to be concentrated near mutual orbital resonances, and with the theoretical finding that planets separated by less than a few Hill radii are unstable."
 Nevertheless. we argue that the separability assumption is sufficiently. accurate {ο provide a powerful tool for analvzing the statistics of multi-planet svstems.," Nevertheless, we argue that the separability assumption is sufficiently accurate to provide a powerful tool for analyzing the statistics of multi-planet systems."
 We describe the evidence on its validitv in re[sectvalid.., We describe the evidence on its validity in \\ref{sec:valid}.
 Let Q-*(w) be the probability that a planet with properties w is detected in the survey labeled by A if its host star is on the target list for this survey and the orientation of the observer is correct (we assume (hat whether or not a planet can be detected is independent of the presence or absence of other planets in the same svstem. which is a reasonable first approximation).," Let $\Theta^{A}(\mathbf{w})$ be the probability that a planet with properties $\mathbf{w}$ is detected in the survey labeled by A if its host star is on the target list for this survey and the orientation of the observer is correct (we assume that whether or not a planet can be detected is independent of the presence or absence of other planets in the same system, which is a reasonable first approximation)."
 Thus the function Ον) describes the survey selection effects for A. but not the geometric selection effects.," Thus the function $\Theta^{A}(\mathbf{w})$ describes the survey selection effects for A, but not the geometric selection effects."
 The probability (hat a planet is detected. ignoring geometric selection effects. is then If the survey target list contains V;' stars with m planets. then using the separability assumption (4)) the expected number of svstems in which / planets will be detected is where the survev selection matrix S is a (A+1)x(IN4+ matrix whose entries are given by the binomial distribution.," The probability that a planet is detected, ignoring geometric selection effects, is then If the survey target list contains $N^{A}_m$ stars with $m$ planets, then using the separability assumption \ref{eq:sep}) ) the expected number of systems in which $k$ planets will be detected is where the survey selection matrix $\mathbf{S}$ is a $(K+1)\times(K+1)$ matrix whose entries are given by the binomial distribution,"
AMevlan (1994) for the whole globular cluster svstem. provides a good fit to the number density profile of the Old Lalo cluster svstem as well.,"Meylan (1994) for the whole globular cluster system, provides a good fit to the number density profile of the Old Halo cluster system as well."
 Ixeeping all three parameters free. we obtain a steeper slope (>c 4.5) coupled. with a larger core.," Keeping all three parameters free, we obtain a steeper slope $-\gamma \simeq -4.5$ ) coupled with a larger core."
 The core reflects the Πατομής of the spatial distribution at small ealactocentric distances. presumably owing to the ereater cllicicney of disruptive processes.," The core reflects the flattening of the spatial distribution at small galactocentric distances, presumably owing to the greater efficiency of disruptive processes."
 lenoring this core region and focusing on the Old Lalo clusters located at galactocentric distances z 3kkpe. that is. where memory of the initial conditions has perhaps been better preserved. we find that both the mass and the number density. profiles of the Old. Halo are well-approximated: by pure power-laws wit1 slope zz3.5 (see Table 2)).," Ignoring this core region and focusing on the Old Halo clusters located at galactocentric distances $\gtrsim
3$ kpc, that is, where memory of the initial conditions has perhaps been better preserved, we find that both the mass and the number density profiles of the Old Halo are well-approximated by pure power-laws with slope $\simeq -3.5$ (see Table \ref{tab:fit_pure_pl}) )."
 The steepness of the Old Lalo spatial distribution is thus similar to that of the whole halo (Zinn 1985)., The steepness of the Old Halo spatial distribution is thus similar to that of the whole halo (Zinn 1985).
 While the mass and number density oofiles show very similar steepness at distances larger than 38kkpe. their overall shapes are also very similar.," While the mass and number density profiles show very similar steepness at distances larger than kpc, their overall shapes are also very similar."
 Fitting he Old Halo mass density profile with the same functions as used. for the number density. profile (Le. equation 1. and the (5. 2.) couples listed. in Table 1)) provides equally good. values of the incomplete gamma function (see the last column of Table 1)).," Fitting the Old Halo mass density profile with the same functions as used for the number density profile (i.e., equation \ref{eq:log_pl_core} and the $\gamma$ , $D_c$ ) couples listed in Table \ref{tab:fit_pl_core}) ) provides equally good values of the incomplete gamma function (see the last column of Table \ref{tab:fit_pl_core}) )."
 Therefore. the number and the mass density. profiles of the Old Lalo are incdistinguishable through the whole extent of the halo.," Therefore, the number and the mass density profiles of the Old Halo are indistinguishable through the whole extent of the halo."
 ‘The previous section shows that theobserved mass density and number density. profiles of the Old Lalo are identical in shape., The previous section shows that the mass density and number density profiles of the Old Halo are identical in shape.
 1 we that the elobular cluster ormation mechanism produced the same mass range an he same mass spectrum for the clusters. irrespective of heir galactocentric distance. then thetial mass anc number density. profiles were identical in shape as well.," If we that the globular cluster formation mechanism produced the same mass range and the same mass spectrum for the clusters, irrespective of their galactocentric distance, then the mass and number density profiles were identical in shape as well."
 Lf he mass density profile has been preserved. (ancl we show in this section that it is actually the case). all together. hese facts imply that the number density profile itself das remained fairly unaltered during evolution in the tida ielel of the Milky Way.," If the mass density profile has been preserved (and we show in this section that it is actually the case), all together, these facts imply that the number density profile itself has remained fairly unaltered during evolution in the tidal field of the Milky Way."
 In what follows. we evolve various outative elobular cluster systems. considering clilferen combinations of initial mass spectra ancl initial spatia distributions.," In what follows, we evolve various putative globular cluster systems, considering different combinations of initial mass spectra and initial spatial distributions."
 We then investigate in which case(s) has he number density profile been reasonably preserved., We then investigate in which case(s) has the number density profile been reasonably preserved.
 We also compare in a least-squares sense the evolved. spatia distributions to the observed ones that we have derived in Section 2., We also compare in a least-squares sense the evolved spatial distributions to the observed ones that we have derived in Section 2.
 To evolve the radial mass and numboer density. profiles ofa cluster system from the time of its formation up to an age of GCOwvr. we adopt the analytic formula of Vesperini llegeie (1997) which supplies at any time/ the mass m oL a star cluster with initial mass m; which is moving along a circular orbit. perpenclicular to the galactic disc at a galactocentric distance D.," To evolve the radial mass and number density profiles of a cluster system from the time of its formation up to an age of Gyr, we adopt the analytic formula of Vesperini Heggie (1997) which supplies at any time$t$ the mass $m$ of a star cluster with initial mass $m_i$ which is moving along a circular orbit perpendicular to the galactic disc at a galactocentric distance $D$."
 “Phe assumption of circular orbits is clearly a simplifving one since it implies that the time variations of the tidal field for clusters on elliptical orbits are not allowed for in our calculations., The assumption of circular orbits is clearly a simplifying one since it implies that the time variations of the tidal field for clusters on elliptical orbits are not allowed for in our calculations.
 Yet. the svstem of relevance here is the Old Halo.," Yet, the system of relevance here is the Old Halo."
 This shows less extreme kinematics than the Younger Halo group of clusters. making this assumption less critical than if we have dealt with the whole halo svstem.," This shows less extreme kinematics than the Younger Halo group of clusters, making this assumption less critical than if we have dealt with the whole halo system."
 As for the inlluence of the cluster orbit inclination with respect to the Galactic disc. Murali Weinberg (1997). found hat. although [ow-inclination halo clusters evolve more rapidly than hieh-inclination ones. the dillerences are. not extreme.," As for the influence of the cluster orbit inclination with respect to the Galactic disc, Murali Weinberg (1997) found that, although low-inclination halo clusters evolve more rapidly than high-inclination ones, the differences are not extreme."
 Furthermore. our sample excluding disce clusters. the assumption of high inclination orbits is a reasonable one.," Furthermore, our sample excluding disc clusters, the assumption of high inclination orbits is a reasonable one."
 “Phe simulations of Vesperini llegeie (1997) were designed in the frame of a host galaxy modelled as a simple isothermal sphere with a constant circular velocity., The simulations of Vesperini Heggie (1997) were designed in the frame of a host galaxy modelled as a simple isothermal sphere with a constant circular velocity.
 This actually constitutes a reasonable assumption for the Old. Halo system. whose racial extent is kkpc. that is. where the mass profile of the Milky Wav (Le. the total Galactic mass enclosed. within a radius D) grows linearly. with the galactocentric distance (Llarris POOL).," This actually constitutes a reasonable assumption for the Old Halo system whose radial extent is kpc, that is, where the mass profile of the Milky Way (i.e, the total Galactic mass enclosed within a radius $D$ ) grows linearly with the galactocentric distance (Harris 2001)."
 We consider the ellect of non-circular orbits in more detail in Section 4. below.," We consider the effect of non-circular orbits in more detail in Section 4, below."
 The relations describing the temporal evolution of the mass of a elobular cluster have been obtained. by fitting the results of a laree set of N-bocly simulations in which Vesperini Llegeic (1997) take into account the effects of stellar evolution as well as two-bocly relaxation. which leads to evaporation through the cluster tical boundary.," The relations describing the temporal evolution of the mass of a globular cluster have been obtained by fitting the results of a large set of N-body simulations in which Vesperini Heggie (1997) take into account the effects of stellar evolution as well as two-body relaxation, which leads to evaporation through the cluster tidal boundary."
 Disc shocking can also be included. (see below)., Disc shocking can also be included (see below).
 In. order to take into account dynamical friction. globular clusters whose time-scale of orbital decay (sec. e.g. Anunev ‘Tremaine 1987) is smaller than / are removed Crom the cluster svstem at that time (see Vesperini: 1905. his Section 2. for Curther details).," In order to take into account dynamical friction, globular clusters whose time-scale of orbital decay (see, e.g., Binney Tremaine 1987) is smaller than $t$ are removed from the cluster system at that time (see Vesperini 1998, his Section 2, for further details)."
 Le is important to note a specific assumption underlying the validity of this analysis., It is important to note a specific assumption underlying the validity of this analysis.
 The large-scale Galactic gravitational potential is assumed constant. that. is. this mocel considers the evolution of a elobular cluster svstem only after it has been assembled in a time-independent Galaxy.," The large-scale Galactic gravitational potential is assumed constant, that is, this model considers the evolution of a globular cluster system only after it has been assembled in a time-independent Galaxy."
 That is the physical basis for a restriction to the svstem of Old Lalo elobular clusters., That is the physical basis for a restriction to the system of Old Halo globular clusters.
 The temporal evolution of the mass of a cluster orbiting at constant galactocentric distance D is found to follow: imus£m; is the fraction of cluster mass lost due to stellar evolution (18 per cent in this particular moclel).," The temporal evolution of the mass of a cluster orbiting at constant galactocentric distance $D$ is found to follow: $\Delta m_{st,ev}/m_i$ is the fraction of cluster mass lost due to stellar evolution (18 per cent in this particular model)."
 The time fis expressed in units of MMwyr ancl £54. à quantity proportional to the initial relaxation time. is definedas:," The time $t$ is expressed in units of Myr and $F_{cw}$ , a quantity proportional to the initial relaxation time, is definedas:"
of 0.25 dex) and -3xlog ms+2 (step of | dex) at a microturbulent velocity. € = 5 km s7!.,"of 0.25 dex), and $-3\le$ $\le+$ 2 (step of 1 dex) at a microturbulent velocity, $\xi$ = 5 km $^{-1}$."
" For each model atmosphere with mes-]. we calculated a second model with (marked by © in Table 2)) following the prediction of the “flash mixing"" scenario. adopting mass fractions of and for carbon and nitrogen. respectively (Lanz et al. 2004))."," For each model atmosphere with $\ge-1$, we calculated a second model with (marked by $^{\rm C}$ in Table \ref{Tab:Par_Rich}) ) following the prediction of the “flash mixing” scenario, adopting mass fractions of and for carbon and nitrogen, respectively (Lanz et al. \cite{labr04}) )."
 We adopted scaled-solar abundanees at co CCen's dominant metallicity ([Fe/H| = —].5)., We adopted scaled-solar abundances at $\omega$ Cen's dominant metallicity ([Fe/H] = $-$ 1.5).
 This abundance ratio by numbers was kept the same for all models. including helium-rich models. which implies that the heavy element mass fraction differs for models with different helium (and C. N) content.," This abundance ratio by numbers was kept the same for all models, including helium-rich models, which implies that the heavy element mass fraction differs for models with different helium (and C, N) content."
 We emphasize. however. that the abundance of tron-peak elements in. EHB stellar photospheres is unknown and probably affected by diffusion processes.," We emphasize, however, that the abundance of iron-peak elements in EHB stellar photospheres is unknown and probably affected by diffusion processes."
 Furthermore. the low abundance of heavy elements limits the effect of metal line blanketing on the atmospheric structure and the predicted emergent spectrum.," Furthermore, the low abundance of heavy elements limits the effect of metal line blanketing on the atmospheric structure and the predicted emergent spectrum."
 Therefore. the resulting uncertainty in our analysis caused by assuming the same [Fe/H] value remains small.," Therefore, the resulting uncertainty in our analysis caused by assuming the same [Fe/H] value remains small."
 Once the atmospheric structure of each model atmosphere converged. we calculated detailed emergent spectra in the 13800-4600 rrange with the spectrum synthesis code. SYNSPEC. using the NLTE populations calculated by TLUSTY.," Once the atmospheric structure of each model atmosphere converged, we calculated detailed emergent spectra in the $\lambda\lambda$ range with the spectrum synthesis code, SYNSPEC, using the NLTE populations calculated by TLUSTY."
 For the helium-poor stars above KK. we also used the TLUSTY models.," For the helium-poor stars above K, we also used the TLUSTY models."
 For the cooler stars. we used models (Moehler et al. 2000)).," For the cooler stars, we used models (Moehler et al. \cite{mosw00}) )."
" Using the atmospheric parameters. a distance modulus of Gn—M);=13°45. and an interstellar absorption of Ay 0747, we derived masses for our target stars as described in Moehler et al. (20000)."," Using the atmospheric parameters, a distance modulus of $(m-M)_0 =
\magpt{13}{45}$, and an interstellar absorption of $A_V =
\magpt{0}{47}$ , we derived masses for our target stars as described in Moehler et al. \cite{mosw00}) )."
 The masses for the helium-rich stars are somewhat underestimated as we used theoretical brightness values for solar-helium atmospheres. which are brighter in the optical range than helium-rich atmospheres.," The masses for the helium-rich stars are somewhat underestimated as we used theoretical brightness values for solar-helium atmospheres, which are brighter in the optical range than helium-rich atmospheres."
 The helium abundances plotted in Fig., The helium abundances plotted in Fig.
 5 shows a clear distinction. between helium-poor stars with P26350I. 6Copensquares. f teryxand GrouplAierea starswithheliumabundane MAW eroóBovelsbl Per PEUrdeOQ roup2eRryrer).," \ref{Fig:Teff_loghe} shows a clear distinction between helium-poor stars with $<-1.6$ (open squares, hereafter) and stars with helium abundances close to or above solar (filled triangles, hereafter)."
 Moehler et al. (2007)), Moehler et al. \cite{modr07}) )
 noted an asymmetric spatial distribution of the heltum-rich stars., noted an asymmetric spatial distribution of the helium-rich stars.
 To verify the significance of this effect. we investigated the spatial distribution of the faint HB stars. B. >17. adopting the combined Advanced Camera for Surveys (ACS) and Wide Field Imager (WFI) photometric catalog (Castellani et al. 2007)).," To verify the significance of this effect, we investigated the spatial distribution of the faint HB stars, $B>$ 17, adopting the combined Advanced Camera for Surveys (ACS) and Wide Field Imager (WFI) photometric catalog (Castellani et al. \cite{cast07}) )."
 We selected candidate helium-rich and helium-poor HB stars according to the magnitudes of the spectroscopically confirmed samples., We selected candidate helium-rich and helium-poor HB stars according to the magnitudes of the spectroscopically confirmed samples.
 We assumed helium-rich stars to be those with B> 18.35 and helium-poor stars to be those with B <18.35., We assumed helium-rich stars to be those with $B>$ 18.35 and helium-poor stars to be those with $B\le$ 18.35.
 The spatial distribution of the two samples does not exhibit any significant asymmetry in the four quadrants of the cluster., The spatial distribution of the two samples does not exhibit any significant asymmetry in the four quadrants of the cluster.
There is mild evidence of an overabundance of hot HB stars in general in the southeast,There is mild evidence of an overabundance of hot HB stars in general in the southeast
event data (exchiding point sources) mn a square region centered ou the pixel.,event data (excluding point sources) in a square region centered on the pixel.
 The region size was determined by requiring at least SOO net (Lo. background. subtracted) counts in the 0.17.0 keV enerev rauge. but with a naxinimui box size of «183 ACTS pixels. or ο”.," The region size was determined by requiring at least 800 net (i.e. background subtracted) counts in the 0.4–7.0 keV energy range, but with a maximum box size of $\times$ 183 ACIS pixels, or $\times$."
 The maxims box size was ouly reached ii the outskirts of the cluster., The maximum box size was only reached in the outskirts of the cluster.
 The total counts iu each region were vtween 1.5 and 2 times the 8SOO count minium to account for backerouud subtraction., The total counts in each region were between 1.5 and 2 times the 800 count minimum to account for background subtraction.
 For each spectrin. a backerouud spectrum was extracted from the blauk sky vackeround event file iu the same region.," For each spectrum, a background spectrum was extracted from the blank sky background event file in the same region."
 RME and ARF files were constructed for specific locations on the CCD. with a spacing of 32 aud 50 pixels; respectively.," RMF and ARF files were constructed for specific locations on the CCD, with a spacing of 32 and 50 pixels, respectively."
 This was done to account for variations in the response across the CCD. without having to create individual RME and ARF files for each region which would be computationally demanding.," This was done to account for variations in the response across the CCD, without having to create individual RMF and ARF files for each region which would be computationally demanding."
 For a given region. the RME and ARF used to fit the spectrum were chosen by selecting the response files with positions closest to the count-weighted average position of the eveuts im each region.," For a given region, the RMF and ARF used to fit the spectrum were chosen by selecting the response files with positions closest to the count-weighted average position of the events in each region."
 The spectra were erouped to have 25 counts per biu aud were fitted in ISIS using the thermal model., The spectra were grouped to have 25 counts per bin and were fitted in ISIS using the thermal model.
 The Calactic Lydrogen column deusitv. redshift. and abundance were fixed to ie values found for the full cluster spectrum 77 above).," The Galactic hydrogen column density, redshift, and abundance were fixed to the values found for the full cluster spectrum \ref{sec:full}
 above)."
 Ouly the teiiperature and normalization of the inoclel were allowed to vary., Only the temperature and normalization of the model were allowed to vary.
 In ecucral. the errors ou 1ο temperature map are about in the temperature.," In general, the errors on the temperature map are about in the temperature."
 Although. for pixels with higher best-fit tempcratures or rose near the edge of the map. the errors are larger. iu rc range of70%.," Although, for pixels with higher best-fit temperatures or those near the edge of the map, the errors are larger, in the range of."
. This is because of the low lieh-energy sensitivity of aud the lower statistics of 1e outer regions., This is because of the low high-energy sensitivity of and the lower statistics of the outer regions.
 The temperature map shown in Figure 8. is colored such that the coolest reeious (ALz| keV) are red.," The temperature map shown in Figure \ref{fig:tmap} is colored such that the coolest regions $kT \approx 4$ keV) are red,"
"for metal-poor stars. we only use spectra that are not affected by saturation effects. which typically start to be noticable at B,~14.0. and we only include spectra with S/N>10 (which roughly corresponds to B;~ 16.4). because at lower S/N an efficient selection of metal-poor stars. by means of a weak or absent Ca K line. is not feasible anymore.","for metal-poor stars, we only use spectra that are not affected by saturation effects, which typically start to be noticable at $B_J\sim 14.0$, and we only include spectra with $S/N>10$ (which roughly corresponds to $B_J\sim 16.4$ ), because at lower $S/N$ an efficient selection of metal-poor stars, by means of a weak or absent Ca K line, is not feasible anymore."
 However. for most other object types. including DAs. we adopt the 56 magnitude limit.," However, for most other object types, including DAs, we adopt the $5\sigma$ magnitude limit."
" The atmospheric cutoff at the blue end. and the sharp sensitivity cutoff of the IIHa-J emulsion (red edge"") result in a wavelength range of 3200A<A<5300A (see Fig. 3)."," The atmospheric cutoff at the blue end, and the sharp sensitivity cutoff of the IIIa-J emulsion (“red edge”) result in a wavelength range of $3200\,\mbox{\AA} < \lambda < 5300\,\mbox{\AA}$ (see Fig. \ref{fig:noisedata_demo}) )."
 The spectral resolution of the HES is primarily seemg-limited., The spectral resolution of the HES is primarily seeing-limited.
 For plates taken during good seeing conditions. the pixel spacings chosen in the digitization process result in an under-sampling. so that in these cases the spectral resolution ts also limited by the sampling.," For plates taken during good seeing conditions, the pixel spacings chosen in the digitization process result in an under-sampling, so that in these cases the spectral resolution is also limited by the sampling."
 The definition of the HES survey area makes use of the mean star density and average column density of neutral hydrogen for each ESO/SERC field (?).., The definition of the HES survey area makes use of the mean star density and average column density of neutral hydrogen for each ESO/SERC field \citep{hespaperIII}.
 The adopted criteria roughly correspond to galactic latitudes of |5b|> 30°., The adopted criteria roughly correspond to galactic latitudes of $|b|>30^{\circ}$ .
 The declination range covered by the HES is |2.5°>6787., The declination range covered by the HES is $+2.5^{\circ}>\delta> -78^{\circ}$.
 In result. the survey area consists of 380 fields.," In result, the survey area consists of 380 fields."
 Between 1989 and 1998. objective-prism plates were taken for all of these. and the plates were subsequently digitized and reduced at Hamburger Sternwarte.," Between 1989 and 1998, objective-prism plates were taken for all of these, and the plates were subsequently digitized and reduced at Hamburger Sternwarte."
 As one ESO Schmidt plate covers approximately RIEN5deg on the sky. the nominal survey area is 9500 ddeg?. or the total southern extragalactic sky.," As one ESO Schmidt plate covers approximately $5\times 5\deg^2$ on the sky, the nominal survey area is $9\,500$ $^2$, or the total southern extragalactic sky."
 Note. however. that the survey area Is ~25 (?)..," Note, however, that the survey area is $\sim 25$ \citep{hespaperIII}."
 Overlapping spectra (hereafter shortly called overlaps) are detected automatically using the direct plate data of the Digitized Sky Survey I (DSS I)., Overlapping spectra (hereafter shortly called overlaps) are detected automatically using the direct plate data of the Digitized Sky Survey I (DSS I).
 For each spectrum to be extracted. it is looked for objects in the dispersion direction on the direct plate.," For each spectrum to be extracted, it is looked for objects in the dispersion direction on the direct plate."
 If there 1s one. the automatic procedure marks the corresponding spectrum. so that it can later be excluded from further processing. 1f this is desired.," If there is one, the automatic procedure marks the corresponding spectrum, so that it can later be excluded from further processing, if this is desired."
" desired for stellar work. since the feature detection and object selection algorithms would get confused otherwise. and a lot of ""garbage"" would enter the candidate samples."," desired for stellar work, since the feature detection and object selection algorithms would get confused otherwise, and a lot of “garbage” would enter the candidate samples."
 The digital HES data base for stellar work consists of —4 million extracted. overlap-free spectra with average S/N>5 in the B; band.," The digital HES data base for stellar work consists of $\sim 4$ million extracted, overlap-free spectra with average $S/N>5$ in the $B_J$ band."
 As described in ?).. the calibration of HES B; magnitudes is done plate by plate with individual photometric sequences.," As described in \cite{hespaperIII}, the calibration of HES $B_J$ magnitudes is done plate by plate with individual photometric sequences."
 The B; band is formally defined by the spectral sensitivity curve of the Kodak IIIa-J emulsion multiplied with the filter curve of a Schott GG395 filter., The $B_J$ band is formally defined by the spectral sensitivity curve of the Kodak IIIa-J emulsion multiplied with the filter curve of a Schott GG395 filter.
 The overall errors of the HES B; magnitudes. including zero point errors. are less than +0.2 mmag.," The overall errors of the HES $B_J$ magnitudes, including zero point errors, are less than $\pm
0.2$ mag."
 Note that B; can be converted to B using the formula which ts valid for main sequence stars in the colour range O1<(BV)<1.6(?)., Note that $B_J$ can be converted to $B$ using the formula which is valid for main sequence stars in the colour range $-0.1<(B-V)<1.6$ \citep{Hewettetal:1995}.
 A global dispersion relation for all HES plates was determined by using A-type stars., A global dispersion relation for all HES plates was determined by using A-type stars.
 In HES spectra of these stars the Balmer lines at least up to Hijo. are resolved (see Fig. 3)).," In HES spectra of these stars the Balmer lines at least up to $_{10}$ are resolved (see Fig. \ref{fig:noisedata_demo}) ),"
 so that a dispersion relation can be derived by comparing the v-positions (scan length in umm) of these limes with the known wavelengths., so that a dispersion relation can be derived by comparing the $x$ -positions (scan length in $\mu$ m) of these lines with the known wavelengths.
" ?) used the position of the “red edge"" of objective-prism spectra to determine the zero point of the wavelength calibration. but noticed that the position depends on the energy distribution of the object."," \cite{Borraetal:1987}
 used the position of the “red edge” of objective-prism spectra to determine the zero point of the wavelength calibration, but noticed that the position depends on the energy distribution of the object."
 Therefore. in the HES we decided to use a zero point specified by an astrometric transformation between direct plates and spectral plates.," Therefore, in the HES we decided to use a zero point specified by an astrometric transformation between direct plates and spectral plates."
 The wavelength calibration is accurate to +10gmm. This corresponds to £4.5 at Hy and £2.3 at A=3500A.," The wavelength calibration is accurate to $\pm 10\,\mu$ m. This corresponds to $\pm 4.5$ at $\gamma$ and $\pm
2.3$ at $\lambda = 3500$."
. Following the approach of ?).. we determine the amplitude of pixel-wise noise as a function of photographic density D plate by plate using A- and F-type stars.," Following the approach of \cite{Hewettetal:1985}, , we determine the amplitude of pixel-wise noise as a function of photographic density $D$ plate by plate using A- and F-type stars."
 A straight line fit is done to the spectral region between Hp and Hy (see Fig. 3))., A straight line fit is done to the spectral region between $\beta$ and $\gamma$ (see Fig. \ref{fig:noisedata_demo}) ).
4 The | G-scatter around this pseudo-continuum fit ts taken as noise amplitude.," The $1\,\sigma$ -scatter around this pseudo-continuum fit is taken as noise amplitude."
 In this approach we assume that the scatter is mainly due to noise. since in early-type stars the spectral region under consideration includes only very few absorption lines at the spectral resolution of the HES.," In this approach we assume that the scatter is mainly due to noise, since in early-type stars the spectral region under consideration includes only very few absorption lines at the spectral resolution of the HES."
 Moreover. itis expected that the population of A- and F-type stars found at high galactic latitudes is dominated by metal-poor stars. so that metal Imes are usuallyvery weak.," Moreover, itis expected that the population of A- and F-type stars found at high galactic latitudes is dominated by metal-poor stars, so that metal lines are usuallyvery weak."
 However. we can not exclude that we," However, we can not exclude that we"
other merger types are occurring. but these cannot dominate the merger process.,"other merger types are occurring, but these cannot dominate the merger process."
 In this final subsection we address the question of whether he asymmetry criteria for locating mergers could. be significant allected by star formation events., In this final subsection we address the question of whether the asymmetry criteria for locating mergers could be significant affected by star formation events.
 While it has oen shown through using the clumpiness index (Conselice 2003). and a comparison between asvmmetries and distorted kinematics (Conseliee et al.," While it has been shown through using the clumpiness index (Conselice 2003), and a comparison between asymmetries and distorted kinematics (Conselice et al."
 2000b).. as well as. visual estimates of mergers (Conselice et al.," 2000b), as well as visual estimates of mergers (Conselice et al."
" 2005). that ultra-high asvnunetrics correlate. with merging galaxies. we provide ""urther evidence here based on the asvmimetrey. time-scale."," 2005), that ultra-high asymmetries correlate with merging galaxies, we provide further evidence here based on the asymmetry time-scale."
 We argue this based on the fact that the merger time-scale is roughly στ0.6 Car. and is no higher than ~11 ινε αἲ ος1.2.," We argue this based on the fact that the merger time-scale is roughly $\tau_{\rm m} \sim 0.6$ Gyr, and is no higher than $\sim 1.1$ Gyr at $z < 1.2$."
 I£ the asymmetric regions in these galaxies were due to star forming complexes. they would last no longer than a few tens of Myr. as the ages of star formation regions are pies no older than 10-20 Myr (e.g... Palla Galli LOOT).," If the asymmetric regions in these galaxies were due to star forming complexes, they would last no longer than a few tens of Myr, as the ages of star formation regions are typically no older than 10-30 Myr (e.g., Palla Galli 1997)."
 Thus. within roughly half a Civr. these star forming regions would no longer be distinct from the rest of the galaxy. and as such would not stand out when measuring asvmmetries.," Thus, within roughly half a Gyr, these star forming regions would no longer be distinct from the rest of the galaxy, and as such would not stand out when measuring asymmetries."
 We conclude that it is unlikely [or star formation to be the cause of the very high asvnimetrics we attribute to merging galaxies., We conclude that it is unlikely for star formation to be the cause of the very high asymmetries we attribute to merging galaxies.
 Lt is possible that star formation re-occurs throughout our time-scale. but the drop in the star formation rate is faster than the derived. merger fraction. suggesting the two are not coupled.," It is possible that star formation re-occurs throughout our time-scale, but the drop in the star formation rate is faster than the derived merger fraction, suggesting the two are not coupled."
 For example. Baldry et al. (," For example, Baldry et al. ("
2005) find that the star formation rate declines from 0.15 PMMpe: 7 at roughly «= 100 ~0.015 DMMpe 70230 2~0.,2005) find that the star formation rate declines from 0.15 $^{-1}$ $^{-3}$ at roughly $z = 1$ to $\sim 0.015$ $^{-1}$ $^{-3}$ at $z \sim 0$.
 While Conselice et al. (, While Conselice et al. (
"2009b) find that the merger fraction declines from fy,=0.13 at οΞ12 to fy=044 at 2=0.2.",2009b) find that the merger fraction declines from $f_{\rm m} = 0.13$ at $z = 1.2$ to $f_{\rm m} = 0.04$ at $z = 0.2$.
 While the star formation rate declines by at least a factor of ten. the merger fraction drops by a factor of three.," While the star formation rate declines by at least a factor of ten, the merger fraction drops by a factor of three."
 We have made the first empirical measurement of the time-scale for mergers within the CAS system. based. on the detailed: merger fraction. evolution. described. in. Conselice et al. (," We have made the first empirical measurement of the time-scale for mergers within the CAS system, based on the detailed merger fraction evolution described in Conselice et al. ("
2009b).,2009b).
 These merger fractions are taken from the Extended Groth Strip and COSMOS surveys. and constitute -20.000. ealaxies with stellar masses M;>LOMAL...," These merger fractions are taken from the Extended Groth Strip and COSMOS surveys, and constitute $> 20,000$ galaxies with stellar masses $_{*} > 10^{10}$."
 Our major result is that the time-scale for CAS mergers ab ο< Lis between 1.1 Gyr and 0.3 Gye., Our major result is that the time-scale for CAS mergers at $z < 1$ is between 1.1 Gyr and 0.3 Gyr.
" Our best estimated time-scale is Tu,=0.6£0.3 Cyr. which gives the total : − ⊔⊔⊔↓∣⋈⋅↓⋅∪⇂⊔↓⋖⊾↓⋅⋏∙≟⋖⋅↓⋅⊳∖⋯⇍≼∼⊔↓⋅↓⋅↓⊔⋏∙≟⋜∐⋅⋅∖∕↓⋅−≽⋜↧⊳∖↓∖⋯∶∪⋅≤⋗∪∩⊽⊐⊽↾⊁⋡∩↽⊔ ⊳∖⊲↓⊔↓∐⋜⊔⋅⋯↓≻↓⋅∢⊾∖⋰↓∪⊔≱∖∖∖⊽∪↓⋅↳∣⋯≱∖⋖⋅∠⇂∩⊔↓∖⊽−∣⋡⇜⇂∙∖⇁≻↕↓↥↓⇂⇂↓⋜↧⇂↕⋖≱↓↥↿↕↓↥↓⋖⊾− scales. and from changes in the mass density of galaxies at οκ1 (Conselice et al."," Our best estimated time-scale is $\tau_{\rm m} = 0.6\pm0.3$ Gyr, which gives the total number of mergers occurring at $z < 1.2$ as $_{\rm m} = 0.90_{-0.23}^{+0.44}$, similar to previous work based on N-body simulation time-scales, and from changes in the mass density of galaxies at $z < 1$ (Conselice et al."
 2007)., 2007).
" We BM that. on average. a galaxy with stellar mass Al,QUU will increase its stellar mass by due to ""emergers."," We calculate that, on average, a galaxy with stellar mass $_{*} > 10^{10}$ will increase its stellar mass by due to these mergers."
 This time-scale also rules out the possibility that star formation is the cause of asvmametries seen in galaxies. as our observed time-scales are over an order of magnitude too long to be produced by single star formation events.," This time-scale also rules out the possibility that star formation is the cause of asymmetries seen in galaxies, as our observed time-scales are over an order of magnitude too long to be produced by single star formation events."
 The fact that there is a good. agreement: between empirically derived merger time-scales and those based on ealaxv merger simulations suggests that we are beginning to understand the role of mergers within galaxy evolution., The fact that there is a good agreement between empirically derived merger time-scales and those based on galaxy merger simulations suggests that we are beginning to understand the role of mergers within galaxy evolution.
" While in the local universe roughly of galaxies. with masses AL,2107 ave disks. the majority of these contain large bulges. ancl very lew are pure disks (e.g. Conselice 2006b)."," While in the local universe roughly of galaxies with masses $_{*} > 10^{10}$ are disks, the majority of these contain large bulges, and very few are pure disks (e.g., Conselice 2006b)."
 Likely. some of these massive galaxies are undergoing more evolution than others. ancl it is possible that some of the more clustered. systems. such as ellipticals are more likely to undergo more than one merger at z<1.2. which would also help nM the increase in sizes for these galaxies (c.g..resultsTrujillo ct al.," Likely, some of these massive galaxies are undergoing more evolution than others, and it is possible that some of the more clustered systems, such as ellipticals are more likely to undergo more than one merger at $z < 1.2$, which would also help explain the increase in sizes for these galaxies (e.g., Trujillo et al."
 2WOT: Duitrago ct al., 2007; Buitrago et al.
 2008)., 2008).
 These show that merecrs are an important part of the galaxy formation process at 2«1.2. when most ealaxies appear to have morphologics similar to todav (e.g. Conselice οἱ al.," These results show that mergers are an important part of the galaxy formation process at $z < 1.2$, when most galaxies appear to have morphologies similar to today (e.g., Conselice et al."
 2005)., 2005).
 Xpplving this methodology to higher redshifts will prove more challenging. due to the active ongoing evolution of these svstems at early. times. and the likelihood that some fraction will undergo more than a single merger.," Applying this methodology to higher redshifts will prove more challenging, due to the active ongoing evolution of these systems at early times, and the likelihood that some fraction will undergo more than a single merger."
 This can be probed in the future when large area surveys for galaxy mergers at z215 are carried out., This can be probed in the future when large area surveys for galaxy mergers at $z > 1.5$ are carried out.
 ] thank the referee. Patrik Jonsson. for his comments which significantly. improved this paper.," I thank the referee, Patrik Jonsson, for his comments which significantly improved this paper."
 L also thank Asa Bluck and Russel White for useful conversations on these topics. and support from the STEC.," I also thank Asa Bluck and Russel White for useful conversations on these topics, and support from the STFC."
for four values of1 and Figure 2. displays X(x) for four values of a.,for four values of $m$ and Figure \ref{fig:plot02-Einasto-profile} displays $\Sigma\left(x\right)$ for four values of $\alpha$.
 In both it can be seen clearly that the respective index 1s very important in determining the overall behavior of the curves., In both it can be seen clearly that the respective index is very important in determining the overall behavior of the curves.
 The Sérrsic profile is characterized by a more steeper central core and extended external wing for larger values of the Sérrsic index 7., The Sérrsic profile is characterized by a more steeper central core and extended external wing for larger values of the Sérrsic index $m$ .
 For low values of ;i the central core is more flat and the external wing is sharply truncated., For low values of $m$ the central core is more flat and the external wing is sharply truncated.
 The Einasto profile has a similar behavior. with the difference that the external wings are most spread out.," The Einasto profile has a similar behavior, with the difference that the external wings are most spread out."
 Also in the inner region for both profiles with low values of the respectively index we obtain larger values of X4 and X., Also in the inner region for both profiles with low values of the respectively index we obtain larger values of $\Sigma_{S}$ and $\Sigma$.
 However. the Einasto profile seems to be less sensitive to the value of the surface mass density for a given a and radius and in the inner region than the Sérrsic profile.," However, the Einasto profile seems to be less sensitive to the value of the surface mass density for a given $\alpha$ and radius and in the inner region than the Sérrsic profile."
 It is in this region where the lensing effect is more important and the difference in the surface mass density determines the lensing properties of the respectively profiles., It is in this region where the lensing effect is more important and the difference in the surface mass density determines the lensing properties of the respectively profiles.
 Given this difference. we see that the lensing properties of the Sérrsic and Einasto profile are not equal.," Given this difference, we see that the lensing properties of the Sérrsic and Einasto profile are not equal."
 Studies of the lensing properties of the Sérrsic profile had been done by ? and ?.., Studies of the lensing properties of the Sérrsic profile had been done by \citet{2004A&A...415..839C} and \citet{2007JCAP...07..006E}.
 The total mass enclosed in a halo deseribed by theEinasto profile can be found by:, The total mass enclosed in a halo described by theEinasto profile can be found by:
same panel as a clashed line. and it is immediately clear that such an approximation is σους for the majority of the galaxy population.,"same panel as a dashed line, and it is immediately clear that such an approximation is good for the majority of the galaxy population."
" To clarify, our understanding of this. the same star formation rates are shown in the right panel as a function of stellar mass."," To clarify our understanding of this, the same star formation rates are shown in the right panel as a function of stellar mass."
 This shows the very strong correlation between current star formation rate. and mean star formation rate. which was discussed in reSSE IL.," This shows the very strong correlation between current star formation rate, and mean star formation rate, which was discussed in \\ref{SSFR}."
 Now. for galaxies which lie on or above this trend. the massive star population is a large enough that they will indeed be the main contributors to the total UV. luminosity. and the strong correlation (6)) holds.," Now, for galaxies which lie on or above this trend, the massive star population is a large enough that they will indeed be the main contributors to the total UV luminosity, and the strong correlation \ref{SFR-M}) ) holds."
 For galaxies below the main trend. this approximation breaks down: less massive stars are so comparatively abundant that they are. responsible for most of the total UV output. despite their poorας contribution to this part of the spectrum.," For galaxies below the main trend, this approximation breaks down; less massive stars are so comparatively abundant that they are responsible for most of the total UV output, despite their poor contribution to this part of the spectrum."
 This is further illustrated by the small peripheral panels which show the star formation histories of four particular salaxies., This is further illustrated by the small peripheral panels which show the star formation histories of four particular galaxies.
 Ln the lower two panels. past star formation episodes were so productive that the stars produced. then are outshining the recently formed stars. even at this high energy end of the spectrum.," In the lower two panels, past star formation episodes were so productive that the stars produced then are outshining the recently formed stars, even at this high energy end of the spectrum."
 The main conclusion of this exercise. is positive: hierarchical formation theory predicts that only a small fraction of galaxies would. diller [from the. assumed correlation., The main conclusion of this exercise is positive; hierarchical formation theory predicts that only a small fraction of galaxies would differ from the assumed correlation.
 Furthermore. such scatter as there is occurs mostly on the lower side: unusually high. star formation rates may still be estimated. correctly as it only serves to accentuate the underlving assumption (6)).," Furthermore, such scatter as there is occurs mostly on the lower side; unusually high star formation rates may still be estimated correctly as it only serves to accentuate the underlying assumption \ref{SFR-M}) )."
 This one-siclecd nature of this error. does means that characteristic star formation rates would beoverestimaled but the practical consequences of this are negligible. particularly when set. aside the comparatively major problems presented by dust extinction. covered in refDust..," This one-sided nature of this error does means that characteristic star formation rates would be but the practical consequences of this are negligible, particularly when set aside the comparatively major problems presented by dust extinction, covered in \\ref{Dust}. ."
"peak tovalley*,, we could have naively expected that the observed time lag/sublimation radius changed by a factor of 20!/2=4.5 (see Eq. 1)).","peak to, we could have naively expected that the observed time lag/sublimation radius changed by a factor of $20^{1/2} = 4.5$ (see Eq. \ref{eq:1}) )."
" Koshidaetal.(2009) conclude that the time lag changes from about ddays in the first 2/3 of the light curve to about ddays in the last 1/3, although at different scaling than (AL)'/?."," \citet{Kos09} conclude that the time lag changes from about days in the first 2/3 of the light curve to about days in the last 1/3, although at different scaling than $(\Delta L)^{1/2}$."
" If such a change were significant, we should have noticed a shift in the peaks when comparing observed and modeled light curves because our models assumes a constant time lag."," If such a change were significant, we should have noticed a shift in the peaks when comparing observed and modeled light curves because our models assumes a constant time lag."
" Over about ddays (19.7ray /c) the shift between observed and modeled light curve would be ~6r,,,/c."," Over about days $\sim13.7\,r_\mathrm{sub}/c$ ) the shift between observed and modeled light curve would be $\sim 6\,r_\mathrm{sub}/c$."
" However, such a shift is not seen in Fig. 6.."," However, such a shift is not seen in Fig. \ref{fig:n4151_mod1}."
 All the peaks and valleys in modeled and observed light curve overlap within less than 1ra5/c.," All the peaks and valleys in modeled and observed light curve overlap within less than $1\,r_\mathrm{sub}/c$."
" This would have also affected the comparison of observed and modeled CCF, but both are consistent within errors (see Fig. 7))."," This would have also affected the comparison of observed and modeled CCF, but both are consistent within errors (see Fig. \ref{fig:n4151_mod1_ccf}) )."
" In order to test even small effects of possible dust destruction and reformation, we removed the assumption of a constant time lag/sublimation radius and account for dust sublimation once it heats over the sublimation temperature (set as a free parameter) and instant or delayed reformation of the dust after cooling."," In order to test even small effects of possible dust destruction and reformation, we removed the assumption of a constant time lag/sublimation radius and account for dust sublimation once it heats over the sublimation temperature (set as a free parameter) and instant or delayed reformation of the dust after cooling."
 This changes the sublimation radius and time lag as the variability progresses through the torus., This changes the sublimation radius and time lag as the variability progresses through the torus.
" However we find that the smallest y? is always found for a model with constant sublimation radius/time lag, i.e. disfavoring significant dust destruction or reformation over the observed time span."," However we find that the smallest $\chi^2_\nu$ is always found for a model with constant sublimation radius/time lag, i.e. disfavoring significant dust destruction or reformation over the observed time span."
" This implies that the dust can either strongly overheat before it is destroyed, or that the dust is efficiently self-shielded."," This implies that the dust can either strongly overheat before it is destroyed, or that the dust is efficiently self-shielded."
 The survival of a dust grain depends on the balance between gas pressure and vapor pressure., The survival of a dust grain depends on the balance between gas pressure and vapor pressure.
" If partial gas pressure dominates, then a dust grain is stable; otherwise it evaporates."," If partial gas pressure dominates, then a dust grain is stable; otherwise it evaporates."
" The vapor pressure of dust, Pyapexp(-1/T), is a strong function of the temperature 7, while the partial pressure, pga,«T, depends only linearly on T."," The vapor pressure of dust, $p_\mathrm{vap}\propto \exp(-1/T)$ , is a strong function of the temperature $T$, while the partial pressure, $p_\mathrm{gas} \propto T$, depends only linearly on $T$."
" Therefore, we would expect that the lifetime of individual dust grains is short once they are heated over the sublimation temperature."," Therefore, we would expect that the lifetime of individual dust grains is short once they are heated over the sublimation temperature."
 As a consequence the observed behavior would favor shielding in a locally-dense environment instead of overheating of dust grains., As a consequence the observed behavior would favor shielding in a locally-dense environment instead of overheating of dust grains.
 This is consistent with the idea of a clumpy torus where the dust is confined in optically-thick clouds., This is consistent with the idea of a clumpy torus where the dust is confined in optically-thick clouds.
 A change in luminosity first acts on individual clouds which may sublimate part of their dust content but can resist longer overall at the same location than smoothly distributed dust that is not shielded locally., A change in luminosity first acts on individual clouds which may sublimate part of their dust content but can resist longer overall at the same location than smoothly distributed dust that is not shielded locally.
" This scenario may also explain the low wy value: If individual clouds close sublimation radius are heated up to the sublimation temperature (and above in corresponding equilibrium temperature) and their dust gets only gradually sublimated from the surface (e.g. as a “melting snowball”), their actual peak temperature would remain essentially constant, leading to a more or less constant K-band flux over some time."," This scenario may also explain the low $w_V$ value: If individual clouds close sublimation radius are heated up to the sublimation temperature (and above in corresponding equilibrium temperature) and their dust gets only gradually sublimated from the surface (e.g. as a “melting snowball”), their actual peak temperature would remain essentially constant, leading to a more or less constant $K$ -band flux over some time."
 Hence only cooler clouds would contribute to the variability on the same time scales as the incident radiation., Hence only cooler clouds would contribute to the variability on the same time scales as the incident radiation.
 We present model simulations of time-variable infrared emission from dust as a consequence of variability of the incident radiation., We present model simulations of time-variable infrared emission from dust as a consequence of variability of the incident radiation.
" For that we first introduce a generalized treatment for temperature variations, which can be used for all kind of dusty environments."," For that we first introduce a generalized treatment for temperature variations, which can be used for all kind of dusty environments."
 We apply this scheme to a simplified model of a (clumpy) dusty torus around AGN and investigate how variability of the accretion disk radiation influences the torus emission in the near- and mid-IR., We apply this scheme to a simplified model of a (clumpy) dusty torus around AGN and investigate how variability of the accretion disk radiation influences the torus emission in the near- and mid-IR.
 The main parameter of this model is the radial brightness distribution of the torus that has previously been shown to be connected to the radial distribution of the dust in the torus., The main parameter of this model is the radial brightness distribution of the torus that has previously been shown to be connected to the radial distribution of the dust in the torus.
 We showed that any variability signal in the optical is smoothened stronger if the brightness distribution is very extended., We showed that any variability signal in the optical is smoothened stronger if the brightness distribution is very extended.
" While this effect is true for both the near- and mid-IR, longer wavelengths show much wider transfer functions than short wavelengths."," While this effect is true for both the near- and mid-IR, longer wavelengths show much wider transfer functions than short wavelengths."
 The time lags between the optical and near-IR emission is mostly representing the light travel time from accretion disk to the sublimation radius independent of the brightness distribution., The time lags between the optical and near-IR emission is mostly representing the light travel time from accretion disk to the sublimation radius independent of the brightness distribution.
" For mid-IR wavelengths, however, time lags can become very long, up to 10s of rsup/c."," For mid-IR wavelengths, however, time lags can become very long, up to 10s of $r_\mathrm{sub}/c$."
" The effect that the brightness distribution influences the time lags seems to be much stronger than any similar effect frominclination (at least in type 1 AGN) or details of the shape of the inner torus, as recently presented by Kawaguchi&Mori (2011).."," The effect that the brightness distribution influences the time lags seems to be much stronger than any similar effect frominclination (at least in type 1 AGN) or details of the shape of the inner torus, as recently presented by \citet{Kaw11}. ."
 This change of lag, This change of lag
Even with the aperture correction it is still possible for there to be a systematic error in the amplitudes of variatious.,Even with the aperture correction it is still possible for there to be a systematic error in the amplitudes of variations.
 This would happen. for example. if there was a systematic error in the ISIS photometry that might result from errors in the subtraction process.," This would happen, for example, if there was a systematic error in the ISIS photometry that might result from errors in the subtraction process."
 To eusure that we are uot uuclerestimating the amplitucles of our Leht curves. aud hience overestimating our precision. we extracted photometry for a haucllul of situulated variable stars.," To ensure that we are not underestimating the amplitudes of our light curves, and hence overestimating our precision, we extracted photometry for a handful of simulated variable stars."
 To add the simulated variable stars we first identified a bright isolated star on one of the images aud extracted a small box arouud the star in every image., To add the simulated variable stars we first identified a bright isolated star on one of the images and extracted a small box around the star in every image.
 We then measured aud subtracted the sky from the box. multiplied the box by a scaling factor aud added the result to another location ou the unage.," We then measured and subtracted the sky from the box, multiplied the box by a scaling factor and added the result to another location on the image."
 In this way we simulated two variables stars with semi-aunuplitude f[Iux-variations of1096.. and196.," In this way we simulated two variables stars with semi-amplitude flux-variations of, and."
. We present the resulting light curves in Fie. 2.., We present the resulting light curves in Fig. \ref{fakelcs}.
 The purpose of this procedure was to test for systematic errors iu the amplitudes. we stress that the overall noise iu the light curves is uot representative of uoise expected for stars of this brightuess as extra nolse is iutrocuced in the sky subtraction process.," The purpose of this procedure was to test for systematic errors in the amplitudes, we stress that the overall noise in the light curves is not representative of noise expected for stars of this brightness as extra noise is introduced in the sky subtraction process."
 As is apparent [rom Fie. 2..," As is apparent from Fig. \ref{fakelcs},"
 the light curves are in good agreement with the simulated signal., the light curves are in good agreement with the simulated signal.
 Iu Fig., In Fig.
 3 we plot the RMS of each light curve versus the average maguituce for that light curve., \ref{lcstat_separate} we plot the RMS of each light curve versus the average magnitude for that light curve.
 We plot each night separately. for both the entire mosaic aud the best individual chip (labeled 21 in Fig. 1)).," We plot each night separately, for both the entire mosaic and the best individual chip (labeled 21 in Fig. \ref{fov}) )."
 For reference we also plot the 6.50 detection limits for Jupiter and Neptune sized trausiting planets., For reference we also plot the $6.5\sigma$ detection limits for Jupiter and Neptune sized transiting planets.
 These lines are defined by eq. [, These lines are defined by eq. [
3] in Mochejskaetal.(2002) where NV is the number of observatious in trausit. AZ? is the amplitude of the trausit. aud σ is set to 6.5.,"3] in \citet{mochejs02}
 where $N$ is the number of observations in transit, $\Delta R$ is the amplitude of the transit, and $\sigma$ is set to $6.5$."
 To calculate NV we use the length of a transit as given by eq. [, To calculate $N$ we use the length of a transit as given by eq. [
1] of Gillilandetal.(2000) where 7 and P? are iu days. aud the stellar mass. M. auc radius. 2). are in solar uuilts.,"1] of \citet{gilliland00}
 where $\tau$ and $P$ are in days, and the stellar mass, $M_{*}$, and radius, $R_{*}$ , are in solar units."
" To obtai AL, aud 2, as Duuctious of ruagnitude we generated isochroues [rom Cürardietal.(2000) usine the parameters for the cluster listed in 82.", To obtain $M_{*}$ and $R_{*}$ as functions of magnitude we generated isochrones from \citet{girardi00} using the parameters for the cluster listed in 2.
 The lines were then caleulated for a P= 3.5dday perio planet asstuning oue observes 3 full transits with two minute integrations taken every 3 minutes [or comparison with night 2. aud oue minute inteeratious taken every 2 minutes for comparison witl wight 3.," The lines were then calculated for a $P=3.5$ day period planet assuming one observes 3 full transits with two minute integrations taken every 3 minutes for comparison with night 2, and one minute integrations taken every 2 minutes for comparison with night 3."
 The implicatious of these lines are ciscussed iu 86., The implications of these lines are discussed in 6.
 There are a total of 378 stars that have RAIS < L πας on the second night. aud 9661 witl RMS < 10 uunae.," There are a total of 378 stars that have RMS $<$ 1 mmag on the second night, and 9661 with RMS $<$ 10 mmag."
 For the third night. with the shorter exposure times. we find 365 stars with RMS < μπας aud 5132 with RAIS < 10 μπας.," For the third night, with the shorter exposure times, we find 365 stars with RMS $<$ 1 mmag and 8132 with RMS $<$ 10 mmag."
 When the two nights are combined we find only 65, When the two nights are combined we find only 65
"the extent of the overlap between Mon, and the Si-rich ejecta depends on the main sequence mass Myg and initial metallicity of the WD progenitor (whichdetermineMore, and the SN brightness (see Figure 2)).","the extent of the overlap between $M_{conv}$ and the Si-rich ejecta depends on the main sequence mass $M_{MS}$ and initial metallicity of the WD progenitor \citep[which determine
$M_{core}$ and the SN brightness (see Figure \ref{fig-2}) )."
" This overlap is only significant for subluminous (Amis> Type Ia SNeoriginated by progenitors with either 1.6)large Ms or low Z, or both."," This overlap is only significant for subluminous $\Delta m_{15} \geq 1.6$ ) Type Ia SNeoriginated by progenitors with either large $M_{MS}$ or low $Z$, or both."
" Chamulaketal.(2008) find an upper limit for the increase of 7 during the simmering phase of An=0.0015, which is comparable to the value of η in solar material."," \citet{chamulak08:reduction_electron_simmering_SNIa} find an upper limit for the increase of $\eta$ during the simmering phase of $\Delta \eta=0.0015$, which is comparable to the value of $\eta$ in solar material."
" The impact of simmering on the Myxs/Mc, ratio can then be estimated by mixing material with Min/Mc,r=0.3 (appropriateforthevalueof Zoderivedby into the incomplete Si burning region, in a proportion2005) equivalent to the extent of the overlap shown in Figure 2.."," The impact of simmering on the $M_{Mn}/M_{Cr}$ ratio can then be estimated by mixing material with $M_{Mn}/M_{Cr}=0.3$ \citep[appropriate for the value of $Z_{\odot}$ derived into the incomplete Si burning region, in a proportion equivalent to the extent of the overlap shown in Figure \ref{fig-2}."
" The green and orange plots in Figure 1 are two examples ofsuch ‘simmering-modified’ models for very subluminous (Amis= 1.8) Type Ia SNe, illustrating our conclusion that C simmering will only modify the My,/Mo; ratio in the SN ejecta for very subluminous SNe, and then only in cases where Marg is large, or Z is low, or both."," The green and orange plots in Figure \ref{fig-1} are two examples ofsuch `simmering-modified' models for very subluminous $\Delta
m_{15}=1.8$ ) Type Ia SNe, illustrating our conclusion that C simmering will only modify the $M_{Mn}/M_{Cr}$ ratio in the SN ejecta for very subluminous SNe, and then only in cases where $M_{MS}$ is large, or $Z$ is low, or both."
 The work in this is motivated by the recent ddetection of Mn and Cr in the X-ray spectrum of the Tycho SN reported by Tamagawaetal. (see Figure 3))., The work in this is motivated by the recent detection of Mn and Cr in the X-ray spectrum of the Tycho SN reported by \citet{tamagawa08:Tycho_Suzaku} (see Figure \ref{fig-3}) ).
" This observational result opens(2008) the possibility of studying the Mjyrn/Mc, ratio in Type Ia SN ejecta, which cannot be done using optical SN spectra due to the 2.7 yr half-life of ??Fe in the decay chain 995Co—55Fe—55Mn."," This observational result opens the possibility of studying the $M_{Mn}/M_{Cr}$ ratio in Type Ia SN ejecta, which cannot be done using optical SN spectra due to the 2.7 yr half-life of $^{55}$ Fe in the decay chain $^{55}$ $\rightarrow ^{55}$ $\rightarrow ^{55}$ Mn."
" Since Mn and Cr are synthesized together in the explosion and have very similar electronic structures, it is possible to estimate their mass ratio from the line flux ratio: Mys/Mo,=1.057x(Fun/Fov)/(Eun Ecv), where 1.057 is the ratio of atomic masses, is the line flux ratio, and Ey/Ecy is the ratio of F'yn/Forspecific emissivities per ion."," Since Mn and Cr are synthesized together in the explosion and have very similar electronic structures, it is possible to estimate their mass ratio from the line flux ratio: $M_{Mn}/M_{Cr}=1.057 \times (F_{Mn}/F_{Cr})/(E_{Mn}/E_{Cr})$ , where $1.057$ is the ratio of atomic masses, $F_{Mn}/F_{Cr}$ is the line flux ratio, and $E_{Mn}/E_{Cr}$ is the ratio of specific emissivities per ion."
" Public data bases for X-ray astronomy do not usually include lines from trace elements like Mn and Cr, but the value of Ey4/Ec, can be estimated by interpolation along the atomic number sequence from elements with available data (Hwangetal.2000).."," Public data bases for X-ray astronomy do not usually include lines from trace elements like Mn and Cr, but the value of $E_{Mn}/E_{Cr}$ can be estimated by interpolation along the atomic number sequence from elements with available data \citep{hwang00:W49B}."
" We have used the ATOMDB data base (Smithetal.2001) to retrieve Ka line emissivities for Si, S, Ar, Ca, Fe, and Ni (Z4—14,16,18,20,26, 28) as a function of ionization timescale n,t and electron temperature kT, the two variables that control the line emission of a plasma in nonequilibrium ionization."," We have used the ATOMDB data base \citep{smith01:H_like_and_He_like_ions} to retrieve $\alpha$ line emissivities for Si, S, Ar, Ca, Fe, and Ni $Z_{A}=14,\,16,\,18,\,20,\,26,\,28$ ) as a function of ionization timescale $n_{e}t$ and electron temperature $kT$, the two variables that control the line emission of a plasma in nonequilibrium ionization."
" Then we performed spline interpolation to obtain Eysn/Ecr, which we aplot in Figure 4,, together with the region of the (n-t,kT) parameter space that is populated by young Type Ia SNRs (seetheAppendixinBadenesetal. 2007).."," Then we performed a spline interpolation to obtain $E_{Mn}/E_{Cr}$ , which we plot in Figure \ref{fig-4}, , together with the region of the $(n_{e}t,kT)$ parameter space that is populated by young Type Ia SNRs \citep[see the Appendix in][]{badenes07:outflows}. ."
 The uncertainty in the value of Ejy5/Ec;. comes from the variation within this region and the error introduced, The uncertainty in the value of $E_{Mn}/E_{Cr}$ comes from the variation within this region and the error introduced
aud a diffraction limited system. a couut rate of Lass.yp photous/sec is expected from ain =29.0 object in the J-baud with NGST. where δε is the total svstem efficiency.,"and a diffraction limited system, a count rate of $\sim 1.8 S_{eff}$ photons/sec is expected from a $m=29.0$ object in the J-band with NGST, where $S_{eff}$ is the total system efficiency."
 For exposure times longer than a few minutes. such observatious will be photon noise dominated. since a background of <10!photons/sec‘resolution eleinent is expected at Lilja.," For exposure times longer than a few minutes, such observations will be photon noise dominated, since a background of $<10^{-1}$photons/sec/resolution element is expected at $1.1\mu m$."
 So the required S/N Is acjeved in δε hrs of exposure., So the required $S/N$ is achieved in $17/S_{eff}$ hrs of exposure.
 For a population of stars at a redshift of +0.5 witha total hinunosity of 10L... the proxbilitv of the necessary variatiow is .so several thousaud such »»pulations need to be monitored to detect a sample of mmicroleusing events. (," For a population of stars at a redshift of $z\sim0.5$ with a total luminosity of $10^7\lsun$, the probability of the necessary variation is, so several thousand such populations need to be monitored to detect a sample of microlensing events. ("
Alhough deeper observations. focusing upo1 the fainter regions of ealaxies. will reveal sinilu scale fluctuatious iu -—DUu and ~56% of the pixels for populations of. respectively. 109L. alu 10 L.).,"Although deeper observations, focusing upon the fainter regions of galaxies, will reveal similar scale fluctuations in $\sim23\%$ and $\sim56\%$ of the pixels for populations of, respectively, $10^6\lsun$ and $10^5\lsun$ )."
 Of course. in a typical field. many resoution clemenuts ou the CCD camera will cover :0.5 galaxies. aud so the monitoring of the popuations may he achieved siuulancously.," Of course, in a typical field, many resolution elements on the CCD camera will cover $z \sim 0.5$ galaxies, and so the monitoring of the populations may be achieved simultaneously."
" [ENGST is resolution limite. each. resohtion clement will cover 0.001017,"," If NGST is resolution limited, each resolution element will cover $0.001 \Box{\scmd}$."
 For each resohtion clement to cove ra 10*L.. population atio0.5. requires the observation of a region of surface brightuess 21.παςΕΙ," For each resolution element to cover a $10^{7}\lsun$ population at $z \sim
0.5$, requires the observation of a region of surface brightness ${\rm
21.5 mag/\Box{\scmd}}$."
" In regions alter than 21.51ag/LI"". boxes larger than a resoltion element can be sunuued up. to eive a toal luminosity 104L..: the variability of these )oxes Cal also be studied with the penalty of asunall amount of extra skv niolse."," In regions fainter than ${\rm 21.5
mag/\Box{\scmd}}$, boxes larger than a resolution element can be summed up, to give a total luminosity $10^7\lsun$; the variability of these boxes can also be studied with the penalty of asmall amount of extra sky noise."
" The TDF field shows that the area du a vpieal 2&2! field. covereL by surface brightuess 2jSnagLU"" reeious of +—(0.5 ealaxies exceeds several teus of LI/, hat is. tens of thousands of NGST resolution elements."," The HDF field shows that the area in a typical $2'\times 2'$ field covered by surface brightness ${\rm > 21.5 mag/\Box{\scmd}}$ regions of $z=0.5$ galaxies exceeds several tens of $\Box{\scmd}$, that is, tens of thousands of NGST resolution elements."
" The above cosmological uicroleusime-iuduce variability wil be observed over a backeround of imtrimsic variability events. due to supernovac. variable stars aud galaxy sclense. as well as due to the inevitable Poisson roise in the observed counts,"," The above cosmological microlensing-induced variability will be observed over a background of intrinsic variability events, due to supernovae, variable stars and galaxy self-lensing, as well as due to the inevitable Poisson noise in the observed counts."
 Ulike current studies of ‘surface brightuess fluctuaions method or distauce deteriuuations out to galaxies at ~LOOALpe Cloury&Schueider1988:Thomsen.al.1998) which essentially requires single epoch observations. fo ideutifv mucrolensine iuduced variability a monitorius program ds required. allowing the ideutification of superuovae by their heht-curves aud peak Iuninosities.," Unlike current studies of `surface brightness fluctuations' method for distance determinations out to galaxies at $\sim100Mpc$ \citep{Tonry1988,Thomsen1997,Lauer1998} which essentially requires single epoch observations, to identify microlensing induced variability a monitoring program is required, allowing the identification of supernovae by their light-curves and peak luminosities."
" Supernuovae are also rare. as are variable stars with a luuinosity sufficient chough to influence the tota Iuninositv of populatious L~LOL... if a survey was fo focus on more luminous source pixels,"," Supernovae are also rare, as are variable stars with a luminosity sufficient enough to influence the total luminosity of populations $L\sim10^7L_\odot$, if a survey was to focus on more luminous source pixels."
 As with supernovae. these weπια also reveal themselves via their charactceristic light curves.," As with supernovae, these would also reveal themselves via their characteristic light curves."
 If the depth of the survey Is increaseLsuch that EL~10°L.. pixels are probed. the ubiquity of their variaions would rule against variatiolis iu the source population.," If the depth of the survey is increased such that $L\sim10^5L_\odot$ pixels are probed, the ubiquity of their variations would rule against variations in the source population."
 Tn the case of selflensing of ealaxy stars by MACTOs in the halo of the same galaxy provides a negligible coutribution as the optical depth is many orders of maenitude snaller than that due to the cosinological τοιoleuses considered here., In the case of self-lensing of galaxy stars by MACHOs in the halo of the same galaxy provides a negligible contribution as the optical depth is many orders of magnitude smaller than that due to the cosmological microlenses considered here.
" The main source of detecteG background eveuts is likely to be due to simple Poisson photon noise,", The main source of detected background events is likely to be due to simple Poisson photon noise.
 However. in the situation outlired above. 30 variations due to Poisson noise are approximately LO times less colon than the 30 uicroleusiug variations.," However, in the situation outlined above, $3\sigma$ variations due to Poisson noise are approximately 40 times less common than the $3\sigma$ microlensing variations."
 Data at two epochs woulk allow an iuifial feasibility study., Data at two epochs would allow an initial feasibility study.
 If he required variability rate is indeed observed. ollow-up oservations at further epochs should be takeu to uonitor the light curves of the variability eveuts. to distinguish microlensing events from uulenuse SHpOOrnova or nove events. and to reject variatiois due to Poisson nolse.," If the required variability rate is indeed observed, follow-up observations at further epochs should be taken to monitor the light curves of the variability events, to distinguish microlensing events from unlensed supernova or nova events, and to reject variations due to Poisson noise."
 The previous Section bas demonstrated. that he vpical fluctuations in the briehtuess of a )jxel is detectable iux Lleuds itself to future space-owed observatories., The previous Section has demonstrated that the typical fluctuations in the brightness of a pixel is detectable and lends itself to future space-based observatories.
 Dut are there amy aspects of nücroleusiug bv a cosmnologicallv. distributed xopulation tha would make them apparent with current technology?, But are there any aspects of microlensing by a cosmologically distributed population that would make them apparent with current technology?
 As noted earlier iu this paper. while the vast majority of stars will be maenified Y oa value cose to the theoretically expected mean (Equation 1)). very rarely a 8ar will undereo an extreme maesnification.," As noted earlier in this paper, while the vast majority of stars will be magnified by a value close to the theoretically expected mean (Equation \ref{meanamp}) ), very rarely a star will undergo an extreme magnification."
 The probabiliv that a particular star ds magnified bv au xtreme value ids fotxd by inteerating fle nuaenificatiou probability distribution. (Equation 5j). which is presented eraphically in Figure 8..," The probability that a particular star is magnified by an extreme value is found by integrating the magnification probability distribution (Equation \ref{probability}) ), which is presented graphically in Figure \ref{fig6}. ."
" For instance. ina lo’L, o»pulation. the LF of Figure elves ~OL stars with L~ 10'L.: if such a star were to be magnified by a factor of 20. it would alter the surface briehtness of the population"," For instance, in a $10^5\lsun$ population, the LF of Figure \ref{fig3} gives $\sim 0.1$ stars with $L \sim 10^4\lsun$ ; if such a star were to be magnified by a factor of 20, it would alter the surface brightness of the population"
"we obtain 47""=0.0007|OSS."" with standard. errors on the coellicients of 0.001. ancl 0.04. respectively.","we obtain $\gamma^{{\rm out}}_i = 0.0007 + 0.84 \gamma^{{\rm in}}_i$, with standard errors on the coefficients of 0.001 and 0.04, respectively."
" For the individual components we obtain 41""=0.002|0.9047"" with errors (.001..05) and 55""=0.0001|0.76523* with errors. (O01...4)."," For the individual components we obtain $\gamma^{{\rm out}}_{1} = 0.002 + 0.90
\gamma^{{\rm in}}_{1}$ with errors (.001,.05) and $\gamma^{{\rm
out}}_{2} = 0.0001 + 0.76 \gamma^{{\rm in}}_{2}$ with errors (.001,.04)."
" For the simulations we similarly obtain consistent results. namely. >SU—(0001|0.7947"" or combined components with respective standard errors of 001 and 0.09"," For the simulations we similarly obtain consistent results, namely $\gamma^{{\rm out}}_{i} = 0.0001 + 0.79 \gamma^{{\rm
in}}_{i}$ for combined components with respective standard errors of 0.001 and 0.091."
 We sec that the measure of shear is symmetrical about zero. but is measuring a slightly smaller shear signal han the input shear.," We see that the measure of shear is symmetrical about zero, but is measuring a slightly smaller shear signal than the input shear."
" In simülar conditions. we should herefore. adjust our shear measures by dividing 5, by 9c0.05 and το by 0.76+0.04 when using this KSB implementation."," In similar conditions, we should therefore adjust our shear measures by dividing $\gamma_1$ by $0.9\pm0.05$ and $\gamma_2$ by $0.76\pm0.04$ when using this KSB implementation."
 A full discussion. of the recovery of rms shears using an extensive statistical analvsis can be found in BIE. including discussion of the recovery of rms shears from sets of simulated fields.," A full discussion of the recovery of rms shears using an extensive statistical analysis can be found in BRE, including discussion of the recovery of rms shears from sets of simulated fields."
 Of sreat practical interest js. the dependence. of the sensitivity of weak lensing measurements on secing., Of great practical interest is the dependence of the sensitivity of weak lensing measurements on seeing.
 To study this dependence. we ran several simulations with the same object catalogue. but with dillerent seeing values. for a setexposure time of 1 hour.," To study this dependence, we ran several simulations with the same object catalogue, but with different seeing values, for a setexposure time of 1 hour."
 For cach simulated S8S simulated field. we computed the rms noise meis=0-VN. where σ. is the rms of shear measures in a single field. and IN is the number of usable galaxies in the field.," For each simulated $8'\times8'$ simulated field, we computed the rms noise $\sigma_{\rm
noise} \equiv \sigma_\gamma/\sqrt{N}$, where $\sigma_\gamma$ is the rms of shear measures in a single field, and $N$ is the number of usable galaxies in the field."
 The quantity mois is à measure of the uncertainty for measuring the average shear in the field., The quantity $\sigma_{\rm noise}$ is a measure of the uncertainty for measuring the average shear in the field.
 The results are shown in table 2) and figure S.., The results are shown in table \ref{tab:seeing} and figure \ref{fig:seeing}.
 As can »* seen in the figure. the seeing degrades the uncertainty almost linearly.," As can be seen in the figure, the seeing degrades the uncertainty almost linearly."
 Interestingly. the loss of sensitivity comes »wimarilv from the loss in the number No of usable galaxies. with no strong increase observed in σ- (see table 2)).," Interestingly, the loss of sensitivity comes primarily from the loss in the number $N$ of usable galaxies, with no strong increase observed in $\sigma_{\gamma}$ (see table \ref{tab:seeing}) )."
 One mieht suppose that this degradation could be countered by onger integrations on the field. to regain the number counts diluted by the larger isotropic smear.," One might suppose that this degradation could be countered by longer integrations on the field, to regain the number counts diluted by the larger isotropic smear."
 However. besides he integration time increase being considerable for such a reclamation of number density (see section 5.5)). many of he regained galaxies will still need to be excluced as their shape information has been erased by a kernel significantly arger than their intrinsic radius.," However, besides the integration time increase being considerable for such a reclamation of number density (see section \ref{time}) ), many of the regained galaxies will still need to be excluded as their shape information has been erased by a kernel significantly larger than their intrinsic radius."
 The noise could. perhaps » reduced by improved shear-measuremoent methods. which reduce the cuts we have to make on small galaxics.," The noise could perhaps be reduced by improved shear-measurement methods, which reduce the cuts we have to make on small galaxies."
 Note that. for worse secing cases. the usable galaxies will be on average brighter and larger ancl will thus have a ower median redshift.," Note that, for worse seeing cases, the usable galaxies will be on average brighter and larger and will thus have a lower median redshift."
 Phis will tend to degrade the lensing signal further., This will tend to degrade the lensing signal further.
" For a cluster normalised CDM που, the shear rms [rom lensing in an N cell is ej,c0.012277 (DIU)."," For a cluster normalised CDM model, the shear rms from lensing in an $\times$ 8' cell is $\sigma_{\rm lens} \simeq 0.012 z_{m}^{0.8}$ (BRE)."
 The median redshift. ο of the galaxies is derived rom the median Z?-magnitude using the results of Cohen et al (2000)., The median redshift $z_{m}$ of the galaxies is derived from the median $R$ -magnitude using the results of Cohen et al (2000).
 “Phe resulting lensing rms aya. is also plotted as a unction of seeing in figure S.. and the signal-to-noise ratio or à single (οκ) cell. S/N=thanf/uoiae ds listed in table 2..," The resulting lensing rms $\sigma_{\rm lens}$ is also plotted as a function of seeing in figure \ref{fig:seeing}, and the signal-to-noise ratio for a single (8'x8') cell, $S/N = \sigma_{\rm lens}/\sigma_{\rm
noise}$ is listed in table \ref{tab:seeing}."
 We find that the reduction of a)... with poorer seeing is rather weak., We find that the reduction of $\sigma_{\rm lens}$ with poorer seeing is rather weak.
 Vhus the reduction of signal-to-noise for shear measurement is again dominated by the decrease in j|., Thus the reduction of signal-to-noise for shear measurement is again dominated by the decrease in $N$.
 ‘Lo optimise weak lensing surveys. one needs to conipromise between depth and width.," To optimise weak lensing surveys, one needs to compromise between depth and width."
 To help in this optimisation. we produced. several sipiulated: images for. dilferent. exposure times. while keeping the seeing at O.S.," To help in this optimisation, we produced several simulated images for different exposure times, while keeping the seeing at 0.8”."
 Table 3. shows the quantities discussed. in the previous section for cillerent exposure times relevant for grouncd-basecl observations., Table \ref{tab:time} shows the quantities discussed in the previous section for different exposure times relevant for ground-based observations.
 The noise and lensing rms are plotted. on figure 9..., The noise and lensing rms are plotted on figure \ref{fig:time}. .
 The dependence of these quantities on exposure time is rather weak., The dependence of these quantities on exposure time is rather weak.
 This is due to the fact that the fainter galaxies which, This is due to the fact that the fainter galaxies which
The study of galaxy. formation and evolution Προς the availability of statistical samples at longe look-back times.,The study of galaxy formation and evolution implies the availability of statistical samples at large look-back times.
 At large redshifts. though. only star forming galaxies will be entering the samples obtained iu the visible bauds aud. to be able to probe their stellar masses. observations at longer waveleuethns are reeded.," At large redshifts, though, only star forming galaxies will be entering the samples obtained in the visible bands and, to be able to probe their stellar masses, observations at longer wavelengths are needed."
 Iu the last decade. deep photometric galaxy. samples have become available. namely through the observations by IST of the ΠΟΤΕ (Williams et citewillams)) aud IIDE-S (Casertano ot citecasertauo)). which have been coordinated with complementary observations from the eround at nem-infrared (NIR) wavelengths (Dickinson et al.2000: da Costa ct citedacosta)).," In the last decade, deep photometric galaxy samples have become available, namely through the observations by HST of the HDF-N (Williams et \\cite{williams}) ) and HDF-S (Casertano et \\cite{casertano}) ), which have been coordinated with complementary observations from the ground at near-infrared (NIR) wavelengths (Dickinson et \cite{dick}; da Costa et \\cite{dacosta}) )."
 At the same time. reliable photometric redshift techuiques have heen developed. allowing estimates of the distances of faint salaxies for which no spectroscopic redshifts can be obtained nowadays. even with the most powerful telescopes CCounolly et al. citecon::," At the same time, reliable photometric redshift techniques have been developed, allowing estimates of the distances of faint galaxies for which no spectroscopic redshifts can be obtained nowadays, even with the most powerful telescopes Connolly et al. \\cite{con};"
 Wang ct οσα Cdallongo ct citegiaz: Fernáuudez-Soto et citefsoto:: Arnouts et citearnouts:: Furusiwa et al. 2000:, Wang et \\cite{wan}; ; Giallongo et \\cite{gia}; Fernánndez-Soto et \\cite{fsoto}; ; Arnouts et \\cite{arnouts}; Furusawa et al. \cite{furu};
 Bodiehiero et citerodighliero: Le Borgne Rocca-Volincrange 2002:: Bolzouclla et citelyperz and the references therein)., Rodighiero et \\cite{rodighiero}; Le Borgne Rocca-Volmerange \cite{leborgne}; Bolzonella et \\cite{hyperz} and the references therein).
 Oue of the nain issues for photometric redshifts is fo studv the evolution of galaxies bevoik the spectroscopic limits., One of the main issues for photometric redshifts is to study the evolution of galaxies beyond the spectroscopic limits.
 The relatively ligh iuuber ofobjects accessible to plotometiy per redshift bin allows to enluge the spectroscopic samples towards the faintest magnitudes. thus inereasing the umber of objects accessible to statistical studies per redshift biu.," The relatively high number of objects accessible to photometry per redshift bin allows to enlarge the spectroscopic samples towards the faintest magnitudes, thus increasing the number of objects accessible to statistical studies per redshift bin."
 Such slicing procedure cau be adopted to derive. for instance. redshift distributions. huuinmositv fictions iu cliffereut xuids. or rest-frame colours as a function of absolute uaenitudes. among the relevant quautities to compare with the predictions derived from the different models of ealaxy formation and evolution.," Such slicing procedure can be adopted to derive, for instance, redshift distributions, luminosity functions in different bands, or rest-frame colours as a function of absolute magnitudes, among the relevant quantities to compare with the predictions derived from the different models of galaxy formation and evolution."
 This approach has con. recently used to infer the star formation history at veh redshift from the UV. huninosity density. to analyse he stellar population aud the evolutionary properties of distant galaxies SSubbaltao ct citesubbar: Carvin Hartwick 1996:: Sawicki ct citesawicki:: Connolly et citecon: Pascarelle et citepascarclle:: Cdallougo et citegia:: Fernánnudoez-Soto et citefsoto:: Poli et citepoli}). or to derive the evolution of the clusteriug properties (Arnouts et citearnouts:: Maeliocchetti Maddox 1999... Arnouts et fa earnouts2)).," This approach has been recently used to infer the star formation history at high redshift from the UV luminosity density, to analyse the stellar population and the evolutionary properties of distant galaxies SubbaRao et \\cite{subba}; Gwyn Hartwick \cite{gwyn}; Sawicki et \\cite{sawicki}; ; Connolly et \\cite{con}; Pascarelle et \\cite{pascarelle}; Giallongo et \\cite{gia}; Fernánndez-Soto et \\cite{fsoto}; Poli et \\cite{poli}) ), or to derive the evolution of the clustering properties (Arnouts et \\cite{arnouts}; Magliocchetti Maddox \cite{maglio}, Arnouts et \\cite{arnouts2}) )."
 We have developed a method to compute ποτν -—uctions (hereafter LEx). based on our public code +> determine photometric redshifts (Bolzonella ct ae tehvperz))," We have developed a method to compute luminosity functions (hereafter LFs), based on our public code to determine photometric redshifts (Bolzonella et \\cite{hyperz}) )."
 This original method is a Monte Carlo o»proach. different from the oues proposed by SubbaRao et al. (1996))," This original method is a Monte Carlo approach, different from the ones proposed by SubbaRao et al. \cite{subba}) )"
 aud Dye et al. (2001)), and Dye et al. \cite{dye}) )
 iu the wav of accounting for the non-eaussianity of the probability fictions. aud specially o include cegenerate solutions in redshift.," in the way of accounting for the non-gaussianity of the probability functions, and specially to include degenerate solutions in redshift."
 Iu this paper we preseut the nethod aud the tests performed ou mock catalogues. aud we apply it specifically to derive NIR LFs aud their evolution ou the IIDE-N ane IIDF-S. The NIR Iuuimositv is directly linked to the tota stellarmass. and barelyaffected by the presence of dust extinction or starbursts.," In this paper we present the method and the tests performed on mock catalogues, and we apply it specifically to derive NIR LFs and their evolution on the HDF-N and HDF-S. The NIR luminosity is directly linked to the total stellarmass, and barelyaffected by the presence of dust extinction or starbursts."
 According to Nanffinann Charlot (1998)). the NIR LF and its evolution coustitute a powerfultest to discriminate between the differeu scenarios of ealaxy formation. nf galaxies were assembled early. according to a mouolithic scenario. or," According to Kauffmann Charlot \cite{kauff}) ), the NIR LF and its evolution constitute a powerfultest to discriminate between the different scenarios of galaxy formation, if galaxies were assembled early, according to a monolithic scenario, or"
where we take Re=5f|Mpe. Because we expect to studs preferentially large voids with a cliameter of 10h*Alpe. tlis scale seems appropriate.,where we take $R_{s}=5\:\hMpcDot$ Because we expect to study preferentially large voids with a diameter of $\sim 10\:\hMpcCom$ this scale seems appropriate.
 Note tha because we have only followed galaxy formation in t1e central. roughly. spherical. high-resolution region of simuation (with radius SOO0kms.+). we also use a shell of Leav-resolution particles immediately bevond to get the correc estimate of the DM density at mesh points near the bouncary.," Note that because we have only followed galaxy formation in the central, roughly spherical, high-resolution region of simulation (with radius $\sim8000\:\kmsKC$ we also use a shell of low-resolution particles immediately beyond to get the correct estimate of the DM density at mesh points near the boundary."
 Once we have sampled the smoothed DX field. we then simply interpolate the overdensities compute on the erid to he positions of the DM haloes (given by their most bound peuticle) or ofthe galaxies.," Once we have sampled the smoothed DM field, we then simply interpolate the overdensities computed on the grid to the positions of the DM haloes (given by their most bound particle) or of the galaxies."
 We consicer then the normalized cumulative counts of he number of galaxies (the population fraction) above a eiven mass overdensity threshold. as a function of decreasing overdensity. starting from ὃςz30 the maximum we fin or the 5h.1Alpe smoothing length we use.," We consider then the normalized cumulative counts of the number of galaxies (the population fraction) above a given mass overdensity threshold, as a function of decreasing overdensity, starting from $\delta_{s}\ga30$ the maximum we find for the $5\:\hMpc$ smoothing length we use."
 Lf the galaxies of some test population reside preferentially in low-density. environments. this will appear as a late rise of the cumulative raction with decreasing DAL overdensity.. compared. for instance. to the behaviour of the reference galaxies.," If the galaxies of some test population reside preferentially in low-density environments, this will appear as a late rise of the cumulative fraction with decreasing DM overdensity, compared, for instance, to the behaviour of the reference galaxies."
 ὃν construction. the cumulative plots obtained. from 10 galaxy positions are mass- rather than voltume-weighted.," By construction, the cumulative plots obtained from the galaxy positions are mass- rather than volume-weighted."
 The visual impression from the pictures of KOO recalled. by 01 is one of very lew simulated galaxies in the voids. with 1e latter filling a substantial fraction of space.," The visual impression from the pictures of K99 recalled by P01 is one of very few simulated galaxies in the voids, with the latter filling a substantial fraction of space."
 A simple way ο assess the departure of the distribution of galaxies from a homogenous one with the tools of this Section is to use 1e regular mesh from which we have interpolated the DM density to the galaxy positions., A simple way to assess the departure of the distribution of galaxies from a homogenous one with the tools of this Section is to use the regular mesh from which we have interpolated the DM density to the galaxy positions.
 In the four plots of Fig 2.. the repeated dotted [line gives the cumulative fraction of mesh »onts above a given. smoothed DAL overdensity threshold: it shoulel be viewed as the simulation volume fraction above he threshold.," In the four plots of Fig \ref{fig:Cumul5MpcFig}, the repeated dotted line gives the cumulative fraction of mesh points above a given smoothed DM overdensity threshold: it should be viewed as the simulation volume fraction above the threshold."
" We will denote this “mesh sample"" with and note that half of the simulation volume has a DM environment density of ὃς below -0.24 and only about a third of it has higher than average density.", We will denote this “mesh sample” with and note that half of the simulation volume has a DM environment density of $\delta_{s}$ below -0.24 and only about a third of it has higher than average density.
 In the same four plots. we also repeat the cumulative fraction of the reference galaxies with a solid linc.," In the same four plots, we also repeat the cumulative fraction of the reference galaxies with a solid line."
 This line is very close to that we find for the DM particles themselves (thus for the “mass” in the simulation) and is a translation bv almost a factor 2 towards higher density from the cumulative fraction: each population fraction is reached in the sample at twice the DM density needed to reach the same fraction for the uniformly. distributed population., This line is very close to that we find for the DM particles themselves (thus for the “mass” in the simulation) and is a translation by almost a factor 2 towards higher density from the cumulative fraction: each population fraction is reached in the sample at twice the DM density needed to reach the same fraction for the uniformly distributed population.
 In the top left panel of Fig., In the top left panel of Fig.
 2 we show with dashed lines the normalized cumulative counts of the halo samples selected by mass (£A)., \ref{fig:Cumul5MpcFig} we show with dashed lines the normalized cumulative counts of the halo samples selected by mass ).
 In each of the four plots of Fig., In each of the four plots of Fig.
 2 that we discuss here. the lowest ancl highest sample indices (/=1 and i£= 7) correspond to the leftmost and rightmost dashed curves. respectively. with a monotonic variation for the samples in between.," \ref{fig:Cumul5MpcFig} that we discuss here, the lowest and highest sample indices $i=1$ and $i=7$ ) correspond to the leftmost and rightmost dashed curves, respectively, with a monotonic variation for the samples in between."
" The first three halo samples to contain haloes with masses Mua<Ad, where as usual we defino AZ, such that e(AM,)=Ooi~1.69 (M,~14410. here)."," The first three halo samples to contain haloes with masses $M_{\rmn{tot}}\la
M_{*}$, where as usual we define $M_{*}$ such that $\sigma(M_{*})=\delta_{\rmn{crit}}\sim1.69$ $M_{*}\sim 1.44\times 10^{13} \msun$ here)."
 The behaviours of the fractions of cumulative counts for these three halo samples are. very similar: at overdensities under ὃς~0.6 they depart slightly from the counts of the sample. favoring lower density environments.," The behaviours of the fractions of cumulative counts for these three halo samples are very similar: at overdensities under $\delta_{\tx{s}}\sim0.6$ they depart slightly from the counts of the sample, favoring lower density environments."
 However. the plots are still far. from. the cumulative fraction for the grid. counts: the population of haloes is complete for ὃς270.3. while a third. of the simulation volume is at such low censities.," However, the plots are still far from the cumulative fraction for the grid counts; the population of haloes is complete for $\delta_{\tx{s}}\geq-0.3$, while a third of the simulation volume is at such low densities."
 While the plot of almost coincides with the cumulative fraction of the ealaxies are central galaxies of haloes. anc of them are central galaxies of haloes). the three most. massive halo bins separate strongly from each other ancl from the fraction.," While the plot of almost coincides with the cumulative fraction of the galaxies are central galaxies of haloes, and of them are central galaxies of haloes), the three most massive halo bins separate strongly from each other and from the fraction."
 This is a clear effect of the non-linearity of halo bias: according to the model of Mo&White(1996).. one WELLES: where 7=derifo(AL).," This is a clear effect of the non-linearity of halo bias: according to the model of \citet{Mo96a}, one writes: where $\nu=\delta_{\rmn{crit}}/\sigma(M)$."
" Haloes less massive than AM, are antibiased. haloes close to Ad. like are unbiased. and the bias becomes more and more substantial as one urther increases the mass."," Haloes less massive than $M_{*}$ are antibiased, haloes close to $M_{*}$ like are unbiased, and the bias becomes more and more substantial as one further increases the mass."
 Llaloes of the most massive sample completely avoid low and mean density. regions (recall also that the particles of a given halo contribute to he smoothed DM density estimation of the regionit resides in)., Haloes of the most massive sample completely avoid low and mean density regions (recall also that the particles of a given halo contribute to the smoothed DM density estimation of the regionit resides in).
" In particular. there are no haloes in the sample ving in environments with 9,<1.5."," In particular, there are no haloes in the sample lying in environments with $\delta_{\tx{s}}\leq1.5$."
 The top right. panel of Fig., The top right panel of Fig.
 2. shows the cumulative raction of the galaxy samples binned by their. luminosity (CL;))., \ref{fig:Cumul5MpcFig} shows the cumulative fraction of the galaxy samples binned by their luminosity ).
 The trends are similar to those of the halo samples selected. by their total DAL mass. but except for the most uminous sample. the range of variation of galaxy bias is much reduced.," The trends are similar to those of the halo samples selected by their total DM mass, but except for the most luminous sample, the range of variation of galaxy bias is much reduced."
 Of course this is due to the fact that there is no tight relation between a halo mass and the luminosity. of its central galaxy. and that a given galaxy. luminosity sample has contributions from several cillering halo samples.," Of course this is due to the fact that there is no tight relation between a halo mass and the luminosity of its central galaxy, and that a given galaxy luminosity sample has contributions from several differing halo samples."
 An example of this dilution is the cumulative fraction of the counts of the first four galaxy saniples. which are very similar. and are very close to the sample.," An example of this dilution is the cumulative fraction of the counts of the first four galaxy samples, which are very similar, and are very close to the sample."
 Phe range of luminosities of the sample encompasses those of the and samples together., The range of luminosities of the sample encompasses those of the and samples together.
 The further mateh with the to samples shows that the population of faint galaxies (i.e. taken globally in the samples and. selected solely by. Luminosity) does not constitute a void population., The further match with the to samples shows that the population of faint galaxies (i.e. taken globally in the samples and selected solely by luminosity) does not constitute a void population.
" and galaxies increasingly tend to avoid underdense regions (9,<= 0) where a few galaxies are found.", and galaxies increasingly tend to avoid underdense regions $\delta_{\tx{s}}\leq0$ ) where a few galaxies are found.
 Phe most luminous bin.€L;.. with only 29 galaxies. contains of course a fair fraction of ealaxies in very dense environments (BCGs in regions with ὃν~ 10).," The most luminous bin, with only 29 galaxies, contains of course a fair fraction of galaxies in very dense environments (BCGs in regions with $\delta_{\tx{s}}\sim10$ )."
 Hlowever. as compared toΛ5.. there also very bright galaxies in the in mean density regions: these are galaxies which have undergone a recent merger and are currently starbursting: among the 7 galaxies of the sample with ὃςx 0.5. 5 have a colour index," However, as compared to, there also very bright galaxies in the in mean density regions: these are galaxies which have undergone a recent merger and are currently starbursting: among the 7 galaxies of the sample with $\delta_{\tx{s}}\leq0.5$ , 5 have a colour index"
profiles with the task inIRAF!.,profiles with the task in.
. We decomposed these mass profiles into a central Sérrsic component plus an outer exponential disk: a Sérrsic law is usually used in modeling bulge light profiles (AndreclakisGraham2001;MacArthuretal. 2003).," We decomposed these mass profiles into a central Sérrsic component plus an outer exponential disk; a Sérrsic law is usually used in modeling bulge light profiles \citep{apb95,g01,mch03}."
. We stress that by decomposing the final density profiles into a “bulge” plus disk component we are not implvine that secular evolution has produced. three-dimensional bulges., We stress that by decomposing the final density profiles into a “bulge” plus disk component we are not implying that secular evolution has produced three-dimensional bulges.
" Nonetheless. lor brevity. we will refer to as “bulges” the central Sérvsic components. and as ""disks"" the exponential components."," Nonetheless, for brevity, we will refer to as “bulges” the central Sérrsic components, and as “disks” the exponential components."
 Our Sérrsic bulge plus exponential disk decompositions are characterized bv live parameters: Mi: Sop. Che disk and (he bulge central surface densities. respectively: A. the scale-length of (he outer exponential disk: Γή. the hall-light radius of the bulge: and à. the index of the Sérrsie profile.," Our Sérrsic bulge plus exponential disk decompositions are characterized by five parameters: $\Sigma_{0,d}$, $\Sigma_{0,b}$, the disk and the bulge central surface densities, respectively; $R_d$, the scale-length of the outer exponential disk; $R_{b,eff}$, the half-light radius of the bulge; and $n_b$, the index of the Sérrsic profile."
" In light of the ill-conditioned fitting described by MacArthuretal.(2003).. mp was held fixed with respect to the remaining four parameters when searching lor the best-fitting models: the best-fitting 7; was then identified as the one giving the smallest. A? when repeating the fits with 0.1xn»,<d in steps of 0.1."," In light of the ill-conditioned fitting described by \citet{mch03}, $n_b$ was held fixed with respect to the remaining four parameters when searching for the best-fitting models; the best-fitting $n_b$ was then identified as the one giving the smallest $\chi^2$ when repeating the fits with $0.1 \leq n_b \leq 4$ in steps of 0.1."
" The five parameters derived from the bulge/disk decompositions allow us to compute three dimensionless structural quantities to compare with observations: nj. Hy,ΕΕ)Πω and B/D. the ratio of bulge to disk nass (we assumed a constant mass-to-light ratio when comparing with the light-weiehted nmeasurenienis available for real galaxies)."," The five parameters derived from the bulge/disk decompositions allow us to compute three dimensionless structural quantities to compare with observations: $n_b$, $R_{b,eff}/R_d$ and $B/D$, the ratio of bulge to disk mass (we assumed a constant mass-to-light ratio when comparing with the light-weighted measurements available for real galaxies)."
 We also measured the bulge ellipticitv. ej. the line-ol-sight. velocity dispersion. a (by averaging the corresponding profiles within some radial range). and Ἐν. the peak line-ol-sight velocity within the same radial range on the disk major-axis.," We also measured the bulge ellipticity, $\epsilon_{\rm b}$, the line-of-sight velocity dispersion, $\bar{\sigma}$ (by averaging the corresponding profiles within some radial range), and $V_p$, the peak line-of-sight velocity within the same radial range on the disk major-axis."
" These allow us to compute V,/6 to investigate the kinematic properties of the resulting bulges in the pi V,/6 versus ει, plane.", These allow us to compute $V_p$ $\bar{\sigma}$ to investigate the kinematic properties of the resulting bulges in the $V_p$ $\bar{\sigma}$ versus $\epsilon_{\rm b}$ plane.
 In (his plane. normal bulges are thought to follow the locus (traced by isotropic oblate rotators (Binnev&Tremaine1987).. and bulges that result from the secular evolution of disks are thought to emerge as svstems (hat are dynamically colder (han isotropic oblate rotators (IXormends.1993:IXormendsyetal.2002).," In this plane, normal bulges are thought to follow the locus traced by isotropic oblate rotators \citep{bt87}, and bulges that result from the secular evolution of disks are thought to emerge as systems that are dynamically colder than isotropic oblate rotators \citep{k93,kbb02}."
. Rigid halo simulations are better suited to svstems in which the disk is dominant in ihe inner regions (as are the simulations discussed here). because the interaction with the halo is then weaker.," Rigid halo simulations are better suited to systems in which the disk is dominant in the inner regions (as are the simulations discussed here), because the interaction with the halo is then weaker."
 While massive disks represent a reasonable assumption for high surface, While massive disks represent a reasonable assumption for high surface
thus. ist the end. of where the bursts cwell.,"thus, in the end, of where the bursts dwell."
 Thei alterglow observaious could fix the enviroumel parameters had been noticed already in the literalre: what is new here is the realization that t1e ciffereice in environmental «ensities controls he tinie-delay as uitch as the ejecta Lorenz [actor. aud thuis that the time-delay can be turned into a sensitive measure of the bursts’ whereabouts.," That afterglow observations could fix the environment parameters had been noticed already in the literature; what is new here is the realization that the difference in environmental densities controls the time–delay as much as the ejecta Lorenz factor, and thus that the time–delay can be turned into a sensitive measure of the bursts' whereabouts."
" Wlat happens between he eud of the bu""p ‘oper aud the οιset of the afterglow?", What happens between the end of the burst proper and the onset of the afterglow?
 ElectrorS acceerated at internal shocks. botl by quasi-iermal aud Fermi p'Ocesses. cool much faster thali the |Nrodsaiunical expausio1 time-scale. (Sari. Narayan aud Piran 1996).," Electrons accelerated at internal shocks, both by quasi–thermal and Fermi processes, cool much faster than the hydrodynamical expansion time–scale, (Sari, Narayan and Piran 1996)."
" However. some electroi« wil je accelerated at the fo""wald shock whicl seyarates the siurroundiug medium from shocked Inhalter already. raked up by the ejecta."," However, some electrons will be accelerated at the forward shock which separates the surrounding medium from shocked matter already raked up by the ejecta."
 Since the rate at which matter is raked up is roughly COLSalt. we cau take as a ivst’ approximatio1 that the total emitted power is a coustaut. [or whic Lan upper limit cau be fou as follows.," Since the rate at which matter is raked up is roughly constant, we can take as a first approximation that the total emitted power is a constant, for which an upper limit can be found as follows."
 The shock slows down when the total swept up mass (inles >) equals the ejecta mass., The shock slows down when the total swept up mass (times $\gamma$ ) equals the ejecta mass.
 Witin this time interval. then. about hall of the total energy is transfered to the swept Up Lass: if this were hielily radiative. then the total emitted power would be of order Ezc£um which is much simaer (by the factor /5/£/4. where €cAv0.1 is the ratio of relative to bulk kineic energy of the winel) iur the burst luminosity.," Within this time interval, then, about half of the total energy is transfered to the swept up mass; if this were highly radiative, then the total emitted power would be of order $\dot{E} \approx \frac{E}{t_d}$ which is much smaller (by the factor $t_{b}/\xi t_d$, where $\xi
\approx 0.1$ is the ratio of relative to bulk kinetic energy of the wind) than the burst luminosity."
" However. this is au ipper lunit. because. thowel electrons are hieuly ""adiative. this estimate imiplies that they are able to racliate away also al ol the thermal energy o ‘the protons."," However, this is an upper limit, because, though electrons are highly radiative, this estimate implies that they are able to radiate away also all of the thermal energy of the protons."
 Since it is generally assuiued. (adit can be checked in the observatious of the afterglow of GRB 970508. Frail. Waxman aud Ixkarni 2000) that ouly a ractlon e«42:0.1 of the protons’ energy can be transfered from the protons to tle electrons. tlis assituption is excessive by the same factor. e;4.," Since it is generally assumed (and it can be checked in the observations of the afterglow of GRB 970508, Frail, Waxman and Kulkarni 2000) that only a fraction $\epsilon_{eq} \approx 0.1$ of the protons' energy can be transferred from the protons to the electrons, this assumption is excessive by the same factor, $\epsilon_{eq}$."
 The exact luminosity racjated duri18oO this coasting pliase 1s «ilficult to predict exactly. since it depends criically upon rateruncertaiu lasina factors. like the elficiency e; with which energy is trauferred [rou protous to electrons. the iciency ej; with whie La near-equipartition magnetic field is built up. aud the relaive efficiency : quasi-therimal to Feruin processes.," The exact luminosity radiated during this coasting phase is difficult to predict exactly, since it depends critically upon ratheruncertain plasma factors, like the efficiency $\epsilon_{eq}$ with which energy is tranferred from protons to electrons, the efficiency $\epsilon_B$ with which a near–equipartition magnetic field is built up, and the relative efficiency of quasi–thermal to Fermi processes."
 However. for the preseut aim. this exact value is unnecessary: {lice it to say that a 'easouable expectation is that What happeus alter shock deceleration has been described. for different values of the parameters. by Mésszárros. Laguna and Rees (1993).," However, for the present aim, this exact value is unnecessary: suffice it to say that a reasonable expectation is that What happens after shock deceleration has been described, for different values of the parameters, by Mésszárros, Laguna and Rees (1993)."
" Basically. a reverse shock wil propagate at moclerate Lorenz factors backwa«d into the ejecta. dissipating au appreciable fract101 of the kinetic energy of the shell within a tinescale Rug/>>7c. which. is. the appareut time. in"" wlicl the shock crosses the ejecta shell. zz /y."," Basically, a reverse shock will propagate at moderate Lorenz factors backward into the ejecta, dissipating an appreciable fraction of the kinetic energy of the shell within a timescale $R_{ag}/\gamma^2 c$, which is the apparent time in which the shock crosses the ejecta shell, $\approx t_d$ ."
 Thus the maximum expeced power is exactly a [racion /5/£fq below hat of the burst., Thus the maximum expected power is exactly a fraction $t_{b}/\xi t_d$ below that of the burst.
 Notice that. in the previous sectiou. this was ouly au upper |init.," Notice that, in the previous section, this was only an upper limit."
 This internal shock provides a new. secouc phase of emission. of total duration comparable [9] he light crossing time oftle ejecta shell. fy.," This internal shock provides a new, second phase of emission, of total duration comparable to the light crossing time of the ejecta shell, $t_d$."
 Alter this peak Iuulnosity we then expec the usual afterglow (x/' |J o begin., After this peak luminosity we then expect the usual afterglow $\propto t^{-\alpha}$ ) to begin.
 A qualitative description of this cat be seen in Fie., A qualitative description of this can be seen in Fig.
 l., 1.
 Diring the afterglow. emission is due to svuclrotron processes (Messzàrros :uc Rees 1997). as evideuced by the simulataneous spectrum of CRB t)r0508 that fits theoretical ex»ectations so nicely (Calama aL... 1998) aud by detectionof polarizatlou," During the afterglow, emission is due to synchrotron processes (Mèsszàrros and Rees 1997), as evidenced by the simulataneous spectrum of GRB 970508 that fits theoretical expectations so nicely (Galama , 1998) and by detectionof polarization"
a rnudoni Poissoien field are less than 3% of the total uber.,a random Poissonian field are less than $3\%$ of the total number.
 These spurIOUS SOTIEECS. causedk by local fluctuations of he background. can be eliminaed by means of a uinimuüal spanning tree (AIST) aleorithin (Ixxuskal 1956.. Pu1n LO57)). acceXtiug only those sources coutainines nore ha ja set mui.1i nunmber of photons.," These spurious sources, caused by local fluctuations of the background, can be eliminated by means of a minimal spanning tree (MST) algorithm (Kruskal \cite{kruska}, , Prim \cite{prim57}) ), accepting only those sources containing more than a set minimum number of photons."
 Since we wait to fin close associaions of phoons. only those trees ο| the MST are considered for which all edec-lenetls are si1aller haji à dnaximally allowed iuer-photon separation daa.," Since we want to find close associations of photons, only those trees of the MST are considered for which all edge-lengths are smaller than a maximally allowed inter-photon separation $d_{max}$ ."
" The value of d,,,, is determiied by the mean iuter-poiut separation expected im au isotropic aud homogeneous Olit distribution.", The value of $d_{max}$ is determined by the mean inter-point separation expected in an isotropic and homogeneous point distribution.
" This separation is given by duy VALN, where Nis the tota -iiber of poiats ancl o ds he area of the region where th IN points are found (see WSV 1997))."," This separation is given by $d_{max}\approx\sqrt{A/N}$ , where $N$ is the total number of points and $A$ is the area of the region where the $N$ points are found (see WSV \cite{wiedenmann}) )."
 An cxrample of the scaling-iidex spectrum is shown in Fie. 1.., An example of the scaling-index spectrum is shown in Fig. \ref{fig:simspec}.
 The upper panes hishow a raudomlv-seucrated.Q smooth PSPC photon ma» (left) aud t1ο scaling iudex a-spectrum (ight).," The upper panels show a randomly-generated, smooth PSPC photon map (left) and the scaling index $\alpha$ -spectrum (right)."
" In au infinite. uuiform nuage. the sSpectruni NOILd be a delta ""unction loc""uaed at a=2."," In an infinite, uniform image, the spectrum would be a delta function located at $\alpha =2$."
 Because the feld is finite axd rot infinitely homogeneous. the spectrum is broadened. iid sleltly offset.," Because the field is finite and not infinitely homogeneous, the spectrum is broadened and slightly offset."
 The lower panels show aji actual PSPC inage and is a-spectrun., The lower panels show an actual PSPC image and its $\alpha$ -spectrum.
 The spikes at k5v o are the xiehtest sources. aud the peak is broadened fiuther due to t1ο presence oD SOMICON.," The spikes at low $\alpha$ are the brightest sources, and the peak is broadened further due to the presence of sources."
 Analyses ο: yxaudonmlv-seunerated μου] PSPC fields with backerotud levels siwil to those in our source fields revealed hat the SIM detected spurious sources with sonrce cotuts up to ~5 photous., Analyses of randomly-generated smooth PSPC fields with background levels similar to those in our source fields revealed that the SIM detected spurious sources with source counts up to $\sim 5$ photons.
 Iu oxer to ensure that no spuriots sources were included iu the source lists; we set the lower nuit ou source counts to teu protons.," In order to ensure that no spurious sources were included in the source lists, we set the lower limit on source counts to ten photons."
 This lat ΠΠIv excluded real sources. but as of vet there is no estimae of source siguificance availadle for the SIM.," This limit undoubtedly excluded real sources, but as of yet there is no estimate of source significance available for the SIM."
 We apied. the SIM. aleorithin he fields in this sunple. trereby creating source lists aud labelne each photon as a source or backeround phot3.," We applied the SIM algorithm to the fields in this sample, thereby creating source lists and labeling each photon as a source or background photon."
" Upon removal of the soPCOS, it was obvious that fre SIM. had not correctly ideutified all photons. as bright sources reiuiinued in the imaees,"," Upon removal of the sources, it was obvious that the SIM had not correctly identified all photons, as bright sources remained in the images."
 Further investigatioi revealed that the SIM algoritlan rad dificulv ideutifving alp rotons associated with a sotree if the photon deusitv wew very high., Further investigation revealed that the SIM algorithm had difficulty identifying all photons associated with a source if the photon density was very high.
 We corrected. lis by identifving all piotons within the SIM-defined ηςmee boundaries as source protons., We corrected this by identifying all photons within the SIM-defined source boundaries as source photons.
 We then applied a ckeround correction based «n the umber of backeround photons «one would expect o find muder the source., We then applied a background correction based on the number of background photons one would expect to find under the source.
 Wule this method is less thau xcal. the resulting background photon maps appear to have! had. all detected ποος COupletely removed.," While this method is less than ideal, the resulting background photon maps appear to have had all detected sources completely removed."
 Tn order to check the effectiveness of the scaliugdudex method. we also determined the diffuse x-ray background flux of cach field using the maxiuuu-likelihood. source-detection alexwithin included in the data r‘eduction software package {Zunuuernunun et al. 1992)).," In order to check the effectiveness of the scaling-index method, we also determined the diffuse x-ray background flux of each field using the maximum-likelihood source-detection algorithm included in the data reduction software package (Zimmermann et al. \cite{zman}) )."
 Our lower likelihood πε was set oat 15. corresponding to a significauce level of ~Sa.," Our lower likelihood limit was set at 15, corresponding to a significance level of $\sim 5\sigma$."
 We set the extrac‘tion radius at 2.5 times the FWIM of cach ποο, We set the extraction radius at 2.5 times the FWHM of each source.
 The backeround-correctedC» plotou counts were then subtraced from the total photon count to eive the raw backeround ploton count., The background-corrected photon counts were then subtracted from the total photon count to give the raw background photon count.
 Vieuetting corrections were not appied. since we assume that vienettiug effects will be similar in cach image and since vignetti18o corrections were not availableal for the SIAL aleorithin.," Vignetting corrections were not applied, since we assume that vignetting effects will be similar in each image and since vignetting corrections were not available for the SIM algorithm."
 We find that the SIAL aanalysis results in backegrouxd levels that are higher than the ΠΕΗΝxl technique backerounds by a Laverage of 158x95 counΤε, We find that the SIM analysis results in background levels that are higher than the maximum-likelihood technique backgrounds by an average of $158\pm 95$ counts.
 The reasol. OY this ¢]screpancv Is not fully clear aud os1o0uld he πο¢xd. before tlre» STA js widely inplemenuted., The reason for this discrepancy is not fully clear and should be understood before the SIM is widely implemented.
 Ilowever. par of the discrepaicv can be explained by noting that oir SIM source flux cut-off of LO counts. while safelv ignoring spurious sources. almost certainly considere nunerous true low-flux sources as spurious. restting in these source photcuns beimg treated as bacseuu counts.," However, part of the discrepancy can be explained by noting that our SIM source flux cut-off of 10 counts, while safely ignoring spurious sources, almost certainly considered numerous true low-flux sources as spurious, resulting in these source photons being treated as background counts."
 Tn this paper. we pertorÜ our analysis 1sine the background count evels as calculated bv. the SIN.," In this paper, we perform our analysis using the background count levels as calculated by the SIM."
 A reanalysis of the data using the numbers from the ΠΠ technique resulted in the same qualitative conclusions. although the resulting quantities dovary.," A reanalysis of the data using the numbers from the maximum-likelihood technique resulted in the same qualitative conclusions, although the resulting quantities dovary."
 The SIM analysis has the benefit of iceutifviug cach backerouud photon. whicrinade spectral aalysis of the backeround photons straightforward.," The SIM analysis has the benefit of identifying each background photon, whichmade spectral analysis of the background photons straightforward."
he parameters in Table. 1).,the parameters in Table. \ref{tab:par}) ).
 In the model used by vanZee Haynes (2006) (henceforth VHO6). this yield is consistent Gwithin he errorbars) with the theoretically expected closed-box yield of 9=0.0074 (Meynet Maeder. 2002).," In the model used by vanZee Haynes (2006) (henceforth VH06), this yield is consistent (within the errorbars) with the theoretically expected closed-box yield of p=0.0074 (Meynet Maeder, 2002)."
 On the other hand. using only he HI mass within the optical disk. the derived por7.510+ is much lower than that expected from closed-box chemical evolution.," On the other hand, using only the HI mass within the optical disk, the derived $\rm{_{eff}}\sim 7.5 \times 10^{-4}$ is much lower than that expected from closed-box chemical evolution."
 If interpreted literally. the above exercise would suggest that NGC 3741 is evolving as a closed-box model. provided that the gas-phase metallicity in the inner disk is the same as the outer disk. i.e. that there is an efficient mixing of the metals throughout the HI disk.," If interpreted literally, the above exercise would suggest that NGC 3741 is evolving as a closed-box model, provided that the gas-phase metallicity in the inner disk is the same as the outer disk, i.e. that there is an efficient mixing of the metals throughout the HI disk."
 However this seems unlikely. given the large size of the HI disk.," However this seems unlikely, given the large size of the HI disk."
 Tassis et al. (, Tassis et al. (
2006) showed that the mixing length of metals in a galaxy increases with a decrease in the galaxy mass.,2006) showed that the mixing length of metals in a galaxy increases with a decrease in the galaxy mass.
 However. whether there is mixing of metals even up to I+ times its optical extent is unclear.," However, whether there is mixing of metals even up to 14 times its optical extent is unclear."
 On the other hand. what evidence do we have for closed-box chemical evolution in dwarf galaxies?," On the other hand, what evidence do we have for closed-box chemical evolution in dwarf galaxies?"
 And can one from the observational data try to make inferences about how much of the HI disk participates in the chemical evolution (i.e. is well mixed)?, And can one from the observational data try to make inferences about how much of the HI disk participates in the chemical evolution (i.e. is well mixed)?
 The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae. hence a priori. one might expect that low mass galaxies would depart from the closed-box chemical evolution. since enriched material could escape via stellar winds and supernova ejecta (Brooks et al.," The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae, hence a priori, one might expect that low mass galaxies would depart from the closed-box chemical evolution, since enriched material could escape via stellar winds and supernova ejecta (Brooks et al."
 2007)., 2007).
 We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. 9[[, We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. \ref{fig:overlay_yield}[ [
A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VHO6 sample with available HI images (the sources of the HI images is given in the figure caption).,A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VH06 sample with available HI images (the sources of the HI images is given in the figure caption).
 The effective yield is computed by considering the entire gas mass., The effective yield is computed by considering the entire gas mass.
 NGC 3741 and DDOIS4 are shown in the plot with extreme values of the HI extent., NGC 3741 and DDO154 are shown in the plot with extreme values of the HI extent.
 As can be seen. there are some galaxies in the sample which are consistent with the closed-box model.," As can be seen, there are some galaxies in the sample which are consistent with the closed-box model."
 However there is no clear trend seen between the effective yield and the extent of the HI disk., However there is no clear trend seen between the effective yield and the extent of the HI disk.
 Figure 9[[B] shows the effective yield for the same sample of galaxies as shown in Fig. 9[[, Figure \ref{fig:overlay_yield}[ [B] shows the effective yield for the same sample of galaxies as shown in Fig. \ref{fig:overlay_yield}[ [
A]. however this time the effective yield is computed by considering the gas fraction within the Holmberg radius.,"A], however this time the effective yield is computed by considering the gas fraction within the Holmberg radius."
 As can be seen. if the effective vield is computed within the Holmberg radius. (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model.," As can be seen, if the effective yield is computed within the Holmberg radius, (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model."
 The theoretically expected closed-box chemical yield depends on assumptions about the IMF. stellar rotation as well as in details of stellar evolution models (Meynet Maeder. 2002).," The theoretically expected closed-box chemical yield depends on assumptions about the IMF, stellar rotation as well as in details of stellar evolution models (Meynet Maeder, 2002)."
 It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties. instead of comparing the observed yield against a model dependent expected yield.," It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties, instead of comparing the observed yield against a model dependent expected yield."
 One possible parameter to use for such a correlation is the tota dynamical mass., One possible parameter to use for such a correlation is the total dynamical mass.
 VHO6 did not tind any significant trend between the dynamical mass and effective yield for the galaxies in their sample. however they computed the dynamical mass using the HI global velocity widths.," VH06 did not find any significant trend between the dynamical mass and effective yield for the galaxies in their sample, however they computed the dynamical mass using the HI global velocity widths."
 We recomputed the dynamical masses for the galaxies in VHO6 sample for which rotation curves are available in literature., We recomputed the dynamical masses for the galaxies in VH06 sample for which rotation curves are available in literature.
 We show in Fig., We show in Fig.
 160. a plot of the effective yield against the total dynamical mass., \ref{fig:yield_mass} a plot of the effective yield against the total dynamical mass.
 The effective yield computec using the entire HI mass is shown as eross. while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points.," The effective yield computed using the entire HI mass is shown as cross, while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points."
 As can be seen. in both cases the effective yield increases with increasing dynamical mass.," As can be seen, in both cases the effective yield increases with increasing dynamical mass."
 The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47). suggesting that. if this model were to be correct. only the gas within the optical disk participates in the chemical evolution of the galaxy.," The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47), suggesting that, if this model were to be correct, only the gas within the optical disk participates in the chemical evolution of the galaxy."
 However we note that the total number of galaxies in our analysis is too small to make any statistical conclusion., However we note that the total number of galaxies in our analysis is too small to make any statistical conclusion.
 Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich. low mass galaxies.," Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich, low mass galaxies."
 In summary. we examine the dark and luminous matter in NGC 3741.," In summary, we examine the dark and luminous matter in NGC 3741."
 Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter. its baryons to dark," Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter, its baryons to dark"
"that the entire triplet is too faint for studies of changes, the line complex around iis strong enough that residual He8 would be detectable.","that the entire triplet is too faint for studies of changes, the line complex around is strong enough that residual $\beta$ would be detectable."
" Also, the higher Ly series lines of are not seen in the difference spectrum."," Also, the higher Ly series lines of are not seen in the difference spectrum."
" We interpret the absence also of high Ly series lines in the difference spectrum as evidence for an increase in the optical depth of the scattering plasma, which could be part of the reformation process of the accretion disk."," We interpret the absence also of high Ly series lines in the difference spectrum as evidence for an increase in the optical depth of the scattering plasma, which could be part of the reformation process of the accretion disk."
 A bit puzzling appears the presence of Lya in the difference spectrum while Ly is not present., A bit puzzling appears the presence of $\alpha$ in the difference spectrum while $\beta$ is not present.
" Except for the Lya line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum."," Except for the $\alpha$ line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum."
 The shape of the continuum in the difference spectrum in Fig., The shape of the continuum in the difference spectrum in Fig.
 14 is the shape of the continuum component in the inner regions., \ref{diffspec} is the shape of the continuum component in the inner regions.
" It has roughly the same shape as the out-of-eclipse spectrum, supporting the interpretation of achromatic Thompson scattering."," It has roughly the same shape as the out-of-eclipse spectrum, supporting the interpretation of achromatic Thompson scattering."
 Close inspection of the RGS and EPIC brightness maps in the bottom panels of Figs., Close inspection of the RGS and EPIC brightness maps in the bottom panels of Figs.
 12 and 13 reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy., \ref{smap} and \ref{smap_epic} reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy.
" In the Rayleigh-Jeans tail, betweenAA,, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. 12))."," In the Rayleigh-Jeans tail, between, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. \ref{smap}) )."
" In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. 13.."," In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. \ref{smap_epic}."
" This could indicate a temperature gradient, however, the hardness light curve in the middle panel of Fig."," This could indicate a temperature gradient, however, the hardness light curve in the middle panel of Fig."
 3 does not indicate a significant temperature change with the eclipse.," \ref{lc2}
 does not indicate a significant temperature change with the eclipse."
 Only the softening after the eclipse appears noteworthy and may have to be attributed to the cooling while nuclear burning is turning off., Only the softening after the eclipse appears noteworthy and may have to be attributed to the cooling while nuclear burning is turning off.
" On the other hand, the hardness light curve contains the emission lines and is a less sensitive indicator for the photospheric temperature."," On the other hand, the hardness light curve contains the emission lines and is a less sensitive indicator for the photospheric temperature."
" In the first of the two oobservations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table 1))."," In the first of the two observations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table \ref{obslog}) )."
" In Fig. 15,,"," In Fig. \ref{smap_om}, ,"
 these spectra are shown in the same format as in Figs., these spectra are shown in the same format as in Figs.
 12 and 13.., \ref{smap} and \ref{smap_epic}.
" In the rangeAA,, the spectrum shows many features which are difficult to identify."," In the range, the spectrum shows many features which are difficult to identify."
 Wavelengths of a few known lines are marked., Wavelengths of a few known lines are marked.
" A weak feature coincides with the position of the resonance doublet but, given the presence of many similar features in the spectrum as well as the uncertainty of the absolute wavelength scale (which depends on the accurate centroiding of the zero order), its identification is uncertain."," A weak feature coincides with the position of the resonance doublet but, given the presence of many similar features in the spectrum as well as the uncertainty of the absolute wavelength scale (which depends on the accurate centroiding of the zero order), its identification is uncertain."
 The wavelength range of the OM grisms overlaps with the long-wavelength range of the International Ultraviolet Explorer (IUE)., The wavelength range of the OM grisms overlaps with the long-wavelength range of the International Ultraviolet Explorer (IUE).
" Five spectra were taken with the IUE during the outburst in 1979: on June 28, June 30, July 2, July 4,and July 10, corresponding to 5, 7, 8, 10, and 16 days after outburst (?).."," Five spectra were taken with the IUE during the outburst in 1979: on June 28, June 30, July 2, July 4,and July 10, corresponding to 5, 7, 8, 10, and 16 days after outburst \citep{williams81}."
" In the top panel of Fig. 15,,"," In the top panel of Fig. \ref{smap_om},"
 the IUE spectra from 8 and 16 days after the 1979 outburst are overplotted in orange and blue (see right legend)., the IUE spectra from 8 and 16 days after the 1979 outburst are overplotted in orange and blue (see right legend).
" The strongest lines in these spectra are, apart from the doublet, at 2512, 2734 and AA,, at aand v]] at2784 and AA.."," The strongest lines in these spectra are, apart from the doublet, at 2512, 2734 and , at and ] at2784 and ."
from [Myr through 13 Cir. including gaseous emission. which signifcantlv affects broad band huuinosities and colours during carly evolutionary stages (see 7 for details).,"from 4 Myr through 13 Gyr, including gaseous emission, which significantly affects broad band luminosities and colours during early evolutionary stages (see \cite*{AndersFritze03} for details)."
 Spectra are then olded with filter unctious for any desired filter svstem to vield the photometric evolution., Spectra are then folded with filter functions for any desired filter system to yield the photometric evolution.
 This is important in order to avoid uucertaimties from transformations )otwoeen filter svstems., This is important in order to avoid uncertainties from transformations between filter systems.
 Models well reproduce eiipirical colour metallicity calibrations over their rauge of validity aud indicate significaut deviations from their inear behaviour towards ligher metallictics., Models well reproduce empirical colour – metallicity calibrations over their range of validity and indicate significant deviations from their linear behaviour towards higher metallicties.
 We showed hat transformations from colour to metallicity are sienificautly age-dependent and that transformations roni colour to age are siguificautlv inctallicitv-depeudenutlg (7)., We showed that transformations from colour to metallicity are significantly age-dependent and that transformations from colour to age are significantly metallicity-dependent \citep{Schulz+02}.
. The effect of dust absorption is included iu CGALEV iodels asstuning a starburst extinction law (2) for a range of values for E(B η...Vjx Lanag), The effect of dust absorption is included in GALEV models assuming a starburst extinction law \citep{Calzetti+00} for a range of values for $E(B-V)$ $0 \leq E(B-V) \leq 1~$ mag).
" GALEV models also iuclude the full set of Lick spectral absorption mdices ou the basis of eimipirical calibratious for the iudices iu ternis of stellar pareuneters for every individual cluster star Tog.logο,[FeΤΠ) as given by (2). and (?).."," GALEV models also include the full set of Lick spectral absorption indices on the basis of empirical calibrations for the indices in terms of stellar parameters for every individual cluster star ${\rm T_{eff},~log~g,~[Fe/H]}$ as given by \citep{Gorgas+93} and \citep{Worthey+94}."
 We showed that the transformation from the age-scusitive Lick index IL; to age is significantly: inetallicity-depeudeut aud that the traustormation from the metallicityv-sensitive Lick indices (Mgb. Me». |MgFe]. ...) to metallicity is age-dependent for ages x:10 Cr (77).," We showed that the transformation from the age-sensitive Lick index $_{\beta}$ to age is significantly metallicity-dependent and that the transformation from the metallicity-sensitive Lick indices (Mgb, $_2$, [MgFe], $\dots$ ) to metallicity is age-dependent for ages $\leq 10$ Gyr \citep{Kurth+99,LillyFritze06}."
 Qur analysis methods use the full iuforxiuation from multi-baud imagine (UV.U.B..... ΑΠ) or/aud Lick spectroscopy available for à SC system. compare thon toa large grid of over 100.000 CALEV models in terius of Spectral Encrey Distributions (SEDs). Lick iudices. or a conibiuation of both (cf. ?.. 7.. Lilly Fritze," Our analysis methods use the full information from multi-band imaging $UV,~U,~B,\dots,~NIR$ ) or/and Lick spectroscopy available for a SC system, compare them to a large grid of over 100.000 GALEV models in terms of Spectral Energy Distributions (SEDs), Lick indices, or a combination of both (cf. \cite*{Anders+04a}, \cite*{LillyFritze06},"
" 2008. submitted), "," Lilly Fritze 2008, )."
SEDs. we recall. are sects of magnitudes in a muuber of filters from short to loug wavelengths. c.g. U.2.K.," SEDs, we recall, are sets of magnitudes in a number of filters from short to long wavelengths, e.g. $U ~ \dots ~ K$."
 Our analysis tools not oulv determinethe best fit model but attribute probabilities to all models that allow us to determine the lo uncertainties for all the SC parameters they return: age. metallicity. E(BV and mass.," Our analysis tools not only determine best fit model but attribute probabilities to all models that allow us to determine the $1 \sigma$ uncertainties for all the SC parameters they return: age, metallicity, $E(B-V)$, and mass."
 Extensive tests with artificial SCs have shown that CV or Ü/— baud observations are essential for age dating of YSCs aud a NIR baud is oeuportaut to obtain accurate moetallicities., Extensive tests with artificial SCs have shown that $UV$ or $U-$ band observations are essential for age dating of YSCs and a NIR band is important to obtain accurate metallicities.
 For YSCs oe1 dusty galaxies four passbauds inchiding CV/U aud IT ov AK with observational uucertaiuties <0.05 mae oei the UV/optical and <0.1 mae in the NIR allow +to largely disentangle ages aud aud metallicities aud to jbtain ages to Aage/agex0.3 and iietallicties to £0.2 ex., For YSCs in dusty galaxies four passbands including $UV/U$ and $H$ or $K$ with observational uncertainties $\leq 0.05$ mag in the UV/optical and $\leq 0.1$ mag in the NIR allow to largely disentangle ages and and metallicities and to obtain ages to $\Delta~{\rm age / age} \leq 0.3$ and metallicties to $\pm 0.2$ dex.
 For intermediate-age SCs or old GCs in dust-free environnieuts. three passbands. again rangiug from C or D through fT or A are enough (?7)..," For intermediate-age SCs or old GCs in dust-free environments, three passbands, again ranging from $U$ or $B$ through $H$ or $K$ are enough \citep{Anders+04a,deGrijs+03c}."
 Applving our SED analvsis tool to TST WEPC? aud NICMOS archival data for some 170. compact YSC's that we identified in the not apparently interacting dwart starburst galaxy NGC 1569. we obtained masses for the bulk of its YSCs iu the range 107LotML..," Applying our SED analysis tool to HST WFPC2 and NICMOS archival data for some 170 compact YSCs that we identified in the not apparently interacting dwarf starburst galaxy NGC 1569, we obtained masses for the bulk of its YSCs in the range ${\rm 10^3 - 10^4~M_{\odot}}$."
. Onulv a handful of these. including the 3 previously known so-called Super Star Clusters. lave asses above a few lo’AL... ic. in the range of GC masses.," Only a handful of these, including the 3 previously known so-called Super Star Clusters, have masses above a few ${\rm 10^5~M_{\odot}}$, i.e. in the range of GC masses."
 We conclude that this strougly starbursting but nof apparently interacting dwirf galaxy docs not fori iu new CCS. or. at most. very few (7?)..," We conclude that this strongly starbursting but not apparently interacting dwarf galaxy does not form any new GCs, or, at most, very few \citep{Anders+04b}."
 For the starburst iu the massive eas-vich spiral — spiral merecr remnant NGC 7252. we could estimate the SE efficiency very conservatively to be at least 35," For the starburst in the massive gas-rich spiral – spiral merger remnant NGC 7252, we could estimate the SF efficiency very conservatively to be at least 35."
 This estimate was based on the amount of new stars formed durug the burst. as obtained from the deep Daher absorption lines in the overall spectrum. aud a vorv eenerous estimate of the σας mass available in the two Se-type progenitor spirals. of which the wuple III still observed all along the extended tidal ails is the proof (77)..," This estimate was based on the amount of new stars formed during the burst, as obtained from the deep Balmer absorption lines in the overall spectrum, and a very generous estimate of the gas mass available in the two Sc-type progenitor spirals, of which the ample HI still observed all along the extended tidal tails is the proof \citep{FG94a,FG94b}."
 Such a high SF efficiency should allow for the formation of massive. conipact. stronelv youd GCs.," Such a high SF efficiency should allow for the formation of massive, compact, strongly bound GCs."
 OST observations indeed revealed a rich o)pulatiou of compact SCs with ages iu the rauge 600900 Myr and metallicities close to solar (?).., HST observations indeed revealed a rich population of compact SCs with ages in the range $600-900$ Myr and metallicities close to solar \citep{FB95}.
 They appareutly have survived may internal crossing iues and the most critical phase in their lives. the infant mortality phase after expulsion of the eas left over at their formation when the first SNe weut off. aud μον are still compact aud bound.," They apparently have survived many internal crossing times and the most critical phase in their lives, the infant mortality phase after expulsion of the gas left over at their formation when the first SNe went off, and they are still compact and bound."
 This is particularly nmupressive since all this happened during the violent relaxation phase that restructured their parent galaxy roni two spiral disks iuto a spherical configuratio- eaturug a de Vaucouleurs profile (?).., This is particularly impressive since all this happened during the violent relaxation phase that restructured their parent galaxy from two spiral disks into a spherical configuration featuring a de Vaucouleurs profile \citep{Schweizer06}.
 These vouug GCs have all chances to survive another Hubble time., These young GCs have all chances to survive another Hubble time.
 Thev have masses in the rauge Lo?10°AD. with cluster W3 even reaching 7SAL. (2?)..," They have masses in the range ${\rm 10^5 - 10^6~M_{\odot}}$ with cluster W3 even reaching ${\rm 7-8~M_{\odot}}$ \citep{FB95,Maraston+04}."
 Enough of tose voung GCs survived until today to secure the ucrecr remnant the typical GC specific frequency of an liptical galaxy. which is twice as high when defined in exis of umber of GCs in relation to galaxy total as for an average spiral (2)..," Enough of those young GCs survived until today to secure the merger remnant the typical GC specific frequency of an elliptical galaxy, which is twice as high when defined in terms of number of GCs in relation to galaxy total as for an average spiral \citep{ZepfAshman93}. ."
 Le. during the strong global starburst accommpanving the merger that transformed wo bright Sc galaxies iuto a dynamically still voune elliptical. a umber of secondary. GCs has formed that is comparable to the uuuber of preexisting GCs iu both xogenitor spirals.," I.e. during the strong global starburst accompanying the merger that transformed two bright Sc galaxies into a dynamically still young elliptical, a number of secondary GCs has formed that is comparable to the number of preexisting GCs in both progenitor spirals."
Bethe&Brown(1998) SUENOOested that merecrs resulting iu short-hard eamuua-ray bursts would be mainly those of LMDITI-NS binaries. with those of NS-NS binarics down bv an order of magnitude from these.,"\citet{Bet98} suggested that mergers resulting in short-hard gamma-ray bursts would be mainly those of LMBH-NS binaries, with those of NS-NS binaries down by an order of magnitude from these."
 The lower umber of the latter resulted from the necessity that the two eiaut progenitors be within of cach other in ZAMS ass so that tjov dDrued He at the same time., The lower number of the latter resulted from the necessity that the two giant progenitors be within of each other in ZAMS mass so that they burned He at the same time.
 Otherwise the first bori pulsar would fux itself in the red elaut euvelope of the coupalion giant as it evolved aud accrete cuough matter to eo into a black hole (BID)., Otherwise the first born pulsar would find itself in the red giant envelope of the companion giant as it evolved and accrete enough matter to go into a black hole (BH).
 Brown(1995) had already estimated this to be true. based on Chevalicr(1993).. and proposed the special wav that two eiauts burn Te at the sale tdue. 1 order to avoid the red giant common envelope evolution of the first 20111 pulsar.," \citet{Bro95} had already estimated this to be true, based on \citet{Che93}, and proposed the special way that two giants burn He at the same time, in order to avoid the red giant common envelope evolution of the first born pulsar."
 If the two eiauts burn Ile at he sane nuc. the two Ue euveopes are assured to eo iuto common euvelope evolution. expelling the conmnaiou envelo]© laatter so that the hel ewelope is lost from cach star.," If the two giants burn He at the same time, the two He envelopes are assumed to go into common envelope evolution, expelling the common envelope matter so that the helium envelope is lost from each star."
 Draun&Langer(1995) showed that there was not sufficieu tuue for either of the stars fo acrete the comnon envelope He. so hat if the two Πο stars had to be nearly equal iu nass. then their progenitor eiauts ust also 0.," \citet{Bra95} showed that there was not sufficient time for either of the stars to accrete the common envelope He, so that if the two He stars had to be nearly equal in mass, then their progenitor giants must also be."
" From the Schalleretal.(1992) miodels for the eiaut progenitors ¢f the neutron stars we coisicler. t1ο elauts have o be within <1% of¢""ch other iu mass in order to buru Πο at the saue time."," From the \cite{Sch92} models for the giant progenitors of the neutron stars we consider, the giants have to be within $\lsim 4\%$ of each other in mass in order to burn He at the same time."
 Of the Bethe&Brown(7908) inerecr 1ate of LOtyr tinor Galaxy. only ~0.1. or 105 1 were estimated o be those of binary NS," Of the \cite{Bet98} merger rate of $10^{-4}$ $^{-1}$ in our Galaxy, only $\sim 0.1$, or $10^{-5}$ $^{-1}$ were estimated to be those of binary NS's."
 A recent detailerL calculation by Dewietal.(2006) οἶνος a ποσο rate of 0.112 |l for Drowu's specia scenario. the upper exd of the calculation iu agreement wih (1998).," A recent detailed calculation by \citet{Dew96} gives a merger rate of $0.1-12$ $^{-1}$ for Brown's special scenario, the upper end of the calculation in agreement with \cite{Bet98}."
. The later authors simply estnauated hat the ολα]ing mergers would be of LMDBII-NS binarics since they calculated that when the pulsar went through ¢Onmuuon eanveloe with the companion star it accretec LAL. of matter. choueh to seudi iuto a DIT.," The latter authors simply estimated that the remaining mergers would be of LMBH-NS binaries since they calculated that when the pulsar went through common envelope with the companion star it accreted $\sim 1\msun$ of matter, enough to sendit into a BH."
 The iuo:ut of accYetion was corrected downwards ~nU& by removal of an approximation of Betlu&Brown(1998) bv Delezvüskicta.(2002)., The amount of accretion was corrected downwards $\sim 25\%$ by removal of an approximation of \citet{Bet98} by \citet{Bel02}.
. In tie present note we try to make a roa calculation of the LMDII-NS binary. NS-NS binary ratio.," In the present note we try to make a real calculation of the LMBH-NS binary, NS-NS binary ratio."
 Pinsomeault&Stauek(2006) assembled evidence that 7Binaries like to be Twius.," \citet{Pin06} assembled evidence that “Binaries like to be Twins""."
 They showed that a recently publishedd sauple of 21 detached eclipsing binaries iu the Simall Magellanic Cloud can be evolve in terms of a flat luass fujction ccontaiuiue of the svsteis aud a “twins” population with q>0.95 containing the remainder.," They showed that a recently published sample of 21 detached eclipsing binaries in the Small Magellanic Cloud can be evolved in terms of a flat mass function containing of the systems and a “twins"" population with $q> 0.95$ containing the remainder."
" All of the binaries had orbital period P<5 davs. wih primary maasses GOAL.<AL,<212Ab.e""n"," All of the binaries had orbital period $P< 5$ days, with primary masses $6.9 \msun <M_1 <27.3 \msun$."
 The iuporaut role of twins is that he two «oκlants are close! enoneh im mass that 1 BreWAL(1995). scenario they Call CVO.ve iuto NS-NS binarics. whereas if they are further apart iu mass they will evolve in oa LMDII-NS binary (CCrevalicrJ993:Bethe&Brown1998).," The important role of twins is that the two giants are close enough in mass that in \citet{Bro95} scenario they can evolve into NS-NS binaries, whereas if they are further apart in mass they will evolve into a LMBH-NS binary \citep{Che93,Bet98}."
. Thus the twins may increase the umber of NS-NS binaries., Thus the twins may increase the number of NS-NS binaries.
 We sugeOOest that the resulting ΠΡΟ of short hard eamuna-rav bursts. which result from the iiereiug of the binaricss. Which to date are muae to differentiate between the two species. wav uot be changed much. some of the predictec large excess of LAIBII-NS biuarcSs appearing rather as NS-NS binaries.," We suggest that the resulting number of short hard gamma-ray bursts, which result from the merging of the binaries, which to date are unable to differentiate between the two species, may not be changed much, some of the predicted large excess of LMBH-NS binaries appearing rather as NS-NS binaries."
 However. because the latter are so mich more easy. to observe. the role betwee ilt we see aud what is present will be tightened.," However, because the latter are so much more easy to observe, the role between what we see and what is present will be tightened."
 Tn Sec., In Sec.
 ?7 we shall show that evoluion of binaries with a flat mass evolution does. i agreement with produce a ratio of |BID | NS) svsteuis of 5. for the population that does not contain twins.," \ref{sec-twin} we shall show that evolution of binaries with a flat mass evolution does, in agreement with \citet{Pin06}
 produce a ratio of $+$ $+$ NS) systems of 5, for the population that does not contain twins."
 This is half the order of magnitude raio found by Bethe&Brown (1998).., This is half the order of magnitude ratio found by \citet{Bet98}. .
 The lower value results from the fact that, The lower value results from the fact that
In this subsection we explore the behavior of this system by direct numerical simulations.,In this subsection we explore the behavior of this system by direct numerical simulations.
 We found this to be helpful in the building of our intuition., We found this to be helpful in the building of our intuition.
 We defer a semi-analytical normal-mode analysis to the next subsection., We defer a semi-analytical normal-mode analysis to the next subsection.
 We follow LO7 and for concreteness concentrate on a specific example; it will be clear that the conclusions we reach are general., We follow L07 and for concreteness concentrate on a specific example; it will be clear that the conclusions we reach are general.
 We choose wo= lrad/second and mass M=1., We choose $\omega_0 = 1$ rad/second and mass $M = 1$.
" We choose a total number of 1000 small pendulae with frequencies ων=(0.5+ n/1000)rad/second and masses m,=m10-7, to mimic the continuum frequency range between 0.5rad/second and 1.5rad/second."," We choose a total number of 1000 small pendulae with frequencies $\omega_n = (0.5 +
n/1000)$ rad/second and masses $m_n=m=10^{-4}$, to mimic the continuum frequency range between $0.5$ rad/second and $1.5$ rad/second."
" 'The simulation is initiated by displacing the large oscillator while keeping the small pendulae relaxed (this mimics the stresses in the crust), and then releasing."," The simulation is initiated by displacing the large oscillator while keeping the small pendulae relaxed (this mimics the stresses in the crust), and then releasing."
 The subsequent motion of the system is then followed numerically by using a second order leapfrog integration scheme which conserves the energy with high precision., The subsequent motion of the system is then followed numerically by using a second order leapfrog integration scheme which conserves the energy with high precision.
 The resulting motion of the large pendulum can be decomposed into three stages (see Fig., The resulting motion of the large pendulum can be decomposed into three stages (see Fig.
 2 and Fig. 3)): (, \ref{Fig2A} and Fig. \ref{Fig2B}) ): (
"1) During the first 50-60 seconds, there is a rapid exponential decay of the large oscillator’s motion, during which most of the energy is transferred to the multitude (i.e., the continuum’) of small oscillators.","1) During the first 50-60 seconds, there is a rapid exponential decay of the large oscillator's motion, during which most of the energy is transferred to the multitude (i.e., the 'continuum') of small oscillators."
" This is the so-called phenomenon of “resonant absorption”, which has been studied for decades in the MHD and plasma physics community (e.g., Ionson 1978, Hollweg 1987, Goedbloed Poedts 2004, L07, Gruzinov 2008b)."," This is the so-called phenomenon of “resonant absorption”, which has been studied for decades in the MHD and plasma physics community (e.g., Ionson 1978, Hollweg 1987, Goedbloed Poedts 2004, L07, Gruzinov 2008b)."
" In this first stage, the amplitude of the big pendulum motions drops by a factor of ~100. ("," In this first stage, the amplitude of the big pendulum motions drops by a factor of $\sim 100$. ("
"2) After ~60 seconds, the exponential decay stops abruptly as the large oscillator now reacts to the collective pull of the small ones.","2) After $\sim 60$ seconds, the exponential decay stops abruptly as the large oscillator now reacts to the collective pull of the small ones."
 This second stage is characterized by a slow algebraic decay of the amplitude of the big pendulum displacement., This second stage is characterized by a slow algebraic decay of the amplitude of the big pendulum displacement.
 Gruzinov (2008b) explains this as being due to the branch cut in the oscillator's response function. (, Gruzinov (2008b) explains this as being due to the branch cut in the oscillator's response function. (
"3) The motion of the large oscillator stabilizes at a constant level (L07 missed this stage in his simulations, which he stopped too early).","3) The motion of the large oscillator stabilizes at a constant level (L07 missed this stage in his simulations, which he stopped too early)."
" Fourier transform reveals 2 QPOs at the frequencies close to the continuum edges, w—0.5 and w=1.5; the same QPO frequencies can be observed in the previous stage (2) as well."," Fourier transform reveals 2 QPOs at the frequencies close to the continuum edges, $\omega=0.5$ and $\omega=1.5$; the same QPO frequencies can be observed in the previous stage (2) as well."
" What is the origin of the QPOs, and how is this eventual stability established?"," What is the origin of the QPOs, and how is this eventual stability established?"
 In Fig., In Fig.
" 4 and 5,, we show how the amplitude of the small oscillators evolves with time."," \ref{Fig5A} and \ref{Fig5AA}, we show how the amplitude of the small oscillators evolves with time."
" After the initial resonant absorption phase, the amplitude is distributed as a Lorentzian centered on the frequency around w=1; this is because the small oscillators in resonance with the large one are the ones which gain the most energy."," After the initial resonant absorption phase, the amplitude is distributed as a Lorentzian centered on the frequency around $\omega=1$; this is because the small oscillators in resonance with the large one are the ones which gain the most energy."
" However, in subsequent times we see that the energy exchange occurs between the smalllators?,, and that the net result of this exchange is the energy flow towards the oscillators whose frequencies are near the edges."," However, in subsequent times we see that the energy exchange occurs between the small, and that the net result of this exchange is the energy flow towards the oscillators whose frequencies are near the edges."
" By the time the third stage begins, the amplitudes of the oscillators near the edge stabilize and their phases become locked."," By the time the third stage begins, the amplitudes of the oscillators near the edge stabilize and their phases become locked."
 They are pulling and pushing the large oscillator in unison., They are pulling and pushing the large oscillator in unison.
" In the next subsection, we"," In the next subsection, we"
Cen A. We show that (vpical blazar-like jet parameters may be used to model the broadband SED. if one allows for an additional cascade contribution to the 5-rav. emission due lo 55 absorption and cascading in the thermal infrared radiation field of the prominent dust emission known to be present in Cen A.,"Cen A. We show that typical blazar-like jet parameters may be used to model the broadband SED, if one allows for an additional cascade contribution to the $\gamma$ -ray emission due to $\gamma\gamma$ absorption and cascading in the thermal infrared radiation field of the prominent dust emission known to be present in Cen A."
binaries that contain significantly evolved companion stars. transferring mass on a time-scale governed by nuclear expansion of the secondary.,"binaries that contain significantly evolved companion stars, transferring mass on a time-scale governed by nuclear expansion of the secondary."
 It is no surprise. then. that GRS | 105. with its long orbital period and huge accretion dise is one of the few svstems in which such behaviour has been observed.," It is no surprise, then, that GRS $+$ 105, with its long orbital period and huge accretion disc is one of the few systems in which such behaviour has been observed."
 MRT acknowledges a PPARC postdoctoral fellowship., MRT acknowledges a PPARC postdoctoral fellowship.
 The simulations were performed on the UK Astrophysical Fluids Facility (UKAFF)., The simulations were performed on the UK Astrophysical Fluids Facility (UKAFF).
 The authors are grateful to Chris Done and also to the referee for helpful and insightful comments., The authors are grateful to Chris Done and also to the referee for helpful and insightful comments.
 The light curve was provided by the RXTE/ASM team at MIT andRXTE SOF and GOF at NASA Goddard SFC., The light curve was provided by the /ASM team at MIT and SOF and GOF at NASA Goddard SFC.
or ongoing gas accretion in nearby galaxies(Sancisietal.2008).,for ongoing gas accretion in nearby galaxies\citep{Sancisi08}.
. However. estimates of the accretion rates in the form of neutral ivdrogen in nearby spirals consistently give values much lower han those required to sustain star formation at their observed rates (See Fraternali (2010) for a recent review).," However, estimates of the accretion rates in the form of neutral hydrogen in nearby spirals consistently give values much lower than those required to sustain star formation at their observed rates (see Fraternali (2010) for a recent review)."
 This leads to the iypothesis that most of the baryons that reside outside galaxies at he present are in the form of ionized gas (e.g. Fukugita. Hogan Peebles 1998).," This leads to the hypothesis that most of the baryons that reside outside galaxies at the present are in the form of ionized gas (e.g. Fukugita, Hogan Peebles 1998)."
 There is also some evidence from observations of ionized silicon in high and intermediate-velocity clouds in the Tilkv Way. that gas in a low-metallicity ionized phase in the halo can provide a substantial CI M./yr) cooling inflow to replenish star ormation in the disk (Shull et al.," There is also some evidence from observations of ionized silicon in high and intermediate-velocity clouds in the Milky Way, that gas in a low-metallicity ionized phase in the halo can provide a substantial (1 $_{\odot}$ /yr) cooling inflow to replenish star formation in the disk (Shull et al."
 2009)., 2009).
 One interesting question that has not been considered. very much in the literature. is whether gas accretes onto all galaxies in à smooth. continuous fashion. or whether accretion is more stochastic.," One interesting question that has not been considered very much in the literature, is whether gas accretes onto all galaxies in a smooth, continuous fashion, or whether accretion is more stochastic."
 If accretion has been stochastic. then galaxies that have recently acquired gas from the external environment might be expected to have unusually high HI mass fractions.," If accretion has been stochastic, then galaxies that have recently acquired gas from the external environment might be expected to have unusually high HI mass fractions."
 The neutral gas content of a galaxy has long been known to correlate with its other physical properties., The neutral gas content of a galaxy has long been known to correlate with its other physical properties.
 HI mass fractions increase smoothly along the Hubble sequence from the early-type (S0) to the late-type (Im) end (Roberts&Haynes1994)., HI mass fractions increase smoothly along the Hubble sequence from the early-type (S0) to the late-type (Im) end \citep{RH94}.
". There are also correlations between HI mass fraction and galaxy properties such as stellar mass (AZ,.). stellar mass surface density (μ.) and broadband colour."," There are also correlations between HI mass fraction and galaxy properties such as stellar mass $M_*$ ), stellar mass surface density $\mu_*$ ) and broadband colour."
 These correlations form the basis for the so-called “photometric gas fraction” technique for predicting the HI gas content galaxies (Kannappan2004:Zhangetal.2009).," These correlations form the basis for the so-called “photometric gas fraction” technique for predicting the HI gas content galaxies \citep{Kannappan04, Zhang09}."
. Rather little attention has been given to thescaffer in gas fraction at a given value of Μ.. µε or colour.," Rather little attention has been given to the in gas fraction at a given value of $M_*$, $\mu_*$ or colour."
 Recently. Zhang et al (2009) found that more gas-rich galaxies were systematically deficient in metals at fixed stellar mass and they interpreted this as evidence for recent cosmological infall of gas in these systems.," Recently, Zhang et al (2009) found that more gas-rich galaxies were systematically deficient in metals at fixed stellar mass and they interpreted this as evidence for recent cosmological infall of gas in these systems."
 However. up to now there has been ho systematic study of how galaxy properties vary as a function of HI over- or under-abundance.," However, up to now there has been no systematic study of how galaxy properties vary as a function of HI over- or under-abundance."
 One problem that has hampered progress on this front has been the lack of suitable data sets., One problem that has hampered progress on this front has been the lack of suitable data sets.
 Blind HI surveys. such as the HI Parkes All Sky Survey (HIPASS. Barnes et al 2001) or the Arecibo Legacy Fast ALFA survey (ALFALFA. Giovanelli et al 2005) have produced large. unbiased samples of galaxies selected by HI mass.," Blind HI surveys, such as the HI Parkes All Sky Survey (HIPASS, Barnes et al 2001) or the Arecibo Legacy Fast ALFA survey (ALFALFA, Giovanelli et al 2005) have produced large, unbiased samples of galaxies selected by HI mass."
 However. these surveys are still relatively shallow. so the fraction of HI-poor galaxies is small.," However, these surveys are still relatively shallow, so the fraction of HI-poor galaxies is small."
 Recently. Catinella et al (2010. hereafter C10) explored how HI gas fraction scales as a function of galaxy stellar mass. galaxy structural parameters and NUV-r colour. using data from the GALEX Arecibo SDSS Survey (GASS).," Recently, Catinella et al (2010, hereafter C10) explored how HI gas fraction scales as a function of galaxy stellar mass, galaxy structural parameters and NUV-r colour, using data from the GALEX Arecibo SDSS Survey (GASS)."
 The survey is an ongoing large programme at the Arecibo radio telescope that is gathering high quality HI-line spectra for an unbiased sample of ~1000 galaxies with stellar masses greater than 107A. and. redshifts in the range 0.025<z< 0.05. selected from the Sloan Digital Sky Survey (SDSS. Yorketal. (2000))) spectroscopic and Galaxy Evolution Explorer (GALEX. Martinetal. (2005))) imaging surveys.," The survey is an ongoing large programme at the Arecibo radio telescope that is gathering high quality HI-line spectra for an unbiased sample of $\sim 1000$ galaxies with stellar masses greater than $10^{10} M_{\odot}$ and redshifts in the range $<z<$ 0.05, selected from the Sloan Digital Sky Survey (SDSS, \citet{York00}) ) spectroscopic and Galaxy Evolution Explorer (GALEX, \citet{Martin05}) ) imaging surveys."
 The galaxies are observed until detected or until a low gas mass fraction limit €1.5-5 ) is reached., The galaxies are observed until detected or until a low gas mass fraction limit (1.5-5 ) is reached.
 CIO quantify in detail how the atomic gas fraction of the galaxies in their sample decreases as a function of stellar mass. stellar mass surface density. galaxy bulge-to-dise ratio (as measured by the concentration index of the r-band light). and global NUV-r colour.," C10 quantify in detail how the atomic gas fraction of the galaxies in their sample decreases as a function of stellar mass, stellar mass surface density, galaxy bulge-to-disc ratio (as measured by the concentration index of the r-band light), and global NUV-r colour."
 The fraction. of galaxies with significant (more than a few percent) HI decreases sharply above a characteristic stellar surface mass density of 107? M. 7., The fraction of galaxies with significant (more than a few percent) HI decreases sharply above a characteristic stellar surface mass density of $10^{8.5}$ $_{\odot}$ $^{-2}$.
 The fraction of gas-rich galaxies decreases much more smoothly with stellar mass., The fraction of gas-rich galaxies decreases much more smoothly with stellar mass.
 In this paper. we extend the study of CIO to study how theresolved UV/optical photometric properties of galaxies depend on atomic gas fraction.," In this paper, we extend the study of C10 to study how the UV/optical photometric properties of galaxies depend on atomic gas fraction."
 We have developed a photometric pipeline that ransforms the SDSS and GALEX images to the same geometry and etfective resolution. so that our photometric measurements race the same part of each galaxy at different wavelengths (Wang et al 2009).," We have developed a photometric pipeline that transforms the SDSS and GALEX images to the same geometry and effective resolution, so that our photometric measurements trace the same part of each galaxy at different wavelengths (Wang et al 2009)."
" We use these images to study UV-optical colours in jeir inner and outer regions of the galaxies in our sample and to Paltudy how colour cand hence specific star formation rate) ""pend on HI content.", We use these images to study UV-optical colours in their inner and outer regions of the galaxies in our sample and to study how colour (and hence specific star formation rate) depend on HI content.
" In order to extend the range in MCHD/AM jit we are able to probe. we combine the sample analyzed in CIO with galaxies from the GASS ""parent sample"" (described in Section 2)) which have HI detections in the ALFALFA survey."," In order to extend the range in $M_*$ that we are able to probe, we combine the sample analyzed in C10 with galaxies from the GASS “parent sample” (described in Section \ref{sec:data}) ) which have HI detections in the ALFALFA survey."
" This considerably improves the statistics for galaxies with large values of MCHD/M,. which are relatively rare."," This considerably improves the statistics for galaxies with large values of $M_*$, which are relatively rare."
 In order to isolate the effect of the presence or absence of gas on the photometric properties of galaxies. we compare our results with three control samples. whieh have similar optical properties to the galaxies in our sample with HI mass measurements. but are selected without regard to HI content.," In order to isolate the effect of the presence or absence of gas on the photometric properties of galaxies, we compare our results with three control samples, which have similar optical properties to the galaxies in our sample with HI mass measurements, but are selected without regard to HI content."
 These control samples are described in detail in Section 2.3.., These control samples are described in detail in Section \ref{subsec:controlsample}.
 Sections 3.1 and 3.3 present the methods used to measure our photometric parameters. and in Section + we discuss the trends in galaxy size. NUV—r and specific star formation rate gradients. and higher order morphological parameters such as asymmetry and smoothness as a function of HI mass fraction.," Sections \ref{subsec:phot_tech} and \ref{subsec:SF_tech} present the methods used to measure our photometric parameters, and in Section 4 we discuss the trends in galaxy size, $NUV-r$ and specific star formation rate gradients, and higher order morphological parameters such as asymmetry and smoothness as a function of HI mass fraction."
 Finally Section 5. summarizes our results., Finally Section \ref{sec:summary} summarizes our results.
" Throughout this paper. we assume a cosmology with 5270 km s! !. Q,,=0.3. and Q,=0.7 (Tegmarketal.2004)."," Throughout this paper, we assume a cosmology with $H_0$ =70 km $^{-1}$ $^{-1}$ , $\Omega_m$ =0.3, and $\Omega_\Lambda$ =0.7 \citep{Tegmark04}."
.. A Chabrier initial mass function is assumed in the stellar population synthesis analysis (Chabrier 2003)., A Chabrier initial mass function is assumed in the stellar population synthesis analysis \citep{Chabrier03}.
" We select galaxies with stellar masses M,>10!A7; in the redshift range 0.025<z«0.05 from the sixth data release (DR6) of the SDSS Survey. which lie within the maximal ALFALFA footprint."," We select galaxies with stellar masses $M_*>10^{10}M_{\odot}$ in the redshift range $0.025<z<0.05$ from the sixth data release (DR6) of the SDSS Survey, which lie within the maximal ALFALFA footprint."
 We match this catalogue with the fourth data release (GR4) of the GALEX survey and this yields a sample of 10468 galaxies., We match this catalogue with the fourth data release (GR4) of the GALEX survey and this yields a sample of 10468 galaxies.
 We further limit the sample to face-on galaxies with b/a>0.4 tor an inclination of less than 66.4 deg) where 5 and à are the minor and major axes of an ellipsoidal tit (from SDSS r band) to each galaxy., We further limit the sample to face-on galaxies with $b/a>0.4$ (or an inclination of less than 66.4 deg) where $b$ and $a$ are the minor and major axes of an ellipsoidal fit (from SDSS $r$ band) to each galaxy.
 This yields a final sample of 8429 galaxies. which we refer to as thesample from now on.," This yields a final sample of 8429 galaxies, which we refer to as the from now on."
 We restrict the sample to face-on systems. so that our estimates of star formation rate. which are derived from the UV/optical photometry. will be less attected by dust attenuation effects (Section 3.3)).," We restrict the sample to face-on systems, so that our estimates of star formation rate, which are derived from the UV/optical photometry, will be less affected by dust attenuation effects (Section \ref{subsec:SF_tech}) )."
 This sample consists of galaxies in the parent sample for which we have catalogued HI detections from the 40% ALFALFA survey (a 40. which will be discussed in Martinetal.(2010) and Haynesetal. 01000). as well as galaxies that are included in the first data release (DRI) of the GASS survey (see CIO for a detailed description).Our HI sample consists of 458 galaxies with amedian HI mass fraction of ~ 30%.," This sample consists of galaxies in the parent sample for which we have catalogued HI detections from the $40\%$ ALFALFA survey $\alpha.40$ , which will be discussed in \citet{Martin10} and \citet{Haynes10}) ), as well as galaxies that are included in the first data release (DR1) of the GASS survey (see C10 for a detailed description).Our HI sample consists of 458 galaxies with amedian HI mass fraction $_*$ of $\sim$ $\%$ ."
 Figure |. shows the distribution of for these galaxies., Figure \ref{fig:HI_frac} shows the distribution of $_*$ for these galaxies.
 The left-top panel of, The left-top panel of
model.,model.
 This arises because the old bright spot model could not describe the complex bright spot profile present and an innacurate value of the mass ratio is found as a result., This arises because the old bright spot model could not describe the complex bright spot profile present and an innacurate value of the mass ratio is found as a result.
" Our new bright spot model is much better in this respect, and is able to take into account a wider variety of geometric effects and orientations."," Our new bright spot model is much better in this respect, and is able to take into account a wider variety of geometric effects and orientations."
 Given that our white dwarf radius is consistent with that of Feline et al. (, Given that our white dwarf radius is consistent with that of Feline et al. (
"2004b), this seems the most likely cause of such a large change.","2004b), this seems the most likely cause of such a large change."
" It is worth noting that our new donor masses for both DV UMa and XZ Eri, are both consistent with the masses obtained by Feline et al. ("," It is worth noting that our new donor masses for both DV UMa and XZ Eri, are both consistent with the masses obtained by Feline et al. ("
"2004b) using the derivative method, which, unlike our parameterised model, does not make any attempt to recreate the bright spot eclipse profile (e.g. Wood et al.","2004b) using the derivative method, which, unlike our parameterised model, does not make any attempt to recreate the bright spot eclipse profile (e.g. Wood et al."
 1986; Horne et al., 1986; Horne et al.
 1994; Feline et al., 1994; Feline et al.
 2004a; Feline et al., 2004a; Feline et al.
 2004b)., 2004b).
" Our new fits to SDSS 1502 decrease the donor mass by 2.90 (AM,= 0.012Μᾳ9) from that of ?.."," \nocite{wood1986, horne1994, feline2004a, feline2004b}
 Our new fits to SDSS 1502 decrease the donor mass by $2.9\sigma$ $\Delta$$M_{r}=0.012M_{\odot}$ ) from that of \citet{littlefair2008}."
" Our mass ratio and inclination are consistent with those of ?,, however our white dwarf radius, Πω, has increased by 13 percent (3.40)."," Our mass ratio and inclination are consistent with those of \citet{littlefair2008}, however our white dwarf radius, $R_{w}$, has increased by $13$ percent $3.4\sigma$ )."
" We believe the primary reason for this change was that the original fit was heavily binned, and thus more susceptible to the bug outlined in section 3.3.."," We believe the primary reason for this change was that the original fit was heavily binned, and thus more susceptible to the bug outlined in section \ref{sec:pme}."
 The most important change of all of our re-modelled systems is for that of SDSS 1501., The most important change of all of our re-modelled systems is for that of SDSS 1501.
" Whilst our donor mass has only increased by 1.90 from that of ?,, we note that our uncertainties are large (cM,= 0.010Μ9) and the mass difference is large enough to take this system from being a post-period-bounce system, to a pre-period-bounce system."," Whilst our donor mass has only increased by $1.9\sigma$ from that of \citet{littlefair2008}, we note that our uncertainties are large $\sigma$$M_{r}=0.010M_{\odot}$ ) and the mass difference is large enough to take this system from being a post-period-bounce system, to a pre-period-bounce system."
Lt is interesting to note that on the opposite side of the nucleus (region E) neither the Ho. nor the kinematic maps show anv remarkable features.,It is interesting to note that on the opposite side of the nucleus (region E) neither the $\alpha$ nor the kinematic maps show any remarkable features.
 The ionization state. however. is similar to region D. “Phe Ha dispersion map doces show a large perturbation in region E. Perhaps this is the signature of the counter jet although it could also be due to interaction with the companion galaxy.," The ionization state, however, is similar to region D. The $\alpha$ dispersion map does show a large perturbation in region F. Perhaps this is the signature of the counter jet although it could also be due to interaction with the companion galaxy."
 The total OLLI] luminosity that we derive. from the lux distribution shown in panel (g) isM 4.2.«107I erg s (ignoring the contribution from region C. which is due to star formation).," The total [OIII] luminosity that we derive from the flux distribution shown in panel (g) is $4.2 \times 10^{40}$ erg $^{-1}$ (ignoring the contribution from region C, which is due to star formation)."
" Thisis equivalent to the Ho. luminosity of he ENLI. Lg,=4. 107""«erg 7."," This is equivalent to the $\alpha$ luminosity of the ENLR, $L_{\rm H\alpha} =
4\times10^{40}$ erg $^{-1}$."
 Note that this will include the contribution from the eas disk. which cannot »e properly separated from the highly ionized extra-planar eas.," Note that this will include the contribution from the gas disk, which cannot be properly separated from the highly ionized extra-planar gas."
 In comparison. the mechanical power of the jet. itself can be estimated. using an empirical conversion from racio uminosity. (equation (1) of Best et al.," In comparison, the mechanical power of the jet itself can be estimated using an empirical conversion from radio luminosity (equation (1) of Best et al."
 2007)., 2007).
" The observed racio Lux (table 1) ) implies' Li,=(4332).«10712 erg roughly an order of magnitude more than the energy which is reracliated as emission lines."," The observed radio flux (table \ref{t:properties}) ) implies $L_{\rm mech} = (4 \pm 2)\times10^{42}$ erg $^{-1}$, roughly an order of magnitude more than the energy which is reradiated as emission lines."
" Phe X-ray luminosity (table 1)) is larger than both £i, and the emission line edies (Hla and ΟΠ) as expected(e.g. Heckman et al.", The X-ray luminosity (table \ref{t:properties}) ) is larger than both $L_{\rm mech}$ and the emission line luminosities $\alpha$ and [OIII]) as expected (e.g. Heckman et al.
 e2004)., 2004).
 If we assume that most of the mechanical energv of the jet is converted. to kinetic energy in the extra-planar eas then we can compute an upper limit on the mass of ionized hydrogen in the IENLIt., If we assume that most of the mechanical energy of the jet is converted to kinetic energy in the extra-planar gas then we can compute an upper limit on the mass of ionized hydrogen in the ENLR.
" Over the lifetime of availablethejet. I0? vr (e.g. Sanders 1984). the upper limit on the encrey in the EENLIU is: s4107 cre +10° ves1.3.107"" erg."," Over the lifetime of the jet, $\lesssim 10^6$ yr (e.g. Sanders 1984), the upper limit on the available energy in the ENLR is: $\lesssim 4
\times 10^{42}$ erg $^{-1} \times \lesssim 10^6$ yr $ \simeq 1.3
\times 10^{56}$ erg."
 The jet lifetime is also consistent with its small size of =5 kpe. assuming a canonical jet velocity of c.," The jet lifetime is also consistent with its small size of $\lesssim 5$ kpc, assuming a canonical jet velocity of $\gtrsim 0.1c$."
 With the typical gas velocities observed in our data of Vins=MAS1oF~300 km this kinetic energy would. correspond to an upper limit on the mass in ionized ivdrogen of ~1.4107M..," With the typical gas velocities observed in our data of $V^2_{\rm RMS} = V^2_{\rm rot} + \sigma^2 \sim 300$ km $^{-1}$, this kinetic energy would correspond to an upper limit on the mass in ionized hydrogen of $\sim1.4 \times10^{8} M_\odot$."
 In our interpretation. we associate the structure observed in region LD with jet driven mass outllow.," In our interpretation, we associate the structure observed in region D with jet driven mass outflow."
 The raction of the total kinetic energy. needed. to. power this outflow is simply the fraction of mass in region D multiplied w the ratio of the bulk velocity (150 km 3) to Vp~ km s+ squared., The fraction of the total kinetic energy needed to power this outflow is simply the fraction of mass in region D multiplied by the ratio of the bulk velocity $\sim 150$ km $^{-1}$ ) to $V_{\rm RMS} \sim 300$ km $^{-1}$ squared.
 Under the assumption of constant eas densitv. the fraction of mass can be estimated. as the raction of OLLI] luminosity in region D. ~0.07.," Under the assumption of constant gas density, the fraction of mass can be estimated as the fraction of [OIII] luminosity in region D, $\sim
0.07$."
 Therefore he fraction of ENLI kinetic energy in this bulk outllow is M13.10.0007«(150/300)?~2.3.1073 erg.," Therefore the fraction of ENLR kinetic energy in this bulk outflow is $\sim 1.3 \times 10^{56} \times 0.07 \times (150/300)^2
\simeq 2.3 \times 10^{54}$ erg."
 Phat is. only about 2 percent of the mechanical energy is requirecl to »ower the outflow.," That is, only about 2 percent of the mechanical energy is required to power the outflow."
 The derived energies are order of magnitude estimates only but are all internally consistent., The derived energies are order of magnitude estimates only but are all internally consistent.
 The low mass loading ancl velocity associated with the outflow makes it unlikely that this process has a profound. impact on the cold. gas content of this galaxy., The low mass loading and velocity associated with the outflow makes it unlikely that this process has a profound impact on the cold gas content of this galaxy.
 However. the implied: mechanical energv of the jet is 50r times greater on this basis only a small fraction of the jet energy is used to power the outflow.," However, the implied mechanical energy of the jet is 50 times greater — on this basis only a small fraction of the jet energy is used to power the outflow."
 A much larger fraction is available to heat the gas which we observe as the highly ionized. large ENNLI in this galaxy.," A much larger fraction is available to heat the gas which we observe as the highly ionized, large ENLR in this galaxy."
" Ht djs notable that the jet energy. is comparable to the cooling luminosity of a 1 keV ealaxy(LOMOAL.) ""m""halo.", It is notable that the jet energy is comparable to the cooling luminosity of a 1 keV $\sim 10^{13.5} {\rm M_{\odot}}$ ) halo.
 This is an important. point in this [rom the AGN seems to have little direct. effect. on the galaxy: any inlluence it can have occurs through the heating of eas in the galaxy’s halo., This is an important point — in this galaxy feedback from the AGN seems to have little direct effect on the galaxy: any influence it can have occurs through the heating of gas in the galaxy's halo.
 This scenario is very much wih current galaxy formation models(ee..," This scenario is very much consistent with current galaxy formation models (eg.,"
. Croton et consistent22006. Bower et 22006nP IS).," Croton et 2006, Bower et 2006, 2008)."
 Compared with powerful. QSOs (eg. Nesvadha et , Compared with powerful QSOs (e.g. Nesvadba et al.
=Yr) and radio galaxies (eg..," 2007) and radio galaxies (eg.,"
". Jost οἱ ""200ACIN) the ""backjet energy is ", Best et 2007) the jet energy is small.
Nevertheless. it is the impact [oc in 1077.-- 1077AL. haloes that is responsible for shaping the galaxy function.," Nevertheless, it is the impact of AGN feedback in $10^{12}$ $10^{13} {\rm M_{\odot}}$ haloes that is responsible for shaping the galaxy luminosity function."
 The jet of this low mass AGN imparts more of its kinetic energy into the cold gas by means of kinetic heating than by directed outflow., The jet of this low mass AGN imparts more of its kinetic energy into the cold gas by means of kinetic heating than by directed outflow.
 LEU observations of galaxies hosting raclio AGN. such as presented in this letter. provide key insight into the coupling between the jet and the gas.," IFU observations of galaxies hosting radio AGN, such as presented in this letter, provide key insight into the coupling between the jet and the gas."
 We thank the referee. Montserrat. Villar-Martin. for the constructive comments and suggestions.," We thank the referee, Montserrat Villar-Martin, for the constructive comments and suggestions."
 We also like to thank Chris Done. Isabelle Gavignaud. Martin Krause and Alare Schartmann for helpful discussions.," We also like to thank Chris Done, Isabelle Gavignaud, Martin Krause and Marc Schartmann for helpful discussions."
We have assumed that a PPA source would appear as aminous AGN. with the gaseous ΠΙΟ perhaps being supplied » the preceding merger of the binarv's host galaxies.,"We have assumed that a PTA source would appear as luminous AGN, with the gaseous fuel perhaps being supplied by the preceding merger of the binary's host galaxies."
 The degree to which galaxy mergers dictate ACN activity remains an open question. and the link between SALBLI παν and GN activity is even less certain.," The degree to which galaxy mergers dictate AGN activity remains an open question, and the link between SMBH binarity and AGN activity is even less certain."
 Lt is possible hat many SMDLILI binaries that are incliviclually detected by *PAs will have no EAL counterpart at all., It is possible that many SMBH binaries that are individually detected by PTAs will have no EM counterpart at all.
 Our results were calculated using a simple semi-analvtic accretion disc model. a central assumption of which is that he binarys tidal torques are able to open a central cavity in the disc.," Our results were calculated using a simple semi-analytic accretion disc model, a central assumption of which is that the binary's tidal torques are able to open a central cavity in the disc."
 In the raciation-dominatec regions of interest. strong horizontal advective Duxes or vertical thickening of he disc may act to close such à cavity ancl wipe out the eatures we predict.," In the radiation-dominated regions of interest, strong horizontal advective fluxes or vertical thickening of the disc may act to close such a cavity and wipe out the features we predict."
 Phe features would also not be present if the disc and binary orbits do not lie on the same plane. as in the binary model sof the variable BL Lac object O.J 287 (Lehto&Valtonen1996).," The features would also not be present if the disc and binary's orbits do not lie on the same plane, as in the binary model of the variable BL Lac object OJ 287 \citep{LV96}."
. Absorption and reprocessing by he binary’s host galaxy may also act to mask or mimic the intrinsic thermal AGN emission we have moclelect., Absorption and reprocessing by the binary's host galaxy may also act to mask or mimic the intrinsic thermal AGN emission we have modeled.
 As we were completing this work. we became aware of a concurrent independent. study by Sesanaetal.(2011). addressing similar questions.," As we were completing this work, we became aware of a concurrent independent study by \cite{Sesana+11}, addressing similar questions."
 “PT acknowledges fruitful discussions. with Alberto Sesana. Massimo. Dotti. and Constanze Roelelig.," TT acknowledges fruitful discussions with Alberto Sesana, Massimo Dotti, and Constanze Röddig."
 Phe authors thank Jules Halpern aud Jeremy Goodman. for insightful. conversations. and are erateful to the anonymous referee. for suggestions that improved the clarity of the manuscript.," The authors thank Jules Halpern and Jeremy Goodman for insightful conversations, and are grateful to the anonymous referee for suggestions that improved the clarity of the manuscript."
 This work was supported by NASA NEEP. grants NNNOSAII35G. (to IXM) and NNITLOZDAOOIN (to ZHI) and by the Polánnyi Program of the Hungarian National Ollice for Rescarch and Technology. (ΝΑΤ to ZL)., This work was supported by NASA ATFP grants NNXO8AH35G (to KM) and NNH10ZDA001N (to ZH) and by the Polánnyi Program of the Hungarian National Office for Research and Technology (NKTH; to ZH).
 This research was supported in part by the Perimeter Institute for Theoretical Physics., This research was supported in part by the Perimeter Institute for Theoretical Physics.
"quasars without detected AALs, matched in redshift and i-band magnitude to the AAL quasars.","quasars without detected AALs, matched in redshift and $i$ -band magnitude to the AAL quasars."
 We create composite spectra using the method described in VandenBerketal. (2001)., We create composite spectra using the method described in \citet[][]{VandenBerk_etal_2001}.
". In short, each spectrum was shifted to restframe, rebinned onto a common dispersion of 1 pper bin, and normalized."," In short, each spectrum was shifted to restframe, rebinned onto a common dispersion of 1 per bin, and normalized."
" The final composite spectrum was generated by taking the median (or geometric mean) flux density in each bin of the shifted, rebinned, and scaled "," The final composite spectrum was generated by taking the median (or geometric mean) flux density in each bin of the shifted, rebinned, and scaled spectra."
An error was generated from the semi-interquantilespectra. range of the spectrumflux densities in each bin scaled by NV. where is the number of spectra contributing to that bin.," An error spectrum was generated from the semi-interquantile range of the flux densities in each bin scaled by $N_{\rm spec}^{1/2}$, where $N_{\rm spec}$ is the number of spectra contributing to that bin."
 We refer the Nopecreader to VandenBerketal.(2001) for more details regarding generating the composite spectra.," We refer the reader to \citet{VandenBerk_etal_2001}
 for more details regarding generating the composite spectra."
 The left panel of 33 shows composite spectra for the above quasar samples., The left panel of 3 shows composite spectra for the above quasar samples.
 AAL quasars have colors lying between normal quasars and the so-called “dust-reddened” quasars in SDSS (with color A(g—i)>0.3; Richards et al., AAL quasars have colors lying between normal quasars and the so-called “dust-reddened” quasars in SDSS (with color $\Delta(g-i)>0.3$; Richards et al.
 2003)., 2003).
" The reddening of AAL quasars relative to the control quasars is well described by a SMC-like extinction curve, with E(B—V)~0.03, consistent with VandenBerketal. (2008)."," The reddening of AAL quasars relative to the control quasars is well described by a SMC-like extinction curve, with $E(B-V)\sim 0.03$, consistent with \cite{Vanden_Berk_etal_2008}."
. The right panel shows flux ratios of the AAL quasar composites to that of the control quasars., The right panel shows flux ratios of the AAL quasar composites to that of the control quasars.
" The “redshifted” and “blueshifted” samples show a prominent excess of narrow eemission, which is absent in the case of the like” sample."," The “redshifted” and “blueshifted” samples show a prominent excess of narrow emission, which is absent in the case of the ``intervening-like'' sample."
" The lack of eemission excess, the similar amount of reddening to classical intervening absorption systems (e.g., York et 22006), and the fact that they join the plateau of the velocity distribution (e.g., reffig:vdist)), suggest that AALs with voy>1500kms""! are in fact mostly classical interveningabsorbers’."," The lack of emission excess, the similar amount of reddening to classical intervening absorption systems (e.g., York et 2006), and the fact that they join the plateau of the velocity distribution (e.g., \\ref{fig:vdist}) ), suggest that AALs with $v_{\rm off}>1500\,{\rm km\,s^{-1}}$ are in fact mostly classical intervening."
. We note that the large-scale fluctuations seen in the composite ratios are due to correlated noise arising from variance in the shape of quasar continua., We note that the large-scale fluctuations seen in the composite ratios are due to correlated noise arising from variance in the shape of quasar continua.
 The correlation between the presence of absorbers with Vorr«1500 ss?! and eemission is of great interest., The correlation between the presence of absorbers with $v_{\rm off}<1500$ $^{-1}$ and emission is of great interest.
" While the composite aabsorption lines are, by construction, offset by hundreds of kms""! with respect to the quasars, the stacked excess eemission is found more or less at the quasar systemic velocity (see below)."," While the composite absorption lines are, by construction, offset by hundreds of ${\rm
km\,s^{-1}}$ with respect to the quasars, the stacked excess emission is found more or less at the quasar systemic velocity (see below)."
"velocity.. The central engine, i.e., the black hole radiation, appears to be similar in AAL quasars and in normal quasars: other than the reddening and aabsorption, no difference is seen in the continuum and broad emission lines between the two quasar populations."," The central engine, i.e., the black hole radiation, appears to be similar in AAL quasars and in normal quasars: other than the reddening and absorption, no difference is seen in the continuum and broad emission lines between the two quasar populations."
 This suggests that dust-reddening is the explanation for the color difference seen in AAL quasars and normal quasars., This suggests that dust-reddening is the explanation for the color difference seen in AAL quasars and normal quasars.
 One might ask if this dust reddening might also cause the apparent eexcess seen in the flux ratio plot in Fig. 3.., One might ask if this dust reddening might also cause the apparent excess seen in the flux ratio plot in Fig. \ref{fig:composite}.
 Dust reddening could occur on spatial scales much smaller than the eemission region but much larger than the continuum plus broad line region., Dust reddening could occur on spatial scales much smaller than the emission region but much larger than the continuum plus broad line region.
" In this case the continuum is attenuated while the eemission is not, an enhancement of sstrength relative to the causingunderlying apparentcontinuum."," In this case the continuum is attenuated while the emission is not, causing an apparent enhancement of strength relative to the underlying continuum."
" Assuming an SMC-like extinction curve, we require E(B—V)~0.12 to achieve the level of eemission enhancement relative to the continuum, substantially larger than the inferred E(B—V)~0.03 from the composite spectra."," Assuming an SMC-like extinction curve, we require $E(B-V)\sim 0.12$ to achieve the level of emission enhancement relative to the continuum, substantially larger than the inferred $E(B-V)\sim 0.03$ from the composite spectra."
 We now focus on the eemission excess., We now focus on the emission excess.
" To quantify it and estimate its significance, we create continuum-subtracted median composites around the eemission line."," To quantify it and estimate its significance, we create continuum-subtracted median composites around the emission line."
 This is done by subtracting a running median, This is done by subtracting a running median
"and variable couplings, as compared to ACDM, and the effect significantly grows with mass (the decreasing behavior found in ? can be explained in view of ?)).","and variable couplings, as compared to $\Lambda $ CDM, and the effect significantly grows with mass (the decreasing behavior found in \cite{Manera_Mota_2006} can be explained in view of \cite{Wintergerst_pettorino_2010}) )."
" In particular, at z©1.5 the halo number density at the high-mass end of our simulated mass functions exceeds the ACDM value by a factor ~10 and ~3 for constant and variable couplings, respectively."," In particular, at $z\approx 1.5$ the halo number density at the high-mass end of our simulated mass functions exceeds the $\Lambda $ CDM value by a factor $\sim 10$ and $\sim 3$ for constant and variable couplings, respectively."
 In Fig. , In Fig. \ref{mass_corr_plot}) )
"we plot the same quantities for our hydrodynamical @)high-resolution simulations, which confirm the trend found in the larger simulation box, although the"," we plot the same quantities for our hydrodynamical high-resolution simulations, which confirm the trend found in the larger simulation box, although the"
AGN and SD components do not seem to experience a strong evolution with redshift up to 2~0.35.,AGN and SB components do not seem to experience a strong evolution with redshift up to $z \sim 0.35$.
 It is now possible to obtain a quantitative estimate of the AGN contribution to the bolometric Iuminosityv. by assuming &—RA?{Re2225; ↴⊺∐≼↲≀↧↴∐≀↧↴↥⋡∖↽∐≺∢≀↧↴↥⊳∖⇁∥↲↕↽≻⊳∖⊽≼⇂≼↲⋝∖⊽≺∢↕⋅↕∣↽≻≼↲≼⇂⊳∖⇁∪↓⋟≀↧↴↕⋅≀⋯," It is now possible to obtain a quantitative estimate of the AGN contribution to the bolometric luminosity, by assuming $\kappa=R^\mathit{agn}/R^\mathit{sb}\sim$ 25: The analytical steps described so far are summarized in Fig. \ref{np},"
↲⋝∖⊽∏∐∐⊔≀↧↴↕⋅↕∠≼↲≼⇂↥∐⊡≸≟⋅∃⋅⋅↕∐∖∖↽∐↕≺∢∐⊔∐↲∣↽≻≼↲⊳∖⇁↥∐↥∪↓≯ ∪↓≯∣↽∣↜∣⋯∣↓⋟∪↕⋅⊔∐↲↥∐≼∐∖↽↕⋔⋯↥⊳∖⇁⋯∐⋅≺∢≼↲⊳∖⊽≀↧↴↕⋅≼↲∐⊳∖⊽∩↲≼⊔∐↴⊺≀↧↴∣↽≻↥≼↲⊥⋅⋅∖∖↽↕⊔↥⊔∐↲⊥⊔≺∢∪∐⇂∎∐⇂≼↲∐≺∢≼↲∐∐↓∐⊳∖⊽⋅," in which the best fit of equation \ref{eq}) ) is shown as a function of $\alpha_\mathit{bol}$, that is $R=\alpha_\mathit{bol}R^\mathit{agn}+(1-\alpha_\mathit{bol})R^\mathit{sb}$."
 ≼↕⊲∪∐≺∢≼↲↕⋅∐↕∐≸↽↔↴⊔∐↲⊥⊳∫⋡∖↽↧⊺∟∐⋩⊂↽⊐⋟∖⊽⋅⋯∐⋅↕⋅≼↲⋟∖⊽∏∐⋟∖⊽≀⋯↲↕∐↖≺↽↔↴∪⋯⇂≀↧↴≸↽↔↴↕⋅≼↲≼↲∐∐↲↕∐∖∖⊽↕⊔↥⊔↥∪⋟∖⇁≼↲∪↓⋟∖⊽≼↲↕∐≼↲∏⇀↸ ," The values of $\alpha_\mathit{bol}$ for the individual sources are listed in Table \ref{t1}, with the $\sigma$ confidence limits."
≼↲↥≀↕↴↥⋅⋜⋡∃∩∩≤∍≀↧∁⋝∶⊔∐↲↕↕⋅≼↲∐⋟∖⇁≼↲∐↓∣↽≻↥≼↲≀↧↴∐≺⇂↕∐≺∐∖↽↕≼⇂∏≀↧↴↥≼↲⋟∖⊽∐∐↓≀↧↴∩↲⋟∖⊽≀↧↴↕⋅≼↲↥≀↧↴↕⋅," Concerning the 1 Jy ULIRGs, our results are in good agreement with those of Veilleux et al. ("
≸↽↔↴≼↲↕⋅⊔↥≀↧↴∐∪⋯⋅⋟∖⊽∣↽≻⋡∖↽↴∿↴∐⊓↽≻≼↲↕⋅ cent. but this seems to be a small svstematic effect related to the AGN/SB (or. in other words. the [actor &).,"2009a): their ensemble and individual estimates are larger than ours by $\sim$ 10 per cent, but this seems to be a small systematic effect related to the AGN/SB (or, in other words, the factor $\kappa$ )."
 The work of Veilleux et al. (, The work of Veilleux et al. (
2009a) explores the connection between ULIBRGs and quasars. and provides six different methods based on the Spi/zer--RS spectra for computing the AGN contribution to the bolometrie luminosity of both kinds of sources.,"2009a) explores the connection between ULIRGs and quasars, and provides six different methods based on the -IRS spectra for computing the AGN contribution to the bolometric luminosity of both kinds of sources."
 The comparison among (hese six independent estimates gives a good measure ol the uncertainties involved when considering the individual sources. which sometimes can be rather huge with respect to the AGN contribution averaged over all methods.," The comparison among these six independent estimates gives a good measure of the uncertainties involved when considering the individual sources, which sometimes can be rather large with respect to the AGN contribution averaged over all methods."
 Such discrepancies can be regarded as (he natural dispersion connected to the use of single indicators. whieh allects our narrow-band analvsis as well.," Such discrepancies can be regarded as the natural dispersion connected to the use of single indicators, which affects our narrow-band analysis as well."
 The scatter around. the best lit of Fig., The scatter around the best fit of Fig.
" 2 is in [act significantly larger than the statistical uncertaintv on the best values of RO"" and R.", \ref{np} is in fact significantly larger than the statistical uncertainty on the best values of $R^\mathit{agn}$ and $R^\mathit{sb}$.
" The actual lo dispersion is 0.18 dex. nearly independent of 05,4. and this should be considered the intrinsic dispersion of the 6 sau to bolometric ratios for the AGN and SB components."," The actual $\sigma$ dispersion is 0.18 dex, nearly independent of $\alpha_\mathit{bol}$, and this should be considered the intrinsic dispersion of the 6 $\mu$ m to bolometric ratios for the AGN and SB components."
 An ecquivalent way of visualizing this point is shown in Fig. 3..," An equivalent way of visualizing this point is shown in Fig. \ref{pd},"
 where the total HR. Iuminosities inferred from our spectral analvsis. assuming (he best values of RO!” and 75 as the true bolometric corrections. are compared to the luminosities nieasured by according to equation (1)).," where the total IR luminosities inferred from our spectral analysis, assuming the best values of $R^\mathit{agn}$ and $R^\mathit{sb}$ as the true bolometric corrections, are compared to the luminosities measured by according to equation \ref{e1}) )."
 The natural dispersion is clearly brought out once again. and (his limits the accuracy. with which the AGN and SB components can be assessed in individual objects.," The natural dispersion is clearly brought out once again, and this limits the accuracy with which the AGN and SB components can be assessed in individual objects."
 We finally remind what are (he possible sources of svstematic error in our approach: 1) the selection of a narrow wavelength range for our analvsis prevents a complete understanding of the gas and dust properties. Chat could be better investigated by considering the whole," We finally remind what are the possible sources of systematic error in our approach: 1) the selection of a narrow wavelength range for our analysis prevents a complete understanding of the gas and dust properties, that could be better investigated by considering the whole"
The interred geometry of the accretion disk in {0 50.55 (i.c.. truncated. and/or iuner parts covered bv corona) nav be conunon features of ACNs with powerful jets.,"The inferred geometry of the accretion disk in 4C 50.55 (i.e., truncated and/or inner parts covered by corona) may be common features of AGNs with powerful jets."
" Receut studies iudicate that radio galaxies also ave relatively narrow irou-Ix. enissionu lines e.g. ry,7 20 ry tefor 3€ 390.3 (Saubrunaetal.2009) and rg2 Ll re for 171.26 (Larssonetal.2008). from the sinele diskline fit. and rg,=(9x1) for 3€ 120 from the iultiple conrponeuts ft (INataokactal.2007)."," Recent studies indicate that radio galaxies also have relatively narrow iron-K emission lines e.g., $r_{\rm in} >$ 20 $r_{\rm g}$ for 3C 390.3 \citep{Sam09} and $r_{\rm
in} >$ 44 $r_{\rm g}$ for 4C +74.26 \citep{Lar08} from the single diskline fit, and $r_{\rm in} = (9\pm1) r_{\rm g}$ for 3C 120 from the multiple components fit \citep{Kat07}."
. This result is in accordance with an expectation from theories that jets are more easily produced by radiatively inefücieut accretion flow than by a standard cisk., This result is in accordance with an expectation from theories that jets are more easily produced by radiatively inefficient accretion flow than by a standard disk.
 Another key paramcter to understand the accretion How is the Eddington ratio. which is estimated to be Lyua/LgaacO.L for [€ 50.55 (section ??)).," Another key parameter to understand the accretion flow is the Eddington ratio, which is estimated to be $L_{\rm bol}/L_{\rm Edd}
\sim 0.4$ for 4C 50.55 (section \ref{differ_SED}) )."
" Similarly. we also estimate that of 3€ 120 to be Lig/Lpgq~0.5. using the 210 keV flux (Ikataokactal.2007). and the black hole mass of LO"" citepPeto L."," Similarly, we also estimate that of 3C 120 to be $L_{\rm bol}/L_{\rm Edd} \sim 0.5$, using the 2–10 keV flux \citep{Kat07} and the black hole mass of $10^{7.7}$ \\citep{Pet04}."
". Thus. these two sources 11av belong to a very similar class of AGNs, except for the radio louduess to the N-rav flux (log Rx=2.1 for 3C 120 and Ίου Rx=3.6 for IC 50.55). which could be partially explained bx the small inclination angle of 3€ 120 (/<1l: see Ikataokaetal. 2007)) couipired with LC 50.55 (/~ 357)."," Thus, these two sources may belong to a very similar class of AGNs, except for the radio loudness to the X-ray flux (log $R_{\rm X} = -2.1$ for 3C 120 and log $R_{\rm
X} = -3.6$ for 4C 50.55), which could be partially explained by the small inclination angle of 3C 120 $i<14^{\circ}$; see \citealt{Kat07}) ) compared with 4C 50.55 $i \sim 35^{\circ}$ )."
 The physical reasou for the difference in their N-ray spectra that the reflection component and mon-kE lines are strouger in 3€ 120 (I— 0.7) is not clear at present., The physical reason for the difference in their X-ray spectra that the reflection component and iron-K lines are stronger in 3C 120 $R\sim0.7$ ) is not clear at present.
 1€ 50.55. and 3€ 120 are rare objects haviug distinctively hieh fractions of Eddington luuinositv compared with other typical BLRGs. for instance. Lyua/Lgg = 0.010.07 for 3€ 390.3 (Sambrunaetal.2009:Lewis&Eracleous 2006).. —0.01 for LC |71.26 (Larssonetal.2008). and 0.0010.002 for Arp 102D (Lewis&Eracleous2006).," 4C 50.55 and 3C 120 are rare objects having distinctively high fractions of Eddington luminosity compared with other typical BLRGs, for instance, $L_{\rm bol}/L_{\rm Edd}$ = 0.01–0.07 for 3C 390.3 \citep{Sam09, Lew06}, $\sim 0.04$ for 4C +74.26 \citep{Lar08}, and 0.001–0.002 for Arp 102B \citep{Lew06}."
. By analogy to the Galactic dack holes. these low Eddiustou ratio sources likely correspond to the low/hard state. where the accretion disk is accompanied by steadyuh jets. while wormal Sevfert ealaxies may do to the lieh state. where the disk extends close to the ISCO with quenchedm jet activity.," By analogy to the Galactic black holes, these low Eddington ratio sources likely correspond to the low/hard state, where the accretion disk is accompanied by steady jets, while normal Seyfert galaxies may do to the high/soft state, where the disk extends close to the ISCO with quenched jet activity."
 The accretion flows in IC 50.55 aud 3€ could be explained as a lieh Πιοτν eud of the low/hard state., The accretion flows in 4C 50.55 and 3C 120 could be explained as a high luminosity end of the low/hard state.
 Alternatively. they may be another state achieved witli even higher mass accretion rates than iu the hieh/soft state. where the disk structure is also simular to that found iu the loxανα state (.0.. truncated disk).," Alternatively, they may be another state achieved with even higher mass accretion rates than in the high/soft state, where the disk structure is also similar to that found in the low/hard state (i.e., truncated disk)."
 For this possibility. itf is iuterestiug to note the similarly to the hieh-Eddiugtouratio Galactic black hole CRS 1915|105. which exhibits a similarly narrow ος cussion liue over a Comptonization clominated coutinuuu. implying that the tuner disk is fully covered by a corona (Uedaetal.2010): in GRS 1915|105. a compact jet is also detected in a steady state with a παντα spectrum. so-called in Class \ (seee.g..Feuder&Belloui2001)..," For this possibility, it is interesting to note the similarly to the high-Eddington ratio Galactic black hole GRS 1915+105, which exhibits a similarly narrow iron-K emission line over a Comptonization dominated continuum, implying that the inner disk is fully covered by a corona \citep{Ued10}; in GRS 1915+105, a compact jet is also detected in a steady state with a hard spectrum, so-called in Class $\chi$ \citep[see e.g.,][]{Fen04a}."
 Iu sununaryv. the unified picture of accretion flows over a wide range of black hole mass is far frou established.," In summary, the unified picture of accretion flows over a wide range of black hole mass is far from established."
 Further svstematic studies of the accretion disk structure of radio loud ACNs at various accretion rates based ou detailed N-ray spectroscopy and multi-waveleneths data are very iurportaut to reveal these fundamental problems., Further systematic studies of the accretion disk structure of radio loud AGNs at various accretion rates based on detailed X-ray spectroscopy and multi-wavelengths data are very important to reveal these fundamental problems.
 We thank Corry Skinner for providing the Suvff/BAT heht curve of 1€ 50.55. and the team for the calibration of the iustrmuents.," We thank Gerry Skinner for providing the /BAT light curve of 4C 50.55, and the team for the calibration of the instruments."
" Part of this work was financially supported by Cwauts-in-Aid for Scicutific Research 20510230. (YU) aud 20710100. (YT). auc by the erant-inaid for the Clobal COE Program ""The Next Generation of Physics. Spun from Universality aud Emergence” from the Ministry of Education. Culture. Sports. Science aud Technology (AIENT) of Japan."," Part of this work was financially supported by Grants-in-Aid for Scientific Research 20540230 (YU) and 20740109 (YT), and by the grant-in-aid for the Global COE Program “The Next Generation of Physics, Spun from Universality and Emergence” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan."
driving velocities.,driving velocities.
" The triangle represents the ""corrected"" 7 value for the run ""C4"" and the star is the corrected value for ""A3""."," The triangle represents the “corrected"" $\eta$ value for the run “C4"" and the star is the corrected value for “A3""."
" The scalings. corresponding to the lines plotted in the Figure. are = VV,=0.1. = 0.147: VV,-0.05 = VV,=0.05 -- Here one can see two different comparable fits for the slow (V,= 0.05) driving experiments. with the scaling based on the corrected value leading to aslightly stronger dependence of Jing 0n 3."," The scalings, corresponding to the lines plotted in the Figure, are = V_d=0.1, = V_d=0.05 - = V_d=0.05 - Here one can see two different comparable fits for the slow $V_d=0.05$ ) driving experiments, with the scaling based on the corrected value leading to aslightly stronger dependence of $J_{max}$ on $\eta$ ."
 However. the correction of the 77 value for the faster driver does not seem to lead to a linear scaling relation.," However, the correction of the $\eta$ value for the faster driver does not seem to lead to a linear scaling relation."
 We now turn to the scaling of the peak current with the driving velocity. for a constant 77 value. which is investigated using the 7=107? experiments listed inΙ.," We now turn to the scaling of the peak current with the driving velocity, for a constant $\eta$ value, which is investigated using the $\eta=10^{-3}$ experiments listed in."
. The result is shown 19.. where it is seen that while the peak current clearly depends on the imposed driving velocity. there is no simple (e.g. linear or exponential) relation that can be obtained to fit the data.," The result is shown in, where it is seen that while the peak current clearly depends on the imposed driving velocity, there is no simple (e.g. linear or exponential) relation that can be obtained to fit the data."
 The dimensions and tilt angle of the current sheet have been measured for the same experiments., The dimensions and tilt angle of the current sheet have been measured for the same experiments.
 They are found to be independent of 7 for a constant driving velocity. to within our measurement accuracy.," They are found to be independent of $\eta$ for a constant driving velocity, to within our measurement accuracy."
 On the other hand. varying the driving velocity while maintaining a constant value for 77. we find that there are significant changes of these dimensions. indicating that they are largely dependent on the amount of imposed stress.," On the other hand, varying the driving velocity while maintaining a constant value for $\eta$, we find that there are significant changes of these dimensions, indicating that they are largely dependent on the amount of imposed stress."
 However. as discussed above. the present domain size and the extent of the driving region limit the current sheet from evolving freely. and thus with the present setup we are unable to provide scaling relations for these quantities.," However, as discussed above, the present domain size and the extent of the driving region limit the current sheet from evolving freely, and thus with the present setup we are unable to provide scaling relations for these quantities."
 The top frame of shows the maximum outflow velocity as a function of time for different driving velocities Vj., The top frame of shows the maximum outflow velocity as a function of time for different driving velocities $V_d$ .
 This showsa significant variation both with time and, This showsa significant variation both with time and
It appears then that Lor large redshifts.,It appears then that for large redshifts.
" Any model with a luminosity distance that grows slower than vields (mi—M)<0 (as SNLO97TID) bevond some z. Perhaps the simplest model one can construct wilh such a property is a flat space wilh a single (hud with constant equation of statew,.", Any model with a luminosity distance that grows slower than yields (m-M)<0 (as SN1997ff) beyond some z. Perhaps the simplest model one can construct with such a property is a flat space with a single fluid with constant equation of state.
. In (Bis case one has in and the lnminosity distance (lor /=2/3) ⋅⋅ ↓⋟∪↕⋅≀↧↴∐∖⇁∣∣⋅↙∕∖∕∖∩⋅⋅⇀∖↕, In this case one has in and the luminosity distance (for =2/3) For <2/3 and large z we have.
∐∐≼↲⋅⊳∖⊽∐↓⋯⇂≼↲↥∩↕∖↽≼↲⋝∖⊽≀↧↴↥∖∖↽≀↧↴∖↽⊳∖⊽↥≀↧↴↕⋅∩≼↲↕⋅≺∐⊳∖⇁↥≀↧↴∐≺∢≼↲⊳∖⊽⋜≀↧↴∐≼⇂⊔∐↲↕⋅≼↲↓≯∪↕⋅≼↲⋟≀↧↴↕∐∩↲↕⋅ ↽ ⊟≻↕⋅∣∣⋅↙↙∖∕∖−≻∕∕∣≡⊰≀↧↴↕∐⊔≀↧↴↕⋅≸≟≼↲⊳∶∖∖↽≼↲∐≀↧↴∖↽≼↲↙∣⊥∾⊳∶−⊔↴−⋅⋅∐↓∪∐∪∖∖⊽⊳∖⊽⊔⋯↥⋅≀↧↴↥↥≀↧↴↕⋅↖↳↴≼↲⊳∶≀↧↴∐≼⇂ ↥∏∐∐∐∪⋝∖⊽∐∖↽⋅↥⋅≼↲⋅↥≀↧↴↕⋅∩≼↲↕⋅≀↧↴↽≻↽≻≀↧↴↕⋅≼↲∐↥∐↓≀↧↴∩∐∐⋯⇂≼↲⋝∖⊽⋝⊔⋯↴∐⊔∐↲⊳∖⇁↕∐∩↥≼↲−∐∏↕≺⇂∐≀↧↴↥−⋝∖⊽↽≻≀↧↴≺∢≼↲≼↲∖↽∪∏∐∪∐⋅ C» .," It follows that, at large z and for any >0, Milne's model gives always larger distances (and therefore fainter luminosity, i.e. larger apparent magnitudes) than the single-fluid flat-space evolution."
J In Fig., In Fig.
" 1η I plot AQ —M)for various values of wy...alone withmodel the reference [lat e ,, =0.65."," 1 I plot (m-M) for various values of, along with the reference flat model =0.65."
".It appears clearly that values of te, 0.4 m are acceptable. as it will be confirmed by the likelihood analvsis below."," It appears clearly that values of around 0.1 are acceptable, as it will be confirmed by the likelihood analysis below."
 llowever. according to (he observations. our universe is composed by a mixture oL καν. of clustered matter (which includes a," However, according to the observations, our universe is composed by a mixture of, say, of clustered matter (which includes a"
"tenth of a magnitude in the (H-K,) color.",tenth of a magnitude in the ) color.
 These offsets were added to the zero-points calculated for our photometry., These offsets were added to the zero-points calculated for our photometry.
 The errors on these zero-point offsets to the magnitudes of the MKO system are smaller than the photometric An analysis to examine the internal photometric uncertainties calculated by ALLSTAR-DAOPHOT routine was made for each filter by means of adding artificial stars to the science images., The errors on these zero-point offsets to the magnitudes of the MKO system are smaller than the photometric An analysis to examine the internal photometric uncertainties calculated by -DAOPHOT routine was made for each filter by means of adding artificial stars to the science images.
 Our 6604 field was divided in two regions: the ‘central region’ and the ‘field region’., Our 604 field was divided in two regions: the `central region' and the `field region'.
" As the main cluster of 6604 does not stand out as an evident increase in the stellar density, the central region limit was set using a NIRI image obtained with the Pa narrow-band filter (details on narrow-band images and analysis will be included in a forthcoming paper)."," As the main cluster of 604 does not stand out as an evident increase in the stellar density, the central region limit was set using a NIRI image obtained with the $\beta$ narrow-band filter (details on narrow-band images and analysis will be included in a forthcoming paper)."
 This is illustrated in Figure 4 where the smoothed Pa contours at 5c used to define the central region limit are shown., This is illustrated in Figure \ref{fig:contornos} where the smoothed $\beta$ contours at $\sigma$ used to define the central region limit are shown.
" The central region, enclosed by a ~150 pc radius circle, is centered at a=01347335.14and 6=--30?47'1.""9 and its area (of 68000 pc?) encompasses the 6604 SOBA."," The central region, enclosed by a $\sim$ 150 pc radius circle, is centered at $\alpha=01^h34^m33^s.14$and $\delta=+30^{\circ}47\arcmin 1.\arcsec9$ and its area (of 68000 $^2$ ) encompasses the 604 SOBA."
" The region outside the circle, the field region, has a surface of ~118000 pc? and was used to account for field star A histogram of magnitude distribution (0.5 mag bin width) was generated separately for each region."," The region outside the circle, the field region, has a surface of $\sim$ 118000 $^2$ and was used to account for field star A histogram of magnitude distribution (0.5 mag bin width) was generated separately for each region."
 A new image was created by adding artificial stars to each region., A new image was created by adding artificial stars to each region.
 The number of added objects represented of the stars at each magnitude interval., The number of added objects represented of the stars at each magnitude interval.
 The artificial star magnitudes were measured following the same procedure employed for the natural stars., The artificial star magnitudes were measured following the same procedure employed for the natural stars.
" By comparing their measured magnitudes with their ‘true’ magnitudes, we found that the differences are in the range of the magnitude uncertainties calculated by the routine."," By comparing their measured magnitudes with their `true' magnitudes, we found that the differences are in the range of the magnitude uncertainties calculated by the routine."
" In Figure ὅ we have plotted the difference between the ‘true’ and measured magnitudes for the artificial stars for theJ,H, and filters in the top, middle, and bottom panels, respectively."," In Figure \ref{fig:error_j} we have plotted the difference between the `true' and measured magnitudes for the artificial stars for the, and filters in the top, middle, and bottom panels, respectively."
 The bars represent the magnitude error calculated by for the measured magnitudes., The bars represent the magnitude error calculated by for the measured magnitudes.
gas is in hwerostatic equilibrium.,gas is in hydrostatic equilibrium.
 Using entropy rather than. for example. the gas density as the basic parametrization is motivated by the theoretical and observed. self-similarity of entropy. profiles in. cluster samples.," Using entropy rather than, for example, the gas density as the basic parametrization is motivated by the theoretical and observed self-similarity of entropy profiles in cluster samples."
 This model can be constrained by SZ and X-ray data to give fitted. eas. and total matter properties of the cluster., This model can be constrained by SZ and X-ray data to give fitted gas and total matter properties of the cluster.
 The model has sensible convergence properties and can be used out to the virial radius of the cluster., The model has sensible convergence properties and can be used out to the virial radius of the cluster.
 By construction. the model does not allow unphysical or inconsistent properties of the cluster gas as can happen if. for example. a parametric fit to the eas density is combined with an unrelated parametric fit to the empoerature.," By construction, the model does not allow unphysical or inconsistent properties of the cluster gas as can happen if, for example, a parametric fit to the gas density is combined with an unrelated parametric fit to the temperature."
 We have tested the model using two detailed N-body xus hydrodynamical simulations of massive clusters with contrasting merger histories., We have tested the model using two detailed N-body plus hydrodynamical simulations of massive clusters with contrasting merger histories.
 In both cases. using realistic mock data from presently available X-ray and SZ telescopes. he mocel is able to accurately fit both the integrated cluster xwameters and. their radial profiles.," In both cases, using realistic mock data from presently available X-ray and SZ telescopes, the model is able to accurately fit both the integrated cluster parameters and their radial profiles."
 LE high-quality. data with very low noise are simulated. the cluster parameters are returned with essentially no bias.," If high-quality data with very low noise are simulated, the cluster parameters are returned with essentially no bias."
 Our fitting code includes roth random. noise and systematic calibration errors in the cata and. Lully includes the elfect. of contamination [roni wimordial CMD. Hluctuations ancl radio sources in the SZ data., Our fitting code includes both random noise and systematic calibration errors in the data and fully includes the effect of contamination from primordial CMB fluctuations and radio sources in the SZ data.
 We also use a hivper-parameter approach to scale the relative constraints [from the two data sets., We also use a hyper-parameter approach to scale the relative constraints from the two data sets.
 C'omparison with the widelv-used isothermal 2 model confirms previous results that this mocel can result in significant biases in fitted: cluster parameters (e.g.??)..," Comparison with the widely-used isothermal $\beta$ model confirms previous results that this model can result in significant biases in fitted cluster parameters \citep[e.g.][]{Kay:2004b, Hallman:2007}."
 The quality of the available SZ data is now high enough to require a more sophisticated modelling approach. especially with data that are sensitive to the outskirts of cluster.," The quality of the available SZ data is now high enough to require a more sophisticated modelling approach, especially with data that are sensitive to the outskirts of cluster."
 This model. however remains simplistic in several potentially important wavs., This model however remains simplistic in several potentially important ways.
 The assumption of hydrostatic equilibrium. is clearly broken badly in the central cores of clusters. anc we are forced. to ignore the data in this region.," The assumption of hydrostatic equilibrium is clearly broken badly in the central cores of clusters, and we are forced to ignore the data in this region."
 Hvdrostatie equilibrium will also be broken in the main body of the cluster due to bulk motions and. οἱher non-thermal support. although in our simulations this does not seem to be a significant impediment to measuring accurate. cluster. profiles.," Hydrostatic equilibrium will also be broken in the main body of the cluster due to bulk motions and other non-thermal support, although in our simulations this does not seem to be a significant impediment to measuring accurate cluster profiles."
 We do not. currently treat. the boundary of the cluster in a Lully consistent way at some radius the virialisecl gas. must. meet a boundary shock of in-falling material and we do not model the corresponding step in pressure., We do not currently treat the boundary of the cluster in a fully consistent way – at some radius the virialised gas must meet a boundary shock of in-falling material and we do not model the corresponding step in pressure.
 We also do not vet. consider. additional observation constraints such as X-rav. spectral ancl optical weak lensing measurements. although these are in. principle straightforward to incorporate in to our analysis Framework.," We also do not yet consider additional observation constraints such as X-ray spectral and optical weak lensing measurements, although these are in principle straightforward to incorporate in to our analysis framework."
 In subsequent papers we will use this model to analyse SZ data from the CDI2 experiment jointly with relevant imaging cata., In subsequent papers we will use this model to analyse SZ data from the CBI2 experiment jointly with relevant X-ray imaging data.
al. (,al. (
"2009), the mass-weighted mean age is a more physical parameter, but it has a much less direct relation with the observables.","2009), the mass-weighted mean age is a more physical parameter, but it has a much less direct relation with the observables."
" Although the mass fraction of a young stellar population might be small, it is much more luminous."," Although the mass fraction of a young stellar population might be small, it is much more luminous."
 Thus their contribution to the luminosity is much higher., Thus their contribution to the luminosity is much higher.
" A secondary parameter to describe the stellar population is the metallicity, also defined as light- and mass- weighted mean metallicity."," A secondary parameter to describe the stellar population is the metallicity, also defined as light- and mass- weighted mean metallicity."
 Both definitions are bounded by the range of Z used in the base., Both definitions are bounded by the range of $Z$ used in the base.
 Results for the metallicity are also presented in the bottom panel of Figure 7., Results for the metallicity are also presented in the bottom panel of Figure 7.
" These results point out to a mean value around solar for both definitions, but the light-weighted average gives higher values for the mean metallicity than the mass-weighted."," These results point out to a mean value around solar for both definitions, but the light-weighted average gives higher values for the mean metallicity than the mass-weighted."
" Again, the light-weighted values are more sensitive to the younger components, while the mass-weighted results are more sensitive to the older components."," Again, the light-weighted values are more sensitive to the younger components, while the mass-weighted results are more sensitive to the older components."
" This result is consistent with a galaxy chemical enrichment scenario, in which the young population is enriched by the evolution of the early massive stars."," This result is consistent with a galaxy chemical enrichment scenario, in which the young population is enriched by the evolution of the early massive stars."
" The power law component is important in the nucleus, as expected, contributing with about 25% of the light."," The power law component is important in the nucleus, as expected, contributing with about $\%$ of the light."
 Cid Fernandes Terlevich (1995) predicted that a broad component in HG becomes distinguishable whenever the scattered FC contributes with > 20% to the optical, Cid Fernandes Terlevich (1995) predicted that a broad component in $\beta$ becomes distinguishable whenever the scattered FC contributes with $\geq$ $\%$ to the optical
 (Ho). Hy!. Hy Hy Ho Ho Hy 3. 4.. 5..," $H_0$ $H_0^{-1}$ $H_0$ $H_0$ $H_0$ $H_0$ $H_0$ \ref{sec:vla} \ref{sec:atca}, \ref{sec:data}."
 6 7 z=2.78. , \ref{sec:discussion} \ref{sec:conclusions} $z=2.78$ 
observing time. 2000BUL33 and 2000BUL34 where our data cover a significant portion of the amplification.,"observing time, 2000BUL33 and 2000BUL34 where our data cover a significant portion of the amplification."
 Phe good coverage and high amplifications of these events allow us to place strict constraints on the fitted. parameters and to exclude the presence of planetary conpanions in the lensing zone 0.6Saflex1.6 being the planetary orbital raclius) with high levels of confidence as discussed in section 6., The good coverage and high amplifications of these events allow us to place strict constraints on the fitted parameters and to exclude the presence of planetary conpanions in the lensing zone ${0.6 \le a/R_{E} \le 1.6}$ being the planetary orbital radius) with high levels of confidence as discussed in section 6.
 2000BUL37 was again covered in the decline and we obtained &ood coverage of the second half of the peak., 2000BUL37 was again covered in the decline and we obtained good coverage of the second half of the peak.
 The OGLE dataset lacks any points in the decline and it is the JIT data that help to define the shape of the lighteurve., The OGLE dataset lacks any points in the decline and it is the JKT data that help to define the shape of the lightcurve.
 2000BUL36 and 2000DBUL39 were low amplification events selected by the priority algorithm mainly because. they were close to maximum amplification while the remaining ongoing events at the time were away from their maximum amplification values., 2000BUL36 and 2000BUL39 were low amplification events selected by the priority algorithm mainly because they were close to maximum amplification while the remaining ongoing events at the time were away from their maximum amplification values.
 Clearly. the information extracted from these last two events is not of the highest quality as their faintness and low amplifications result in poorer data points ancl a deviation should be more pronounced to be detected.," Clearly, the information extracted from these last two events is not of the highest quality as their faintness and low amplifications result in poorer data points and a deviation should be more pronounced to be detected."
 All data is available upon request., All data is available upon request.
 Following the S-parameter PSPL fit. we refit the data assuming a binary lens (?:?)| ancl proceed to calculate he net detection probability (for a given. mass ratio q) for each of the sampled. events.," Following the 8-parameter PSPL fit, we refit the data assuming a binary lens \cite{witt90,Schneider86} and proceed to calculate the net detection probability (for a given mass ratio $q$ ) for each of the sampled events."
 This involves two additional xwameters. d and q. where d is the projected. separation xtween the planet and the star. and q the planet to star mass ratio.," This involves two additional parameters, $d$ and $q$, where $d$ is the projected separation between the planet and the star, and $q$ the planet to star mass ratio."
 A similar analysis using a cilferent method has n recently presented in (?:7)..," A similar analysis using a different method has been recently presented in \cite{gaudi00,Albrow01}."
 Prior to calculating the detection. probability for a xanet of mass ratio d we set up a fine eric of planet positions in .r.y on the lens plane and for each of these positions we it the binary model to the data optimizing all parameters.," Prior to calculating the detection probability for a planet of mass ratio $q$ we set up a fine grid of planet positions in $x,y$ on the lens plane and for each of these positions we fit the binary model to the data optimizing all parameters."
 The density of sampling in wey has to be dense enough so hat planetary fits are not missed.," The density of sampling in $x,y$ has to be dense enough so that planetary fits are not missed."
 Our grid step size spacing was defined as J/q/4. where q is the mass ratio.," Our grid step size spacing was defined as $\sqrt{q}/4$, where $q$ is the mass ratio."
 This sets up à very fine grid. for each selected. mass ratio., This sets up a very fine grid for each selected mass ratio.
 We then make a Ay? map versus planet position by subtracting the minimum X? of the PSPL fit from the minimum X7 of the binary fit for each wey.," We then make a $\Delta\chi^2$ map versus planet position by subtracting the minimum $\chi^2$ of the PSPL fit from the minimum $\chi^2$ of the binary fit for each $x,y$."
 Examples of such maps are shown in figure 7..., Examples of such maps are shown in figure \ref{fig:chi}.
 Albay values where the Ay? exceeds the threshold value GNATyp 760) are shown in black.," All $x,y$ values where the $\Delta\chi^2$ exceeds the threshold value ${\Delta\chi^2}_{\mbox{thr}}$ =60) are shown in black."
 These “black zones? show us where the PSPL mocdel gives a better fit to the data., These `black zones' show us where the PSPL model gives a better fit to the data.
For various reasous. such as camera optics. aliguimenut errors. filter irregularities. non-Ilat CCDs. and CCD manufacturing defects. the mapping of the square array of square pixels of a detector outo the tangent-plane projection of the sky requires a nou-linear trauslormation.,"For various reasons, such as camera optics, alignment errors, filter irregularities, non-flat CCDs, and CCD manufacturing defects, the mapping of the square array of square pixels of a detector onto the tangent-plane projection of the sky requires a non-linear transformation."
 Positious measured within the pixel grid need to be corrected. [or geometric distortion. (CD) before they cau be accurately compared with other positious in tlie same image. or compared with positions measured iu other image.," Positions measured within the pixel grid need to be corrected for geometric distortion (GD) before they can be accurately compared with other positions in the same image, or compared with positions measured in other image."
 While almost all scientific programse nuust make use of the distortiou solution. most are relatively insensitive to it.," While almost all scientific programs must make use of the distortion solution, most are relatively insensitive to it."
 So loug as each detector pixel is mappecl to within a fraction of a pixel of its true, So long as each detector pixel is mapped to within a fraction of a pixel of its true
The fundamental assumption here is that the galaxies seen al 2e6 are (he remnants of star-Formation responsible for reionization.,The fundamental assumption here is that the galaxies seen at $z\sim6$ are the remnants of star-formation responsible for reionization.
 It is plausible that the ο6 galaxies (hat are seen in deep surveys are actually comprised of Population I stars with a Salpeter IME which are responsible for a second late epoch of reionization., It is plausible that the $z\sim6$ galaxies that are seen in deep surveys are actually comprised of Population II stars with a Salpeter IMF which are responsible for a second late epoch of reionization.
 In (hat scenario. the earlier epochs would be entirely due to Population I1I stars which do not contribute to the ultraviolet and visible light huminosity density al z~6. à scenario that has been considered previously (e.&2005).," In that scenario, the earlier epochs would be entirely due to Population III stars which do not contribute to the ultraviolet and visible light luminosity density at $z\sim6$, a scenario that has been considered previously \citep[e.g][]{Cen:03, Furl:05}."
. These stars. which are more more massive (han MAL. evolve into black holes within 30 Myr. ie. bv z6.," These stars, which are more more massive than $_{\sun}$ evolve into black holes within 30 Myr, i.e. by $z\sim6$."
 The number of ionizing photons required io keep the IGM ionized between 15<z6 is 11 photons/barvon., The number of ionizing photons required to keep the IGM ionized between $15<z<6$ is $\sim$ 11 photons/baryon.
 An IMFE. extending between 10—100 MM... with a Salpeter slope of 2.3 provides a total of 1.38 photons per barvon for a stellar mass densitv of 2.5x 10mun..," An IMF extending between $10-100$ $_{\sun}$, with a Salpeter slope of $2.3$ provides a total of 1.38 photons per baryon for a stellar mass density of $\times$ $^{6}$."
 The stellar mass density in massive Population IHE stars must therefore be 2x 10*7., The stellar mass density in massive Population III stars must therefore be $\times$ $^{7}$.
 Thus. if reionization was initiated by massive stars which evolve into neutron stars aud black holes by 2~6. there must be as much mass density in (hese remnants as in (he stars (hat we detect in the galaxies.," Thus, if reionization was initiated by massive stars which evolve into neutron stars and black holes by $z\sim6$, there must be as much mass density in these remnants as in the stars that we detect in the galaxies."
 If in a contrived scenario. the initial z13 epoch of reionization from Population II stars was relatively brief. lasting A:=2 (e.g.e.CCen2003).. it would require that the stellar mass densitv in the initial burst was ~ 10°mun.," If in a contrived scenario, the initial $z\sim13$ epoch of reionization from Population III stars was relatively brief, lasting $\Delta z=2$ \citep[e.g.][]{Cen:03}, it would require that the stellar mass density in the initial burst was $\sim$ $^{6}$."
. This corresponds to of barvons that are in stars al 2ον6., This corresponds to of baryons that are in stars at $z\sim6$.
 Since the lifetime of stars are ~30 Myr while (he interval between 13<215 spans 60 Myr. the first epoch of reionization must be relatively inhomogeneous ancl will depend on the exact epoch al which starlormation in dark matter halos was initiated.," Since the lifetime of $_{\sun}$ stars are $\sim$ 30 Myr while the interval between $13<z<15$ spans 60 Myr, the first epoch of reionization must be relatively inhomogeneous and will depend on the exact epoch at which star-formation in dark matter halos was initiated."
 Furthermore. (he iruncation of Population HI star-formation through [feedback processes argues against them being significant. contributors to reionization (Greil&Bromm|.," Furthermore, the truncation of Population III star-formation through feedback processes argues against them being significant contributors to reionization \citep{Greif_Bromm}."
O006).. Measuring the distribution of Stromgren sphere size using hieh spatial resolution IHE observations will reveal the true nature of the reionization historv at z>10., Measuring the distribution of Stromgren sphere size using high spatial resolution HI observations will reveal the true nature of the reionization history at $z>10$.
 It should be noted that Population HI star formation could potentially extend down to lower redshifts. depending on the effect of feedback on the metallicity of the star-lormine environments.," It should be noted that Population III star formation could potentially extend down to lower redshifts, depending on the effect of feedback on the metallicity of the star-forming environments."
 The rates of star-Dormation in such stars are however thought to be 3x10.! of the Population Ε star-formation rate and are inconsequential to the ultraviolet luminosity density or tlie co-moving star-formation rate density 2OOT)..," The rates of star-formation in such stars are however thought to be $3\times10^{-4}$ of the Population II star-formation rate and are inconsequential to the ultraviolet luminosity density or the co-moving star-formation rate density \citep{Tornatore, Brook:07}. ."
The svstems we selected can be grouped into three categories based on their broad-banud spectral energy. distribution (SED).,The systems we selected can be grouped into three categories based on their broad-band spectral energy distribution (SED).
" VW Cha. Sz τὸ, and Sz 102 have significant excess enussion relative to the photospheric [lux from near- through to far-infrared wavelengths (Gauvin&Strom1992:IIughesetal.1994:Nessler-Silacci2006)."," VW Cha, Sz 73, and Sz 102 have significant excess emission relative to the photospheric flux from near- through to far-infrared wavelengths \citep{gauvin92,hughes94,kessler06}."
. Such broad SEDs can be well reproduced bydisks. extending [rom a few stellar radii out to hundreds of AU.," Such broad SEDs can be well reproduced by, extending from a few stellar radii out to hundreds of AU."
 TW Ilva. CS Cha. and T Cha are classified asdisks in the literature.," TW Hya, CS Cha, and T Cha are classified as in the literature."
 Their SEDs present a stronglv reduced (or lack of) near-inlrared excess emission but large mid- and far-infrared emission., Their SEDs present a strongly reduced (or lack of) near-infrared excess emission but large mid- and far-infrared emission.
 Detailed modeling of their SEDs points to relatively large inner dust cavities almost devoid of sub-micron- aud micron-sized dust grains: e 1-4AAU for TW Iva (Calvetetal.2002:Ratzka2007). e-43AAU for CS Cha (Espaillatetal.2007).. and ~15 AAU for T Cha (Brownetal.2007).," Detailed modeling of their SEDs points to relatively large inner dust cavities almost devoid of sub-micron- and micron-sized dust grains: $\sim$ AU for TW Hya \citep{calvet02,ratzka07}, $\sim$AU for CS Cha \citep{espaillat07}, and $\sim$ AU for T Cha \citep{brown07}."
". There is no evidence of gas inner holes in these svstems: TW [va is accretingdisk gas at a rale o[ e5xLO MAL. /vr (Muzerolleetal.2000).. the spectroscopic binary CS Cha at <10 M, /vr (Espaillatetal.2007)star. while the small (< LOA)) but variable Ho. equivalent width from T Cha suggests low-level and possibly episodic accretion (Alealaetal.1993)."," There is no evidence of gas inner holes in these systems: TW Hya is accretingdisk gas at a rate of $\sim 5 \times 10^{-10}$ $_{\sun}$ /yr \citep{muzerolle00}, the spectroscopic binary CS Cha at $< 10^{-8}$ $_{\sun}$ /yr \citep{espaillat07}, while the small $< 10$ ) but variable $\alpha$ equivalent width from T Cha suggests low-level and possibly episodic accretion \citep{alcala93}."
. Finally. the SED of WD 347004 has little excess enission al all wavelengths produced by a (enuous dust disk. possibly adish (Sylvester&Skinner1996).," Finally, the SED of HD 34700A has little excess emission at all wavelengths produced by a tenuous dust disk, possibly a \citep{sylvester96}."
. We performed long-slit high-resolution spectroscopy wilh the spectrograph VISIR mounted on the VLT telescope Melipal (Lagageetal. 2004).., We performed long-slit high-resolution spectroscopy with the spectrograph VISIR mounted on the VLT telescope \citep{lagage04}. .
 The observations were executed, The observations were executed
The key difference is that RISE is a frame transfer CCD whose dead time is the frame transfer time. 35 milliseconds for observations longer than | second.,"The key difference is that RISE is a frame transfer CCD whose dead time is the frame transfer time, 35 milliseconds for observations longer than 1 second."
 For the brightest comparison star in our field. (Vz 9). we found the optimum exposure times with RISE are approximately 2.7. 7.8. 10.8 seconds during bright. gray and dark time. respectively.," For the brightest comparison star in our field, $V \approx 9$ ), we found the optimum exposure times with RISE are approximately 2.7, 7.8, 10.8 seconds during bright, gray and dark time, respectively."
 We iterate that the improvement in signal-to-noise for defocussed observations. reported by ? is only due to deadtime losses: hence. the defocussing needed is proportional to the CCD readout time.," We iterate that the improvement in signal-to-noise for defocussed observations, reported by \citet{Southworth2009} is only due to deadtime losses; hence, the defocussing needed is proportional to the CCD readout time."
 If the deadtime was zero the best theoretical signal-to-noise would always be for focused observations. mainly due to the increase in background noise for wider profiles.," If the deadtime was zero the best theoretical signal-to-noise would always be for focused observations, mainly due to the increase in background noise for wider profiles."
 Moreover. in our case. the improvement on signal-to-noise between | second and 10.8 seconds exposure times is quite small on the order of 10 ppm per 30 sec bin.," Moreover, in our case, the improvement on signal-to-noise between 1 second and 10.8 seconds exposure times is quite small on the order of $10\,$ ppm per $30\,$ sec bin."
 As we will see below. the strongest reason for defocussing is to minimise systematic noise which. due to its nature. is not accounted for in the ealeulation and can substantially increase the noise in a transit light curve.," As we will see below, the strongest reason for defocussing is to minimise systematic noise which, due to its nature, is not accounted for in the calculation and can substantially increase the noise in a transit light curve."
 Figure shows systematic noise variations larger than 400 ppm., Figure \ref{complc} shows systematic noise variations larger than 400 ppm.
 Exoplanet transit observations are often dominated by systematic noise., Exoplanet transit observations are often dominated by systematic noise.
 Therefore. to improve the precision of the light curves it is important to determine and minimise this noise source.," Therefore, to improve the precision of the light curves it is important to determine and minimise this noise source."
 For the 2009 September 09 observations. the brightest comparison star (c1) on the field was affected by systematic noise.," For the 2009 September 09 observations, the brightest comparison star (c1) on the field was affected by systematic noise."
 This can clearly be seen in Figure 2.. where we show the flux of cl relative to the ensemble of comparison stars used in the final 2009 WASP-?21 ight curve.," This can clearly be seen in Figure \ref{complc}, where we show the flux of c1 relative to the ensemble of comparison stars used in the final 2009 WASP-21 light curve."
 This shows a variation of 400 ppm., This shows a variation of 400 ppm.
 We found that his systematic noise was correlated with the star position in the CCD. which during the transit observation varied by 10 pixels in he .r direction and 8 in the jy.," We found that this systematic noise was correlated with the star position in the CCD, which during the transit observation varied by 10 pixels in the $x$ direction and 8 in the $y$."
 Given that we used an aperture radius of 22 pixels. this implies that only half of the pixels used o perform aperture photometry were common for the duration of he observation.," Given that we used an aperture radius of 22 pixels, this implies that only half of the pixels used to perform aperture photometry were common for the duration of the observation."
 Hence. we concluded that the systematic noise was due to variations in the pixel-to-pixel sensitivity which were not corrected by flat fielding.," Hence, we concluded that the systematic noise was due to variations in the pixel-to-pixel sensitivity which were not corrected by flat fielding."
 In fact. the systematic noise is slightly uigher if we flat field the data.," In fact, the systematic noise is slightly higher if we flat field the data."
 Our master flat is a combination of 150 frames. each with a mean of 35000 counts.," Our master flat is a combination of 150 frames, each with a mean of 35000 counts."
 The uncertainty in this flat is 0.5 millimags per pixel which is smaller than the johetometrie error (~4.4 milimags per unbinned point) and the observed systematic noise., The uncertainty in this flat is 0.5 millimags per pixel which is smaller than the photometric error $\sim 4.4$ milimags per unbinned point) and the observed systematic noise.
 After careful analysis of the data. we ound that the οἱ comparison star crossed a reflection feature in the CCD that is rotator dependent (LT is on an. alt-azimuth mount) and thus was not corrected by flat tielding.," After careful analysis of the data, we found that the c1 comparison star crossed a reflection feature in the CCD that is rotator dependent (LT is on an alt-azimuth mount) and thus was not corrected by flat fielding."
 This experience demonstriites the importance of good guiding in decreasing the sources of systematic noise., This experience demonstrates the importance of good guiding in decreasing the sources of systematic noise.
 If the observations were performed in focus and assuming the seeing was | arcsec. the FHWM would have been —2 pixels.," If the observations were performed in focus and assuming the seeing was 1 arcsec, the FHWM would have been $\sim 2$ pixels."
 Using an aperture radius of 1.5... FWHM pixels. it would have implied that there were no common pixels during the observations.," Using an aperture radius of $1.5 \times\,$ FWHM $=3\,$ pixels, it would have implied that there were no common pixels during the observations."
 Therefore. we infer. if the observations were focused. the amount of systematic noise would have doubled.," Therefore, we infer, if the observations were focused, the amount of systematic noise would have doubled."
 Note that the defocussing does not affect the guiding since the guide camera is always kept in focus., Note that the defocussing does not affect the guiding since the guide camera is always kept in focus.
 After this incident the RISE instrument was upgraded., After this incident the RISE instrument was upgraded.
 The source of the reflected feature was identified and removed from the instrument field of view., The source of the reflected feature was identified and removed from the instrument field of view.
 We also improved the telescope guiding system's stability., We also improved the telescope guiding system's stability.
 This led to an improvement in the precision of the light curves which is evident in the latest light curve of WASP- taken after the upgrades (see Fig., This led to an improvement in the precision of the light curves which is evident in the latest light curve of WASP-21 taken after the upgrades (see Fig.
 1)., 1).
 In the November 2010 observations the variation in position is less than 2 pixels in the or direction and 4 pixels in the y., In the November 2010 observations the variation in position is less than 2 pixels in the $x$ direction and 4 pixels in the $y$.
 An accurate estimate of the photometric errors is important to obtain reliable system. parameters., An accurate estimate of the photometric errors is important to obtain reliable system parameters.
 Our first estimate of errors or each light curve includes only the shot noise. readout and background noise. which underestimates the true errors.," Our first estimate of errors for each light curve includes only the shot noise, readout and background noise, which underestimates the true errors."
 To obtain a more reliable estimate we begin by scaling the errors of each ight curve so that the reduced X7 of the best fitting model is 1.0., To obtain a more reliable estimate we begin by scaling the errors of each light curve so that the reduced $\chi^2$ of the best fitting model is 1.0.
 This resulted in the multiplication of the errors by 1.97. 1.22 and 44. for the 2008. 2009 and 2010 light curves. respectively.," This resulted in the multiplication of the errors by $1.97$ , $1.22$ and $1.44$, for the 2008, 2009 and 2010 light curves, respectively."
 We jen. calculated the time-correlated noise following the procedure rom ?.., We then calculated the time-correlated noise following the procedure from \citet{gillon2009}.
 Using the residuals of the best fit model. we estimated ye amplitude of the red noise. σι. to be 150 ppm. 250 ppm and 50 ppm. for the 2008. 2009 and 2010 light curves. respectively.," Using the residuals of the best fit model, we estimated the amplitude of the red noise, $\sigma_r$ to be $150\,$ ppm, $250\,$ ppm and $150\,$ ppm, for the 2008, 2009 and 2010 light curves, respectively."
 These were added in quadrature to the rescaled photometric errors and were used in the final Markov Chain Monte Carlo (MCMC) chains., These were added in quadrature to the rescaled photometric errors and were used in the final Markov Chain Monte Carlo (MCMC) chains.
" However. ? found that this ""time-averaging"" method of estimating the correlated noise can still underestimate the uncertainties by 15-30 per cent."," However, \citet{carter2009} found that this “time-averaging” method of estimating the correlated noise can still underestimate the uncertainties by 15-30 per cent."
 To determine the planetary and orbital parameters. we fitted the three RISE light curves of WASP-21b simultaneously.," To determine the planetary and orbital parameters, we fitted the three RISE light curves of WASP-21b simultaneously."
" We used the ?. transit model parametrised by the normalised separation of the planet. @//?,.. ratio of planet radius to star radius. £2),/22). orbital inclination. 7. and the transit epoch. 76. of each light curve."," We used the \citet{Mandel2002} transit model parametrised by the normalised separation of the planet, $a/R_*$, ratio of planet radius to star radius, $ R_p/R_* $, orbital inclination, $i$, and the transit epoch, $T_0$, of each light curve."
 Our model was originally. developed © measure transit timing variations of exoplanets., Our model was originally developed to measure transit timing variations of exoplanets.
 Following ? qat found no evidence for a significant orbital eccentricity of WASP-21b we adopt a circular orbit., Following \citet{Bouchy2010} that found no evidence for a significant orbital eccentricity of WASP-21b we adopt a circular orbit.
 We included the quadratic limb diirkening (LD) coefficients for the RISE filter V+R from the mocels of α=0.45451 and b=0.21017, We included the quadratic limb darkening (LD) coefficients for the RISE filter V+R from the models of \citet{Howarth2010}: $a=0.45451$ and $b=0.210172$.
 These were calculated for ει= 5800K. g=44.2 and [M/H] 0.5 to match 1e Stellar parameters from ?..," These were calculated for $T_{eff} = 5800\,$ K, 4.2 and [M/H] $-$ 0.5 to match the stellar parameters from \citet{Bouchy2010}."
 We initially kept the limb darkening parameters fixed during the fit., We initially kept the limb darkening parameters fixed during the fit.
 For each light curve. we included two extra parameters to account for a linear normalization.," For each light curve, we included two extra parameters to account for a linear normalization."
 Therefore. 12. parameters were fitted.," Therefore, 12 parameters were fitted."
 Besides the linear normalization. no extra trends were removed fromthe light curve.," Besides the linear normalization, no extra trends were removed fromthe light curve."
 To obtain the best tit parameters and uncertainties. we used," To obtain the best fit parameters and uncertainties, we used"
Based on equation (1). the investigation of the EAS inverse problem. which is the reconstruction of cherey spectra of primary nuclei by the observable EAS electron and muon size spectra at observation level males sense ouly using given functions for Πο primary energy spectra with given uuknown spectral parameters (so called parameterization of equation (1)) as it is done in[S.18.19. 201.,"Based on equation (1), the investigation of the EAS inverse problem, which is the reconstruction of energy spectra of primary nuclei by the observable EAS electron and muon size spectra at observation level makes sense only using given functions for unknown primary energy spectra with given unknown spectral parameters (so called parameterization of equation (1)) as it is done in\cite{Glass,STPB,TH,TB}. ."
(2010).,.
". In a recent paper, analysed the multiwavelength data from the 2007-2008 WEBT campaign, including three pointings by XMM-Newton."," In a recent paper, analysed the multiwavelength data from the 2007–2008 WEBT campaign, including three pointings by XMM-Newton."
" The XMM-Newton data revealed a UV excess, which was interpreted to be due to thermal emission from the accretion disc, as well as a spectral curvature in the X-ray band."," The XMM-Newton data revealed a UV excess, which was interpreted to be due to thermal emission from the accretion disc, as well as a spectral curvature in the X-ray band."
" The authors constructed spectral energy distributions (SEDs) of BL Lacertae corresponding to various epochs where the source was in different brightness states, using both their own data and data from the literature."," The authors constructed spectral energy distributions (SEDs) of BL Lacertae corresponding to various epochs where the source was in different brightness states, using both their own data and data from the literature."
" They applied the inhomogeneous, rotating helical jet model by 1999,,2003,, 2004)mainBodyCitationEnd220] to fit the SEDs, and suggested that the broad-band spectral properties of BL Lacertae may result from the combination of two synchrotron emission components with their self inverse-Compton emission, plus a thermal component from the disc."," They applied the inhomogeneous, rotating helical jet model by , ] to fit the SEDs, and suggested that the broad-band spectral properties of BL Lacertae may result from the combination of two synchrotron emission components with their self inverse-Compton emission, plus a thermal component from the disc."
" Subsequently, analysed optical spectra acquired in the same period with the 3.56 m Telescopio Nazionale Galileo (TNG)."," Subsequently, analysed optical spectra acquired in the same period with the 3.56 m Telescopio Nazionale Galileo (TNG)."
" They found a broad Ha emission line, with luminosity of ~4x10*'ergs! and FWHM of ~ 4600kms'!, even brighter than that found in 1997 by and2000)."," They found a broad $\alpha$ emission line, with luminosity of $\sim 4 \times 10^{41} \, \rm erg \, s^{-1}$ and FWHM of $\sim 4600 \rm \, km \, s^{-1}$ , even brighter than that found in 1995--1997 by and."
". This favours the hypothesis that the UV excess is caused by thermal emission from the accretion disc, the most likely source of ionising photons for the broad line region."," This favours the hypothesis that the UV excess is caused by thermal emission from the accretion disc, the most likely source of ionising photons for the broad line region."
" The multiwavelength data available for the analysis lacked simultaneous information in the y- band, so that the inverse-Compton spectral region was poorly constrained."," The multiwavelength data available for the analysis lacked simultaneous information in the $\gamma$ -ray band, so that the inverse-Compton spectral region was poorly constrained."
" But in 2008 the Fermi satellite was able to detect BL Lacertae2010a),, even if in a low state compared to the past detections by the Compton Gamma Ray (CGRO,1999,, 1997))."," But in 2008 the Fermi satellite was able to detect BL Lacertae, even if in a low state compared to the past detections by the Compton Gamma Ray (CGRO, )."
" In the same period, observations in the UV and bands were performed by Swift, while in the optical, near- mm and cm radio bands the source was monitored by the GLAST-AGILE Support Program (GASP) of the WEBT."," In the same period, observations in the UV and X-ray bands were performed by Swift, while in the optical, near-IR, mm and cm radio bands the source was monitored by the GLAST-AGILE Support Program (GASP) of the WEBT."
 This offered the unique opportunity to study the source emission over a very extended spectral range., This offered the unique opportunity to study the source emission over a very extended spectral range.
 The results of this further investigation effort on BL Lacertae are presented in this paper., The results of this further investigation effort on BL Lacertae are presented in this paper.
" The GASP was born in 2007 as a WEBT project, with the aim of monitoring a list of 28 y-ray loud blazars in the optical, near- mm, and cm radio bands during the y-ray observations of the and (formerly GLAST) satellites2009a)."," The GASP was born in 2007 as a WEBT project, with the aim of monitoring a list of 28 $\gamma$ -ray loud blazars in the optical, near-IR, mm, and cm radio bands during the $\gamma$ -ray observations of the and (formerly GLAST) satellites."
". Data are collected periodically by the WEBT President, who checks the consistency of the various datasets."," Data are collected periodically by the WEBT President, who checks the consistency of the various datasets."
" The GASP light curves are then available for multiwavelength studies, mostly in the framework of the GASP collaboration with the AGILE and Fermi research teams."," The GASP light curves are then available for multiwavelength studies, mostly in the framework of the GASP collaboration with the AGILE and Fermi research teams."
 The GASP data presented in this paper were taken at the observatories listed in Table 1.., The GASP data presented in this paper were taken at the observatories listed in Table \ref{obs}.
" The optical data were calibrated with respect to a common choice of reference stars in the same field of the source in U and B bands; in V, R, and J)."," The optical data were calibrated with respect to a common choice of reference stars in the same field of the source in $U$ and $B$ bands; in $V$, $R$, and $I$ )."
" The source photometry was evaluated from a circular region with an 8 arcsec aperture radius, while the background was taken in a surrounding annulus with 10 and 16 arcsec radii."," The source photometry was evaluated from a circular region with an 8 arcsec aperture radius, while the background was taken in a surrounding annulus with 10 and 16 arcsec radii."
 In this way the measureis essentially seeing-independent and all datasets are affected by, In this way the measureis essentially seeing-independent and all datasets are affected by
are operated on the island of La Palma by. the Isaac Newton Group in the Spanish Observatorio cel Roque de los) Muchachos of the Instituto. de Astrolisica cde Canarias.,are operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
 This research. has mace use of the NASA/IPAC Extragalactic Database (NIZD) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics ancl 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."
 The authors thank Neville Shane for both helping out with the observations and calculations provided in this paper., The authors thank Neville Shane for both helping out with the observations and calculations provided in this paper.
 We also thank the referee for comments which improved the content of this paper., We also thank the referee for comments which improved the content of this paper.
our study.,our study.
 This comparison clearly shows the strong correlation between high mass loss rates and variability., This comparison clearly shows the strong correlation between high mass loss rates and variability.
 Mauas et al. (2006)), Mauas et al. \cite{Mauas06}) )
 derive a mass loss rate of a few 107? Μο on the upper part of the giant branch of NGC 2808 from the analysis of chromospheric lines., derive a mass loss rate of a few $^{-9}$ $M_{\odot}$ on the upper part of the giant branch of NGC 2808 from the analysis of chromospheric lines.
 Ho line components at an outflow velocity were found in a large sample of red giants by Cacciari et al. (2004))., $\alpha$ line components at an outflow velocity were found in a large sample of red giants by Cacciari et al. \cite{Cacciari04}) ).
" A Spitzer study of this cluster has been obtained already (Fabbri et al. 2008)),"," A Spitzer study of this cluster has been obtained already (Fabbri et al. \cite{Fabbri08}) ),"
 but the results are not available yet., but the results are not available yet.
 From the horizontal branch morphology of this cluster D'Antona Caloi (2008)) and Dalessandro et al. (2011)), From the horizontal branch morphology of this cluster D'Antona Caloi \cite{dAC08}) ) and Dalessandro et al. \cite{dal10}) )
 derive an average mass lost before the red clump phase of Me., derive an average mass lost before the red clump phase of $M_{\odot}$.
 We have shown that modelling of the LPVs in 47 Tuc allows one to derive theamount of mass lost on the RGB (Lebzelter Wood 2005))., We have shown that modelling of the LPVs in 47 Tuc allows one to derive theamount of mass lost on the RGB (Lebzelter Wood \cite{LW05}) ).
 It is our aim to carry out the same pulsation analysis for NGC 362 and NGC 2808., It is our aim to carry out the same pulsation analysis for NGC 362 and NGC 2808.
" In addition, given the large range in the helium abundance suspected in NGC 2808, we aim to see how the helium abundance affects the LPV pulsation periods."," In addition, given the large range in the helium abundance suspected in NGC 2808, we aim to see how the helium abundance affects the LPV pulsation periods."
" In particular, we aim to see if the position on the period-luminosity diagram can give a clue to the helium abundance."," In particular, we aim to see if the position on the period-luminosity diagram can give a clue to the helium abundance."
" Based on the summary of abundance measurements in the two clusters detailed in the Introduction, we assume a metal abundance Z=0.001 for both clusters."," Based on the summary of abundance measurements in the two clusters detailed in the Introduction, we assume a metal abundance Z=0.001 for both clusters."
" Models have been made with helium mass fractions Y=0.25, 0.3 and 0.4."," Models have been made with helium mass fractions Y=0.25, 0.3 and 0.4."
" Note that these are, respectively, the estimated helium mass fractions given by Dalessandro et al. (2011))"," Note that these are, respectively, the estimated helium mass fractions given by Dalessandro et al. \cite{dal10}) )"
" for red horizontal branch, blue horizontal branch and extreme horizontal branch stars in NGC 2808."," for red horizontal branch, blue horizontal branch and extreme horizontal branch stars in NGC 2808."
 Mass loss was added to some models assuming a Reimers’ Law (Reimers 1975))., Mass loss was added to some models assuming a Reimers' Law (Reimers \cite{r75}) ).
 The Reimers mass loss rate was multiplied by a factor 7=0.4., The Reimers mass loss rate was multiplied by a factor $\eta$ =0.4.
 This factor was chosen as it leads to a termination of the AGB near the maximum observed luminosity of the variable stars in NGC 362 and NGC 2808., This factor was chosen as it leads to a termination of the AGB near the maximum observed luminosity of the variable stars in NGC 362 and NGC 2808.
" It also closely reproduces the masses estimated for the horizontal branch stars in the two clusters (see below), and it is close to the value of 0.33 we found to apply in 47 Tuc."," It also closely reproduces the masses estimated for the horizontal branch stars in the two clusters (see below), and it is close to the value of 0.33 we found to apply in 47 Tuc."
" In order to compute the declining stellar mass along the RGB and AGB in the presence of mass loss, evolution rates as a function of luminosity were obtained from the evolution tracks of Bertelli et al (2008))."," In order to compute the declining stellar mass along the RGB and AGB in the presence of mass loss, evolution rates as a function of luminosity were obtained from the evolution tracks of Bertelli et al \cite{Bertelli08}) )."
 Teg in our calculations was forced to be the same as the mean observed Τεῃ on the giant branch (see Fig., $T_{\rm eff}$ in our calculations was forced to be the same as the mean observed $T_{\rm eff}$ on the giant branch (see Fig.
 9 or Fig. 11)), \ref{hrd_mconst} or Fig. \ref{hrd_eta0.4}) )
 so that the radius used in the Reimers’ Law formula was appropriate for NGC 362 and NGC 2808., so that the radius used in the Reimers' Law formula was appropriate for NGC 362 and NGC 2808.
" Following the discussion in the Introduction, we have assumed an age of 10x10? years for both clusters and for each population of different helium abundance."," Following the discussion in the Introduction, we have assumed an age of $\times 10^{9}$ years for both clusters and for each population of different helium abundance."
 The tracks and isochrones of Bertelli et al. (2008)), The tracks and isochrones of Bertelli et al. \cite{Bertelli08}) )
" were used to obtain the initial mass appropriate for giant branch stars of this age, Y and Z. Initial masses of 0.86, 0.79 and 0.65 Μο were found for helium abundances of 0.25, 0.3 and 0.4, respectively."," were used to obtain the initial mass appropriate for giant branch stars of this age, Y and Z. Initial masses of 0.86, 0.79 and 0.65 $M_{\odot}$ were found for helium abundances of 0.25, 0.3 and 0.4, respectively."
 Linear pulsation models were computed with the code described in Lebzelter Wood (2005))., Linear pulsation models were computed with the code described in Lebzelter Wood \cite{LW05}) ).
 A mixing length of 1.7 pressure scale heights was used in all models as this was found to reproduce the observed Τεῃ of the giant branch well., A mixing length of 1.7 pressure scale heights was used in all models as this was found to reproduce the observed $T_{\rm eff}$ of the giant branch well.
 Models without mass loss are shown in the Hertzsprung- in Fig. 9.., Models without mass loss are shown in the Hertzsprung-Russell-diagram in Fig. \ref{hrd_mconst}. .
 The My. and Teg values of the, The $M_{\rm bol}$ and $T_{\rm eff}$ values of the
at magnetic poles rather than at stellar equator.,at magnetic poles rather than at stellar equator.
 This completely changes the topology of accretion How but the major conchisious about the effect ou stellar cooling are likely to hold., This completely changes the topology of accretion flow but the major conclusions about the effect on stellar cooling are likely to hold.
 Indeed. the magnetically channeled eas travels towards the stellar surface at a &ood fraction of the free-fall velocity ancl at some point it nist pass through the radiative shock. after which it acciunulates at the top of the maeuetospheric colunn of accreted material. as schematically indicated in Figure 6..," Indeed, the magnetically channeled gas travels towards the stellar surface at a good fraction of the free-fall velocity and at some point it must pass through the radiative shock, after which it accumulates at the top of the magnetospheric column of accreted material, as schematically indicated in Figure \ref{fig:mag_pole}."
 Total energv release within the shock aud maguetospheric column is comparable to that occurring if the accretion disk were extending all the wav to the stellar surface., Total energy release within the shock and magnetospheric column is comparable to that occurring if the accretion disk were extending all the way to the stellar surface.
 This hot cohuun of accreted material illuniuates the surface of the star leading to the same suppression of intrinsic stellar τις as we discussed in this work., This hot column of accreted material illuminates the surface of the star leading to the same suppression of intrinsic stellar flux as we discussed in this work.
 In this case. however. irradiation 1s strongest near the magnetic poles while the magnetic equator is likely to be the coolest part of the stellarsurface’.," In this case, however, irradiation is strongest near the magnetic poles while the magnetic equator is likely to be the coolest part of the stellar."
.. Caleulatiou of stellar radiation and mteerated huuinositv iu this case would involve coustructing a model for the maguetosphieric cohuun structure and its radiative propertics., Calculation of stellar irradiation and integrated luminosity in this case would involve constructing a model for the magnetospheric column structure and its radiative properties.
 The impact of these details on the structure and evolution of young stars should be addressed by. future work., The impact of these details on the structure and evolution of young stars should be addressed by future work.
 Liuninosity of voung stars actively accreting from the civetuustellar disk can be siguificautlv affected bv the radiation which is produced in the inner parts of the disk ancl is intercepted by the stellar surface., Luminosity of young stars actively accreting from the circumstellar disk can be significantly affected by the radiation which is produced in the inner parts of the disk and is intercepted by the stellar surface.
 We showed that if a star gaius its mass via disk accretion on timescale of several 10° vr then the radiative flux caused by viscous dissipation in the disk is more than sufiicicut to increase the surface temperature of the star above the photospheric temperature that an isolated star with the same mass and radius would lave., We showed that if a star gains its mass via disk accretion on timescale of several $10^5$ yr then the radiative flux caused by viscous dissipation in the disk is more than sufficient to increase the surface temperature of the star above the photospheric temperature that an isolated star with the same mass and radius would have.
 πασάο by the disk is strongest iu the equatorial regions aud is almost neelieible near the poles., Irradiation by the disk is strongest in the equatorial regions and is almost negligible near the poles.
 Au outer radiative zone of almost constant temperature forms above the fully convective iuterior iu the strongly iradiated parts of he stellar surface., An outer radiative zone of almost constant temperature forms above the fully convective interior in the strongly irradiated parts of the stellar surface.
 This leads to the local suppression of iutrinsic enerev flux escaping from the stellar iuterior., This leads to the local suppression of intrinsic energy flux escaping from the stellar interior.
 We have demonstrated that there are two distinct nodes in which a fully convective object. can cool: nainly through the cool high-latitude polar regious or oxedonuünautlv through the low-latitude parts of the stellar surface., We have demonstrated that there are two distinct modes in which a fully convective object can cool: mainly through the cool high-latitude polar regions or predominantly through the low-latitude parts of the stellar surface.
 A particular regime of cooling iu a given object is set by the opacity behavior aud the adiabatic cluperature eradicut μμ iu the outer radiative zone., A particular regime of cooling in a given object is set by the opacity behavior and the adiabatic temperature gradient $\nabla_{ad}$ in the outer radiative zone.
 Accreting voung stars and brown dwirfs cool mainly hrough the polar regious while forming giaut planets cool through the whole surface., Accreting young stars and brown dwarfs cool mainly through the polar regions while forming giant planets cool through the whole surface.
 luteerated stellar Lhuninositv iu accreting case Is suppressed compared to the case of an isolated object. by up to a factor of several in some classes. of objects (actively accreting brown dwarts aud planets stars forming in gravitationally unstable disks in galactic unclei).," Integrated stellar luminosity in accreting case is suppressed compared to the case of an isolated object, by up to a factor of several in some classes of objects (actively accreting brown dwarfs and planets, stars forming in gravitationally unstable disks in galactic nuclei)."
 This leads to larger radii of bracdiated objects aud ay affect the initial conditions which are used to calculate the evolution of the low-mass objects ou timescales of ~10 Myr after their formation., This leads to larger radii of irradiated objects and may affect the initial conditions which are used to calculate the evolution of the low-mass objects on timescales of $\sim 10$ Myr after their formation.
 Existence of external radiative zoue may facilitate retention of dust in the atmospheres of brown chwarfs aud planets. aud may affect the streneth of magnetic Bold generated by internal dynamo in convective objects.," Existence of external radiative zone may facilitate retention of dust in the atmospheres of brown dwarfs and planets, and may affect the strength of magnetic field generated by internal dynamo in convective objects."
 Some of the results obtained iu this work iav be yplicable to accreting white dwarf and neutron star SVSTCLUS., Some of the results obtained in this work may be applicable to accreting white dwarf and neutron star systems.
 Tain grateful to Cilles Chabricr for careful reading of the manuscript aud many useful sugecstion., I am grateful to Gilles Chabrier for careful reading of the manuscript and many useful suggestion.
 The financial support for this work is provided by the Canada Researcli Chairs program aud a NSERC Discovery eraut., The financial support for this work is provided by the Canada Research Chairs program and a NSERC Discovery grant.
 Performing au iutegral over o in eq. (5)) we find , Performing an integral over $\phi$ in eq. \ref{eq:irr_flux}) )
"Ly rieht)). where D?=(47|1)?Le?siu?0 aud su,ναι,"," we find ), where $D^2=(x^2+1)^2-4x^2\sin^2\theta$ and $x_{in}=1/\sin\theta$."
 For ΕΠ) obeviug (6)) equation (A2)) can be rewrittenas eq. (7)), For $F_d(R)$ obeying \ref{eq:vis_dissip}) ) equation \ref{eq:1D}) ) can be rewrittenas eq. \ref{eq:irr_flux_mod}) )
 with, with
lifetime (~20 Myr). which ts 1n turn short compared to the global gas consumption timescale of several Gyr.,"lifetime $\sim20\,$ Myr), which is in turn short compared to the global gas consumption timescale of several Gyr."
 To establish whether the replenishment achievable in supershells is sufficient to make this mechanism feasible. we first convert the replenishment rates given in refdeltarho— into a replenished mass per SN event.," To establish whether the replenishment achievable in supershells is sufficient to make this mechanism feasible, we first convert the replenishment rates given in \\ref{deltarho} into a replenished mass per SN event."
 A replenishment rate proportional to the SFR density is also proportional to the rate of supernova type Il (SNID)), A replenishment rate proportional to the SFR density is also proportional to the rate of supernova type II ).
 Converting a proportionality to SFR density into one depending on the SNII rate. Paxjj1. depends on the assumed IMF.," Converting a proportionality to SFR density into one depending on the SNII rate, $\dot{\rho}_{\rm SNII}$, depends on the assumed IMF."
 From Hopkins&Beacom(2006) psxiy=(0.00915/42..) for the SalA IMF.," From \citet{HB:06} $\dot{\rho}_{\rm SNII}=(0.00915/M_{\odot})\,\dot{\rho}_*$ for the SalA IMF."
 The replenishment rate A(*)=1.65. becomesp. Att)=L?LOPsxuM..," The replenishment rate $K(t)=1.6\dot{\rho}_*$ becomes $K(t)=174.9\dot{\rho}_{\rm SNII}\,M_{\odot}$."
 The other extreme choice of IMF consistent with the normalization of the SFH (Hopkins&Beacom2006) is that of Baldry&Glazebrook(2003.hereaftertheBG IMF).., The other extreme choice of IMF consistent with the normalization of the SFH \citep{HB:06} is that of \citet[hereafter the BG IMF]{Bal:03}. .
 For the BG IMF PSU=(0.00532/A/.)p..," For the BG IMF $\dot{\rho}_{\rm SNII}=(0.0132/M_{\odot})\,\dot{\rho}_*$."
 The recycled fraction is R=0.56 (Hopkins&Beacom2006).. changing the consumption term in Equation (1)) ο. Πρ.," The recycled fraction is $R=0.56$ \citep{HB:06}, changing the consumption term in Equation \ref{theeqn}) ) to $-1.44\dot{\rho}_*$."
 The corresponding replenishment rate is A(f)109.1505x11AL...," The corresponding replenishment rate is $K(t)=109.1\dot{\rho}_{\rm SNII}\,M_{\odot}$."
 These extremes imply that. depending on the IMF. sufficient gas replenishment to maintain a constant HI mass density with redshift would be achieved if each SN event caused the recombination and cooling of =10180 of gas.," These extremes imply that, depending on the IMF, sufficient gas replenishment to maintain a constant HI mass density with redshift would be achieved if each SN event caused the recombination and cooling of $\approx 110-180\,M_{\odot}$ of gas."
 These IMFs are the extrema given the SFH normalization.. limits. and most reasonable IMFs should result in masses within this range.," These IMFs are the extrema given the SFH normalization limits, and most reasonable IMFs should result in masses within this range."
 Detailed measurements to confirm molecular gas formation within supershells are observationally challenging., Detailed measurements to confirm molecular gas formation within supershells are observationally challenging.
 We use the limited data currently available to assess the replenishmentrates associated with supershells. and to establish whether at least one well-studied supershell achieves the required rate.," We use the limited data currently available to assess the replenishmentrates associated with supershells, and to establish whether at least one well-studied supershell achieves the required rate."
 MeClure-Griffiths(2005) and Dawsonetal.(2008) have shown explicit cases of molecular clumps along the edges of supershells. suggestive of some degree of formation. with a significant amount of molecular material associated with the supershell walls.," \citet{McCG:05} and \citet{Daw:08} have shown explicit cases of molecular clumps along the edges of supershells, suggestive of some degree of formation, with a significant amount of molecular material associated with the supershell walls."
 The supershell investigated by Dawsonetal.(2008) is associated with about 2«10°M.. of molecular gas. of which those authors estimate that 80% likely comes from a pre-existing giant molecular cloud.," The supershell investigated by \citet{Daw:08} is associated with about $2\times10^5\,M_{\odot}$ of molecular gas, of which those authors estimate that $80\%$ likely comes from a pre-existing giant molecular cloud."
 Of the remaining xΕν10!M. of molecular gas it is difficult to determine how much is pre-existing and how much has been cooled and recombined by the expansion of the shell.," Of the remaining $\approx 4\times10^4\,M_{\odot}$ of molecular gas it is difficult to determine how much is pre-existing and how much has been cooled and recombined by the expansion of the shell."
 We can use z|<101AF. as an upper limit to the replenishment rate.," We can use $\approx 4\times10^4\,M_{\odot}$ as an upper limit to the replenishment rate."
 About 30 stars with stellar mass A.>7WM are required to form this supershell. including stars that may not.. yet have gone supernova.," About 30 stars with stellar mass $M_*> 7\,M_{\odot}$ are required to form this supershell, including stars that may not yet have gone supernova."
" This gives =13002000ΑΓ, of molecular mass replenished per SN event. a limit comfortably encompassing the required rate."," This gives $\lesssim 1300 - 2000\,M_{\odot}$ of molecular mass replenished per SN event, a limit comfortably encompassing the required rate."
 This upper limit could change significantly depending on the fraction of pre-existing molecular material and also on the fraction of stars that have not yet gone supernova., This upper limit could change significantly depending on the fraction of pre-existing molecular material and also on the fraction of stars that have not yet gone supernova.
 Not all SNe lie within supershells. although Higdon&Lin-genfelter(2005) estimate that a minimum of65% of SNII should occur in superbubbles.increasing to =SO904 when the spatial and temporal correlations of stellar —clusters are considered.," Not all SNe lie within supershells, although \citet{HL:05} estimate that a minimum of $65\%$ of SNII should occur in superbubbles, increasing to $\approx 80-90\%$ when the spatial and temporal correlations of stellar clusters are considered."
 If 80% of SNII are associated with supershells. for example. this would increase the required. replenishment rate per SN to z110230A...," If $80\%$ of SNII are associated with supershells, for example, this would increase the required replenishment rate per SN to $\approx 140-230\,M_{\odot}$."
 But even if as few as of all SNII contribute in this way to the replenishment. the rate implied by the results of Dawsonetal.(2008) would still be sufficient.," But even if as few as of all SNII contribute in this way to the replenishment, the rate implied by the results of \citet{Daw:08} would still be sufficient."
 This confirms that the necessaryreplenishment rates are likely to be achievable within supershells., This confirms that the necessary replenishment rates are likely to be achievable within supershells.
 The observed decline by a factor of two in the HI mass density may be a natural consequence of a replenishment rate about of that required to match consumption. as shown by the heavy solid line in Figure 2..," The observed decline by a factor of two in the HI mass density may be a natural consequence of a replenishment rate about of that required to match consumption, as shown by the heavy solid line in Figure \ref{fig:gasmodels}."
 If the actual replenishment rate from supershells Hes somewhere between the required rate and our derived upper limit. though. there may in fact be too much newly replenished gas to allow any decline in the neutral gas mass density.," If the actual replenishment rate from supershells lies somewhere between the required rate and our derived upper limit, though, there may in fact be too much newly replenished gas to allow any decline in the neutral gas mass density."
 A possible resolution in this scenario would be increasing the proportionality between the gas outflow rates and the SER as redshift decreases., A possible resolution in this scenario would be increasing the proportionality between the gas outflow rates and the SFR as redshift decreases.
 This is not unreasonable. as the SFH is becoming progressively more dominated by lower-mass galaxies with decreasing redshift (Juneauetal.2005;Panteral.Mobasheret2008).," This is not unreasonable, as the SFH is becoming progressively more dominated by lower-mass galaxies with decreasing redshift \citep{Jun:05,Pan:07,Mob:08}."
". Galaxies with stellar masses AL,3007:X107""A£.. dominate the SFH at :<1 (Mobasheretal.2008)."," Galaxies with stellar masses $M_* \lesssim 10^{10}\,M_{\odot}$ dominate the SFH at $z\lesssim 1$ \citep{Mob:08}."
.. Such low-mass galaxies lose more mass in gas outflows in proportion to their SFR than high-mass galaxies. simply due to the former's shallower potential wells (e.g..Dekel&Silk1986:ΜαςLow&Ferrara1999:Tolstoy 2000).," Such low-mass galaxies lose more mass in gas outflows in proportion to their SFR than high-mass galaxies, simply due to the former's shallower potential wells \citep[e.g.,][]{DS:86,MF:99,FT:00}."
. This effect may contribute to the slow decline in the HI mass density., This effect may contribute to the slow decline in the HI mass density.
 We have treated a number of complex physical processes in very general terms., We have treated a number of complex physical processes in very general terms.
 While being cautious of oversimplification. we have attempted to capture the essential interactions between star formation. recycling from stellar evolutionary. processes. ISM processes of heating and ionization. recombination. cooling and molecule formation. together with infall from the IGM. and outflow of ISM material.," While being cautious of oversimplification, we have attempted to capture the essential interactions between star formation, recycling from stellar evolutionary processes, ISM processes of heating and ionization, recombination, cooling and molecule formation, together with infall from the IGM, and outflow of ISM material."
 Most of this complexity 1s concealed within the replenishment factor A(f)., Most of this complexity is concealed within the replenishment factor $K(t)$.
 One issue is that stellar winds and SNe contribute to all components of the ISM rather than solely to page., One issue is that stellar winds and SNe contribute to all components of the ISM rather than solely to $\rho_{\rm SFG}$.
" In a “galactic fountain"" (Shapiro&Field1976;HouckBreg- 1990). infalling gas will contribute to. and outflowing gas will strip from. all components."," In a “galactic fountain"" \citep{SF:76,HB:90}, infalling gas will contribute to, and outflowing gas will strip from, all components."
 If recycled gas includes a component that never subsequently forms stars (such as some recycled gas in the ionized phase being ejected from the galaxy before contributing to star formation). the factor |Rp.(f) in Equation (1)) will be reduced. and (f) will need to be increased to compensate.," If recycled gas includes a component that never subsequently forms stars (such as some recycled gas in the ionized phase being ejected from the galaxy before contributing to star formation), the factor $+R\dot{\rho}_*(t)$ in Equation \ref{theeqn}) ) will be reduced, and $K(t)$ will need to be increased to compensate."
 Our quantitative results strongly depend on the assumed gas outflow rate., Our quantitative results strongly depend on the assumed gas outflow rate.
 Variations by a factor of two or so in. either direction will still result in a constant or slowly varying HI mass density. as long as a proportionality with the SFR of the host galaxies remains (assuggestedbyVeilleuxetal.2005).," Variations by a factor of two or so in either direction will still result in a constant or slowly varying HI mass density, as long as a proportionality with the SFR of the host galaxies remains \citep[as suggested by][]{Vei:05}."
. The chosen outflow rate is an effective average over all star forming galaxies. and is consistent with observed trends (e.g..Martin1999;Pettinietal.2000:Veilleux 2005).," The chosen outflow rate is an effective average over all star forming galaxies, and is consistent with observed trends \citep[e.g.,][]{Mar:99,Pet:00,Vei:05}."
. While individual galaxies show a large observed scatter between outflow rates and SERs. for the ensemble properties of the total population this assumption should be robust.," While individual galaxies show a large observed scatter between outflow rates and SFRs, for the ensemble properties of the total population this assumption should be robust."
 The proposed replenishment through the supershell mechanism is not inconsistent with some simultaneous— replenishment through infall., The proposed replenishment through the supershell mechanism is not inconsistent with some simultaneous replenishment through infall.
 Metallicity considerations. which we do not address here. do require infall of some low metallicity gas (Erb2008). and gas infall in local galaxies is well established (e.g..Bland-Hawthornetal.2007:Sancisi 2008).. although the observed infall rate is insufficient to match consumption.," Metallicity considerations, which we do not address here, do require infall of some low metallicity gas \citep{Erb:08},, and gas infall in local galaxies is well established \citep[e.g.,][]{Bla:07,San:08}, , although the observed infall rate is insufficient to match consumption."
therefore. a PAGD sar (Ilrivnak 1995. νοκ 1993).,"therefore, a PAGB star (Hrivnak 1995, Kwok 1993)."
 Even on a low resolution sceterum. Lrivnak (1995) could see the enhancement. of lines of s-process elements.," Even on a low resolution spectrum, Hrivnak (1995) could see the enhancement of lines of s-process elements."
 From the UDV photometry. Arkhipova ct al. (," From the UBV photometry, Arkhipova et al. ("
2003) found. this star to be pulsating variable with a period of  90 davs.,2003) found this star to be pulsating variable with a period of $\sim$ 90 days.
 Long term monitoring of this star using high resolution spectra has been carried out by. IxIochkova. Panchuck ‘Tavolzhanskava (2010) with following interesting findings.," Long term monitoring of this star using high resolution spectra has been carried out by Klochkova, Panchuck Tavolzhanskaya (2010) with following interesting findings."
 The strong absorption lines such as low excitation line of Ballat 6141 not only show asvounetries in the profile with short wavelength: side of the profile showing extended wing than the red wine: these strong lines also show large amplitude profile variations (with time) caused by variations in blue wing while red wing remained unchanged., The strong absorption lines such as low excitation line of at 6141 not only show asymmetries in the profile with short wavelength side of the profile showing extended wing than the red wing; these strong lines also show large amplitude profile variations (with time) caused by variations in blue wing while red wing remained unchanged.
 The spectrum contains C» lines most likely formed. in. the circumstellar shell., The spectrum contains $_{2}$ lines most likely formed in the circumstellar shell.
 At the epoch of largest asvmmetry in strong. line the €» (0:1). band head at A 5635 is seen in emission., At the epoch of largest asymmetry in strong line the $_{2}$ (0;1) band head at $\lambda$ 5635 is seen in emission.
 The cores of hwdrogen lines show larger variations in radial velocities ( 8 kms 1) while weak metallic lines show smaller amplitude variations in radial velocities (~ 1 i)., The cores of hydrogen lines show larger variations in radial velocities $\sim$ 8 $^{-1}$ ) while weak metallic lines show smaller amplitude variations in radial velocities $\sim$ 1 $^{-1}$ ).
 Molecular Cs lines remain stationary with time: the shift in. circumstellar features relative to systemic velocity. gives an expansion velocity Voss Of 15.0 |., Molecular $_{2}$ lines remain stationary with time; the shift in circumstellar features relative to systemic velocity gives an expansion velocity $_{exp}$ of 15.0 $^{-1}$.
 Our spectrum taken on Dec 27. 2009 also exhibits the features mentioned in Wlochkova. Panchuck Tavolzhanskava (2010).," Our spectrum taken on Dec 27, 2009 also exhibits the features mentioned in Klochkova, Panchuck Tavolzhanskaya (2010)."
 This star was analysed by Van Winckel and. Revniers (2000). (hereinafter: WR2000) who found it moderately metal-poor Fe/H] of 0.82 dex and showing enhancement of s-process elements., This star was analysed by Van Winckel and Reyniers (2000) (hereinafter WR2000) who found it moderately metal-poor [Fe/H] of $-$ 0.3 dex and showing enhancement of s-process elements.
 The present analysis covers additional elements Na. Mg and Zn and uses larger number of lines for many species (see Table S).," The present analysis covers additional elements Na, Mg and Zn and uses larger number of lines for many species (see Table 8)."
 Since the solar abundances usec in WR2000 are dillerent from our work. we have transformed. these abundances to solar abundances of Asplund et al. (," Since the solar abundances used in WR2000 are different from our work, we have transformed these abundances to solar abundances of Asplund et al. ("
2005) to facilitate comparison.,2005) to facilitate comparison.
 All elements agree within £0.15 dex., All elements agree within $\pm$ 0.15 dex.
 IRAS 22223]4827's progenitor was most probably a thermally pulsing ACB star., IRAS 22223+4327's progenitor was most probably a thermally pulsing AGB star.
 This is. indicated. by the C/O ratio of unity and the about one dex enrichment. of the s-process elements., This is indicated by the C/O ratio of unity and the about one dex enrichment of the $s$ -process elements.
 Two of our program stars LRAS 17279-1119 ancl LIGAS 22223|4327 show significant s-process enhancement., Two of our program stars IRAS 17279-1119 and IRAS 22223+4327 show significant s-process enhancement.
 We have compared the spectra of these two objects with HAS 07140-2321 with similar temperature but without s-process enhancement in Although this object has been mentioned in several papers on PAGB stars. a contemporary abundance analysis using high-quality digital spectra. modern model atmospheres aud refined atomic data has not been undertaken.," We have compared the spectra of these two objects with IRAS 07140-2321 with similar temperature but without s-process enhancement in Although this object has been mentioned in several papers on PAGB stars, a contemporary abundance analysis using high-quality digital spectra, modern model atmospheres and refined atomic data has not been undertaken."
 Abundance data from Ixodaira et al. (, Abundance data from Kodaira et al. (
1970) show strong ellects of dust-eas winnowing.,1970) show strong effects of dust-gas winnowing.
 Yet. this star unlike other stars exhibiting severe dust-gas winnowing does not have an infrared excess.," Yet, this star unlike other stars exhibiting severe dust-gas winnowing does not have an infrared excess."
 Llowever. the star is a spectroscopic binary. as are many or even all other stars exhibiting severe dust-gas winnowing.," However, the star is a spectroscopic binary, as are many or even all other stars exhibiting severe dust-gas winnowing."
gas Is dissipated from the disk.,gas is dissipated from the disk.
 On the contrary. for Vega-like objects no giant planet needs to be formed and/or migrate inward.," On the contrary, for Vega-like objects no giant planet needs to be formed and/or migrate inward."
 The gas may dissipate and still the planetesimal in the external part of the disk may produce dust by collisions., The gas may dissipate and still the planetesimal in the external part of the disk may produce dust by collisions.
 We tentatively analyzed two small sub-sets of Vega-like objects: the Vega-like stars with planets and the Vega-like group with no Doppler detected planets., We tentatively analyzed two small sub-sets of Vega-like objects: the Vega-like stars with planets and the Vega-like group with no Doppler detected planets.
 The first group is composed of 7 stars: 6 with 70 jm excess detected by Spitzer (HD33636.HD50554.52265.82943.HD128311and117176:Beichmanetal.2006) and € Eri with infrared and submillimieter excesses (Greavesetal.1998:Zuckerman2001).," The first group is composed of 7 stars: 6 with 70 $\mu$ m excess detected by Spitzer \citep[HD 33636, HD 50554, HD 52265, HD 82943, HD 128311 and HD 117176; ][]{beichman06}
 and $\epsilon$ Eri with infrared and submillimieter excesses \citep{greaves98,zuckerman01}."
. In the second group we include 5 stars without Exoplanets detected by the Doppler technique (Santosetal.2004:Gilli2006) and showing infrared excess in 24 or 70 jim (HD7570.HD38858.Beichmanetal.2006:Bryden 2006).," In the second group we include 5 stars without Exoplanets detected by the Doppler technique \citep{santos04,gilli06} and showing infrared excess in 24 or 70 $\mu$ m \citep[HD 7570, HD 38858, HD 69830, HD 76151 and HD 115617; ][]{beichman06,bryden06}."
. The median metallicity of Vega-like stars with planets is +0.07 dex and the dispersion is 0.16 dex., The median metallicity of Vega-like stars with planets is $+$ 0.07 dex and the dispersion is 0.16 dex.
 For the Vega-like objects without planets these values are: 20.08 and 0.18 dex. respectively.," For the Vega-like objects without planets these values are: $-$ 0.08 and 0.18 dex, respectively."
 It seems that when a Vega-like star has a planet the metallicity increases slightly., It seems that when a Vega-like star has a planet the metallicity increases slightly.
 However the small number of objects available as well as the dispersions prevent us from giving any statistical significance to this mitial trend., However the small number of objects available as well as the dispersions prevent us from giving any statistical significance to this initial trend.
 Greavesetal.(2007) proposed that the solid-mass (1.e.. metals) content in primordial disks. called Ms. is the fundamental parameter that regulates the planet/disk formation.," \citet{greaves07} proposed that the solid-mass (i.e., metals) content in primordial disks, called $_{\rm S}$, is the fundamental parameter that regulates the planet/disk formation."
 If Ma is small. the star will form a Vega-like disk. while if Ms is larger. a giant planet may be formed.," If $_{\rm S}$ is small, the star will form a Vega-like disk, while if $_{\rm S}$ is larger, a giant planet may be formed."
 Table | of Greavesetal.(2007) shows the range of metallicity and the final configurations (planet+debris.," Table 1 of \citet{greaves07}
 shows the range of metallicity and the final configurations $+$ debris,"
ISM.,ISM.
 According to the models by ? a lower rratio would indicate larger densities., According to the models by \citet{snijders07} a lower ratio would indicate larger densities.
 In Fig., In Fig.
 13 the 12.81 line ratios are also lower in the center than around it., \ref{fig:line-ratios} the 12.81 line ratios are also lower in the center than around it.
" This ratio ranges between 0.002 and 0.013 in the center, which indicate densities larger than 106cm? in a >5 Myr old starburst system with solar metallicity and relatively high (q=8x10%) ionization parameter (?,theirFig.5).."," This ratio ranges between 0.002 and 0.013 in the center, which indicate densities larger than $10^6~\3cm$ in a $>$ 5 Myr old starburst system with solar metallicity and relatively high $\rm q=8\times10^8$ ) ionization parameter \citep[][their Fig.5]{snijders07}."
" Based on our observed rratios, the rratios predicted with the model by ?,theirequation2 are about ten times larger than the observed ratios."," Based on our observed ratios, the ratios predicted with the model by \citet[][their equation 2]{pereira10} are about ten times larger than the observed ratios."
 These can be a consequence of the about 10 times higher extinction found in NGC 4945 than in the sample of galaxies used by ?.., These can be a consequence of the about 10 times higher extinction found in NGC 4945 than in the sample of galaxies used by \citet{pereira10}.
 The lline ratios obtained with the extinction correction in Fig. 13)), The line ratios obtained with the extinction correction in Fig. \ref{fig:line-ratios}) )
 are just ~9% larger than without correction., are just $\sim$ larger than without correction.
" This relatively small change after the extinction correction is because even in a high-extinction situation the differential extinction between aand lis small, given that both lines are closely spaced in wavelength and not in one of the silicate absorption features."," This relatively small change after the extinction correction is because even in a high-extinction situation the differential extinction between and is small, given that both lines are closely spaced in wavelength and not in one of the silicate absorption features."
" On the other hand, because of their larger differential (wavelength) extinction, the rratios corrected for extinction do change significantly from a factor —50 in the center (where the extinction is larger) to a factor 3 away from the center (where the extinction is lower)."," On the other hand, because of their larger differential (wavelength) extinction, the ratios corrected for extinction do change significantly from a factor $\sim$ 50 in the center (where the extinction is larger) to a factor 3 away from the center (where the extinction is lower)."
" Note that only the ratios from our co-added fluxes (Table 1)) can be compared to other galactic nuclei, as the 10x10 aperture is comparable to the size probed in any of the more distant galaxy nuclei."," Note that only the ratios from our co-added fluxes (Table \ref{tab-c4:fluxes-fov}) ) can be compared to other galactic nuclei, as the $\times$ 10 aperture is comparable to the size probed in any of the more distant galaxy nuclei."
 The rratio at the position of the H?O mega maser is about lower than the ratio obtained from the fluxes of the 10x10 co-added spectrum (Table 1))., The ratio at the position of the $_2$ O mega maser is about lower than the ratio obtained from the fluxes of the $\times$ 10 co-added spectrum (Table \ref{tab-c4:fluxes-fov}) ).
" Since in starburst environments the aand eemission lines are expected to be driven mainly by ionization (e.g.,?),, the lower ratios found along the southwest axis are likely due to a eemission enhanced by the starburst ring."," Since in starburst environments the and emission lines are expected to be driven mainly by photo-ionization \citep[e.g.,][]{ho07}, the lower ratios found along the northeast-southwest axis are likely due to a emission enhanced by the starburst ring."
" Although, these low ratios are also consistent with a ratio II] €O.1 found in shocks (?) where the low ionization line ccan also be enhanced (2)."," Although, these low ratios are also consistent with a ratio $\leq$ 0.1 found in shocks \citep{binette85} where the low ionization line can also be enhanced \citep{voit92}."
". On the other hand, the highest rratios found above and below the starburst ring are larger than those typically found in shocks."," On the other hand, the highest ratios found above and below the starburst ring are larger than those typically found in shocks."
 These higher ratios could actually be tracing an additional contribution to the [NellI] emission by a conically shaped narrow line region (NLR)., These higher ratios could actually be tracing an additional contribution to the [NeIII] emission by a conically shaped narrow line region (NLR).
" Previously, no evidence was found for the existence of such a NLR, given the absence of emission in the central 800pcx800pc (?).."," Previously, no evidence was found for the existence of such a NLR, given the absence of emission in the central $\times$ 800pc \citep{moorwood96a}."
 Instead the conical cavity traced by optical and near-infrared line and continuum tracers (??) was associated with a starburst super wind.," Instead the conical cavity traced by optical and near-infrared line and continuum tracers \citep{moorwood96a, marconi00} was associated with a starburst super wind."
" However, given the high extinction implied by our observations, optical eemission can be easily attenuated; mid-infrared eemission less so."," However, given the high extinction implied by our observations, optical emission can be easily attenuated; mid-infrared emission less so."
 A hypothetical conical NLR would be, A hypothetical conical NLR would be
Since in microlensing experiments the event durations are found by photometric fitüng and since the optical depth is proportional to the sum of the fit /zs. when making corrections [or blending it is important to properly relate the lens-light lraction of each event to the underlying event duration.,"Since in microlensing experiments the event durations are found by photometric fitting and since the optical depth is proportional to the sum of the fit $\te$ 's, when making corrections for blending it is important to properly relate the lens-light fraction of each event to the underlying event duration."
 and ((1997) (WP) studied the degeneracy of blend fits and concluded that in many cases blended and unblended lightcurves cannot be distinguished by photometric fitüng., and (1997) (WP) studied the degeneracy of blend fits and concluded that in many cases blended and unblended lightcurves cannot be distinguished by photometric fitting.
 They described areas of parameter space where blend fits would be useful and areas where they would not., They described areas of parameter space where blend fits would be useful and areas where they would not.
" While we think that WP did an accurate and very useful caleulation, and we agree with their conclusion that blend fits are usually not very useful, we wanted to repeat their analysis for several reasons."," While we think that WP did an accurate and very useful calculation, and we agree with their conclusion that blend fits are usually not very useful, we wanted to repeat their analysis for several reasons."
" First, WP did not include the baseline magnitude in their fits. reasoning that since many measurements are taken before and aller the event, the error in baseline magnitude was not significant."," First, WP did not include the baseline magnitude in their fits, reasoning that since many measurements are taken before and after the event, the error in baseline magnitude was not significant."
" In fact, we find that error in the baseline magnitude is one of the most severe problems in blend fits."," In fact, we find that error in the baseline magnitude is one of the most severe problems in blend fits."
 We find that errors even at the few percent level can drasucally alter the parameter values extracted [rom the fit., We find that errors even at the few percent level can drastically alter the parameter values extracted from the fit.
" Second, WP considered only evenly spaced observations and we wanted to consider whether different [ollow-up strategies could improve the ability to extract the parameters."," Second, WP considered only evenly spaced observations and we wanted to consider whether different follow-up strategies could improve the ability to extract the parameters."
" In our studies, we find the error in fit parameters three ways."," In our studies, we find the error in fit parameters three ways."
 First we create artificial lightcurves using the theoretical formula and add Gaussian random noise to each measurement., First we create artificial lightcurves using the theoretical formula and add Gaussian random noise to each measurement.
 We perform blended and unblended fits on these lghtcurves using Minuit (CERN Lib., We perform blended and unblended fits on these lightcurves using Minuit (CERN Lib.
 2003)., 2003).
 Second we calculate the error matrix by inverting the Hessian matrix as discussed in Gould (2003)., Second we calculate the error matrix by inverting the Hessian matrix as discussed in Gould (2003).
" Finally to understand the e[Iect of the non-Gaussianity of the errors in real microlensing experiments we create. artificial lensing lighteurves by adding microlensing signal into actual non-microlensing lightcurves obtained by the MACHO collaboration, and then fit these."," Finally to understand the effect of the non-Gaussianity of the errors in real microlensing experiments we create artificial lensing lightcurves by adding microlensing signal into actual non-microlensing lightcurves obtained by the MACHO collaboration, and then fit these."
" Since the method of calculating the error matrix is closest to what WP did, we first give these results."," Since the method of calculating the error matrix is closest to what WP did, we first give these results."
" Briefly, we calculate the Hessian matrix (the matrix of second derivatives of the light curve residuals with respect to each parameter) then invert it."," Briefly, we calculate the Hessian matrix (the matrix of second derivatives of the light curve residuals with respect to each parameter) then invert it."
 The square root of the diagonal elements of the resulting matrix are then the one sigma errorbars of the parameters., The square root of the diagonal elements of the resulting matrix are then the one sigma errorbars of the parameters.
" This accounts for correlations in the parameters, but not any nonlineariues."," This accounts for correlations in the parameters, but not any nonlinearities."
" WP used a very similar method, but used it to calculate the ο of the error bars."," WP used a very similar method, but used it to calculate the $\Delta \chi^2$ instead of the error bars."
In figure 3. we show that our method brackets WP's.,In figure \ref{fig:wp} we show that our method brackets WP's.
" We show limits calculated as both the one sigma lower limit on. { for an unblended hghtcurve and the value of fy that gives fj,ση= 1. ", We show limits calculated as both the one sigma lower limit on $f_{ll}$ for an unblended lightcurve and the value of $f_{ll}$ that gives $f_{ll}+\sigma_{f_{ll}} = 1$ 
In the case of narrow line or edge features. in different combinations of spectral order. data reduction method aud binning size. we identify possible structure in residuals al 26.5. 21.6. 34.4. 32.4. and 35.9 (emission like features). and at 28.2. 39.1. and 86.5 (absorption like features). that might be tempting to attribute to the source.,"In the case of narrow line or edge features, in different combinations of spectral order, data reduction method and binning size, we identify possible structure in residuals at 26.5, 27.6, 34.4, 32.4, and 35.9 (emission like features), and at 28.2, 39.1, and 86.5 (absorption like features), that might be tempting to attribute to the source."
 ILowever. we cannot exclude the possibility that anv are chance fluctuations at the level.," However, we cannot exclude the possibility that any are chance fluctuations at the level."
 The issue is complicated by possible calibration uncertainties on smaller scales. believed to be at a level of about oor less. that should be largely smoothed out by dither.," The issue is complicated by possible calibration uncertainties on smaller scales, believed to be at a level of about or less, that should be largely smoothed out by dither."
 We have also used a 60ks observation (ObsID 331) of2155-304. currently thought to be a featureless continuum in the speclral range we are concerned wilh here (Marshall οἱ al..," We have also used a 60ks observation (ObsID 331) of, currently thought to be a featureless continuum in the spectral range we are concerned with here (Marshall et al.,"
 in preparation). as a flat field source lo aid in feature identification.," in preparation), as a flat field source to aid in feature identification."
 This spectrum comprises about eight limes (he number of first order counts of the combined ddata., This spectrum comprises about eight times the number of first order counts of the combined data.
 Moreover. we have imposed a constraint that features must appear in both positive and negative orders in the sspectrum.," Moreover, we have imposed a constraint that features must appear in both positive and negative orders in the spectrum."
 We examined deviations [rom the model on scales up to 3 aad find only the expected normal distribution of residuals after allowing [for smooth departures resulting [rom calibration., We examined deviations from the model on scales up to 3 and find only the expected normal distribution of residuals after allowing for smooth departures resulting from calibration.
 The Ixolmogorov-5Smürnov. test applied to deviations on different scales also revealed no evidence for significant features (hese scales., The Kolmogorov-Smirnov test applied to deviations on different scales also revealed no evidence for significant features these scales.
 In summary. all significant deviations in the residuals (hat have been found can reasonably be explained bv instrumental effects.," In summary, all significant deviations in the residuals that have been found can reasonably be explained by instrumental effects."
 Equivalent width upper limits were derived by applying counting statistics to a convolution of the spectrum with a triangular kernel (Figure 2))., Equivalent width upper limits were derived by applying counting statistics to a convolution of the spectrum with a triangular kernel (Figure \ref{f:ew}) ).
" The distance of 62 pe derived by Walter (2001) seems at odds with the neutral HE column density. Vj). of LO?"" ? derived [rom the Chandra spectra: measured Vy, values for objects al this distance based on different techniques are typically in the range 107-10?) 7 FFruscione οἱ 1994)."," The distance of 62 pc derived by Walter (2001) seems at odds with the neutral H column density, $N_H$ , of $10^{20}$ $^{-2}$ derived from the Chandra spectra: measured $N_H$ values for objects at this distance based on different techniques are typically in the range $10^{18}$ $10^{19}$ $^{-2}$ Fruscione et 1994)."
 Walter (2001) indeed remarked on (his. citing reddening values Epv olf up to 0.1 derived by Ixnude Hog (1998) in support of the distance.," Walter (2001) indeed remarked on this, citing reddening values $E_{B-V}$ of up to 0.1 derived by Knude g (1998) in support of the distance."
 However. these redclening values show considerable scatter at low reddening and are based only on a relalively coarse attribution of spectral twpe to the stars considered.," However, these reddening values show considerable scatter at low reddening and are based only on a relatively coarse attribution of spectral type to the stars considered."
" We have estimated Ny, and the mean local neutral hvdrogen number density. 2,;. in the line-of-sight. toward aas a [unetion of distance by spatial interpolation in (he measurements compiled by Fruscione et ((1994) ancl Diplas Savage(1994) using a technique developed by P. Jelinsky"," We have estimated $N_H$ and the mean local neutral hydrogen number density, $n_H$, in the line-of-sight toward as a function of distance by spatial interpolation in the measurements compiled by Fruscione et (1994) and Diplas Savage(1994) using a technique developed by P. Jelinsky"
Ou the large scale (Figure 2)) we can see extremely faint. diffuse ciuission that exteuds for ~675 (20 kpc} in the east-west direction.,"On the large scale (Figure \ref{fig:1549ls}) ) we can see extremely faint, diffuse emission that extends for $\sim6\farcs5$ (20 kpc) in the east-west direction."
 The north-south exteusion. as noted bv Prestage&Peacock(1983).. cam be seen.," The north-south extension, as noted by \citet{pandp83}, can be seen."
 This Figure shares simul features to the deep Very Large Telescope Comm rk image of IT06 (their Figure 1)., This Figure shares similar features to the deep Very Large Telescope Gunn $r$ image of H06 (their Figure 1).
 The authors note that the north-south extended features appear to contain knots of enuüssiou., The authors note that the north-south extended features appear to contain knots of emission.
" Πας we cau see poiut-like sources im similar positious to these knots. which could be foreground stars but may also be super star clusters associated with the tidal tails of PISSIS19-το,"," Here we can see point-like sources in similar positions to these knots, which could be foreground stars but may also be super star clusters associated with the tidal tails of PKS1549-79."
 The radio15 source PISS 1315112 las also hac wach previous work carried out on it., The radio source PKS 1345+12 has also had much previous work carried out on it.
 Again. a brief outline of its main properties will be given before the new data are presented.," Again, a brief outline of its main properties will be given before the new data are presented."
 Readers iuterested iu a more thorough review are directed toward ITALO3., Readers interested in a more thorough review are directed toward HTM03.
 PISS 1315)12 (1€ 12.50) is one of the closest GPS sources., PKS 1345+12 (4C 12.50) is one of the closest GPS sources.
" This allows the compact double jet and core structure. noted frou, VLBI (δα) and VLBA (Gein) radio observatious. to preseut proportions of ~0715."," This allows the compact double jet and core structure, noted from VLBI (2cm) and VLBA (6cm) radio observations, to present proportions of $\sim0\farcs15$."
 The more pronünent S-shaped jet componcut extends to the south-cast before beudiug aud expanding into a diffuse lobe., The more prominent S-shaped jet component extends to the south-east before bending and expanding into a diffuse lobe.
 Protruding to the north-west of the core (the core being identified from the relative fatness of the radio spectimm) weak radio cussion is detected., Protruding to the north-west of the core (the core being identified from the relative flatness of the radio spectrum) weak radio emission is detected.
 On larger scales. diffuse radio cussion is detected exteudiue 35700 (NU kpe) to the north. aud 25700 (~55 kpc) to the south (Stanghellinietal.2005).," On larger scales, diffuse radio emission is detected extending 0 $\sim$ 80 kpc) to the north, and 0 $\sim$ 55 kpc) to the south \citep{stang05}."
. Optically. PISS 1315|12 shows a couples morphology characterized by two nuclei; the western most of which. identified as a 17.5(V) magnitude elliptical. possessing an extended curved tail.," Optically, PKS 1345+12 shows a complex morphology characterized by two nuclei, the western most of which, identified as a 17.5(V) magnitude elliptical, possessing an extended curved tail."
 PreviousAST studies. which are unable to resolve structure down to the scale of the radio mmorphology. have shown the western nucleus to be associated with the radio source (Axonetal.2000).," Previous studies, which are unable to resolve structure down to the scale of the radio morphology, have shown the western nucleus to be associated with the radio source \citep{axon00}."
. From the ACS data presented here we find optical radio offsets (Table 2)) similar to those fouud by Axonetal. (2000).. which coufizius the western nucleus as the host of the radio source.," From the ACS data presented here we find optical – radio offsets (Table \ref{tab:astro}) ) similar to those found by \citet{axon00}, which confirms the western nucleus as the host of the radio source."
 The double nuuceus and distorted appearance of PISS 1315|12 shows tha tagnereer event Is taking place., The double nucleus and distorted appearance of PKS 1345+12 shows that a merger event is taking place.
 As with the other source in this study; PISS 1315|12 shows a voung stellar populaion (Tadluuteretal. 2005).. a FIR excess (ULIRG) and near-UV cussion (Evansctal.1999.Labianoetal..inprep).. mdicatiug the presence of considerable star formation.," As with the other source in this study, PKS 1345+12 shows a young stellar population \citep{tad05}, a FIR excess (ULIRG) and near-UV emission \citep[][Labiano et al., in prep]{evans99}, indicating the presence of considerable star formation."
 Using optical spectroscopy. ITTAL03 lave observed 3. distinct unclear kineniatical componcuts in PERS 1315|12. the narrowest of which (PWIIMz310kans1) is interpreted as the systemic velocity.," Using optical spectroscopy, HTM03 have observed 3 distinct nuclear kinematical components in PKS 1345+12, the narrowest of which $\approx340{\rm~km~s^{-1}}$ ) is interpreted as the systemic velocity."
 The two other compoucuts. designated “intermediate” and “broad”. show FATAL of ~1250kins and ~L950kins| respectively. with corresponding bluc-shifts of ~lOOlas+ and L980last with respect to the rest frame.," The two other components, designated “intermediate” and “broad”, show FWHM of $\sim1250{\rm~km~s^{-1}}$ and $\sim1950{\rm~km~s^{-1}}$ respectively, with corresponding blue-shifts of $\sim400{\rm~km~s^{-1}}$ and $\sim1980{\rm~km~s^{-1}}$ with respect to the rest frame."
 Due to the reddening observed in cach component. it is proposed that the broad component originates from the imnoer most reeions closest to the obscured quasar. whilst the narrow component represents a quiesceut halo.," Due to the reddening observed in each component, it is proposed that the broad component originates from the inner most regions closest to the obscured quasar, whilst the narrow component represents a quiescent halo."
 Iu Figure 3. we preseut the new ACS data for PIS 1315|12., In Figure \ref{fig:1345acs} we present the new ACS data for PKS 1345+12.
 Iu both the Πα and [OTH] line aud coutiuuun nuages we find the two separate nuclei clearly visible within an extended diffuse euvelope., In both the $\alpha$ and [OIII] line and continuum images we find the two separate nuclei clearly visible within an extended diffuse envelope.
 The 270 (~5 kpc) separation of the two nuclei measured here is ~(71 ercater than the separation reported by Weckmanetal.(19056) aud Cülinore&Shaw(1986)., The $2\farcs0$ $\sim5$ kpc) separation of the two nuclei measured here is $\sim0\farcs1$ greater than the separation reported by \citet{heck86} and \citet{gands86}.
. The continuuni subtracted emission line dmages (Figures 2cc aud £f) show hat an insignificant amount of line cussion ομαλάτος roni the easteru component when compared to the western uucleus., The continuum subtracted emission line images (Figures \ref{fig:1345acs}c c and f) show that an insignificant amount of line emission emanates from the eastern component when compared to the western nucleus.
" To the northwest of this western micleus there is an extended cussion line filament (6.8.. Figures Saa. ο, d and f)."," To the north-west of this western nucleus there is an extended emission line filament (e.g., Figures \ref{fig:1345acs}a a, c, d and f)."
 haniediately north-east of the nai nuclear structure there is a separate island of ΟΠΠ enission (see Figure 300) and a “mushroom Like norpholoey to the Ta coutiuuua (see Figure 3bb): this is clear evidence of a dust lane running approximatcly south-cast to uorth-west., Immediately north-east of the main nuclear structure there is a separate island of [OIII] emission (see Figure \ref{fig:1345acs}e e) and a “mushroom” like morphology to the $\alpha$ continuum (see Figure \ref{fig:1345acs}b b); this is clear evidence of a dust lane running approximately south-east to north-west.
 On the larger scale we can again compare this data to the findings of Heckmanotal.(1986)., On the larger scale we can again compare this data to the findings of \citet{heck86}.
. Figure 1. highlights the distorted morphology and lints at some of the south-west curved tail exteusions mentioned by TWeckmanetal.(1986)., Figure \ref{fig:1345ls} highlights the distorted morphology and hints at some of the south-west curved tail extensions mentioned by \citet{heck86}.
.. We also see that the halo of PISS 1315112 coutams similar point like sources (to the south of the eastern nucleus) to the foreground stars or possible star cluster seen around PISS 1519-79., We also see that the halo of PKS 1345+12 contains similar point like sources (to the south of the eastern nucleus) to the foreground stars or possible star cluster seen around PKS 1549-79.
 Further study has shown these sources to be super star cluster with voung stellar populations (RodriguezZaurinetal.2006)., Further study has shown these sources to be super star cluster with young stellar populations \citep{rod06}.
. Iu this section we closely examune the iuner structures of the observed nuclei aud determine the most likely position of the ACN in the ACS emission line images (and therefore the likely position of the radio cores)., In this section we closely examine the inner structures of the observed nuclei and determine the most likely position of the AGN in the ACS emission line images (and therefore the likely position of the radio cores).
 Di-couical structures will sugecst that the outflows are wind driven. whereas structures similar to the radio morphologies will suggest that the outflows are driven by the radio jets.," Bi-conical structures will suggest that the outflows are wind driven, whereas structures similar to the radio morphologies will suggest that the outflows are driven by the radio jets."
" However. first we cxamine the relative astromietrv in the ACS data in order to estimate the ""uncertainties in derived positions."," However, first we examine the relative astrometry in the ACS data in order to estimate the uncertainties in derived positions."
 There are two clemenuts that could contribute to differeuces hetween the spatial offsets of objects measured ou the WECT aud URC frames: the errors iu measuring the positious themselves. i.e. true positions as related to iieasured positions. aud he residual errors in the correction of the spatial distortiou by the pipeline reduction.," There are two elements that could contribute to differences between the spatial offsets of objects measured on the WFC1 and HRC frames: the errors in measuring the positions themselves, i.e., true positions as related to measured positions, and the residual errors in the correction of the spatial distortion by the pipeline reduction."
 By quautifviug these errors we cau estimate the astrometric uncertainties present 1 ithe ACS images., By quantifying these errors we can estimate the astrometric uncertainties present in the ACS images.
in probing these scales in order to understand them on their own terms. describing substructure and. the cuspiness of halos: cosmic flexion is also complementary to cosmic shear. probing small scales in an isolated. fashion. whereas cosmic shear has a broad window function for power.,"in probing these scales in order to understand them on their own terms, describing substructure and the cuspiness of halos; cosmic flexion is also complementary to cosmic shear, probing small scales in an isolated fashion, whereas cosmic shear has a broad window function for power."
 The cosmic Hexion signal will be a useful means of testing theories of stable clustering or stable merging (ef., The cosmic flexion signal will be a useful means of testing theories of stable clustering or stable merging (c.f.
 Smith et al 2003)., Smith et al 2003).
 lt should be noted that in this analysis we have neglected the power that might exist from intrinsic. physical llexion correlations between galaxies.," It should be noted that in this analysis we have neglected the power that might exist from intrinsic, physical flexion correlations between galaxies."
 The analogous intrinsic cllipticity correlation between galaxies has been shown (e.g. Llevmans et al 2004) to be small: however. further work will be necessary to measure the level of contamination of cosmic Llexion due to intrinsic. [lexion alignments.," The analogous intrinsic ellipticity correlation between galaxies has been shown (e.g. Heymans et al 2004) to be small; however, further work will be necessary to measure the level of contamination of cosmic flexion due to intrinsic flexion alignments."
 In addition to the Hexion power spectrum. we are also able to calculate the convergence-Hexion. cross power spectrum. which can easily be related to the shear-Dexion cross power spectrum.," In addition to the flexion power spectrum, we are also able to calculate the convergence-flexion cross power spectrum, which can easily be related to the shear-flexion cross power spectrum."
 We note that to do this we can again use Limber's equation (79)). but this time using £5 from the outset rather than 2s).," We note that to do this we can again use Limber's equation \ref{eq:limber}) ), but this time using $P_\delta$ from the outset rather than $P_{\delta'}$."
 In this case. from our final power spectrum: for Uexion (equation 84)) we see that the relevant choice of q for llexion in Limber’s equation is 1n αστοι. [rom equationi (74)). we see that the choice of q suitable for convergence is llence the cross-power spectrum between convergence and Hexion can be written as ‘This is shown in Figure Ll. together with the associated convergence-I[exion. cross-correlation function in Figure 12 with appropriate errors for a 100. square degree survey.," In this case, from our final power spectrum for flexion (equation \ref{eqn:pf}) ) we see that the relevant choice of $q$ for flexion in Limber's equation is In addition, from equation \ref{eqn:kappa}) ), we see that the choice of $q$ suitable for convergence is Hence the cross-power spectrum between convergence and flexion can be written as This is shown in Figure 11, together with the associated convergence-flexion cross-correlation function in Figure 12 with appropriate errors for a 100 square degree survey."
 We see that this quantity has a measurement limit on an intermediate scale to shear and flexion limits ( 2’)., We see that this quantity has a measurement limit on an intermediate scale to shear and flexion limits $\simeq 2'$ ).
 Ht is a valuable quantity to measure. as it gives a stronger signal-to-noise than cosmic flexion. anc olfers a stringent check on svstematic errors between the shear or convergence and llexion signals.," It is a valuable quantity to measure, as it gives a stronger signal-to-noise than cosmic flexion, and offers a stringent check on systematic errors between the shear or convergence and flexion signals."
 In this paper. we have cxamined how Uexion can be applied," In this paper, we have examined how flexion can be applied"
how systems with negative heat capacity evolve (Lyudeu-Bell1999).,how systems with negative heat capacity evolve \citep{l99}.
. However the theory does uot describe accurately real clusters. at least those of modest population on which we lave focused.," However the theory does not describe accurately real clusters, at least those of modest population on which we have focused."
 The two main [actors ehanging the pleture are binary beating aud stellar evolution., The two main factors changing the picture are binary heating and stellar evolution.
 Both processes are. of course. well understood. but their combined effect lias uot been appreciatect.," Both processes are, of course, well understood, but their combined effect has not been appreciated."
 All clusters are born with a largeDm fraction of binaries. but these do not provide the largestDm effect.," All clusters are born with a large fraction of binaries, but these do not provide the largest effect."
 It is the systems most massive stars coupling together that generate most of the heating through three-body interactions., It is the system's most massive stars coupling together that generate most of the heating through three-body interactions.
 This heating easily reverses inciplent core contraction. so that the central cleusity climbs only. slightly before the uew phase of global expansion begius.," This heating easily reverses incipient core contraction, so that the central density climbs only slightly before the new phase of global expansion begins."
 This phase resembles. at least qualitatively. the post-collapse evolution described by Hénou(1972).," This phase resembles, at least qualitatively, the post-collapse evolution described by \citet{h72}."
. However. the reversal [rom coutraction occurs at wach lower density thai iu earlier accounts.," However, the reversal from contraction occurs at much lower density than in earlier accounts."
 Mass loss accompanying stellar evolution moclilies the picture. but does uot change it qualitatively.," Mass loss accompanying stellar evolution modifies the picture, but does not change it qualitatively."
 Siuce the most massive stars die out belore they cau couple with others. the degree of binary heating. aud therefore the vigor of global expausion. is less.," Since the most massive stars die out before they can couple with others, the degree of binary heating, and therefore the vigor of global expansion, is less."
 Iu addition. the earlier phase of core contraction lasts longerOm aud leads to a higherfae) central density before reversal.," In addition, the earlier phase of core contraction lasts longer and leads to a higher central density before reversal."
 Both moclificatious iucrease with the cluster population NV., Both modifications increase with the cluster population $N$.
 We thus see why some globular clusters iudeed reach the point of true core collapse. which cau be reversed ouly by the tightest of binaries.," We thus see why some globular clusters indeed reach the point of true core collapse, which can be reversed only by the tightest of binaries."
 The new picture of cluster evolution preseuted here is more complex than tle classical oue. but it is motivated by the basic physical effects that are incorporated in moderni uumerical simulatious.," The new picture of cluster evolution presented here is more complex than the classical one, but it is motivated by the basic physical effects that are incorporated in modern numerical simulations."
 With the beneli X hiudsight. i is easy to see why earlier. simplified methods reinforced the impression that cyuamical relaxation is ubiquitous.," With the benefit of hindsight, it is easy to see why earlier, simplified methods reinforced the impression that dynamical relaxation is ubiquitous."
 Iu sinele mass mocels. binary formation is so delayed that it becomes irrelevant.," In single mass models, binary formation is so delayed that it becomes irrelevant."
 Statistical models. based ou solving the Fokker-Plauck equation. ieglect three-bocly effects eutirely.," Statistical models, based on solving the Fokker-Planck equation, neglect three-body effects entirely."
—- Finally. the contraction of Lagrangian nass shells is not a reliable sien of core contraction. but may reflect a differeut phenomenon. mass segregation.," Finally, the contraction of Lagrangian mass shells is not a reliable sign of core contraction, but may reflect a different phenomenon, mass segregation."
 Our uew picture is itself far [roin complete., Our new picture is itself far from complete.
 Future simulations carried out at higher JN. will reveal iu detail how the ransition is mace to a more vigorously contractiug central core., Future simulations carried out at higher $N$ will reveal in detail how the transition is made to a more vigorously contracting central core.
 We are grateful to Douglas Hegegle and Simou Portegies-Zwart for hielpiug us navigate the literature of dynamical relaxation., We are grateful to Douglas Heggie and Simon Portegies-Zwart for helping us navigate the literature of dynamical relaxation.
 Ousi Fakhourt also provided useful suggestious ou the visualization of energy transfer., Onsi Fakhouri also provided useful suggestions on the visualization of energy transfer.
 This research was supported by NSF gerant. AST 0008573., This research was supported by NSF grant AST 0908573.
ercater than those of NGC 7603 and its companion galaxy.,greater than those of NGC 7603 and its companion galaxy.
 Thus we have preseuted a very well known svstenmi with anomalous redshifts. NCC 7603. to be an apparently much more anomalous than was previously thought.," Thus we have presented a very well known system with anomalous redshifts, NGC 7603, to be an apparently much more anomalous than was previously thought."
 There are | objects with very different redshifts apparently commected by a filament associated with the lower redshift galaxy., There are 4 objects with very different redshifts apparently connected by a filament associated with the lower redshift galaxy.
 This svstem is at prescut the most spectacular case that we know among the caudidates for anomalous redshift., This system is at present the most spectacular case that we know among the candidates for anomalous redshift.
 Future studies of this system are clearly warranted., Future studies of this system are clearly warranted.
 Acknowledements: We eratefully acknowledge the anonviuous referee for helpful conunents., Acknowledgments: We gratefully acknowledge the anonymous referee for helpful comments.
 Thanks are also eivon to Victor P. Debattista aud Ciustav Tanunaun (Astron., Thanks are also given to Victor P. Debattista and Gustav Tammann (Astron.
 Inst., Inst.
 Basel) for helpfu discussion about the present paper., Basel) for helpful discussion about the present paper.
the remnant at the center.,the remnant at the center.
 A reduction in the infall mass brings z15D closer to reproducing observations., A reduction in the infall mass brings z15D closer to reproducing observations.
 Two dimensional versions of the one dimensional simulations presented in the higher energy explosions of 7 and ? might eject more of the pproduced in the more energetic explosions., Two dimensional versions of the one dimensional simulations presented in the higher energy explosions of \citet{Heger&Woosley:2008} and \citet{Nomoto:2007} might eject more of the produced in the more energetic explosions.
" Rotating models (7) create more primary nitrogen, which can lead to an increase in the rate of CNO burning at the base of the hydrogen shell, causing some models die as larger red supergiants rather than a compact blue supergiants."," Rotating models \citep{Hirschi:2008} create more primary nitrogen, which can lead to an increase in the rate of CNO burning at the base of the hydrogen shell, causing some models die as larger red supergiants rather than a compact blue supergiants."
" In this case, Rayleigh-Taylor mixing would play out in a similar way to the solar models presented in this paper, and more iron would "," In this case, Rayleigh-Taylor mixing would play out in a similar way to the solar models presented in this paper, and more iron would be ejected by these stars."
point out that the supernova explosion mechanism is probably inherently multidimensional and asymmetric.," Recent simulations \citep{Scheck:2004,Scheck:2006,Burrows:2007a,Burrows:2007b, Burrows:2007c} point out that the supernova explosion mechanism is probably inherently multidimensional and asymmetric."
" Asymmetry in the explosion, whether in the form of a jet or a perturbation described by Legendre polynomials of order of |=1 or |=2, might also mix more of the nickel core out of the star, bringing the models closer to reproducing observations."," Asymmetry in the explosion, whether in the form of a jet or a perturbation described by Legendre polynomials of order of $l=1$ or $l=2$, might also mix more of the nickel core out of the star, bringing the models closer to reproducing observations."
" 7 have suggested that HMP stars may be ""chemically peculiar"" stars, in which low iron abundance is caused by separation of gas and dust beyond the stellar surface, followed by accretion of dust-depleted gas."," \citet{Venn&Lambert:2008} have suggested that HMP stars may be ”chemically peculiar” stars, in which low iron abundance is caused by separation of gas and dust beyond the stellar surface, followed by accretion of dust-depleted gas."
 If this is the case-and the authors note that a definitive answer requires additional information—the stars’ true metallicity is closer to [X/H] z—2 rather than -5., If this is the case–and the authors note that a definitive answer requires additional information--the stars' true metallicity is closer to [X/H] $\approx -2$ rather than -5.
 'The supernova light curve is affected by the amount of 56ΝΙ in the center of the star that falls back onto the black hole at the center of the explosion., The supernova light curve is affected by the amount of $^{56}$ Ni in the center of the star that falls back onto the black hole at the center of the explosion.
 The models for the first supernovae presented in this work are intrinsically dimmer than corresponding supernovae arising from stars of solar composition provided they explode with the same amount of energy., The models for the first supernovae presented in this work are intrinsically dimmer than corresponding supernovae arising from stars of solar composition provided they explode with the same amount of energy.
" In our models of primordial composition supernovae, all or nearly all of the synthesized in the supernova falls back onto the remnant left behind at the center of the explosion."," In our models of primordial composition supernovae, all or nearly all of the synthesized in the supernova falls back onto the remnant left behind at the center of the explosion."
 Energy from the radioactive decay of powers the tail of core-collapse supernova light curves., Energy from the radioactive decay of powers the tail of core-collapse supernova light curves.
" When the energy released in its radioactive decay to °°Fe is no longer observable, the supernova light curves will loose their radioactive tails, making them briefer and dimmer than ordinary core-collapse supernova light curves."," When the energy released in its radioactive decay to $^{56}$ Fe is no longer observable, the supernova light curves will loose their radioactive tails, making them briefer and dimmer than ordinary core-collapse supernova light curves."
 The presupernova structure of a star is determined largely by its initial mass and by the initial composition of the gas from which it formed., The presupernova structure of a star is determined largely by its initial mass and by the initial composition of the gas from which it formed.
" The symmetry and energy of the explosion, along with the presupernova structure, influence where and to what extent Rayleigh- instabilities will grow, as well as how much mass will fall back onto the remnant at the center."," The symmetry and energy of the explosion, along with the presupernova structure, influence where and to what extent Rayleigh-Taylor instabilities will grow, as well as how much mass will fall back onto the remnant at the center."
" The non-rotating zero metallicity models studied are far more compact than solar-composition models of the same mass, in part because CNO burning proceeds at higher temperatures and densities."," The non-rotating zero metallicity models studied are far more compact than solar-composition models of the same mass, in part because CNO burning proceeds at higher temperatures and densities."
" CNO burning is responsible for energy production during the main sequence for all stars at the masses studied here, but in metal poor stars CNO burning proceeds at higher temperatures and densities."," CNO burning is responsible for energy production during the main sequence for all stars at the masses studied here, but in metal poor stars CNO burning proceeds at higher temperatures and densities."
" For zero-metalicity stars, the star must first contract to a temperature of 10? K, hot enough to initiate helium burning."," For zero-metalicity stars, the star must first contract to a temperature of $^8$ K, hot enough to initiate helium burning."
" This helium burning produces a small amount of carbon, which is enough to act as a catalyst to enable hot CNO burning to proceed."," This helium burning produces a small amount of carbon, which is enough to act as a catalyst to enable hot CNO burning to proceed."
" In addition, non-rotating stars with a metallicity Z below 10-? will never reach the red giant branch, since they end helium burning with effective temperatures above 104."," In addition, non-rotating stars with a metallicity Z below $^{-3}$ will never reach the red giant branch, since they end helium burning with effective temperatures above $^4$."
" Below this temperature, the opacity is large enough that the star will expand toward the red giant branch."," Below this temperature, the opacity is large enough that the star will expand toward the red giant branch."
 The more compact structure of these stars causes their reverse shocks to propagate more quickly to the origin than those in solar stars., The more compact structure of these stars causes their reverse shocks to propagate more quickly to the origin than those in solar stars.
" Larger remnants are left behind in the more compact stars because the rate at which mass accretes onto the stellar remnant is higher, as predicted by ? and shown in the 1D simulations of ?.."," Larger remnants are left behind in the more compact stars because the rate at which mass accretes onto the stellar remnant is higher, as predicted by \citet{Chevalier:1989} and shown in the 1D simulations of \citet{Zhang:2008}."
 The time scale over which the Rayleigh-Taylor instabilities can develop is also set by the reverse shock., The time scale over which the Rayleigh-Taylor instabilities can develop is also set by the reverse shock.
" For the case of the compact primordial composition progenitors modeled here, the Rayleigh-Taylor instabilities have little time to develop."," For the case of the compact primordial composition progenitors modeled here, the Rayleigh-Taylor instabilities have little time to develop."
 This means that a smaller portion of the isotopic layers of the star will be mixed., This means that a smaller portion of the isotopic layers of the star will be mixed.
" The Rayleigh-Taylor instabilities do not have time to become fully nonlinear in our simulations, so the scale of the instability as well as the degree of mixing is set by the scale of the initial seed perturbations."," The Rayleigh-Taylor instabilities do not have time to become fully nonlinear in our simulations, so the scale of the instability as well as the degree of mixing is set by the scale of the initial seed perturbations."
" In the case of the solar-composition progenitor models, the Rayleigh-Taylor instability became fully nonlinear and the size and shape of the initial perturbation was no longer apparent at late times."," In the case of the solar-composition progenitor models, the Rayleigh-Taylor instability became fully nonlinear and the size and shape of the initial perturbation was no longer apparent at late times."
" A smaller region of the primordial-composition stars is unstable, compared to solar-composition stars, which also contributes to the reduced mixing we see in our zero-metal models."," A smaller region of the primordial-composition stars is unstable, compared to solar-composition stars, which also contributes to the reduced mixing we see in our zero-metal models."
 The small amount of mixing, The small amount of mixing
As the largest virtalized objects in. the Universe. galaxy clusters are a powerful cosmological tool once their mass distribution is univocally determined.,"As the largest virialized objects in the Universe, galaxy clusters are a powerful cosmological tool once their mass distribution is univocally determined."
 In the recent past. there have been several claims that cluster masses obtained from X-ray analyses of the intracluster plasma. taken to be in hydrostatic equilibrium with the gravitational potential well. are significantly smaller (up to a factor of two: but see Wu et 11998: Allen 1998; Bóhhringer et 1998; Allen et 22001) than the ones derived from gravitational lensing (see Mellier 1999 for a review).," In the recent past, there have been several claims that cluster masses obtained from X-ray analyses of the intracluster plasma, taken to be in hydrostatic equilibrium with the gravitational potential well, are significantly smaller (up to a factor of two; but see Wu et 1998; Allen 1998; Böhhringer et 1998; Allen et 2001) than the ones derived from gravitational lensing (see Mellier 1999 for a review)."
 In this paper we report on the mass distribution. of the cluster 1224 by combining the results from weak lensing analysis of deep FORSI-VLT images with those obtained from a spatially-resolved spectroscopic X-ray analysis of a observation., In this paper we report on the mass distribution of the cluster $-$ 1224 by combining the results from weak lensing analysis of deep FORS1-VLT images with those obtained from a spatially-resolved spectroscopic X-ray analysis of a observation.
 1224 is a rich galaxy cluster at redshift 0.302 that has been part of the Einstein Medium Sensitivity Survey sample (Gioia Luppino 1994) and of the CNOC survey (Carlberg et 11996)., $-$ 1224 is a rich galaxy cluster at redshift 0.302 that has been part of the Einstein Medium Sensitivity Survey sample (Gioia Luppino 1994) and of the CNOC survey (Carlberg et 1996).
 Lombardi et ((2000) presented a detailed weak lensing analysis of the FORSI-VLT data., Lombardi et (2000) presented a detailed weak lensing analysis of the FORS1-VLT data.
 Figure | shows the X-ray Isophotes overplotted to the optical V-band image., Figure \ref{opt_xray} shows the X-ray isophotes overplotted to the optical V-band image.
" In the following we adopt the conversion 1aremin=376kpe (:= 0.302. If,=οτμkms.|!Μρο 1O,-21Oy-- 0.3) απά quote all the errors at Lo (68.3% confidence level)."," In the following we adopt the conversion $1 \mbox{ arcmin} =
376 \mbox{ kpc}$ $z=0.302$ , $H_0 = 50 \, h_{50} \mbox{ km s}^{-1}
\mbox{ Mpc}^{-1}$, $\Omega_{\rm m} = 1 - \Omega_{\Lambda} = 0.3$ ) and quote all the errors at $1 \sigma$ $68.3\%$ confidence level)."
 We retrieved the primary and secondary data products from the archive., We retrieved the primary and secondary data products from the archive.
 The exposure of 1224 was done on June 11. 2000 using the ACIS-I configuration.," The exposure of $-$ 1224 was done on June 11, 2000 using the ACIS-I configuration."
 We reprocessed the levelz1 events file in the Very Faint Mode and. then. with the software 11.38: Townsley et 22000).," We reprocessed the level=1 events file in the Very Faint Mode and, then, with the software 1.38; Townsley et 2000)."
 The light curve was checked for high background flares that were not detected., The light curve was checked for high background flares that were not detected.
 About [1.0ksec (out of [1.2 ksec. the nominal exposure time) were used and a total number of counts of about 20000 were collected from the region of interest in the 0.5-7 keV band.," About $44.0 \mbox{ ksec}$ (out of $44.2 \mbox{ ksec}$ , the nominal exposure time) were used and a total number of counts of about $20 \, 000$ were collected from the region of interest in the 0.5–7 keV band."
 We used (v. 2.2: Elvis et 22002. in prep.)," We used (v. 2.2; Elvis et 2002, in prep.)"
 and our own routines to prepare the data to the imaging and spectral studies., and our own routines to prepare the data to the imaging and spectral studies.
" The X-ray center was fixed to the peak of the projected mass from weak lensing analysis (Lombardi. et 22000) at (RA. Dec: =(LOHLOM@32°68,12?39/58.87 )."," The X-ray center was fixed to the peak of the projected mass from weak lensing analysis (Lombardi et 2000) at (RA, Dec; ${} =
(10^\mathrm{h} 10^\mathrm{m} 32\fs68, -12^{\circ} 39' 58.8"")$ ."
" Note that the maximum value in à 5""-smoothed image of the cluster X-ray emission is at (RA. =(105109327LL.12739/55.6""). Le. less than 5 aresec apart from the adopted center."," Note that the maximum value in a $5\arcsec$ -smoothed image of the cluster X-ray emission is at (RA, ${} = (10^\mathrm{h} 10^\mathrm{m} 32\fs44,
-12^{\circ} 39' 55.6"")$, i.e. less than 5 arcsec apart from the adopted center."
 With respect to the adopted center. a clear asymmetry in the surface brightness distribution is however detected. suggesting an excess in emission in the northern region (see Fig. 2)).," With respect to the adopted center, a clear asymmetry in the surface brightness distribution is however detected, suggesting an excess in emission in the northern region (see Fig. \ref{xray_asi}) )."
 We detected extended emission at 20 confidence level up to 4.1 aremm(1.55 Mpe)and we were able to extract a total of four, We detected extended emission at $2 \sigma$ confidence level up to 4.1 arcmin$1.55 \mbox{ Mpc}$ )and we were able to extract a total of four
lines. as can be seen from Fig.,"lines, as can be seen from Fig."
 5 in MWT99.., 5 in \cite{martini}.
 The results obtained for this date are particularly uncertain. and. should be regarded with caution., The results obtained for this date are particularly uncertain and should be regarded with caution.
 They are based on rough estimates of the VR/ magnitudes made from the spectral observations., They are based on rough estimates of the $VRI$ magnitudes made from the spectral observations.
 Besides. judging from the estimated effective temperature the observations covered only the shortwavelength Wien's part of the spectrum.," Besides, judging from the estimated effective temperature the observations covered only the shortwavelength Wien's part of the spectrum."
 The bulk of the energy of the object was presumably emitted in the infrared where no measurements were made., The bulk of the energy of the object was presumably emitted in the infrared where no measurements were made.
 Finally. our fits for this date. result from extrapolation beyond the range of the standard spectra (the latest types for which intrinsic colours are available are: Μό--7 for giants and M5-6 for supergiants).," Finally, our fits for this date result from extrapolation beyond the range of the standard spectra (the latest types for which intrinsic colours are available are: M6–7 for giants and M5–6 for supergiants)."
 Figure 3. shows the results of observations in. 1998. 1999 and 2003.," Figure \ref{sp03} shows the results of observations in 1998, 1999 and 2003."
 Asterisks indicate the 2MASS measurements obtained on 18 May 1998., Asterisks indicate the 2MASS measurements obtained on 18 May 1998.
 Triangles show the DENIS results derived on 11 September 1999., Triangles show the DENIS results derived on 11 September 1999.
 Circles represent the spectrum observed in May-September 2003 (see above for the sources fo the data)., Circles represent the spectrum observed in May-September 2003 (see above for the sources fo the data).
 First we discuss the observations obtained in 2003 as they cover the largest spectral range., First we discuss the observations obtained in 2003 as they cover the largest spectral range.
 The whole spectrum. 1.8. all the circles in Fig. 3..," The whole spectrum, i.e. all the circles in Fig. \ref{sp03},"
 cannot be fitted with a single standard spectrum., cannot be fitted with a single standard spectrum.
 This can only be done for shorter wavelengths., This can only be done for shorter wavelengths.
 In Fig., In Fig.
 5 we show the best fits of the supergiant (full curve) and giant (dotted curve) spectra for the VR./..7 measurements., \ref{sp03} we show the best fits of the supergiant (full curve) and giant (dotted curve) spectra for the $VR_cI_cJ$ measurements.
 The parameters of the fits are given in Table 3.., The parameters of the fits are given in Table \ref{evol_t}.
 The B magnitude has not been taken into account in the fitting procedure because of its significant uncertainty., The $B$ magnitude has not been taken into account in the fitting procedure because of its significant uncertainty.
 However. as can be seen from Fig. 3..," However, as can be seen from Fig. \ref{sp03},"
 it fits well the obtained spectra., it fits well the obtained spectra.
 In the long wavlength range the H and. particularly. K magnitudes show a clear excess compared to the spectra fitted in the shorter wavelengths.," In the long wavlength range the $H$ and, particularly, $K$ magnitudes show a clear excess compared to the spectra fitted in the shorter wavelengths."
 With the L and M magnitudes measured by BVAOA (not shown in Fig. 3)), With the $L$ and $M$ magnitudes measured by \cite{bva} (not shown in Fig. \ref{sp03}) )
 one can easily conclude that the source of this excess dominates the brightness of the object in the infrared., one can easily conclude that the source of this excess dominates the brightness of the object in the infrared.
 This infrared excess will be discussed in Sect. 6.., This infrared excess will be discussed in Sect. \ref{ire}.
 The infrared observations displayed in Fig., The infrared observations displayed in Fig.
 3. show that V4332 Ser evolved systematically between 1998 and 2003., \ref{sp03} show that V4332 Sgr evolved systematically between 1998 and 2003.
 It was becoming fainter in 7 (and /) but brighter in K., It was becoming fainter in $J$ (and $I$ ) but brighter in $K$.
 This can be interpreted as due to a gradual fading of the main object (seen in J and /) and the increasing infrared excess in K., This can be interpreted as due to a gradual fading of the main object (seen in $J$ and $I$ ) and the increasing infrared excess in $K$.
 Therefore when fitting the standard spectra to the DENIS magnitudes obtained on 11 September 1999 (triangles in Fig. 3)).," Therefore when fitting the standard spectra to the DENIS magnitudes obtained on 11 September 1999 (triangles in Fig. \ref{sp03}) ),"
 expecting that K may be affected by the IR excess. we considered only / and J.," expecting that $K$ may be affected by the IR excess, we considered only $I$ and $J$."
 Indeed. as can be seen from Fig. 3..," Indeed, as can be seen from Fig. \ref{sp03},"
 the K magnitude ts -0.5 magnitude above the fitted spectrum., the $K$ magnitude is $\sim$ 0.5 magnitude above the fitted spectrum.
 Note. however. that if all the three (77K) measurements are taken into account the fits would be quite poor and 7. would lower by - 100KK for class IIl and -200 KK for class I compared to the values given in Table 3..," Note, however, that if all the three $IJK$ ) measurements are taken into account the fits would be quite poor and $T_\mathrm{eff}$ would lower by $\sim$ K for class III and $\sim$ K for class I compared to the values given in Table \ref{evol_t}."
 No fit to the 2MASS data on 18 May 1998 (asterisks) is shown in Fig. 3.., No fit to the 2MASS data on 18 May 1998 (asterisks) is shown in Fig. \ref{sp03}.
 The spectral range of the data is quite narrow and hence any Τομ between «3000 K and «4500 K could be considered to satisfactorily fit the data., The spectral range of the data is quite narrow and hence any $T_\mathrm{eff}$ between $\sim$ 3000 K and $\sim$ 4500 K could be considered to satisfactorily fit the data.
 Fortunately for this wide Ty range. log 4 of the fits varies by less than 0.20.," Fortunately for this wide $T_\mathrm{eff}$ range, log $\theta$ of the fits varies by less than 0.20."
 The mean values of log 8 from these fits are given in Table 3.., The mean values of log $\theta$ from these fits are given in Table \ref{evol_t}.
 The last two columns in Table 3. show the stellar radius and luminosity (given in solar units) of V4332 Ser calculated from the angular radius (8) and the effective temperature (Το) assuming a distance of 1.8 kpe., The last two columns in Table \ref{evol_t} show the stellar radius and luminosity (given in solar units) of V4332 Sgr calculated from the angular radius $\theta$ ) and the effective temperature $T_\mathrm{eff}$ ) assuming a distance of 1.8 kpc.
 Figure 4 displays the evolution of principal parameters of V4332 Sgr taken from Table 3.., Figure \ref{evol_f} displays the evolution of principal parameters of V4332 Sgr taken from Table \ref{evol_t}.
 The time is in days since 24 February 1994. Le. since the discovery of V4332 Ser in eruption.," The time is in days since 24 February 1994, i.e. since the discovery of V4332 Sgr in eruption."
 The effective temperature is in units of 10° K. while the stellar radius and luminosity are in solar units.," The effective temperature is in units of $10^3$ K, while the stellar radius and luminosity are in solar units."
 Open symbols show the results from fitting the standard supergiant (I) spectra to the observations., Open symbols show the results from fitting the standard supergiant (I) spectra to the observations.
 The same but using the giant (IIL) spectra is presented with the full points., The same but using the giant (III) spectra is presented with the full points.
 Asterisks in panel denote the effective temperatures derived by MWT99 from fitting stellar atmosphere models to their spectra.," Asterisks in panel denote the effective temperatures derived by \cite{martini}
 from fitting stellar atmosphere models to their spectra."
 Let us first discuss the spectral types obtainec from our analysis., Let us first discuss the spectral types obtained from our analysis.
" As can be seen from Table 3 no matter which luminosity class of the standard spectra (I or IL) is used. the resultant spectral types are always very similar,"," As can be seen from Table \ref{evol_t} no matter which luminosity class of the standard spectra (I or III) is used, the resultant spectral types are always very similar."
 Moreover. our spectral classes are also very close to those obtained by MWT99 from the classification of their spectra.," Moreover, our spectral classes are also very close to those obtained by \cite{martini} from the classification of their spectra."
 This shows that the general approach adopted in our analysis of the photometric data is consistent and reliable., This shows that the general approach adopted in our analysis of the photometric data is consistent and reliable.
 The consistency of the effective temperatures derived in the different ways is not as good as that of the spectral types., The consistency of the effective temperatures derived in the different ways is not as good as that of the spectral types.
 As can be seen from Table 3 and Fig. 4, As can be seen from Table \ref{evol_t} and Fig. \ref{evol_f}
 initially. when the object was of the K type. both kinds of standard spectra give practically the same values of," initially, when the object was of the K type, both kinds of standard spectra give practically the same values of"
"by The plasma wave energy density, E.,(r,t), close to the Sun at time t=25 s is displayed in Figure 3 with the corresponding scale of the background plasma inhomogeneity.","by The plasma wave energy density, $E_w(r,t)$, close to the Sun at time $t=25$ s is displayed in Figure \ref{fig:pert_wave_energy_1} with the corresponding scale of the background plasma inhomogeneity."
 The unperturbed case has been over plotted for comparison., The unperturbed case has been over plotted for comparison.
 Lines have been drawn to indicate the 1010 cm wavelength of sinusoid perturbation to the background plasma., Lines have been drawn to indicate the $10^{10}$ cm wavelength of sinusoid perturbation to the background plasma.
 Periodic oscillation of the background plasma is evident together with the corresponding periodic nature of the plasma wave energy density., Periodic oscillation of the background plasma is evident together with the corresponding periodic nature of the plasma wave energy density.
" The magnitude of E,(r,t) in the unperturbed case is generally larger than the perturbed case, showing clearly the reduction in wave growth when the background plasma is significantly perturbed."," The magnitude of $E_w(r,t)$ in the unperturbed case is generally larger than the perturbed case, showing clearly the reduction in wave growth when the background plasma is significantly perturbed."
" As we get further away from the Sun (5, compared with 2R,) the radial drop of density plays a less dominant role allowing small scale fluctuations to become more important, seen in |L|-!."," As we get further away from the Sun $5R_s$ compared with $2R_s$ ) the radial drop of density plays a less dominant role allowing small scale fluctuations to become more important, seen in $|L|^{-1}$."
" With this increased role, the small scale fluctuations increase the suppression of induced plasma wave energy density with respect to the unperturbed case."," With this increased role, the small scale fluctuations increase the suppression of induced plasma wave energy density with respect to the unperturbed case."
" Despite fluctuations suppressing plasma waves, the perturbed case displays plasma wave energy density greater than the unperturbed case at peaks in its oscillation."," Despite fluctuations suppressing plasma waves, the perturbed case displays plasma wave energy density greater than the unperturbed case at peaks in its oscillation."
 The instability of the electron beam which induces the plasma waves (Of/Ov> 0) is not fully relaxed to thermal velocities in areas of space where plasma wave production is suppressed., The instability of the electron beam which induces the plasma waves $\partial f/\partial v > 0$ ) is not fully relaxed to thermal velocities in areas of space where plasma wave production is suppressed.
" Another striking feature of Figure 3 is the double peak and trough behaviour of E,(r,t) within one wavelength of background plasma fluctuation."," Another striking feature of Figure \ref{fig:pert_wave_energy_1} is the double peak and trough behaviour of $E_w(r,t)$ within one wavelength of background plasma fluctuation."
" The distribution of E,(r,t) in space is substantially different at the latter time of t=100 s, shown in Figure 3.."," The distribution of $E_w(r,t)$ in space is substantially different at the latter time of $t=100$ s, shown in Figure \ref{fig:pert_wave_energy_1}."
 There is a larger discrepancy in magnitude between the unperturbed and perturbed case., There is a larger discrepancy in magnitude between the unperturbed and perturbed case.
" Moreover, the second peak of E,(r,t) within one wavelength clearly seen at t=25 s is suppressed at the later time of t—100 s. The one remaining pronounced peak does not stay co-spatially with the small scale fluctuation wavelength but shifts backwards with respect to increasing distance from the Sun for this single point in time."," Moreover, the second peak of $E_w(r,t)$ within one wavelength clearly seen at $t=25$ s is suppressed at the later time of $t=100$ s. The one remaining pronounced peak does not stay co-spatially with the small scale fluctuation wavelength but shifts backwards with respect to increasing distance from the Sun for this single point in time."
" Density fluctuations at distances &7R, become influential enough over the radial density decrease to generate some positive background density gradients.", Density fluctuations at distances $\approx 7R_s$ become influential enough over the radial density decrease to generate some positive background density gradients.
 A positive gradient causes plasma waves to move to higher phase velocities and causes the streaking seen at t=100 s in Figure 2.., A positive gradient causes plasma waves to move to higher phase velocities and causes the streaking seen at $t=100$ s in Figure \ref{fig:pert_movie_1}.
" Despite the plasma wave distribution being substantially different, the electron flux remains almost unchanged, agreeing with the numerical results from ?.."," Despite the plasma wave distribution being substantially different, the electron flux remains almost unchanged, agreeing with the numerical results from \cite{Kontar2001_a}. ."
" The group velocity of plasma waves, 3v2.,/v, is small in magnitude, within the range 4x107 cm/s to 4x108 cm/s. At t—25 s (Figure 3)) the removal of the group velocity term has minimal effect."," The group velocity of plasma waves, $3v_{Te}^2/v$, is small in magnitude, within the range $4\times 10^7$ cm/s to $4\times10^8$ cm/s. At $t=25$ s (Figure \ref{fig:pert_wave_energy_1}) ) the removal of the group velocity term has minimal effect."
 Waves are moved in space by a small distance dependent upon the magnitude of the group velocity., Waves are moved in space by a small distance dependent upon the magnitude of the group velocity.
 The slower energetic electrons at the back of the beam produce waves with higer group velocity and hence the wave energy density is displaced further., The slower energetic electrons at the back of the beam produce waves with higer group velocity and hence the wave energy density is displaced further.
" At the later time of t=100 s, E,(r,t) is substantially different when the group velocity term is notpresent,"," At the later time of $t=100$ s, $E_w(r,t)$ is substantially different when the group velocity term is notpresent,"
c005AL. are able to eject a common envelope and form an sdD. Claims have been mace that the primaries of AA Dor (Rauch2000;Rucinski2009) and IS 2231-2441 (Ostensen2008) are low mass sdDs and the companions therefore substellar.,"$\simeq0.08\,M_{\rm \odot}$ are able to eject a common envelope and form an sdB. Claims have been made that the primaries of AA Dor \citep{rauch00,rucinski09} and HS $+$ 2441 \citep{oestensen08} are low mass sdBs and the companions therefore substellar."
 However. in the former case (his has been refuted by the measurement of the companions radial velocity (RV) curve (Vuékoviéetal.2003). and in the latter case bv the gravity measurement. 2010).," However, in the former case this has been refuted by the measurement of the companion's radial velocity (RV) curve \citep{vuckovic08} and in the latter case by the gravity measurement \citep{for10}."
. Substellar companions to sdD stars have been found using the light travel time technique (Schuh2010.andreferencestherein).., Substellar companions to sdB stars have been found using the light travel time technique \citep[][and references therein]{schuh10}.
 ILowever. these svstems have wide orbits and are therefore unlikely to have experienced a common envelope phase.," However, these systems have wide orbits and are therefore unlikely to have experienced a common envelope phase."
 None of these companions influenced the evolution of its host star. but the presence of such objects in wide orbits may be an indication of current or former close substellar companions to sdDs.," None of these companions influenced the evolution of its host star, but the presence of such objects in wide orbits may be an indication of current or former close substellar companions to sdBs."
 llere we report the discovery of the short-period eclipsing IW Vir type binary JO8205-+0008 from the MUCIIFUSS project., Here we report the discovery of the short-period eclipsing HW Vir type binary J08205+0008 from the MUCHFUSS project.
 This svstem is regarded as the first one in which a close substellar companion to an sdD star has been detected unambiguously., This system is regarded as the first one in which a close substellar companion to an sdB star has been detected unambiguously.
 The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCIIFUSS) aims at finding sdBs with compact companions like massive white dwarfs (WDs. Ad>1.0M. ). neutron stars or black holes.," The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims at finding sdBs with compact companions like massive white dwarfs (WDs, $M>1.0\,M_{\rm \odot}$ ), neutron stars or black holes."
 Details on the survey and target selection procedure are provided in Geieretal.(2010a).. and an analvsis of seven sdB binaries in Geileretal.(2010b).," Details on the survey and target selection procedure are provided in \citet{geier10}, and an analysis of seven sdB binaries in \citet{geier11}."
. The same selection criteria that we applied to find such binaries are also well suited to single out hot subcdwarl stars with constant high radial velocities in the Galactic halo and search for hypervelocity stars., The same selection criteria that we applied to find such binaries are also well suited to single out hot subdwarf stars with constant high radial velocities in the Galactic halo and search for hypervelocity stars.
 First results of the search for hvpervelocity stars are presented in Tillichetal.(2010)., First results of the search for hypervelocity stars are presented in \citet{tillich10}.
. The MUCTIIFUSS target selection strategy is tailored to single out RV variations on time scales of half an hour or less., The MUCHFUSS target selection strategy is tailored to single out RV variations on time scales of half an hour or less.
 Such variations may indicate the presence of short-period svslenms of relatively low RV amplitude or longer-period binaries with high RY amplitudes., Such variations may indicate the presence of short-period systems of relatively low RV amplitude or longer-period binaries with high RV amplitudes.
 The latter are the prime targets for the core programme of MUCIIFUSS., The latter are the prime targets for the core programme of MUCHFUSS.
 Obviously. the campaign is also bound to find short-period. low RV amplitude systemswith low mass stellar or even substellar companions.," Obviously, the campaign is also bound to find short-period, low RV amplitude systemswith low mass stellar or even substellar companions."
 JJO82053.53+000843.4 JJO82053.6+000843. in short JOS205+0008. 14.9 mae) was classified as an sdD star by colour selection ancl visual inspection of SDSS spectra (Abazajianetal. 2009).. whieh are flux. calibrated and cover the wavelength range from 3800Ato 9200A with a resolution of R= 1800.," J082053.53+000843.4 J082053.6+000843, in short J08205+0008, $g=14.9\,{\rm mag}$ ) was classified as an sdB star by colour selection and visual inspection of SDSS spectra \citep{abazajian09}, , which are flux calibrated and cover the wavelength range from $3800\,{\rm \AA}$to $9200\,{\rm \AA}$ with a resolution of $R=1800$ ."
 The six individual sub-spectra showed, The six individual sub-spectra showed
of 111404. and 60062 galaxy spectra had been obtained in jo SCP and NGP regions respectively.,of 111404 and 60062 galaxy spectra had been obtained in the SGP and NGP regions respectively.
 From these objects we remove those which did not receive accurate redshifts («3. Colless ct al.," From these objects we remove those which did not receive accurate redshifts $Q<3$, Colless et al."
 2001). repeated: observations ancl spectra with particularly low signal-to-noise ratio (< 10).," 2001), repeated observations and spectra with particularly low signal-to-noise ratio $\le10$ )."
 ‘This leaves us with 78994 (SGP) and 44937 (NCDP) galaxies or use in our spectral analysis., This leaves us with 78994 (SGP) and 44937 (NGP) galaxies for use in our spectral analysis.
" Because of interference [rom gakv emission and atmospheric absorption we have made a ""urther restriction to our redshift range such that 2x0.15.", Because of interference from sky emission and atmospheric absorption we have made a further restriction to our redshift range such that $z\le0.15$.
 This cut. ensures that the Πα line in our spectra is not corrupted., This cut ensures that the $\alpha$ line in our spectra is not corrupted.
 Note that this is only a problem for the small redshift range 0.15.<zQT. however. we have also excluded the galaxies with z20.17 in order to simplify our analvsis.," Note that this is only a problem for the small redshift range $0.15 < z < 0.17$, however, we have also excluded the galaxies with $z>0.17$ in order to simplify our analysis."
 Imposing this cut and removing spectra observed in poor quality fields. (Section 4.1) leaves us with 43440 (SGP) and 32140 (NGP) galaxies., Imposing this cut and removing spectra observed in poor quality fields (Section 4.1) leaves us with 43449 (SGP) and 32140 (NGP) galaxies.
 A total of 75589 unique galaxies will therefore be used in our subsequent. analysis and measurement of the LE., A total of 75589 unique galaxies will therefore be used in our subsequent analysis and measurement of the LF.
" The spectral classification presented. here is based. upon a Principal Component Analysis. (PCA) of the galaxy spectra,", The spectral classification presented here is based upon a Principal Component Analysis (PCA) of the galaxy spectra.
 PCA is a statistical technique which has been used with considerable success by multiple authors in the past (e.g. Connolly et al., PCA is a statistical technique which has been used with considerable success by multiple authors in the past (e.g. Connolly et al.
 1995: Folkes. Lahav Macldox. 1996: Glazebrook. Oller Doeclev 1998: Bromley et al.," 1995; Folkes, Lahav Maddox 1996; Glazebrook, Offer Deeley 1998; Bromley et al."
 1998: E99) to deal with large multi-cimensional data sets., 1998; F99) to deal with large multi-dimensional data sets.
 A detailed mathematical formulation of the PCA adopted here in is given in FOO., A detailed mathematical formulation of the PCA adopted here in is given in F99.
 Note that the most significant dillerence between this formulation and that used hy οrer authors (e.g. Connolly 1995) is that our spectra have been mean-subtracted (Fig. 1)), Note that the most significant difference between this formulation and that used by other authors (e.g. Connolly 1995) is that our spectra have been mean-subtracted (Fig. \ref{aver}) )
 before constructing the covariance matrix., before constructing the covariance matrix.
 This makes no substantial dillerence to the analysis since using other methods simply vields the mean spectrum as the first component., This makes no substantial difference to the analysis since using other methods simply yields the mean spectrum as the first component.
 We note that throughout the remainder of this paper we will denote the cigenvectors (herein eigenspectra) as PCA.PC» otc., We note that throughout the remainder of this paper we will denote the eigenvectors (herein eigenspectra) as $\bmath{PC_1}$ $\bmath{PC_2}$ etc.
 and the projections onto these axes by per. peo etc.," and the projections onto these axes by $pc_1$, $pc_2$ etc."
 PCA is a useful technique in that it allows us to. easily visualise a multi-dimensional population in terms of just a handful of significant components., PCA is a useful technique in that it allows us to easily visualise a multi-dimensional population in terms of just a handful of significant components.
 It does this by identifying the components of the data (in this case the galaxy spectra) which are the most discriminatory between each galaxy., It does this by identifying the components of the data (in this case the galaxy spectra) which are the most discriminatory between each galaxy.
 The significance of each. component is measured. in terms of its contribution to the variance over the sample and is determined in the PCA., The significance of each component is measured in terms of its contribution to the variance over the sample and is determined in the PCA.
 This allows us to identify just the most significant components for future use., This allows us to identify just the most significant components for future use.
 Lt is clear from such a formalism that any clustering in a space defined by the PCA is indicative of distinct sub-populations within the sample In terms of reduced. climensionality we find. after applving the PCA to our galaxy spectra. that rather than using the original 738 spectral channels to describe. each," It is clear from such a formalism that any clustering in a space defined by the PCA is indicative of distinct sub-populations within the sample In terms of reduced dimensionality we find, after applying the PCA to our galaxy spectra, that rather than using the original 738 spectral channels to describe each"
Putting these results together. a clear and direct way to constrain AGN feedback preseuts itself,"Putting these results together, a clear and direct way to constrain AGN feedback presents itself."
" This can be sununarized as follows: The results of carrving out this procedure over (2.2 deg) ""nof sky calculated frou: our simulations. are shown in Figure 11.", This can be summarized as follows: The results of carrying out this procedure over (2.2 $^2$ of sky calculated from our simulations are shown in Figure \ref{fig:Eplot}.
 Tere we have grouped all bulges iu logavithimic bius of stellar mass with width 0.25. again takine a fixed ratio of LOO between μοι and Mp. To calculate the uncertainty in each bin we have accounted both for Poisson noise and intrinsic scatter. talking iubErica)=[Εμμbiu|8onceEyhorual)|VN. where τα] Is the average thermal cucrey du a eiven bin. OyeήEnea) Is the RAIS scatter between sources du a eiven bin. where we computed Nu conservatively as the number of sources iu a eiven bin relative to a signal realization ofthe map (1/1 of the [2.2 deg)? region iu the AGN feedback zun and 1/16 of this region iu the comparison run).," Here we have grouped all bulges in logarithmic bins of stellar mass with width $0.25$, again taking a fixed ratio of 400 between $M_{\rm
bulge}$ and $M_{\rm BH}.$ To calculate the uncertainty in each bin we have accounted both for Poisson noise and intrinsic scatter, taking $\sigma_{\rm bin}(E_{\rm thermal}) = [\bar E_{\rm thermal,bin} +
\sigma_{\rm source}(E_{\rm thermal})]/\sqrt{N_{\rm bin}},$ where $\bar
E_{\rm thermal,bin}$ is the average thermal energy in a given bin, $\sigma_{\rm source}(E_{\rm thermal})$ is the RMS scatter between sources in a given bin, where we computed $N_{\rm bin}$ conservatively as the number of sources in a given bin relative to a signal realization of the map (1/4 of the [2.2 $^2$ region in the AGN feedback run and 1/16 of this region in the comparison run)."
 At both high and low redshifts the ACN feedback un shows a clear excess; which scales linearly with ALiape. as expected from (111.," At both high and low redshifts the AGN feedback run shows a clear excess, which scales linearly with $M_{\rm bulge}$ as expected from \ref{eq:ekin}) )."
 For comparison. we use this equation to plot the euergv added to the ICM. as a function of bulge mass.," For comparison, we use this equation to plot the energy added to the IGM as a function of bulge mass."
 Since kinetic energy is converted iuto thermal energy as the outflows accrete material. and ax radiative losses are siall for these objects Oli Benson 2003: Scannapiceco Ol 2001). we expect that most of this energy should be observable as Eua. Iu fact. this figure shows that at both low and high redshift. the thermal SZ excess closely traces this energy input as a function of bulge mass.," Since kinetic energy is converted into thermal energy as the outflows accrete material, and as radiative losses are small for these objects Oh Benson 2003; Scannapieco Oh 2004), we expect that most of this energy should be observable as $E_{\rm thermal}.$ In fact, this figure shows that at both low and high redshift, the thermal SZ excess closely traces this energy input as a function of bulge mass."
 Thus ACN feedback is not only detectable by the SZ effect. but the level of this feedback as a function of mass can be obtained cirectly from SZ micasurcmicuts.," Thus AGN feedback is not only detectable by the SZ effect, but the level of this feedback as a function of mass can be obtained directly from SZ measurements."
Accepted for publication in the Astrophysical Journal,Accepted for publication in the Astrophysical Journal
input tanecutial velocities (Cransce ταν) Normalized by the expected error (Ανω) for a set of GO experiments onu our idealized data sets.,"input tangential velocities $v_{\rm tan, rec}-v_{\rm tan}$ ) normalized by the expected error $\Delta v_{\rm tan}$ ) for a set of 60 experiments on our idealized data sets."
 Note that the method for bootstrapping estimates of errors from observed data sets adopted by vanderMarel&Corhathakurta(2008) was found to agree well with this cstimate., Note that the method for bootstrapping estimates of errors from observed data sets adopted by \citet{2008VanDerMarel} was found to agree well with this estimate.
 Using our results so far we can assess which real galaxy clusters iav be interesting targets for a study of PR ic. those for which our estimated uncertainty (Ac) is less thau the expected signal ( which is comparable to σ for galaxy clusters)., Using our results so far we can assess which real galaxy clusters may be interesting targets for a study of PR — i.e. those for which our estimated uncertainty $\Delta v_{\rm tan}$ ) is less than the expected signal $\sim \sigma_{\rm pec}$ — which is comparable to $\sigma$ for galaxy clusters).
" yxFigure 2. shows contours of f=Acfo for objects of various 0, aud IN. with current values for some nearby galaxy clusters overlaid."," Figure \ref{fig:nrho} shows contours of $f=\Delta v_{\rm tan}/\sigma$ for objects of various $\theta_{\rm max}$ and $N$, with current values for some nearby galaxy clusters overlaid."
 It is clear that the πο” of measurements for these objects is just become interesting for our purpose those that have f£<1 (ie. within lightest-eray area ofthe plot) should have errors due to random motions of order σ which is simular in amplitude to what we are trviug to measure., It is clear that the number of measurements for these objects is just becoming interesting for our purpose — those that have $f \le1$ (i.e. within lightest-gray area ofthe plot) should have errors due to random motions of order $\sigma$ which is similar in amplitude to what we are trying to measure.
" Nevertheless.a straightforward application of our erid-based search to the N=379.0,44;=3.1 Virgo galaxies selected by Rines&Celler(2008). from the Sloan Digital Sky Survey spectroscopic data base. and augmented to N=520.0444—4.67 with the Bineechctal.(1987) siuuple. found a tangential velocity of several thousand liun/s with even larger error bars."," Nevertheless,a straightforward application of our grid-based search to the $N=379, \theta_{\rm max}=3.4^{\circ}$ Virgo galaxies selected by \citet{rines08} from the Sloan Digital Sky Survey spectroscopic data base, and augmented to $N=520, \theta_{\rm max}=7.7^\circ$ with the \citet{binggeli87} sample, found a tangential velocity of several thousand km/s with even larger error bars."
 We interpret this as a null result. most Likely due to svstematic motions of eroups of galaxies falling in to Vireo.," We interpret this as a null result, most likely due to systematic motions of groups of galaxies falling in to Virgo."
" Indeed. Virgo is classified as an ""regular"" ealaxy cluster for just this reason (c.g.Bohringeretal.199 1)."," Indeed, Virgo is classified as an “irregular” galaxy cluster for just this reason \citep[e.g.][]{bohringer94}. ."
". When we applied the search to the Ursa Major cluster using a sample with Vi=90.Oya,7.5? galaxies culled from Tullyetal.(1996) aud Trenthametal.(2001) we found ey.=919439 ας, exo—310τε556 Imifs. μα=ΟδETOL Kms aud στ378£30 kis (GvlierevanderMarel&Corhathakurta 2008)."," When we applied the search to the Ursa Major cluster using a sample with $N=90, \theta_{\rm max}=7.8^{\circ}$ galaxies culled from \citet{tully96} and \citet{trentham01} we found $v_{\rm sys}=919\pm 39$ km/s, $v_{\rm North}=370 \pm 556$ km/s, $v_{\rm West}=980 \pm 794$ km/s and $\sigma=378 \pm 30$ km/s \citep[where the errorbars are from the bootstrap method outlined in][]{2008VanDerMarel}."
 Unfortunately. while the measurements in this case fall within our expectations for clusters’ peculiar velocitics. this simple interpretation is unlikely to be correct.," Unfortunately, while the measurements in this case fall within our expectations for clusters' peculiar velocities, this simple interpretation is unlikely to be correct."
 Since we live in the epoch of galaxy cluster formation. our problem with Virgo (contamination of the sample by substructure) is likely to be oue shared by oher galaxy clusters.," Since we live in the epoch of galaxy cluster formation, our problem with Virgo (contamination of the sample by substructure) is likely to be one shared by other galaxy clusters."
 In order to assess how significant fjs concern is. we conipared the known spaceanotious o:galaxw clusters in the seni-analytic galaxw catalogue produced for the Millenium Simulation (Crotonetal.2006).. with those we derived bv “observing” the same galaxy clusters from random viewpoiuts. at a distance of 10Mpc.," In order to assess how significant this concern is, we compared the known space-motions of galaxy clusters in the semi-analytic galaxy catalogue produced for the Millenium Simulation \citep{croton06}, with those we derived by “observing” the same galaxy clusters from random viewpoints, at a distance of 10Mpc."
 In all. we analyzed GU sets of simulated observations of galaxy clusters. witli aneular sizes of order μμ757 and muubers of galaxies iu each iu the range /Nο250.700.," In all, we analyzed 60 sets of simulated observations of galaxy clusters, with angular sizes of order $\theta_{\rm max}\sim 5^\circ$ and numbers of galaxies in each in the range $N\sim 250-700$."
 The dotted histogram in Figure d. shows our results we find only ~ 10 of our exporiuents eive estimates within our expected uncertaintv due to randoni motions., The dotted histogram in Figure \ref{fig:histo} shows our results — we find only $\sim$ 10 of our experiments give estimates within our expected uncertainty due to random motions.
 The reniüniug 90% fall outside the plot., The remaining $\sim 90$ fall outside the plot.
 While these results are somewhat ciscouragine. the sizes of the real and simmlated catalogues of spectra are still mich smaller * more than an order of magnitude than the actual wuubers of galaxies in clusters.," While these results are somewhat discouraging, the sizes of the real and simulated catalogues of spectra are still much smaller — by more than an order of magnitude — than the actual numbers of galaxies in clusters."
 By takine spectra of fainter cluster πας it still may be possible to gather sufficient data that svstcmatic internal motions (substructure aud rotation) can be separated from PR., By taking spectra of fainter cluster members it still may be possible to gather sufficient data that systematic internal motions (substructure and rotation) can be separated from PR.
 Moreover. these siuuples could be augmented by dutra-cluster elobular clusters. planctary nebulae aud ejaut stars.," Moreover, these samples could be augmented by intra-cluster globular clusters, planetary nebulae and giant stars."
" The collisional nature of gas suggests that the intra-cluster mediuu (ICM) could provide a cleaner probe of PR than cluster galaxies naively. the ICM. πο]! be expected to follow a more svnunetrie distribution of velocities around the svstem mean. and to have lower random local motions (10. sumaller cj, terii iu equation 2))."," The collisional nature of gas suggests that the intra-cluster medium (ICM) could provide a cleaner probe of PR than cluster galaxies — naively, the ICM might be expected to follow a more symmetric distribution of velocities around the system mean, and to have lower random local motions (i.e. smaller $v_{\rm local}$ term in equation \ref{eq:LOSvel}) )."
 The measurement of eas velocities from X-rav spectroscopy of the ICAL is just becoming feasible: for example Dupke&Dregnmau(2006) report direct detections of velocity differences from N-aray observations of the ICAL across the Centaurus galaxy cluster of 2000 kms. Tudeed. the planned Iuternational X-ray Observatory (INO) is aiming to have the capability of surveviue ealaxy cluster gas at high spectral resolution (AF~ 2.5eV foy E—(0.3. TkeV ou few avciiuute scales) in order to study turbulent motions of cluster gas with 100 kis resolution at +~2 (Arnaudetal.2009).," The measurement of gas velocities from X-ray spectroscopy of the ICM is just becoming feasible: for example \citet{dupke06} report direct detections of velocity differences from X-ray observations of the ICM across the Centaurus galaxy cluster of $~$ 2000 km/s. Indeed, the planned International X-ray Observatory (IXO) is aiming to have the capability of surveying galaxy cluster gas at high spectral resolution $\Delta E \sim 2.5$ eV for $E \sim 0.3-7$ keV on few arcminute scales) in order to study turbulent motions of cluster gas with 100 km/s resolution at $z\sim 2$ \citep{arnaud09}."
.. While PR. with an expected signal of order ~θα έν (see equation 3)) would be barely detectable iu the largest nearby galaxy clusters with this resolution. the INO design does at least demonstrate the technical feasibility of these neasureimoenuts.," While PR, with an expected signal of order $\sim 100$ km/s (see equation \ref{eq:signal}) ) would be barely detectable in the largest nearby galaxy clusters with this resolution, the IXO design does at least demonstrate the technical feasibility of these measurements."
 Uufortunately. the interpretation of anv such observations is likely to be difficult: nnuuerical simulations do imply the existence of long-Iived turbuleut velocities and bulk flows of order a 300-600 kin/s on scales of 100-500kpc in the typical ICAL (Norman&Bryan 1999).. iux a comparable degree of rotational support throughott the inner parts of the cluster (as over-cooling)..," Unfortunately, the interpretation of any such observations is likely to be difficult: numerical simulations do imply the existence of long-lived turbulent velocities and bulk flows of order a 300-600 km/s on scales of 100-500kpc in the typical ICM \citep{norman99}, and a comparable degree of rotational support throughout the inner parts of the cluster \citep[as seen in][although these results may in part be due to numerical effects such as over-cooling]{fang09}. ."
 Tudeed. numerical studies sugeestOO that the rotation of gas following mergers of clusters may be longer lived than for ealaxies (Rocttiger&Flores 2000)..," Indeed, numerical studies suggest that the rotation of gas following mergers of clusters may be longer lived than for galaxies \citep{roettiger00}. ."
 Another wav to nmieasuregalaxy cluster motions is to look for distortions of the Cosmic Microwave Backeround (CA\IB) due to the clusters intervene gas., Another way to measuregalaxy cluster motions is to look for distortions of the Cosmic Microwave Background (CMB) due to the cluster's intervening gas.
"sources but vertical and horizontal sizes of the sources, which is required for examining the density structures of the chromosphere.","sources but vertical and horizontal sizes of the sources, which is required for examining the density structures of the chromosphere."
 Theoretical relationships were compared with observations to find the density structure of the chromosphere., Theoretical relationships were compared with observations to find the density structure of the chromosphere.
 The vertical size of the X-ray sources is found to be larger than the ones predicted by a hydrostatic atmosphere in thick-target scenario., The vertical size of the X-ray sources is found to be larger than the ones predicted by a hydrostatic atmosphere in thick-target scenario.
" However, assuming that the electrons are propagating along several narrow threads with different density profiles can explain the measured vertical sizes of the sources."," However, assuming that the electrons are propagating along several narrow threads with different density profiles can explain the measured vertical sizes of the sources."
 The spatial information about an X-ray source measured by RHESSI for a given energy range and time interval can be presented (??) as two dimensional Fourier components or X-ray visibilities where is the observed image at photon energy e.," The spatial information about an X-ray source measured by RHESSI for a given energy range and time interval can be presented \citep{hurford2002,schmahl2007}
 as two dimensional Fourier components or X-ray visibilities where $I(x,y; \epsilon)$ is the observed image at photon energy $\epsilon$."
" Then, I(x,y;€)reconstructed X-ray image I(x,y;¢) is the inverse Fourier transformation of measured X-ray visibilities V(u,v;e)."," Then, reconstructed X-ray image $I(x,y; \epsilon)$ is the inverse Fourier transformation of measured X-ray visibilities $V (u,v; \epsilon )$."
" Each of the nine RHESSI Rotating Modulating Collimators measures V(u,v; at a fixed spatial frequency (or a (RMC)circle in the (u,v) €)plane) corresponding to its angular resolution and with a position angle along the circles, which varies continuously as the spacecraft rotates."," Each of the nine RHESSI Rotating Modulating Collimators (RMC) measures $V(u,v; \epsilon)$ at a fixed spatial frequency (or a circle in the $(u,v)$ plane) corresponding to its angular resolution and with a position angle along the circles, which varies continuously as the spacecraft rotates."
" Nine detector grids with angular resolutions growing with detector number are logarithmically spaced in the (u,v) plane."," Nine detector grids with angular resolutions growing with detector number are logarithmically spaced in the $(u,v)$ plane."
" Since the measured visibilities sparsely populate the plane and have statistical uncertainties, the direct (u,v)inverse Fourier transform is impractical (???) and alternative methods should be used."," Since the measured visibilities sparsely populate the $(u,v)$ plane and have statistical uncertainties, the direct inverse Fourier transform is impractical \citep{hurford2002,schmahl2007,Massone_etal2009}
 and alternative methods should be used."
" Assuming a characteristic shape of X-ray source, one can find the position and characteristic sizes directly by fitting a 2D Fourier image of the model to the RHESSI visibilities."," Assuming a characteristic shape of X-ray source, one can find the position and characteristic sizes directly by fitting a 2D Fourier image of the model to the RHESSI visibilities."
" Here, we assume that the sources can be presented as elliptical Gaussian sources where 2/21n2e, and 2y21n2e, are FWHMs of an elliptical Gaussian source in x and y direction respectively, zo(c), yo(e) is the position of the source, and Jo is the total photon flux of the source."," Here, we assume that the sources can be presented as elliptical Gaussian sources where $2\sqrt{2\ln2}\sigma_x$ and $2\sqrt{2\ln2}\sigma_y$ are FWHMs of an elliptical Gaussian source in $x$ and $y$ direction respectively, $x_0(\epsilon)$, $y_0(\epsilon)$ is the position of the source, and $I_0$ is the total photon flux of the source."
" One major advantage of the visibility forward fit approach is that knowing the errors on visibilities V(u,v;€) one can readily propagate the errors to forward fit parameters of the model in Equation "," One major advantage of the visibility forward fit approach is that knowing the errors on visibilities $V(u,v; \epsilon )$ one can readily propagate the errors to forward fit parameters of the model in Equation \ref{eq:Imodel}) )."
Reliable error estimates for images reconstructed with (2)).other algorithms are currently unavailable., Reliable error estimates for images reconstructed with other algorithms are currently unavailable.
" Using HXR data from RHESSI we analysed a limb event on January 6th, 2004 (GOES M5.8 class)."," Using HXR data from RHESSI we analysed a limb event on January 6th, 2004 (GOES M5.8 class)."
" As shown previously by (?), this event is ideally suited for our analysis having two well separated footpoints: one bright and a second much weaker footpoint."," As shown previously by \citep{Kontar_etal08}, this event is ideally suited for our analysis having two well separated footpoints: one bright and a second much weaker footpoint."
" In addition, the location of the flare at the limb greatly reduces albedo flux (??),, so that the albedo correction (?) becomes negligible."," In addition, the location of the flare at the limb greatly reduces albedo flux \citep{BaiRamaty1978,2010A&A...513L...2K}, so that the albedo correction \citep{Kontar_etal2006} becomes negligible."
" The flare occurred at the eastern limb near (—975,75) arcseconds from the disk center at ~0622 UT (Figure 1))."," The flare occurred at the eastern limb near $(-975,75)$ arcseconds from the disk center at $\sim 06:22$ UT (Figure \ref{fig:lc}) )."
" It was imaged during the time of peak emission >50 keV 06:22:20-06:23:00 UT indicated by the vertical dotted lines in Figure 1,, using four different image algorithms (see Figure 2)): Clean (?),, MEM NJIT (?),, PIXON (??) and visibility forward fit (??).."," It was imaged during the time of peak emission $>50 $ keV 06:22:20-06:23:00 UT indicated by the vertical dotted lines in Figure \ref{fig:lc}, using four different image algorithms (see Figure \ref{fig:images_jan06}) ): Clean \citep{hurford2002}, MEM NJIT \citep{schmahl2007}, PIXON \citep{PinaPuetter1993,Metcalfetal1996} and visibility forward fit \citep{hurford2002,schmahl2007}."
 'The resulting images in five energy bands covering the nonthermal emission are shown in Figure 2.., The resulting images in five energy bands covering the nonthermal emission are shown in Figure \ref{fig:images_jan06}.
 Each image was made using the front segments of detectors2 to 7., Each image was made using the front segments of detectors2 to 7.
 Grid 1 with the highest spatial resolution had no significant signal and grids 8-9 are too coarse for our flaring region., Grid 1 with the highest spatial resolution had no significant signal and grids 8-9 are too coarse for our flaring region.
 Previously the flare was imaged using ten energy bins (?) and simple circular gaussian fit but this was reduced to five wider bins in this paper to improve signal to noise., Previously the flare was imaged using ten energy bins \citep{Kontar_etal08} and simple circular gaussian fit but this was reduced to five wider bins in this paper to improve signal to noise.
" Figures 2,,3 demonstrate that the brighter source has an elliptical shape at various energies, so an elliptical Gaussian could be used as natural X-ray distribution model (Figure 3))."," Figures \ref{fig:images_jan06}, \ref{fig:ff_fit}
 demonstrate that the brighter source has an elliptical shape at various energies, so an elliptical Gaussian could be used as natural X-ray distribution model (Figure \ref{fig:ff_fit}) )."
 Comparing the different algorithm results we find that CLEANed images have systematically larger sizes than the other algorithms., Comparing the different algorithm results we find that CLEANed images have systematically larger sizes than the other algorithms.
 This is related to the fact that CLEAN images are determined by the user choices for analysis (clean beam size) and not the requirements of the data and hence should be used with great care to measure source sizes., This is related to the fact that CLEAN images are determined by the user choices for analysis (clean beam size) and not the requirements of the data and hence should be used with great care to measure source sizes.
" MEM NJIT has produced smaller source sizes, which could be the tendency of the algorithm to over-resolve sources (?).."," MEM NJIT has produced smaller source sizes, which could be the tendency of the algorithm to over-resolve sources \citep{schmahl2007}."
 PIXON (??) gave source sizes similar to those of X-ray visibility forward fit.," PIXON \citep{PinaPuetter1993,metcalf1995} gave source sizes similar to those of X-ray visibility forward fit."
 ? have also analysed this event and confirmed the finding of ?.., \citet{dennis2009} have also analysed this event and confirmed the finding of \citet{Kontar_etal08}.
" We choose to forward fit a circular Gaussian source for the northern footpoint and an elliptical Gaussian source (Equation 2)) for the southern footpoint to the visibilities (Equation 1)), the image shown is a reconstruction of the fit results."," We choose to forward fit a circular Gaussian source for the northern footpoint and an elliptical Gaussian source (Equation \ref{eq:Imodel}) ) for the southern footpoint to the visibilities (Equation \ref{eq:vis}) ), the image shown is a reconstruction of the fit results."
 These fits are shown in Figure 3 and will be discussed in detail in refsec:fit.., These fits are shown in Figure \ref{fig:ff_fit} and will be discussed in detail in \\ref{sec:fit}. .
" Assuming two elliptical sources, the weaker"," Assuming two elliptical sources, the weaker"
"frequency in the Jj, curves). lower than P. as for these lugh frequencies the source is nof monochromatic over the observation tine.","frequency in the $h_c$ curves), lower than $h$, as for these high frequencies the source is not monochromatic over the observation time."
 Such simply consideration naturally leads to define fi. aud fp., Such simply consideration naturally leads to define $h_c$ and $h_B$.
 Consider now a binary system at comoving distance rt)., Consider now a binary system at comoving distance $r(z)$.
" The strain amplitude (sky-aud-polarisation averaged) at |the rest-frame frequency— f, is where Mo=οOAL|MS)? is the erp mass” of the binary. and all the other sviubols have their standard meaning."," The strain amplitude (sky-and-polarisation averaged) at the rest-frame frequency $f_r$ is where ${\mathcal M}=(M_1 M_2)^{3/5}/(M_1+M_2)^{1/5}$ is the “chirp mass” of the binary, and all the other symbols have their standard meaning."
 The strain is averaged over a wave period., The strain is averaged over a wave period.
 The rest-frame cnerey fiux (enerev per unit area per unit time) associated to the CAV is As discussed above. the important quantity to consider is the παρα of cycles spent in a frequency interval Afcof around a eiven frequency f.," The rest-frame energy flux (energy per unit area per unit time) associated to the GW is As discussed above, the important quantity to consider is the number of cycles spent in a frequency interval $\Delta f \simeq f$ around a given frequency $f$."
 Asstumine that the backreaction from CAV ciuission dominates the orbital decay of a binary. durug the spiralin phase oue can write where we have used the rest-frame frequency shift rate Note that η cau be computed either im the rest or iu the observer frame.," Assuming that the backreaction from GW emission dominates the orbital decay of a binary, during the spiral-in phase one can write where we have used the rest-frame frequency shift rate Note that $n$ can be computed either in the rest or in the observer frame."
 The characteristic straiu in an observation of (observed) duration 7 is then aud where f=f./(1|2) is the observed frequency., The characteristic strain in an observation of (observed) duration $\tau$ is then and where $f=f_r/(1+z)$ is the observed frequency.
 Using Parseval theoreni. if is easy to see that Jj is related to the Fourier transform of the strain ὃν as he--2f.) where A is defined over the positive frequency axis.," Using Parseval theorem, it is easy to see that $h_c$ is related to the Fourier transform of the strain $\tilde h$, as $h_c^2=2 f_r^2 \tilde h^2(f_r)$, where $\tilde h$ is defined over the positive frequency axis."
" The specific energy per uut area is then auc. from equation (6)). we obtain Note that dE/df,Xf, DOS while (eq. 3))"," The specific energy per unit area is then and, from equation \ref{eq1h_c}) ), we obtain Note that $dE/df_r\propto f_r^{-1/3}$ , while (eq. \ref{eqenergyflux}) )"
 10/3 , $dE/dt\propto f_r^{10/3}$ .
Tn an operating interferometer. auv stochastic signal will add up n quadrature) to 7p to form the effective nis noise of the instrument. γιο.," In an operating interferometer, any stochastic signal will add up (in quadrature) to $h_B$ to form the effective rms noise of the instrument, $h_{\rm rms}$ ."
 An inspiraling binary is then detected if the signal-to-noise ratio is larger than the assumed. threshold for detection. where the iutegrated S/N is giveu by Tere. f is the (observed) frequency euüutted at the starting time f=0 of the observation. aud Af is the (observed) frequency shift iu a tine 7 starting from f.," An inspiraling binary is then detected if the signal-to-noise ratio is larger than the assumed threshold for detection, where the integrated $S/N$ is given by Here, $f$ is the (observed) frequency emitted at the starting time $t=0$ of the observation, and $\Delta f$ is the (observed) frequency shift in a time $\tau$ starting from $f$."
" The latter is auplicitly given by where dff=(1df,fon ", The latter is implicitly given by where $df/\dot f=(1+z)df_r/\dot f_r$.
The frequency at the ISCÓ is. strictly speaking. defined ouly in the test particle luit Mo«AL.," The frequency at the ISCO is, strictly speaking, defined only in the test particle limit $M_2 \ll M_1$."
 Iu the general case. various estimate of the transition poiut from m-spiral to plunge exist. aud differ bv à factor of 3 at most (e.g... INadder. Will Wisciman 1993: Cook 1991).," In the general case, various estimate of the transition point from in-spiral to plunge exist, and differ by a factor of 3 at most (e.g., Kidder, Will Wiseman 1993; Cook 1994)."
 Such uucertiünties do not affect our results iu any niuuner. so we use. for the observed frequency at the ISCO. the conventional Neplerian defintion: Replacing f|Af with κου in equation (11)) gives To. the time needed. to span the frequency interval Lf.fisco]. to be compared to 7.," Such uncertainties do not affect our results in any manner, so we use, for the observed frequency at the ISCO, the conventional Keplerian defintion: Replacing $f+\Delta f$ with $f_{\rm ISCO}$ in equation \ref{eqfmax}) ) gives $\tau_{\rm ISCO}$, the time needed to span the frequency interval $[f,f_{\rm ISCO}]$, to be compared to $\tau$."
 Iu the case ToTyco. we then set f|Af=μου in equation (10)).," In the case $\tau>\tau_{\rm ISCO}$, we then set $f+\Delta f=f_{\rm ISCO}$ in equation \ref{eqSN}) )."
" In Figure 2. we plot 5, for different MDIIDs at different redshifts. compared to the μμ (see L1) multiplied by a factor of 5. assumniug a 3-vear observation."," In Figure \ref{singlesource} we plot $h_c$ for different MBHBs at different redshifts, compared to the $h_{\rm rms}$ (see 4.1) multiplied by a factor of 5, assuming a 3-year observation."
 If hs.cShays. then the sgual has. approximately. an integrated S/N>5.," If $h_c > 5h_{\rm rms}$, then the signal has, approximately, an integrated $S/N>5$."
 This is for illustrative purposes ouly. as the actual S/N iust be integrated over the observing period using equation (10)).," This is for illustrative purposes only, as the actual $S/N$ must be integrated over the observing period using equation \ref{eqSN}) )."
" At frequencies higher than the ""kuec. the time speut around a eiven frequency is less than 3 vears. aud fi,xf 8.) "," At frequencies higher than the “knee”, the time spent around a given frequency is less than 3 years, and $h_c\propto f^{-1/6}$ ."
The sienal shifts toward higher frequency during he observation. and reaches the ISCO and the coalescence ghase in ost cases.," The signal shifts toward higher frequency during the observation, and reaches the ISCO and the coalescence phase in most cases."
 The lowest curve represents a low nass. hieh redshift equal mass binary.," The lowest curve represents a low mass, high redshift equal mass binary."
 As we shall see low. these sources are common in our licrarclical model or MBIT assembly.," As we shall see below, these sources are common in our hierarchical model for MBH assembly."
 In terms of their detectability hyLISA. they represent a somewhat different class of events.," In terms of their detectability by, they represent a somewhat different class of events."
 Coutrary to the case of more massive binaries present at ower z. the final coalescence phase of light binarics lies at oo high frequecies. well below the threshold.," Contrary to the case of more massive binaries present at lower $z$, the final coalescence phase of light binaries lies at too high frequecies, well below the threshold."
 For frequencies much below the knec. the characteristic strain is proportional to f°. as the timescale for requencv shift is longer than 3 vears.," For frequencies much below the knee, the characteristic strain is proportional to $f^{7/6}$, as the timescale for frequency shift is longer than 3 years."
 The signal amplitude is then limited bv the observation time. not w the intrinsic properties of the source.," The signal amplitude is then limited by the observation time, not by the intrinsic properties of the source."
 The source will be observed as a “stationary source”. a quasi wave forthe whole duration of the observation.," The source will be observed as a “stationary source"", a quasi-monochromatic wave forthe whole duration of the observation."
 Au increase in the observation time will result im a shift of the knee toward lower frequencies., An increase in the observation time will result in a shift of the knee toward lower frequencies.
 The time needed for the sources to reach the ISCO, The time needed for the sources to reach the ISCO
where Vis the volume and ο is the surface. as in L94. and A(s) is a parameter that depends on the scale of the analysis.,"where $V$ is the volume and $S$ is the surface, as in L94, and $K(s)$ is a parameter that depends on the scale of the analysis."
 We want L(s) to have the following behaviour: zero For very filamentary structures and | for spherical ones., We want $L(s)$ to have the following behaviour: zero for very filamentary structures and $1$ for spherical ones.
 This may be achieved. putting A=362. but only for those scales not allected by the granular nature of the analysis.," This may be achieved putting $K=36 \pi$, but only for those scales not affected by the granular nature of the analysis."
" We choose the value 36z only for the scales s=2"" pixels with £z2.", We choose the value $36 \pi$ only for the scales $s=2^r$ pixels with $r \ge 2$.
 For the smallest scales the constant 367 is not adequate. since we are close to the erid resolution and the geometry of the substructures cannot be spherical.," For the smallest scales the constant $36 \pi $ is not adequate, since we are close to the grid resolution and the geometry of the substructures cannot be spherical."
 Since we want to consider as spherical a one-pixel structure. we adopt the values: Then. for every. detection. threshold. we caleulate the values: where Nos; is the number of objects detected at scale ," Since we want to consider as spherical a one-pixel structure, we adopt the values: Then, for every detection threshold we calculate the values: where $N_{obj}$ is the number of objects detected at scale $s$."
Our model clusters are engendered by randomly assembling a number of clumps. cach characterized. by the position of their centers.," Our model clusters are engendered by randomly assembling a number of clumps, each characterized by the position of their centers."
 As coordinates we choose two angular coordinates and the line-of-ight velocity: (8.0.Όμως)," As coordinates we choose two angular coordinates and the line-of-sight velocity: $(\theta,\phi,v_{los})$."
" Given the position of the center. of cach clump (8,4.6,4.04). ealaxies are distributed. about the center according to a gaussian distribution in real space of width a,."," Given the position of the center of each clump $(\theta_{cl},\phi_{cl},v_{cl})$, galaxies are distributed about the center according to a gaussian distribution in real space of width $\sigma_{r}$."
 Velocities are then specified. by adding to the Llubble flow à random component drawn from a maxwellian. distribution with a given dispersion σι., Velocities are then specified by adding to the Hubble flow a random component drawn from a maxwellian distribution with a given dispersion $\sigma_{cl}$.
 Each simulated cluster is then made of a collection of these clumps., Each simulated cluster is then made of a collection of these clumps.
" This method allows a partial superposition of the To each galaxy in the cluster we also attribute an absolute magnitude. cdrewn rancomly from ai Schechter luminosity function: The values for m,=25Log(L.).ó* and a are appropriate to the central region of the Coma. cluster (Bivianoetal.1996)."," This method allows a partial superposition of the To each galaxy in the cluster we also attribute an absolute magnitude drawn randomly from a Schechter luminosity function: The values for $m_{\ast}=-2.5{\rm Log}(L_{\ast}), \phi^{\ast}$ and $\alpha$ are appropriate to the central region of the Coma cluster \cite{bdglflms}."
. We show in Fig., We show in Fig.
 1 the projected positions of galaxies in atypical mock catalogue obtained with these prescriptions. and in Fig.," 1 the projected positions of galaxies in a typical mock catalogue obtained with these prescriptions, and in Fig."
 2 the corresponding wedge diagram., 2 the corresponding wedge diagram.
 Lt is evident [rom these plots that substructure in these mock catalogues is mace of independent. eroups which overlap each other., It is evident from these plots that substructure in these mock catalogues is made of independent groups which overlap each other.
 We also applied. our test to. the result. of à. N-bocky simulation. where density cistribution is clearly hierarchical.," We also applied our test to the result of a N-body simulation, where density distribution is clearly hierarchical."
 We have considered. a 1075.Αν) box extracted. fron a l6-million. particles simulation of a 50 hlA4pe. box (Antonuccio-Delogu ct al..," We have considered a $10^{3} h^{-3} Mpc^{3}$ box extracted from a 16-million particles simulation of a 50 $h^{-1} Mpc$ box (Antonuccio-Delogu et al.,"
 in preparation)., in preparation).
 Using SIXKID. a standard gravitationally bound. groups finder (Stadel οἱ al..," Using SKID, a standard gravitationally bound groups finder (Stadel et al.,"
 in preparation) we have found. 5 groups on a scale of 500 hb| kpe within this box., in preparation) we have found 5 groups on a scale of 500 $h^{-1}$ kpc within this box.
 In order to assess the capability of our code to recover substructures we simulate five clusters of galaxies at a fixed distance mace of an increasing number of well separated clumps: from only 1 clump to 15., In order to assess the capability of our code to recover substructures we simulate five clusters of galaxies at a fixed distance made of an increasing number of well separated clumps: from only 1 clump to 15.
 Clusters are identified by the names C13 (containing 1 clump. 528 galaxies). C14 (3 clumps. 1224 galaxies). Cl (5 clumps. 1512 galaxies). C15 (8 clumps. 3456 galaxies) and C16 (15 clumps. 8750 galaxies).," Clusters are identified by the names C13 (containing 1 clump, 528 galaxies), C14 (3 clumps, 1224 galaxies), C1 (5 clumps, 1512 galaxies), C15 (8 clumps, 3456 galaxies) and C16 (15 clumps, 8750 galaxies)."
 Phe mean separation between two clumps inside a cluster is set equal to 2.7+ Alpe.," The mean separation between two clumps inside a cluster is set equal to $2.7 \, h^{-1}$ Mpc."
 As one can see [rom ‘Table P. substructures are well detected., As one can see from Table \ref{tab1} substructures are well detected.
 Unfortunately. an intrinsic drawback of the DWT is the unability to distinguish the typical scale. of substructures (Diajoui. private communication).," Unfortunately, an intrinsic drawback of the DWT is the unability to distinguish the typical scale of substructures (Biajoui, private communication)."
 Substructures “ereated™ by our simulations. are on a tvpical. scale of⋅ about ⋅271 we can detect them looking at the right scale.," Substructures ”created” by our simulations are on a typical scale of about $2 \, h^{-1}$ Mpc, so we can detect them looking at the right scale."
 We simulate four cillerent clusters of galaxies with distances ranging [rom 8 to GSf+ Ape with step 205+ Alpe.," We simulate four different clusters of galaxies with distances ranging from $8$ to $68 \, h^{-1}$ Mpc with step $20 \, h^{-1}$ Mpc."
 Clusters are identified by the names €1 (set at a distance 68ht Alpe from the observer). C2 (48h1 Alpe). C3 (28h1 Alpe) and C4 (Sf+ Alpe).," Clusters are identified by the names C1 (set at a distance $68 \, h^{-1}$ Mpc from the observer), C2 $48 \, h^{-1}$ Mpc), C3 $28 \, h^{-1}$ Mpc) and C4 $8 \, h^{-1}$ Mpc)."
 ALL clusters ave mace of 1512, All clusters are made of 1512
.2in,.2in
thus soft EoSs (Weber 1999) would be in auy case required.,thus soft EoSs (Weber 1999) would be in any case required.
 So one might sav that the existence of these stars hinges ou oue uncertainty only. the EoS of nuclear matter.," So one might say that the existence of these stars hinges on one uncertainty only, the EoS of nuclear matter."
" Besides the barvonclean euvironmoents, SupraNovae have another advantage over rival mocdlels only the lowest censity regions would be left behind. precisely those with the smallest neutrino losses."," Besides the baryon–clean environments, SupraNovae have another advantage over rival modlels: only the lowest density regions would be left behind, precisely those with the smallest neutrino losses."
 The powering of the burst can thus occur through accretion caused by removal of angular moment by maenuctic stresses. without the parallel. unproductive. neutrino generation.," The powering of the burst can thus occur through accretion caused by removal of angular momentum by magnetic stresses, without the parallel, unproductive, neutrino generation."
 It is difficult to eud on au upbeat note: we cannot expect in the near future a rate of progress simular to the one we wituessed in the past three years., It is difficult to end on an upbeat note: we cannot expect in the near future a rate of progress similar to the one we witnessed in the past three years.
 In particulu. it nay be expected that the next fiy of excitement will come with the beginning of the SWIFT unissiou. which promises to collect relevant data (vedshifts. ealaxv vpes. location within or without galaxies. absorption or cussion features iu the optical and in the Nrav) for a few hundred bursts.," In particular, it may be expected that the next flurry of excitement will come with the beginning of the SWIFT mission, which promises to collect relevant data (redshifts, galaxy types, location within or without galaxies, absorption or emission features in the optical and in the X–ray) for a few hundred bursts."
 This data will nail the major characteristics of the environment (at large) in which bursts take place. aud we may © able to rule out a few models.," This data will nail the major characteristics of the environment (at large) in which bursts take place, and we may be able to rule out a few models."
 Ou the other hand. the enerev release process. shrouded as it is in optical depths >1079. will remain iuvsterious. our only hope in us direction being gravitational waves.," On the other hand, the energy release process, shrouded as it is in optical depths $> 10^{10}$, will remain mysterious, our only hope in this direction being gravitational waves."
 Judging by the analogy with radio pulsars. this will correspond to the fattening of the learning curve.," Judging by the analogy with radio pulsars, this will correspond to the flattening of the learning curve."
 Aside from this. we iav lope to locate the equivalent of the ΗΝ radio pulsar. but. differeutly from Jo Tavlor. we have to be awfully quick iu erabbius it.," Aside from this, we may hope to locate the equivalent of the binary radio pulsar, but, differently from Jo Taylor, we have to be awfully quick in grabbing it."
 in the We have caleulateck the critical density of complete ionization assuming at first the Schródinger equation and a Coulomb potential., in the We have calculated the critical density of complete ionization assuming at first the ${\ddot {\rm o}}$ dinger equation and a Coulomb potential.
 Next. we implemented the Ixohn-Sham equation which takes into account the exchange interaction due to the [ree electrons and the screening. by them.," Next, we implemented the Kohn-Sham equation which takes into account the exchange interaction due to the free electrons and the screening by them."
 Comparison of our results with the NPA method vields a very σους agreement for the case of metallic BeryIHium., Comparison of our results with the NPA method yields a very good agreement for the case of metallic Beryllium.
 We mention that when the bouncary condition implemented in the INS equation is ele»x)=0 23), We mention that when the boundary condition implemented in the KS equation is $\psi(r \rightarrow \infty)=0$ \citealt{MW98})
 We mention that when the bouncary condition implemented in the INS equation is ele»x)=0 23)., We mention that when the boundary condition implemented in the KS equation is $\psi(r \rightarrow \infty)=0$ \citealt{MW98})
We have presented an analysis of the properties of the \ISPs ancl placed constraints on the magnetic field and the spin period. distributions of the AISPs at the time they turn on as radio emitters.,We have presented an analysis of the properties of the MSPs and placed constraints on the magnetic field and the spin period distributions of the MSPs at the time they turn on as radio emitters.
 We find that if we assume a braking index m=3. the field. distribution can be represented by a Gaussian in the logarithm with mean logD(CG)=S.1 and Toe=0.4 and the birth spin period by a Gaussian with mean {ντ4 ms and op=1.3 ms.," We find that if we assume a braking index $n=3$, the field distribution can be represented by a Gaussian in the logarithm with mean $\log B({\rm G})=8.1$ and $\sigma_{\log B}=0.4$ and the birth spin period by a Gaussian with mean $P_0=4$ ms and $\sigma_P=1.3$ ms."
 Our study. which allows for acceleration ellects on. the observed. spin-down rate. shows that (1) most λος are born with periods that are close to the currently observed values (ii) the characteristic ages of MSPs are typically much larger than their true age. and (iii) sub-millisecond. pulsars are rare or do not exist.," Our study, which allows for acceleration effects on the observed spin-down rate, shows that (i) most MSPs are born with periods that are close to the currently observed values (ii) the characteristic ages of MSPs are typically much larger than their true age, and (iii) sub-millisecond pulsars are rare or do not exist."
" We also find a Galactic birth rate for the ISPs of 23.2.10"" vrl.", We also find a Galactic birth rate for the MSPs of $\gsimeq 3.2\times 10^{-6}$ yr $^-1$.
 We have used our results to discuss the relative merits ( ‘the LMXD(GCCO/INXD(GUC) and ALC scenarios that have been proposed for explaining the origin of the AISPs., We have used our results to discuss the relative merits of the LMXB(CC)/IMXB(CC) and AIC scenarios that have been proposed for explaining the origin of the MSPs.
 Our main conclusions can be summarised as follows., Our main conclusions can be summarised as follows.
 We diller a more detailed. discussion of the expected outcomes from the ALC route to a subsequent. paper (Pout et al., We differ a more detailed discussion of the expected outcomes from the AIC route to a subsequent paper (Tout et al.
 2007). where we present a detailed comparison of rw birth rates anc orbital period. distributions of the ilferent. types of radio. AISPs that result. from the usual LMXD(GCCO/IMXD(GCC) route and the ALC route.," 2007), where we present a detailed comparison of the birth rates and orbital period distributions of the different types of radio MSPs that result from the usual LMXB(CC)/IMXB(CC) route and the AIC route."
 We conclude by noting that if the ICs provide the ominant route leading to the AISPs. one has to make 16 proposition that neutron star fields. co not decay. even in accreting stars. which remains contentious at the present time.," We conclude by noting that if the AICs provide the dominant route leading to the MSPs, one has to make the proposition that neutron star fields do not decay, even in accreting stars, which remains contentious at the present time."
" ""This issue is likely to be resolved by detailed observations. as has been done in the case of white dwarls where the general consensus appears to be that there is no evidence for field decay. either in single magnetic white chvarts. or in accreting magnetic white clhwarls in binaries."," This issue is likely to be resolved by detailed observations, as has been done in the case of white dwarfs where the general consensus appears to be that there is no evidence for field decay either in single magnetic white dwarfs, or in accreting magnetic white dwarfs in binaries."
 We thank Chris Tout anc Jarrocl Llurley for helpful discussions and the anonymous Iteferee for a careful reacing of our manuscript and for numerous useful comments., We thank Chris Tout and Jarrod Hurley for helpful discussions and the anonymous Referee for a careful reading of our manuscript and for numerous useful comments.
The only sure way of measuring magnetic fields is bv observing the electron-evcelotron line.,The only sure way of measuring magnetic fields is by observing the electron-cyclotron line.
 The many observed. electron-evelotron measurements of magnetic fields in X-ray binaries indicate fields >>10*G: Coburnetal.(2002): (2001).. Coburnοἱal. (2002).. BATSE Pulsarteam!.. Coburnοἱ (2002).. BATSE Pulsar team. Coburnοἱal.(2002):Davkalet (2001).. citecob02.. BATSE Pulsar team: Negueruelaetal.(2000).. Coburnetal. (2002).. LaBarberaetal.(2001).. Coburn(2002):vanIxerkwijketal. (19983).. BATSE Pulsar team. Coburnοἱal.(2002):Nelsonetal. (1997).. DATSE Pulsar team: Shirakawa&Lai(2002): Coburnetal. (2002).. Coburnetal.(2002):Oosterbroek(2001 ).. BATSE Pulsar team.," The many observed electron-cyclotron measurements of magnetic fields in X-ray binaries indicate fields $\gg 10^{8}$ G: \cite{cob02,del01}, \cite{cob02}, , BATSE Pulsar, \cite{cob02}, BATSE Pulsar team, \cite{cob02,bay01}, , \\cite{cob02}, BATSE Pulsar team; \cite{neg00}, \cite{cob02}, , \cite{lab01}, \cite{cob02,van98}, BATSE Pulsar team, \cite{cob02,nel97}, BATSE Pulsar team; \cite{shi02}; \cite{cob02}, \cite{cob02,oos01}, BATSE Pulsar team."
 No evelo(von measurement has indicated a magnetic field ~105 miC on ihe neutron star., No cyclotron measurement has indicated a magnetic field $\sim 10^{8}$ G on the neutron star.
 To be complete. the lack of detection of evclotron lines in the X-vav spectra of LMXDs could be used. however. to support the view that their fields are low.," To be complete, the lack of detection of cyclotron lines in the X-ray spectra of LMXBs could be used, however, to support the view that their fields are low."
 The fields measured in accreting neutron stars using evelotron lines are those of neutron stars in High Mass \-Rayv Binaries. which are still very voung and mostly wind accretors.," The fields measured in accreting neutron stars using cyclotron lines are those of neutron stars in High Mass X-Ray Binaries, which are still very young and mostly wind accretors."
 If the fields of neutron stars in LAINRBs were of the order of 10° Gauss. the evelotvon lines would be in the optical spectral band.," If the fields of neutron stars in LMXRBs were of the order of $10^8$ Gauss, the cyclotron lines would be in the optical spectral band."
 Such lines. arising from extremely small accretion shocks. would be swamped bythe radiationfrom the accretion diskand would thus be hidden from detection.," Such lines, arising from extremely small accretion shocks, would be swamped bythe radiationfrom the accretion diskand would thus be hidden from detection."
(i) the spectra taken for two enussionu line candidates showed that thev are Lya objects,(iii) the spectra taken for two emission line candidates showed that they are $\alpha$ objects.
" None of the acquired spectra showed the typical [OTT doublet expected in real Όλο,", None of the acquired spectra showed the typical [OIII] doublet expected in real PNe.
 We can set au upper ΙΤ to the number of PNe at 10 Apc. associated wit ithe WI cloud. of 1-51 PN in the first 2 magnitudes fainter than the PNLF bright cut-off:," We can set an upper limit to the number of PNe at 10 Mpc, associated with the HI cloud, of $1\pm1$ PN in the first 2 magnitudes fainter than the PNLF bright cut-off:"
Notwithstaudiusg these reservations. Fie.,"Notwithstanding these reservations, Fig."
 12 does exhibit the eeueral profile of the celestial spectra: the stronger peaks do not deviate frou the observed positions by more than 654: nearly all observed peaks are present with approximately the right relative intensities: the continua is distinctly building up as the uunuber of structures im each family iuereases. and πο strong undesirable feature emerges.," 12 does exhibit the general profile of the celestial spectra: the stronger peaks do not deviate from the observed positions by more than $\%$; nearly all observed peaks are present with approximately the right relative intensities; the continuum is distinctly building up as the number of structures in each family increases, and no strong undesirable feature emerges."
 Sole defects are. however. obvious.," Some defects are, however, obvious."
 The lines at 5.6 aud 19 jin. both associated with trios. appear to be too strong: this sugeestsCC» that trios should not carry hydroxyl groups. which cnuhauce those features.," The lines at 5.6 and 19 $\mu$ m, both associated with trios, appear to be too strong; this suggests that trios should not carry hydroxyl groups, which enhance those features."
 The peak at 6.55 gan is too red by 6 %: this. unfortunately cannot be remedied with the present software.," The peak at 6.55 $\mu$ m is too red by 6 $\%$; this, unfortunately cannot be remedied with the present software."
 The line density in the 7.7-;221 complex is insufficient. as is also the case near 12.5 jun. incicating that more. aud different. structures are required. so as to provide more nodes. etc.," The line density in the $\mu$ m complex is insufficient, as is also the case near 12.5 $\mu$ m, indicating that more, and different, structures are required, so as to provide more modes, etc."
 Not shown in Fig.12 are 2 isolated lines near 313 sou (F=10). due to ΟΠ wageing in trios (d) and (0).," Not shown in Fig.12 are 2 isolated lines near 34.3 $\mu$ m $I$ =10), due to OH wagging in trios (d) and (e)."
 They cau be seen in Fie., They can be seen in Fig.
 13., 13.
 The spectra. in the latter figure was obtained by adding to the concatenation of Fig., The spectrum in the latter figure was obtained by adding to the concatenation of Fig.
"The X-ray emission [rom 10""— LOIN plasma in the gravitational potentials of massive clusters and groups of galaxies has proved to be an invaluable means by which these svstenis can be robustly detected ancl (quantified. e.g. Gioiaetal.(1990).","The X-ray emission from $10^6-10^8$ K plasma in the gravitational potentials of massive clusters and groups of galaxies has proved to be an invaluable means by which these systems can be robustly detected and quantified, e.g. \citet{gio90}."
. The use of all- or partial- A-rav data (Ebelingetal.1997:Ilenry.1992:Gioia1990). and archival pointed data (Rosatietal.1995:Scharl1997:Vikhlinin1998) in constructing statistically complete catalogs of clusters ancl groups has dramatically fillel in our picture ol their evolution. from low redshifts to z~1 (Borganietal.2001).," The use of all- or partial-sky X-ray data \citep{ebe97,hen92,gio90} and archival pointed data \citep{ros95,sch97,vik98} in constructing statistically complete catalogs of clusters and groups has dramatically filled in our picture of their evolution, from low redshifts to $z\sim 1$ \citep{bor01}."
. The new Chandra and AMM-Newton observatories promise to further extend (his early work. aud in combination with measurements of the S9unvaev Zeldovich (5-Z) CAIB decrement. will allow us to refine," The new Chandra and XMM-Newton observatories promise to further extend this early work, and in combination with measurements of the Sunyaev Z'eldovich (S-Z) CMB decrement, will allow us to refine"
requenucies (svuchrotron) and high frequencies (dust): and. in fact. at all frequencies at low Galactic latitudes.,"frequencies (synchrotron) and high frequencies (dust); and, in fact, at all frequencies at low Galactic latitudes."
 However. observing at ligh/low requenucies vields template distributions for those contaminants. and these templates can be cross-correlated with data in the preferred frequency γαι] to estimate their contamination level.," However, observing at high/low frequencies yields template distributions for those contaminants, and these templates can be cross-correlated with data in the preferred frequency band to estimate their contamination level."
 This xocedure has provided robust confirmation that. at hieh latitudes. the recognised Galactic foregrounds o not significantly contaminate the CODE DMR ata (Ikogut et al 1996).," This procedure has provided robust confirmation that, at high latitudes, the recognised Galactic foregrounds do not significantly contaminate the COBE DMR data (Kogut et al 1996)."
 Althougho robust. the method we have just escribed clearly cannot be applied if there is uo template for the foreground.," Although robust, the method we have just described clearly cannot be applied if there is no template for the foreground."
 This is) the üureunustanee we are faced with if the Calactic dark matter has a substantial compoucut iu the form of cold seas clouds. as has been proposed by a number of authors (Pfcuniger. Combes aud ALutimet 1991: De Paolis et al 1995: Teuriksen and Widrow 1995: Cerhard and Silk 1996: Walker and Wardle 1908: Sciama 20000).," This is the circumstance we are faced with if the Galactic dark matter has a substantial component in the form of cold gas clouds, as has been proposed by a number of authors (Pfenniger, Combes and Martinet 1994; De Paolis et al 1995; Henriksen and Widrow 1995; Gerhard and Silk 1996; Walker and Wardle 1998; Sciama 2000a)."
 Such clouds enüt primarily in the microwave baud. aux tha Cluission is thermal at temperatures of onlv a few degrees: consequently the magnitude of this putative foreground is at preseut only subjec to very weak direct observational constraints.," Such clouds emit primarily in the microwave band, and that emission is thermal at temperatures of only a few degrees; consequently the magnitude of this putative foreground is at present only subject to very weak direct observational constraints."
 ludirect coustraimts — from the simall auplitude of fluctuations in the Cosmic Microwave Dackeroun (CAIB). and from Big Bane Nucleosvuthesisi are generally. supposed. to exclude ay sieuificaur aluonnt ¢: barvonic dark matter (e.g. Turner ας Tysou 1999). but these arguineuts are not cutirely free of loopholes (Hogan 1993: Walker auc Wardle 1999) anc direct constraints are desirable.," Indirect constraints – from the small amplitude of fluctuations in the Cosmic Microwave Background (CMB), and from Big Bang Nucleosynthesis – are generally supposed to exclude any significant amount of baryonic dark matter (e.g. Turner and Tyson 1999), but these arguments are not entirely free of loopholes (Hogan 1993; Walker and Wardle 1999) and direct constraints are desirable."
 Cüvenu the great sensitivity of the microwave data which are now beime acquired. it is therefore prudent to cousider what Galactic microwave endssion is expected for mocels i which the dark matter is composed of cold gas.," Given the great sensitivity of the microwave data which are now being acquired, it is therefore prudent to consider what Galactic microwave emission is expected for models in which the dark matter is composed of cold gas."
 To proceed with a calculation we need to specity a particular model., To proceed with a calculation we need to specify a particular model.
 The success of the now-standard structure formation paracdienm. exenplified by the Cold Dark Matter model (c.g. Pechles 1992). argues that anv acceptable model ust possess clustering properties that are similar to those of CDAL. in order to match the data on ]arge-scale-structure. aud consequently we utilise the properties of CDM. halos as a guide.," The success of the now-standard structure formation paradigm, exemplified by the Cold Dark Matter model (e.g. Peebles 1992), argues that any acceptable model must possess clustering properties that are similar to those of CDM, in order to match the data on large-scale-structure, and consequently we utilise the properties of CDM halos as a guide."
 It then relmains to specify the properties of the iudividual clouds., It then remains to specify the properties of the individual clouds.
 Radioavave scintillation data specifically the Extreme Scattering Eveuts (Fiedler et al 1987: Fiedler et al 1991) SugeestOO a vast population of ~AU-sized clouds. cach of pluietary mass (Walker and Wardle 1995). and we assume that these properties are appropriate to the individual CLOTICLS.," Radio-wave scintillation data – specifically the Extreme Scattering Events (Fiedler et al 1987; Fiedler et al 1994) – suggest a vast population of $\sim{\rm AU}$ -sized clouds, each of planetary mass (Walker and Wardle 1998), and we assume that these properties are appropriate to the individual clouds."
 The present paper is organised as follows: in §22 we derive the augular spectu for au unclustered ClO distribution: iu 833 the influence of CDALlike clusteringo js considered: LL combines the results of 822.3 mto a xedietion for the root-mean-square teniperature anisotropy spectrum. under the assuniptiou of erey-body cinission. aud considers the constraints which existing data place upon the input model: $55 then considers how these results are modified in the case where the clouds have “dusty clission spectra.," The present paper is organised as follows: in 2 we derive the angular spectrum for an unclustered cloud distribution; in 3 the influence of CDM-like clustering is considered; 4 combines the results of 2,3 into a prediction for the root-mean-square temperature anisotropy spectrum, under the assumption of grey-body emission, and considers the constraints which existing data place upon the input model; 5 then considers how these results are modified in the case where the clouds have “dusty” emission spectra."
 Asa tool to describe the statistical propertics of the microwave sky. it is conventional to enmiploy the power-spectrmu where the απο coefficieuts in the expansion of the brightness temperature field. 67. in terms of the spherical harmouic fictions τη] We will model oulv the power-spectrma which would be derived from measurements over a small yatch of sky so that we need only consider he case /z9d. for which some mathematical siupliücations are possible.," As a tool to describe the statistical properties of the microwave sky, it is conventional to employ the power-spectrum where the $a_{lm}$ are coefficients in the expansion of the brightness temperature field, $\delta T$, in terms of the spherical harmonic functions $Y_{lm}$: We will model only the power-spectrum which would be derived from measurements over a small patch of sky, so that we need only consider the case $l\gg1$, for which some mathematical simplifications are possible."
 The restriction to aree / also means that we do not have to model he structure of the Galaxy in anv detailed. way. vecatise We are considering angular scales which are sufficiently simall that the source (cloud) )ositious are essentially raudoun.," The restriction to large $l$ also means that we do not have to model the structure of the Galaxy in any detailed way, because we are considering angular scales which are sufficiently small that the source (cloud) positions are essentially random."
 The starting poiut for our calculation is the white-noise spectrum (Cy)=CT. independent of 4) which is introduced by a rancdom distribution of point sources. each of flux Ff. with a mean ΠΠΟΟ," The starting point for our calculation is the white-noise spectrum $C_l=C_l^w$, independent of $l$ ) which is introduced by a random distribution of point sources, each of flux $F$ , with a mean number"
be noted that the lack of evolution in the gas-phase metallicity of the HOST3 sample is essentially due to our selection method.,be noted that the lack of evolution in the gas-phase metallicity of the HOST3 sample is essentially due to our selection method.
 In order to enter this sample. host galaxies must have young stars with metallicity lower than ZO.1Z..," In order to enter this sample, host galaxies must have young stars with metallicity lower than $Z\leq0.1Z_{\odot}$."
 In the model used in this study. stars form with the metallicity of the component. so the adopted selection requires host galaxies to have gas-phase metallicity close to the adopted threshold (it will be typically higher because the model adopts an instantaneous recycling approximation).," In the model used in this study, stars form with the metallicity of the component, so the adopted selection requires host galaxies to have gas-phase metallicity close to the adopted threshold (it will be typically higher because the model adopts an instantaneous recycling approximation)."
 Another important and well studied relation is the luminosity-metallicity relation., Another important and well studied relation is the luminosity-metallicity relation.
 This has been measured fora very large sample of star forming galaxies from the Sloan Digital Sky Survey (SDSS) by ?.. and for smaller samples of galaxies by other authors.," This has been measured for a very large sample of star forming galaxies from the Sloan Digital Sky Survey (SDSS) by \citet{Tremonti_etal_2004}, and for smaller samples of galaxies by other authors."
 In particular. ? have recently suggested a technique to identify extremely metal-poor galaxies which share very similar properties (age. metallicity. star formation rates) with hosts of LGRBs.," In particular, \citet*{Brown_Kewley_Geller_2008} have recently suggested a technique to identify extremely metal-poor galaxies which share very similar properties (age, metallicity, star formation rates) with hosts of LGRBs."
 The data from ? are plotted in Fig., The data from \citet{Brown_Kewley_Geller_2008} are plotted in Fig.
 9 as blue circles. together with the observed relations by 2.. and by ?. for a sample of irregular galaxies.," \ref{fig:metallum} as blue circles, together with the observed relations by \citet{Tremonti_etal_2004}, and by \citet{Richer_McCall_1995} for a sample of irregular galaxies."
 Model results for the HOSTS sample are plotted as magenta asterisks and lie in the same region occupied by the Brown et al., Model results for the HOST3 sample are plotted as magenta asterisks and lie in the same region occupied by the Brown et al.
 data., data.
 Dark crosses show the corresponding results for the HOST? sample., Dark crosses show the corresponding results for the HOST2 sample.
 As explained above. the adopted selection results in clear metallicity cuts in Fig. 9..," As explained above, the adopted selection results in clear metallicity cuts in Fig. \ref{fig:metallum}."
 Observational studies of gas-phase metallicity of GRB hosts could therefore provide important iiformation on the metallicity of the progenitor stars. although in10mogeneous mixing of metals could complicate the interpretation.," Observational studies of gas-phase metallicity of GRB hosts could therefore provide important information on the metallicity of the progenitor stars, although inhomogeneous mixing of metals could complicate the interpretation."
 The few objects in the HOST3 samples with high metallicity are galaxies with very high star formation rate (which coupled with the instantaneous recycling approximation. results in quite high metallicities of the inter-stellar medium).," The few objects in the HOST3 samples with high metallicity are galaxies with very high star formation rate (which coupled with the instantaneous recycling approximation, results in quite high metallicities of the inter-stellar medium)."
 The physical environment of LGRB host galaxies can provide important information on the origin of LGRBs., The physical environment of LGRB host galaxies can provide important information on the origin of LGRBs.
 The analysis of GRB hosts environments is. however. quite difficult from the," The analysis of GRB hosts environments is, however, quite difficult from the"
As ds discussed above. the origin of IPs as a result of the MIP scattering far from the enission region can account for a number of distinctions in the properties of the AIP and IP emissions.,"As is discussed above, the origin of IPs as a result of the MP scattering far from the emission region can account for a number of distinctions in the properties of the MP and IP emissions."
 At the same time. our model implies a physical connection between these enissions. which is believed (o manilest itself as a correlation of the temporal fIuctuations of the MIP aud IP. ancl also as à consisteney of the angular aud frequency structures in the two components.," At the same time, our model implies a physical connection between these emissions, which is believed to manifest itself as a correlation of the temporal fluctuations of the MP and IP and also as a consistency of the angular and frequency structures in the two components."
 The idea of the MP-IP connecton is strongly supported by a number of observational results., The idea of the MP-IP connection is strongly supported by a number of observational results.
 Recent observations of PSR. D1702-19 (Weltevredeetal.2007) have shown that the subpulse pattern in the IP is characterized by exactly the same periodicities as that in the MP., Recent observations of PSR B1702-19 \citep{welt07} have shown that the subpulse pattern in the IP is characterized by exactly the same periodicities as that in the MP.
 Moreover. the intensity fluctuations appear correlated. with a delay of about a half of the pulsar period.," Moreover, the intensity fluctuations appear correlated with a delay of about a half of the pulsar period."
 This is just what can be expected if the MP is partially scattered into ihe IP., This is just what can be expected if the MP is partially scattered into the IP.
 As the subpulse pattern is independent of frequency. the subpulse modulation in the scaltered component should repeat Chat in the incident radiation.," As the subpulse pattern is independent of frequency, the subpulse modulation in the scattered component should repeat that in the incident radiation."
 The MP and the IP seen bv an observer originate at different phases of pulsar rotation. ancl therefore they. should arise al different phases of subpulse drift and the intensities should be correlated with a certain temporal delay.," The MP and the IP seen by an observer originate at different phases of pulsar rotation, and therefore they should arise at different phases of subpulse drift and the intensities should be correlated with a certain temporal delay."
 It is worth noting that this delay should not exactly correspond to the longitudinal separation between the. MP. ancl IP in the profile. since (he components travel somewhat different distances to the observer.," It is worth noting that this delay should not exactly correspond to the longitudinal separation between the MP and IP in the profile, since the components travel somewhat different distances to the observer."
 The microstructure characteristic of the MP emission is also expected to be present in (he scattered component., The microstructure characteristic of the MP emission is also expected to be present in the scattered component.
 The observations of PSR 0020-05 have indeed revealed the microstructure in the IP at the timescale τιν=90 i. whereas in the MP mip=130 ys (Hankins&Corcles1931:HankinsBoriakoll1981).," The observations of PSR B0950+08 have indeed revealed the microstructure in the IP at the timescale $\tau_{\rm
IP}=90\,\mu$ s, whereas in the MP $\tau_{\rm MP}=130\,\mu$ s \citep{hc81,hb81}."
. In our model. the relationship between the microstructure timescales in the two components can be estimated as follows.," In our model, the relationship between the microstructure timescales in the two components can be estimated as follows."
 The intensiv is translerred between thephoton states related as p(1—9cos0)=im(1-—»cos64)., The intensity is transferred between thephoton states related as $\nu (1-\beta\cos\theta)=\nu_1 (1-\beta\cos\theta_1)$.
 Differentiating (his at fixed [requencies vields p/6.N9=r4. N22. where it is taken (hal [or θιεπ.," Differentiating this at fixed frequencies yields $\nu\theta\Delta\theta =\nu_1\Delta\theta^2$ , where it is taken that $\sin\theta_1\approx\Delta\theta_1$ for $\theta_1\approx\pi$."
" As ""p/Typ=AMALAND and vt?f2oviPV. one can find that TipVy 2/ν0.λ0, "," As $\tau_{\rm IP}/\tau_{\rm MP}=\Delta\theta_1/\Delta\theta$ and $\nu\theta^2/2\approx 2\nu_1$, one can find that $\tau_{\rm
IP}(\nu_1)/\tau_{\rm MP}(\nu)=2/\sqrt{\theta\Delta\theta}$ ."
Taking into account that the microstructure timescaleevolves with [recquency.," Taking into account that the microstructure timescaleevolves with frequency,"
"The inferred miass-loss rates AL~10£M. vrἩ, is much higher than any reasonable mass-loss rate from au O-star primary and suggests that it is connected with the unusual short-lived pliase £133 is expericucing (see LL).","The inferred mass-loss rate, $\dot{M}\sim
10^{-4}\,M_{\odot}\,$ $^{-1}$, is much higher than any reasonable mass-loss rate from an O-star primary and suggests that it is connected with the unusual short-lived phase 433 is experiencing (see 4.1)."
 Tt could be mass loss from a common cuvelope that has already. started to form around the binary. or a hot coronal wind from the outer parts of the accretion disk driven. e.g. by the N-ray radiation from the central compact source.," It could be mass loss from a common envelope that has already started to form around the binary, or a hot coronal wind from the outer parts of the accretion disk driven, e.g., by the X-ray irradiation from the central compact source."
 With unique sampling iu the UV-plane. we have imaged the L135 system at Gecu aud 2Ocem and securely detected at both wavelengths s1000thi eiission extending over a few hundred AU perpendicular to the jet axis.," With unique sampling in the UV-plane, we have imaged the 433 system at cm and cm and securely detected at both wavelengths smooth emission extending over a few hundred AU perpendicular to the jet axis."
 The most likely interpretation of this radiation is enission frou matter which has been ejected from the disk as a thermal wind with an outward speed of ~3001s.1.," The most likely interpretation of this radiation is emission from matter which has been ejected from the disk as a thermal wind with an outward speed of $\sim 300\,{\rm km\,s^{-1}}$."
 tthauks the Roval Society for a Uuiversity Research Fellowship., thanks the Royal Society for a University Research Fellowship.
 MERLIN is a unational facility operated by the University of Manchester ou behalf of PPARC., MERLIN is a national facility operated by the University of Manchester on behalf of PPARC.
 The VLBA aud VLA are facilities of NRAO operated by AUT. under cooperative agreement with the NSF.," The VLBA and VLA are facilities of NRAO operated by AUI, under cooperative agreement with the NSF."
systems domiuated by metal-rich globular clusters.,systems dominated by metal–rich globular clusters.
 However. noue of these cases were as extreme as NGC 3311 was previously thowelt to be.," However, none of these cases were as extreme as NGC 3311 was previously thought to be."
 The existetce of a blue (metal-poor) population iu these galaxies is not excluded by hese data (because of sinall sample statistics) but Gebhardt ]xissler-Patig suggest that it is not likely to be siguilicaut. as in IC. [051.," The existence of a blue (metal–poor) population in these galaxies is not excluded by these data (because of small sample statistics) but Gebhardt Kissler-Patig suggest that it is not likely to be significant, as in IC 4051."
 Iu suminary. no system has yet been observed to have a globular cluster color distribution as extremely rec as the previous claiti lor NGC 3311.," In summary, no system has yet been observed to have a globular cluster color distribution as extremely red as the previous claim for NGC 3311."
 In particular.dex.," In particular,."
 NGC 3311 representecl the best case of an almost. excusively metal-rich globular cluster population., NGC 3311 represented the best case of an almost exclusively metal–rich globular cluster population.
 As such it raised serious questions about our un(lerstaucding of elobular cluster and ealaxy formation. since the existence of a metal-poor poptatiou is implicit in all the current sSCellarlos.," As such it raised serious questions about our understanding of globular cluster and galaxy formation, since the existence of a metal–poor population is implicit in all the current scenarios."
 In the merger picture a1 elliptical galaxy. is formed. [ro idie merger of two gas-rich spiral sealaxies., In the merger picture an elliptical galaxy is formed from the merger of two gas–rich spiral galaxies.
 The resultaut galaxy contaius a blue. metal-poor )opulation of globular clusters from the progenitor spirals aud a uetal-rich population formed di‘ine tle mereer.," The resultant galaxy contains a blue, metal–poor population of globular clusters from the progenitor spirals and a metal–rich population formed during the merger."
 In this scenario the metal-poor population shoud peak at the meclian metalliciM7 of “ilthe globular cluster systems of spiral galaxies. i.e. [Fe/H] —1.5 dex.," In this scenario the metal–poor population should peak at the median metallicity of the globular cluster systems of spiral galaxies, i.e. [Fe/H] $\sim -1.5$ dex."
 It is generally recogiizecl. 1howh. that mergers are unlikely. by themselves. to result i iligh specilic (requeney. galaxie. slcl as NGC 3311 (Ashina1 Zepl L998: Forbes. Brodie Crithairy 1997).," It is generally recognized, though, that mergers are unlikely, by themselves, to result in high specific frequency galaxies, such as NGC 3311 (Ashman Zepf 1998; Forbes, Brodie Grillmair 1997)."
 In the multi-plase ρα.re. ie blue population is fo‘inecl in a pre-ealaxy pliase. or during galaxy assembly. [roii relatively iuenriched gas and so. by definition. is metal-poor.," In the multi–phase picture, the blue population is formed in a pre–galaxy phase, or during galaxy assembly, from relatively unenriched gas and so, by definition, is metal–poor."
 The red globular clister population a1 the ilk of tje galaxy stars are formed later rou enriched material., The red globular cluster population and the bulk of the galaxy stars are formed later from enriched material.
 In the accretio1 model. the origial elliptical galaxy. (formed in a single 5) aceretes smaller (lower meallicitv) galaxies with tleir retiuues of low-metallicity globular clusters.," In the accretion model, the original elliptical galaxy (formed in a single burst) accretes smaller (lower metallicity) galaxies with their retinues of low–metallicity globular clusters."
" αἱ galaxies at tlie ceuters o ‘rich galaxy «‘luste ""Quay aso be expected to strip Globular clusters from the ouskirs of neighboring [n]galaxies.", Giant galaxies at the centers of rich galaxy clusters may also be expected to strip metal--poor globular clusters from the outskirts of neighboring galaxies.
" Because of the globular cluster uean metallicity — pareut galaxy Undaity relation (BrocieandHuclra1991: accreted/stripped globulars must be. o1 average. of lower metallicity han those belonging to the ""seed"" elliptical."," Because of the globular cluster mean metallicity – parent galaxy luminosity relation \citep{bro91,for96}
 accreted/stripped globulars must be, on average, of lower metallicity than those belonging to the “seed” elliptical."
 Coté.MarzkeandWest(1998) show bow accretion processes and the luminosity [uuction of galaxies will lead to bi-iuodal globular cluster systems iu bieht galaxies with blue ancl red peaks at [Fe/H] ~—1.5 aud ~—0.5 dex. as geerally observed.," \citet{cot98} show how accretion processes and the luminosity function of galaxies will lead to bi–modal globular cluster systems in bright galaxies with blue and red peaks at [Fe/H] $\sim -1.5$ and $\sim -0.5$ dex, as generally observed."
 Sketchy arguments cau be imagined to accommodate au absence o ‘wetal-poor clusters wiltli any of the above formation scenarios., Sketchy arguments can be imagined to accommodate an absence of metal–poor clusters within any of the above formation scenarios.
" To produce oly. or predominanty. netal-rich clusters uu the ""in situ scenario would require rapid star foru€ion prior to cluste ‘formation in the saine st: formation event."," To produce only, or predominantly, metal–rich clusters under the “in situ” scenario would require rapid star formation prior to cluster formation in the same star formation event."
 Iun a deep gravitational potential te metals produced N the stars are retained aud the average metallicity of the system is driven to a igh value (see also Woodworth Harris 2000). conceivably before any clusters are formed.," In a deep gravitational potential, the metals produced by the stars are retained and the average metallicity of the system is driven to a high value (see also Woodworth Harris 2000), conceivably before any clusters are formed."
 In acereion scenarios. the metal-poor population in the," In accretion scenarios, the metal–poor population in the"
or temporal variations in the grain size distributions.,or temporal variations in the grain size distributions.
 As with the Reference case. these disces are simulated. purely to analyse the energeties since we do not expect these disces to fragment.," As with the Reference case, these discs are simulated purely to analyse the energetics since we do not expect these discs to fragment."
 We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass clensity as the Reference case., We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass density as the Reference case.
 We do this by changing the initial Foomre stability parameter profiles such that Quin=1.0.75 and 0.5 (simulations Qminl. OQmin0.75 and Qmin0.5. respectively).," We do this by changing the initial Toomre stability parameter profiles such that $Q_{\rm min} = 1, 0.75$ and $0.5$ (simulations Qmin1, Qmin0.75 and Qmin0.5, respectively)."
 This is equivalent to reducing the disc aspect ratios to ΗΝ~22.107. L7«10> and l.l10 respectively.," This is equivalent to reducing the disc aspect ratios to $H/R \sim 2.2 \times 10^{-2}$, $1.7 \times 10^{-2}$ and $1.1 \times 10^{-2}$, respectively."
 We reiterate that the boundary emperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature olile. but it also changes the boundary temperature profile.," We reiterate that the boundary temperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature profile, but it also changes the boundary temperature profile."
 Furthermore. we consider a combination of the above actors by simulating clises with €i=0.75 and opacitics hat are 0.1. and 0.01. the interstellar opacity values.," Furthermore, we consider a combination of the above factors by simulating discs with $Q_{\rm min} = 0.75$ and opacities that are $0.1\times$ and $0.01\times$ the interstellar opacity values."
 The unfavourable conditions for fragmentation at small radii have been discussed at great. length in the past (c.g.????7)..," The unfavourable conditions for fragmentation at small radii have been discussed at great length in the past \citep[e.g.][]{Rafikov_unrealistic_conditions, Stamatellos_no_frag_inside_40AU, Boley_CA_and_GI,Rafikov_SI,Clarke2009_analytical}."
 We therefore expand: our parameter. space o include disces that are a factor of 12 larger with a radii range of 3xHox300A., We therefore expand our parameter space to include discs that are a factor of 12 larger with a radii range of $3 \le R \le 300 \rm AU$.
 These dises have the same mass as the 25AU dises ancl are set up so that Quin=1., These discs have the same mass as the 25AU discs and are set up so that $Q_{\rm min}=1$.
 We simulate three different opacity values (1:10. ancl 0.1 the interstellar Rosscland mean opacities).," We simulate three different opacity values $1\times, 10\times$ and $0.1\times$ the interstellar Rosseland mean opacities)."
 In addition. we also simulate a Large disc with Quin=0.75 with interstellar opacity values.," In addition, we also simulate a large disc with $Q_{\rm min} = 0.75$ with interstellar opacity values."
 In order to keep these disc masses ancl initial Toomre stability profiles the same as the smaller 25AU. disces. we require both the surface. mass density anc absolute temperature to be reduced.," In order to keep these disc masses and initial Toomre stability profiles the same as the smaller 25AU discs, we require both the surface mass density and absolute temperature to be reduced."
 Fhese clises are therefore not only larger. but also colder than their equivalent. (in terms of initial Toomre stability profiles) small clises.," These discs are therefore not only larger, but also colder than their equivalent (in terms of initial Toomre stability profiles) small discs."
 ‘The simulations have been analysed in three main wavs: (i) we compare the azimuthally averaged “Toone stability profiles of the initial and final (or in the case of [ragmenting cises. shortly before. fragmentation). discs which indicates whether the bulk of the dises were able to reach a state of thermal equilibrium: with their boundary.," The simulations have been analysed in three main ways: (i) we compare the azimuthally averaged Toomre stability profiles of the initial and final (or in the case of fragmenting discs, shortly before fragmentation) discs which indicates whether the bulk of the discs were able to reach a state of thermal equilibrium with their boundary."
 The surface mass density does not change significantlv throughout the simulations anc hence. changes in the ‘Toone stability parameter are due to changes in the disc temperature., The surface mass density does not change significantly throughout the simulations and hence changes in the Toomre stability parameter are due to changes in the disc temperature.
 This enables us to determine which disces are more likely to fragment., This enables us to determine which discs are more likely to fragment.
" Note that we assume s,=O in equation (", Note that we assume $\kappa_{\rm ep} = \Omega$ in equation \ref{eq:Toomre}. (
i) we examine the timescale on which the disces coo (bx considering the energy passed. from. the gas to. the radiation within the cise as well as that which is assume to be instantly raciated away from the cise surface by the boundary particles).,ii) we examine the timescale on which the discs cool (by considering the energy passed from the gas to the radiation within the disc as well as that which is assumed to be instantly radiated away from the disc surface by the boundary particles).
 In past simulations that have neglecte the heating elfects of stellar. irradiation. (e.g.22). the cooling. C'. in a steady-state disc balances the heating due to eravitational stresses. Z/04. and the heating due to artificia viscosity. Jf. such that If the artificial viscosity is low. Czc£o.," In past simulations that have neglected the heating effects of stellar irradiation \citep[e.g.][]{Gammie_betacool,Rice_beta_condition}, the cooling, $C$, in a steady-state disc balances the heating due to gravitational stresses, $H_{\rm GI}$, and the heating due to artificial viscosity, $H_{\rm \nu}$, such that If the artificial viscosity is low, $C \approx H_{\rm GI}$."
 In this case.thecooling timescale in units of the orbital timescale. .7 (section 1)). can be related to the gravitational stress in the disc. oc C?) ? and ? have shown that the maximum gravitational stress that a disc can support is acy=0.06. bevond which fragmentation will occur.," In this case,thecooling timescale in units of the orbital timescale, $\beta$ (section \ref{sec:intro}) ), can be related to the gravitational stress in the disc, $\alpha_{GI}$ \citep{Gammie_betacool}: \cite{Gammie_betacool} and \cite{Rice_beta_condition} have shown that the maximum gravitational stress that a disc can support is $\alpha_{GI} = 0.06$, beyond which fragmentation will occur."
 In clises that do not take into account heating duc to external irradiation. this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale. 3. to be smaller than the critical values. described in section 1.. for fragmentation.," In discs that do not take into account heating due to external irradiation, this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale, $\beta$, to be smaller than the critical values, described in section \ref{sec:intro}, for fragmentation."
 In our steacky-state dises. not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity. but it also has to balance the heating due to stellar irraciation. σι. such that: In what follows. we calculate the parameter. c. which," In our steady-state discs, not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity, but it also has to balance the heating due to stellar irradiation, $H_{SI}$ such that: In what follows, we calculate the parameter, $\psi$ , which"
to predict the LE LL bubble size. distribution. curing the reionization epoch.,to predict the H II bubble size distribution during the reionization epoch.
 In Barkana(2007) we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers. using the two-step approximation which Scannapieco&Barkana(2002) had applied to the two-point constant barrier problem.," In \citet{b07} we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers, using the two-step approximation which \citet{sb} had applied to the two-point constant barrier problem."
 Finding the joint. probability distribution of the density. and ionization state of two points allows the calculation of the 2lem correlation function. or power spectrum (Barkana2007)., Finding the joint probability distribution of the density and ionization state of two points allows the calculation of the 21-cm correlation function or power spectrum \citep{b07}.
. Following Purlanettoetal.(2004).. the appropriate oxwrier for reionization is found bv setting the ionized raction in a region C£! equal to unity. where Zug is he collapse fraction (i.e. the gas fraction in galactic halos) and & is the overall efficiency. factor. which is the number of ionizing photons that escape Lrom galactic halos per ivdrogen atom (or ion) contained in these halos.," Following \citet{fzh04}, the appropriate barrier for reionization is found by setting the ionized fraction in a region $\zeta F_{\rm coll}$ equal to unity, where $F_{\rm coll}$ is the collapse fraction (i.e., the gas fraction in galactic halos) and $\zeta$ is the overall efficiency factor, which is the number of ionizing photons that escape from galactic halos per hydrogen atom (or ion) contained in these halos."
 This simple version of the model remains approximately valid even with recombinations if the ellective ¢ is divided. by one. plus he number of recombinations per hvdrogen atom in the IGAL assuming this factor is roughly uniform.," This simple version of the model remains approximately valid even with recombinations if the effective $\zeta$ is divided by one plus the number of recombinations per hydrogen atom in the IGM, assuming this factor is roughly uniform."
 In order to ind fap a good starting point is the formula of ShethTormen (1999).. which accurately fits the cosmic mean 1alo abundance in simulations.," In order to find $F_{\rm
coll}$, a good starting point is the formula of \citet{Sheth}, which accurately fits the cosmic mean halo abundance in simulations."
 However. an exact analytical &eneralization is not known for the biased. δω in regions of various mean density [uctuation à.," However, an exact analytical generalization is not known for the biased $F_{\rm coll}$ in regions of various mean density fluctuation $\del$."
 Barkana&Loch(2004) suggested a hybrid prescription hat adjusts the abundance in various regions based on he extended: Press-Schechter formula (Bondetal.1991).. and showed that it fits a broad. range of simulation results.," \citet{BLflucts} suggested a hybrid prescription that adjusts the abundance in various regions based on the extended Press-Schechter formula \citep{bc91}, and showed that it fits a broad range of simulation results."
 In. general. we denote by f(9.(2).9)dS the mass raction contained at z within halos with mass in the range corresponding to variance S to S|dS. where ὃς) is the critical density for halo collapse at z.," In general, we denote by $f(\del_c(z),S)\, dS$ the mass fraction contained at $z$ within halos with mass in the range corresponding to variance $S$ to $S+d S$, where $\del_c(z)$ is the critical density for halo collapse at $z$."
" Phen the biased mass ""unction in a region of size f? (corresponding todensity variance Sy) and mean density [luctuation 0 is (Barkana&Loeb2004) where firs and. for are. respectively. the Press-Schechter anc Sheth-VTormen halo mass functions."," Then the biased mass function in a region of size $R$ (corresponding todensity variance $S_R$ ) and mean density fluctuation $\del$ is \citep{BLflucts} where $f_{\rm PS}$ and $f_{\rm ST}$ are, respectively, the Press-Schechter and Sheth-Tormen halo mass functions."
" The valuc of {μου(C).ὃςI.9) is the integral of fii over S. from 0 up o the value Syin that corresponds to the minimum halo mass My, or circular velocity Vi.=VOMwinHa (where Rey is the virial radius of a halo of mass Mj, at 2)."," The value of $F_{\rm coll}(\del_c(z),\delta,R,S)$ is the integral of $f_{\rm bias}$ over $S$, from 0 up to the value $S_{\rm min}$ that corresponds to the minimum halo mass $M_{\rm min}$ or circular velocity $V_{\rm
c}=\sqrt{G M_{\rm min}/R_{\rm vir}}$ (where $R_{\rm vir}$ is the virial radius of a halo of mass $M_{\rm min}$ at $z$ )."
 We hen numerically find the value of o that gives Choy=1 at S=0 and its derivative with respect to S. vielding the incar approximation to the barrier: 605)z7|ps.," We then numerically find the value of $\delta$ that gives $\zeta F_{\rm
coll}=1$ at $S=0$ and its derivative with respect to $S$, yielding the linear approximation to the barrier: $\delta(S) \approx \nu + \mu
S$."
 Note hat Barkana(2007) and Darkana&Loeb(2008). used an approximation in which effectively each factor on the right-1and side of equation (1)) was integrated separately over 5. vielding a simple analytical formula for the ellective linear xurier.," Note that \citet{b07} and \citet{diffPDF} used an approximation in which effectively each factor on the right-hand side of equation \ref{eq:bias}) ) was integrated separately over $S$, yielding a simple analytical formula for the effective linear barrier."
 Here we solve numerically for the barrier using the exact formulas (though the cillerence in the final results is small)., Here we solve numerically for the barrier using the exact formulas (though the difference in the final results is small).
 ὃν the relonization epoch. there are expected. to. be sullicient. radiation. backgrounds of X-ravs and of Lya photons so that the cosmic gas has been heated to well above the cosmic microwave background. temperature and the 21-cm level occupations have come into equilibrium with the ea," By the reionization epoch, there are expected to be sufficient radiation backgrounds of X-rays and of $\alpha$ photons so that the cosmic gas has been heated to well above the cosmic microwave background temperature and the 21-cm level occupations have come into equilibrium with the gas temperature \citep{Madau}."
s temperature (Macauctal.1997)..," In this case, the observed 21-cm brightness temperature relative to the CMB is independent of the spin temperature and, for our assumed cosmological parameters, is given by \citep{Madau} T_b = _b(z) _b(z) = 25, with, where $x^n$ is the neutral hydrogen fraction and the linear overdensity at $z$ is the growth factor $D(z)$ times $\del$ (which is the density linearly extrapolated to redshift 0)."
 In this case. the obser," Under these conditions, the 21-cm power spectrum is thus $P_{21} = \tilde{T}_b^2 P_\Psi$, and thus a model of the relation between the density and the ionization is all that is needed for calculating the 21-cm power spectrum."
ved 21-em brightness ," The analytical model thus consists of the following: For a given efficiency $\zeta$ and minimum halo circular velocity $V_{\rm c}$ at redshift $z$, find the corresponding linear barrier coefficients $\nu$ and $\mu$, calculate the 21-cm correlation function as a function of separation $d$ (where at each $d$ we numerically integrate equation (49) of \citet{b07})), and then Fourier transform to find the power spectrum at the desired values of $k$."
temperature relative t," Even with the analytical model, this procedure is too slow to apply directly in the $\chi^2$ fitting, but the power spectrum can be interpolated from a large precomputed table as a function of the three variables $\zeta$, $V_{\rm c}$, and $z$."
o the CALB is in, Note that our assumption of a fixed $\zeta$ (at a given $z$ ) for all halos above the minimum $V_{\rm c}$ is not as strong a restriction as it may appear.
dependent of the s," Since the halo mass function declines rapidly with mass at the high redshifts of the reionization era, once $V_{\rm c}$ is fixed, most of the ionizing sources are close in mass (i.e., within a factor of a few) to the minimum mass."
pin temperature and.," Thus, even if in the real universe $\zeta$ varies with mass at a given redshift, it is unlikely that the total ionized volume will receive large contributions from a wide range of halo masses."
 for our as," With the basic setup just described, we are free to apply any values of $\zeta$ and $V_{\rm c}$ at various redshifts where the power spectrum can be observed."
sumed cosmo, The simplest model we use is thus a two-parameter model where $\zeta$ and $V_{\rm c}$ are both assumed to be constant with redshift.
logical parameters. is given ," However, complex, time-variable feedbacks are likely to be operating during reionization, such as X-ray and UV photo-heating, supernovaeand stellar winds, metal enrichment (and the consequent changes in gas cooling and stellar populations), feedback from mini-quasars, and radiative feedbacks that affect $H_2$ formation and destruction."
by (Macauetal.," Many of these feedbacks involve scales that are far too small for direct numerical simulation, certainly within a cosmological context, so instead of trying to use particular models we prefer to parametrize our ignorance using additional free parameters."
1997) posee ," The third parameter that we add is a coefficient that gives $V_{\rm c}$ a linear dependence on $z$, and the fourth allows a linear redshift-dependence in $\zeta$."
btepma ΠΠ”.," Similarly, a fifth and sixth parameter allow a quadratic redshift-dependence in $\zeta$ and $V_{\rm
c}$, thus permitting these parameters to vary more flexibly with redshift (including a slope that may even change in sign during reionization)."
" 11D]. where xà"" is the ne "," Our main goal is to see whether the 21-cm power spectrum can help determine both the reionization history and key properties of the ionizing sources, even if we allow for such flexible models of the ionizing sources with six free parameters that are not restricted based on specific models of feedback."
Numerical simulations of reionization are a rapidly developing field., Numerical simulations of reionization are a rapidly developing field.
 Current simulations are based. on purely eravitational N-bocky codes that are used to locate and weigh forming halos as a function of time., Current simulations are based on purely gravitational N-body codes that are used to locate and weigh forming halos as a function of time.
 Radiative transfer codes are then used to find the reionization topology clue o ionizing photons coming from the source halos., Radiative transfer codes are then used to find the reionization topology due to ionizing photons coming from the source halos.
 “Phus. simulations oller the potential advantages of fully realistic source halo distributions ancl accurate racliative transfer.," Thus, simulations offer the potential advantages of fully realistic source halo distributions and accurate radiative transfer."
 tesources. though. are still stretched when attempts are made to resolve the smallest. source. halos while having sulliciently large. boxes for tracking ionizing photons with he longest mean free paths.," Resources, though, are still stretched when attempts are made to resolve the smallest source halos while having sufficiently large boxes for tracking ionizing photons with the longest mean free paths."
 Also. while prospects are good or also including hydrodynamics. it seems that astrophysics or the foreseeable future must be included: schematically. as in an analvtical model.," Also, while prospects are good for also including hydrodynamics, it seems that astrophysics for the foreseeable future must be included schematically, as in an analytical model."
 The important aspects of astrophysics that are inserted by. hand include at least. the star formation rate within each halo. properties of the stellar populations. supernova feedback. (including suppression of star formation. metal enrichment. ancl dust. formation). photo-heating feedback. and the escape of ionizing photons from each galaxy.," The important aspects of astrophysics that are inserted by hand include at least the star formation rate within each halo, properties of the stellar populations, supernova feedback (including suppression of star formation, metal enrichment, and dust formation), photo-heating feedback, and the escape of ionizing photons from each galaxy."
 Since the analytical model we use is. limited. in using spherical statistics as à simple approximation for radiative transfer. it is useful to compare ijt to results of numerical simulations.," Since the analytical model we use is limited in using spherical statistics as a simple approximation for radiative transfer, it is useful to compare it to results of numerical simulations."
 We compare our 21-cm power spectrum. predictions based on Barkana(2007) to those measured in numerical simulations of Zahnetal.(2007)simulation... Lievetal.(2008). ancl Santosetal.(2008). in Figures 1.. 2 and 3.. respectively.," We compare our 21-cm power spectrum predictions based on \citet{b07} to those measured in numerical simulations of \citet{zahn}, \citet{iliev} and \citet{santos} in Figures \ref{f:test1}, \ref{f:test2} and \ref{f:test3}, respectively."
 For comparison. the figures also show the shape of the 21-cm power spectrum if it arose purely from density Huctuations: the normalization of these curves Corresponds to a uniformly ionizing universe (see also the next subsection).," For comparison, the figures also show the shape of the 21-cm power spectrum if it arose purely from density fluctuations; the normalization of these curves corresponds to a uniformly ionizing universe (see also the next subsection)."
 Phe figures show the brightness temperature [uctuation , The figures show the brightness temperature fluctuation .
The simulations are all in reasonable agreement with the analytical mocdel., The simulations are all in reasonable agreement with the analytical model.
 The agreement is especially good with Zahnοἱal. (2007).. where the typical error in As) is ~10% although it ranges up to ~ 25%.," The agreement is especially good with \citet{zahn}, , where the typical error in $\Delta_{21}$ is $\sim 10\%$ although it ranges up to $\sim 25\%$ ."
 The agreement with Lievοἱ is good at >= 12. when density [uctuations are completely dominant. but. later curing reionization a 25% dilference is typical. with the simulation curves showing a somewhat dillerent shape that includes a decrease with & at hk Lh/Alpe.," The agreement with \citet{iliev} is good at $z=12$ , when density fluctuations are completely dominant, but later during reionization a $25\%$ difference is typical, with the simulation curves showing a somewhat different shape that includes a decrease with $k$ at $k \ga 1h$ /Mpc."
 There is good agreement (typically ~ 1054)," There is good agreement (typically $\sim
10\%$ )"
integrations at fixed positions 1n the disk.,integrations at fixed positions in the disk.
 This enabled us to achieve good sensitivity but was at the cost of undersampling the source., This enabled us to achieve good sensitivity but was at the cost of undersampling the source.
 We obtained deep observations at nine positions of the galaxy with a total on source integration time of 11 hours (Figure 1)., We obtained deep observations at nine positions of the galaxy with a total on source integration time of 11 hours (Figure 1).
 The observations were frequency switched., The observations were frequency switched.
 The intrinsic velocity resolution was 2.7 km s!: the data was then smoothed using a Hanning squared function., The intrinsic velocity resolution was 2.7 km $^{-1}$; the data was then smoothed using a Hanning squared function.
 We reduced the data using the CLASS software of the GILDAS package by fitting a first order baseline to all spectra within a window going from -400 to ss! about the galaxys’ systemic velocity of 13830 km s7!., We reduced the data using the CLASS software of the GILDAS package by fitting a first order baseline to all spectra within a window going from -400 to $^{-1}$ about the galaxys' systemic velocity of 13830 km $^{-1}$.
 This window was the same for all nine spectra., This window was the same for all nine spectra.
 The noise level is not the same for all receivers: the lowest is 0.7mK and the highest is 1.6 mK in the 10.9 km/s channels., The noise level is not the same for all receivers; the lowest is 0.7mK and the highest is 1.6 mK in the 10.9 km/s channels.
 The noise is also not uniform across the band., The noise is also not uniform across the band.
 Hence we computed the baseline and the noise in the -400 +400 window using emission free channels only., Hence we computed the baseline and the noise in the -400 +400 window using emission free channels only.
 All the details are given in Table 2., All the details are given in Table 2.
 The conversion factor from K to Jy is 8.6 Jy ΚΙ., The conversion factor from K to Jy is 8.6 Jy $^{-1}$.
" To convert from the antenna temperature scale 71 to the main beam temperature Τρ we multiplied 7) by the factor F;;;/B,;;=1.67 where F,;, is the forward beam efficiency and δι, is the main beam efficiency.", To convert from the antenna temperature scale $T_A^*$ to the main beam temperature $T_{mb}$ we multiplied $T_A^*$ by the factor $F_{eff}/B_{eff}~=~1.67$ where $F_{eff}$ is the forward beam efficiency and $B_{eff}$ is the main beam efficiency.
 We have detected CO(2-1) emission from several positions in the disk as well as from the center of Malin 2., We have detected CO(2-1) emission from several positions in the disk as well as from the center of Malin 2.
 In the following paragraphs we present our results and discuss their FFigure 2 shows the CO(2-1) emission spectra observed from nine locations across Malin 2., In the following paragraphs we present our results and discuss their Figure 2 shows the CO(2-1) emission spectra observed from nine locations across Malin 2.
 The offsets from the galaxy center are indicated in each box., The offsets from the galaxy center are indicated in each box.
 CO(2-1) emission was detected from four out of nine positions at line intensities above 3c., CO(2-1) emission was detected from four out of nine positions at line intensities above $3\sigma$.
 The line at (-24. 24) 1s a a hint of emission rather than a sure detection.," The line at (-24, 24) is a a hint of emission rather than a sure detection."
 At (0. 0) the line is broad but ts a 3c detection.," At (0, 0) the line is broad but is a $3\sigma$ detection."
 We estimated the line parameters (flux. width and central velocity) by fitting à gaussian to each spectrum.," We estimated the line parameters (flux, width and central velocity) by fitting a gaussian to each spectrum."
 We determined the noise level for each of the nine positions., We determined the noise level for each of the nine positions.
 The results are listed in Table 2 and the best fit gaussians are overlaid on the spectra in Figure 2., The results are listed in Table 2 and the best fit gaussians are overlaid on the spectra in Figure 2.
 Molecular gas has been detected earlier in this. galaxy by Das et al. (, Molecular gas has been detected earlier in this galaxy by Das et al. (
2006) with the IRAM 30m telescope and the BIMA array.,2006) with the IRAM 30m telescope and the BIMA array.
 However. due to a correlator setup problem the BIMA map was incomplete. it was covering a velocity range corresponding to CO(I-0) line emission from the east side of the galaxy only.," However, due to a correlator setup problem the BIMA map was incomplete, it was covering a velocity range corresponding to CO(1–0) line emission from the east side of the galaxy only."
" In addition. the 30m telescope was pointed toward two directions only at 7"" and ~35” east of the nucleus (see 11)."," In addition, the 30m telescope was pointed toward two directions only at $''$ and $\sim$ $''$ east of the nucleus (see 1)."
 Although the source was observed simultaneously at GGHz and 230GGHz with the 30m telescope. only CO(1-0) emission was detected: the CO(2-I) line was not detected from either positions.," Although the source was observed simultaneously at GHz and GHz with the 30m telescope, only CO(1–0) emission was detected; the CO(2--1) line was not detected from either positions."
 Our present observations cover the CO emission over a wider velocity and spatial extent than these previous observations and hence give a better idea of the distribution of molecular gas in the inner disk of Malin 2., Our present observations cover the CO emission over a wider velocity and spatial extent than these previous observations and hence give a better idea of the distribution of molecular gas in the inner disk of Malin 2.
 These observations are also the first detections of the CO(2-1) πο in Malin 2., These observations are also the first detections of the CO(2–1) line in Malin 2.
 Our detection lies below the detection limit of the older observations of Das et al. (, Our detection lies below the detection limit of the older observations of Das et al. (
2006).,2006).
 Their CO(2-1) emission spectrum had a noise (rms) of 2.6 mK whereas our line detections have a peak of 2 to 3 mK (Figure 2)., Their CO(2–1) emission spectrum had a noise (rms) of 2.6 mK whereas our line detections have a peak of 2 to 3 mK (Figure 2).
 Near the galaxy center. where there is overlap with the previous CO detection. the CO line velocities are in the same direction and are similar in shape and in width.," Near the galaxy center, where there is overlap with the previous CO detection, the CO line velocities are in the same direction and are similar in shape and in width."
 Close to the center of the galaxy the CO(I-0) line as detected by Das et al. (, Close to the center of the galaxy the CO(1–0) line as detected by Das et al. (
2006) is broad (~200kkmss~') and asymmetric with the red side being slightly more prominent than the blue side.,2006) is broad $\sim$ $^{-1}$ ) and asymmetric with the red side being slightly more prominent than the blue side.
 The CO(2A-1) line detected at the center of the galaxy by our new HERA observations is 243+76Kms! wide and at a centroid position offset by 77+34kins! relative to the systemic velocity given in Table |., The CO(2­-1) line detected at the center of the galaxy by our new HERA observations is $243\pm76~km~s^{-1}$ wide and at a centroid position offset by $77\pm34~km~s^{-1}$ relative to the systemic velocity given in Table 1.
 —Investigating the cause of this offset would require interferometric observations., Investigating the cause of this offset would require interferometric observations.
 As the beams and pointing directions are different (23” for the CO(I—O0) line and 11 for the CO(2-1) line) the fluxes cannot be directly compared., As the beams and pointing directions are different $''$ for the CO(1--0) line and $''$ for the CO(2–1) line) the fluxes cannot be directly compared.
 But if the molecular gas were uniformly distributed we would expect a line ratio in temperature scale close m the range of values found by Braine Combes (1992) with the same telescope te.. 0.4 to 1.2.," But if the molecular gas were uniformly distributed we would expect a line ratio in temperature scale close in the range of values found by Braine Combes (1992) with the same telescope i.e., 0.4 to 1.2."
 We checked this for the HERA central beam whose pointing. direction is the closest to the central pointing of Das et al (2006)., We checked this for the HERA central beam whose pointing direction is the closest to the central pointing of Das et al (2006).
 ⋀∣⋪∪∐∶↔⊺∣↴∁⋂⋯∣⊃⋯⋪≣⋯∏∪↑↴↾∣↴⊜⇂↴∣⋪≣∶↔⊺∣⇈∏⊖⋋⋋≣∏∣⊔∣∖↗∣∖⊳⋯⊳√∶↔⊺≣∖⇁⊖⋋ ∣ ∣⊂⊲≺≻≼∶⊣⊳∕∣⊂⊲≺≻≼⊢⋯∶∩↜−↓∍∕⊔∥∶↭↜−↓∍⋖∖∖⇁∣↴⊜∣⋪⊜⋔⊜⊂↻⋖⊐∣−⊓∥∏⊜ intensity from the HERA central pointing is 0.43 and the CO(1—0) intensity from IRAM ts 1.01)., A rough comparison of the brightness in $mK~km~s^{-1}$ gives $I_{\rm CO(2-1)}/I_{\rm CO(1-0)}$ = 0.43/1.01 = 0.43 (where the CO(2–1) line intensity from the HERA central pointing is 0.43 and the CO(1–0) intensity from IRAM is 1.01).
 This value is at the lower end of the line ratio range for most galaxies but given the uncertainties (e.g. gas distribution). the value shows that," This value is at the lower end of the line ratio range for most galaxies but given the uncertainties (e.g. gas distribution), the value shows that"
Tt should be noted that the nuuvey of stars decreases rapidly with the increasing &á—/ colour.,It should be noted that the number of stars decreases rapidly with the increasing $r'-i'$ colour.
 A slight chanee in the zero point of the photometric calibration in r or may change slightly our couclusiois., A slight change in the zero point of the photometric calibration in $r'$ or $i'$ may change slightly our conclusions.
 We estimate from Tables 4. 5 aud 6 that a systematic slift of 0.05 magnitude ine’/ would produce a chiuse of about 0.5 on the slope a.," We estimate from Tables 4, 5 and 6 that a systematic shift of 0.05 magnitude in $r'-i'$ would produce a change of about 0.5 on the slope $\alpha$."
 IHowever such a shift is iuprobab eas it would be seen also at the blue cud of the sequence (7.7= 0) which is not the case. ax seen in Figure 9.," However such a shift is improbable as it would be seen also at the blue end of the sequence $r'-i'=0$ ) which is not the case, as seen in Figure 9."
 Zheng et al. (2001)), Zheng et al. \cite{Zheng}) )
 determined the luminosity function fromn a sample of about 11400 NI dwurfs iu 118 fields using the WEC?2 aud 162 fields frou PCT with the UST., determined the luminosity function from a sample of about 1400 M dwarfs in 148 fields using the WFC2 and 162 fields from PC1 with the HST.
 Their sample is characterized by a mean height above the plane of 1.5 kpe. with very few stars at vertical height «1 kpe.," Their sample is characterized by a mean height above the plane of 1.5 kpc, with very few stars at vertical height $<$ 1 kpc."
 They derive their LF aud IME taking iuto account a probable metallicity eradieut. by adopting a metallicitv of 0.5 dex at 1.5 kpc. aud a colom-absolute," They derive their LF and IMF taking into account a probable metallicity gradient, by adopting a metallicity of –0.5 dex at 1.5 kpc, and a colour-absolute"
1n contrast with the methods based on integral transformation techniques. πο formalism developed here does not require that the mass density has an analytic continuation to complex arguments.,"In contrast with the methods based on integral transformation techniques, the formalism developed here does not require that the mass density has an analytic continuation to complex arguments."
 Indeed. this is the principal disadvantage involved in such methods.," Indeed, this is the principal disadvantage involved in such methods."
 Moreover. our fractional derivative approach can be regarded as a general method that contains. as particular cases. the results obtained by Fricke (1952)... IXalnajs(1976) and Jiang&Ossipkov(2007).," Moreover, our fractional derivative approach can be regarded as a general method that contains, as particular cases, the results obtained by \cite{fricke}, , \cite{kal} and \cite{jiang}."
. The method developed here can be applied to a wider variety of axisvmmetrie models. due to the generic form of the density as a function.," The method developed here can be applied to a wider variety of axisymmetric models, due to the generic form of the density as a function."
 Another advantage of this formalism is that it can be applied directly both to tridimensional svstenis and to [lat systems. without the implementation of a pseudo-volume density.," Another advantage of this formalism is that it can be applied directly both to tridimensional systems and to flat systems, without the implementation of a pseudo-volume density."
 Therefore. taking into account all the above statements. the present formalism represents a powerful tool on the construction of self-consistent stellar models.," Therefore, taking into account all the above statements, the present formalism represents a powerful tool on the construction of self-consistent stellar models."
 J. IC. wants to thank the financial support from.Académica. Vniversidad Industrial deSantander.," J. R-C. wants to thank the financial support from, Universidad Industrial deSantander."
The results thus obtained are shown in Table 2 and the fit itself is compared to the data in Figure 2..,The results thus obtained are shown in Table \ref{tab:results} and the fit itself is compared to the data in Figure \ref{fig:fit}.
 The reduced chi-squared for this fit is 0.63. which suggests we have slightly overestimated the uncertainties in our data.," The reduced chi-squared for this fit is 0.63, which suggests we have slightly overestimated the uncertainties in our data."
 Thus the uncertainties in our results are somewhat conservative., Thus the uncertainties in our results are somewhat conservative.
 We also note that there are unavoidable correlations between some parameters., We also note that there are unavoidable correlations between some parameters.
" Besides the exc ccorrelation mentioned in section ??.. the strongest of these are between aH,. b and FfI."," Besides the $e$ correlation mentioned in section \ref{subsec:fitting}, the strongest of these are between $a/\rs$, $b$ and $\rp/\rs$."
" Phere are also significant correlations between aandz.. and also between A,ήδη and the normalisation actor For the LO data."," There are also significant correlations between and, and also between $\rp/\rs$ and the normalisation factor for the IGO data."
 The uncertainties in results include he effects of all these correlations., The uncertainties in results include the effects of all these correlations.
 Since we used the values of the period (121). eccentricity (c) ancl argument of periastron (a)) from LOO as clirect constraints in the Gt. we obtained results that agree with hose values.," Since we used the values of the period ), eccentricity $e$ ) and argument of periastron ) from L09 as direct constraints in the fit, we obtained results that agree with those values."
 We did find a larger uncertainty foro. but a more precise value for the eccentricity.," We did find a larger uncertainty for, but a more precise value for the eccentricity."
 Our results also agree well with the parameters reported x POO. GOO and WO09.," Our results also agree well with the parameters reported by P09, G09 and W09."
 Phe only significant exception to this is the period. where our result is 37 smaller than the other analyses.," The only significant exception to this is the period, where our result is $3\sigma$ smaller than the other analyses."
 We note. however. that we have essentially forced our simulations to agree with the period reported by LOO.," We note, however, that we have essentially forced our simulations to agree with the period reported by L09."
 If we repeat our fit without the direct constraints onL?.. ¢ and ((see section 22)). the best-fit period is almost unchanged. but the uncertainty in its value is four times ereater.," If we repeat our fit without the direct constraints on, $e$ and (see section \ref{subsec:fitting}) ), the best-fit period is almost unchanged, but the uncertainty in its value is four times greater."
 “This means our photometric cata are in fact consistent with the period reported by POO. CO9 ancl WOO.," This means our photometric data are in fact consistent with the period reported by P09, G09 and W09."
 We also find a planet-to-star radius ratio that is marginally smaller (by 1.80) than the values reported. by WO09 and. GOO., We also find a planet-to-star radius ratio that is marginally smaller (by $1.8\sigma$ ) than the values reported by W09 and G09.
 A possible cause for this is the nature of our data from the LOO. which contains the majority. of the in-transit points. but. no out-of-transit. points on the same night.," A possible cause for this is the nature of our data from the IGO, which contains the majority of the in-transit points, but no out-of-transit points on the same night."
 This means the normalisation of those data is not strongly constrained. ancl leads to the correlation noted above.," This means the normalisation of those data is not strongly constrained, and leads to the correlation noted above."
 In. addition. the LOO cata appear to show a significant svstematic trend in the middle of the transit. which we were unable to remove by de-correlation against anv physical paramctrers of the observations (such as airmass or position on the CCD).," In addition, the IGO data appear to show a significant systematic trend in the middle of the transit, which we were unable to remove by de-correlation against any physical parametrers of the observations (such as airmass or position on the CCD)."
 We have obtained multi-site observations of a transit ingress and a complete transit. of LID SOGOG b. across. its. host star., We have obtained multi-site observations of a transit ingress and a complete transit of HD 80606 b across its host star.
 We analvsed. these data independently of any other photometric data. and found system parameters consistent with previously reported values.," We analysed these data independently of any other photometric data, and found system parameters consistent with previously reported values."
 These observations were made using four telescopes at different sites., These observations were made using four telescopes at different sites.
 This allowed: us to obtain near-continuous coverage of this 12-hour event., This allowed us to obtain near-continuous coverage of this 12-hour event.
 However. the cillerences between the instruments. telescopes ancl time-allocation procedures were. t0 an extent. limitations on our ability to obtain a uniform data set.," However, the differences between the instruments, telescopes and time-allocation procedures were, to an extent, limitations on our ability to obtain a uniform data set."
 In the near future. the completion of LCOC'TE's network of Im robotic telescopes (Brownetal. ," In the near future, the completion of LCOGT's network of 1m robotic telescopes \citep{Brown2010} "
then became globally stable.,then became globally stable.
 A well studied case in which both conditions could be satisfied. is in self-gravitating protoplanetary disks where the heating is due to gravito-driven turbulence.," A well studied case in which both conditions could be satisfied, is in self-gravitating protoplanetary disks where the heating is due to gravito-driven turbulence."
" Gane (2001) showed that. turbulence heat the gas such the svstem becomes stable on all scales (Q > 1). when tooo> Stan. being toooandtay, the cooling and orbital times."," Gammie (2001) showed that turbulence heat the gas such the system becomes stable on all scales (Q $>$ 1), when $\rm t_{cool} \,
 > \, 3 \, t_{dyn}$ , being $\rm t_{cool} \,\, and \,\, t_{dyn}$ the cooling and orbital times."
" Such disk is in an equilibrium state (so-called qreveitoturbulence ) that experiences sienilicant fluctuations. but the disk is stable against fragmentation and maintains itself in the brink of instability (Ralikov 2009) Galaxies are indeed observed (o be close to equilibrium (Martin Kennicutt 2001: Downes Solomon 1998). with observed Toomre Q parameters never too [ar from 1 (averaged over the whole svstem and using the turbulent version of (he Toomre parameter: Qua,=μμ GM)."," Such disk is in an equilibrium state (so-called $gravitoturbulence$ ') that experiences significant fluctuations, but the disk is stable against fragmentation and maintains itself in the brink of instability (Rafikov 2009) Galaxies are indeed observed to be close to equilibrium (Martin Kennicutt 2001; Downes Solomon 1998), with observed Toomre Q parameters never too far from 1 (averaged over the whole system and using the turbulent version of the Toomre parameter; $\rm Q_{turb} = v_{\rm turb} \kappa / \pi G \Sigma$ )."
" This is due (to sell-regulation heating/cooling processes: if Qiu22 1. in the absence of heating driven by instabilities the disk will cool rapidly and the svstem will eventually become unstable. while if μι<< 1. then the sell-gravityv. aud star formation feedback will be so efficient that will produce enough turbulence to heat the disk towards Qi,7 1."," This is due to self-regulation heating/cooling processes: if $\rm Q_{turb} >>$ 1, in the absence of heating driven by instabilities the disk will cool rapidly and the system will eventually become unstable, while if $\rm Q_{turb} <<$ 1, then the self-gravity and star formation feedback will be so efficient that will produce enough turbulence to heat the disk towards $\rm Q_{turb} \sim$ 1."
 llowever. galaxies are in au state that departs somewhat from the ‘gracvilolurbulent one found by Ganmamie (2001).," However, galaxies are in an state that departs somewhat from the $gravitoturbulent$ ' one found by Gammie (2001)."
 Because in galaxies only the turbulent Q Toonmre parameter is close to one. not the thermal Q which is the one that guarantees stability (like in grevitoturbulent state).," Because in galaxies only the turbulent Q Toomre parameter is close to one, not the thermal Q which is the one that guarantees stability (like in $gravitoturbulent$ ' state)."
 Galaxies are only close to stability. the runaway. growth of density [Inetuations is nol suppressed and the formation of bound objects on different scales is ongoing (i.e. star formation. GAIC formation. etc).," Galaxies are only close to stability, the runaway growth of density fluctuations is not suppressed and the formation of bound objects on different scales is ongoing (i.e. star formation, GMC formation, etc)."
 They are probably oscillating around marginal stability due to the sell-regulation feedback process. in a more dynamical fashion (and with larger oscillations) than the one studied in Gammie (2001).," They are probably oscillating around marginal stability due to the self-regulation feedback process, in a more dynamical fashion (and with larger oscillations) than the one studied in Gammie (2001)."
 Besides this more complex behavior of ISM in galaxies compared. with the classical sell-regulated *qrevitoturbulent! state studied in protoplanetary disks. (he threshold is still well defined ancl there is sell-regulation processes toward (his marginal state.," Besides this more complex behavior of ISM in galaxies compared with the classical self-regulated $gravitoturbulent$ ' state studied in protoplanetary disks, the threshold is still well defined and there is self-regulation processes toward this marginal state."
" The marginal stability is well defined at thermal Q=1 and this happens when the following two conditions are salisfied: Qj,~1 and to;>Usa.", The marginal stability is well defined at thermal Q=1 and this happens when the following two conditions are satisfied: $\rm Q_{turb} \sim 1$ and $\rm t_{cool} > t_{heat}$.
 Besides most disks in galaxies are in the same state of being close to marginal Toomre stability. still some disks like nucleardisks in starbursts are able to be much more turbulent," Besides most disks in galaxies are in the same state of being close to marginal Toomre stability, still some disks like nucleardisks in starbursts are able to be much more turbulent"
short time-scale (~ 1 vr).,short time-scale $\sim$ 1 Gyr).
 During the second one. the thin clise is formed. on a much longer time-scale (being  7 Civr at the solar ring and increasing with increasing CalactocentLic distance) oul of matter of primordial chemical composition plus traces of halo gas.," During the second one, the thin disc is formed, on a much longer time-scale (being $\sim$ 7 Gyr at the solar ring and increasing with increasing Galactocentric distance) out of matter of primordial chemical composition plus traces of halo gas."
 For a complete. description of the model basic assumptions and equations we address the interested reader to Chiappini et al. (, For a complete description of the model basic assumptions and equations we address the interested reader to Chiappini et al. (
1997. 2001. 2003).,"1997, 2001, 2003)."
 Hore we only briefly outline how novae have been included. in the model. (see also D'Xntona Matteucci 1991 and Romano et al., Here we only briefly outline how novae have been included in the model (see also D'Antona Matteucci 1991 and Romano et al.
 1999)., 1999).
" The rate of formation of nova systems at à given time £ is computed as a fraction à of the rate of formation of white chwarts (Ds) at à previous time /.—4M: where 7,, is the lifetime of the star of mass m. wo!) is the star formation rate and q(m) is the IME."," The rate of formation of nova systems at a given time $t$ is computed as a fraction $\alpha$ of the rate of formation of white dwarfs (WDs) at a previous time $t - \Delta t$: where $\tau_m$ is the lifetime of the star of mass $m$ , $\psi(t)$ is the star formation rate and $\varphi(m)$ is the IMF."
 The Scalo (1986) LXME is assumed., The Scalo (1986) IMF is assumed.
 All the stars between m = 0.8 M. and m = S AM. end up as WDs., All the stars between $m$ = 0.8 $M_\odot$ and $m$ = 8 $M_\odot$ end up as WDs.
 Af is a suitable clelav- which guarantees the cooling of the WD at a level that ensures a strong enough nova outburst., $\Delta t$ is a suitable delay-time which guarantees the cooling of the WD at a level that ensures a strong enough nova outburst.
 Llere we assume Af = 2 Gyr. which is a typical value for novae (see also tomano et al.," Here we assume $\Delta t$ = 2 Gyr, which is a typical value for novae (see also Romano et al."
 1999 and D'AXntona Mazzitelli 1982)., 1999 and D'Antona Mazzitelli 1982).
 Phe »wameter à represents the fraction of WDs which belong to nova svstenis and its value (constant in time) is fixed by the request of reproducing the current rate of nova outbursts in the Galaxy., The parameter $\alpha$ represents the fraction of WDs which belong to nova systems and its value (constant in time) is fixed by the request of reproducing the current rate of nova outbursts in the Galaxy.
 Unfortunately. this is a free parameter.," Unfortunately, this is a free parameter."
 Here we set a~ 0.01.," Here we set $\alpha 
\sim$ 0.01."
 Phe rate of nova outbursts is computed rom the rate of formation of nova systems hy assuming hat each nova sullers roughly 107 outbursts during its life (Bath Shaviv 1978)., The rate of nova outbursts is computed from the rate of formation of nova systems by assuming that each nova suffers roughly $^4$ outbursts during its life (Bath Shaviv 1978).
 A value of à between ~ 0.01 and  0.02 leads to μαπας(oa)  330⋅⋅ 1c. which: has o be compared with the value inferred. from scalings from extragalactic: nova surveys. Reobsya(lou) = 550 vr1 (Della Valle Livio 1994: see also Shafter 1997).," A value of $\alpha$ between $\sim$ 0.01 and $\sim$ 0.02 leads to $R_{\mathrm{outbursts}}(t_{\mathrm{Gal}})$ $\sim$ 30 $^{-1}$, which has to be compared with the value inferred from scalings from extragalactic nova surveys, $R_{\mathrm{outbursts}}^{\mathrm{obs}}(t_{\mathrm{Gal}})$ = 50 $^{-1}$ (Della Valle Livio 1994; see also Shafter 1997)."
 Since the evolution of the CNO isotopic ratios (as well as that of the other elemental ratios) depends mainly on the nucleosvnthesis prescriptions. rather than on the parameters of the galactic evolution like star formation and infall rates. chemical evolution models can put. constraints mainly on 10 nucleosynthesis ancl time-scales for clement production.," Since the evolution of the CNO isotopic ratios (as well as that of the other elemental ratios) depends mainly on the nucleosynthesis prescriptions, rather than on the parameters of the galactic evolution like star formation and infall rates, chemical evolution models can put constraints mainly on the nucleosynthesis and time-scales for element production."
 The validity. of this statement rests on the fact that any variation in the star formation and/or infall laws allects 10 main and the minor isotopesertent., The validity of this statement rests on the fact that any variation in the star formation and/or infall laws affects the main and the minor isotopes.
 Hn the ramework of a model where nova nucleosvnthesis is taken into account. the situation is more complicated.," In the framework of a model where nova nucleosynthesis is taken into account, the situation is more complicated."
 In fact. in us case the evolution of the CNO isotopic ratios depends Uso on the parameters which enter the computation of the jeoretical nova outburst. rate.," In fact, in this case the evolution of the CNO isotopic ratios depends also on the parameters which enter the computation of the theoretical nova outburst rate."
 Since novae produce large amounts of theisolopes. whereas their contribution o the main ones is almost negligible. cach variation in the xwameters regulating the nova rate does not cancel out in he €NO isotopic ratios.," Since novae produce large amounts of the, whereas their contribution to the main ones is almost negligible, each variation in the parameters regulating the nova rate does not cancel out in the CNO isotopic ratios."
 One should always keep in. mind his when discussing predictions from models in which nova nucleosvnthesis is included., One should always keep in mind this when discussing predictions from models in which nova nucleosynthesis is included.
 We will come back on this issue in Section 4.3., We will come back on this issue in Section 4.3.
 The nucleosvnthesis. prescriptions adopted here. are. [rom van den Llock Ciroenewegen (1997) and Ventura. D'XAntona Mazzitelli (2002) for LIAIS:4; either Woosley Weaver (1995) or Nomoto et al. (," The nucleosynthesis prescriptions adopted here are from van den Hoek Groenewegen (1997) and Ventura, D'Antona Mazzitelli (2002) for LIMS; either Woosley Weaver (1995) or Nomoto et al. ("
1997) for Type LE SNe:ii) Vhiclemann ct al. (,1997) for Type II SNe; Thielemann et al. (
1993) for “Pype Ia SNe:ze) Jose llernanz (1998) for novac.,1993) for Type Ia SNe; José Hernanz (1998) for novae.
 lt is worth emphasizing that metallicity dependent vields are available from ai limitecl number of studies. especially in the range of massive stars (n 10 AL. ).," It is worth emphasizing that metallicity dependent yields are available from a limited number of studies, especially in the range of massive stars $m >$ 10 $M_\odot$ )."
 Moreover. nucleosvnthesis studies are usually restricted to specilic mass ranges (c.g. m 88.0 AL. van den Lock Grocnewegen 1997: m~ 66.0 AL. | Ventura et al.," Moreover, nucleosynthesis studies are usually restricted to specific mass ranges (e.g., $m \sim$ 8.0 $M_\odot$ – van den Hoek Groenewegen 1997; $m \sim$ 6.0 $M_\odot$ – Ventura et al."
 2002: mi— 440 AL. Woosley Weaver 1995: m— 710 M. Nomoto et al., 2002; $m \sim$ 40 $M_\odot$ – Woosley Weaver 1995; $m \sim$ 70 $M_\odot$ – Nomoto et al.
 1997) and/or do not deal with some specific chemical species. so that it is neither possible to homogeneously cover the mass spectrum over which stars clistribute (m 1100 AZ.) nor to treat all the relevant chemical species hy adopting a single stellar nucleosvnthesis study.," 1997) and/or do not deal with some specific chemical species, so that it is neither possible to homogeneously cover the mass spectrum over which stars distribute $m \sim$ 100 $M_\odot$ ) nor to treat all the relevant chemical species by adopting a single stellar nucleosynthesis study."
" For instance. van den LHoek CGroenewegen (1997) give metallicity dependent: viclds of πο, 1€. ο. HN and ο Ὁ for stars. in the mass range m~ SR AL... but do not provide the vields of 1O. Therefore. one must complete their. grid of stellar vields by means of LO vields coming from some other study."," For instance, van den Hoek Groenewegen (1997) give metallicity dependent yields of $^4$ He, $^{12}$ C, $^{13}$ C, $^{14}$ N and $^{16}$ O for stars in the mass range $m \sim$ 8.0 $M_\odot$ , but do not provide the yields of $^{17}$ O. Therefore, one must complete their grid of stellar yields by means of $^{17}$ O yields coming from some other study."
 We adopt. the 11Ο. vields recently computed by Ventura et al. (, We adopt the $^{17}$ O yields recently computed by Ventura et al. (
2002) [or stars in the mass range m~ 66.0 M... for cilferent initial chemical compositions.,"2002) for stars in the mass range $m 
\sim$ 6.0 $M_\odot$, for different initial chemical compositions."
 Since their vields cdo not extend. to metallicities higher than Z = 0.01. we must extrapolate them to supersolar metallicities.," Since their yields do not extend to metallicities higher than $Z$ = 0.01, we must extrapolate them to supersolar metallicities."
 This makes the mocielisation of ο evolution in the inner disk inaccurate., This makes the modelisation of $^{17}$ O evolution in the inner disk inaccurate.
 Stars with m« 2.0 AL. are not ο Ο. producers. since they do not go through the NO evele during which this element is synthesized.," Stars with $m <$ 2.0 $M_\odot$ are not $^{17}$ O producers, since they do not go through the NO cycle during which this element is synthesized."
 Pherefore. we set to zero the 1 O vields from stars in the mass range m~ 22.0 AZ...," Therefore, we set to zero the $^{17}$ O yields from stars in the mass range $m~\sim$ 2.0 $M_\odot$."
 We also set to zero the FN production [rom LIMS., We also set to zero the $^{15}$ N production from LIMS.
 In fact. the net viele of this element from LIAIS is negative. due to the elect of the first and. second dredege-up for stars in the mass range 33.5 M. and to LBB for higher mass stars (Alarigo 2001).," In fact, the net yield of this element from LIMS is negative, due to the effect of the first and second dredge-up for stars in the mass range 3.5 $M_\odot$ and to HBB for higher mass stars (Marigo 2001)."
 Among the input. parameters of nova hvdrodsnamical models with a deep influence on the nova nucleosvnthesis there is the chemical. composition of the II-rich. envelope accreted by the WD from the main-sequence. companion which fills its Roche lobe., Among the input parameters of nova hydrodynamical models with a deep influence on the nova nucleosynthesis there is the chemical composition of the H-rich envelope accreted by the WD from the main-sequence companion which fills its Roche lobe.
 The problem of the chemical composition of nova envelopes is complex and far from being understood., The problem of the chemical composition of nova envelopes is complex and far from being understood.
 The matter transferred from the companion is assumed to be solarlike and is mixed in a given fraction with the outermost shells of the underlving core (e.g. Politano et al.," The matter transferred from the companion is assumed to be solarlike and is mixed in a given fraction with the outermost shells of the underlying core (e.g., Politano et al."
 1995: JoséLHernanz 1998)., 1995; JoséHernanz 1998).
 This is done in order to get the enhanced CNO or ONeAle abundances required. both to power the explosion and to account. for the spectroscopic abundance determination., This is done in order to get the enhanced CNO or ONeMg abundances required both to power the explosion and to account for the spectroscopic abundance determination.
 Lt is not clear how the composition of the nova cjecta changesduring the evolution of the Galaxy. as a function. e.g.. of the," It is not clear how the composition of the nova ejecta changesduring the evolution of the Galaxy, as a function, e.g., of the"
Lomb-Scargle analysis and the position ancl amplitude of the highest peak in the power spectrum determined.,Lomb-Scargle analysis and the position and amplitude of the highest peak in the power spectrum determined.
 The data sample was then moved on by ld and the process repeated., The data sample was then moved on by 1d and the process repeated.
 The results are presented in the lower two panels of Figure 1: (cach SOd block result is displaved at the mid point of the time interval being investigated)., The results are presented in the lower two panels of Figure 1 (each 80d block result is displayed at the mid point of the time interval being investigated).
 From this it can immediately be seen that there is a strong increase in the pulse amplitude associated with the 394d cvcele peaking at optical outburst., From this it can immediately be seen that there is a strong increase in the pulse amplitude associated with the 394d cycle peaking at optical outburst.
 Furthermore the modulation. period. is also often substantially disturbed at the same epochs., Furthermore the modulation period is also often substantially disturbed at the same epochs.
 The occasional points at 6-7d. represent times when the power spectrum becomes more complex - see Figure 2 for two examples of the power spectra from individual SOd samples., The occasional points at 6-7d represent times when the power spectrum becomes more complex - see Figure 2 for two examples of the power spectra from individual 80d samples.
 The observed optical modulation in AX 0049.477323 is not unique in the published literature., The observed optical modulation in AX J0049.4-7323 is not unique in the published literature.
 There are at least three further svstems in which a similar optical moculation is observed., There are at least three further systems in which a similar optical modulation is observed.
 These are listed in Table 1., These are listed in Table 1.
 In each case the MLACTIO lighteurve in the red. band was extracted from the archive and the data folded at the binary period., In each case the MACHO lightcurve in the red band was extracted from the archive and the data folded at the binary period.
 The resulting folded lighteurves are presented in Figure 3., The resulting folded lightcurves are presented in Figure 3.
 The lighteurves are all very assvymetric. and show strong evidence for a sharp rise followed by a slower decline.," The lightcurves are all very assymetric, and show strong evidence for a sharp rise followed by a slower decline."
 This ellect is clear in all the lighteurves shown. even though the binary periods range from 394d to 16d. (AX J0049.4-7323 to A0538-66).," This effect is clear in all the lightcurves shown, even though the binary periods range from 394d to 16d (AX J0049.4-7323 to A0538-66)."
We have performed spectral analysis of the PSPC observations for sources with more than 60 counts |.,We have performed spectral analysis of the PSPC observations for sources with more than 60 counts $^{-1}$.
 The timing analysis has been performed for all sources., The timing analysis has been performed for all sources.
 Tn this paper we only show light curves of sources with sieuificaut N-vav variability., In this paper we only show light curves of sources with significant X-ray variability.
 Spectral information from the survey data could be obtained for 59 Sevtert 1 galaxies aud ouly for oue Sevfert 2 eailaxy., Spectral information from the survey data could be obtained for 59 Seyfert 1 galaxies and only for one Seyfert 2 galaxy.
 The optical aud N-ray properties of Sevfert 1 2 galaxies of this sample are listed iu tables C1 C2.., The optical and X-ray properties of Seyfert 1 2 galaxies of this sample are listed in tables \ref{rafdats1.tab} \ref{rafdats2.tab}.
" The tables quote he name of the Sevtert calaxy (column 2). ROSAT name (colunn 23). vedshift τ (coluun 1). diameter of the Sevtert galaxy. D, (colui 5).E diameter of the conraiuioln ealaxv D, (column 6). separation between the components ο (column 7). dineusionless eravitatioual interaction streugth Q (cohunn 58) (for description see Sect. 3.2.2) "," The tables quote the name of the Seyfert galaxy (column 2), ROSAT name (column 3), redshift $z$ (column 4), diameter of the Seyfert galaxy $D_{\rm p}$ (column 5), diameter of the companion galaxy $D_{\rm c}$ (column 6), separation between the components $S$ (column 7), dimensionless gravitational interaction strength $Q$ (column 8) (for description see Sect. \ref{interaction}) )"
and the apparent visual magnitude V (coluun 9)., and the apparent visual magnitude $V$ (column 9).
" The values of : and V are taken frou Verou-Cetty Veron catalogue (1991) and he uuits of D,. D. aud 5 are mui (POSS plates) with a scale ~19.funn (Rataucli et al."," The values of $z$ and $V$ are taken from Veron-Cetty Veron catalogue (1991) and the units of $D_{\rm p}$, $D_{\rm c}$ and $S$ are mm (POSS plates) with a scale $\sim 13.4''/\rm mm$ (Rafanelli et al.,"
 1995)., 1995).
 Columus 10 aud 11 show the qualitv of the N-vav identifications both iu the poiutiug aud the survey observatious. the identifications labeled either with 1 or 2. 1 and 2 indicating high aud lower degree of reliability. respectively.," Columns 10 and 11 show the quality of the X-ray identifications both in the pointing and the survey observations, the identifications labeled either with 1 or 2, 1 and 2 indicating high and lower degree of reliability, respectively."
" In the last column we have liste the classification of the Sevfert type (Sv1.0. Sv1.2. Sv1.5. 5vas. ον, Sx2.0) taken from the (Lipovetski et aL."," In the last column we have listed the classification of the Seyfert type (Sy1.0, Sy1.2, Sy1.5, Sy1.8, Sy1.9, Sy2.0) taken from the (Lipovetski et al.,"
 1987)., 1987).
 We have modifier tje Rafauelli ct al., We have modified the Rafanelli et al.
 couventious (Sl = Sv1.0 | Sv1.3 | Sv1.5 aud S2 = Syl. | Svl.9 | Sv2.0) to S1 = Sv1.0 | Svl2 | $Sy1.5 | Syl.5 | Sy1.9 and S2 = 82.0., conventions (S1 = Sy1.0 + Sy1.2 + Sy1.5 and S2 = Sy1.8 + Sy1.9 + Sy2.0) to S1 = Sy1.0 + Sy1.2 + Sy1.5 + Sy1.8 + Sy1.9 and S2 = S2.0.
" The Classifications marked by a hash ()) indicate Narrow Line Seyfert 1 galaxies (NLSI) (οιο, Osterbrock Posee: Boller. Brandt Fins 1996: Ciyupoe Tn Appendix AppendixC: the X-ray properties obtained from the timing and spectral analysis are listed imn tables C3 aud CL."," The classifications marked by a hash ) indicate Narrow Line Seyfert 1 galaxies (NLS1) (e.g. Osterbrock Pogge; Boller, Brandt Fink 1996; Grupe In Appendix \ref{tables_light} the X-ray properties obtained from the timing and spectral analysis are listed in tables \ref{Xdats1.tab} and \ref{Xdats2.tab}."
 Columus 2 and 3 contain the position., Columns 2 and 3 contain the position.
 We mostly eive the centroid source position from the pointed observation with the higher exposure tines., We mostly give the centroid source position from the pointed observation with the higher exposure times.
" The cols baud 5 list the count rates. columns 6 and 7 the corresponding exposure times. columns 8 aud 9 the fluxes and coluuns 10 an 1l the huuiunosities of the sources detected in pointing aud survey observations. respectively,"," The columns 4 and 5 list the count rates, columns 6 and 7 the corresponding exposure times, columns 8 and 9 the fluxes and columns 10 and 11 the luminosities of the sources detected in pointing and survey observations, respectively."
 The SUPVCN count rates were taken roni the RASS II catalogue and the pointing count rates were computed from the helt curves of the sources., The survey count rates were taken from the RASS II catalogue and the pointing count rates were computed from the light curves of the sources.
 The apices p aud fin column | indicate that the source data are taken from a PSPC or IIRI observation., The apices $p$ and $h$ in column 4 indicate that the source data are taken from a PSPC or HRI observation.
 Iu the columns 8 aud 9 we apply the apices f and ο to mark the data produced by spectral fit or bv count rates., In the columns 8 and 9 we apply the apices $f$ and $c$ to mark the data produced by spectral fit or by count rates.
 This specification applies also for columns 10 aud 11., This specification applies also for columns 10 and 11.
 The Galactic colin denusitv is eiven in column 12 (Dickey Lockuman. 1990). while the cohunn deusitv obtained frou the spectral fit is given iu cohunn 13.," The Galactic column density is given in column 12 (Dickey Lockman, 1990), while the column density obtained from the spectral fit is given in column 13."
 The other spectral fit parameters. namely the monochromatic flux at UseV and the photon index are also given in columus Ll aud 15. respectively.," The other spectral fit parameters, namely the monochromatic flux at 1keV and the photon index are also given in columns 14 and 15, respectively."
 The value P=2.3 was used. if no reliable spectral At could be obtained.," The value $\Gamma=-2.3$ was used, if no reliable spectral fit could be obtained."
 When spectral information was available from the survey as well as from the poiuted data. we quote the results from the pointed Iu inost cases for optically separated close pairs. we detected iu the N-rav baud an unresolved single source (see overlavs!)).," When spectral information was available from the survey as well as from the pointed data, we quote the results from the pointed In most cases for optically separated close pairs, we detected in the X-ray band an unresolved single source (see )."
 The results of these spectral fits are listed in tables C3 and CL., The results of these spectral fits are listed in tables \ref{Xdats1.tab} and \ref{Xdats2.tab}.
 When woe detected two separate X-rav coniponents. we created two spectra and we show the suu of the count rates. fluxes aud hmunuinosities aud the sinele fit parameters CNT. Fig D) of the Sevtert galaxy in the tables.," When we detected two separate X-ray components, we created two spectra and we show the sum of the count rates, fluxes and luminosities and the single fit parameters $N_{\rm H}$, $f_{\rm 1keV}$, $\Gamma$ ) of the Seyfert galaxy in the tables."
" Iu this section we present tle spectral properties of Sevtert laud Sevfert 2 galaxies im terms of the relations between the photon iudex TE. the interaction strength Q. tle X-ray DIuunositv Zx. the far-infrared bhuuinositv Lg, aud the Sevtert type."," In this section we present the spectral properties of Seyfert 1 and Seyfert 2 galaxies in terms of the relations between the photon index $\Gamma$, the interaction strength $Q$, the X-ray luminosity $L_{\rm X}$, the far-infrared luminosity $L_{\rm fir}$ and the Seyfert type."
 Iu Fig., In Fig.
 l we have correlated the photon iudex obtained roni the power-law fit with the N-ray Iuninositv., 1 we have correlated the photon index obtained from the power-law fit with the X-ray luminosity.
 Different subtypes of Sevtert 1 galaxies are marked with ciffercut aboels., Different subtypes of Seyfert 1 galaxies are marked with different labels.
" For loxc-Inninositv Sevfert Ls. below about Lol?ergsLl. where a significant contribution from the starburst is expected to contribute to the total huninosity. iere is no clear trend between Py, aud Zx."," For low-luminosity Seyfert 1's, below about $\rm 10^{42}\ erg\ s^{-1}$, where a significant contribution from the starburst is expected to contribute to the total luminosity, there is no clear trend between $ \Gamma_{\rm fit}$ and $L_{\rm X}$."
 However. »* nonual Sevfert 1l type galaxies. a clear trend of a steepeniug of the ταν προ with increasing X-ray uuimositv is detected.," However, for 'normal' Seyfert 1 type galaxies, a clear trend of a steepening of the X-ray spectrum with increasing X-ray luminosity is detected."
 A possible. explanation for this ffect muehlt be a shifted aud streugthened accretion disk spectrin in bhieli-Inninosity Sevferts., A possible explanation for this effect might be a shifted and strengthened accretion disk spectrum in high-luminosity Seyferts.
 This is expected. as 1e high N-rav luminosity is most probably related to the ceretion rate and/or the black hole mass (Frau. Nine. Raine. 1985).," This is expected, as the high X-ray luminosity is most probably related to the accretion rate and/or the black hole mass (Frank, King, Raine, 1985)."
 When fitting a siuple-power law to the spectral data in the ROSAT energy. baud. steeper values or the photon index are expected to arise in the hieh mnulmositv Sevfer ealaxies.," When fitting a simple-power law to the spectral data in the ROSAT energy band, steeper values for the photon index are expected to arise in the high luminosity Seyfert 1 galaxies."
 Another well-known effect is also present in Fig., Another well-known effect is also present in Fig.
 1. i.c. the steeper X-ray continua of NLS1s compared to broad-line Sevfert 1 galaxies (Boller. Braudt Fink 1996).," 1, i.e. the steeper X-ray continua of NLS1s compared to broad-line Seyfert 1 galaxies (Boller, Brandt Fink 1996)."
 For Sevtert 2 galaxies. we found no significant trend or an ducreasing photon iudex with increasing N-rav inuinositv.," For Seyfert 2 galaxies, we found no significant trend for an increasing photon index with increasing X-ray luminosity."
 Ilüeher seusitivitv measurements. e.g. with NADIENewton. are necessary to search for a correlation )etween the photon index aud the N-rav lDunünositv. for Sevtert 2 ealaxies.," Higher sensitivity measurements, e.g. with XMM-Newton, are necessary to search for a correlation between the photon index and the X-ray luminosity for Seyfert 2 galaxies."
step by treating the parameter 5 in the discrete Lagrangian describing an integrator as a funelion of the positions through the step: Because the sequence of. positions⋅⋅ qi.qi.....qiVIE«qe encodes all available. informationn. about the trajectory. essentially technique lor choosing a timestep can be recast in (his [ashion.,"step by treating the parameter $h$ in the discrete Lagrangian describing an integrator as a function of the positions through the step: Because the sequence of positions $q_1, q'_1, \ldots, q_1^{(n)},
q_2$ encodes all available information about the trajectory, essentially technique for choosing a timestep can be recast in this fashion."
 We do not change the integrator equations Assuming that the timestep function P(n.qei’) is invariant under the same coordinate variations which leave 77 invariant (his will be the case if both 77 and η inherit the sanie svimmetries [rom the continuous Lagrangian). then (he proof of momentum conservation in equation still holds.," We do not change the integrator equations Assuming that the timestep function $h\left( q_1, q'_1, \ldots,
q_1^{(n)}, q_2 \right)$ is invariant under the same coordinate variations which leave $H$ invariant (this will be the case if both $H$ and $h$ inherit the same symmetries from the continuous Lagrangian), then the proof of momentum conservation in equation still holds."
 All terms in 077 proportional to Q4((n.qiqu.i»)a7 vanish because 9/ also vanishes.," All terms in $\delta H$ proportional to $\partial_0 H \left( h\left( q_1, q'_1, \ldots,
q_1^{(n)}, q_2 \right), q_1, q'_1, \ldots, q^{(n)}_1, q_2 \right)$ vanish because $\delta h$ also vanishes."
 Adaptive stepping poses no threat to momentum conservation. provided (hat the steps are chosen in a wav which respects (he svmuuetries in (he continuous mechanical problem.," Adaptive stepping poses no threat to momentum conservation, provided that the steps are chosen in a way which respects the symmetries in the continuous mechanical problem."
 Unfortunatelv. adaptive stepping does pose a threat to svinplecticitv.," Unfortunately, adaptive stepping does pose a threat to symplecticity."
" With a Gimestep function h(n.qequU.4»). the expression for dS (see eqrekl5)) gets additional ternis: , . ∐∐∐↲⊳∖⊽∩↲↕↽≻⊳∖⇁⋅⊔∐↲↕⋅≼↲↕⋝∖⊽∐∪↥∖∖⊽∪−↓⋟∪↕⋅∐↓∪∐⊔∐↲⊳∖⊽↥≀↧↴∥↲⋝∖⊽↕↽≻≀↧↴≺∢≼↲∖∖↽∐↕≺∢∐↕⋝∖⊽≺∢∪∐⊳∖⇁≼↲↕⋅∖↽≼↲≼⇂∪∖⇁≼↲↕⋅≀↧↴∐⇀↸≼↲≼⇂∐∏↕∐∣↽≻≼↲↕⋅∪↓≯⋅⋅ JA ⋅⊳ ∏∐↲⋟∖⊽≼↲≼↲⇀↸⊔⋅≀↧↴∩↲↕⋅∐↓⋟∖⊽↕↽≻↕⋅≼↲∖↽≼↲↕∐∏⋟∖⊽∐⋅∪∐⊔∖⊽↕⋅↕⊔∐≸↽↔↴↙∣−↺∶∩≀↧⊔∖⊽⊔∐↲≼∐∐≼↲↕⋅≼↲∐≺∢↩∪↓↥∖∖⇁∪↓∪↕⋅"," With a timestep function $h\left( q_1, q'_1, \ldots,
q_1^{(n)}, q_2 \right)$, the expression for $d \mathcal{S}$ (see ) gets additional terms: These extra terms prevent us from writing $d^2\mathcal{S} = 0$ as the difference of two forms, one of which is the pushforward of the other, as we did in equation."
∐↓⋟∖⊽⋅∪∐≼↲ ∪↓⋟∖∖↽∐↥≺∢∐↕⊳∖⇁⊔∐↲↕↽≻∏⊳∖⇁∐↓≯∪↕⋅∖∖↽≀↧↴↕⋅≼⇂∪↓≯⊔∐↲∪⊔∐↲↕⋅⋅≀↧↴⊳∖⊽∖∖↽≼↲≼∐≼⊔∐≼↲≺⇂∏≀↧↴∐∪∐≼⋝∏⋅⋅∖∖⊽↕⊔↥↖≺↽↔↴≼↲∐≼↲↕⋅≀↧↴↥≀↧↴≼⇂≀↧↴↕↽≻∐∖↽≼↲ sleps.," With general adaptive timesteps, there is no two-form on the state space which is conserved over a fixed number of steps."
VAL1,$^{-1}$.
 The mass model determined from the X-ray data may be compared to the mass implied by the observed. lensing configuration in the cluster (Section 1)., The mass model determined from the X-ray data may be compared to the mass implied by the observed lensing configuration in the cluster (Section 1).
 Since only a single. putative gravitational arc is seen. and to be consistent with the X-ray analysis. we have only carried out a simple. spherically-svnimetric analysis of the lensing data.," Since only a single, putative gravitational arc is seen, and to be consistent with the X-ray analysis, we have only carried out a simple, spherically-symmetric analysis of the lensing data."
 For a spherical mass distribution. the projected mass within the tangential critical radius. which we assume to be equal to the are vraclius. r0=15 aresee (071.8 kpe). is given by where Dene. Dave and Dareons are respectively the angular diameter distances from. the observer to the cluster. the observer to the lensed object. and the cluster to the Iensed object.," For a spherical mass distribution, the projected mass within the tangential critical radius, which we assume to be equal to the arc radius, $r_{\rm arc}= 15$ arcsec (71.8 kpc), is given by where $D_{\rm clus}$, $D_{\rm arc}$ and $D_{\rm arc-clus}$ are respectively the angular diameter distances from the observer to the cluster, the observer to the lensed object, and the cluster to the lensed object."
 Fig., Fig.
 4 shows the projected mass within the critical radius as a function of the redshift of the are (solid curve)., 4 shows the projected mass within the critical radius as a function of the redshift of the arc (solid curve).
" The horizontal dashed. ancl dotted. lines mark the best fit (projected) mass measurement and 90 per cent confidence limits determined. from the X-ray data. within the same radius (3.8""Lot? ))."," The horizontal dashed and dotted lines mark the best fit (projected) mass measurement and 90 per cent confidence limits determined from the X-ray data, within the same radius $3.8^{+1.0}_{-0.6} 
\times 10^{13}$ )."
 We see that the X-ray and lensing mass measurements are consistent for any are redshift zi20.7., We see that the X-ray and lensing mass measurements are consistent for any arc redshift $z_{\rm arc} > 0.7$.
 The best match between the N-rayv and lensing mass measurements is obtained for an are recdshift of 1.5., The best match between the X-ray and lensing mass measurements is obtained for an arc redshift of 1.5.
 The ROSAT URL image of the powerful raclio galaxy 4€155.16 shows extended X-ray emission. peaking at the radio galaxy indicating cluster enmüssion with a strong cooling Low., The ROSAT HRI image of the powerful radio galaxy 4C+55.16 shows extended X-ray emission peaking at the radio galaxy indicating cluster emission with a strong cooling flow.
 A spectral study of the ASCA data suggests the N- emitting gas to be multi-phase., A spectral study of the ASCA data suggests the X-ray emitting gas to be multi-phase.
 An absorbed. cool component is found in the spectrum.," An absorbed, cool component is found in the spectrum."
 The muti-phase spectral analysis indicates that the temperature of the ambient. cluster medium is στ5.4 keV. A single-phase mocel fitted to the data gives a temperature lower by ~1 keV. typical of a cooling How cluster.," The muti-phase spectral analysis indicates that the temperature of the ambient cluster medium is $kT \simeq 5.4$ keV. A single-phase model fitted to the data gives a temperature lower by $\sim 1$ keV, typical of a cooling flow cluster."
 The mass deposition rate of the cooling low. 110021544. ver+. derived from the spectral analysis is consistent with that (070.το ver1 0) estimated: from⋅ the image. analysis. when corrected [or excess absorption.," The mass deposition rate of the cooling flow, $1100^{+240}_{-410}$ $^{-1}$, derived from the spectral analysis is consistent with that $970^{+270}_{-450}$ $^{-1}$ ) estimated from the image analysis when corrected for excess absorption."
 Agreements between mass deposition rates derived from the two methods have been found for other distant cooling-How clusters (Allen 1998b)., Agreements between mass deposition rates derived from the two methods have been found for other distant cooling-flow clusters (Allen 1998b).
 The optical spectrum of 4€155.16. (Lawrence ct al 1996) is indeed very similar to the other cooling Low galaxies (Crawford et al L999)., The optical spectrum of 4C+55.16 (Lawrence et al 1996) is indeed very similar to the other cooling flow galaxies (Crawford et al 1999).
 The La luminosity is about S810K ((Lawrence et al 1996)., The $\alpha $ luminosity is about $8\times 10^{42}$ (Lawrence et al 1996).
 The relatively laree Balmer decriment. (La 11:32 5.5) suggests a significant reddening. which is often observed in cooling flows.," The relatively large Balmer decriment $\alpha $ $\beta \simeq 5.5$ ) suggests a significant reddening, which is often observed in cooling flows."
 The inferred absorption column density is slightly smaller than observed in the X-ray. spectrum., The inferred absorption column density is slightly smaller than observed in the X-ray spectrum.
 The absorption-corrected. 2.10. keV. and. bolometric Iumiosities. computed from the multi-phase model. are 8.010tere st. and 2.2«LOMerela respectively == 50 aan == 0.5).," The absorption-corrected 2–10 keV and bolometric lumiosities, computed from the multi-phase model, are $8.0\times 10^{44}$ , and $2.2\times 10^{45}$, respectively = 50 and = 0.5)."
 About 60 per cent of the bolometric luminosity is due to the cooling How., About 60 per cent of the bolometric luminosity is due to the cooling flow.
 The bolometric luminosity execeds that predicted. for the single-phase temperature of4 keV from the correlation between emission-weighted cluster temperature ancl luminosity (Mushotzky 1984: Eclee Stewart 1991: David ct al 1998: Fabian οἱ al 1994: Alushotzky Sharl 1997: White ct al 1997)., The bolometric luminosity exceeds that predicted for the single-phase temperature of 4 keV from the correlation between emission-weighted cluster temperature and luminosity (Mushotzky 1984; Edge Stewart 1991; David et al 1993; Fabian et al 1994; Mushotzky Sharf 1997; White et al 1997).
 A similar deserepancy is found for the other strong cooling How clusters (e.g Fabian ct al 1994: Allen Fabian 19982: Alarkevich 1998).," A similar descrepancy is found for the other strong cooling flow clusters (e.g., Fabian et al 1994; Allen Fabian 1998a; Markevich 1998)."
 Taking the temperature derived from the multi-phase spectral analwsis. 4€155.16 fits well the &7x Lia correlation obtained from a similar analysis of other luminous (Ly.1OMere t)) clusters for which the cllect of cooling Lows is included. (Allen Fabian 1998a). and is consistent with LpxS expected. [rom simple eravitational collapses for formation of clusters (Ixaiser 1986: Navarro. Frenk White 1995).," Taking the temperature derived from the multi-phase spectral analysis, 4C+55.16 fits well the $kT_{\rm X}$ $L_{\rm Bol}$ correlation obtained from a similar analysis of other luminous $L_{\rm Bol}>10^{45}$ ) clusters for which the effect of cooling flows is included (Allen Fabian 1998a), and is consistent with $L_{\rm Bol}\propto T_{\rm X}^2$ expected from simple gravitational collapses for formation of clusters (Kaiser 1986; Navarro, Frenk White 1995)."
 As shown in Section 6 (and Lig., As shown in Section 6 (and Fig.
 4). the mass estimated using the tentatively-identified. lensing are and the eravitational mass derived from the X-ray deprojection," 4), the mass estimated using the tentatively-identified lensing arc and the gravitational mass derived from the X-ray deprojection"
rate due to ms needs to be be comparable to the resonant effect but of opposite sigu.,rate due to $m_2$ needs to be be comparable to the resonant effect but of opposite sign.
 Cousidering the precession rate of meo. we estimate that i5 corresponds to TO orbits iu the prograde seuse while the resonant terii corresponds to 70/2 orbits in the retrograde sense.," Considering the precession rate of $m_2,$ we estimate that $\omega_{pr2}$ corresponds to $70$ orbits in the prograde sense while the resonant term corresponds to $70/2$ orbits in the retrograde sense."
 Thus the combined effect produces a precession period of 70 orbits iu the retrograde seuse as seen in the simulation., Thus the combined effect produces a precession period of $70$ orbits in the retrograde sense as seen in the simulation.
 Iu sunuuary our simulation gives plasuble eccentricity values for the two plauets that can be uuderstood in outline bv use of a simplified analytic theory and are consistent with the current observatious.," In summary our simulation gives plasuble eccentricity values for the two planets, that can be understood in outline by use of a simplified analytic theory and are consistent with the current observations."
 Iun addition. to the analytic model preseuted im section (2)) aud the lvdrodvuaimic simulations prescuted in section (27)). we lave also performed three-body orbit iutegratious using a fifth-order Runge-Kutta scheme (e.g. Press et al.," In addition to the analytic model presented in section \ref{mod}) ) and the hydrodynamic simulations presented in section \ref{simulation}) ), we have also performed three-body orbit integrations using a fifth-order Runge-Kutta scheme (e.g. Press et al."
 1993)., 1993).
 The basic assunptious of the model are that the wo plauets exist Wiun the imuer cavitv of a tically runcaed dise that lies exterior to the outer planet., The basic assumptions of the model are that the two planets exist within the inner cavity of a tidally truncated disc that lies exterior to the outer planet.
 Tidal interaction with this dise causes inwards migration of the outer planet. and also leads to eccentricity damping of he outer plauet.," Tidal interaction with this disc causes inwards migration of the outer planet, and also leads to eccentricity damping of the outer planet."
" It is further assumed that as he plancts uierate dwards and approach their final semi-major axes. he disc isperses on Some prescribed tine scale f45;,,. Iu our nunerical calculations. a torque was applied to the outermost plauet such that it nierated inwards on a time scale of ting local orbital periods as defined iu sectiou(2}). and a damping force was applied iu the radial direction ο dap the eccentricity on a ine scale of f. local orbital yeriods also as defined iu section (2))."," It is further assumed that as the planets migrate inwards and approach their final semi-major axes, the disc disperses on some prescribed time scale $t_{disp}.$ In our numerical calculations, a torque was applied to the outermost planet such that it migrated inwards on a time scale of $t_{mig}$ local orbital periods as defined in \ref{mod}) ), and a damping force was applied in the radial direction to damp the eccentricity on a time scale of $t_c$ local orbital periods also as defined in section \ref{mod}) )."
 These integrations used initial conditions corresponding to the more nassive. outermost planct reine located initially at 5 AU. with the lighter inuex-most λαο located initially at 2.5 AU.," These integrations used initial conditions corresponding to the more massive, outermost planet being located initially at 5 AU, with the lighter inner-most planet located initially at 2.5 AU."
 The planct niasses adopted for the orbit integrations are the same as the uinimuuni masses reported for the planets im the svsteus around CJsT6 by Marcy et al. (2001)) (, The planet masses adopted for the orbit integrations are the same as the minimum masses reported for the planets in the system around GJ876 by Marcy et al. \cite{Marcy4}) ) (
ie. Lae M; ancl 0.56 NL;).,i.e. 1.87 $_{J}$ and 0.56 $_{J}$ ).
 The stellar mass is taken to be 0.32 AL..., The stellar mass is taken to be 0.32 $_{\odot}$.
 Whülst these caleulatious provide onlv a crude approximation to the detailed plysics of disecompanion iuteractions. their simplicity allows us to perform many calculations. covering a wide area of parameter space. and also to run for much longer time scales than is possible for sinulatious of the type described in section(? ?)).," Whilst these calculations provide only a crude approximation to the detailed physics of disc–companion interactions, their simplicity allows us to perform many calculations, covering a wide area of parameter space, and also to run for much longer time scales than is possible for simulations of the type described in \ref{simulation}) )."
 A qnunber of calculations have been performed to examine the relationship between the final values of ey. ey. and their ratio ο ουν to the various input parameters fig te ANC των.," A number of calculations have been performed to examine the relationship between the final values of $e_1$, $e_2$, and their ratio $e_1/e_2$ , to the various input parameters $t_{mig}$, $t_c$, and $t_{disp}$."
" The results of some of these caleulations are preseuted in table Ἐν, aud are discussed below."," The results of some of these calculations are presented in table \ref{tab1}, and are discussed below."
 The unit of time used iu the abscissa of the figures 3. to 5. is the orbital period for au object at 1 AU in orbit around a star with mass 0.32 Li and is denoted as P(1 AU).," The unit of time used in the abscissa of the figures \ref{fig3} to \ref{fig5}
 is the orbital period for an object at 1 AU in orbit around a star with mass $0.32$ $_{\odot}$, and is denoted as P(1 AU)."
" Equation Ls shows that the eccentricity of the outer plauet. ej. depeuds ou the ratio of f./f,,;4."," Equation \ref{e1} shows that the eccentricity of the outer planet, $e_1$, depends on the ratio of $t_c/t_{mig}$."
" Mere we preseut results of simulations that explore how the ecceutricitv ratio ¢y/e, depends ou f. aud τω. Figure 3.Pa shows the evolution of the sonimajor axes and eccentricities for the rum R1. whose model parameters are described iu table 1.."," Here we present results of simulations that explore how the eccentricity ratio $e_2/e_1$ depends on $t_c$ and $t_{mig}.$ Figure \ref{fig3} shows the evolution of the semi–major axes and eccentricities for the run R1, whose model parameters are described in table \ref{tab1}."
 This figure shows the invard uueration of the outer plauct that subsequeutlv locks to the iuuer planet as it reaches the 2:1 conuuensurability., This figure shows the inward migration of the outer planet that subsequently locks to the inner planet as it reaches the 2:1 commensurability.
 The subsequent evolution is such that the two planets. nowresonautly locked. migrate wards.," The subsequent evolution is such that the two planets, nowresonantly locked, migrate inwards."
 The eccentricities, The eccentricities
Type I AGN (20).,Type I AGN $2\sigma$ ).
 The ratio of Type I quasars to Type II AGN increases for both bright and dim equasars with decreasing scale. but less dramatically as the ratio to Tvpe E AGN.," The ratio of Type I quasars to Type II AGN increases for both bright and dim quasars with decreasing scale, but less dramatically as the ratio to Type I AGN."
 The ratio between dimmer Type I quasars and Tvpe II AGN is approximately consistent with unitv lor scales 150hlkpeSR<2.0Alpe: the ratio between brighter Type I quasars aud Type I AGN is 1.3 CZ 26) for scales RZ500hz!kpe., The ratio between dimmer Type I quasars and Type II AGN is approximately consistent with unity for scales $150\kpchseventy \lesssim R \leqslant 2.0\Mpchseventy$; the ratio between brighter Type I quasars and Type II AGN is 1.3 $\gtrsim2\sigma$ ) for scales $R\gtrsim500\kpchseventy$.
 On smaller scales. both ratios increase.," On smaller scales, both ratios increase."
 At scales 2zz150hlkpe. the ratio of brighter Type I quasars to Type II AGN is 1.6 (220). and the ratio of dimmer Type I quasars to Type IL AGN is 1.3 (>Lo).," At scales $R\approx150\kpchseventy$, the ratio of brighter Type I quasars to Type II AGN is 1.6 $\approx2\sigma$ ), and the ratio of dimmer Type I quasars to Type II AGN is 1.3 $>1\sigma$ )."
 This scale dependeney could be evidence for (he merger origin of quasars. since one would expect (o see a higher density of environment galaxies al small scales where merger events are likely to take place (Ilopkinsetal.2008).," This scale dependency could be evidence for the merger origin of quasars, since one would expect to see a higher density of environment galaxies at small scales where merger events are likely to take place \citep{Hopkins2007}."
. Evidence (hat dimuner quasars and lower-Iuminosity AGN are located in environments wilh similar overclensitv might suggest that cdimmer quasars could be a transition population between low-liminosity AGN (likely fueled in dry mergers. close encounters. or secular processes) and high-Iuminositv AGN (likely fueled in major mergers).," Evidence that dimmer quasars and lower-luminosity AGN are located in environments with similar overdensity might suggest that dimmer quasars could be a transition population between low-luminosity AGN (likely fueled in dry mergers, close encounters, or secular processes) and high-luminosity AGN (likely fueled in major mergers)."
 Rather than disparate populations of merger-fueled and secularlv fueled AGN. there may be a continuum of galaxy interactions from major mergers to close encounters or harassment that cause AGN Iuninosityv differences.," Rather than disparate populations of merger-fueled and secularly fueled AGN, there may be a continuum of galaxy interactions from major mergers to close encounters or harassment that cause AGN luminosity differences."
 Alternatively. a mix of mergers and secular processes could drive the AGN population near (he quasar-Sevlert divide (GV;2005b).," Alternatively, a mix of mergers and secular processes could drive the AGN population near the quasar-Seyfert divide \citep[$M_{i}."
 We have compared the AGN samples without redshilt cuts. but we note that in Section ?? we demonstrated (hat evolution of quasar environments with redshift is negligible.," We have compared the AGN samples without redshift cuts, but we note that in Section \ref{redshiftsubsec} we demonstrated that evolution of quasar environments with redshift is negligible."
 The significant dillerence in (he environments of bright Type I quasars aud (he environments ol both Type I and Type II AGN could imply that these populations have different fueling mechanisms., The significant difference in the environments of bright Type I quasars and the environments of both Type I and Type II AGN could imply that these populations have different fueling mechanisms.
 This result is consistent with results presented by Lietal.(2006.2008).. who find that there is only a weak link between nearby neighbors of narrow-line AGN and their nuclear activily.," This result is consistent with results presented by \citet{Li2006, Li2008}, who find that there is only a weak link between nearby neighbors of narrow-line AGN and their nuclear activity."
 Finally. we combine our analysis of tvpe. redshift and luminosity effects on environment overdensitv in Figures 11.. 12.. and 13..," Finally, we combine our analysis of type, redshift and luminosity effects on environment overdensity in Figures \ref{scale_spectargs_Mandz_higherz}, \ref{scale_spectargs_Mandz_lowerz}, and \ref{scale_qso_newMzcompare}."
 Our ὃς cuts on the photometric galaxies around the spectroscopic targets as well as around the random positions to which they are compared (as described in Section ??)) allow us to make meaningful comparisons of objects in different, Our $\delta z$ cuts on the photometric galaxies around the spectroscopic targets as well as around the random positions to which they are compared (as described in Section \ref{deltazcutsection}) ) allow us to make meaningful comparisons of objects in different
absorbed mid-IR emissiou re-radiated in the FIR docs not exceed the observed poiuts.,absorbed mid-IR emission re-radiated in the FIR does not exceed the observed points.
 If the FIR emission is powered bv the ACN this is UV radiation re-processed by dust., If the FIR emission is powered by the AGN this is UV radiation re-processed by dust.
 However. if the AGN emits —2«JUL. im UV photons. high excitation gas chussiou lines should also be observed.," However, if the AGN emits $\sim 2\xten{10}\Lo$ in UV photons, high excitation gas emission lines should also be observed."
 The abseuce of high ionization lines like rur|A5007.LO59A (CMoorwood c al. 1996a}) ," The absence of high ionization lines like $\lambda 5007,4959$ (Moorwood et al. \cite{moorwood96a}) )"
or [NeVJALL3pau (Genzelet al. 1998)), or $\lambda 14.3\MIC$ (Genzel et al. \cite{genzel98}) )
 aud the low excitation observed in the wind-blown cone strongly argues that uo ioniziug UV photous (ie. 13.6<hr 00ο) escape frou the inuer region., and the low excitation observed in the wind-blown cone strongly argues that no ionizing UV photons (i.e. $13.6\le \HNU < 500\EV$ ) escape from the inner region.
" The low excitation IT, /Pao map. associated with the peak in IH» cluission close to the nucleus location. indicates that ALL ultraviolet photons must be absorbed within R<175. Le. T?30pe along ALL lines of sight."," The low excitation $_2$ $\alpha$ map, associated with the peak in $_2$ emission close to the nucleus location, indicates that ALL ultraviolet photons must be absorbed within $R<1\farcs5$, i.e. $R<30\PC$ along ALL lines of sight."
 This is in contrast with the standard unified model of AGN where ionizing radiation escapes along directions close to the torus axis., This is in contrast with the standard unified model of AGN where ionizing radiation escapes along directions close to the torus axis.
 If. the AGNUM is duoenmibedded5B ini a; thickTEM dustydx mediunm then two effects will contribute to its obsewmration., If the AGN is embedded in a thick dusty medium then two effects will contribute to its obscuration.
 First. dust will compete] with the otgas in ‘absorbing© UV. photons which will be directly converted iuto infrared radiation (e.g. Netzer Laor 1993.. Oliva. Marconi AMoorwood 1999a)).," First, dust will compete with the gas in absorbing UV photons which will be directly converted into infrared radiation (e.g. Netzer Laor \cite{netzer93}, Oliva, Marconi Moorwood \cite{oliva99}) )."
 Second. emission lines originating πι this. medium. will: be suppressed. by dust absorption.," Second, emission lines originating in this medium will be suppressed by dust absorption."
. To00 ⋅ . ↸∖↴∖↴↑∐⊔⋜↧↑↸∖↑∐↸∖⋜⋯⋯∏∐∪↕↥⋅↸∖≺∣∏∐⋅↸∖≺↸∖⊼↑⋯≼⊳↕∪∐⋅∐∪↑↸∖↑↕⋯↑∐↓↽∙⊽↴∙↴⋅↴∙⋅∙. ⋅∙⋅ ∙ ≼⊲∐⋅↸⊳↕∐∏↴∖↴⊪∖⊽↸∖∖⊳∏↓∙∶≩∕∣⋯⊪∖⊽↸∖∐∫⊔∙≺∖∖∕∣⋯∶∩∙↓≺↸∖↘⊓∐↸⊳↑↕∪∐ coirected) aud iu NGC 1915 0.008 (both ratios are from Cienzel et al. 19908)).," To estimate the amount of required extinction, note that in Circinus $\NeV 14.3\MIC/\NeII 12.8\MIC=0.4$ (extinction corrected) and in NGC 4945 $\le 0.008$ (both ratios are from Genzel et al. \cite{genzel98}) )."
 TE NGC1915. has the same iutrinsie ratio as Circinus. then the observed rratiov] requiresui] {οyon)2 L2maeg correspondiug to Ay> LlOmag aud in aereeimeut with the above estimates.," If NGC4945 has the same intrinsic ratio as Circinus, then the observed ratio requires $A(14.3\MIC)>4.2$ mag corresponding to $\AV>110$ mag and in agreement with the above estimates."
 We conclude that the ACN can power the FIR cnussion if it is properly obscured., We conclude that the AGN can power the FIR emission if it is properly obscured.
 Inferring the black hole mass from the nunuaser observatious (1.1ον109NI.. Greenhill.," Inferring the black hole mass from the maser observations $1.4\xten{6}\Mo$, Greenhill."
 et al. 1997)).," et al. \cite{greenhill}) ),"
 we find im this scenario that the ACN is eidttine at ~50% of its Eddineton Lumiuosity., we find in this scenario that the AGN is emitting at $\sim 50\%$ of its Eddington Luminosity.
 As discussed above. if an ACN powers the FIR cuission of NGC 1915. it aust be hidden up to midIR wavelengths aud does not fitJ inH the standard uuifedf model.," As discussed above, if an AGN powers the FIR emission of NGC 4945, it must be hidden up to mid-IR wavelengths and does not fit in the standard unified model."
 The possible: existence: of: such a class of: Active: Nuelei.-: detectable onlv at >10keV. would have important cousequeuces ou the interpretation of IR huuinous objects whose power source is still debated.," The possible existence of such a class of Active Nuclei, detectable only at $>10\KEV$, would have important consequences on the interpretation of IR luminous objects whose power source is still debated."
 Genzel et al. (1998)), Genzel et al. \cite{genzel98}) )
 and Lutz et al (1998) , and Lutz et al. \cite{lutz98}) )
compared iiid-IR spectra of Ultra Luninous IRAS ealaxies (ULIRGs. see Sanders Mirabel 1996 for a review) with those of AGN aud starburst templates.," compared mid-IR spectra of Ultra Luminous IRAS galaxies (ULIRGs, see Sanders Mirabel \cite{sanders96} for a review) with those of AGN and starburst templates."
 They concluded that the absence of high excitation lines (e.g. [Nev]}) and the presence of PAT features undiluted bv strong thermal coutimmun in CLIRGSs spectra strongly Sugeest that the starburst component is dominaut., They concluded that the absence of high excitation lines (e.g. ) and the presence of PAH features undiluted by strong thermal continuum in ULIRGs spectra strongly suggest that the starburst component is dominant.
 They also show that. after a proper extinction correction. the observed star formation activity can power FIR cussion.," They also show that, after a proper extinction correction, the observed star formation activity can power FIR emission."
 In their papers. NCC 11915 is classified as a starburst because of its mid-IR properties but. as shown in the previous. section. NGC 1915. could also be powered by a highly obscured AGN aud the same scenario could iu principle apply to all ULIRGs.," In their papers, NGC 4945 is classified as a starburst because of its mid-IR properties but, as shown in the previous section, NGC 4945 could also be powered by a highly obscured AGN and the same scenario could in principle apply to all ULIRGs."
 Their bolometric cussion cau be powered by an active nucleus completely obscured even at mil-IR wavelengths., Their bolometric emission can be powered by an active nucleus completely obscured even at mid-IR wavelengths.
 The same aremnent could be used for the sources detected at submillimeter wavelengths by SCUBA which cai be considered as the high redshift counterpart of local ULIRGs., The same argument could be used for the sources detected at submillimeter wavelengths by SCUBA which can be considered as the high redshift counterpart of local ULIRGs.
 If they are powered by hidden active uuclei then their enormous FIR ciission would uot require star formation rates in excess of >LOOMxr.| (e.g. Hughes et al. 1998)).," If they are powered by hidden active nuclei then their enormous FIR emission would not require star formation rates in excess of $>100\Mo\YR\1$ (e.g. Hughes et al. \cite{hughes98}) ),"
 and this would have important consequences :for understanding: the history: of. star formationJ: in: hieh: yedshift ealaxies., and this would have important consequences for understanding the history of star formation in high redshift galaxies.
 Iu additiou.⋅⋅ it∙∙ is well known that in⋅ order to explai⋅— he Nav background a huge fraction of obscured ACN0 is required.," In addition, it is well known that in order to explain the X-ray background a large fraction of obscured AGN is required."
 However Calli et al. (1999)), However Gilli et al. \cite{gilli99}) )
 have shown that. dm order to reconcile the observed Xaay background with ↕⋜⋯∟∖≓⋯⋅↖↸⊳∪∏∐↑↴∖∙⋜⋃⋜∏⋯∐⋅↖↸∖↖∪↕∏∐∶↴∙↻∪↴⋯↕⋜↧↕∪∐∪↕∐⋜⋯↧∙↽∙⊽ ↴ ∙⋅⊽⊽⊽⋅↜ ⋅ ⊳∙ ∙↴⋅⊳ ⊸∖≓⋯⋅↖↴∖≺∏∐∏∖↴∖↕↴∖↥↸∖≺∣∏∐↸∖≼↧∏↻↑∪⊓∖," have shown that, in order to reconcile the observed X-ray background with hard X-ray counts, a rapidly evolving population of hard X-ray sources is required up to redshift $\sim 1.5$."
≼⊔∐⇈∿↓∙⋅⊐∙⋀∖∪↴∖⋯⊳↕ »pulatiou is known at the moment aud the oulv class of objects which are known to undergo such a rapid density evolution are local ULIRGs (iim et al. 1998)), No such population is known at the moment and the only class of objects which are known to undergo such a rapid density evolution are local ULIRGs (Kim et al. \cite{kim98}) )
 anc. at higher redshift. the SCUBA sources (Suail ct al. 1997)).," and, at higher redshift, the SCUBA sources (Smail et al. \cite{smail97}) )."
 SCUBA sources ave therefore candidates to host a population of hiehlv obscured ACNs., SCUBA sources are therefore candidates to host a population of highly obscured AGNs.
 Almaini et al. (1999)), Almaini et al. \cite{almaini99}) )
 sueeestOO that. if the SED of high redshift ACN is simular to those observed locally. oue cau explain of the SSCUDA sources at 1 idw.," suggest that, if the SED of high redshift AGN is similar to those observed locally, one can explain of the SCUBA sources at 1 mJy."
 This fraction could be significantly higher if à laree population of AGN are Compton thick at N-rav wavelengths., This fraction could be significantly higher if a large population of AGN are Compton thick at X-ray wavelengths.
 Trentham. Blain Coldader (1999)) show that if the SCUBA sources are completely powered by a dust cushrouded ACN then they iav help in explaining the discrepancy between the local density iu super massive black holes aud the lieh redshift AGN component (sce also Fabian Twasawa 1999)).," Trentham, Blain Goldader \cite{trentham}) ) show that if the SCUBA sources are completely powered by a dust enshrouded AGN then they may help in explaining the discrepancy between the local density in super massive black holes and the high redshift AGN component (see also Fabian Iwasawa \cite{fabian99}) )."
 Establishing the nature of SCUBA sourees could beD extremelyWwrayhon difficultHMC if theD embeddedDB ACNsUN arepvo likeepo οςSOC[0451915. re.5 completely.Fols obscuredCIO ini alb; directions.vecti: because they would then not be identifiable with the standard optical/IR diagnostics.," Establishing the nature of SCUBA sources could be extremely difficult if the embedded AGNs are like NGC4945, i.e. completely obscured in all directions, because they would then not be identifiable with the standard optical/IR diagnostics."
 Iucidlentallv. this fact could possibly account for the sparse detections of type 2 ACNs at high redshifts (Akivama et al. 1999).," Incidentally, this fact could possibly account for the sparse detections of type 2 AGNs at high redshifts (Akiyama et al. \cite{akiyama}) )."
 The best possibility for the detection of NGC1915-Ilike ACINs is via their hard X-ray cussion but. uufortunatelv. the sensitivity of existing παν surveys is still. not high cnough to detect high : AGN and the low spatial resolution makes ideutificatious uncertain iu the case of faint optical/ucar-IR counterparts.," The best possibility for the detection of NGC4945-like AGNs is via their hard X-ray emission but, unfortunately, the sensitivity of existing X-ray surveys is still not high enough to detect high $z$ AGN and the low spatial resolution makes identifications uncertain in the case of faint optical/near-IR counterparts."
 Moreover. hard N-ravs," Moreover, hard X-rays"
extended. a slowly varving evrosvuchrotron source aud a liehh-polarizecdl maser source.,"extended, a slowly varying gyrosynchrotron source and a highly-polarized maser source."
 Iu the high resolution WLBI data. ouly one poiutlike source is observed.," In the high resolution VLBI data, only one pointlike source is observed."
 We identify this as the southern component T Tau Sb., We identify this as the southern component T Tau Sb.
 Tutercoutinental VLA-Effelsbere baselines in the carly part of the experiment allow us to constrain the size of this source to o less than 115 R. in radius., Intercontinental VLA-Effelsberg baselines in the early part of the experiment allow us to constrain the size of this source to be less than 14.5 $_{\odot}$ in radius.
 Circular polarization indicates the Yesenuce of magnetic fields in the source region., Circular polarization indicates the presence of magnetic fields in the source region.
 Short timescale variability is observed. in the form of two distiuct. step-ike fux increases. cach followed by steady imereased dux.," Short timescale variability is observed, in the form of two distinct step-like flux increases, each followed by steady increased flux."
 During the first of these. the observed polarization changed from left- to right-handed.," During the first of these, the observed polarization changed from left- to right-handed."
 The second seems to rave added ouly rielit-hand polarized flux., The second seems to have added only right-hand polarized flux.
 We argue that lis stronely indicates coherent enüssiou. nost probably an electrou-eyclotron maser.," We argue that this strongly indicates coherent emission, most probably an electron-cyclotron maser."
 Based ou this interpretation he magnetic field strength in the maser ciitting region can be estimated to be in the kilogauss range., Based on this interpretation the magnetic field strength in the maser emitting region can be estimated to be in the kilogauss range.
 By areuine that the quiesceut enusslon 1u the fist 6 hours represents evrosvuchrotron cussion frou. rou-therimal electrous and requiring the brightuess eniperature for this cCluission fto lie below scusible inits. we argue that the cmitting magnetic region must ο af least 1 R. in size. and probably larger.," By arguing that the quiescent emission in the first 6 hours represents gyrosynchrotron emission from non-thermal electrons and requiring the brightness temperature for this emission to lie below sensible limits, we argue that the emitting magnetic region must be at least 1 $_{\odot}$ in size, and probably larger."
 The evrosvuchrotron endütting regions have sizes of the same order as those expected for an accreting magnuetospliere., The gyrosynchrotron emitting regions have sizes of the same order as those expected for an accreting magnetosphere.
 At low resolutiou the svstem is resolved into the two components. N and ο. T Tau N is consistent with a point source iu our VLA maps.," At low resolution the system is resolved into the two components, N and S. T Tau N is consistent with a point source in our VLA maps."
" T Tau S shows evidence of resolved flux. indicating that there is either diffuse enissionu. or additional comiponeuts in the «ποια, or both."," T Tau S shows evidence of resolved flux, indicating that there is either diffuse emission, or additional components in the system, or both."
 The nou-detection of T Tau N in the high resolution data indicates that this is a wind source., The non-detection of T Tau N in the high resolution data indicates that this is a wind source.
 The non-detectiou of T Tau Sa iav indicate that this source is below our detection lit. although it is possible that it is resolved out bv our shortest VLBI baseline.," The non-detection of T Tau Sa may indicate that this source is below our detection limit, although it is possible that it is resolved out by our shortest VLBI baseline."
Calmore&Reid(1983) andreferencestherein).. (ey.Majewski2007) —a-cuhan,"\citet{Gilmore1983} \citep[for reviews see][and references therein]{Reid1993, Buser1999, Norris1999}, \citep{Robin1996, Ojha2001, Chen2001, Larsen2003}. \citep{Nissen1995, Chiba2000, Gilmore2002, Soubiran2003, Parker2004, Wyse2006}."
ced2005)..," \citep[\egc][]{Reid1993, Chiba2000, Bochanski2007a} $\alpha$."
 Moreoever. thin and thick disk attributes are not unique to the Milky Way but a ubiquitous feature for late type galaxies (Dursteim 2007).," Moreoever, thin and thick disk attributes are not unique to the Milky Way but a ubiquitous feature for late type galaxies \citep{Burstein1979, vanderKruit1981, Abe1999, Neeser2002, Yoachim2005, Yoachim2006, Yoachim2007}."
. Receutlv. several SDSSbased. studies have provided further strong observational constraints on the structural. kinematic and chemical properties of stars in the solar cevliuder.," Recently, several SDSS–based studies have provided further strong observational constraints on the structural, kinematic and chemical properties of stars in the solar cylinder."
 απόetal.(2008.hereafterJOS) used a photometric parallax method ou SDSS data to estimate distances to ~ LS million stars and studied their spatial distribution.," \citet[hereafter J08]{Juric2008}
 used a photometric parallax method on SDSS data to estimate distances to $\sim$ 48 million stars and studied their spatial distribution."
 Because SDSS provides accurate photometry. which enables reasonably robust distances 15%... Sesaretal. 2008)). as well as faint magnitude limits ἐν< 22) and a laree sky coverage (6500 deg? ). 105 were able to robustly coustrain the parameters of a model for the elobal spatial distribution of stars in the Milky Way.," Because SDSS provides accurate photometry, which enables reasonably robust distances , \citealt{Sesar2008}) ), as well as faint magnitude limits $r<22$ ) and a large sky coverage (6500 $^2$ ), J08 were able to robustly constrain the parameters of a model for the global spatial distribution of stars in the Milky Way."
 The JOS model is qualitatively similar to previous work Dalicall&Soncira 1980)) which ideutifies a clear change of slope in the counts of disk stars as a function of distance from the Calactic plane: this changein slope is usually iuterpreted as the transition from the thin to thick disk 2002)..," The J08 model is qualitatively similar to previous work \citealt{Bahcall1980}) ) which identifies a clear change of slope in the counts of disk stars as a function of distance from the Galactic plane; this changein slope is usually interpreted as the transition from the thin to thick disk \citep{Gilmore1983, Siegel2002}. ."
Traclitional theories of planetary formation (Safronov 1969) predict that the giant planets form yw accretion of gas outo rocky cores of 5—2084. while lower mass planets form via a clifferent jecliauisin.,"Traditional theories of planetary formation (Safronov 1969) predict that the giant planets form by accretion of gas onto rocky cores of $5-20 M_\oplus$, while lower mass planets form via a different mechanism."
 Here we evaluate the likelihood for SIM to detect planets with am<p20M, Here we evaluate the likelihood for SIM to detect planets with $m \le 20 M_\oplus$.
 [f the primary goal is to detect planets with n:«2OAL. then of the four observing plaus we ave cousidered. the one with 2 µας single measurement. precision is optimal (see 55a) and ‘ould be expected to detect 11-ε or 2549 planets with masses €20M. [or five- ac| len-year lissions. respectively (see 33 top).," If the primary goal is to detect planets with $m< 20 M_\oplus$, then of the four observing plans we have considered, the one with 2 $\mu$ as single measurement precision is optimal (see 5a) and could be expected to detect $11\pm6$ or $25\pm9$ planets with masses $\le20
M_\oplus$ for five- and ten-year missions, respectively (see 3 top)."
 A five- or teu-vear mission ix expected to make |i or 124-6 ass and orbital parameter determinations with accuracy (see 33 middle right) and 323 or 87 mass aud orbital parameter determinatious with accuracy (see 33 bottom right, A five- or ten-year mission is expected to make $4^{+4}_{-3}$ or $12\pm6$ mass and orbital parameter determinations with accuracy (see 3 middle right) and $3\pm3$ or $8^{+5}_{-4}$ mass and orbital parameter determinations with accuracy (see 3 bottom right).
 The two-tier strategy would detect. ~5 Or 1TX9 planets with masses aX20M. during a [ive- or ten-year mission. respectively.," The two-tier strategy would detect $\sim5^{+2}_{-3}$ or $\sim17\pm9$ planets with masses $m\le 20 M_\oplus$ during a five- or ten-year mission, respectively."
 Lt woulcl measure masses aud orbits with accuracy for ⋅∣ −≻↓≽∩↕⋅↙=6 ⋮↥↽≻↥⋜⋃≺↵↕⊳∖⋜↕∐≼⊔∐≺↵⋜↕⊳∖⋃⋅≺↵↕↕≺↵∐↕⋜↕⊳∖⊳∖≺↵⊳∖⋜↕∐≺⇂∩↓⋅∣≻∐⋜↕↥↥↽≻⋜⋃⋅⋜⋃∐≺↵↕≺↵↕∷∖∖∖↽∐∐∐⋗↸⋰∣⋰∡⋜⊔∙∢∙⇂⊔⋅⋜↕∢∙⊽∖⊽↥∩↓⋅−≻ ⋅↽∣ ⋅⋅∣ Or 9p such planets depending on the length of the mission., It would measure masses and orbits with accuracy for $2^{+4}_{-2}$ or $7^{+6}_{-5}$ planets and measure the masses and orbital parameters with accuracy for $2^{+3}_{-2}$ or $5^{+5}_{-4}$ such planets depending on the length of the mission.
 Again. it is important to remember that these estimates depend on an extrapolation of the planet mass functiou observed for larger masses. although in this case the extrapolation iu mass is relatively small. since radial velocity surveys already detect 3044 plauets.," Again, it is important to remember that these estimates depend on an extrapolation of the planet mass function observed for larger masses, although in this case the extrapolation in mass is relatively small, since radial velocity surveys already detect $\sim30 M_\oplus$ planets."
 Auy of the ten-year SIM surveys which we considered is likely to detect oue planet with a mass LAL. for any of the target lists we cousider.," Any of the ten-year SIM surveys which we considered is likely to detect one planet with a mass $\sim1 M_\oplus$, for any of the target lists we consider."
 Similarly. a 1 µας five-year SIM survey is likely to detect one planet with a mass LOAL and the other five-year surveys would likely detect one planet with a iass 2—3M. (see Ll aud 10).," Similarly, a 1 $\mu$ as five-year SIM survey is likely to detect one planet with a mass $\sim1.5 M_\oplus$ and the other five-year surveys would likely detect one planet with a mass $\sim2-3M_\oplus$ (see 4 and 10)."
 Of course. the mass of the smallest planet that SIM will actually detect mmay be siguificantly larger or sinaller than these precictious due to s1nall number statistics and uncertaiuties in the mass function.," Of course, the mass of the smallest planet that SIM will actually detect may be significantly larger or smaller than these predictions due to small number statistics and uncertainties in the mass function."
 Either a 1. LoL. or 2 gras survey is likely to measure with accuracy the mass aud orbital parameters of one planet with a imass SAL [or a five-year survey.," Either a 1, 1.4, or 2 $\mu$ as survey is likely to measure with accuracy the mass and orbital parameters of one planet with a mass $\sim5 M_\oplus$ for a five-year survey."
 During a ten-year survey. SIM would likely measure with accuracy the mass aid orbital parameters of oue planet with a mass ολ with the 1 µας survey aud ~2À£. with either the l.l or 2 pras surveys.," During a ten-year survey, SIM would likely measure with accuracy the mass and orbital parameters of one planet with a mass $\sim 1.5 M_\oplus$ with the 1 $\mu$ as survey and $\sim2 M_\oplus$ with either the 1.4 or 2 $\mu$ as surveys."
 The two-tier strategy would likely measure with accuracy the mass aud orbital parameters of one planet with a mass 2 or L.OAL [or five- or teu-vear surveys.," The two-tier strategy would likely measure with accuracy the mass and orbital parameters of one planet with a mass $\sim5$ or $1.5
M_\oplus$ for five- or ten-year surveys."
be. we create synthetic galaxy images using Lattened Sérrsic profiles with dilferent [lattenings e=1O(1 bfe) and Séresic exponents 7.,"be, we create synthetic galaxy images using flattened Sérrsic profiles with different flattenings $\epsilon = 10(1-b/a)$ and Sérrsic exponents $n$."
 The hall-light radius is then measured as the geometric mean of the semi-major axis and semi-minor axis of the elliptical isophote that cneloses half the light and by integrating over circular isophotes., The half-light radius is then measured as the geometric mean of the semi-major axis and semi-minor axis of the elliptical isophote that encloses half the light and by integrating over circular isophotes.
 Phe dillerence between the two approaches is plotted. in Fig., The difference between the two approaches is plotted in Fig.
 3. as à function of Hlattening ο anc Sérrsic p., \ref{fitre} as a function of flattening $\epsilon$ and Sérrsic $n$.
 The maximum deviation is obtained for small » and strong [Dattening and is not larger than Aloe(h..)0.15.," The maximum deviation is obtained for small $n$ and strong flattening and is not larger than $\Delta \log({\rm R}_{\rm e}) \approx
0.15$."
 his is smaller than the scatter on the observed scaling relations., This is smaller than the scatter on the observed scaling relations.
 We therefore do not expect to see any significant systematic trend of half-light radius with Ilattening as à result of the particular way it was measured., We therefore do not expect to see any significant systematic trend of half-light radius with flattening as a result of the particular way it was measured.
 Although the data show considerable scatter. especially in the cdwarl regime. it is striking that galaxies [rom a wicle range of environments trace a continuous Aly vs. Ry relation over a range οἱ 6 orders of magnitude in luminosity.," Although the data show considerable scatter, especially in the dwarf regime, it is striking that galaxies from a wide range of environments trace a continuous $_V$ vs. $_{\rm e}$ relation over a range of 6 orders of magnitude in luminosity."
 ]t is well known that earlv-tvpe galaxies brighter than Aly14 mag trace a single Aly vs. 0 relation.," It is well known that early-type galaxies brighter than $_V \sim
-14$ mag trace a single $_V$ vs. $n$ relation."
 This relation is quantified as log(n)=L4.0.1:Mg by Jerjen&Bingecli (LOOT). as log(n)=Lss|0.125Mpoocw. by Graham&Guzman (2003).. and as log(n)=1.520.11Mz » Graham&Worley(2008).," This relation is quantified as $\log(n) = -1.4 - 0.1 \times {\rm M}_B$ by \citet{jb97}, as $\log(n) = -1.88 - 0.12 \times {\rm M}_{\rm F606W}$ by \citet{gg03}, and as $\log(n) = -1.52 - 0.11 \times {\rm M}_B$ by \citet{gw08}."
. These authors fit Sérrsic wofiles to the observed surface brightness profiles. evaluated as function of equivalent. radius.," These authors fit Sérrsic profiles to the observed surface brightness profiles, evaluated as function of equivalent radius."
 Llowever. it is also possible o fit the growth curve. constructed by integrating a galaxy image over circular apertures. with the growth curve of he Sérrsic profile.," However, it is also possible to fit the growth curve, constructed by integrating a galaxy image over circular apertures, with the growth curve of the Sérrsic profile."
 This approach is advocated by, This approach is advocated by
have. until now. prevented detailed studies of HE in the bars of AGN hosts.,"have, until now, prevented detailed studies of HI in the bars of AGN hosts."
 The ‘fuelling’ of an AGN requires gas from the outer regions of a galaxy to be delivered. to its centre with essentially zero angular momentum. in order to form (ancl refuel) an aceretion cise around a central black hole (Cunn. 1979: Shlosman et abl.," The `fuelling' of an AGN requires gas from the outer regions of a galaxy to be delivered to its centre with essentially zero angular momentum, in order to form (and refuel) an accretion disc around a central black hole (Gunn, 1979; Shlosman et al.,"
 1990)., 1990).
 Although. controversial. gas streaming in galactic bars may play an important role in the carly stages of this process (Simkin. Su Schwarz. 1980). with significant angular momentum loss occurring when two different: families of gas orbits meet and. formi. dissipative shocks. allowing gas to move inward (Prendergast. 1983: Athanassoula. 1992a.b).," Although controversial, gas streaming in galactic bars may play an important role in the early stages of this process (Simkin, Su Schwarz, 1980), with significant angular momentum loss occurring when two different families of gas orbits meet and form dissipative shocks, allowing gas to move inward (Prendergast, 1983; Athanassoula, 1992a,b)."
 Until now. direct evidence for this has been difficult to obtain (Lindblad J6rrsater. LOSS: Sellhvood Wilkinson. 1993: Teuben. 1996) since optical studies are restricted by the small amounts of ionisecl eas in bar shocks (Lindblad et al.," Until now, direct evidence for this has been difficult to obtain (Lindblad Jörrsater, 1988; Sellwood Wilkinson, 1993; Teuben, 1996) since optical studies are restricted by the small amounts of ionised gas in bar shocks (Lindblad et al.,"
 1996). and. detailed: studies of more ubiquitous neutral hydrogen in the bars of AGN hosts. and indeed. normal galaxies. have been limited by inadequate angular resolution and sensitivity.," 1996), and detailed studies of more ubiquitous neutral hydrogen in the bars of AGN hosts, and indeed, normal galaxies, have been limited by inadequate angular resolution and sensitivity."
 Although the physical conditions in the host galaxy of an AGN may be intimately related to the nuclear activity. to date there have been relatively lew detailed: synthesis studies of HIE in ACN hosts.," Although the physical conditions in the host galaxy of an AGN may be intimately related to the nuclear activity, to date there have been relatively few detailed synthesis studies of HI in AGN hosts."
 As part of an ongoing project to study the distribution and kinematics of HE in AGN (Sevferts) we present here. the highest angular resolution observations of the neutral hydrogen in the bar of the archetypal Sevfert. galaxy NGCAISL. obtained using the VLA in B configuration.," As part of an ongoing project to study the distribution and kinematics of HI in AGN (Seyferts) we present here, the highest angular resolution observations of the neutral hydrogen in the bar of the archetypal Seyfert galaxy NGC4151, obtained using the VLA in B configuration."
 NOCAI5I is a woell-studied nearby eas-rich spiral galaxy with a central oval distortion (Bosma. IEkers. Lequeux. 1977) and a Sevfert 1.5 nucleus (Osterbrock Ixoski. 1976).," NGC4151 is a well-studied nearby gas-rich spiral galaxy with a central oval distortion (Bosma, Ekers, Lequeux, 1977) and a Seyfert 1.5 nucleus (Osterbrock Koski, 1976)."
 Phe oval cistortion. identified kinematically in early LIL stuclies (Bosma et al.," The oval distortion, identified kinematically in early HI studies (Bosma et al.,"
 1977. Bosma. 1981) and evident in deep optical exposures (Arp. 1977). and. subsequent LIE maps (Pedlar ct al..," 1977, Bosma, 1981) and evident in deep optical exposures (Arp, 1977) and subsequent HI maps (Pedlar et al.,"
. 1992). is elongated. along. PA ~130° and has dimensions of 3.35«2.1 (12.9 kpe 8.2 kpe).," 1992), is elongated along PA $\sim$ $^o$ and has dimensions of $3.3' \times 2.1'$ (12.9 kpc $\times$ 8.2 kpc)."
 In this paper. we establish the oval distortion as a weak. fat bar and concentrate particularly on the gas dynamics in this region: we relate our study of the gas flows in the bar to models of eas Hows in non-axisvmmoetrie barred. potentials.," In this paper, we establish the oval distortion as a weak, 'fat' bar and concentrate particularly on the gas dynamics in this region; we relate our study of the gas flows in the bar to models of gas flows in non-axisymmetric barred potentials."
 Assuming a heliocentric velocity of 998 km +. and Εν = τὸ km | +. the distance to NGC4ISL is 13.3 Alpe (see also Muncdell et al.," Assuming a heliocentric velocity of 998 km $^{-1}$ , and $_0$ = 75 km $^{-1}$ $^{-1}$, the distance to NGC4151 is 13.3 Mpc (see also Mundell et al.,"
 1998). so 1 corresponels to 65pc in the galaxy.," 1998), so 1"" corresponds to 65pc in the galaxy."
 Full details of the observations ancl subsequent data processing techniques (including production of the moment maps) are presented in Muncell et al. (, Full details of the observations and subsequent data processing techniques (including production of the moment maps) are presented in Mundell et al. (
1998).,1998).
" Ehe data used in this paper were obtained [rom a 63-channel. naturalA weighted spectral line cata cube which has an angular resolution. of ⋅⋅∕∕ ∕∕ à spectral resolution: of ⋅⋅10.3 km s"" and a greater sensitivity (lowest detectable column density of⋅⋅⋅ 1.32 x 107""οι em2 7) than the higher. resolution.. uniformly"" weighted cube."," The data used in this paper were obtained from a 63-channel, naturally weighted spectral line data cube which has an angular resolution of $'' \times$ $''$, a spectral resolution of 10.3 km $^{-1}$ and a greater sensitivity (lowest detectable column density of 1.32 x $^{20}$ $^{-2}$ ) than the higher resolution, uniformly weighted cube."
 NOGC4151 shares some of the basic characteristics of barred spirals as summarised by Roberts et al. (, NGC4151 shares some of the basic characteristics of barred spirals as summarised by Roberts et al. (
1979): for example the “lack of dominance of the bar in photometric studies. which is indeed the case for NGOC4151 where the underlying mass distribution is only a mild. oval distortion. (Bosma et al.,"1979); for example the “lack of dominance of the bar in photometric studies”, which is indeed the case for NGC4151 where the underlying mass distribution is only a mild oval distortion (Bosma et al.,"
" 1977: Arp. 1977): the ""sharp bend. of the bar into spiral arms” which is evident in the HE image of NOGC4151 (Alundell ct ab."," 1977; Arp, 1977); the “sharp bend of the bar into spiral arms” which is evident in the HI image of NGC4151 (Mundell et al.,"
" 1998). and. ""gas streaming along the bar (sce Section 3)."," 1998), and “gas streaming along the bar” (see Section 3)."
 However. the amount of neutral hydrogen present in the oval region (central 3.3s2.4) of NGCAI5I is unusually high. compared. with other early tvpe barred spirals (e.g. Roberts et al.," However, the amount of neutral hydrogen present in the oval region (central $3.3' \times 2.1'$ ) of NGC4151 is unusually high compared with other early type barred spirals (e.g. Roberts et al.,"
 1979: Regan et al..," 1979; Regan et al.,"
. 1996)., 1996).
 Optical photometry of the outer. spiral structure (Simkin. 1975) found a major axis position angle of 26 and an inclination of 21.," Optical photometry of the outer spiral structure (Simkin, 1975) found a major axis position angle of $\sim$ $^{\circ}$ and an inclination of $^{\circ}$."
 Similarly. Peclar et al.," Similarly, Pedlar et al.,"
 reported thatthe overall LIL velocity field of NCCHI51 was approximately consistent with circular rotation and an inclination of 21 for the galaxy: a change in position angle of the line of nodes in the oval region. however. indicated the presence of non-circular motions.," reported thatthe overall HI velocity field of NGC4151 was approximately consistent with circular rotation and an inclination of $^{\circ}$ for the galaxy; a change in position angle of the line of nodes in the oval region, however, indicated the presence of non-circular motions."
" Pheir observations also sugeested structure in the oval but were limited by angular resolution (717""« 22"") and the strong central absorption feature.", Their observations also suggested structure in the oval but were limited by angular resolution $\sim17'' \times 22''$ ) and the strong central absorption feature.
 They detected regions of high LIL concentration (Nw M15 107 7) inthe north-west and south-cast regions of the bar which appeared to be small spiral arms. with their concave edges facing toward the major axis of the bar (see Section 3.2).," They detected regions of high HI concentration $_H$ $\sim$ 1.5 $\times$ $^{21}$ $^{-2}$ ) in the north-west and south-east regions of the bar which appeared to be small spiral arms, with their concave edges facing toward the major axis of the bar (see Section 3.2)."
" Ifa uniform circular disc is viewed at. some inclination. i. to the line of sight it appears as an ""oval. with a axis. a. and semi-münor axis of (b = a cos i)."," If a uniform circular disc is viewed at some inclination, i, to the line of sight it appears as an `oval', with a semi-major axis, a, and semi-minor axis of (b = a cos i)."
 In the dise is rotating. the tilting of the disc will result in an observed radial velocity field where the zero velocity (or line of constant/svstemic velocity or kinematic minor axis) lies along the spatial minor axis. b. In NGCAISL. the central region is also oval but. the iso-velocity contours are very. cillerent compared. to those expected from an inclined circularly rotating disc.," If the disc is rotating, the tilting of the disc will result in an observed radial velocity field where the zero velocity (or line of constant/systemic velocity or kinematic minor axis) lies along the spatial minor axis, b. In NGC4151, the central region is also oval but the iso-velocity contours are very different compared to those expected from an inclined circularly rotating disc."
 The iso-velocity contours are elongated. the oval. indicating he presence of significant deviations from circular motion.," The iso-velocity contours are elongated the oval, indicating the presence of significant deviations from circular motion."
 'rendergast (1983) points out that. in barred. galaxies. the gas response leads the bar and so the larger the angle oween the eas (or kinematic) major axis ancl the bar (spatial) major axis. the weaker the bar.," Prendergast (1983) points out that, in barred galaxies, the gas response leads the bar and so the larger the angle between the gas (or kinematic) major axis and the bar (spatial) major axis, the weaker the bar."
 For. NGCALSL. assuming the bar lies in the plane of the galaxy ancl taking he average PA of the [ine of nodes in the bar to be 28(Muncdell et al..," For NGC4151, assuming the bar lies in the plane of the galaxy and taking the average PA of the line of nodes in the bar to be $^{\circ}$(Mundell et al.,"
 1998). this angle is 772. (Le. the kinematic major axis lies almost on the spatial minor axis). indicating," 1998), this angle is $\sim$ $^{\circ}$ , (i.e., the kinematic major axis lies almost on the spatial minor axis), indicating"
the V I bands.,the V I bands.
 We overplotted the errors for all five fields. since the cata were obtained with the same (or similar) exposure times and have similar properties.," We overplotted the errors for all five fields, since the data were obtained with the same (or similar) exposure times and have similar properties."
 We have no a priori knowledge of the star-formation history (SEL) o£ CLUVCs., We have no a priori knowledge of the star-formation history (SFH) of CHVCs.
" CLIVCs could have just started to form stars. and then their CALDs would exhibit nothing but the ""blue plume”."," CHVCs could have just started to form stars, and then their CMDs would exhibit nothing but the “blue plume""."
 This seems somewhat unlikely given the non-detection of stellar content. on. survey. plates., This seems somewhat unlikely given the non-detection of stellar content on survey plates.
 LE CIIVCS started to form stars more than a Gyr ago. thew CMDs should exhibit the cred plume”.," If CHVCs started to form stars more than a Gyr ago, their CMDs should exhibit the “red plume""."
 Indeed. the cwarl galaxies of the Local Group. which experienced a variety of SELL. always show stars on the red. plume.," Indeed, the dwarf galaxies of the Local Group, which experienced a variety of SFHs, always show stars on the red plume."
 The CALDs of Local Group cwarfs exhibit either the red. plume only (dSph). a weak blue plume as well as a red. plume (clLir/dSph). or a strong blue plume combined with a red plume (dli).," The CMDs of Local Group dwarfs exhibit either the red plume only (dSph), a weak blue plume as well as a red plume (dIrr/dSph), or a strong blue plume combined with a red plume (dIrr)."
 οσο morphologics serve as a guide to our exploration of ονο CMDs., These morphologies serve as a guide to our exploration of CHVC CMDs.
 We display in Figure 4 the V-L I] CMD of the transition αςαρ galaxy. Phoenix.," We display in Figure 4 the [V-I, I] CMD of the transition dIrr/dSph galaxy Phoenix."
" The observations were obtained with the VEEP UT2. ""IXOYIEN and FORS2 under good secing conditions."," The observations were obtained with the VLT UT2 “KOYEN"" and FORS2 under good seeing conditions."
 Phe exposure times were 3 300s each. in V and Lb. Phe data were reduced. and single-star photometry applied in the same wav. as described above for the CLIVCS.," The exposure times were 3 $\times$ 300s each, in V and I. The data were reduced, and single-star photometry applied in the same way, as described above for the CHVCs."
 We measure a EWILM in V of 07554. and in L of 0777.," We measure a FWHM in V of 54, and in I of 7."
 Ehe total number of stars detected in. V. and Eis S780. much higher iui in anv of the. CIIVC. fields.," The total number of stars detected in V and I is 8780, much higher than in any of the CHVC fields."
 Phe DAOPLIOT photometric errors are. clisplavecl in Figure 5. in order to emphasise that the quality of these cata is similar to that of the CLIVC data sets.," The DAOPHOT photometric errors are displayed in Figure 5, in order to emphasise that the quality of these data is similar to that of the CHVC data sets."
 Phoenix. is located at. high Galactic latitude. near 69°.," Phoenix is located at high Galactic latitude, near $^o$."
 Phe foreground contamination and extinction are small., The foreground contamination and extinction are small.
 H has a distance modulus of about 23.25 (Mateo. 1998) or a distance of about 450 Ixpc., It has a distance modulus of about 23.25 (Mateo 1998) or a distance of about 450 Kpc.
 The CALD of Phoenix shows why it is classed as having a mixed morphology: it exhibits both a blue. plume of relatively voung stars. and a red plume which includes the ROB.," The CMD of Phoenix shows why it is classed as having a mixed morphology: it exhibits both a blue plume of relatively young stars, and a red plume which includes the RGB."
 The stellar distributions on the CALDs of the CLVCs are quite dilferent from that of known Local Group carts., The stellar distributions on the CMDs of the CHVCs are quite different from that of known Local Group dwarfs.
 The morphology of the CLIVC CALDs does not reveal cither of the two plumes., The morphology of the CHVC CMDs does not reveal either of the two plumes.
 Instead. the CALDs of the CLIVCs are reminiscent of other. deep HIST. pointings into the clisk and halo of our Galaxy (e... Richer et al.," Instead, the CMDs of the CHVCs are reminiscent of other, deep HST pointings into the disk and halo of our Galaxy (e.g., Richer et al."
 2002)., 2002).
 We overplotted on Fig., We overplotted on Fig.
 1 theoretical isochrones from the database of Girardi et al. (, 1 theoretical isochrones from the database of Girardi et al. (
2000) for ages of LO and 100 Myr. and for 1 and 10 Civr.,"2000) for ages of 10 and 100 Myr, and for 1 and 10 Gyr."
 We adopted a metallicity of 1/5 of Solar. as cwarft galaxies tend to have sub-Solar metallicities.," We adopted a metallicity of 1/5 of Solar, as dwarf galaxies tend to have sub-Solar metallicities."
 1n general. the elfect of varving metallicity at a given age is that more metal-poor isochrones shift to bluer V-I colors. while more metal-rich ones show redder colors.," In general, the effect of varying metallicity at a given age is that more metal-poor isochrones shift to bluer V-I colors, while more metal-rich ones show redder colors."
" This shift in minimal for the voung"" isochrones (e.g.. 10 LOO Myr). but noticable for the ""old"" isochrones (1 10 Cyr)."," This shift in minimal for the “young"" isochrones (e.g., 10 100 Myr), but noticable for the “old"" isochrones (1 10 Gyr)."
 We show the set with a metallicity of 1/5 of Solar because the 1 10 Gyr isochrones have sullicicntly rec colors to encompass the data clistribution., We show the set with a metallicity of 1/5 of Solar because the 1 10 Gyr isochrones have sufficiently red colors to encompass the data distribution.
 When comparing the data with the “voung™ isochrones. we notice there are virtually no stars observed with V-l< 1. where we expect to find a voung population.," When comparing the data with the “young"" isochrones, we notice there are virtually no stars observed with $<$ 1, where we expect to find a young population."
 This emphasises the absence of young MS and blue supergiant stars in the CLIVCs., This emphasises the absence of young MS and blue supergiant stars in the CHVCs.
 The brightest’ evolutionary phase of stars with ages larger than about one Civr occurs on the red eiant. branch., The brightest evolutionary phase of stars with ages larger than about one Gyr occurs on the red giant branch.
 Furthermore. the PROB. at M; of 4. is a well calibrated distance indicator (Lee. Freedman Madore 1983). and at a distance of 1 Alpe. it would appear at Iz221.," Furthermore, the TRGB, at $_I$ of –4, is a well calibrated distance indicator (Lee, Freedman Madore 1983), and at a distance of 1 Mpc, it would appear at $\approx$ 21."
 We overplotted on Fig., We overplotted on Fig.
 1 theoretical isochrones with ages of 1 ancl LO Cie., 1 theoretical isochrones with ages of 1 and 10 Gyr.
 Note that the Cirardi et al., Note that the Girardi et al.
 isochrones extend. above the RGB into the thermally pulsing ACB phase., isochrones extend above the RGB into the thermally pulsing AGB phase.
 A PROB would have been detected for the entire metallicity range appropriate for cwarl galaxies. to L magnitudes of at least 22.5. or to a distance of up to 2 Alpe. in the four CIIVCS whose CMDs are shown in Fig.," A TRGB would have been detected for the entire metallicity range appropriate for dwarf galaxies, to I magnitudes of at least 22.5, or to a distance of up to 2 Mpc, in the four CHVCs whose CMDs are shown in Fig."
 1., 1.
 Notice that the absence of stars with V-E« 1 rules out extremely metal-poor ICDs. which can be observed in dwarf Spheroidal galaxies.," Notice that the absence of stars with $<$ 1 rules out extremely metal-poor RGBs, which can be observed in dwarf Spheroidal galaxies."
 Since no ROB is obvious. a straightforward conclusion is that there is none. and that these objects are not faint galaxies within the Local Group.," Since no RGB is obvious, a straightforward conclusion is that there is none, and that these objects are not faint galaxies within the Local Group."
 The absence of a PROB with Lz21 suggests the hypothesis hat LIIPASS J1712-64 is a faint cwarl ealaxy of the Local Group is similarly unliklev., The absence of a TRGB with $\leq$ 21 suggests the hypothesis that HIPASS J1712-64 is a faint dwarf galaxy of the Local Group is similarly unlikley.
 To illustrate the expected ocations of RGDs in our data if ΤΗΑΡ 1712-64 were at à distance of 3.2 Alpe as proposed by Ixilborn et al. (, To illustrate the expected locations of RGBs in our data if HIPASS J1712-64 were at a distance of 3.2 Mpc as proposed by Kilborn et al. (
2000). we overplotted in Fig.,"2000), we overplotted in Fig."
 2 the shifted Globular Cluster ridgelines rom da Costa ArcmandrolT (1990) of M 15. Fe/11]—-2.17. GO 6397. 21.91. NL 2. -1.58. NGC 6752. -1.54. NGC 1551. -1.29. and 47 Tuc. -0.71.," 2 the shifted Globular Cluster ridgelines from da Costa Armandroff (1990) of M 15, [Fe/H]=-2.17, NGC 6397, -1.91, M 2, -1.58, NGC 6752, -1.54, NGC 1851, -1.29, and 47 Tuc, -0.71."
 Even i£ HIDPASS J1712-64 were as ar as 3.2 Mpe. with a corresponding PROB I-magnitude of 23.5. we could. have detected. it if its metallicity were ow enough. although this is clearly at the very limit. of our data.," Even if HIPASS J1712-64 were as far as 3.2 Mpc, with a corresponding TRGB I-magnitude of 23.5, we could have detected it if its metallicity were low enough, although this is clearly at the very limit of our data."
 Lewis et al. (, Lewis et al. (
2002) recently presented. single-star whotometry obtained under sub-aresee secing conditions in a 0755 [field of view centered at 17 12 35.7. 64 38 12 J2000) and reaching magnitudes fainter than r—24 and e=25.,"2002) recently presented single-star photometry obtained under sub-arcsec seeing conditions in a $\times$ 5 field of view centered at 17 12 35.7, –64 38 12 (J2000) and reaching magnitudes fainter than r=24 and g=25."
 They. too. Failed to detect an obvious stellar content associated with LIEPASS J1712-64.," They, too, failed to detect an obvious stellar content associated with HIPASS J1712-64."
 Furthermore. they rule out any uncderlving unresolved dilfuse components within their large field of view to deep surface-brightness limits.," Furthermore, they rule out any underlying unresolved diffuse components within their large field of view to deep surface-brightness limits."
 We can set upper limits on the non-detection of a possible οΝΟ stellar. population in the VET/FORS data. by constructing CALDs and luminosity functions (LE) with ποσο sub-populations.," We can set upper limits on the non-detection of a possible CHVC stellar population in the VLT/FORS data, by constructing CMDs and luminosity functions (LF) with added sub-populations."
" This is accomplished by using the VLT FORS2 observation of Phoenix obtained. under very similar conditions and with similar photometric limits. as a template stellar population with which we 7contaminate"" the observed. CLIVCG CMDs."," This is accomplished by using the VLT FORS2 observation of Phoenix obtained under very similar conditions and with similar photometric limits, as a template stellar population with which we “contaminate"" the observed CHVC CMDs."
 We added: Phoenix stars to the IVC οος at their location in the Phoenix €MD., We added Phoenix stars to the HVC CMDs at their location in the Phoenix CMD.
 ln other words. we added," In other words, we added"
during the day. even on days when the general RFI level should be quite low (e.g.. the Easter holiday).,"during the day, even on days when the general RFI level should be quite low (e.g., the Easter holiday)."
 Dipoles deployed at ground level should suppress RFI sources located near the horizon and should enable more sensitive RRL (Ellingson2009). (Kogan&," Dipoles deployed at ground level should suppress RFI sources located near the horizon and should enable more sensitive RRL \citep{ellingson09}. \citep{kc09},"
Cohen.2009)... 4— 5c 107 The Η15>265(115MHz «v190MHz). (Payneetal..1959).," \ref{tab:lwadetect} $5\sigma$ $10^{-3}$ The $11.5> z > 6.5$ $115\,\mathrm{MHz}
< \nu < 190\,\mathrm{MHz}$ \citep{1989ApJ...341..890P}."
" 1077 21"" ?2))", $10^{-3}$ $21^{\mathrm{st}}$ \ref{sec:cosmo})
" 1077 21"" ?2)).", $10^{-3}$ $21^{\mathrm{st}}$ \ref{sec:cosmo})
Since the advent. of high qualiy CCDs there has been a great deal of effort to obtain (inillimagnuitude. or less than 15€)) time-series. optical aud infrared photometry lor laree uumbers of stars.,"Since the advent of high quality CCDs there has been a great deal of effort to obtain high-precision (millimagnitude, or less than ) time-series, optical and infrared photometry for large numbers of stars."
 Photometry at te inillimagnitude leve of precision is considered a prerequisite in searches [or trausiting Jupiter-sized planets arouud sdlar-type stars., Photometry at the millimagnitude level of precision is considered a prerequisite in searches for transiting Jupiter-sized planets around solar-type stars.
 As a result. the number oL groups that have achieved. this level of precisiou is oo mauy to list here (see for example Horne2003 for a list of trausitit& planet searches).," As a result, the number of groups that have achieved this level of precision is too many to list here (see for example \citealt{horne03} for a list of transiting planet searches)."
 Tie search [or transiting planets has uot been in vain: at the time of writing there are 7 known ransitiug planets. 6 of which were first identiliel photometrically (see e.g. Udalskietal.2001 αιd Ixouackietal. 2004)).," The search for transiting planets has not been in vain; at the time of writing there are 7 known transiting planets, 6 of which were first identified photometrically (see e.g. \citealt{udalski04}
 and \citealt{konacki04}) )."
 Milliniagnuitude photometry bas also contributed to the study of stars near the hydrogen fusion limit, Millimagnitude photometry has also contributed to the study of stars near the hydrogen fusion limit
especially near (he centre of the svstem.,especially near the centre of the system.
 Of course the svstem may not be fully relaxed when the black hole is growing., Of course the system may not be fully relaxed when the black hole is growing.
" Results are shown in Figure 1. [or black hole masses from zero through 0.001. 0.01. 0.1 and 1.0 as labelled by increasing, effect."," Results are shown in Figure \ref{fig:iso} for black hole masses from zero through $0.001$ , $0.01$, $0.1$ and $1.0$ as labelled by increasing effect."
 These dimensionless masses correspond to plivsical masses in the range of about 10* to LOM AL. if we use (he values of py and ry given in section yoQu., These dimensionless masses correspond to physical masses in the range of about $10^7$ to $10^{10}$ $M_{\odot}$ if we use the values of $\rho_0$ and $r_0$ given in section \ref{sec:growth}.
 We find the same characteristic density cusp of 2/7?> as obtained by Young(1980).. and the radial velocity profiles are also similar.," We find the same characteristic density cusp of $R^{-3/2}$ as obtained by \citet{you80}, and the radial velocity profiles are also similar."
 Although Young(L980) did not show results for the anisotropy parameter. defined as 3=1—<Vg>/«2Vg9>. our results do agree with the prediction of Quinlanefaf(1995). lor distributions of this (wpe.," Although \citet{you80} did not show results for the anisotropy parameter, defined as $\beta = 1 - <V_T^2> / <2 V_R^2>$, our results do agree with the prediction of \citet{qui95} for distributions of this type."
 We observe that (here is at most about a 106 anisotropy in favour of tangential motion. due to the increasing binding energv of a particle aud the resultant decrease in eccentricity al constant. angular momentum.," We observe that there is at most about a $10$ anisotropy in favour of tangential motion, due to the increasing binding energy of a particle and the resultant decrease in eccentricity at constant angular momentum."
 Moreover (he perturbation extends as far as the core radius only when (he mass is comparable to that of the core. as is to be expected.," Moreover the perturbation extends as far as the core radius only when the mass is comparable to that of the core, as is to be expected."
 These results are (he main (test of our progralni., These results are the main test of our program.
 We explore here the aclabatic growth of a central black hole in a collisionless dark matter halo that possesses a central cusp., We explore here the adiabatic growth of a central black hole in a collisionless dark matter halo that possesses a central cusp.
 For initial svstems. we choose (wo very dillerent starting points.," For initial systems, we choose two very different starting points."
 The first is an isotropic sell-similar svstem. meant (o represent the final state of a halo undergoing self-similar relaxation (Ilenriksen&Widrow1995).," The first is an isotropic self-similar system, meant to represent the final state of a halo undergoing self-similar relaxation \citep{hen95}."
. The other svstem is the NEW system of Navarro.Frenk&White(1996).. which fits a wide range of dark matter halo sizes.," The other system is the NFW system of \citet{nav96}, which fits a wide range of dark matter halo sizes."
 The self-similar svstem is described by the DF where 6 is a[ree parameter (2/3<901.0> 1) that essentially controls (he logarithmic slope of the initial density and potential. given by," The self-similar system is described by the DF where $\delta$ is afree parameter $2/3 < \delta < 1,\ \delta > 1$ ) that essentially controls the logarithmic slope of the initial density and potential, given by"
"keV band is 9.241012P cre 1 "" ↸⊳⋯−↸⊳∪↥⋅↥⋅↸∖↴∖↴↻∪↕∐∐∐∶↴∙↑∪⋅⋝ a huninosty of L1 « 10/9 ere |.",keV band is $\times10^{-12}$ erg $^{-1}$ $^{-2}$ corresponding to a luminosity of 1.1 $\times$ $^{40}$ erg $^{-1}$.
 The contribulon of t1 power-law component. the thermal black body coll)OLnont. aud the thermal thin plasma comiponenu to the total O.3-8.0 keV flux are 77C. 16% aud respectiveY.," The contribution of the power-law component, the thermal black body component, and the thermal thin plasma component to the total 0.3-8.0 keV flux are 77, 16 and, respectively."
 However. a longer EPIC-PN exposure Is nieed to discutangle a possible extended ticrinal thin plasnua ficun the »)ut-like power-law and thermal tick plasna couponenuts.," However, a longer EPIC-PN exposure is needed to disentangle a possible extended thermal thin plasma from the point-like power-law and thermal thick plasma components."
 Tle spectral analysis of the combined NAAI data has coufirmed two spectral compoucuts in Toll N-1., The spectral analysis of the combined XMM data has confirmed two spectral components in HoII X-1.
 The hare COLL2011011 is best described by a powerlaw (D~ 2.6). aud the soft component is fitted by thermal nodels with relatively ow temperatures (AL~0.110.22 keV).," The hard component is best described by a powerlaw $\Gamma\sim2.6$ ), and the soft component is fitted by thermal models with relatively low temperatures $kT\sim0.14-0.22$ keV)."
 The intrinsic N-rav ΠΟ ΕΕΠΠ isotroplic emission) is about H9 oye tin the 0.3-8.0 keV band, The intrinsic X-ray luminosity (assuming isotrophic emission) is about $^{40}$ erg $^{-1}$ in the 0.3-8.0 keV band.
" Before we discuss the nature of the ultraluminuots Νταν source ΠΟ N-1 we stuuarize our resits: There are three niodels for ULX extensively discussed in the literature: 1) ULX 1iuav be black holes of “normal” stellar masses (~ LOAL. ) in binaries. which accrete gas in a supercritical ποσο,"," Before we discuss the nature of the ultraluminous X-ray source HoII X-1 we summarize our results: There are three models for ULX extensively discussed in the literature: i) ULX may be black holes of ”normal” stellar masses $\sim 10$ $_{\sun}$ ) in binaries, which accrete gas in a supercritical regime."
 They are 33-like objects or mücroquasars m their transicut activity staCs. Wwrose hard radiation can be collimated (and heaued) along Jes ancl accretion cisks axes (Fabrika Moeschervakov. 012001.. Iàiug et al. 20013).," They are 433-like objects or microquasars in their transient activity states, whose hard radiation can be collimated (and beamed) along jets and accretion disks axes (Fabrika Mescheryakov, \cite{Fa01}, King et al., \cite{Ki01}) )."
 i) ULX may be black holes wihi ew tens of soar Wass (~ LOAD: ) and that heir ταν enidesbons ds from the disk shining at super-Eddiieton Iuuinosities (Beecluan 20023)., ii) ULX may be black holes with few tens of solar mass $\sim 10$ $_{\sun}$ ) and that their X-ray emissions is from the disk shining at super-Eddington luminosities (Begelman \cite{Beg02}) ).
 The slim disk luocl (A»yenmowiez ct al. 1988..," The slim disk model (Abramowicz et al. \cite{Abra88},"
 Ebisawa et al. 20033) , Ebisawa et al. \cite{Ebi03}) )
alows to explain the observed super-Eddineton hunuinosity. hard A-rav spectra and spectral variations.," allows to explain the observed super-Eddington luminosity, hard X-ray spectra and spectral variations."
 ii) The ULN may be iuteriiediate mass black holes (IMBUs). ~ 107M; (€'olbert Mushotzky 19993). which were formed from the very first stars (Aladau Rees 20013) or in globular clusters (Miller ILuuiltou 2002)).," iii) The ULX may be intermediate mass black holes (IMBHs), $\sim 10^3$ $_{\sun}$ (Colbert Mushotzky \cite{Col99}) ), which were formed from the very first stars (Madau Rees \cite{Mad01}) ) or in globular clusters (Miller Hamilton \cite{Mil02}) )."
 The IMDBII could. acciTo eas frou a close companion or even from the interstellar medium aud become bright XPav SOULCCS when they are in dense Bas environments., The IMBH could accrete gas from a close companion or even from the interstellar medium and become bright X--ray sources when they are in dense gas environments.
 Spectra of some ULX (Miller et al. 20033) , Spectra of some ULX (Miller et al. \cite{Mil03}) )
support the idea that they ave IMDITs., support the idea that they are IMBHs.
We call sources “trausicuts” when the iutrinsic duration of UIIECR production at a source 07 is shorter than the characteristic time profile spread. τς) at the observed euergv of £.,"We call sources ""transients"" when the intrinsic duration of UHECR production at a source $\delta T$ is shorter than the characteristic time profile spread $\tau(E)$ at the observed energy of $E$."
 Itf the time dispersion is longer thaw the time scale of UITECT. observatious. we nüsperceive that ΤΕΠΟ bursts ave steady sources. aud therefore can define the “apparent” number density of UITECR sources DUE).," If the time dispersion is longer than the time scale of UHECR observations, we misperceive that UHECR bursts are steady sources, and therefore can define the ""apparent"" number density of UHECR sources $n_s(E)$."
" The source muuber deusity is related to the rate of UIIECR bursts p, as The source nuuber deusitv generally depends on UIIECR cnereies. since the apparent duration is dependent on cucreics explicitly."," The source number density is related to the rate of UHECR bursts $\rho_s$ as The source number density generally depends on UHECR energies, since the apparent duration is dependent on energies explicitly."
| UIIECTs observed at the Earth suffer from the GME and EGAIFs embedding their sources., UHECRs observed at the Earth suffer from the GMF and EGMFs embedding their sources.
The GME typically as order of pO for a disk component. aud it also hasrandom and halo components.,"The GMF typically has order of $\mu {\rm G}$ for a disk component, and it also hasrandom and halo components."
" In principle. p, cau be estimated by equation (6)) if the time spread. by these Ποια» and the ECAIF in voids can be well estimated."," In principle, $\rho_s$ can be estimated by equation \ref{eq:estrate}) ) if the time spread by these fields and the EGMF in voids can be well estimated."
 However. the ECGME in voids is lighly uncertain as discussed in the last subsection. but could contribute o the total time spread significantly because of large xopagation distance compared to the size of Galactic space and the magnetic structures around sources.," However, the EGMF in voids is highly uncertain as discussed in the last subsection, but could contribute to the total time spread significantly because of large propagation distance compared to the size of Galactic space and the magnetic structures around sources."
 This uucertainty leads to a finite range of allowed values of py., This uncertainty leads to a finite range of allowed values of $\rho_s$.
 Given inevitable contributions of the CME aud ECGMES clubedding UITECT. sources to the apparent duration. TZuinCE). aud the allowed maximal time spread incliding the contribution from the poorly known EGALIF iu voids. ΤικE). the rate of UITECT bursts is linuted as Tere. Ες). cau be. i principle. estimated from. anisotropy iu the arrival distribution of VITECRs2009).. assuming that the time spread is loneer than the VITECR observation timescale.," Given inevitable contributions of the GMF and EGMFs embedding UHECR sources to the apparent duration, $\tau_{\rm min}(E)$, and the allowed maximal time spread including the contribution from the poorly known EGMF in voids, $\tau_{\rm max}(E)$, the rate of UHECR bursts is limited as Here, $n_s(E)$ can be, in principle, estimated from anisotropy in the arrival distribution of UHECRs, assuming that the time spread is longer than the UHECR observation timescale."
" However, one should keep in munud that equation (6)) is valid when cach UITECR. burst. can be inclividually identified as a burst2009)."," However, one should keep in mind that equation \ref{eq:estrate}) ) is valid when each UHECR burst can be individually identified as a burst."
. If more than one bursts or flares occurring in au angular patch contribute to UMECRs observed in the same time-window. ie. the time profiles of two independent CHECR bursts from the same direction (within the size of the augular patch) are overlapped at the Earth. equation (6)) cannot be used as it is.," If more than one bursts or flares occurring in an angular patch contribute to UHECRs observed in the same time-window, i.e., the time profiles of two independent UHECR bursts from the same direction (within the size of the angular patch) are overlapped at the Earth, equation \ref{eq:estrate}) ) cannot be used as it is."
 Therefore. one has to focus on CUECRs with higher energies to exaiine cases where 7(£) is shorter than the appareut time interval between bursts or flares occurring in the same aneular patch. AT.," Therefore, one has to focus on UHECRs with higher energies to examine cases where $\tau(E)$ is shorter than the apparent time interval between bursts or flares occurring in the same angular patch, $\Delta T$."
 In reality. UHECRs have finite deviation angles due to cosinic magnetic fields. so UIIECTs from a source arrives within a finite solid augle AQ=we? around the source. which can be regarded as the appropriate size of the finite augular patch.," In reality, UHECRs have finite deviation angles due to cosmic magnetic fields, so UHECRs from a source arrives within a finite solid angle $\Delta \Omega = \pi \psi^2$ around the source, which can be regarded as the appropriate size of the finite angular patch."
 For a given py. the apparent tine interval between bursts in the region of the sky with AQ is estimated to be where 0s=/5?aud pay=pQ/109 Cpe% t.," For a given $\rho_s$, the apparent time interval between bursts in the region of the sky with $\Delta \Omega$ is estimated to be where $\psi_5 \equiv \psi / 5^{\circ}$and $\rho_{s,0} = \rho_s / 10^0$ $^{-3}$ $^{-1}$."
 Wo ake the typical positional correlation scale as ος and mse c005? as a reference choice. which correspouds o Boch’?<2 ut Mpc/7.," We take the typical positional correlation scale as $\psi$, and use $\psi \sim 5^{\circ}$ as a reference choice, which corresponds to $B_{\rm eff} {\lambda_{\rm eff}}^{1/2} \lesssim 2$ nG $^{1/2}$."
 This is reasonable. since lis is consistent with the effective. EGAIFs estimated in the last subsection and a current upper limit of the void EGAIF from a plausible cosmological model is 2.5 we for Ay=1 Ape2010).. but more conservative discussions with larger values of c are also possible.," This is reasonable, since this is consistent with the effective EGMFs estimated in the last subsection and a current upper limit of the void EGMF from a plausible cosmological model is 2.5 nG for $\lambda_{\rm v} = 1$ Mpc, but more conservative discussions with larger values of $\psi$ are also possible."
 Equation (8)) imuplies that a smaller AQ gives areer AT. but AT should be limited to the burst/flare intermittence m a host galaxy. zΠρι. where ny is the iiuber density of host galaxies of UITECR sources.," Equation \ref{eq:deltat}) ) implies that a smaller $\Delta \Omega$ gives larger $\Delta T$, but $\Delta T$ should be limited to the burst/flare intermittence in a host galaxy, $\approx n_h/\rho_s$, where $n_h$ is the number density of host galaxies of UHECR sources."
" Iu other words. AQ smaller than the corresponding lower Πιτ is meanineless, at which one host galaxy should exist in a volume with a solid angle AQ within {ως1)."," In other words, $\Delta \Omega$ smaller than the corresponding lower limit is meaningless, at which one host galaxy should exist in a volume with a solid angle $\Delta \Omega$ within $D_{\rm max}(E)$."
 We call the case “bursting case” that only one burst or flare contributes to arviving UIIECTis at a time in a direction. Le. TLE)AT.," We call the case ""bursting case"" that only one burst or flare contributes to arriving UHECRs at a time in a direction, i.e., $\tau(E) < \Delta T$."
 Then. the requirement TE)<AT gives a sufficient coucition to apply equation (6)). which leads to with the usage of equation (6)).," Then, the requirement $\tau(E) < \Delta T$ gives a sufficient condition to apply equation \ref{eq:estrate}) ), which leads to with the usage of equation \ref{eq:estrate}) )."
 As demonstrated in Figure 2.. the range of (CE). in which equation (6)) can be applied. is extended to larger κ1) at higher energies. because the aller nunmiber of sources contributiug to the observed flux. decreases the probability that two bursts are temporally overlapped in a region of the skv (see also equation (8))).," As demonstrated in Figure \ref{fig:nlim}, the range of $n_s(E)$ , in which equation \ref{eq:estrate}) ) can be applied, is extended to larger $n_s(E)$ at higher energies, because the smaller number of sources contributing to the observed flux decreases the probability that two bursts are temporally overlapped in a region of the sky (see also equation \ref{eq:deltat}) ))."
" Thus. we especially focus. on cases of E~10°"" eV to demonstrate constrünts on psu Sections 3. and L. although discussions are general for other E."," Thus, we especially focus on cases of $E \sim {10}^{20}$ eV to demonstrate constraints on $\rho_s$ in Sections \ref{prop} and \ref{results}, although discussions are general for other $E$."
 Note that. although we here fix e even at higher enereies. stualler values of c are expected there. so that the extension of the curve to higher enereies would be more casily justified.," Note that, although we here fix $\psi$ even at higher energies, smaller values of $\psi$ are expected there, so that the extension of the curve to higher energies would be more easily justified."
" Ou the other haud. if τε)>AT. another UITECR burst may start to contribute before the eud of the former CHECR burst is observed. aud equation (8)) nuplies. Since n4CE) can be determined by the auto-correlation analysis. equation (6)) enables us to estimate p, from observational quantities. if TLE) cau be evaluated by ECAIF simulations aud observations."," On the other hand, if $\tau(E) > \Delta T$, another UHECR burst may start to contribute before the end of the former UHECR burst is observed, and equation \ref{eq:deltat}) ) implies, Since $n_s(E)$ can be determined by the auto-correlation analysis, equation \ref{eq:estrate}) ) enables us to estimate $\rho_s$ from observational quantities, if $\tau(E)$ can be evaluated by EGMF simulations and observations."
 Iuportautly. 7.2) has the characteristic energv dependence. which is demonstrated in Figure 2..," Importantly, $n_s(E)$ has the characteristic energy dependence, which is demonstrated in Figure \ref{fig:nlim}."
 Here. the case that oulv the ECAIF in filamentary structures affects the time spread of VITZECR bursts is considered for demonstration. 1.6.. Bade?~03 ας: P.," Here, the case that only the EGMF in filamentary structures affects the time spread of UHECR bursts is considered for demonstration, i.e., $B_{\rm eff} {\lambda_{\rm eff}}^{1/2} \sim 0.3$ nG $^{-3}$ ."
" Two represeutative cases for p, are shown. Lo. p,=1  yrt and 10? ? lo "," Two representative cases for $\rho_s$ are shown, i.e., $\rho_s = 1$ $^{-3}$ $^{-1}$ and $10^2$ $^{-3}$ $^{-1}$ ."
One sees that n.(E) changes by more than one order of magnitude when £ increases by the cubic root of ten., One sees that $n_s(E)$ changes by more than one order of magnitude when $E$ increases by the cubic root of ten.
 This mieaus that anisotropy features are different among energies., This means that anisotropy features are different among energies.
 Thus. observations of UITEC's above 107 eX. are crucial to identify this tendency clearly.," Thus, observations of UHECRs above $10^{20}$ eV are crucial to identify this tendency clearly."
 Future CIECRexperiments with huge exposures may, Future UHECRexperiments with large exposures may
"To acquire precise O-isotope data for Iris. we developed a sample mount consisting of an Al round. which supported the potted butt at a fixed altitude. covered by an Al annulus which both supported a 500nm-thick membrane (made of gold-coated S1; N, with a 3800s ion-millecl hole) and incorporated polished standards surrounding the central hole.","To acquire precise O-isotope data for Iris, we developed a sample mount consisting of an Al round, which supported the potted butt at a fixed altitude, covered by an Al annulus which both supported a 500nm-thick membrane (made of gold-coated $_3$ $_4$ with a $\mu$ m ion-milled hole) and incorporated polished standards surrounding the central hole."
 San Carlos olivine was used to standardize Iris olivine. ancl Mivakajima plagioclase and Burma. spinel were used to standardize Iris mesostasis ancl chromite. respectively.," San Carlos olivine was used to standardize Iris olivine, and Miyakajima plagioclase and Burma spinel were used to standardize Iris mesostasis and chromite, respectively."
 We measured three oxvgen isotopes in Iris using the University of Hawaii Cameca inis 1280 ion microprobe in multicollection mode (!O on a Faraday cup. YO and PO on electron multipliers).," We measured three oxygen isotopes in Iris using the University of i Cameca ims 1280 ion microprobe in multicollection mode $^{16}$ O on a Faraday cup, $^{17}$ O and $^{18}$ O on electron multipliers)."
 A 2530 pA primary ion beam was focused to ~2 jan to allow for analvsis of Iris., A 25–30 pA $^{+}$ primary ion beam was focused to $\sim$ 2 $\mu$ m to allow for single-grain analysis of Iris.
 The data was corrected for background. deacltime. detector vield. and interference from MOLL to FO (typically <0.2%.).," The data was corrected for background, deadtime, detector yield, and interference from $^{16}$ $^{-}$ to $^{17}$ O (typically $<$ $\permil$ )."
 We corrected measured compositions of (he mineral phases in Iris for instrumental mass fractionation by comparing wilh appropriate mineral standards of known composition., We corrected measured compositions of the mineral phases in Iris for instrumental mass fractionation by comparing with appropriate mineral standards of known composition.
 We measured (he oxvgen isotopic composition ol San Carlos olivine mounted analogously to Iris in order (ο understand instrumental mass fractionation associated with the mounting of the unknown sample relative to (he standards., We measured the oxygen isotopic composition of San Carlos olivine mounted analogously to Iris in order to understand instrumental mass fractionation associated with the mounting of the unknown sample relative to the standards.
 We found (that there was a reproducible instrumental fractionation effect between (he San Carlos olivine surrounding the central hole and the San Carlos olivine in the central hole (the center olivine plotted ος lower in 0O than the surrounding olivine along the terrestrial fractionation line)., We found that there was a reproducible instrumental fractionation effect between the San Carlos olivine surrounding the central hole and the San Carlos olivine in the central hole (the center olivine plotted $\sim$ $\permil$ lower in $\delta^{18}$ O than the surrounding olivine along the terrestrial fractionation line).
 We applied this offset to the final Iris oxvgen measurements., We applied this offset to the final Iris oxygen measurements.
 Our conservative estimate of the uncertainties in the final ratios comes [from adding in quadrature the statistical uncertainty of the individual measurements. the standard deviation of the standard measurements. and (he uncertainty in the instrumental mass fractionation olIset.," Our conservative estimate of the uncertainties in the final ratios comes from adding in quadrature the statistical uncertainty of the individual measurements, the standard deviation of the standard measurements, and the uncertainty in the instrumental mass fractionation offset."
 Olivine. chromite. and mesostasis in Iris have oxvgen isotopic compositions indistinguishable from terrestrial oxvgen (Figure 2)).," Olivine, chromite, and mesostasis in Iris have oxygen isotopic compositions indistinguishable from terrestrial oxygen (Figure \ref{oiso}) )."
 The oxvgen isotopic compositions of the three mineral phases are consistent with co-crvstallization [rom a single melt., The oxygen isotopic compositions of the three mineral phases are consistent with co-crystallization from a single melt.
 Iris has oxvgen-isotope composition higher in both “O/'O and !' O/!O than most chondriules in meteorites and other chondrule-like objects in the Stardust collection (Figure 2))., Iris has oxygen-isotope composition higher in both $^{18}$ $^{16}$ O and $^{17}$ $^{16}$ O than most chondrules in meteorites and other chondrule-like objects in the Stardust collection (Figure \ref{oiso}) ).
 The oxveen isotopes of nebular solids can evolve toward isotopically heavier compositions through processes such as interaction with water (partitioning between liquid ancl solid) or evaporation (Ravleigh-like distillation)., The oxygen isotopes of nebular solids can evolve toward isotopically heavier compositions through processes such as interaction with water (partitioning between liquid and solid) or evaporation (Rayleigh-like distillation).
 Iris apparently lormed from a relatively evolved oxygen isotopic reservoir., Iris apparently formed from a relatively evolved oxygen isotopic reservoir.
The inerease of rogsry in blue earlv-tvpe dwarfs (Fig.,The increase of $r_{e B}/r_{e H}$ in blue early-type dwarfs (Fig.
 reflects the existence of a (strong) negative gradient in 11 and in V along the radial coordinate (Fig., 2) reflects the existence of a (strong) negative gradient in $-$ H and in $-$ V along the radial coordinate (Fig.
 3)., 3).
 The data show that this is a necessary but not sullicient condition however., The data show that this is a necessary but not sufficient condition however.
 This trend is not foun in giant I5 and SO galaxies. which span a broad range in r.g/r.g. though their 11 color is almost as red as in red earlv-tvpe diwarfs.," This trend is not found in giant E and S0 galaxies, which span a broad range in $r_{e B}/r_{e H}$, though their $-$ H color is almost as red as in red early-type dwarfs."
 Raclial color eracdients observed. in individual giant. elliptical and lenticular galaxies are commonly. interpreted. as a product either of age/moetallicitv gradients of the stellar populations along the radial coordinate or of dust attenuation (cl., Radial color gradients observed in individual giant elliptical and lenticular galaxies are commonly interpreted as a product either of age/metallicity gradients of the stellar populations along the radial coordinate or of dust attenuation (cf.
 Sect., Sect.
 1)., 1).
 These interpretations do not imply a correlation between Γρ ond BLL. In the Following sections. these three theoretical interpretations will be extended. to our results for carly-type dvarfs and ciscussed individually. in relation with some scenarios of earlv-tvpe dwarf galaxy formation and evolution which may justify the trend seen in Fig.," These interpretations do not imply a correlation between $r_{e B}/r_{e H}$ and $-$ H. In the following sections, these three theoretical interpretations will be extended to our results for early-type dwarfs and discussed individually, in relation with some scenarios of early-type dwarf galaxy formation and evolution which may justify the trend seen in Fig."
 2., 2.
 The lack of data does not allow us to achieve a direct. proof of the valiclity of any of these three interpretations., The lack of data does not allow us to achieve a direct proof of the validity of any of these three interpretations.
 Moreover. the absence of a one-to-one correlation between reesra and the strength ofthe gradient in LL. i£ not due to errors in data analysis. may indicate that the interpretation of Fig.," Moreover, the absence of a one-to-one correlation between $r_{e B}/r_{e H}$ and the strength of the gradient in $-$ H, if not due to errors in data analysis, may indicate that the interpretation of Fig."
 2 is complex., 2 is complex.
 The integrated broacd-banc colors of E and SO galaxies become progressively Επομ toward fainter magnitudes (Faber 1973: see however Scodegeio 2001)., The integrated broad-band colors of E and S0 galaxies become progressively bluer toward fainter magnitudes (Faber 1973; see however Scodeggio 2001).
 This correlation. known as the colormagniude relation. is universal and very σαι in he optical for ellipticals and lenticulars in clusters al z=0 Bower. Lucey Ellis 1992a.b).," This correlation, known as the color–magnitude relation, is universal and very tight in the optical for ellipticals and lenticulars in clusters at z=0 (Bower, Lucey Ellis 1992a,b)."
 Relying on the commonly accopled interpretation of the colormagnitude relation (Ixodama Arimoto 1997). Wwe c'onclude that. in blue carby-type diwvarfs. either the averaee metallicity is lower than in red earlv-tvpe. dwarls of je same L-banel luminosity or star formation is still going «on.," Relying on the commonly accepted interpretation of the color–magnitude relation (Kodama Arimoto 1997), we conclude that, in blue early-type dwarfs, either the average metallicity is lower than in red early-type dwarfs of the same H-band luminosity or star formation is still going on."
 Here we make the. hypothesis that the blue colors of the VCC sample cwarls are due to the presence of a voung sellar population., Here we make the hypothesis that the blue colors of the VCC sample dwarfs are due to the presence of a young stellar population.
 ‘This hypothesis is supported by spectrosco[ow (GOL) for some individual samyge galaxies and is consisten with the results of Terlevich et al. (, This hypothesis is supported by spectroscopy (G01) for some individual sample galaxies and is consistent with the results of Terlevich et al. (
1999).,1999).
 IDe., Fig.
 5h srows that most of the B-bancl emission of the chwarls is contributed by the. st«αρ populations distributed wihin an cxponential-cisk c“OMIpeHen., 5b shows that most of the B-band emission of the dwarfs is contributed by the stellar populations distributed within an exponential-disk component.
 This disk-componen. M present. is also responside for more than of the tota L-band luminosity (Fig.," This disk-component, if present, is also responsible for more than of the total H-band luminosity (Fig."
 5a)., 5a).
 Lowe make the asstunption that early-type dwarls are rotaionally [lattened (cf., If we make the assumption that early-type dwarfs are rotationally flattened (cf.
 Sect., Sect.
 1). tr¢ wavelength-dependence of their. effective radius. and the relation between total coor and sign and streneth of the color. gradients. may be understood: as," 1), the wavelength-dependence of their effective radius, and the relation between total color and sign and strength of the color gradients may be understood as"
 (e.g.Bellonterαἱ.2001:Tomsick& (e.g.," \citep[e.g.][]{Bel01,Tom01,Rod02}. \citep[e.g.][]{Now99,Mis00,Cui99,Pou99,Nob01}."
 in black hole and neutron star systems. can be explainec in a model where the global disk resonates nonlinearly with the stochastic fluctuations (Abramowiezefal.2003).," in black hole and neutron star systems, can be explained in a model where the global disk resonates nonlinearly with the stochastic fluctuations \citep{Aba03}."
. More compelling model independent evidence has been givel by Uttleyοἱal.(2005). (see also Timmereraf.(2000) and Thieleta£. (2001))). who argue that the log-normal distribution of the fluxes and the linear relationship betweer RMS and flux imply that the response of the disk is non-," More compelling model independent evidence has been given by \cite{Utt05} (see also \cite{Tim00} and \cite{Thi01}) ), who argue that the log-normal distribution of the fluxes and the linear relationship between RMS and flux imply that the response of the disk is non-linear."
 They show that an exponential response can explaui these observations., They show that an exponential response can explain these observations.
 Earlier Mineshigeefαἱ.(1994)... had suggested that the behavior of the observed fluctuations could be because the accretion disk is in self-organized critical state.," Earlier \cite{Min94}, had suggested that the behavior of the observed fluctuations could be because the accretion disk is in self-organized critical state."
 In all these models the temporal behavior of the system is driven by underlying stochastic variations., In all these models the temporal behavior of the system is driven by underlying stochastic variations.
 Moreover. they address the short (<10 sec) time-scale variability of the systems. although many systems also exhibit quite dramatic long time-scale variability.," Moreover, they address the short $ < 10 $ sec) time-scale variability of the systems, although many systems also exhibit quite dramatic long time-scale variability."
 Variability of a system may not necessarily be driven by an underlying stochastic variation., Variability of a system may not necessarily be driven by an underlying stochastic variation.
 The system can show complicated temporal behavior if the governing differential equations are non-linear and have unstable steady state solutions., The system can show complicated temporal behavior if the governing differential equations are non-linear and have unstable steady state solutions.
 In other words. although these systems do not have an explicit time dependent term in the equations describing their structure. they exhibit sustained time variability.," In other words, although these systems do not have an explicit time dependent term in the equations describing their structure, they exhibit sustained time variability."
 In fact. the standard aceretion disk theory predicts that the disk is unstable when it is radiation pressure dominated and when the viscous stress scales with the total pressure.," In fact, the standard accretion disk theory predicts that the disk is unstable when it is radiation pressure dominated and when the viscous stress scales with the total pressure."
 Numerical hydro-dynamie simulations reveal that under such circumstances. the disk would undergo large amplitude oscillations around the unstable solution (Chen&Taam1994).," Numerical hydro-dynamic simulations reveal that under such circumstances, the disk would undergo large amplitude oscillations around the unstable solution \citep{Che94}."
. These variations occur on a viscous time-scale that may be as large as hundreds of seconds., These variations occur on a viscous time-scale that may be as large as hundreds of seconds.
 Specific dynamic models for the temporal behavior of accretion disk. like the Dripping Handrail (Young&Seargle 1996).. have been proposed where the apparent random behavior is actually deterministic.," Specific dynamic models for the temporal behavior of accretion disk, like the Dripping Handrail \citep{You96}, have been proposed where the apparent random behavior is actually deterministic."
 The Galactic micro quasar GRS 19154105 1s a highly variable black hole system., The Galactic micro quasar GRS 1915+105 is a highly variable black hole system.
 It shows a wide range of long term variability (Chenefaf1997; which required Bellonieraf(2000) to classify the behavior in no less than twelve temporal," It shows a wide range of long term variability \citep{Che97,Pau97,Bel97a} which required \cite{Bel00} to classify the behavior in no less than twelve temporal"
The magnetorotational instability is. one. of the most important instajlities in astrophysical Ες dynamics.,The magnetorotational instability is one of the most important instabilities in astrophysical fluid dynamics.
 |t applies to a οercntially rotating. electrically. conducting Iluid in which t1e angular velocity. decreases in magnitude awav [rom the axis of 1n the presence of a weak magnetic ielel of arbitrary. configuration. such a Low is subject to a dynamical instability. with a growth rate comparable to he shear rate of the low (Velikhoy 1959: Chandrasekhar 1960: Fricke 1969: Acheson LOTS: Balbus Lawley 1991. 1992: Papaloizou Szuszkiewicz 1992: Balbus 1995: lFoglizzo Vagger 1995: Ogilvie Pringle 1996: Terquem Papaloizou 1996).," It applies to a differentially rotating, electrically conducting fluid in which the angular velocity decreases in magnitude away from the axis of In the presence of a weak magnetic field of arbitrary configuration, such a flow is subject to a dynamical instability, with a growth rate comparable to the shear rate of the flow (Velikhov 1959; Chandrasekhar 1960; Fricke 1969; Acheson 1978; Balbus Hawley 1991, 1992; Papaloizou Szuszkiewicz 1992; Balbus 1995; Foglizzo Tagger 1995; Ogilvie Pringle 1996; Terquem Papaloizou 1996)."
 The xincipal application of the magnetorotational instability is) to accretion discs. in which the profile of angular velocity ds. fixed by Kepler's third law.," The principal application of the magnetorotational instability is to accretion discs, in which the profile of angular velocity is fixed by Kepler's third law."
 The non-linear development of the instability leads to sustained magnetohycdrodyvnamuc (MED) turbulence. which ransports angular momentum outwards in a vain attonipt o neutralize the destabilizing eradient of angular. velocity (Llawles. Gammie albus 1995: Brandenburg et al.," The non-linear development of the instability leads to sustained magnetohydrodynamic (MHD) turbulence, which transports angular momentum outwards in a vain attempt to neutralize the destabilizing gradient of angular velocity (Hawley, Gammie Balbus 1995; Brandenburg et al."
 1995: Stone et al., 1995; Stone et al.
 1996: Dalbus Lawley 1998)., 1996; Balbus Hawley 1998).
 Owing to the generality of the conditions or instability. however. further applications exist to stellar interiors ancl other astrophysical objects. ancl possibly to," Owing to the generality of the conditions for instability, however, further applications exist to stellar interiors and other astrophysical objects, and possibly to"
"O.Struecm In every as .r passes through c. the number of sign changes in (fo(r).fiGr))decreases by L if g(«»-Q. and increases by-- | if g(«0. If e is a root of g;with /=1....A. then it is neither a root of y;, nor a root of g;,. and g;1f«160)«0. by the of the sequence.","0.5truecm In every as $x$ passes through $c$, the number of sign changes in $(f_0(x),f_1(x))$ decreases by $1$ if $g(c)>0$ , and increases by $1$ if $g(c)<0$ If $c$ is a root of $g_i$with $i=1,...k$, then it is neither a root of $g_{i-1}$ nor a root of $g_{i+1}$, and $g_{i-1}(c)g_{i+1}(c)<0$, by the definition of the sequence."
 Passing through c does not lead to any modification of the number of sign changes in (f;Gr).fir).LC6r7))in this case.," Passing through $c$ does not lead to any modification of the number of sign changes in $(f_{i-1}(x),f_i(x),f_{i+1}(x))$in this case."
 Using g=1 in previous theorem., Using $g=1$ in previous theorem.
Rees(1988) assumed that the debris is uniformly distributed in mass between —AL and +AR.,\citet{ree88} assumed that the debris is uniformly distributed in mass between $-\Delta E$ and $+ \Delta E$ .
 Numerical simulations (Evans&Iwochanek1950:Aval.Livio.Piran2000) have shown (hat this is a reasonable approximation.," Numerical simulations \citep{eva89,aya00} have shown that this is a reasonable approximation."
 The bound material then returns to pericenter al the rate (Phinney1959:Evans&lxochanek1959) where {ο is thetime of the initial tidal disruption. AA/ is the actual mass Chat [alls back to pericenter. which is a fraction f of the original mass of the star. ancl ↕∐∐≼↲≼↲⋟∖⊽∎∪↕⋅↕≸↽↔↴↕∐≀↕↴∐⊔⋯⇂≼↲↥⋅⊔∐↲∖∖⊽∐∪↥≼↲⋟∖⊽↥≀↧↴↕⋅↕⋟∖⊽≼∐⋟∖⊽↕⋅∏↕↽≻∩↲≼⇂≀↧↴↕∐⇂↥⋯↴∐⋟⊔∐↲≼⇂≼↲∣↽≻∏⋟∖⊽↕⋟∖⊽∪∐∣↽≻∪∏∐≺⇂∪," The bound material then returns to pericenter at the rate \citep{phi89,eva89}
 where $t_D$ is thetime of the initial tidal disruption, $\Delta M$ is the actual mass that falls back to pericenter, which is a fraction $f$ of the original mass of the star, and In Rees' original model, the whole star is disrupted and half the debris is on bound orbits, so that $f = 0.5$."
↕⋅∣↽≻∐⋟∖⊽⋅ ⋟∖⊽∪⊔⋯↥∙∕⋮∶∩⋅⇀↱≻⋅∐∪∖∖⊽≼↲∖⇁≼↲↕⋅⋅≀↧↴↕⋅≼↲≺∢≼↲∐↥∐∏∐∐↲↕⋅↕≺∢≀↧↴↥⋟∖⊽↕∐↓∏↥≀↧↴∐∪∐⋟∖⊽∐∪∖∖⇁⋟∖⊽⊔⋯↴↥∐∪↥≀↧↴∐⊔∐↲↕⋅≼↲⊓∐⋅∐↕∐≸≟ ∐↓≀↧↴∩↲↕⋅↕≀↧↴⊔⋟∖⊽≺∢≀↧↴↕↽≻⊓∐⋅≼↲≼⊓↽≻⋡∖↽⊔∐↲∣↽≻↥≀↧↴≺∢↳↽∐∪↥≼↲∶≀↧↴∣↽≻∪⋯⊺⇀↱≻↖∕⋡∣⋪↙∪↓⋟⊔∐↲↕⋅≼↲⋯↕⋅∐↕∐≸≟∐↓≀↕⊍∖⋱∖⊽∣↽≻≼↲≺∢∪∐∐↲⋟∖⊽∏∐∣↽≻∪," However, a recent numerical simulation shows that not all the returning material is captured by the black hole: about $75\%$ of the returning mass becomes unbound following the large compression it experiences on the way back \citep{aya00}."
∏∐≼⇂ ↓≯∪∐∪∖∖↽↕∐≸↽↔↴⊔∐↲↥≀↧↴↕⋅≸↽↔↴≼↲≺∢∪∐↓↕↽≻↕⋅≼↲⋝∖⊽, This gives rise to a smaller $f\approx 0.1$.
⊳∖⇁↕∪∐∐≼↲⇀↸↕↽≻≼↲↕⋅↕≼↲∐≺∢≼↲⊳∖⊽∪∐⊔∐↲∖∖↽≀↧∶∖⇁∣↽≻≀↧↴≺∢↳↽≼⋝↼≚∡∖⇁≀↧↴↥⋅⊔∖↽↥∪⋅≪↽∖↽↥↴↕↕⋅≀↧↴∐∃∪∩∩↕⋝⋅⋅ ↴⊺∐↕⋝∖⊽≸↽↔↴↕∖↽≼↲⋝∖⊽↕⋅↕⋟∖⊽≼↲↥∪≀↧↪∖⊽∐⋯∐≼↲↕⋅∙∕⋅≈∪⋅⊥⋅↼≚∐∪⊔∐↲↕⋅↕↽≻∪⊳∖⊽⊳∖⇁↕∣↽≻∐∐∡∖↽≸↽↔↴↕∖⇁↕∐≸≟↕⋅↕⊳∖⊽≼↲↥∪≀↧↪∖⇁∐⋯∐∙∕⋅↕⊳∖⊽⊔⋯↴↥⊔∐↲ ⋝∖⊽↥≀↧↴↕⋅↥⊳∖⊽∪∐↥∡∖⇁↕↽≻≀↧↴↕⋅∐≀↧↴∐⋡∖↽≼∐⊳∖⊽↕⋅∏↕↽≻∩↲≺⇂∶∐⊳∖⊽≼↲∐∖↽≼↲↥∪↕↽≻≼↲≺∢⋯∏≼⇂∣↽≻≼↲⊳∖⊽∏⋅∏↽≻↕↽≻≼↲≼⇂∣↽≻∡∖↽⊔∐↲∣↽≻↥≀↧↴≺∢↕≶∐∪↥≼↲⋅↥≼↲≀↧↴∖↽↕∐≸↽↔↴∐↓∪⋝∖⊽↥ ol its core nearlv intact. (IRenzini et al.," Another possibility giving rise to a small $f$ is that the star is only partially disrupted: its envelope could be stripped by the black hole, leaving most of its core nearly intact (Renzini et al."
 1995: see also 855 below)., 1995; see also 5 below).
 Here we treat. f/ as a [ree parameter., Here we treat $f$ as a free parameter.
 The gravitational potential energv available from fallback is determined bv the difference between (he specific binding energy of the circularization orbit al r=2rpνε and the specific binding energy of the incoming material., The gravitational potential energy available from fallback is determined by the difference between the specific binding energy of the circularization orbit at $r = 2 r_P = 2r_T$ and the specific binding energy of the incoming material.
" Since Mj;S>AL,. all the bound debris is on hiehlv eccentric orbils wilh a specilic binding energy much smaller than the binding energy ol the final circular orbit."," Since $M_H \gg M_\star$, all the bound debris is on highly eccentric orbits with a specific binding energy much smaller than the binding energy of the final circular orbit."
 Thus. assuming that the fallback material racdiates the energy release promptly. the radiation efficiency. € is independent of time during fallback: The huminositv of the fallback process is then given by The luminosity peaks at /=/p+ Afy. ie. when the most bound debris falls back to the pericenter. sowe have," Thus, assuming that the fallback material radiates the energy release promptly, the radiation efficiency $\epsilon$ is independent of time during fallback: The luminosity of the fallback process is then given by The luminosity peaks at $t = t_D + \Delta t_1$ , i.e. when the most bound debris falls back to the pericenter, sowe have"
"For tvpical parameters (e.g.. o,~LO7) 7; can be measured to &10s (e.g.. Brown et 22001: Holman et 22006).","For typical parameters (e.g., $\sigma_{ph}\sim~10^{-3}$ ), $t_i$ can be measured to $\simeq10$ s (e.g., Brown et 2001; Holman et 2006)."
 The period can be measured much more accurately (han ἐν rom observations of multiple transits separated by many orbits.," The period can be measured much more accurately than $t_i$, from observations of multiple transits separated by many orbits."
 For small amplitude libration about L4/L5 and circular orbits. the transit timing perturbation is given by NMGS)/(8). where NM(f) is the angular displacement of the Trojan from L4/L5 at the time of the /th transit.," For small amplitude libration about L4/L5 and circular orbits, the transit timing perturbation is given by $\delta t_i \simeq \epsilon
P_s \Delta M(t_i) / (2\pi)$ , where $\Delta M(t_i)$ is the angular displacement of the Trojan from L4/L5 at the time of the $i$ th transit."
 The TTVs can be modeled by a sinusoid. 07/;=Aqsin(2x(1—14)(Peppy+6). where Aq is the aaplitude of the transit timing variations and Pp744.," The TTVs can be modeled by a sinusoid, $\delta t_i = K_{\rm tt} \sin\left(2\pi\left(t-t_0\right)/P_{\rm TTV}+\phi\right)$, where $K_{\rm tt}$ is the amplitude of the transit timing variations and $P_{\rm TTV}\sim\tau_{\rm slow}$."
 L the dominant periodicity of the transit timing variations (Jj) is well determined. then the remaining parameters can be determined via linear least squares fitting to the observed (ransil times.," If the dominant periodicity of the transit timing variations $P_{\rm
TTV}$ ) is well determined, then the remaining parameters can be determined via linear least squares fitting to the observed transit times."
" The transit timing variations will have an amplitiucle ens (o ge where A4, is the amplitude of the Trojans angular displacement from (he Lagrange point."," The transit timing variations will have an amplitude 60s ) ) ) ), where $K_{\Delta M}$ is the amplitude of the Trojan's angular displacement from the Lagrange point."
 For small amplitude libration. A4;&max|AAS and rms(0/;)cWy/V2 (see Fig.," For small amplitude libration, $K_{\Delta M}\simeq\mathrm{max}\left|\Delta M\right|$ and $\mathrm{rms}(\delta t_i)\simeq K_{\rm tt} / \sqrt{2}$ (see Fig."
 1) Libration amplitudes of A4;~5—25 are common for Trojans orbiting near the sun-Jupiter Lagrange points (Murray Dermott 2000)., 1) Libration amplitudes of $K_{\Delta M}\sim~5-25^\circ$ are common for Trojans orbiting near the Sun-Jupiter Lagrange points (Murray Dermott 2000).
 The Lomb-Scargle5 periocogram5 can be easily adapted to efficiently scan a range5 of putative periods aud identily any signilicant periodicities (Cumming 2004)., The Lomb-Scargle periodogram can be easily adapted to efficiently scan a range of putative periods and identify any significant periodicities (Cumming 2004).
" If we assume that ihere are many V4) transit (aiming observations with uncorrelated Gaussian unicertainties σι=Gg. that the transit timing5 observations are evenly distributed. and the duration of observations (2,,,) is greater than than P. (en a periodogram-stvle analvsis results in a chance of detecting a Trojan 1 Ny,>Nyeoy,(atlog|Tin./(2FTD.i) (Cumming 2004). where F is the false alarm probability. which we set to 107."," If we assume that there are many $N_{\rm tt}$ ) transit timing observations with uncorrelated Gaussian uncertainties $\sigma_{t_i}=\sigma_{tt}$, that the transit timing observations are evenly distributed, and the duration of observations $T_{\rm obs}$ ) is greater than than $P_{\rm TTV}$, then a periodogram-style analysis results in a chance of detecting a Trojan if $K_{tt}\ge K_{1/2} \simeq \sigma_{tt}\left(\frac{4}{N_{\rm tt}}
\log\left[T_{\rm obs} / \left(2 F P_s\right) \right] \right)^{1/2}$ (Cumming 2004), where $F$ is the false alarm probability, which we set to $10^{-3}$."
 For Vay=L/P.40. Nyyc04. so sub-Earth-mass Trojans could be reaclily detected.," For $N_{\rm tt} = T_{\rm obs}/P_s = 40$, $K_{1/2}
\simeq \sigma_{tt}$, so sub-Earth-mass Trojans could be readily detected."
 We note that all published transit timing data sets have Ay<20. which results in a significantly reduced sensitvitv. if [ιν is unknown p," We note that all published transit timing data sets have $N_{\rm tt}<20$, which results in a significantly reduced sensitvity, if $P_{\rm TTV}$ is unknown ."
riori ln this small-Nq regime. a simple 4? test of the null hypothesis (0/;= 0) is more sensitive for detecting transit timing variations.," In this $N_{\rm
tt}$ regime, a simple $\chi^2$ test of the null hypothesis $\delta
t_i=0$ ) is more sensitive for detecting transit timing variations."
 However. if only a single periodicity (e.g.. 744) is lo be tested. then even a modest number of observations can be quite sensitive (e.g... Ayo22.504even lor Nyy= 13).," However, if only a single periodicity (e.g., $\tau_{\rm slow}$ ) is to be tested, then even a modest number of observations can be quite sensitive (e.g., $K_{1/2}\simeq 2.5\sigma_{\rm tt}$even for $N_{\rm
tt}=13$ )."
rotation curve of the receding half drops in the outer parts.,rotation curve of the receding half drops in the outer parts.
" The masini rotation speed. leaving out the bump at110"".. occurs around a radius of (1.87 ΚΡΟ) at a speed of 25|."," The maximum rotation speed, leaving out the bump at, occurs around a radius of (1.87 kpc) at a speed of 25."
.. Stil Israel (2002) give a rotation speed Vsini of 17.543.9 aat a radius of {for DDO 43., Stil Israel (2002) give a rotation speed $V \sin i$ of $\pm$ 3.9 at a radius of for DDO 43.
 At that radius our Vsin/ would be the same at 17.60.58 !., At that radius our $V \sin i$ would be the same at $\pm$ 0.8.
. To examine the quality of the lit. we made a model of the velocity field. (hen subtracted it from the observed. velocity Ποια.," To examine the quality of the fit, we made a model of the velocity field, then subtracted it from the observed velocity field."
 The resilual map is shown in Figure 24.., The residual map is shown in Figure \ref{fig:resid}.
 The values of the residuals range [rom -6.6 to 7.1!.. so in general. the fit seems quite good.," The values of the residuals range from -6.6 to 7.1, so in general, the fit seems quite good."
 We have plotted. contours Irom the model velocity [field on the residual map in Figure 25. and the observed. velocity [field contours on (he residual map in Figure 26.., We have plotted contours from the model velocity field on the residual map in Figure \ref{fig:modelonresid} and the observed velocity field contours on the residual map in Figure \ref{fig:m1onresid}.
 The model successfully recreates (he weak turnover in each side of the velocity field. but the residual map shows (hat it had. difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north.," The model successfully recreates the weak turnover in each side of the velocity field, but the residual map shows that it had difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north."
 There is another region of higher-than-average residuals just south of the center of the galaxy: (his area slightly overlaps the west sides of the large hole and knot in the “Thhis is also near (he region of hiehest velocity dispersion in the galaxy. so perhaps it is nol surprising that the velocity residuals are larger here as well.," There is another region of higher-than-average residuals just south of the center of the galaxy; this area slightly overlaps the west sides of the large hole and knot in the \\.Thhis is also near the region of highest velocity dispersion in the galaxy, so perhaps it is not surprising that the velocity residuals are larger here as well."
 From Figure 26.. it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp.," From Figure \ref{fig:m1onresid}, it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp."
 The residuals are still small however. indicating (hal its not a significant warp.," The residuals are still small however, indicating that it's not a significant warp."
 The original listing of DDO 43 as a candidate tidal dwarf by Hunter ((2000) was based on a suggested rotation speed of order 9|., The original listing of DDO 43 as a candidate tidal dwarf by Hunter (2000) was based on a suggested rotation speed of order 9.
.. As a result. on a plot of Mg; versus the masini rotation speed (Figure 1 of IIunter al.)) DDO 43 stood oul as unusually huninous for its rotation speed.," As a result, on a plot of $_B$ versus the maximum rotation speed (Figure 1 of Hunter ) DDO 43 stood out as unusually luminous for its rotation speed."
 This could imply a deficit of dark matter. a characteristic of dal dwarls (Barnes Hernequist 1992).," This could imply a deficit of dark matter, a characteristic of tidal dwarfs (Barnes Hernquist 1992)."
 However. with a maximum rotation speed of 25s... found here. DDO 43 now lies close to (he mean of the relationship defined bv other Im galaxies ancl spirals in (hat plot.," However, with a maximum rotation speed of 25, found here, DDO 43 now lies close to the mean of the relationship defined by other Im galaxies and spirals in that plot."
 Thus. DDO 43 is unlikely to be without dark matter. and unlikely to be a tidal dwarl.," Thus, DDO 43 is unlikely to be without dark matter, and unlikely to be a tidal dwarf."
 This is comforting since there was no obvious nearby postnerger object to have been the parent of DDO 43 if il were a tidal dwarl., This is comforting since there was no obvious nearby post-merger object to have been the parent of DDO 43 if it were a tidal dwarf.
 A erev-scale display of the velocity dispersion map from the ddata is shown in Figure 27 with contours of the integrated ssuperposed., A grey-scale display of the velocity dispersion map from the data is shown in Figure \ref{fig:veldisp} with contours of the integrated superposed.
 Within the optical body of the galaxy. the velocity dispersion is around LOτ," Within the optical body of the galaxy, the velocity dispersion is around 10."
"ν, This is the value found in most quiescent gas disks.", This is the value found in most quiescent gas disks.
 There are a few spots with higher, There are a few spots with higher
the absorption features at 71.47 keV and ~2.71 keV. now both appear as a resolved line pair. with the energy spacing of the respective Lee and. Lye resonance lines of Mg aid 5. Furthermore. additional narrow absorption features are seen to mateh with same Ix-shell resonance Lines of Ne. οἱ and. possibly Ar.,"the absorption features at $\sim$ 1.47 keV and $\sim$ 2.71 keV now both appear as a resolved line pair, with the energy spacing of the respective $\alpha$ and $\alpha$ resonance lines of Mg and S. Furthermore, additional narrow absorption features are seen to match with same K-shell resonance lines of Ne, Si and possibly Ar."
 To quantify these absorption features we explored. the ALOS data with Nspec., To quantify these absorption features we explored the MOS data with Xspec.
. We first. fitted the MOS data at 1-5 keV with a power law to provide a baseline: below l keV the spectrum rises steeplv due to strong soft. X-rav emission (Pounds. and. Reeves 2006)., We first fitted the MOS data at 1-5 keV with a power law to provide a baseline; below 1 keV the spectrum rises steeply due to strong soft X-ray emission (Pounds and Reeves 2006).
 Several narrow features clearly visible in the data-to-power-law-mocdel ratio plot (figure 3.2 upper panel) contributed to à poor statistical fit (\7=351266).," Several narrow features clearly visible in the data-to-power-law-model ratio plot (figure 3, upper panel) contributed to a poor statistical fit $\chi^{2}$ =351/266)."
 Fitting gaussians to the visible features. with a fixed width of a= 10eV. found 6 significant negative (absorption) lines.," Fitting gaussians to the visible features, with a fixed width of $\sigma$ = 10eV, found 6 significant negative (absorption) lines."
 Ehe overall improvement to the fit was very significant with X7 reduced to 270/254., The overall improvement to the fit was very significant with $\chi^{2}$ reduced to 270/254.
 The fitted line energies and I[uxes are listed in Table 1 where the observe line energy is in each case compared: with the most likely identification. chosen as the nearest resonance transition of an abundant ion.," The fitted line energies and fluxes are listed in Table 1 where the observed line energy is in each case compared with the most likely identification, chosen as the nearest resonance transition of an abundant ion."
" Crucially. α 6 line energies exhibit a ""blue shift in the range ~5-7 %.."," Crucially, all 6 line energies exhibit a `blue shift' in the range $\sim$ 5-7."
 Assuming the same ratio for the absorption line observed at 731.07 keV. gives a preferrec identification with Llea of FeXXV. (figure 2)., Assuming the same ratio for the absorption line observed at $\sim$ 7.07 keV gives a preferred identification with $\alpha$ of FeXXV (figure 2).
 In the res frame o£ tthe revised. identification of the absorption spectrum now vields an increased. outllow velocity in the range vo 0.13-0.15c., In the rest frame of the revised identification of the absorption spectrum now yields an increased outflow velocity in the range $\sim$ 0.13-0.15c.
 To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised. gas modelled using the NSTAIU code (Kallman et al 1996)., To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised gas modelled using the XSTAR code (Kallman et al 1996).
 Free. parameters of the absorber in this comparison were the column density and. ionisation parameter. with outflow (or inflow) velocities included as an adjustment to the apparent. redshift of the absorbing gas.," Free parameters of the absorber in this comparison were the column density and ionisation parameter, with outflow (or inflow) velocities included as an adjustment to the apparent redshift of the absorbing gas."
 Alb relevant abundant elements from Ne to Fe were include with the relative abundances constrained to within a factor 2 of solar., All relevant abundant elements from Ne to Fe were included with the relative abundances constrained to within a factor 2 of solar.
 Since our primary aim was to check the energies an relative strength of the principal absorption lines identifiec in the visual spectral fit shown in figure 2. the mocdel clic not attempt to match the broad. excess Lux near 6 keV: it therefore consisted only of a power law with photolonisec absorber.," Since our primary aim was to check the energies and relative strength of the principal absorption lines identified in the visual spectral fit shown in figure 2, the model did not attempt to match the broad excess flux near $\sim$ 6 keV; it therefore consisted only of a power law with photoionised absorber."
 Fitting over the 1-10. keV band. the addition of he photoionisec absorber improved the spectral fit. [rom v of 522 for 358 degrees of freedom to 465/345., Fitting over the 1-10 keV band the addition of the photoionised absorber improved the spectral fit from $\chi^{2}$ of 522 for 358 degrees of freedom to 465/345.
 The vest-fit column density was Ny21077 em with an ionisation parameter of logé=2.9-+0.4 and nominal relative abundances of Ne. Mg. Si. S. Ar and Fe of 0.5. 1. 0.5. 1. 1.5 and 0.5.," The best-fit column density was $_{H}$$\sim$$2\times 10^{22}$ $^{-2}$, with an ionisation parameter of $\xi$ $\pm$ 0.4 and nominal relative abundances of Ne, Mg, Si, S, Ar and Fe of 0.5, 1, 0.5, 1, 0.5 and 0.5."
 Figure 3 (mid. panel) reproduces this absorbed power Law model. with the strongest. predicted: absorption ines (in order of increasing energy) corresponding to Ix-shell resonance transitions of Ne. Me. Si. S. Ar and Fe. supporting he visual assessment of figure 2.," Figure 3 (mid panel) reproduces this absorbed power law model, with the strongest predicted absorption lines (in order of increasing energy) corresponding to K-shell resonance transitions of Ne, Mg, Si, S, Ar and Fe, supporting the visual assessment of figure 2."
 Additionally. we note the Ly? line of Μο would occur at 1.83 keV. sugeesting," Additionally, we note the $\beta$ line of MgXII would occur at $\sim$ 1.83 keV, suggesting"
V405 Xurigae. 0558.015353) was discovered. in the Al-Sky Survey ancl identified as απ intermediate polar (a cataclysmic variable with a magnetic white-cwarl primary) by Llaberl (1994).,V405 Aurigae J0558.0+5353) was discovered in the All-Sky Survey and identified as an intermediate polar (a cataclysmic variable with a magnetic white-dwarf primary) by Haberl (1994).
 lt is notable. firstly. for showing a soft blackbocdvy component in the X-ray spectrum. one of a number of such objects discovered. withZosal.," It is notable, firstly, for showing a soft blackbody component in the X-ray spectrum, one of a number of such objects discovered with."
. Secondly. its soft-N-ray and optical emission shows a double-pealked. modulation at the white-dwarl spin period AAllan 11996). whereas most of these stars show a single-peakecl moculation (see. ce.g.. Patterson 1994 or Hellier 2001 for reviews of this class).," Secondly, its soft-X-ray and optical emission shows a double-peaked modulation at the white-dwarf spin period Allan 1996), whereas most of these stars show a single-peaked modulation (see, e.g., Patterson 1994 or Hellier 2001 for reviews of this class)."
 The hard X-ray. emission in intermediate polars (LPs) originates below a. stanc-oll aceretion shock near the magnetic poles of the white dwarf., The hard X-ray emission in intermediate polars (IPs) originates below a stand-off accretion shock near the magnetic poles of the white dwarf.
 The soft. blackhocky emission is then understood. as arising from heated: white-dwarf surface around the accretion footprints., The soft blackbody emission is then understood as arising from heated white-dwarf surface around the accretion footprints.
 his is nearly always seen in the AM Ller class of cataclysmic variable. but it is seen only in some LPs. for which the reason is unclear.," This is nearly always seen in the AM Her class of cataclysmic variable, but it is seen only in some IPs, for which the reason is unclear."
 The issue of why some LPs show a single-peaked pulsation. whereas others show a clouble-peakecl pulsation. is also unclear.," The issue of why some IPs show a single-peaked pulsation, whereas others show a double-peaked pulsation, is also unclear."
 One idea Lblellier 1996: Allan 11996: Norton 1999) notes that LPs with shorter spin periods will have smaller magnetospheres in which the accretion clises are disrupted nearer the white cwarf., One idea Hellier 1996; Allan 1996; Norton 1999) notes that IPs with shorter spin periods will have smaller magnetospheres in which the accretion discs are disrupted nearer the white dwarf.
 This could result in shorter. fatter ‘accretion curtains’ of material which might have lower opacity in the vertical direction. thus. preferentially beaming X-ravs along magnetic field lines.," This could result in shorter, fatter `accretion curtains' of material which might have lower opacity in the vertical direction, thus preferentially beaming X-rays along magnetic field lines."
 The two magnetic poles would combine to. produce a double-peaked pulsation., The two magnetic poles would combine to produce a double-peaked pulsation.
 With longer spin periods. where disc clisruption occurs further out. the opposite might hold. with tall. thin accretion curtains preferentially bcaming rays out of the sides.," With longer spin periods, where disc disruption occurs further out, the opposite might hold, with tall, thin accretion curtains preferentially beaming X-rays out of the sides."
 Phe two poles would then act in phase. producing a single-peakecl pulsation.," The two poles would then act in phase, producing a single-peaked pulsation."
 The X-ray satellite has a larger collecting area ancl better spectral resolution thanfosef.. allowing us to return to V405 Aur with better N-rav. cata than previously obtained.," The X-ray satellite has a larger collecting area and better spectral resolution than, allowing us to return to V405 Aur with better X-ray data than previously obtained."
 We report here on a 30-ks. observation aimed at understanding the pulsation at the 545-8 spin period of V405 Aur., We report here on a 30-ks observation aimed at understanding the pulsation at the 545-s spin period of V405 Aur.
(SAIBLL masses for our sample are estimated. from. stellar velocity clispersions: see Section 4.3 for further details: see Column 7 o£ Table 1). e(0.2 20)«107eres1M.lt the luminosity completeness linit (Lxz107ergs +) and assuming a similar distribution in bExddington ratios. the smallest SAIBLLE which could conceivably be in our sample is Mag=510M.: this is a factor z10 below the lowest mass Compton-thick ΑΝ identified here (Albu=5OPAL. ).,"(SMBH masses for our sample are estimated from stellar velocity dispersions; see Section 4.3 for further details; see Column 7 of Table 1), $\approx (0.2$ $20) \times
10^{35} \ergps \Msun^{-1}$, at the luminosity completeness limit $L_{\rm X} \goa 10^{42} \ergps$ ) and assuming a similar distribution in Eddington ratios, the smallest SMBH which could conceivably be in our sample is $\Mbh \approx 5 \times 10^5 \Msun$; this is a factor $\approx 10$ below the lowest mass Compton-thick AGN identified here $\Mbh \approx 5 \times 10^6 \Msun$ )."
" We may now estimate how many Conpton-thick AGNs may contain SAIBLIs in the mass region Myg25(0.5 5)«I0""M.. and hence constrain the number of Compton-hick .ACGNs not included in our space-density estimate clue o the lower mass limit of the SDSS."," We may now estimate how many Compton-thick AGNs may contain SMBHs in the mass region $\Mbh \approx
(0.5$ $5) \times 10^6 \Msun$, and hence constrain the number of Compton-thick AGNs not included in our space-density estimate due to the lower mass limit of the SDSS."
 Η the five most conservatively identified Compton-thick ACGNs with Mpg estimates contained SMDlIISs which were a factor z10 smaller in mass but had the same Lx/Mpg ratio. our (=SO percent) would still have Lyz1072eres+ and would therefore be included in our estimate of the space density of Compton-thick ACGNs as shown in Fig. 6..," If the five most conservatively identified Compton-thick AGNs with $\Mbh$ estimates contained SMBHs which were a factor $\approx 10$ smaller in mass but had the same $L_{\rm X} / \Mbh$ ratio, four $\approx 80$ percent) would still have $L_{\rm X} \goa 10^{42}
\ergps$ and would therefore be included in our estimate of the space density of Compton-thick AGNs as shown in Fig. \ref{fig:space_dens}. ."
" Based on a simple extrapolation of the SMDII mass function of 7.. AGNs hosting SAIBIIs with Alpyz(0.5 5)10""M. are a factor &1.5 more abundant than those with Mig25(0.5 5)-10AL.."," Based on a simple extrapolation of the SMBH mass function of \citet{marconi04}, AGNs hosting SMBHs with $\Mbh
\approx (0.5$ $5) \times 10^{6} \Msun$ are a factor $\approx 1.5$ more abundant than those with $\Mbh \approx (0.5$ $5) \times 10^{7}
\Msun$."
" Hence. based on this simplistic formalisim. we estimate that approximately half of all Compton-thick AGNs with Lyz1077ergs may contain SAIBLIs with Mayzm(0.5 5)10""AL. which are not included in our parent sample."," Hence, based on this simplistic formalism, we estimate that approximately half of all Compton-thick AGNs with $L_{\rm X} \goa
10^{42} \ergps$ may contain SMBHs with $\Mbh \approx (0.5$ $5) \times
10^{6} \Msun$ which are not included in our parent sample."
 Obscuration and host-ealaxy contamination may further prevent us from identifving all Compton-thick ACGNs in our considered. volume., Obscuration and host-galaxy contamination may further prevent us from identifying all Compton-thick AGNs in our considered volume.
 Obscured AGNsS can be mis-classified whenthe host-ealaxy over-shines the nuclear emission., Obscured AGNs can be mis-classified whenthe host-galaxy over-shines the nuclear emission.
 In the absence of extinction. a NL-AGN with Lx21077ergs can be almost totally eluted by a star-Lormation rate of I0M. 1 (Le. z95r percent of the observed. 41:23 emission is produced in regions: e.g. 7).," In the absence of extinction, a NL-AGN with $L_{\rm
 X} \approx 2 \times 10^{42} \ergps$ can be almost totally diluted by a star-formation rate of $10 \Msun$ $^{-1}$ (i.e., $\goa 95$ percent of the observed $H \beta$ emission is produced in regions; e.g., \citealt{yan10}) )."
 The contribution of these sources to our observed space density is dillicult to quantify., The contribution of these sources to our observed space density is difficult to quantify.
 However. it is predicted that as many z50 percent of AGNs may. show no evidence for AGN activity in their optical spectroscopy (eg. ?:: Goulding Alexander 2009). anc would therefore not be included in our optically selected AGN sample.," However, it is predicted that as many $\approx 50$ percent of AGNs may show no evidence for AGN activity in their optical spectroscopy (e.g., \citealt{maiolino03}; Goulding Alexander 2009), and would therefore not be included in our optically selected AGN sample."
 Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick. we suggest that our derived space density can be broadly consistent with the ΧΙ models.," Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick, we suggest that our derived space density can be broadly consistent with the XRB models."
 Some theoretical models predict that Compton-thick ACGNs may harbour SAIBLIs which are undergoing an evolutionary phase of rapid growth (c.g.. ??2)).," Some theoretical models predict that Compton-thick AGNs may harbour SMBHs which are undergoing an evolutionary phase of rapid growth (e.g., \citealt{Fabian99,Granato06,Hopkins08}) )."
 In this section we consider the implied. Ecllington ratios Gp~Laon/Leaa: where Leam126«lo(AlbuΔΙ.Jeres 13 for the Compton-thick ACGNs identified in our sample with publicly available black-hole mass (Alby) estimates.," In this section we consider the implied Eddington ratios $\eta \sim L_{\rm AGN} / L_{\rm
 Edd}$; where $ L_{\rm Edd} \approx 1.26 \times 10^{38} (\Mbh /
\Msun) \ergps$ ) for the Compton-thick AGNs identified in our sample with publicly available black-hole mass $\Mbh$ ) estimates."
 Stellar velocity dispersion measurements have been computed for 13 of the LE ΑΝ» in our sample. at least five of whieh we conservatively identify as Compton-thick AGNs.," Stellar velocity dispersion measurements have been computed for 13 of the 14 AGNs in our sample, at least five of which we conservatively identify as Compton-thick AGNs."
 These measurements are publicly available in the MDPA-JIEU release of SDSS-DIU and ave derived. [rom the fitting of stellar population synthesis models to the SDSS 1-D Using the A o relation of 2? we convert the stellar velocity dispersions to Alby (sec Column 7 of Table 1)) in order to calculate Leap for these sources., These measurements are publicly available in the MPA-JHU release of SDSS-DR7 and are derived from the fitting of stellar population synthesis models to the SDSS 1-D Using the $M$ $\sigma$ relation of \citet{gebhardt00} we convert the stellar velocity dispersions to $\Mbh$ (see Column 7 of Table \ref{tab:srce_props}) ) in order to calculate $L_{\rm Edd}$ for these sources.
 The median SALBLL mass for our sample is AlpymA105M.(ic. these AGNs host SMDLI which are similar to those identified in the optical studs of Heckman et al.," The median SMBH mass for our sample is $\Mbh \approx 3 \times 10^7 \Msun$(i.e., these AGNs host SMBHs which are similar to those identified in the optical study of Heckman et al."
 2004)., 2004).
" In order to estimate η for our Compton-thick ACGNs. we use Loy, as a proxy [or Lage and we assume the bolometric corrections of ?.."," In order to estimate $\eta$ for our Compton-thick AGNs, we use $L_{6
 \mu m}$ as a proxy for $L_{\rm AGN}$ and we assume the bolometric corrections of \citet{marconi04}."
 Phe use of the 6pum continuum emission to infer £Lxcoy bas the advantage that it is an independent measure of the intrinsic luminosity of the AGN. whilst the NL emission arises from a similar region to that of Oru] which was used for the selection of the sources considered. here.," The use of the $6 \um$ continuum emission to infer $L_{\rm AGN}$ has the advantage that it is an independent measure of the intrinsic luminosity of the AGN, whilst the NL emission arises from a similar region to that of ] which was used for the selection of the sources considered here."
 Twelve of our 14 sources have both Alby estimates and 6tum measurements., Twelve of our 14 sources have both $\Mbh$ estimates and $6 \um$ measurements.
 We find that our sample of AGNs are spread: over a wide-range of Edclington ratio. ye0.002 0.3 (median =0.014: see Column Ll of Table 2): the five Compton-thick ACiNs are at systematically higher Eddington ratios. rjz0.01 0.3 (median z0.2). Similarly. we find that the wellestucdied local Compton-thick AGNs (Circinus. Mrk 3. NGC LOGS and NGC 6240) have a similar range in Ecdclineton ratio. 4s0.002 1 (median z 0.2).," We find that our sample of AGNs are spread over a wide-range of Eddington ratio, $\eta \approx 0.002$ –0.3 (median $\approx 0.014$; see Column 11 of Table 2); the five Compton-thick AGNs are at systematically higher Eddington ratios, $\eta \approx 0.01$ $0.3$ (median $\approx 0.2$ Similarly, we find that the well-studied local Compton-thick AGNs (Circinus, Mrk 3, NGC 1068 and NGC 6240) have a similar range in Eddington ratio, $\eta
\approx 0.002$ –1 (median $\approx 0.2$ )."
 Lt is important to note the large uncertainties involved. with caleulating bolometric luminosities and subsequent LEclclington ratios: the large scatter in the 6pum relation combined with a possible LEcclineton ratio dependent bolometric correction (e.g... 2)) could vield an uncertainty [actor of the order z10 for the highest Iddington ratio sources.," It is important to note the large uncertainties involved with calculating bolometric luminosities and subsequent Eddington ratios; the large scatter in the $6
\um$ relation combined with a possible Eddington ratio dependent bolometric correction (e.g., \citealt{vasudevan07}) ) could yield an uncertainty factor of the order $\goa 10$ for the highest Eddington ratio sources."
 None of the AGNs in our sample appear to be Ededington-limited on the basis of the 6tun luminosity. and any uncertainties would apply equally to all of the AGNs considered. bere. hence. our. [finding of systematically higher Exldington ratios for Compton-thick AGNs. to first-order. appears to be relatively robust.," None of the AGNs in our sample appear to be Eddington-limited on the basis of the $6 \um$ luminosity, and any uncertainties would apply equally to all of the AGNs considered here, hence our finding of systematically higher Eddington ratios for Compton-thick AGNs, to first-order, appears to be relatively robust."
 Llowever. we suggest that this result may be driven by our selection of Oiu]-bright AGNsas well as our sensitivity towards the identification of Compton-thick ACNs.," However, we suggest that this result may be driven by our selection of ]-bright AGNsas well as our sensitivity towards the identification of Compton-thick AGNs."
" For example. with deeper X-ray. data we may icentily further Compton-thick ACiNs in our sample which have lower values of η, and hence reducing the median Eddington ratio for the Compton-thick ACN subsample."," For example, with deeper X-ray data we may identify further Compton-thick AGNs in our sample which have lower values of $\eta$, and hence reducing the median Eddington ratio for the Compton-thick AGN subsample."
 ὃν comparison. for the total population of Typc-2 ACGNSs identified from optical emission-line diagnostics in the SDSS. ? find that basedon the use of Ori] emission. to infer Lycoy. <0.5 percent of Evpe-2 AGNs hosting SMDIIS with Migz3OAL. are accreting above 4j;8 0.1: by contrast. we find that z30 percent of our sample have ne 0.1.," By comparison, for the total population of Type-2 AGNs identified from optical emission-line diagnostics in the SDSS, \citet{heckman04} find that basedon the use of ] emission to infer $L_{\rm AGN}$ , $< 0.5$ percent of Type-2 AGNs hosting SMBHs with $\Mbh \approx 3
\times 10^7 \Msun$ are accreting above $\eta \approx 0.1$ ; by contrast, we find that $\goa 30$ percent of our sample have $\eta \goa
0.1$ ."
 A particular advantage to a direct comparison with the study of Leckman et al. (, A particular advantage to a direct comparison with the study of Heckman et al. (
2004) is that selection processes ancl biases are likely to be identical between both studies.,2004) is that selection processes and biases are likely to be identical between both studies.
7 tuclicates that: 1) brown dwarfs in the ONC dorofl depart Grom the £x - mass relationship we observe for higher mass stars. and 2) the mean BD N-ray luminosity is of the order of 107 eres. F.,"\ref{fig:BD} indicates that: 1) brown dwarfs in the ONC do depart from the $L_X$ - mass relationship we observe for higher mass stars, and 2) the mean BD X-ray luminosity is of the order of $10^{28.5}$ $\cdot$ $^{-1}$."
 Ou average this is higher than the recent. results obtained for BDs in IC 318 by (2001).. but lower than the £x reported by Imanishietal.(2001) for oue detected BD and one BD caudidate in the voung p Ophiuchi cloud.," On average this is higher than the recent results obtained for BDs in IC 348 by \citet{pre01}, , but lower than the $L_X$ reported by \citet{ima01} for one detected BD and one BD candidate in the young $\rho$ Ophiuchi cloud."
 Although the relationship with mass explains a good deal of the scatter in activity levels of our sample. the deviations from this treuc are still siguificant.," Although the relationship with mass explains a good deal of the scatter in activity levels of our sample, the deviations from this trend are still significant."
 The next stellar parameter we investigate in order to uuderstaud this residual scatter is the age. as iuferred from the SDF evolutiouary tracks.," The next stellar parameter we investigate in order to understand this residual scatter is the age, as inferred from the SDF evolutionary tracks."
 Figure 8. shows the Log(Lx) vs. Log(.Age) plot Dor stars iu our sample with mass between 0.2 aud 1.0 M.., Figure \ref{fig:LXvsA0a} shows the $Log(L_X)$ vs. $Log(Age)$ plot for stars in our sample with mass between 0.5 and 1.0 $M_{\odot}$.
 The median Ly appears to decrease with increaslug age. but we must exercise special care in the tuterpretation of this treud: there is a widespread coucern that the age spread iudicated yy the position of low mass stars still ou the Hayashi tracks may be largely. or even eutirely. due ο an artificial spread in the heometric luminosities (cf.Hartimann2001).," The median $L_X$ appears to decrease with increasing age, but we must exercise special care in the interpretation of this trend: there is a widespread concern that the age spread indicated by the position of low mass stars still on the Hayashi tracks may be largely, or even entirely, due to an artificial spread in the bolometric luminosities \citep[cf.][]{har01}."
. The sources of error hat may contribute to uncertainties tu £j4; aud consequent age are indeed utimerous aud include uncertainties in: adopted distance. spectral type and extinction. photometric variability. unresolved companions. aud accretion luminosity.," The sources of error that may contribute to uncertainties in $L_{bol}$ and consequent age are indeed numerous and include uncertainties in: adopted distance, spectral type and extinction, photometric variability, unresolved companions, and accretion luminosity."
 Ou the other haud. if oue were to concede a real age spread in the ONC (plausible as star formation is still talkiug place at the present day). stellar ages 1might Carry a statistical aud relative significauce. though still uncertain on an individual basis: stars tliat we place lower on the Hayashi tracks may be older. on average. than those that we place higher.," On the other hand, if one were to concede a real age spread in the ONC (plausible as star formation is still taking place at the present day), stellar ages might carry a statistical and relative significance, though still uncertain on an individual basis: stars that we place lower on the Hayashi tracks may be older, on average, than those that we place higher."
 This latter hypotliesis is supported by the time evolution of ONC stellar radii recently observed » Rhodeοἱal.(2001)., This latter hypothesis is supported by the time evolution of ONC stellar radii recently observed by \citet{rho01}.
. Although our correlation of Ly with age also seems to argue in favor of a ‘eal age spread. it could also be an artifact of au interrelation between inferred) Ly aud L4. aud he matter remains open.," Although our correlation of $L_X$ with age also seems to argue in favor of a real age spread, it could also be an artifact of an interrelation between inferred $L_X$ and $L_{bol}$, and the matter remains open."
 Indeed the treud in Figure 8. corresponds to a constant ratio of X-ray to iometric lumiuosity at different ages aud cau be interpreted equally well in two different. ways: 1) Stars of equal mass have equal bolometric αμα X-ray luminosities. but there are effects that act in exactly the same way on both Ly auc Lo: 2) These stars are saturated and stay saturated hrough their contraction on the Hayashi tracks. thus keeping La/Lig constant.," Indeed the trend in Figure \ref{fig:LXvsA0a}
 corresponds to a constant ratio of X-ray to bolometric luminosity at different ages and can be interpreted equally well in two different ways: 1) Stars of equal mass have equal bolometric and X-ray luminosities, but there are effects that act in exactly the same way on both $L_X$ and $L_{bol}$ ; 2) These stars are saturated and stay saturated through their contraction on the Hayashi tracks, thus keeping $L_X/L_{bol}$ constant."
 Figure 9 presents a plot of ουν) vs. [ουσε) [οι stars iu the 2—3AL. mass bin ancl 'eveals an age clepeucdence aud a sudden drop of Ly at LogAye)6.5 (a similar drop is also seen in Lxy/Ly4)., Figure \ref{fig:LXvsA0b} presents a plot of $Log(L_X)$ vs. $Log(Age)$ for stars in the $2-3~M_{\odot}$ mass bin and reveals an age dependence and a sudden drop of $L_X$ at $Log(Age) \sim 6.5$ (a similar drop is also seen in $L_X/L_{bol}$ ).
 This is just the age at which a 2.5AL. star dissipates its convective envelope accordingo the SDF modclels. leudiug further evidence for the convection —activity counection found iu," This is just the age at which a $2.5~M_{\odot}$ star dissipates its convective envelope accordingto the SDF models, lending further evidence for the convection –activity connection found in"
where r is the timescale over which the mass is lost.,where $\tau$ is the timescale over which the mass is lost.
 The magnetic energv density is equal to the kinetic energy density at the Alfvénn radius which we find to be We consider this further in Section 4. where we apply our model to the recurrent nova U Sco., The magnetic energy density is equal to the kinetic energy density at the Alfvénn radius which we find to be We consider this further in Section \ref{usco} where we apply our model to the recurrent nova U Sco.
 We parametrise the dipole moment with the magnetic field strength at the stellar surface. Da. so that where fs is the stellar radius of the companion which woe find with equation (13)).," We parametrise the dipole moment with the magnetic field strength at the stellar surface, $B_{\rm
 star}$, so that where $R_2$ is the stellar radius of the companion which we find with equation \ref{rl}) )."
 The specific angular momentum of the ejectec mass that is forced to corotate with the secondary is (63|AUG)0 assuming that the secondary is tically locked.," The specific angular momentum of the ejected mass that is forced to corotate with the secondary is $(a_2^2+KR_{\rm A}^2)\,\Omega$ assuming that the secondary is tidally locked."
 The distance from the centre of mass to the secondary star is The constant A depends on the distribution of the material within the Alfvénn radius., The distance from the centre of mass to the secondary star is The constant $K$ depends on the distribution of the material within the Alfvénn radius.
 ΕΕ it were distributed uniformly within a spherical shell. then A.=22/3.," If it were distributed uniformly within a spherical shell, then $K=2/3$."
 Because the density within the shell varies and the shell itsell will not be perfectly spherical. we take fy=I.," Because the density within the shell varies and the shell itself will not be perfectly spherical, we take $K=1$."
" Thus. the angular momentum. loss from the binary to the ejected material is eiven by We estimate the fraction of the ejected mass that gains angular momentum in this wav to be Now with equations (2)) : We substitute this into equation (6)) with AM,=Am, and AAI=0 to find the change in separation We note that this reduces to equation (7)) when there is no magnetic field."," Thus, the angular momentum loss from the binary to the ejected material is given by We estimate the fraction of the ejected mass that gains angular momentum in this way to be Now with equations \ref{da}) ) and \ref{jobs}) ) we find We substitute this into equation \ref{change}) ) with $\Delta M_1=-\Delta m_1$ and $\Delta M_2=0$ to find the change in separation We note that this reduces to equation \ref{over}) ) when there is no magnetic field."
 In Fig., In Fig.
 2 we plot APP as a function of the mass ratio for cillerent values of the πμAlfvénn radius.," \ref{dadm2} we plot $\frac{\Delta P/P}{\Delta
 m_1/M}$ as a function of the mass ratio for different values of the Alfvénn radius."
 The larger magnetic fields are even capable of producing an overall decrease to the orbital period. during the nova for small mass ratios., The larger magnetic fields are even capable of producing an overall decrease to the orbital period during the nova for small mass ratios.
 In Fig., In Fig.
 I. we also plot MUSmena [orfor anan. Mfvénn.Alfvénn radius of O.75e@ (long dashed line) for comparison with the other models we have considered.," \ref{dadm} we also plot $\frac{\Delta P/P}{\Delta m_1/M}$ for an Alfvénn radius of $0.75\,a$ (long dashed line) for comparison with the other models we have considered."
 For this strong magnetic field. the period change is smaller than with mass transfer to the secondary or [rictional angular momentum losses.," For this strong magnetic field, the period change is smaller than with mass transfer to the secondary or frictional angular momentum losses."
 Lf a secondary star has a large magnetic field then it will significantIv. alter the orbital period. change during a nova outburst., If a secondary star has a large magnetic field then it will significantly alter the orbital period change during a nova outburst.
 ‘There is a critical mass ratio where the additional terni in equation (29)) causes no change to the separation (or orbital period) Ig<qon then the cjeetecd material that is forced to corotate with the secondary gains angular momentum. angular momentum is lost [rom the orbit and so the separation decreases.," There is a critical mass ratio where the additional term in equation \ref{cor}) ) causes no change to the separation (or orbital period) If $q<q_{\rm crit}$ then the ejected material that is forced to corotate with the secondary gains angular momentum, angular momentum is lost from the orbit and so the separation decreases."
 Similarly the orbital period change is smaller than previously predicted., Similarly the orbital period change is smaller than previously predicted.
 Llowever. if dder. then the material Forced. to corotate loses angular moment and the orbital period increases.," However, if $q>q_{\rm crit}$, then the material forced to corotate loses angular momentum and the orbital period increases."
 We plot this in the solidunm. line in Fie. 3.., We plot this in the solid line in Fig. \ref{qc}.
 We note that most observed systems have a mass ratio qd1 (Ritter&Ixolb2003). because there is a critical mass ratio. that depends on AM». above which the mass transfer becomes unstable (e.g.Smith&VanelePutte 2006).," We note that most observed systems have a mass ratio $q\lesssim 1$ \citep{ritter03} because there is a critical mass ratio, that depends on $M_2$, above which the mass transfer becomes unstable \citep[e.g.][]{smith06}."
. Hence in most systems the orbital period will decrease when the effects of à magnetic field are considered., Hence in most systems the orbital period will decrease when the effects of a magnetic field are considered.
 We also plot the dashed line for the mass ratio below which the period change is negative., We also plot the dashed line for the mass ratio below which the period change is negative.
 We see that for the larger magnetic fields it is possible that the orbital period may actually decrease for all mass ratios., We see that for the larger magnetic fields it is possible that the orbital period may actually decrease for all mass ratios.
 This effect. could be significant even for larger mass ratios., This effect could be significant even for larger mass ratios.
 Frictional angular momentum losses only dominate for g=0.01 (Sharactal. so this new mechanism potentially has a greater effect on the orbital period change., Frictional angular momentum losses only dominate for $q\lesssim 0.01$ \citep{shara86} so this new mechanism potentially has a greater effect on the orbital period change.
 There are now ten recurrent novae known in our galaxy ," There are now ten recurrent novae known in our galaxy \citep[the tenth
 one was discovered last year;][]{pagnotta09} "
populate the ERO class.,populate the ERO class.
 The best examples are provided by LBDS53W001 (ROAN= 5.8 2=1.55: Dunlop et al., The best examples are provided by LBDS 53W091 $R-K=5.8$ ; $z=1.55$; Dunlop et al.
 1996: Spinrad et al., 1996; Spinrad et al.
 1997). ERO CL 09039143713D (29.Wy=à: 2o1.6: Soifer et al.," 1997), ERO CL 0939+4713B $R-K=7$; $z\sim 1.6$; Soifer et al."
 1999). and. by most of the EROs ats~1.3 around the QSO 1213-0017 (Liu et al.," 1999), and by most of the EROs at $z\sim 1.3$ around the QSO 1213-0017 (Liu et al."
 2000)., 2000).
 Also near-LR. spectroscopy confirmed that both dusty and old galaxies contribute to the ERO population (Cimatti et al., Also near-IR spectroscopy confirmed that both dusty and old galaxies contribute to the ERO population (Cimatti et al.
 1999)., 1999).
 Understanding the nature and deriving the abundance of EROs is important to shed light on the controversial Issue of the deficit of high-z elliptical galaxies: according to some results. the number of galaxies with the red colours expected for high-z passively evolved. spheroidals is lower compared to the predictions of passive luminosity evolution. (e.g. Ixaullmann. Charlot White 1996: Zepf 1997: Franceschini et al.," Understanding the nature and deriving the abundance of EROs is important to shed light on the controversial issue of the deficit of $z$ elliptical galaxies: according to some results, the number of galaxies with the red colours expected for $z$ passively evolved spheroidals is lower compared to the predictions of passive luminosity evolution (e.g. Kauffmann, Charlot White 1996; Zepf 1997; Franceschini et al."
 1998: Bareer et al., 1998; Barger et al.
 1999)., 1999).
 Llowever. other works cid not confirm the existence of such a deficit up to z~2 (e.g. 'l'otani Yoshii 1997: Benitez ct al.," However, other works did not confirm the existence of such a deficit up to $z\sim 2$ (e.g. Totani Yoshii 1997; Benitez et al."
 1999: Broadhurst. Bowens 1999: Schade et al., 1999; Broadhurst Bowens 1999; Schade et al.
 1999)., 1999).
" As a first step to understand the nature of EROs. we started an imaging survey program aimed at selecting complete samples of such galaxies both in ""empty fields and around. high-z radio-loud. AGN."," As a first step to understand the nature of EROs, we started an imaging survey program aimed at selecting complete samples of such galaxies both in “empty” fields and around $z$ radio-loud AGN."
 In this paper. we present the results of our survey around racdio-Ioud CN at ο>1.5.," In this paper, we present the results of our survey around radio-loud AGN at $z>1.5$."
 The main motivations of such a survey are to investigate whether EROs are more numerous around high-z ACN (as suspected. in previous works: e.g. AleCarthy et al., The main motivations of such a survey are to investigate whether EROs are more numerous around $z$ AGN (as suspected in previous works; e.g. McCarthy et al.
 1992: Dev et al., 1992; Dey et al.
 1995). to select. old. passively evolving galaxies abozI1. hy weir optical/near-I1t. colours. to study the environment of high-z racio-loud XN (e.g. Hall. Green Cohen 1998: Hall Creen 1998 and references therein). ane to search for galaxy cluster candidates at 5.," 1995), to select old passively evolving galaxies at $z>1$ by their optical/near-IR colours, to study the environment of $z$ radio-loud AGN (e.g. Hall, Green Cohen 1998; Hall Green 1998 and references therein), and to search for galaxy cluster candidates at $z>1.5$ ."
 We recal that the most distant. spectroscopically confirmed. cluster known to date bas z=1.27 (Stanford et al., We recall that the most distant spectroscopically confirmed cluster known to date has $z=1.27$ (Stanford et al.
 LOOT: Rosati et al., 1997; Rosati et al.
 1999)., 1999).
 Other works selected cluster candidates aroun quasars at z1.3 and suggested a significant heterogeneity of the cluster galaxies. including both passively evolving ol ellipticals as well as vounger and custy systems (e.g. Hal Green 1998: Liu et al.," Other works selected cluster candidates around quasars at $z>1.3$ and suggested a significant heterogeneity of the cluster galaxies, including both passively evolving old ellipticals as well as younger and dusty systems (e.g. Hall Green 1998; Liu et al."
 2000)., 2000).
" Phroughout this paper we assume Ly=50 + 1 Oy2d) and QO,=0 unless otherwise statect."," Throughout this paper we assume $H_0=50$ $^{-1}$ $^{-1}$, $\Omega_0=1$ and $\Omega_{\Lambda}=0$ unless otherwise stated."
 The survey presented here is based on 2 and. A7 -baux imagine., The survey presented here is based on $R$ - and $K^{\prime}$ -band imaging.
 We observed totally 12. fields: 6 around. racio galaxies (Gs) taken from the ALRC sample selected at 408 Az (AleCarthy et al., We observed totally 14 fields: 6 around radio galaxies (RGs) taken from the MRC sample selected at 408 MHz (McCarthy et al.
 1997. IxXapahii ct al.," 1997, Kapahi et al."
 1998). S arounc raclio-loud quasars (ILOs) taken from the PIS) sample selected at 2.7 Gllz (Wright Ostrupeek 1990).," 1998), 8 around radio-loud quasars (RLQs) taken from the PKS sample selected at 2.7 GHz (Wright Ostrupcek 1990)."
 We note that AIRC101-220 is a broad line radio galaxy (Ixapahi e al., We note that MRC1017-220 is a broad line radio galaxy (Kapahi et al.
 1998)., 1998).
 All the targeted AGN have 1.5«z2.0. with the exception of the quasars PIS 1351-018 (2= 3.71) ane PINS 1556-245 (2= 2.82).," All the targeted AGN have $1.5<z<2.0$, with the exception of the quasars PKS 1351-018 $z=3.71$ ) and PKS 1556-245 $z=2.82$ )."
 The radio powers at rest-frame 5 CllzrangeΓΕ  for RGs to 430.1077--  for RLOs., The radio powers at rest-frame 5 GHz range from $2-5 \times 10^{27}$ $^{-1}$ for RGs to $4-30 \times 10^{27}$ $^{-1}$ for RLQs.
 Table 1 lists the relevant information about the sample., Table 1 lists the relevant information about the sample.
 “Phe fields were selected according to the redshifts of the AGN. to their Galactic latitude (>207) and to their good observability curing the telescope runs.," The fields were selected according to the redshifts of the AGN, to their Galactic latitude $>20^{\circ}$ ) and to their good observability during the telescope runs."
 We have used the predictions of the Bruzual Charlot (1999) evolutionary svnthesis models to define a colour selection. criterion capable to select a complete sample of EROs at high-z., We have used the predictions of the Bruzual Charlot (1999) evolutionary synthesis models to define a colour selection criterion capable to select a complete sample of EROs at $z$.
" In particular. we used instantaneous burst models (also called simple stellar population models. SSP) with cillerent redshifts of formation (2,=2.3.4.5.6) o describe old. spheroidal galaxies."," In particular, we used instantaneous burst models (also called simple stellar population models, SSP) with different redshifts of formation $z_{f}=2,3,4,5,6$ ) to describe old spheroidal galaxies."
 In addition. we also considered. models with exponential time-scale for the star ormation rate. SLRxecp(F/r7). with 7=0.1.0.3 Ce or QO=1.0.1 respectively.," In addition, we also considered models with exponential time-scale for the star formation rate, $SFR \propto exp(-t/\tau)$, with $\tau=0.1,0.3$ Gyr for $\Omega=
1,0.1$ respectively."
 Such models. correspond. to cases with low residual star formation at 2< (ic. <1 M.vr | for a galaxy with mass Maur=10 M. ). and hey are capable to reproduce the colours and the spectra of local ellipticals. as well as the faint galaxy optical colour and vecshift distributions (Pozzetti. Bruzual Zamorani 1996).," Such models correspond to cases with low residual star formation at $z<2$ (i.e. $<1$ $_{\odot}$ $^{-1}$ for a galaxy with mass $_{gal}=10^{11}$ $_{\odot}$ ), and they are capable to reproduce the colours and the spectra of local ellipticals, as well as the faint galaxy optical colour and redshift distributions (Pozzetti, Bruzual Zamorani 1996)."
 A Salpeter IME (0.1.<a<125 M.) and. solar metallicity have been adopted., A Salpeter IMF $0.1<m<125$ $_{\odot}$ ) and solar metallicity have been adopted.
 Models with Scalo IME or with supersolar metallicities reach even redder colours at high-:., Models with Scalo IMF or with supersolar metallicities reach even redder colours at $z$.
 Optical to near-Ht AA. colours derived from the acloptecl evolutionary models are shown in Fig., Optical to near-IR $R-K$ colours derived from the adopted evolutionary models are shown in Fig.
" 1 for two cosmologies (44,=50 + |. Q—0.1)."," 1 for two cosmologies $H_0=50$ $^{-1}$ $^{-1}$, $\Omega=0.1,1$ )."
 The colour selection threshold adopted in our survey is Rolv>6., The colour selection threshold adopted in our survey is $R-K>6$.
 This allows us to select old galaxies at z>1.2 [ormed at zr;23 in both cosmologics., This allows us to select old galaxies at $z>1.2$ formed at $z_{f}>3$ in both cosmologies.
 Ht is relevant to note that for τ 20.3 Gyr and zy<3. colours 2.AN>6 are never reached.," It is relevant to note that for $\tau>$ 0.3 Gyr and $z_{f}<3$, colours $R-K>6$ are never reached."
 In other words. colours 2A6 select old. galaxies whieh had a short episode of star formation in carly cosmological epochs.," In other words, colours $R-K>6$ select old galaxies which had a short episode of star formation in early cosmological epochs."
 For instance. assuming no cust extinction. a galaxy at z 21.5 with RoA>6 should have SpIOX. an age C2 Gaver (04= 1.0) or 3 Gyr (04=0.1) and SER<<1 M.vyr. +.," For instance, assuming no dust extinction, a galaxy at $z\approx$ 1.5 with $R-K>6$ should have $z_{f}>3$, an age $>$ 2 Gyr $\Omega_0=1.0$ ) or $>$ 3 Gyr $\Omega_0=0.1$ ) and $SFR<<1$ $_{\odot}$ $^{-1}$ ."
 eear-infrared imagine was done on 1997 April 1-3 with rw ESO/AIPL 2.2m telescope. with the HUXC2D. camera (Moorwood ct al., Near-infrared imaging was done on 1997 April 1-3 with the ESO/MPI 2.2m telescope with the IRAC2B camera (Moorwood et al.
" 1992) equipped with a 256 11οςαΤο array (0.506"" /pixel).", 1992) equipped with a $\times$ 256 HgCdTe array $^{\prime \prime}$ /pixel).
" We used the A"" filter in order to reduce 1e thermal noise.", We used the $K^{\prime}$ filter in order to reduce the thermal noise.
 The sky conditions were photometric and 10 seeing. was around 1.07. o, The sky conditions were photometric and the seeing was around $^{\prime \prime}$.
sPhe observations. were done aking a number of background-limited. images (typically 10-14) with the telescope moved LO” between cach image., The observations were done taking a number of background-limited images (typically 10-14) with the telescope moved $10^{\prime \prime}$ between each image.
 In each telescope position. theexposures were typically 120 seconds long (c.g. 12 images cach with an exposuretime of 10 seconds).," In each telescope position, theexposures were typically 120 seconds long (e.g. 12 images each with an exposuretime of 10 seconds)."
 “Phe data reduction was performed. using the ΗΛ reduction package and using the method outlined by Villani di Serego Alighieri (1099)., The data reduction was performed using the IRAF reduction package and using the method outlined by Villani di Serego Alighieri (1999).
 Photometric calibration was obtained observing standard. stars from the Carter Meadows. (1995). sample., Photometric calibration was obtained observing standard stars from the Carter Meadows (1995) sample.
 Phe typical night-to-night scatter in the zero-points was around 0.03 magnitudes., The typical night-to-night scatter in the zero-points was around 0.03 magnitudes.
" The conversion from A"" to A magnitudes inthe SAAO-Carter", The conversion from $K^{\prime}$ to $K$ magnitudes inthe SAAO-Carter
showing weak or even abscut thermal features) display very high peak frequencics: in IIBL. which appear to be the less powerful objects (with typical Iuuinosities 107 ere cm? 1) the first peals falls in the UV-soft Naav baud aud the high energv component can peak near the TeV reeion.,"showing weak or even absent thermal features) display very high peak frequencies: in HBL, which appear to be the less powerful objects (with typical luminosities $10^{42}$ erg $^{-2}$ $^{-1}$ ) the first peak falls in the UV-soft X-ray band and the high energy component can peak near the TeV region."
 This behaviour has been iuterpreted (Cbisellini et al., This behaviour has been interpreted (Ghisellini et al.
 1998. recently revisited in (κοπια et al.," 1998, recently revisited in Ghisellini et al."
 2002) as the result of a balance. between a acceleration i1 cooling suffered. by the electrons producing the radiation at the peaks., 2002) as the result of a balance between a acceleration an cooling suffered by the electrons producing the radiation at the peaks.
 Iu the assumption that the acceleration rate is coustant in all the sources. the sequence ean be successfully interpreted as due to au increasing cooling rate (dominated iu most of the sources by IC losses) from the low-power BL Lacs to the powerful FSRQs.," In the assumption that the acceleration rate is constant in all the sources, the sequence can be successfully interpreted as due to an increasing cooling rate (dominated in most of the sources by IC losses) from the low-power BL Lacs to the powerful FSRQs."
 SEDs can be satisfactorily reproduced by simple cussion models (e.g. Clisellini et al., SEDs can be satisfactorily reproduced by simple emission models (e.g. Ghisellini et al.
 1998. Tavecchio et al.," 1998, Tavecchio et al."
 1998). vielding the value of the main plwvsical quautitics of the jet. such as electron density and cnereyv. magnetic fold. size of the region.," 1998), yielding the value of the main physical quantities of the jet, such as electron density and energy, magnetic field, size of the region."
 In particular miecasuring the N-ray spectra aud adapting a broad band model to their SEDs vields reliable estimates of the total ΙΟ: of relativistic particles involved. which is dominated by those at the lowest energies.," In particular measuring the X-ray spectra and adapting a broad band model to their SEDs yields reliable estimates of the total number of relativistic particles involved, which is dominated by those at the lowest energies."
 This is interesting iu view of a determination of the total cnerey fiux along the jet (e.g. Celotti et al., This is interesting in view of a determination of the total energy flux along the jet (e.g. Celotti et al.
 1997. Sikora ct al.," 1997, Sikora et al."
 1997)., 1997).
 The total  kinetic” power of the jet can be written as: where AR is the jet radius. D ds the bulk Lorentz factor aud Ü is the total energy deusitv in the jet. including radiation. magnetic field. relativistic particles aud eventually protous.," The total "" kinetic"" power of the jet can be written as: where $R$ is the jet radius, $\Gamma$ is the bulk Lorentz factor and $U$ is the total energy density in the jet, including radiation, magnetic field, relativistic particles and eventually protons."
 If one assumes that there is 1 (cold) proton per relativistic electron. the proton contribution is usually dominant.," If one assumes that there is 1 (cold) proton per relativistic electron, the proton contribution is usually dominant."
 Iu Fig., In Fig.
 2 the derived radiative huninosity £44 aud kinetic power of the jet Pia for a group of sources with sufficieutlv good spectral information are compared., 2 the derived radiative luminosity $L_{\rm jet}$ and kinetic power of the jet $P_{\rm jet}$ for a group of sources with sufficiently good spectral information are compared.
" The ratio between these two quantities eives directly the ""radiative efficiency? of the jet. which turis out to be jj20.1. though with large scatter."," The ratio between these two quantities gives directly the “radiative efficiency” of the jet, which turns out to be $\eta\simeq 0.1$, though with large scatter."
 The line traces the result of a least-squares ft: we found a slope ~1.3. suggesting a decrease ofthe radiative efficiency. with decreasing power.," The line traces the result of a least-squares fit: we found a slope $\sim 1.3$, suggesting a decrease of the radiative efficiency with decreasing power."
 Two iain classes of models for the production of jets has been proposed., Two main classes of models for the production of jets has been proposed.
 The frst class considers the extraction of rotational enerev from the black, The first class considers the extraction of rotational energy from the black
"dashed lines uutil they eventually intersect the cooling inflow at some large radius r,..",dashed lines until they eventually intersect the cooling inflow at some large radius $r_c$.
"audThe europe of the bubbles and flow are identical atr, the bubbles provide Bonjust chough gas to maintain the inflowing cooling flow that radius.", The entropy of the bubbles and flow are identical at $r_c$ and the bubbles provide just enough gas to maintain the inflowing cooling flow from that radius.
 The third row of paucls(ο. aud. À) shows the uegative cooling inflow with solid lines aud he much faster outward motion of the riiug bubbles. ej>.0. with dashed lines.," The third row of panels, and ) shows the negative cooling inflow with solid lines and the much faster outward motion of the rising bubbles, $u_b > 0$, with dashed lines."
 The variation of the bubble radius ois shown in thebottom row of panels(df aud 2 with dash- lines.," The variation of the bubble radius $r_b(r)$ is shown in the bottom row of panels, and ) with dash-dotted lines."
 The dashed lines iu these bottom panels show the variation of the inflow volume filling factor f(r)., The dashed lines in these bottom panels show the variation of the inflow volume filling factor $f(r)$.
 As h approaches the highest possible value for each bubble mass mp. ho» huyus thebubbles nearly fill the eutire available volume at kj where f0 0. as explained by Condition (21).," As $h$ approaches the highest possible value for each bubble mass $m_b$, $h \rightarrow h_{max}$ , the bubbles nearly fill the entire available volume at $r_h$ where $f \rightarrow 0$ , as explained by Condition (21)."
" For the most massive bubbles cousidered. ay,=LO A... solutions for two heating parameters are shown. )—3 and 6 for which the circulation radi are r,LO and 25 kpe respectively."," For the most massive bubbles considered, $m_b = 10^6$ $M_{\odot}$, solutions for two heating parameters are shown, $h = 3$ and 6 for which the circulation radii are $r_c = 10$ and 25 kpc respectively."
 The deusity. temperature and velocity profiles for the cooling inflows for these two solutions are alinost ideutical.," The density, temperature and velocity profiles for the cooling inflows for these two solutions are almost identical."
" We have not considered larger values of h because thebubble velocity «, for the f=6 solution the sound speed iu the cooling flow (50/3)?=ee(T/lO Klaus. |.", We have not considered larger values of $h$ because the bubble velocity $u_b$ for the $h = 6$ solution approaches the sound speed in the cooling flow $(5 \theta /3)^{1/2} = 476~(T/10^7~{\rm K})$ km $^{-1}$.
 Larger / would result in supersonic bubble velocities that would drive shocks iuto the cooling eas. drsinatficallv increasing its temperature.," Larger $h$ would result in supersonic bubble velocities that would drive shocks into the cooling gas, dramatically increasing its temperature."
 Also the bubble size attorj for the f=6 solution. η)~1 kpc Is Colmparable rp. again arene agaist larger values of h.," Also the bubble size at $r_h$ for the $h = 6$ solution, $r_b(r_h) \sim 1$ kpc is comparable to $r_h$, again arguing against larger values of $h$."
 The ceutral column of Fiewe 2 illustrates two circulation flows forbubbles of mass me=Q0 AL. for h —3aud 6.5., The central column of Figure 2 illustrates two circulation flows for bubbles of mass $m_b = 10^5$ $M_{\odot}$ for $h = 3$ and 6.5.
" The circulation with —x6.5 extends out to =[8 kpc. but the flow fillime factor f less than abou Ll atory so there are uo circulations with fo6.5zchi, (Condition 21)."," The circulation with $h = 6.5$ extends out to $r_c = 18$ kpc, but the flow filling factor $f$ is less than about 0.1at $r_h$ so there are no circulations with $h > 6.5 \approx h_{max}$ (Condition 21)."
" Iu order for this mareial flow to suppor unss flux M. the relative flow muo nuust as SOory, and the drag increases accordinely."," In order for this marginal flow to support mass flux ${\dot M}$ , the relative flow $u_b - u$ must increase as $r \rightarrow r_h$ and the drag increases accordingly."
" The pirebubble velocity a, is secu to decline toward +).", The bubble velocity $u_b$ is seen to decline toward $r_h$.
" As a result he laree drag. the effective eravity g,. (Equation 15) is directed outward near ry,lL kpe where the flow woul Ravleigh-Tavlor unstable."," As a result of the large drag, the effective gravity $g_e$ (Equation 15) is directed outward near $r_h = 1$ kpc where the flow would be Rayleigh-Taylor unstable."
 This region of instability vecolmcs larger for higher values of 5., This region of instability becomes larger for higher values of $h$.
" Because of the approximations we have made. the deusitv in the flow region ry«or<r, is somewhat higher than the density observed iu NCC I172 (dotted lines)."," Because of the approximations we have made, the density in the flow region $r_h < r < r_c$ is somewhat higher than the density observed in NGC 4472 (dotted lines)."
" However. if this flow were observed. the appareut density iyap, would be owered since the flow only occupies a fraction. f£ of the volume. Le. n,app!)29f2r)."," However, if this flow were observed, the apparent density $n_{e,app}$ would be lowered since the flow only occupies a fraction $f$ of the volume, i.e., $n_{e,app}(r) \approx f^{1/2} n_e(r)$."
 The frst cohuun in Fieure 2 shows the circulation ραίσα for bubbles of mass ney«10! AL. for two flows with h=3 aud , The first column in Figure 2 shows the circulation pattern for bubbles of mass $m_b = 3 \times 10^4$ $M_{\odot}$ for two flows with $h = 3$ and 3.6.
The flow fllius factor f is dropping rapidly as ro>ry for the f=3.6 solution so lis is close to the maximum possible heating (and 7.) for hese smallerbubbles., The flow filling factor $f$ is dropping rapidly as $r \rightarrow r_h$ for the $h = 3.6$ solution so this is close to the maximum possible heating (and $r_c$ ) for these smaller bubbles.
" We were unable to achieve fully convergent flow solutions with even sinallerbubbles of nass nn,S&SLO’ ALL.", We were unable to achieve fully convergent flow solutions with even smaller bubbles of mass $m_b \lta 10^4$ $M_{\odot}$ .
" While our search for such solutions was not exhaustive. if is apparent from the trend im pauclsk »g > ein Figure 2 that the maximaun values of u;. 7 and r,. all decrease with my. as expected frou condition 22),"," While our search for such solutions was not exhaustive, it is apparent from the trend in panels $\rightarrow$ $\rightarrow$ in Figure 2 that the maximum values of $u_b$, $h$ and $r_c$ all decrease with $m_b$, as expected from condition (22)."
" Bubbles of mass ai,=3<104 AL. are approaching the minima 25 necessary to carry the cooling mass flow AT foy auy heating 5h21.", Bubbles of mass $m_b = 3 \times 10^4$ $M_{\odot}$ are approaching the minimum $m_b$ necessary to carry the cooling mass flow ${\dot M}$ for any heating $h > 1$.
 Nou-circulating flows with bubbles of lower mass must ultimately cool radiativelv to temperatures mich lower than Trj). iu disagreement with NADAL observations.," Non-circulating flows with bubbles of lower mass must ultimately cool radiatively to temperatures much lower than $T(r_h)$, in disagreement with XMM observations."
 One of the motivations for our exploration of nou-rocks circulation flows is to estimate the influence of the bubbles on the apparent eas temperature which typically has a nuninuun near the origin., One of the motivations for our exploration of non-cooling circulation flows is to estimate the influence of the bubbles on the apparent gas temperature which typically has a minimum near the origin.
 To simulate the apparcut temperature that would be inferred when viewiug the cooling inflow aud the hot rising bubbles aloug the same lue of sight. we calculated the local cuission-weighted telpcrature which is plotted as dotted lines for each of the flows in panels5.f audj of Figure 2.," To simulate the apparent temperature that would be inferred when viewing the cooling inflow and the hot rising bubbles along the same line of sight, we calculated the local emission-weighted temperature which is plotted as dotted lines for each of the flows in panels, and of Figure 2."
 For most circulation flows (7) is nearly iudistinguisliable frou the temperature of the cooling flow component., For most circulation flows $\langle T\rangle$ is nearly indistinguishable from the temperature of the cooling flow component.
 Consequcuth. a sinele phase interpretation of the temperature profile would show a mildly positive eradieut. dffdro>0. similar to those observed aud consisteut with traditional cooling flows.," Consequently, a single phase interpretation of the temperature profile would show a mildly positive gradient, $dT/dr > 0$, similar to those observed and consistent with traditional cooling flows."
 This is a desirable feature of the circulation model., This is a desirable feature of the circulation model.
 Qu for the least iuassive bubbles cousidered. mdifferential«10! AL... does (P3 vise slightly as r>ry. but the change in the temperature profile caused by the hot bubbles is xnall.," Only for the least massive bubbles considered, $m_b = 3 \times 10^4$ $M_{\odot}$, does $\langle T\rangle$ rise slightly as $r \rightarrow r_h$, but the differential change in the temperature profile caused by the hot bubbles is small."
 Tle apparent density pap)(C023)72. and eutropy profiles are also similar to those of the cooling flow component alouc.," The apparent density $\rho_{app} =
(\langle \rho^2 \rangle)^{1/2}$ and entropy profiles are also similar to those of the cooling flow component alone."
" We stress that these results differ from normal couvection where (1) there is a single temperature and density at every radius (apart from fluctuations). (2) the temperature eradieut is determined by the gravitational potential. dffdr=(270,ΕΙ fdr). aud theretore has a sig opposite to that observed. aud (3) the entropy is constant."," We stress that these results differ from normal convection where (1) there is a single temperature and density at every radius (apart from fluctuations), (2) the temperature gradient is determined by the gravitational potential, $dT/dr = -(2 \mu m_p/5 k)(d \Phi /dr)$ , and therefore has a sign opposite to that observed, and (3) the entropy is constant."
" The ratio of Pd/V heating to drag heating is where a,«|e] appropriateand sve use qzzLAF«10Ln cms ? whichis for lXors 1003 NCC 1172.", The ratio of $PdV$ heating to drag heating is where $u_b \ll |u|$ and we use $g \approx 4.47 \times 10^{-7} r_{kpc}^{-0.85}$ cm $^{-2}$ which is appropriate for $1 \lta r_{kpc} \lta 100$ in NGC 4472.
" The result Z,4;/2,471 follows nunediately frou Equation (13) provided dui, ΠΜ "," The result ${\dot \varepsilon}_{pdv}/{\dot \varepsilon}_d 
\sim 1$ follows immediately from Equation (13) provided $u_b \ll |u|$."
"of the uncertain physical nature of these two comparablebubble-flow heating mechanisimnis. we cousider heating due to bubble expansion and drag separately,"," In view of the uncertain physical nature of these two comparable bubble-flow heating mechanisms, we consider heating due to bubble expansion and drag separately."
 Figure 23 illustrates four represcutative cooling flow models in which the work done by the drag force is assuned to leat the local cooling flow eas with various efficiencies ο) (aud Cyd.= 0)., Figure 3 illustrates four representative cooling flow models in which the work done by the drag force is assumed to heat the local cooling flow gas with various efficiencies $e_d$ (and $e_{pdv} = 0$ ).
" As before AT07 M. t and ry,=1d kpe for allflows.", As before ${\dot M} = 0.7$ $M_{\odot}$ $^{-1}$ and $r_h = 1$ kpc for allflows.
" The fourflows also have the same bubble mass a,=10° M. and heating factor 5h=6. but thebubble drag heating cfiicieucy has values e,= 0. 0.1. 0.3 and0.7."," The fourflows also have the same bubble mass $m_b = 10^5$ $M_{\odot}$ and heating factor $h = 6$, but the bubble drag heating efficiency has values $e_d = 0$ , 0.1, 0.3 and0.7."
 Flows with progressively lugher T. 75 aud » near the heating radius ky correspoud to increasing efficiencies.," Flows with progressively higher $T$, $T_b$ and $n$ near the heating radius $r_h$ correspond to increasing efficiencies."
 By contrast. the circulation radii. velocitics.filling factors audbubble radii are inscusitive to the heating efficieucy.," By contrast, the circulation radii, velocities,filling factors and bubble radii are insensitive to the heating efficiency."
 However. the flow with the largest heating efiicieucy. ο=OF is less satisfactory because flow teniperature aud particularly the appareut temperature(75 develop appreciable negative radial gradieuts ucar rj.," However, the flow with the largest heating efficiency, $e_d = 0.7$ is less satisfactory because flow temperature and particularly the apparent temperature$\langle T \rangle$ develop appreciable negative radial gradients near $r_h$ ."
 Because of, Because of
seven of them show neeligible absorption. or do not show any band or line so they. were discarded for the gas mixtures.,"Seven of them show negligible absorption, or do not show any band or line so they were discarded for the gas mixtures."
 We have chosen high puritv gases commercially. available with deeper absorptions and wider spectral coverage. adding and/or replacing individual eases with new ones. includiug acetvlene. nitrous oxide. hydrocarbons ancl chloromethans. using different partial pressures.," We have chosen high purity gases commercially available with deeper absorptions and wider spectral coverage, adding and/or replacing individual gases with new ones, including acetylene, nitrous oxide, hydrocarbons and chloromethans, using different partial pressures."
 All of them are safe (ο use at this small concentrations. are nol corrosive and are gaseous al room temperature: (his makes (hem suitable for regular eround-based In total we have worked with five new different. mixtures (see Figure 5)).," All of them are safe to use at this small concentrations, are not corrosive and are gaseous at room temperature; this makes them suitable for regular ground-based In total we have worked with five new different mixtures (see Figure \ref{fig2}) )."
 We have listed the composition in Table 4.., We have listed the composition in Table \ref{tab2}.
 Due to the number of gas cells available. only three have been measured twice for stability. study.," Due to the number of gas cells available, only three have been measured twice for stability study."
 The first two new mixtures (namely Mixture-I. 111. included nitrous oxide. acetvlene. methane and/or ehloromethans: only Mixture-I was measured on (wo occasions three months apart.," The first two new mixtures (namely Mixture-I, II), included nitrous oxide, acetylene, methane and/or chloromethans; only Mixture-I was measured on two occasions three months apart."
 We found Mixture-I to be stable. with differences on the measurements lower than on band absorption intensity and nnm on line position.," We found Mixture-I to be stable, with differences on the measurements lower than on band absorption intensity and nm on line position."
 Dased on (his mixture. three additional mixtures introducing ammonia and hydrocarbons were produced. namely NIL;i-I. HH: and HII.," Based on this mixture, three additional mixtures introducing ammonia and hydrocarbons were produced, namely $_{3}$ -I, II and III."
 The mixture δα Π was measured eight months apart and remained stable with time ancl temperature. but we have discarded methane because of the atmospheric absorption.," The mixture $_{3}$ -II was measured eight months apart and remained stable with time and temperature, but we have discarded methane because of the atmospheric absorption."
 We have carried ont a characterization of the NIL4-HI gas cell bv means of an Infrared Fourier Transform (FTIR) Spectrometer (Domen DAS). located at the University of Central Florida (USA).," We have carried out a characterization of the $_{3}$ -III gas cell by means of an Infrared Fourier Transform (FTIR) Spectrometer (Bomen DA8), located at the University of Central Florida (USA)."
 The instrument makes use of a InSb (€ Indium Antimonice) detector. a cquartz-halogen lamp as source and a quartz beam-splitter.," The instrument makes use of a InSb ( Indium Antimonide) detector, a quartz-halogen lamp as source and a quartz beam-splitter."
 The spectrum was obtained wider vacuum (< 5mTorr) at 23°C with a resolution of 0.1 + (R = 40000 at 2.5 jm)., The spectrum was obtained under vacuum $<$ 5mTorr) at $\degr$ C with a resolution of 0.1 $^{-1}$ (R = 40000 at 2.5 $\mu$ m).
 The cell was measured with Cary 5 and on two separate occasions wilh FTIR. three and eight months apart., The cell was measured with Cary 5 and on two separate occasions with FTIR three and eight months apart.
" Figure ?? compares a high resolution measurement with the low resolution measurement. an ammonia gas cell NIL, + Argon). a M9 brown dwar moclel (I. ~ 65000) and a telluric spectra in absorption (from top to bottom)."," Figure \ref{3} compares a high resolution measurement with the low resolution measurement, an ammonia gas cell $_{3}$ + Argon), a M9 brown dwarf model (R $\sim 65000$ ) and a telluric spectra in absorption (from top to bottom)."
" This gas cell consists on a mixture of NoO. Πο, CICIL,. CISCIIS. NIE. a-Dutvlene and Trans--butvlene."," This gas cell consists on a mixture of $_{2}$ O, $_{2}$ $_{2}$, $_{3}$, $_{2}$ $_{2}$, $_{3}$, $\alpha$ -Butylene and $\beta$ -butylene."
 There are (wo main bands covering a significant fraction of the II-band (red vertical lines) which are not heavily affected by telluric absorptions and (thus make them object of interest for accurate velocity measurements., There are two main bands covering a significant fraction of the H-band (red vertical lines) which are not heavily affected by telluric absorptions and thus make them object of interest for accurate velocity measurements.
 The first one is clearly seen as a forest [rom 1.471.54 jan. mainly due to acetvlene absorption (53 lines resolved al 0.1 ! between mn: Ίου 66000) but also ammonia.," The first one is clearly seen as a forest from 1.47–1.54 $\mu$ m, mainly due to acetylene absorption (53 lines resolved at 0.1 $^{-1}$ between $\mu$ m; $\sim 66000$ ) but also ammonia."
 Acetvlene was one of the first candidates and was already used, Acetylene was one of the first candidates and was already used
instead: based: purely. upon whether the periodic signal is persistent in time and frequency. and upon the shape of the pulse profile. with little or no indication of whether à source is actually terrestrial in origin.,"instead based purely upon whether the periodic signal is persistent in time and frequency, and upon the shape of the pulse profile, with little or no indication of whether a source is actually terrestrial in origin."
 This led to there being an overwhelming number of candidates. especially at low DM.," This led to there being an overwhelming number of candidates, especially at low DM."
 A typical single beam from the survey would generate ~ 170 candidates. leading to à total of over 3.5 million candidates in the survey.," A typical single beam from the survey would generate $\sim$ 170 candidates, leading to a total of over 3.5 million candidates in the survey."
 This large number of candidates is impossible to filter ov eve and so some automated filters were designed to reduce he number to be viewed., This large number of candidates is impossible to filter by eye and so some automated filters were designed to reduce the number to be viewed.
 As the MMD receiver has multiple »eanms. it allows us to compare each of the beams from the same observation. and assume that if à periodic signal is detected in many beams. then it is likely to be grouncd-based VL," As the MMB receiver has multiple beams, it allows us to compare each of the beams from the same observation, and assume that if a periodic signal is detected in many beams, then it is likely to be ground-based RFI."
 Fherefore. any periodicities which appeared in two or more beams from the same pointing and had a period which matched within a tolerance of 10 ns were rejected.," Therefore, any periodicities which appeared in two or more beams from the same pointing and had a period which matched within a tolerance of 10 ns were rejected."
 As shown in equation (4)). the S/N of a periodic signal decreases as the elfective pulse width increases for a given set of observing parameters.," As shown in equation \ref{senseq}) ), the S/N of a periodic signal decreases as the effective pulse width increases for a given set of observing parameters."
 The effective width is given by where Wap is equal to the sampling rate and. 7; is a distortion in the pulse width due to scattering in the LSAL (given by equation (6)))., The effective width is given by where $W_{\mathrm{samp}}$ is equal to the sampling rate and $\tau_\mathrm{s}$ is a distortion in the pulse width due to scattering in the ISM (given by equation \ref{bhatscatter}) )).
 Equation (3)) can be used to give Af. where Av is now the bandwidth of a single filterbank channel.," Equation \ref{dispersion}) ) can be used to give $\Delta t$, where $\Delta\nu$ is now the bandwidth of a single filterbank channel."
 This broadening of the pulse arises due to the decispersion process and the finite width of the filterbank channels in the observing svstem., This broadening of the pulse arises due to the dedispersion process and the finite width of the filterbank channels in the observing system.
 Fig., Fig.
 G shows S/N against trial DAL error for signals with duty eveles of50%.. and it can be seen that S/N drops olf more quickly Xfor narrower pulses.," \ref{snr_vs_dm_w} shows S/N against trial DM error for signals with duty cycles of, and; it can be seen that S/N drops off more quickly for narrower pulses."
 Fhus. a filter was applied. to the candidates to reject any with a width greater than of the period. which eliminated sinusoidal signals often indicative of REL which are often of high S/N for à very large range of trial DAIs.," Thus, a filter was applied to the candidates to reject any with a width greater than of the period, which eliminated sinusoidal signals often indicative of RFI, which are often of high S/N for a very large range of trial DMs."
 In total. these two filters removed ~15% of the candidates from the processing pipeline.," In total, these two filters removed $\sim$ of the candidates from the processing pipeline."
 During the inspection of the candidates. a further cut was made. removing all candidates with S/N κ 9.," During the inspection of the candidates, a further cut was made, removing all candidates with S/N $<$ 9."
 This removed. a further of the candidates. with many of those remaining clustered around common REL frequencies.," This removed a further of the candidates, with many of those remaining clustered around common RFI frequencies."
 ]t is common. curing the inspection process. to visualise the candidates in. Period-DAL space (for an example using the JReaper software. soe Fig.," It is common, during the inspection process, to visualise the candidates in Period-DM space (for an example using the JReaper software, see Fig."
 2 in 2)). so that any ‘clustering’ of the candidates at RET frequencies is highly apparent. making it easier for such candidates to be ignored.," 2 in \citet{kel+09}) ), so that any `clustering' of the candidates at RFI frequencies is highly apparent, making it easier for such candidates to be ignored."
 This reduced the number of candidates to 10000. and given that it takes only a few seconds to classify a cancidate. this allowed visual inspection of this subset of the survey output.," This reduced the number of candidates to $\sim10000$, and given that it takes only a few seconds to classify a candidate, this allowed visual inspection of this subset of the survey output."
 The first. processing of the data. by2.. uncovered. one previously unknown pulsar. the voung and highly energetic PSR. 6132.," The first processing of the data, by\citet{obrien08}, uncovered one previously unknown pulsar, the young and highly energetic PSR $-$ 6132."
 ? noted that the pulsar was within the error box of the ECRET source 3E: 6147 and it is within that of the Fermi source 6128c (C2).., \citet{obrien08} noted that the pulsar was within the error box of the EGRET source 3EG $-$ 6147 and it is within that of the Fermi source $-$ 6128c \citep{abdoetal}.
 The pulsar is regularly observed at Parkes as part of the timing support for the Fermi mission (2).. but as vet pulsations in eamma-ravs have not been detected (?)..," The pulsar is regularly observed at Parkes as part of the timing support for the Fermi mission \citep{weltevrede2010}, but as yet pulsations in gamma-rays have not been detected \citep{fermipsrcat}."
 One further pulsar. PSR 0812. with a period of 491 ms and a DM o£ 1023em?pe was discovered during the reprocessing of the Galactic-plane data (detailed in Section 77)).," One further pulsar, PSR $-$ 0812, with a period of 491 ms and a DM of $1023\,\mathrm{cm}^{-3}\,\mathrm{pc}$ was discovered during the reprocessing of the Galactic-plane data (detailed in Section \ref{sec:reprocessing}) )."
" As seen in the top panel of Fig. Ἐν,"," As seen in the top panel of Fig. \ref{1834prof},"
 the pulse profile αἱ 6.5 Gilg is narrow with a duty evele of only2:4... which ensured that the S/N was significantly lower away from the true value of DM. as shown in Fi .," the pulse profile at 6.5 GHz is narrow with a duty cycle of only, which ensured that the S/N was significantly lower away from the true value of DM, as shown in Fig. \ref{1834snrdm}."
 The pulsar has been observed at a frequency of 4.85Giz using the IElfelsberg 100-m radio telescope. and at 1.4 Cillz with the Lovell telescope.," The pulsar has been observed at a frequency of $4.85\,\mathrm{GHz}$ using the Effelsberg 100-m radio telescope, and at 1.4 GHz with the Lovell telescope."
 The profile is extremely. scatter broacdencd at this. frequency. with a scattering. time of 7150 ms.," The profile is extremely scatter broadened at this frequency, with a scattering time of $\sim$ 150 ms."
 “Phe pulse profiles at 4.55 ancl 1.4 Cllz are shown in the bottom two panels of Fig. 7.., The pulse profiles at 4.85 and 1.4 GHz are shown in the bottom two panels of Fig. \ref{1834prof}.
 Processing of the data taken around the Galactic centre was completed in August 2006 and resulted in an excellent candidate., Processing of the data taken around the Galactic centre was completed in August 2006 and resulted in an excellent candidate.
 Lhe candidate was subsequently confirmed to be a pulsar. PSR J1746 2850. with a period of 1077ms and a DM of 963em.?pe in an observation made on October 29. 2006.," The candidate was subsequently confirmed to be a pulsar, PSR $-$ 2850, with a period of $1077\,\mathrm{ms}$ and a DM of $963\,\mathrm{cm}^{-3}\,\mathrm{pc}$ in an observation made on October 29, 2006."
 Subsequently. this pulsar was also seen by2.. who have published a full timing solution.," Subsequently, this pulsar was also seen by\citet{deneva2009}, who have published a full timing solution."
 A folded. pulse profile of this pulsar from a confirmation observation taken with the MMD receiver is shown in Fig. 9.., A folded pulse profile of this pulsar from a confirmation observation taken with the MMB receiver is shown in Fig. \ref{1746prof}. .
 Parameters for PSRs 2850 and. 0812 are shown in Table 2.. including DAI distances estimated," Parameters for PSRs $-$ 2850 and $-$ 0812 are shown in Table \ref{psrpars}, , including DM distances estimated"
through the proper motions of the LAIC or probing the local ISM.,through the proper motions of the LMC or probing the local ISM.
 We thank Sarah Brough. our support astrononicr. for help απο the observing run.," We thank Sarah Brough, our support astronomer, for help during the observing run."
 We thank Jaroszvüsski for the helpful discussion on MOS | 700210.1., We thank Jaroszyńsski for the helpful discussion on MQS $-$ 700210.1.
. We also. thank. the anonvunious referee. whose coments helped us to nuprove the mauuscript.," We also thank the anonymous referee, whose comments helped us to improve the manuscript."
 This research was mace based ou observations with the Anelo-Australian Telescope. for which the observing time was erated bv the Optical Infrared Coordination Network for Astronomy (OPTICON).," This research was made based on observations with the Anglo-Australian Telescope, for which the observing time was granted by the Optical Infrared Coordination Network for Astronomy (OPTICON)."
 This research has mace use of the SIMDAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France."
 This research has also made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory (JPL). California Tustitute of Technologv (Caltech). uuder contract with the National Aeronautics aud Space Administration (NASA).," This research has also made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory (JPL), California Institute of Technology (Caltech), under contract with the National Aeronautics and Space Administration (NASA)."
" Support for this work was provided by the Polish Ministry of Science and IHügher Education (NENISW) through the program ""Iuveutus Plus. award ΙΟ IP2010 020170 to SA. AALS. and A.U. This work das been supported bx NSF erants AST-OTOSOS2 and AST-1009756G to C.S.K. The OGLE is supported by the Enropean Research. Council wader the European Coumuuity’s Seventh Framework Programe (FP7/2007-2013). ERC eraut agreement no."," Support for this work was provided by the Polish Ministry of Science and Higher Education (MNiSW) through the program “Iuventus Plus”, award number IP2010 020470 to S.K., A.M.J., and A.U. This work has been supported by NSF grants AST-0708082 and AST-1009756 to C.S.K. The OGLE is supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013), ERC grant agreement no."
 216678 to AU., 246678 to A.U.
very narrow.,very narrow.
 The last column in Table 1. shows whether we have achieved convergent migration or not., The last column in Table \ref{tab1} shows whether we have achieved convergent migration or not.
" In this table ""convergent/divergent means that the relative migration of the planets reversed during the evolution."," In this table ""convergent/divergent"" means that the relative migration of the planets reversed during the evolution."
 Similarly as in our previous paper. we have tried to determine the initial conditions appropriate for the convergent migration using the analytic formulae given by equations (13) for the Super-Earth ancl (3)) or (4)) for the eas giant.," Similarly as in our previous paper, we have tried to determine the initial conditions appropriate for the convergent migration using the analytic formulae given by equations \ref{tanaka}) ) for the Super-Earth and \ref{kl}) ) or \ref{redgar}) ) for the gas giant."
 Llowever. we have found as in Edgar(2007) hat in an isothermal viscous disc a giant planet does not obey the standard tvpe LL migration and. hence migration does not proceed on the viscous timescale.," However, we have found as in \citet{edgar} that in an isothermal viscous disc a giant planet does not obey the standard type II migration and hence migration does not proceed on the viscous timescale."
 That is why we iive performed a series of numerical experiments in order o examine under which conditions it is possible to obtain convergent migration., That is why we have performed a series of numerical experiments in order to examine under which conditions it is possible to obtain convergent migration.
 Using the full 2D hvdrodynamical code NIRVANA we nave caleulated the evolution of the orbital elements of the rlanets embedded in the gaseous disc in the region where he exterior first order mean motion resonances are located., Using the full 2D hydrodynamical code NIRVANA we have calculated the evolution of the orbital elements of the planets embedded in the gaseous disc in the region where the exterior first order mean motion resonances are located.
 The gas giant planet has been placed always at the distance lin our units and the Super-Earth further away from the star (see Table 12). starting from a small separation between planets of the order of a few Jupiters Lill radii. and then increasing it.," The gas giant planet has been placed always at the distance 1 in our units and the Super-Earth further away from the star (see Table \ref{tab1}) ), starting from a small separation between planets of the order of a few Jupiter's Hill radii, and then increasing it."
 Planets are not allowed to accrete matter and their masses are fixed for the whole time of the calculations., Planets are not allowed to accrete matter and their masses are fixed for the whole time of the calculations.
 We have analyzed dillerent. disc models changing the aspect ratio. the kinematic viscosity and the surface density of the disc.," We have analyzed different disc models changing the aspect ratio, the kinematic viscosity and the surface density of the disc."
 These investigations allowed: us to find the conditions under which the migration is convergent at the beginning of the evolution., These investigations allowed us to find the conditions under which the migration is convergent at the beginning of the evolution.
 This does not imply that it will remain convergent throughout the whole run., This does not imply that it will remain convergent throughout the whole run.
 In fact. in most of our mocdels clivergent migration is the final outconie.," In fact, in most of our models divergent migration is the final outcome."
" If the kinematic viscosity is high. for instance 7—5-10"" (h=0.05 and X— Xu). the migration of the Jupiter is fast and the relative migration of both planets is divergent (‘Table 1.. model 1)."," If the kinematic viscosity is high, for instance $\nu=5\cdot 10^{-6}$ $h=0.05$ and $\Sigma=\Sigma_0$ ), the migration of the Jupiter is fast and the relative migration of both planets is divergent (Table \ref{tab1}, model 1)."
 For eas giants the migration speed. is evaluated. to be proportional to the viscosity of the disc (Lin&Papaloizou1993).. so if we take a lower value of UV. the migration of the Jupiter is slower.," For gas giants the migration speed is evaluated to be proportional to the viscosity of the disc \citep{linpap93}, so if we take a lower value of $\nu$, the migration of the Jupiter is slower."
 Assuming for the kinematic viscosity the value v=2-10° without changing other parameters (Table 1.. model 2). we have obtained indeed a slower migration than in model 1 as it is shown in Fig. 2..," Assuming for the kinematic viscosity the value $\nu=2 \cdot 10^{-6}$ without changing other parameters (Table \ref{tab1}, model 2), we have obtained indeed a slower migration than in model 1 as it is shown in Fig. \ref{modrho},"
 but still the relative motion of both planets is divergent., but still the relative motion of both planets is divergent.
 We have noted that the migration of the gas giu is faster than that of the Super-Earth even after pushing the kinematic viscosity as low as p=8:10.7., We have noted that the migration of the gas giant is faster than that of the Super-Earth even after pushing the kinematic viscosity as low as $\nu=8 \cdot 10^{-7}$.
 We conclude that convergent migration cannot be achieved. changing only the viscosity of the disc., We conclude that convergent migration cannot be achieved changing only the viscosity of the disc.
 lt was shown by (Edgar2007) that the migration of the gas giant depends also on the surface density. so we have continued our search for convergent migration changing other cise properties.," It was shown by \citep{edgar} that the migration of the gas giant depends also on the surface density, so we have continued our search for convergent migration changing other disc properties."
 A full. analysis of the influence of the dise parameters on the gap profile and thus on the migration of the planet can be found. in Cridaetal.(2006)., A full analysis of the influence of the disc parameters on the gap profile and thus on the migration of the planet can be found in \citet{crida}.
. We have performed. simulations with relatively low v7 (2-10 °) changing P and X., We have performed simulations with relatively low $\nu$ $2 \cdot 10^{-6}$ ) changing $h$ and $\Sigma$.
 First. we have set X—Ny and achieved the convergent mieration of both planets for a very thin disc with aspect ratio fp=0.03 (for example model 4).," First, we have set $\Sigma =\Sigma_0$ and achieved the convergent migration of both planets for a very thin disc with aspect ratio $h=0.03$ (for example model 4)."
 In this case. the gap opened by the eas giant is very wide and the migration of the Jupiter is slower than that of the Super-Earth. which causes that the radial distance between the planets decreases.," In this case, the gap opened by the gas giant is very wide and the migration of the Jupiter is slower than that of the Super-Earth, which causes that the radial distance between the planets decreases."
 Convergent migration has been obtained also keeping the aspect ratio fixed (bh= 0.05) and changing the surface density., Convergent migration has been obtained also keeping the aspect ratio fixed $h=0.05$ ) and changing the surface density.
 Taking =2X (as in model 7) we have got a migration of the Super-Earth which is faster than in model 2 in accordance to the simple approximation of tvpe E migration (Tanakactal.2002) and at the same time the migration is convergent.," Taking $\Sigma=2\Sigma_0$, (as in model 7) we have got a migration of the Super-Earth which is faster than in model 2 in accordance to the simple approximation of type I migration \citep{tanaka02} and at the same time the migration is convergent."
" ln PNOS it has been discussed the evolution of a two-planet system containing a low-mass planet with a mass in the range of 3.520M, and à Jupiter mass planet. both embedded: in a cise with the surface density Xxr""7."," In PN08 it has been discussed the evolution of a two-planet system containing a low-mass planet with a mass in the range of $3.5-20M_{\oplus}$ and a Jupiter mass planet, both embedded in a disc with the surface density $\Sigma \propto r^{-3/2}$."
 According to PNOS this evolution should end up with the trapping of the low-mass planet near the outer edge of the eap produced by the Jupiter mass planet., According to PN08 this evolution should end up with the trapping of the low-mass planet near the outer edge of the gap produced by the Jupiter mass planet.
 In this Section we are interested in the possibility of resonant. locking of a Super-Earth with mass 5.54/) and a Jupiter mass planet embedded: in a dise with a fat surface density. profile., In this Section we are interested in the possibility of resonant locking of a Super-Earth with mass $5.5M_{\oplus}$ and a Jupiter mass planet embedded in a disc with a flat surface density profile.
 In order to check whether the outcome of the evolution of the system considered. here is the same as in PNOS. we have performed a series of simulations which are described below.," In order to check whether the outcome of the evolution of the system considered here is the same as in PN08, we have performed a series of simulations which are described below."
 In Fig., In Fig.
 8 we show the evolution of the semi-major axis ratio of the planets in the case where the initial planetary orbital separation is 0.35 (Lable 1.. model 3).," \ref{fig2} we show the evolution of the semi-major axis ratio of the planets in the case where the initial planetary orbital separation is 0.35 (Table \ref{tab1}, model 3)."
 The semi-major axis ratio has been calculated. by dividing the semi-major axis of the Super-Earth by the semi- axis of the gas giant., The semi-major axis ratio has been calculated by dividing the semi-major axis of the Super-Earth by the semi-major axis of the gas giant.
 The convergent migration brings planets into the 2:3 mean motion commensurabilitv., The convergent migration brings planets into the 2:3 mean motion commensurability.
 The horizontal lines in Fig., The horizontal lines in Fig.
 3. show the width of this resonance," \ref{fig2}
 show the width of this resonance"
= 1 - = where à is the complex conjugate of O.,= 1 -; = where $\bar\partial$ is the complex conjugate of $\partial$.
 The Jacobian determinant is J= |parlialomega\|? = |=.(9) and on the critical curve y=(," The Jacobian determinant is J = |^2 = 1 -, and on the critical curve =."
10) The critical⋅⋅ curve is⋅ an ellipse., The critical curve is an ellipse.
⋅ z= + ibsin thela)), z= + i b ).
(11) The corresponding caustic is a equadroid (or astroid) with the four cusps on the real and Imaginary axes (or svnuuelry axes)., The corresponding caustic is a quadroid (or astroid) with the four cusps on the real and imaginary axes (or symmetry axes).
 The precusps can be found using (he same method as in RhieandB, The precusps can be found using the same method as in \citet{RCB}.
ennett(2009).. Since Oe is real. the precusp condition 0=J becomes 0-z290J— partial J (," Since $\partial\omega$ is real, the precusp condition $0 = \partial_- J$ becomes 0 = z J - z J ."
12) The equation leads to sin20= 0. hence the precusps are al 9—0. /&/2. x. and 37/2.," The equation leads to $\sin 2\theta = 0$ , hence the precusps are at $\theta = 0$, $\pi/2$, $\pi$, and $3\pi/2$."
 The precusps are mapped (o cusps on (the positive real. negative imaginary. negative real. ancl positive imaginary axisrespectivelv.o weer —," The precusps are mapped to cusps on the positive real, negative imaginary, negative real, and positive imaginary axisrespectively._0 - = -"
2009).,.
.. The more general case πιοµιαας will be studied iu a forthcoming work., The more general case including will be studied in a forthcoming work.
 Several reasons inclined us to focus on non force-free equilibria instead of force-free oues: let us briefly describe them here., Several reasons inclined us to focus on non force-free equilibria instead of force-free ones; let us briefly describe them here.
 First.Reiscueceecr(2009). τοις us that no configuration can be force-free evervwhere.," First,\citet{Reisenegger:2009} reminds us that no configuration can be force-free everywhere."
 Although there do exist “force-free” coufiguratious. they must be confined bv some region or boundary leer with non-zero or singular Lorentz force.," Although there do exist “force-free"" configurations, they must be confined by some region or boundary layer with non-zero or singular Lorentz force."
 Discoutimuities such as curent sheets are unlikely to appear in nature except in a transient manucr., Discontinuities such as current sheets are unlikely to appear in nature except in a transient manner.
 Second. uou force-free equilibria have been ideutified in plasma plysics as the result of relaxationMIID). by Montgomery&Phillips(1988):Shaikhetal. (2008)...," Second, non force-free equilibria have been identified in plasma physics as the result of relaxation, by \citet{Montgomery:1988,Shaikh:2008}. ."
 Third. as shown by Duez&Mathis(2010).. this family of equilibria is a generalization of Tavlor states im a stellay context. where the stratification of the ποπ plays a crucial role.," Third, as shown by \cite{Duez:2010b}, this family of equilibria is a generalization of Taylor states in a stellar context, where the stratification of the medium plays a crucial role."
 Let us briefly recall the asstuptious made in building the semi-analytical model of maeuetolydrostatic (MIIS) equilibrium described by Duez&Mathis(2010).., Let us briefly recall the assumptions made in building the semi-analytical model of magnetohydrostatic (MHS) equilibrium described by \cite{Duez:2010b}.
". The axisviunietrie maenetic field B(r.0) is expressed as a function of a poloidal flux η.0). a toroidal potential F(r.0). and the potential vector A(70) so that it is diverecnee-free by coustruction: where in splierical coordinates the poloidal component is iu the mnerdional plane (é,.é5) aud the toroidal component is aloug the azinuthal direction (6.)."," The axisymmetric magnetic field $\bB(r, \theta)$ is expressed as a function of a poloidal flux $\Psi(r,\theta)$ a toroidal potential $F(r,\theta)$, and the potential vector $\bA\left(r,\theta\right)$ so that it is divergence-free by construction: where in spherical coordinates the poloidal component is in the meridional plane $\er,\etheta$ ) and the toroidal component is along the azimuthal direction $\ephi$ )."
 The AMIS equation expressing balance between the pressure eracdieut force. eravity and the Loreutzforce is where Vois the gravitational potential which satisfies the Poisson equation: V?V=παρ.," The MHS equation expressing balance between the pressure gradient force, gravity and the Lorentzforce is where $V$ is the gravitational potential which satisfies the Poisson equation: $\nabla^{2}V=4\pi G\rho$."
 Tere. we focus on the minimi cuerey non force-free MOIS equilibrium iu stably stratified radiation zones.," Here, we focus on the minimum energy non force-free MHS equilibrium in stably stratified radiation zones."
 Given the field strengths iu real stars. the ratio of the Loreutz force to gravity is very low: stellar interiors are iu a regne where 3=P/Pyecd. PyDJ(Quy) being the magnetic pressure.," Given the field strengths in real stars, the ratio of the Lorentz force to gravity is very low: stellar interiors are in a regime where $\beta=P/P_{\rm Mag}>\!\!>1$, $P_{\rm Mag}=B^2/\left(2\mu_0\right)$ being the magnetic pressure."
 We then ideutifv the two ΑΠΟ invariants relaxed states iu the uou force-free context: the maguctic helicity H=f.A-Bay aud the mass cneompassed iu poloidal maguetic surfaces My=p dY. conserved because of the stable stratification.," We then identify the two MHD invariants relaxed states in the non force-free context: the magnetic helicity ${\mathcal H}=\int_{\mathcal V}{\bA}\cdot{\bB}\:{\rm d}{\mathcal V}$ and the mass encompassed in poloidal magnetic surfaces $M_{\Psi}=\int_{\mathcal V}\Psi\:{\overline \rho}\:{\rm d}{\mathcal V}$ , conserved because of the stable stratification."
" fXAsstuning a selective decay during relaxation (the magnetic οποίον decays much faster thaw H and My time). a variational method allows us to derive the elliptic lincar partial cditterential equation governing W POLO): p 3s the density iu the non-magnetic case. NU=OU|sindOy(μπι)ἐν the Grad-Shafranoy operator iu spherical coordinates. A, a coctiicicnt to be determined. Ra characteristic radius. and oy ds constrained bv the field’s intensity."," Assuming a selective decay during relaxation (the magnetic energy decays much faster than ${\mathcal H}$ and $M_{\Psi}$ ), a variational method allows us to derive the elliptic linear partial differential equation governing $\Psi$ \citep{Woltjer:1959b,Duez:2010b}: $\overline \rho$ is the density in the non-magnetic case, $\Delta^* \Psi \equiv \partial_{rr}{\Psi} + \sin \theta \: \partial_{\theta} \left(\partial_{\theta}{\Psi}/\sin \theta\right)/r^2$ the Grad-Shafranov operator in spherical coordinates, $\lambda_1$ a coefficient to be determined, $R$ a characteristic radius, and $\beta_0$ is constrained by the field's intensity."
 This equation is simul to the Crad-Shafrauov equation used to fud equilibria in magnetically confined plasmas (Caacl&Rubin1958:Shatranov1966).. the source termi being here related to the stellar structure through p (seeITeiuc-formofthisequationiuastroplivsics)..," This equation is similar to the Grad-Shafranov equation used to find equilibria in magnetically confined plasmas \citep{Grad:1958, Shafranov:1966}, the source term being here related to the stellar structure through $\overline{\rho}$ \citep[see][for a discussion of the general form of this equation in astrophysics]{Heinemann:1978}."
 Furthermore. this equilibrimmn is in a barotropic state (n the meaning of the teri. isghar and iso-deusity surfaces coincide) where the field is explicitly coupled with stellar structure through: V«(Fe/p)=ο. where Fe is the Lorentz force.," Furthermore, this equilibrium is in a barotropic state (in the meaning of the term, isobar and iso-density surfaces coincide) where the field is explicitly coupled with stellar structure through: ${\bm\nabla}\times\left(\FLor/{\overline\rho}\right)={\textit{\textbf{0}}}$, where $\FLor$ is the Lorentz force."
 This is a ecueralization of Preudergasts equilibria taking into account compressibility. first studied in polvtropic cases by Woltjer(1960).," This is a generalization of Prendergast's equilibrium taking into account compressibility, first studied in polytropic cases by \cite{Woltjer:1960}."
. The boundary couditious have naw to be discussed., The boundary conditions have now to be discussed.
 Iu Duezetal.(2010):&Mathis(2010).. we considered the general case of a field. confined between two radii. owing to the possible presence of both a couvective core and a convective envelope and to cusure the conservation of mmaenctic helicitv.," In \cite{Duez:2010a, Duez:2010b}, we considered the general case of a field confined between two radii, owing to the possible presence of both a convective core and a convective envelope and to ensure the conservation of magnetic helicity."
 We here choose to cancel both radial ancl latitucinal fields at thesurface. to avoid any current sheets. couscrving once again magnetic helicity.," We here choose to cancel both radial and latitudinal fields at thesurface, to avoid any current sheets, conserving once again magnetic helicity."
 Owing to its sinall extension. the couvective core on the large-scale strouncding field are ucelected.," Owing to its small extension, the convective core on the large-scale surrounding field are neglected."
 Using Green's function method we finally obtain the purely dipolar. eeucral solutions indexed by /: R being the upper boundary coufiniug the magnetic field: Aj are the set of eigenvalues indexed by. 7 allowing to verity the boundary conditions.," Using Green's function method we finally obtain the purely dipolar, general solutions indexed by $i$: $R$ being the upper boundary confining the magnetic field; $\lambda_{1}^{i}$ are the set of eigenvalues indexed by $i$ allowing to verify the boundary conditions."
 jj aud yp are respectively the spherical Bessel fictions of the first and the second kind., $j_{l}$ and $y_{l}$ are respectively the spherical Bessel functions of the first and the second kind.
1. The toroidal magnetic fieldis then given usine FW)=AqV/R:iuthe case of astratified i=3 polvtrope aud for the simulation purposes where we set R=0.55 Ro.we have Ay= 32.95. while for a constantdensity profile Gua zero eravitv mediun). we have Ayz 5.76.," The toroidal magnetic fieldis then given using $F(\Psi) = \lambda_1 \Psi/R$; in the case of a $n=3$ polytrope and for the simulation purposes where we set $R=0.85\: R_*$ ,we have $\lambda_1\simeq 32.95$ , while for a constantdensity profile (in a zero gravity medium), we have $\lambda_1 \simeq 5.76$ ."
 The solution for the 122 polvtrope is represented in 1.., The solution for the n=3 polytrope is represented in \ref{FigBPsi}. .
 Thesetup of the uuuercal model is simülar to that in Braithwaite Nordland 2006. where a fuller account," Thesetup of the numerical model is similar to that in Braithwaite Nordlund 2006, where a fuller account"
An increase in ccan be observed. across a sequence from isolated galaxies to strongly interacting svstenis.,An increase in can be observed across a sequence from isolated galaxies to strongly interacting systems.
 Color variations are consistent with the emergence of a FIR continuum component whose luminosity and colors are correlated., Color variations are consistent with the emergence of a FIR continuum component whose luminosity and colors are correlated.
 This component can be associated (to thermal bv dust of hot stars continuum emission., This component can be associated to thermal re-radiation by dust of hot stars continuum emission.
 In the most extreme cases of isolated CS galaxies. we may have only a cold cirrus component. T~20° Ix. At the other end of the FIR. color-color diagram. a “hot” component peaking around. LOO-GO jm may have become prominent.," In the most extreme cases of isolated CS galaxies, we may have only a cold cirrus component, $\sim 20^\circ$ K. At the other end of the FIR color-color diagram, a “hot” component peaking around 100-60 $\mu$ m may have become prominent."
 The increase in ccan be lareely ascribed to an increase in the SER. as shown in many previous studies (Ixennicutt.(1998).. and references (herein: Sauvage&Thuan (1992))).," The increase in can be largely ascribed to an increase in the SFR, as shown in many previous studies \citet{k98}, and references therein; \citet{st92}) )."
" For the ""hottest? sources (F(25jm)/F(60jm) & 0.2). however. the reprocessed continuum may be due (ο a non-thermal source (deGrijpetal.1992)."," For the “hottest” sources $\mu$ $\mu$ $\simgt$ 0.2), however, the reprocessed continuum may be due to a non-thermal source \citep{dg92}."
" The dillerence in aand (la factor of more than 100 from mergers to isolated CS objects. see Table 2) suggests (hat strong interactions (dp.Z;30 INpc) are a necessary and sullicient condition Dor an extreme SFR. and for a ""starburst (defined as star formation that cannot be maintained over (he IIubble time). at least for the ealaxies of our sample (this result max not be generally irue if not all mergers of gas rich-galaxies are infrared hluminous)."," The difference in and (a factor of more than 100 from mergers to isolated CS objects, see Table 2) suggests that strong interactions $d_P \simlt 30$ Kpc) are a necessary and sufficient condition for an extreme SFR and for a “starburst” (defined as star formation that cannot be maintained over the Hubble time), at least for the galaxies of our sample (this result may not be generally true if not all mergers of gas rich-galaxies are infrared luminous)."
 A companion that has approached to less than 30 Ixpe to a galaxy may need a ime 33x10snipe?uh. νι to move bevond this distance.," A companion that has approached to less than 30 Kpc to a galaxy may need a time $\simgt 3\times 10^8 d_{30Kpc}
v^{-1}_{100 Km s^{-1}}$ yr to move beyond this distance."
 The mean depletion time for strongly interacting galaxies is z5xLO“ vr (Table 2).," The mean depletion time for strongly interacting galaxies is $\approx
5\times10^8$ yr (Table 2)."
 In this case. the interaction time and the τμ aare comparable.," In this case, the interaction time and the $\tau_H$ are comparable."
 This means that a galaxv may exhaust ils σας before an interaction episode is over. on a time much less than the IInbble tine.," This means that a galaxy may exhaust its gas before an interaction episode is over, on a time much less than the Hubble time."
 On the other hand. the SFRs of weakly interacting galaxies (CS galaxies with dpZ 30 Kpe) do not show values that may be considered extraordinarv (SFR x09211./ yr).," On the other hand, the SFRs of weakly interacting galaxies (CS galaxies with $d_P \simgt$ 30 Kpc) do not show values that may be considered extraordinary (SFR $\approx 0.52 M_\odot/yr$ )."
 For objects whose companion is separated by dp<30 Ixpc. the average d» lis approximately 112 Kpe aud 67 Ixpc in the CS and in the BIRG sample respectively.," For objects whose companion is separated by $d_P \simgt 30 $ Kpc, the average $d_P$ is approximately 112 Kpc and 67 Kpc in the CS and in the BIRG sample respectively."
 The SFR is ez 10 times larger in the BIRG than in the CS., The SFR is $\approx$ 10 times larger in the BIRG than in the CS.
 This is consistent with tidal forces Cxdi? ) driving the SER increase., This is consistent with tidal forces $\propto d_P^{-3}$ ) driving the SFR increase.
 A weak interaction may produce a moderate enhancement of the SFR. of a ealaxy. but not lead to dramatic effects on its secular evolution.," A weak interaction may produce a moderate enhancement of the SFR of a galaxy, but not lead to dramatic effects on its secular evolution."
 An important implication of our resulis is (hat at least part of the large dispersion (a factor 10) for the SFR. in ealaxies of a particular morphological (vpe (see Ixennicutt. (1998))) may be explained by weak interactions (cf HlernándezToledo.Dultzin-Hacvan.&Sulentic (2001)))., An important implication of our results is that at least part of the large dispersion (a factor $\sim$ 10) for the SFR in galaxies of a particular morphological type (see \citet{k98}) ) may be explained by weak interactions (cf \citet{ht01}) ).
Where Τονοις 15 the time for the neutron star to (traverse the limit evcle once.,where $\tau_\rmscr{cycle}$ is the time for the neutron star to traverse the limit cycle once.
 This is essentially equal to the time for the star to spin up by AQ from the bottom of the limit evele to the top., This is essentially equal to the time for the star to spin up by $\Delta {\tilde \Omega}$ from the bottom of the limit cycle to the top.
 νυν is the (ime it (takes (he neutron star (o spin up as an accreting LMXD to the final spin rate Ojap. ancl rijip is (he rate of Formation of MSPs in the Galaxy e3x10?vr1 1(??)..," $t_\rmscr{LMXB}$ is the time it takes the neutron star to spin up as an accreting LMXB to the final spin rate $\Omega_\rmscr{MSP}$, and $r_\rmscr{MSP}$ is the rate of formation of MSPs in the Galaxy $\sim 3 \times 10^{-5}~\rmmat{yr}^{-1}$ \citep{1995Natur.376..393L,1998MNRAS.295..743L}."
 The ratio of Tyee {ο Ming is inferred from Eq. 1.., The ratio of $\tau_\rmscr{cycle}$ to $t_\rmscr{LMXB}$ is inferred from Eq. \ref{eq:dodt}.
 Estimating the (vpical strain amplitude that would be observed from one of these sources is also straightforward since the total angular momentum radiated is proportional to AQ., Estimating the typical strain amplitude that would be observed from one of these sources is also straightforward since the total angular momentum radiated is proportional to $\Delta \Omega$.
 This vields wf quie aTxlO οί where o is a constant which depends on geometry ils mean value is 2.9 (?).., This yields h = ( 10 7 ( where $\alpha$ is a constant which depends on geometry – its mean value is 2.9 \citep{Brad98}.
 To obtain the final approximation. AQ—0.12 and <Q>=0.2 which is appropriate for 1=0.1.," To obtain the final approximation, $\Delta {\tilde \Omega}=0.12$ and $<{\tilde \Omega}>=0.2$ which is appropriate for $A = 0.1$."
 This is thirty times larger than (he strain lor the brightest source. Seo X-1. if the GW emission is continuous (7). and should be easily detected with the initial LIGO (?)..," This is thirty times larger than the strain for the brightest source, Sco X-1, if the GW emission is continuous \citep{1998ApJ...501L..89B} and should be easily detected with the initial LIGO \citep{Brad98}."
" One could possibly detect such sources even in MBL. so for z,4~10! vr. one could expect to find several sources in the Local Group."," One could possibly detect such sources even in M31, so for $\tau_\rmscr{on} \sim
10^4$ yr, one could expect to find several sources in the Local Group."
 If cds greater than a few hundred. vears. the radiation from the surface will reflect the heightened core temperature (?)..," If $\tau_\rmscr{on}$ is greater than a few hundred years, the radiation from the surface will reflect the heightened core temperature \citep{1998PhR...292....1T}."
 The X-ray radiation is powered bv the dissipation of the r—modes., The X-ray radiation is powered by the dissipation of the $r-$ modes.
" The typical core temperature as the star is spinning down is 6x105 1. vielding a effective temperature of 3xLO"" IX and a soft-N-ray. luminosity of 107? erg/s (?).."," The typical core temperature as the star is spinning down is $6 \times 10^8$ K, yielding a effective temperature of $3 \times 10^6$ K and a soft-X-ray luminosity of $10^{35}$ erg/s \citep{Heyl98numens}."
" Assuming that the source is found at the maximum possible distance for an enhanced LIGO with P,LO7*> (?).. — ynd ( (Xr)""URL"," Assuming that the source is found at the maximum possible distance for an enhanced LIGO with $h_\rmscr{min}
\sim 10^{-27}$ \citep{Brad98}, = 7 ( (."
' {his vields an observed. X-ray. flux of ⊑≓⊋⋗⋖⊥∩↓⋎≼↲↕⋅∩≺∢∐↓∶∃⋝∖⊽∶⊥ Un ↓↓⊔⊳≞↓≓−⋯⊔↽⋅2) GAME Cook due to the dissipation of the r—-mode energv alone., this yields an observed X-ray flux of F = 2 ( )^2 ( ( due to the dissipation of the $r-$ mode energy alone.
 The tvpical Galactic source (αἱ a distance of 10 kpc). discussed earlier would be 500.000 times brighter with a flux of about 3.2 mCrab.," The typical Galactic source (at a distance of 10 kpc), discussed earlier would be 500,000 times brighter with a flux of about 3.2 mCrab."
 ? discussed (he X-ray emission produced if the GW emission is steady. and derive constraints on either the accretion or the r—modes., \citet{2000ApJ...536..915B} discussed the X-ray emission produced if the GW emission is steady and derive constraints on either the accretion or the $r-$ modes.
 If the GW. emission is transient. the," If the GW emission is transient, the"
trapped inertial modes. which are of considerable interest.,"trapped inertial modes, which are of considerable interest."
 On the other hand. there are many uncertainties in his calculations anc be did not discuss the origin or nature of the elobal deformations.," On the other hand, there are many uncertainties in his calculations and he did not discuss the origin or nature of the global deformations."
 In this paper we develop and generalize WKato’s ideas on this excitation mechanism anc make detailed numerical calculations of the modes and growth rates for rotating black holes., In this paper we develop and generalize Kato's ideas on this excitation mechanism and make detailed numerical calculations of the modes and growth rates for rotating black holes.
 We include a dynamical treatment of the warp or eccentricitv but defer to a second paper a broader discussion of the origin anc global propagation of these deformations., We include a dynamical treatment of the warp or eccentricity but defer to a second paper a broader discussion of the origin and global propagation of these deformations.
 In Section 2 we review the trapping of inertial oscillations in a simple. pseudo-relativistic cise model.," In Section 2 we review the trapping of inertial oscillations in a simple, pseudo-relativistic disc model."
 In Section 3 we describe the excitation mechanism for trapped inertial modes. which relies on a coupling between waves in the disc and. global deformations.," In Section 3 we describe the excitation mechanism for trapped inertial modes, which relies on a coupling between waves in the disc and global deformations."
 In Section 4 we discuss the dependence of the inertial modes! growth rates on clise parameters and. black hole spin., In Section 4 we discuss the dependence of the inertial modes' growth rates on disc parameters and black hole spin.
 C'onelusions are. presented in Section 5., Conclusions are presented in Section 5.
 The trapping of oscillations can be easily. understood. by analvsing the fluid equations in a simple. isothermal disc model (Lubow&Pringle1993:Ixato2001).," The trapping of oscillations can be easily understood by analysing the fluid equations in a simple isothermal disc model \citep{lubowpringle1993,rkato2001}."
.. Although this trapping happens only in disces around. compact objects. a fully relativistic niodel is not necessary.," Although this trapping happens only in discs around compact objects, a fully relativistic model is not necessary."
 The most important cllects can be included. by supplementing a Newtonian treatment with the correct relativistic expressions for the characteristic frequencies in the disc (ato2001)., The most important effects can be included by supplementing a Newtonian treatment with the correct relativistic expressions for the characteristic frequencies in the disc \citep{rkato2001}.
. For simplicity. anc clarity. we adopt this. pseudo-relativistic approach and consider a strictly isothermal disc with a ratio of specifie heats 5.=1.," For simplicity and clarity, we adopt this pseudo-relativistic approach and consider a strictly isothermal disc with a ratio of specific heats $\gamma=1$."
 legnoring viscosity and. magnetic fields. the fundamental hyerocynamic equations can be written as where =czlog pis the enthalpy and ὃς is the constant sound speed in the disc.," Ignoring viscosity and magnetic fields, the fundamental hydrodynamic equations can be written as where $h=c_\mathrm{s}^2\log\rho$ is the enthalpy and $c_\mathrm{s}$ is the constant sound speed in the disc."
 We neglect. sell-eravitation and consider a fixed axisvmmetrie gravitational potential er.z). where (17.0.2) are evlindrical polar coordinates.," We neglect self-gravitation and consider a fixed axisymmetric gravitational potential $\Phi(r,z)$, where $(r,\phi,z)$ are cylindrical polar coordinates."
 As in the case of stars (Christensen-Dalsgaard2002)... to study. oscillations one needs to analyse what happens to this svstem of equations when the velocity and enthalpy are perturbed: q=qu|q'.," As in the case of stars \citep{cd2002}, to study oscillations one needs to analyse what happens to this system of equations when the velocity and enthalpy are perturbed: $q=q_0+q'$."
" Ehe equilibrium state of the disc is independent of time and azimuth: uo=Ωr= rO(r)e... where © is the angular velocity. which is independent. of z in a strictly isothermal disc. while ho(r.z) satisfies Why=re,— Vo."," The equilibrium state of the disc is independent of time and azimuth: $\bmath{u}_0=\bmath{\Omega}\times\bmath{r}=r
\Omega(r)\bmath{e}_\phi$ , where $\Omega$ is the angular velocity, which is independent of $z$ in a strictly isothermal disc, while $h_0(r,z)$ satisfies $\bmath{\nabla}h_0=r\Omega^2\bmath{e}_r-\bmath{\nabla}\Phi$ ."
 Thus the perturbations acting on it can be ΑΕΤΟΠ as where m is the azimuthal mode number and w is the oscillation frequency., Thus the perturbations acting on it can be written as where $m$ is the azimuthal mode number and $\omega$ is the oscillation frequency.
 Dropping. for simplification. the tildes and zeros. the linearized equations for the perturbed quantities can be written in the form where w@=wm is the Doppler-shilted wave frequeney. which is zero at the corotation radius. and &s aud O. are the epicvelic and: vertical frequencies. respectively (Binney&“TremaineLOSS)," Dropping, for simplification, the tildes and zeros, the linearized equations for the perturbed quantities can be written in the form where $\hat{\omega}=\omega-m\Omega$ is the Doppler-shifted wave frequency, which is zero at the corotation radius, and $\kappa$ and $\Omega_z$ are the epicyclic and vertical frequencies, respectively \citep{galacticdynamics}."
 We apply the thin. disc approximation (Ofὃς=O22). and neglect the term uLOhfr in the last equation.," We apply the thin disc approximation $\partial h/\partial z=-\Omega_z^2z$ ), and neglect the term $u'_r\partial h/\partial r$ in the last equation."
 Vhe latter approximation is valid if the radial wavelength for perturbations is smaller than the radial scale on which the enthalpy varies in the basic state., The latter approximation is valid if the radial wavelength for perturbations is smaller than the radial scale on which the enthalpy varies in the basic state.
 Variables can then be further separated. inr and 2. using (Okazakictal.1987) ⊔↿∖⇀∖∣⋡↓⋅⋜⋯↓∩∖∖⋰⊔∠⊾∖↽∺↿∢⋅⋏∙≟⊔⊔↓≤⋗⊤⇉∃↦∖∖⋰∐↓↥⊔∶∪⋡↓⋡∫≻ ∣⋡⋖⋅⋠↓⊔⋏↳≱↥↓↥∢⊾∖⇁⋖⋅↓⋅↿⊲⊔∼⋜↧↓⊔↓⋯⇂⋖⊾⊔⊔⊔↓∣⋈⋅↓⋅⋜⋯∠⇂∐∶∖∠⋅∖≤≥↝↿↓⊔⋅ ∖⇁∢⊾↓⋅⇂↕≼⇍⋜↧↓⊳∖≼∼⋜↧↓∢⋅↓∐⋅⊀↓⋏∙≟↓∐∪⇂⋅↿↓⊔⋅∠∐⊳∖≼⋱↿∖∺⊀↓⊔≼⇍⋖⊾∐∢⋅⊥↕≻↓↕⋖⋟∣∠⇂⋖⊾↕↕↓↕⋖⋅∠⇂⋡ ⇂⋅∩↓⋅⊔∶∪∖∖⊽⋖⊾∐⋜↧∖⇁⋖⋅∣∣∕↚∶," Variables can then be further separated in $r$ and $z$ , using \citep{okazakietal1987}
 where $\textrm{He}_n$ is the modified Hermite polynomial of order $n$ \citep{abramowitzstegun}, with $n=0,1,2,3,\dots$ being the vertical mode number and $H=\sqrt{c_\mathrm{s}/\Omega_z}$ the vertical scaleheight of the disc. ("
∪⋡⊐∐⋡∖↓↥∪⊔↓∠⇂∣⋡⋖⊾⊔∪⇂⋯⇂∣∐⋜⊔∣∐↓⊳∖ ,"Since $\textrm{He}_{-1}$ is not defined, for $n=0$ we have $u'_z=0$ .)"
separation of variables is not exact since // depends on r (as described by ato(2001).. this separation is valid to lowest WIXD order: Nowak&Wagoner(1992). use à slowly varving function of r to separate variables).," It should be noted that this separation of variables is not exact since $H$ depends on $r$ (as described by \cite{rkato2001}, this separation is valid to lowest WKB order; \cite{nowakwagoner1992} use a slowly varying function of $r$ to separate variables)."
 The variation of Lf with p couples different vertical modes (CIanakactal.2002) but this elfect is weak when the radial wavelength is short. and we neglect it.," The variation of $H$ with $r$ couples different vertical modes \citep{tanakaetal2002} but this effect is weak when the radial wavelength is short, and we neglect it."
 The final set of ordinary. dillerential equations in r for the perturbecl quantities reads The dispersion relation for wave modes in the disc can be determined by further assuming that the radial wavelengthof the perturbed quantities is much smaller than both the azimuthal wavelength and the characteristicscale for racial variations of the equilibrium. quantities., The final set of ordinary differential equations in $r$ for the perturbed quantities reads The dispersion relation for wave modes in the disc can be determined by further assuming that the radial wavelengthof the perturbed quantities is much smaller than both the azimuthal wavelength and the characteristicscale for radial variations of the equilibrium quantities.
 Lt can then be verified that perturbations with local radial wavenumboer A obey (Okazakictal.LOST) ," It can then be verified that perturbations with local radial wavenumber $k$ obey \citep{okazakietal1987}
 "
should be possible with the current sample. but is not expected to improve the coustraints on (2) significautly.,"should be possible with the current sample, but is not expected to improve the constraints on $w(z)$ significantly."
 The basic approach to the error estimation is a standard onc., The basic approach to the error estimation is a standard one.
" Arranging the statistics one is estimating (iu our case power spectrum and bispectrmm) iuto a vector x and the parameters oue is interested in into vector y the Fisher matrix is giveu by where Cy,=(orpωςoQe ", Arranging the statistics one is estimating (in our case power spectrum and bispectrum) into a vector $\bf x$ and the parameters one is interested in into vector $\bf y$ the Fisher matrix is given by where $C_{ij}=\langle (x_i-\langle x_i\rangle) (x_j-\langle x_j\rangle) \rangle$.
One must thus compute both the covariance matrix aud the derivatives with respect to the parameters on the statistic than one is using., One must thus compute both the covariance matrix and the derivatives with respect to the parameters on the statistic than one is using.
 We lave ound that combining the bispectrum aud the power spectrum information sienificautly improves the determumation of the amplitude of fluctuations., We have found that combining the bispectrum and the power spectrum information significantly improves the determination of the amplitude of fluctuations.
 The reason for this is a degeneracy between the mean flux absorption aud the incar amplitude., The reason for this is a degeneracy between the mean flux absorption and the linear amplitude.
 Chaneine the mean flux changes the power spectrum of the Hux significautlv. as docs the variation in the linear amplitude.," Changing the mean flux changes the power spectrum of the flux significantly, as does the variation in the linear amplitude."
 The mean Hux absorption is a free parameter. «nce it is governed by the amount of UV ckeround that controls the fraction of ucutral gas in joniziug equilibrim.," The mean flux absorption is a free parameter, since it is governed by the amount of UV background that controls the fraction of neutral gas in ionizing equilibrium."
 Wile it can be determined directly using iudependent methods such as conti fittingor principal component analysisof spectra. the precision of these methods is not sufficient to break the degeneracies eutirely.," While it can be determined directly using independent methods such as continuum fitting or principal component analysis of spectra, the precision of these methods is not sufficient to break the degeneracies entirely."
 However. at the 3-poiut tuction level eravity predicts a very specific pattern of correlations. which cannot be mimicked by the mean flux variation.," However, at the 3-point function level gravity predicts a very specific pattern of correlations, which cannot be mimicked by the mean flux variation."
 A full analysis reveals that lis can naprove the precision of amplitude determination by a factor of 3., A full analysis reveals that this can improve the precision of amplitude determination by a factor of 3.
 To compute the covariance matrix of power spectimm and bispectruii we use lydro-PAL simmlations to simulate the forest. apply the analysis ou Μαιν realizations of the simulations and compute the mean and covariance uatrix of the statistics.," To compute the covariance matrix of power spectrum and bispectrum we use hydro-PM simulations to simulate the forest, apply the analysis on many realizations of the simulations and compute the mean and covariance matrix of the statistics."
" We use power spectrum aud. bispectrum information or 10""s/nho210μη which is the range of interest for the SDSS data."," We use power spectrum and bispectrum information for $10^{-3}s/km<k<2\times 10^{-2}s/km$, which is the range of interest for the SDSS data."
 We then vary by stall amount the parameters of interest one at a time. rerun the simulation with the same initial conditions to niuinize the sampling variance and recompute the mean.," We then vary by small amount the parameters of interest one at a time, rerun the simulation with the same initial conditions to minimize the sampling variance and recompute the mean."
 This allows us to compute the derivatives μην) ot the statistic; with respect to the parameter y;., This allows us to compute the derivatives $dx_i/dy_j$ of the statistic $x_i$ with respect to the parameter $y_j$.
 The parameters we vary are the amplitude of fuctuatious as a function of redshift (we use 9 bius between 2.2<2« 3.8). mean flux as a function of redshift. slope aud curvature of the primoridal spectruui aud temperature deusitv relation parametrized as a power law with amplitude aud slope as the parameters. both of which cau vary with redshift.," The parameters we vary are the amplitude of fluctuations as a function of redshift (we use 9 bins between $2.2<z<3.8$ ), mean flux as a function of redshift, slope and curvature of the primoridal spectrum and temperature density relation parametrized as a power law with amplitude and slope as the parameters, both of which can vary with redshift."
 The asstuued redshift distribution of the seuuple ος the SDSS distribution in the curent data., The assumed redshift distribution of the sample mimics the SDSS distribution in the current data.
 We lave scaled. the leugth of the forest to match the overall umber of quasars to 3000. which is significantly less than the fal," We have scaled the length of the forest to match the overall number of quasars to 3000, which is significantly less than the final"
in some cases. but svnchrotron emission efliciency may indeed. vary from galaxy to galaxy.,"in some cases, but synchrotron emission efficiency may indeed vary from galaxy to galaxy."
 The median for the whole sample is 1.1. but it is reduced to 1.0 if the two clear radio AGN hosts are removed.," The median for the whole sample is 1.1, but it is reduced to 1.0 if the two clear radio AGN hosts are removed."
 Therefore. on average. the non-thermal svichrotron emission [rom {hese clusty starbursts appear to follow the Galactic normalization adopted by (1992).," Therefore, on average, the non-thermal synchrotron emission from these dusty starbursts appear to follow the Galactic normalization adopted by ."
". In summary. we adopt 7;=58 Ix. 2=1.35. and. fy),=1.0 for our photometric redshilt SED template."," In summary, we adopt $T_d=58$ K, $\beta=1.35$ , and $f_{nth}=1.0$ for our photometric redshift SED template."
 This relatively fIat ο is in good agreement with the analvsis of 102 galaxies bv(2000b).. but the mean dust temperature we adopt is significantly warmer (han the mean of Ty=3645 Ik Dunne et al.," This relatively flat $\beta$ is in good agreement with the analysis of 102 galaxies by, but the mean dust temperature we adopt is significantly warmer than the mean of $T_d = 36 \pm 5$ K Dunne et al."
 derived using 60 ji. LOO ji. and 850 j( measurements.," derived using 60 $\mu$, 100 $\mu$, and 850 $\mu$ measurements."
 The main difference is that the dust emission from our IR selected. bumninous cdusty starbursts are on average significantly warmer (han those of the Dunne et al.," The main difference is that the dust emission from our IR selected, luminous dusty starbursts are on average significantly warmer than those of the Dunne et al."
 sample. which includes a large number of late (wpe field galaxies.," sample, which includes a large number of late type field galaxies."
" Once the dusty starburst SED template is chosen. then (he entire radio-to-EIR. continuum spectrum for any given galaxy can be described in terms of just the total star formation rate SFR and the Iuminosity distance D,."," Once the dusty starburst SED template is chosen, then the entire radio-to-FIR continuum spectrum for any given galaxy can be described in terms of just the total star formation rate $SFR$ and the luminosity distance $D_L$."
 The dust spectrum Sy in Eq., The dust spectrum $S_d$ in Eq.
 4. can be rewritten as Combined with tlie expressions for Iree-[ree and non-thermal svnchrotron emission given in Eqs., \ref{eq:Sd3} can be re-written as Combined with the expressions for free-free and non-thermal synchrotron emission given in Eqs.
" 12 13.. the entire radio-to-EIR. continuum spectrum can be written as. where SFR is in M. t. Dy inMpc. and vs=(1+z)pu, in Gllz."," \ref{eq:Sff}~ \ref{eq:nth2}, , the entire radio-to-FIR continuum spectrum can be written as, where $SFR$ is in $M_\odot$ $^{-1}$, $D_L$ in, and $\nu_\circ=(1+z)\nu_{obs}$ in GHz."
 A (1+2) term is needed for sources at. cosmological distances im order (o account for the frequency. or wavelength folding bv the Doppler effect., A $(1+z)$ term is needed for sources at cosmological distances in order to account for the frequency or wavelength folding by the Doppler effect.
 The redshift z ancl the FIR luminosity (SF HR) ofa particular galaxy can be determined simultaneouslv by comparing the observed SEDwith the dusty starburst template in the, The redshift $z$ and the FIR luminosity $SFR$ ) ofa particular galaxy can be determined simultaneously by comparing the observed SEDwith the dusty starburst template in the
of SCEPREL to handle distributions departing from the Lernquist distribution (the SCTE basis set).,of SCFTREE to handle distributions departing from the Hernquist distribution (the SCF basis set).
 The distributions ave the Lernquist density profile (MHlernquist.1990)... the hummer density profile (Plummer1911).. and the Lowered Evans model (Evans1993).," The distributions are the Hernquist density profile \cite{h90}, the Plummer density profile \cite{pl11}, and the Lowered Evans model \cite{e93}."
 Phe Lowereck Evans mocel iis been shown to be useful for the practical modelling of dark halos (Ixuijken&Dubinski1994).. and as such is our preferred model in many of the tests.," The Lowered Evans model has been shown to be useful for the practical modelling of dark halos \cite{kd94}, and as such is our preferred model in many of the tests."
" With reference to he parameters in Ixuijken Dubinski (1994) we use the ollowing for all our Lowerecl Evans models: Wy=5.0. mym 15.q10. (fr)?=10046, =10."," With reference to the parameters in Kuijken Dubinski (1994) we use the following for all our Lowered Evans models: $\Psi_0=-5.0$, $v_0=1.5$, $q=1.0$, $(r_c/r_k)^2=1.0$, $r_a=1.0$."
 In these tests the models are populated with up to 107 xuwticles ancl a specified fraction of them are designated. as xwticles to be dealt. with by the Tree. part of the codo. referred. to hereafter as “Tree particles.," In these tests the models are populated with up to $10^5$ particles and a specified fraction of them are designated as particles to be dealt with by the Tree part of the code, referred to hereafter as `Tree particles'."
 The remainder of he particles are dealt with bv the SCE part of the code and referred to as SCE particles’., The remainder of the particles are dealt with by the SCF part of the code and referred to as `SCF particles'.
 Analogous to the investigations of Llozumi and Lernquist (1995) who perform tests on the pure SCE code. we examine the behaviour of SCETIRELE in systems which are not in equilibrium.," Analogous to the investigations of Hozumi and Hernquist \shortcite{hh95} who perform tests on the pure SCF code, we examine the behaviour of SCFTREE in systems which are not in equilibrium."
 For this purpose we construct a uniform density sphere with velocity clispersions assigned according to a specified initial virial ratio. the evolution of he svstem is followed until it reaches its final relaxed. state.," For this purpose we construct a uniform density sphere with velocity dispersions assigned according to a specified initial virial ratio, the evolution of the system is followed until it reaches its final relaxed state."
 Extending these tests of SCEPRIEL to more interesting systems we perform test runs on a disk svstem., Extending these tests of SCFTREE to more interesting systems we perform test runs on a disk system.
 A. clisk. )ulee. and halo model is set up as prescribed in Dubinski and Ixuijken (1995).," A disk, bulge, and halo model is set up as prescribed in Dubinski and Kuijken (1995)."
 Such a system is well suited to the SCIFRIEL technique whereby the disk particles are assigned o the Tree and the halo ancl bulee particles are assigned o the SCE svstem., Such a system is well suited to the SCFTREE technique whereby the disk particles are assigned to the Tree and the halo and bulge particles are assigned to the SCF system.
 Here we merely examine the effect of increasing the number of halo particles on the stability of he disk., Here we merely examine the effect of increasing the number of halo particles on the stability of the disk.
 The individual timing performances of tree and SCE codes rave been shown to scale to OUN)logNi). (Barnes&Llut 1986).. and OCNseu). (Llernquist&Ostriker1992).. respectively.," The individual timing performances of tree and SCF codes have been shown to scale to ${\cal O}(N_{tree}\log N_{tree})$, \cite{bh86}, and ${\cal O}(N_{SCF})$, \cite{ho92}, respectively."
 For the combined. code we have to consider he CPU time spent on the interaction between the two components., For the combined code we have to consider the CPU time spent on the interaction between the two components.
" The calculation of the Tree force on cach SCL xwuticle would. at worst. scale as O(NseulogNip). and hat of the SCE force on the tree particles scales as Q(GN,,,,)."," The calculation of the Tree force on each SCF particle would, at worst, scale as ${\cal O}(N_{SCF}\log N_{tree})$, and that of the SCF force on the tree particles scales as ${\cal
O}(N_{tree})$."
 So overall we would expect the CPU time to scale as Nis) Αννα Nscr]]]., So overall we would expect the CPU time to scale as ) + ].
 As the major advantage of SCETRIEE is expected: to be its elliciency in dealing with svstems with substructure. we perform tests varving the fraction of tree. particles in the svstem and changing the initial distribution of these particles.," As the major advantage of SCFTREE is expected to be its efficiency in dealing with systems with substructure, we perform tests varying the fraction of tree particles in the system and changing the initial distribution of these particles."
 The models used here for the performance checks are the Lowered I2vans mocels., The models used here for the performance checks are the Lowered Evans models.
 We examine how the timing of SCE'THERE behaves with the total number of particles., We examine how the timing of SCFTREE behaves with the total number of particles.
 The fraction of tree particles is set at of the total and they are distributed randomly throughout the system., The fraction of tree particles is set at of the total and they are distributed randomly throughout the system.
 The random clistribution of particles implies that there will not be any advantage in time saved due to the Tree structure., The random distribution of particles implies that there will not be any advantage in time saved due to the Tree structure.
 This is demonstrate in Figure 2(a) where we compare purely Free. purely SCE. and SCETPREE timings as the total number of particles is increased. up to 107.," This is demonstrated in Figure 2(a) where we compare purely Tree, purely SCF, and SCFTREE timings as the total number of particles is increased up to $10^5$."
 As expected. no advantage is ollerec by SCLEIUS with rancomiby distributed particles over the pure ‘Tree treatment., As expected no advantage is offered by SCFTREE with randomly distributed particles over the pure Tree treatment.
 The great advantage of SCE'TREI is. demonstrate in Figure 2(b) where the Tree. particles are. assigned. to a satellite system orbiting à more Massive syvsteni conmposec of the SCE particles., The great advantage of SCFTREE is demonstrated in Figure 2(b) where the Tree particles are assigned to a satellite system orbiting a more massive system composed of the SCF particles.
 This is compared to a pure Tree reatment of the same binary svstem., This is compared to a pure Tree treatment of the same binary system.
 The Figure clearly demonstrates the strength. of SCETREE when the Tree xuticles are assigned to à distinct. substructure., The Figure clearly demonstrates the strength of SCFTREE when the Tree particles are assigned to a distinct substructure.
 We see hat for SCETREE the CPU time per timestep scales approximately as QGV). a substantial improvement over the »ure Tree timings.," We see that for SCFTREE the CPU time per timestep scales approximately as ${\cal O}(N)$, a substantial improvement over the pure Tree timings."
 Finally we examine the performance of the code as the raction of Tree particles is increased., Finally we examine the performance of the code as the fraction of Tree particles is increased.
 Figure 2(0) shows the CPU time spent both on the whole SCETREE timestep and just on the Tree timestep in à system with a randomly distributed. fraction of Tree particles., Figure 2(c) shows the CPU time spent both on the whole SCFTREE timestep and just on the Tree timestep in a system with a randomly distributed fraction of Tree particles.
 It can be seen that [or such a system the fraction of Tree particles must remain below ~1014 to gain any reasonable advantages., It can be seen that for such a system the fraction of Tree particles must remain below $\sim 10$ to gain any reasonable advantages.
 lt is instructive to follow the behaviour of. two-body relaxation as the svstem evolves., It is instructive to follow the behaviour of two-body relaxation as the system evolves.
 As anindicator of two-body relaxation we take the mean square fractional energy change of the particles. Ranay=(ARSE PS.," As anindicator of two-body relaxation we take the mean square fractional energy change of the particles, $R_{2-body}=\left< | \Delta E/E|^2\right>$ ."
" We define this as Loli| αι LI;, and £75 are the total energy (kinetic plus potential) of particle 7 at times / ancl O respectively."," We define this as | |^2, $E_{i,t}$ and $E_{i,0}$ are the total energy (kinetic plus potential) of particle $i$ at times $t$ and 0 respectively."
 In. Figure (3)) we see that by our measure the average relaxation remains less than Ma for the period of the simulation., In Figure \ref{rel}) ) we see that by our measure the average relaxation remains less than $1\%$ for the period of the simulation.
 Phe initial sharp rise is expected. due to the initial random placing of the particles. meaning that many pairs of particles will have initial separations less than the tree softening length. c.," The initial sharp rise is expected due to the initial random placing of the particles, meaning that many pairs of particles will have initial separations less than the tree softening length, $\epsilon$."
 Relaxation tells us how close our models approach the behaviour of a collisionless svstem. providing us with a quantitive estimate of over what timescales our simulations can be applied.," Relaxation tells us how close our models approach the behaviour of a collisionless system, providing us with a quantitive estimate of over what timescales our simulations can be applied."
 We may also look at the change in the energv of each particle over a suitable time period and compare the behaviour of SCE and tree particles., We may also look at the change in the energy of each particle over a suitable time period and compare the behaviour of SCF and tree particles.
 This gives another gauge of relaxation of particles this time as a function of the binding energy. £.," This gives another gauge of relaxation of particles this time as a function of the binding energy, $E$ ."
 We follow a similar analvsis as 11O92 and plot££E vs E for both SCE and tree particles. Figure(5)), We follow a similar analysis as HO92 and plot$\Delta E/E$ vs $E$ for both SCF and tree particles. \ref{pen}) )
and backeround particles or waves (Wuetal.2005).,and background particles or waves \citep{wu05}.
. In other words. DC-electric field in the reconnection site alone max not be able to explain the observed spectral features of nonthermal electrons.," In other words, DC-electric field in the reconnection site alone may not be able to explain the observed spectral features of nonthermal electrons."
 The combination of DC-electric field ancl (he turbulence may finally lead to single or double power-law spectral distributions. which were derived [rom IIXR observations.," The combination of DC-electric field and the turbulence may finally lead to single or double power-law spectral distributions, which were derived from HXR observations."
 This is definitelv an issue requiring further investigation., This is definitely an issue requiring further investigation.
 One of the authors (WIL) thanks V. V. Zharkova and Y. Dai for their helpful cliseussions and suggestions., One of the authors (WJL) thanks V. V. Zharkova and Y. Dai for their helpful discussions and suggestions.
 This research is supported by the Chinese foundations GYIIY200706013. FANEDD (200226). 2006CD306302. NSFC (10221001. 10403003. and 10673004).," This research is supported by the Chinese foundations GYHY200706013, FANEDD (200226), 2006CB806302, NSFC (10221001, 10403003, and 10673004)."
2006).,.
. Velocity observatious were startedbefore the expected beeimning of the transit. aud were continued uitil after the expeced cud of the trausit.," Velocity observations were started before the expected beginning of the transit, and were continued until after the expected end of the transit."
 At total of LS spectra. cach 15 minutes in leneth. were obtained.," At total of 18 spectra, each 15 minutes in length, were obtained."
 Table 1 gives the relative racial velocities for the ILJST 6servations of 1)71156," Table \ref{tab:HJSvels}
 gives the relative radial velocities for the HJST observations of 17156."
 IET observations wore mace ou the sale nieht (25 December 2007 UT) using the Wiech Resolution Spectrograph (Tull1998) iu its R60.000 luocde.," HET observations were made on the same night (25 December 2007 UT) using the High Resolution Spectrograph \citep{Tu98} in its $R = 60,000$ mode."
 Due to its fxed-zenith-distance design. we were Oily able to observe 117156 froni shortly before ic beeiuuiug of the traidt to just past past mid-trausit.," Due to its fixed-zenith-distance design, we were only able to observe 17156 from shortly before the beginning of the transit to just past past mid-transit."
 The observations were planned to obtai as ima GOOss exposures of 117156 as possible durius 2.] hour track leneli., The observations were planned to obtain as many s exposures of 17156 as possible during the 2.1 hour track length.
 The Y tayeet exposure on the WET was ternratedl after 4155s when tjio. fiber-iiustrumicut-feed reached the cud of track., The $^{th}$ target exposure on the HET was terminated after s when the fiber-instrument-feed reached the end of track.
 Details of iInstrmuent configuration and the data reduclon aud analysis procedures are given. by Cochranetal.(20— 2007).," Details of the instrument configuration and the data reduction and analysis procedures are given by \citet{CoEnMA04,CoEnWi07}."
. Table 2 eives the relative racial velocities for IIET observations of 117156, Table \ref{tab:HETvels} gives the relative radial velocities for the HET observations of 17156.
 For both the IIJST aud WET data. observation tines ad velocities Lave been corrected to the solar system xuveenter.," For both the HJST and HET data, observation times and velocities have been corrected to the solar system barycenter."
 The uncertainty 6 for each velocity iu the able is anGaferenal eror computed from the variance about the mean of the velocities from each. of the ~2À small chunks into which the spectrum is divided or the velocity computation., The uncertainty $\sigma$ for each velocity in the table is an error computed from the variance about the mean of the velocities from each of the $\sim 2$ small chunks into which the spectrum is divided for the velocity computation.
 Thus. it represents the relative uucertainty of one velocity measurement with respect to the others for that iustrunment. based ou he quality aud observing couditious of the spectrum.," Thus, it represents the relative uncertainty of one velocity measurement with respect to the others for that instrument, based on the quality and observing conditions of the spectrum."
 This uncertainty does not include other iutriusic stellar sources of uncertaiuty. uor any unidentified sources of systematic errors.," This uncertainty does not include other intrinsic stellar sources of uncertainty, nor any unidentified sources of systematic errors."
 The two different spectrographs have independent arbitrary velocity zero points. and thus there is some constant offset velocity (determined below and denoted as 5) between the data sets preseuted im Tables 1 and 2..," The two different spectrographs have independent arbitrary velocity zero points, and thus there is some constant offset velocity (determined below and denoted as $\gamma$ ) between the data sets presented in Tables \ref{tab:HJSvels} and \ref{tab:HETvels}."
 A varicty of different tvpes of models have been used by others to analyze observations of the MeLaneglilin (RM). (Rossiter1921:AlcLanghlin οπου for transiting planets.," A variety of different types of models have been used by others to analyze observations of the Rossiter-McLaughlin (RM) \citep{Ro24,ML24}
 effect for transiting planets."
" Quelozetal.(2000) divided a model stellar photosphere iuto a larec umber of cells. and then used a ""σαι shape CYORS-correlation with a near lint darkening law to conrpute themodel radial velocity anomaly."," \citet{QuEgMa00} divided a model stellar photosphere into a large number of cells, and then used a “Gaussian shape cross-correlation model” with a linear limb darkening law to compute the radial velocity anomaly."
 Olitactal.(2005) developed analytic expressions for the apparent radial velocity perturbation during a transit. in several different approxinations.," \citet{OhTaSu05} developed analytic expressions for the apparent radial velocity perturbation during a transit, in several different approximations."
 Cüniénez(2006) developed another set of analytic expressions for the RM effect which utilize a inore generalized higher order limb darkening expressiou., \citet{Gi06} developed another set of analytic expressions for the RM effect which utilize a more generalized higher order limb darkening expression.
 A more elaborate technique was developed by Winnetal. (2005).. who first computed an approximation to the disk-iutegrated stellar spectrum.," A more elaborate technique was developed by \citet{WiNoHo05}, who first computed an approximation to the disk-integrated stellar spectrum."
 They then computed à Doppler shifted. aud. intensity scaled spectrum of the portion of the disk that would be blocked by the transiting plauet and subtracted this frou their disk-integrated spectrum., They then computed a Doppler shifted and intensity scaled spectrum of the portion of the disk that would be blocked by the transiting planet and subtracted this from their disk-integrated spectrum.
 This spectrum was then iuultiplied by their high-resolution iodiue spectrum. aud the result was processed through their radial velocity code to compute model velocities iu the same mauuer as the observed data.," This spectrum was then multiplied by their high-resolution iodine spectrum, and the result was processed through their radial velocity code to compute model velocities in the same manner as the observed data."
 We analyzed our data uie a niοςοἱ that is a hybrid of these methods., We analyzed our data using a model that is a hybrid of these methods.
" We started by adc»tiug the 117156) system parameters frou, Naritaetal.(2008).", We started by adopting the 17156b system parameters from \citet{NaSaOh08}.
. We then computed the orbit of the planet around the star. as we would view it from Earth.," We then computed the orbit of the planet around the star, as we would view it from Earth."
 This eave us the appareut offset of the plauet from the center of the star as a function of time through the transit., This gave us the apparent offset of the planet from the center of the star as a function of time through the transit.
 We divided he stellar disk iuto a LOO«100 exid of cells. iu the nanuecr of Quelozetal.(2000).. Suellen (2001)... or Winnetal.(2005).," We divided the stellar disk into a $400 \times 400$ grid of cells, in the manner of \citet{QuEgMa00}, \citet{Sn04}, or \citet{WiNoHo05}."
. For cach photospheric cell. we colmputed a specific intcusity using the nou-Inear four-xuineter lub darseniug law of Claret(2000).," For each photospheric cell, we computed a specific intensity using the non-linear four-parameter limb darkening law of \citet{Cl00}."
. Each xiotosphlierie cell is also assigned : vradial velocity due to )oth the stellar orbital motion aid the stellar rotation. with the stellar esl1j as a node] parameter.," Each photospheric cell is also assigned a radial velocity due to both the stellar orbital motion and the stellar rotation, with the stellar $v \sin i$ as a model parameter."
 For each nue ste> during the transit. frou first contact to fourth contact. we compute which stelay photospheric cells are blocked by the transiting plaact.," For each time step during the transit, from first contact to fourth contact, we compute which stellar photospheric cells are blocked by the transiting planet."
 We then iutegrate he unblocked Doppler-shitted aud intensity weighted stellar photospleric cells to couite both the RM racial, We then integrate the unblocked Doppler-shifted and intensity weighted stellar photospheric cells to compute both the RM radial
Dillerent authors have reported the discovery of an excess in the Near Infrared. Background (NIB) which cannot be accounted For by normal galaxies (see Hauser Dwek 2001 and references therein).,Different authors have reported the discovery of an excess in the Near Infrared Background (NIRB) which cannot be accounted for by normal galaxies (see Hauser Dwek 2001 and references therein).
 This unaccounted excess can be well fitted by the redshifted light of the first population of stars born inside the so-called Population HI objects (Pop ELLs) (Santos. Dromm Ixamionkowski 2001. Salvaterra Ferrara 2003 SE03]).," This unaccounted excess can be well fitted by the redshifted light of the first population of stars born inside the so-called Population III objects (Pop IIIs) (Santos, Bromm Kamionkowski 2001, Salvaterra Ferrara 2003 [SF03])."
 More recently. Ixashlinskvy et al. (," More recently, Kashlinsky et al. ("
2002) have observed small-scale. NIRB Uuetuations in the J. 1 and [x bands. which cannot be due to local or low redshift sources.,"2002) have observed small-scale NIRB fluctuations in the J, H and K bands, which cannot be due to local or low redshift sources."
" The aim of this paper is to show that. Popllls are indeed: required. to account. for the observed: small-scale (0X 200"") background fluctuations at least in the J) band.", The aim of this paper is to show that PopIIIs are indeed required to account for the observed small-scale $\theta\simlt 200^{\prime\prime}$ ) background fluctuations at least in the J band.
" Their contribution — dominant for A= 1.255 is found o rapidly decrease at. longer wavelengths until it becomes negligible for A= 2.1750. We will also show that ""normal. ügh (£2)29 3) redshift and highly clustered star-forming galaxies of the kind found in the Llubble Deep Fields can oovide for the missing power in the LE and Ix hands. so that the joint. contribution from these two populations can reproduce. within the errors. the observed. power spectrum of intensity [uctuations at all NIU wavelengths."," Their contribution – dominant for $\lambda=1.25\mu$ m – is found to rapidly decrease at longer wavelengths until it becomes negligible for $\lambda=2.17 \mu$ m. We will also show that “normal”, high $\langle z \rangle\simeq 3$ ) redshift and highly clustered star-forming galaxies of the kind found in the Hubble Deep Fields can provide for the 'missing' power in the H and K bands, so that the joint contribution from these two populations can reproduce, within the errors, the observed power spectrum of intensity fluctuations at all NIR wavelengths."
 Note that. due to the high redshifts of the two candidate populations (2c8S. as found by SEO3. for Popllls and z2 for “normal” star-forming galaxies). this is only true a small angular scales.," Note that, due to the high redshifts of the two candidate populations $z\ga 8.8$, as found by SF03, for PopIIIs and $z\ga 2$ for “normal” star-forming galaxies), this is only true at small angular scales."
 Signals on intermecdiate-to-LIarge scales detected by other experiments (6—0.77: see e.g. Ixashlinsky Odenwald. 2000: Matsumoto. ct al., Signals on intermediate-to-large scales detected by other experiments $\theta\sim 0.7^\circ$; see e.g. Kashlinsky Odenwald 2000; Matsumoto et al.
 2000) are. insteac expected to require populations of more local sources., 2000) are instead expected to require populations of more local sources.
 The outline of the paper is as follows: in Sec., The outline of the paper is as follows: in Sec.
 2 we briellv describe the adopted: model for the birth and evolution of Pop LLU protogalaxies., 2 we briefly describe the adopted model for the birth and evolution of Pop III protogalaxies.
 Sec., Sec.
 3 presents our predictions for the intensity fluctuations of the NIRB due to the clustering of Pop ΗΙ sources. while Sec.," 3 presents our predictions for the intensity fluctuations of the NIRB due to the clustering of Pop III sources, while Sec."
 4 compares such predictions with the available cata and ciscusses the results., 4 compares such predictions with the available data and discusses the results.
 Finally. Sec.," Finally, Sec."
 5 summarizes our conclusions., 5 summarizes our conclusions.
 SFOS have shown that the NIRB data (see e.g. Hauser Dwek (2001) and references therein) are well fitted by a, SF03 have shown that the NIRB data (see e.g. Hauser Dwek (2001) and references therein) are well fitted by a
Iu the last two decades. discoveries of the Ixuiper belt (Jewitt&Luu1993).. as well as planets orbiti stars other han the Suu (Mavor&Queloz1995).. have supplice the ceuturies-old quest to uudorstaud 1C formation of the soar system with fresh constraints and insights into plivsical processes at play.,"In the last two decades, discoveries of the Kuiper belt \citep{1993Natur.362..730J}, as well as planets orbiting stars other than the Sun \citep{1995Natur.378..355M}, have supplied the centuries-old quest to understand the formation of the solar system with fresh constraints and insights into physical processes at play."
 AmoueT a multitude of newly xoposed. for1nafion scenarios. “Nice” inode (Tsieausetal.205:Comes2005:Alorbidellietal.2005) as particuarly notable. as it has attained a coισαe amount of success n reproducing the various observed euures of the solar system.," Among a multitude of newly proposed formation scenarios, the “Nice"" model \citep{2005Natur.435..459T, 2005Natur.435..466G, 2005Natur.435..462M} is particularly notable, as it has attained a considerable amount of success in reproducing the various observed features of the solar system."
 Witiu the contest of the scejudo envisiored by the Nice inodol. ejut plaucts start heim post-uebular evolution im a conrpact. multiaesonal configuration. aud following a brief period of ανα iustabiity. scatter onto their current orbits (Morbidelliσα].etal.207:Batvein2010:Walshctal.20]1).," Within the context of the scenario envisioned by the Nice model, giant planets start their post-nebular evolution in a compact, multi-resonant configuration, and following a brief period of dynamical instability, scatter onto their current orbits \citep{2007AJ....134.1790M, 2010ApJ...716.1323B, 2011Natur.475..206W}."
 The first success of the Nice model lies iji its ability to quantitatively reproduce the observed orbits of the ejut plaucts. as we] as their dvuamical architecure (i.e. secular eigenniodes of the system) (Tsigauiseal.2005:Morbidellieta. 2009)..," The first success of the Nice model lies in its ability to quantitatively reproduce the observed orbits of the giant planets, as well as their dynamical architecture (i.e. secular eigenmodes of the system) \citep{2005Natur.435..459T, 2009A&A...507.1041M}."
 Simultauncousv. the brief lustabilitv. mbhereut o the model. provides a natural trigecrCoco» o the Late IIeavy. Donibimrcaueut (Comeseal. 2005).. as well as a traisport mmechanisin for euplacement of dvuanically “hot” Kuiper belt objects (KDOs) from inside of ~ 35AU (Levisonetal.2008)...," Simultaneously, the brief instability, inherent to the model, provides a natural trigger to the Late Heavy Bombardment \citep{2005Natur.435..466G}, as well as a transport mechanism for emplacement of dynamically “hot"" Kuiper belt objects (KBOs) from inside of $\sim 35$ AU \citep{2008Icar..196..258L}."
 Meauschile. it has been recently demonstrated that survival of a dvuanücalle “cold” primordial population between Neptune's current 3:?2 and 2:1 exterior ΓΗ POSOMALCCS (AIMIRs) is fully consistent with a Nice modeLlike evolution of the planets muplviug an formation of fi6 cold classical population of the Kuiper belt (Batvei1etal.2011)..," Meanwhile, it has been recently demonstrated that survival of a dynamically “cold"" primordial population between Neptune's current 3:2 and 2:1 exterior mean-motion resonances (MMRs) is fully consistent with a Nice model-like evolution of the planets, implying an formation of the cold classical population of the Kuiper belt \citep{2011arXiv1106.0937B}."
 Finally. the presence of πας and Ncptune’s Trojan asteroids has been attributed to chaotic: capture ofplauctesimals during the instability (ALorbidelietal.2005:Nesvorny2007)..," Finally, the presence of Jupiter's and Neptune's Trojan asteroids has been attributed to chaotic capture of planetesimals during the instability \citep{2005Natur.435..462M, 2007AJ....133.1962N}."
 All successful reaizatious of the Nice model to date have been comprise exclusively of the four currently present eiaut planes., All successful realizations of the Nice model to date have been comprised exclusively of the four currently present giant planets.
 However. there exists uo strong evidence that sugeess that additional planets were not preseut im the solar sveto at the epoch of the dispersion of the nebula.," However, there exists no strong evidence that suggests that additional planets were not present in the solar system, at the epoch of the dispersion of the nebula."
 In fac. theoretical arguments. presented by Goldreichetal.(20010) point to a possibility of initially formune as many as five ice giants; three owhich eet subsequently axq4uoved xia ejections (see however Levisoi&Morbidelli (2007))).," In fact, theoretical arguments, presented by \citet{2004ApJ...614..497G} point to a possibility of initially forming as many as five ice giants, three of which get subsequently removed via ejections (see however \citet{2007Icar..189..196L}) )."
 The dynamical sensibility of such a scenario is further strenethenc: by the fact that a considerable fraction of standard Nice nodel simula1ος result in au ejection of an iceeiut after an encounter with at least one of the eas eiauts., The dynamical sensibility of such a scenario is further strengthened by the fact that a considerable fraction of standard Nice model simulations result in an ejection of an ice-giant after an encounter with at least one of the gas giants.
 In this paper. we explore απ instahility-driven dynamical evolution of a 5-plauet svstem (2 eas giants | 32 ice giauts) with an eve towards idewifving a patlwayv owards reproducticπι of solar svstem-like ανασα] architecture.," In this paper, we explore an instability-driven dynamical evolution of a 5-planet system (2 gas giants + 3 ice giants) with an eye towards identifying a pathway towards reproduction of solar system-like dynamical architecture."
 Iu principle. the reahu of possibility available to this stulv is enormous.," In principle, the realm of possibility available to this study is enormous."
 Consequently. rather han performing a ος1uprelienusive paramoeter-search. here we nit ourselves t«) svstenus that contain au additional Uranus-like plauct. with the aim of prescuting a few xoof-of-concept. uumerical experiuents," Consequently, rather than performing a comprehensive parameter-search, here we limit ourselves to systems that contain an additional Uranus-like planet, with the aim of presenting a few proof-of-concept numerical experiments."
 The plan of hne paper is as follows., The plan of the paper is as follows.
 Iu section 2. we describe our mmerical setup.," In section 2, we describe our numerical setup."
 hhi section 3. we show that in our uodel. the planetar *oorbits. their secular clecuimodes. as well as various ]»pulatious of the άρα belt are approxinuatelv reproduced.," In section 3, we show that in our model, the planetary orbits, their secular eigenmodes, as well as various populations of the Kuiper belt are approximately reproduced."
 We couclude and diseuss our results in section L., We conclude and discuss our results in section 4.
proper time 7: signs in (2)) and (3)) can be chosen independently. £.,"proper time $\tau$; signs in \ref{eqmotr}) ) and \ref{eqmotth}) ) can be chosen independently. $E$,"
 L and Q are the three constants of the particle motion: £7 and L are. respectively. the energy. and the angular momentum in the azimutal direction as seen bv an observer at rest at infinitv: ( is related to Carter's constant of motion (see e.g. Chandrasekhar (1983). and cle Felice (1980))) characterizes the @ motion.," $L$ and $Q$ are the three constants of the particle motion: $E$ and $L$ are, respectively, the energy and the angular momentum in the azimutal direction as seen by an observer at rest at infinity; $Q$ is related to Carter's constant of motion (see e.g. Chandrasekhar \shortcite{cha} and de Felice \shortcite{def}) ) and characterizes the $\theta$ motion."
 As Wilkinsuem(1972) showed. bound. motion is possible only if E?«1 Q30: moreover. for given € and L and ||«1l. there may be at most. one.region of binding.," As Wilkins \shortcite{wil} showed, bound motion is possible only if $E^2<1$ and $Q\geq 0$; moreover, for given $Q$ and $L$ and $|E|<1$, there may be at most oneregion of binding."
 Analysis of the @ effective. potential shows that every orbit either remains in the equatorial plane (ῷ=0) or Crosses it repeteacdhy (0.2 0).," Analysis of the $\theta$ effective potential shows that every orbit either remains in the equatorial plane $Q=0$ ), or crosses it repeteadly $Q > 0$ )."
 For every bound. motion. introducing the angle-action variables. we can define the three fundamental proper frequencies where Τρ. Τον and την are the proper time periods for Ó. 8 and r motions respectively.," For every bound motion, introducing the angle-action variables, we can define the three fundamental proper frequencies where $\tau_{\phi,p}$, $\tau_{\theta,p}$ and $\tau_{r,p}$ are the proper time periods for $\phi$, $\theta$ and $r$ motions respectively."
 Unlike the Newtonian case of particle motion around a spherically svmmetric central object. where all orbits close and the three fundamental frequencies are equal. in the Werr field (ez 0) there is no degeneracy. Lc. The same is also true for coordinate frequencies ον. va and b," Unlike the Newtonian case of particle motion around a spherically symmetric central object, where all orbits close and the three fundamental frequencies are equal, in the Kerr field $a\neq 0$ ) there is no degeneracy, i.e. The same is also true for coordinate frequencies $\nu_{\phi}$ , $\nu_{\theta}$ and $\nu_{r}$."
 Let us first consider a circular geodesic in the equatorial plane (06= z/2)., Let us first consider a circular geodesic in the equatorial plane $\theta=\pi/2$ ).
" We have. for the coordinate angular velocities measured by an observer. static at. infinity (Bardeenetal.1972 the angular velocity O,, deviates from. its. Weplerian value at small radii."," We have, for the coordinate angular velocities measured by an observer static at infinity \cite{bpt}
 the angular velocity $\Omega_\phi$ deviates from its Keplerian value at small radii."
 The upper sign refers to progracde orbits and the lower to retrograde ones., The upper sign refers to prograde orbits and the lower to retrograde ones.
" Lf we slightly perturb a circular orbit introducing velocity components in the r and 8 directions. we can compute the coordinate. [requencies of the small amplitude oscillations within the plane (the epievclic frequeney O,) and in the perpendicular direction (the vertic [requeney Qe) (Okazaki. Kato Pulue(198 kato (1990)... pnade Felice Usseglio-Tomasset (1906).. Perez et al. "," If we slightly perturb a circular orbit introducing velocity components in the $r$ and $\theta$ directions, we can compute the coordinate frequencies of the small amplitude oscillations within the plane (the epicyclic frequency $\Omega_r$ ) and in the perpendicular direction (the vertical frequency $\Omega_\theta$ ) (Okazaki, Kato Fukue \shortcite{okf}, Kato \shortcite{ka}, de Felice Usseglio-Tomasset \shortcite{dut}, Perez et al. \shortcite{per}) ):"
1n the case of the Sehwarzschild metric (e= 0). there is a partial degeneracy. as the vertical frequeney coincides with the azimutal one.,"In the case of the Schwarzschild metric $a=0$ ), there is a partial degeneracy, as the vertical frequency coincides with the azimutal one."
 The epieyclie Frequency. instead. is always lower than the other two. reaching a maximum for r—8M and &oing to zero at kc=GAL (Okazakictal.1987).," The epicyclic frequency, instead, is always lower than the other two, reaching a maximum for $r=8M$ and going to zero at $r=6M$ \cite{okf}."
. These qualitative behaviour of the epyciclie frequency is preserved in the Ixerr field (e40). and is a key feature for the existence of trapped dliskoscismic &-mocdes (Perez et al (1997))).," These qualitative behaviour of the epyciclic frequency is preserved in the Kerr field $a\neq 0$ ), and is a key feature for the existence of trapped diskoseismic g-modes (Perez et al \shortcite{per}) )."
 We now confine ourselves to the study of those orbits with constant r which are arbitrarily (not infinitesimallv) lifted over the equatorial plane. ie. with a finite value of Q.," We now confine ourselves to the study of those orbits with constant $r$ which are arbitrarily (not infinitesimally) lifted over the equatorial plane, i.e. with a finite value of $Q$."
 The conditions for the stability of a spherical orbit with radius r—ro are (see eq. (2))), The conditions for the stability of a spherical orbit with radius $r=r_0$ are (see eq. \ref{eqmotr}) ))
 Conditions (9)) anc (10)) introduce two relations between rand the constants of motion £. L and 6). reducing the freeparameters that characterize the orbit to two: thus. given a specilie Ixerr black hole (i.e. given the values of Al ancl e). a spherical orbit. is completely determinated. for example. by specilving its radius ancl the value of €. which fixes the amplitude of motion in the @ direction. (Wilkins (1912))).," Conditions \ref{cond:R}) ) and \ref{cond:dR}) ) introduce two relations between $r$ and the constants of motion $E$, $L$ and $Q$, reducing the freeparameters that characterize the orbit to two; thus, given a specific Kerr black hole (i.e. given the values of $M$ and $a$ ), a spherical orbit is completely determinated, for example, by specifying its radius and the value of $Q$, which fixes the amplitude of motion in the $\theta$ direction (Wilkins \shortcite{wil}) )."
" The motion is open. since the two fundamental frequencies #7, anc ove (proper or coordinate) are incommensurate: then the Fourier spectra of every function of the position of the test particle will contain a superposition of the two fundamental frquencies ancl of all their harmonies and will be of the kine where ιτ is an arbitrary. phase."," The motion is open, since the two fundamental frequencies $\nu_\phi$ and $\nu_\theta$ (proper or coordinate) are incommensurate; then the Fourier spectra of every function of the position of the test particle will contain a superposition of the two fundamental frquencies and of all their harmonics and will be of the kind where $\beta$ is an arbitrary phase."
 'herefore. the most natural signals to look for in such ἃ svstem are the two fundamental coordinate frequencies themselves anc the cillerence between them. that. as we will show. coincide with the unique correct definition of precession frequency. of the nodes of à spherical orbit.," Therefore, the most natural signals to look for in such a system are the two fundamental coordinate frequencies themselves and the difference between them, that, as we will show, coincide with the unique correct definition of precession frequency of the nodes of a spherical orbit."
 In fact we can compute exactly the coordinate period of the @ motion: i£ we call 64 (with 6«8 ) the two roots of the equation O(9)= 0. we see from (3)) that the particle oscillates on the coordinate sphere between the angles ϐ and w/2|4 ," In fact we can compute exactly the coordinate period of the $\theta$ motion: if we call $\theta_\pm$ (with $\theta_-<\theta_+$ ) the two roots of the equation $\Theta(\theta)=0$ , we see from \ref{eqmotth}) ) that the particle oscillates on the coordinate sphere between the angles $\theta_-$ and $\pi/2+\theta_-$ ."
Dividing (5)) by (3)) and integrating. we obtain where f=1. EPk=&fe (with za=cos? +) and dy(A) and EG) are the elliptic integrals of the first and second. kind. respectively.," Dividing \ref{eqmott}) ) by \ref{eqmotth}) ) and integrating, we obtain where $\beta=1-E^2$ , $k^2=z_-/z_+$ (with $z_{\pm}=cos^2\theta_\pm$ ) and $K(k)$ and $E(k)$ are the elliptic integrals of the first and second kind, respectively."
 The change of azimuth during onequarter oscillation of latitucle is given by, The change of azimuth during onequarter oscillation of latitude is given by
"Approximately 150 off-nuclear Ultraluminous X-ray Sources (ULXs) in nearby galaxies have been discovered with luminosities greater (han LO"" erg |. exceeding the Eddington Launinosityv for à ~10A. black hole (e.g..Fabbiano1988:Colbert&AMushotzky1999:Colbert&Ptak2002;LinAlirabel 2005).","Approximately 150 off-nuclear Ultraluminous X-ray Sources (ULXs) in nearby galaxies have been discovered with luminosities greater than $10^{39}$ erg $^{-1}$, exceeding the Eddington Luminosity for a $\sim 10 M_{\odot}$ black hole \citep[e.g.,][]{fabbiano88,cm99,cp02,lm05}."
. While some can be identified as supernova remnants. background. Active Galactic Nuclei. or faint foreground. stars 2006).. most seem to be the result of accretion from a high-mass star onto a compact object.," While some can be identified as supernova remnants, background Active Galactic Nuclei, or faint foreground stars \citep[e.g.,][]{g06}, most seem to be the result of accretion from a high-mass star onto a compact object."
 Short-term variability of some of these ULXs indicates that (μον are not simply unresolved superposilions of several lower-Iuminositv sources (e.g..Matsumotoetal.2001:etal. 2003).," Short-term variability of some of these ULXs indicates that they are not simply unresolved superpositions of several lower-luminosity sources \citep[e.g.,][]{matsumoto01,fabbiano03}."
". Thus. the hieh huninosity implies accretion onto black holes with masses 504.<AL10V... Gntermediatemassblackholes:IMDIIs:Colbert&Mushotzky.1999:Makishimaetal.2000:πα,Ixrolik&IIubeny2005:Machusucdhan2006) or superEddington accretion."," Thus, the high luminosity implies accretion onto black holes with masses $50 M_{\odot} < M < 10^4 M_{\odot}$, \citep[intermediate mass black holes; IMBHs;][]{cm99,metal00,hui05,metal06} or super--Eddington accretion."
 SuperEcddington accretion can be achieved in (wo different wavs: an Inhomogeneous accretion-disk structure in which the photon flux is spatially separated from (he bulk of the matter influx. or strongly. anisotropic radiation.," Super–Eddington accretion can be achieved in two different ways: an inhomogeneous accretion-disk structure in which the photon flux is spatially separated from the bulk of the matter influx, or strongly anisotropic radiation."
" Anisotropic emission (lxingetal.2001) may originate. e.g.. from jet sources associated wilh accretion onto solar-mass black holes (microquasars) in which the jet is oriented at a small angle with respect to our line of sight — (he so-called ""miceroblazar model (Georganopoulos.2002:Nording.Faleke&Markolf 2002)."," Anisotropic emission \citep{king01} may originate, e.g., from jet sources associated with accretion onto solar-mass black holes (microquasars) in which the jet is oriented at a small angle with respect to our line of sight — the so-called “microblazar” model \citep{gak02,kfm02}."
 The latter model is now considered unlikely based on recent observations of X-ray ionization of optical nebulae associated with some ULXs (Pakull&Mirioni2003:Gutierrez2006).," The latter model is now considered unlikely based on recent observations of X-ray ionization of optical nebulae associated with some ULXs \citep{pm03, g06}."
. A promising mechanism for sustaining super-Eddington accretion in a iinaateed. magnetized accretion flow. is provided by the so-called photon bubble instability (Arons1992:Gammie1998:Begelman2001.2002.2006).," A promising mechanism for sustaining super-Eddington accretion in a ed, magnetized accretion flow, is provided by the so-called photon bubble instability \citep{a92,g98,begelman01,begelman02,begelman06}."
. In this model. radiation can escape along low-density regions (LDIs) aligned with predominantly vertical magnetic field lines.," In this model, radiation can escape along low-density regions (LDRs) aligned with predominantly vertical magnetic field lines."
 The accretion flow is concentrated in thin. optically Chick high-density regions (1112115). where (he magnetic pressure of field lines oriented predominantly within the disk dominates over (he gas pressure. (hus confining the gas and preventing the radiation pressure from disrupting the accretion flow.," The accretion flow is concentrated in thin, optically thick high-density regions (HDRs), where the magnetic pressure of field lines oriented predominantly within the disk dominates over the gas pressure, thus confining the gas and preventing the radiation pressure from disrupting the accretion flow."
 In such a configuration. the total disk Iuminosity can exceed the Eddington luminosity by à factor approximately equal to the ratio of the magnetic field pressure (o (he gas pressure (Beeelmman2001.2002) in the HIDRs.," In such a configuration, the total disk luminosity can exceed the Eddington luminosity by a factor approximately equal to the ratio of the magnetic field pressure to the gas pressure \citep{begelman01,begelman02} in the HDRs."
 Given (he variety. of different promising candidate models for (he nature of ULXs. the obvious question is: Can one distinguish between these models with ULXs X-ray spectra?," Given the variety of different promising candidate models for the nature of ULXs, the obvious question is: Can one distinguish between these models with ULXs' X-ray spectra?"
 If so. what are (he characteristic spectral features of the individual models?," If so, what are the characteristic spectral features of the individual models?"
 From an accreting ]IMDLIL it is generally believed that à multi-color disk blackbody (AICDBB) spectrum wilh an inner temperature of £T;~ 0.1 0.3 keV (that is. the disk temperature at the innermost," From an accreting IMBH it is generally believed that a multi-color disk blackbody (MCDBB) spectrum with an inner temperature of $kT_{in} \sim$ 0.1 — 0.3 keV (that is, the disk temperature at the innermost"
"kinetic encrey Z4, have lower values than considered. for Figures 3 and 4.",kinetic energy $E_k$ have lower values than considered for Figures 3 and 4.
 The elfect of these parameters is illustrated in Figure 5 for η=10*em and P=100.," The effect of these parameters is illustrated in Figure 5 for $n=10^3\, \cm3$ and $\Gamma = 100$."
 A Kinetic energy [y lower than 107 cres or magnetic field parameter zg below LO vield an carly afterglow emission too dim to have been detected with the past capabilities of ROWSE or LOTIS. but within their reach in the future.," A kinetic energy $E_k$ lower than $10^{52}$ ergs or magnetic field parameter $\varepsilon_B$ below $10^{-6}$ yield an early afterglow emission too dim to have been detected with the past capabilities of ROTSE or LOTIS, but within their reach in the future."
 For a lower electron energy. past detections were more cillicult. but not impossible.," For a lower electron energy, past detections were more difficult, but not impossible."
 We note that such low values for £2; and the + - output energy Lo. obtained by Bloom. Frail Sari (2001) for bursts with known redshifts. ranging [rom 10757 to 10737 erg. would imply high burst. efficiencies.," We note that such low values for $E_k$ and the $\gamma$ -ray output energy $E_\gamma$ obtained by Bloom, Frail Sari (2001) for bursts with known redshifts, ranging from $10^{51.5}$ to $10^{54.5}$ erg, would imply high burst efficiencies."
" Furthermore. the above low values for 2. and zg are below the values 2,20.1 and 7g>10+ determined by Panaitescu Kumar (2002) from fits to the 0.5im100 days broadband afterglow emission ol several GRB afterglows."," Furthermore, the above low values for $\varepsilon_e$ and $\varepsilon_B$ are below the values $\epsilon_e > 0.1$ and $\epsilon_B > 10^{-4}$ determined by Panaitescu Kumar (2002) from fits to the 0.5–100 days broadband afterglow emission of several GRB afterglows."
"o VPherclore. barring a substantial increase of the 2, and pg parameters [ron 10510 sto 107 s after the burst. the non-detections by LOTIS and ROTSE of GIUD optical counterparts brighter than #= 13 162at/«35107 s imply that the medium surrounding the GRB source is less dense jun p—100em."" up to à distance r0.01 pe."," Therefore, barring a substantial increase of the $\epsilon_e$ and $\epsilon_B$ parameters from $10^2-10^3$ s to $10^5$ s after the burst, the non-detections by LOTIS and ROTSE of GRB optical counterparts brighter than $R = 13$ –16 at $t < 3\times 10^3$ s imply that the medium surrounding the GRB source is less dense than $n = 100\, \cm3$ up to a distance $r \sim 0.01$ pc."
 Figures 6 and 7 present the afterglow light-curves expected when the circumburst medium is a stellar wind of ensitv profile n=clr7 ejected by the GIU. progenitor. as expected. in the hvpernova. scenario.," Figures 6 and 7 present the afterglow light-curves expected when the circumburst medium is a stellar wind of density profile $n = A r^{-2}$ ejected by the GRB progenitor, as expected in the hypernova scenario."
 In. contrast with the homogeneous medium case considered in Figures 3 and the brightening produced. by the pair wind is stronger (23 mags). occurs earlier. and has a weak dependence on the normalization constant zd. the wind density). but a stronger dependence on the ejecta Lorentz factor.," In contrast with the homogeneous medium case considered in Figures 3 and 4, the brightening produced by the pair wind is stronger (2–3 mags), occurs earlier, and has a weak dependence on the normalization constant $A$ the wind density), but a stronger dependence on the ejecta Lorentz factor."
 For the canonical burst parameters used here. optical afterglows brighter than some of the IROTSIZ and LOIS limits are obtained even for tenuous stellar wincds corresponding to a mass-loss rate to wind speed ratio of LOOAL./vr/(10kms) ," For the canonical burst parameters used here, optical afterglows brighter than some of the ROTSE and LOTIS limits are obtained even for tenuous stellar winds corresponding to a mass-loss rate to wind speed ratio of $10^{-6}\, M_\odot/{\rm yr}/ (10^3\, {\rm km/s})$ ."
"Assuming that GRBs are produced. by internal shocks at 1015—107 em. a smell fraction of the eaniuma-ray photons is converted. into. clectron-positron pairs al a. distance of less than rj;=101"" em from the center of explosion."," Assuming that GRBs are produced by internal shocks at $10^{13}-10^{14}$ cm, a small fraction of the gamma-ray photons is converted into electron-positron pairs at a distance of less than $r_{pair} = 10^{16}$ cm from the center of explosion."
" The fractional energy carried. away by this. palr-wind is ~10""n. where » is the particle density in em of the unperturbed. cireumburst. medium."," The fractional energy carried away by this pair-wind is $\sim 10^{-6} n$, where $n$ is the particle density in $\cm3$ of the unperturbed, circumburst medium."
 “Phe number of pairs created per external electron is of order a few hundred anc 10 average Lorentz factor of the pairs is a few., The number of pairs created per external electron is of order a few hundred and the average Lorentz factor of the pairs is a few.
 For plausible values of the fireball kinetic energy. electron. ancl magnetic. field parameters in. the shocker circumburst. medium. and for an external density η=100em the optical afterglow from. the forward shock »eaks around. LO minutes from the burst (when the peak of 16 synchrotron spectrum reaches the optical domain) zu magnitude #2~14 (Figure 3).," For plausible values of the fireball kinetic energy, electron and magnetic field parameters in the shocked circumburst medium, and for an external density $n=100\, \cm3$ , the optical afterglow from the forward shock peaks around 10 minutes from the burst (when the peak of the synchrotron spectrum reaches the optical domain) and at magnitude $R \sim 14$ (Figure 3)."
 For a tenfold increase in 1ο density. the peak brightens by one magnitude 43]]) and occurs earlier due to the electron cooling.," For a tenfold increase in the density, the peak brightens by one magnitude ]) and occurs earlier due to the electron cooling."
 By softening the afterglow spectrum and by increasing 1e number of radiating particles. the pair-wincd brightens re rise of the optical light-curve.," By softening the afterglow spectrum and by increasing the number of radiating particles, the pair-wind brightens the rise of the optical light-curve."
 Fordensities higher iun mcLO?em the peak optical emission. occurs," Fordensities higher than $n \sim 10^3\, \cm3$ the peak optical emission occurs"
SNRs have Όσο identified in the SAIC by work done in thle radio. optical aud N-ray regine (Mills et al.,"SNRs have been identified in the SMC by work done in the radio, optical and X-ray regime (Mills et al."
 1982. 1981).," 1982, 1984)."
 Iu the work of Ye Turtle (1993). some 15 SNRs aud SNR candidates are detected in a 8125 MITz survey.," In the work of Ye Turtle (1993), some 15 SNRs and SNR candidates are detected in a 843 MHz survey."
 We applied the selection criteria likelihood. of extent and in order to derive a candidate sample of SNRs aud other extended structures., We applied the selection criteria likelihood of extent and in order to derive a candidate sample of SNRs and other extended structures.
 We find 19 objects fulfilling these criteria Gneludiug four SNRs detected byEiusteiu.. although they have a LIL. below our classification threshold: sources 86. 128. ]7T aud 182).," We find 19 objects fulfilling these criteria (including four SNRs detected by, although they have a $_{\rm ext}$ below our classification threshold: sources 86, 128, 177 and 182)."
 These sources are classified as class=R iu Table 1., These sources are classified as class=R in Table 1.
 The sources with catalogue ummber 95. 132. aud 136 may be detector artifacts.," The sources with catalogue number 95, 132, and 136 may be detector artifacts."
 They have the class=R/D. For 13 sources an lidentification has beeu found., They have the class=R/D. For 13 sources an identification has been found.
 We eive the munber and the identification for these sources in Table 5., We give the number and the identification for these sources in Table 5.
 12 of these sources actually are kuown SNRs., 12 of these sources actually are known SNRs.
 The bright voung oxvecu-rich SNR 0102-723 (Amy Ball 1993) has two cutrics (182 aud 183) in our catalog due to the mereime of two pointed observations at differcut off-anis-aneles., The bright young oxygen-rich SNR 0102-723 (Amy Ball 1993) has two entries (182 and 183) in our catalog due to the merging of two pointed observations at different off-axis-angles.
 Entry 183 is the more accurate one., Entry 183 is the more accurate one.
 An additional classified source (31) correlates with a SNR proposed by Filipovié ct al. (, An additional classified source (34) correlates with a SNR proposed by Filipović et al. (
1998).,1998).
 We find new candidate SNRs in our N-rav survey: RN JOT01.8-7219 (source 165) aud RN JOLL2.7-7207 {223) wore not reported before. while RN J019.1-7301 {215) was already detected. with (BINGS 30. Brulaveiler et al.," We find new candidate SNRs in our X-ray survey: RX J0101.8-7249 (source 165) and RX J0112.7-7207 (223) were not reported before, while RX J019.4-7301 (245) was already detected with (BKGS 30, Bruhweiler et al."
 1987). however not classified as SNR.," 1987), however not classified as SNR."
 We ndss a few well known SNRs in the SAIC with this selection., We miss a few well known SNRs in the SMC with this selection.
 They have au extent likelihood ratio 210 and fulfill the criteria of being extended. sugecsting we have chosen too strict an extent criterion iu order to be ou the secure side.," They have an extent likelihood ratio $>$ 10 and fulfill the criteria of being extended, suggesting we have chosen too strict an extent criterion in order to be on the secure side."
 It also sugecsts that there are still uurecognized SNRs in our sample (see discussion iu Filipovic et al., It also suggests that there are still unrecognized SNRs in our sample (see discussion in Filipović et al.
 1998)., 1998).
 We list these SNRs in the lower part of Table 5., We list these SNRs in the lower part of Table 5.
 It is not trivial το select this sample just from the N-ray characteristics., It is not trivial to select this sample just from the X-ray characteristics.
 Stars are coronal ciuitters with temperatures in the range of a few toK., Stars are coronal emitters with temperatures in the range of a few to.
 The ΠΕΙ would then fall into the regine0.5.. aud the likelihood of extent50.," The HR1 would then fall into the regime, and the likelihood of extent."
. Actually. all ealactic foreground stars detected in a field centered ou the SAIC and observed durius the RASS have values of (INahabka Pietsch 1993).," Actually, all galactic foreground stars detected in a field centered on the SMC and observed during the RASS have values of (Kahabka Pietsch 1993)."
 This meaus that we may be too conservative in sclecting stars in our sample with the criteria mentioned above., This means that we may be too conservative in selecting stars in our sample with the criteria mentioned above.
 We find 19 candidates aud we classify these sources as class=F iu Table 1., We find 19 candidates and we classify these sources as class=F in Table 1.
 For seven objects. a match exists.," For seven objects, a match exists."
" Six of these identifications appear to be reliable as the distance to the source is <60"".", Six of these identifications appear to be reliable as the distance to the source is $<60''$.
 Five of thei correlate with stars of spectral type O. A or F and they are given in Table 6.," Five of them correlate with stars of spectral type O, A or F and they are given in Table 6."
 Source 138 coincides with au O star., Source 138 coincides with an O star.
" Asstuning a conversion factor of 0.76«10°""erects+ we derive for the O-star in the SAIC an Nay. luminosity of 10eres1 from the measured count rate.", Assuming a conversion factor of $0.76\times10^{37}\ {\rm erg}\ {\rm cts}^{-1}$ we derive for the O-star in the SMC an X-ray luminosity of $10^{34}\ {\rm erg}\ {\rm s}^{-1}$ from the measured count rate.
 The nature of the other LL sources remains unclear., The nature of the other 14 sources remains unclear.
 Dackeround objects ire selected as0.5.. and extent likehhood50.," Background objects are selected as, and extent likelihood."
. The same criterion has already. been applied in Paper I, The same criterion has already been applied in Paper I
the CMD plus the contribution coming from the BS and HB stars: star counts has been limited at the magnitude V<15.5.,the CMD plus the contribution coming from the BS and HB stars; star counts has been limited at the magnitude $V\le18.5$.
 This relatively bright limit corresponds approximately to the limit of the visual star counts by Kingetal.(1968) on the plate ED-2134 (in order to make the comparison easier we used the same radial bins of King)., This relatively bright limit corresponds approximately to the limit of the visual star counts by \cite{King68} on the plate ED-2134 (in order to make the comparison easier we used the same radial bins of King).
 Our counts have been transformed to surface brightness and adjusted 1n zero point to fit the al.(1991) profile of MSS., Our counts have been transformed to surface brightness and adjusted in zero point to fit the \cite{Pryor91} profile of M55.
 The agreement with the data presented by Pryor is good everywhere but in the outer parts where our CCD star counts are clearly above those of Kingetal.(1968)., The agreement with the data presented by Pryor is good everywhere but in the outer parts where our CCD star counts are clearly above those of \cite{King68}.
. This difference is probably due to our better estimate of the background star contamination., This difference is probably due to our better estimate of the background star contamination.
" In the plot we have shown also the raw star counts (crosses) prior to the background star subtraction: it can be clearly seen that our star counts go well beyond the tidal radius. r;=977"". published by Trageretal.(1995)."," In the plot we have shown also the raw star counts (crosses) prior to the background star subtraction: it can be clearly seen that our star counts go well beyond the tidal radius, $r_t=977''$, published by \cite{Trager95}."
.. This allow us to estimate in a better way than in the past the stellar background contribution., This allow us to estimate in a better way than in the past the stellar background contribution.
 The background star counts show a small radial gradient: we will discuss this point in greater detail in the next Section., The background star counts show a small radial gradient: we will discuss this point in greater detail in the next Section.
 Here. the minimum value has been taken as an estimate of the background level.," Here, the minimum value has been taken as an estimate of the background level."
 We point out that the differences present in. the central zones of the cluster could be in part due to some residual incompleteness of our star counts. to the absence in the starcounts of the brightest saturated stars. and to the difficulties in finding the center of the cluster.," We point out that the differences present in the central zones of the cluster could be in part due to some residual incompleteness of our star counts, to the absence in the starcounts of the brightest saturated stars, and to the difficulties in finding the center of the cluster."
 We searched for the center using a variant of the mirror autocorrelation technique developed by Djorgovski(1988)., We searched for the center using a variant of the mirror autocorrelation technique developed by \cite{DJ88}.
". In the case of M55 we encountered some problems due to a surface density which is almost constant inside a radius of ~100"".", In the case of M55 we encountered some problems due to a surface density which is almost constant inside a radius of $\simeq100\arcsec$.
 In order to evaluate the structural parameters of M55. we have fitted the profile Figure 9. with a multi-mass isotropic King(1966) model as deseribed in the previous Section.," In order to evaluate the structural parameters of M55, we have fitted the profile Figure \ref{profile} with a multi-mass isotropic \cite{King66}
 model as described in the previous Section."
 In the following table we show the parameters of the best fitting model and we compare them with the results of Trageret (1995).. Pryoretal. (1991).. and Irwin&Trimble(1984): The concentration parameter of M55 is one of the smallest known for a globular cluster.," In the following table we show the parameters of the best fitting model and we compare them with the results of \cite{Trager95}, \cite{Pryor91}, and \cite{Irwin84}: The concentration parameter of M55 is one of the smallest known for a globular cluster."
 Such à small concentration implies strong dynamical evolution and indicates that the cluster is probably in a state of high disgregation 1988;Gnedin&Ostriker. 1997).," Such a small concentration implies strong dynamical evolution and indicates that the cluster is probably in a state of high disgregation \cite[]{Aguilar88,Gnedin97}."
. Our value of the tidal radius is well in agreement with that of Trageretal.(1995) who used a similar method to fit the data., Our value of the tidal radius is well in agreement with that of \cite{Trager95} who used a similar method to fit the data.
 Pryoretal.(1991) give a value of rc smaller than ours., \cite{Pryor91} give a value of $r_t$ smaller than ours.
 We note that Pryor and Trager used the same observational data set., We note that Pryor and Trager used the same observational data set.
 The difference with Irwin&Trimble(1984) i$ probably due to the fact that the authors have not fitted their data directly but made only a comparison with a plot of King models., The difference with \cite{Irwin84} is probably due to the fact that the authors have not fitted their data directly but made only a comparison with a plot of King models.
"we suegeest that the velocity width is due to expansion such that 02,—Ae/2.","we suggest that the velocity width is due to expansion such that $v_{exp} =
\Delta v / 2$."
 Assiuuing 64LausLowe estimate the cucrey required to form this shell is ou the order of ~10°! ores. which is consistent with the amount of cnerey expected from stellar winds over the lifetime of a single massive star.," Assuming $v_{exp}\sim4$, we estimate the energy required to form this shell is on the order of $\sim 10^{51}$ ergs, which is consistent with the amount of energy expected from stellar winds over the lifetime of a single massive star."
 Because of the low expansion velocity. the formation energv for a shell whose expansion has stalled is comparable.," Because of the low expansion velocity, the formation energy for a shell whose expansion has stalled is comparable."
 We sueecst that the sshell and depression around ROW 91 are the signatures of a molecular cloud eucircliug the iregion., We suggest that the shell and depression around RCW 94 are the signatures of a molecular cloud encircling the region.
" Iu this case. the iregion appears to be αμοσα, in a molecular cloud. displaving various stages of ionization and dissociation related to the interior stars."," In this case, the region appears to be embedded in a molecular cloud, displaying various stages of ionization and dissociation related to the interior stars."
 Interior to the ~21 pe iuncr shell radius the UV photons from the stars ionize the jeutral gas. producing the rregion.," Interior to the $\sim 24$ pc inner shell radius the UV photons from the stars ionize the neutral gas, producing the region."
 The stars photo-cdissociate the surrounding uolecular gas. producing an sshell which extends to a radius of ~29 pc.," The stars photo-dissociate the surrounding molecular gas, producing an shell which extends to a radius of $\sim 29$ pc."
 The uinmorphologv correspondence with the continuum uorphologv especially supports this lypothesis., The morphology correspondence with the continuum morphology especially supports this hypothesis.
 In articular. the region of deuse comission in the concave portion on the right-hand side of he iregion indicates that the expansion of the ploto-dissociation region (PDR) was impeded bv a density enhancement in the external mediun prestunalbly chuups of molecular material.," In particular, the region of dense emission in the concave portion on the right-hand side of the region indicates that the expansion of the photo-dissociation region (PDR) was impeded by a density enhancement in the external medium, presumably clumps of molecular material."
 The extension of the shell smrounding the compact source to the upper left. iucdicates that the shape of the shell is directly related to the shape of the iregion. and that they are therefore correlated.," The extension of the shell surrounding the compact source to the upper left, indicates that the shape of the shell is directly related to the shape of the region, and that they are therefore correlated."
 Comparison with the CO images of Bronufinanetal.(1989) indicates molecular gas at the position aud velocity of ROW 91., Comparison with the CO images of \citet{bronfman89} indicates molecular gas at the position and velocity of RCW 94.
 Tnuneciately exterior to the sshell we can expect to see chussion from polycyclic aromatic hvdrocarbous (PAIIS) at 6.2.7.7.8.6. or 11.3 citepsinpson09..," Immediately exterior to the shell we can expect to see emission from polycyclic aromatic hydrocarbons (PAHs) at $6.2,
7.7, 8.6,$ or 11.3 \\citep{simpson99}."
 Close examination of MSX band A data does reveal au increase in cussion exterior to the shell. which also supports the theory that this iregion and its sshell are embedded in a molecular cloud.," Close examination of MSX band A data does reveal an increase in emission exterior to the shell, which also supports the theory that this region and its shell are embedded in a molecular cloud."
 Gacuslerctal.(2000a) explore the polarization properties of this region and find that the depolarization is consistent with being caused by an iregion enibedded im molecular gas with several lavers of ionization and photo-dissociation., \citet{gaensler00a} explore the polarization properties of this region and find that the depolarization is consistent with being caused by an region embedded in molecular gas with several layers of ionization and photo-dissociation.
 The ddepressioun around ROW 91. appears to exteud towards the Plane at lower longitudes where it traces the morphology of the large bow shaped structure. 1326.96|0.03. seen at the bottom of the continu inage.," The depression around RCW 94 appears to extend towards the Plane at lower longitudes where it traces the morphology of the large bow shaped structure, G326.96+0.03, seen at the bottom of the continuum image."
 This source is seen in the MOST images. as well as the MSN tages. aud therefore appears to be a thermal source.," This source is seen in the MOST images, as well as the MSX images, and therefore appears to be a thermal source."
 We measure aabsorptiou towards the knot of enuüssiou at 7—326795. b= 4002.," We measure absorption towards the knot of emission at $l=326\fdg95$, $b=+0\fdg02$ ."
 Though the spectra is rather noisy (Fie., Though the spectrum is rather noisy (Fig.
 7 left). we see a strong absorption feature at e=G0[2o which indicates that this region may be slightly more distaut than ROW 91-95 (d=3.9 kpc). though still iu the Scutuuni-Crux arin.," \ref{fig:g327abs} left), we see a strong absorption feature at $v=-60$, which indicates that this region may be slightly more distant than RCW 94-95 $d=3.9$ kpc), though still in the Scutum-Crux arm."
 There is an extended reeion of eenission to the left of these ivegious which is mach brighter than that surrounding ROW 91-95., There is an extended region of emission to the left of these regions which is much brighter than that surrounding RCW 94-95.
 The cohluuu density in this region. over the rauge of channels spauniug the depression {ο=38.bhansD toe 33.15kinsP) is a factor of two larger than it is suvrounding the sshell.," The column density in this region, over the range of channels spanning the depression $v=-38.4~{\rm km~s^{-1}}$ to $v=-33.45~{\rm km~s^{-1}}$ ), is a factor of two larger than it is surrounding the shell."
 Whereas iregious and SNRs draw a connection between the Tine aud coutimmiun cussion. the impact of massive stars ou the ISM can also be seeu with sshells. where no continuum object exists.," Whereas regions and SNRs draw a connection between the line and continuum emission, the impact of massive stars on the ISM can also be seen with shells, where no continuum object exists."
 These cavities survive much longer than the radiative lifetime of à SNR or an ivregion. allowing us to explore the lasting effects of massive stars on the ISAL," These cavities survive much longer than the radiative lifetime of a SNR or an region, allowing us to explore the lasting effects of massive stars on the ISM."
 sshells are often detected as voids in the wwith brightened “walls” of swept-up iuatenal., shells are often detected as voids in the with brightened “walls” of swept-up material.
 These shells can range iu size frou tens of parsecs to kiloparsecs., These shells can range in size from tens of parsecs to kiloparsecs.
 The majority of the shells. especially the smaller ones. are caused by the combined effects of stellar winds aud supernovae (IIeiles198D).," The majority of the shells, especially the smaller ones, are caused by the combined effects of stellar winds and supernovae \citep{heiles84}."
. The ultimate destruction of au Sμαhell occurs on the time-scale of τοις of millions of vears when they eventually dissipate as a result of turbulent motions in the ISM aud shear due to ditfereutial rotation in the Galaxy., The ultimate destruction of an shell occurs on the time-scale of tens of millions of years when they eventually dissipate as a result of turbulent motions in the ISM and shear due to differential rotation in the Galaxy.
 We have detected two simall shells in the ο Test Reeion (AleChire-Caitithsetal.2000a)., We have detected two small shells in the SGPS Test Region \citep{mcgriff00a}.
. The first of these appears as an vvokl at /= 32973. b=οι. e=108i. the terminal velocity for this line of sight.," The first of these appears as an void at $l=329\fdg3$ , $b=+0\fdg4$, $v=-108$, the terminal velocity for this line of sight."
 The velocity implics a kinematic distance of 7.3 kpc., The velocity implies a kinematic distance of $7.3$ kpc.
 Fig., Fig.
 9 is an echannel image ate=Los sshowing a small shell of angular ciameter is ~OFL., \ref{fig:term} is an channel image at $v=-108$ showing a small shell of angular diameter is $\sim 0\fdg4$.
 At a distance of 7.3 kpe the shell has a plysical diameter of HO pc., At a distance of $7.3$ kpc the shell has a physical diameter of $\sim 50$ pc.
 Because of its position at the terminal velocity it is very dithcult to distinguish the front and back caps. we detect only the frout cap.," Because of its position at the terminal velocity it is very difficult to distinguish the front and back caps, we detect only the front cap."
 It is not unusual to detect ouly one cap. though.," It is not unusual to detect only one cap, though."
 There is oulv oue detectable cap for a large majority of the shells catalogued by Ieies(1981)., There is only one detectable cap for a large majority of the shells catalogued by \citet{heiles84}.
. Detecting only one cap males it difficult to estimate an expansion velocity., Detecting only one cap makes it difficult to estimate an expansion velocity.
 It may be that the shell is stalled or that the structure is mostly cylindrical and expanding in the plane of the sky., It may be that the shell is stalled or that the structure is mostly cylindrical and expanding in the plane of the sky.
 Though we cannot measure the expansion velocity. we interpret this structure as a stalled wind or supernova blown shell.," Though we cannot measure the expansion velocity, we interpret this structure as a stalled wind or supernova blown shell."
 The secoud shell is observed in the local gas at e—2 ὃν 7=33075. and b=| 2212.," The second shell is observed in the local gas at $v=-2.1$ , $l=330\fdg5$, and $b=+2\fdg12$ ."
 This shell is shown in Fig. 10.. ," This shell is shown in Fig. \ref{fig:local}, ,"
a channel πμασο of the aaf ο=2.1|., a channel image of the at $v=-2.1$.
 The shell is remarkably circular with an aneular diameter of ~225., The shell is remarkably circular with an angular diameter of $\sim 2\fdg5$.
 Because of its low velocity its distance is very uncertain. we estimate D= pc.which tuplics a plysical radius of ouly15 pe.," Because of its low velocity its distance is very uncertain, we estimate $D=
350 - 500$ pc,which implies a physical radius of only$\sim 15$ pc."
 Given its stall size we speculatethat this shell nav have been formed by an old SNR., Given its small size we speculatethat this shell may have been formed by an old SNR.
 There areno associated features in the continu dnaaee., There areno associated features in the continuum image.
"where the M, are independent of w.",where the ${\bf M}_{n}$ are independent of $\omega$.
" With the appropriate substitutions, this can then be turned into a single eigenvalue equation Mss wT,, where if M is NxN elements, Mss is 5Nx5N, and T,=GA,O(wM,)!Xa,Θ(ωΜιη)”O(uM,2O(oM,)*3) is constructed from combinations of the M,, X, and w."," With the appropriate substitutions, this can then be turned into a single eigenvalue equation ${\bf M}_{\rm 5x5}\,\bar{T}_{a} = \omega\,\bar{T}_{a}$ , where if ${\bf M}$ is $NxN$ elements, ${\bf M}_{\rm 5x5}$ is $5Nx5N$ and $\bar{T}_{a} = 
(\bar{\Sigma}_{a},\,
\mathcal{O}(\omega\,{\bf M}_{n})^{1}\,\bar{\Sigma}_{a},\,
\mathcal{O}(\omega\,{\bf M}_{n})^{2}\,\bar{\Sigma}_{a},\,
\mathcal{O}(\omega\,{\bf M}_{n})^{3}\,\bar{\Sigma}_{a},\,
\mathcal{O}(\omega\,{\bf M}_{n})^{4}\,\bar{\Sigma}_{a})$ is constructed from combinations of the ${\bf M}_{n}$, $\bar{\Sigma}_{a}$ and $\omega$."
 It is then straightforward to solve for all eigenvalues and eigenvectors., It is then straightforward to solve for all eigenvalues and eigenvectors.
" Figure 1 illustrates the spectrum of eigenvalues of growing modes, in power-law disks, as a function of the softening (3), slope (7), and disk cutoff radius/mass (a)."," Figure \ref{fig:eigenvalues} illustrates the spectrum of eigenvalues of growing modes, in power-law disks, as a function of the softening $\beta$ ), slope $\eta$ ), and disk cutoff radius/mass $a$ )."
" For now, we simply show all eigenvalues of the above equations that fall in the plotted range, making no discrimination between local or global modes."," For now, we simply show all eigenvalues of the above equations that fall in the plotted range, making no discrimination between local or global modes."
" We focus on the growing modes, but see that in all cases there is a very large spectrum of stable modes; there are also decaying modes, but these correspond to the complex conjugate pairs of the growing modes shown."," We focus on the growing modes, but see that in all cases there is a very large spectrum of stable modes; there are also decaying modes, but these correspond to the complex conjugate pairs of the growing modes shown."
" The nearly continuous lines traced out by the eigenvalues correspond to solutions that cover some finite dynamic range well inside the cutoff a wwhere the disk is still scale-free), so that the solution can simply be shifted in r and w."," The nearly continuous lines traced out by the eigenvalues correspond to solutions that cover some finite dynamic range well inside the cutoff $a$ where the disk is still scale-free), so that the solution can simply be shifted in $r$ and $\omega$."
" Broadly speaking, the growing modes range in growth rates from ~0.01-1|Q,|, and the pattern speeds 2, for both stable and growing modes tend to fall in a similar range."," Broadly speaking, the growing modes range in growth rates from $\gamma\sim0.01-1\,|\Omega_{p}|$, and the pattern speeds $\Omega_{p}$ for both stable and growing modes tend to fall in a similar range."
 We will show how this relates to the characteristic scales of the modes below., We will show how this relates to the characteristic scales of the modes below.
" At fixed η and a (or Ma/Msau), increasing the softening 3 decreases the mode growth rates 7/Q,, and decreases the overall fraction of unstable modes, as expected."," At fixed $\eta$ and $a$ (or $M_{d}/M_{\rm BH}$ ), increasing the softening $\beta$ decreases the mode growth rates $\gamma/\Omega_{p}$, and decreases the overall fraction of unstable modes, as expected."
" However, growing modes exist even for large 9=0.25."," However, growing modes exist even for large $\beta\gtrsim0.25$."
" These are global modes, where there is a large contribution to the instability from the indirect potential, which is not treated inthe WKB limit."," These are global modes, where there is a large contribution to the instability from the indirect potential, which is not treated inthe WKB limit."
" Hence,our previous conclusions regarding sufficient 3 for stability should be regarded as only pertaining to local instabilities."," Hence,our previous conclusions regarding sufficient $\beta$ for stability should be regarded as only pertaining to local instabilities."
" ? found similar results,"," \citet{adams89:eccentric.instab.in.keplerian.disks} found similar results,"
"model predicts an asymptotic behaviour ~170-332? after the end of the fall back of the envelope, which covers the range of variability of our απο.","model predicts an asymptotic behaviour $\sim t^{-(1.3\div2.7)}$ after the end of the fall back of the envelope, which covers the range of variability of our $\alpha_{normal}$."
" However, this does not constrain the spectral index of the final decay to be related to the one of the previous accretion phase, as we found in Fig. 2.."," However, this does not constrain the spectral index of the final decay to be related to the one of the previous accretion phase, as we found in Fig. \ref{BETAtype}."
" On the contrary, since the late time decay should be produced by the same mechanism than the early steep decay, a similar spectral behaviour should be expected."," On the contrary, since the late time decay should be produced by the same mechanism than the early steep decay, a similar spectral behaviour should be expected."
" The comparison of the properties of the present sample with the X-ray light curves of GRBs showing flaring activity in Marguttietal.(2011) shows that flares occur more likely in Type II light curves (73% of the flare light curves are Type II, while only 23% of the light curves without flares, as first noticed in Marguttietal. 2010))."," The comparison of the properties of the present sample with the X-ray light curves of GRBs showing flaring activity in \citet{2011MNRAS.410.1064M} shows that flares occur more likely in Type II light curves $73\%$ of the flare light curves are Type II, while only $23\%$ of the light curves without flares, as first noticed in \citealt{giantflares10}) )."
 We argue that the presence of the steep decay is related to suitable conditions for the occurrence of early-time flares., We argue that the presence of the steep decay is related to suitable conditions for the occurrence of early-time flares.
 A connection between the flares and the steep decay has been found in Marguttietal.(2011):: the average luminosity of flares decays in time as the average slope of the steep decay., A connection between the flares and the steep decay has been found in \citet{2011MNRAS.410.1064M}: the average luminosity of flares decays in time as the average slope of the steep decay.
 In that work we also noted that light curves with multiple flares are associated with shallower decays., In that work we also noted that light curves with multiple flares are associated with shallower decays.
" A hint of a steeper distribution of the power-law index for the light curves without flares is found in Fig. 4.,"," A hint of a steeper distribution of the power-law index for the light curves without flares is found in Fig. \ref{alpha},"
 as if there is a transition from steep to shallow decays depending on the number of flares., as if there is a transition from steep to shallow decays depending on the number of flares.
" However, the moderate difference is not conclusive."," However, the moderate difference is not conclusive."
 The association of the steep decay with the flaring activity is an argument for a possible contribution of the central engine to the steep decay emission., The association of the steep decay with the flaring activity is an argument for a possible contribution of the central engine to the steep decay emission.
" In this case, the slope of the steep decay in the accretion model depends on the rotation rate of the progenitor core: the faster the rotation, the shallower the decay (seeFig.5inKumaretal.2008).."," In this case, the slope of the steep decay in the accretion model depends on the rotation rate of the progenitor core: the faster the rotation, the shallower the decay \citep[see Fig.~5 in][]{2008MNRAS.388.1729K}."
" A fast rotation of the infall material is needed to create the suitable conditions for instabilities, which are supposedly responsible for accretion models (Pernaetal.2006;Kumar2008).."," A fast rotation of the infall material is needed to create the suitable conditions for instabilities, which are supposedly responsible for accretion models \citep{2006ApJ...636L..29P,2008MNRAS.388.1729K}."
" A change in the rotation rate of the core produces a change in the peak jet power and of the duration over which the luminosity is high, as shown in Fig."," A change in the rotation rate of the core produces a change in the peak jet power and of the duration over which the luminosity is high, as shown in Fig."
 5 of Kumaretal.(2008).., 5 of \citet{2008MNRAS.388.1729K}.
" However, we do not observe any significant difference in the Lj, and E;;, distributions of the GRBs with and without flares."," However, we do not observe any significant difference in the $L_{pk}$ and $E_{iso}$ distributions of the GRBs with and without flares."
This second consistency test is based on the comparison of the parameter [o5] computed in two different wavs.,This second consistency test is based on the comparison of the parameter $[\sigma_{\rm BG}^2]$ computed in two different ways.
 We call [oj] to the variance produced by galaxies with magnitudes within a given interval: where m. is the magnitude corresponding to a Πας fy. and my to fy.," We call $[\sigma_{\rm BG}^2]$ to the variance produced by galaxies with magnitudes within a given interval: where $m_{A}$ is the magnitude corresponding to a flux $f_{A}$, and $m_{B}$ to $f_{B}$."
 Defined in this way. [onc] is the difference between the variances computed with two values of nj. namely Me=nma and my=mg: The nGn)-estimated and SBF-measured [oj] can be now compared.," Defined in this way, $[\sigma_{\rm BG}^2]$ is the difference between the variances computed with two values of $m_{\rm c}$ , namely $m_{\rm
 c}=m_{A}$ and $m_{\rm c}=m_{B}$: The $n(m)$ -estimated and SBF-measured $[\sigma_{\rm BG}^2]$ can be now compared."
 To do this. the nagnitude interval [27.8. 28.8] has been considered.," To do this, the magnitude interval [27.8, 28.8] has been considered."
 As the Williamsetal...(1996) photometric catalogue has been used to ereate (he window unctions. only objects found by them in the magnitude interval [27.8. 28.8] contribute to the SBF-neasurecl 9 |o5;].," As the \citet{W96} photometric catalogue has been used to create the window functions, only objects found by them in the magnitude interval [27.8, 28.8] contribute to the SBF-measured $[\sigma_{\rm BG}^2]$ ."
 In particular. some of the objects within⋅⋅ the interval⋅ [27.8.- 28.8] in (he Metealleetal...(2001) catalogue will remain masked. namely those which. following Metealleetal.(2001).. are merged in the Williamsetal.(1996) catalogue.," In particular, some of the objects within the interval [27.8, 28.8] in the \citet{Met01} catalogue will remain masked, namely those which, following \citet{Met01}, are merged in the \citet{W96} catalogue."
 This implies that the SBF-measured [55] is not expected to coincide with the n(n)-estimated. [oj] computed using the Metcalfeοἱal.(2001) data., This implies that the SBF-measured $[\sigma_{\rm BG}^2]$ is not expected to coincide with the $n(m)$ -estimated $[\sigma_{\rm BG}^2]$ computed using the \citet{Met01} data.
 On the other hand. the n(m)-estimated lo] computed using the Williamsetal.(1996) data should. for rigor. be similar to the SDF-measured |o] only if all the objects of the Williamsetal.(1996) catalogue in the interval [27.8. 28.8] are unmerged.," On the other hand, the $n(m)$ -estimated $[\sigma_{\rm BG}^2]$ computed using the \citet{W96} data should, for rigor, be similar to the SBF-measured $[\sigma_{\rm BG}^2]$ only if all the objects of the \citet{W96} catalogue in the interval [27.8, 28.8] are unmerged."
" However. if merged galaxies exist in other intervals (Metcalfeetal,2001).. there is no reason why they should not be present here also."," However, if merged galaxies exist in other intervals \citep{Met01}, there is no reason why they should not be present here also."
 The elfect of mergers on [oo] can be tested considering that a fraction of objects in the interval (27.8. 28.8] are the result of a merger between two fainter galaxies with integrated [lixes fy ancl ο.," The effect of mergers on $[\sigma_{\rm BG}^2]$ can be tested considering that a fraction of \citet{W96} objects in the interval [27.8, 28.8] are the result of a merger between two fainter galaxies with integrated fluxes $f_1$ and $f_2$."
 We have considered three simple situations: i) fy=for ti) fy= [ος and ii) fj=3/5., We have considered three simple situations: i) $f_1=f_2$; ii) $f_1=2f_2$ ; and iii) $f_1=3f_2$.
 It should be noted that since SBFs are a measure ol the second moment of the brightness function. the more similar fy and /> are. the larger is the effect introduced in [o5].," It should be noted that since SBFs are a measure of the second moment of the brightness function, the more similar $f_1$ and $f_2$ are, the larger is the effect introduced in $[\sigma_{\rm BG}^2]$."
 So case 1) is the most pessimistic and. although it is unrealistic. will give the maximum expected effect on [oj] for a given fraction of mergers.," So case i) is the most pessimistic and, although it is unrealistic, will give the maximum expected effect on $[\sigma_{\rm BG}^2]$ for a given fraction of mergers."
 In Figure4. we show the results of n(m)-estimated [o4] for the three cases and the FOOGWfiller. considering different values of thepercentage of merged objects.," In Figure\ref{mergers} we show the results of $n(m)$ -estimated $[\sigma_{\rm BG}^2]$ for the three cases and the F606Wfilter, considering different values of thepercentage of merged objects."
 It can be seen, It can be seen
In the above equations V=(0/0x.0.0/00) and sina.,"In the above equations $\nabla=(\da/\da x,0,\da/\da\theta)$ and $w=v_{\parallel}\cos\alpha-v_{\perp}\sin\alpha$ ."
" Equations (17))-(26)) will be used in the following sections to derive the governing equation for the resonant waves inside the dissipative layer and to find the nonlinear corrections,", Equations \ref{eq:masscontinuity1}) \ref{eq:solenoid1}) ) will be used in the following sections to derive the governing equation for the resonant waves inside the dissipative layer and to find the nonlinear corrections.
 In order to derive the governing equation for wave motions in the dissipative layer we employ the method of matched asymptotic expansions (22)..," In order to derive the governing equation for wave motions in the dissipative layer we employ the method of matched asymptotic expansions \citep{nayfeh1981, bender1999}."
 This method requires to find the so-called and expansions and then match them in the overlap regions., This method requires to find the so-called and expansions and then match them in the overlap regions.
 This nomenclature ts ideal for our situation., This nomenclature is ideal for our situation.
 The outer expansion corresponds to the solution outside the dissipative layer and the inner expansion corresponds to the solution inside the dissipative layer., The outer expansion corresponds to the solution outside the dissipative layer and the inner expansion corresponds to the solution inside the dissipative layer.
 A simplified version of the method of matched asymptotic expansions. developed by ?.. is adopted here.," A simplified version of the method of matched asymptotic expansions, developed by \citet{Ballai1998a}, is adopted here."
 The typical largest nonlinear term in the system of MHD equations is of the form gdg/dz while the typical dissipative term is of the form g/Oz. where g is any ‘large’ variable.," The typical largest nonlinear term in the system of MHD equations is of the form $g\da g/\da z$ while the typical dissipative term is of the form $\overline{\eta}\da^2 g/\da z^2$, where $g$ is any `large' variable."
 Linear theory predicts that ‘large’ variables have an ideal singularity 17' in the vicinity of x=0., Linear theory predicts that `large' variables have an ideal singularity $x^{-1}$ in the vicinity of $x=0$.
" This implies that the ""large"" variables have dimensionless amplitudes in the dissipative layer of the order of εδο."," This implies that the `large' variables have dimensionless amplitudes in the dissipative layer of the order of $\epsilon
R^{1/3}$."
" It is now straightforward to estimate the ratio of a typical quadratic nonlinear and dissipative term. where the quantity @, can be considered as theparameter."," It is now straightforward to estimate the ratio of a typical quadratic nonlinear and dissipative term, where the quantity $\phi_q$ can be considered as the."
 ΓΕ the condition eR?«| is satisfied. linear theory is applicable.," If the condition $\epsilon R^{2/3}\ll1$ is satisfied, linear theory is applicable."
 On the other hand. if eR?>| then nonlinearity has to be taken into account when studying resonant waves in dissipative layers.," On the other hand, if $\epsilon R^{2/3}\gtrsim 1$ then nonlinearity has to be taken into account when studying resonant waves in dissipative layers."
 Using the same scalings. ? showed that nonlinearity has to be considered whenever slow resonant waves are studied in the solar photosphere.," Using the same scalings, \citet{ruderman3} showed that nonlinearity has to be considered whenever slow resonant waves are studied in the solar photosphere."
 For a typical dimensionless amplitude of e~1077 linear theory can be applied if the total Reynolds number is less than 10°., For a typical dimensionless amplitude of $\epsilon\sim10^{-2}$ linear theory can be applied if the total Reynolds number is less than $10^3$.
 This value is much less than the resistive and shear viscosity Reynolds number (10!—10'7)., This value is much less than the resistive and shear viscosity Reynolds number $10^{10}-10^{12}$ ).
 This conclusion implies that in the solar atmosphere resonant absorption should be a nonlinear phenomenon., This conclusion implies that in the solar atmosphere resonant absorption should be a nonlinear phenomenon.
" In order to describe the role of dissipation and nonlinearity equally we assume that 4,~|.", In order to describe the role of dissipation and nonlinearity equally we assume that $\phi_q\sim1$.
 Far away from the dissipative layer the amplitudes of perturbations are small. so we use linear ideal MHD equations in order to deseribe the wave motion.," Far away from the dissipative layer the amplitudes of perturbations are small, so we use linear ideal MHD equations in order to describe the wave motion."
 The full set of nonlinear dissipative MHD equations are used for describing wave motion the dissipative layer where the amplitudes can be large., The full set of nonlinear dissipative MHD equations are used for describing wave motion the dissipative layer where the amplitudes can be large.
 We. therefore. look for solutions in the form of asymptotic expansions.," We, therefore, look for solutions in the form of asymptotic expansions."
 The equilibrium quantities change only slightly across the dissipative layer so it 1s possible to approximate them by the first non-vanishing term in their Taylor series expansion with respect to x., The equilibrium quantities change only slightly across the dissipative layer so it is possible to approximate them by the first non-vanishing term in their Taylor series expansion with respect to $x$.
 Similar to linear theory. we assume that the expansions of equilibrium quantities are valid in a region embracing the ideal resonant position. which is assumed to be much wider than the dissipative layer.," Similar to linear theory, we assume that the expansions of equilibrium quantities are valid in a region embracing the ideal resonant position, which is assumed to be much wider than the dissipative layer."
 This implies that there are two overlap regions. one to the left and one to the right of the dissipative layer. where both the outer (the solution to the linear ideal MHD equations) and inner (the solution to the nonlinear dissipative MHD equations) solutions are valid.," This implies that there are two overlap regions, one to the left and one to the right of the dissipative layer, where both the outer (the solution to the linear ideal MHD equations) and inner (the solution to the nonlinear dissipative MHD equations) solutions are valid."
 Hence. both solutions must coincide in the overlap regions which provides the matching conditions.," Hence, both solutions must coincide in the overlap regions which provides the matching conditions."
 Before deriving the nonlinear governing equation we ought to make a note., Before deriving the nonlinear governing equation we ought to make a note.
 In linear theory. perturbations of physical quantities are harmonie functions of 8 and their mean values over a period are zero.," In linear theory, perturbations of physical quantities are harmonic functions of $\theta$ and their mean values over a period are zero."
 In nonlinear theory. however. the perturbations of variables can have non-zero mean values às a result of nonlinear interaction of different harmonics.," In nonlinear theory, however, the perturbations of variables can have non-zero mean values as a result of nonlinear interaction of different harmonics."
 Due to the absorption of wave momentum. a mean shear flow is generated outside the dissipative layer (2)..," Due to the absorption of wave momentum, a mean shear flow is generated outside the dissipative layer \citep{ofman1995}."
 This result is true for our analysis also. however. due to the length of this stucv we prefer to deal with this problem in a forthcoming paper.," This result is true for our analysis also, however, due to the length of this study we prefer to deal with this problem in a forthcoming paper."
 We suppose that nonlinearity and dissipation are of the same order so we have eR?=O(1). ie. R~εἰ.," We suppose that nonlinearity and dissipation are of the same order so we have $\epsilon R^{2/3}=\mathscr{O}(1)$, i.e. $R\sim
\epsilon^{-3/2}$."
 We can. therefore. substitute € for R in Eq. (15))," We can, therefore, substitute $\epsilon^{-3/2}$ for $R$ in Eq. \ref{eq:reycoefscales}) )"
 to rescale viscosity and finite electrical resistivity às We do not rewrite the MHD equations as they are easily obtained from Eqs. (17))-(26)), to rescale viscosity and finite electrical resistivity as We do not rewrite the MHD equations as they are easily obtained from Eqs. \ref{eq:masscontinuity1}) \ref{eq:solenoid1}) )
 by substitution of Eq. (28))., by substitution of Eq. \ref{eq:rescalecoeffquadratic}) ).
The philosophy of microlensing monitoring has been based on (he premise (liat events are generated by lenses (hat are not known For mesolenses. though. (his is not always the case.,"The philosophy of microlensing monitoring has been based on the premise that events are generated by lenses that are not known For mesolenses, though, this is not always the case."
 For example. when the lens producing a short-duration event happens to be a planet in orbit with a nearby star. there is a good chance that the star has already been detected. especially when the region has been monitored over an interval of vears.," For example, when the lens producing a short-duration event happens to be a planet in orbit with a nearby star, there is a good chance that the star has already been detected, especially when the region has been monitored over an interval of years."
we encourage the use of this diagnostic tool in (he search for exoplanets via (ransils to reduce the large nmmbers of candidates that require resource-consumineg Iollow-up observations.,we encourage the use of this diagnostic tool in the search for exoplanets via transits to reduce the large numbers of candidates that require resource-consuming follow-up observations.
Figure 9 shows the distribution of Ni Gvhich decays iuto Fe) aud 19O at the homologous expansion pliase or the models with Αννα=10M... (ve. out inodel LOD. because it produces very little amount of DANI,"Figure \ref{f9} shows the distribution of $^{56}$ Ni (which decays into $^{56}$ Fe) and $^{16}$ O at the homologous expansion phase for the models with $M_{\rm ZAMS} = 40\msun$ (we omit model 40D, because it produces very little amount of $^{56}$ Ni)."
 Along the jet axis. matter experiences a strong shock. hus beime reprocessed throueh complete silicon burning.," Along the jet axis, matter experiences a strong shock, thus being reprocessed through complete silicon burning."
 It produces a large amount of PPNi, It produces a large amount of $^{56}$ Ni.
 Ou the other laud. uatter coutinucs to accrete from the side.," On the other hand, matter continues to accrete from the side."
 When the nass accretion rate becomes low enough. matter gets outward momentum laree enough to compete with inflow.," When the mass accretion rate becomes low enough, matter gets outward momentum large enough to compete with inflow."
 The peak temperatures of those materials are. however. oo low to cause significant nuclear reactions.," The peak temperatures of those materials are, however, too low to cause significant nuclear reactions."
 Thus their isotopic patterus reflect those of initial composition before he eravitational collapse., Thus their isotopic patterns reflect those of initial composition before the gravitational collapse.
 The result is characterized. by he high velocity 9Nixich matter alone the jet. aud ow velocity Ον matter near the ceuter.," The result is characterized by the high velocity $^{56}$ Ni-rich matter along the jet, and low velocity $^{16}$ O-rich matter near the center."
 Maeda et al. (, Maeda et al. (
2002) aud Mazzali et al. (,2002) and Mazzali et al. (
2001) discussed that such configuration could uaturally explain- nebular spectra of SN L998bw.,2001) discussed that such configuration could naturally explain nebular spectra of SN 1998bw.
 The comparison among the models in Figure 9 reveals row the overall asplericity is affected by the property of the jets., The comparison among the models in Figure \ref{f9} reveals how the overall asphericity is affected by the property of the jets.
 A lareer opening anele (jet) leads to a ess aspherical explosion as expected (LOA vs. LOB)., A larger opening angle $\theta{\rm jet}$ ) leads to a less aspherical explosion as expected (40A vs. 40B).
 Larger eficiency (0) leads to a amore energetie aud a less aspherical explosion (LOA vs. LOD)., Larger efficiency $\alpha$ ) leads to a more energetic and a less aspherical explosion (40A vs. 40D).
 The reason for the atter is as follows: a stronger shock (larger o) deposits a arecr amount of enerev in the surrounding material at the working surface and causes a stronger lateral expansion., The reason for the latter is as follows: a stronger shock (larger $\alpha$ ) deposits a larger amount of energy in the surrounding material at the working surface and causes a stronger lateral expansion.
 These are also obvious in Figure 6.. which shows that uodels LOB and LOC) keep the accretion rate smaller han LOA. indicating the stronger lateral expansion.," These are also obvious in Figure \ref{f6}, which shows that models 40B and 40C keep the accretion rate smaller than 40A, indicating the stronger lateral expansion."
 In addition. final kinetic cuereies listed in Table 1 support lis explanation.," In addition, final kinetic energies listed in Table 1 support this explanation."
 The final eucreies of models LOB and 10C are simaller than £3410.9«(toa/0.01). which is expected if the accretion rate is the same as in iiodel. LOA. This result is cousisteut with MacEadyen et al. (," The final energies of models 40B and 40C are smaller than $E_{51} = 10.9 \times (\alpha/0.01)$, which is expected if the accretion rate is the same as in model 40A. This result is consistent with MacFadyen et al. ("
2001). who exanüned the interaction between bipolar jets and euvelopes of failed superuovae by the similar forializii we adopt in this paper.,"2001), who examined the interaction between bipolar jets and envelopes of failed supernovae by the similar formalism we adopt in this paper."
 We note that in model LOA. the jet material really daills the hole along its wav up to the stellar surface.," We note that in model 40A, the jet material really drills the hole along its way up to the stellar surface."
 Iu this section. we discuss further details of the ueucleosvuthetie feature. ic. the isotopic composition of the bipolar explosions.," In this section, we discuss further details of the neucleosynthetic feature, i.e., the isotopic composition of the bipolar explosions."
 The isotopic abundance patterns of model LOA along the z-axis aud the r-asis. as well as that averaged over all directions are shown in Figure 10..," The isotopic abundance patterns of model 40A along the $z$ -axis and the $r$ -axis, as well as that averaged over all directions are shown in Figure \ref{f10}."
 The abundance pattern of the spherical model LOSI is also shown., The abundance pattern of the spherical model 40SH is also shown.
" Iu explosive nucleosvuthesis in a supernova explosion. the isotopic ratios depend on the peak temperature attained at the passing of the shock wave as follows ίσιο, Thiclemmanun. Nomoto. Hashimoto."," In explosive nucleosynthesis in a supernova explosion, the isotopic ratios depend on the peak temperature attained at the passing of the shock wave as follows (e.g., Thielemann, Nomoto, Hashimoto."
 1996): Iu spherical models. higher temperature is attained in inner regions. because the temperature after the passing of the shock wave decreases as the shock wave moves outward (TRCCE? where Ris the radius of the position of the shock wave: sce equations (3) aud (£13).," 1996): In spherical models, higher temperature is attained in inner regions, because the temperature after the passing of the shock wave decreases as the shock wave moves outward $T \propto R^{-3/4} E^{1/4}$ where $R$ is the radius of the position of the shock wave; see equations (3) and (4))."
" Thus. spherical models predict in general the following pattern in order of increasing radi: strong a-vich freezcout (0.8... ο Ti (Ca). Cu (Co). 51 Ge (Zu)). coniplete silicon burning (e.g. PONG (Fe)). iucomplete silicon burning (e... I9 Co (Nu). oxveen burning (e.g. 778i, 78, °° Ay), and no significant burning (ee. Te. ο, 190). ("," Thus, spherical models predict in general the following pattern in order of increasing radii: strong $\alpha$ -rich freezeout (e.g., $^{44}$ Ti (Ca), $^{59}$ Cu (Co), $^{64}$ Ge (Zn)), complete silicon burning (e.g., $^{56}$ Ni (Fe)), incomplete silicon burning (e.g., $^{40}$ Ca, $^{55}$ Co (Mn)), oxygen burning (e.g., $^{28}$ Si, $^{32}$ S, $^{36}$ Ar), and no significant burning (e.g., $^{4}$ He, $^{12}$ C, $^{16}$ O). ("
Tho stable isotopes after decavs are indicated iu pareuthesis.),The stable isotopes after $\beta$ -decays are indicated in parenthesis.)
 This feature in spherical models is evident iu Figure 10d., This feature in spherical models is evident in Figure 10d.
 We are interested iu the isotopic vields iu the whole ejecta. as these are responsible for the Cadactic chemica evolution.," We are interested in the isotopic yields in the whole ejecta, as these are responsible for the Galactic chemical evolution."
 In couveutional spherical models. the vields depend ou the “ass cut’. which divides the stellar materia into those Παν ejected and accreted onto a centra roiunant.," In conventional spherical models, the yields depend on the 'mass cut', which divides the stellar material into those finally ejected and accreted onto a central remnant."
 We show how the resultant yields depend ou Mew (the mass contained below the mass cut) in spherica models. to clarity the deference between spherical models and the bipolar models in the later part.," We show how the resultant yields depend on $M_{\rm cut}$ (the mass contained below the mass cut) in spherical models, to clarify the deference between spherical models and the bipolar models in the later part."
 Figure ll shows the isotopic patterns of spherical wmode 10SII for different mass cuts., Figure \ref{f11} shows the isotopic patterns of spherical model 40SH for different mass cuts.
 The isotopic distribution iu the ejecta of model 10SIT shown in Figure 10d explains the behavior., The isotopic distribution in the ejecta of model 40SH shown in Figure 10d explains the behavior.
 For lavee Mas. AC Ni) is ial aud the isotopes produced iu the deepest regions such as 9!Zu (produced as 061663 and 7? Co (produced as CW) are not ejected (Figure 11a).," For large $M_{\rm cut}$, $M$ $^{56}$ Ni) is small and the isotopes produced in the deepest regions such as $^{64}$ Zn (produced as $^{64}$ Ge) and $^{59}$ Co (produced as $^{59}$ Cu) are not ejected (Figure 11a)."
 For πια] Ma. on the coutrary a aree amount of !Zu aud 7? Co are ejected (Figure 11b).," For small $M_{\rm cut}$, on the contrary, a large amount of $^{64}$ Zn and $^{59}$ Co are ejected (Figure 11b)."
 The isotopes with mass nunibers 4dX140 are produces uanulv in the lavers well above the mass cut. so that their abuudances do not depeud on the mass cut.," The isotopes with mass numbers $A \lsim 40$ are produced mainly in the layers well above the mass cut, so that their abundances do not depend on the mass cut."
 For these elements (CA<< LO). therefore. the abundances normalizes wiron. es [NX/Fo|2log(X/Fe)logN/Fo)... are simaller or lavger AL (Ni)," For these elements $A \lsim 40$ ), therefore, the abundances normalized by iron, i.e., $\rm{[X/Fe]} = \log (X/Fe) - \log (X/Fe)_{\odot}$, are smaller for larger $M$ $^{56}$ Ni)."
 The spherical models thus. predict hat the ejecta with smaller Mo has larger |(Zu. Co)/Fe and smaller [((O. Me. Mu)Το] (the latter because of larger AC Ni). unless the musing and fallback process takes dace (Uineda Nomoto 2002).," The spherical models thus predict that the ejecta with smaller $M_{\rm cut}$ has larger [(Zn, Co)/Fe] and smaller [(O, Mg, Mn)/Fe] (the latter because of larger $M$ $^{56}$ Ni)), unless the mixing and fallback process takes place (Umeda Nomoto 2002)."
" Such a correlation is not he case for the bipolar models because of the following ΤΟΞΟ,", Such a correlation is not the case for the bipolar models because of the following reason.
 Figure 12 shows the peak temperatures of individual lnass particles against the deusitics at the passing of the, Figure \ref{f12} shows the peak temperatures of individual mass particles against the densities at the passing of the
for galactic scales (several hundred kpe at ze3) coincides roughly with the for the Lyman αἱ absorption line. as shown in fie. 1..,"for galactic scales (several hundred kpc at $\sim 3$ ) coincides roughly with the for the Lyman $\alpha$ absorption line, as shown in fig. \ref{cog}."
 The hydro-inulatious picture a Lyo forest caused by a cohereut network of flaments. sheets. aud knots of eas. in which more spherical. higher density condensations. galaxies or nini-halos. are cmbedded.," The hydro-simulations picture a $\alpha$ forest caused by a coherent network of filaments, sheets, and knots of gas, in which more spherical, higher density condensations, galaxies or mini-halos, are embedded."
 The fractionof baryous iu Lyman a clouds in CDAL based models is indeed very high [|7].. with (even by zg ~ 2) of order of all barvous in low cobuun deusity clouds. dominated by the range (11 < logN « 15.5) |6]..[1]..," The fractionof baryons in Lyman $\alpha$ clouds in CDM based models is indeed very high \cite{pet}, with (even by z $\sim$ 2) of order of all baryons in low column density clouds, dominated by the range (14 $<$ $\log N$ $<$ 15.5) \cite{me}, \cite{hern}. ."
 The spatial arrangement of this barvouic reservoir is illustrated by fig. 2.., The spatial arrangement of this baryonic reservoir is illustrated by fig. \ref{densdist}.
 Colm deusitv contours at a level as Ligh. as ↽104 cu?9 are stretching⋅ coutiuuouslv⋅ over may hundreds of. kes.f," Column density contours at a level as high as $10^{14}$ $^{-2}$ are stretching continuously over many hundreds of kpcs.,"
ilaments. without having collapsed iuto Lyman limit svstenis. virialized galaxies or damped Lyo systems vet.," without having collapsed into Lyman limit systems, virialized galaxies or damped $\alpha$ systems yet."
 The lvdvodvuaiiic simulations are illustrative aud have furthered the iuterpretatiou of QSO absorption spectra immensely. but they cau also be used for quantitative mmcastrelents. e... by comparing laree sets of simulated QSO spectra with observed ones.," The hydrodynamic simulations are illustrative and have furthered the interpretation of QSO absorption spectra immensely, but they can also be used for quantitative measurements, e.g., by comparing large sets of simulated QSO spectra with observed ones."
 The problemi is as usual to find observables which cau be measured at a reasonable precision. do not depend seusitivelv ou the shortcomings of the modelling aud at the same time correspond iu a unique way to the ineredicuts of the simulated model.," The problem is as usual to find observables which can be measured at a reasonable precision, do not depend sensitively on the shortcomings of the modelling and at the same time correspond in a unique way to the ingredients of the simulated model."
 One of the most easily measurable quantities is the distribution of pixel intensities £ — ο (or alternatively. flux decrements D=1 FJ. or optical depths 7). ie. the amount of lieht per unit velocity absorbedbv ἵνα of," One of the most easily measurable quantities is the distribution of pixel intensities $I$ = $ e^{-\tau}$ (or alternatively, flux decrements $D = 1 - I$ , or optical depths $\tau$ ), i.e. the amount of light per unit velocity absorbedby $\alpha$ of"
"uncover large numbers of these sources, which can then be used to constrain timescales related to AGN activity and study the interaction between radio plasma and the ICM in clusters and galaxy groups.","uncover large numbers of these sources, which can then be used to constrain timescales related to AGN activity and study the interaction between radio plasma and the ICM in clusters and galaxy groups."
"We have artificially, aud somewhat arbitrarily. iucreased the opacity from the vicinity of ooutward.","We have artificially, and somewhat arbitrarily, increased the opacity from the vicinity of outward."
" We have uot found an appreciable differcutial effect withει, and have therefore not pursued this aveuue with more detailed modelling."," We have not found an appreciable differential effect with, and have therefore not pursued this avenue with more detailed modelling."
" Finally,-- the insensitivity of the slope to fg males us believe. that the linearization of the raciatiou hwdrodyuanües equatious instead of the common equilibrimu diffusion equation (vequiring a serious coding effort) would also make little cüffereuce."," Finally, the insensitivity of the slope to $f_E$ makes us believe that the linearization of the radiation hydrodynamics equations instead of the common equilibrium diffusion equation (requiring a serious coding effort) would also make little difference."
 We conclude that the discrepancy between the models and the observations is not due to an inadequate treatineut of the radiation transport., We conclude that the discrepancy between the models and the observations is not due to an inadequate treatment of the radiation transport.
 Could compositional make-wp be more portant than expected?, Could compositional make-up be more important than expected?
 We have computed a nunuber of RR Lyrac models with various combinations of Y aud Z. but fiud that the effect on E is negligible.," We have computed a number of RR Lyrae models with various combinations of Y and Z, but find that the effect on $\Xi$ is negligible."
 Next we lave artificially increased the abundances of the easily ionizable light elements such as Me aud Na in the OPAL opacities., Next we have artificially increased the abundances of the easily ionizable light elements such as Mg and Na in the OPAL opacities.
 Again this las such a neglieible effect on E that the inclusion of this data would unnecessarily clutter Figure 2., Again this has such a negligible effect on $\Xi$ that the inclusion of this data would unnecessarily clutter Figure 2.
 An inhomogcucous composition is uulikelv to exist iu RR Larac euvelopes because of couvection. but even if existed our tests with various changes ii composition make us doubt that it would resolve the discrepancy.," An inhomogeneous composition is unlikely to exist in RR Lyrae envelopes because of convection, but even if existed our tests with various changes in composition make us doubt that it would resolve the discrepancy."
 Could rotation be responsible for the discrepancy?, Could rotation be responsible for the discrepancy?
 Iu order to estimate the magnitude of the effect of rotation we have included a spherical pseudo-ceutrifugal acceleration we? rin the equilibrimu model iud iu the computation of the periods aud erowth rates., In order to estimate the magnitude of the effect of rotation we have included a spherical pseudo-centrifugal acceleration $\omega^2\th r$ in the equilibrium model and in the computation of the periods and growth rates.
 We fiud that a rather short rotation period. of order of a few davs. would be necessary," We find that a rather short rotation period, of order of a few days, would be necessary"
In this paper we have shown that the standard prescriptions for svuthesizing the NRB from the integrated chussion of ACNs are uot consistent with a umuber of recent observational constraints. and some of then must be relaxed.,"In this paper we have shown that the standard prescriptions for synthesizing the XRB from the integrated emission of AGNs are not consistent with a number of recent observational constraints, and some of them must be relaxed."
" We have worked out inodels (AL and A2) which take into account detailed input spectra of Ανα, the NW istribution observed iu local Seyfert 2s. aud the XLF and evolution newly determined frou the larges ROSAT sample."," We have worked out models (A1 and A2) which take into account detailed input spectra of AGNs, the $N_{\rm H}$ distribution observed in local Seyfert 2s, and the XLF and evolution newly determined from the largest ROSAT sample."
 The latter ata do not define a unique parametrization. anc the wo iuodels explore cüffereu variants.," The latter data do not define a unique parametrization, and the two models explore different variants."
 As prescribed by he standard model. the NLF and evolution of tvpe 2 ACGNs are taken from type H5. and the spectra of both types are taken indepeuden of redshift: the only fitting parameter is the nuuber ratio R of type 2s to type 1s.," As prescribed by the standard model, the XLF and evolution of type 2 AGNs are taken from type 1s, and the spectra of both types are taken independent of redshift; the only fitting parameter is the number ratio $R$ of type 2s to type 1s."
 We find that model Ad reproduces the NRBD aud the soft counts with a ratio A> compatible with the local value. but underestimates the uud counts," We find that model A1 reproduces the XRB and the soft counts with a ratio $R$ compatible with the local value, but underestimates the hard counts."
 Model À2 is less discrepant as far as the counts are concerned. but requires a ratio AR cefiuitely arecr than observed locally.," Model A2 is less discrepant as far as the counts are concerned, but requires a ratio $R$ definitely larger than observed locally."
 We have also computed a nodel adopting a canonical pure huninosity evolution (imiodel B)., We have also computed a model adopting a canonical pure luminosity evolution (model B).
 In agreement with the results of Co95. model D cau reproduce the NRB. the soft Nrav counts aud he ASCA hard couuts in the 210 keV baud.," In agreement with the results of Co95, model B can reproduce the XRB, the soft X–ray counts and the ASCA hard counts in the 2–10 keV band."
 It is also consistent within 26 (or discrepant at 20) with the xeliniuuw BeppoSAN counts in the 510 keV baud., It is also consistent within $\sigma$ (or discrepant at $\sigma$ ) with the preliminary BeppoSAX counts in the 5–10 keV band.
 Nevertheless. it requires a inuuber of type 2 QSOs much ueher than the local upper luüt. aud perhaps already ruled out by the deep X.rav surveys.," Nevertheless, it requires a number of type 2 QSOs much higher than the local upper limit, and perhaps already ruled out by the deep X–ray surveys."
 The discrepancies found in all models are to ποιο extent uodel depeudent. bu all of them out iu the sane direction. aud sugees that hard spectrum. sources at mterinediate or high redshifts are needec iu addition o the xedietious of the standard scenario.," The discrepancies found in all models are to some extent model dependent, but all of them point in the same direction, and suggest that hard spectrum sources at intermediate or high redshifts are needed in addition to the predictions of the standard scenario."
 The Xrav Spectitu of these additiona sources could be flattened by absorption. or could be intrinsically hard.," The X–ray spectrum of these additional sources could be flattened by absorption, or could be intrinsically hard."
 In the former ivpothesis reasonable candiate counterparts could be rapidly evolving. “normal” Seyfert 2s.," In the former hypothesis reasonable candidate counterparts could be rapidly evolving, “normal” Seyfert 2s."
 One should also rote that a fraction of ULIRGs secur to be powered Nw ACNS and their cosmological evolution sccius faster han that of unabsorbed QSOs.," One should also note that a fraction of ULIRGs seem to be powered by AGNs, and their cosmological evolution seems faster than that of unabsorbed QSOs."
 The alternate lypothesis could imstead require the xeseuce of ADAFs., The alternate hypothesis could instead require the presence of ADAFs.
 Optical identifications of the hard X.ray sources are still largely incomplete aud do not allow vet to decide between the various possibilities., Optical identifications of the hard X–ray sources are still largely incomplete and do not allow yet to decide between the various possibilities.
 We have computed a canonical svuthesis model of the ARD bv adopting the NLF and PLE of Jones ct al. (, We have computed a canonical synthesis model of the XRB by adopting the XLF and PLE of Jones et al. (
1997): since only ACNs with broad optical lines are PENcluded. there is uo need to correct for the contribution M type 2 ACNs.,"1997); since only AGNs with broad optical lines are included, there is no need to correct for the contribution of type 2 AGNs."
" This sample is smaller than \G99a. aud prestunably low ""numositv sources at high redshifts are uderrreppresseuted."," This sample is smaller than Mi99a, and presumably low luminosity sources at high redshifts are sented."
 Our model B. assuines the ΝΤΕ aud PLE indicated above. iucludes QSO 2s as nuuerous as the Sev 2x. and adopts the absorption distribution of Risaliti et al. (," Our model B assumes the XLF and PLE indicated above, includes QSO 2s as numerous as the Sey 2s, and adopts the absorption distribution of Risaliti et al. ("
1999) at all redshifts aud all Iuninosities.,1999) at all redshifts and all luminosities.
 Iu the cosmology adopted here. model D makes only ~30% of the soft ΑΠΌ with type 1 ACNs. aud one needs Ry=7.7 to fit the overall background (Fig.," In the cosmology adopted here, model B makes only $\sim 30\%$ of the soft XRB with type 1 AGNs, and one needs $R_{\rm S}=R_{\rm Q}=7.7$ to fit the overall background (Fig."
 Al)., A1).
 Due to the large coutribution of tvpe 2 ACNs. the model NRB spectrum is very lard.," Due to the large contribution of type 2 AGNs, the model XRB spectrum is very hard."
" Furthermore. due to the high ""effective"" huninosity nuplied by QSO 2s, the ASC'A counts are reproduced."," Furthermore, due to the high “effective” luminosity implied by QSO 2s, the ASCA counts are reproduced."
 The discrepancy with the data in the 510 keV banc. ou the coutrary. is not eliminated. although it is reduced to a 2a level.," The discrepancy with the data in the 5–10 keV band, on the contrary, is not eliminated, although it is reduced to a $2\sigma$ level."
 Because of the preliminary nature of the TELLAS data oue might debate about its significance., Because of the preliminary nature of the HELLAS data one might debate about its significance.
 At any rate. one should stress that this mareinal result can be obtained only bx assundue a strong (a factor > 1) differcutial evolution of QSO 2s with respect to QSO Is. so that at τε the former would outummber the latter by a factor —8.," At any rate, one should stress that this marginal result can be obtained only by assuming a strong (a factor $>$ 4) differential evolution of QSO 2s with respect to QSO 1s, so that at $z_{cut}$ the former would outnumber the latter by a factor $\sim$ 8."
This annihilation luminosity depends on some simple considerations.,This annihilation luminosity depends on some simple considerations.
" We assume that PBHs have not evaporated yet, which is valid for Mppy210:15Mo; and that most of the dark matter is made of WIMPs and not PBHs, otherwise there would be too few WIMPs to form a UCMH."," We assume that PBHs have not evaporated yet, which is valid for $M_{\rm PBH} \ga 10^{-18}\ \Msun$; and that most of the dark matter is made of WIMPs and not PBHs, otherwise there would be too few WIMPs to form a UCMH."
 We require that the density profile along a WIMP’s orbit not evolve significantly., We require that the density profile along a WIMP's orbit not evolve significantly.
" Most importantly, we require that dark matter accretion after ze, does not increase the mass within Reg."," Most importantly, we require that dark matter accretion after $z_{\rm eq}$ does not increase the mass within $R_{\rm eq}$."
" Such accretion would initially increase the UCMH luminosity, but would also shorten the time WIMPs survive in the UCMH."," Such accretion would initially increase the UCMH luminosity, but would also shorten the time WIMPs survive in the UCMH."
 We also assume that annihilation of WIMPs with small apocenters does not affect our calculations., We also assume that annihilation of WIMPs with small apocenters does not affect our calculations.
" As a limiting case, if WIMPs annihilate into a constant density core with p= then Las,© this weakens our p(Req),bounds by a factor 0.42Lo(Mppu/Mo)mo;of ~60, but still implies Oppy«0.1 for mpc?S10TeV."," As a limiting case, if WIMPs annihilate into a constant density core with $\rho = \rho(R_{\rm eq})$, then $L_{\rm ann} \approx 0.42 \Lsun (M_{\rm PBH} / \Msun) m_{100}^{-1}$; this weakens our bounds by a factor of $\sim 60$, but still implies $\Omega_{\rm PBH} \ll 0.1$ for $m_{\rm DM} c^2 \la 10\ \TeV$."
" Furthermore, since the PBH dominates the mass within Reg, adiabatic contraction should be unimportant."," Furthermore, since the PBH dominates the mass within $R_{\rm eq}$, adiabatic contraction should be unimportant."
" Perhaps the most important other effects we do not consider are those of accreted baryonic material, which may cool radiatively and collapse efficiently."," Perhaps the most important other effects we do not consider are those of accreted baryonic material, which may cool radiatively and collapse efficiently."
 Adiabatic contraction will not be important if the PBH dominates the mass within Reg., Adiabatic contraction will not be important if the PBH dominates the mass within $R_{\rm eq}$.
" However, baryonic matter can be optically thick to gamma rays, reducing the apparent UCMH luminosity."," However, baryonic matter can be optically thick to gamma rays, reducing the apparent UCMH luminosity."
 We estimate the optical depth as 7neorReg., We estimate the optical depth as $\tau \approx n_e \sigma_T R_{\rm eq}$.
" If the mass of baryons within Reg is fpMpm~fpMppu, then τ2”0.5f(Mppnu/Mo)'/ 5."," If the mass of baryons within $R_{\rm eq}$ is $f_b M_{\rm DM} \approx f_b M_{\rm PBH}$, then $\tau \approx 0.5 f_b (M_{\rm PBH} / \Msun)^{1/3}$ ."
 Klein-Nishina effects will reduce this optical depth., Klein-Nishina effects will reduce this optical depth.
" Thus for smaller PBHs (M<10 Mo), we can ignore baryonic opacity."," Thus for smaller PBHs $M \la 10\ \Msun$ ), we can ignore baryonic opacity."
 Neutrino limits are unaffected by opacity., Neutrino limits are unaffected by opacity.
 Annihilation of dark matter can produce gamma rays with significant power near mpc”., Annihilation of dark matter can produce gamma rays with significant power near $m_{\rm DM} c^2$.
 Gamma rays below ~100GeV contribute directly to the extragalactic background., Gamma rays below $\sim 100\ \GeV$ contribute directly to the extragalactic background.
" Gamma rays with energy Z100GeV for zZ1 cascade down in energy by pair production and Inverse Compton processes with ambient photons, contributing to the background at lower energies."," Gamma rays with energy $\ga 100\ \GeV$ for $z \ga 1$ cascade down in energy by pair production and Inverse Compton processes with ambient photons, contributing to the background at lower energies."
 The gamma-ray emissivity of the Universe at energies above 100 MeV is limited by EGRET observations to Qmax=8x107?ergs!cm? (Coppi&Aharonian1997)., The gamma-ray emissivity of the Universe at energies above 100 MeV is limited by EGRET observations to $Q_{\rm max} = 8 \times 10^{-35}\ \ergscm3$ \citep{Coppi97}.
". The number density of PBHs is then limited to be npgyC /(LannBr(y)), where Br(y) is the branching fraction into gamma rays."," The number density of PBHs is then limited to be $n_{\rm PBH} \la Q_{\rm max} / (L_{\rm ann} \Br(\gamma))$ , where $\Br (\gamma)$ is the branching fraction into gamma rays."
" If dark matter annihilates into charged particles, there must be internal bremsstrahlung, with branching ratio Br(y)©az0.01, which we take as a minimum branching fraction."," If dark matter annihilates into charged particles, there must be internal bremsstrahlung, with branching ratio $\Br (\gamma) \approx \alpha \approx 0.01$, which we take as a minimum branching fraction."
" This number density is converted into a limit on Ώρμη the mass of the PBH and dividing by the bycritical multiplyingdensity, byo.=9.20Azox10?gcm, so that ΏρμηSOmaxMpau/(PcLannBr(y)): The upper limits on Qppy are essentially independent of PBH mass: the number of PBHs for a given Qpgy scales as Mp, but the luminosity of each scales as Mpgg."," This number density is converted into a limit on $\Omega_{\rm PBH}$ by multiplying by the mass of the PBH and dividing by the critical density, $\rho_c = 9.20\ h_{70} \times 10^{-30}\ \gram\ \cm^{-3}$, so that $\Omega_{\rm PBH} \la Q_{\rm max} M_{\rm PBH} / (\rho_c L_{\rm ann} \Br (\gamma))$: The upper limits on $\Omega_{\rm PBH}$ are essentially independent of PBH mass: the number of PBHs for a given $\Omega_{\rm PBH}$ scales as $M_{\rm PBH}^{-1}$, but the luminosity of each scales as $M_{\rm PBH}$."
 Stronger constraints can be obtained by taking advantage of the higher-than-average number density of PBHs in the Milky Way., Stronger constraints can be obtained by taking advantage of the higher-than-average number density of PBHs in the Milky Way.
" PBHs in the Milky Way are close enough that annihilation gamma rays are not attenuated; such gamma do not have to compete with the entire raysbackground above 100 MeV, but only with that neargamma-ray mMpMC.."," PBHs in the Milky Way are close enough that annihilation gamma rays are not attenuated; such gamma rays do not have to compete with the entire gamma-ray background above 100 MeV, but only with that near $m_{\rm DM} c^2$."
" Suppose the density of PBHs, npgy(s), tracks the dark matter density."," Suppose the density of PBHs, $n_{\rm PBH} (\vec{s})$, tracks the dark matter density."
" Then the integrated gamma-ray intensity on a line of sight out of the Milky Way is 1=Lana(ΠΡΒΗ)Br(7) where 5 is the dark matter overdensity3 over the [9()ds,average cosmic dark matter density and (nppu) is the average PBH density in the Universe."," Then the integrated gamma-ray intensity on a line of sight out of the Milky Way is $I = \frac{1}{4\pi} L_{\rm ann} \mean{n_{\rm PBH}} \Br (\gamma) \int \delta (\vec{s}) ds$ , where $\delta$ is the dark matter overdensity over the average cosmic dark matter density and $\mean{n_{\rm PBH}}$ is the average PBH density in the Universe."
" Then the abundance of PBHs is limited by To find the background [ους the UCMH radiation competes with, we use the Fermi--measured extragalactic background spectrum (Abdoetal.2010) for E«x100GeV."," Then the abundance of PBHs is limited by To find the background $I_{\rm obs}$ the UCMH radiation competes with, we use the -measured extragalactic background spectrum \citep{Abdo10} for $E \le 100\ \GeV$."
" For annihilation into gamma rays or internal bremsstrahlung from charged particles, most of the power is within one log bin in energy of ων. (Bell&Jacques2009)."," For annihilation into gamma rays or internal bremsstrahlung from charged particles, most of the power is within one log bin in energy of $m_{\rm DM} c^2$ \citep{Bell09}."
". We therefore find Io», by integrating the gamma-ray background as such.", We therefore find $I_{\rm obs}$ by integrating the gamma-ray background as such.
" We use an NFW for the distribution of UCMHs in the Milky Way, densityó(r)profile=6,(r/rs)'(.+r/rs), with ὃν&45000 and r,=27kpc (Stoehretal.2003)."," We use an NFW density profile for the distribution of UCMHs in the Milky Way, $\delta(r) = \delta_s (r/r_s)^{-1} (1 + r/r_s)^{-2}$, with $\delta_s \approx 45000$ and $r_s = 27\ \kpc$ \citep{Stoehr03}."
. The line of sight integral is not sensitive to the distribution of UCMHs in the inner Galaxy., The line of sight integral is not sensitive to the distribution of UCMHs in the inner Galaxy.
" The integral is more like that for dark matter decay than diffuse annihilation, since the intensity is proportional to npgy(7)."," The integral is more like that for dark matter decay than diffuse annihilation, since the intensity is proportional to $n_{\rm PBH} (r)$."
" We consider a sightline aimed directly away from the Galactic Center, where the uncertainty in the profile should have the least effect and the signal is smallest, for a conservative result."," We consider a sightline aimed directly away from the Galactic Center, where the uncertainty in the profile should have the least effect and the signal is smallest, for a conservative result."
 The dependence of Qpgy with WIMP mass is shown in Figure 1 for various final states., The dependence of $\Omega_{\rm PBH}$ with WIMP mass is shown in Figure \ref{fig:BoundsWithMass} for various final states.
 The Galactic gamma-ray bounds in Figure | (solid)) include the cosmic background bounds above 100 GeV. The annihilation luminosity falls as the WIMP mass increases (Eq. 8))., The Galactic gamma-ray bounds in Figure \ref{fig:BoundsWithMass} ) include the cosmic background bounds above 100 GeV. The annihilation luminosity falls as the WIMP mass increases (Eq. \ref{eqn:LannPBH}) ).
 Since the competing, Since the competing
"we chose for the cooling funcüon vielded an accretion rate-weighted mean specific enthalpy that was well-described by /~1+0.0310/.4/)""5,",we chose for the cooling function yielded an accretion rate-weighted mean specific enthalpy that was well-described by $h \simeq 1 + 0.031 (r/M)^{-0.8}$.
" At large radius. where the Newtonian approximation applies. the ratio of /—1 to the net binding οποιον is c0.06(7/2)""?. while al the ISCO this ratio is ον0.1."," At large radius, where the Newtonian approximation applies, the ratio of $h-1$ to the net binding energy is $\simeq 0.06 (r/M)^{0.2}$, while at the ISCO this ratio is $\simeq 0.1$."
 Thus. this tov-mocdel does assure (hat the majority of the dissipated heat is racdiatec.," Thus, this toy-model does assure that the majority of the dissipated heat is radiated."
 If the accretion flow were in a strict steady-state. the local (i.e. shell-integrated) mass accretion rate M(r) would be the same at a] radii al all times and the mass interior to a given radius would likewise be constant.," If the accretion flow were in a strict steady-state, the local (i.e., shell-integrated) mass accretion rate $\dot M(r)$ would be the same at all radii at all times and the mass interior to a given radius would likewise be constant."
 I1 these turbulent disks fed bv a finite mass reservoir. (he most we can hope [ον is that 1je. (ime-average local accretion rate is nearly constant as a function of r through most of the accreting region. and the mass of the inner disk. after an initial period of growth. eventualv levels off and fluctuates within some range.," In these turbulent disks fed by a finite mass reservoir, the most we can hope for is that the time-average local accretion rate is nearly constant as a function of $r$ through most of the accreting region, and the mass of the inner disk, after an initial period of growth, eventually levels off and fluctuates within some range."
 The degree to which we approach (hese goals is shown in Figures 4 and 5.., The degree to which we approach these goals is shown in Figures \ref{fig:inflowequil} and \ref{fig:massfillin}.
 In the left-hand panel of Figure 4.. we see that the accretion rate (measured al (he event horizon) varies by roughly a [actor of [ive in an extremely irregular wav.," In the left-hand panel of Figure \ref{fig:inflowequil}, we see that the accretion rate (measured at the event horizon) varies by roughly a factor of five in an extremely irregular way."
 Nonetheess. as shown in the panel. (he time-averaged M(7) is very nearly constant [rom the horizon to r2LLAS for the latter 8000. of the simulation.," Nonetheless, as shown in the right-hand panel, the time-averaged $\dot M(r)$ is very nearly constant from the horizon to $r\simeq 14M$ for the latter $8000M$ of the simulation."
 The reason why we choose tje interval 7000. 150001 for averaging is shown in Figure 5.., The reason why we choose the interval $7000M$ $15000M$ for averaging is shown in Figure \ref{fig:massfillin}.
 As this figure demonstrates. it takes roughly the first TOOOAL of the simulation Lor the nass of the inner clisk to reaci à rough plateau.," As this figure demonstrates, it takes roughly the first $7000M$ of the simulation for the mass of the inner disk to reach a rough plateau."
 Because {he mass interior {ο a given radius fIuctuates. we chose the starting point for time-averaged «quantities to be the point at which essentially all the inner disk had reached at least 90% of ils final mass. which is approximately /=τουίLM.," Because the mass interior to a given radius fluctuates, we chose the starting point for time-averaged quantities to be the point at which essentially all the inner disk had reached at least $90\%$ of its final mass, which is approximately $t = 7000M$."
" llowever. lor the purposes of esiimaliig (he radiative efficiency, we require a tighter definition of inflow equilibrium."," However, for the purposes of estimating the radiative efficiency, we require a tighter definition of inflow equilibrium."
 This is bec:wise we wish to contrast the computed radiation rate with the NT rate a( an accuracy of a ew percent or better., This is because we wish to contrast the computed radiation rate with the NT rate at an accuracy of a few percent or better.
 In the NT model. 23% of the total light is emitted between 1247 and 25A/. where our simulation shows significant departures from intlow equilibrium: a further. 27% comes from outside 25. where our simulation is not an accretion [low and we do not compute the luminosity at all.," In the NT model, $23\%$ of the total light is emitted between $12M$ and $25M$, where our simulation shows significant departures from inflow equilibrium; a further $27\%$ comes from outside $25M$, where our simulation is not an accretion flow and we do not compute the luminosity at all."
 For these reasons. When we contrast the NT luminosity with Chat produced in the simulation. we adjust the local accretion rates to mimic inflow equilibrium and attach a carefully-chosen representation of large-radius emission where needed (see below [ον details).," For these reasons, when we contrast the NT luminosity with that produced in the simulation, we adjust the local accretion rates to mimic inflow equilibrium and attach a carefully-chosen representation of large-radius emission where needed (see below for details)."
for spectrally resolved lines (?)..,for spectrally resolved lines \citep{landi_deglinnocenti_polarization_2004}.
" We shall in this work use the full theory, but in the following paragraphs and in the sake of illustration, we will voluntarily simplify our description of the Hanle effect and limit it to just those two modifications of the polarization generated at every single scattering event."," We shall in this work use the full theory, but in the following paragraphs and in the sake of illustration, we will voluntarily simplify our description of the Hanle effect and limit it to just those two modifications of the polarization generated at every single scattering event."
" Even further, rather than going into a detailed description of those two modifications we shall first take the opposite direction and make use of a widely known geometric property of the Hanle effect: a magnetic field perfectly aligned with the direction of illumination produces no effect on the resonance scattering polarization."," Even further, rather than going into a detailed description of those two modifications we shall first take the opposite direction and make use of a widely known geometric property of the Hanle effect: a magnetic field perfectly aligned with the direction of illumination produces no effect on the resonance scattering polarization."
" Such simplifications capture still the essence of the Hanle effect in the case under study without burdening it with unnecesary details, unneeded at this point and incorporated nevertheless in the computations below."," Such simplifications capture still the essence of the Hanle effect in the case under study without burdening it with unnecesary details, unneeded at this point and incorporated nevertheless in the computations below."
 It is time now to set the example that will explain our proposed diagnostic., It is time now to set the example that will explain our proposed diagnostic.
" Let us suppose a spherical star rotating around an axis in the plane of the sky, that is with the equator seen edge-on."," Let us suppose a spherical star rotating around an axis in the plane of the sky, that is with the equator seen edge-on."
 The density and temperature of the star are spherically symmetric and it presents limb darkening., The density and temperature of the star are spherically symmetric and it presents limb darkening.
 We shall be interested in relatively weak photospheric lines for which the last scattering approximation applies ? Let us suppose a global dipolar field with strength Bo at the stellar surface.," We shall be interested in relatively weak photospheric lines for which the last scattering approximation applies \cite{stenflo_hanle_1982}
 Let us suppose a global dipolar field with strength $B_0$ at the stellar surface."
 We will further suppose in our first example that the dipole is perfectly aligned with the rotation axis., We will further suppose in our first example that the dipole is perfectly aligned with the rotation axis.
 For rays from most of the equator line the dipole field will primarily induce a depolarization of the background resonance scattering polarization., For rays from most of the equator line the dipole field will primarily induce a depolarization of the background resonance scattering polarization.
 At the poles however the dipolar field will be strictly aligned with the vertical direction of illumination and will result in no modification of the resonance scattering polarization., At the poles however the dipolar field will be strictly aligned with the vertical direction of illumination and will result in no modification of the resonance scattering polarization.
 The three inset images of Fig., The three inset images of Fig.
 1 show the polarization degree at every point in the resolved disk and illustrate the loss of symmetry described at two different dipole field strengths., 1 show the polarization degree at every point in the resolved disk and illustrate the loss of symmetry described at two different dipole field strengths.
 It can be seen that the polarization amplitude in the poles is no longer compensated by the diminished polarization at the equator and the integral around the limb will not be zero., It can be seen that the polarization amplitude in the poles is no longer compensated by the diminished polarization at the equator and the integral around the limb will not be zero.
" Explained in such simple terms, a dipole field results in measurable linear polarization from the star."," Explained in such simple terms, a dipole field results in measurable linear polarization from the star."
" To estimate the expected polarization degree from this effect we will use a spectral line arising from an atomic system with angular momenta J,=1 and J;=0 for the upper and lower levels respectively.", To estimate the expected polarization degree from this effect we will use a spectral line arising from an atomic system with angular momenta $J_u=1$ and $J_l=0$ for the upper and lower levels respectively.
 This simplification allows us to use in our computations the analytic results of ? for this atomic system!., This simplification allows us to use in our computations the analytic results of \cite{casini_hanle_2002} for this atomic system.
". All lines that can be acceptably simulated by such an atomic system are characterized by a critical Hanle field B., defined as the field at which the Zeeman splitting of the sublevels equals the natural width of the level (cr being the Larmor frecuency of a 1G field, A the Einstein coefficient of the level in MHz and g, the Landé factor of the upper level)."," All lines that can be acceptably simulated by such an atomic system are characterized by a critical Hanle field $B_c$, defined as the field at which the Zeeman splitting of the sublevels equals the natural width of the level $\omega_L$ being the Larmor frecuency of a 1G field, $A$ the Einstein coefficient of the level in MHz and $g_u$ the Landé factor of the upper level)."
" With the dipole field strength put in terms of this critical Hanle field, the Hanle behavior of all such spectral lines is identical."," With the dipole field strength put in terms of this critical Hanle field, the Hanle behavior of all such spectral lines is identical."
 Fig., Fig.
 1 shows the linear polarization of such lines in the presence of a dipole field integrated over the observable stellar disk., 1 shows the linear polarization of such lines in the presence of a dipole field integrated over the observable stellar disk.
 At zero field we are in the conditions of resonance scattering polarization that for symmetry reasons cancels out over the disk., At zero field we are in the conditions of resonance scattering polarization that for symmetry reasons cancels out over the disk.
" As the magnetic field increases, depolarization at the equator happens but not at the poles, as described."," As the magnetic field increases, depolarization at the equator happens but not at the poles, as described."
 Cancellation is not complete and a linear net polarization appears over the star., Cancellation is not complete and a linear net polarization appears over the star.
 The effect grows for increasing field strengths and then saturates beyond the Hanle critical field., The effect grows for increasing field strengths and then saturates beyond the Hanle critical field.
 The reason is that Hanle effect can only take place whilst the Zeeman sublevels are not separated in energy more than their natural width., The reason is that Hanle effect can only take place whilst the Zeeman sublevels are not separated in energy more than their natural width.
 When the sublevels reach this critical field the quantum interference between the sublevels drops and the magnetic field can not further modify them., When the sublevels reach this critical field the quantum interference between the sublevels drops and the magnetic field can not further modify them.
" For reference, Fig."," For reference, Fig."
" 2 shows the value in G of the Hanle critical field for about 500 Hanle-sensitive lines in the visible and near-IR spectral region (0.4 through 2.5 microns), extending previous compilations ?.."," \ref{Bc} shows the value in G of the Hanle critical field for about 500 Hanle-sensitive lines in the visible and near-IR spectral region (0.4 through 2.5 microns), extending previous compilations \cite{ignace_hanle_2001}."
 The computed polarization in Fig., The computed polarization in Fig.
 1 is given in terms of the zero-field polarization amplitude Qo of the line., 1 is given in terms of the zero-field polarization amplitude $Q_0$ of the line.
 Unfortunately the actual value of Qo is unknown for most (if not all) spectral lines., Unfortunately the actual value of $Q_0$ is unknown for most (if not all) spectral lines.
 The reason for this is that it strongly depends on the actual anisotropy of the radiation field that illuminates the scattering atom., The reason for this is that it strongly depends on the actual anisotropy of the radiation field that illuminates the scattering atom.
" This anisotropy may depend on the formation height of the line in each stellar atmosphere, on the limb darkening conditions and on the pattern of intensities in the photosphere below the line."," This anisotropy may depend on the formation height of the line in each stellar atmosphere, on the limb darkening conditions and on the pattern of intensities in the photosphere below the line."
 For example granulation in solar- stars is known to influence this anisotropy and modifies the zero-field polarization Qo in these atmospheres (?).., For example granulation in solar-like stars is known to influence this anisotropy and modifies the zero-field polarization $Q_0$ in these atmospheres \citep{trujillo_bueno_scattering_2007}. .
No such are-shaped nebula ds. seen around3219.,No such arc-shaped nebula is seen around.
 Our relatively low detection sensitivity could explain part of the observed differences., Our relatively low detection sensitivity could explain part of the observed differences.
 However. in the known bow shock nebulae Daliner emission usually shows the highest surface brightuess ahead of motion.," However, in the known bow shock nebulae Balmer emission usually shows the highest surface brightness ahead of motion."
 At the apex the nebula extends perpendicular to the trajectory thus tracing the shape of the frout-shocked reeion., At the apex the nebula extends perpendicular to the trajectory thus tracing the shape of the front-shocked region.
 Iu the present case. the ceimission appears clongated in the direction of motion.," In the present case, the emission appears elongated in the direction of motion."
 Such a seeometry cannot be matched by any isotropic wind model since one would uaively expect a larecr extent in the direction perpendicular to the motion than iu the direction of motion., Such a geometry cannot be matched by any isotropic wind model since one would naively expect a larger extent in the direction perpendicular to the motion than in the direction of motion.
 Iu the absence of detailed modeling. it is unclear whether pulsar wind beaming could account for the observed eecomoetrv.," In the absence of detailed modeling, it is unclear whether pulsar wind beaming could account for the observed geometry."
 If no strong wind blows from cemission could still arise from au X-ray ionized nebula., If no strong wind blows from emission could still arise from an X-ray ionized nebula.
 Blaes et al. (1995)), Blaes et al. \cite{blaes1995}) )
 have shown that ionization of the local interstellar medimu by the N-ray aud UV radiation field of the hot neutron star combined with proper motion would produce cometary ΠΙ resious., have shown that ionization of the local interstellar medium by the X-ray and UV radiation field of the hot neutron star combined with proper motion would produce cometary HII regions.
 Their properties depend on the details of the ionizatio- reconibinatiou. heatingC» and coolingC» rates (seo van Kerkwijk-M Ίνα-. :2001b.. for. a detailed. modeling: including dvuamical effects).," Their properties depend on the details of the ionization, recombination, heating and cooling rates (see van Kerkwijk Kulkarni \cite{vk2001b}, for a detailed modeling including dynamical effects)."
 The isotropic ionizing field should create a spherical lead nebula ceutered on the neutron star with an extent oein the direction perpendicular to motion at least as large as in the direction of motion. shuilar to the case of bow shock ucbulac.," The isotropic ionizing field should create a spherical head nebula centered on the neutron star with an extent in the direction perpendicular to motion at least as large as in the direction of motion, similar to the case of bow shock nebulae."
 Also. because of the rather loug cooling time. most of the cemission will occur in the wake of the neutron star. again at variance with the observation.," Also, because of the rather long cooling time, most of the emission will occur in the wake of the neutron star, again at variance with the observation."
 Scaling the observed surface briehtuess to that of (wan Kerkwijlk I&ulleuni 2001)) would imply local densities of the order of ug~ 9 bean  quueh[um larger than expected for normal ISM densities.," Scaling the observed surface brightness to that of (van Kerkwijk Kulkarni \cite{vk2001b}) ) would imply local densities of the order of $n_{\rm H} \ \sim$ 9 $^{-1}$ $^{-3}$, much larger than expected for normal ISM densities."
" Such hig[um deusities would however viekl a cooling time of z,,, ~ yr roughly comparable to the nebula crossing fine Των LYVE as estimated from its angular size (~ 6001228 ahead) and observed proper otio-", Such high densities would however yield a cooling time of $\tau_{cool}$ $\sim$ yr roughly comparable to the nebula crossing time $\tau_{cross}$ $\sim$ yr as estimated from its angular size $\sim$ mas ahead) and observed proper motion.
 The geometry of the nebula is in principle consistent with that expected from a bipolar jet., The geometry of the nebula is in principle consistent with that expected from a bipolar jet.
 Such jets have been observed in X-rays from very voung neutron stars. the best documented cases being those of the Crab (Weisskopf.— et al. 2000))," Such jets have been observed in X-rays from very young neutron stars, the best documented cases being those of the Crab (Weisskopf et al. \cite{weisskopf2000}) )"
" and of the Vela pulsar (Helfand et al, 2001)).", and of the Vela pulsar (Helfand et al. \cite{helfand2001}) ).
 Their power-law X-rav spectra are iuterprete Las due to optically thin svuchrotron cussion from ultza-relativistic particles., Their power-law X-ray spectra are interpreted as due to optically thin synchrotron emission from ultra-relativistic particles.
 Obviously. some other mechanism invoked to explain: Ha comission: redshift∙⋅ < —⋠↴≻↽↽∖⋅ 28 0.03 (the maxima allowed by the filter band pass) frou such a jet.," Obviously, some other mechanism must be invoked to explain emission at redshift $\leq$ 0.03 (the maximum allowed by the filter band pass) from such a jet."
 One possibility could be the interaction of the beamed particle fow with the interstellar medimm., One possibility could be the interaction of the beamed particle flow with the interstellar medium.
 lf the main direction of the nnebula would indeed traceLea the vexspin axis.axe wwould«uw be Lsauothe∖⋅ case of appareut aligunieut of spin axis aud proper motion direction (Lai et al. 20013).," If the main direction of the nebula would indeed trace the spin axis, would be another case of apparent alignment of spin axis and proper motion direction (Lai et al. \cite{lai2001}) )."
 Alternatively. if the main axis of the nebula would exactly follow the trajectory. as would be the case for au N-ravO ionized or bow shocked nebula unperturbed by the interstellar uveditiu. the apparent proper motion direction should not be exactly aligned with the nebula as a result of solu motion.," Alternatively, if the main axis of the nebula would exactly follow the trajectory, as would be the case for an X-ray ionized or bow shocked nebula unperturbed by the interstellar medium, the apparent proper motion direction should not be exactly aligned with the nebula as a result of solar motion."
 In principle. this effect could be used to derive mdepeudenut estimates of the distance of the neutron star.," In principle, this effect could be used to derive independent estimates of the distance of the neutron star."
 However. the accuracy with which we cau deteriune the anele difference 0 = LOE iis nof vet large chough to be useful.," However, the accuracy with which we can determine the angle difference $\theta$ = $\pm$ is not yet large enough to be useful."
 Nevertheless. the sigu of the anele difference between the nebula aud the appareut proper motion is that expected due to the different positions of the Sun between 1999 aud 2003.," Nevertheless, the sign of the angle difference between the nebula and the apparent proper motion is that expected due to the different positions of the Sun between 1999 and 2003."
 Using the Sun velocity parameters determined by Tipparcos (Dehuen Binney 1998)) we compute an anele difference 0 = +., Using the Sun velocity parameters determined by Hipparcos (Dehnen Binney \cite{db98}) ) we compute an angle difference $\theta$ = $^{-1}$.
 Considering the absence of calibration of the iustruimeutal ssettiug. it is clear that the astonishing gcoietry of the nebula needs to be confirmed aud specified by other observations before exteusive couchisious on its lature can bedraw.," Considering the absence of calibration of the instrumental setting, it is clear that the astonishing geometry of the nebula needs to be confirmed and specified by other observations before extensive conclusions on its nature can be drawn."
 Orr deep Subaru iiagiug reveals the high proper motion of aaud thus confirms the optical identification. proposed by EKaplau et al. (2003a))., Our deep Subaru imaging reveals the high proper motion of and thus confirms the optical identification proposed by Kaplan et al. \cite{kaplan03a}) ).
 The correspoudiug large space motion most probably excludes accretion. from the interstellar inedimn as the source of the radiated XN-rav eucrgy., The corresponding large space motion most probably excludes accretion from the interstellar medium as the source of the radiated X-ray energy.
 Similarly to aand JOT20.63125.. 1 likely a cooling neutron star with an age younger than ~ 10° vr.," Similarly to and , is likely a cooling neutron star with an age younger than $\sim$ $^{6}$ yr."
 Evidence for residual magnetospheric activity comes frou the relatively red BR iudex which iudicates the presence of an excess of red light above the expected Ravieigh-Jeans tail. a picture comparable to that seen in Cemunga or in PSR D0656|11.," Evidence for residual magnetospheric activity comes from the relatively red $-$ R index which indicates the presence of an excess of red light above the expected Rayleigh-Jeans tail, a picture comparable to that seen in Geminga or in PSR B0656+14."
 A sinall size unebula 1s detected approximately centered ou the neutron star aud extended aloug the direction of the trajectory., A small size nebula is detected approximately centered on the neutron star and extended along the direction of the trajectory.
 The lack of photometric calibration auc fla-ficlding does not wake it possible to draw stringent conclusions on its nature., The lack of photometric calibration and flat-fielding does not make it possible to draw stringent conclusions on its nature.
 However. the ualb size and geometry of the nebula are mmique and no standard bow-shock or X-ray jonisation model can account. for these peculiarities 1n a straightforwardmanner.," However, the small size and geometry of the nebula are unique and no standard bow-shock or X-ray ionisation model can account for these peculiarities in a straightforward manner."
 Forthcomingdeeper observations should allow us to confirm the unusual features detected in 1999., Forthcoming deeper observations should allow us to confirm the unusual features detected in 1999.
 Finally. we find that nuuay have been born iu the same nearby Sco OB2 OB association J1856.5-3751m perhapsale RXκ JU720.," Finally, we find that may have been born in the same nearby Sco OB2 OB association as and also perhaps."
1-3125.πε This could nuplv that the bright part of the observed LogN-LogS curve for S-ray dima isolated neutron starsis by the dominated of productionthis single OB association., This could imply that the bright part of the observed LogN-LogS curve for X-ray dim isolated neutron starsis dominated by the production of this single OB association.
densities aud velocity dispersions for those (wo groups.,densities and velocity dispersions for those two groups.
 We thank Oded Aharonson aud Andrew MeFadven for useful discussions., We thank Oded Aharonson and Andrew McFadyen for useful discussions.
 MP is supported by an NSF graduate research fellowship., MP is supported by an NSF graduate research fellowship.
(load atxd resolution (sce vanderlis1989:Pressetal.1992:Vaughan 2003).,"domain and resolution (see \citealt{1989tns..conf...27V,1992nrca.book.....P,2003MNRAS.345.1271V}) )."
 Given the frequencies of interest and the total duration of the simulation. we can afford to tase only No=| independeut time series. which inereases he significance of the averaged PSD by a factor of two over the unaveraged case.," Given the frequencies of interest and the total duration of the simulation, we can afford to take only $N=4$ independent time series, which increases the significance of the averaged PSD by a factor of two over the unaveraged case."
 Figure 3 shows he PSDs of the azimuthal magnetic field over the same regions depictec in Figure 2., Figure 3 shows the $\overline{\rm PSD}$ s of the azimuthal magnetic field over the same regions depicted in Figure 2.
 As iu Figure 2. we SCC cas (now broadeied. but at higher significance) tha sit oapproxiuatelv ten to tweuty times below the local orbital period.," As in Figure 2, we see peaks (now broadened, but at higher significance) that sit approximately ten to twenty times below the local orbital period."
 While the peaks are sufficiently broad tha hev overlap for different radii. the frequency resolution of the PSD is iisufücieut to determine how sieuifican lis overlap is.," While the peaks are sufficiently broad that they overlap for different radii, the frequency resolution of the $\overline{\rm PSD}$ is insufficient to determine how significant this overlap is."
" Figure lL shows the PSD of the azimuthal maguetic ficld as a ""uctiou of both frequency and radius. so tha we are hxtter able to evaluate the racial depeudenuce of the pxwer profile."," Figure 4 shows the PSD of the azimuthal magnetic field as a function of both frequency and radius, so that we are better able to evaluate the radial dependence of the power profile."
 As in Figure 2. the PSD has )COLL COLLmuted over the cutive time series;," As in Figure 2, the PSD has been computed over the entire time series."
 The vertical σαος 1du Figure | illustrate that power is shared a istic‘t+ frequencies across large racial intervals. with singe peaks often stretching across radial ranges of 10 ory or more.," The vertical features in Figure 4 illustrate that power is shared at distinct frequencies across large radial intervals, with single peaks often stretching across radial ranges of 10 $r_{\rm g}$ or more."
 Taken iu agerceate. however. the power disbution reflects the radial run of the orbital frequency.," Taken in aggregate, however, the power distribution reflects the radial run of the orbital frequency."
 Specifically. the power is bounded by ~v16 on fie high-frequency cud and ~voy/30 on the low.," Specifically, the power is bounded by $\sim \nu_{\rm orb}/6$ on the high-frequency end and $\sim \nu_{\rm orb}/30$ on the low."
 So even frough a given power peak may racially spau multiple orbital fequeucies. the range of peak frequencies ronuadns ao»proxinatelv proportional to the local orbital frequency.," So even though a given power peak may radially span multiple orbital frequencies, the range of peak frequencies remains approximately proportional to the local orbital frequency."
" This pattern only stands out clearly from the noise for A?z10 το, ", This pattern only stands out clearly from the noise for $R \gtorder 10$ $_{\rm g}$.
Toward of this region. the broadbaud Lolse assocliatec with accretion across the ISCO masks any ουνlous Trexc.," Inward of this region, the broadband noise associated with accretion across the ISCO masks any obvious trend."
 To further eueidate the nature of this variability. Figure 5 presents analyses of the azimuthal feld at R=20ry after various cuts and segregations have been imposed.," To further elucidate the nature of this variability, Figure 5 presents analyses of the azimuthal field at $R=20~{\rm r_g}$ after various cuts and segregations have been imposed."
 Tn the left panel of Figure 5. we show the PSDs for this region when it is divided iito two independent tiue series (TL represcuts the first half of he simulation. T2 the secoud). each of whic Lois approximately 5<101 GAL/c? in duration.," In the left panel of Figure 5, we show the PSDs for this region when it is divided into two independent time series (T1 represents the first half of the simulation, T2 the second), each of which is approximately $5 \times 10^4$ $^3$ in duration."
 Note hat the oeaks are not coustant in frequency. sugecstingOO that the nntiple peaks in Figures 2-1 are at least partly caused »* yequencics nüeratine in time.," Note that the peaks are not constant in frequency, suggesting that the multiple peaks in Figures 2-4 are at least partly caused by frequencies migrating in time."
 It is tempting to cain lia the peaks move from higher to lower frequencies over ine. but it is challenging in practice to follow individual ICA swithout a auch longer time baseline.," It is tempting to claim that the peaks move from higher to lower frequencies over time, but it is challenging in practice to follow individual peaks without a much longer time baseline."
 The middle xuel of Figure 5 shows the PSD for the tll time series. now comparing the regious above aud rclow t1e midplane.," The middle panel of Figure 5 shows the PSD for the full time series, now comparing the regions above and below the midplane."
" These peaks. too. fail to perfectly align even thoteh the disk starts from an approximatcly sviuuctvic staο,"," These peaks, too, fail to perfectly align even though the disk starts from an approximately symmetric state."
 This is perhaps not surprising eiven hat feaures iu the disk turbulence are also secu to evolve asviunnetrcally about the midplane., This is perhaps not surprising given that features in the disk turbulence are also seen to evolve asymmetrically about the midplane.
 That said. this top-ottonuü asviuuctry sugeests that the exact frequency of a siicle field oscillation may be less useful as a diagnosic tool than the rauge of frequencies observed.," That said, this top-bottom asymmetry suggests that the exact frequency of a single field oscillation may be less useful as a diagnostic tool than the range of frequencies observed."
 The rightinost panel of Figure 5 conrpares the PSDs, The rightmost panel of Figure 5 compares the PSDs
hence the [or r given S will be For the Schechter form of the luninosity function. let us define a characteristic distance ry. which is a distance to a galaxy with a given flix 5 and a characteristic luminosity Ly: Then for the SchechterLE. ((A3)) simplifies to with F(a) being the Gamma. function.,"hence the for $r$ given $S$ will be For the Schechter form of the luminosity function, let us define a characteristic distance $r_S$, which is a distance to a galaxy with a given flux $S$ and a characteristic luminosity $L_*$: Then for the SchechterLF, \ref{eq:r_mean}) ) simplifies to with $\Gamma(a)$ being the Gamma function."
 Similarly. (he lor r given S. denoted here as ry. will be obtained [rom the implicit equation with respect to Fy. where 5(a..0) and ία.ο) are respectively (he lower ancl upper incomplete Gamma. functions.," Similarly, the for $r$ given $S$, denoted here as $\bar{r}_S$, will be obtained from the implicit equation which for the Schechter LF is equivalent to solving with respect to $\bar{r}_S$, where $\gamma(a,x)$ and $\Gamma(a,x)$ are respectively the lower and upper incomplete Gamma functions."
" In the particular case of the ἐν band. taking a=—1.16 (?).. we obtain and Note that especially the median conditional distance gives a value very. close to the characteristic distance rs. which could be the ""first-guess. effective cdistauce (Tully 2008. private communication)."," In the particular case of the $K$ band, taking $\alpha=-1.16$ \citep{6dF_Fi}, we obtain and Note that especially the median conditional distance gives a value very close to the characteristic distance $r_S$ , which could be the `first-guess' effective distance (Tully 2008, private communication)."
"in which the breaking of the €O bond and the production of Cll; + OIL is again the rate-limiting step. in (his case via (he reaction Note that the of the two reactions (15ee) or (19dd) will serve as the rate-limiting step because this represents Che fastest overall pathway available in our model for the CO — CL, conversion process.","in which the breaking of the C–O bond and the production of $_{3}$ + OH is again the rate-limiting step, in this case via the reaction Note that the of the two reactions \ref{comech}e e) or \ref{cobypass}d d) will serve as the rate-limiting step because this represents the fastest overall pathway available in our model for the CO $\rightarrow$ $_{4}$ conversion process."
 ILowever. although the thermal decomposition of methanol (reaction 15ee) remains the dominant rate-limiting reaction over the range of A... values (10*—10? cnp +t) shown in Figure 2.. the contribution from reaction 19dd) is significant enough (i.e.. it is [ast enough) that it must be considered when estimating the quench CO abundance via a timescale approach.," However, although the thermal decomposition of methanol (reaction \ref{comech}e e) remains the dominant rate-limiting reaction over the range of $K_{zz}$ values $10^{3}-10^{9}$ $^{2}$ $^{-1}$ ) shown in Figure \ref{figure:monoxide}, the contribution from reaction \ref{cobypass}d d) is significant enough (i.e., it is fast enough) that it must be considered when estimating the quench CO abundance via a timescale approach."
 Using the kinetic schemes identilied above. we revisit the (ime-scale approach (hat was previously developed (e.g..Prim&Barshayv1977;ΓοσίονPrinn1985.1983:FeeleyLodcders1996:Lodders&Feglev2002) o estimate the quenched abundance of CO in the atmosphere of cool giant planets aud brown dwarls.," Using the kinetic schemes identified above, we revisit the time-scale approach that was previously developed \citep[e.g.,][]{prinn1977,fegley1985apj,fegley1988,fegley1996,lodders2002} to estimate the quenched abundance of CO in the atmosphere of cool giant planets and brown dwarfs."
 Considering reactions (15ee) ancl (104) as a combined rate-limiting step for CO destruction. (he chemical lifetime of CO is eiven by This expression is useful for considering the dominant contribution from either pathway breaking the CO bond and forming Cll; + OIL," Considering reactions \ref{comech}e e) and \ref{cobypass}d d) as a combined rate-limiting step for CO destruction, the chemical lifetime of CO is given by This expression is useful for considering the dominant contribution from either pathway breaking the C–O bond and forming $_{3}$ + OH."
" For example. if reaction (15ee) is much faster (han reaction (19dd). Tepe,(CO) will be mostly determined by the rate of the methanol decomposition reaction."," For example, if reaction \ref{comech}e e) is much faster than reaction \ref{cobypass}d d), $\tau_{chem}(\textrm{CO})$ will be mostly determined by the rate of the methanol decomposition reaction."
" The reaction rate coefficients A45. and A49; are calculated al each temperature in (he model from their respective “forward” rate coefficients for CIT4OLIEN and I+CIISOII—Cl,+OIL from Jasperetal. (2007).. using equation (12)) in the reversal procedure described above."," The reaction rate coefficients $k_{\ref{comech}e}$ and $k_{\ref{cobypass}d}$ are calculated at each temperature in the model from their respective “forward” rate coefficients for $\textrm{CH}_{3}\textrm{OH} \xrightarrow{\textrm{M}} \textrm{CH}_{3} + \textrm{OH}$ and $\textrm{H} + \textrm{CH}_{2}\textrm{OH} \rightarrow \textrm{CH}_{3} + \textrm{OH}$ from \citet{jasper2007}, , using equation \ref{eq:reversal}) ) in the reversal procedure described above."
" The parameters used lor calculating the forwarcl rate coelficients are given below in our discussion of Cll, quench chemistry on ID 189723b.", The parameters used for calculating the forward rate coefficients are given below in our discussion of $_{4}$ quench chemistry on HD 189733b.
 The vertical mixing time scale is given by where A.. is the ecldy diffusion coefficient ancl £ isthe characteristic lengthi scale over which the mixing operates., The vertical mixing time scale is given by where $K_{zz}$ is the eddy diffusion coefficient and $L$ isthe characteristic length scale over which the mixing operates.
 Although the atmospheric pressure scale height {1 has commonly, Although the atmospheric pressure scale height $H$ has commonly
"where we have taken £j=E,/£.",where we have taken $F_p=E_p/\xi$.
 Eq. (10)), Eq. \ref{vcrit}) )
 was found in the numerical simulations of the dynamics of an isolated vortex in a random potential (2).., was found in the numerical simulations of the dynamics of an isolated vortex in a random potential \citep{link09}.
 This equation shows that pinning is weakened by vortex tension., This equation shows that pinning is weakened by vortex tension.
" For £j,2 1 MeV and £=10 (m. the eritical velocity is e245107+."," For $E_p=$ 1 MeV and $\xi=10$ fm, the critical velocity is $v_c\simeq
4\times 10^5$."
 The corresponding dillerential angular velocity between the superlluid and the erust is as large as I rrad |. but still much less than the angular velocity of the star when the superlluid condensed.," The corresponding differential angular velocity between the superfluid and the crust is as large as $\sim 1$ rad $^{-1}$, but still much less than the angular velocity of the star when the superfluid condensed."
 Ehe relative Low between the superfluid and the erust will thus be close to or comparable the local critical velocity in regions where there is pinning., The relative flow between the superfluid and the crust will thus be close to or comparable the local critical velocity in regions where there is pinning.
 We now examine the stability of this cillerentiallv-rotating state., We now examine the stability of this differentially-rotating state.
 The problem of the coupled dynamics of the superlluid ancl vortex lattice can be studied using the hydrodynamic theory of ? which accounts for vortex degrees of freedom.," The problem of the coupled dynamics of the superfluid and vortex lattice can be studied using the hydrodynamic theory of \citet{bc83}
 which accounts for vortex degrees of freedom."
 The local quantities of Duid. velocity. vortex density. and. vortex velocity are averaged over a length scale that is large compared to the inter-vortex spacing fo: the theory is valid. for wavenumboers that satisfy Af.<<1.," The local quantities of fluid velocity, vortex density, and vortex velocity are averaged over a length scale that is large compared to the inter-vortex spacing $l_v$; the theory is valid for wavenumbers that satisfy $kl_v<<1$."
 We treat the superlluid as a single-component [uid at zero temperature. and ignore dissipation in the bulk [uid and the small ellects of vortex inertia.," We treat the superfluid as a single-component fluid at zero temperature, and ignore dissipation in the bulk fluid and the small effects of vortex inertia."
 Fhese approximations are justified in a tvpical neutron star. for which the temperature of the inner crust is much less than the condensation temperature of the superlluid.," These approximations are justified in a typical neutron star, for which the temperature of the inner crust is much less than the condensation temperature of the superfluid."
 We also treat the crust as infinitely rigid and ignore local shear deformations. an approximation that will be justified below.," We also treat the crust as infinitely rigid and ignore local shear deformations, an approximation that will be justified below."
 The motion of the superlluid does not couple to the electrons. so electron viscosity is not relevant.," The motion of the superfluid does not couple to the electrons, so electron viscosity is not relevant."
 Magnetic fields are not relevant either. as they do not interact with the vortices of the inner crust.," Magnetic fields are not relevant either, as they do not interact with the vortices of the inner crust."
 We will consider only shear modes in the superlluid. so that the Dow velocity e(r./) is divergence-free.," We will consider only shear modes in the superfluid, so that the flow velocity $\vbf(\rbf,t)$ is divergence-free."
 Ehe rotation axis lies along 2. and r.(r./) denotes the continuum vortex displacement. vector. with components in thee jy plane only.," The rotation axis lies along $\hat{z}$, and $\rbf_v(\rbf,t)$ denotes the continuum vortex displacement vector, with components in the $x-y$ plane only."
" The equations of motion in the laboratory frame are (?) where w—Vo.v is the vorticity due to the existence of vortices in the uid. ji is the chemical potential. o is the eravitational potential. 9,4/p is the elastic force per unit volume that arises from bending of the vortex lattice. ancl f/p is the force per unit volume exerted on the Iuid by the normal matter."," The equations of motion in the laboratory frame are \citep{bc83}
 where $\omegabf\equiv\nabla\times\vbf$ is the vorticity due to the existence of vortices in the fluid, $\mu$ is the chemical potential, $\phi$ is the gravitational potential, $\sigmabf_{el}/\rho$ is the elastic force per unit volume that arises from bending of the vortex lattice, and $\fbf/\rho$ is the force per unit volume exerted on the fluid by the normal matter."
 The clastic force is where V4. denotes a derivative with components in the wy plane onlv., The elastic force is where $\nabla_\perp$ denotes a derivative with components in the $x-y$ plane only.
 Here ez=(004m)? is the Tkachenko wave speed. (27)... and © is the spin rate of the superlluid.," Here $c_T=(\hbar\Omega/4m)^{1/2}$ is the Tkachenko wave speed \citep{tk2a,tk2}, and $\Omega$ is the spin rate of the superfluid."
" The quantity ei=(hO/2m)In(Q,/0) is related to wave propagation along the rotation axis: Q.=fh(am) [or a triangular vortex lattice.", The quantity $c^2_V=(\hbar\Omega/2m)\ln(\Omega_c/\Omega)$ is related to wave propagation along the rotation axis; $\Omega_c=h/(\sqrt{3}m\xi^2)$ for a triangular vortex lattice.
 For à typical neutron star rotation rate of O=100 rad 7 er—0409 em | and ey=9er.," For a typical neutron star rotation rate of $\Omega=100$ rad $^{-2}$, $c_T=0.09$ cm $^{-1}$ and $c_V=9\,c_T$."
" The areal density of vortices in the.4 plane is /,2=2mQO/h for a uniform vortex lattice: hence. the requirement that Af.<< Lis equivalent to beg<<ο."," The areal density of vortices in the $x-y$ plane is $l_v^{-2}=2m\Omega/h$ for a uniform vortex lattice; hence, the requirement that $kl_v<<1$ is equivalent to $kc_T<<\Omega$."
 Ίσα. (13)), Eq. \ref{lineforce}) )
 is an expression of balance of the Magnus force. the elastic force of the deformed. vortex Lattice. and the force exerted on the fluid by the normal matter.," is an expression of balance of the Magnus force, the elastic force of the deformed vortex lattice, and the force exerted on the fluid by the normal matter."
" LE the vortex array is perfectly pinned to the normal matter of the inner crust moving at velocity v,. so that Or./Of=v,,. the force is For imperfect. pinning. the Magnus force and elastic force drive vortex motion with respect to the normal matter."," If the vortex array is perfectly pinned to the normal matter of the inner crust moving at velocity $\vbf_n$, so that $\partial\rbf_v/\partial t=\vbf_n$, the force is For imperfect pinning, the Magnus force and elastic force drive vortex motion with respect to the normal matter."
 For imperfect pinning. the force above can be generalized. as The first two terms of this force are. present in the mutual friction force introduced by 2..," For imperfect pinning, the force above can be generalized as The first two terms of this force are present in the mutual friction force introduced by \citet{hv56}."
 We emphasize the generality of the Force law of eq. (16))., We emphasize the generality of the force law of eq. \ref{fl}) ).
 Phe first two terms represent the force exerted on the fluid by vortices that are moving with respect to the normal matter: the first term corresponds to the force transverse to the vortex motion. while the second term," The first two terms represent the force exerted on the fluid by vortices that are moving with respect to the normal matter; the first term corresponds to the force transverse to the vortex motion, while the second term"
Let us recousider the highly idealized clusters with which we began - oue with stars of identical mass. and the other with a continuous range of stellar masses.,"Let us reconsider the highly idealized clusters with which we began - one with stars of identical mass, and the other with a continuous range of stellar masses."
 In both cases. the initial systems contaiued neither binaries nor higher-order multiple systems.," In both cases, the initial systems contained neither binaries nor higher-order multiple systems."
 The evolving. siugle-1uass cluster spawned no new binaries over the duration of our simulation.," The evolving, single-mass cluster spawned no new binaries over the duration of our simulation."
 However. Makino(1996) founcl. in lis more extensive investigation of the single-1nass model. that binaries do eventually form i[un the contracting[n] interior. and that their heating reverses core collapse atfretax.," However, \citet{m96} found, in his more extensive investigation of the single-mass model, that binaries do eventually form in the contracting interior, and that their heating reverses core collapse at."
. The core subsequeutly uudergoes the eravothermal oscillations predicted by Bettwieser&Sugimoto(1981 aud Goodman(1987). usiug fluid mocels with an internal euergy. source., The core subsequently undergoes the gravothermal oscillations predicted by \citet{bs84} and \citet{g87} using fluid models with an internal energy source.
 In our cluster with a realistic stellar mass distribution. the interior contraction euds much sooner. within a single tuitial relaxation time.," In our cluster with a realistic stellar mass distribution, the interior contraction ends much sooner, within a single initial relaxation time."
 Is this prompt reversal also due to binary. leatine’, Is this prompt reversal also due to binary heating?
 The answer is ves., The answer is yes.
 We have confirmed that the turnaround at coincides with the appearauce oL the first hard binary., We have confirmed that the turnaround at coincides with the appearance of the first hard binary.
 Here. we remiud the reader that a ανα binary is one whose gravitational biudiug[n]) energy exceeds the average. center-o[-mass kinetic energy of all other stellar systems.," Here, we remind the reader that a “hard” binary is one whose gravitational binding energy exceeds the average, center-of-mass kinetic energy of all other stellar systems."
 It is ouly such pairs that donate euergy to ueleliboring stars duriug a close flybsy. aud thereby become even harder.," It is only such pairs that donate energy to neighboring stars during a close flyby, and thereby become even harder."
 This is the esseuce of binary heating (HeeeieMD1975)., This is the essence of binary heating \citep{he75}.
. Why do binaries form so much earlier in this cluster thau in the sinele-miass model?, Why do binaries form so much earlier in this cluster than in the single-mass model?
 Closer inspection reveals that these new systems are comprisect ol stars that are appreciably more massive than the average cluster member., Closer inspection reveals that these new systems are comprised of stars that are appreciably more massive than the average cluster member.
 This fact is readily understood in a qualitative sense., This fact is readily understood in a qualitative sense.
 In clusters with no initial mass segregation. the relatively massive stars promptly sink to the center.," In clusters with no initial mass segregation, the relatively massive stars promptly sink to the center."
 Once in close proximity. these objects have a stronger mutual attraction than other cluster members. aud are thus more prone to forming binaries.," Once in close proximity, these objects have a stronger mutual attraction than other cluster members, and are thus more prone to forming binaries."
 Iu more detail. a gravitationally bound. pair of such stars cau only. orm by giving energy to a third star.," In more detail, a gravitationally bound pair of such stars can only form by giving energy to a third star."
 Binary formation is thus a three-bocly process., Binary formation is thus a three-body process.
 In the traditional analysis of cluster evolution based ou single-1nass models. three-body encounters throughout the bulk of the system are considered {ου rare to be of significance.," In the traditional analysis of cluster evolution based on single-mass models, three-body encounters throughout the bulk of the system are considered too rare to be of significance."
 Binney&Tremaine(2008.p.558) show that /7. the time for the first binary to form via tliis route. is much longer that /4444.," \citet[][p.~558]{bt08} show that $t_b^\ast$, the time for the first binary to form via this route, is much longer than $t_{\rm relax}$."
 Specifically. they estimate that Our superscript on /7 emphasizes that this time pertaius to the highly specialized case of equal-iiass stars.," Specifically, they estimate that Our superscript on $t_b^\ast$ emphasizes that this time pertains to the highly specialized case of equal-mass stars."
 The derivation of equation (5) assumes that the binary-forming stars reside in a region of average cdeusity., The derivation of equation (5) assumes that the binary-forming stars reside in a region of average density.
 This assumption breaks down if the iuteractious occur iu a deeply collapsing core., This assumption breaks down if the interactions occur in a deeply collapsing core.
 Three-body interactions proceed here efficiently (e.g.HeeeieOoy1981).," Three-body interactions proceed here efficiently \citep[e.g.,][]{he84}."
. However. the process is too slow iu regions where the cleusity is not greatly," However, the process is too slow in regions where the density is not greatly"
"outside eclipses (SchacterL990: Schacter&Rine-1905)). we derive a color excess of E(By=(B.V).=0.56 Tere. suffixes e and o represcut the theoretically calculated aud the observational values. respectively,","outside eclipses \cite{sch90}; ; \cite{sch95}) ), we derive a color excess of $E(B-V)= (B-V)_o - (B-V)_c= 0.56$ Here, suffixes $c$ and $o$ represent the theoretically calculated and the observational values, respectively."
 Then. we expect an absorption of 4=1E(BVy=Le and Ap=ely|ECBOV)23.," Then, we expect an absorption of $A_V= 3.1 ~E(B-V)= 1.8$ and $A_B= A_V + E(B-V) = 2.3$."
 Thus. we are forced to have a rather short distance to U Sco of 7.5 kpe.," Thus, we are forced to have a rather short distance to U Sco of 7.5 kpc."
 Iu our case of à=0.7 ancl ο)=0.30. the accretion disk is completely occulted at mid-eclipse.," In our case of $\alpha=0.7$ and $\beta=0.30$, the accretion disk is completely occulted at mid-eclipse."
 The color iudex of (B.V).=0.53 at mid-eclipse indicates a spectral type of Fe for the cool component MS. which is in good agreement with the spectral type of F8E2 sugeested by Joluston να (1992).," The color index of $(B-V)_c= 0.53$ at mid-eclipse indicates a spectral type of F8 for the cool component MS, which is in good agreement with the spectral type of $\pm$ 2 suggested by Johnston Kulkarni (1992)."
 anes (1985) also suggested that a spectral type nearer F7 is preferred., Hanes (1985) also suggested that a spectral type nearer F7 is preferred.
 For other mass accretion rates of HN= «10.CAL. to we obtain similar short distauces to U Sco. as stunumarized in Table 1..," For other mass accretion rates of $\dot M_{\rm acc}=$ $\times 10^{-7} M_\odot$ $^{-1}$, we obtain similar short distances to U Sco, as summarized in Table \ref{tbl-1}."
 It should be noted that. although the luminosity of the model depends ou our various asstuuptions of the radiation efficiencies. the zepowered law of the disk. and the intrinsic hDunuinositv of the WD. the derived distance to U Sco itself is aliuost independent of these assuniptions. as seen from Table 2..," It should be noted that, although the luminosity of the model depends on our various assumptions of the irradiation efficiencies, the $\varpi$ -powered law of the disk, and the intrinsic luminosity of the WD, the derived distance to U Sco itself is almost independent of these assumptions, as seen from Table \ref{tbl-2}."
 Therefore. the relatively short distance to U Sco (~ 6S kpe) is a rather robust conclusion. at least. from the theoretical point of view.," Therefore, the relatively short distance to U Sco $\sim$ 6---8 kpc) is a rather robust conclusion, at least, from the theoretical point of view."
 Matsiunuoto et al. (, Matsumoto et al. (
"2000) observed a few eclipses divine the 1999 outburst and. for the first time. detected a sjeuificaut period-change of Pi/P=(VT#O07)<108 Ἡ,","2000) observed a few eclipses during the 1999 outburst and, for the first time, detected a significant period-change of $\dot P / P = (-1.7 \pm 0.7) \times 10^{-6}$ $^{-1}$."
" Tf we assmne the conservative mass transfer. this period change requires a ias transfer rate of >10OAL, vr) in quiescence."," If we assume the conservative mass transfer, this period change requires a mass transfer rate of $\gtrsim 10^{-6} M_\odot$ $^{-1}$ in quiescence."
 Such a mass trausfer for 12 vears is too lüeh to be compatible with the euvelope mass on the white dwarf. thus implying a non-conservative mass transfer m U Sco.," Such a mass transfer for 12 years is too high to be compatible with the envelope mass on the white dwarf, thus implying a non-conservative mass transfer in U Sco."
" We have estimated the mass trauster rate for à non-conservative case by assuming that matter is escaping frou the outer Lagrangian poiuts and thus the specific augular momentum of the escaping matter is 1.70670,,4, (Sawadaet 198 ITachlisuetal. 1999a)). where « is the separation aud Qo,=2r/P."," We have estimated the mass transfer rate for a non-conservative case by assuming that matter is escaping from the outer Lagrangian points and thus the specific angular momentum of the escaping matter is $1.7 a^2 \Omega_{\rm orb}$ \cite{saw84}; \cite{hac99a}) ), where $a$ is the separation and $\Omega_{\rm orb} \equiv 2 \pi /P$."
" Then the mass trausfer rate from the conrpanion Is Mya=(5.521.)«10AL. 3 for AAs—08. 2,0 M. under the assuuptiou that the WD receives natter at a rate of AL=25<10“AL 1L", Then the mass transfer rate from the companion is $\dot M_{\rm MS}= (-5.5 \pm 1.5) \times 10^{-7} M_\odot$ $^{-1}$ for $M_{\rm MS}= 0.8$ —2.0 $M_\odot$ under the assumption that the WD receives matter at a rate of $\dot M_{\rm acc} = 2.5 \times 10^{-7} M_\odot$ $^{-1}$.
" The residual (~3«10TAL, !). which is escaping fron the system. forms an excretion disk outside the orbit of the binary."," The residual $\sim 3 \times 10^{-7} M_\odot$ $^{-1}$ ), which is escaping from the system, forms an excretion disk outside the orbit of the binary."
 Such an extended excretion disk/torus may cause a laree color excess of E(BV)=0.56., Such an extended excretion disk/torus may cause a large color excess of $E(B-V)= 0.56$.
 Iahabka et al. (, Kahabka et al. (
"1999) reported the hwdrosen column deusity of «1073 2. which is much larger han the Calactic absorption iu the direction of U Sco 007! 2, Dickey&Lockman 1990)). inclicating a substantial intrinsic absorption.","1999) reported the hydrogen column density of $\times 10^{21}$ $^{-2}$, which is much larger than the Galactic absorption in the direction of U Sco $\times 10^{21}$ $^{-2}$, \cite{dic90}) ), indicating a substantial intrinsic absorption."
 It should also be noted rere that Barlow ct al. (, It should also be noted here that Barlow et al. (
1981) estimated the absorption oward U Sco by three wavs: (1) the Galactic absorption im he direction ofU Sco. E(BVy~0.2 and Ay~0.7. (2) he hue ratio of Te II during the 1979 outburst (f~ 12 davs after πιακα). A(BV)—0.2 aud ely~0.6. aud (3) he Balmer line ratio during the 1979 outburst (f.~ davs after maxi). £(BV)~0.35 aud Ay~1.1.,"1981) estimated the absorption toward U Sco by three ways: (1) the Galactic absorption in the direction of U Sco, $E(B-V) \sim 0.24$ and $A_V \sim 0.7$, (2) the line ratio of He II during the 1979 outburst $t \sim$ 12 days after maximum), $E(B-V) \sim 0.2$ and $A_V \sim 0.6$, and (3) the Balmer line ratio during the 1979 outburst $t \sim$ days after maximum), $E(B-V) \sim 0.35$ and $A_V \sim 1.1$."
" The last one is siguifcautle lareer than the other two estimates,", The last one is significantly larger than the other two estimates.
 They sueeested the breakdown of their case D approximation in ligh density regious., They suggested the breakdown of their case B approximation in high density regions.
" Ποπονα, we may point out another possibility that the svstemic mass outtlow frou the binary system has already: beeun at f~ 33 davs auc. as a result. au iutrinsic absorption is eradually ΠιοΡΟ,"," However, we may point out another possibility that the systemic mass outflow from the binary system has already begun at $t \sim$ 33 days and, as a result, an intrinsic absorption is gradually increasing."
 The mass of the companion star can be constrained from the mass transfer rate., The mass of the companion star can be constrained from the mass transfer rate.
 Such a lieh trauster rate as AnasM5510*M. + stronelv indicates a thermally uustable mass transfer (c.e.. vandeuIHeuveletal.1992)). which is realized when the mass ratio is larger than 1.0Lilie. g=Ahis/AAvp> 1.0Ll for zero-age πιαποιος stars (Webbink19853).," Such a high transfer rate as $\dot M_{\rm MS} \sim 5.5
\times 10^{-7} M_\odot$ $^{-1}$ strongly indicates a thermally unstable mass transfer (e.g., \cite{heu92}) ), which is realized when the mass ratio is larger than 1.0—1.1, i.e., $q= M_{\rm MS}/ M_{\rm WD} >$ 1.0—1.1 for zero-age main-sequence stars \cite{web85}) )."
 This may pose a requiremieut Ais=LAL..., This may pose a requirement $M_{\rm MS} \gtrsim 1.4 M_\odot$.
 We estimate the most likely colupanion mass of Lt1.6 AZ.. from equation (11) in Tachisu et al. (, We estimate the most likely companion mass of 1.4—1.6 $M_\odot$ from equation (11) in Hachisu et al. (
19990).,1999b).
 If the distance to U Sco is  6.08.0 kpe. it is located ~ 2.5.3.0 kpc above the Galactic plane (5=22°).," If the distance to U Sco is $\sim$ 6.0—8.0 kpc, it is located $\sim$ 2.3—3.0 kpc above the Galactic plane $b=22\arcdeg$ )."
 The zero-age Inasses of the progenitor system to U Sco are rather massive (ce. S.0M.|2.5 from EHachisu et al.," The zero-age masses of the progenitor system to U Sco are rather massive (e.g., $8.0 ~M_\odot + 2.5 ~M_\odot$ from Hachisu et al."
 19995) aud it is uulikelv that such massive stars were born in the halo., 1999b) and it is unlikely that such massive stars were born in the halo.
 Some normal B-type main-sequence stars have been found iu the halo (e.g. PCO009|036 is located ~ 5 kpe below the Galactic disk. Sclumidtetal.1996)). which were ejected from the Galactic disk because of their relatively high moving velocities ~100 200 lan +.," Some normal B-type main-sequence stars have been found in the halo (e.g., PG0009+036 is located $\sim$ 5 kpc below the Galactic disk, \cite{smt96}) ), which were ejected from the Galactic disk because of their relatively high moving velocities $\sim$ 100—200 km $^{-1}$."
 The radial velocity of U Sco is not known but it is sueeested that the ~-velocity is ~50) 100 kan | from the absorption liue velocities (Joluuston&I&ullzuui1992: Schacter&wald 19051)., The radial velocity of U Sco is not known but it is suggested that the $\gamma$ -velocity is $\sim$ 50—100 km $^{-1}$ from the absorption line velocities \cite{joh92}; \cite{sch95}) ).
 If so. it secus likely that U Sco was ejected from the Galactic disk with a vertical velocity faster than ~20 kn +t and has reached at the preseut place within the 1idu-sequeuce lifetimes of a ~3.0AL.. star (~3.5«105 vr}.," If so, it seems likely that U Sco was ejected from the Galactic disk with a vertical velocity faster than $\sim 20$ km $^{-1}$ and has reached at the present place within the main-sequence lifetimes of a $\sim 3.0 M_\odot$ star $\sim 3.5\times 10^8$ yr)."
 Now. we can understaud the current evolutionary status and a further evolution of U Sco system.," Now, we can understand the current evolutionary status and a further evolution of U Sco system."
 The white chwart has aduass 1.37m0.0LAL... It is verv likely that the WD has reached such a large μας by mass accretion., The white dwarf has a mass $1.37 \pm 0.01 M_\odot$ It is very likely that the WD has reached such a large mass by mass accretion.
" Iu fact the WD is currently increasing the mass of the lelimu laver at a rate of Al,oo10.10SAL. 3 (Tlachisuetal. 2000)).", In fact the WD is currently increasing the mass of the helium layer at a rate of $\dot M_{\rm He} \sim 1.0 \times 10^{-7} M_\odot$ $^{-1}$ \cite{hac2000}) ).
 We then predict that the WD will evolve as follows., We then predict that the WD will evolve as follows.
 When the mass of the helium laver reaches a critical mass after many eveles of recurrent nova outbursts. a helium shell flash will occur.," When the mass of the helium layer reaches a critical mass after many cycles of recurrent nova outbursts, a helium shell flash will occur."
 Its streneth is as weak as those of ACD stars because of the high mass accretion rate (Nomoto 1982))., Its strength is as weak as those of AGB stars because of the high mass accretion rate \cite{nom82}) ).
 A part of the helium laver will be blown off in the wind. but virtually all of the helimm laver will be burnt iuto carbon-oxygen aud accumulates in the white dwiuf (I&ato&Uachisu 1999)).," A part of the helium layer will be blown off in the wind, but virtually all of the helium layer will be burnt into carbon-oxygen and accumulates in the white dwarf \cite{kat99h}) )."
 Therefore. the WD mass can grow until au SN Ia explosion is triggered (Nomotoct 1)).," Therefore, the WD mass can grow until an SN Ia explosion is triggered \cite{nom84}) )."
 We thauk the anouvinous referee for iuauv critical cohmuents to inuprove the manuscript., We thank the anonymous referee for many critical comments to improve the manuscript.
" This research has been supported in part by the Grant-in-Aid for Scicutific Research (O7TCE200. O86L0321. 09610325. 11610226, 20283591) of the Japauese Ministry of Education. Scieuce. Culture. and Sports."," This research has been supported in part by the Grant-in-Aid for Scientific Research (07CE200, 08640321, 09640325, 11640226, 20283591) of the Japanese Ministry of Education, Science, Culture, and Sports."
KAD has been financially supported as a Research Fellow for Young Scieutistsbv the Japan Society for the Promotion of Science.,KM has been financially supported as a Research Fellow for Young Scientistsby the Japan Society for the Promotion of Science.
backeround sublraction. aud the flare Lrequeney-peak flux. ancl wailine-lime cistributions are analvzed.,"background subtraction, and the flare frequency-peak flux, and waiting-time distributions are analyzed."
 The Irequency-peak flux distribution for the background-subtracted events reveals an absence of large events by comparison wilh (he expected power-law [orm., The frequency-peak flux distribution for the background-subtracted events reveals an absence of large events by comparison with the expected power-law form.
 The deficiency is clearly seen in a cumulative number representation of the distribution (lower panels of Figures 3 and 4)., The deficiency is clearly seen in a cumulative number representation of the distribution (lower panels of Figures 3 and 4).
 A quantitative comparison is made with a simple power-law model. and a power-law plus upper exponential rollover model. using Davesian methods. outlined in the appendices.," A quantitative comparison is made with a simple power-law model, and a power-law plus upper exponential rollover model, using Bayesian methods, outlined in the appendices."
 The power-law plus rollover model is strongly favored by the data: the odds ratio for the (wo models is 2220. or 23dD. for a prior odds ratio of unity.," The power-law plus rollover model is strongly favored by the data: the odds ratio for the two models is $\approx 220$, or $23\,{\rm dB}$, for a prior odds ratio of unity."
 This means that. if the (wo models are assumed a priori to be equally likely. (hen the power-law plus rollover moclel is more (han 200 times more probable. based on the data.," This means that, if the two models are assumed a priori to be equally likely, then the power-law plus rollover model is more than $200$ times more probable, based on the data."
 The model comparison takes into account all possible values of the model parameters., The model comparison takes into account all possible values of the model parameters.
 The result represents strong evidence in favor of a departure from power-law behavior in the Blrequency-peak fhix distribution., The result represents strong evidence in favor of a departure from power-law behavior in the frequency-peak flux distribution.
 As discussed in section 3.2. the power-law plus rollover model is chosen for convenience. and other models aa broken power law) are also possible.," As discussed in section 3.2, the power-law plus rollover model is chosen for convenience, and other models a broken power law) are also possible."
 It is expected that a broken power law model would also be strongly [avored over a simple power law for this data., It is expected that a broken power law model would also be strongly favored over a simple power law for this data.
 The important result is Chat the events shows departure [rom the power law peak-Iux distribution al large peak fIux., The important result is that the events shows departure from the power law peak-flux distribution at large peak flux.
 The wailing-lime distribution for the backgrounmnd-subtracted. events (lower panel οἱ Figure 5) has a double-exponential form. which may be explained via a piecewise-constaul Poisson model with two different rates.," The waiting-time distribution for the background-subtracted events (lower panel of Figure 5) has a double-exponential form, which may be explained via a piecewise-constant Poisson model with two different rates."
 The active region initially produced [ares at a low rate (prior to 26 Oct). then at a high rate (26 Oct and 27 Oct). and then at a low rate again. with the second low rate comparable to the first low rate.," The active region initially produced flares at a low rate (prior to 26 Oct), then at a high rate (26 Oct and 27 Oct), and then at a low rate again, with the second low rate comparable to the first low rate."
 A Bayesian analvsis identilies the three intervals. and (he model piecewise-constant Poisson wailing-lime distribution produced by the analvsis reproduces the observed waiting-time distribution.," A Bayesian analysis identifies the three intervals, and the model piecewise-constant Poisson waiting-time distribution produced by the analysis reproduces the observed waiting-time distribution."
 The reported departure of the Irequency-peak flux distribution from the simple form is the first (ime such a result has been seen lor an individual active region., The reported departure of the frequency-peak flux distribution from the simple power-law form is the first time such a result has been seen for an individual active region.
 Evidence for a size-linit was reported for a large statistical saaiple of small solar active regions (INucera et 11997). ancl a departure is expected on energetics grounds IHIudson 1991). but in eeneral it has proven difficult to identilv the effect in data Wheatland 2000a: Lhidson 2007).," Evidence for a size-limit was reported for a large statistical sample of small solar active regions (Kucera et 1997), and a departure is expected on energetics grounds Hudson 1991), but in general it has proven difficult to identify the effect in data Wheatland 2000a; Hudson 2007)."
 This study has certain advantages over previous studies., This study has certain advantages over previous studies.
 First. a small region is observed at a time of very low solar activitv. leading to GOES event lists for the region which are particularlv complete above the chosen peak-flux threshold.," First, a small region is observed at a time of very low solar activity, leading to GOES event lists for the region which are particularly complete above the chosen peak-flux threshold."
 The low background. also allows careful background subtraction of each event to determine the intrinsic peak flux., The low background also allows careful background subtraction of each event to determine the intrinsic peak flux.
 The lower panel of Figuree 3 suggestsOO the importance of backgrounde subtraction for the analvsis., The lower panel of Figure 3 suggests the importance of background subtraction for the analysis.
 Previous studies of flare statisües. in particular using the GOES events. have suffered from," Previous studies of flare statistics, in particular using the GOES events, have suffered from"
"""energv crisis” for this model. aud possibly violating upper limits from EGRET (Energetic Gamma-Ray Experiment Telescope) (Gonzalez&Sanchez2005:Ando.NakarSari2008).","“energy crisis"" for this model, and possibly violating upper limits from EGRET (Energetic Gamma-Ray Experiment Telescope) \citep{gs05,ans08}."
. This problem is generic ancl il does not depend on the specilic details of (he overall moclel., This problem is generic and it does not depend on the specific details of the overall model.
 The above analvsis is oversimplified and (wo [actors may alleviate (he energy catastrophe., The above analysis is oversimplified and two factors may alleviate the energy catastrophe.
 First. the frequency of the seed photons may differ from that where upper limits exist. allowing larger seed flux and reducing the lower limits on Y.," First, the frequency of the seed photons may differ from that where upper limits exist, allowing larger seed flux and reducing the lower limits on $Y$."
 Second. the Ixlein-Nishina (IXN) suppression. which does not affect the first scattering. mav affect the second. resulting ina lower Y parameter for the second scattering than the first one.," Second, the Klein-Nishina (KN) suppression, which does not affect the first scattering, may affect the second, resulting in a lower $Y$ parameter for the second scattering than the first one."
 In (his article. we explore (he parameter space (o see weather (here exist a regime where a combination of these two factors allows lor less energv in (lie second IC: component (Typically in the TeV range) than in (he 5-ravs.," In this article, we explore the parameter space to see weather there exist a regime where a combination of these two factors allows for less energy in the second IC component (Typically in the TeV range) than in the $\gamma$ -rays."
 We find (hat possible solutions are limited (to a very small region in (he parameters space in which (he seed photons are in the IR. the bulk Lorentz factor is verv low (< 200) and the electrons’ Lorentz factor is verv large (>2000).," We find that possible solutions are limited to a very small region in the parameters space in which the seed photons are in the IR, the bulk Lorentz factor is very low $(\le 200$ ) and the electrons' Lorentz factor is very large $\ge 2000)$."
 Llowever. (his solution implies a healthy. emission in the It. while self absorption limits it.," However, this solution implies a healthy emission in the IR, while self absorption limits it."
 Therefore. when taking sell-absorption into account. this solution is ruled out as well.," Therefore, when taking self-absorption into account, this solution is ruled out as well."
 A second possible solution exists if the seed photons are in the UV., A second possible solution exists if the seed photons are in the UV.
 This solution requires a very low electrons Lorentz lactor <LOO. and a seed photon flux that carries comparable energy to the observed prompti 5-ravs.," This solution requires a very low electrons' Lorentz factor $\le 100$, and a seed photon flux that carries comparable energy to the observed prompt $\gamma$ -rays."
 Furthermore. prompt. X-ray. observations limit the high energy tail of the UV component and practically rule out this model.," Furthermore, prompt X-ray observations limit the high energy tail of the UV component and practically rule out this model."
 We (ake the Lorentz [actor of the electrons ancl the bulk Lorentz [actor as [ree parameters and we estimate what is the second IC fluence (at TeV or multi GeV) given the observed prompt ganmia-ray flux and the limits on the prompt optical band., We take the Lorentz factor of the electrons and the bulk Lorentz factor as free parameters and we estimate what is the second IC fluence (at TeV or multi GeV) given the observed prompt gamma-ray flux and the limits on the prompt optical band.
 Most of our analvsis is insensitive to the size of the source. which appears only in the final section when we estimate the self absorption flux.," Most of our analysis is insensitive to the size of the source, which appears only in the final section when we estimate the self absorption flux."
 In our numerical examples we use very conservative parameters., In our numerical examples we use very conservative parameters.
" For exalple we use Ro magnitude of 11.2 as an upper limit on the optical flux. while many limits are much stronger and the 5-rav [lux we take. 10?""ergem7s11,1 is quite mocest."," For example we use R magnitude of 11.2 as an upper limit on the optical flux, while many limits are much stronger and the $\gamma$ -ray flux we take, $10^{-26} {\rm erg\,cm^{-2}\,s^{-1}\,Hz^{-1}}$, is quite modest."
 Similarly we use conservative rather rather than “canonical” values for the spectral slopes.," Similarly we use conservative rather rather than “canonical"" values for the spectral slopes."
 Consider electrons that move wilh a bulk Lorentz factor EDs>1 while in the bulk (or fluid), Consider electrons that move with a bulk Lorentz factor $\G \gg 1$ while in the bulk (or fluid)
"p=pe+dp V.—Vw+50V. Fryxelletal.(2000) (MacNeiceetal.:LO09).. rr, li (see.e.g..Binney&Tremaije.2008).. Mj Aly AL, (see.ancreferencestherein). ryisis","$\rho=\rho_w+\delta\rho$ $\vct{V}=\vct{V_w}+\delta\vct{V}$ \citet{fry00} \citep{mac99}, $r_\ast$ \citep[see, e.g.,][]{bin08}, $M_p$ $M_J$ $M_J$ \citep[see, 
e.g.,][and references therein]{vil09}."
" ri; ru ‘sareV. Vi.c. (+=1.00001) c; icy. M,=0.5-10. Mf,«11. 1 rg=GAL,*fez.Hcay (MM,=10) (Map5) r7 ‘thes dar? r, ", $r_p$ $r_s$ $r_s$ $V_p$ $V_w$$\cs$ $\gamma=1.00001$ $\cs$ $\cs$ $\mach_p=0.5$ $\mach_w<11$ \ref{tab:para} $r_B=GM_p/\cs^2$ $\mach_w=10$ $\mach_w=5$ $r^{-2}$ $r^{-2}$ $r_\ast$ 
In. the past few decades. discrepancies in. the. solar neighborhood age-metallicity relation have implied that effective radial migration. (1e... redistribution of angular momentum) must be taking place in the Milky Way disk (Edvardssonetal.1993:Haywood2008:SchónrichandBin-ney 2009:; see Minchev&Famaey2010 for a comprehensive discussion).,"In the past few decades, discrepancies in the solar neighborhood age-metallicity relation have implied that effective radial migration (i.e., redistribution of angular momentum) must be taking place in the Milky Way disk \citealt{edvardson93,
haywood08, schonrich09}; ; see \citealt{mf10} for a comprehensive discussion)."
 In parallel. there is now considerable observational evidence that the non-axisymmetry of the Galactic potential can cause significant perturbations in the motion of stars of all ages.," In parallel, there is now considerable observational evidence that the non-axisymmetry of the Galactic potential can cause significant perturbations in the motion of stars of all ages."
 Evidence for this comes from. e.g. the moving groups in the solar neighbourhood (Dehnen.1998). containing stars of very different ages (Famaeyetal..2005) or the non-zero value of the C and K Oort constants for red giant stars in the extended local disk (Olling&Dehnen.2003: 2010).," Evidence for this comes from, e.g, the moving groups in the solar neighbourhood \citep{dehnen98} containing stars of very different ages \citep{famaey05} or the non-zero value of the $C$ and $K$ Oort constants for red giant stars in the extended local disk \citep{od03, siebert10}."
. All of these can be explained by the etfect of resonances associated with a central bar (Minchevetal..2010.2007) or spiral structure (SS) (QuillenandMinchev.2005:Quillenal.. 2010).," All of these can be explained by the effect of resonances associated with a central bar \citep{minchev10,mnq07} or spiral structure (SS) \citep{qm05,quillen10}."
. Until recently 1t was accepted that efficient radial mixing of stars in galactic disks was caused solely by transient spirals (SellwoodandBinney.2002.hereafterSBO2)., Until recently it was accepted that efficient radial mixing of stars in galactic disks was caused solely by transient spirals \citep[][hereafter SB02]{sellwood02}.
. However. Quillenetal.(2009) showed that small satellites on radial. plane orbits can cause mixing in the outer disk and thus account for the fraction of low-metallicity stars present in the solar neighborhood (Haywood.2008).," However, \cite{quillen09} showed that small satellites on radial, in-plane orbits can cause mixing in the outer disk and thus account for the fraction of low-metallicity stars present in the solar neighborhood \citep{haywood08}."
. Moreover. we have recently demonstrated Ainchev&Famaey2010.. hereafter ΜΕΤΟ) that à strong exchange of angular momentum occurs when a stellar disk is perturbed by a central bar and SS. simultaneously: our test-particle simulations allowed us to attribute this effect to the overlap or first and second order resonances of each perturber.," Moreover, we have recently demonstrated \citealt{mf10}, hereafter MF10) that a strong exchange of angular momentum occurs when a stellar disk is perturbed by a central bar and SS simultaneously: our test-particle simulations allowed us to attribute this effect to the overlap or first and second order resonances of each perturber."
 The presence of multiple patterns in galactic disks has been observed both in external galaxies (e.g.. etal. 1992)) and N-body simulations (e.g.. RautiainenandSalo 1999)).," The presence of multiple patterns in galactic disks has been observed both in external galaxies (e.g., \citealt{elmegreen92}) ) and N-body simulations (e.g., \citealt{rautiainen99}) )."
 Given that more than two-thirds of disk galaxies. including our own Milky Way. contain both central bars and SS. it is imperative to establish a strong understanding of the implications of this mechanism.," Given that more than two-thirds of disk galaxies, including our own Milky Way, contain both central bars and SS, it is imperative to establish a strong understanding of the implications of this mechanism."
 Therefore. in this work we study a range of fully self-consistent. Tree-SPH simulations. as Well as high resolution pure N-body simulations. searching for the signature of spiral-bar interaction in the distribution of angular momentum: MF1O predicted that when both bar and spirals are present in the disk. one finds that the changes in angular momentum form a bimodal distribution. with two local maxima close to the corotation and outer Lindblad resonance of the bar. regardless of the pattern speed of the spiral.," Therefore, in this work we study a range of fully self-consistent, Tree-SPH simulations, as well as high resolution pure N-body simulations, searching for the signature of spiral-bar interaction in the distribution of angular momentum: MF10 predicted that when both bar and spirals are present in the disk, one finds that the changes in angular momentum form a bimodal distribution, with two local maxima close to the corotation and outer Lindblad resonance of the bar, regardless of the pattern speed of the spiral."
 While not self-consistent. test-particle simulations allow for a full control over the simulation parameters. such as the amplitudes and pattern speeds of bar and SS. and still provide a good approximation to self-consistent simulations.," While not self-consistent, test-particle simulations allow for a full control over the simulation parameters, such as the amplitudes and pattern speeds of bar and SS, and still provide a good approximation to self-consistent simulations."
 Employing this method in MFIO. we were able to suppress the effect of transient spirals and thus identify the non-linear effect of resonance overlap.," Employing this method in MF10, we were able to suppress the effect of transient spirals and thus identify the non-linear effect of resonance overlap."
 We showed that the most important signature of this mechanism was a bimodality in the changes in angular momentum in the disk. AZ. with maxima near the bar's corotation and its outer Lindblad resonance (OLR) regardless of the SS pattern speed.," We showed that the most important signature of this mechanism was a bimodality in the changes in angular momentum in the disk, $\Delta L$, with maxima near the bar's corotation and its outer Lindblad resonance (OLR) regardless of the SS pattern speed."
 Hereafter. we analyze self-consistent simulations with strong bars and spirals. therefore mixing from transient spirals (SBO2) and resonance overlap (MFIO) is expected.," Hereafter, we analyze self-consistent simulations with strong bars and spirals, therefore mixing from transient spirals (SB02) and resonance overlap (MF10) is expected."
 However. we hope to be able to identify the latter mechanism by detecting the aforementioned bimodality. given that the predicted distribution of ALgenerated by transient spirals without a bar is rather smooth and not bimodal (see SBO2).," However, we hope to be able to identify the latter mechanism by detecting the aforementioned bimodality, given that the predicted distribution of $\Delta L$generated by transient spirals without a bar is rather smooth and not bimodal (see SB02)."
 We test the predictions of ΜΕΙΟ by analyzing fully.self- simulations of isolated disk galaxies. from. the GalMer database!.. including a gas component as well as star formation (DiMatteoetal..2007:Chilingarian 2010).," We test the predictions of MF10 by analyzing fullyself-consistent simulations of isolated disk galaxies from the GalMer , including a gas component as well as star formation \citep{dimatteo07,chilingarian10}. ."
Qur reference model at 10 000 Ix. retains from to of its turmoll angular momentum. depending on whether solid-body rotation is enforced in the core or whether the angular momentum deposited in the core remains there.,"Our reference model at 10 000 K retains from to of its turnoff angular momentum, depending on whether solid-body rotation is enforced in the core or whether the angular momentum deposited in the core remains there."
 Ouce on the horizontal brauch. the surface rotation rate will depeud upon whether augular iruomentum from the core is redistributed to the envelope.," Once on the horizontal branch, the surface rotation rate will depend upon whether angular momentum from the core is redistributed to the envelope."
 For local conservation of augular momeutuim from the giaut branch tip to the horizontal branch. the predicted surface rotation rates are extremely low. of order 0.01 kins f.," For local conservation of angular momentum from the giant branch tip to the horizontal branch, the predicted surface rotation rates are extremely low, of order 0.01 km $^{-1}$."
 If angular momentum is redistributed from the core to the envelope ou the horizontal branch the surface rotation rate for our reference model is inthe range 0.21 kms 1102.23 kan ! depending upon whether or not angular momentuim was preserved iu the core on the giaut brauch., If angular momentum is redistributed from the core to the envelope on the horizontal branch the surface rotation rate for our reference model is in the range 0.24 km $^{-1}$ to 2.23 km $^{-1}$ depending upon whether or not angular momentum was preserved in the core on the giant branch.
 The expected surface rotation rates ou the horizontal brauch for models in this class will be low for all assumptious about internal angular mouentum trausport outhe giaut aud borizoutal branch., The expected surface rotation rates on the horizontal branch for models in this class will be low for all assumptions about internal angular momentum transport on the giant and horizontal branch.
 If there is constant specific angular momentum in giant brauch convective envelopes. there are two ellects that limit the amount of envelope augular momeutuim loss.," If there is constant specific angular momentum in giant branch convective envelopes, there are two effects that limit the amount of envelope angular momentum loss."
" First. the fraction of he envelope angular momentum which is lost is proportional to either the fraction of the mass above the poiut of maximum couvectiou zoue depth (local couservation of angular ruonientum i he core) or to the fraction of the convective envelope which is lost (solid body rotation in the ""adiative core)."," First, the fraction of the envelope angular momentum which is lost is proportional to either the fraction of the mass above the point of maximum convection zone depth (local conservation of angular momentum in the core) or to the fraction of the convective envelope which is lost (solid body rotation in the radiative core)."
 There will therefore be more aueular momentum available on the horizontal braucl or this case (Figure 1)., There will therefore be more angular momentum available on the horizontal branch for this case (Figure 4).
 Our reference model retains from to of its turnoll augular uomentunm [or models with solid body core rotation and local angular momenttun couservatior in the core respectively., Our reference model retains from to of its turnoff angular momentum for models with solid body core rotation and local angular momentum conservation in the core respectively.
 The inferred surface rotation rates ou the horizontal brauch rauge from a ow of 0.01 km + for local conservation of angular momentum from the giant. branch tip to the iorizontal branch to a range of 6.01 - 8.12 kins | i£ there is horizontal branch angular momentum ‘eclistribution., The inferred surface rotation rates on the horizontal branch range from a low of 0.01 km $^{-1}$ for local conservation of angular momentum from the giant branch tip to the horizontal branch to a range of 6.04 - 8.42 km $^{-1}$ if there is horizontal branch angular momentum redistribution.
 All of these cases are well below the observed rotation rates of blue horizontal branch stars. inclicating that for solid body main sequence rotation a higher main sequence rotation rate than 1 ans Lis needed to explain the data.," All of these cases are well below the observed rotation rates of blue horizontal branch stars, indicating that for solid body main sequence rotation a higher main sequence rotation rate than 1 km $^{-1}$ is needed to explain the data."
 In the case of solid-body rotation in the couvective envelope ou the elant brauch. the required main sequence rotation rates are prohibitively lieh: a similar conclusion was reached in Pinsouueault.Delivauuls&Demarque(1991).," In the case of solid-body rotation in the convective envelope on the giant branch, the required main sequence rotation rates are prohibitively high; a similar conclusion was reached in \cite{PDD}."
. Dillerent amounts of giant branch mass loss will produce horizontal branch. models: with different T7.py: models which lose more mass will also lose more angular momentum., Different amounts of giant branch mass loss will produce horizontal branch models with different $T_{eff}$; models which lose more mass will also lose more angular momentum.
 Bluer horizontal branch models will therefore have systematically less total angular momentum than redder horizoutal brauch models., Bluer horizontal branch models will therefore have systematically less total angular momentum than redder horizontal branch models.
 However. the moment of inertia decreases strougly for the bluer horizontal branch mioclels. aud it is therefore not clear a priori that lower stulace rotation velocities would be preclictος.," However, the moment of inertia decreases strongly for the bluer horizontal branch models, and it is therefore not clear a priori that lower surface rotation velocities would be predicted."
 The overall structural properties of our horizontal brauch. models are suutarizect in Table 1., The overall structural properties of our horizontal branch models are summarized in Table 1.
 All models are shown at the zero age horizontal branch., All models are shown at the zero age horizontal branch.
 There is a strong trend to decreased, There is a strong trend to decreased
mionentun. and magnetic fiux.,"momentum, and magnetic flux."
 We solve the equations of ideal isothermal MITID. and where ος Land P=cp are the isothermal sonud speed and pressure. on a threc-dimeusional periodic Cartesian erid of length £=1.," We solve the equations of ideal isothermal MHD, and where $c_s = 1$ and $P = c_s^2 \rho$ are the isothermal sound speed and pressure, on a three-dimensional periodic Cartesian grid of length $L = 1$."
 We use an approximate nonlinear Riecruaun solver (IILLD: \livoshi Ixusauo 2005) for our MIID runs aud au exact noulinear Riemauu solver for our lvdrocwnamic ruus., We use an approximate nonlinear Riemann solver (HLLD; Miyoshi Kusano 2005) for our MHD runs and an exact nonlinear Riemann solver for our hydrodynamic runs.
 We inteerate our siuulatious for roughly { clwnamical times bevond the saturation time using a directionallv-unsplit vau Leer scheme (Stone Cardiner 2008)., We integrate our simulations for roughly 4 dynamical times beyond the saturation time using a directionally-unsplit van Leer scheme (Stone Gardiner 2008).
" Here we have defied the dvnamucal tine to be fag,=£/(2M). where Mo= is the Mach uimnber aud σι=(ipp1/2 is the velocity dispersion of the eas. caleulated using a mass-weighted average."," Here we have defined the dynamical time to be $t_{\rm dyn} = L/(2\mathcal{M})$, where $\mathcal{M} \equiv \sigma_v/c_s$ is the Mach number and $\sigma_v = \langle v^2 \rho/\bar{\rho} \rangle^{1/2}$ is the velocity dispersion of the gas, calculated using a mass-weighted average."
 For further details on our umnuerical methods as applied to turbulence. see Paper I. We drive our turbulence here im a numer very simular to Ss.," For further details on our numerical methods as applied to turbulence, see Paper I. We drive our turbulence here in a manner very similar to S98."
 We initialize a uniform. stationary zuubient medium with deusity p=1 aud magnetic Ποιά parallel to the w-axis whose amplitude By is fixed by the value of $=jJ203p/Da.," We initialize a uniform, stationary ambient medium with density $\bar{\rho} = 1$ and magnetic field parallel to the $x$ -axis whose amplitude $B_0$ is fixed by the value of $\beta = 2c_s^2\bar{\rho}/B_0^2$."
 We apply divergence-free velocity perturbations before every time step. following a Gaussian randoms distribution peaked at hy.f/27=3.," We apply divergence-free velocity perturbations before every time step, following a Gaussian random distribution peaked at $k_{\rm pk}L/2\pi = 2$."
 Before applying the perturbations. we shift them such that no uct momentum will be added to the grid.," Before applying the perturbations, we shift them such that no net momentum will be added to the grid."
 We also norinalize them to eive the desired energy injection rate. E/pL?ci.," We also normalize them to give the desired energy injection rate, $\dot{E}/\bar{\rho}L^2c_s^3$."
 For our decaying runs. we bogin with a snapshot of fully-developed turbulence from a driven ruu and allow it to evolve without further energy injection.," For our decaying runs, we begin with a snapshot of fully-developed turbulence from a driven run and allow it to evolve without further energy injection."
 We investigate strone-ficld MITD (3= 0.02) as well as lydrodvuamic (9= x) turbulence., We investigate strong-field MHD $\beta = 0.02$ ) as well as hydrodynamic $\beta = \infty$ ) turbulence.
" The magnetic fields we use in our simulations correspond to plivsical values of B=2.0pC}HOQTAOK)?(ngu,1050213, where T i the temperature axl] ng is the muuber density of molecular livdrogen."," The magnetic fields we use in our simulations correspond to physical values of $B = 2.0 \unit{\mu G} \beta^{-1/2} (T/10 \unit{K})^{1/2}
(n_{H_2}/10^2 \unit{cm^{-3}})^{1/2}$, where $T$ is the temperature and $n_{H_2}$ is the number density of molecular hydrogen."
 Our simulations are scale-free. allowing them to be scaled to any set of plysical paranueters using appromiate choices of p. ey. and L.," Our simulations are scale-free, allowing them to be scaled to any set of physical parameters using appropriate choices of $\bar{\rho}$, $c_s$, and $L$ ."
" Utilizing the same valuc""s eiven du SOS. e. £=2pc. Hoy=Lan”. and T=10h. vields au euerev injection rate of E—0.2L. with magnetic field streneth B=Llp."," Utilizing the same values given in S98, i.e. $L = 2 \unit{pc}$, $n_{H_2} = 10^3 \unit{cm^{-3}}$, and $T = 10 \unit{K}$, yields an energy injection rate of $\dot{E} = 0.2 L_\odot$ with magnetic field strength $B = 44 \unit{\mu G}$."
 Turbulence iu molecular clouds causes couverging flows where the gas can be compressed to very high deusities., Turbulence in molecular clouds causes converging flows where the gas can be compressed to very high densities.
 The PDF of the densiv tells us the fraction of the lnass or voluue within a cloud that obtains a given density., The PDF of the density tells us the fraction of the mass or volume within a cloud that obtains a given density.
 Since sclferaviating clumps can form iu the lugh-density regions. understanding PDFs is critical for gaining insight iuto the stellar IPM aud SER.," Since self-gravitating clumps can form in the high-density regions, understanding PDFs is critical for gaining insight into the stellar IFM and SFR."
 If colmpression and rarefacion events in the turbulent eas within a molecular cloud are spatially aud temporally independent. the PDF o: deusitv will have a loe-normal distribution (Passot Vazquez-Semadeui 1998).," If compression and rarefaction events in the turbulent gas within a molecular cloud are spatially and temporally independent, the PDF of density will have a log-normal distribution (Passot Vazquez-Semadeni 1998)."
 The PDF of the logarithm of density. then. will have a normal distribution given by where y=lu(p/p). p dis the mean of the distribution. and 6? is the dispersion. with |u|=07/2.," The PDF of the logarithm of density, then, will have a normal distribution given by where $y \equiv \ln (\rho/\bar{\rho})$, $\mu$ is the mean of the distribution, and $\sigma^2$ is the dispersion, with $|\mu| = \sigma^2/2$."
 Our goal iu this Letter is to analyze the relationship between the mean of the distribution. which represeuts the median density within the cloud. aud the Mach uunber.," Our goal in this Letter is to analyze the relationship between the mean of the distribution, which represents the median density within the cloud, and the Mach number."
 We have investigated this mean-\Mach relation over a range of Mach uunbers 1.2xM<7.0 for both driven lbydrodvuamic and strone-feld ΑΠΟ turbulence., We have investigated this mean-Mach relation over a range of Mach numbers $1.2 \le \mathcal{M} \le 7.0$ for both driven hydrodynamic and strong-field MHD turbulence.
 We found that a resolution of 512? eave «πουher-looking PDFs that could be fitted more accurately than those frou 256? simmlatious. justifving the computational expense.," We found that a resolution of $512^3$ gave smoother-looking PDFs that could be fitted more accurately than those from $256^3$ simulations, justifying the computational expense."
 Higher resolution also allows us to study scatter in the PDF iu sub-voluues of the domain., Higher resolution also allows us to study scatter in the PDF in sub-volumes of the domain.
 We show in Paper I that the simulations have couvereed by this resolution: thus. increasing it further is wulikely to affect the results.," We show in Paper I that the simulations have converged by this resolution; thus, increasing it further is unlikely to affect the results."
 To müiuiuize the influence of mteruütteucyv. we time-average the PDFs obtained from seven suapshots in the saturated state spamming almost 3 dwuamical times before fitting thon.," To minimize the influence of intermittency, we time-average the PDFs obtained from seven snapshots in the saturated state spanning almost 3 dynamical times before fitting them."
 Since the tails of the PDFs will deviate from normal form due to the effects of intermittency. we fit oulv bius with values of at least LOW of the peak value.," Since the tails of the PDFs will deviate from normal form due to the effects of intermittency, we fit only bins with values of at least $10\%$ of the peak value."
 We perform a Levenbere-Alarquardt least-squares fit with uuiforii weighting., We perform a Levenberg-Marquardt least-squares fit with uniform weighting.
 Once we lave obtained the mean. µ. of the best-fit distribution. we plot it against a function of Mach muuber. £M)=lul|aC].," Once we have obtained the mean, $\mu$, of the best-fit distribution, we plot it against a function of Mach number, $\xi(\mathcal{M}) = \ln[1+\alpha\mathcal{M}^2]$."
" With the appropriate choice of a. we can obtain a luear relation between the PDF mean aud this function £(,V()."," With the appropriate choice of $\alpha$, we can obtain a linear relation between the PDF mean and this function $\xi(\mathcal{M})$."
 We note that Ixowal et al. (, We note that Kowal et al. (
2007) have recently shown that higher order statistics can also provide insight iuto the properties of Supersonic turbulence. however iu this Letter we will focus only on the density PDF.,"2007) have recently shown that higher order statistics can also provide insight into the properties of supersonic turbulence, however in this Letter we will focus only on the density PDF."
 Observations show a wide range of star formation rates for different clouds., Observations show a wide range of star formation rates for different clouds.
 To inter frou our sinulatious the level of cloud-to-cloud variation we would likely observe. we also investigate the meau-Alach relation for regious of size comparable to the driving scale.," To infer from our simulations the level of cloud-to-cloud variation we would likely observe, we also investigate the mean-Mach relation for regions of size comparable to the driving scale."
 To do this. we divide our computational domain iuto eight equal sub-domains. cach of resolution 256°.," To do this, we divide our computational domain into eight equal sub-domains, each of resolution $256^3$."
 We compute the PDF in each of these sub-boxes (which we will refer to as sub-PDEs) individually and plot their means against the Mach number within that sub-box., We compute the PDF in each of these sub-boxes (which we will refer to as sub-PDFs) individually and plot their means against the Mach number within that sub-box.
 We do not tinie-average our results. vieldiug 56 mcau-AMach pairs for each run.," We do not time-average our results, yielding 56 mean-Mach pairs for each run."
 Although the suapshots are at iutervals of just wader half a cvnamical time on the elobal scale. the iuterval between snapshots is closer to a flow crossing time on the scale of the sub-boxes. making the snapshots sufficieutlv uncorrelated for our analysis.," Although the snapshots are at intervals of just under half a dynamical time on the global scale, the interval between snapshots is closer to a flow crossing time on the scale of the sub-boxes, making the snapshots sufficiently uncorrelated for our analysis."
 Substantial scatter iu the values within a run nueght help explain the observed cloud-to-cloud variation in the star formation rate in molecular clouds., Substantial scatter in the values within a run might help explain the observed cloud-to-cloud variation in the star formation rate in molecular clouds.
 The time-averaged PDFs over the full domain are very snooth and approximate Ciussiaus. particularly iu the hydro case.," The time-averaged PDFs over the full domain are very smooth and approximate Gaussians, particularly in the hydro case."
 Although we have not plotted such a PDFin this Letter. a similar example can be seen in Figure 3 of Writsuk et al. (," Although we have not plotted such a PDFin this Letter, a similar example can be seen in Figure 3 of Kritsuk et al. ("
2007).,2007).
 Presented ii Table 1. are, Presented in Table \ref{tab:runs} are
dust by vouug stars (Telesco Cezar 1992)).,dust by young stars (Telesco Gezari \cite{telesco9}) ).
" Ii contrast. the bulk of the CO eas is located bevoud ~LO”,"," In contrast, the bulk of the CO gas is located beyond $\sim10''$."
" The gas traced by the ICN molecule resides in very deuse clouds that are better sliclded against the radiation Ποια,", The gas traced by the HCN molecule resides in very dense clouds that are better shielded against the radiation field.
 We have performed high-resolution observations of in the CO (dL 0) line using the Plateau de Bure interferometer., We have performed high-resolution observations of in the $^{13}$ $\rightarrow$ 0) line using the Plateau de Bure interferometer.
 The distribution and kinematics of this molecular species have been derived and analyzed. aud a first comparison is made with existing interferometric data in the lines of πο 30) and 20).," The distribution and kinematics of this molecular species have been derived and analyzed, and a first comparison is made with existing interferometric data in the lines of $^{12}$ $\rightarrow$ 0) and $\rightarrow$ 0)."
 The complex kinematic structure unveiled ia previous studies is confirmed., The complex kinematic structure unveiled in previous studies is confirmed.
 Together with the asvunuetric morphology of the observed distribution of the molecular eas it makes it dificult o 1naintaiu the hypothesis of au edge-on molecular torus. au idea advanced when the first low-resolution sinele-dish maps of the CO eas iu the ceutre of became available.," Together with the asymmetric morphology of the observed distribution of the molecular gas it makes it difficult to maintain the hypothesis of an edge-on molecular torus, an idea advanced when the first low-resolution single-dish maps of the CO gas in the centre of became available."
 We rather propose that what we observe is the signature of a bar. the ceutral (projected) 200 pe portion of which is relatively void of CO eas aud probably subject to strong dissociation.," We rather propose that what we observe is the signature of a bar, the central (projected) 200 pc portion of which is relatively void of CO gas and probably subject to strong dissociation."
 A 130 peavide cunission hole is secu iu our PCO data cube: i coincides with a region of enhanced high-J lines. recombination Hues enüssiou peaks. aud strong frec-free and cmission.," A 130 pc-wide emission hole is seen in our $^{13}$ CO data cube; it coincides with a region of enhanced high-J lines, recombination lines emission peak, and strong free-free and emission."
 It also hosts the young SNR. 11.9|58., It also hosts the young SNR 41.9+58.
 We think that this CO hole reflects a bubble inside which the gas is ionized aud the molecules dissociated., We think that this CO hole reflects a bubble inside which the gas is ionized and the molecules dissociated.
 Maps of several transitions of the rare CO isotopomcrs would be needed to better constrain the cloud properties., Maps of several transitions of the rare CO isotopomers would be needed to better constrain the cloud properties.
 Together with one aresec resolution maps of CO aud IICN. which could be directly compared to the optical pictures. they couk vield a real understanding of how is trigeereao and fueled he most spectacular starburst in the vicinity of the Calaxy.," Together with one arcsec resolution maps of CO and HCN, which could be directly compared to the optical pictures, they could yield a real understanding of how is triggered and fueld the most spectacular starburst in the vicinity of the Galaxy."
 It is a pleasure to thank JJ. Shen anc Ix.Y. Lo for making available to us their 17200(1-0) data from DINLA., It is a pleasure to thank J. Shen and K.Y. Lo for making available to us their $^{12}$ CO(1-0) data from BIMA.
 We are very grateful to the referec. DD. Jalle. for his many helpful suggestions.," We are very grateful to the referee, D. Jaffe, for his many helpful suggestions."
 Ulx is very. indebted to HAN [or the warm hospitality and financial support., UK is very indebted to IRAM for the warm hospitality and financial support.
"If the above scenario is correct, each successive stellar generation would leave a different signature in frequently observed diagnostic planes, such as the [Na/Fe] vs. [O/Fe] diagram.","If the above scenario is correct, each successive stellar generation would leave a different signature in frequently observed diagnostic planes, such as the [Na/Fe] vs. [O/Fe] diagram."
 This diagram is schematically shown in panel g of Figure 1.., This diagram is schematically shown in panel g of Figure \ref{FIGNonMassiveGC}.
" The anticipated impact on the HR diagram is shown in Figure 2,, where our new set of Princeton-Goddard-PUC (PGPUC) isochrones has been used(?)."," The anticipated impact on the HR diagram is shown in Figure \ref{FIGNonMassiveGCIso}, where our new set of Princeton-Goddard-PUC (PGPUC) isochrones has been used."
". A schematic representation of the second stage of the formation of intermediate-mass PSs, which are related to the progenitors of GCs like NGC 2808 (and possibly NGC 2419), is shown in panels b through f of Figure 3,, and can be summarized as follows: In panel g of Figure 3 we show schematically the expected shape of the diagnostic [Na/Fe] vs. [O/Fe] diagram."," A schematic representation of the second stage of the formation of intermediate-mass PSs, which are related to the progenitors of GCs like NGC 2808 (and possibly NGC 2419), is shown in panels b through f of Figure \ref{FIGFairlyMassiveGC}, and can be summarized as follows: In panel g of Figure \ref{FIGFairlyMassiveGC} we show schematically the expected shape of the diagnostic [Na/Fe] vs. [O/Fe] diagram."
 The corresponding HR diagrams for this class of PS are shown in Figure 4.., The corresponding HR diagrams for this class of PS are shown in Figure \ref{FIGFairlyMassiveGCCMD}.
" Figure 5 is a schematic representation of our scenario for massive PSs, which is explained in the following paragraphs."," Figure \ref{FIGMassiveGC} is a schematic representation of our scenario for massive PSs, which is explained in the following paragraphs."
" Here, one can identify w Cen as a prototype of massive PSs — but other posssible examples include M22, M54, and Terzan 5 (see refintro))."," Here, one can identify $\omega$ Cen as a prototype of massive PSs – but other posssible examples include M22, M54, and Terzan 5 (see \\ref{intro}) )."
"The identification of the disk pixels ts made taking into account that most of the pixels outside of the solar disk correspond to black pixels (/,,[/.j]=0).","The identification of the disk pixels is made taking into account that most of the pixels outside of the solar disk correspond to black pixels $I_m[i,j] = 0$ )."
 In this way. we segment the image employing a simple threshold.," In this way, we segment the image employing a simple threshold."
 Note that by applying this threshold the annotation's pixels outside of the disk will also be identified as disk pixels., Note that by applying this threshold the annotation's pixels outside of the disk will also be identified as disk pixels.
 In order to deal with this problem. we search for the feature with the largest area.," In order to deal with this problem, we search for the feature with the largest area."
" To distinguish the magnetic active regions from the quiet Sun. we segment the disk magnetograms (X,,,) employing by a threshold where X, is the intensity level that corresponds to 0 Gauss and Xj,;; 1s the threshold."," To distinguish the magnetic active regions from the quiet Sun, we segment the disk magnetograms $X_{m,p}$ ) employing by a threshold where $X_{m,0}$ is the intensity level that corresponds to 0 Gauss and $X_{m,th}$ is the threshold."
 One example of the binary image resulting from the segmentation is shown in Figure 2cc. White regions represent magnetic active regions. the quiet Sun is shown in black.," One example of the binary image resulting from the segmentation is shown in Figure \ref{FigHMI1}c c. White regions represent magnetic active regions, the quiet Sun is shown in black."
 Next. we perform a connected-component labeling. which ts a method for identifying each object in a binary image.," Next, we perform a connected-component labeling, which is a method for identifying each object in a binary image."
 The connectivity 15 four (4). which means that we search for 4-connected neighborhood.," The connectivity is four (4), which means that we search for 4-connected neighborhood."
 The area of each object. which is employed to classify the objects. is then computed.," The area of each object, which is employed to classify the objects, is then computed."
 We remove objects with small areas (less than 10 pixels)., We remove objects with small areas (less than 10 pixels).
 We identify sunspots (umbrae and penumbrae) m the solar disk intensity images., We identify sunspots (umbrae and penumbrae) in the solar disk intensity images.
 The procedure is similar to the one used to identify magnetic active regions., The procedure is similar to the one used to identify magnetic active regions.
 However. as sunspots are dark features m the solar disk. we search for pixels that are below a given threshold.," However, as sunspots are dark features in the solar disk, we search for pixels that are below a given threshold."
 In order to distinguish umbrae and penumbrae. we apply two thresholds.," In order to distinguish umbrae and penumbrae, we apply two thresholds."
" where X,.9 is the reference level and X.,,. and X,,; are the thresholds for umbrae and penumbrae. respectively."," where $X_{c,0}$ is the reference level and $X_{c,th_u}$ and $X_{c,th_u}$ are the thresholds for umbrae and penumbrae, respectively."
 An example of a binary image obtained is presented in 2dd. The sunspots identified are presented in white., An example of a binary image obtained is presented in \ref{FigHMI1}d d. The sunspots identified are presented in white.
 —| Figure 2ος we observe that bipolar regions oceur in a continuum size spectrum ?.., In Figure \ref{FigHMI1}c c we observe that bipolar regions occur in a continuum size spectrum \cite{harvey1993}.
 However. it is convinient to divide the spectrum into active regions and ephemeral regions.," However, it is convinient to divide the spectrum into active regions and ephemeral regions."
 Here we divide the spectra into four classes according to the filling factors of individual structures. 1.e.. the fraction of the solar dise covered by an individual magnetic structure.," Here we divide the spectra into four classes according to the filling factors of individual structures, i.e., the fraction of the solar disc covered by an individual magnetic structure."
 The classes are determined from the empirical cumulative distribution function (ECDF) of the features identified from Sep/2010 to Dec/2010., The classes are determined from the empirical cumulative distribution function (ECDF) of the features identified from Sep/2010 to Dec/2010.
 Note that the ithe thresholds employed for the segmentation of the imagess are fixed taking into account that the noise should be removed., Note that the ithe thresholds employed for the segmentation of the imagess are fixed taking into account that the noise should be removed.
 The threshold values affect the distribution of the filing factors of individual structures., The threshold values affect the distribution of the filing factors of individual structures.
 In Figure 2ος we observe that bipolar regions occur in a continuum size spectrum 9?.., In Figure \ref{FigHMI1}c c we observe that bipolar regions occur in a continuum size spectrum \cite{harvey1993}.
 However. it is convenient to consider separately the spectral contribution from active regions," However, it is convenient to consider separately the spectral contribution from active regions"
corresponds to a constant rock mass fraction (RAIP) = 0.719.,corresponds to a constant rock mass fraction (RMF) = 0.719.
 At 7=O.1 Gyr. we see that ColtoT-7 b may have started with considerably. more than its current mass.," At $t = 0.1$ Gyr, we see that CoRoT-7 b may have started with considerably more than its current mass."
" For example. ife1. Ad,ini could have been as large as about 9.2 Mg4,5."," For example, if $\epsilon = 1$, $M_{p, init}$ could have been as large as about 9.2 $M_{Earth}$."
 Even for c as small as 0.1. Minis was about 0.5 Meorin larger than My.," Even for $\epsilon$ as small as 0.1, $M_{p, init}$ was about 0.5 $M_{Earth}$ larger than $M_{p, cur}$."
" As time moves forward. dAZ,fd drops. largely as à result of the decrease in fe. and. by assumption. all mass evolution lines converge on Adjcm 5.6 Alpes al E=2.3 Gyr."," As time moves forward, $dM_p/dt$ drops, largely as a result of the decrease in $F_{xuv}$ , and, by assumption, all mass evolution lines converge on $M_{p, cur}$ = 5.6 $M_{Earth}$ at $t = 2.3$ Gyr."
" Though the current mass loss rate is smaller than in the past. for c=1. dM,/dlντ10* ke/s (about 0.4. Mun fxr)."," Though the current mass loss rate is smaller than in the past, for $\epsilon = 1$, $dM_p/dt \sim 7\times10^{7}$ kg/s (about 0.4 $M_{Earth}$ /Gyr)."
 Obviously. smaller c-values eive smaller mass loss rates.," Obviously, smaller $\epsilon$ -values give smaller mass loss rates."
" As time continues into the future. the mass loss rate continues to drop. and for ¢=I. the planet will lose about Ll Alea, in a few billion In such proximity to its host star. tides likely do drive significant orbital migration."," As time continues into the future, the mass loss rate continues to drop, and for $\epsilon = 1$, the planet will lose about 1 $M_{Earth}$ in a few billion In such proximity to its host star, tides likely do drive significant orbital migration."
 Figure 3. illustrates the mass evolution for the same ei; Mou. and (IMP) values as in the previous figure. but this time the calculation includes orbital evolution for a range of stellar ή.," Figure \ref{fig:plot_evol_tide_solid} illustrates the mass evolution for the same $a_{cur}$, $M_{p, cur}$ , and (RMF) values as in the previous figure, but this time the calculation includes orbital evolution for a range of stellar $Q_{*}^{\prime}$ ."
 We can see from this figure that orbital migration plavs an important role in both the planet's past and. Starting again at /= 0.1 Civr ancl moving forward in time.. consider. first⋅ the red lines.+ forB which+ ΟνH=n10'.," We can see from this figure that orbital migration plays an important role in both the planet's past and Starting again at $t =$ 0.1 Gyr and moving forward in time, consider first the red lines, for which $Q_{*}^{\prime} = 10^7$."
 In this case. ColtoT-7 bs orbit changes little: and aii is only about 0.001 AU larger than a...," In this case, CoRoT-7 b's orbit changes little, and $a_{init}$ is only about 0.001 AU larger than $a_{cur}$."
 Fhus. the planet receives more XUV radiation at all points in time than if (Q5 were smaller.," Thus, the planet receives more XUV radiation at all points in time than if $Q_{*}^{\prime}$ were smaller."
 As a consequence. Alpini is larger for larger (Q4.," As a consequence, $M_{p, init}$ is larger for larger $Q_{*}^{\prime}$."
 For example. for «=1 and Q)=107. the planet loses about 4 Aguas between §= 0.1 and 2.3 Gyr.," For example, for $\epsilon = 1$ and $Q_{*}^{\prime} = 10^7$, the planet loses about 4 $M_{Earth}$ between $t =$ 0.1 and 2.3 Gyr."
" By comparison. for εξ Land QC=10"". the total mass lost in the same period is about 3 Alea."," By comparison, for $\epsilon = 1$ and $Q_{*}^{\prime} = 10^6$, the total mass lost in the same period is about 3 $M_{Earth}$ ."
 Thus. the total mass lost by ColtoT-7 b depends on QZ and c.," Thus, the total mass lost by CoRoT-7 b depends on $Q_{*}^{\prime}$ and $\epsilon$."
 Now consider orbital evolution proceeding forward. in ime starting at /= 2.3 Civr., Now consider orbital evolution proceeding forward in time starting at $t =$ 2.3 Gyr.
" Again. by assumption. the mass and orbital evolution lines pass through M, and (tous Ub= 2.3 Grr."," Again, by assumption, the mass and orbital evolution lines pass through $M_{p, cur}$ and $a_{cur}$ at $t =$ 2.3 Gyr."
" ColtoT-Y b's orbit quickly decays. and he planet encounters the stellar surface and is destroyed in ess than 2 billion vears for Q5<10""."," CoRoT-7 b's orbit quickly decays, and the planet encounters the stellar surface and is destroyed in less than 2 billion years for $Q_{*}^{\prime} \le 10^6$."
" In this case. the planet only loses about 0.5. Ades, before it dis. destroved."," In this case, the planet only loses about 0.5 $M_{Earth}$ before it is destroyed."
" For Q),=-10'. orbital. evolution D.is much slower. and the planet oses more mass: for ο=1. about 1.25 Alea, over the next few billion vears."," For $Q_{*}^{\prime} = 10^7$, orbital evolution is much slower, and the planet loses more mass: for $\epsilon = 1$, about 1.25 $M_{Earth}$ over the next few billion years."
 Comparing the e=1 lines in Figures 2 and 3.. we see that the planet loses about 0.25 AMgd) more bv /=10 Cyr with orbital evolution than without.," Comparing the $\epsilon = 1$ lines in Figures \ref{fig:plot_evol_notide_solid} and \ref{fig:plot_evol_tide_solid}, we see that the planet loses about 0.25 $M_{Earth}$ more by $t = 10$ Gyr with orbital evolution than without."
 Also. we see that cdillerent choices of c-values result. in slightly cilferent orbital evolution rates. as indicated by the divergence of the different linestvles in panel (b) of Figure 3..," Also, we see that different choices of $\epsilon$ -values result in slightly different orbital evolution rates, as indicated by the divergence of the different linestyles in panel (b) of Figure \ref{fig:plot_evol_tide_solid}."
" Given the short time ColtoT-7 b has left for Q7«10"". we might conclude that Q5 is much larger."," Given the short time CoRoT-7 b has left for $Q_{*}^{\prime} \le 10^6$, we might conclude that $Q_{*}^{\prime}$ is much larger."
 Otherwise. il nmüght seem unlikely that we would see ColtoT-7 b at all.," Otherwise, it might seem unlikely that we would see CoRoT-7 b at all."
 7? propose a similar argument for the planet WASD-19 b. which also seems on the verge of plummeting into its host star [ον (QJ107.," \citet{2010ApJ...708..224H} propose a similar argument for the planet WASP-19 b, which also seems on the verge of plummeting into its host star for $Q_{*}^{\prime} \le 10^9$."
 On the other αμα. close-in exoplauiets may well be commonly destroved. through orbital decay (?2).. so Cohol-7 b and WASP-19 b may just be next in a long line of planets to be destroved.," On the other hand, close-in exoplanets may well be commonly destroyed through orbital decay \citep{2009ApJ...698.1357J}, so CoRoT-7 b and WASP-19 b may just be next in a long line of planets to be destroyed."
 Although the amount of mass lost by ColtodT-7 b depends on (Q4 and c. the planets. current orbit. mass ancl (ας. as well as its composition. are also important or determining the total mass lost by the planet over its ifetime.," Although the amount of mass lost by CoRoT-7 b depends on $Q_{*}^{\prime}$ and $\epsilon$, the planet's current orbit, mass and radius, as well as its composition, are also important for determining the total mass lost by the planet over its lifetime."
" However. by considering the full range allowed for hese parameters. we can constrain the change in mass and he accompanying change in semi-major Figure 4. shows the range allowed for the mass lost w CobloT-7 b (AM,=AlpiniAMyoue) and the range allowed for (;,;5. as functions of QQ) and c."," However, by considering the full range allowed for these parameters, we can constrain the change in mass and the accompanying change in semi-major Figure \ref{fig:smallest_largest_solid} shows the range allowed for the mass lost by CoRoT-7 b $\Delta M_p = M_{p, init} - M_{p, cur}$ ) and the range allowed for $a_{init}$, as functions of $Q_{*}^{\prime}$ and $\epsilon$."
" In. panel (a). 10 solid. contours show the value for AAL, as a function of Q4 and c. while the dashed. contours showje value."," In panel (a), the solid contours show the value for $\Delta M_p$ as a function of $Q_{*}^{\prime}$ and $\epsilon$, while the dashed contours showthe value."
 ForB example. consider. Q;/=107n2 and €=0-4. values suggested by 2? and the mass loss rate for LID 209458 b (Section. 1). respectively.," For example, consider $Q_{*}^{\prime} = 10^{5.5}$ and $\epsilon = 0.4$ , values suggested by \citet{2008ApJ...678.1396J} and the mass loss rate for HD 209458 b (Section 1), respectively."
" Phat point. lies to yw left of the 72 Alearg,” dashed contour. which indicates re total mass loss cannot exceed 2 Alewan."," That point lies to the left of the “2 $M_{Earth}$ ” dashed contour, which indicates the total mass loss cannot exceed 2 $M_{Earth}$."
 The point also ies to the right of the 70.5 Αμ solid contour. which --ndicates the total mass loss must exceed 0.5. ΑΕ.," The point also lies to the right of the “0.5 $M_{Earth}$ ” solid contour, which indicates the total mass loss must exceed 0.5 $M_{Earth}$."
" lor je same (Q4 ancl cvalues. panel (b) tells us ColtoT-7 b's tina day between 0.022 and 0.024 AU. at least 30 larger lal Coup. In interpreting Figure 4. panel (a). it’s important. to keep in mind that a dashed. contour provides constraints on AAL, only for the region to the left. of the contour. while a solid. contour provides constraints only for the region to the right of the contour."," For the same $Q_{*}^{\prime}$ and $\epsilon$ -values, panel (b) tells us CoRoT-7 b's $a_{init}$ lay between 0.022 and 0.024 AU, at least 30 larger than $a_{cur}$ In interpreting Figure \ref{fig:smallest_largest_solid}, panel (a), it's important to keep in mind that a dashed contour provides constraints on $\Delta M_p$ only for the region to the left of the contour, while a solid contour provides constraints only for the region to the right of the contour."
" For example. consider the region sandwiched between the. dashed Meri” and the solid 70.5 Mews, contours."," For example, consider the region sandwiched between the dashed “1 $M_{Earth}$ ” and the solid “0.5 $M_{Earth}$ ” contours."
 In this region. we can only conclude the change in mass in this region is less than 2 Αρ because it lies to the left of the dashed ο contour.," In this region, we can only conclude the change in mass in this region is less than 2 $M_{Earth}$ because it lies to the left of the dashed “2 $M_{Earth}$ ” contour."
 The contours nearest this region co not cirectly provide constraints on this region., The contours nearest this region do not directly provide constraints on this region.
" Otherwise. we might conclude paracloxically that. in this region. the total mass lost is greater than | Ade, and less than 0.5 Movin."," Otherwise, we might conclude paradoxically that, in this region, the total mass lost is greater than 1 $M_{Earth}$ and less than 0.5 $M_{Earth}$."
 Stilar considerations apply to panel (b). except that constraints from a dashed contour apply to the region the contour. ancl constraints from a solid contour to the region Figure 4— also illustrates how the total mass lost depends on the orbital evolution and. how. to a lesser extent. the orbital evolution depends on the mass. oss.," Similar considerations apply to panel (b), except that constraints from a dashed contour apply to the region the contour, and constraints from a solid contour to the region Figure \ref{fig:smallest_largest_solid} also illustrates how the total mass lost depends on the orbital evolution and how, to a lesser extent, the orbital evolution depends on the mass loss."
 In panel (a). for⋅ smaller ∕€. the contour lines. become more horizontal.," In panel (a), for smaller $Q_{*}^{\prime}$, the contour lines become more horizontal."
 Vhis trend rellects the fact that. for faster orbital evolution. the total mass lost bv ColtoT-7 b depends more sensitively on the chosen Qi-value. as well as on e.," This trend reflects the fact that, for faster orbital evolution, the total mass lost by CoRoT-7 b depends more sensitively on the chosen $Q_{*}^{\prime}$ -value, as well as on $\epsilon$."
 A similar but less pronounced. trend. is evident in panel (b)., A similar but less pronounced trend is evident in panel (b).
 The slight. upward slope of the lines reflects the fact that. [or a fixed. Q-value. larger c-values result in more orbital migration during the planets history.," The slight upward slope of the lines reflects the fact that, for a fixed $Q_{*}^{\prime}$ -value, larger $\epsilon$ -values result in more orbital migration during the planet's history."
" The presence of Coltod-7 c ina nearby orbit. (with a=0.046 AU. ΤΕ) would seem toprovidesome dynamical constraints on the allowed AM,;,;; and e;,;;-values for planet b. We expect that. whatever theoriginal niass and orbit of ColoT-7 b. gravitational interactions between the planets should never have ejectecl either planet from the system or changed the ordering of their orbits. Ze... the systemhas always been dynamically stable."," The presence of CoRoT-7 c ina nearby orbit (with $a = 0.046$ AU \citealt{2009A&A...506..303Q}] ]) would seem toprovidesome dynamical constraints on the allowed $M_{p, init}$ and $a_{init}$ -values for planet b. We expect that, whatever theoriginal mass and orbit of CoRoT-7 b, gravitational interactions between the planets should never have ejected either planet from the system or changed the ordering of their orbits, , the systemhas always been dynamically stable."
Unfortunately no simple criteria have been found that determines whether a given svstem is dvnamicallv stable in this way.,Unfortunately no simple criteria have been found that determines whether a given system is dynamically stable in this way.
 However. based on," However, based on"
"If we adopt an escape rate corresponding to of the LO3 value. ic. a reduction by a factor 100. im order for he planet to reach a Neptune-iass within 1 Covr. the initia mass nist be ΜΗ&18M4, (0.056 A1). as illustrated in Fie. 5..","If we adopt an escape rate corresponding to of the L03 value, i.e. a reduction by a factor 100, in order for the planet to reach a Neptune-mass within $\sim 1$ Gyr, the initial mass must be $m_{\rm i} \simeq 18 \mearth$ (0.056 $\mjup$ ), as illustrated in Fig. \ref{figL100}."
 This corresponds to a ~20% inass loss of he planet envelope., This corresponds to a $\sim 20\%$ mass loss of the planet envelope.
 For this initial mass. our formation nodels predict an envelope chrichment Zi4420.4.," For this initial mass, our formation models predict an envelope enrichment $Z_{\rm env} \simeq 0.4$."
 This abunance of heavy elements strongly cdepeuds ou the treatinent of planctesimal accretion (size of the Ροestaρα. mechanical cestruction im the enveloe. convection in the envelope. see 85.2).," This abundance of heavy elements strongly depends on the treatment of planetesimal accretion (size of the planetesimals, mechanical destruction in the envelope, convection in the envelope, see 5.2)."
 To test how seusitive our evolutionary models are to these issues. we performed a comparison calculation in which we assuued that all the accreted planctesimals sink through the euvelope without mass loss and fall onto the core.," To test how sensitive our evolutionary models are to these issues, we performed a comparison calculation in which we assumed that all the accreted planetesimals sink through the envelope without mass loss and fall onto the core."
 Tn such a model. a plauct with an initial mass of 18 AL). is found to have a core iass of ~ 11 AL). surrounded by an euvelope esscutially composed of IT aud Ue.," In such a model, a planet with an initial mass of 18 $\mearth$ is found to have a core mass of $\sim$ 11 $\mearth$ surrounded by an envelope essentially composed of H and He."
 In that case. the evolutionary properties ave very similar to the ones obtained with our nonüual model (characterized by ων M. aud Zac 70.1) for LUS evaporation rates divided by 100.," In that case, the evolutionary properties are very similar to the ones obtained with our nominal model (characterized by $\mcore$ =6 $\mearth$ and $Z_{\rm enve}$ =0.4) for L03 evaporation rates divided by 100."
 The radius found i the former case is 7 0.55 Ry at LO Cii. instead of 0.6 Ry for the nominal model (solid curve in Fig. 5)).," The radius found in the former case is $\sim$ 0.55 $\rjup$ at 10 Gyr, instead of $0.6$ $\rjup$ for the nominal model (solid curve in Fig. \ref{figL100}) )."
 The different evolutionary sequences are sunamiarized in Table 1.., The different evolutionary sequences are summarized in Table \ref{summary}. .
" Our results predict that if the formation and evolution of a hot-Neptuue. such as the planet around μ-Άτα, sroceeds as described by one of the sequences displayed in Fies. 2-5."," Our results predict that if the formation and evolution of a hot-Neptune, such as the planet around $\mu$ -Ara, proceeds as described by one of the sequences displayed in Figs. \ref{fig2}- \ref{figL100},"
 its radius should be ereater than ~ L6 Ry. regardless of t1 escape rate adopted.," its radius should be greater than $\sim$ 0.6 $\rjup$, regardless of the escape rate adopted."
 Daraffe et al. (, Baraffe et al. (
2005) reached simular conclusions for corcless evolutionary sequences and imaximal escape rate.,2005) reached similar conclusions for coreless evolutionary sequences and maximal escape rate.
 The esent work coufinus tus prediction with more realistic dlanetary structures. cousistent with the core accretiou nodel scenario.," The present work confirms this prediction with more realistic planetary structures, consistent with the core accretion model scenario."
 It is nu)ortant to understand the reason or such a luge radis and thus to disentaugle the various effects. evaporation. imadiation aud heavy element enrichment.," It is important to understand the reason for such a large radius and thus to disentangle the various effects, evaporation, irradiation and heavy element enrichment."
 This is illustrated in Table ο which displavs a few values of the radius of Neptune mass planets evolvedat coustaut mass with cifferent ων aud with or," This is illustrated in Table \ref{neptune}
 which displays a few values of the radius of Neptune mass planets evolvedat constant mass with different $\zenv$ and with or"
How and its subsequent gravitational focusing around. the neutron star.,flow and its subsequent gravitational focusing around the neutron star.
 The accretion. column is. predicted. το be optically thin to Thomson scattering. while the fan beam. photons are produced by exclotron resonance scattering.," The accretion column is predicted to be optically thin to Thomson scattering, while the fan beam photons are produced by cyclotron resonance scattering."
 The overall situation is summarized in the bottom panel of Figure 8 in Scott ct al. (, The overall situation is summarized in the bottom panel of Figure 8 in Scott et al. (
2000). while their Figures 10a-Lob illustrate the evolution of the pulse profiles predicted during the main-on and short-on respectively.,"2000), while their Figures 10a-10b illustrate the evolution of the pulse profiles predicted during the main-on and short-on respectively."
 A number of the features observed. in our data are qualitatively reproduced., A number of the features observed in our data are qualitatively reproduced.
 At 3;=0.17. the hard emission shows two main peaks (LV and 7D)? in Figure 2)). and à third. lower peak ο in Figure 2)).," At $\Phi_{35}=0.17$, the hard emission shows two main peaks (`A' and `B' in Figure \ref{fold}) ), and a third, lower peak (`C' in Figure \ref{fold}) )."
 This situation is close to that. modeled by Scott et al. (, This situation is close to that modeled by Scott et al. (
2000) at similar 35. during the progressive occultation of leading and training peaks of the hard beam.,"2000) at similar $\Phi_{35}$, during the progressive occultation of leading and training peaks of the hard beam."
" At sy,~0.27. when the main components are occulted. we only observe the survival of a broad. underlying modulation that is attributed to the magneto-spheric emission."," At $\Phi_{35} \sim 0.27$, when the main components are occulted, we only observe the survival of a broad, underlying modulation that is attributed to the magneto-spheric emission."
 Since this component is emitted [rom a larger region at some distance from the neutron star. it ds naturally expected to have a lower modulation as well as à broad maximum (Figure 2)).," Since this component is emitted from a larger region at some distance from the neutron star, it is naturally expected to have a lower modulation as well as a broad maximum (Figure \ref{fold}) )."
 The pulse profile close to the short-on is also similar o that. presented. by. Scott ct al. (, The pulse profile close to the short-on is also similar to that presented by Scott et al. (
2000) at ωςz0.58 (sce their. Figure. 10b).,2000) at $\Phi_{35}\approx 0.58$ (see their Figure 10b).
 In. the EPIC data. we can in act recognize à main peak D as well a less prominent »eak ο (Figure 2)).," In the EPIC data, we can in fact recognize a main peak `D' as well a less prominent peak `E' (Figure \ref{fold}) )."
 X cross-correlation between cillerent datasets. does. not. allow a proper. phase alignment between main-on and. short-on peaks based on 16 extrapolation of the pulse timing ephemeris., A cross-correlation between different datasets does not allow a proper phase alignment between main-on and short-on peaks based on the extrapolation of the pulse timing ephemeris.
 However. rvecause the peak “LE is the hardest feature. spectral 'onsiderations suggest that this maximum is associated with 1e small hard. peak and the feature D with the soft peak liscussed by Scott et al. (," However, because the peak `E' is the hardest feature, spectral considerations suggest that this maximum is associated with the small hard peak and the feature `D' with the soft peak discussed by Scott et al. ("
2000).,2000).
" Lf this is the case. ""I7. is vetually due to direct emission from the pencil beam. while D' is the radiation redirected into the fan beam from the antipodal accretion column."," If this is the case, `E' is actually due to direct emission from the pencil beam, while `D' is the radiation redirected into the fan beam from the antipodal accretion column."
 Given the complexity of the. source..— pulse-phase spectroscopy is of paramount importance to separate the dillerent. spectral components observed. in. Lier N-1.," Given the complexity of the source, pulse-phase spectroscopy is of paramount importance to separate the different spectral components observed in Her X-1."
 Using £instein (MeCray et al., Using $Einstein$ (McCray et al.
 1982) and BepposSar data (Oosterbrock et al., 1982) and $BeppoSax$ data (Oosterbroek et al.
 LOOT. 2000) it has been shown that. during the main-on state. the maximum of the thermal component and the power law components are shifted by 250 and that the maximum of the unresolved. feature at ] keV is in phase with that of the blackbody component.," 1997, 2000) it has been shown that, during the main-on state, the maximum of the thermal component and the power law components are shifted by $\sim 250^\circ$ and that the maximum of the unresolved feature at $\sim 1$ keV is in phase with that of the blackbody component."
 The situation is less consistent as far as the 6.4 keV be Ix line is concerned: Choi et al. (, The situation is less consistent as far as the 6.4 keV Fe K line is concerned: Choi et al. (
1994). have shown that its intensity is moclulatecl in phase with the πο emission. sugecsting a common origin for the two Le lines. while Oosterbroek et al. (,"1994) have shown that its intensity is modulated in phase with the soft emission, suggesting a common origin for the two Fe lines, while Oosterbroek et al. ("
2000) have found it correlated with the hard (power law) emission.,2000) have found it correlated with the hard (power law) emission.
 The shift in phase between hard and soft emission can be explained if the latter results [rom re-processing of hard X-rays in the inner part of the accretion disk., The shift in phase between hard and soft emission can be explained if the latter results from re-processing of hard X-rays in the inner part of the accretion disk.
 La non-tilted disk intercepts (and re-processes) a substantial fraction of the hard beam from the neutron star. the expected. phase dilference between direct. ancl rellected. component is 1807.," If a non-tilted disk intercepts (and re-processes) a substantial fraction of the hard beam from the neutron star, the expected phase difference between direct and reflected component is $180^\circ$."
 Therefore. the value of ~250° determined using J£instein andl Bepposar data has been associated: with the clisk having a tilt angle.," Therefore, the value of $\sim 250^\circ$ determined using $Einstein$ and $BeppoSax$ data has been associated with the disk having a tilt angle."
 Hf the tilt of the disk changes with phase along the 35 d evele (as predicted. by the precessing clisk models. see Gerend Bovndon 1976) the shift in phase should therefore vary with 35.," If the tilt of the disk changes with phase along the 35 d cycle (as predicted by the precessing disk models, see Gerend Boyndon 1976) the shift in phase should therefore vary with $\Phi_{35}$ ."
 However. both Einstein and Sax data were obtained at the same ως Le. during the main-on state (ως=0.1 for Einstein: a;=0.007O15 [or Bepposar in 1997 and «an=OL0.2 lor Bepposar in 2000).," However, both Einstein and Sax data were obtained at the same $\Phi_{35}$, i.e. during the main-on state $\Phi_{35} =0.1$ for $Einstein$; $\Phi_{35} =0.07-0.15$ for $BeppoSax$ in 1997 and $\Phi_{35} =0.1-0.2$ for $BeppoSax$ in 2000)."
 Oosterbroek οἱ al. (, Oosterbroek et al. (
2000) also observed the source at us=0.5 and found that the pulse phase dillerence in 10 short-on and main-on state are consistent.,2000) also observed the source at $\Phi_{35} =0.5$ and found that the pulse phase difference in the short-on and main-on state are consistent.
 This is not surprising. since symmetry considerations allow for the same behaviour at $55;=0.0 and 0.5.," This is not surprising, since symmetry considerations allow for the same behaviour at $\Phi_{35} =0.0$ and 0.5."
 A tracking of the phase ilference between the two components over the entire evcle was therefore required., A tracking of the phase difference between the two components over the entire cycle was therefore required.
 llere. we have found that not. only the phase shift erived. from. main-on data is considerably ilferent. from. previous observations made in the main-on. rut it continues to change dramatically curing the other two observations.," Here we have found that not only the phase shift derived from main-on data is considerably different from previous observations made in the main-on, but it continues to change dramatically during the other two observations."
 This suggests that we are observing. for the irst time. adisk. which is what we would expect. [rom a svstem which had a precessine accretion dise.," This suggests that we are observing, for the first time, a, which is what we would expect from a system which had a precessing accretion disc."
" Lt should. be noted hat the interpretation of the phase shift observed at the short-on may. be alfected. by a systematic error. depending on whether during the observation the soft peak D"" is higher han the small hard. peak “LE” or vice-versa (see τι)."," It should be noted that the interpretation of the phase shift observed at the short-on may be affected by a systematic error, depending on whether during the observation the soft peak `D' is higher than the small hard peak `E' or vice-versa (see \ref{enres}) )."
 ‘To investigate in more detail the possible common origin of the soft component and the Fe line at 6.4 keV. we have derived the line parameters as a function of the spin phase. Oxpin (SCC 6 and Figure 5)).," To investigate in more detail the possible common origin of the soft component and the Fe line at 6.4 keV, we have derived the line parameters as a function of the spin phase, $\phi_{spin}$ (see \ref{pulsespec} and Figure \ref{fitph}) )."
 At &35=0.26 and 0.60. there is little evidence for a significant variation in the line parameters.," At $\Phi_{35}$ =0.26 and 0.60, there is little evidence for a significant variation in the line parameters."
" The observation made during the main-on (Φως 0.17) clearly shows that the soft [flux below 0.7 keV and the equivalent width all exhibit a common minimum. at 0.20,,,,00.4. which. in turn. is shifted with respect to that of the hard emission."," The observation made during the main-on $\Phi_{35}=0.17$ ) clearly shows that the soft flux below 0.7 keV and the equivalent width all exhibit a common minimum at $\phi_{spin}$ 0.4, which, in turn, is shifted with respect to that of the hard emission."
 This supports the idea that the 6.4 keV Le line originates from lluorescence from the relatively cold matter of the illuminated. spot where the soft. emission is reprocessed., This supports the idea that the 6.4 keV Fe line originates from fluorescence from the relatively cold matter of the illuminated spot where the soft emission is reprocessed.
 In this case. the [lux emitted in the line may provide a lower limit to the size of the spot because the observed line energy allows us to put an upper limit to the ionization degree and to the temperature of the emitting region. 70.3 keV Csallman AleCray 1982).," In this case, the flux emitted in the line may provide a lower limit to the size of the spot because the observed line energy allows us to put an upper limit to the ionization degree and to the temperature of the emitting region, $T$ 0.3 keV (Kallman McCray 1982)."
 This is in principle appealing since it allows us to constrain the size of the illuminated spot in a way which is lesssubject to absorption (compared with the usual methods based on the value of the soft flux)., This is in principle appealing since it allows us to constrain the size of the illuminated spot in a way which is lesssubject to absorption (compared with the usual methods based on the value of the soft flux).
 However. assuming a spherical spot," However, assuming a spherical spot"
plugged with the maximum ones.,plugged with the maximum ones.
 Compared with the KN frequency we have LEND»n4. then reach the conclusion that the synchrotron self-absorption ts negligible.," Compared with the KN frequency we have $\nukn_\ob\gg\nu_a$, then reach the conclusion that the synchrotron self-absorption is negligible."
 There are uncertainties in the afterglow model parameters. especially for the poorly constrained eg. which is usually coupled with 7 in the afterglow modelling.," There are uncertainties in the afterglow model parameters, especially for the poorly constrained $\eps_B$, which is usually coupled with $n$ in the afterglow modelling."
 We should scan all the possible parameter space., We should scan all the possible parameter space.
 However. when IC cooling is important and KN correction is important to IC cooling. the electron distribution (after cooling modified) and synchrotron spectrum become quite complicated compared to the cases when synchrotron cooling dominates or IC scattering takes place in Thomson limit (e.g..Nakaretal.2009;Wang2009. 2010).," However, when IC cooling is important and KN correction is important to IC cooling, the electron distribution (after cooling modified) and synchrotron spectrum become quite complicated compared to the cases when synchrotron cooling dominates or IC scattering takes place in Thomson limit \citep[e.g.,][]{nakar09,wz09,wang10}."
. It is better to pin down some relations between the characteristic frequencies in the spectrum. and cancel the other cases in the parameter space.," It is better to pin down some relations between the characteristic frequencies in the spectrum, and cancel the other cases in the parameter space."
 As we are going to consider the >100 MeV emission of 10°s scale in GRBs 080916C and 090902B (with isotropic equivalent gamma-ray energy E. of order 10°terg) and of 1019 scale in GRB090510 (E.~ IOPerg). we will consider only two eases with (E.r)=(IOerg.101) and (DOSerg.1079).," As we are going to consider the $>100$ MeV emission of $10^3$ s scale in GRBs 080916C and 090902B (with isotropic equivalent gamma-ray energy $E_\gamma$ of order $10^{54}$ erg) and of $10^2$ s scale in GRB090510 $E_\gamma\sim10^{53}$ erg), we will consider only two cases with $(E,t)=(10^{54}{\rm erg},10^3{\rm s})$ and $(10^{53}{\rm erg},10^2{\rm s})$."
" In. these. two cases. with the presumed parameter ranges mentioned in refsec:assume.. we examine the above calculations and find the followings are always satisfied. and Depending on the relation between ο and 7. there aretwo regimes for the bulk postshock injected electrons: ""slow cooling"" regime with 14,—74 and ""fast cooling"" regime with Usvy."," In these two cases, with the presumed parameter ranges mentioned in \\ref{sec:assume}, we examine the above calculations and find the followings are always satisfied, and Depending on the relation between $\nu_m$ and $\nu_c$, there aretwo regimes for the bulk postshock injected electrons: ""slow cooling"" regime with $\nu_m<\nu_c$ and ""fast cooling"" regime with $\nu_c<\nu_m$."
" Consider the critical case when v,,=7. then the synchrotron emission is peaking atiC1)."," Consider the critical case when $\nu_m=\nu_c$, then the synchrotron emission is peaking at$\nu_m(=\nu_c)$."
" Given vkN> 1. the IC scattering does not suffer KN suppression. and if only single IC scattering is considered. then Y,,=Y.(e./e,)!: (Sar&Esim20010... which substituted into eq.(13)). and Vy,=, leads to a critical ej value For eg<€p,4 electrons are slow cooling. and vice verse."," Given $\nukn_m>\nu_m$ , the IC scattering does not suffer KN suppression, and if only single IC scattering is considered, then $Y_m=Y_c=(\eps_e/\eps_B)^{1/2}$ \citep{se01}, which substituted into \ref{eq:nuc}) ) and $\nu_m=\nu_c$ leads to a critical $\eps_B$ value For $\eps_{B}<\eps_{B,\rm cr}$ electrons are slow cooling, and vice verse."
" As the wide parameter space may allow both regimes to happen. in what follows we derive Y, in these two regimes separately."," As the wide parameter space may allow both regimes to happen, in what follows we derive $Y_\ob$ in these two regimes separately."
" In this case the 7f,, spectrum of the synchrotron radiation peaks at 1. Le. the total energy density in. synchrotron photons is tyyn©umC1)."," In this case the $\nu f_\nu$ spectrum of the synchrotron radiation peaks at $\nu_c$, i.e., the total energy density in synchrotron photons is $u_{\rm ph,syn}'\approx u_{\rm ph}'(<\nu_c)$."
 Let us first derive Y.., Let us first derive $Y_c$.
" As only the electrons with 57€>>!/ efficiently cool. let us denote i)=(74/1,7*7«| the fraction of postshock injected electron energy that is rapidly radiated 2001)."," As only the electrons with $\gamma_e'>\gamma_c'$ efficiently cool, let us denote $\eta\equiv(\nu_m/\nu_c)^{(p-2)/2}<1$ the fraction of postshock injected electron energy that is rapidly radiated \citep{se01}."
. If pz2 then the value of 4) is usually order of unity., If $p\approx2$ then the value of $\eta$ is usually order of unity.
" A lower limit can be obtained by taking Y,2O. then eqs. (11) "," A lower limit can be obtained by taking $Y_c=0$, then eqs. \ref{eq:num}) )"
and (13)) implies jj>0.4(E3465κεΕαν). for pz2.2.," and \ref{eq:nuc}) ) implies $\eta>0.4(E_{54}\eps_{B,-5}^2\eps_{e,-1}^2f_p^2n_0/t_3)^{0.1}$ for $p=2.2$."
" As the synchrotron spectrum follows f,X7V3 at p. Xi—py2 ab,<w<<. and then decreases with v above 7."," As the synchrotron spectrum follows $\nu f_\nu\propto \nu^{4/3}$ at $\nu<\nu_m$, $\propto\nu^{(3-p)/2}$ at $\nu_m<\nu<\nu_c$, and then decreases with $\nu$ above $\nu_c$."
 The spectralshape above r. is affectedby KN correction. but is not interested to this work.," The spectralshape above $\nu_c$ is affectedby KN correction, but is not interested to this work."
" Following Wangetal.(2010).. we can set up equations for ¥.. depending on the relations between ve"".KN 1, and 14: where. assuming 1f, 1/777*7 for v>1. the correction factors are. approximately. c,©£—pyp—2) if VENο.Mo 2%p—2ME vyRmLEN«p and es=Dif peopEN."," Following \cite{wang10}, we can set up equations for $Y_c$, depending on the relations between $\nukn_c$ , $\nu_m$ and $\nu_c$: where, assuming $\nu f_\nu\propto\nu^{-(p-2)/2}$ for $\nu>\nu_c$ , the correction factors are, approximately, $c_1\approx{3\over8}(3-p)(p-2)$ if $\nukn_c<\nu_m\ll\nu_c$ , $c_2\approx p-2$if $\nu_m\ll\nukn_c<\nu_c$ and $c_3\approx1$ if $\nu_c\ll\nukn_c$."
 Now substituting eqs. (11)). (13) ," Now substituting eqs. \ref{eq:num}) ), \ref{eq:nuc}) )"
and (14)) into eq.(22)). Y; can be solved out.," and \ref{eq:oc}) ) into \ref{eq:slowcoolingYc}) ), $Y_c$ can be solved out."
 Since inthe parameter space that we concern. we have conditions of eqs. (19))," Since inthe parameter space that we concern, we have conditions of eqs. \ref{eq:cond1}) )"
 and (20)). there are only several interesting cases for Yop: where the correction factors are approximately c4~] if 1LEN«VESyy cs zmi&G-m if LEN.«EN.ZO. and cg©μ.ο.z(3—ρερ- If iSobKNπμνοας," and \ref{eq:cond2}) ), there are only several interesting cases for $Y_\ob$: where the correction factors are approximately $c_4\approx1$ if $\nukn_\ob<\nukn_c<\nu_m\ll\nu_c$ $c_5\approx{3\over8}(3-p)$ if $\nukn_\ob<\nu_m\ll\nukn_c<\nu_c$, and $c_6\approx{3\over8}(3-p)(p-2)$ if $\nukn_\ob<\nu_m\ll\nu_c\ll\nukn_c$."
" For the case with the lowest eg value allowed. eg=1075. and with the other parameters beingEs,2£1272066,=I. the condition for slow cooling regime is maremally satisfied. €pSa."," For the case with the lowest $\eps_B$ value allowed, $\eps_B=10^{-5}$, and with the other parameters being$E_{54}=t_3=n_0=\eps_{e,-1}=1$, the condition for slow cooling regime is marginally satisfied, $\eps_B\la\eps_{B,\rm cr}$."
 We derive ἕωμ to be. as shown in Appendix. where p2 is used when p appears in indices.," We derive $Y_\ob$ to be, as shown in Appendix, where $p=2$ is used when $p$ appears in indices."
 We neglect the redshift effect so far., We neglect the redshift effect so far.
 Considering this effect. Le. voyPaἜσ) απά »r/(bI. the rh.s.," Considering this effect, i.e., $\nu_\ob\rightarrow\nu_\ob(1+z)$ and $t\rightarrow t/(1+z)$, the r.h.s."
 of eq. (24)), of eq. \ref{eq:Yob_eq:eB=1e-5}) )
 should be multiplied by (14-2)9., should be multiplied by $(1+z)^{-7/6}$.
" When ej>ep, is satisfied. we have vy.«14, (45« 51)."," When $\eps_B>\eps_{B,\rm cr}$ is satisfied, we have $\nu_c<\nu_m$ $\gamma_c'<\gamma_m'$ )."
 This means all the postshock injected electron energy ts radiated rapidly. 7)=1.," This means all the postshock injected electron energy is radiated rapidly, $\eta=1$."
" Since in the parameter space we are interested we have pENsopa. the electrons with 27=57, do not suffer KN suppression in IC scattering the synchrotron photons. and the synchrotron vf, spectrum is peaking at τη."," Since in the parameter space we are interested we have $\nukn_m>\nu_m$, the electrons with $\gamma_e'=\gamma_m'$ do not suffer KN suppression in IC scattering the synchrotron photons, and the synchrotron $\nu f_\nu$ spectrum is peaking at $\nu_m$ ."
" Now that 7,4;7 , we have v8%>(BNs pu ie. electrons around >/ even have less KN correction in IC scattering synchrotron photons."," Now that $\gamma_m>\gamma_c$ , we have $\nukn_c>\nukn_m>\nu_m$ , i.e., electrons around $\gamma_c'$ even have less KN correction in IC scattering synchrotron photons."
" In this case. the electron distribution at .—,<+,, still follows the result derived in Thomson limit. dn,οικ (Sari 2001).."," In this case, the electron distribution at $\gamma_c<\gamma_e<\gamma_m$ still follows the result derived in Thomson limit, $dn_e/d\gamma_e\propto\gamma_e^{-2}$ \citep{se01}. ."
" Therelevant synchrotron spectrum vfollowsUhκpMVS ate«ops xwpU ates<< pQ and then turnover"" napeat ο.withHu Un/sgALUSC» η)."," Therelevant synchrotron spectrum follows$\nu f_\nu\propto\nu^{4/3}$ at $\nu<\nu_c$, $\propto\nu^{1/2}$ at $\nu_c<\nu<\nu_m$ , and then turnover at $\nu_m$,with $u'_{\rm ph,syn}\approx u'_{\rm
ph}(<\nu_m)$ ."
" WithoutH KN effect.CCau the Compton parameter Y,,of electrons with / is still the same as the solution inThomson limit (Sari&Esin+,, 2001).. Using the spectral form of synchrotron radiation and depending on the relations of vSob with v. and τμ. the"," Without KN effect, the Compton parameter $Y_m$of electrons with $\gamma_m'$ is still the same as the solution inThomson limit \citep{se01}, , Using the spectral form of synchrotron radiation and depending on the relations of $\nukn_\ob$ with $\nu_c$ and $\nu_m$ , the"
"intermediate metallicity) objects with blue horizontal branches can have auy vaue of e, whereas nearly round clusters all have red horizontal braneies.","intermediate metallicity) objects with blue horizontal branches can have any value of $\epsilon$, whereas nearly round clusters all have red horizontal branches."
 A better way to look iuto this problem is provide by using the larecr axd amore recent sample of € ar| WB-inedes values Lised by Mackey va1 deu Bergh., A better way to look into this problem is provided by using the larger and more recent sample of $\epsilon$ and HB-index values listed by Mackey van den Bergh.
 Their IB iudex is defined as CD-R)/DB|VR) in which D is the umber of stars that Be to the blue of ITB instability strip. V is the unniber of stars in this strip. ane Rois the umuber of «ars to the red of the horizontal braich instanlity strip.," Their HB index is defined as (B-R)/B+V+R) in which B is the number of stars that lie to the blue of HB instability strip, V is the number of stars in this strip, and R is the number of stars to the red of the horizontal branch instability strip."
" Ator onittiug (1) lighly redderκα clusters with Ay.> 1.0 mag (for which he apparent flattening nieht )o due to asvinunuetrie redd:q1nuej.(2)1 itriusically faint clusters M,> -6.0 (n swich fattening ueasureimenuts are iutrinsically uncertaüu because of low total stelar conent). aud (3) w Ceu and M51 (ανuch ndsit he strippce ealaxy cores). one obtaius a sample of 51 Calactic globular clusters."," After omitting (1) highly reddened clusters with $A_{v} >$ 1.0 mag (for which the apparent flattening might be due to asymmetric reddening),(2) intrinsically faint clusters $M_{v} >$ -6.0 (in which flattening measurements are intrinsically uncertain because of low total stellar content), and (3) $\omega$ Cen and M54 (which might be stripped galaxy cores), one obtains a sample of 54 Galactic globular clusters."
 alt of these custers have a jiorizoutal branch iudex < 10.6 and ialf of them Lave ali IID-iudex |0.6., Half of these clusters have a horizontal branch index $<$ +0.6 and half of them have an HB-index $>$ +0.6.
 A IlKolinogorov-Suiruov test shows twat there is no statistically siguficaut difkrence beween the ellipticitv distributions of the Galactic oelobular clusters with red aud with bτο 10rizonta branches., A Kolmogorov-Smirnov test shows that there is no statistically significant difference between the ellipticity distributions of the Galactic globular clusters with red and with blue horizontal branches.
 Since the preseut sample is exactly twice as aree as that used by Norris if is concluled that his restIt. which was siguificaibat the level. was xobablv due to the well-uown perversity of sinalLiunuber statistics.," Since the present sample is exactly twice as large as that used by Norris it is concluded that his result, which was significant at the level, was probably due to the well-known perversity of small-number statistics."
 Iu lis origina] paper Norris considered. oulv those elobular clusters with intermicejate metallicities in the range 1.1 < [FeTT & -1.9., In his original paper Norris considered only those globular clusters with intermediate metallicities in the range 1.4 $\leqslant$ [Fe/H] $\leqslant$ -1.9.
 If oue applies he same restriction to the siuuple discussed above fheu one is left with oulv 29 chsters., If one applies the same restriction to the sample discussed above then one is left with only 29 clusters.
 For these objects a Ίντο test againoO shows uo significantoO differeuce between the flattenme distributions of the clusters with « 10.6 aud IIDB-1ndex > |0.6., For these objects a K-S test again shows no significant difference between the flattening distributions of the clusters with HB-index $<$ +0.6 and HB-index $>$ +0.6.
 It is therefore concluded that the best preseulv available data provide no evidence to support the couclusion by Norris (1983) that the flattening of Caactic elobular clusters is correlated with their horizoutal brauch morphology., It is therefore concluded that the best presently available data provide no evidence to support the conclusion by Norris (1983) that the flattening of Galactic globular clusters is correlated with their horizontal branch morphology.
 About a quarter of all elobular clusters exhibit au unusually extended horizoutal brauch: (Lee οἳ al., About a quarter of all globular clusters exhibit an unusually extended horizontal branch (Lee et al.
 2007)., 2007).
" This ""blue hook” morphology probably indicates that such clusters had au unusual evolutionary historv.", This “blue hook” morphology probably indicates that such clusters had an unusual evolutionary history.
 Ou averageg these clusters are of above-average8 Iuniuositv., On average these clusters are of above-average luminosity.
 A comparison between the distribution ∪↕⋟↑∐↸∖↴∖↴⋯⋜↧∐↻∪↻∏↕⋜↧↑↕∪∐∪↕⋟∐↑↑↕↸∖↥⋅↸∖≺∐∐∖∐↸∖≺∏⋝↕⋯∖∐∪∪↨↘↽↸⊳↕∏↴∖↴↑↸∖↥⋅↴∖↴↖↖↽↕↑∐⋜↧↴∖↴↕↕⊔∐⋜∐⋅↻∪↻∏↕⋜↧↑↕∪∐∪↕≯↕⋯⊔↕∐∪∏↴∖↴∶↴∙⊾↕∪↴⋝∏↕⋜∐⋅↴∖↴ ↖↖⇁↕↑∐∐∪↥⋅⋯⋜↧↕∐∪∏∑∪∐↑⋜↧↕↴⋝↥⋅⋜⋯↸⊳∐↸∖↴∖↴↴∖↴∐∪↖↖⇁↴∖↴∐∪↴∖↴↑⋜↧↑↕↴∖↴↑↕↸⊳⋜↧∐⋅↖↽↴∖↴↕∶↴∙⊾∐↕∱∎⊔⊳⋜⋯↑≼∐↕−↥⋅↸∖↥⋅↸∖∐↸⊳↸∖↕∐↑, A comparison between the distribution of the small population of little reddened blue hook clusters with a similar population of luminous globulars with normal horizontal branches shows no statistically significant difference in the distribution of cluster flattenings.
↕∐∖≼∐↴∖↴⊓⋅∏⋝∏↑↕∪∐∪↕⋟↸⊳↕∏↴∖↴↑↸∖↥⋅ ∏⋜↧↑↑↸∖∐↕∐∶↴∙∷∖↴∙↕↑↴∖↴∐∪∏∐∙↕↓∪↖↖↽↸∖↖↽↸∖↥⋅∙↴⋝↸∖↸∖∐∏≻∐⋜↧↴∖↴↕," It should, however, be emphasized that this conclusion is based on small samples."
∑↸∖≼⇂↑∐⋜↧↑↑↕∐↴∖↴↸⊳∪∐↸⊳↕∏↴∖↴↕∪∐↕↴∖↴↴⋝⋜↧↴∖↴↸∖≼↧∪∐↴∖↴⋯⋜↕∐↴∖↴⋜⋯∏≻↕↸∖↴∖↴∙ Data in the larger dataose that is now available do not confirma Norris's (4983) surprising conclusion that the flattenius of Galactic οobular clusters correlaes with their horizoutal brauc1 iiorphologv., Data in the larger database that is now available do not confirm Norris's (1983) surprising conclusion that the flattening of Galactic globular clusters correlates with their horizontal branch morphology.
" Furthermore it is found that there is no cditfference between tlic| flattesine distributions ainom© old halo. vouug halo iux bulee/disk clusters (as «chiic by Mackeyv vau clen Beveh (2005),"," Furthermore it is found that there is no difference between the flattening distributions among old halo, young halo and bulge/disk clusters (as defined by Mackey van den Bergh (2005)."
 Finally t1e present data strengthen ai confirm the conclusion o Davoust Prueniel (199n tha huninous Galactic ek)bular clusters are. ou average. rounder than are less nui1οιs elobular clusters.," Finally the present data strengthen and confirm the conclusion of Davoust Prugniel (1990) that luminous Galactic globular clusters are, on average, rounder than are less luminous globular clusters."
 Iu this respect the Galaxy appears to resenibles MI iux NOC 5128. but differs frou the Alagellanic Clotds (Freuk Fall 1982. Vall den Bergh 1983a. CGoodewiu 1997).," In this respect the Galaxy appears to resembles M31 and NGC 5128, but differs from the Magellanic Clouds (Frenk Fall 1982, van den Bergh 1983a, Goodewin 1997)."
 The reasous for tLOSE ¢iference are presenly no understood., The reasons for these difference are presently not understood.
" The coichsions listed above could be ercatly strenetiened by oltaining values for Galactic globular clusDES with 4, 1 Oat infrarec wavelengths.", The conclusions listed above could be greatly strengthened by obtaining values for Galactic globular clusters with $A_{v} >$ 1.0 at infrared wavelengths.
 81ich fatteniiie (letermunatious woud be uuch less affected by pachy foregrouid absorption than are existi15 leastPOMCits at shorter wavecneths., Such flattening determinations would be much less affected by patchy foreground absorption than are existing measurements at shorter wavelengths.
 however. such ineasurements will rot provide a panacea because the inewes of clusters in the iutra-recd are strongly afecte by small uunbers of cool rec stars. whereas the imacss of clusters in blue liel: previde more nearly COLLxrable coutributlous from rec eqauts aud blue horizonal brauch stars.," However, such measurements will not provide a panacea because the images of clusters in the infra-red are strongly affected by small numbers of cool red stars, whereas the images of clusters in blue light provide more nearly comparable contributions from red giants and blue horizontal branch stars."
 It would also be of interest to obtain flattening oservations of elobular clusters in other nearby dwarf galaxies., It would also be of interest to obtain flattening observations of globular clusters in other nearby dwarf galaxies.
 Such observations wieght allow oue to see 1 they exhibi, Such observations might allow one to see if they exhibit
the unclear mass also correlates with the overall mass of a galaxy (Ferrarese et al.,the nuclear mass also correlates with the overall mass of a galaxy (Ferrarese et al.
 2006: Tlopkins et al., 2006; Hopkins et al.
 2007)., 2007).
 These results all indicate that the unclear mass in a ealaxy is intimately connected to the dynamics of its disk and halo., These results all indicate that the nuclear mass in a galaxy is intimately connected to the dynamics of its disk and halo.
" If so. then it is not suprising that o, iu our sample of barred galaxies is correlated with Q, or zo."," If so, then it is not suprising that $\sigma_{e}$ in our sample of barred galaxies is correlated with $Q_g$ or $A_{2}$."
 It suggests that the erowth of a central mass aud evolution of the bar for spiral galaxies may be closely linked., It suggests that the growth of a central mass and evolution of the bar for spiral galaxies may be closely linked.
 Our results have important inplications for the secular evolution of barred galaxies., Our results have important implications for the secular evolution of barred galaxies.
 Simulations siegeVA+ that there may be several factors responsible for the dissolution of a bar., Simulations suggest that there may be several factors responsible for the dissolution of a bar.
 One is the CAIC erowth (asa Norman 1990: Friedl Ptfenniecr 1991) which weakens the bar-upportiug «c4 orbits aud increases the raction of chaotic orbits in the ealaxy ceuter., One is the CMC growth (Hasan Norman 1990; Friedli Pfenniger 1991) which weakens the bar-supporting $x_1$ orbits and increases the fraction of chaotic orbits in the galaxy center.
 Secoud is the inflow of gas towards the galaxy. center which results in the transfer of angular momentum to the uw wave which then weakens the bar itself (Bournaud. Combes Semeliu 2005).," Second is the inflow of gas towards the galaxy center which results in the transfer of angular momentum to the bar wave which then weakens the bar itself (Bournaud, Combes Semelin 2005)."
 The buckling instability is au iuportant bar thickening mechauisu that results in a )oxv/peauut bulge which cau temporarily weaken a bar (Raha et al., The buckling instability is an important bar thickening mechanism that results in a boxy/peanut bulge which can temporarily weaken a bar (Raha et al.
 1991: Bereutzen et al., 1991; Berentzen et al.
 1998: Athanassoula Alisiviotis 2002: Martiuez-Valpuesta. Shlosuiu Ueller 2006: Debattista et al.," 1998; Athanassoula Misiriotis 2002; Martinez-Valpuesta, Shlosman Heller 2006; Debattista et al."
 2006)., 2006).
 All these effects result iu a 1uore massive and dvnanucally hotter ceutral conrponeut and a weaker bar., All these effects result in a more massive and dynamically hotter central component and a weaker bar.
 The correlatious that we see in Figures 1 aud 2 may be observational incdicatious of this ongoing evolution., The correlations that we see in Figures 1 and 2 may be observational indications of this ongoing evolution.
" In particular. while the appareut drop of Q, with ceutral velocity dispersion night be an artifact caused by the bulge dilution effect (sce Laurikainen. Salo Buta 2001: a bias could follow sjuce nuclear velocity dispersion and bulge mass are strouglv correlated). the simular correlation between the bar intensity contrast “lo suggest that the effect is real."," In particular, while the apparent drop of $Q_g$ with central velocity dispersion might be an artifact caused by the bulge dilution effect (see Laurikainen, Salo Buta 2004; a bias could follow since nuclear velocity dispersion and bulge mass are strongly correlated), the similar correlation between the bar intensity contrast $A_2$ suggest that the effect is real."
 The found correlation between A» aud σι MEL also consistent with Das ct al. (, The found correlation between $A_2$ and $\sigma_e/v_g$ is also consistent with Das et al. (
2003) who found that the bar ellipticitv (closely related. to Ae) drops with central mass concentration.,2003) who found that the bar ellipticity (closely related to $A_2$ ) drops with central mass concentration.
 The evolution of bars by secular processes im galaxies Is an dssue which is expected to gain more attention iu the near future., The evolution of bars by secular processes in galaxies is an issue which is expected to gain more attention in the near future.
 Recent observational evidence shows that the fraction of strong bars in bright salaxies increases from under at redshift z=0.81 to about in the local universe (Sheth et 2007)., Recent observational evidence shows that the fraction of strong bars in bright galaxies increases from under at redshift z=0.84 to about in the local universe (Sheth et 2007).
 Also. it has been shown by (Laurikainen ct al.," Also, it has been shown by (Laurikainen et al."
 2007) that among the carly-type barred galaxies the bulge-to-total flux ratios are on average smaller than in the uou-barred galaxies., 2007) that among the early-type barred galaxies the bulge-to-total flux ratios are on average smaller than in the non-barred galaxies.
 These results. together with ours. may indicate that bars evolve with their parent galaxies.," These results, together with ours, may indicate that bars evolve with their parent galaxies."
 This research Las mace use of the NASA/TPAC Infrared Science Archive (NED). which is operated bv the JPL. California Institute of Technology. uuder coutract with NASA.," This research has made use of the NASA/IPAC Infrared Science Archive (NED), which is operated by the JPL, California Institute of Technology, under contract with NASA."
 We also acknowledge the usage of the ILvperLeda database (http://leda.univ-Ivonl.fr)., We also acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).
 R.D. is supported by NSF eraut AST 05-07110., R.B. is supported by NSF grant AST 05-07140.
 E.L aud ILS acknowledge the support by the Academy of Fiulaud., E.L and H.S acknowledge the support by the Academy of Finland.
 ," \nocite{*}
 "
"Rfriena(Z=0.5) 2.8 Mpch-* and Ufriend(zZ=0.5) 900 kms""! after which clusters are merged together creating highly unphysical structures.",$R_{friend}(z=0.5) = $ 2.8 Mpc$h^{-1}$ and $v_{friend}(z=0.5) = $ 900 $^{-1}$ after which clusters are merged together creating highly unphysical structures.
" This sets an upper limit on both of the parameters, although we would intuitively expect the value of Rfriena(z=0.5) to be much lower."," This sets an upper limit on both of the parameters, although we would intuitively expect the value of $R_{friend}(z=0.5)$ to be much lower."
" For vfriend(z=0.5)> 400 kms the catalogue is fully complete in the range 0.35<Rfriena(z!,=0.5) 0.87 Mpc h! and fully pure out to Ryriena(z=0.5) 0.28 Mpc h! for both the unique and non-unique regimes."," For $v_{friend}(z=0.5) > $ 400 $^{-1}$, the catalogue is fully complete in the range $ 0.35 < R_{friend}(z=0.5) < $ 0.87 Mpc $h^{-1}$ and fully pure out to $R_{friend}(z=0.5) = $ 0.28 Mpc $h^{-1}$ for both the unique and non-unique regimes."
" Since Reriena(z=0.5) has a greater effect on the completeness and purity, we can fix vfriena(z=0.5) to the limit imposed by the top panel of fig.4 and examine how the completeness and purity vary with just Rriena(z=0.5)."," Since $R_{friend}(z=0.5)$ has a greater effect on the completeness and purity, we can fix $v_{friend}(z=0.5)$ to the limit imposed by the top panel of \ref{fig:rfriends00} and examine how the completeness and purity vary with just $R_{friend}(z=0.5)$."
" Fig.5 shows the variations in completeness and purity as a function of Rriena(z=0.5) for different richness cuts using a fixed value of Vfriena(z=0.5) 900 kms""", \ref{fig:pure_test} shows the variations in completeness and purity as a function of $R_{friend}(z=0.5)$ for different richness cuts using a fixed value of $v_{friend}(z=0.5) = $ 900 $^{-1}$.
 The richness cuts show what the completeness and purity !.would look like if we remove groups that have fewer members than some given threshold., The richness cuts show what the completeness and purity would look like if we remove groups that have fewer members than some given threshold.
 It should be noted that the value of Nnratoes is unchanged and therefore haloes which have fewer members than the richness cut threshold are no longer matched., It should be noted that the value of $N_{haloes}$ is unchanged and therefore haloes which have fewer members than the richness cut threshold are no longer matched.
" This figure indicates that the richer clusters are more pure, but less complete, as one would expect."," This figure indicates that the richer clusters are more pure, but less complete, as one would expect."
" Because it is not possible to produce a catalogue that is complete and pure, it is necessary to choose one or the other, or some compromise between the two requirements."," Because it is not possible to produce a catalogue that is complete and pure, it is necessary to choose one or the other, or some compromise between the two requirements."
" If we choose a catalogue that is ~ complete, fig.5 shows it can be cut by richness to improve the purity."," If we choose a catalogue that is $\sim$ complete, \ref{fig:pure_test} shows it can be cut by richness to improve the purity."
" Finally, the DFoF code was run on the real 28LAQ catalogue to investigate the number of clusters found for a given set of linking parameters."," Finally, the DFoF code was run on the real 2SLAQ catalogue to investigate the number of clusters found for a given set of linking parameters."
 Fig.6 shows the total number of clusters found in the 2SLAQ catalogue as a function of Rfriena(z=0.5) and veriena(z=0.5)., \ref{fig:rfriends01} shows the total number of clusters found in the 2SLAQ catalogue as a function of $R_{friend}(z=0.5)$ and $v_{friend}(z=0.5)$.
 Both this figure and the top panel of fig.4 have the largest Nex contours roughly in the range 2.5€Ryriena(z=0.5)<4.0 Mpc hot., Both this figure and the top panel of \ref{fig:rfriends00} have the largest $N_{\textrm{clt}}$ contours roughly in the range $2.5\leq R_{friend}(z=0.5)\leq4.0$ Mpc $h^{-1}$.
" Therefore in order to obtain a fully complete catalogue with high purity and the largest number of clusters possible, based on the results in fig.4,, 5 and 6,, values of Rfriena(z= Mpc h! and vfriena(z=0.5)900 kms were chosen to find groups and clusters in the 25LAQ catalogue."," Therefore in order to obtain a fully complete catalogue with high purity and the largest number of clusters possible, based on the results in \ref{fig:rfriends00}, \ref{fig:pure_test} and \ref{fig:rfriends01}, , values of $R_{friend}(z=0.5)=0.87$ Mpc $h^{-1}$ and $v_{friend}(z=0.5)=900$ $^{-1}$ were chosen to find groups and clusters in the 2SLAQ catalogue."
! These values correspond to a 28LAQ mock cluster catalogue that is 9896 complete and 5296 pure., These values correspond to a 2SLAQ mock cluster catalogue that is $\%$ complete and $\%$ pure.
with p the vertically intcerated pressure and & the eravitational potential.,with $p$ the vertically integrated pressure and $\Phi$ the gravitational potential.
 We consider iuviscid disks only. and ignore the sclberavity of the eas. so that d is due to the ceutral star only.," We consider inviscid disks only, and ignore the self-gravity of the gas, so that $\Phi$ is due to the central star only."
 We will consider a strictly isothermal equation of state; p=(2X. with e; the sound speed.," We will consider a strictly isothermal equation of state, $p=c_s^2 \Sigma$, with $c_s$ the sound speed."
" The disk surface density profile is à power law initially. M=Myréry)""S with ry a reference radius. most often the initial location of the vortex."," The disk surface density profile is a power law initially, $\Sigma=\Sigma_0 (r/r_0)^{-\alpha}$, with $r_0$ a reference radius, most often the initial location of the vortex."
 Since we do not consider selferavitv. Xy is arbitrary.," Since we do not consider self-gravity, $\Sigma_0$ is arbitrary."
 The sound speed is set bv choosing a scale height LF at ry. My. which determinesthe sound speed ος=Που.," The sound speed is set by choosing a scale height $H$ at $r_0$, $H_0$, which determinesthe sound speed $c_s=H_0\Omega_0$."
 We then have IH=Ho(riry)*7., We then have $H=H_0(r/r_0)^{3/2}$.
" The angular velocity Q is Keplerian. initially, with a sinall correction due to a radial pressure evacicut."," The angular velocity $\Omega$ is Keplerian, initially, with a small correction due to a radial pressure gradient."
 Ta some of the analysis. it is advantageous to have a coustant aspect ratio Γη.," In some of the analysis, it is advantageous to have a constant aspect ratio $H/r$."
 This cau be achieved by having a racially varving. but coustant im time. sound speed.," This can be achieved by having a radially varying, but constant in time, sound speed."
 Physically. this correspoucds to a disk that relaxes to an equilibriun temperature profile ou a very short time scale (the cooling time scale is formally zero. so no temperature fluctuations are allowed).," Physically, this corresponds to a disk that relaxes to an equilibrium temperature profile on a very short time scale (the cooling time scale is formally zero, so no temperature fluctuations are allowed)."
 It is possible to combine equatious (1)) aud (2)) iuto a single equation for the vortensity o/h. where Ξκ:(V svk showing that in 2D barotropic flow. for which p=p(X). vorteusitv is conserved aloug streamlines.," It is possible to combine equations \ref{eqCont}) ) and \ref{eqMom}) ) into a single equation for the vortensity $\omega/\Sigma$, where $\omega={\bf \hat k} \cdot (\nabla \times {\bf v})$ : showing that in 2D barotropic flow, for which $p=p(\Sigma)$, vortensity is conserved along streamlines."
 This of course includes the isothermal case., This of course includes the isothermal case.
 It is no longer true when ie sound speed varies racially. which makes the flow ton-barotropic. or when 3D inotious are allowed for.," It is no longer true when the sound speed varies radially, which makes the flow non-barotropic, or when 3D motions are allowed for."
 Iu iat case. à more eeneral quantity (V.«v):VQ/p. with Q any quantity that is couserved on fluid elements aud p ie density. is conserved aloug streamlines.," In that case, a more general quantity $(\nabla \times {\bf v})\cdot \nabla Q/\rho$, with $Q$ any quantity that is conserved on fluid elements and $\rho$ the density, is conserved along streamlines."
 For example. or an adiabatic flow Q can be taken to be the specific eutropy.," For example, for an adiabatic flow $Q$ can be taken to be the specific entropy."
 The resulting quautity is sometimes called the otential vorticity., The resulting quantity is sometimes called the potential vorticity.
 Ou top of the equilibrium configuration we introduce a vortical perturbation., On top of the equilibrium configuration we introduce a vortical perturbation.
 In elobal models. this is clone by applving a circular velocity perturbation with a specified uaxinumni over a circular patch of the disk.," In global models, this is done by applying a circular velocity perturbation with a specified maximum over a circular patch of the disk."
 The velocity )orturbdion is usually a sizeable fraction ( 0.5) of he local sound speed. and the patch a sizeable fraction of the local scale height. typically fy/2.," The velocity perturbation is usually a sizeable fraction $\sim 0.5$ ) of the local sound speed, and the patch a sizeable fraction of the local scale height, typically $H_0/2$."
 The velocity serturbation tapers off exponentially away from the uaxinumn., The velocity perturbation tapers off exponentially away from the maximum.
 The exact form of the perturbation was found ος to be important. as the system relaxes to a similar vorteusitv profile on a dynamical time scale regardless.," The exact form of the perturbation was found not to be important, as the system relaxes to a similar vortensity profile on a dynamical time scale regardless."
 Note that the subcritical baroclinic instability will teud ο produce vortices of a size comparable to LF (?).., Note that the subcritical baroclinic instability will tend to produce vortices of a size comparable to $H$ \citep{lesur10}.
 For our global disk models. we solve equations (1)) and (2)) in evlindrical geometry (57.47) using (2)... which is a second-order fuite volume method using an approximate Riemann solver duc to ?..," For our global disk models, we solve equations \ref{eqCont}) ) and \ref{eqMom}) ) in cylindrical geometry $(r,\varphi)$ using \citep{rodeo}, , which is a second-order finite volume method using an approximate Riemann solver due to \cite{roe}."
 It has been successfully applied to the study of disk-eubedded planets (2?) aud disks im tight binary svstems (?)..," It has been successfully applied to the study of disk-embedded planets \citep{comparison,paardpap08} and disks in tight binary systems \citep{binary}."
" The computational domain consists of an annulus at a reference radius rg. with muer aud outer boundaries located at 0.2 ry and 2.5 rg. respectively,"," The computational domain consists of an annulus at a reference radius $r_0$, with inner and outer boundaries located at $0.2$ $r_0$ and $2.5$ $r_0$, respectively."
 We use noureflective boundary couditious (?7).. to allow the waves excited by the vortex to leave the computational onn freely.," We use non-reflective boundary conditions \citep{godon}, , to allow the waves excited by the vortex to leave the computational domain freely."
 Although cesiened to be non-reflective for 1D simple waves only. we have observed no wave reflection in our 2D non-linear simulations.," Although designed to be non-reflective for 1D simple waves only, we have observed no wave reflection in our 2D non-linear simulations."
 As explained -iu mmore detail in ?.. the use of a characteristies-based Rictuann solver eusures that information is always drawn from the rieht places.," As explained in more detail in \cite{rodeo}, the use of a characteristics-based Riemann solver ensures that information is always drawn from the right places."
 At the boundary. αν incoming characteristics are treated as if they originate from au unperturbed disk.," At the boundary, any incoming characteristics are treated as if they originate from an unperturbed disk."
 This eusures that no waves cuter the computational domain., This ensures that no waves enter the computational domain.
 We consider the full 27 in azimuth., We consider the full $2\pi$ in azimuth.
 For fy=0.τω we use a typical exid size of 1536 iu the radial and 6111 in the azimuthal direction. varving this up aud down by factors of 2 to study effects of resolution.," For $H_0=0.1 r_0$, we use a typical grid size of 1536 in the radial and 6144 in the azimuthal direction, varying this up and down by factors of 2 to study effects of resolution."
 Our typical exid therefore has 67 zones per scale height., Our typical grid therefore has 67 zones per scale height.
 When considering smaller values of fy. we increase the resolution to maintain a fixed ΠΙΟ of eric cells per scale height.," When considering smaller values of $H_0$, we increase the resolution to maintain a fixed number of grid cells per scale height."
 Within the code. we set ry=1 for numerical couvenicnee.," Within the code, we set $r_0=1$ for numerical convenience."
 Tn this section. we consider au isothermal disk with o=3/2 and Hy=Ory.," In this section, we consider an isothermal disk with $\alpha=3/2$ and $H_0=0.1r_0$."
 Note that this is a disk with coustant vorteusitv. aud that. fornmuerical convenience. it is relatively thick for a protoplauctary disk.," Note that this is a disk with constant vortensity, and that, fornumerical convenience, it is relatively thick for a protoplanetary disk."
 The dependence on fy is discussed in Sect. 7.., The dependence on $H_0$ is discussed in Sect. \ref{secGlob}. .
 We give the disk a circular velocity perturbation of maguitude ος{3 over a scale Ly/2., We give the disk a circular velocity perturbation of magnitude $c_{s}/2$ over a scale $H_0/2$.
 The resulting vortensity aud. deusity perturbations after LO orbits at 7=1 are shown in Fig. 1.., The resulting vortensity and density perturbations after 10 orbits at $r=1$ are shown in Fig. \ref{figvortdens}. .
 From Fig., From Fig.
 1 we seethat thevortensitv perturbation, \ref{figvortdens} we seethat thevortensity perturbation
the LMC disk. or are not associated with the LMC disk.,"the LMC disk, or are not associated with the LMC disk."
 The RDP should be seen in the original heliocentric racial velocities ο better than it is seen in the disk-fit residuals Ac., The KDP should be seen in the original heliocentric radial velocities $v$ better than it is seen in the disk-fit residuals $\Delta v$.
 We therefore fit the data to a functions of the form, We therefore fit the data to a functions of the form
Although the warm ionized meditm (WIM). also called. the dilfuse ionized) gas (DIC). is a principal component of the interstellar medium iu our Calaxy and others. the source of its,"Although the warm ionized medium (WIM), also called the diffuse ionized gas (DIG), is a principal component of the interstellar medium in our Galaxy and others, the source of its"
dispersion relations presented in Figs.,dispersion relations presented in Figs.
 2. and 4. (hat the I-frame moves relativisically with respect to the pulsar (E.>>1) for RZ10., \ref{circulardispersion} and \ref{lineardispersion} that the H-frame moves relativistically with respect to the pulsar $\Gamma_>\gg1$ ) for $R\gtrsim10$.
" An instability that grows locally in the lL-füame with growth-rate comparable to the wave frequency in (hat Iraune. propagates a distance of F2, wavelengths in the pulsar reference frame in one e-Iolding time."," An instability that grows locally in the H-frame with growth-rate comparable to the wave frequency in that frame, propagates a distance of $\Gamma_>^2$ wavelengths in the pulsar reference frame in one $e$ -folding time."
 Thus. alihough such instabilities may be present. (heir effect on the structure of the pulsar wind or (he termination shock might not be dramatic.," Thus, although such instabilities may be present, their effect on the structure of the pulsar wind or the termination shock might not be dramatic."
 In relresulls we show that superluminal waves are capable of carrying the particle. energy and magnetic fields thought to be transported by a pulsar wind when they reach the termination shock of an isolated pulsar. except lor a range of latitudes around the (rotation) pole.," In \\ref{results} we show that superluminal waves are capable of carrying the particle, energy and magnetic fields thought to be transported by a pulsar wind when they reach the termination shock of an isolated pulsar, except for a range of latitudes around the (rotation) pole."
 In fact. at most latitudes. there is a large range of radii between pj and py. in which propagation is possible.," In fact, at most latitudes, there is a large range of radii between $\rho_{\rm cr}$ and $\rho_{\rm ts}$ in which propagation is possible."
 Our results do not address the question of where conversion from a striped wind to a superluminal wave might occur., Our results do not address the question of where conversion from a striped wind to a superluminal wave might occur.
 However. since these waves are subsequently camped. it would seem likely that they could be sustained only within an extinction length of the termination shock itself. in which case their excitation and dampius can be regarded as forming a part of this structure.," However, since these waves are subsequently damped, it would seem likely that they could be sustained only within an extinction length of the termination shock itself, in which case their excitation and damping can be regarded as forming a part of this structure."
 ? suggested (he physics of the termination sshould differ from that of an MIID shock auc permit reconnection of the alternating component of the incoming magnetic field., \citet{lyubarsky03} suggested the physics of the termination should differ from that of an MHD shock and permit reconnection of the alternating component of the incoming magnetic field.
 A quantitative investigation based on analytic considerations and 1D PIC simulations (?) found that the effectiveness of reconnection depends on the ratio of the Larmor radii of electrons in the downstream flow to the wavelength of the stripes., A quantitative investigation based on analytic considerations and 1D PIC simulations \citep{petrilyubarsky07} found that the effectiveness of reconnection depends on the ratio of the Larmor radii of electrons in the downstream flow to the wavelength of the stripes.
 Since (his quantity increases monolonically with radius in a striped wind. these results imply thal reconnection can be important only outside of a," Since this quantity increases monotonically with radius in a striped wind, these results imply that reconnection can be important only outside of a"
»etween the lifetime and the SN.,between the lifetime and the SN.
 Those orbits surviving the whole integration are also those with small SN while orbits with relatively larger SN escape from the resonance before he integration ends., Those orbits surviving the whole integration are also those with small SN while orbits with relatively larger SN escape from the resonance before the integration ends.
 Particularly. in the lower panel we see our orbits with 7=137.147.15.16 lose their stability after 4.2. 0.24. 1.1 and GGvr respectively.," Particularly, in the lower panel we see four orbits with $i_0=13^\circ, 14^\circ, 15^\circ, 16^\circ$ lose their stability after 4.2, 0.24, 1.1 and Gyr respectively."
 These points are on the blue arc in 33. i.c. the chaotic property «i hese orbits has been correctly. predicted by the relativeA arge SN calculated from our short-term integration.," These points are on the blue arc in 3, i.e., the chaotic property of these orbits has been correctly predicted by the relatively large SN calculated from our short-term integration."
 We should point out that several orbits with small 8 (crecen ones in 66) can not sustain the solar svstem age., We should point out that several orbits with small SN (green ones in 6) can not sustain the solar system age.
" They are all at the border of stable region. and escape onA after very long evolution (LO"" vvr)."," They are all at the border of stable region, and escape only after very long evolution $\sim 10^9$ yr)."
 Perhaps the instabiliE is introduced through very slow chaotic dillusion. which the SN fails to detect.," Perhaps the instability is introduced through very slow chaotic diffusion, which the SN fails to detect."
 Nevertheless. one can see that elobally the SN is still a successful indicator of orbital stability.," Nevertheless, one can see that globally the SN is still a successful indicator of orbital stability."
 Another conclusion can be macle from 66. nameA ‘Trojans with highIn inclinations 4j750° can survive thesolar system age.," Another conclusion can be made from 6, namely Trojans with high inclinations $i_0>50^\circ$ can survive thesolar system age."
 fy=35 is not the upper limit in inclination for potentially stable Trojans. as one also can see from Fig.22 and 33.," $i_0=35^\circ$ is not the upper limit in inclination for potentially stable Trojans, as one also can see from 2 and 3."
" The most cistinguishable features in the dynamical map are two white (unstable) regions: the high. inclination region with fo61"" and an unstable gap at iy44.", The most distinguishable features in the dynamical map are two white (unstable) regions: the high inclination region with $i_0>61^\circ$ and an unstable gap at $i_0\sim 44^\circ$.
 Orbits in these two regions are strongly chaotic and they cannot survive in the resonance even in our short-term integration., Orbits in these two regions are strongly chaotic and they cannot survive in the resonance even in our short-term integration.
 There must be some strong mechanisms driving them out., There must be some strong mechanisms driving them out.
 For orbits with high inclination. the Ixozai resonance (Ixozai1962:Winoshita&Nakai2007) is acting as the responsible mechanism.," For orbits with high inclination, the Kozai resonance \citep{koz62,kin07} is acting as the responsible mechanism."
 In ai Ixozal resonance the perihelion argument c librates while the cecentricity and inclination undergo variations such that the quantity ffi=Vlc=eos? remains constant., In a Kozai resonance the perihelion argument $\omega$ librates while the eccentricity and inclination undergo variations such that the quantity $H_K=\sqrt{1-e^2}\cos i$ remains constant.
 When the inclination of a ‘Trojan decreases its eccentricity increases. as a result. it will cross Uranus! orbit ancl the probability. of close encounter with Uranus is enhanced significantLy.," When the inclination of a Trojan decreases its eccentricity increases, as a result, it will cross Uranus' orbit and the probability of close encounter with Uranus is enhanced significantly."
 We checked the evolution of some orbits with fy2GL and found that the instability is really clue to the Ixozai resonance., We checked the evolution of some orbits with $i_0>61^\circ$ and found that the instability is really due to the Kozai resonance.
 A typical orbit is shown in 77 We see clearly that w enters a small-amplitude libration state at MMwyr after a transient period., A typical orbit is shown in 7 We see clearly that $\omega$ enters a small-amplitude libration state at Myr after a transient period.
 From then on w is nearly constant. e increases as / decreases till MMSyr when e reaches a value of 0.358.," From then on $\omega$ is nearly constant, $e$ increases as $i$ decreases till Myr when $e$ reaches a value of 0.358."
 Phe perihelion distance is now q=alο).m30.20.(10.358)—19.39 AAU. which is in the range of Uranus distance to the Sun.," The perihelion distance is now $q=a(1-e)\approx 30.20 \times
(1-0.358)=19.39$ AU, which is in the range of Uranus distance to the Sun."
 A close encounter with Uranus then destrovs the 1:1: mean motion resonance between the ‘Trojan ancl Neptune. as shown by the deviation of σ from libration in the bottom panel of 77.," A close encounter with Uranus then destroys the 1:1 mean motion resonance between the Trojan and Neptune, as shown by the deviation of $\sigma$ from libration in the bottom panel of 7."
 After that the object is finally scattered out from the solar svstem through a series of encounters with planets., After that the object is finally scattered out from the solar system through a series of encounters with planets.
 Generally. the Ixozai mechanism protects an object [rom close encounters with the perturber (usually a planet) either fororbits at high inclination where w librates around. 90 or 210 (Vhomas&.Morbidelli 1996).. or for orbits at. low inclination where w oscillates around. O° or 1807 (Michel 1996)..," Generally, the Kozai mechanism protects an object from close encounters with the perturber (usually a planet) either fororbits at high inclination where $\omega$ librates around $90^\circ$ or $270^\circ$ \citep{tho96}, , or for orbits at low inclination where $\omega$ oscillates around $0^\circ$ or $180^\circ$ \citep{mith96}. ."
 But in our case of Neptune Trojans. as," But in our case of Neptune Trojans, as"
model to the 850500) data point we find that for a couple of the objects (SAIAT J163658.78|105728.1 at a redshift of 1.2 aud MAL J163639|1056 at a redshift of 1.5) the cinrus imodel seems to be adequate for explaining the spectral cucrey distribution.,model to the $\mu m$ data point we find that for a couple of the objects (SMM J163658.78+405728.1 at a redshift of 1.2 and MM J163639+4056 at a redshift of 1.5) the cirrus model seems to be adequate for explaining the spectral energy distribution.
 For SAINT J10521]5719 a cirrus model with 6=18 is also adequate for explaining the SED., For SMM J10521+5719 a cirrus model with $\psi =18$ is also adequate for explaining the SED.
 For the rest ofthe objects the model falls short of matching the observed mid-infrared spectruni sugecstingCoco either that the PATT abundance is higher than assuued or there is contribution iu the mid-infrared froma starburst., For the rest of the objects the model falls short of matching the observed mid-infrared spectrum suggesting either that the PAH abundance is higher than assumed or there is contribution in the mid-infrared from a starburst.
 Iu Sect., In Sect.
 Land 5 we will explore the latter possibility., 4 and 5 we will explore the latter possibility.
 In Fig., In Fig.
 9 we also explore the possibility that a starburst alone can explain the complete spectral energy distribution., \ref{cirrus.ps} we also explore the possibility that a starburst alone can explain the complete spectral energy distribution.
 To do that we take a single starburst spectrum from the SED library of Sicheumoregen νήσου (2007)., To do that we take a single starburst spectrum from the SED library of Siebenmorgen Krüggel (2007).
" We choose a starburst model with a total huuiuositv of 10)Το, à nuclear radius of J3kpe and a visual extinction from the edge to the center of Ἱδιιαο"," We choose a starburst model with a total luminosity of $10^{13.1}$, a nuclear radius of 3kpc and a visual extinction from the edge to the center of 18mag."
", For each ealaxy this model spectrum is normalized to the mid-infrared observations.", For each galaxy this model spectrum is normalized to the mid-infrared observations.
 It is clear that a starburst-only model falls short of matching the submillimeter photometry by at least an order of mmaenitude., It is clear that a starburst-only model falls short of matching the submillimeter photometry by at least an order of magnitude.
 The model, The model
"were (he compact objects that could be clusters or galaxies. and as a result the numbers ol ""possible clusters” were the greatest especially in the central regions.","were the compact objects that could be clusters or galaxies, and as a result the numbers of “possible clusters” were the greatest especially in the central regions."
 As the contrast and scaling were changed. some objects smoothly grew. some were a faint smear with no sharp edges. and others could be seen to displav spiral shape.," As the contrast and scaling were changed, some objects smoothly grew, some were a faint smear with no sharp edges, and others could be seen to display spiral shape."
 If the object had smooth contours and ilit was in a group of other objects that were clearly galaxies. (he object was likely to be a galaxy and not a star cluster.," If the object had smooth contours and if it was in a group of other objects that were clearly galaxies, the object was likely to be a galaxy and not a star cluster."
 Group 4 objects did not look like a cluster. a cluster-canclidate. a galaxy or à star.," Group 4 objects did not look like a cluster, a cluster-candidate, a galaxy or a star."
 As noled above. the influence of background contamination by galaxies on this selection process should not be underestimated.," As noted above, the influence of background contamination by galaxies on this selection process should not be underestimated."
 In essence. this is a needles-in-a-havstack process where we are attempting to find a small number of clusters in a huge population of contaminants. and even though our selection and culling is rigorous. there remain a large number of objects whose nature is ambiguous from the current data.," In essence, this is a needles-in-a-haystack process where we are attempting to find a small number of clusters in a huge population of contaminants, and even though our selection and culling is rigorous, there remain a large number of objects whose nature is ambiguous from the current data."
 Higher resolution imaging. imaging in the near infrared where the cluster red giants would be better resolved (and which also can have better seeing). or ultimately spectroscopy. will be required for more definitive elimination of the last contaminants.," Higher resolution imaging, imaging in the near infrared where the cluster red giants would be better resolved (and which also can have better seeing), or ultimately spectroscopy, will be required for more definitive elimination of the last contaminants."
 There was only one definite new outer halo cluster discovered in our study αἱ a projected radius of 87 (or 22 kpe. assuming a distance to M33 of 570. kpe).," There was only one definite new outer halo cluster discovered in our study at a projected radius of 87” (or 22 kpc, assuming a distance to M33 of 870 kpc)."
 It was founcl using the automated search., It was found using the automated search.
 The new cluster is named M33E following the naming convention begun in ?.., The new cluster is named M33E following the naming convention begun in \cite{2009ApJ...698L..77H}.
 Four of the five previouslv-known outer halo clusters (2?) were easily recovered.," Four of the five previously-known outer halo clusters \citep{2008AJ....135.1482S, 2009ApJ...698L..77H} were easily recovered."
 Cluster D was identified but. was too compact to have been recovered without prior knowledge., Cluster D was identified but was too compact to have been recovered without prior knowledge.
 Clusters A to E and $ are shown in Figure 5.. where S is thecluster found by 2..," Clusters A to E and S are shown in Figure \ref{m33ag}, where S is thecluster found by \cite{2008AJ....135.1482S}. ."
The final step of inae involves combining the Parkes and ATCA data.,The final step of imaging involves combining the Parkes and ATCA data.
 The data may be combined in the Fourier domain after deconvolution of the iucividual images or in thewe plane prior to deconvolution., The data may be combined in the Fourier domain after deconvolution of the individual images or in the plane prior to deconvolution.
 Stanimirovic(1999). showed that the results are comparable using either method. but that combining after deconvolution produced results that were typically more cousisteut than with other methods.," \citet{stanimirovic99} showed that the results are comparable using either method, but that combining after deconvolution produced results that were typically more consistent than with other methods."
 Comparison of our data conibiue in both wavs shows simula results., Comparison of our data combined in both ways shows similar results.
 We have chosen. therefore. to combine the data in the Fourier domain after deconvolution.," We have chosen, therefore, to combine the data in the Fourier domain after deconvolution."
 Iu this method. the interferometric data aand contiuuun data are müased and cecouvolved. the sinele-dish data are inmaged aud the clean interferometric and sinele-dish images are Fourier trausforiued aux conibined.," In this method, the interferometric data and continuum data are imaged and deconvolved, the single-dish data are imaged and the clean interferometric and single-dish images are Fourier transformed and combined."
 This technique is implemented im the task imunerec., This technique is implemented in the task immerge.
 Slieht differences in calibration can leac to the necessity of a relative calibration factor bv which the single-dish dataset is multiplied before combination., Slight differences in calibration can lead to the necessity of a relative calibration factor by which the single-dish dataset is multiplied before combination.
 This calibration factor is deteriuned bv comparing the datasets in the Fourier plane at every pixel and frequency +oi the ranee of overlapping spatial frequencies., This calibration factor is determined by comparing the datasets in the Fourier plane at every pixel and frequency in the range of overlapping spatial frequencies.
 In order o calculate the calibration factor both images must be aAeconvolved. a step which requires a good knowledge of ie sinele-dish bean (Stanimirovic1999).," In order to calculate the calibration factor both images must be deconvolved, a step which requires a good knowledge of the single-dish beam \citep{stanimirovic99}."
. Using a two dimensional Gaussian with FWIIM 15/5 for the Parkes beam and by comparing the Parkes and ATCA continua Huages of a strong. compact source in the Test Reeion. we calculated a relative calibration factor of 1.19.," Using a two dimensional Gaussian with FWHM $15\farcm5$ for the Parkes beam and by comparing the Parkes and ATCA continuum images of a strong, compact source in the Test Region, we calculated a relative calibration factor of 1.19."
 Two combined ddata cubes were created. one containing the continua enüssion for absorption studies aud one which had the onutiunmua subtracted for euidssion studies.," Two combined data cubes were created, one containing the continuum emission for absorption studies and one which had the continuum subtracted for emission studies."
 The continua nuages were combined m the same wav as the cube aud with the same calibration factor., The continuum images were combined in the same way as the cube and with the same calibration factor.
 The combined Parkes aud ATCA 21-cii contimmun image is shown in Fie. 1, The combined Parkes and ATCA 21-cm continuum image is shown in Fig. \ref{fig:21cont}.
 The combined data are sensitive to all angular scales from the svuthesized beam size. 12179«10775 (a <8). up to theimage size. S7& τς 5) for the Test Reeion.," The combined data are sensitive to all angular scales from the synthesized beam size, $124\farcs9 \times 107\farcs5$ $\alpha \times \delta$ ), up to the image size, $8\arcdeg \times 4 \arcdeg$ $l \times b$ ) for the Test Region."
 Because of the fine scale structure seen iu the velocity domain. uo Tanning smoothing was applied to the data.," Because of the fine scale structure seen in the velocity domain, no Hanning smoothing was applied to the data."
 Each channel image has a velocity separation of 0.821., Each channel image has a velocity separation of $0.82$.
 Channel images from the coutimmun subtracted combined data cube are shown iu Fie. 2.., Channel images from the continuum subtracted combined data cube are shown in Fig. \ref{fig:chans1}.
 Every fourth channel frou e—στις Πο ο=19 tis shown., Every fourth channel from $v=-127$ to $v=79$ is shown.
 The rus noise iu the channel images is ~2.1 K of Tp for the ATCA data. ~LOO mls of Tp for the Parkes data and ~2.3 Iv of Tp for the combined dataset.," The rms noise in the channel images is $\sim 2.4$ K of ${\rm T_B}$ for the ATCA data, $\sim 100$ mK of ${\rm T_B}$ for the Parkes data and $\sim 2.3$ K of ${\rm
T_B}$ for the combined dataset."
 The rius noise in the continu images is —5.5mJybeam| for the ATCA data. ~500iiybeam+ for the Parkes data (boa size 15/5« 15/5). and ~Τι]beam| for the combined data.," The rms noise in the continuum images is $\sim 5.5~{\rm mJy~beam^{-1}}$ for the ATCA data, $\sim 500~{\rm
mJy~beam^{-1}}$ for the Parkes data (beam size $15\farcm5 \times
15\farcm5$ ), and $\sim 7~{\rm mJy~beam^{-1}}$ for the combined data."
 The combined A21-cni coutimmiun nuage of the SGPS Test Reeion is shown in Fig. l.., The combined $\lambda$ 21-cm continuum image of the SGPS Test Region is shown in Fig. \ref{fig:21cont}.
 Most sources have beeu previously catalogued as rreeious or SNRs CAvedisova1997:Caswell&Tavues1987:Creeon2000:Whiteoak&Cacen 1996).," Most sources have been previously catalogued as regions or SNRs \citep{avedisova97,caswell87,green00,whiteoak96}."
. There are also many unresolved sources scattered throughout the Test Reeion., There are also many unresolved sources scattered throughout the Test Region.
 aabsorption measurements towards many of these sugecst that most are extragalactic., absorption measurements towards many of these suggest that most are extragalactic.
 This region has been studied iu Ha bv Ceoreclinetal.(1991). as part of an extensive Πα survey of the Southern Calactic Plane., This region has been studied in ${\rm \alpha}$ by \citet{georgelin94} as part of an extensive ${\rm \alpha}$ survey of the Southern Galactic Plane.
 As shown in the Fig. 2...," As shown in the Fig. \ref{fig:diag},"
 a diagram of the expected velocities aud spiral ars in the fourth quadrant. the Test Region line of sight crosses both the Saeittarius-Carina aud ΠΜαν.spiral zs and uus tangent to the Norma armi at /23277," a diagram of the expected velocities and spiral arms in the fourth quadrant, the Test Region line of sight crosses both the Sagittarius-Carina and Scutum-Crux spiral arms and runs tangent to the Norma arm at $l\approx 327\arcdeg$."
",As a result this region has a particularly high deusitv of coutiumuu SOULCOS.", As a result this region has a particularly high density of continuum sources.
 We describe here the more prominent discrete sources in the SGPS Test Region., We describe here the more prominent discrete sources in the SGPS Test Region.
 These sources are marked i ou the MOST 813 MIIz coutimmum image shown in Fig. 3.., These sources are marked in on the MOST 843 MHz continuum image shown in Fig. \ref{fig:most}.
 Several individual sources are discussed in detail below with conunent given about their associated cclussion., Several individual sources are discussed in detail below with comment given about their associated emission.
" Starting at the lower longitude cud. the first strong source is ROW 91(Rodgers.Campbell.&Whiteoak1960:Shaver.AleGec,&Pottasch1970). at7=32625. b=[0S with an aueulur diameter of aboutδ"," Starting at the lower longitude end, the first strong source is RCW 94\citep{rodgers60, shaver79} at$l=326\fdg3$, $b=+0\fdg8$, with an angular diameter of about."
"ι, This vine-like structure is an region. with strongest cussion to the lower left."," This ring-like structure is an region, with strongest emission to the lower left."
 There is a smaller region adjoiuing the rroegion at /—32621. b=1079.," There is a smaller region adjoining the region at $l=326\fdg4$, $b=+0\fdg9$."
 At --32ο b=|OFS is another region. ROW 5.," At $l=326\fdg7$, $b=+0\fdg8$ is another region, RCW 95."
 Directly below RCW 95 is the brighter. extended iregion (326.65|0.59 (Ceorgelinet.al.1991).," Directly below RCW 95 is the brighter, extended region G326.65+0.59 \citep{georgelin94}."
.. Closer to the Plane at higher longitudes is a very exteuded thermal filamentary structure 326.96|0.03., Closer to the Plane at higher longitudes is a very extended thermal filamentary structure G326.96+0.03.
 This source has arcs of cliuission above and below a ceutralized. bright knot., This source has arcs of emission above and below a centralized bright knot.
 Because these sources are all at the same ere we refer to the erouping of RCW 91. ROW 95. 326.65|0.59. aud (326.9610.03 as the ROW 91-95 rreeion coniplex.," Because these sources are all at the same distance, we refer to the grouping of RCW 94, RCW 95, G326.65+0.59, and G326.96+0.03 as the RCW 94-95 region complex."
 Above the high longitude edge of the (326.96|0.03 arc is SNR C327.ELO.L. a large shell tvpe SNR with euliauced iub brightening to the lower left.," Above the high longitude edge of the G326.96+0.03 arc is SNR G327.4+0.4, a large shell type SNR with enhanced limb brightening to the lower left."
 Further from the Plaue hau (221110. is a snaller. weaker supernova relunant. SNR C€C327.1]there1.0.," Further from the Plane than G327.4+0.4 there is a smaller, weaker supernova remnant, SNR G327.4+1.0."
 This source has a nearly closed arc extending to higher latitudes., This source has a nearly closed arc extending to higher latitudes.
 At slightly higher ouegitudes there is a region of extended emission conrised of several thermal sources grouped at 2327.83|0.11., At slightly higher longitudes there is a region of extended emission comprised of several thermal sources grouped at G327.83+0.11.
 At üeher longitudes aud lower latitudes than these sources here is another region. )0-0.00.," At higher longitudes and lower latitudes than these sources there is another region, G327.99-0.09."
" Near /2328"" is the compact rregion CO28.31|0.15 and the extremely bright Crab-like SNR C328.1]0.2 (Caeusleretal.20005).", Near $l=328\arcdeg$ is the compact region G328.31+0.45 and the extremely bright Crab-like SNR G328.4+0.2 \citep{gaensler00b}.
. At higher longitudes. the compact source 6328.81-0.08 is Classified as an region in CaswellTavues(1987.hereafterCIIST) ou the basis of a recombination line detection.," At higher longitudes, the compact source G328.81-0.08 is classified as an region in \citet[ hereafter CH87]{caswell87} on the basis of a recombination line detection."
 However. cxanunation of the Midcourse Space Experineut. (MSX: Egan et 11998)) band A (6.8—LOLS µια) image shows oulv a small infrared source. TRAS 15550-5306. slightly offset from the ceuter of G328.81-0.08.," However, examination of the Midcourse Space Experiment (MSX; Egan et \nocite{egan98}) ) band A $6.8-10.8$ ) image shows only a small infrared source, IRAS 15550-5306, slightly offset from the center of G328.81-0.08."
" This iufrared source has a EWIIM of ~30"". whereas the offset A21-cii source has a EWIINME of ~Y."," This infrared source has a FWHM of $\sim 30\arcsec$, whereas the offset $\lambda$ 21-cm source has a FWHM of $\sim 3\arcmin$."
 It is unclear whether the infrared source is tle same as the radio source., It is unclear whether the infrared source is the same as the radio source.
 About 30/ from C328S.SL-0.08 there is an extended source centered at /=32876. L1 b=07.," About $30\arcmin$ from G328.81-0.08 there is an extended source centered at $l=328\fdg6$ , $b=0\arcdeg$ ."
 , Fig.
SGPSFie. E. shows the combined Parkes aud ATCA Gz continmmiu image of this region and the MOST 813 MIIz image of the same area., \ref{fig:newsnr} shows the combined Parkes and ATCA 1.4 GHz SGPS continuum image of this region and the MOST 843 MHz image of the same area.
this paper. equivalent to HST's resolution of 0.17 at a distance of 150 pe.,"this paper, equivalent to HST's resolution of 0.1” at a distance of 150 pc."
 We use a sample of eight jets: DG Tau. HN Tau. CW Tau. UZ Tau E. RW Aur. HH34. HH30 and HL Tau (Fig. 1).," We use a sample of eight jets: DG Tau, HN Tau, CW Tau, UZ Tau E, RW Aur, HH34, HH30 and HL Tau (Fig. \ref{Fig_observations}) )."
 In order to determine the width of the jets in our models. we use a method which is às close as possible to that applied by the observers.," In order to determine the width of the jets in our models, we use a method which is as close as possible to that applied by the observers."
 We create convolved synthetic maps for the emission in the [SII] 446731 and [OI] 26300 lines for each numerical model and each run of OpenSESAMe and determine the jet width from the map’s FWHM as a function of distance along the axis., We create convolved synthetic maps for the emission in the [SII] $\lambda$ 6731 and [OI] $\lambda$ 6300 lines for each numerical model and each run of OpenSESAMe and determine the jet width from the map's FWHM as a function of distance along the axis.
 Throughout the first paper. we used only the dimensionless quantities in which PLUTO performs its calculations.," Throughout the first paper, we used only the dimensionless quantities in which PLUTO performs its calculations."
 In order to compare our results with observations. however. ie. in order to run OpenSESAMe correctly. we have to scale them to physical units by providing sealing factors for density po. pressure po. velocity vo. magnetic field strength Bo. a length scale Ro and a mass scale At.," In order to compare our results with observations, however, i.e. in order to run OpenSESAMe correctly, we have to scale them to physical units by providing scaling factors for density $\rho_0$ , pressure $p_0$, velocity $v_0$, magnetic field strength $B_0$, a length scale $R_0$ and a mass scale $\mathcal{M}$."
 However. in terms of the normalizations used in the PLUTO code. only three of those quantities are independent.," However, in terms of the normalizations used in the PLUTO code, only three of those quantities are independent."
 A possible choice is the mass of the central object. velocity scale and density scale. while the remaining factors are calculated from these.," A possible choice is the mass of the central object, velocity scale and density scale, while the remaining factors are calculated from these."
" Here we use three different “coordinate systems"": 1) the computational grid of cells with indices (./) from (0.0) to (199,399), i1) the PLUTO domain from (0.6) to (50.100) and in) the physical scale of the jet in AU. which is simply the PLUTO domain multiplied with a length scale Ro."," Here we use three different “coordinate systems”: i) the computational grid of cells with indices $i$ $j$ ) from (0,0) to (199,399), ii) the PLUTO domain from (0,6) to (50,100) and iii) the physical scale of the jet in AU, which is simply the PLUTO domain multiplied with a length scale $R_0$."
 In the solution of VOO. the length scale Ao is connected to the mass of the central object and the velocity normalization via From the velocity and density normalization directly follow the normalizations for the magnetic field and pressure as The mass of the central object affects only the length scale.," In the solution of V00, the length scale $R_0$ is connected to the mass of the central object and the velocity normalization via From the velocity and density normalization directly follow the normalizations for the magnetic field and pressure as The mass of the central object affects only the length scale."
 The pressure and temperature of the Jet and thus the synthetic emission maps are affected only by the unit density and unit velocity., The pressure and temperature of the jet and thus the synthetic emission maps are affected only by the unit density and unit velocity.
 As typical jet velocities in YSOs we assumed values of 100. 300. 600 and 1000 km s'. as typical masses of T Tauri stars 0.2. 0.5 and 0.8 M.. (Hartiganetal.1995).. and as Jet number densities valuesof 125. 500. 1000 and 5x10! em.," As typical jet velocities in YSOs we assumed values of 100, 300, 600 and 1000 km $^{-1}$, as typical masses of T Tauri stars 0.2, 0.5 and 0.8 $_{\odot}$ \citep{HEG95}, and as jet number densities valuesof 125, 500, 1000 and $5\times10^4$ $^{-3}$ ."
 We adopt the nomenclature for our runs as e.g. Gr. via. M) with m4 in em. vj in km s! and M in Ms.," We adopt the nomenclature for our runs as e.g. $n_{\rm jet}$, $v_{\rm jet}$, $M$ ) with $n_{\rm jet}$ in $^{-3}$, $v_{\rm jet}$ in km $^{-1}$ and $M$ in $_{\odot}$."
 In order to find the normalizations listed above. we needed to have typical values of jet density and velocity at a certain position (R. z) for a given mass M. and iteratively solved the Eq. (19).," In order to find the normalizations listed above, we needed to have typical values of jet density and velocity at a certain position $R$, $z$ ) for a given mass $M$, and iteratively solved the Eq. \ref{length_scale}) )."
 Details of this algorithm and also a graphical picture of this approach are given in Appendix AppendixA:., Details of this algorithm and also a graphical picture of this approach are given in Appendix \ref{app_norm}.
. The normalizations vary from numerical model to numerical model. therefore we used the corresponding different values for each model.," The normalizations vary from numerical model to numerical model, therefore we used the corresponding different values for each model."
 As another constraint. we require that Ro is small enough that the FWHM of the Gaussian of 15 AU is sampled by a reasonable number of pixels.," As another constraint, we require that $R_0$ is small enough that the FWHM of the Gaussian of 15 AU is sampled by a reasonable number of pixels."
 Because the resolution of our numerical simulations was four pixels per Ro. requiring at least two pixels per FWHM requires Ro<30 AU.," Because the resolution of our numerical simulations was four pixels per $R_0$, requiring at least two pixels per FWHM requires $R_0 < 30$ AU."
 This limit highly reduces the number of runs. from 576 to 180.," This limit highly reduces the number of runs, from 576 to 180."
 The only valid runs are The corresponding values of Ro are listed in Table 2.., The only valid runs are The corresponding values of $R_0$ are listed in Table \ref{tbl_R0}.
 After plotting transverse intensity cuts through the convolved emission maps. it can be seen that the maximum emission does not come from the axis. but from a small shell at a finite radius (Fig. 2..," After plotting transverse intensity cuts through the convolved emission maps, it can be seen that the maximum emission does not come from the axis, but from a small shell at a finite radius (Fig. \ref{Fig_limb_brightening},"
 left)., left).
 This effect of limb-brightening. which has beer never observed up to now in real protostellar jets. is a direct consequence of the density and pressure/temperature profiles 11 the analytical solution and ts present in all our models and runs. the untruncated model ADO as well as our truncated models.," This effect of limb-brightening, which has been never observed up to now in real protostellar jets, is a direct consequence of the density and pressure/temperature profiles in the analytical solution and is present in all our models and runs, the untruncated model ADO as well as our truncated models."
 Detailsof the physical reasons for this behavior are given 1 Appendix Appendix B:.., Detailsof the physical reasons for this behavior are given in Appendix \ref{app_limb}. .
 Because the analytical solution isnot well defined close to the axis and we had to interpolate it in our numerical, Because the analytical solution isnot well defined close to the axis and we had to interpolate it in our numerical
Iscussed in Section 6.,discussed in Section 6.
 In Figure l(a) the variation of the total usiencd magnetic flux within the selected. active region can be seen as a fiction of time., In Figure \ref{fig:fig3}( (a) the variation of the total unsigned magnetic flux within the selected active region can be seen as a function of time.
" The fiux values ave eiven in units of 107 Mx. aud time in davs from 16"" December 1996 19.12.05 UT.", The flux values are given in units of $10^{22}$ Mx and time in days from $^{th}$ December 1996 19.12.05 UT.
 The solid line in Figure 1((a) shows the total unsigned Hix as derived froii the individual magnetograms., The solid line in Figure \ref{fig:fig3}( (a) shows the total unsigned flux as derived from the individual magnetograms.
 The flux values are cousistent with a medi sized active region., The flux values are consistent with a medium sized active region.
 Initially over the first dav the Hux values are secu to increase shelth. possibly due to LOS changes as the region rotates toward central meridian and the cierecuce of a sinall dipole ou the south-western edee of the active reeion.," Initially over the first day the flux values are seen to increase slightly, possibly due to LOS changes as the region rotates toward central meridian and the emergence of a small bipole on the south-western edge of the active region."
 However. between davs 1-1 the flux decays away as cancellation becomes significant along he iuterual PIL (Creen&μοι2009).," However, between days 1-4 the flux decays away as cancellation becomes significant along the internal PIL \citep{gree09}."
. By the eud of day { the flux has dropped bv 20% of its original value., By the end of day 4 the flux has dropped by $20\%$ of its original value.
 This behavior fits well with the observation that it is a cdecaving active recion., This behavior fits well with the observation that it is a decaying active region.
 The peak flux densities found within both the positive and negative poluities are around LkC. Iu Figure {10} the flix difference (flix imbalance) calculated for each magnetogram can be seen as a function of time., The peak flux densities found within both the positive and negative polarities are around $1$ kG. In Figure \ref{fig:fig3}( (b) the flux difference (flux imbalance) calculated for each magnetogram can be seen as a function of time.
 Over the four dav period the inbalance is svstematically negative. possibly duc oa dominanutlv negative surrounding siiall scale fields.," Over the four day period the imbalance is systematically negative, possibly due to a dominantly negative surrounding small scale fields."
 At worst it is 1054 that of the total flux of he active region., At worst it is $10\%$ that of the total flux of the active region.
 As this value is iuall. the active reeion may be regarded to be iu flux balance to a uel degree of accuracy.," As this value is small, the active region may be regarded to be in flux balance to a high degree of accuracy."
 To use the magnetoeramso as a lower boundary condition in the ummerical simulations complete Hux balauce is required., To use the magnetograms as a lower boundary condition in the numerical simulations complete flux balance is required.
 Therefore in cach maeuetogram 1e ubalauce per pixel is deteriuiued and subtracted roni each pixel., Therefore in each magnetogram the imbalance per pixel is determined and subtracted from each pixel.
 This correction varies from one -ragnetoeram to the next., This correction varies from one magnetogram to the next.
 In general it is less iu |6 [G and so is comparable to the noise vel within the magnetograms and siguificautlv ess that the peak flux density., In general it is less than $\mid 6 \mid$ G and so is comparable to the noise level within the magnetograms and significantly less that the peak flux density.
 After correction. je variation of the total unsigned flux is eiven by 1ο dotted line in Fieure ία).," After correction, the variation of the total unsigned flux is given by the dotted line in Figure \ref{fig:fig3}( (a)."
 It can be seen that us line follows the uncorrected fix very closely and applying the correction docs uot significantly effect the net flux of the active region., It can be seen that this line follows the uncorrected flux very closely and applying the correction does not significantly effect the net flux of the active region.
 To simulate the evolution of the coronal maguctic, To simulate the evolution of the coronal magnetic
the number of correctly functioning PCUs.,the number of correctly functioning PCUs.
 For the lightcurve analysis PCUs 2. 3. and 4+ were used: whilst for the spectral analysis only PCU 2 was used.," For the lightcurve analysis PCUs 2, 3, and 4 were used; whilst for the spectral analysis only PCU 2 was used."
 Only the top layer of each PCU was included in the measurements and the time resolution of the data was 16 s. Background subtracted light curves were constructed in four energy bands: 2-- keV. 4-6 keV. 6-10 keV and 10-20 keV. as well as a combined 2-10 keV band for maximum signal-to-noise.," Only the top layer of each PCU was included in the measurements and the time resolution of the data was 16 s. Background subtracted light curves were constructed in four energy bands: 2–4 keV, 4–6 keV, 6–10 keV and 10–20 keV, as well as a combined 2–10 keV band for maximum signal-to-noise."
 In the presence of white noise in the data. the power values in the power spectrum are expected to follow an exponential distribution.," In the presence of white noise in the data, the power values in the power spectrum are expected to follow an exponential distribution."
 However. any correlated noise e.g. red noise. will mean the distribution becomes frequency dependent.," However, any correlated noise e.g. red noise, will mean the distribution becomes frequency dependent."
 This makes estimating the significance limits in the power spectra non-trivial., This makes estimating the significance limits in the power spectra non-trivial.
 As accreting systems usually show flickering in their lighteurves. it is feasible to believe that there may be a significant red noise component in the data.," As accreting systems usually show flickering in their lightcurves, it is feasible to believe that there may be a significant red noise component in the data."
 In order to take this into account in the analysis. the technique introduced in was used.," In order to take this into account in the analysis, the technique introduced in \citet{hakala04} was used."
 The data were equally spaced (apart from the large gaps in between different orbits). so the red noise component was modelled by fitting a second order autoregressive process model to the lightcurves.," The data were equally spaced (apart from the large gaps in between different orbits), so the red noise component was modelled by fitting a second order autoregressive process model to the lightcurves."
 This model was then used to generate 500000 synthetic lighteurves with similar red and white noise properties. as well as observing window. to the original datasets.," This model was then used to generate 000 synthetic lightcurves with similar red and white noise properties, as well as observing window, to the original datasets."
 The95.2%... and (2. 3 and dc respectively) significance limits (as a function of frequency) were then calculated.," The, and (2, 3 and $\sigma$ respectively) significance limits (as a function of frequency) were then calculated."
 To estimate the error on the measured periods we folded the raw data at the period found from the period analysis., To estimate the error on the measured periods we folded the raw data at the period found from the period analysis.
 We then fitted a curve to this folded data., We then fitted a curve to this folded data.
 This curve (repeatec over the whole data set) was then subtracted from the raw data leaving residual values., This curve (repeated over the whole data set) was then subtracted from the raw data leaving residual values.
 These were then shuffled and addec to the fitted curve. yielding a new synthetic raw data set.," These were then shuffled and added to the fitted curve, yielding a new synthetic raw data set."
 This synthetic data was then analysed as before., This synthetic data was then analysed as before.
 This whole process was repeated ~200 times and the resulting periods were ther used to calculate à standard deviation of periods. which was then used as the error estimate.," This whole process was repeated $\sim200$ times and the resulting periods were then used to calculate a standard deviation of periods, which was then used as the error estimate."
 A mean X-ray spectrum was also extracted for each source. and two spectral nodels applied to find the best fit. using the package.," A mean X-ray spectrum was also extracted for each source, and two spectral models applied to find the best fit, using the package."
 The models considered were a photoelectrically absorbed single temperature bremsstrahlung with a Gaussian at the iron line emission energy (model A). and a photoelectrically absorbed power law with a similar Gaussian (model B).," The models considered were a photoelectrically absorbed single temperature bremsstrahlung with a Gaussian at the iron line emission energy (model A), and a photoelectrically absorbed power law with a similar Gaussian (model B)."
 10056 was observed over two consecutive days (see Table 1))., J0056 was observed over two consecutive days (see Table \ref{observing_log}) ).
 The total good time on target 8800 3) comprised fourteen approximately equal segments of one satellite orbit each., The total good time on target 800 s) comprised fourteen approximately equal segments of one satellite orbit each.
 In the 2-10 keV energy band the raw count rate varied between 3.9 and 9.1 et s! PCU-'., In the 2–10 keV energy band the raw count rate varied between 3.9 and 9.1 ct $^{-1}$ $^{-1}$.
 The background count rate. generated from the calibration files. varied between 2.9 and 4ος ΡΟ.," The background count rate, generated from the calibration files, varied between 2.9 and 4.1 ct $^{-1}$ $^{-1}$."
 A significant (> 407) peak was present in the periodogram at ~ 185 cyeles day”! in the 2-10 keV energy band (see Fig. 1))., A significant $>4\sigma$ ) peak was present in the periodogram at $\sim$ 185 cycles $^{-1}$ in the 2–10 keV energy band (see Fig. \ref{J00564_red_noise}) ).
 Analysis of the peak gave a pulsation period of 465.6840.07 s. The data were then folded in each energy band at this period. Fig.," Analysis of the peak gave a pulsation period of $\pm$ 0.07 s. The data were then folded in each energy band at this period, Fig."
 2 shows the result of the 2-10 keV energy band., \ref{J00564_folded} shows the result of the 2–10 keV energy band.
 In each energy band a sinusoid was fitted to the folded data to estimate the modulation depth of the variation (see Table 2))., In each energy band a sinusoid was fitted to the folded data to estimate the modulation depth of the variation (see Table \ref{modulation_depths}) ).
 There is a clear decreasing trend m the modulation depth with increasingenergy., There is a clear decreasing trend in the modulation depth with increasingenergy.
 Clustered around the 185 cycles day! peak were a series of smaller peaks. spaced apart by ~8 cycles day!. the largest of which was at 489.040.7 s. There was also one other peak detected at above the 4c level at ~41 cycles day! (21109 s).," Clustered around the 185 cycles $^{-1}$ peak were a series of smaller peaks, spaced apart by $\sim8$ cycles $^{-1}$ , the largest of which was at $\pm$ 0.7 s. There was also one other peak detected at above the $\sigma$ level at $\sim41$ cycles $^{-1}$ 109 s)."
 The best spectral fit was a simple photoelectrically absorbed bremsstrahlung model with a Gaussian added., The best spectral fit was a simple photoelectrically absorbed bremsstrahlung model with a Gaussian added.
 This fit had the parameters AT=22+2 keV. ny=(0.6404)107 em- and a Gaussian at 6.540.1 keV with a width of 0.340.1 keV. which was interpreted as a iron feature 0.8). as shown in Fig.," This fit had the parameters $kT=22\pm2$ keV, $n_{\rm
 H}=(0.6\pm0.4)~\times10^{22}$ $^{-2}$ and a Gaussian at $\pm$ 0.1 keV with a width of $\pm$ 0.1 keV, which was interpreted as a iron feature $\chi_{\rm reduced}^2=0.8$ ), as shown in Fig."
 3 and summarised in Table 3.., \ref{J00564_spectrum} and summarised in Table \ref{spectral_fits}.
" The table also shows the Galactic column density to the object as derived from the HEASARC sy tool"".", The table also shows the Galactic column density to the object as derived from the HEASARC $n_{\rm H}$ .
 Data were takenover two consecutive days (see Table 1))., Data were takenover two consecutive days (see Table \ref{observing_log}) ).
 The total good time on target (359936 s) was split over twelve, The total good time on target 936 s) was split over twelve
elliptical galaxies. it 1s reasonable to assume that the environment may play a crucial role in their evolution.,"elliptical galaxies, it is reasonable to assume that the environment may play a crucial role in their evolution."
 Segregation within the dwarf ellipticals in Virgo itself has already. been noted by several authors (Ferguson&Sandage1989:OhLin2000).. who point out that the nucleated dE's occupy the cluster core. whereas the majority of nou-nucleated oues are [οι in the peripheral regious.," Segregation within the dwarf ellipticals in Virgo itself has already been noted by several authors \citep{FS89,Oh00}, who point out that the nucleated dE's occupy the cluster core, whereas the majority of non-nucleated ones are found in the peripheral regions."
 Furthermore. as discussed in Section 3. ram pressure stripping is an efficieut mechauisi to remove the ISM from cluster members. regardless of total mass.," Furthermore, as discussed in Section 3, ram pressure stripping is an efficient mechanism to remove the ISM from cluster members, regardless of total mass."
 Infall of galaxies into the Virgo Cluster is au ongoing process (Tully&Shaya1051Couseliceetal.2003):: oue thus expects that small eroups of galaxies similar to the Local Group continue to fall into the Virgo Cluster.," Infall of galaxies into the Virgo Cluster is an ongoing process \citep{TS84,COGW03}; one thus expects that small groups of galaxies similar to the Local Group continue to fall into the Virgo Cluster."
 Given the simple surface mass deusity criteria for ram pressure stripping (Camu&Gott1972).. essentially all low mass dwarl irregular galaxies falling into the Virgo cluster will be stripped of their gas 2003).," Given the simple surface mass density criteria for ram pressure stripping \citep{GG72}, essentially all low mass dwarf irregular galaxies falling into the Virgo cluster will be stripped of their gas \citep[e.g.,][]{MBD03}."
. Indeed. there is evideuce of a very recent. case of stripping ola Virgo dwarf galaxy (UGC7636.Sancisi.Thounarcd.&Ekers1957:PattersouThuan1992).," Indeed, there is evidence of a very recent case of stripping of a Virgo dwarf galaxy \citep[UGC 7636,][]{STE87,PT92}."
. Unless one imagines that all dwarl galaxies that [all 1[uno the Virgo cluster are already dEs. (aud he [act that they are falling in from low deusity envirouments argues strongly against this). then it would appear to be inevitable that some of the «Es in the Virgo cluster are stripped cls.," Unless one imagines that all dwarf galaxies that fall into the Virgo cluster are already dEs (and the fact that they are falling in from low density environments argues strongly against this), then it would appear to be inevitable that some of the dEs in the Virgo cluster are stripped dIs."
 Siuce dwarf irregular galaxies are clark matter dominated. removal of their ISM will have only a uodest effect ou their kinematics.," Since dwarf irregular galaxies are dark matter dominated, removal of their ISM will have only a modest effect on their kinematics."
 However. subsequent passages through the cluster could further disrupt the stellar kinematies via galaxy harassiuent or mereing events.," However, subsequent passages through the cluster could further disrupt the stellar kinematics via galaxy harassment or merging events."
 Thus. if dls are converted into «Es via ram pressure strippiug. one might expect a correlation between the location of dwarl elliptical galaxies with significant rotation aud the cluster center.," Thus, if dIs are converted into dEs via ram pressure stripping, one might expect a correlation between the location of dwarf elliptical galaxies with significant rotation and the cluster center."
 While the present sample is ‘el:ively sinall. Figure 5 shows a lint of such a relationship. in the sense that galaxies with rotation appear to be located. predominantly tu the cluster core or in high density. elumps. while those with significant rotation are in the outskirts of the cluster.," While the present sample is relatively small, Figure \ref{fig:cluster} shows a hint of such a relationship, in the sense that galaxies with little-to-no rotation appear to be located predominantly in the cluster core or in high density clumps, while those with significant rotation are in the outskirts of the cluster."
 This is cousisteut with the idea that gas-richi dwarl galaxies are stripped of their gas during a passage through the intracluster uediun: the uou-rotating cdwarl elliptical galaxies may be remuauts of eas-rich systems that have uace multiple passes through the ICM. or hada catastropliie event occur.," This is consistent with the idea that gas-rich dwarf galaxies are stripped of their gas during a passage through the intracluster medium; the non-rotating dwarf elliptical galaxies may be remnants of gas-rich systems that have made multiple passes through the ICM, or had a catastrophic event occur."
 We caution. however. tliat he present sample size is relatively sinall aud. biased toward the more luminous cluster dEs: further observations of a larger sample of dwarl elliptical galaxies throughout the cluster euviroument are ieeced to investigate this suggestive trend.," We caution, however, that the present sample size is relatively small and biased toward the more luminous cluster dEs; further observations of a larger sample of dwarf elliptical galaxies throughout the cluster environment are needed to investigate this suggestive trend."
 Although we have argued above that the available observations do not allow us to establish he relative streugtlis of the rotatioually supported aud non-rotationally supported dE populatious. we canuot close without some speculation ou the preseuce of nou-rotatiug dE galaxies.," Although we have argued above that the available observations do not allow us to establish the relative strengths of the rotationally supported and non-rotationally supported dE populations, we cannot close without some speculation on the presence of non-rotating dE galaxies."
 Following he same liue of arguimeute eοἶνοι above. Le.. that it is almost inescapable that some of the dEs observed in the Virgo cluster must have lost their gas to rain pressure stripping. it is also likely hat some clwarl galaxies entered the Virgo cluster as dEs before they encountered sullicient hot eas for strippiug.," Following the same line of argument given above, i.e., that it is almost inescapable that some of the dEs observed in the Virgo cluster must have lost their gas to ram pressure stripping, it is also likely that some dwarf galaxies entered the Virgo cluster as dEs before they encountered sufficient hot gas for stripping."
 It also seems inescapable that some cll galaxies interact tidally with more massive @alaxies. aud thereby lose gas in this manuer.," It also seems inescapable that some dI galaxies interact tidally with more massive galaxies, and thereby lose gas in this manner."
 Civen that it is difficult to quantity the relative inportance of these {νου different clianuels of cluster dE galaxy formation. we caution agalust sinele Channel evolutionary scenarios.," Given that it is difficult to quantify the relative importance of these three different channels of cluster dE galaxy formation, we caution against single channel evolutionary scenarios."
 Specifically. we uote that explanations for the deusity-morphology," Specifically, we note that explanations for the density–morphology"
Apart from the reflex peculiar motion of the Sun treated in Section 2.. we observe the heliocentric velocity field AGYrgdy—oy.,"Apart from the reflex peculiar motion of the Sun treated in Section \ref{sun.sec}, we observe the heliocentric velocity field $\Delta \vec
v = \vec a + \vec \omega - \vec a_0 -\vec \omega_0$."
 Projections of this vector field onto the local tangential coordinate frames (7.75) introduced in Appendix A. are substituting the model (3)) into Eqs.," Projections of this vector field onto the local tangential coordinate frames $(\vec
\tau_\ell, \vec \tau_b)$ introduced in Appendix A, are Substituting the model \ref{model.eq}) ) into Eqs."
 4 and retaining only. teris to QU). we obtain alter some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the D(z) terms. let us compare (his equation with the classical expansion of thevelocity field via (he fundamental Oort's constants (e.g..Torraetal.2000).. which in the veetor harmonies notation takes the form E," \ref{proj.eq} and retaining only terms to $O(\frac{r}{\rho_0})$, we obtain after some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the $\Gamma(z)$ terms, let us compare this equation with the classical expansion of thevelocity field via the fundamental Oort's constants \citep[e.g.,][]{tor}, which in the vector harmonics notation takes the form ."
 4 and retaining only. teris to QU). we obtain alter some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the D(z) terms. let us compare (his equation with the classical expansion of thevelocity field via (he fundamental Oort's constants (e.g..Torraetal.2000).. which in the veetor harmonies notation takes the form EM," \ref{proj.eq} and retaining only terms to $O(\frac{r}{\rho_0})$, we obtain after some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the $\Gamma(z)$ terms, let us compare this equation with the classical expansion of thevelocity field via the fundamental Oort's constants \citep[e.g.,][]{tor}, which in the vector harmonics notation takes the form ."
 4 and retaining only. teris to QU). we obtain alter some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the D(z) terms. let us compare (his equation with the classical expansion of thevelocity field via (he fundamental Oort's constants (e.g..Torraetal.2000).. which in the veetor harmonies notation takes the form EMG," \ref{proj.eq} and retaining only terms to $O(\frac{r}{\rho_0})$, we obtain after some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the $\Gamma(z)$ terms, let us compare this equation with the classical expansion of thevelocity field via the fundamental Oort's constants \citep[e.g.,][]{tor}, which in the vector harmonics notation takes the form ."
 4 and retaining only. teris to QU). we obtain alter some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the D(z) terms. let us compare (his equation with the classical expansion of thevelocity field via (he fundamental Oort's constants (e.g..Torraetal.2000).. which in the veetor harmonies notation takes the form EMG)," \ref{proj.eq} and retaining only terms to $O(\frac{r}{\rho_0})$, we obtain after some toil the general expansion where we made use of the functional forms of the vector spherical harmonics in galactic coordinates specified in Appendix A. Disregarding for now the $\Gamma(z)$ terms, let us compare this equation with the classical expansion of thevelocity field via the fundamental Oort's constants \citep[e.g.,][]{tor}, which in the vector harmonics notation takes the form ."
Fitted orbital parameters for PSR D19134-16 are listed in Table 3..,Fitted orbital parameters for PSR B1913+16 are listed in Table \ref{table:orbfits}.
 As we have emphasized belore (Tavlor& Weisberg1989).. values for each of the Damour-Deruelle post-Ixeplerian parameters expected in general relativitv can be expressed in terms of (he Ixeplerian parameters and (he initially unknown masses of the pulsar aid its companion. m ancl mo.," As we have emphasized before \citep{tw89}, values for each of the Damour-Deruelle post-Keplerian parameters expected in general relativity can be expressed in terms of the Keplerian parameters and the initially unknown masses of the pulsar and its companion, $m_1$ and $m_2$."
" The appropriate expressions for (0) and 5 are In (he second line of each equation we have substituted values for 77, ancl e from Table 3.. and used the constants GM,ο)=4925490947x10.5 s and 1 Julian vr =86400x365.25 s. The figures in parentheses represent uncertainties in (he last quoted digit. determined by propagating the uncertainties listed in Table 3.."," The appropriate expressions for $\langle\dot\omega\rangle$ and $\gamma$ are In the second line of each equation we have substituted values for $P_b$ and $e$ from Table \ref{table:orbfits}, and used the constants $G
M_{\sun}/c^3=4.925490947\times10^{-6}$ s and 1 Julian yr $=86400
\times 365.25$ s. The figures in parentheses represent uncertainties in the last quoted digit, determined by propagating the uncertainties listed in Table \ref{table:orbfits}."
 In each case. the uncertainties are dominated bv the experimental uncertainty in orbital eccentricity. €.," In each case, the uncertainties are dominated by the experimental uncertainty in orbital eccentricity, $e$."
 Eq. (, Eq. (
1) may be solved for the total mass of the PSR B19134-16 system. vielding M=0.000007 AL..,"1) may be solved for the total mass of the PSR B1913+16 system, yielding $M=m_1 + m_2=2.828378 \pm 0.000007~M_{\sun}$ ."
 The additional constraint. privided bv Eq. (, The additional constraint privided by Eq. (
2) permits a solution for each stars mass individually. 224=1.4398+0.0002AZ. ancl 0.0002 Af..,"2) permits a solution for each star's mass individually, $m_1=1.4398\pm0.0002 \ M_{\sun}$ and $m_2=1.3886\pm0.0002 \ M_{\sun}$ ."
 As far as we know. these are the most accurately determined stellar masses outside the solar svstem.," As far as we know, these are the most accurately determined stellar masses outside the solar system."
" It is interesting to note that since the value of Newton's constant Gis known to a fractional accuracy of only 1x10.1, AL can be expressed more accurately in solar masses than in grams."," It is interesting to note that since the value of Newton's constant $G$ is known to a fractional accuracy of only $1\times10^{-4}$, $M$ can be expressed more accurately in solar masses than in grams."
 According to general relativity a binary star svstem should radiate energy in the form ol gravitational waves., According to general relativity a binary star system should radiate energy in the form of gravitational waves.
 Peters ancl Matthews (1963) showed that the resulting rate of change, Peters and Matthews (1963) showed that the resulting rate of change
but are in very good agreement with the observed data in the solar neighbourhood and in the outer parts of the disk.,but are in very good agreement with the observed data in the solar neighbourhood and in the outer parts of the disk.
 The higher SER in the inner parts of the MW disk can be due to the presence of a bar. as suggested in Portinart Chiosi (2000). and therefore cannot be reproduced by simple chemical evolution models.," The higher SFR in the inner parts of the MW disk can be due to the presence of a bar, as suggested in Portinari Chiosi (2000), and therefore cannot be reproduced by simple chemical evolution models."
 The stellar surface density of the MW is in agreement with the observed values but models with à smaller threshold (MW-À2 and MW-B) overestimate the stellar content in the outer region of the disk., The stellar surface density of the MW is in agreement with the observed values but models with a smaller threshold (MW-A2 and MW-B) overestimate the stellar content in the outer region of the disk.
 Unlike other observational constraints. the variable efficiency in the SFR does not play an important role for the results relative to the stellar sufarce density. indicating that the threshold ts a stronger mechanism to regulate it.," Unlike other observational constraints, the variable efficiency in the SFR does not play an important role for the results relative to the stellar sufarce density, indicating that the threshold is a stronger mechanism to regulate it."
 In summary. the model that fits best the observational constraints for the Milky Way is the model with variable efficiency for the the star formation (MW-B).," In summary, the model that fits best the observational constraints for the Milky Way is the model with variable efficiency for the the star formation (MW-B)."
 The evolution of the disk of M31 is well reproduced by assuming a faster evolution (faster means a more intense SFR which is due both to the higher efficiency of SF and to the shorter infall timescale) than in the disk of the MW and a higher star formation threshold., The evolution of the disk of M31 is well reproduced by assuming a faster evolution (faster means a more intense SFR which is due both to the higher efficiency of SF and to the shorter infall timescale) than in the disk of the MW and a higher star formation threshold.
 Since the disk of M31 is more massive than the MW one. this implies that more massive disks should form faster and therefore that they are older than less massive ones (see also Botssier et al.," Since the disk of M31 is more massive than the MW one, this implies that more massive disks should form faster and therefore that they are older than less massive ones (see also Boissier et al."
 2003)., 2003).
 The O abundance gradient fron HII regions is well reproduced by all models for M31., The O abundance gradient from HII regions is well reproduced by all models for M31.
 This result confirms the predictions for the MW. showing that the present day abundance gradient is not so sensitive to the changes in the star formation efficiency.," This result confirms the predictions for the MW, showing that the present day abundance gradient is not so sensitive to the changes in the star formation efficiency."
 On the other hand. the time evolution of the O gradient is very dependent on this efficiency. steepening or flattening in time according to the chosen v.," On the other hand, the time evolution of the O gradient is very dependent on this efficiency, steepening or flattening in time according to the chosen $\nu$."
 This fact can be confirmed with the results obtained for M31-Bk1.25 where we used the same efficiency but a different exponent for the SER., This fact can be confirmed with the results obtained for M31-Bk1.25 where we used the same efficiency but a different exponent for the SFR.
 Models with constant efficiency in the star formation (M31- and M31-À2) provide an exponential distribution of the present day gas surface density. while models M31-B. and M31-Bk1.25 with variable efficiency. predict a more realistic scenario with a peak in the gas distribution around 12 kpe which can be related to M31 spiral arms.," Models with constant efficiency in the star formation (M31-A1 and M31-A2) provide an exponential distribution of the present day gas surface density, while models M31-B and M31-Bk1.25 with variable efficiency predict a more realistic scenario with a peak in the gas distribution around 12 kpc which can be related to M31 spiral arms."
 , 
implementation of the method. as described. above.,"implementation of the method, as described above."
 The resulting S4BR) will be representative of the stars which where used in the construction of the likelihood matrix., The resulting $SFR(t)$ will be representative of the stars which where used in the construction of the likelihood matrix.
 To normalize the various inferred οκ) [rom samples having dillerent AA limits. ancl hence complete out to dillerent distances. we apply the following kinematic and geometric corrections.," To normalize the various inferred $SFRs(t)$ from samples having different $M_{V}$ limits, and hence complete out to different distances, we apply the following kinematic and geometric corrections."
 Let F(v.h) be the fraction of the time a star having vertical velocity at the disk plane e spends between heights h and |.," Let $F(v,h)$ be the fraction of the time a star having vertical velocity at the disk plane $v$ spends between heights $-h$ and $+h$."
 Then. for a cylindrical saniple complete to height h above and below the disk plane. where ΑΟ} is the number of stars a stellar population of age / contains. IN.(/) the number of stars of age | observed. and a(/) the time dependent: velocity. dispersion of the several populations.," Then, for a cylindrical sample complete to height $h$ above and below the disk plane, where $N(t)$ is the number of stars a stellar population of age $t$ contains, $N_{o}(t)$ the number of stars of age $t$ observed and $\sigma(t)$ the time dependent velocity dispersion of the several populations."
 As volunie-limitecd samples are generally spherical around. the Sun. a further. geometric [actor is required. giving: where 2 is the radius of the observed spherical volume limited sample. ris a radial coordinate and AF=Rork2," As volume-limited samples are generally spherical around the Sun, a further geometric factor is required, giving: where $R$ is the radius of the observed spherical volume limited sample, $r$ is a radial coordinate and $h^2=R^2-r^2$."
 ‘To estimate {ο/)) one requires the detailed: vertical force law of the galactic disk at the solar neighbourhood.," To estimate $F(v,h)$ one requires the detailed vertical force law of the galactic disk at the solar neighbourhood."
 The best direct estimate of this function remains that of Ixuijken and Gilmore(1989). who show this function to deviate [rom that of à harmonic potential to a large degree.," The best direct estimate of this function remains that of Kuijken and Gilmore (1989), who show this function to deviate from that of a harmonic potential to a large degree."
 This detailed force law we integrate numerically to obtain £fc.hh).," This detailed force law we integrate numerically to obtain $F(v,h)$."
 We use c(t)=20km/s which is appropriate for the metallicity anc age ranges we are studving (Ixlvardsson et al., We use $\sigma(t) \; = \; 20 \; {\rm km/s} $ which is appropriate for the metallicity and age ranges we are studying (Edvardsson et al.
 1993. \Woyse Cilmore 1995.," 1993, Wyse Gilmore 1995)."
 —Note also that the scatter in metallicity within NO pc is small(Garnett and Ixobulnickv. 1999) and will not change significantly our results.," Note also that the scatter in metallicity within 80 pc is rather small (Garnett and Kobulnicky, 1999) and will not change significantly our results."
 1n this way. assuming a Gaussian distribution for the vertical velocities of the stars. and a given e(/). an observed ING) can be transformed into a total ΑΟ]. which is equal to the total projected. disk quantity.," In this way, assuming a Gaussian distribution for the vertical velocities of the stars, and a given $\sigma(t)$, an observed $N_{o}(t)$ can be transformed into a total $N(t)$ , which is equal to the total projected disk quantity."
 In our case the SIBI) eiven by the method. takes the place of /NS(D). and equation (6) is used to. obtain a final star formation history. which accounts for the kinematic ancl geometric factors described.," In our case the $SFR(t)$ given by the method takes the place of $N_{o}(t)$, and equation (6) is used to obtain a final star formation history, which accounts for the kinematic and geometric factors described."
 This function is then normalized through the total number of stars in the relevant sample. to give the deduced: SAAC) in units of Al. tkpe27.," This function is then normalized through the total number of stars in the relevant sample, to give the deduced $SFR(t)$ in units of $M_{\odot}$ $^{-1}$ $^{-2}$."
 ligure (4) shows the CALD corresponding to a volume-limited sample complete to Ady<3.15 for stars in the llipparcos catalogue having errors in. parallax of less than 20% and my«7.25 (loft. panel)., Figure (4) shows the CMD corresponding to a volume-limited sample complete to $M_{V}<3.15$ for stars in the Hipparcos catalogue having errors in parallax of less than $20 \%$ and $m_{V}<7.25$ (left panel).
 The right panel of this figure shows the result of applying our inversion method to this CMD. solid curve.," The right panel of this figure shows the result of applying our inversion method to this CMD, solid curve."
" The dotted envelope encloses several alternative reconstructions arising [rom dillerent. A, cuts. and gives an estimate of the errors likely to be present. in ourresult. which can be seen to increase with time."," The dotted envelope encloses several alternative reconstructions arising from different $M_{V}$ cuts, and gives an estimate of the errors likely to be present in ourresult, which can be seen to increase with time."
 The, The
(consistent with the difference in the burst tails in Figure 1). and they show much larger burst to burst variations than observed.,"(consistent with the difference in the burst tails in Figure 1), and they show much larger burst to burst variations than observed."
 Also. whereas the observed bursts are well fit by a two-timescale decay. some of the model bursts show a more complex decay profile. which we have fitted with three timescales.," Also, whereas the observed bursts are well fit by a two-timescale decay, some of the model bursts show a more complex decay profile, which we have fitted with three timescales."
 We have presented a first comparison between multizone burst models and the observed bursts from1826-24., We have presented a first comparison between multizone burst models and the observed bursts from.
. The good agreement further confirms ads a “textbook” burster., The good agreement further confirms as a “textbook” burster.
". For a distance of (6.07+ (where ¢, is the burst emission anisotropy factor). our solar metallicity models closely match. the observed lighteurves."," For a distance of $(6.07\pm 0.18)\ {\rm kpc}\ \xi_b^{-1/2}$ (where $\xi_b$ is the burst emission anisotropy factor), our solar metallicity models closely match the observed lightcurves."
 Both the long rise and decay times arise naturally from rp-process hydrogen burning., Both the long rise and decay times arise naturally from rp-process hydrogen burning.
 From the very regular nature of the bursting. GO4 argued that the accreted material covers the entire surface of the neutron star: this is supported by the excellent agreement of our spherically-symmetric models.," From the very regular nature of the bursting, G04 argued that the accreted material covers the entire surface of the neutron star; this is supported by the excellent agreement of our spherically-symmetric models."
 Solar metallicity models agree best with the observed lighteurves., Solar metallicity models agree best with the observed lightcurves.
 Low metallicity models produce too little helium by hot CNO burning prior to ignition. leading to a lower peak luminosity and a longer rp-process tail.," Low metallicity models produce too little helium by hot CNO burning prior to ignition, leading to a lower peak luminosity and a longer rp-process tail."
 This agrees with the conclusions of GO4. who argued for solar metallicity based on the burst energetics.," This agrees with the conclusions of G04, who argued for solar metallicity based on the burst energetics."
 The estimate of the distance is based on a comparison of mean burst lighteurve at asingle epoch. with the lightcurve predicted by the model for parameters giving the same recurrence time.," The estimate of the distance is based on a comparison of mean burst lightcurve at a single epoch, with the lightcurve predicted by the model for parameters giving the same recurrence time."
 It is possible that lightcurve comparisons at different epochs (1.e. values of the recurrence time) may result in different values of the distance and/or anisotropy parameters., It is possible that lightcurve comparisons at different epochs (i.e. values of the recurrence time) may result in different values of the distance and/or anisotropy parameters.
 Such comparisons will provide an additional consistency check for the distance estimation. which we will undertake in a future paper.," Such comparisons will provide an additional consistency check for the distance estimation, which we will undertake in a future paper."
" Our models reproduce the observed variation in. burst recurrence times. energies. and à values with accretion rate for a ratio of anisotropy factors for the persistent and burst emission of €,/€»=1.55."," Our models reproduce the observed variation in burst recurrence times, energies, and $\alpha$ values with accretion rate for a ratio of anisotropy factors for the persistent and burst emission of $\xi_p/\xi_b=1.55$."
 This is within the range discussec by Fujimoto(1988) and similar to that inferred for other sources (e.g. Sztajnoetal.1987))., This is within the range discussed by \cite{fuji88} and similar to that inferred for other sources (e.g. \citealt{sztajno}) ).
 GO4 found that the ignitior models of Cumming&Bildsten(2000) reproduced the change in a. but not the scaling of ignition column with M.," G04 found that the ignition models of \cite{CB00} reproduced the change in $\alpha$, but not the scaling of ignition column with $\dot M$."
 In these models. there is less time for helium productior between bursts at higher M. delaying the ignition. and leading to increasing ignition mass.," In these models, there is less time for helium production between bursts at higher $\dot M$, delaying the ignition, and leading to increasing ignition mass."
 However. our time-dependent models show that the chemical and thermal inertia associated with the ashes from previous bursts (Taam 1980) outweighs the lower helium abundance. heating the layer. and leading to asmaller ignition mass as M increases. in agreement with observations.," However, our time-dependent models show that the chemical and thermal inertia associated with the ashes from previous bursts (Taam 1980) outweighs the lower helium abundance, heating the layer, and leading to a ignition mass as $\dot M$ increases, in agreement with observations."
 A change in the covering fraction of accreted fuel. as speculated by GO4. is not required.," A change in the covering fraction of accreted fuel, as speculated by G04, is not required."
 Despite the good agreement. there are several differences between the observations and the models which need to be investigated in future work.," Despite the good agreement, there are several differences between the observations and the models which need to be investigated in future work."
 These comparisons promise to constrain the nuclear physics of the rp-process. the thermal properties of the burning layers. spreading of the nuclear burning. and neutron star parameters.," These comparisons promise to constrain the nuclear physics of the rp-process, the thermal properties of the burning layers, spreading of the nuclear burning, and neutron star parameters."
 The model burst lightcurves show a distinct two-component rise which is not present in the data. as well as a slightly shorter burst tail.," The model burst lightcurves show a distinct two-component rise which is not present in the data, as well as a slightly shorter burst tail."
 Another difference in burst shape is that. unlike the observations. some of the model lightcurves show a three-stage rather than two-stage decay.," Another difference in burst shape is that, unlike the observations, some of the model lightcurves show a three-stage rather than two-stage decay."
 These differences may relate to our treatment of heat transport (especially convection) or nuclear physics., These differences may relate to our treatment of heat transport (especially convection) or nuclear physics.
" WO4. confirmed previous findings that burst tails are sensitive to nuclear flows above the iron group (Schatzetal.2001a;Koike1999)., and also pointed out that the rise times are sensitive to nuclear decays the iron group."," W04 confirmed previous findings that burst tails are sensitive to nuclear flows above the iron group \citep{sch01a,koi99}, and also pointed out that the rise times are sensitive to nuclear decays the iron group."
" An alternative for the rise is that a finite propagation time for the burning around the star of Is (e.g. Fryxell&Woosley1982:: Spitkovskyetal. 2002)) might act to “wash out"" the kink.", An alternative for the rise is that a finite propagation time for the burning around the star of $\sim 1\ {\rm s}$ (e.g. \citealt{fryxellwoosley}; \citealt{spitkovsky}) ) might act to “wash out” the kink.
 The neutron star mass and radius also change the predicted burst properties., The neutron star mass and radius also change the predicted burst properties.
 In this paper. we have considered a neutron star with redshift factor z20.26. corresponding to M21.4M. and R=11.2 km.," In this paper, we have considered a neutron star with redshift factor $z=0.26$, corresponding to $M=1.4\ M_\odot$ and $R=11.2\ {\rm km}$ ."
 A smaller radius of 10.6km would reduce the predicted burst energies by5%.. and would increase the redshift factor and therefore a. bringing both of these quantities into better agreement with observations (Fig.," A smaller radius of $10.6\ {\rm km}$ would reduce the predicted burst energies by, and would increase the redshift factor and therefore $\alpha$, bringing both of these quantities into better agreement with observations (Fig."
 2)., 2).
 We will investigate the constraints on the neutron star mass and radius in detail in future work., We will investigate the constraints on the neutron star mass and radius in detail in future work.
 AH is supported by the Department of Energy under grant W-7405-ENG-36 to the Los Alamos National Laboratory., AH is supported by the Department of Energy under grant W-7405-ENG-36 to the Los Alamos National Laboratory.
 AC is grateful for support from NSERC. CIfAR. FQRNT. and is an Alfred P. Sloan Research Fellow.," AC is grateful for support from NSERC, CIfAR, FQRNT, and is an Alfred P. Sloan Research Fellow."
 SW acknowledges support from the NSF (AST 02-06111). NASA (NAGS-12036). andthe DOE Program for Scientific Discovery through Advanced Computing (SciDAC:; DE-," SW acknowledges support from the NSF (AST 02-06111), NASA (NAG5-12036), andthe DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DE-FC02-01ER41176)."
As suggested by Soderbergetal.(2006).. there is an empirical relation between the kinetic energy (Εκ) and the velocity (ic) of the hypernova ejecta. parameterized as Ex=10°70140.15. where T=(0178?) ,"As suggested by \citet{Soderberg2006}, there is an empirical relation between the kinetic energy $E_K$ ) and the velocity $\beta c$ ) of the hypernova ejecta, parameterized as $E_K = 10^{52} (\Gamma \beta / 0.1)^{-2}$ , where $\Gamma = (1 - \beta^2)^{-1/2}$ ."
The low velocity component with D./—0.1 corresponds to à very energetic supernova. while the high velocity component with D;~| corresponds to the mildly relativistic ejecta.," The low velocity component with $\Gamma \beta \simeq 0.1$ corresponds to a very energetic supernova, while the high velocity component with $\Gamma \beta \simeq 1$ corresponds to the mildly relativistic ejecta."
 It is assumed that the energy of the ejecta components Is dissipated when they start to decelerate. going into relativistic particles.," It is assumed that the energy of the ejecta components is dissipated when they start to decelerate, going into relativistic particles."
 The deceleration occurs as a result of interaction with the surrounding matter. which we assume ts provided by the mass loss of the massive progenitor (Wolf-Rayet type) star.," The deceleration occurs as a result of interaction with the surrounding matter, which we assume is provided by the mass loss of the massive progenitor (Wolf-Rayet type) star."
" We adopt a fiduciary mass-loss rate of M=107M.. and a wind velocity v,210° km s7!.", We adopt a fiduciary mass-loss rate of $\dot M = 10^{-5} M_{\sun}$ and a wind velocity $v_w = 10^3$ km $^{-1}$.
 The density profile is then pu2OM/Azvar?=8«10!72 g em! ," The density profile is then $\rho(r) = (\dot M / 4 \pi v_w) r^{-2} 
= 5 \times 10^{11} r^{-2}$ g $^{-1}$ ."
In this case. the kinetic energy (Ey=10? erg) of the mildly relativistic ejecta (D./= 1) starts to be dissipated when it reaches at radius rzRc109 em.," In this case, the kinetic energy $E_K = 10^{50}$ erg) of the mildly relativistic ejecta $\Gamma \beta = 1$ ) starts to be dissipated when it reaches at radius $r = R \simeq
10^{16}$ cm."
 The corresponding dynamical time scale is fa=R/cE3«10° s. a few days.," The corresponding dynamical time scale is $t_{\rm dyn} = R/ c \Gamma
\beta = 3 \times 10^5$ s, a few days."
 Around that time. the hypernova luminosity is still very large.," Around that time, the hypernova luminosity is still very large."
 On the other hand. if we consider sub-relativistic but more energetic ejecta. the dynamical time scale is significantly larger. by which time the hypernova luminosity has decreased. a situation that is not interesting for the present purposes.," On the other hand, if we consider sub-relativistic but more energetic ejecta, the dynamical time scale is significantly larger, by which time the hypernova luminosity has decreased, a situation that is not interesting for the present purposes."
 The hypernova luminosity around a few days after the explosion is roughly Ls=107 erg s! and we assume the spectrum is black body with a temperature of ~ 1 eV: a typical photon energy is 5.=2.7 eV. The photon number density at the dissipation radius R is then given by n.2Lau/cR7.= em? ," The hypernova luminosity around a few days after the explosion is roughly $L_{\rm SN} = 10^{43}$ erg $^{-1}$, and we assume the spectrum is black body with a temperature of $\sim$ 1 eV; a typical photon energy is $\varepsilon_\gamma = 2.7$ eV. The photon number density at the dissipation radius $R$ is then given by $n_\gamma = L_{\rm SN} / \pi c R^2 \varepsilon_\gamma = 4 \times
10^{11}$ $^{-3}$."
We note that the parameter values above are very similar to those in Wangetal.(2007) and AsanoMészáros (2005)., We note that the parameter values above are very similar to those in \citet{Wang2007} and \citet{Asano2008}.
" When dissipation starts. we assume a fraction. e, of the kinetic energy goes into primary electrons accelerated to relativistic speed inthe shock. and their initial spectrum is a power law with index —p."," When dissipation starts, we assume a fraction $\epsilon_e$ of the kinetic energy goes into primary electrons accelerated to relativistic speed inthe shock, and their initial spectrum is a power law with index $-p$ ."
" A typical Lorentz factor (in the ejecta frame) of the primary electrons 1s then given by 5,=een),fimdT260(e,/0.1)."," A typical Lorentz factor (in the ejecta frame) of the primary electrons is then given by $\gamma_m = \epsilon_e (m_p / m_e) \Gamma =
260 (\epsilon_e/0.1)$."
" In addition. we assume a fraction ερ of Ex goes into magnetic fields. yielding τα G. We shall study the dependence of results on these parameters in the following. but unless stated. we adopt e,= 0.1. egy=107. and p=2.5 as fiducial values. according to the analogy to GRB emission."," In addition, we assume a fraction $\epsilon_B$ of $E_K$ goes into magnetic fields, yielding $B = [8 \pi \epsilon_B \rho(R) c^2]^{1/2} =
1 (\epsilon_B/10^{-2})^{1/2}$ G. We shall study the dependence of results on these parameters in the following, but unless stated, we adopt $\epsilon_e = 0.1$ , $\epsilon_B
= 10^{-2}$, and $p = 2.5$ as fiducial values, according to the analogy to GRB emission."
 After acceleration. these electrons immediately lose their energies through radiation unless the cooling time scale fi is longer than the dynamical time scale fy).," After acceleration, these electrons immediately lose their energies through radiation unless the cooling time scale $t_{\rm cool}$ is longer than the dynamical time scale $t_{\rm dyn}$ ."
 Relevant radiation mechanisms include synchrotron radiation due to magnetic field. inverse-Compton scatterings off hypernova photons (external inverse-Compton: EIC) and synchrotron photons (synchrotron self-Compton: SSC).," Relevant radiation mechanisms include synchrotron radiation due to magnetic field, inverse-Compton scatterings off hypernova photons (external inverse-Compton; EIC) and synchrotron photons (synchrotron self-Compton; SSC)."
 The ratio of cooling time scales of EIC and synchrotron processes is given by (hic/fyn= 1072).," The ratio of cooling time scales of EIC and synchrotron processes is given by $t_{\rm EIC} / t_{\rm syn} = U_B / \varepsilon_\gamma
n_\gamma \approx 0.05 (\epsilon_B / 10^{-2})$ ."
" Inaddition. unless e, is much larger than eg. the SSC cooling time scale is at most comparable to that of synchrotron radiation."," Inaddition, unless $\epsilon_e$ is much larger than $\epsilon_B$, the SSC cooling time scale is at most comparable to that of synchrotron radiation."
" Thus. among those three. EIC is the most efficient mechanism for electron energy losses. and we have foool©fidc<faa for xe25,710. where , represents the electron Lorentz factor in the ejecta frame."," Thus, among those three, EIC is the most efficient mechanism for electron energy losses, and we have $t_{\rm cool}
\approx t_{\rm EIC} < t_{\rm dyn}$ for $\gamma_e > \gamma_c \simeq
70$, where $\gamma_e$ represents the electron Lorentz factor in the ejecta frame."
" When the electrons are in the ""fast-cooling"" regime. defined as the case when .(«7,4, (or equivalently e,>0.03 in the current context). the electron spectrum is given by where the normalization is set so that we have correct number of electrons N,=Ex5.10° after integration (e.g..Sart&Esin2001).."," When the electrons are in the “fast-cooling” regime, defined as the case when $\gamma_c < \gamma_m$ (or equivalently $\epsilon_e > 0.03$ in the current context), the electron spectrum is given by where the normalization is set so that we have correct number of electrons $N_e = E_K / \Gamma m_p c^2 = 5 \times 10^{52}$ after integration \cite[e.g.,][]{Sari2001}. ."
"Diner On the other hand. in ""slow-cooling"" regime (7,75,,). we have The synehrotron. mechanism. gives. the dominant contribution at radio wavebands. and also provides seed photons for the SSC process."," On the other hand, in “slow-cooling” regime $\gamma_c > \gamma_m$ ), we have The synchrotron mechanism gives the dominant contribution at radio wavebands, and also provides seed photons for the SSC process."
" The typical frequency. and power from an electron with 7, is where ay, is the Thomson cross section (Rybicki&Light-man1979).. and we define 1,—1444(5,,) and 1—Áo)."," The typical frequency and power from an electron with $\gamma_e$ is where $\sigma_T$ is the Thomson cross section \citep{Rybicki1979}, and we define $\nu_m \equiv \nu_{\rm syn} (\gamma_m)$ and $\nu_c \equiv
\nu_{\rm syn}(\gamma_c)$."
" The flux of3 synchrotron photons f°"".. is then givenη by for the slow-cooling phase. where Fi=N,.PaGu/dMdrauGu). and d is distance to the source (Sari.Piran.&Narayan1998)."," The flux of synchrotron photons $F_\nu^{\rm syn}$ is then given by for the fast-cooling phase, and for the slow-cooling phase, where $F_{\nu,{\rm max}}^{\rm syn} = N_e P_{\rm
syn}(\gamma_e) / 4\pi d^2 \nu_{\rm syn}(\gamma_e)$ , and $d$ is distance to the source \citep*{Sari1998}."
. Here we neglected the effect of synchrotron self-absorption. which however might become important at low-frequency radio bands.," Here we neglected the effect of synchrotron self-absorption, which however might become important at low-frequency radio bands."
" We note that the radio flux at 10 GHz with this model and d=100 Mpe is 1600 mJy for e,=0.1 and ej=107 and 10 my for e,210 and ey=1071: the self-absorption is irrelevant at this frequeney.", We note that the radio flux at 10 GHz with this model and $d = 100$ Mpc is 1600 mJy for $\epsilon_e = 0.1$ and $\epsilon_B = 10^{-2}$ and 10 mJy for $\epsilon_e = 10^{-2}$ and $\epsilon_B = 10^{-4}$; the self-absorption is irrelevant at this frequency.
 For comparison. the radio fluxes around similar frequencyat a peak time were 0.5 mJy forGRB 060218 (Soderbergetal.2006) and 50 mJy for GRB 980425 (Kulkarnietal. 1998)..," For comparison, the radio fluxes around similar frequencyat a peak time were $0.5$ mJy forGRB 060218 \citep{Soderberg2006} and $50$ mJy for GRB 980425 \citep{Kulkarni1998}. ."
" Given that theradio flux strongly depends onboth e, and eg. and that this model predicts a substantialflux. radio observations would enable strong test to constrain these parameters or others."," Given that theradio flux strongly depends onboth $\epsilon_e$ and $\epsilon_B$, and that this model predicts a substantialflux, radio observations would enable strong test to constrain these parameters or others."
 If the magnetic fields are highly inhomogeneous on very smallspatial scales. then the photon spectrum would," If the magnetic fields are highly inhomogeneous on very smallspatial scales, then the photon spectrum would"
the MEKAL (Mewe et al.,the MEKAL (Mewe et al.
 1985. 1995)code*.. KELLY (Kelly 1987) and the database of the National Institute of Standards and Technology (NIST). which is also available on the Wela have also: compared.an with⇁↼⋅↼ a list ofu lines observedad ini the solar corona (Doschek Cowan 1984. hereafter D&CC).," 1985, 1995), KELLY (Kelly 1987) and the database of the National Institute of Standards and Technology (NIST), which is also available on the We have also compared with a list of lines observed in the solar corona (Doschek Cowan 1984, hereafter C)."
 Further we compare our measured iron lines with the results from: laboratory experiments. such as the Lawrence Livermore. National. Laboratory's Electron Beam Ion Trap (EBIT) (see Beiersdorfer et al., Further we compare our measured iron lines with the results from laboratory experiments such as the Lawrence Livermore National Laboratory's Electron Beam Ion Trap (EBIT) (see Beiersdorfer et al.
 1999 and Lepson et al., 1999 and Lepson et al.
 2002 for Fe and Lepson et al., 2002 for Fe VIII--X and Lepson et al.
 2000 for Fe XII-XIID., 2000 for Fe XII–XIII).
 A number of lines in Table 2 (see note “d™) are in close wavelength agreement to lines identified in EBIT.," A number of lines in Table 2 (see note ""d"") are in close wavelength agreement to lines identified in EBIT."
 Finally in Table 1 the fluxes. from the multi-temperature global fitting of Sect.," Finally in Table 1 the fluxes, from the multi-temperature global fitting of Sect."
 3.2. have been added.," 3.2, have been added."
 Some possible line identifications have been omitted from Table 2. due to the absence of comparable lines belonging to the same multiplet or ton (Table 3) or due to ambiguity of the lateriification concernsof teelines atin 60989atomicA databasesο ' 1987).," Some possible line identifications have been omitted from Table 2, due to the absence of comparable lines belonging to the same multiplet or ion (Table 3) or due to ambiguity of the identification of lines in atomic databases (Kelly 1987)."
 (Si VIL VII. IX) and 61.852 (Si VUE IX).," The latter concerns lines at 60.989 (Si VII, VIII, IX) and 61.852 (Si VIII IX)."
 Earlier benchmarks with a solar flare spectrum (Phillips et al., Earlier benchmarks with a solar flare spectrum (Phillips et al.
 1999) and with RGS and LETGS spectra of Capella (Audard et al., 1999) and with RGS and LETGS spectra of Capella (Audard et al.
 2001a: Mewe et al., 2001a; Mewe et al.
 2001) have already shown that the current atomic databases are lacking quite a number of. spectral lines for L-shell transitions of Ne. Mg. Si. and S. that appear in the long-wavelength region above about 40A.," 2001) have already shown that the current atomic databases are lacking quite a number of spectral lines for L-shell transitions of Ne, Mg, Si, and S, that appear in the long-wavelength region above about 40."
. This is illustrated by the many identifications present in the third Col. (, This is illustrated by the many identifications present in the third Col. (
RELLY).; which. are absent in. MEKAL.,"KELLY), which are absent in MEKAL."
 For the Fe L-shell Behar et al. (, For the Fe L-shell Behar et al. (
2001) have shown that the HULLAC atomic data are fairly accurate.,2001) have shown that the HULLAC atomic data are fairly accurate.
 first characterize the thermal structure and the elemental 49.696 of Procyon's corona., We first characterize the thermal structure and the elemental composition of Procyon's corona.
 To this end. we fitted multi- 49.975models using SPEX (Kaastra et al.," To this end, we fitted multi-T models using SPEX (Kaastra et al."
 19962) of the spectra 50.327 and LETGS)., 1996a) of the spectra (RGS+MOS and LETGS).
 For both the observations the 50.520 require two dominant temperature components., For both the observations the calculations require two dominant temperature components.
 A | (small and not very significant) temperature component 52306 needed to account for the lines of low stages of ionization. 52.594 in the LETGS spectrum.," A third (small and not very significant) temperature component is needed to account for the lines of low stages of ionization, present in the LETGS spectrum."
 The reduced 4? is relatively mys fits., The reduced $\chi^2$ is relatively high (1.3–2) for the fits.
 This ts due to a lack of lines in the AES — m Nt MEKAL code and to the high resolution of the instrument., This is due to a lack of lines in the MEKAL code and to the high resolution of the instrument.
 Small wavelength deviations (about 1-2 bins re. 0.02-0.04 ) between lines in the spectrum and in the model are often present (see Table 2)., Small wavelength deviations (about 1-2 bins i.e. 0.02-0.04 ) between lines in the spectrum and in the model are often present (see Table 2).
 This effect results in à sharp maximum and minimum in the value of the normalized difference between model and observation around the peak of the line (see also Fig., This effect results in a sharp maximum and minimum in the value of the normalized difference between model and observation around the peak of the line (see also Fig.
 4)., 4).
 The results of RGS and LETGS are very In Table 4 results for temperatures T (in MK).emission measures EAM. and abundances are given.," The results of RGS and LETGS are very In Table 4 results for temperatures $T$ (in MK),emission measures $EM$ and abundances are given."
 Statistic Ia , Statistic $\sigma$ 
Blazar-type active ealactic nuclei (ACUNs) are cliaracterized by a luminous aud rapidly variable spectral euergy distribution (SED) exteudiug from radio up to GeV aud TeV energies 1995).,Blazar–type active galactic nuclei (AGNs) are characterized by a luminous and rapidly variable spectral energy distribution (SED) extending from radio up to GeV and TeV energies \citep{urry95}.
. The blazar SED is characterized by two coimponeuts., The blazar SED is characterized by two components.
 The first one peaks at IR to X-ray energies aud it is most probably synelirotron radiation from electrons in a relativistic jet j»oiutineOm close to the line of sight., The first one peaks at IR to X-ray energies and it is most probably synchrotron radiation from electrons in a relativistic jet pointing close to the line of sight.
e The second one peaks at CieV-TeV energiese aud. accordingOm to leptonic models (Lor a recent review see Botttcher 1999). is inverse Compton (IC) emission [rom the," The second one peaks at GeV-TeV energies and, according to leptonic models (for a recent review see Bötttcher 1999), is inverse Compton (IC) emission from the"
where Py=5/3 is the adiabatic index of the surrounding IGM.,where $\Gamma_{\rm x}=5/3$ is the adiabatic index of the surrounding IGM.
 The lobe is treated as consisting of small volume elements 21. each with varving fluid properties.," The lobe is treated as consisting of small volume elements $\delta V$, each with varying fluid properties."
 A fluid element is injected at some time /; from the hotspot over a time interval δὲ., A fluid element is injected at some time $t_{\rm i}$ from the hotspot over a time interval $\delta t_{\rm i}$.
 The element oV(Ha) is related to δὲ by: using thermodynamie relations assuming adiabatie expansion of the volume element over the time interval (equation C19) in 23)., The element $\delta V(t_{\rm i})$ is related to $\delta t_{\rm i}$ by: using thermodynamic relations assuming adiabatic expansion of the volume element over the time interval (equation (19) in \cite{1999AJ....117..677B}) ).
" Ay, is the area of the hotspot (the hotspot is assumed to have a fixed radius of 2.5 kpey. Lj=4/3 is the adiabatic index of the lobe and py is the pressure in the lobe. which we equate with the pressure in the head given by equation (6)) divided by a factor of 6. adopted from ?.. to allow for the pressure gradient along the lobe."," $A_{\rm hs}$ is the area of the hotspot (the hotspot is assumed to have a fixed radius of $2.5~{\rm kpc}$ ), $\Gamma_{\rm l}=4/3$ is the adiabatic index of the lobe and $p_{\rm l}$ is the pressure in the lobe, which we equate with the pressure in the head given by equation \ref{eq:phead}) ) divided by a factor of $6$, adopted from \cite{1999AJ....117..677B}, to allow for the pressure gradient along the lobe."
 Then. assuming furtheradiabatic expansion. the volume element changes ds: The volume of each lobe at time / can be found by integrating equation (8)).," Then, assuming furtheradiabatic expansion, the volume element changes as: The volume of each lobe at time $t$ can be found by integrating equation \ref{eq:dV}) )."
 That is. for /x£s: For a general time /. we want to set the integration limit to minἐς/;]. as nothing is injected into the lobes once the jet has shut down.," That is, for $t\leq t_{\rm j}$: For a general time $t$, we want to set the integration limit to $\min [t,t_{\rm j}]$, as nothing is injected into the lobes once the jet has shut down."
 We call the axial ratio of the lobe /?=/?(/) (nucleus-hotspot distance divided by full width of the lobe). so that the volume of a lobe is: (the lobe is assumed to have a cylindrical shape).," We call the axial ratio of the lobe $R=R(t)$ (nucleus-hotspot distance divided by full width of the lobe), so that the volume of a lobe is: (the lobe is assumed to have a cylindrical shape)."
 For /xfi. we know how Y; and £; evolve and thus can determine how 7? grows with expansion.," For $t\leq t_{\rm j}$, we know how $V_{\rm l}$ and $L_{\rm j}$ evolve and thus can determine how $R$ grows with expansion."
 Now we will describe the evolution of the lobe after the jet has turned off., Now we will describe the evolution of the lobe after the jet has turned off.
" The expansion of the lobe for /7/; is governed by where p, is the ambient density at £;(/). which we know from equation GE)."," The expansion of the lobe for $t>t_{\rm j}$ is governed by where $\rho_{\rm a}$ is the ambient density at $L_{\rm j}(t)$, which we know from equation \ref{eq:environment}) )."
 It is not reasonable to assume that the source continues o expand according to equation (5)) once the jet activity has discontinued since at this point Q;=0 and we do not have a characteristic length., It is not reasonable to assume that the source continues to expand according to equation \ref{eq:Lj}) ) once the jet activity has discontinued since at this point $Q_{\rm j}=0$ and we do not have a characteristic length.
 To proceed. we assume that the axial ratio or /2[5 will be given by its value at /?(/;). that is. the axial ratio at the time when the jet turned off.," To proceed, we assume that the axial ratio for $t>t_{\rm j}$ will be given by its value at $R(t_{\rm j})$, that is, the axial ratio at the time when the jet turned off."
 This is a reasonable assumption if the axial ratio is small enough and the distance from the galaxy arge enough so that the external pressure at the heads and sides of he jet are similar. even in an ambient environment with density described by a power-law decline.," This is a reasonable assumption if the axial ratio is small enough and the distance from the galaxy large enough so that the external pressure at the heads and sides of the jet are similar, even in an ambient environment with density described by a power-law decline."
 The assumption is useful for obtaining an analytic solution for the problem. and has been made or the entirety of the evolution of sources in other models such as hose of ?.. ?.. 2.. and ?..," The assumption is useful for obtaining an analytic solution for the problem, and has been made for the entirety of the evolution of sources in other models such as those of \cite{1997MNRAS.286..215K}, \cite{1997MNRAS.292..723K}, and \cite{2010MNRAS.tmp.1004N}."
 Noticing from equation (9)) that for /.>fg we have and using equation (10)) we findafter substitution from equation CLE that for />>4).where With the assumption that A(/)=—(Ig) for post-jet conditions. we tind an analytic solution for the evolution of £L; at [oc[ by solving the differential equation (139) with appropriate boundary condition at time /: with From L;(/) we can determine \1(/) and consequently ji(/) from equation (12)). for /f.," Noticing from equation \ref{eq:V}) ) that for $t>t_{\rm j}$ we have and using equation \ref{eq:volume}) ), we findafter substitution from equation \ref{eq:evo2}) ) that for $t>t_{\rm j}$,where With the assumption that $R(t)=R(t_{\rm j})$ for post-jet conditions, we find an analytic solution for the evolution of $L_{\rm j}$ at $t>t_{\rm j}$ by solving the differential equation \ref{eq:diffeq}) ) with appropriate boundary condition at time $t_{\rm j}$: with From $L_{\rm j}(t)$ we can determine $V_{\rm l}(t)$ and consequently $p_{\rm l}(t)$ from equation \ref{eq:volevo}) ), for $t>t_{\rm j}$ ."
 We assume that the initial electron energy distribution when injected into the lobe is a power law in energy given by: with. for case [A]. p=2.14 as in ? and ; ranging between Sain=dl and μοι10° (Lorentz factors of +~10° are required to produce upscattering of the CMB in the X-ray and Lorentz factors of 10 are needed for GHz synchrotron radiation in the radio for typical magnetic field strengths).," We assume that the initial electron energy distribution when injected into the lobe is a power law in energy given by: with, for case [A], $p=2.14$ as in \cite{1997MNRAS.292..723K} and $\gamma_{\rm i}$ ranging between $\gamma_{\rm min}=1$ and $\gamma_{\rm max}=10^6$ (Lorentz factors of $\gamma\sim10^3$ are required to produce upscattering of the CMB in the X-ray and Lorentz factors of $\gamma\geq 10^4$ are needed for GHz synchrotron radiation in the radio for typical magnetic field strengths)."
" The constant no 1s found by integration: Increasing ,,445 has little effect onthe luminosity.", The constant $n_0$ is found by integration: Increasing $\gamma_{\rm max}$ has little effect onthe luminosity.
" However. pecan range from 2 to 3 (2) and the 7""—a correlation of ? suggests sources with higher jet power have higher p."," However, $p$ can range from $2$ to $3$ \citep{1987MNRAS.225....1A} and the $P$ $\alpha$ correlation of \cite{1999AJ....117..677B} suggests sources with higher jet power have higher $p$."
 Also. μμ. often assumed to be 1 in previous models. may infact be higher and influence the luminosities. an issue we explore in 22..," Also, $\gamma_{\rm min}$, often assumed to be $1$ in previous models, may infact be higher and influence the luminosities, an issue we explore in \ref{sec:params}. ."
" The minimum injected Lorentz factor j, has taken various values from 1 to 107 for describing individual sources (2).. ", The minimum injected Lorentz factor $\gamma_{\rm min}$ has taken various values from $1$ to $10^4$ for describing individual sources \citep{2006ApJ...644L..13B}. .
We also assume and that is. the ratio of theenergy density in the particles to that in the magnetic field is a constant —(1| p)/4. based on minimum energy arguments. adopted from ?.. ," We also assume and that is, the ratio of theenergy density in the particles to that in the magnetic field is a constant $r=(1 + p)/4$ , based on minimum energy arguments, adopted from \cite{1997MNRAS.292..723K}. ."
"We now describe the determination of ; and ασ ας,", We now describe the determination of $\gamma_{\rm i}$ and $d\gamma_{\rm i} / d\gamma$ .
 First, First
"The GCs were assigned individual weights in the sums that combine in quadrature the individual observational uncertaintv. το in e, and the random velocity component. 2,404,454. Of the GCS.","The GCs were assigned individual weights in the sums that combine in quadrature the individual observational uncertainty, $\varepsilon_v$, in $v_r$ and the random velocity component, $\varepsilon_{random}$, of the GCS."
 The dominance of the latter is evident by the large dispersion in (he GC velocities in (he kinematic fitting (see Figure 4))., The dominance of the latter is evident by the large dispersion in the GC velocities in the kinematic fitting (see Figure \ref{fig:kin_plot}) ).
 In other words. the clusters have individual weights. wyτοοτμ]5 the main purpose of this is (o assign a bit more importance to the clusters with more securely measured. velocities.," In other words, the clusters have individual weights, $\omega_i = (\varepsilon_v^2 +
\varepsilon_{random}^2)^{-1}$; the main purpose of this is to assign a bit more importance to the clusters with more securely measured velocities."
 This random velocity term dominates in nearly every case. leaving the GC's with very similar base weights in the kinematic fitting.," This random velocity term dominates in nearly every case, leaving the GCs with very similar base weights in the kinematic fitting."
 The three kinematic parameters - rotation aunplitude. rotation axis. aud velocity dispersion - are determined with three different binning methods.," The three kinematic parameters - rotation amplitude, rotation axis, and velocity dispersion - are determined with three different binning methods."
 The first involves binning the GCs in racially projected circular annuli from (he center of NGC 5128., The first involves binning the GCs in radially projected circular annuli from the center of NGC 5128.
 The chosen bins keep a minimum of 15 clusters in each. ranging as high as 124 clusters.," The chosen bins keep a minimum of 15 clusters in each, ranging as high as 124 clusters."
 The bins are 0-5. 5-10. 10-15. 15-25. and 25-50 kpe.," The bins are 0-5, 5-10, 10-15, 15-25, and 25-50 kpc."
 Also. we include 0-50 kpe to determine the overall kinematies of the svslenm.," Also, we include 0-50 kpc to determine the overall kinematics of the system."
 The second method adopts bins with equal numbers of clusters., The second method adopts bins with equal numbers of clusters.
 The entire population of clusters had nine bins of 38 clusters each. the metal-poor clusters hac nine bins of 20 clusters. ancl the metal-rich clusters had eight bins of 20 elusters.," The entire population of clusters had nine bins of 38 clusters each, the metal-poor clusters had nine bins of 20 clusters, and the metal-rich clusters had eight bins of 20 clusters."
 The base weighting is applied to the clusters in both the first and second binning methods., The base weighting is applied to the clusters in both the first and second binning methods.
 The third method uses an exponential weighting function. outlined in (2006).. to generate a smoothed profile.," The third method uses an exponential weighting function, outlined in \cite{bergond06}, to generate a smoothed profile."
" This method determines each. kinematic parameter al the radial position. H. of every GC in the entire sample by exponentially weighting all other GC's surrounding that position based on their radial separation. /2—H;. following In Equation 3.. (6; is (he determined weight on each GC in the sample. aud a, is the half-width of the window size."," This method determines each kinematic parameter at the radial position, $R$, of every GC in the entire sample by exponentially weighting all other GCs surrounding that position based on their radial separation, $R - R_i$, following In Equation \ref{eqn:exp_wei}, $w_i$ is the determined weight on each GC in the sample, and $\sigma_R$ is the half-width of the window size."
" For this study. o, is incrementally varied in a linear fashion for the total sample fom a,=1.0 kpe at the radius of the innermost GC in the sample oul lo gp=4.5 kpe at the radius of the outermost GC. where the population is lowest."," For this study, $\sigma_R$ is incrementally varied in a linear fashion for the total sample from $\sigma_R
= 1.0$ kpc at the radius of the innermost GC in the sample out to $\sigma_R = 4.5$ kpc at the radius of the outermost GC, where the population is lowest."
 The metal-poor population was given a half-width window of συ=1.0—6.5 kpc. and the metal-rieh population was given a half-width window of o;=2—5.3 kpc. again [rom the innermost to outermost cluster.," The metal-poor population was given a half-width window of $\sigma_R = 1.0-6.5$ kpc, and the metal-rich population was given a half-width window of $\sigma_R = 2-5.3$ kpc, again from the innermost to outermost cluster."
" The progressive radial increase in ao), ensured (hat each point H had roughly equal total weights.", The progressive radial increase in $\sigma_R$ ensured that each point $R$ had roughly equal total weights.
"with respect to the fore and background galaxies in the field, but not being too restrictive so that a sufficient number of candidate cluster members was selected.","with respect to the fore and background galaxies in the field, but not being too restrictive so that a sufficient number of candidate cluster members was selected."
 The galaxy iso-density contours are shown in Fig. 2.., The galaxy iso-density contours are shown in Fig. \ref{fig:xray}.
" The cluster shows a pronounced bimodal structure, with two cores separated by about 700 kpc."," The cluster shows a pronounced bimodal structure, with two cores separated by about 700 kpc."
 The cluster extends somewhat further in the east-west direction than the X-ray emission from ROSAT., The cluster extends somewhat further in the east-west direction than the X-ray emission from ROSAT.
" The cD galaxy 2MASX J00112171+5231437 belongs to the western subcluster (i.e., it is located at the center of the subcluster)."," The cD galaxy 2MASX J00112171+5231437 belongs to the western subcluster (i.e., it is located at the center of the subcluster)."
" The eastern subcluster also hosts a separate cD galaxy J00121892+5233460,, see Fig. 13))."," The eastern subcluster also hosts a separate cD galaxy , see Fig. \ref{fig:SD}) )."
" Although we do not have a spectroscopic redshift for this galaxy, the (i) color and (ii) R and K magnitudes are in agreement with a subcluster located at the same redshift as the western subcluster (e.g.,??).. "," Although we do not have a spectroscopic redshift for this galaxy, the (i) color and (ii) R and K magnitudes are in agreement with a subcluster located at the same redshift as the western subcluster \citep[e.g.,][]{2003MNRAS.339..173W, 2007A&A...464..879D}."
"The same is true for the other massive elliptical galaxies found in both subclusters, see Sect. 1.."," The same is true for the other massive elliptical galaxies found in both subclusters, see Sect. \ref{sec:agn}."
" Therefore, both the X-ray and optical observations point towards a bi-modal galaxy cluster, indicative of an ongoing merger event."," Therefore, both the X-ray and optical observations point towards a bi-modal galaxy cluster, indicative of an ongoing merger event."
" As we will show in the next sections, the radio observations also point towards a merger scenario."," As we will show in the next sections, the radio observations also point towards a merger scenario."
 The WSRT 1382 MHz image is shown in Fig. 3.., The WSRT 1382 MHz image is shown in Fig. \ref{fig:wsrt21cm}.
" It reveals a large arc of diffuse emission on the east side of the cluster and a smaller faint diffuse source on the west side of the cluster, symmetrically with respect to the cluster center."," It reveals a large arc of diffuse emission on the east side of the cluster and a smaller faint diffuse source on the west side of the cluster, symmetrically with respect to the cluster center."
" We classify these sources as radio relics based on their location with respect to the cluster center, their morphology, and the lack of optical counterparts."," We classify these sources as radio relics based on their location with respect to the cluster center, their morphology, and the lack of optical counterparts."
 The relics are located about 850 kpc from the center of the X-ray emission., The relics are located about 850 kpc from the center of the X-ray emission.
" Several complex tailed radio sources, related to AGN activity, are also visible."," Several complex tailed radio sources, related to AGN activity, are also visible."
" The WSRT 1714 MHz image is similar to the 1382 MHz image, although the overall signal to noise ratio is less, therefore revealing less of the diffuse extended relics."," The WSRT 1714 MHz image is similar to the 1382 MHz image, although the overall signal to noise ratio is less, therefore revealing less of the diffuse extended relics."
 The radio relics are also visible in the GMRT 610 and 241 MHz images (Figs., The radio relics are also visible in the GMRT 610 and 241 MHz images (Figs.
" 5 and 6)), although at 241 MHz the SNR on the relics is x5 per beam."," \ref{fig:gmrt610} and \ref{fig:gmrt241}) ), although at 241 MHz the SNR on the relics is $\lesssim 5$ per beam."
 To facilitate the discussion we have labeled various sources in Figs., To facilitate the discussion we have labeled various sources in Figs.
 3 and 7.., \ref{fig:wsrt21cm} and \ref{fig:gmrt610_labels}.
 Optical overlays can be found Sect. 1.., Optical overlays can be found Sect. \ref{sec:agn}.
" The integrated fluxes, spectral indices, radio power and largest linear size for the two relics (RE RW) are displayed in Table 3.."," The integrated fluxes, spectral indices, radio power and largest linear size for the two relics (RE RW) are displayed in Table \ref{tab:relicflux}."
" Relic RE consist of two parts, a smaller region of emission to the north and a larger one in the south (most clearly seen in Figs."," Relic RE consist of two parts, a smaller region of emission to the north and a larger one in the south (most clearly seen in Figs."
 5 and 7))., \ref{fig:gmrt610} and \ref{fig:gmrt610_labels}) ).
 In the 1382 MHz image the two regions are seen connected., In the 1382 MHz image the two regions are seen connected.
" The eastern boundary of RE is somewhat more pronounced, while on the western side the emission fades more slowly in the direction of the cluster center."," The eastern boundary of RE is somewhat more pronounced, while on the western side the emission fades more slowly in the direction of the cluster center."
 The relic has a total extent of 1.4 Mpc., The relic has a total extent of 1.4 Mpc.
 The surface brightness varies across the relic fading at the extreme northern and southern ends., The surface brightness varies across the relic fading at the extreme northern and southern ends.
" The northern diffuse patch has a ""notch"" like region of higher surface brightness.", The northern diffuse patch has a “notch” like region of higher surface brightness.
 Relic RW has a muchsmaller extent of 290 kpc., Relic RW has a muchsmaller extent of 290 kpc.
 The western boundary is more pronounced in the, The western boundary is more pronounced in the
Or an outer cireumstellar envelope.,or an outer circumstellar envelope.
 The high 7; values of these objects also corstrain the physical origins of their veilites., The high $r_{k}$ values of these objects also constrain the physical origins of their veilings.
 In Paper [we showed that veiliugs rz>1 cannot be procluced by a simple optically thick. geomerically thin reprocessing disk around a low-mass PMS sta5.," In Paper I we showed that veilings $r_{k} 
> 1$ cannot be produced by a simple optically thick, geometrically thin reprocessing disk around a low-mass PMS star."
 Consequently. we argued that these lel veilings are inost likely produced by eitlier actively accreting circumstellar disks or circuimstellar envelopes associated with these objects., Consequently we argued that these high veilings are most likely produced by either actively accreting circumstellar disks or circumstellar envelopes associated with these objects.
 Furthermore we found that veilings iu the rauge meas‘ed for IRS Sl aud IRS 63. rj = 3— fL. can be caused by luminous accretion disks οων<3 .," Furthermore we found that veilings in the range measured for IRS 51 and IRS 63, $r_{k}$ = 3 – 4, can be caused by luminous accretion disks $L_{disk}/L_{*} \leq 3$ )."
" Veiliugs iu the range observed for GSS 26. 7%,25—10. could be explained by extremely Iumiuos accretion disks (Lapων2 3)."," Veilings in the range observed for GSS 26, $r_{k} \simeq 5 - 10$, could be explained by extremely luminous accretion disks $L_{disk}/L_{*} \geq 3$ )."
 In either case. these accretion disks would have to have relaively large central holes to avoid procucing strong CO absorptiou-line systems in the clisk photos]yhere itself.," In either case, these accretion disks would have to have relatively large central holes to avoid producing strong CO absorption-line systems in the disk photosphere itself."
 However. because there is no obvious plivsical mechanism for produciig central holes of the needed sige. Calvet.Hartinaih.&Strom(1997. suggested tha the veiling flux must origin:de in some other circuiustellar structure such as the inner regious of the protosellar euvelope.," However, because there is no obvious physical mechanism for producing central holes of the needed size, \citet{CHS97} suggested that the veiling flux must originate in some other circumstellar structure such as the inner regions of the protostellar envelope."
 On the other haud. this seems to be inconsistent. with the observation by Lulimaun&Rieke that tve Ax- baud excesses of flat-spectrum YSOs are correlated with their HI Br 5 line fluxes which iu tu‘LL suggests that the veiling flux should originate iu the disk.," On the other hand, this seems to be inconsistent with the observation by \citeauthor{LR99} that the $K$ -band excesses of flat-spectrum YSOs are correlated with their HI Br $\gamma$ line fluxes which in turn suggests that the veiling flux should originate in the disk."
 More detailed knowledge of the couclitiois required to produce CO absorption line systems in au accretion disk may )e needed to resolve tUs Issue., More detailed knowledge of the conditions required to produce CO absorption line systems in an accretion disk may be needed to resolve this issue.
 The flat-spectrum source YLÀV 13B was found tolave H Br > absorption by Lulula1&Rieke.. who estimate its spectral type to be earier than 190.," The flat-spectrum source YLW 13B was found to have H Br $\gamma$ absorption by \citeauthor{LR99}, who estimate its spectral type to be earlier than K0."
 However. tlev also fiud it to be sieuilicantly veiled with rg>1. so it is possibly an intermectiate mass PAS cloud population vember.," However, they also find it to be significantly veiled with $r_{k} > 1$, so it is possibly an intermediate mass PMS cloud population member."
 Our uou-cdetection of CO absorption does not coustraim this source fu‘ther., Our non-detection of CO absorption does not constrain this source further.
 We do uot detect CO absorptious in any of the Class I YSOs wlich we observed (Figure 2). confirming earlier low resolution spectroscopic observatious tha found. all t1ese objects to be featureless aud highly. veiled (Paper E: Lulinau& Rieke)).," We do not detect CO absorptions in any of the Class I YSOs which we observed (Figure 2), confirming earlier low resolution spectroscopic observations that found all these objects to be featureless and highly veiled (Paper I; \citeauthor{LR99}) )."
 Cousedqtently heir spectral types are unknown. however all of these Class E sources exhibit HI Br > eimissio1 (Pa »rkLdunan&Rieke) ).," Consequently their spectral types are unknown, however all of these Class I sources exhibit HI Br $\gamma$ emission (Paper I; \citeauthor{LR99}) )."
 Analysis of our new data coustraius the natures of these objecs., Analysis of our new data constrains the natures of these objects.
 Ta)e 2 stows thlat they all have large velliugs. rjF>L if they are late-type ( MO) stars.," Table 2 shows that they all have large veilings, $r_{k} > 4$, if they are late-type $\sim$ M0) stars."
 GSS :0. IRS [E)). aud WL 6. all have estimatecl uiniunum veilines of 7j.2225—8. overlapping with the flat-svecLe1l saldle.," GSS 30, IRS 43, and WL 6, all have estimated minimum veilings of $r_{k} \simeq 5-8$, overlapping with the flat-spectrum sample."
 These sources all have bolomeric luminosities Li]€13 L. (WLY)., These sources all have bolometric luminosities $_{\rm bol} \leq 13$ $_{\odot}$ (WLY).
 This is consistent wihi their being low-mass (M < 1 M.) protostars accreting matter at rates M~sxlo® M. ÉL the value expected for the T ~ 20 Ix gas temperatures in the p Oph cloud (see ALS)..," This is consistent with their being low-mass (M $<$ 1 $_{\odot}$ ) protostars accreting matter at rates $\dot{M} \simeq 5 \times 10^{-6}$ $_{\sun}$ $^{-1}$, the value expected for the T $\simeq$ 20 K gas temperatures in the $\rho$ Oph cloud \citep[see][hereafter ALS]{ALS87}."
 Veiliugs in the observed ange. rj27L—10. are also predicted by theoretical models of Class [ circumstellar envelopes (Paper I: Calvet et al.).," Veilings in the observed range, $r_{k} > 4 - 10$, are also predicted by theoretical models of Class I circumstellar envelopes (Paper I; Calvet et al.)."
 Montijerleοἱal... note thi othe maximum possible mass of IRS 13 (also known as YLW 15) is 2.2 M. which is derived frou PMS models given its bolometric luminosity (Lb  10 L.) aud, \citeauthor{MGTK00} note that the maximum possible mass of IRS 43 (also known as YLW 15) is 2.2 $_{\odot}$ which is derived from PMS models given its bolometric luminosity (L $\sim$ 10 $_{\odot}$ ) and
To improve our understanding of how planets migrate in Gl-active disks that are not fragmenting. we have begun a systematic study. using numerical 3D radiative hyvdrodinamies. where we investigate the elfects on both the disk and the planet of inserting a planel-mass object into disks susceptible to Gls.,"To improve our understanding of how planets migrate in GI-active disks that are not fragmenting, we have begun a systematic study, using numerical 3D radiative hydrodynamics, where we investigate the effects on both the disk and the planet of inserting a planet-mass object into disks susceptible to GIs."
 Using techniques developed in earlier research by our group (Pickettetal.2003:Mejfa2005:Cal2006.2008:Dolevetal.2006.2007a:Michael&Durisen 2010).. we can identify the dominant spiral waves in a simulation and analyze how (he waves interact will the planets motion.," Using techniques developed in earlier research by our group \citep{pickett2003, mejia2005,cai2006,cai2008,boley2006,boley2007b,michael2010}, we can identify the dominant spiral waves in a simulation and analyze how the waves interact with the planet's motion."
 Our goal is to determine both the effect of eiut. planets on GIs and the effect of GIs on planet migration., Our goal is to determine both the effect of giant planets on GIs and the effect of GIs on planet migration.
 Because Gls are sensitive to radiative physics. we use a well-tested radiative scheme and realistic opacities (D'Alessioetal.2001).," Because GIs are sensitive to radiative physics, we use a well-tested radiative scheme \citep{boley2007b} and realistic opacities \citep{dalessio2001}."
 section 2 below presents our numerical methods and initial conditions., Section 2 below presents our numerical methods and initial conditions.
 We describe the simulation results in 823. and discuss them in 844.," We describe the simulation results in 3, and discuss them in 4."
 The CHYMERA (Computational HYcdrodyvnamies with MultiplE. Radiation Algorithms) code (Bolevetal.2007a) is a second-order. explicit. Eulerian scheme on a 3D cvlindrical grid.," The CHYMERA (Computational HYdrodynamics with MultiplE Radiation Algorithms) code \citep{boley2007b} is a second-order, explicit, Eulerian scheme on a 3D cylindrical grid."
 The code uses a realistic equation of state for Ils and integrates an energy equation that includes Pd work. net heating or cooling due to radiative fIux divergence. and heating by artificial bulk viscositv.," The code uses a realistic equation of state for $_2$ \citep{boley2007} and integrates an energy equation that includes $PdV$ work, net heating or cooling due to radiative flux divergence, and heating by artificial bulk viscosity."
 Calculations are done on a uniform cvlindyical grid with reflection symmetry. about the disk midplane aud a grid size (zc.6.2) = (512.512.64).," Calculations are done on a uniform cylindrical grid with reflection symmetry about the disk midplane and a grid size $\varpi$ $\phi$ ,z) = (512,512,64)."
 The z-axis is the rotation axis of the disk., The $z$ -axis is the rotation axis of the disk.
 The large nunmber of azimuthal zones is necessary (o resolve (he planets Hill sphere aud the planets wake., The large number of azimuthal zones is necessary to resolve the planet's Hill sphere and the planet's wake.
 These simulations utilize the radiative cooling scheme developed and tested in, These simulations utilize the radiative cooling scheme developed and tested in
"luminosity fraction (B/T) of 30 per cent (i.e. B/T,« 0.3).",luminosity fraction (B/T) of 30 per cent (i.e. $_r < 0.3$ ).
 The reasons for this selection are two-fold., The reasons for this selection are two-fold.
" First, the selection of disk-dominated galaxies based solely on their quantitative B/T is relatively robust(??),, minimising the additional cuts necessary to identify a ‘clean’ morphological tracer from the catalogue."," First, the selection of disk-dominated galaxies based solely on their quantitative B/T is relatively robust, minimising the additional cuts necessary to identify a `clean' morphological tracer from the catalogue."
" Second, we expect disks to be heavily affected by their environments."," Second, we expect disks to be heavily affected by their environments."
" Both the truncation of star formation in, and tidal disruption of, a galaxy’s disk component will lead to rapid evolution toward higher values of B/T, making the fraction of disk light in disk-dominated systems a sensitive probe of such interactions."," Both the truncation of star formation in, and tidal disruption of, a galaxy's disk component will lead to rapid evolution toward higher values of B/T, making the fraction of disk light in disk-dominated systems a sensitive probe of such interactions."
" As in Figure we remove galaxies with disk b/a<0.5 to limit the [7],attenuation of bulge flux by dusty, edge on disks."," As in Figure \ref{fig:red_fraction}, we remove galaxies with disk $b/a < 0.5$ to limit the attenuation of bulge flux by dusty, edge on disks."
 In Figure we plot the late-type galaxy fraction as a function of radius[5 in each of our environment samples., In Figure \ref{fig:bulge_fraction} we plot the late-type galaxy fraction as a function of radius in each of our environment samples.
" In all samples we observe an apparent morphology density relation such that the fraction of late-type, disk-dominated galaxies decreases as a function of decreasing group-centric radius."," In all samples we observe an apparent morphology density relation such that the fraction of late-type, disk-dominated galaxies decreases as a function of decreasing group-centric radius."
" The average fraction of disk-dominated galaxies around isolated compact groups appears to increase steeply outside of the CG core, mirroring the red fraction trend shown in Figure "," The average fraction of disk-dominated galaxies around isolated compact groups appears to increase steeply outside of the CG core, mirroring the red fraction trend shown in Figure \ref{fig:red_fraction}."
"In contrast, both embedded CGs and rich groups follow a [7].shallower increase in late-type fraction outside of 200 kpc, commensurate with their comparatively shallow red fraction and number-density radial relations."," In contrast, both embedded CGs and rich groups follow a shallower increase in late-type fraction outside of 200 kpc, commensurate with their comparatively shallow red fraction and number-density radial relations."
" Finally, inside ~200 kpc all systems — that is, isolated and embedded compact groups, as well as rich groups — host a similar fraction of late-type galaxies despite probing a broad range of both global and local environments."," Finally, inside $\sim$ 200 kpc all systems – that is, isolated and embedded compact groups, as well as rich groups – host a similar fraction of late-type galaxies despite probing a broad range of both global and local environments."
 We have so far considered the general properties of galaxies in the volume around CGs without explicitly examining the characteristics of CGs themselves; it is to this comparison that we now turn., We have so far considered the general properties of galaxies in the volume around CGs without explicitly examining the characteristics of CGs themselves; it is to this comparison that we now turn.
" A detailed comparison of CG galaxies with other galaxies in other environments is the focus of a future paper, so here we restrict ourselves to a broad-brush comparison of isolated and embedded CG properties."," A detailed comparison of CG galaxies with other galaxies in other environments is the focus of a future paper, so here we restrict ourselves to a broad-brush comparison of isolated and embedded CG properties."
" The separation of isolated and embedded CGs based on their relationship to large-scale structure says nothing about the physical properties of the groups themselves; it is therefore interesting to ask if this distinction can be made given the set of parameters that define a compact group, e.g. isolation or surface brightness."," The separation of isolated and embedded CGs based on their relationship to large-scale structure says nothing about the physical properties of the groups themselves; it is therefore interesting to ask if this distinction can be made given the set of parameters that define a compact group, e.g. isolation or surface brightness."
" We show in Figure[] the distributions of group physical size, ra; group surface brightness, µα; and relative isolation, On/0c."," We show in Figure \ref{fig:group_prop} the distributions of group physical size, $r_G$ ; group surface brightness, $\mu_G$; and relative isolation, $\theta_N/\theta_G$."
" Isolated and embedded compact groups are shown as solid (red) and dashed (black) histograms, respectively."," Isolated and embedded compact groups are shown as solid (red) and dashed (black) histograms, respectively."
" In terms of physical extent, the median size of embedded CGs is ~10 kpc smaller than that of isolated groups (80 versus 90 kpc)."," In terms of physical extent, the median size of embedded CGs is $\sim$ 10 kpc smaller than that of isolated groups (80 versus 90 kpc)."
" While there is no clear division between the size distributions of isolated and embedded CGs, a two-sample Kolmogorov-Smirnov (KS) shows that the two are unlikely to be drawn from the same parent sample at just under 3c significance (0.5 per cent)."," While there is no clear division between the size distributions of isolated and embedded CGs, a two-sample Kolmogorov–Smirnov (KS) shows that the two are unlikely to be drawn from the same parent sample at just under $\sigma$ significance $\sim$ 0.5 per cent)."
" The systematic offset between CG sizes is also reflected in their distributions of surface brightness; embedded CGs have on average higher surface brightness, as expected given that ugc05."," The systematic offset between CG sizes is also reflected in their distributions of surface brightness; embedded CGs have on average higher surface brightness, as expected given that $\mu_G \propto \theta_G^{-2}$."
" 'The comparison of surface brightnesses — and, by extension, sizes — also suggests that the selecting CGs using cuts in surface brightness may bias the resulting sample towards predominantly embedded CGs."," The comparison of surface brightnesses – and, by extension, sizes – also suggests that the selecting CGs using cuts in surface brightness may bias the resulting sample towards predominantly embedded CGs."
" From our comparisons with large-scale structure, we know that isolated CGs are distinct from rich groups in terms of their global distribution; the comparison of relative isolation in Figure|9] shows that isolated CGs are also more isolated from other galaxies."," From our comparisons with large-scale structure, we know that isolated CGs are distinct from rich groups in terms of their global distribution; the comparison of relative isolation in Figure \ref{fig:group_prop} shows that isolated CGs are also more isolated from other galaxies."
" In our sample of SDSS groups, the split between isolated and embedded CGs is roughly equal."," In our sample of SDSS groups, the split between isolated and embedded CGs is roughly equal."
" Based on the distribution of relative isolations, we could bias our sample towards isolated CGs using amore strict isolation criteria in our initial group selection."," Based on the distribution of relative isolations, we could bias our sample towards isolated CGs using amore strict isolation criteria in our initial group selection."
 If we, If we
accounts explicitly for 16 chemical clements. and the thermonuclear reaction rates are those described in Althaus ct al. (,"accounts explicitly for 16 chemical elements, and the thermonuclear reaction rates are those described in Althaus et al. ("
"2005a). with the exception of Pe py ey BN q5 »BO | ol|n aud PCQ. 5)HIN, ποσο] are tien. from Aneulo ct al. (","2005a), with the exception of $^{12}$ $\ +\ $ $ \rightarrow \ ^{13}$ N + $\gamma
\rightarrow \ ^{13}$ C + $^+ + \nu_{\rm e}$ and $^{13}$ C(p, $\gamma)^{14}$ N, which are taken from Angulo et al. ("
1999).,1999).
 The ote.2 190 reaction rate is taken from Aneulo et al. (," The $^{12}$ $\alpha,\gamma)^{16}$ O reaction rate is taken from Angulo et al. ("
1999) as well. aud is about twice as luge as that of Caughlan Fowler (1988).,"1999) as well, and is about twice as large as that of Caughlan Fowler (1988)."
 The final carbou-oxvecn colposition is a relevant issuc. as a proper computation of the euergv released by phase separation markedly depends on the chemical profile of the core.," The final carbon-oxygen composition is a relevant issue, as a proper computation of the energy released by phase separation markedly depends on the chemical profile of the core."
 The standard musing leugth theory for convection with the free paralcter a=1.61 has been adopted., The standard mixing length theory for convection — with the free parameter $\alpha=1.61$ — has been adopted.
 With this value. the prescut luminosity aud effective temperature of the Sum. at au age of 1570 Myr. are reproduced by LPCODE when Z=0.0161 aud .X=0.711 are adopted in agreement with the Z/.X value of Grevesse Sauval (1998).," With this value, the present luminosity and effective temperature of the Sun, at an age of 4570 Myr, are reproduced by when $Z=0.0164$ and $X=0.714$ are adopted — in agreement with the $Z/X$ value of Grevesse Sauval (1998)."
 Except for the evolutionary stages correspondius to the thermally-pulsing asviuptotie giant branch (AGB) phase. we considered the occurrence of extra-nüxiug episodes bevond cach convective boundary followine the prescription of Uerwig ct al. (," Except for the evolutionary stages corresponding to the thermally-pulsing asymptotic giant branch (AGB) phase, we considered the occurrence of extra-mixing episodes beyond each convective boundary following the prescription of Herwig et al. ("
1997).,1997).
 Extra-musing episodes largely determine the final chemical profile of white dwarfs., Extra-mixing episodes largely determine the final chemical profile of white dwarfs.
 We treated extranixing as a diffusion process by assuming that mixing velocitics decay exponentially bevoud cach convective botudary., We treated extra-mixing as a diffusion process by assuming that mixing velocities decay exponentially beyond each convective boundary.
" Specifically, we asstmed a diffusion coefficient. eiven by Dov=Doοσο24 where /Tp is the pressure scale height at the couvectiveFIT). boundary, Dj is the diffusion cocficient of unstable regions close to the convective boundary. and + is the ecometric distauce frou the edge of the convective boundary (Herwig ct al."," Specifically, we assumed a diffusion coefficient given by $D_{\rm OV}= D_{\rm O}\ \exp(-2z/f H_{\rm p})$, where $H_{\rm
 P}$ is the pressure scale height at the convective boundary, $D_{\rm
 O}$ is the diffusion coefficient of unstable regions close to the convective boundary, and $z$ is the geometric distance from the edge of the convective boundary (Herwig et al."
 1997)., 1997).
 We adopted f£=0.016 iu all of our sequences. a value inferred from the width of the upper main sequence.," We adopted $f=0.016$ in all of our sequences, a value inferred from the width of the upper main sequence."
 Other physical iugredieuts considered im are the radiative opacities from the OPAL project (Igesjas Rogers 1996). incliding C- aud. O-vich composition. supplemented at low temperatures with the molecular opacities of Alexander Fereuson (1991).," Other physical ingredients considered in are the radiative opacities from the OPAL project (Iglesias Rogers 1996), including C- and O-rich composition, supplemented at low temperatures with the molecular opacities of Alexander Ferguson (1994)."
 During the white dwarf oregunue. the metal mass fraction Z in the envelope is not assumed to be fixed.," During the white dwarf regime, the metal mass fraction $Z$ in the envelope is not assumed to be fixed."
 Iustead. it is specified consistently according to the prediction of clement diffusion.," Instead, it is specified consistently according to the prediction of element diffusion."
 To account for this. we lave considered radiative opacities tables frou: OPAL for arbitrary inctallicities.," To account for this, we have considered radiative opacities tables from OPAL for arbitrary metallicities."
 For effective temperatures less than 10.000 I& we have incluced the effects of molecular opacitiv bv asstuuine pure lydrogen composition frou the computations of Mavigo Avineer (2009).," For effective temperatures less than 10,000 K we have included the effects of molecular opacitiy by assuming pure hydrogen composition from the computations of Marigo Aringer (2009)."
 This assuniptfiou is justified because element diffusion leads to pure hydrogen cuvelopes in cool white dwrfs., This assumption is justified because element diffusion leads to pure hydrogen envelopes in cool white dwarfs.
 It is worth noting that these opacity calculations do not cover the higli-deusitv regine characteristic of the euvelopes of cool white cliwarts., It is worth noting that these opacity calculations do not cover the high-density regime characteristic of the envelopes of cool white dwarfs.
 Nevertheless. because the derivation of the outer boundary conditions for our evolving models involves the inteeration of cletailed non-grav model atmospheres down to very large optical depths (7= 25) these opacities are only required at large τ and low effective. temperatures.," Nevertheless, because the derivation of the outer boundary conditions for our evolving models involves the integration of detailed non-gray model atmospheres down to very large optical depths $\tau=25$ ) these opacities are only required at large $\tau$ and low effective temperatures."
 However. at the high densities reached at the cud of the atmospheric iutegration. energv transfer is niainlv by convection. which at such depths is essentially adiabatic.," However, at the high densities reached at the end of the atmospheric integration, energy transfer is mainly by convection, which at such depths is essentially adiabatic."
 Indeed. we find that at 7=25. the radiative flux amounts to LY at most.," Indeed, we find that at $\tau=25$, the radiative flux amounts to $4\%$ at most."
 Consequently. the temperature stratification characterizing these decp lavers becomes stronely tied to the equation of state. so a detailed knowledge of the radiative opacity becomes almost relevant.," Consequently, the temperature stratification characterizing these deep layers becomes strongly tied to the equation of state, so a detailed knowledge of the radiative opacity becomes almost irrelevant."
 The couductive opacities are those of Cassisi et al. (, The conductive opacities are those of Cassisi et al. (
2007). and the neutrino emission rates are taken from Itoh et al. (,"2007), and the neutrino emission rates are taken from Itoh et al. ("
1996) and Haft et al. (,1996) and Haft et al. (
199D).,1994).
 For the high density regime characteristics of white dwarts. we have used the equation of state of Seeretaim et al. (," For the high density regime characteristics of white dwarfs, we have used the equation of state of Segretain et al. ("
1991). which accounts for all the important contributions for both the liquid aud solid phascs sec Althaus et al. (,"1994), which accounts for all the important contributions for both the liquid and solid phases — see Althaus et al. ("
2007) and references therein.,2007) and references therein.
 We have also considered the abundance chauges resulting frou clement ciffusiou in the outer lavers of white dwarts., We have also considered the abundance changes resulting from element diffusion in the outer layers of white dwarfs.
 As a result. our sequences develop pure hydrogen euvelopes. je thickness of which gradually increases as evolution xoceeds;," As a result, our sequences develop pure hydrogen envelopes, the thickness of which gradually increases as evolution proceeds."
 We have cousidered eravitational settling aud iorial and chemical diffusion. see Althaus ot al. (," We have considered gravitational settling and thermal and chemical diffusion, see Althaus et al. ("
2003) x details.,2003) for details.
 InLPCODE. diffusion becomes operative once je Wind limit is reached at high effective teniperatures (Cuelaub Bues 2000).," In, diffusion becomes operative once the wind limit is reached at high effective temperatures (Unglaub Bues 2000)."
 Chemical rehomoegcnization of ie Taner carbon-oxveen profile induced by Ravleigh-Tavlor iustabilities las been considered following Salaris al. (, Chemical rehomogenization of the inner carbon-oxygen profile induced by Rayleigh-Taylor instabilities has been considered following Salaris et al. (
1997).,1997).
 These instabilities arise because the positive -iolecular weight eradicuts that remain above the flat chemical profile left by convection during helium core mde., These instabilities arise because the positive molecular weight gradients that remain above the flat chemical profile left by convection during helium core burning.
" Finally, we enplov outer boundary conditions for our evolving white dwarf models as provided bv detailed uou-eray ιούς atimospheres that include ron-ideal effects in the gas equation of state and chemical equilibrimm based on the occupation probability ormalism."," Finally, we employ outer boundary conditions for our evolving white dwarf models as provided by detailed non-gray model atmospheres that include non-ideal effects in the gas equation of state and chemical equilibrium based on the occupation probability formalism."
 The level occupation probabilities are sclconsistently incorporated in the calculation of the ine aud continuum opacitics., The level occupation probabilities are self-consistently incorporated in the calculation of the line and continuum opacities.
 Model atimosphercs also consider collisiounduced absorption due to Πο Πο. T.- Ie. aud IL-ITe pairs. aud the Lya quasiinuolecular opacity hat result frou perturbations of hwdrosen atoms by interactions with other particles. mainly HH aud IT».," Model atmospheres also consider collision-induced absorption due to $_2$ $_2$, $_2$ -He, and H-He pairs, and the $\alpha$ quasi-molecular opacity that result from perturbations of hydrogen atoms by interactions with other particles, mainly H and $_2$."
 These nodel atmospheres have been developed by Rolamaun et al. (, These model atmospheres have been developed by Rohrmann et al. (
2002. 2010). and we refer the reader to those works and to Renedo et al. (,"2002, 2010), and we refer the reader to those works and to Renedo et al. ("
2010) for a full description ofthei.,2010) for a full description of them.
 In the interest of reducing computing timc. we have computed from these models a exid of pressure. temperature. radial thickuess aud outer mass fraction values at an optical depth 7=25 from which we derive the outer boundary conditions.," In the interest of reducing computing time, we have computed from these models a grid of pressure, temperature, radial thickness and outer mass fraction values at an optical depth $\tau=25$ from which we derive the outer boundary conditions."
 At advanced stages of white dwarf evolution. the ceutral temperature becomes strouely tied to the temperature stratification of the very outer lavers. thus the ciploviment of nou-grav modcl atinosplhieres is lighly desired for an accurate assessineut of cooling times of cool white dwarts (Prada Moroui Stranicro 2007).," At advanced stages of white dwarf evolution, the central temperature becomes strongly tied to the temperature stratification of the very outer layers, thus the employment of non-gray model atmospheres is highly desired for an accurate assessment of cooling times of cool white dwarfs (Prada Moroni Straniero 2007)."
 Our model atmuoshperes also provide detailed colors aud magnitudes for effective temperatures lower than 60.000]. for a pure hydrogen composition aud for the IST ACS filters (Veea-mag syste) and BVRI photometry.," Our model atmoshperes also provide detailed colors and magnitudes for effective temperatures lower than 60,000K for a pure hydrogen composition and for the HST ACS filters (Vega-mag system) and $UBVRI$ photometry."
 The cnereyv contribution resulting from the gravitational settling of ??Ne is treated in a similar— wav as it was done in CarefaaBerro et al. (, The energy contribution resulting from the gravitational settling of $^{22}$ Ne is treated in a similar way as it was done in a–Berro et al. (
2008). except thatnow we have asstuned that the liquid behaves as a sinele backerouug one-component plasmnia consistiug of the average by. uunuber of carbon aud oxvecu the,"2008), except thatnow we have assumed that the liquid behaves as a single backgroung one-component plasma consisting of the average by number of carbon and oxygen — the"
Grandiοἱal. 2007)).,\citealt{grandi07}) ).
 Below we give a detailed description of these emission lines. utilizing the full spectral resolution of the Chandra/LIZEG.," Below we give a detailed description of these emission lines, utilizing the full spectral resolution of the Chandra/LETG."
 We return in Section 4 to discuss more physical models lor both the absorber and emitter. using the photoionization code (Ixallmanetal.2004).," We return in Section 4 to discuss more physical models for both the absorber and emitter, using the photoionization code \citep{kallman04}."
. To analvse the emission lines in detail. (he LETG spectra were binned more finely (o sample the resolution of the detector. αἱ approximately the FWIIM spectral resolution (e.g. AA=0.05À bbins).," To analyse the emission lines in detail, the LETG spectra were binned more finely to sample the resolution of the detector, at approximately the FWHM spectral resolution (e.g. $\Delta\lambda
=0.05$ bins)."
" Thus the spectral resolution is E/.NEe500 (or ! FWIIM) at Κον), For the fits. the C-statistic was adopted (Cash1979). rather than 47. as there are fewer than 10 counts in some of the resolution bins."," Thus the spectral resolution is $E/\Delta E \sim 500$ (or $^{-1}$ FWHM) at keV. For the fits, the C-statistic was adopted \citep{cash79} rather than $\chi^{2}$, as there are fewer than 10 counts in some of the resolution bins."
 The emission lines were modeled wilh Gaussian profiles and the best-fit partial covering continuum model was adopted from above. allowing the continuum and absorption parameters to vary.," The emission lines were modeled with Gaussian profiles and the best-fit partial covering continuum model was adopted from above, allowing the continuum and absorption parameters to vary."
 Table 1 Lists the detected lines with their observed ancl inferred. properties. aud (heir significance as per the C-statistic.," Table 1 lists the detected lines with their observed and inferred properties, and their significance as per the C-statistic."
 Figures 2 and 3 show (he portions of the LETG spectrum containing (he strongest lines. with the model overlaid.," Figures 2 and 3 show the portions of the LETG spectrum containing the strongest lines, with the model overlaid."
 Overall the [it statistic improves considerably upon the addition of the emission lines to the continuum model. ie. from C/dol=720.2/444 without emission lines (rejected. at. >99.99% confidence) to C/dof=448.3/425 upon adding the emission lines (rejected at only confidence).," Overall the fit statistic improves considerably upon the addition of the emission lines to the continuum model, i.e. from ${\rm C/dof} = 720.2/444$ without emission lines (rejected at $>99.99$ confidence) to ${\rm C/dof} = 448.3/425$ upon adding the emission lines (rejected at only confidence)."
 Indeed the majority of the individual emission lines in Table 1 and are detected at high confidence. corresponding to AC>14. or >99.9% significance for 2 parameters of interest (note lines detected with a lower level of confidence are noted).," Indeed the majority of the individual emission lines in Table 1 and are detected at high confidence, corresponding to $\Delta C>14$, or $>99.9\%$ significance for 2 parameters of interest (note lines detected with a lower level of confidence are noted)."
 For instance the Ile-a ancl Lyiman-a lines are detected with AC>50., For instance the $\alpha$ and $\alpha$ lines are detected with $\Delta C > 50$.
 The strongest emission lines correspond to the IIe-like (EHe-a) and H-like (Lvman-a) transitions fromlexiscvii-viil..lexiscix-x..lexiscxi-xii.. and lextiscxiii-xiv.," The strongest emission lines correspond to the He-like $\alpha$ ) and H-like $\alpha$ ) transitions from, and ."
. Fluorescence lines may also be present [rom Ίνα ancl Ka at 2.3 and kkeV respectively. which may originate [rom reflection off Compton thick matter (see Section 4.1).," Fluorescence lines may also be present from $\alpha$ and $\alpha$ at 2.3 and keV respectively, which may originate from reflection off Compton thick matter (see Section 4.1)."
 Most of the rest.[rame energies of the emission lines areclose, Most of the rest–frame energies of the emission lines areclose
A possible caveat is the following: ouly the velocity dispersion is observed. while it is the pressure which is the miportaut plvsical quautity.,"A possible caveat is the following: only the velocity dispersion is observed, while it is the pressure which is the important physical quantity."
 The estimate of the oressure as the numerical density inultiplied bw the ocity dispersion is correct if there is no equipartitiou ween small and large galaxy masses. or expressed differently if the velocity dispersion docs not depend ou he ealaxy nass.," The estimate of the pressure as the numerical density multiplied by the velocity dispersion is correct if there is no equipartition between small and large galaxy masses, or expressed differently if the velocity dispersion does not depend on the galaxy mass."
 We have checked in a ceutral region of ) aresec radius that the velocity dispersion docs not 201. on he magnitude: assunidne a constaut mass to ight ratio for all galaxies. this nuplies that the velocity dispersion docs not depend ou galaxy mass.," We have checked in a central region of 750 arcsec radius that the velocity dispersion does not depend on the magnitude; assuming a constant mass to light ratio for all galaxies, this implies that the velocity dispersion does not depend on galaxy mass."
 The combined large field photographic plate aud simall field CCD nuage catalogues. coupled with exteusive spectroscopic data. have led us to eather oue of the arecst amounts of data for a single cluster.," The combined large field photographic plate and small field CCD imaging catalogues, coupled with extensive spectroscopic data, have led us to gather one of the largest amounts of data for a single cluster."
 These data rave been used in the preseut paper to analyze several xoperties of ABC'C 85., These data have been used in the present paper to analyze several properties of ABCG 85.
 Some of these properties have already been discussed in the past by various authors (see Tutroduction). but the large amount of data now available allows a more refined analysis. leading either to derive new properties or to confirma previous results with a hieh confidence level.," Some of these properties have already been discussed in the past by various authors (see Introduction), but the large amount of data now available allows a more refined analysis, leading either to derive new properties or to confirm previous results with a high confidence level."
 Fist. we have compared the distributions of enission line (ELCs) ancl i0n-enüssion line galaxies (NoELGs). and shown that ELGs secu. intrinsically fainter than NoELCx. and clo not appear as ceutrally condensed NoELCGsx. ]oth spatially aud in velocity space.," First, we have compared the distributions of emission line (ELGs) and non-emission line galaxies (NoELGs), and shown that ELGs seem intrinsically fainter than NoELGs, and do not appear as centrally condensed as NoELGs, both spatially and in velocity space."
 ELCs slow zu eubhauceiment souh of the uucleus. where groups are falling outo the main cluster (as discussed in our previous paper by Duet et al.," ELGs show an enhancement south of the nucleus, where groups are falling onto the main cluster (as discussed in our previous paper by Durret et al."
 1998b)., 1998b).
 This fits in well with the general view of lis cluster: the eas in the galaxie:μα belongiug to these groups is expected to be shocked aud consequcutly star formation should be more miportant iu the impact region at the epoch of actual galaxy iufall. aud less iniportaut in the central regions of clusters where star formation appears to be truncated.," This fits in well with the general view of this cluster: the gas in the galaxies belonging to these groups is expected to be shocked and consequently star formation should be more important in the impact region at the epoch of actual galaxy infall, and less important in the central regions of clusters where star formation appears to be truncated."
 This has been shown be the case for two clusters at redshifts 0.2 aud MED Abraham et al. (, This has been shown to be the case for two clusters at redshifts 0.2 and 0.4 by Abraham et al. (
1996) aud Morris ct al. (,1996) and Morris et al. (
1998).,1998).
 Doesides. the cluster analyzed by. Abraham et al..," Besides, the cluster analyzed by Abraham et al.,"
" ABCC 2300. κrows evidence for a subcomponcut infalline onto he main cluster. as the south blob is falling onto ABC sh,"," ABCG 2390, shows evidence for a subcomponent infalling onto the main cluster, as the south blob is falling onto ABCG 85."
 Second. we have analyzed im detail the bhpuuünositv muetion of ABCC 85 in the R band. using a wavelet reconstruction technique.," Second, we have analyzed in detail the luminosity function of ABCG 85 in the R band, using a wavelet reconstruction technique."
 We have shown with a high confidence level that a dip was preseut at an absolute uaeguitude Mg—20.5., We have shown with a high confidence level that a dip was present at an absolute magnitude $_{\rm R}\simeq -20.5$.
 This feature has also heen detected m several other clusters aud can be accounted for w the distributions of the various types of galaxies prescut in the cluster., This feature has also been detected in several other clusters and can be accounted for by the distributions of the various types of galaxies present in the cluster.
 In this scenario. the dip would correspond o the separation between elliptical aud dwarf galaxies.," In this scenario, the dip would correspond to the separation between elliptical and dwarf galaxies."
 Third. parametric aud nou-paranmetric methods applied to our redshift catalogue have allowed us to derive εje dyaianical properies of the cluster.," Third, parametric and non-parametric methods applied to our redshift catalogue have allowed us to derive the dynamical properties of the cluster."
 We find that the dvuamical mass profes derived roni the XN-raw gas and ealaxy distributions aerce if the temperature of the N-rav οuitting plasma ds alout 8 keV. Between 250 and LOOO arcsec. whatever techlique we apply (parametric or not). iid whatever data wο Tse (X-ray or optical). the slopes of the dvuaniical mass profiles are the σα11ο e(Mir)xr).," We find that the dynamical mass profiles derived from the X-ray gas and galaxy distributions agree if the temperature of the X-ray emitting plasma is about 8 keV. Between 250 and 1000 arcsec, whatever technique we apply (parametric or not), and whatever data we use (X-ray or optical), the slopes of the dynamical mass profiles are the same $M(r) \propto r$ )."
" Tn this region. both he N-rav plasma aud ""eas of ealaxies are isothermal. aud the galaxy veocity dispersion Is isotropic."," In this region, both the X-ray plasma and the “gas” of galaxies are isothermal, and the galaxy velocity dispersion is isotropic."
 If we take into account the temperature eraclicut of the N-vay gas. the dynamical nlass is reduced.," If we take into account the temperature gradient of the X-ray gas, the dynamical mass is reduced."
 If we ake iuto account a possible temperature eracdicut of the N-rav gas. the ls reuced at very laree scae but is stil conrparable to the in the X-ray cluitting region.," If we take into account a possible temperature gradient of the X-ray gas, the is reduced at very large scale but is still comparable to the in the X-ray emitting region."
 Alhough this pa])r dst re last one of the series ou ABCG 85. the analysis of a nnch. larger area in that region of the skv is planes in a near future: we have recently obtained about 300 new redshifts in the direction of ABCC 87 (in collal)oration wit1 M. Colless). aud have the project of obtaining redsufts for the various clusters and eroups aligued along PA~16F aud in which ABCC 85 sees enibedded.," Although this paper is the last one of the series on ABCG 85, the analysis of a much larger area in that region of the sky is planned in a near future: we have recently obtained about 300 new redshifts in the direction of ABCG 87 (in collaboration with M. Colless), and have the project of obtaining redshifts for the various clusters and groups aligned along $\sim 160^\circ$ and in which ABCG 85 seems embedded."
 We also inteud to discuss the large scale structure properties of μοι niverse in the direction of ABCG 85. based on the large scale volociv features of our velocity catalogue.," We also intend to discuss the large scale structure properties of the universe in the direction of ABCG 85, based on the large scale velocity features of our velocity catalogue."
simple assumption is probably sullicientIy accurate for most applications.,simple assumption is probably sufficiently accurate for most applications.
 We remarked that the term. A'(7)could.-- be thought of as the correlation function of the o., We remarked that the term $\lambda_{cc}({\bm r})$ could be thought of as the correlation function of the subclumps.
 To see why. suppose there is no mass in the smooth component. and all the subelumps are infinitesimally small: ie. we replace all factors of the subclump density profile. f; with celta functions 9p(r;).," To see why, suppose there is no mass in the smooth component, and all the subclumps are infinitesimally small: i.e., we replace all factors of the subclump density profile $f_i$ with delta functions $\delta_{\rm D}({\bm r}_i)$ ."
 Phen. when rz0. only the third term in equation (5)) contributes any pairs.," Then, when ${\bm r}\ne 0$, only the third term in equation \ref{lambdar}) ) contributes any pairs."
" Using the delta functions reduces this terni to which is proportional to the convolution of. the subclump cistribution p, with itself.", Using the delta functions reduces this term to which is proportional to the convolution of the subclump distribution $\rho_c$ with itself.
 We can use a similar argument to compute the cross correlation between subclumps anc mass., We can use a similar argument to compute the cross correlation between subclumps and mass.
 Fhat is. we imagine we sit at the center of the ith subclump anc we then compute the typical density at distance 7 from it.," That is, we imagine we sit at the center of the $i$ th subclump and we then compute the typical density at distance ${\bm r}$ from it."
 Jecause the first term in equation (5)) is not centered. on a subclump it no longer contributes., Because the first term in equation \ref{lambdar}) ) is not centered on a subclump it no longer contributes.
 Since our constraint only requires one. member of cach pair of positions to be centered on a subclump we now need to replace one factor of f; with a delta function., Since our constraint only requires one member of each pair of positions to be centered on a subclump we now need to replace one factor of $f_i$ with a delta function.
 This means In the limit in which the subelumps are much smaller in size than the parent halo the last term simplifies to give. When ορP this becomes and further. if the total mass in subelumps is small we obtain lt is easy to verily that the result for €&. can be obtained simply by averaging over all realizations of subclump positions. p(r;) and plr;).," This means so that the subclump–mass cross correlation function is In the limit in which the subclumps are much smaller in size than the parent halo the last term simplifies to give, When $\rho_c/\bar\rho\propto F$ this becomes and further, if the total mass in subclumps is small we obtain It is easy to verify that the result for $\xi_\times$ can be obtained simply by averaging over all realizations of subclump positions, $p({\bm r}_i)$ and $p({\bm r}_j)$."
 The power spectrum is the Fourier ‘Transform of the correlation function., The power spectrum is the Fourier Transform of the correlation function.
 Since the correlation function involves a number of convolution-tvpe integrals. the power spectrum is given. by simple multiplications of the various density prolile factors.," Since the correlation function involves a number of convolution-type integrals, the power spectrum is given by simple multiplications of the various density profile factors."
 Let denote the Fourier. transform of the density run of the smooth component 7 normalized. by the total mass contained in the profile. and define (ΑΛ) and CLE) similarly (we have assumed: we are working in three-dimensions).," Let denote the Fourier transform of the density run of the smooth component $F$ normalized by the total mass contained in the profile, and define $u_i(k)$ and $U_c(k)$ similarly (we have assumed we are working in three-dimensions)."
 Then which we could write as A similar calculation shows that the cross spectrum.between subelumps and mass is and the power spectrum of the subelumps is, Then which we could write as A similar calculation shows that the cross spectrumbetween subclumps and mass is and the power spectrum of the subclumps is
"Bag)=0.43120.008 respectively,",$R_{100} = 0.134 \pm 0.008$ respectively.
" Au unbroken DL—1.9 power law up to 300 keV. svouk result in flux ratios of 0.178 and 0.129. respectively,"," An unbroken $\Gamma = 1.9$ power law up to 300 keV would result in flux ratios of 0.178 and 0.129, respectively."
 A P=1.9 power law extending up to 500 keV would result in a (300500 keV)/(1250 keV) fiux ratio of 0.028. while CDM measures esseutiallv no flux above 300 keV. που=0.006dE0.010. consisteut with a steepeuiug or cut off somewhere near 300 keV. The CDM results appear to be consistent with the steepening seen in the OSSE-COMPTEL Spectra.," A $\Gamma = 1.9$ power law extending up to 500 keV would result in a (300–500 keV)/(12–50 keV) flux ratio of 0.028, while GBM measures essentially no flux above 300 keV, $R_{300} = 0.006 \pm 0.010$, consistent with a steepening or cut off somewhere near 300 keV. The GBM results appear to be consistent with the steepening seen in the OSSE-COMPTEL spectra."
" The ealactic iicroquasar CRS 19151105 i$ à LMXD with the compact object being a massive black hole (Greiner.Cubyv,&MeCaughlreau 2001).", The galactic microquasar GRS 1915+105 is a LMXB with the compact object being a massive black hole \citep{Greiner2001}.
. It was highly variable over the 9-vear observation period of theCGRO inission (Paciesas with significant Cluission observed out to ~1 MeV (Zdzimrskietal.2001:Case 2005).," It was highly variable over the 9-year observation period of the mission \citep{Paciesas1995,Case2005} with significant emission observed out to $\sim 1$ MeV \citep{Zdziarski2001,Case2005}."
. Combining the BATSE data from imultiple outbursts vields a PActim best fit bv a broken power law. with PAectral iudex P—2.7 below 300 keV flattening to D~1.5 above 300 keV. The spectrum derived from DATSE data shows ua evidence of the thermal spectrum seen in Cyg X-1.," Combining the BATSE data from multiple outbursts yields a spectrum best fit by a broken power law, with spectral index $\Gamma \sim 2.7$ below 300 keV flattening to $\Gamma \sim 1.5$ above 300 keV. The spectrum derived from BATSE data shows no evidence of the thermal spectrum seen in Cyg X-1."
 By contrast. observations with JNTEGRAL/SPI in the 20500 keV enuerev range (Droulans&Jourdain2009) showed evidence for a. time-variable thermal Comptonization component below ~100 keV along with a relatively steady. hard power law at lieher cuereies. indicating that different emission reeions are likely responsible for the soft aud hard CLUISSIOL.," By contrast, observations with /SPI in the 20–500 keV energy range \citep{Droulans2009} showed evidence for a time-variable thermal Comptonization component below $\sim 100$ keV along with a relatively steady, hard power law at higher energies, indicating that different emission regions are likely responsible for the soft and hard emission."
" The CDM daily fluxcs integrated over 730 davs (Table 1)) show sienificant ciuission above 100 τον, consistent with the relatively hard power law spectrum seen in BATSE and SPI data."," The GBM daily fluxes integrated over 730 days (Table \ref{Flux_table}) ) show significant emission above 100 keV, consistent with the relatively hard power law spectrum seen in BATSE and SPI data."
 The GBA ight curve (Fie. 5)), The GBM light curve (Fig. \ref{GRS1915}) )
 shows distinct variability vclow LOO keV. with statistics above 100 keV iusufficieut to determine the level of variability of he cuuission.," shows distinct variability below 100 keV, with statistics above 100 keV insufficient to determine the level of variability of the emission."
 The fux ratios observed bv CBA (Roy=WOLLEO.00L and Riyy=0.010+ 0.001) are close to the flux ratios expected frou a power aw spectrum with D~3 (R=)=0.016. ane Hoo—001 L)., The flux ratios observed by GBM $R_{50} = 0.044 \pm 0.001$ and $R_{100} = 0.010 \pm 0.001$ ) are close to the flux ratios expected from a power law spectrum with $\Gamma \sim 3$ $R_{50} = 0.046$ and $R_{100} = 0.014$ ).
The color distribution of globular clusters in most galaxies has long been known to be bimodal (e.g.Nanda&Whitmore2001:Larsenοἱal.2001).,"The color distribution of globular clusters in most galaxies has long been known to be bimodal \citep[e.g.][]{Kundu01,Larsen01}."
. The standard understanding of (his feature is that the red. aud blue subpopulations for a given galaxy represent a difference in metallicity. with the blue clusters being on average more metal poor than (he red clusters.," The standard understanding of this feature is that the red and blue subpopulations for a given galaxy represent a difference in metallicity, with the blue clusters being on average more metal poor than the red clusters."
 The correspondence of the blue clusters with lower metallicity and red clusters with higher metallicity follows directly [rom studies of the Milkv Wav globular cluster svstem (e.g.Harris 1991).. and has been confirmed in a number of extragalactic globular cluster svstenis (e.g.Cohenetal.2003:Strader2007;Ixundu&Zepl2001).," The correspondence of the blue clusters with lower metallicity and red clusters with higher metallicity follows directly from studies of the Milky Way globular cluster system \citep[e.g.][]{AZ98,Harris91}, and has been confirmed in a number of extragalactic globular cluster systems \citep[e.g.][]{CBC03,SBB07,KZ07}."
. Recently. several studies of the globular cluster svstems of early type galaxies have suggested a relation between (he color and Iuminositv of the blue metal-poor clusters. with brighter clusters appearing more red (IIlaurisetal.2006: 2006)..," Recently, several studies of the globular cluster systems of early type galaxies have suggested a relation between the color and luminosity of the blue metal-poor clusters, with brighter clusters appearing more red \citep{Harris06,Strader,Mieske}."
" This ""blue ült has been taken as evidence of a relation between (he mass and metallicitv of these clusters.", This “blue tilt” has been taken as evidence of a relation between the mass and metallicity of these clusters.
 If such a trend were real. it would suggest an important role [ου sell-eurichment in huminous globular clusters (Strader&Smith2008).," If such a trend were real, it would suggest an important role for self-enrichment in luminous globular clusters \citep{StraderSmith08}."
. It might also suggest that eglobular clusters are surrounded by more massive halos when they form. in order to allow them to retain metals from multiple generations of stars.," It might also suggest that globular clusters are surrounded by more massive halos when they form, in order to allow them to retain metals from multiple generations of stars."
 Alternatively. the absence ol a mass-metallicitv relation would strongly limit the degree to which sell-enrichment is a [actor in the observed cluster metallicities.," Alternatively, the absence of a mass-metallicity relation would strongly limit the degree to which self-enrichment is a factor in the observed cluster metallicities."
 Such an absence also emphasizes the differences between the formation histories of globular clusters and galaxies. which are known to have a strong mass-metallicitv relation.," Such an absence also emphasizes the differences between the formation histories of globular clusters and galaxies, which are known to have a strong mass-metallicity relation."
 Firmly establishing anv such relation requires determining the color and huninosities of the eglobular clusters over a large range in brightness to detect anv effect. over a significant luminosity and mass scale., Firmly establishing any such relation requires determining the color and luminosities of the globular clusters over a large range in brightness to detect any effect over a significant luminosity and mass scale.
 Unfortunately. many of the results that show evidence of this blue tilt do so using fairly shallow single orbit ACS data. with comparably low signal to noise for the remaining more distant galaxies.," Unfortunately, many of the results that show evidence of this blue tilt do so using fairly shallow single orbit ACS data, with comparably low signal to noise for the remaining more distant galaxies."
 In. (his paper. we present the results of an exiraordinarilv deep 50 orbit ACS study of the central region of M87.," In this paper, we present the results of an extraordinarily deep 50 orbit ACS study of the central region of M87."
 This deep data allows, This deep data allows
The luminosity fuuction of galeusdes Is one of the most basic properties of he ealaxy pomulation: vet it contains many valuable chies to the process of galaxy formation.,The luminosity function of galaxies is one of the most basic properties of the galaxy population; yet it contains many valuable clues to the process of galaxy formation.
 The basic physical uechliaisuis Wwuch determine the forme of the DIuniuositv fiuction were first described wRees& an White&Rees(1978)., The basic physical mechanisms which determine the form of the luminosity function were first described by\citet{ro} and \citet{wr}.
. In this picture. ealaxv formation is regulated by the rate at which gas ix able to cool in the parent dark matter halos.," In this picture, galaxy formation is regulated by the rate at which gas is able to cool in the parent dark matter halos."
 These authors sugecsted hat the sharp cut-off iu the galaxy huninosity function arose frou the long cooling times of eas du Hel mass halos (or ligli πας protogalaxies in the case of Rees Ostriker)., These authors suggested that the sharp cut-off in the galaxy luminosity function arose from the long cooling times of gas in high mass halos (or high mass protogalaxies in the case of Rees Ostriker).
 The model has been developed by nuiv authors to follow iu ereat detail the formation of galasdes du a hierarchical 1universe., The model has been developed by many authors to follow in great detail the formation of galaxies in a hierarchical universe.
 Rev iniprovemeuts are the inclusion of galaxy ucreius aud the evolution of stelar populations (White&Freuk1991:Colelac.|999:Coleetal.2000:Benson 2002).," Key improvements are the inclusion of galaxy merging and the evolution of stellar populations \citep{wf,cole91,kwg,lacey93,cole94,kauff99,sp,cole00,benson02}."
. Such inodels are now being stronglv tested. by high-precision east‘olmcuts of the galaxy Iuuiinositv function fou large redshift surveys stch as the 2dFCRS aud 2MASS (Coleal.2001:IXochaucket2001 ).," Such models are now being strongly tested by high-precision measurements of the galaxy luminosity function from large redshift surveys such as the 2dFGRS and 2MASS \citep{cole2mass,koch01}."
. While the key physics of gas cooling aud mereiue are now thought to be modeled with reasonable accuracy (Bensonetal.Re]OL.2002:YoshidaTellyetal.2003:Voit 2002).. other physics crucial to establishing the shape of the Iuninositv finction read poorly uudersQO(C.," While the key physics of gas cooling and merging are now thought to be modeled with reasonable accuracy \citep{benson01,benson02,yoshida02,helly02,voit02}, other physics crucial to establishing the shape of the luminosity function remain poorly understood."
" The first uncertainty is he ""feedback necded to regulate the formatio1 of dwart ealaxies. aud hence reconcile the rather shallow slope o| fhe fait cud of the observed huunmositv function with the relatively steep mass function of dark mater halos."," The first uncertainty is the “feedback” needed to regulate the formation of dwarf galaxies, and hence reconcile the rather shallow slope of the faint end of the observed luminosity function with the relatively steep mass function of dark matter halos."
 While outflows of eas from galaxies have been observe at both low and high redshift (Martin1999:Pettinietal.2002).. the conrplex physics at work has not vet been uuderstood iu detail. aud most mocels of galaxy. formatio1 simply. adopt phenomenological rules to describe their effects;," While outflows of gas from galaxies have been observed at both low and high redshift \citep{martin99,pettini02}, the complex physics at work has not yet been understood in detail, and most models of galaxy formation simply adopt phenomenological rules to describe their effects."
 Previous work has typically assmucd tha the doniuaut feedback miechanisui is the reheating of cold gas πι he disk to the temperature of the diffuse eas halo (White&Freuk1991:OstrikeY(1977) 2000).. although complete expulsion of disk eas from the halo," Previous work has typically assumed that the dominant feedback mechanism is the reheating of cold gas in the disk to the temperature of the diffuse gas halo \citep{wf,cole94,kauff99,efst00}, , although complete expulsion of disk gas from the halo"
Approximately thirteen. billion years ago. the cosmic neighbourhood destined eventually to become our Local. Group of galaxies underwent a dramatic transition: a giant ionization front swept through. engulfing it in à sea of ionizing radiation.,"Approximately thirteen billion years ago the cosmic neighbourhood destined eventually to become our Local Group of galaxies underwent a dramatic transition: a giant ionization front swept through, engulfing it in a sea of ionizing radiation."
 This occurred as a local manifestation of a global transition of the intergalactic medium in the whole universe referred to as Cosmic Reionization. caused by the radiation from the first galaxies.," This occurred as a local manifestation of a global transition of the intergalactic medium in the whole universe referred to as Cosmic Reionization, caused by the radiation from the first galaxies."
 This process converted the intergalactic medium from neutral and cold gas during the Cosmic Dark Ages before any galaxies existed. into a hot. ionized plasma.," This process converted the intergalactic medium from neutral and cold gas during the Cosmic Dark Ages before any galaxies existed, into a hot, ionized plasma."
 The absorption spectra of QSOs from redshift 0 to about 6 show that the intergalactic medium has been almost fully ionized for most of the lifetime of the Universe., The absorption spectra of QSOs from redshift 0 to about 6 show that the intergalactic medium has been almost fully ionized for most of the lifetime of the Universe.
 On the other hand. the recent data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite yielded a rather large optical depth for scattering the Cosmic Microwave Background photons on free electrons.," On the other hand, the recent data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite yielded a rather large optical depth for scattering the Cosmic Microwave Background photons on free electrons."
 This strongly suggests that the reionization epoch started well before redshift [0 and therefore was fairly extended in time., This strongly suggests that the reionization epoch started well before redshift 10 and therefore was fairly extended in time.
 It also contirmed independently the existence of a reionization epoch. required by this additional optical. depth.," It also confirmed independently the existence of a reionization epoch, required by this additional optical depth."
 The process of reionization had. far-reaching consequences for subsequent galaxy formation., The process of reionization had far-reaching consequences for subsequent galaxy formation.
 The photoionization heating which accompanies reionization increased the gas temperature from the very low one. of order a few K or less. during the Cosmic Dark Ages before the first stars formed. to 107 K or more.," The photoionization heating which accompanies reionization increased the gas temperature from the very low one, of order a few K or less, during the Cosmic Dark Ages before the first stars formed, to $\sim10^4$ K or more."
 This in turn increased the corresponding Jeans mass. the mass above which gas pressure cannot sucessfully counteract gravity. by about 5 orders of magnitude.," This in turn increased the corresponding Jeans mass, the mass above which gas pressure cannot sucessfully counteract gravity, by about 5 orders of magnitude."
 This strongly suppressed the formation of low-mass galaxies and cut off the star formation in previously-formed ones. and thereby should have significantly influenced the early population of dwarf satellite galaxies.," This strongly suppressed the formation of low-mass galaxies and cut off the star formation in previously-formed ones, and thereby should have significantly influenced the early population of dwarf satellite galaxies."
 For this reason. retonization is often invoked as a plausible explanation for the observed lack of galaxy satellites compared to the numbers predicted by pure dark matter simulations (2222)..," For this reason, reionization is often invoked as a plausible explanation for the observed lack of galaxy satellites compared to the numbers predicted by pure dark matter simulations \citep{2000ApJ...539..517B, 2009MNRAS.400.1593M,
2010MNRAS.402.1995M,2010ApJ...710..408B}."
 The same ionization and heating process also changed significantly the character of star formation. as stars whose formation starts out from hot. ionized gas. even those with a primordial element abundance. are different from the ones forming out of initially cold gas (e.g. ο).," The same ionization and heating process also changed significantly the character of star formation, as stars whose formation starts out from hot, ionized gas, even those with a primordial element abundance, are different from the ones forming out of initially cold gas \citep[e.g.][]{2003ApJ...586....1M}. ."
2001).,.
. ere we attempt to calibrate these correction factors using theoretical models of dusty rreglons., Here we attempt to calibrate these correction factors using theoretical models of dusty regions.
 The MacOS version of the MAPPINGS IIIc code was used to generate spherical-shell clusty photoionized models appropriate to rregions excited by clusters of OD stars., The MacOS version of the MAPPINGS IIId code was used to generate spherical-shell dusty photoionized models appropriate to regions excited by clusters of OB stars.
 MAPPINGS Id includes a nunber of advances in (he treatment of dust physics and absorption., MAPPINGS IIId includes a number of advances in the treatment of dust physics and absorption.
 The dust model includes three types of grains. “astronomical” silicates ancl graphite or amorphous carbon grains having a &Nordsiek(1977). (MBN) distribution for grain sizes between aand2500A.," The dust model includes three types of grains, “astronomical” silicates and graphite or amorphous carbon grains having a \citet{MRN77} (MRN) distribution for grain sizes between and."
 For these grains the extinction curve is based on the Laor&Draine(1993) data for silica ancl graphite., For these grains the extinction curve is based on the \citet{Laor93} data for silica and graphite.
 In addition. we have the option of including complex PAII-like organic molecules.," In addition, we have the option of including complex PAH-like organic molecules."
 For (hese. the photoionization cross-section per carbon atom Lollow the vield factors given by Vastraeteοἱal.(1990) which. are based on pyrene and coronene.," For these, the photoionization cross-section per carbon atom follow the yield factors given by \citet{Vestraete90} which are based on pyrene and coronene."
 These have been extrapolatecl (using the same slope as (he Vestraete curve) to NV.=80. which seems {ο be appropriate for interstellar PAIIs (Allain.Leach&Sedlimavr199Ga.h:IIlollenbach&Tielens1999:Peetersetal 2002).," These have been extrapolated (using the same slope as the Vestraete curve) to $N_{{\rm c}}=80$, which seems to be appropriate for interstellar PAHs \citep{Allain96a, Allain96b, Hollenbach99, Peeters02}."
. For PAIL molecules of these dimensions. the ionization potential is about 6 eV. The PAIL opacities are taken from the recent publication by Li&Draine(2002).," For PAH molecules of these dimensions, the ionization potential is about 6 eV. The PAH opacities are taken from the recent publication by \cite{Li02}."
. With our present state of knowledge on the physies of PAL molecules. it is not at all clear whether such molecules can survive lor significant leneths of time in the hostile environment offered by the ionized zones of an rreeion.," With our present state of knowledge on the physics of PAH molecules, it is not at all clear whether such molecules can survive for significant lengths of time in the hostile environment offered by the ionized zones of an region."
 Provided that the heating rate by the absorption of photons in the ISM can be al least matched bv the infrared. radiative rate. then the survival of polvevelic aromatic hvdroearbons. PAIIs. is set by the competition between photoclissociation (by the ejection ol an acetvleneic group) and its repair through accretion of carbon atoms (Allain.sedlmavr," Provided that the heating rate by the absorption of photons in the ISM can be at least matched by the infrared radiative rate, then the survival of polycyclic aromatic hydrocarbons, PAHs, is set by the competition between photodissociation (by the ejection of an acetyleneic group) and its repair through accretion of carbon atoms \citep{Allain96a,Allain96b}."
 1996a.b).. IL T4; is the radiative dissociation timescale. and τις is the C atom accretion timescale. (hen these are given by," If $\tau _{{\rm
diss}}$ is the radiative dissociation timescale, and $\tau _{{\rm acc}}$ is the C atom accretion timescale, then these are given by"
This inference. must. be qualified: as follows. (,This inference must be qualified as follows. (
i) The Core parameters used are very uncertain. in. particular the core masses. (,"i) The core parameters used are very uncertain, in particular the core masses. ("
ii) Many of the cores appear already to have formed protostars (as evidenced. by their association with LRAS sources). and. even those that have not may already be in an advanced state of collapse.,"ii) Many of the cores appear already to have formed protostars (as evidenced by their association with IRAS sources), and even those that have not may already be in an advanced state of collapse."
" Therefore the observed values of Z4, and οι, may not be ""initial, in the sense we have defined them. (", Therefore the observed values of $R_{_{\rm O}}$ and $\Omega_{_{\rm O}}$ may not be “initial” in the sense we have defined them. (
ii) Our simulations do not take account of the low levels of turbulence observed. in such cores. (,iii) Our simulations do not take account of the low levels of turbulence observed in such cores. (
iv) We do not rule out the possibility that at a later stage. once infall ceases. some of these protostellar disces cool and fragment. particularly if more cllicient cooling due to dust operates.,"iv) We do not rule out the possibility that at a later stage, once infall ceases, some of these protostellar discs cool and fragment, particularly if more efficient cooling due to dust operates."
 We have performed simulations of the collapse of rigidly rotating prestellar cores., We have performed simulations of the collapse of rigidly rotating prestellar cores.
 Each core is initially a mildly supercritical Bonnor-Ebert. sphere (ἐν= 6.9). with its densitv. increased byLO%.. ancl contained. by external pressure.," Each core is initially a mildly supercritical Bonnor-Ebert sphere $\xi_{_{\rm B}}=6.9$ ), with its density increased by, and contained by external pressure."
" The gas is pure molecular hydrogen with 2=δι (hence isothermal sound speed 0.3410’ems +). the initial central density is p.=10Pgem*and hence the core mass is AL,=6.1ΔΕ. its initial radius is 74,=17.000AU. and its external pressure is P4=A,5.5.10em. IN."," The gas is pure molecular hydrogen with $T=28\,{\rm K}$ (hence isothermal sound speed $0.34\times 10^5\,{\rm cm}\,{\rm s}^{-1}$ ), the initial central density is $\rho_{_{\rm C}}=10^{-18}\,{\rm g}\,{\rm cm}^{-3}$,and hence the core mass is $M_{_{\rm O}}=6.1\,{\rm M}_\odot$, its initial radius is $R_{_{\rm O}}=17,000\,{\rm AU}$, and its external pressure is $P_{_{\rm EXT}}=k_{_{\rm B}}\,5.5\times 10^5\,{\rm cm}^{-3}\,{\rm K}$ ."
" Phe initial angular speed is varied from Q,,—0.610Ls1 to Q,-—lLs.LoLs1 (corresponding to 0.013«4< 0.12)."," The initial angular speed is varied from $\Omega_{_{\rm O}}=0.6\times 10^{-13}\,{\rm s}^{-1}$ to $\Omega_{_{\rm O}}=1.8\times 10^{-13}\,{\rm s}^{-1}$ (corresponding to $0.013<\beta<0.12$ )."
 A slowly rotating core collapses to form a relatively massive primary protostar. and then a protostcllar disc erows around this protostar.," A slowly rotating core collapses to form a relatively massive primary protostar, and then a protostellar disc grows around this protostar."
FPhe cisc is massive. but quite hot and. compact. and so it does not. fragment: 1 simply aecretes onto the primary protostar.,"The disc is massive, but quite hot and compact, and so it does not fragment; it simply accretes onto the primary protostar."
 There is some observational evidence for the existence of massive disces (e.g. 7777)..," There is some observational evidence for the existence of massive discs \citep[e.g.][]{Eisner2005, Rodriguez2005, Greaves2008, Mann2009}."
 However. the phase we have simulated is short lived ancl still deeply embedded in the parental core. so our disces would. be rather hard. to observe.," However, the phase we have simulated is short lived and still deeply embedded in the parental core, so our discs would be rather hard to observe."
 We conjecture that such disces will show signatures of crystalline silicates out to disc raclit of several AU., We conjecture that such discs will show signatures of crystalline silicates out to disc radii of several AU.
 A rapidly rotating core collapses initially to form a protostellar. disc. and then a protostar condenses out. at the centre.," A rapidly rotating core collapses initially to form a protostellar disc, and then a protostar condenses out at the centre."
 “Phe protostar acquires almost all its mass via the disc. ancl therefore it grows. quite slowly.," The protostar acquires almost all its mass via the disc, and therefore it grows quite slowly."
 The disc is extended. cool and thin. and tends to fragment.," The disc is extended, cool and thin, and tends to fragment."
 On the basis ofan analytic model. we obtain a condition on the mass. initial radius and initial angular speed of a core (Iqn. 13))," On the basis of an analytic model, we obtain a condition on the mass, initial radius and initial angular speed of a core (Eqn. \ref{EQN:MULT}) )"
 such that its protostellar disc will fragment. whilst material is still infalling. from. the core envelope.," such that its protostellar disc will fragment, whilst material is still infalling from the core envelope."
 Applying this condition to observed. samples of cores we predict that such fragmentation is unlikely., Applying this condition to observed samples of cores we predict that such fragmentation is unlikely.
 In a companion paper (Walch et al..," In a companion paper (Walch et al.,"
 in preparation). we explore how these results are fundamentally. changed if a prestellar core is turbulent. but has the same net angular momentum as the cores modeled here.," in preparation), we explore how these results are fundamentally changed if a prestellar core is turbulent, but has the same net angular momentum as the cores modeled here."
 We thank D. Neufeld for. providing the cooling tables., We thank D. Neufeld for providing the cooling tables.
" 5. Walch. performed. this work with support from the International Alax-Planck Research School. the DEG Cluster of Excellence. (www.universe-cluster.doe) and. the Marie Curie REN (MICEN-C""I-2006-035800)."," S. Walch performed this work with support from the International Max-Planck Research School, the DFG Cluster of Excellence (www.universe-cluster.de) and the Marie Curie RTN (MRTN-CT-2006-035890)."
 We thank the referee for his/her detailed and thoughtful comments. which were very helpful.," We thank the referee for his/her detailed and thoughtful comments, which were very helpful."
 We develop here a simple model to explain. why rapidly rotating cores tend to fragment (and. thereby presumably produce multiple systems). whereas slowly rotating cores do not.," We develop here a simple model to explain why rapidly rotating cores tend to fragment (and thereby presumably produce multiple systems), whereas slowly rotating cores do not."
" For simplicity we assume that the initial core is cvlindrical. with height equal to its diameter and hence initial density p,=AM/27PR): we make this assumption purely because it allows us to formulate analytically the structure of the resulting disc."," For simplicity we assume that the initial core is cylindrical, with height equal to its diameter and hence initial density $\rho_{_{\rm O}}=M_{_{\rm O}}/2\pi R_{_{\rm O}}^3$; we make this assumption purely because it allows us to formulate analytically the structure of the resulting disc."
" Phe core is initially in solicl-body rotation with angular speed O,,.... and we assume that during the Isothermal Collapse Phase. during the carly Protostellar Disc. Phase. angular momentum is conserved minutely."," The core is initially in solid-body rotation with angular speed $\Omega_{_{\rm O}}$, and we assume that during the Isothermal Collapse Phase, during the early Protostellar Disc Phase, angular momentum is conserved minutely."
" Consequently the material initially in an annulus at radius 5, has mass M,=Mors ΜΥ to it in the disc. and ends up at radius r with angular speed r7."," Consequently the material initially in an annulus at radius $r_{_{\rm O}}$ has mass $M_{r_{\rm o}}=M_{_{\rm O}}r_{_{\rm O}}^2/R_{_{\rm O}}^2$ “interior to it” in the disc, and ends up at radius $r$ with angular speed $\Omega_{_{\rm D}}(r)=\Omega_{_{\rm O}}r_{_{\rm O}}^2/r^2$."
" Contrifugal balance then requires that ~OF(r)r. and hence The edge of the dise is therefore at and lt follows that the final surface clensity of the disc is Infallingὃν material impinges1oO on the disc at racius r with speed and continues arriving at a constant rate until time 26,07)."," Centrifugal balance then requires that $GM_{r_{\rm o}}/r^2\simeq\Omega_{_{\rm D}}^2(r)r$, and hence The edge of the disc is therefore at and It follows that the final surface density of the disc is Infalling material impinges on the disc at radius $r$ with speed We shall assume that it starts arriving at time and continues arriving at a constant rate until time $2t_{_{\rm D}}(r)$."
" Hence. in the time interval /,(0)xf= 2607). the Hux of materialonto one side of the disc at radius r is the instantaneous surlace-censity of the disc is"," Hence, in the time interval $t_{_{\rm D}}(r)\leq t\leq 2t_{_{\rm D}}(r)$ the flux of materialonto one side of the disc at radius $r$ is the instantaneous surface-density of the disc is"
de Oliveira 2005: da Rocha οἱ 22008) indicate that most CGs are indeed real physical associations.,de Oliveira 2005; da Rocha et 2008) indicate that most CGs are indeed real physical associations.
 since (he first catalog of CGs by Iickson (1982). many other catalogs have been built from different survevs (lovino et ((2003): de Carvalho et ((2005): Prandoni. Iovino. MacGillivray (1994): Iovino (2002): Focardi Ixelm (2002): Barton et ((1996): Allam Tucker 2000).," Since the first catalog of CGs by Hickson (1982), many other catalogs have been built from different surveys (Iovino et (2003); de Carvalho et (2005); Prandoni, Iovino, MacGillivray (1994); Iovino (2002); Focardi Kelm (2002); Barton et (1996); Allam Tucker 2000)."
 Particularly relevant for this paper are the 5D55-based catalogues (Lee et ((2004); MeConnachie et ((2009). hereafter MCO09).," Particularly relevant for this paper are the SDSS-based catalogues (Lee et (2004); McConnachie et (2009), hereafter MC09)."
 Those catalogs have been built using basically the criteria established originally by Hickson (1982) based on the ΠΠο of galaxy members (2 4) within some specific magnitude range. a given isolation criterion in order to avoid considering CGs as transient or projected associations of galaxies within larger structures. and compactness.," Those catalogs have been built using basically the criteria established originally by Hickson (1982) based on the number of galaxy members $\geq 4$ ) within some specific magnitude range, a given isolation criterion in order to avoid considering CGs as transient or projected associations of galaxies within larger structures, and compactness."
 The exact values of such parameters must be selected in order to get an optimum balance between completeness and (he presence of [oreground or backeround contaminants., The exact values of such parameters must be selected in order to get an optimum balance between completeness and the presence of foreground or background contaminants.
 The fraction of contaminants present in a eiven catalog depends critically on the value adopted for the surface brightness of the CG. as was explicitly demonstrated by: NICOO.," The fraction of contaminants present in a given catalog depends critically on the value adopted for the surface brightness of the CG, as was explicitly demonstrated by MC09."
 The SDSS-based catalogs have allowed for the first time the detection of a large number of CG candidates at redshift z>0.2., The SDSS-based catalogs have allowed for the first time the detection of a large number of CG candidates at redshift $z\geq 0.2$.
 In particular. MC09 have compiled (wo different catalogs containing 2.297 (catalog A) and 74.791 (catalog D) CG candidates. imposing limits for their members of r=18 mag and 21 mag respectively.," In particular, MC09 have compiled two different catalogs containing 2,297 (catalog A) and 74,791 (catalog B) CG candidates, imposing limits for their members of $r=18$ mag and 21 mag respectively."
 The mean number of ealaxies per CG candidate is 4.2 (i.e. most of the candidates have four galaxies).," The mean number of galaxies per CG candidate is 4.2 (i.e., most of the candidates have four galaxies)."
 The fraction of CG candidates with a spectroscopic determination of redshift is 44% and for catalogs A and B respectively., The fraction of CG candidates with a spectroscopic determination of redshift is 44 and for catalogs A and B respectively.
 There are 2.002 CG candidates at estimated redshift 20.3 (the most distant. has," There are 2,062 CG candidates at estimated redshift $z>0.3$ (the most distant has"
We selected a few well-studied. very bright. very small HE regions that previous observations sugeest have one or more of the three properties of the small ILLI regions.,"We selected a few well-studied, very bright, very small HII regions that previous observations suggest have one or more of the three properties of the small HII regions."
" For each source we have one observation of the IHI30o. line made with the Submillimeter Array (SALA) and one or more observations of centimeter wavelength RRLs made with the National Radio Astronomy Observatory Very Large Array The SALA observations of the [130 line (231.900959 GIIz) in the HII regions NGCT7538-IRSL. W51e2. and G28.20-0.04 were made in 2005 September wilh a spectral resolution of 0.83 km f. a bandwidth of 2 GlIz. and an angular resolution of 1.0""."," For each source we have one observation of the $\alpha$ line made with the Submillimeter Array (SMA) and one or more observations of centimeter wavelength RRLs made with the National Radio Astronomy Observatory Very Large Array The SMA observations of the $\alpha$ line (231.900959 GHz) in the HII regions G10.6-0.04, NGC7538-IRS1, W51e2, and G28.20-0.04 were made in 2005 September with a spectral resolution of 0.83 km $^{-1}$, a bandwidth of 2 GHz, and an angular resolution of $^{\prime\prime}$."
" Observations of G45.07-+0.14 were made in 2005 October with an angular resolution of 0.4"".", Observations of G45.07+0.14 were made in 2005 October with an angular resolution of $^{\prime\prime}$.
 The noise level obtained in each observation was 60 mJv ! !.., The noise level obtained in each observation was 60 mJy $^{-1}$ $^{-1}$.
 Analysis of the data indicated that some of the baselines were not well-defined. hence the positions ancl [lux densities of the sources are uncertain.," Analysis of the data indicated that some of the baselines were not well-defined, hence the positions and flux densities of the sources are uncertain."
 The standard deviation of the flux of 3€C454.4. measured. once [or each observation. is of the average measured value (table 1)).," The standard deviation of the flux of 3C454.4, measured once for each observation, is of the average measured value (table \ref{millimetercalibration}) )."
 IE we exclude the low measurement of 3C454.4 corresponding to the G45.07+0.14 data. then the standard deviation falls to ol the average.," If we exclude the low measurement of 3C454.4 corresponding to the G45.07+0.14 data, then the standard deviation falls to of the average."
 Our positions from the SALA agree with those of the VLA to better than the angular resolution., Our positions from the SMA agree with those of the VLA to better than the angular resolution.
 The LIL regions are unresolved by the SALA observations. and hence the widths of their spectral lines are unallectecl by baseline errors.," The HII regions are unresolved by the SMA observations, and hence the widths of their spectral lines are unaffected by baseline errors."
 The SALA data were processed in the SMA data reduction package MIR. and in MIRIAD.," The SMA data were processed in the SMA data reduction package MIR, and in MIRIAD."
 Most of the VLA observations were made in 2003 and 2005., Most of the VLA observations were made in 2003 and 2005.
 We reprocessed observations ol the 76a line in G45.072-0.14 (Garayetal.1986). from the VLA archives., We reprocessed observations of the $\alpha$ line in G45.07+0.14 \citep{Garay1986} from the VLA archives.
 The observations of the Πόσα line in G10.6-0.4 were previously reported in Ixeto(2002a)., The observations of the $\alpha$ line in G10.6-0.4 were previously reported in \citet{Keto2002a}.
. The other observations have not previously been published., The other observations have not previously been published.
 Details of (he observations are presented in table 2.., Details of the observations are presented in table \ref{VLAobs}.
 The VLA data were processed in AIPS: calibration data are given in table 3.., The VLA data were processed in AIPS; calibration data are given in table \ref{centimetercalibration}.
 The recombination line spectra are shown in figures 1 to 5.Hr and the line widths ancl velocities based are given in table 4..," The recombination line spectra are shown in figures 1 to 5, and the line widths and velocities based are given in table \ref{CMrrl}. ."
 mide⋅2A ⋅lt?) | glLOdo⋅⋅με)”. (31) ⋅ 17 17 (Us|Thus intrinsic metri,"The equation of the hypersurface is then $v=t \pm \rb(r,\theta)=constant$, with $\rb=\rho(r,\theta,\lambda(r,\theta))$ and the function $\lambda(r,\theta) \equiv\sin^2\thetab$ determined by the constraint $F=0$."
"cof these 3-spaces is ΠΑΣ fds? yp, Ξ-1 |Rosi? (do αμ)”. showing ", We now prove the rather remarkable result that quasi-spherical light cones are free of caustics for all positive values of the Kerr radial coordinate $r$.
that thegenerators rotate with ZAASO aneular velocityrelative tostationary observers at infinity. (Thisis direct," This is trivially true if $m=0$, when these surfaces are simply light cones in Minkowski space with vertices at the spatial origin, represented by $r=0$, $\theta=0$ or $\pi$ in oblate spheroidal coordinates according to \ref{oblate}) )."
"ly from (27)). which showsthat (,,= 0for anaxisvuuuetr"," We shall prove that it is true for $m>0$ by effectively showing that when $m$ is larger, the generators converge rapidly as $r \rightarrow 0^+$."
ic hyper," As noted in Sec. \ref{gen_prop},"
surface). From(33)) wesee that caustics Lind >0 (ποσα μις thatAhasa fixed," formation of a caustic along a generator is signalled by We consider in turn the behaviour of each factor in \ref{caust}) ) along an ingoing generator, so that $r$ is positive and decreasing, with $\lambda$ fixed."
developvalue along cach degenerategenerator). calls upou(73). (8)). (13)) aud(25)) itself. vicl," Because of the equatorial symmetry we need only consider “northern” generators, i.e., we may assume $\thetab$ (which specifies the initial, asymptotic value of $\theta$ when $r=+\infty$ ) to be acute, and $P(\theta,\lambda)$ positive, at least initially. ("
ds a? (Opt∙∙JIN — ypagsSR? (31) > wherethesubscript Tuversionofthe differcutial relati,"Note from \ref{drb}) ) that equatorial symmetryof $\rb(r,\theta)$ implies $P(\lambda, \pi-\theta)=-
P(\lambda,\theta)$ Since $\theta$ decreases with $r$ at fixed $\lambda$ according to \ref{dl_mu}) ), the factor $P=a\sqrt{\lambda-\sin^2\theta}$ must and remain positive."
ons(10)) aud (25)) gives XgUde = AQUI., Any possible caustic in the Kerr $r$ sheet cannot arise from the behaviour of $P$.
 pp PPdd). XR? d0 =PUNdr. QA)., We proceed to consider the other factors in \ref{caust}) ).
 Quasi-spherical hypersurfaces which asvuiptoticallv approach Miukowski spher," From the definition \ref{pq}) ), We shall further show that Thus, none of the three factors $\mu$, $Q$ and $\sin\theta$ can reach zero sooner for positive $m$ than they do in flat space, and hence they do not reach zero for any positive value of $r$."
icallight conesat infinity. Defiue an angle 0.(r. 0)bv A= su0..," To establish \ref{tiq}) ), we note that the function $\theta(r,\lambda,m)$ is determined by the vanishing of $F(r,\theta,\lambda,m)$ as given by \ref{Fqs}) )."
 indistiunguishable, Taking the differential at fixed $r$ $\lambda$ and using \ref{pq}) ) gives which is manifestly positive.
from spherical coordinates. so we ," Turning to $\mu$ , this is defined as a function of $r,\theta,\lambda,m$ by $\mu = -\partial F/ \partial \lambda$ according to \ref{dl_mu}) )."
lavethe condition 0.(rx0)0 eenerates," Inverting the order of partial differentiation and using \ref{Fqs}) ), Hence"
Associating the dark cored filaments with individual fux tubes inbed:led in a amore vertical magnetic field. as sugecstor by Solauki ame ALoutavon (1993) is possible. but would imply tha such flux tubes unst follow very closely her=1 surface to be visible over lengths of several 1000 il. al he same niust o true for tιο Evershed flow aud he maeguetic fled withi the fhx be.,"Associating the dark cored filaments with individual flux tubes imbedded in a more vertical magnetic field, as suggested by Solanki and Montavon (1993) is possible, but would imply that such flux tubes must follow very closely the $\tau=1$ surface to be visible over lengths of several 1000 km, and the same must be true for the Evershed flow and the magnetic field within the flux tube."
 While we do not completely rejec the possibilitv tha these structures are iucividal flux tibes coifaiming siphon fiows. we believe hat the aree radlal exteion of the dark cored filameuts nakes fus unlikev ancl cefinitelv qiestion the suggestion o» Schlichemmaicr aud Solanki (2003) that such flows xovide the heat flux to the pemmubra.," While we do not completely reject the possibility that these structures are individual flux tubes containing siphon flows, we believe that the large radial extension of the dark cored filaments makes this unlikely and definitely question the suggestion by Schlichenmaier and Solanki (2003) that such flows provide the heat flux to the penumbra."
 As discussed by Scliichemmaicr aid Solanki (2003) we cau also rule out iuterchauge of flux tubes. proposed by Jalin aud Schinidt (1991). as a viae inechanisni to heat the penuunbra sinuplv on the basis of the loug life times of these dark cored filaments. that preserve their identity during more than one hour (Langhans et al 2005a).," As discussed by Schlichenmaier and Solanki (2003) we can also rule out interchange of flux tubes, proposed by Jahn and Schmidt (1994), as a viable mechanism to heat the penumbra simply on the basis of the long life times of these dark cored filaments, that preserve their identity during more than one hour (Langhans et al 2005a)."
 retcores2 shows a coutimmiu dare of a arly regular spot recorded at a heliocentric angle of 617 The disk center (DC) and solar North (CN) directions axο mdicated., \\ref{cores2} shows a continuum image of a fairly regular spot recorded at a heliocentric angle of $^\circ$ The disk center (DC) and solar North (N) directions are indicated.
 This Huaee eives several nuications sugecstiιο that the 7=1 surace in the penuulπα ds not a flat but a corrugated surace., This image gives several indications suggesting that the $\tau=1$ surface in the penumbra is not a flat but a corrugated surface.
 Dark cores are not seen i most of the peuumbra., Dark cores are not seen in most of the penumbra.
 Ou the lub side. darς cores are clearv seen du several filaucuts.," On the limb side, dark cores are clearly seen in several filaments."
 At aziuiths away from the direcion to the lib. lar’s cores shift away roni the center of brielt filaments towards the Iib direction.," At azimuths away from the direction to the limb, dark cores shift away from the center of bright filaments towards the limb direction."
" At agiuutlis around 90 degτου», dar& cores cannot casily be seen but hints of the neare seen as dark streaks (shown as bright ou this necative priit) separating two filaments."," At azimuths around 90 degrees, dark cores cannot easily be seen but hints of them are seen as dark streaks (shown as bright on this negative print) separating two filaments."
 We also note, We also note
claimed convergence of the fIux-weighted dipole. was ο=0.40£0.09.,"claimed convergence of the flux-weighted dipole, was $\beta=0.40\pm0.09$."
 A somewhat larger value was obtained by ?.. where the peculiaw. velocity field within 65Mpc/h predicted from ΛΑΟΣ photometry and public redshift data was compared to three independent peculiar velocity. surveys based on Type la supernovae. surface brightness [luctuations in elliptical galaxies. and Tullv-Fisher distances to spiral galaxies.," A somewhat larger value was obtained by \cite{PH}, where the peculiar velocity field within $65\Mpch$ predicted from 2MASS photometry and public redshift data was compared to three independent peculiar velocity surveys based on Type Ia supernovae, surface brightness fluctuations in elliptical galaxies, and Tully-Fisher distances to spiral galaxies."
 The best-fit from this comparison was ο=0.4940.04., The best-fit from this comparison was $\beta=0.49\pm0.04$.
 On the other hand. our value ol 3 agrees within the errors with that obtained by 2.. who reconstructed the cosmological large scale flows in the nearby Universe using the SFI++ sample of Tullvs-Fisher measurements of galaxies and compared it with the whole sky distribution of galaxies in the 2\IRS to derive 0.28<90.37 confidence).," On the other hand, our value of $\beta$ agrees within the errors with that obtained by \cite{Davis11}, who reconstructed the cosmological large scale flows in the nearby Universe using the SFI++ sample of Tully-Fisher measurements of galaxies and compared it with the whole sky distribution of galaxies in the 2MRS to derive $0.28<\beta<0.37$ confidence)."
 Finally. in a recent paper. ? used the galaxy. distribution in (he 2AIRS to solve for the peculiar velocity [ield. estimated absolute magnitudes of galaxies and constrained ;2 by minimizing (heir spread.," Finally, in a recent paper, \cite{NBD11b} used the galaxy distribution in the 2MRS to solve for the peculiar velocity field, estimated absolute magnitudes of galaxies and constrained $\beta$ by minimizing their spread."
 They found a value in excellent agreement with our determination: ¢=0.3540.1., They found a value in excellent agreement with our determination: $\beta=0.35\pm0.1$.
 The motion of the Local Group of galaxies through the Universe can be used as a tool to constrain Cosmological parameters., The motion of the Local Group of galaxies through the Universe can be used as a tool to constrain cosmological parameters.
 One of the applications is to estimate the peculiar acceleration of the LG and compare it within the linear theory. with its peculiar velocity. known from the dipole anisotropy of the cosmic microwave background.," One of the applications is to estimate the peculiar acceleration of the LG and compare it within the linear theory with its peculiar velocity, known from the dipole anisotropy of the cosmic microwave background."
 This comparison may be used to directly measure j—QUfb. and hence the cosmological parameter of matter density. Qi.," This comparison may be used to directly measure $\beta=\Omm^{0.55}/b$, and hence the cosmological parameter of matter density, $\Omm$."
 In (his paper. as the estimator of the LG acceleration we have used the clustering dipole οἱ the galaxies [rom the 2\LASS Extended Source Catalog. which contains positions ancl fluxes of almost one million sources.," In this paper, as the estimator of the LG acceleration we have used the clustering dipole of the galaxies from the 2MASS Extended Source Catalog, which contains positions and fluxes of almost one million sources."
 As we wanted to reach as [ar [rom the Local Group as possible with the state-of-the-art observations. we have decided to trade the advantages of redshift survevs lor the huge number of objects ancl unprecedented sky coverage of the 2\IASS NSC.," As we wanted to reach as far from the Local Group as possible with the state-of-the-art observations, we have decided to trade the advantages of redshift surveys for the huge number of objects and unprecedented sky coverage of the 2MASS XSC."
 This allowed us to measure the dipole up to 300Mpc/h. which is almost 3 (mes Farther (han lor the deepest existing all-sky survey of galaxies wilh measured. redshifts. the 2\LASS Redshift Survey (2MBRS. a subset of ihe 2AIASS NSC. containing ~ 43.000 galaxies).," This allowed us to measure the dipole up to $300\Mpch$, which is almost 3 times farther than for the deepest existing all-sky survey of galaxies with measured redshifts, the 2MASS Redshift Survey (2MRS, a subset of the 2MASS XSC, containing $\sim$ 43,000 galaxies)."
 The price to pay was our inability to weight galaxies with the inverse of their selection function. (which would require redshifts to be known). so we could," The price to pay was our inability to weight galaxies with the inverse of their selection function (which would require redshifts to be known), so we could"
energy distribution for HI by constructing analytic approximations to the HI ionization and excitation cross-sections.,energy distribution for HI by constructing analytic approximations to the HI ionization and excitation cross-sections.
 In his calculation. the leading order behavior is x(1|£/£7)2. although he also includes several other corrective terms proportional to higher powers of this same factor (see also 2).," In his calculation, the leading order behavior is $\propto (1+E/E_i)^{-2}$, although he also includes several other corrective terms proportional to higher powers of this same factor (see also \citealt{omidvar69}) )."
 This has a similar (though not identical) shape to our choice. and there is no simple way to extend it to the other relevant ions.," This has a similar (though not identical) shape to our choice, and there is no simple way to extend it to the other relevant ions."
 We include collisional excitation processes in a similar way to collisional ionization. by making use of the CCC database.," We include collisional excitation processes in a similar way to collisional ionization, by making use of the CCC database."
 This provides cross-sections for all excitations from the n=1 to n=2.3. and 4 states of HI. Hel. and Hell. including separately all angular momentum sublevels as well as separate estimates for the singlet and triplet configurations in the case of Hel. We again extrapolate to /7>|keV using the Bethe approximation.," This provides cross-sections for all excitations from the $n=1$ to $n=2,\,3,$ and 4 states of HI, HeI, and HeII, including separately all angular momentum sublevels as well as separate estimates for the singlet and triplet configurations in the case of HeI. We again extrapolate to $E>1 \keV$ using the Bethe approximation."
 This explicit separation is useful to us because some applications (particularly estimates of the high-redshift 21 em signal) require the production rate of HI photons through collisional excitation., This explicit separation is useful to us because some applications (particularly estimates of the high-redshift 21 cm signal) require the production rate of HI photons through collisional excitation.
 For the n«4 levels. this is relatively easy (see ? and ? for discussions of analogous photo-excitation Atoms excited to the 2s state obviously produce no photons.," For the $n < 4$ levels, this is relatively easy (see \citealt{pritchard06} and \citealt{hirata06} for discussions of analogous photo-excitation Atoms excited to the $2s$ state obviously produce no photons."
 Atoms excited to the 3« or 3d levels must either decay through the 2p state (producing a photon) or directly to the ground state., Atoms excited to the $3s$ or $3d$ levels must either decay through the $2p$ state (producing a photon) or directly to the ground state.
 But in the latter case the resulting line photon will quickly be re-absorbed by a nearby atom (assuming that neutrals are encountered before the photon redshifts out of resonance). and it will eventually cascade into a photon.," But in the latter case the resulting line photon will quickly be re-absorbed by a nearby atom (assuming that neutrals are encountered before the photon redshifts out of resonance), and it will eventually cascade into a photon."
 On the other hand. atoms excited to the 3p state must decay to 2s and then to the ground state via two-photon decay.," On the other hand, atoms excited to the $3p$ state must decay to $2s$ and then to the ground state via two-photon decay."
 Thus they do not produce photons at all., Thus they do not produce photons at all.
 The cascade possibilities become more complicated atin=4., The cascade possibilities become more complicated at $n=4$.
 For example. excitation to ts can result in decay directly to the ground state (which is irrelevant for our purposes. since the photon is re-absorbed) or indirectly through the 3p state Gin which case no photon is produced) or the 2p state (which produces a photon).," For example, excitation to $4s$ can result in decay directly to the ground state (which is irrelevant for our purposes, since the photon is re-absorbed) or indirectly through the $3p$ state (in which case no photon is produced) or the $2p$ state (which produces a photon)."
" The relative fractions of these are given by the decay probabilities. where νε, is the spontaneous emission coefficient from level n to m."," The relative fractions of these are given by the decay probabilities, (4s) = , where $A^e_{nm}$ is the spontaneous emission coefficient from level $n$ to $m$."
 Similar exercises yield the decay probabilities for the other »=4 sublevels., Similar exercises yield the decay probabilities for the other $n=4$ sublevels.
 It is important to include excitations to the different n.=2 angular momentum sublevels separately. because they feedinto differently: most previous work has included only n<2 (e.g. 2). averaged over all the sublevels (e.g.. 2). or included only excitation to the np sublevels (e.g. 29).," It is important to include excitations to the different $n \ge 2$ angular momentum sublevels separately, because they feedinto differently; most previous work has included only $n \le 2$ (e.g., \citealt{shull85}) ), averaged over all the sublevels (e.g., \citealt{xu91}) ), or included only excitation to the $np$ sublevels (e.g., \citealt{valdes08}) )."
 Note that. in the case of Hel and Hell excitations. the decay photons can ionize other elements.," Note that, in the case of HeI and HeII excitations, the decay photons can ionize other elements."
 In detail. we should follow the radiative cascades of these excited atoms or ions. propagate each decay photon through the IGM. and follow the resulting ionizations.," In detail, we should follow the radiative cascades of these excited atoms or ions, propagate each decay photon through the IGM, and follow the resulting ionizations."
 However. we take a cruder approach and simply assume that each excited atom or ion immediately decays to the ground state. producing a photon equal to the energy of the excitation.," However, we take a cruder approach and simply assume that each excited atom or ion immediately decays to the ground state, producing a photon equal to the energy of the excitation."
 We then assume that this photon ionizes another atom and follow the resulting photo-electron., We then assume that this photon ionizes another atom and follow the resulting photo-electron.
 We use the photoionization cross-sections from ? for this purpose., We use the photoionization cross-sections from \citet{verner96} for this purpose.
 We therefore eventually recycle the Hel and Hel excitation energy into ionization or heating. rather than allowing a fraction to escape.," We therefore eventually recycle the HeI and HeII excitation energy into ionization or heating, rather than allowing a fraction to escape."
 However. we find that ©1.554 of the initial electron energy is typically lost to Hel excitation (and even smaller than that for HeID in the high energy limit. and most of that is direct excitation to 2p. for which our assumption is accurate.," However, we find that $\la 1.5\%$ of the initial electron energy is typically lost to HeI excitation (and even smaller than that for HeII) in the high energy limit, and most of that is direct excitation to $2p$, for which our assumption is accurate."
 This approximation is therefore a small correction to our results (comparable to many other processes that we ignore. and smaller than uncertainties in our cross-sections).," This approximation is therefore a small correction to our results (comparable to many other processes that we ignore, and smaller than uncertainties in our cross-sections)."
 It will. however. affect the results more strongly near the Hel threshold (e.g.. Fig.," It will, however, affect the results more strongly near the HeI threshold (e.g., Fig."
 | of 25)., 1 of \citealt{shull85}) ).
 The CCC database does not include cross-sections for transitions to nl states. and in any case it is impractical to include arbitrarily many final states.," The CCC database does not include cross-sections for transitions to $n>4$ states, and in any case it is impractical to include arbitrarily many final states."
 We therefore approximate the effects of higher evels based on the analytic calculations of ? and 2.., We therefore approximate the effects of higher levels based on the analytic calculations of \citet{johnson72} and \cite{xu91}.
" In the Bethe approximation. the leading coefficient ;1, (for excitation from the ground state to the nth level) is proportional o the oscillator strength. of the equivalent radiative absorption ransition. f,,."," In the Bethe approximation, the leading coefficient $A_{n}$ (for excitation from the ground state to the $n$ th level) is proportional to the oscillator strength of the equivalent radiative absorption transition, $f_n$."
" This depends on the quantum number of the upper evel through fi,xgu/(n&,Y where, =1.(1/n) and Gu δα correction factor (the “Gaunt factor"") that depends on the quantum mechanical details of the interaction."," This depends on the quantum number of the upper level through $f_n \propto g_n/(n k_n)^{3}$, where $k_n=1-(1/n)^2$ and $g_n$ is a correction factor (the “Gaunt factor"") that depends on the quantum mechanical details of the interaction."
" Thus we can approximate the otal cross-section to all levels above »=4. relative to that for n= tas 60 ,∙ ez Tr"," Thus we can approximate the total cross-section to all levels above $n=4$, relative to that for $n=4$, as = 60 (k_n 1.58."
a Because of the details that we have ignored (namely the Gaunt factor). the actual cross-section of the higher levels is somewhat smaller than this estimate.," Because of the details that we have ignored (namely the Gaunt factor), the actual cross-section of the higher levels is somewhat smaller than this estimate."
 ? explicitly included all η<=10 in their calculation Cutilizing the analytic approximate cross-section of 2)): they found that the »= 5-10 states increased the interaction rate by a factor of 1.17. as opposed to the 1.29 suggested by truncating the sum in equation (4)) at»=10.," \citet{xu91} explicitly included all $n \le 10$ in their calculation (utilizing the analytic approximate cross-section of \citealt{johnson72}) ); they found that the $n=5$ –10 states increased the interaction rate by a factor of 1.17, as opposed to the 1.29 suggested by truncating the sum in equation \ref{eq:ngt4}) ) at $n=10$."
 We therefore increase the n=+ cross-sections by a factor (1.17/1.29)1.58=145 (fet actiducial estimate of the importance of higher-level transitions., We therefore increase the $n=4$ cross-sections by a factor $(1.17/1.29) \times 1.58 = 1.43$ for a fiducial estimate of the importance of higher-level transitions.
 Fortunately. varying this enhancement level by a factor of two affects our heating. ionization. and excitation fractions by less than a percent.," Fortunately, varying this enhancement level by a factor of two affects our heating, ionization, and excitation fractions by less than a percent."
" We further assume that the fraction of such excitations producing photons is identical to that for η=4. which is a reasonable estimate (2). but does not substantially affect our results anyway,"," We further assume that the fraction of such excitations producing photons is identical to that for $n=4$, which is a reasonable estimate \citep{pritchard06} but does not substantially affect our results anyway."
 We also apply this same »z4 enhancement to Hel and Hell. although this is no more than a guess.," We also apply this same $n>4$ enhancement to HeI and HeII, although this is no more than a guess."
" Again. this makes only a negligible differenceto our results,"," Again, this makes only a negligible differenceto our results."
 A fast electron will share its kinetic energy with its surroundings by scattering off of ambient electrons., A fast electron will share its kinetic energy with its surroundings by scattering off of ambient electrons.
 The energy loss rate is (2) where InX is the Coulomb logarithm (to be discussedΠρ in," The energy loss rate is \citep{spitzer69}
 = - , where $\ln \Lambda$ is the Coulomb logarithm (to be discussed in"
 The energy loss rate is (2) where InX is the Coulomb logarithm (to be discussedΠρ in1," The energy loss rate is \citep{spitzer69}
 = - , where $\ln \Lambda$ is the Coulomb logarithm (to be discussed in"
 The energy loss rate is (2) where InX is the Coulomb logarithm (to be discussedΠρ in11," The energy loss rate is \citep{spitzer69}
 = - , where $\ln \Lambda$ is the Coulomb logarithm (to be discussed in"
rule out unobscured black holes with mass greater than 10A.. in the direction of the galactic bulge (3257) at distances less than 150AU.,"rule out unobscured black holes with mass greater than $10\,M_\sun$ in the direction of the galactic bulge $\beta\ge5\degr$ ) at distances less than $150\,\mbox{AU}$."
 These distauce limits improve dramatically with deeper surveys., These distance limits improve dramatically with deeper surveys.
 Should a xetro-AIACTIO ever be observed. it would afford au unprecedented opportunity to study the strone-field aspects of eeucral relativity.," Should a retro-MACHO ever be observed, it would afford an unprecedented opportunity to study the strong-field aspects of general relativity."
 These objects probe very near the horizon of the holesin the perfect aliguineut case. the nuage represents plotous that have passed within 3.507=ντος of the sineularitv (where kr; is the Schwarzschild radius). as deep iuto the strong field regime as we are ever likely to probe via light.," These objects probe very near the horizon of the holes—in the perfect alignment case, the image represents photons that have passed within $ 3.5 m=1.75 r_s$ of the singularity (where $r_s$ is the Schwarzschild radius), as deep into the strong field regime as we are ever likely to probe via light."
 A retro-MACTIO observation would be au impressive confrinatiou of the theory of general relativity. and would leave little doubt as to the existence of Eiusteiu black holes.," A retro-MACHO observation would be an impressive confirmation of the theory of general relativity, and would leave little doubt as to the existence of Einstein black holes."
 It is a pleasure to acknowledge diseussious with Evic Agol. Doug Eardley. Warner Miller. Bolidan Paczviisski. James Peebles. Sterl Phinney. Bob Rutledec. aud Johucale Solem iu the course of tlis work.," It is a pleasure to acknowledge discussions with Eric Agol, Doug Eardley, Warner Miller, Bohdan Paczyńsski, James Peebles, Sterl Phinney, Bob Rutledge, and Johndale Solem in the course of this work."
 We thauk Enuly Bemuctt for providing invaluable assistance iu the preparation of the mamuscript., We thank Emily Bennett for providing invaluable assistance in the preparation of the manuscript.
"The non-fossil populations (see Figure 5)) could have either lost their stellar populations, or had their primordial populations increase in size to the point where they are undetectable by the SDSS.","The non-fossil populations (see Figure \ref{LF.pristine}) ) could have either lost their stellar populations, or had their primordial populations increase in size to the point where they are undetectable by the SDSS."
" Near the Milky Way, we assume they lost their enüre primordial stellar population to tidal interactions."," Near the Milky Way, we assume they lost their entire primordial stellar population to tidal interactions."
" After falling into the Milky Way halo, the non-fossils were unable to form a significant younger stellar population."," After falling into the Milky Way halo, the non-fossils were unable to form a significant younger stellar population."
 At larger radii. the non-fossils are less likely to have their primordial populations stripped.," At larger radii, the non-fossils are less likely to have their primordial populations stripped."
" However, as the stars expand to fill the spatial extent of the dark matter halo, the non-fossils end up with a primordial populauon with X4:~Lyx Ri? where Li: is the luminosity of the primordial population and 7t is the radius of the primordial population."," However, as the stars expand to fill the spatial extent of the dark matter halo, the non-fossils end up with a primordial population with $\Sigma_V \sim L_V \times R_p^{-2}$ , where $L_V$ is the luminosity of the primordial population and $R_p$ is the radius of the primordial population."
" Figure 15. shows the fraction of the non-lossils with a primordial population with surface brightness, X4. for Ry,=Rye, and Ry,=0.25xRear. where 765,4, is the radius of the maximum circular velocity."," Figure \ref{SigmaV.nf}
 shows the fraction of the non-fossils with a primordial population with surface brightness, $\Sigma_V$, for $R_p = R_{max}$ and $R_p =
0.25 \times R_{max}$, where $R_{max}$ is the radius of the maximum circular velocity."
" We find that for 2,=Rya» about 1% of non-lossils would have an extended primordial halo above the SDSS detection limits (to the right of the dashed line), and. when Zi, is decreased to 0.25x/7,,,,. the detectable fraction only rises to 20%."," We find that for $R_p = R_{max}$ about $1\%$ of non-fossils would have an extended primordial halo above the SDSS detection limits (to the right of the dashed line), and, when $R_p$ is decreased to $0.25 \times R_{max}$, the detectable fraction only rises to $~20\%$."
 If these non-fossils formed few or no stars aller reionization the majority would be undetectable by SDSS., If these non-fossils formed few or no stars after reionization the majority would be undetectable by SDSS.
" The non-lossils which did form stars aller reionization today coulds be dhr or one of the [ew isolated dSphs or dSphs/Irrs:e.g... Cetus, Tucana, Anta."," The non-fossils which did form stars after reionization today coulds be dIrr or one of the few isolated dSphs or dSphs/Irrs:, Cetus, Tucana, Antlia."
" In our scenario, they would be surrounded by “ghost halos” of primordial stars 12 Gyr old with [Fe/H]&—2."," In our scenario, they would be surrounded by “ghost halos” of primordial stars $\sim 12$ Gyr old with $[Fe/H]
\simlt -2$."
 But does the dispersal of the primordial population into “ghost halos” solve the “bright satellite problem?, But does the dispersal of the primordial population into “ghost halos” solve the “bright satellite problem”?
 We quantitatively approximate this for our simulations by using a circular velocity cul., We quantitatively approximate this for our simulations by using a circular velocity cut.
 We look at the primordial luminosity functions as if all the ghost halos are either stripped or below SDSS detection limits., We look at the primordial luminosity functions as if all the ghost halos are either stripped or below SDSS detection limits.
" Pracücallv, we set the luminosities to zero for all the non-fossils."," Practically, we set the luminosities to zero for all the non-fossils."
 We look to see if this cut solves the bright satellite problem while preserving the fossils better than lowering the star formation efficiency., We look to see if this cut solves the bright satellite problem while preserving the fossils better than lowering the star formation efficiency.
 We find it to be a good solution to the bright satellite problem., We find it to be a good solution to the bright satellite problem.
" Since setting the non-fossils luminosities to zero is able to decrease the number of luminous satellites, we look at the luminosity function it produces in more detail."," Since setting the non-fossils luminosities to zero is able to decrease the number of luminous satellites, we look at the luminosity function it produces in more detail."
 All the curves in Figure 16 are the same as in Figure 5.. excepung the red curve [or the non-[ossils that now represents only the polluted fossils.," All the curves in Figure \ref{LF.nonf} are the same as in Figure \ref{LF.pristine}, excepting the red curve for the non-fossils that now represents only the polluted fossils."
 We now look at each distance bin to see what turning olf the non-fossil population has done to our various arguments., We now look at each distance bin to see what turning off the non-fossil population has done to our various arguments.
" For 50 kpe «A100 kpe, the necessity of a primordial dwarf population is even stronger when we only consider the fossil and polluted fossil populations."," For $50$ kpc $<R<100$ kpc, the necessity of a primordial dwarf population is even stronger when we only consider the fossil and polluted fossil populations."
 There are only ~7 polluted fossils within LOO kpc. less than one-fifth of what is required to account for the ~50 observed satellites.," There are only $\sim 7$ polluted fossils within $100$ kpc, less than one-fifth of what is required to account for the $\sim 50$ observed satellites."
" For Ly>101LL. , the luminosity function now sits below observations."," For $L_V > 10^4 L_\odot$ , the luminosity function now sits below observations."
 This gives the remaining star forming halos room to form additional stars without overproducing subhalos with Ly;>104L.., This gives the remaining star forming halos room to form additional stars without overproducing subhalos with $L_V>10^4 L_\odot$.
 The total number of subhalos within LOO kpe decreasing to 35 is consistent with observations., The total number of subhalos within $100$ kpc decreasing to 35 is consistent with observations.
" First, our MW.3 is on the low end of the mass range lor the Milky Way for both observational estimates and simulations."," First, our MW.3 is on the low end of the mass range for the Milky Way for both observational estimates and simulations."
" Second, as seen in Figure 8.. there are more than enough stripped down fossils which formed in halos with AZ>10*AL. and Ly>1021. to fill in the deficit."," Second, as seen in Figure \ref{LF.MF.part}, there are more than enough stripped down fossils which formed in halos with $M >10^7
M_\odot$ and $L_V >10^5 L_\odot$ to fill in the deficit."
 Since these objects would lack a cloud of tracer particles. they are marked as unboundby the halo finder AHF and would be included in the luminosity and mass of the host halo andnot in any luminosity function of the satellites.," Since these objects would lack a cloud of tracer particles, they are marked as unboundby the halo finder AHF and would be included in the luminosity and mass of the host halo andnot in any luminosity function of the satellites."
Molecular clouds are known to exhibitas supersonic. chaotic. dvnamics (?7?777) which are thought to control star formation⋅. and determine. the properties. of⋅ protostellar cores .(?)..,"Molecular clouds are known to exhibit supersonic chaotic dynamics \citep{Heyer2004,Ossenkopf2002,Falgarone1990,Perault1985,
Hayashi1989,Larson1981}, which are thought to control star formation and determine the properties of protostellar cores \citep{MacLow2004}."
 Although referred. to as .turbulence.: the origin and nature of. these motions. are not Lully⋅ understood.," Although referred to as 'turbulence', the origin and nature of these motions are not fully understood."
 jsThe most general definition⋅↔ of ⋅↴LSAT turbulence. is. simply. that the eas exhibitsa random motions. on many scales ;(2)., The most general definition of ISM turbulence is simply that the gas exhibits random motions on many scales \citep{MacLow2004}.
" However there is: a consistent. correlation. observed in. molecular clouds between the velocity. dispersion. and. size scale (the ? relation).. approximately: axr""us (e.g. 23. ??7))."," However there is a consistent correlation observed in molecular clouds between the velocity dispersion and size scale (the \citet{Larson1981} relation), approximately $\sigma \propto r^{0.5}$ (e.g. \citet{Myers1983,Solomon1987,Brunt2003}) )."
 This has invoked many comparisons between interstellar turbulence ancl classical turbulence. c.g. Ixolmorogov. incompressible turbulence (2?) (0x L7): Burgers shock dominated turbulence (2). (6x L7: and the She-Leveque model for incompressible turbulence (22). (0xL7 (?))).," This has invoked many comparisons between interstellar turbulence and classical turbulence, e.g. Kolmorogov incompressible turbulence \citep{Passot1988,Falgarone1990} $\sigma \propto L^{0.33}$ ); Burger's shock dominated turbulence \citep{Scalo1998} $\sigma \propto
L^{0.5}$ ); and the She-Leveque model for incompressible turbulence \citep{She1994,Boldyrev2002} $\sigma \propto L^{0.42}$ \citep{Bold2002}) )."
 The possible sources of turbulence can be summarised as follows: gravitational. magnetic or. hvdromagnetic instabilities: galactic rotation. through magneto-rotational instabilities. shocks in spiral arms or collisions of clouds on dillerent. epievelic orbits: stellar. feedback: via. supernovae. stellar winds and LIE regions.," The possible sources of turbulence can be summarised as follows: gravitational, magnetic or hydromagnetic instabilities; galactic rotation, through magneto-rotational instabilities, shocks in spiral arms or collisions of clouds on different epicyclic orbits; stellar feedback via supernovae, stellar winds and HII regions."
 Recent simulations have indicated that turbulence induced by a large scale driving force (e.g. large scale. Hows from supernovae or galactic rotation) is more consistent with observed molecular cloud structures. 29(??)..," Recent simulations have indicated that turbulence induced by a large scale driving force (e.g. large scale flows from supernovae or galactic rotation) is more consistent with observed molecular cloud structures \citep{Brunt2003,
Klessen2001}."
" Supernovac; have. been shown to produce sullicientD. energy to generate the velocity. clispersions. observed ""€2)..", Supernovae have been shown to produce sufficient energy to generate the velocity dispersions observed \citep{MacLow2004}.
 However observations. of. turbulent velocities.. in. regions.which. do not contain. massive. star formation⋅. suggests that other mechanisms.. such as magneto-rotational. instabilities (72)— and. colliding flows. (7) must also be important.," However observations of turbulent velocities in regionswhich do not contain massive star formation suggests that other mechanisms, such as magneto-rotational instabilities \citep{Piontek2005,Sellwood1999} and colliding flows \citep{Ball1999} must also be important."
 Interestingly. recent observations have suggested that the clongations of molecular clouds are more compatible with galactic rotation mocdels rather than stellar. feedback (nUT," Interestingly, recent observations have suggested that the elongations of molecular clouds are more compatible with galactic rotation models rather than stellar feedback \citep{Koda2006}."
 Galactic cisk simulations have investigated gravity driven turbulence. (2). stellar feedback. (7277) ancl the influence of spiral density waves on ISM. dynamics (?)..," Galactic disk simulations have investigated gravity driven turbulence \citep{Wada2002}, stellar feedback \citep{Wada2001,Avillez2005,
Dib2006} and the influence of spiral density waves on ISM dynamics \citep{Dobbs2006}."
 Analytical results also inelica ethat vorticity is generated in centrally condensed clouds subject to galactic shocks (?).. and the induced. velocities folow the observed velocity size-scale relation.," Analytical results also indicate that vorticity is generated in centrally condensed clouds subject to galactic shocks \citep{Kornreich2000}, and the induced velocities follow the observed velocity size-scale relation."
 vrevious numerical work on colliding Lows showed that density and veloc‘ity perturbations occur even in uniformi [lows subject to cooing instabilities (2).. although a velocity length. scale. correlation was not. investigated.," Previous numerical work on colliding flows showed that density and velocity perturbations occur even in uniform flows subject to cooling instabilities \citep{Heitsch2005}, , although a velocity length scale correlation was not investigated."
"In the last few vears gravitational lensing has proved useful not only in the determination of cosmological parameters, such as the Llubble constant (c.g. Refsdal 1964. 1966) and he cosmological constant (e.g. Kochanek 1996). but alsoin he studs of the mass distribution in the universe ane the mass distribution of lensing galaxies.","In the last few years gravitational lensing has proved useful not only in the determination of cosmological parameters, such as the Hubble constant (e.g. Refsdal 1964, 1966) and the cosmological constant (e.g. Kochanek 1996), but also in the study of the mass distribution in the universe and the mass distribution of lensing galaxies."
 To obtain a sample of gravitational lens systems. relatively unbiased. compared o optical lens surveys (Ixochanek 1991). which suller from secing elfects and dust obscuration. two large radio surveys. he Jodrell-Dank. VLA Astrometric Survey (JVAS: Patnaik et al.," To obtain a sample of gravitational lens systems, relatively unbiased compared to optical lens surveys (Kochanek 1991), which suffer from seeing effects and dust obscuration, two large radio surveys, the Jodrell-Bank VLA Astrometric Survey (JVAS; Patnaik et al."
 1992: Wing et al..," 1992; King et al.,"
 in preparation: Wilkinson et al..," in preparation; Wilkinson et al.,"
 in reparation) and the Cosmic Lens All Sky Survey (CLASS: Alvers et al.," in preparation) and the Cosmic Lens All Sky Survey (CLASS; Myers et al.,"
 in preparation). were set up.," in preparation), were set up."
 Together these surveys targeted. ~ 12.000 Lat spectrum radio sources with flus densities kuweer than 25 and 200 mJy for CLASS and JVAS. respectively.," Together these surveys targeted $\sim$ 12,000 flat spectrum radio sources with flux densities larger than 25 and 200 mJy for CLASS and JVAS, respectively."
 All sources were observed with the Very Large Array (VLA) in A-array at 84 Gllz with 0.2 arsec resolution., All sources were observed with the Very Large Array (VLA) in A-array at 8.4 GHz with 0.2 arsec resolution.
 Objects that showed signs of multiple compact components. or structure that could be due to lensing. were listed for further high. resolution radio observations with MERLIN.," Objects that showed signs of multiple compact components, or structure that could be due to lensing, were listed for further high resolution radio observations with MERLIN."
 Those objects still exhibiting compact structure in the MERLIN image were subsequently observed with the VLBA to confirm their identification as a lens svsteni and sometimes LIST to observe the optical emission of the lens galaxy and lens images., Those objects still exhibiting compact structure in the MERLIN image were subsequently observed with the VLBA to confirm their identification as a lens system and sometimes HST to observe the optical emission of the lens galaxy and lens images.
 In the following sections we give a detailed description, In the following sections we give a detailed description
AfAX 2950 in IN. For a more comprehensive description of the instrument. refer to Vanzi ct al. (L997)).,"$\lambda/\Delta\lambda\simeq$ 950 in K. For a more comprehensive description of the instrument, refer to Vanzi et al. \cite{Vea97}) )."
 Observations were conducted in March 1998 πια’ nou-photometric conditions., Observations were conducted in March 1998 under non-photometric conditions.
 The slit had dimensions aand was orieuted N-S. The sccing duriug the observations was in the rauee, The slit had dimensions $\times$ and was oriented N-S. The seeing during the observations was in the range.
UNCC 2316 was observe at three slia positions labeled as E. S. W aud shown in Fig.," NGC 2346 was observed at three slit positions labeled as E, S, W and shown in Fig."
 1 superimposed on the image im he LL-OS(1) line., \ref{fig:imh2} superimposed on the image in the 1-0S(1) line.
 Position E anc Ware centerce on the peaks of the line enüssion located cast and west of the ceutral star. respectively (sce Zuckerman aud Catley 19858).," Position E and W are centered on the peaks of the line emission located east and west of the central star, respectively (see Zuckerman and Gatley 1988)."
 Position S is ceutered on the star., Position S is centered on the star.
 At cach erating position we performed 5 ABBA cycles (A=ou source. D—on skv) with an ou-chip inteeration time of 60 sec. or a total of 10 uiu iuteeration on source.," At each grating position we performed 5 ABBA cycles (A=on source, B=on sky) with an on-chip integration time of 60 sec, for a total of 10 min integration on source."
 Data reduction was performed with the ESO package MIDAS. within the context IRSPEC. modified to take into account LonCGSp iustrmucutal characteristics.," Data reduction was performed with the ESO package MIDAS, within the context IRSPEC, modified to take into account LonGSp instrumental characteristics."
 The frames were corrected for bad pixels. flat-ficlded. sky subtracted and waveleneth calibrated using the OID sky lines preseut in all the frames (Oliva Orvielia 10051).," The frames were corrected for bad pixels, flat-fielded, sky subtracted and wavelength calibrated using the OH sky lines present in all the frames (Oliva Origlia \cite{OO92}) )."
 After direct subtraction. skv removal was optiuized by miuimuizug he standard deviation in selected reas where the OT sky lines were poorly subtracted but no object emission was present.," After direct subtraction, sky removal was optimized by minimizing the standard deviation in selected areas where the OH sky lines were poorly subtracted but no object emission was present."
 The wavelength calibration was performed to vetter than 1/5 of a pixel (22A))., The wavelength calibration was performed to better than 1/5 of a pixel $\simeq$ ).
 The spectra were them corrected for telluric absorption by dividing the spectra x the spectrum of the A star BS 2711 after removing its yhotospheric features GQuainly Bre}., The spectra were then corrected for telluric absorption by dividing the spectra by the spectrum of the A star BS 2714 after removing its photospheric features (mainly $\gamma$ ).
 For more details ou LouCGSp data reduction. see Vauzi ct al. 1997..," For more details on LonGSp data reduction, see Vanzi et al. \cite{Vea97}."
 Flux calibration of the spectra was achieved by rescaling the observed flix distribution along the slit to match that obtained from the ARNICA imaee in the OS(1) line at the positions of the slits., Flux calibration of the spectra was achieved by rescaling the observed flux distribution along the slit to match that obtained from the ARNICA image in the 1-0S(1) line at the positions of the slits.
 The image in the 11-0S(1) line is shown in Fie. L., The image in the 1-0S(1) line is shown in Fig. \ref{fig:imh2}.
 As verified with the spectra. the continua emission is evervwhere negligible but at the position of the ceutral star. ic. in a radius region centered on the star.," As verified with the spectra, the continuum emission is everywhere negligible but at the position of the central star, i.e. in a radius region centered on the star."
 The 11-08(1) image of Fig., The 1-0S(1) image of Fig.
 1 shows the well-known NGC 2316 inorphology. with a bright central region of size ~ «207 aud two very exteuded lobes of weaker emission (Ixastuer et al.," \ref{fig:imh2} shows the well-known NGC 2346 morphology, with a bright central region of size $\sim$ $\times$ and two very extended lobes of weaker emission (Kastner et al."
 1991)., 1994).
 The central region has two peaks of emission. to the cast aud west of the star and matches well the bright torus. tilted with respect to the line of sight. seen in optical tracers and in CO (Walsh 1983: Bachiller et al.," The central region has two peaks of emission, to the east and west of the star and matches well the bright torus, tilted with respect to the line of sight, seen in optical tracers and in CO (Walsh 1983; Bachiller et al."
 1989)., 1989).
 The IL; 1-0S(1) intensity is ~1.34101 ou both peaks., The $_2$ 1-0S(1) intensity is $\sim 1.3\times 10^{-4}$ on both peaks.
 The total luninosity of the nebula iu this line is about 0.06 L.(for D=N00 pc). of which about is contributed by the torus.," The total luminosity of the nebula in this line is about 0.06 (for $D=800$ pc), of which about is contributed by the torus."
 The average line intensity over the torus (defined as the central region of size 4.507)) is ~G«10.3x, The average line intensity over the torus (defined as the central region of size $\times$ ) is $\sim 6\times 10^{-5}$.
 These nuubers are very similar (within )) to those derived by Zuckerman aud Gatley (1988)., These numbers are very similar (within ) to those derived by Zuckerman and Gatley (1988).
 The Is. baud spectra in the three positious E. S aud Ware shown in Fig. 2..," The K band spectra in the three positions E, S and W are shown in Fig. \ref{fig:spec}."
 The spectra have been averaged over a reeiou of ~20” (12 pix) along the slit ceutered on the torus midplane., The spectra have been averaged over a region of $\sim$ (12 pix) along the slit centered on the torus midplane.
 The line intensities are given in Table 1. which gives in Column 1 the line identification. in C'oluun 2 the wavelength of the ine. In Column 3 he intensity in the W position. in Columu 1 that ou the E position. iu Cohuun 5 that in the S position of the slit.," The line intensities are given in Table 1, which gives in Column 1 the line identification, in Column 2 the wavelength of the line, in Column 3 the intensity in the W position, in Column 4 that on the E position, in Column 5 that in the S position of the slit."
 The lines are normalized to he L-OS(1) line set equal to 100: the intensity of the 1-08(1) liue is given in the Tables note., The lines are normalized to the 1-0S(1) line set equal to 100; the intensity of the 1-0S(1) line is given in the Table's note.
 Typica tuicertainties ou the line ratios are ~LO% for ratios 250. and ~30% for the others.," Typical uncertainties on the line ratios are $\sim$ for ratios $>$ 50, and $\sim$ for the others."
 Lines whose iuteusitv is particularly nucertain are marked with a semicolon., Lines whose intensity is particularly uncertain are marked with a semicolon.
 The variations in intensity along the slit positions E and W aud S of the 11-0S(1) and 2-18(1) lines iud of Hs shown in Fig. 3.., The variations in intensity along the slit positions E and W and S of the 1-0S(1) and 2-1S(1) lines and of is shown in Fig. \ref{fig:cuts}.
 The intensity profiles show that the cession in the 1-08S(1) line. peaks in the torus (i.c.. for LI= 10)) and has extended cuussion with intensity that declines more sharply oward the north than toward the," The intensity profiles show that the emission in the 1-0S(1) line peaks in the torus (i.e., for $|\delta|\simless$ ) and has extended emission with intensity that declines more sharply toward the north than toward the"
"of mass then sets the electron density within the core to be n9l fewtimes 0.1. and we adopt m,=0.2 from the Allen (2006) sample.","of mass then sets the electron density within the core to be $\nCore\/ \sim 0.1-$ fewtimes $0.1$, and we adopt $\nCore\/ = 0.2$ from the Allen \shortcite{AllenEA06} sample."
 Following observations of Cvgnus A (Beeelman&το1989) we also set 2p-2.0. corresponding to a jet opening angle of 31 (IxaiserAlexander 1997).," Following observations of Cygnus A \cite{BegelmanCioffi89} we also set $\RT\/ = 2.0$, corresponding to a jet opening angle of $31^\circ$ \cite{KA97}."
. Given durations of jet on ancl olf timescales. we can now »ediet the racio Luminosity fanction (REE) fora population of such sources observed at random stages in their evolution.," Given durations of jet on and off timescales, we can now predict the radio luminosity function (RLF) for a population of such sources observed at random stages in their evolution."
 ligure 7. explores the dependence of the RLF on input xwameters., Figure \ref{fig:parameterSpace} explores the dependence of the RLF on input parameters.
" We adopt the same base quantities as above. in addition taking the scatter in jet power (as expected from he observed. MiiAl.(llavring&Rus2004:Magorrianetal.1998). and Qi,Adin, (Allenetal.2006). relations) o be OS dex."," We adopt the same base quantities as above, in addition taking the scatter in jet power (as expected from the observed $\Mbh\/-\Mstar\/$\cite{HaeringRix04,MagorrianEA98} and $\Qjet\/-\Mbh\/$ \cite{AllenEA06} relations) to be 0.8 dex."
" The jet is active for £4,=2«107 vears. and olf for time fay=2f."," The jet is active for $\tOn\/ = 2 \times 10^8$ years, and off for time $\tOff\/ = 2 \tOn\/$."
 To explore the sensitivity of our predicted. cumulative tLES on model. parameters. cach of these parameters is varied in turn (with the others fixed).," To explore the sensitivity of our predicted cumulative RLFs on model parameters, each of these parameters is varied in turn (with the others fixed)."
 The relative animportance of the exact density profile of the atmosphere into which the source is expanding. as discussed: above. is the reason very similar LES are predicted. for various Moan ANC Fara. values in Figure τα ancl6.," The relative unimportance of the exact density profile of the atmosphere into which the source is expanding, as discussed above, is the reason very similar RLFs are predicted for various $\rTrans\/$ and $\betaCluster\/$ values in Figure \ref{fig:parameterSpace}{ and."
 Significantly. this implies that very similar ιν are also predicted. for sources of very cillerent ages. so long as the duty evele (Leo. Lula) remains the same. and. sources are not. old enough for inverse Compton losses to dominate.," Significantly, this implies that very similar RLFs are also predicted for sources of very different ages, so long as the duty cycle (i.e. $\tOn\//\tOff\/$ ) remains the same, and sources are not old enough for inverse Compton losses to dominate."
 This is shown in Figure το where we vary the jet on time. while keeping ἐς constant.," This is shown in Figure \ref{fig:parameterSpace}{, where we vary the jet on time, while keeping $\tOn\//\tOff\/$ constant."
 The duty evele is the main factor determining the number of radio quiet. sources. since the fraction of sources old enough to drop below the luminosity detection threshold is expected to be relatively small.," The duty cycle is the main factor determining the number of radio quiet sources, since the fraction of sources old enough to drop below the luminosity detection threshold is expected to be relatively small."
" This is illustrated in Figure τα, where duration of the active phase is kept constant. while the length of the quiescent phase is varied."," This is illustrated in Figure \ref{fig:parameterSpace}{, where duration of the active phase is kept constant, while the length of the quiescent phase is varied."
 The Uatness of the tracks for /< few Alves [or a range of power-law exponents in Figure ο also. implies that the ILE is also not very sensitive to changes in the density profile within the galaxy., The flatness of the tracks for $t<$ few Myrs for a range of power-law exponents in Figure \ref{fig:exampleTracks} also implies that the RLF is also not very sensitive to changes in the density profile within the galaxy.
 This is seen in Figure 7c., This is seen in Figure \ref{fig:parameterSpace}{.
" The ""characteristic luminosity of a source before it sullers significant inverse Compton losses is largely. determined. by mean jet power(Figure 7/. core radius (Figure το) and density (Figure 75). and axial ratio (Figure 77) of the source. in the sense that higher values of Qua. rss Poor aud lower value of 4 result in higher characteristic luminosities."," The “characteristic” luminosity of a source before it suffers significant inverse Compton losses is largely determined by mean jet power(Figure \ref{fig:parameterSpace}{ ), core radius (Figure \ref{fig:parameterSpace}{ ) and density (Figure \ref{fig:parameterSpace}{ ), and axial ratio (Figure \ref{fig:parameterSpace}{ ) of the source, in the sense that higher values of $\Qjet\/$, $\rCore\/$, $\rhoCore\/$ and lower value of $\RT\/$ result in higher characteristic luminosities."
 Finally. effects of scatter in jet power are shown in Figure 17.," Finally, effects of scatter in jet power are shown in Figure \ref{fig:parameterSpace}{."
" As expected. larger scatter in jet power results in less sources at the break (or ""characteristic) luminosity. ancl hence a broader distribution of sources across the radio luminosity bins."," As expected, larger scatter in jet power results in less sources at the break (or “characteristic”) luminosity, and hence a broader distribution of sources across the radio luminosity bins."
 The crucial feature of these plots is that they clearly show that changes in most of the parameters only result in recistributing the radio Loud. sources in luminosity., The crucial feature of these plots is that they clearly show that changes in most of the parameters only result in redistributing the radio loud sources in luminosity.
 The only parameter that can significantly alter the predicted radio Loud. fraction is μμ. be. the duty evele.," The only parameter that can significantly alter the predicted radio loud fraction is $\tOff\//\tOn\/$, i.e. the duty cycle."
 Hence observed. radio loud fractions place tight. constraints on relative clurations of the radio active ane quiescent: phases in our sample., Hence observed radio loud fractions place tight constraints on relative durations of the radio active and quiescent phases in our sample.
 Our sample is complete to Ly)—81072 . rather than the 1077 plotted in. Figure Y...," Our sample is complete to $L_{\rm 1.4} = 8 \times 10^{22}$ , rather than the $10^{22}$ plotted in Figure \ref{fig:parameterSpace}. ."
 Therefore. only sources. with luminosities brighter than this value can be used to constrain the models.," Therefore, only sources with luminosities brighter than this value can be used to constrain the models."
 Inspection of Figure 7 shows that the discussion, Inspection of Figure \ref{fig:parameterSpace} shows that the discussion
Although we have assumed in Sect.,Although we have assumed in Sect.
" 3.2 that the simulated temperature function based on Τον by ? is only accidentally in good agreement with the potential-based temperature function including spherical collapse because of the overcooling problem in the central parts of simulated clusters, it is remarkable that the spherical function gives results that are compatible with results from both the WMAP5+BAO+SN analysis and classical mass functions."," \ref{subsec:propTemp} that the simulated temperature function based on $T_\mathrm{ew}$ by \citet{Borgani2004} is only accidentally in good agreement with the potential-based temperature function including spherical collapse because of the overcooling problem in the central parts of simulated clusters, it is remarkable that the spherical function gives results that are compatible with results from both the WMAP5+BAO+SN analysis and classical mass functions."
" At this point, it is definitely worth analysing whether this is only a coincidence or it really describes temperature functions based on observed temperatures better."," At this point, it is definitely worth analysing whether this is only a coincidence or it really describes temperature functions based on observed temperatures better."
" The latter would imply that one either has to identify the measured temperature directly with the temperature that is used in the theoretical model and to include additional merger effects, or one has to convert the measured temperature using Eq."," The latter would imply that one either has to identify the measured temperature directly with the temperature that is used in the theoretical model and to include additional merger effects, or one has to convert the measured temperature using Eq."
 to a theoretical temperature which is then used in the model., to a theoretical temperature which is then used in the model.
" However, in the latter case it seems that one has to exclude merger effects since including both corrections result in values for cs and €25 that are inconsistent with other cosmological probes."," However, in the latter case it seems that one has to exclude merger effects since including both corrections result in values for $\sigma_8$ and $\Omega_\mathrm{m0}$ that are inconsistent with other cosmological probes."
 Another reason for the discrepancy between the results from the simulations and the comparison with cluster samples could be that simulated clusters are more elongated than those which are actually observed., Another reason for the discrepancy between the results from the simulations and the comparison with cluster samples could be that simulated clusters are more elongated than those which are actually observed.
 The clusters for the sample by ? for example are selected to appear regular., The clusters for the sample by \citet{Vikhlinin2009a} for example are selected to appear regular.
" Furthermore, the different temperature definitions are related in different ways to the potential shape."," Furthermore, the different temperature definitions are related in different ways to the potential shape."
" While Tq traces better the cluster potential and hence agrees well with the temperature function built on ellipsoidal collapse (see Fig. 1)),"," While $T_\mathrm{mw}$ traces better the cluster potential and hence agrees well with the temperature function built on ellipsoidal collapse (see Fig. \ref{fig:sphEllFunc}) ),"
" observed temperatures as well as Ταν, and T; as inferred from simulations follow the more spherical shape of the emitting gas.", observed temperatures as well as $T_\mathrm{ew}$ and $T_\mathrm{sl}$ as inferred from simulations follow the more spherical shape of the emitting gas.
" The approach including merger effects is more physically motivated since in the theoretical derivation of the pure X-ray temperature function, we explicitly assume virial equilibrium, which only relaxed clusters should have reached."," The approach including merger effects is more physically motivated since in the theoretical derivation of the pure X-ray temperature function, we explicitly assume virial equilibrium, which only relaxed clusters should have reached."
" Combining the results of ?,, who also found that mergers do have a significant impact on the inferred values for Qno and cs, with the conclusions of Sect. 4,,"," Combining the results of \citet{Randall2002}, who also found that mergers do have a significant impact on the inferred values for $\Omega_\mathrm{m0}$ and $\sigma_8$, with the conclusions of Sect. \ref{sec:mergers},"
 we believe that correcting for merger effects should be a necessary step., we believe that correcting for merger effects should be a necessary step.
" Note additionally that the scaling relation between both temperatures, Eq."," Note additionally that the scaling relation between both temperatures, Eq."
" was established for clusters at z=0 and hence, it is not known how this relation evolves with redshift."," was established for clusters at $z=0$ and hence, it is not known how this relation evolves with redshift."
" In the preceding discussion, however, we should keep in mind that measurements of σᾳ from CMB data are degenerate with the optical depth due to reionisation."," In the preceding discussion, however, we should keep in mind that measurements of $\sigma_8$ from CMB data are degenerate with the optical depth due to reionisation."
" Breaking this degeneracy requires polarisation data, e.g. the T-E cross-power spectrum."," Breaking this degeneracy requires polarisation data, e.g. the $T$ $E$ cross-power spectrum."
" Thus, its value is sensitive to uncertainties in particular in the reionisation parameters and has changed significantly several times with subsequent data releases."," Thus, its value is sensitive to uncertainties in particular in the reionisation parameters and has changed significantly several times with subsequent data releases."
" Additional information from baryonic acoustic oscillations and type-Ia supernovae do not directly constrain os either, but rather tighten constraints on the matter density Q,o/7 through information on the cosmological constant at fixed spatial curvature."," Additional information from baryonic acoustic oscillations and type-Ia supernovae do not directly constrain $\sigma_8$ either, but rather tighten constraints on the matter density $\Omega_\mathrm{m0} h^2$ through information on the cosmological constant at fixed spatial curvature."
 We thus hesitate to accept og as derived from WMAP data as a firm reference., We thus hesitate to accept $\sigma_8$ as derived from WMAP data as a firm reference.
" Weak-lensing data, that are in principle capable of constraining os more directly, still yield a fairly broad range of results, σα~0.6—0.9; tthe compilation in ?.."," Weak-lensing data, that are in principle capable of constraining $\sigma_8$ more directly, still yield a fairly broad range of results, $\sigma_8\sim0.6-0.9$; the compilation in \cite{Bartelmann2010}."
 Some tension between expectations and data are also reflected in the literature., Some tension between expectations and data are also reflected in the literature.
" For example, while ? prefer a high normalisation of the power spectrum to be consistent with numerical simulations, ? concludes that data from the sample prefer a low o."," For example, while \citet{Evrard2008} prefer a high normalisation of the power spectrum to be consistent with numerical simulations, \citet{Reiprich2006} concludes that data from the sample prefer a low $\sigma_8$."
 ? take merger effects into account by splitting the clusters of their samples into relaxed and unrelaxed ones by looking at their respective X-ray morphology., \citet{Vikhlinin2009a} take merger effects into account by splitting the clusters of their samples into relaxed and unrelaxed ones by looking at their respective X-ray morphology.
" If a cluster is classified as unrelaxed, the mass estimate using Eq."," If a cluster is classified as unrelaxed, the mass estimate using Eq."
" ismultiplied by a factor of 1.17, assuming that the M-T relation for these two cluster samples evolves separately but similarly."," ismultiplied by a factor of 1.17, assuming that the $M$ $T$ relation for these two cluster samples evolves separately but similarly."
 This approach is inspired by results of a numerical simulation by ?.., This approach is inspired by results of a numerical simulation by \citet{Kravtsov2006}.
 We think that this rigorous classification of clusters into relaxed and unrelaxed objects is problematic and should be avoided if possible., We think that this rigorous classification of clusters into relaxed and unrelaxed objects is problematic and should be avoided if possible.
 This can be done using our model of merger effects from Sect. 4.., This can be done using our model of merger effects from Sect. \ref{sec:mergers}.
 The resulting solid red contour in the lower panel of Fig., The resulting solid red contour in the lower panel of Fig.
 6 is in good agreement with ? (see their Fig., \ref{fig:confidence} is in good agreement with \citet{Vikhlinin2009b} (see their Fig.
" 3), where the rigorous classification was made."," 3), where the rigorous classification was made."
" This and the compatibility with other cosmological probes indicate that our merger model can improve the determination of cosmological parameters from X-ray data without having to decide individually if a cluster is relaxed or not, at least if mass functions and an empirical M-T relation are used to model an X-ray temperature function."," This and the compatibility with other cosmological probes indicate that our merger model can improve the determination of cosmological parameters from X-ray data without having to decide individually if a cluster is relaxed or not, at least if mass functions and an empirical $M$ $T$ relation are used to model an X-ray temperature function."
" In the first part of the paper, we have refined the theoretical X-ray temperature function of ? in two different ways: First, we have used the ellipsoidal-collapse model by ? to account for effects of the dynamics of ellipsoidal rather than spherical collapse and second, we have developed a simple analytic and parameter-free model that takes into account the net effect of temporary X-ray temperature boosts of galaxy clusters that previously underwent mergers on the temperature function."," In the first part of the paper, we have refined the theoretical X-ray temperature function of \citet{Angrick2009} in two different ways: First, we have used the ellipsoidal-collapse model by \citet{Angrick2010} to account for effects of the dynamics of ellipsoidal rather than spherical collapse and second, we have developed a simple analytic and parameter-free model that takes into account the net effect of temporary X-ray temperature boosts of galaxy clusters that previously underwent mergers on the temperature function."
" Comparing these two modifications to an N-body simulation by ?,, we have found the following results:"," Comparing these two modifications to an $N$ -body simulation by \citet{Borgani2004}, , we have found the following results:"
two-sample IKolhinosorov-Suirnov test indicates that the probability that these two populatious are identical is,two-sample Kolmogorov-Smirnov test indicates that the probability that these two populations are identical is.
 The statistical similarity is striking. although we note that there secs to be trend for higher οsin/ values amoung the BSS in [7 Tuc.," The statistical similarity is striking, although we note that there seems to be trend for higher $v\sin i$ values among the BSS in 47 Tuc."
 Thus. in line with the conclusions from the previous section. we ideutifv the slow rotation of some hot Jupiter host stars as tle main pitfall of the binary merser hypothesis.," Thus, in line with the conclusions from the previous section, we identify the slow rotation of some hot Jupiter host stars as the main pitfall of the binary merger hypothesis."
 Iu stellar inergers. accretion of chionicallv fractionated material mav be cuhanuced over normal stars as shown bv Desidera et al. (," In stellar mergers, accretion of chemically fractionated material may be enhanced over normal stars as shown by Desidera et al. ("
2007) iu the case of ΠΟ 113981 AD. a wide binary svsteii where the primary is a BSS with au iron conteut 0.25 dex lower than the secondi star.,"2007) in the case of HD 113984 AB, a wide binary system where the primary is a BSS with an iron content 0.25 dex lower than the secondary star."
 A subpopulation of C aud ο depleted. BSS las been identified in the lí Tue cluster bv Ferraro ct al. (, A subpopulation of C and O depleted BSS has been identified in the 47 Tuc cluster by Ferraro et al. (
2006). indicating again that stellar imucergeers cau sometimes produce chemical abundance anomalies.,"2006), indicating again that stellar mergers can sometimes produce chemical abundance anomalies."
 We have preseuted the working hwpothesis that hot Jupiter plauets could form iu binary mergers., We have presented the working hypothesis that hot Jupiter planets could form in binary mergers.
 The final uereer of W λα stars is a possibility. but the direct uereer of lower mass binaries that have not gone through an extended Wo λαπρο contact plase ds likely to contribute as well.," The final merger of W UMa stars is a possibility, but the direct merger of lower mass binaries that have not gone through an extended W UMa-type contact phase is likely to contribute as well."
 We estimate that the frequency of these ynaries in the Milkv Wav is cousistent with what would © needed to account for the observed frequency of hot Jupiters., We estimate that the frequency of these binaries in the Milky Way is consistent with what would be needed to account for the observed frequency of hot Jupiters.
 To test our hwpothesis we looked for a correlation )etxeen the radius anomaly aud the life time of the plauct ofore spiral-in by tidal interaction with the host star., To test our hypothesis we looked for a correlation between the radius anomaly and the life time of the planet before spiral-in by tidal interaction with the host star.
 Using a value (Q.—105 for the stellar dissipation coustaut we found that about half of the hot Jupiters could have ages of about 1 Cyr or vouuger., Using a value $\qpe = 10^6$ for the stellar dissipation constant we found that about half of the hot Jupiters could have ages of about 1 Gyr or younger.
 However. the usefulness of this age indicator is limited by its strong depenudoeuce on the value of Q. which is highly uncertain.," However, the usefulness of this age indicator is limited by its strong dependence on the value of $\qpe$, which is highly uncertain."
 Ao quergor scenario agrees with the peculiar distribution of orbital distances of transiting planets., A merger scenario agrees with the peculiar distribution of orbital distances of transiting planets.
 The concentration near 0.05 AU. with a rapid decline at arecr distances. indicates an origiu close to the lost star.," The concentration near 0.05 AU, with a rapid decline at larger distances, indicates an origin close to the host star."
 Mereer eveuts are likely to produce planets even closer iu as well. but these would have disappeared rapidly from he population owing to the steep dependence of spiral-iu ine on distance.," Merger events are likely to produce planets even closer in as well, but these would have disappeared rapidly from the population owing to the steep dependence of spiral-in time on distance."
 To bring thei radii iu agreement with stancdaid cooling curves (Baraffe et al., To bring their radii in agreement with standard cooling curves (Baraffe et al.
 2003). the ios inflated alanets would need to be vounger than about 0.1 Cor.," 2003), the most inflated planets would need to be younger than about 0.1 Gyr."
 A correlation between degree of inflation aud the rotation rate of the rost star would be expected from the merecr scenario., A correlation between degree of inflation and the rotation rate of the host star would be expected from the merger scenario.
 It is found to be ouly weaklv preseut in the observations. overshadowed by large scatter.," It is found to be only weakly present in the observations, overshadowed by large scatter."
 In agrecuent with the scenario. however. the average rotation rate of the josts of inflated planets is ercater han in normal stars of he same (inferred) age. as roted xeviouslv (Pout 209. Tartinan 2010).," In agreement with the scenario, however, the average rotation rate of the hosts of inflated planets is greater than in normal stars of the same (inferred) age, as noted previously (Pont 2009, Hartman 2010)."
 The inclined. aud retrograde orbits identified through he Rossiter-AlcLaueghlin effect παπα et al., The inclined and retrograde orbits identified through the Rossiter-McLaughlin effect Triaud et al.
 2010) require explanation iu the merger interpretation. since the angular moment of a disk formed in a merger would wave the same direction as that of he star.," 2010) require explanation in the merger interpretation, since the angular momentum of a disk formed in a merger would have the same direction as that of the star."
 We sugecst wre that planet formation im he massive. compact disk resulting from merger on a dvuaimical tine scale. would wave produced a number of planets in closely packed orbits.," We suggest here that planet formation in the massive, compact disk resulting from merger on a dynamical time scale, would have produced a number of planets in closely packed orbits."
 Caavitational interaction iu such compact svstenis of planets causes their orbits to be seculazly unstable., Gravitational interaction in such compact systems of planets causes their orbits to be secularly unstable.
 This would scatter them iuto stochastic orbits CChatterjee et al., This would scatter them into stochastic orbits Chatterjee et al.
 2008). including retrograde ones. (," 2008), including retrograde ones. ("
The total angular moment vector aud a corresponding prepondoerauce of prograde orbits would be conserved).,The total angular momentum vector and a corresponding preponderance of prograde orbits would be conserved).
 The process is also consistent with the ligh frequency of exceutric orbits., The process is also consistent with the high frequency of excentric orbits.
(Gru. 2).,"$x,y,z$ )."
" The mapping data are also weighted according to the relevant...Caussian-smoothed (2 EWLIAL and 5' cut-olf. radius) based on the Mopra beam EWILM Aun=2 appropriate for the NIL, lines we detected. and pixel masked to remove noisy edge: pixels."," The mapping data are also weighted according to the relevant,Gaussian-smoothed $^\prime$ FWHM and $^\prime$ cut-off radius) based on the Mopra beam FWHM $\theta_{\rm mb}=2^\prime$ appropriate for the $_3$ lines we detected, and pixel masked to remove noisy edge pixels."
 Analysis of position-switchecl deep. pointings employed. with time-averagine. weighting by the relevant ancl bascline subtracted using a linear fit after masking of the 15 channels at cach bandpass edge.," Analysis of position-switched deep pointings employed with time-averaging, weighting by the relevant and baseline subtracted using a linear fit after masking of the 15 channels at each bandpass edge."
 In. both mapping ancl position-switched data. the antenna temperature (corrected. for atmospheric attenuation anc rearward loss) is converted to the main beam brightness temperatureZin. such that = than where man is the main beam ellicieney.," In both mapping and position-switched data, the antenna temperature (corrected for atmospheric attenuation and rearward loss) is converted to the main beam brightness temperature, such that = $\eta_{\rm mb}$ where $\eta_{\rm mb}$ is the main beam efficiency."
" Based on the frequencies of the detected NIL, lines (ο Εν12) WO ASSUDIC Jul.0.6 following Urquhartetal.(2010).", Based on the frequencies of the detected $_3$ lines $\sim$ GHz) we assume $\eta_{\rm mb}=0.6$ following \citet{mopra_beam}.
 This data reduction procedure vields an UMS error in of Tuus0.05 1 per channel for mapping data with LOPS overlap ancl ~0.08 WIS per channel for mapping data without., This data reduction procedure yields an RMS error in of $\sim0.05$ K per channel for mapping data with HOPS overlap and $\sim0.08$ K per channel for mapping data without.
 As a result. of their increased. exposure. position- observations achieve a Zi;ο ~—0.02 WIN per channel.," As a result of their increased exposure, position-switched observations achieve a of $\sim0.02$ K per channel."
 ‘Table 1 lists the lines detected in our mapping and position-switched. deep spectra observations., Table \ref{tab:lines} lists the lines detected in our mapping and position-switched deep spectra observations.
 In mapping data. the so called. peak-pixel map for emission is shown in ligure 2 along with the locations of position-switehed deep »ointingga," In mapping data, the so called peak-pixel map for emission is shown in Figure \ref{fig:peakpixmapNH311} along with the locations of position-switched deep pointings."
 Deak-pixel maps highlight only the brightest pixel along he velocity axis (2 axis) and serve as a useful wav to search or pointlike and moderately extended features., Peak-pixel maps highlight only the brightest pixel along the velocity axis $z$ axis) and serve as a useful way to search for pointlike and moderately extended features.
 Of the 29 molecular lines listed in Table 1. within he MIOPS bandwidth. about half. were detected.," Of the 29 molecular lines listed in Table \ref{tab:lines} within the MOPS bandwidth, about half were detected."
 From he mapping observations we detected. H2O.. NIL; ((1.1). A14 ((2.2). NID; (03.3). NIL; (6.6). HICSNOGS2). HCSN(IO LIGOo. Πόσα and όσα. with the criterion for detection »opng a 3 line peak signal.," From the mapping observations we detected $_{2}$ O, $_{3}$ (1,1), $_{3}$ (2,2), $_{3}$ (3,3), $_{3}$ (6,6), $_{3}$ N(3–2), $_{5}$ N(10--9), $\alpha$, $\alpha$ and $\alpha$, with the criterion for detection being a 3 line peak signal."
 Since position-switched deep spectra observations were more sensitive than mapping. several additional lines were revealed as can be seen in Table 1..," Since position-switched deep spectra observations were more sensitive than mapping, several additional lines were revealed as can be seen in Table \ref{tab:lines}."
 Maps of position-velocity. (PV). integrated intensity. and spectra for all detected. lines can be. found in the online appendix.," Maps of position-velocity (PV), integrated intensity, and spectra for all detected lines can be found in the online appendix."
 Presented in Figures 3.. 4. and 5) are integrated. intensity ancl position-velocity (PV) plots.," Presented in Figures \ref{fig:11cores}, \ref{fig:22cores} and \ref{fig:33cores} are integrated intensity and position-velocity (PV) plots."
 The PY plots reveal the velocitv-space structure of the NIL; ((1.1). (2.2) and (3.3) emission regions or cores in the Wes field.," The PV plots reveal the velocity-space structure of the $_{3}$ (1,1), (2,2) and (3,3) emission regions or cores in the W28 field."
 A Lanning smoothing in velocity (width ~6 kims)) was applied to reduce random fluctuations. and then the Galactic latitucle axis was Llattened into a single laver.," A Hanning smoothing in velocity (width $\sim$ ) was applied to reduce random fluctuations, and then the Galactic latitude axis was flattened into a single layer."
 1n this way we show the intrinsic velocity location and width of the gas without confusion., In this way we show the intrinsic velocity location and width of the gas without confusion.
 Dased on the PV maps. it is clear that much of the NIL; emission is found in the velocity range 7-5 to —20 which is quite consistent with the molecular gas found in CO studies (Aharonianetal.2008b:Fukui2008:Lisztetal.2009) towards the W28 region.," Based on the PV maps, it is clear that much of the $_3$ emission is found in the velocity range $\sim$ -5 to $\sim$ which is quite consistent with the molecular gas found in CO studies \citep{hess_w28, nanten21,liszt} towards the W28 region."
 The four satellite lines of NIL; ((1.1) ave clearly visible towards most of the cores as co-located peaks with 7 and separation [rom the main line for the inner and outer satellite lines respectively.," The four satellite lines of $_3$ (1,1) are clearly visible towards most of the cores as co-located peaks with 7 and separation from the main line for the inner and outer satellite lines respectively."
 “Phese satellite lines spread. the (1.1) emission over a wider -20 to range.," These satellite lines spread the (1,1) emission over a wider -20 to range."
 The intensity maps also in Figures 3.. 4. and 5- are integrated. over. velocity ranges designed. to encompass the bulk of the NII; emission. and show that it is found generally towards the TeV. gamma-ray sources. and concentrated into clumps or cores.," The intensity maps also in Figures \ref{fig:11cores}, \ref{fig:22cores} and \ref{fig:33cores} are integrated over velocity ranges designed to encompass the bulk of the $_3$ emission, and show that it is found generally towards the TeV gamma-ray sources, and concentrated into clumps or cores."
 For simplicity we label the detected NIL; features as Cores 1 to 6 and Triple Core, For simplicity we label the detected $_{3}$ features as Cores 1 to 6 and Triple Core
small region of parameter space that is available when an object is to be a BAL (high Eddington ratio. high accretion rate) and radio-Ioud (large black hole mass).,"small region of parameter space that is available when an object is to be a BAL (high Eddington ratio, high accretion rate) and radio-loud (large black hole mass)."
 As noted by Laor(2000).. it might be expected that three parameters. black hole mass. Eddington ratio. ancl orientation. would determine the observable characterises of AGNs.," As noted by \citet{Laor00}, it might be expected that three parameters, black hole mass, Eddington ratio, and orientation, would determine the observable characteristics of AGNs."
 While the picture developed in this paper includes the first two. there has been little inclication of anvthing (hat could be interpreted as orientation.," While the picture developed in this paper includes the first two, there has been little indication of anything that could be interpreted as orientation."
 This is. in some sense. in conflict with (he “standard unification model in which orientation plavs a major role in providing context for the classification of AGNs (Antonucei1993;UrryandPaclovani1995).," This is, in some sense, in conflict with the ""standard unification model"" in which orientation plays a major role in providing context for the classification of AGNs \citep{Antonucci93,Urry95}."
. The unification model. based on the ideas of relativistically beamed emission and a thick (verlically and optically) torus. receives support [rom scattered broad line emission seen in some Sev[ert 2 galaxies. the “alignment effect seen in high redshift radio galaxies. as well as a ΠΠο of consistency arguments applied to various statistical samples.," The unification model, based on the ideas of relativistically beamed emission and a thick (vertically and optically) torus, receives support from scattered broad line emission seen in some Seyfert 2 galaxies, the ""alignment effect"" seen in high redshift radio galaxies, as well as a number of consistency arguments applied to various statistical samples."
 Within the samples considered in (his study. the most obvious groups (o explore for orientation effects are the core-dominated (flat-spectirum) aud Iobe-dominated (steep-spectrum) raclio-loud QSOs.," Within the samples considered in this study, the most obvious groups to explore for orientation effects are the core-dominated (flat-spectrum) and lobe-dominated (steep-spectrum) radio-loud QSOs."
 It has been conjectured (hat if a raclio-loud QSO is seen along its jet. il will appear as a core-dominated source. wilh the core radio emission enhanced by relativistic beamune.," It has been conjectured that if a radio-loud QSO is seen along its jet, it will appear as a core-dominated source, with the core radio emission enhanced by relativistic beaming."
 If (he jet is close to the plane of the sky. however. the lobes will dominate. and will be well apart from the cental source.," If the jet is close to the plane of the sky, however, the lobes will dominate, and will be well apart from the cental source."
 Studies comparing the (wo twpes suffer from the difficulty of picking samples that include objects of similar intrinsic properties., Studies comparing the two types suffer from the difficulty of picking samples that include objects of similar intrinsic properties.
 Although Figure 6 shows little obvious separation between the core-dominated (open triangles) ancl lobe-dominated (open circles) objects. a Ixolmogrov-9niirnov test indicates a significant difference (chance probability < 0.5%)) in the distribution of PCL. with objects having lower values of PCI by about 1.0 in the median than objects.," Although Figure 6 shows little obvious separation between the core-dominated (open triangles) and lobe-dominated (open circles) objects, a Kolmogrov-Smirnov test indicates a significant difference (chance probability $<$ ) in the distribution of PC1, with core-dominated objects having lower values of PC1 by about 1.0 in the median than lobe-dominated objects."
 OF course. log Rois a component of PCL (as log Ro increases. PCI increases). but the median log Ro value for the core-dominated objects is larger than that of the lobe-dominated objects: 3.14 as opposed to 2.56 No significant difference is seen in PC.," Of course, log R is a component of PC1 (as log R increases, PC1 increases), but the median log R value for the core-dominated objects is larger than that of the lobe-dominated objects: 3.14 as opposed to 2.56 No significant difference is seen in PC2."
 What would be expected?, What would be expected?
 If core-dominated objects have weaker intrinsic radio Iuminositv but their emission is enhanced bv beaming and if the orientation has no effect on any property other than log Π. used in our analvsis. then (his is qualitatively a consistent linding.," If core-dominated objects have weaker intrinsic radio luminosity but their emission is enhanced by beaming and if the orientation has no effect on any property other than log R used in our analysis, then this is qualitatively a consistent finding."
 Within this simplistic picture. an enhancement of 2.8 in log I is required (o explain the location of the core-dominated objects.," Within this simplistic picture, an enhancement of 2.8 in log R is required to explain the location of the core-dominated objects."
 This is extremely. speculative as it depends on (a) unquantifiable selection effects in the samples considered here. (b) unknown additional effects (hat orientation might have ou other properties (hat went into (he analvsis. and (ο) a derivation of principal components that was based on the assumption that the log Ro values ol core- and lobe-dominated objects have the same intrinsic meaning.," This is extremely speculative as it depends on (a) unquantifiable selection effects in the samples considered here, (b) unknown additional effects that orientation might have on other properties that went into the analysis, and (c) a derivation of principal components that was based on the assumption that the log R values of core- and lobe-dominated objects have the same intrinsic meaning."
find that the time scale for the period change of R να corresponds to a longer time after the maximal huninosity of the Ποιο flash than that of R Aq.,find that the time scale for the period change of R Hya corresponds to a longer time after the maximum luminosity of the He-shell flash than that of R Aql.
 This could explain the Tc curichiment of R Ίνα aud its AI6-M9S spectral The period change for R Cen is steeper than for R Ίνα and thus Wawkins et al. (, This could explain the Tc enrichment of R Hya and its M6-M9S spectral The period change for R Cen is steeper than for R Hya and thus Hawkins et al. (
2001) ooOive two possible explanations: either R Cen is m a stage right after the »eiunniug ofthe flash. with a total mass less than 2-3 M. or it is ina stage right after where the huuinositv of the Hash reaches the stellar surface with a much larger rauge of allowed stellar mass.,"2001) give two possible explanations: either R Cen is in a stage right after the beginning of the flash, with a total mass less than 2-3 ${\cal M}_{\sun}$ or it is in a stage right after where the luminosity of the flash reaches the stellar surface with a much larger range of allowed stellar mass."
 We πια that R Cen is the most Ix uuimous LPV but its 25-12 index is this of au ο star. at he Μι between O aud C-rich LPVs. aud is assigned8 to DD. the eroup of the most massive stars.," We find that R Cen is the most K luminous LPV but its 25-12 index is this of an S star, at the limit between O and C-rich LPVs, and is assigned to BD, the group of the most massive stars."
 Therefore. our results stronglv favor the second possibilitv: Ro Cen is iu a stage right after the huninosity of the fash reaches the stellar surface.," Therefore, our results strongly favor the second possibility: R Cen is in a stage right after the luminosity of the flash reaches the stellar surface."
 Furthermore the ITe-shell flash cuhances the efficiency of the third dredge-up Ulerwig. 2000). tha can explai- the verv peculiar location. compared to the oue of that IIBD caudidates. of Ro Cen in the diagram (Ix.25-12).," Furthermore the He-shell flash enhances the efficiency of the third dredge-up (Herwig, 2000), that can explain the very peculiar location, compared to the one of that HBB candidates, of R Cen in the diagram (K,25-12)."
 This so huuiuous O-rich LPV inight become a carbon star exceptionally brighter than the usual Iunuinositv lim+ accepted for these stars., This so luminous O-rich LPV might become a carbon star exceptionally brighter than the usual luminosity limit accepted for these stars.
 A few such luminous carbon starμα exist in the Maecllanic Clouds as observed by van Loon et al. (, A few such luminous carbon stars exist in the Magellanic Clouds as observed by van Loon et al. (
1999) and moceled by Frost et al. (,1999b) and modeled by Frost et al. (
1998).,1998).
 Our results confini that the ACB evolution depends o- the initial mass of the progenitor ou the main sequenuce., Our results confirm that the AGB evolution depends on the initial mass of the progenitor on the main sequence.
 The study of LPVs with peculiar properties. often associated with trausition states in the stellar evolution. elucidates some points of the very complex evolution along the AGB.," The study of LPVs with peculiar properties, often associated with transition states in the stellar evolution, elucidates some points of the very complex evolution along the AGB."
 The simmultancous study of the behaviour of the circuunstellar envelope provides further imtormation on the evolutive state of the stars alone the AGB., The simultaneous study of the behaviour of the circumstellar envelope provides further information on the evolutive state of the stars along the AGB.
 However. this study is mainly statistical and so results for individual stars can be erroneous because the coufideuce level of a probabilistic discrimination can never reach The proposed evolutivo scenario. schematically represented in figure T.. da: The study of LPVs enriched in Te confinis that thev are at different stages along the AGB but after a receut dredge-up.," However, this study is mainly statistical and so results for individual stars can be erroneous because the confidence level of a probabilistic discrimination can never reach The proposed evolutive scenario, schematically represented in figure \ref{fig_schema}, is: The study of LPVs enriched in Tc confirms that they are at different stages along the AGB but after a recent dredge-up."
 It allows us to confirm the location of the first dredee-ip at A5;=3.5 and the quite carly operative third dredge-p ou the The uo-Te S-type LPVs (except Ro Aud). are. faint in WW. 12 aud 25. and they are coufirmed as extriusic S stars enriched not by their own uucleosvuthesis but by mass exchauge from a iore evolved. companion.," It allows us to confirm the location of the first dredge-up at $M_{bol}=-3.5$ and the quite early operative third dredge-up on the The no-Tc S-type LPVs (except R And), are faint in K, 12 and 25, and they are confirmed as extrinsic S stars enriched not by their own nucleosynthesis but by mass exchange from a more evolved companion."
 The extrinsic carichment iu s-clements may accelerate the evolution along the AGB and lead to the formation of an envelope closer to being carbonated than silicated before any intrinsic eurichineut by successive The examination of the brightest LPVs allows us to propose a list of stars with peculiar spectral. envelope aud huninosity properties that may be Hot Bottom Burning candidates.," The extrinsic enrichment in s-elements may accelerate the evolution along the AGB and lead to the formation of an envelope closer to being carbonated than silicated before any intrinsic enrichment by successive The examination of the brightest LPVs allows us to propose a list of stars with peculiar spectral, envelope and luminosity properties that may be Hot Bottom Burning candidates."
 The most luminous of them. R Cen. a star iu a ILIe-shell flash. could become. before leaving AGB. a C-ich LPV brighter than the usual hDunuinositv huit of carbon stars.," The most luminous of them, R Cen, a star in a He-shell flash, could become, before leaving AGB, a C-rich LPV brighter than the usual luminosity limit of carbon stars."
Similarly. the expected number of false alarms is given by: In Fig.,"Similarly, the expected number of false alarms is given by: In Fig."
 δε) we plot the expected number of transiting planet detections (continuous curves) and false alarms (dashed curves) for all stars as functions of Siniq With Ninin land 1.2415., \ref{fig:Ndet_vs_thresh_Allstar} we plot the expected number of transiting planet detections (continuous curves) and false alarms (dashed curves) for all stars as functions of $S_{\mbox{\small min}}$ with $N_{\mbox{\small min}}~=~1$ and $R_{\mbox{\small p}} = 1.2 R_{\mbox{\small J}}$ .
 Each curve is labelled with the period range to whichfp it corresponds., Each curve is labelled with the period range to which it corresponds.
 Similarly. each of Figs.," Similarly, each of Figs."
 ο) - (4) corresponds to a different period range in which we plot the expected number of transiting planet detections for the F. G. K and M stars in our sample as a function of Spin With Vining= Land Rp= 1.270.," \ref{fig:Ndet_vs_thresh_P1to3}~ - (d) corresponds to a different period range in which we plot the expected number of transiting planet detections for the F, G, K and M stars in our sample as a function of $S_{\mbox{\small min}}$ with $N_{\mbox{\small min}}~=~1$ and $R_{\mbox{\small p}} = 1.2 R_{\mbox{\small J}}$ ."
 For a limited range 7gig19. the “curves” for Άι in all of Figs.," For a limited range $7 \le S_{\mbox{\small min}} \le 15$, the “curves” for $N_{\mbox{\small det}}$ in all of Figs."
" S¢a)-(d) can be approximated by straight lines. allowing us to express our results in the form of an approximate empirical relationship: where -Lis a constant that may be determined for each set of starsY and period range /?, to 1; considered."," 5(a)-(d) can be approximated by straight lines, allowing us to express our results in the form of an approximate empirical relationship: where $A$ is a constant that may be determined for each set of stars$Y$ and period range $P_{1}$ to $P_{M}$ considered."
 We note that the transit detection statistic 5j; is equivalent to the signal-to-noise (S/N) of the fitted transit signal and that: where Xf/fy is the fractional transit depth., We note that the transit detection statistic $S_{\mbox{\small tra}}$ is equivalent to the signal-to-noise (S/N) of the fitted transit signal and that: where $\Delta f / f_{0}$ is the fractional transit depth.
 Now. since we have SuaoxI5. we may infer that for a fixed t the equivalent detectionthreshold varies as 5;min⋅XRy≻⊐ .," Now, since we have $S_{\mbox{\small tra}}~\propto~R_{\mbox{\small p}}^{2}$, we may infer that for a fixed $S_{\mbox{\small tra}}$ the equivalent detectionthreshold varies as $S_{\mbox{\small min}}~\propto~R_{\mbox{\small p}}^{-2}$ ."
 UsingTei thisDo fact.£u we may rewrite Eqn.," Using this fact, we may rewrite Eqn."
 13. as:, \ref{eqn:empirical1} as:
The recent analysis of the angular power spectrum of the Cosmic Microwave Background (CMB) obtained from WMAP (Bennett et al.,The recent analysis of the angular power spectrum of the Cosmic Microwave Background (CMB) obtained from WMAP (Bennett et al.
 2003) has provided constraints on the cosmological parameters (Spergel et al., 2003) has provided constraints on the cosmological parameters (Spergel et al.
 2003) that contirms with greater accuracy the current energy density of the Universe to be comprised by about 73 per cent of dark energy and 27 per cent of matter. mostly non-baryonic and dark.," 2003) that confirms with greater accuracy the current energy density of the Universe to be comprised by about 73 per cent of dark energy and 27 per cent of matter, mostly non-baryonic and dark."
 In particular. the quoted constraint on the baryon density. Qj. is 0.0224+0.00005. and on the matter. density. ) m ubvlanormOOS2 *.η o hen ↘↝ -—el," In particular, the quoted constraint on the baryon density, $\Omega_{\rm b}$, is $0.0224 \pm 0.0009 h_{100}^{-2}$, and on the matter density, $\Omega_{\rm m}$, is $0.135^{+0.008}_{-0.009} 
h_{100}^{-2}$."
"snon-thermal 0.Az.hfVar.IS Istal equalto ο uentotaput ""atio theo Tatio b:Darvonparsonbetween fri ane' dark matter density. 106$9.eua=O4,THEOn. is equal to 0.199.Mnyas"," Consequently, the cosmic baryon fraction, $\Omega_{\rm b} / \Omega_{\rm m}$, is equal to $0.166^{+0.012}_{-0.013}$ and the ratio between baryon and dark matter density, $\Omega_{\rm c} = \Omega_{\rm m}-\Omega_{\rm b}$, is equal to $0.199^{+0.017}_{-0.019}$."
 These values are expected to be maintained— in regions at high overdensities2. that collapse to form: galaxy clusters., These values are expected to be maintained in regions at high overdensities that collapse to form galaxy clusters.
 The clusters baryon budget is composed mainly from the X- luminous baryons. A.- of the intracluster medium (ICM) that becomes hotter upon falling into the cluster dark matter halo by gravitational collapse.," The clusters baryon budget is composed mainly from the X-ray luminous baryons, $M_{\rm gas}$, of the intracluster medium (ICM) that becomes hotter upon falling into the cluster dark matter halo by gravitational collapse."
" Other contributions come from the baryonic stellar mass in galaxies. 1,4. and from other ""exotic"" sources. ike intergalactic stars and a still poorly defined baryonic dark matter."," Other contributions come from the baryonic stellar mass in galaxies, $M_{\rm gal}$, and from other “exotic” sources, like intergalactic stars and a still poorly defined baryonic dark matter."
" Given the large uncertainties on the relative contribution Tom baryons that are not accounted for in either Ad... or Ma. I qualify these as ""other baryons”. Ai. as already done in a orevious work (Ettori 2001) in which I discussed the constraints on cluster baryon budget from BOOMERANG and MAXIMA-I data."," Given the large uncertainties on the relative contribution from baryons that are not accounted for in either $M_{\rm gas}$ or $M_{\rm gal}$, I qualify these as “other baryons"", $M_{\rm ob}$, as already done in a previous work (Ettori 2001) in which I discussed the constraints on cluster baryon budget from BOOMERANG and MAXIMA-I data."
 The tighter constraints on the cosmological parameters provided rom WMAP allow now more firm conclusions., The tighter constraints on the cosmological parameters provided from WMAP allow now more firm conclusions.
 Therefore. one can put the following relation between the relative of amountbaryons in the Universe and in clusters with total gravitating mass. A: where fu.=Muy/Moa. foiMya/Moa 6m1010Ha in —Fukugita et al.," Therefore, one can put the following relation between the relative amount of baryons in the Universe and in clusters with total gravitating mass, $M_{\rm tot}$: where $f_{\rm gas} = M_{\rm gas}/M_{\rm tot}$, $f_{\rm gal} = M_{\rm gal}/M_{\rm tot}$ $\approx 
0.010^{+0.005}_{-0.004} h_{100}^{-1}$ in Fukugita et al."
 1998). fan=AL(Adi. and Y is the parameterμι representing the cosmic depletion of baryons at the virial radius with respect to the global value (0.92+).06 from the hydrodynamical simulations of the Santa Barbara Project: Frenk et al.," 1998), $f_{\rm ob} = M_{\rm ob}/M_{\rm tot}$ , and $Y$ is the parameter representing the cosmic depletion of baryons at the virial radius with respect to the global value $\approx 0.92 \pm 0.06$ from the hydrodynamical simulations of the Santa Barbara Project; Frenk et al."
 1999)., 1999).
 T parametrize the uncertainties on the measurements of the total gravitating mass and gas mass through he factors /? and C'. respectively.," I parametrize the uncertainties on the measurements of the total gravitating mass and gas mass through the factors $B$ and $C$, respectively."
 These factors act to increase the otal mass estimates (1.8. 17 1) if corrections to the hydrostatic equilibrium equation are required for bulk motions of the ICM or pressure support. and to lower the true gas mass (i.e. Aff CIp Dif. clumpiness. .is present 1in the ICM. that is assumed to be smoothly distributed (e.g. Mathiesen et al.," These factors act to increase the total mass estimates (i.e. $B>1$ ) if corrections to the hydrostatic equilibrium equation are required for bulk motions of the ICM or non-thermal pressure support, and to lower the true gas mass (i.e. $C>1$ ) if clumpiness is present in the ICM that is assumed to be smoothly distributed (e.g. Mathiesen et al."
 1999)., 1999).
 In this Letter. I will analyze the equation |. (i) to assess the consistency between the cosmic and the cluster baryon budget and (ii) to put Significant constraints on fi...," In this Letter, I will analyze the equation \ref{eq:fbar} (i) to assess the consistency between the cosmic and the cluster baryon budget and (ii) to put significant constraints on $f_{\rm ob}$."
 In a consistent way. I adopt the WMAP results on the Hubble constant. //4: ΟΕ TLoi kms. | ! to rescale all the measured quantities.," In a consistent way, I adopt the WMAP results on the Hubble constant, $H_0$, of $71^{+0.04}_{-0.03}$ km $^{-1}$ $^{-1}$ to rescale all the measured quantities."
 Figure‘ | shows the allowed Lo region from the WMAP results on the cosmic baryon budget with respect to the observed gus and baryon fraction for a sample of relaxed galaxy clusters both at low and high redshift., Figure \ref{fig:dat} shows the allowed $1 \sigma$ region from the WMAP results on the cosmic baryon budget with respect to the observed gas and baryon fraction for a sample of relaxed galaxy clusters both at low and high redshift.
" All these values are estimated at the overdensity of 200 with respect to the critical density (νο, within the cluster region that numerical simulations show to be virialized in a Q,, independent way: see. er. Evrard et al."," All these values are estimated at the overdensity of 200 with respect to the critical density (i.e. within the cluster region that numerical simulations show to be virialized in a $\Omega_{\rm m}$ independent way; see, e.g., Evrard et al."
 2002), 2002).
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0."
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.1," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.1"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.11," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.11"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 "
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \p"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm "
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0.," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0."
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0.0," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0.0"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0.01," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0.01"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0.010," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0.010"
 Using a Bayesian approach (Press 1996). I measure the average gas (baryon) fraction and confirm. that is consistent between the two samples: 0.107rois(0.133ime] and 0.111.50s(0.133.052) (he. error-weighted means of the gas fraction distribution are 0.116+0.005 and0.111+0.010," Using a Bayesian approach (Press 1996), I measure the average gas (baryon) fraction and confirm that is consistent between the two samples: $0.107^{+0.028}_{-0.019} (0.133^{+0.029}_{-0.026})$ and $0.111^{+0.069}_{-0.063} (0.133^{+0.063}_{-0.067})$ (the error-weighted means of the gas fraction distribution are $0.116 \pm 0.005$ and$0.111 \pm 0.010$"
Surveys of large-scale structure in the universe provide a rich resource for testing our understanding of cosmology.,Surveys of large-scale structure in the universe provide a rich resource for testing our understanding of cosmology.
 Future surveys will cover nearly the full sky to redshifts [ar deeper than are currently studied. mapping out some 10 billion vears of history.," Future surveys will cover nearly the full sky to redshifts far deeper than are currently studied, mapping out some 10 billion years of history."
 The great statistical power and leverage from depth will allow detailed examination of the cosmological framework by carrying out a simultaneous fit of a substantial suite of relevant parameters., The great statistical power and leverage from depth will allow detailed examination of the cosmological framework by carrying out a simultaneous fit of a substantial suite of relevant parameters.
 One particularly attractive prospect is the capability to put to the test the predictions of Einstein gravity for the growth of structure and its Consisteney with the cosmic expansion history., One particularly attractive prospect is the capability to put to the test the predictions of Einstein gravity for the growth of structure and its consistency with the cosmic expansion history.
 We consider next-generation surveys mapping the distribution of galaxies in three dimensions to redshifts of order z=2., We consider next-generation surveys mapping the distribution of galaxies in three dimensions to redshifts of order $z=2$.
 A goal of this study is to. determine the capabilities of such surveys., A goal of this study is to determine the capabilities of such surveys.
 In. particular we aim to estimate realistic constraints from a global. parameter fit on the gravitational growth index 5. which can characterize deviations from general relativitv.," In particular we aim to estimate realistic constraints from a global parameter fit on the gravitational growth index $\gamma$, which can characterize deviations from general relativity."
 Phe second goal is to examine how the survey characteristics such as redshift range. resolution. and galaxy selection allect those capabilities.," The second goal is to examine how the survey characteristics such as redshift range, resolution, and galaxy selection affect those capabilities."
 In Sec., In Sec.
 ?? we review the formalism lor extracting cosmological information from galaxy correlation measurements in terms of the matter.— power spectrum. ancl diseuss the anisotropic distortion due to measuring in redshift space (rather than position space).," \ref{smethod} we review the formalism for extracting cosmological information from galaxy correlation measurements in terms of the matter power spectrum, and discuss the anisotropic distortion due to measuring in redshift space (rather than position space)."
 We discuss the relevant set of cosmological parameters in Sec., We discuss the relevant set of cosmological parameters in Sec.
 ?? and their influence on the matter power spectrum., \ref{ssolve} and their influence on the matter power spectrum.
 The results are analyzed with emphasis on the role of degeneracies between factors that influence growth. including the gravitational erowth index. the dark energy equation of state. anc neutrino mass.," The results are analyzed with emphasis on the role of degeneracies between factors that influence growth, including the gravitational growth index, the dark energy equation of state, and neutrino mass."
 ln Sec., In Sec.
 2? we turn to astrophysical and survey characteristics and. analyze the cllect of the bias level of the selected. galaxy populations. the form. of the small-scale velocity. damping. the spectroscopic survey redshift) resolution. and the redshift range of the survey.," \ref{ssurvey} we turn to astrophysical and survey characteristics and analyze the effect of the bias level of the selected galaxy populations, the form of the small-scale velocity damping, the spectroscopic survey redshift resolution, and the redshift range of the survey."
 This allows quantitative comparison of the capabilities of next-generation (Stage LV) experiments from both eround and space. as well as nearer term (Stage HI) experiments.," This allows quantitative comparison of the capabilities of next-generation (Stage IV) experiments from both ground and space, as well as nearer term (Stage III) experiments."
 We conclude in Sec., We conclude in Sec.
 ?? with a summary of the prospects for testing the standard. cosmology and revealing clues to dark cnerey or the breakdown of Einstein gravity., \ref{sconcl} with a summary of the prospects for testing the standard cosmology and revealing clues to dark energy or the breakdown of Einstein gravity.
ddata we find @=17241.8 eV. τς265.6+100.0 clays and b=106.242.5 eV (42=0.34 for 11 οι).,"data we find $a=17.2\pm1.8$ eV, $\tau=265.6 \pm 100.0$ days and $b=106.2\pm2.5$ eV $\chi^2_{\nu}=0.34$ for 11 d.o.f.),"
 which is consistent with the (fit., which is consistent with the fit.
 Although an exponential decay provides an acequate description of the data ofτό as has been found for other sources2010).. mathematically a neutron star crust is expected to cool via a (broken) powerlaw2," Although an exponential decay provides an adequate description of the data of, as has been found for other sources, mathematically a neutron star crust is expected to cool via a (broken) powerlaw."
009).. Lowe fit a single powerlaw of the form yh)=Afo)? to the dedata. we find an index of D=0403+ normalisation of A=134.441.0 eV (4Z—=0.13 ," If we fit a single powerlaw of the form $y(t)=A(t-t_0)^{B}$ to the data, we find an index of $B=-0.03\pm0.01$ and a normalisation of $A=134.4\pm1.0$ eV $\chi^2_{\nu}=0.13$ for 2 d.o.f.)."
For the oobservations we find B=0.05c0.01 and sl=144.7+Bs eV (AZ=0-4 for 12 d.o.)., For the observations we find $B=-0.05\pm0.01$ and $A=144.7\pm3.8$ eV $\chi^2_{\nu}=0.4$ for 12 d.o.f.).
 These powerlaw fits are indicated by the dashed lines in Fig. 5.., These powerlaw fits are indicated by the dashed lines in Fig. \ref{fig:temp_chanfit}.
 A broken powerlaw also vields an acceptable fit to the clelata (AZ=0.3 for 10 cho)., A broken powerlaw also yields an acceptable fit to the data $\chi^2_{\nu}=0.3$ for 10 d.o.f.).
 We find a normalisation of eh=135.0417.8 eV. a break at 166.023:99.2 davs anedecay indices of 0.0340.03 and 0.06+0.02 before ancl after the break. respectively.," We find a normalisation of $A=135.0\pm17.8$ eV, a break at $166.0\pm99.2$ days anddecay indices of $-0.03\pm0.03$ and $-0.06\pm0.02$ before and after the break, respectively."
 This fit is indicated by the dotted curve in Fig. 5.., This fit is indicated by the dashed-dotted curve in Fig. \ref{fig:temp_chanfit}.
 Phere are not sullicient: oobservations to lita broken powerlaw decay., There are not sufficient observations to fit a broken powerlaw decay.
 We note that the shape of the decay curve of iis not strongly allected by our choice of spectral parameters (Ny. My. Hey. and D) or assumed distance3005).," We note that the shape of the decay curve of is not strongly affected by our choice of spectral parameters $N_{\mathrm{H}}$, $M_{\mathrm{NS}}$, $R_{\mathrm{NS}}$, and $\Gamma$ ) or assumed distance."
.. The quiescent lightcurve presented.in Fig., The quiescent lightcurve presentedin Fig.
 4. shows indications that the thermal Dux and temperature inferred rom the oobservations Πο below the trend of the οσα points., \ref{fig:temp} shows indications that the thermal flux and temperature inferred from the observations lie below the trend of the data points.
 “Phis possible shift (~6 percent for the [lux ighteurve) may. be due to cross-calibration issues between he two satellites., This possible shift $\sim 6$ percent for the flux lightcurve) may be due to cross-calibration issues between the two satellites.
 X study of the Crab nebula: indeed revealed an ollsct between aanelSuwiff.. whereas such a discrepancy was not found πλ aand]kusch2005.," A study of the Crab nebula indeed revealed an offset between and, whereas such a discrepancy was not found between and."
. Phis might be rellected in our results as well. since the deata point appears to line up with the trend indicated. by the ddata.," This might be reflected in our results as well, since the data point appears to line up with the trend indicated by the data."
 Llowever. our aand ddata points may also be (partly) olfset due to the fact that we cannot constrain the powerlaw component in the delata. which we therefore fixed to contribute LO percent of the total 0.510 keV. unabsorbed [ux (see Section 7?) ," However, our and data points may also be (partly) offset due to the fact that we cannot constrain the powerlaw component in the data, which we therefore fixed to contribute $10$ percent of the total 0.5–10 keV unabsorbed flux (see Section \ref{subsec:spectraldata}) )."
We discuss.ρα. aanc oobservations obtained alter the cessation of the very ong (~24 vear) active period of676.," We discuss, and observations obtained after the cessation of the very long $\sim$ 24 year) active period of."
. Fitting he spectral data with a neutron star atmosphere niodelNSATMOS.. did not reveal clear indications of a changing hermal spectrum. during the first. five months of the cquiescent phase20090).," Fitting the spectral data with a neutron star atmosphere model, did not reveal clear indications of a changing thermal spectrum during the first five months of the quiescent phase."
. However. now that he quiescent monitoring has extended to 19 months (1.6 vears). we find a significant decrease in neutron star ellective emperature from AT;~124 to 109 eV. The thermal xlometric Hux was observed. to decay from Hs1012160 0.9-10ereemost.," However, now that the quiescent monitoring has extended to 19 months (1.6 years), we find a significant decrease in neutron star effective temperature from $kT^{\infty}_{\mathrm{eff}}\sim124$ to $109$ eV. The thermal bolometric flux was observed to decay from $F_{\mathrm{bol}}^{\mathrm{th}}\sim1.5\times10^{-12}$ to $0.9\times10^{-12}~\flux$."
 In addition to a soft. thermal component. the aanc oobservations show evidence for a hard. powerlaw tail with index DL-—1.7.," In addition to a soft, thermal component, the and observations show evidence for a hard powerlaw tail with index $\Gamma=1.7$."
 Phe fractional contribution of the hard spectral Component to the total unabsorbed 0.510 keV. [lux initially clecreasecl from ~20 percent. in 2008 October to 4 percent in 2009 June., The fractional contribution of the hard spectral component to the total unabsorbed 0.5–10 keV flux initially decreased from $\sim20$ percent in 2008 October to $\sim4$ percent in 2009 June.
 However. observations carried out in 2010 April suggest. that. the powerlaw fraction increased again to 15 percent.," However, observations carried out in 2010 April suggest that the powerlaw fraction increased again to $\sim15$ percent."
 Similar behaviour has been observed. for several other quicscent neutron star svstenis2008).. although others show more irregular behaviour2010).," Similar behaviour has been observed for several other quiescent neutron star systems, although others show more irregular behaviour."
. In Cen ο the powerlaw tail in the quiescent spectrum. shows variations that appear to be linked to changes in the thermal component. possibly caused by low-level accretion2010).," In Cen X-4, the powerlaw tail in the quiescent spectrum shows variations that appear to be linked to changes in the thermal component, possibly caused by low-level accretion."
. The gradual decrease in thermal [ux and neutron star temperature observed for ccan be interpreted as the neutron star crust cooling down in quiescence after it has been heated during its long accretion outburst., The gradual decrease in thermal flux and neutron star temperature observed for can be interpreted as the neutron star crust cooling down in quiescence after it has been heated during its long accretion outburst.
 Fig., Fig.
 6. compares our data of wwith the crust cooling curves observed for the neutron star X-ray binaries260.. aand462.," \ref{fig:sources} compares our data of with the crust cooling curves observed for the neutron star X-ray binaries, and."
. This plot shows that the amount of cooling following the end of the outburst is markedly smaller or than for the other three sources., This plot shows that the amount of cooling following the end of the outburst is markedly smaller for than for the other three sources.
 We have observed. our arget over the first 19 months alter the cessation of the outburst and during this time the thermal bolometric Iux jas decreased. by a factor of ~1.7., We have observed our target over the first 19 months after the cessation of the outburst and during this time the thermal bolometric flux has decreased by a factor of $\sim1.7$.
 In a similar time span. he thermal bolometric Huxes of260.. aand thacl decreased by a [actor of ~3.5. 6 and 2.5. respectively2010).," In a similar time span, the thermal bolometric fluxes of, and had decreased by a factor of $\sim3.5$, 6 and 2.5, respectively."
. The ellective neutron star temperature of thas decreased by about LO percent. compared to 30. 40 and 20 percent for260.. aand162.," The effective neutron star temperature of has decreased by about 10 percent, compared to $\sim30$, 40 and 20 percent for, and."
. Although the observed. fractional changes in. neutron star temperature and. thermal bolometric Dux are smaller for tthan for the other three sources. the decay. itself may. not be markedly different.," Although the observed fractional changes in neutron star temperature and thermal bolometric flux are smaller for than for the other three sources, the decay itself may not be markedly different."
 Phe equiescent lighteurves of 260.. aand οσα be fit with an exponential decay function levelling olf to a constant. value. vielding e-folding times of ~305+ 50. 465x25 and ~120x25 days. respectively," The quiescent lightcurves of , and can be fit with an exponential decay function levelling off to a constant value, yielding e-folding times of $\sim305\pm50$ , $\sim465\pm25$ and $\sim120\pm25$ days, respectively"
as part of SDSS aud are included im DRI.,as part of SDSS and are included in DR4.
 Redshitt accuracy is better than 30 kim/s and the overall completcuess is ~90%.., Redshift accuracy is better than 30 km/s and the overall completeness is $\sim$.
 For our study we compute rest frame absolute magnitudes in the e-baud from, For our study we compute rest frame absolute magnitudes in the g-band from
with AA=64 the FWHLIAT of the redshifted Ila filter and Fur) and ωμή) the total number of counts inside a circular aperture with radius i of respectively the Ho| Nu] and the continuum image.,with $\Delta \lambda=64$ the FWHM of the redshifted $\alpha$ filter and $F_{\rm em}(r)$ and $F_{\rm cont}(r)$ the total number of counts inside a circular aperture with radius $r$ of respectively the $\alpha+$ ] and the continuum image.
 We find: Given the possible sources of error. (photon. shot-noise. sky and. continuum subtraction) that can allect our meastwements. we consider these values in good agreement with the EWs measured by Drinkwater (2001)..," We find: Given the possible sources of error (photon shot-noise, sky and continuum subtraction) that can affect our measurements, we consider these values in good agreement with the EWs measured by Drinkwater \cite{dri}."
 Pure. Ho| Nu]emission. images of FCCO4G and ECC207 are presented in Figures 9 and LO., Pure $\alpha+$ ]emission images of FCC046 and FCC207 are presented in Figures \ref{FCC046_Ha} and \ref{FCC207_Ha}.
 For ECC046. we find PFRQUCCO46)=153.L5T«10.PWom7. corresponding ο a total luminosity Loy(ECC€046)=6.21107 Ww.," For FCC046, we find $F_{\rm em}({\rm FCC046}) = 1.53 - 1.57 \times 10^{-18}\,{\rm
W~m}^{-2}$, corresponding to a total luminosity $L_{\rm em}({\rm
FCC046}) = 6.21 - 6.37 \, h_{75}^{-2} \times 10^{30}\,{\rm W}$ ."
 Phe range of values is given Lor πο”.2 (see Figure 11)).," The range of values is given for $F_{\rm{[N{\sc
ii}]}_2}/F_{\rm{H}\alpha}=0-2$ (see Figure \ref{Fem2a}) )."
 The central emission peak comprises yout half of the Iuminosity., The central emission peak comprises about half of the luminosity.
 Lt alone has a luminosity o£ xit 3o107 NV. Phe total lux of ECC207 is somewhat righer: FU(ECC207)=1.93.21s.10Wom 7. which vields a total luminosity Loay(PCC207)=7.89.S.S4hoo107 AV.," It alone has a luminosity of about $3 \times 10^{30}$ W. The total flux of FCC207 is somewhat higher: $F_{\rm em}({\rm FCC207}) = 1.93 - 2.18 \times
10^{-18}\,{\rm W~m}^{-2}$ , which yields a total luminosity $L_{\rm
em}({\rm FCC207}) = 7.83 - 8.84 \, h_{75}^{-2} \times 10^{30}\,{\rm
W}$ ."
" ""Phese numbers can be compared to those found by Duson (1993).. Ixim. (1989).. Phillips (1986) and Shields (1991). for normal elliptical ancl SO galaxies."," These numbers can be compared to those found by Buson \cite{bus}, Kim \cite{kim}, Phillips \cite{phi}
 and Shields \cite{shi} for normal elliptical and S0 galaxies."
 The luminosities of the central emission peaks in. ECCOA6 and ECC207 are compared to those of ellipticals in Figure 12.., The luminosities of the central emission peaks in FCC046 and FCC207 are compared to those of ellipticals in Figure \ref{buson}.
 Twpical emission luminosities for these galaxies lic in he range Low=10*.—10*' W. re. more than a 1000 times xiehter.," Typical emission luminosities for these galaxies lie in the range $L_{\rm em}
= 10^{33} - 10^{35}$ W, i.e. more than a 1000 times brighter."
 Phe fact that the luminosity of the nuclear emission in these dls agrees fairly well with the trend of normal Es extrapolated over more than 2 magnitudes — suggests that he ionising mechanism. at least for the central emission. is the same and. therefore somehow related. to the stellar »opulation.," The fact that the luminosity of the nuclear emission in these dEs agrees fairly well with the trend of normal Es – extrapolated over more than 2 magnitudes – suggests that the ionising mechanism, at least for the central emission, is the same and therefore somehow related to the stellar population."
" The total Hlo-Iux of ECCOA46 is fy,=417.15.7)[1IWom.2 7) depending. on the value of galeyay1 f/f."," The total $\alpha$ -flux of FCC046 is $F_{{\rm H}\alpha}=4.17 - 15.7
\times 10^{-19}\,{\rm W~m}^{-2}$ , depending on the value of $F_{\rm{[N{\sc ii}]}_2}/F_{\rm{H}\alpha}$ ."
" οThis ranslates into a total Lo luminosity Lg,=1.696.37 POW about half of which is emitted by the central peak ""orresponding to the galaxy’s nucleus."," This translates into a total $\alpha$ luminosity $L_{{\rm H}\alpha}=1.69- 6.37 \,
h_{75}^{-2} \times 10^{30}\,{\rm W}$ , about half of which is emitted by the central peak corresponding to the galaxy's nucleus."
" The total Lla-flux of FCC207 is somewhat higher: fy.=5.9519.3)wm 7. corresponding to Lg,=2.44.T.8S3Rh2 POW."," The total $\alpha$ -flux of FCC207 is somewhat higher: $F_{{\rm
H}\alpha}=5.95-19.3\times 10^{-19}\,{\rm W~m}^{-2}$ , corresponding to $L_{{\rm H}\alpha}=2.41 - 7.83 \, h_{75}^{-2} \times 10^{30}\,{\rm
W}$ ."
 Binette (1994) propose photo-ionisation by post-AGB stars as a source for the central emission in elliptical galaxies., Binette \cite{bin} propose photo-ionisation by post-AGB stars as a source for the central emission in elliptical galaxies.
 Using their prescriptions. we clerive central Ho luminosities of the order of 2107 W. Le. comparable to what is observed.," Using their prescriptions, we derive central $\alpha$ luminosities of the order of $2 \times 10^{30}$ W, i.e. comparable to what is observed."
 Hence. blindly interpreting the central Ho. emission as evidence for star-Formation may be somewhat aucacious.," Hence, blindly interpreting the central $\alpha$ emission as evidence for star-formation may be somewhat audacious."
" We can however check our results and use Ixennieutts (1983). calibration between the total SER and the Ho. luminosity. with £y,=1 mag the internal extinction factor."," We can however check our results and use Kennicutt's \cite{ken}
 calibration between the total SFR and the $\alpha$ luminosity, with $E_{{\rm H}\alpha}=1$ mag the internal extinction factor."
 We obtain in good agreement with the estimates based on the EWs eiven by Drinkwater (2001).., We obtain in good agreement with the estimates based on the EWs given by Drinkwater \cite{dri}.
" The total mass in ionised hyelrogen canbe written as with £g, the total Ho. luminosity. 2g the mass of the hvdrogen atom and the electron density in the gas."," The total mass in ionised hydrogen canbe written as with $L_{{\rm H}\alpha}$ the total $\alpha$ luminosity, $m_{\rm H}$ the mass of the hydrogen atom and $N_e$ the electron density in the gas."
 The hvdrogen Lla emissivity jua is given by in “case Dy recombination. i.e. complete re-absorption of all. Lyman photons in an optically thick nebula (Osterbrock (1989)... Spitzer (1978)... Alaechetto ad (1990))).," The hydrogen $\alpha$ emissivity $j_{{\rm H}\alpha}$ is given by in “case B” recombination, i.e. complete re-absorption of all Lyman photons in an optically thick nebula (Osterbrock \cite{ost}, , Spitzer \cite{spi}, Macchetto \cite{mac2}) )."
 Each Lyman photon emitted.[rom alevel with n>3 is later on converted to (a) Balmer photon(s) plus one Lyman à photon. thus raising the [ux in the Balmer lines.," Each Lyman photon emittedfrom alevel with $n \ge 3$ is later on converted to (a) Balmer photon(s) plus one Lyman $\alpha$ photon, thus raising the flux in the Balmer lines."
" The production cocllicient og (Cealeulated for 2=107 Is) is insensitive to the electron density (it changes by only if AN, is raised from len το10 ) and varies as Z77 as a function of temperature."," The production coefficient $\alpha_{{\rm
H}\alpha}$ (calculated for $T=10^4$ K) is insensitive to the electron density (it changes by only if $N_e$ is raised from 1 $^{-3}$ to$^6$ $^{-3}$ ) and varies as $T^{-0.8}$ as a function of temperature."
 Using equations (13)) and (14)). the ionised hydrogen mass canbe written concisely as: cl.," Using equations \ref{mhy}) ) and \ref{e1}) ), the ionised hydrogen mass canbe written concisely as: cf."
 Wim (1989).., Kim \cite{kim}.
" In the following. we will assume the value Ny=1000 em7?for the electron. density to be in accord with most other authors and to be able to directly compare ourtonised hydrogen masses with the literature (however. Spitzer (LOTS) advocates IN,=100 em"" asa typical value for both Galactic regions with cliaumeters of the order of 100 pe and for supernova remnants)."," In the following, we will assume the value $N_e =
1000$ $^{-3}$for the electron density to be in accord with most other authors and to be able to directly compare ourionised hydrogen masses with the literature (however, Spitzer \cite{spi} advocates $N_e
= 100$ $^{-3}$ as a typical value for both Galactic regions with diameters of the order of 100 pc and for supernova remnants)."
 Using equation (15)). the mass of the ionisecl hvdrogen gas in FCCOLG canbe estimated at Aly;;z40.150. and at AM;©G0—1905.AL. in ECC207.," Using equation \ref{mhy2}) ), the mass of the ionised hydrogen gas in FCC046 canbe estimated at $M_{{\rm H}{\sc ii}}
\approx 40 - 150 \,M_\odot$ and at $M_{{\rm H}{\sc ii}} \approx 60 -
190 \, h_{75}^{-2} \,M_\odot$ in FCC207."
 The Ler emission of FCCOAG is distributed overa bright centralregion ancl six fainter clouds. labeled to in ligure 9.. C11. C12. 015. ," The ${{\rm H}{\sc ii}}$ emission of FCC046 is distributed overa bright centralregion and six fainter clouds, labeled to in Figure \ref{FCC046_Ha}. . , , ,"
and areidentifiable in the 1t color map., and areidentifiable in the $-$ R color map.
 and are part of the bluish nebulosity to the north of the nucleus whereas and, and are part of the bluish nebulosity to the north of the nucleus whereas and
denoted NI but lacking planetesimal self-gravitv.,denoted N1 but lacking planetesimal self-gravity.
 Phe semi-major axis ancl eecentricity distributions for this simulation are. shown in Figure 2., The semi-major axis and eccentricity distributions for this simulation are shown in Figure \ref{fig:10000-noselfgrav}.
 The increase in eccentricity dispersion of particles in the outer disk seen in the selt-eravitating disk is not present in simulation NI., The increase in eccentricity dispersion of particles in the outer disk seen in the self-gravitating disk is not present in simulation N1.
 Thus the eccentricity dispersion increase in the sell-gravitating outer disk is likely caused by gravitational stirring of the planetesimals by themselves., Thus the eccentricity dispersion increase in the self-gravitating outer disk is likely caused by gravitational stirring of the planetesimals by themselves.
 Pwo dominant scattering surfaces are seen as broad in the semi-major axis vs eccentricity distributions of strokesFigure 1 and 2e one ewh from the inner and outer planet.," Two dominant scattering surfaces are seen as broad strokes in the semi-major axis vs eccentricity distributions of Figure \ref{fig:10000} and \ref{fig:10000-noselfgrav}, one each from the inner and outer planet."
 These surfaces. correspond. to. particles with, These surfaces correspond to particles with
determine if was undergoing a flaring event.,determine if was undergoing a flaring event.
 The June 2002 observation (Fig. 3)), The June 2002 observation (Fig. \ref{fig:lc}) )
" shows significant variability. with the count rate decreasing rather irregularly during the observation. but without a clear decay (or rise) which could be associated with a ""classic"" flare."," shows significant variability, with the count rate decreasing rather irregularly during the observation, but without a clear decay (or rise) which could be associated with a “classic” flare."
 Also. the hardness ratio does not change significantly during the observation. pointing to a constant (rather than decreasing. as expected in the decay phase of a flare) plasma temperature.," Also, the hardness ratio does not change significantly during the observation, pointing to a constant (rather than decreasing, as expected in the decay phase of a flare) plasma temperature."
 Most solar flares have typical duration of tens of minutes (although some very long ones. up to a day. have been observed). and such short event would have a very clear signature in the two hour span of the observation.," Most solar flares have typical duration of tens of minutes (although some very long ones, up to a day, have been observed), and such short event would have a very clear signature in the two hour span of the observation."
 Long-duration flares. up to days. have been observed in very active stars: while 81809'ss activity level is higher than solar. even when considering surface X-ray flux rather than luminosity. it still is much less active than the very active stars in which long duration flaring events have so far been observed to be common.," Long-duration flares, up to days, have been observed in very active stars; while s activity level is higher than solar, even when considering surface X-ray flux rather than luminosity, it still is much less active than the very active stars in which long duration flaring events have so far been observed to be common."
 Very significant X-ray long term variability is present in (Fig. 2))., Very significant X-ray long term variability is present in (Fig. \ref{fig:sim}) ).
 This alone is a significant result. as in all X- active stars monitored with a sufficient time base the long term variability is very small (typically a factor <2. see Stern.1998)).," This alone is a significant result, as in all X-ray active stars monitored with a sufficient time base the long term variability is very small (typically a factor $\le 2$, see \citealp{ste98b}) )."
 The X-ray luminosity of81809.. which is not a high-activity star. varies by more than an order of magnitude in two years. with a systematic pattern.," The X-ray luminosity of, which is not a high-activity star, varies by more than an order of magnitude in two years, with a systematic pattern."
 If the June 2002 observation were discounted as due to a long-duration flare. the total light curve amplitude would still be a factor of approximately 5.," If the June 2002 observation were discounted as due to a long-duration flare, the total light curve amplitude would still be a factor of approximately 5."
 The amplitude of cycle-related modulation in the X-ray luminosity is thus higher in tthan that recently reported for 61 Cyg (a factor of 2.5. Hempelmannetal.. 2003))," The amplitude of cycle-related modulation in the X-ray luminosity is thus higher in than that recently reported for 61 Cyg (a factor of 2.5, \citealp{hsb+2003}) )."
 While more luminous than the Sun in absolute terms. lis a subgiant. with a typical radius of Ji~376...," While more luminous than the Sun in absolute terms, is a subgiant, with a typical radius of $R \simeq 3 R_\odot$."
 The observed X-ray luminosity range. corresponds(considering only the primary star) to a surface flux 1.6>logFx5.4. somewhat higher than the corresponding solar values.," The observed X-ray luminosity range corresponds(considering only the primary star) to a surface flux $4.6 \ge \log F_{\rm X} \ge 5.5$, somewhat higher than the corresponding solar values."
 At the same time. the surface flux μις is almost identical in aand in the Sun (losHj=LOO versus logRy=195 respectively. Baliunasetal.. 1995)).," At the same time, the surface flux $R_{\rm HK}$ is almost identical in and in the Sun $\log R_{\rm HK} = -4.90$ versus $\log R_{\rm HK} = -4.92$ respectively, \citealp{bds+95}) )."
 The X-ray surface flux of us plotted. in Fig. 4..," The X-ray surface flux of is plotted, in Fig. \ref{fig:lxev},"
 together with the range of values observed in the Sun during the cycle., together with the range of values observed in the Sun during the cycle.
 The coronal temperature of is (except for the June 2002 observation) rather constant. and somewhat higher than the coronal temperature of the disk-integrated Sun.," The coronal temperature of is (except for the June 2002 observation) rather constant, and somewhat higher than the coronal temperature of the disk-integrated Sun."
 The coronal emission measure of the Sun (when filtered through the response of a CCD X-ray detector. see Peresetal..2000 for details) has a bulk component whose temperature varies little. between 0.16 and 0.19 keV between the minimum and the maximum of the cycle. with the addition of a hotter component (Z7=0.19 keV). which is only present at cycle maximum.," The coronal emission measure of the Sun (when filtered through the response of a CCD X-ray detector, see \citealp{por+99} for details) has a bulk component whose temperature varies little, between 0.16 and 0.19 keV between the minimum and the maximum of the cycle, with the addition of a hotter component $T = 0.49$ keV), which is only present at cycle maximum."
 Whether the June 2002 ts part of the cycle behavior of oor Is an exceptional event is something which can only be clarified by further observations., Whether the June 2002 is part of the cycle behavior of or is an exceptional event is something which can only be clarified by further observations.
 Figure 2 shows our determination of the X-ray luminosity of pplotted together with the last years of 5 index measurements (due to wildfires that threatened the Mt. Wilson area. very few observations were obtained in 2003).," Figure \ref{fig:sim} shows our determination of the X-ray luminosity of plotted together with the last years of $S$ index measurements (due to wildfires that threatened the Mt. Wilson area, very few observations were obtained in 2003)."
 The chromospheric cycle had a well defined maximum in 2001. and it is now in its descending phase; based on the previous cycles this," The chromospheric cycle had a well defined maximum in 2001, and it is now in its descending phase; based on the previous cycles this"
"The fLlatfielded WECS3/UVIS images in each filter were co-added using the MULTIDRIZZLE task (IXoekemoer et 22002). with a final pixel scale of 0.0396"" pix! (based on the best calibration available lor WFCS3 at the time the data were reduced. and accurate lo 21%...)","The flatfielded WFC3/UVIS images in each filter were co-added using the MULTIDRIZZLE task (Koekemoer et 2002), with a final pixel scale of $0.0396^{\prime\prime}$ $^{-1}$ (based on the best calibration available for WFC3 at the time the data were reduced, and accurate to $\approx1$ .)"
 A color image of the observed. M33 field is shown in Figure 1.., A color image of the observed M83 field is shown in Figure \ref{fig:colorimage}.
 The field covers the nuclear starburst region in M83. as well as a portion of a spiral arm and the inter-auim region.," The field covers the nuclear starburst region in M83, as well as a portion of a spiral arm and the inter-arm region."
 Figure is an enlargement of the nuclear region. ancl shows (hat recent star formation has cleared out most of the dust over much of the area.," Figure \ref{fig:nuclearimage} is an enlargement of the nuclear region, and shows that recent star formation has cleared out most of the dust over much of the area."
 A dust lane along the inner edge of the spiral arn is seen to the north and west of the nucleus. which appears as the vellowish object in (he upper left of the image.," A dust lane along the inner edge of the spiral arm is seen to the north and west of the nucleus, which appears as the yellowish object in the upper left of the image."
 Fieure 3. shows an enlargement of a tvpical portion of our fielcl outside of the nuclear region. including three large str-Iorming complexes containing compact star clusters.," Figure \ref{fig:triangle_region} shows an enlargement of a typical portion of our field outside of the nuclear region, including three large star-forming complexes containing compact star clusters."
 In order (o detect as many sources as possible. we aligned ancl co-adcded together the final. diizzled broad-band images in the U. D. V. and 7 filters. based on RAIS-normalized images (o eive roughly equal weight to all wavelengths.," In order to detect as many sources as possible, we aligned and co-added together the final, drizzled broad-band images in the $U$, $B$, $V$, and $I$ filters, based on RMS-normalized images to give roughly equal weight to all wavelengths."
 This procedure allows us to include objects that are very. blue or very red in our source list. such as blue aud red supergiant stars. that might otherwise be missing in anv single filler.," This procedure allows us to include objects that are very blue or very red in our source list, such as blue and red supergiant stars, that might otherwise be missing in any single filter."
 Using a mecian-divided version of the “white light image (see discussion in Miller 1997). we identified all sources. both point-like ancl slightly extended. using the ΗΑΕ task DAOFIND.," Using a median-divided version of the “white light” image (see discussion in Miller 1997), we identified all sources, both point-like and slightly extended, using the IRAF task DAOFIND."
 This resulted in a total list οἱ z68.000 objects. which includes a combination ol individual stars. close blends of a few stars. star clusters. and background galaxies.," This resulted in a total list of $\approx 68,000$ objects, which includes a combination of individual stars, close blends of a few stars, star clusters, and background galaxies."
 We perform circular aperture photometry of all detected sources on the drizzled images for each filter using the IRAF task PIIOT. using an aperture radius of 3 pixels and a backeround annulus between 10 and 13 pixels.," We perform circular aperture photometry of all detected sources on the drizzled images for each filter using the IRAF task PHOT, using an aperture radius of 3 pixels and a background annulus between 10 and 13 pixels."
 We have checked. however. (hat our results for the Iuminosity and mass functions are not sensiüve to the exact choice of aperture.," We have checked, however, that our results for the luminosity and mass functions are not sensitive to the exact choice of aperture."
 For the narrow-band E657N (Ho) image. we perform photometry on the drizzled image without subtracting the stellar continuum flux.," For the narrow-band F657N $H\alpha$ ) image, we perform photometry on the drizzled image without subtracting the stellar continuum flux."
 We convert the ΓΕ magnitudes to ihe VEGAMAG magnitude svstem by applving the following zeropoints: F336GW = 23.46. F438W = 24.98. F555W = 25.81. F657N = 22.35. and ΕΡΙΧ = 24.67. which are provided by SIScl at the following URL: /www.stsciedu/hst/phot_zzp_llbn.," We convert the instrumental magnitudes to the VEGAMAG magnitude system by applying the following zeropoints: F336W = 23.46, F438W = 24.98, F555W = 25.81, F657N = 22.35, and F814W = 24.67, which are provided by STScI at the following URL: lbn."
" We will loosely reler to (hese as ""UV. 7U. 7B. ον and 17 band magnitudes. although we do not make anv transformations to the Johnson-Cousins svstem."," We will loosely refer to these as $UV$ ,” $U$ $B$ ,” $V$ ,” and $I$ ” band magnitudes, although we do not make any transformations to the Johnson-Cousins system."
 We use (wo different approaches to determine aperture corrections. which convert our fixecl aperture magnitudes to total magnitudes.," We use two different approaches to determine aperture corrections, which convert our fixed aperture magnitudes to total magnitudes."
 Both approaches make use of the Concentration Index (C). measured in (he V. band image and defined as the difference in aperture magnitudes determined using a3 pix and a 0.5 pix radius.," Both approaches make use of the Concentration Index $C$ ), measured in the $V$ band image and defined as the difference in aperture magnitudes determined using a 3 pix and a 0.5 pix radius."
 In the first approach. a single value (0.30) is used for the aperture correction of point sources (i.e. objects with C< 2.3). and a different," In the first approach, a single value (0.30) is used for the aperture correction of point sources (i.e., objects with $C < 2.3$ ), and a different"
to far. or vice versa).,"to far, or vice versa)."
 Finally. we choose only those satellites in front of or behind the giants (with the relative direction within 60 degrees of the line of sight). so that any motion due to inlall shows up well in radial velocity.," Finally, we choose only those satellites in front of or behind the giants (with the relative direction within 60 degrees of the line of sight), so that any motion due to infall shows up well in radial velocity."
 To see the order of magnitude of the effect we are looking for. consider a galaxy of LOY solar masses. acting at a distance of 1 Mpe over 10-13 billion vears.," To see the order of magnitude of the effect we are looking for, consider a galaxy of $10^{12}$ solar masses, acting at a distance of 1 Mpc over 10-13 billion years."
 That results in a change in speed of 44-67 km | so we look for something in the tens. but not hundreds. of kim st.," That results in a change in speed of 44-67 km $^{-1}$; so we look for something in the tens, but not hundreds, of km $^{-1}$."
 The average of satellites behind the giant galaxy should show a blueshilt (negative). and those before a redshift: the difference should be on the order of 100 km !.," The average of satellites behind the giant galaxy should show a blueshift (negative), and those before a redshift; the difference should be on the order of 100 km $^{-1}$."
 There should be some noise from those satellites having made a close approach. but given the observed peculiar velocities we do nol expect verv many of them.," There should be some noise from those satellites having made a close approach, but given the observed peculiar velocities we do not expect very many of them."
 There are not enough satellite galaxies around most of the bright ones to give a clear picture. so the data from all eroups outside the Local Group are averaged together in Table (5)).," There are not enough satellite galaxies around most of the bright ones to give a clear picture, so the data from all groups outside the Local Group are averaged together in Table \ref{cherry}) )."
" There being no satellites ""before"" the Milky Way. and only one for M31. the numbers listed for those giants are all ""behind""."," There being no satellites “before” the Milky Way, and only one for M31, the numbers listed for those giants are all “behind”."
CP as the parameters used in the simulation correspond to the regime of the abcrratecl backward circular polarization (ABCD) (Melrose Luo 2004a).,CP as the parameters used in the simulation correspond to the regime of the aberrated backward circular polarization (ABCP) (Melrose Luo 2004a).
 In this regine. waves propagate backward in the local plasma rest frame. and are clliptically polarized.," In this regime, waves propagate backward in the local plasma rest frame, and are elliptically polarized."
 The simulated: pulses show substructures that are similar to the microstructrue seen in observations., The simulated pulses show substructures that are similar to the microstructrue seen in observations.
 The profiles shown in Figure 2. are the snapshots of the radiation. pattern produced. from a random. distribution of subsources., The profiles shown in Figure \ref{fig:profile} are the snapshots of the radiation pattern produced from a random distribution of subsources.
 The pulse structures are due to the transverse (across the field lines) elfect. only., The pulse structures are due to the transverse (across the field lines) effect only.
 Because of the relativistic beaming each subsource has a natural angular width of L/P.. which gives rise to a twpical time scale given by (Cordes 1979) The recent study of cascade above the PC confirms that the secondary pairs have a broad. distribution. peaked. at a moderate Lorentz factor around E;2107. which is not particularly sensitive to the pulse period (Zhang Llarcling 2000: Llibschman Arons 2001: Arendt Lilek 2002).," Because of the relativistic beaming each subsource has a natural angular width of $1/\Gamma_s$, which gives rise to a typical time scale given by (Cordes 1979) The recent study of cascade above the PC confirms that the secondary pairs have a broad distribution peaked at a moderate Lorentz factor around $\Gamma_s\approx 10^2$, which is not particularly sensitive to the pulse period (Zhang Harding 2000; Hibschman Arons 2001; Arendt Eilek 2002)."
 Lence. (5)) predicts a approximately linear relation with 2’.," Hence, \ref{eq:micro1}) ) predicts a approximately linear relation with $P$."
 Observations of microstructures secm consistent with this linear relation (Ixramoer. Johnston van Straten 2002).," Observations of microstructures seem consistent with this linear relation (Kramer, Johnston van Straten 2002)."
" For Py=100. P—0.1s. one has 7,=159gis."," For $\Gamma_s=100$, $P=0.1\, \rm s$, one has $\tau_\mu=159\,\mu\rm s$."
 The pulse structure can be smeared out substantially if, The pulse structure can be smeared out substantially if
since the thermal desorption is ineffective al 10 IX. στα surface reactions do not affect isolope ratios of gaseous species.,"Since the thermal desorption is ineffective at 10 K, grain surface reactions do not affect isotope ratios of gaseous species."
 Then the isotope fractionation of the gaseous species is mostly determined by the gas phase reactions and the depletion of CO., Then the isotope fractionation of the gaseous species is mostly determined by the gas phase reactions and the depletion of CO.
 Before a few 104 vr the abundance ratio of CO/MCO is significantly smaller than 60 because of the reaction (1)., Before a few $^4$ yr the abundance ratio of ${\rm CO/^{13}CO}$ is significantly smaller than 60 because of the reaction (1).
 As the abundance of CO increases with time and CO becomes the dominant carbon-bearing species. the isotope ratio gets close to the elemental abundance ratio of [C/C] = 60.," As the abundance of CO increases with time and CO becomes the dominant carbon-bearing species, the isotope ratio gets close to the elemental abundance ratio of $^{12}$ $^{13}$ C] = 60."
 For example. the CO/MCO ratio is 54 at 10? vr.," For example, the ${\rm CO/^{13}CO}$ ratio is 54 at $^5$ yr."
 In contrast. the /PC ratio is larger than 60 because of the reaction (1).," In contrast, the $^+$ $^{13}$ $^+$ ratio is larger than 60 because of the reaction (1)."
 Many carbon species are produced by reactions starting from or C. which is produced by recombination of C.," Many carbon species are produced by reactions starting from $^+$ or C, which is produced by recombination of $^+$."
" Therefore the isotope ratios of these ""carbon isotope pool” species are similar to the C ratio before 10* vr and the ος ratio alter 10 vr. although actual values vary among species depending on their production pathways."," Therefore the isotope ratios of these ""carbon isotope pool"" species are similar to the $^+$ $^{13}$ $^+$ ratio before $^3$ yr and the $^{13}$ C ratio after $^3$ yr, although actual values vary among species depending on their production pathways."
 For example. the CN/MCN ratio is 83. while CS/PCS ratio is 109 at 10! vr.," For example, the $^{13}$ CN ratio is 83, while $^{13}$ CS ratio is 109 at $^4$ yr."
" The evolution of the — ο ratio is similar to those of ""carbon isotope pool” at /< 10° vr. but the ratio is lowered by the reaction(2) alter a few 10* vr: the /HPCO ralio is 45 at LO? vr."," The evolution of the $^+$ $^{13}$ $^+$ ratio is similar to those of ""carbon isotope pool"" at $t <$ $^3$ yr, but the ratio is lowered by the reaction(2) after a few $^3$ yr; the $^+$ $^{13}$ $^+$ ratio is 45 at $^5$ yr."
" To investigate the clensity dependence of the isotope ratios. we also performed calculations with my, — 5 x 107 and 5 x LO? ?."," To investigate the density dependence of the isotope ratios, we also performed calculations with $n_{\rm {H_2}}$ = 5 $\times$ $^3$ and 5 $\times$ $^5$ $^{-3}$ ."
 The evolution is in general faster at hieher densiües., The evolution is in general faster at higher densities.
 Since we are interested in carbon-bearing species. we compare isotope ratios of these molecules at the time of peak carbon-chain abundance: 1 x 107. 2 x 104 and 14 x 10* vr for densities of 5x107. 5x10! and 5x10? 7. respectively.," Since we are interested in carbon-bearing species, we compare isotope ratios of these molecules at the time of peak carbon-chain abundance; 1 $\times$ $^5$, 2 $\times$ $^4$ and 4 $\times$ $^3$ yr for densities of $5 \times 10^3$, $5 \times 10^4$ and $5 \times 10^5$ $^{-3}$, respectively."
 We found that the isotope ratios do not significantly depend on density., We found that the isotope ratios do not significantly depend on density.
 For example. the CN/MCN ratio al the selected (ime is 83. 81 and 80. and the CS/MCS ratio is 83. 92 and. 105 for densities of 5xn 10*. 5x10! and 5x10 . respectively.," For example, the ${\rm CN/^{13}CN}$ ratio at the selected time is 83, 81 and 80, and the ${\rm CS/^{13}CS}$ ratio is 83, 92 and 108 for densities of $5 \times 10^3$ , $5 \times 10^4$ and $5 \times 10^5$ $^{-3}$, respectively."
 The isotope ratios of otherspecies in each density model are listed in Table 3., The isotope ratios of otherspecies in each density model are listed in Table 3.
previous analyses have made use of this theory to measure 5.,previous analyses have made use of this theory to measure $\beta$.
 On quasi-linear and non-linear scales we are instead reduced to making approximations. or using fitting formulae based on numerical simulations.," On quasi-linear and non-linear scales we are instead reduced to making approximations, or using fitting formulae based on numerical simulations."
" The standard approach is to use a ""streaming? model. where linear theory is spliced together with an approximation for random motion of particles in collapsed objects (see section 2). Tinker.Weinber"," The standard approach is to use a `streaming' model, where linear theory is spliced together with an approximation for random motion of particles in collapsed objects (see section \ref{sec:zspace_theory}) )."
g&Zheng(2006). and Tinker(2007)... which are developments of work in Hatton&Cole(1999). discuss a number of possible improvements to the streaming model based on fits to numerical simulation results.," \citet{TinWeiZhe06} and \citet{Tin07}, which are developments of work in \citet{HatCol99}, discuss a number of possible improvements to the streaming model based on fits to numerical simulation results."
 These approaches aim to allow us to extract information on £ from scales where the power spectrum does not match its linear form., These approaches aim to allow us to extract information on $\beta$ from scales where the power spectrum does not match its linear form.
 One concernis that the theoretical dependence on £ might change in the quasi-linear regime. leading to complicated dependencies and that fits to simulations will only be correct in a subset of cosmologies and galaxy formation models similar to those from which the fits were.," One concernis that the theoretical dependence on $\beta$ might change in the quasi-linear regime, leading to complicated dependencies and that fits to simulations will only be correct in a subset of cosmologies and galaxy formation models similar to those from which the fits were."
. A better approach would be to analyse the physics behind redshift-space distortions. and to try to use this to devise the best estimator with which to extract cosmological information.," A better approach would be to analyse the physics behind redshift-space distortions, and to try to use this to devise the best estimator with which to extract cosmological information."
 Because galaxy velocities only depend on the distribution of matter. we can devise an estimator Pt) that is not affected by galaxy bias: instead it measures the large-scale shape of the matter power spectrum.," Because galaxy velocities only depend on the distribution of matter, we can devise an estimator $\hat{P}(k)$ that is not affected by galaxy bias: instead it measures the large-scale shape of the matter power spectrum."
" Because the estimator is based on the velocity power spectrum. the large-scale amplitude is / times that of matter fluctuations. where / is the logarithmic derivative of the linear growth rate with respect to the scale factor, /2dinD/dIna."," Because the estimator is based on the velocity power spectrum, the large-scale amplitude is $f^2$ times that of matter fluctuations, where $f$ is the logarithmic derivative of the linear growth rate with respect to the scale factor, $f\equiv d\ln D/d\ln
a$."
 From this estimator. we can Measure fOnus. Which is proportional to dD/d Ina. and orovides a good discriminant between modified gravity and dark energy models (Song&Perc," From this estimator, we can measure $f\sigma_{8,\,{\rm mass}}$, which is proportional to $dD/d\ln a$ , and provides a good discriminant between modified gravity and dark energy models \citep{song08b}."
ival2008).. PUO is expected to match he linear matter power spectrum shape on large scales. so small- differences will help us to determine the scales on which he theory is breaking down.," $\hat{P}(k)$ is expected to match the linear matter power spectrum shape on large scales, so small-scale differences will help us to determine the scales on which the theory is breaking down."
 For ACDM models. we show that a simple Gaussian smoothing of the redshift-space power along he line-of-sight is able to match most of this break-down.," For $\Lambda$ CDM models, we show that a simple Gaussian smoothing of the redshift-space power along the line-of-sight is able to match most of this break-down."
 This ylaces redshift-space distortion measurements on the same footing as weak lensing measurements in the sense that they both allow us o test the matter distribution directly., This places redshift-space distortion measurements on the same footing as weak lensing measurements in the sense that they both allow us to test the matter distribution directly.
 They provide complementary information. as non-relativistic velocity measurements only depend on temporal metric perturbations. while weak lensing tests the sum of the temporal and spatial metric perturbations.," They provide complementary information, as non-relativistic velocity measurements only depend on temporal metric perturbations, while weak lensing tests the sum of the temporal and spatial metric perturbations."
 The layout of our paper is as follows., The layout of our paper is as follows.
 We first review the theory behind redshift-space distortions (Section 2)) in the linear. quasi-linear and non-linear regimes.," We first review the theory behind redshift-space distortions (Section \ref{sec:zspace_theory}) ) in the linear, quasi-linear and non-linear regimes."
 In Section 3.. we introduce a new estimator. based on the monopole and quadrupole from a Legendre decomposition of the redshift-space power spectrum. which is designed to recover a power spectrum given by /* times the matter power spectrum on large scales.," In Section \ref{sec:estimators}, we introduce a new estimator, based on the monopole and quadrupole from a Legendre decomposition of the redshift-space power spectrum, which is designed to recover a power spectrum given by $f^2$ times the matter power spectrum on large scales."
 Section 4 introduces the N-body simulation used to test this theory and our new estimator., Section \ref{sec:sims} introduces the N-body simulation used to test this theory and our new estimator.
 We use spherically averaged power spectra where we include distortions along multiple axes to analyse this simulation. an approach described in Section 5..," We use spherically averaged power spectra where we include distortions along multiple axes to analyse this simulation, an approach described in Section \ref{sec:pk_sph_av}."
 Our analytic theory is compared with results from the numerical simulation in Section 6.., Our analytic theory is compared with results from the numerical simulation in Section \ref{sec:sim_results}.
 The paper ends with a discussion of our results., The paper ends with a discussion of our results.
 The redshift-space position of a galaxy differs from its real-space position due to its peculiar velocity. where w(x) is the line-of-sight component of the galaxy velocity (assumed non-relativistic) in units of the Hubble velocity. and we have taken the line-of-sight to be the z-axis.," The redshift-space position of a galaxy differs from its real-space position due to its peculiar velocity, where $u_z({\bf x})$ is the line-of-sight component of the galaxy velocity (assumed non-relativistic) in units of the Hubble velocity, and we have taken the line-of-sight to be the $z$ -axis."
 We shall adopt the “plane-parallel” approximation. so this direction is fixed for all gulaxies.," We shall adopt the “plane-parallel” approximation, so this direction is fixed for all galaxies."
 The galaxy overdensity field in redshift-space can be obtained by imposing mass conservation. (10;kPs=CEὃν]r. and the exact Jacobian for the real-space to redshift-space transformation is In the limit where we are looking at scales much smaller than the mean distance to the pair. w/c is small and it is only the second term that is important (Kaiser1987: but see Papal2008). If we assume an irrotational velocity field we can write it.=O[ÜzN -@ where @=V-u. and V is the inverse Laplacian operator.," The galaxy overdensity field in redshift-space can be obtained by imposing mass conservation, $(1+\delta_g^s)d^3s=(1+\delta_g)d^3r$, and the exact Jacobian for the real-space to redshift-space transformation is In the limit where we are looking at scales much smaller than the mean distance to the pair, $u_z/z$ is small and it is only the second term that is important \citealt{Kai87}; but see \citealt{PapSza08}) ), If we assume an irrotational velocity field we can write $u_z=\partial/\partial z\,\nabla^{-2}\theta$ , where $\theta\equiv\nabla\cdot{\bf u}$, and $\nabla^{-2}$ is the inverse Laplacian operator."
" In Fourier space. (0/02=(ΚΚ4C. where µ is the cosine of the line-of-sight angle.V so we have that including second order convolutions in 6} and 6,(4). while neglecting third and higher order terms."," In Fourier space, $(\partial/\partial
z)^2\nabla^{-2}=(k_z/k)^2=\mu^2$, where $\mu$ is the cosine of the line-of-sight angle, so we have that including second order convolutions in $\theta(k)$ and $\delta_g(k)$, while neglecting third and higher order terms."
" If @ and o, are small. then we can drop the second and higher order terms from Eq. (49. "," If $\theta$ and $\delta_g$ are small, then we can drop the second and higher order terms from Eq. \ref{eq:del_full}) ),"
and Often it is further assumed that the velocity field comes from linear perturbation theory., and Often it is further assumed that the velocity field comes from linear perturbation theory.
 Then where f=dInD/dlnaQO! (Peebles1980)., Then where $f\equiv d\ln D/d\ln a \approx \Omega_m^{0.6}$ \citep{Pee80}.
" For a population of galaxies. which we denote with a subscript ο, the linear redshift-space power spectrum can be written where P.)= δι). Βικ=(0.UK00K)). Palky= (8E). are the galaxy-galaxy. galaxy-@ and 6-4 power spectra respectively for modes k."," For a population of galaxies, which we denote with a subscript $g$, the linear redshift-space power spectrum can be written where $P_{gg}(k)\equiv\langle |\delta_g({\bf k})|^2\rangle$ , $P_{g\theta}(k)\equiv\langle\delta_g({\bf k})\theta({\bf k})\rangle$, $P_{\theta\theta}(k)\equiv\langle |\theta({\bf k})|^2\rangle$ , are the galaxy–galaxy, $\theta$ and $\theta$ $\theta$ power spectra respectively for modes ${\bf k}$ ."
 A subscript 9 shows that a variable is determined from the velocity field of the galaxies. which we have assumed is irrotational and small compared with the real-space distance to the galaxies (see Fig. 1}).," A subscript $\theta$ shows that a variable is determined from the velocity field of the galaxies, which we have assumed is irrotational and small compared with the real-space distance to the galaxies (see Fig. \ref{fig:pksim}) )."
 In the followingwe often drop explicitlyshowing the K dependence of these power spectra. for convenience.," In the followingwe often drop explicitlyshowing the $k$ dependence of these power spectra, for convenience."
On a more formal basis. electrons with energy less than the escape energy (that is. the Fermi energy) that are directed towards the surface along the curving magnetic field lines must be reflected. since they cannot escape.,"On a more formal basis, electrons with energy less than the escape energy (that is, the Fermi energy) that are directed towards the surface along the curving magnetic field lines must be reflected, since they cannot escape."
 Therefore there must be two populations of electrons in motion along a flux tube: those that are moving towards the surface. and those that are moving towards the interior. having been reflected at some point.," Therefore there must be two populations of electrons in motion along a flux tube: those that are moving towards the surface, and those that are moving towards the interior, having been reflected at some point."
 This is similar to the magnetic bottle effect (Boyd&Sanderson2003) where charged particles are reflected at magnetic field concentrations: note that the analogy is not perfect. though. since in the magnetic bottle. particles are reflected simply because energy is transferred from parallel motion along the tield to perpendicular motion in the form of larmor orbits.," This is similar to the magnetic bottle effect \citep{2003phpl.book.....B} where charged particles are reflected at magnetic field concentrations; note that the analogy is not perfect, though, since in the magnetic bottle, particles are reflected simply because energy is transferred from parallel motion along the field to perpendicular motion in the form of larmor orbits."
 Such counter-streaming electrons will lead to density instabilities if the perturbations on each stream happen to evolve in phase such that they reinforce each other., Such counter-streaming electrons will lead to density instabilities if the perturbations on each stream happen to evolve in phase such that they reinforce each other.
" The full dispersion relation for electrons moving parallel and anti-parallel to the magnetic field direction with speed # is given by Boyd&Sanderson(2003) in which ""m=nycfGum,) is the square of the plasma Tequencey for electrons moving parallel to the magnetic field with speed i. where », is the number density of such electrons: c3 is similarly defined for electrons moving anti-parallel to the field."," The full dispersion relation for electrons moving parallel and anti-parallel to the magnetic field direction with speed $u$ is given by \citet{2003phpl.book.....B}
 in which $\omega_1^2=n_1e^2/(\epsilon_0m_e)$ is the square of the plasma frequency for electrons moving parallel to the magnetic field with speed $u$, where $n_1$ is the number density of such electrons; $\omega_2^2$ is similarly defined for electrons moving anti-parallel to the field."
" We lave assumed symmetry in the modelling. for simplicity: clearly we expect n,zm. which is equivalent to saying that the electron oss-rate is small: hence we also expect &;©iy. i£=1.2."," We have assumed symmetry in the modelling, for simplicity; clearly we expect $n_1\approx n_2$, which is equivalent to saying that the electron loss-rate is small; hence we also expect $\omega_i \approx \omega_p$, $i=1,2$."
 The frequeney and wavenumber of the common perturbation on he electron streams are given by c and f# respectively., The frequency and wavenumber of the common perturbation on the electron streams are given by $\omega$ and $k$ respectively.
 We must solve Eq. (22)), We must solve Eq. \ref{twostream}) )
 in order to arrive at the criteria for instability., in order to arrive at the criteria for instability.
" Tanipulation of the algebra reveals that the dispersion relation is biquadratic in c. and that there are imaginary components of Tequeney (or wavenumber) when tv<Qu,A."," Manipulation of the algebra reveals that the dispersion relation is biquadratic in $\omega$, and that there are imaginary components of frequency (or wavenumber) when $u<\sqrt{2}\omega_p/k$."
" Put another way. any density perturbations with a wavelength A satisfying must be unstable. where we have taken the upper limit on the wavelength to be the maximum scalelength in the star itself. that is. the pulsar radius /,."," Put another way, any density perturbations with a wavelength $\lambda$ satisfying must be unstable, where we have taken the upper limit on the wavelength to be the maximum scalelength in the star itself, that is, the pulsar radius $R_*$."
" Since the lower limit is at most Dire(2x)xh.10 ""me2005I. then it is always possible for instabilities to affect the counterstreaming flows. in the form of longitudinal plasma oscillations at the plasma frequency."," Since the lower limit is at most $2\pi c /(\sqrt{2}\omega_p)\approx 5 \times 10^{-10}$ m $\approx 200\hat{\rho}\ll R_*$, then it is always possible for instabilities to affect the counterstreaming flows, in the form of longitudinal plasma oscillations at the plasma frequency."
 There are further assumptions in this simple treatment. namely that the plasma density is uniform. and the electrons are monoenergetic.," There are further assumptions in this simple treatment, namely that the plasma density is uniform, and the electrons are monoenergetic."
 These assumptions are fine in the context of an idealised cold plasma treatment: we contend that they serve as an adequate illustration in the context of the pulsar flux tube., These assumptions are fine in the context of an idealised cold plasma treatment; we contend that they serve as an adequate illustration in the context of the pulsar flux tube.
 The nature of this streaming instability is to induce electrostatic oscillations on the dynamic electron population inside the flux tube., The nature of this streaming instability is to induce electrostatic oscillations on the dynamic electron population inside the flux tube.
 These plasma oscillations produce a self electric field because of the compression and rarefaction of electron density: there is no associated Magnetic perturbation. since the particle and displacement currents cancel perfectly.," These plasma oscillations produce a self electric field because of the compression and rarefaction of electron density; there is no associated magnetic perturbation, since the particle and displacement currents cancel perfectly."
 Note that this is a pure electron plasma with a fixed positive ion background. and so density enhancements here are pure electron overdensities.," Note that this is a pure electron plasma with a fixed positive ion background, and so density enhancements here are pure electron overdensities."
 There is however a maximum amplitude of electric field associated with such oscillations., There is however a maximum amplitude of electric field associated with such oscillations.
" If the wavenumber is A. then in the limit. this maximum electric field. Z4,1990):: This result can be extended to the relativistic case: where 5,=(1|pz/Gn7c))*7 is the relativistic factor for maximum associated electron momentum p,, in the oscillation."," If the wavenumber is $k$ , then in the non-relativistic limit, this maximum electric field $E_{\text{max}}$: This result can be extended to the relativistic case: where $\gamma_\phi = (1+p_\phi^2/(m^2c^2))^{1/2}$ is the relativistic factor for maximum associated electron momentum $p_\phi$ in the oscillation."
 This is the limiting field before coherent motion breaks down and wavebreaking occurs. at which point part of the electron population begins free-streaming at speeds greater than the phase velocity of the oscillation itself (Mori&Katsouleas1990:Kruer1990)..," This is the limiting field before coherent motion breaks down and wavebreaking occurs, at which point part of the electron population begins free-streaming at speeds greater than the phase velocity of the oscillation itself \citep{1990PhST...30..127M,1990PhST...30....5K}."
 Consider the case of an electrostatic oscillation in a flux tube. very close to the surface near the magnetic pole.," Consider the case of an electrostatic oscillation in a flux tube, very close to the surface near the magnetic pole."
 If the oscillation is at the point of wavebreaking. then the maximum energy ὃς that can be gained by an electron falling through the self-field of the oscillation before free-streaming must be given by This electron will escape to the surface if it has an energy greater than the Fermi energy.," If the oscillation is at the point of wavebreaking, then the maximum energy $\delta\varepsilon$ that can be gained by an electron falling through the self-field of the oscillation before free-streaming must be given by This electron will escape to the surface if it has an energy greater than the Fermi energy."
 Hence for escaping electrons. which can be expressed as using Eqs. 6. (109) ," Hence for escaping electrons, which can be expressed as using Eqs. \ref{ne_lattice}) ), \ref{plasfreq}) )"
and. 060)., and \ref{efermi1dclassical}) ).
" Por the typical pulsar ὁ -= 426.yieldingAll. « —1.31am~,1Inmagnetic"," For the typical pulsar magnetic field, $b\approx 426$, yielding $k<1.7\times 10^{11}$ $^{-1}$."
 field.other words. plasma oscillations with wavelengths (or scale variations)À. = 2afhexceeding4 QO Imcan eject electrons from the surface. providing such oscillations are at maximum amplitude.," In other words, plasma oscillations with wavelengths (or scale $\lambda=2\pi/k$ exceeding $4 \times 10^{-11}$ m can eject electrons from the surface, providing such oscillations are at maximum amplitude."
 This minimum wavelength is considerably greater than pom2.6.107 the width of the flux-tube (and the effective inter-ion spacing). suggesting that whilst the breakdown of ultra-short wavelength oscillations can't provide sufficient energy for electrons to escape the surface. longer wavelength oscillations will readily do SO.," This minimum wavelength is considerably greater than $\hat{\rho}\approx 2.6\times 10^{-12}$, the width of the flux-tube (and the effective inter-ion spacing), suggesting that whilst the breakdown of ultra-short wavelength oscillations can't provide sufficient energy for electrons to escape the surface, longer wavelength oscillations will readily do so."
 Thus we have shown that instabilities in the electron dynamics within the flux tube are sufficient to eject electrons from the pulsar interior., Thus we have shown that instabilities in the electron dynamics within the flux tube are sufficient to eject electrons from the pulsar interior.
" Given that the opacity of the pulsar to photons of frequency w is reduced by a factor (ifo)? for propagation parallel to the magnetic field direction (Lai2001:Canuto1975)... where c,ebm is the electron cyclotron frequency. there is the enhanced orospect of photons characteristic of the oscillation within the flux ube escaping directly to the pulsar atmosphere: in this context. w=wy. und (esos)?cm64bIx0.12 for magnetic fields of 10T. leading to the enhanced probability that the magnetic dolar regions are transparent to the emission of keV photons (from he plasma oscillation) produced inside the flux tubes by the bulk dasmadynamics."," Given that the opacity of the pulsar to photons of frequency $\omega$ is reduced by a factor $(\omega/\omega_c)^2$ for propagation parallel to the magnetic field direction \citep{2001RvMP...73..629L,1975NYASA.257..108C}, where $\omega_c=eB/m$ is the electron cyclotron frequency, there is the enhanced prospect of photons characteristic of the oscillation within the flux tube escaping directly to the pulsar atmosphere; in this context, $\omega = \omega_p$, and $(\omega_p/\omega_c)^2\approx 6.4b^{-0.65}\approx 0.12$ for magnetic fields of $10^8$ T, leading to the enhanced probability that the magnetic polar regions are transparent to the emission of keV photons (from the plasma oscillation) produced inside the flux tubes by the bulk plasmadynamics."
 Note that for magnetic fields of around 4. 10T. his opacity enhancement disappears. and so direct emission of οποίος below O.tkeV by this process wouldn't be expected.," Note that for magnetic fields of around $4\times 10^6$ T, this opacity enhancement disappears, and so direct emission of photons below $0.4$ keV by this process wouldn't be expected."
"show that our dynamical estimate of M. is proportional to (re/rap)U?Tapo”=(rap/re)""! reo?.","show that our dynamical estimate of $M_*$ is proportional to $(r_e/r_{ap})^{0.9}\,r_{ap}\sigma^2 = (r_{ap}/r_e)^{0.1}\, r_e\sigma^2$ ."
 Figure 2 shows that there is little scatter around this relation., Figure \ref{fig:lambda} shows that there is little scatter around this relation.
" However, our sample has essentially fixed c, and rap/re has only a small scatter, so Figure 5 is almost a plot of re vs re, with the zero-point being set by the mean c and rap/re values in the sample."," However, our sample has essentially fixed $\sigma$, and $r_{ap}/r_e$ has only a small scatter, so Figure \ref{fig:comp1} is almost a plot of $r_e$ vs $r_e$, with the zero-point being set by the mean $\sigma$ and $r_{ap}/r_e$ values in the sample."
 This is why the slope is close to unity., This is why the slope is close to unity.
" Of course, if the stellar distribution were not homologous, or the dark matter was a significant fraction of the total mass, then Ταρ/Τε need not have small scatter."," Of course, if the stellar distribution were not homologous, or the dark matter was a significant fraction of the total mass, then $r_{ap}/r_e$ need not have small scatter."
" The diamonds, squares, triangles show these same relations, but now obtained from a sample of z~2.3 objects by Bezanson et al. ("," The diamonds, squares, triangles show these same relations, but now obtained from a sample of $z\sim 2.3$ objects by Bezanson et al. ("
"2009), Damjanov et al. (","2009), Damjanov et al. ("
"2009), Mancini et al. (","2009), Mancini et al. ("
2010) and Longhetti et al. (,2010) and Longhetti et al. (
"2007), respectively.","2007), respectively."
 A number of studies have noted that the z~2 objects are significantly smaller than z~0 objects of the same M. (dotted or dashed curves)., A number of studies have noted that the $z\sim 2$ objects are significantly smaller than $z\sim 0$ objects of the same $M_*$ (dotted or dashed curves).
" Note that Bezanson et al,"," Note that Bezanson et al.,"
" Mancini et al.,"," Mancini et al.,"
 Longhetti et al., Longhetti et al.
 and Damjanov et al., and Damjanov et al.
" computed their stellar masses with different IMF (Kroupa, Chabrier, Salpeter and Baldry Glazebrook) and different stellar population models (Bruzual Charlot 2003 and Maraston 2005)."," computed their stellar masses with different IMF (Kroupa, Chabrier, Salpeter and Baldry Glazebrook) and different stellar population models (Bruzual Charlot 2003 and Maraston 2005)."
 The fit from Hyde Bernardi (2009) and Shen et al. (, The fit from Hyde Bernardi (2009) and Shen et al. (
2003) were computed using à Chabrier IMF.,2003) were computed using a Chabrier IMF.
 In order to compare these different samples werecalibrated, In order to compare these different samples werecalibrated
and the parameter fo describes the hole size in space plasma distribution (see Fig. 6)).,and the parameter $f_0$ describes the hole size in space plasma distribution (see Fig. \ref{fig0}) ).
" As was already stressed, in this paper we are going to discuss the theoretical ground of propagation effects only."," As was already stressed, in this paper we are going to discuss the theoretical ground of propagation effects only."
 For this reason we assume here for simplicity the intensity of radio emission in the emission region to be proportional to the number density of outgoing plasma., For this reason we assume here for simplicity the intensity of radio emission in the emission region to be proportional to the number density of outgoing plasma.
 In reality the directivity pattern may differ drastically from the particle profile., In reality the directivity pattern may differ drastically from the particle profile.
" To determine the number density ne of the outgoing plasma in the arbitrary point of the magnetosphere, we use quasi-stationary formalism, which is valid for quantities that are functions of—Qt."," To determine the number density $n_{\rm e}$ of the outgoing plasma in the arbitrary point of the magnetosphere, we use quasi-stationary formalism, which is valid for quantities that are functions of."
. For such functions all time derivatives can be reduced to spatial derivatives by the following rules (Beskin 2009): for any scalar (Q) and vector (V) functions., For such functions all time derivatives can be reduced to spatial derivatives by the following rules (Beskin 2009): for any scalar $Q$ ) and vector ${\bf V}$ ) functions.
" Here Using now the continuity equation where the velocity is given by Eqn. (27)),"," Here Using now the continuity equation where the velocity is given by Eqn. \ref{vdrift1}) ),"
" one can obtain Hence, the product remains constant along the field lines (BGI, Gruzinov 2006)."," one can obtain Hence, the product remains constant along the field lines (BGI, Gruzinov 2006)."
" Taking now intoaccount only the first order by Qr/c and assuming that the velocity of the outflowing particles is close to the light velocity c, we finally obtain Thus, to determine the number density ne. at an arbitrary point along the ray trajectory it is enough to know the number density and magnetic field B at the base of a given field line on the neutron star surface."," Taking now intoaccount only the first order by $\Omega r/c$ and assuming that the velocity of the outflowing particles is close to the light velocity $c$, we finally obtain Thus, to determine the number density $n_{\rm e}$ at an arbitrary point along the ray trajectory it is enough to know the number density and magnetic field $B$ at the base of a given field line on the neutron star surface."
 But for this it is necessary to produce the back integration along the field line from any point along the trajectory up to the star surface., But for this it is necessary to produce the back integration along the field line from any point along the trajectory up to the star surface.
 In Fig., In Fig.
 7 we show the dependences of the distance of the foot points to the magnetic axis γι within the polar cap as a function of the distance r along the ray for rotating dipole (model B) and for magnetic field including the monopole wind (model C) for the phase point ¢=—5°., \ref{figres0} we show the dependences of the distance of the foot points to the magnetic axis $r_{\perp}$ within the polar cap as a function of the distance $r$ along the ray for rotating dipole (model B) and for magnetic field including the monopole wind (model C) for the phase point $\phi =-5^{\circ}$.
" As for model B the appropriate value can be obtained analytically (dashed curve) where jm is the angle between local point on the ray vector and momentary magnetic axis, one can conclude that the precision of our procedure is high enough."," As for model B the appropriate value can be obtained analytically (dashed curve) where $\psi_m$ is the angle between local point on the ray vector and momentary magnetic axis, one can conclude that the precision of our procedure is high enough."
" As was shown by Andrianov Beskin (2010), for large enough shear of the magnetic field along the ray (as will be shown below, this condition does hold in the pulsar magnetosphere), all the polarization characteristics of outgoing radiation depend on the diagonal components of dielectric tensor, that are not sensitive to the difference of the ete” distribution functions."," As was shown by Andrianov Beskin (2010), for large enough shear of the magnetic field along the ray (as will be shown below, this condition does hold in the pulsar magnetosphere), all the polarization characteristics of outgoing radiation depend on the diagonal components of dielectric tensor, that are not sensitive to the difference of the $e^{+}e^{-}$ distribution functions."
 This fundamental property allows us to consider the electron and positron energy distribution functions to be identical., This fundamental property allows us to consider the electron and positron energy distribution functions to be identical.
 Our particularchoice is (see Fig. 8)), Our particular is (see Fig. \ref{fig1}) )
" This distribution has the maximum for y=yo that is assumed as a typical Lorentz-factor of plasma particles, and has power-law spectrum Υ for large Lorentz-factors > yo."," This distribution has the maximum for $\gamma = \gamma_0$ that is assumed as a typical Lorentz-factor of plasma particles, and has power-law spectrum $\gamma^{-2}$ for large Lorentz-factors $\gamma \gg \gamma_0$ ."
" Thus, it models well enough the energy distribution function obtained numerically (Daugherty Harding 1982; BGI)."," Thus, it models well enough the energy distribution function obtained numerically (Daugherty Harding 1982; BGI)."
late-twpe galaxies. already accounting for our selection ellect due to the axial ratio eut.,"late-type galaxies, already accounting for our selection effect due to the axial ratio cut."
 Ες is below the estimates in both ancl 2.. but consistent with that in ?.. with the uncertainties they quote.," This is below the estimates in both and , but consistent with that in , with the uncertainties they quote."
 Most. likely. our estimate is below these previous results due to our eut in total stellar mass at the low mass end.," Most likely, our estimate is below these previous results due to our cut in total stellar mass at the low mass end."
 and include galaxies with masses below our mass cut. and thus a significantly larger fraction of late-tvpe galaxies. as the fraction of late-type galaxies is stronglv increasing as one goes lower in mass.," and include galaxies with masses below our mass cut, and thus a significantly larger fraction of late-type galaxies, as the fraction of late-type galaxies is strongly increasing as one goes lower in mass."
 The larger dillerence with respect to might be at least partially a result from the cillerent relations used to estimate Αρη., The larger difference with respect to might be at least partially a result from the different relations used to estimate $M_{\rm{BH}}$ .
 also investigate quantitatively how late-twpe galaxies can be misclassified as carly-type galaxies. duc to dust reddening alone. if one applies a colour cut in order to co such a classification in the SDSS?).," also investigate quantitatively how late-type galaxies can be misclassified as early-type galaxies, due to dust reddening alone, if one applies a colour cut in order to do such a classification in the SDSS."
. Γον find that the ratio of red to blue galaxies changes from 1:1 to 1:2 when going [rom observed to intrinsic colours., They find that the ratio of red to blue galaxies changes from 1:1 to 1:2 when going from observed to intrinsic colours.
 Therefore. the true fraction ofdisc galaxies rises bv a factor of about 1.3.," Therefore, the true fraction of disc galaxies rises by a factor of about 1.3."
 This results only from inclined disc galaxies being misclassified as ellipticals because dust attenuation makes their colours too red for a tvpical disc galaxy., This results only from inclined disc galaxies being misclassified as ellipticals because dust attenuation makes their colours too red for a typical disc galaxy.
 Our estimate of the fraction of the total black hole mass in bulges is a factor of 1.5 higher than that in2.. and a factor of 2 higher than that in?.," Our estimate of the fraction of the total black hole mass in bulges is a factor of 1.5 higher than that in, and a factor of 2 higher than that in."
. Thus. the elfects of dust reddening alone cannot explain this dillerence.," Thus, the effects of dust reddening alone cannot explain this difference."
 Llowever. we argue that an important fraction of intrinsically red and concentrated lenticulars and earlv-tvpe spirals (with massive bulges and black holes) are present in the earlv-type/red samples in both studies mentioned. and thus the masses of their black holes are. being computed together with black holes in ellipticals.," However, we argue that an important fraction of intrinsically red and concentrated lenticulars and early-type spirals (with massive bulges and black holes) are present in the early-type/red samples in both studies mentioned, and thus the masses of their black holes are being computed together with black holes in ellipticals."
 Since lenticulars and. earlv-tvpe spirals generally have a relatively low dust content. this ellect is not being account for in the estimate of?.," Since lenticulars and early-type spirals generally have a relatively low dust content, this effect is not being account for in the estimate of."
. Hence. the Larger fraction of the total black hole mass we find in bulges is not an unexpected result.," Hence, the larger fraction of the total black hole mass we find in bulges is not an unexpected result."
 The results described. above indicate. that pseudo-bulges have higher @ for their masses. as compared to classical bulges. which also have. on average. higher σ for their masses when compared to elliptical galaxies.," The results described above indicate that pseudo-bulges have higher $\sigma$ for their masses, as compared to classical bulges, which also have, on average, higher $\sigma$ for their masses when compared to elliptical galaxies."
 We have kept the low σ estimates from SDSS for pseudo-bulges to avoid artificially strengthening these results., We have kept the low $\sigma$ estimates from SDSS for pseudo-bulges to avoid artificially strengthening these results.
 For these svstenis. it is unclear. however. if such results arise from the inability of SDSS measurements to correctly measure o in cases where he true velocity. dispersion is lower than. or close to. the instrumental resolution.," For these systems, it is unclear, however, if such results arise from the inability of SDSS measurements to correctly measure $\sigma$ in cases where the true velocity dispersion is lower than, or close to, the instrumental resolution."
 In. other words. one could argue hat the pseucdo-bulges for which e is available are only those at the high end of the velocity. dispersiondistribution.," In other words, one could argue that the pseudo-bulges for which $\sigma$ is available are only those at the high end of the velocity dispersiondistribution."
 As mentioned above. we have e estimates for only 30 per cent of he pscuclo-bulges in our sample.," As mentioned above, we have $\sigma$ estimates for only 30 per cent of the pseudo-bulges in our sample."
 In such a case. our results would only indicate that pseuclo-bulges displav a very large scalter around the Aus;—0 relation.," In such a case, our results would only indicate that pseudo-bulges display a very large scatter around the $M_{\rm{Bulge}}-\sigma$ relation."
 While we can no »esently rule out such possibility. we note that there seems o be a gradual transition from elliptical galaxies to classica )ulees ancl pseudo-bulges in Fig.," While we can not presently rule out such possibility, we note that there seems to be a gradual transition from elliptical galaxies to classical bulges and pseudo-bulges in Fig."
 1. and in the edge-on view of the fundamental plane (Paper D)., \ref{fig:smbh} and in the edge-on view of the fundamental plane (Paper I).
 This suggests tha our results are the outcome of a real οσο. since classica )ulees have σ estimates typically substantially larger than he SDSS instrumental resolution.," This suggests that our results are the outcome of a real effect, since classical bulges have $\sigma$ estimates typically substantially larger than the SDSS instrumental resolution."
 The result. that) pseuco-bulges have higher velocity dispersion. than classical bulges. at a fixed. stellar mass. gocs in the opposite direction as one would naively infer from the virial theorem. particularly because pseudo-bulges are more rotationally supported than classical bulges.," The result that pseudo-bulges have higher velocity dispersion than classical bulges, at a fixed stellar mass, goes in the opposite direction as one would naively infer from the virial theorem, particularly because pseudo-bulges are more rotationally supported than classical bulges."
 Llowever. pseuclo-bulges are not expected to be Lully relaxed systems. which is one of the main assumptions in the virial theorem.," However, pseudo-bulges are not expected to be fully relaxed systems, which is one of the main assumptions in the virial theorem."
 Concerning this result. one may worry that disc contamination in the SDSS fibre (from which the spectra. and thus e. are obtained) could artificially rise the values of a in pseudo-bulges. where such contamination is expected to be present to some degree.," Concerning this result, one may worry that disc contamination in the SDSS fibre (from which the spectra, and thus $\sigma$, are obtained) could artificially rise the values of $\sigma$ in pseudo-bulges, where such contamination is expected to be present to some degree."
 In fact. disce rotation can result in overestimated e values. since with SDSS data alone one can not distinguish. true dispersion from rotation.," In fact, disc rotation can result in overestimated $\sigma$ values, since with SDSS data alone one can not distinguish true dispersion from rotation."
 This is also true for bulge rotation and. again. such elect is expected to be more significant for pseudo-bulges than for classical bulges.," This is also true for bulge rotation and, again, such effect is expected to be more significant for pseudo-bulges than for classical bulges."
 However. given that we have only selected: galaxies with θα0.9. Le. face-on galaxies. both disc and bulge rotation should have negligible components along the line of sight. and the elfects from. rotation are expected to be present.," However, given that we have only selected galaxies with $b/a\geq0.9$, i.e. face-on galaxies, both disc and bulge rotation should have negligible components along the line of sight, and the effects from rotation are expected to be present."
 Indeed. the intrinsic axial ratio of discs seems to be closer to 0.9 rather than exactly 122).," Indeed, the intrinsic axial ratio of discs seems to be closer to 0.9 rather than exactly 1."
. Although recent numerical experiments. vield. similar results(2)... it remains to be verified if the dillerent behaviour of pseudo-bulges5 in the Apuoo relation is not only a consequence of the presence of bars2).," Although recent numerical experiments yield similar results, it remains to be verified if the different behaviour of pseudo-bulges in the $M_{\rm{Bulge}}-\sigma$ relation is not only a consequence of the presence of bars."
.. A bar is expected to enhance the central velocity dispersion in its host galaxygalaxies. M it has evolved. lor à. sullicient imetherein).. and such elfect should ος more dramatic in galaxies with less conspicuous bulges.," A bar is expected to enhance the central velocity dispersion in its host galaxy, if it has evolved for a sufficient time, and such effect should be more dramatic in galaxies with less conspicuous bulges."
 1t should also be noted that it is likely that a fraction of our unbarred galaxies contain small bars (smaller than 2.3 kpe in semi-major axis) which have been missed due to he relatively poor spatial resolution of SDSS images., It should also be noted that it is likely that a fraction of our unbarred galaxies contain small bars (smaller than $2-3$ kpc in semi-major axis) which have been missed due to the relatively poor spatial resolution of SDSS images.
 Such raction should be larger in galaxies with pseucdo-bulges. since these bars are more often hosted by galaxies with small xulge-to-total ratios.," Such fraction should be larger in galaxies with pseudo-bulges, since these bars are more often hosted by galaxies with small bulge-to-total ratios."
 This could explain the few pseudo-σος in αραο galaxies that are also outliers in the Meuse0 relation. should the exception caused by xilees be only due to the presence of a bar.," This could explain the few pseudo-bulges in “unbarred” galaxies that are also outliers in the $M_{\rm{Bulge}}-\sigma$ relation, should the exception caused by pseudo-bulges be only due to the presence of a bar."
 have recently shown that the relation between clliptical/hulgeΠοστ L and e in the local sample of galaxies with black hole mass measurements appears to differ from that in a sample of SDSS earlv-tvpe galaxies., have recently shown that the relation between elliptical/bulge $L$ and $\sigma$ in the local sample of galaxies with black hole mass measurements appears to differ from that in a sample of SDSS early-type galaxies.
 It is presently unclear if this is a selection or à physical effect. but it has important consequences. since the distributions of black hole masses estimated using SDSS data depends on whether luminosity or σ is used to derive Adpy.," It is presently unclear if this is a selection or a physical effect, but it has important consequences, since the distributions of black hole masses estimated using SDSS data depends on whether luminosity or $\sigma$ is used to derive $M_{\rm{BH}}$."
 The results in indicate that once barred. galaxies are removed. from the samples with measurements of Alpy the £0 relation so obtained is consistent with that in the SDSS sample., The results in indicate that once barred galaxies are removed from the samples with measurements of $M_{\rm{BH}}$ the $L-\sigma$ relation so obtained is consistent with that in the SDSS sample.
 It also seems that one should not consider all bulges together in these analyses 2).. although again such discrepaney between classical ancl pseudo-bulges is likely to be related to the presence ofa bar. as argued in," It also seems that one should not consider all bulges together in these analyses , although again such discrepancy between classical and pseudo-bulges is likely to be related to the presence of a bar, as argued in"
In the first step. the mass ancl period. cistributions among those three groups were studied.,"In the first step, the mass and period distributions among those three groups were studied."
 The result confirms common knowledge that the massive systems are likely to be found in the group of the “CO and the less massive systems are likely to be found among the “ALIS” group. so ib is not displaved.," The result confirms common knowledge that the massive systems are likely to be found in the group of the `G' and the less massive systems are likely to be found among the `MS' group, so it is not displayed."
 However. it is of interest. το display the period distribution (Fig.," However, it is of interest to display the period distribution (Fig."
 5) among the €. SG. and. MS systems.," 5) among the G, SG, and MS systems."
 The SCO group shows nearly a normal distribution with the peak at six days anc a range of orbital periods from 0.79 to 50 days., The `SG' group shows nearly a normal distribution with the peak at six days and a range of orbital periods from 0.79 to 50 days.
 The group of σα prefers not only more massive systems but also the systems with the longest orbital periods., The group of `G' prefers not only more massive systems but also the systems with the longest orbital periods.
 According to Fig., According to Fig.
 5. systems containing a giant star prefer an orbital period. of 10 days or longer. but rarely shorter periods.," 5, systems containing a giant star prefer an orbital period of 10 days or longer, but rarely shorter periods."
 Notice the sharp decrease of the short period. binaries in the αν group., Notice the sharp decrease of the short period binaries in the `G' group.
" The ""MS. systems are mostly less than 10 days down to the shortest. period of 0.476533 days.", The `MS' systems are mostly less than 10 days down to the shortest period of 0.476533 days.
 Our sample does not have many shorter »eriods because CAB are detached systems., Our sample does not have many shorter periods because CAB are detached systems.
 Much. shorter »eriods are common among the contact (WU Ma) and semi contact (2 Lyvrea) binaries., Much shorter periods are common among the contact (W UMa) and semi contact $\beta$ Lyrea) binaries.
" His interesting to note that he range of ""MS. periods covers quite a range of the most oeferred “Ge group periods with a smooth decrease.", It is interesting to note that the range of `MS' periods covers quite a range of the most preferred `G' group periods with a smooth decrease.
 This decrease may. well be due to the selection cllect that main sequence long period systems are harder to be noticed than he long period binaries with a giant or two., This decrease may well be due to the selection effect that main sequence long period systems are harder to be noticed than the long period binaries with a giant or two.
 However. similar selection elfect. cannot be true for the decrease of the 77 systems towards the shorter periods.," However, similar selection effect cannot be true for the decrease of the `G' systems towards the shorter periods."
 Fig., Fig.
 6 compares the orbital period. distributions tween the kinematically vounger (MG) and. older. (field) »opulations in our sample., 6 compares the orbital period distributions between the kinematically younger (MG) and older (field) populations in our sample.
 Both groups have about the same range of orbital periods., Both groups have about the same range of orbital periods.
 However. the vounger MC. group shows a rather smoother distribution. without a clistinet »ak. contrasting with the older population. which shows a peak of a gaussian at 11.3. (fog?= 1.053) cdavs.," However, the younger MG group shows a rather smoother distribution, without a distinct peak, contrasting with the older population, which shows a peak of a gaussian at 11.3 $logP=1.053$ ) days."
 At inst. the composition rates of G. SG. ancl MS svstems in xh groups were investigated.," At first, the composition rates of G, SG, and MS systems in both groups were investigated."
 There are SS systems in the vounger population in Fig., There are 88 systems in the younger population in Fig.
 Ga which is composed. of 344 C. 244 σα. and 42% AIS systems.," 6a which is composed of $34\%$ G, $24\%$ SG, and $42\%$ MS systems."
 On the other hand. here are 127 of the stars in the older population in Fig.," On the other hand, there are 127 of the stars in the older population in Fig."
 Gh which is composed of 434 of €. 25% of SG. and 32% of MS systems.," 6b which is composed of $43\%$ of G, $25\%$ of SG, and $32\%$ of MS systems."
 There is not much dillerence in the distributions of the subgroups. between the two groups., There is not much difference in the distributions of the subgroups between the two groups.
 Therefore. the period preferences of the sub groups (6. SG. and. MS) alone cannot not explain the displaved dillerence between Fig.," Therefore, the period preferences of the sub groups (G, SG, and MS) alone cannot not explain the displayed difference between Fig."
 6a and Vie., 6a and Fig.
 6, 6b.
 Nevertheless. the decrease in the number of systems in the longer and shorter periods in field stars (the older sample) may be an ellect in the binary evolution.," Nevertheless, the decrease in the number of systems in the longer and shorter periods in field stars (the older sample) may be an effect in the binary evolution."
 According to Demircan (1999). mass loss from a binary is associated with the momentum loss causing the decrease of the semi-major axis of the orbit.," According to Demircan (1999), mass loss from a binary is associated with the momentum loss causing the decrease of the semi-major axis of the orbit."
 X shrinking orbit forces the orbital period to decrease., A shrinking orbit forces the orbital period to decrease.
 Fig., Fig.
 6 appears to support this scenario., 6 appears to support this scenario.
 1ας is because. assuming that the Ποια stars” have a similar period distribution as “ALCO at the origin when they were vounger. the number decrease of longer period svstenis could. be interpreted with the above prediction.," This is because, assuming that the `field stars' have a similar period distribution as `MG' at the origin when they were younger, the number decrease of longer period systems could be interpreted with the above prediction."
 Llowever. the number decrease. of short. period. svstems appears to contradict the scenario.," However, the number decrease of short period systems appears to contradict the scenario."
 That is. normally one expects to count more systems with shorter periods among the older binaries if orbital periods decrease curing evolution.," That is, normally one expects to count more systems with shorter periods among the older binaries if orbital periods decrease during evolution."
 However. it should. not be forgotten that the binaries in our sample are all detached systems.," However, it should not be forgotten that the binaries in our sample are all detached systems."
 Apparently. the period decrease and radius increase in the evolution changed those short period systems into contact or semi contact form. thus they are no longer in our sample anc we see their number," Apparently, the period decrease and radius increase in the evolution changed those short period systems into contact or semi contact form, thus they are no longer in our sample and we see their number"
all cases. (he mean eccentricity is zero initially because of the cireular shape of the field loops.,"all cases, the mean eccentricity is zero initially because of the circular shape of the field loops."
 Later in the evolution. large /2 cases tend to evolve into a state of large eccentricity in the steady state.," Later in the evolution, large $R$ cases tend to evolve into a state of large eccentricity in the steady state."
 This is caused by a rapid expansion of the interface induced by the strong elobal field., This is caused by a rapid expansion of the interface induced by the strong global field.
 In short. large 72 induces more distorted local fiekd loops and less tangled total field due to fast interlace expansion. while small f? values results in less eccentric local field loops but will more tangled total field and strong magnetic reconnection.," In short, large $R$ induces more distorted local field loops and less tangled total field due to fast interface expansion, while small $R$ values results in less eccentric local field loops but with more tangled total field and strong magnetic reconnection."
 To compute the estimated heat transfer rate in the simulation. we caleulate the averaged slope of the curve plotted in Figure 7((b). and compare it to the analvtie model in Section 4.," To compute the estimated heat transfer rate in the simulation, we calculate the averaged slope of the curve plotted in Figure \ref{fig07}( (b), and compare it to the analytic model in Section 4."
 Although the equilibration rate represented by the slope of the curves in Figure T((b) is changing throughout the evolution. an early phase of the evolution can be chosen when the field configuration has not been modified significantly lor which we can then comptute the averaged heat. Gansfer rate.," Although the equilibration rate represented by the slope of the curves in Figure \ref{fig07}( (b) is changing throughout the evolution, an early phase of the evolution can be chosen when the field configuration has not been modified significantly for which we can then comptute the averaged heat transfer rate."
 By normalizing the resulting heat. (ransler rate (o the isotropic value. we can determine the heat (rausler efficiency. for. different maegnelic structures.," By normalizing the resulting heat transfer rate to the isotropic value, we can determine the heat transfer efficiency for different magnetic structures."
 From Figure 10.. we can see (hat the analvtic prediction and the simulation resulis agree quite well except [or the situation when Ais below 0.2.," From Figure \ref{fig10}, we can see that the analytic prediction and the simulation results agree quite well except for the situation when $R$ is below $0.2$."
 The simulation result does not converge to point. (0.0) but ends at an intercept on the y axis.," The simulation result does not converge to point (0,0) but ends at an intercept on the $y$ axis."
 This intercept indicates Chat even if there are initially. negligibly [few channels for energy transfer. (he magnetic reconnection can open up channels aud allow heat transfer.," This intercept indicates that even if there are initially negligibly few channels for energy transfer, the magnetic reconnection can open up channels and allow heat transfer."
 Ex.(19) is valid for predicting the cooling rate of the hot material throughout Che early phase of the heat equilibration process., Eq.(19) is valid for predicting the cooling rate of the hot material throughout the early phase of the heat equilibration process.
 It also provides insight on the strength of the local field in the vicinity of the interface once we know the cooling rate and global magnetic field strength., It also provides insight on the strength of the local field in the vicinity of the interface once we know the cooling rate and global magnetic field strength.
 To summarize our results we find first that the average heat [Iux at the end of our simulations is lower (han at the beginning for all R values., To summarize our results we find first that the average heat flux at the end of our simulations is lower than at the beginning for all $R$ values.
 Thus we see an approach to, Thus we see an approach to
computed usine the Eiseustein IIu (1999) transfer function.,computed using the Eisenstein Hu (1999) transfer function.
" Iu both ruus. as iu our previous work Scammapicco. Thacker. Davis 2001). simulations were conducted with ao parallel OpenMDP based nuplemieutatioun of the ""UHYDRA'"" code (Thacker Couchinau 2006) that uses the Adaptive Particle-Particle. Particle-Alesh aleorithuu to calculate eravitational forces (Couchinan 1991). and the smooth particle lvdrocdwuamic (SPILT) method to calculate gas forces (Lucy 1977: Gingold Monaghlau 19:7)."," In both runs, as in our previous work Scannapieco, Thacker, Davis 2001), simulations were conducted with a parallel OpenMP based implementation of the “HYDRA” code (Thacker Couchman 2006) that uses the Adaptive Particle-Particle, Particle-Mesh algorithm to calculate gravitational forces (Couchman 1991), and the smooth particle hydrodynamic (SPH) method to calculate gas forces (Lucy 1977; Gingold Monaghan 1977)."
 As the details of this code aud our outflow Huplementation are described in detail elsewhere (Scannapieco. Thacker. Davis 2001: TSC06) here we ouly sununiarize the aspects most relevant to the SZ effect.," As the details of this code and our outflow implementation are described in detail elsewhere (Scannapieco, Thacker, Davis 2001; TSC06) here we only summarize the aspects most relevant to the SZ effect."
 Om study is tareeted to relatively large aud late ornüue structures. and for both ruus we have kept the netallicity coustaut at Z=0.05. to mimic a moclerate evel of eurichment.," Our study is targeted to relatively large and late forming structures, and for both runs we have kept the metallicity constant at $Z=0.05$, to mimic a moderate level of enrichment."
 Stmilark. because the epoch of reionization is poorly known aud because reionization has ittle impact ou mass scales exeater than LO? (Barkana. Loel 1999). we did not imeclide a photoionization background iu either simulation.," Similarly, because the epoch of reionization is poorly known and because reionization has little impact on mass scales greater than $10^{9}$ (Barkana, Loeb 1999), we did not include a photoionization background in either simulation."
 In our ACN feedhack run. which was designed to cover a aree range in the ACN luminosity function. we used a siumlation box of size 1165.+ Mpe filled with 2<610° articles. which corresponded to a dark-imatter particle nass of 1.9«LOSAL.. and a gas particle mass of 2.7.s10 A£... Our comparison simmlation. which was carried out purely for the purposes of the current study. used 320° particles in à box 73h|! comoving Mpe ou a side. correspouding to the same particle masses as in the ACN run.," In our AGN feedback run, which was designed to cover a large range in the AGN luminosity function, we used a simulation box of size $146 h^{-1}$ Mpc filled with $2\times
640^3$ particles, which corresponded to a dark-matter particle mass of $1.9
\times 10^{8} \msun$ and a gas particle mass of $2.7 \times 10^{7} \msun.$ Our comparison simulation, which was carried out purely for the purposes of the current study, used $320^3$ particles in a box $73 h^{-1}$ comoving Mpc on a side, corresponding to the same particle masses as in the AGN run."
 Both runs were terminated at 2=1.2. at which poit integration was beconuug expensive due to the sinele-stepping nature of the ντα code. and imupracticeal in à shared queue cuviroument.," Both runs were terminated at $z = 1.2$, at which point integration was becoming expensive due to the single-stepping nature of the Hydra code, and impractical in a shared queue environment."
 This means that our results do not coutain the SZ contribution from lower redshifts. during which most galaxw clusters are formed.," This means that our results do not contain the SZ contribution from lower redshifts, during which most galaxy clusters are formed."
 Tlowever. as :=1.2 is well past the peak epoch of AGN activity UUeda 2003: Barecr 2005). our results should do well at quantitving the ACN contribution to the SZ effect. which is our main cus here.," However, as $z=1.2$ is well past the peak epoch of AGN activity Ueda 2003; Barger 2005), our results should do well at quantifying the AGN contribution to the SZ effect, which is our main focus here."
" As in Τος bright quasar-phase ACN are associated with galaxy 060,mergers. which are tracked by labeling gas articles aud ideutifvine new eroups in which at least of the accreted mass does uot come from a sinele nassive progenitor."," As in TSC06, bright quasar-phase AGN are associated with galaxy mergers, which are tracked by labeling gas particles and identifying new groups in which at least of the accreted mass does not come from a single massive progenitor."
 Όπου a imerecr has been identified. we compute the mass of the associated supermassive lack hole. Afpy. from the circular velocity of the remnant. ος using the observed Afpyος relation (Merit Forrarese 2001: Tremaie 2001: Forrarese 2002) which gives = 2.8 4105 (4," Once a merger has been identified, we compute the mass of the associated supermassive black hole, $M_{\rm BH},$ from the circular velocity of the remnant, $v_{\rm c}$ using the observed $M_{\rm BH}- v_{\rm c}$ relation (Merrit Ferrarese 2001; Tremaine 2001; Ferrarese 2002) which gives = 2.8 10^8 ( )^5."
" Ogre eods estimated as = Gp, (n2)2(2Qywhere Gis the eyavitational coustaut. p(t) is the virial density as a function of redshift. and 5 is the implied virial radius for a group of No eas particles with mass my "," Here $v_{\rm c}$ is estimated as = G ^2,where $G$ is the gravitational constant, $\rho_{\rm v}(z)$ is the virial density as a function of redshift, and $r_{\rm v}$ is the implied virial radius for a group of $N$ gas particles with mass $m_{\rm g}$."
"Following ντο Loeb (2002) aud Scaunapieco Oh (2001). we assume that for cach merecr the accreting black hole shines at its Eddineton Iuninosity (1.2«107 ores 1 AL,lj for a time takeu to be a fixed fraction of the dvuamical time of the system. ty=(σος=Ds«107006)V?IT) 1."," Following Wyithe Loeb (2002) and Scannapieco Oh (2004), we assume that for each merger the accreting black hole shines at its Eddington luminosity $1.2 \times 10^{38}$ ergs $^{-1}$ $\msun^{-1}$ ) for a time taken to be a fixed fraction of the dynamical time of the system, $t_{\rm d} = 0.055 r_{\rm v}/v_{\rm c} =
 5.8 \times 10^{-3} \Omega(z)^{-1/2} H(z)^{-1}$ ."
 In TSCOG it was demonstrated that. apart from a discrepancy for the very Iuninous eud. this simple model does extremely well at reproducing the observed ACN hunuinositv functiou as well as the laree and simall-scale clustering of AGN over the full range of sinmlated redshifts.," In TSC06 it was demonstrated that, apart from a discrepancy for the very luminous end, this simple model does extremely well at reproducing the observed AGN luminosity function as well as the large and small-scale clustering of AGN over the full range of simulated redshifts."
 Furthermore. the discrepancy at the verv luminous eud for the «λαΊο as compared to the semi-analytic model could be attributed to the relative cficicucy of shock heating ou substructure (e.g. see Agertz 2006 for a discussiou of nunierical “stripping” issues).," Furthermore, the discrepancy at the very luminous end for the simulation as compared to the semi-analytic model could be attributed to the relative efficiency of shock heating on substructure (e.g. see Agertz 2006 for a discussion of numerical ""stripping"" issues)."
" Note that while our approach does uot distiuguish between ACN formed. in eas-rich ""wet"" merecrs and saspoor Udrv inorgers. uulike at lower redshift Bell 2006). dry mergers are likely to be relatively unimportant at the :>1.2 redshifts we are studyviug."," Note that while our approach does not distinguish between AGN formed in gas-rich “wet” mergers and gas-poor “dry” mergers, unlike at lower redshift Bell 2006), dry mergers are likely to be relatively unimportant at the $z \ge 1.2$ redshifts we are studying."
 Tn our fiducial rui. we also assume that a fixed fraction ες=0.05 of the bolometric cucrey of cach ACN is channeled iuto a kinetic outflow.," In our fiducial run, we also assume that a fixed fraction $\epsilon_{\rm k} =0.05$ of the bolometric energy of each AGN is channeled into a kinetic outflow."
 This value is consistent with other literature estimates Furlanctto Loch 2001: Nath Rovchowdhury 2002). as well as obscrvatious (Chartas 2007).," This value is consistent with other literature estimates Furlanetto Loeb 2001; Nath Roychowdhury 2002), as well as observations (Chartas 2007)."
 Each outflow is then launched with au cucrey input of —6 | )erg., Each outflow is then launched with an energy input of =6 ) ).
" Civen the uncertainties surrounding AGN outflows. we simply model cach expanding outflow as a splerical shell at a radius 254. which is coustructed by rearranging all the eas within this radius. but outside r4. and below a deusity threshold of 2.5... Finall. the radial velocity e. and temperature Z4, of the shell are determuncecd by fiàug the postshock temperature. Ti. to be T,=13.640|e,(issnp and choosing ce; such that the sium of the thermal aud kinetic energv of the shell equals Ly munus the eucrev used to move particles from their initial positions iuto the shell."," Given the uncertainties surrounding AGN outflows, we simply model each expanding outflow as a spherical shell at a radius $2r_{\rm v}$ which is constructed by rearranging all the gas within this radius, but outside $r_{\rm v},$ and below a density threshold of $2.5\rho_{\rm v}.$ Finally, the radial velocity $v_s$ and temperature $T_s$ of the shell are determined by fixing the postshock temperature, $T_s$, to be $T_s = 13.6
K [v_s/({\rm km} {\rm s}^{-1})]^2$ and choosing $v_s$ such that the sum of the thermal and kinetic energy of the shell equals $E_{\rm k}$ minus the energy used to move particles from their initial positions into the shell."
 As shown in TSC'O06. this prescription results in a level of preheating iu galaxy clusters and eroups that is in good aegrecient with observations.," As shown in TSC06, this prescription results in a level of preheating in galaxy clusters and groups that is in good agreement with observations."
 In Fieure 1.. we show the imass-averaged eas telperatize in our ACN feedback aud comparison runs.," In Figure \ref{fig:norm}, we show the mass-averaged gas temperature in our AGN feedback and comparison runs."
 The preseuce of outflows has a substantial impact ou the IGAL raising the mean gas temperature in the station by z 50%.," The presence of outflows has a substantial impact on the IGM, raising the mean gas temperature in the simulation by $\approx 50 \%$ ."
 Furthermore. as discussed iu TSCOG. most of this heating is targeted toward the densest regions. exactly those that contribute most to the SZ," Furthermore, as discussed in TSC06, most of this heating is targeted toward the densest regions, exactly those that contribute most to the SZ"
"where Ay,=αμαdr)) is the mixing length. αμ being a constant of order unity. (OT/àr),=Vaal(dnP/dr). and the subscript P? denotes evaluation at constant pressure.","where $\Lambda_{\rm ml}=|\alpha_{ml}P/(dP/d r)|$ is the mixing length, $\alpha_{ml}$ being a constant of order unity, $\left(
\partial T/\partial r \right)_{s} = \nabla_{\rm ad} T \left( d \ln
P / d r \right)$, and the subscript $P$ denotes evaluation at constant pressure."
 The different thermodynamic parameters needed in the above equation are given by Chabrier et al. (, The different thermodynamic parameters needed in the above equation are given by Chabrier et al. (
1992). and we fix a41.,"1992), and we fix $\alpha_{\rm ml}=1$."
 We have (o solve the above equations lor the three variables P. M. and FT as a function of r.," We have to solve the above equations for the three variables $P$ , $M$ and $T$ as a function of $r$."
 Accordingly. we need three boundary. conditions.," Accordingly, we need three boundary conditions."
 Following Bodenheimer Pollack (1986) and Pollack et al. (, Following Bodenheimer Pollack (1986) and Pollack et al. (
1996). we take for the mass density of the core p.=3.2 ο .,"1996), we take for the mass density of the core $\rho_{c} = 3.2$ g $^{-3}$."
" The inner boundary of the atmosphere is equal to the core radius r.. given bv: The first boundary condition is that M(r;)=AL. We denote ray, the outer boundary of the atmosphere. ancl we assume this radius to be lixed."," The inner boundary of the atmosphere is equal to the core radius $r_c$, given by: The first boundary condition is that $M(r_c)=M_{c}.$ We denote $r_{\rm atm}$ the outer boundary of the atmosphere, and we assume this radius to be fixed."
" In the caleulations presented below. we will take ray, to be either a lew core radii or the Roche lobe radius rj. which is assumed to be the same as the Hill radius. and is given by: where « is the orbital radius of the protoplanet aud. AM, is the mass of the central star."," In the calculations presented below, we will take $r_{\rm atm}$ to be either a few core radii or the Roche lobe radius $r_L$, which is assumed to be the same as the Hill radius, and is given by: where $a$ is the orbital radius of the protoplanet and $M_{\star}$ is the mass of the central star."
" Throughout the paper. we take M,=1M... When ram<rp. we assume thal the space above the atmosphere and in the Roche lobe of the protoplanet is filled with a cold accretion How."," Throughout the paper, we take $M_{\star}=1~{\rm M}_{\odot}.$ When $r_{\rm atm} < r_L$, we assume that the space above the atmosphere and in the Roche lobe of the protoplanet is filled with a cold accretion flow."
" Then the temperature 7; and the pressure 7, al the surface 7=ray, Can be approximated by the stancared photospheric conditions (e.g.. IxXippenhahn Weigert 1990. Boclenheimer οἱ al."," Then the temperature $T_s$ and the pressure $P_s$ at the surface $r=r_{\rm atm}$ can be approximated by the standard photospheric conditions (e.g., Kippenhahn Weigert 1990, Bodenheimer et al."
" 2000): where σ is the StefanBoltzmann constant. ancl: where &,;=#(ps.T) and py is the mass density al r=Pain."," 2000): where $\sigma$ is the Stefan–Boltzmann constant, and: where $\kappa_s = \kappa \left( \rho_s, T_s \right)$ and $\rho_s$ is the mass density at $r=r_{\rm atm}$."
 Silay boundary conditions have beenused by Palla Stabler (1992) for computing (he evolution ofa protostar accreting from a dise., Similar boundary conditions have beenused by Palla Stahler (1992) for computing the evolution ofa protostar accreting from a disc.
 The validity of these boundary. conditions will be discussed in section 3.1.., The validity of these boundary conditions will be discussed in section \ref{sec:accretion}. .
The ouset of collisional erosion is determined by the value of the material parameter οὖν,The onset of collisional erosion is determined by the value of the material parameter $c^*$.
 With e=1.9 aud he initial mass ratios in typical N-body simulations. erosion begins with impact velocities of about 2 to 3 nues the mutual escape velocity for head-on collisious and imereases with impact parameter (Fieure 1))," With $c^*=1.9$ and the initial mass ratios in typical $N$ -body simulations, erosion begins with impact velocities of about 2 to 3 times the mutual escape velocity for head-on collisions and increases with impact parameter (Figure \ref{fig:collmap}) )."
 For collisions between sinibulv sized bodies. the transition οσοι accretion and catastrophic disruptiou occurs over a very sinall range in impact velocity.," For collisions between similarly sized bodies, the transition between accretion and catastrophic disruption occurs over a very small range in impact velocity."
" For example. he critical impact velocities required to beein croding and to catastrophically disrupt au embryo by a body ια its mass are oulv 2.01525 and 2.510. at b=0. respectively,"," For example, the critical impact velocities required to begin eroding and to catastrophically disrupt an embryo by a body half its mass are only $2.0V_{\rm esc}$ and $2.5V_{\rm esc}$ at $b=0$, respectively."
 As the mass ratio becomes more extrene. he impact velocities required to reach catastrophic isruption increase sienificauth.," As the mass ratio becomes more extreme, the impact velocities required to reach catastrophic disruption increase significantly."
 In Figure LAA. erosion iens at 2.5. and disruption at 5.9. for a uass ratio of 1:10.," In Figure \ref{fig:collmap}A A, erosion begins at $2.5V_{\rm esc}$ and disruption at $5.9V_{\rm esc}$ for a mass ratio of 1:10."
 For the 1:10 amass ratio shown oei Fiewre LBB. the disruption of an enmbrvo by a auetesimnal would require an imipact velocity of at least 18V.," For the 1:40 mass ratio shown in Figure \ref{fig:collmap}B B, the disruption of an embryo by a planetesimal would require an impact velocity of at least $18V_{\rm
 esc}$."
 The contours of constaut largest remnant have a ifferent shape for the reverse impact in the hit-aud-run reeiue compared to the forward scenario., The contours of constant largest remnant have a different shape for the reverse impact in the hit-and-run regime compared to the forward scenario.
" For iupact parameters near bei, aud MQj/M,zxü.l. the interacting mass of the target is approximately equal to the projectile mass."," For impact parameters near $b_{\rm crit}$ and $M_{\rm
 p}/M_{\rm t} \le 0.1$, the interacting mass of the target is approximately equal to the projectile mass."
 As the impact anele increases. the reverse projectile-to-tarect nass ratio decreases.," As the impact angle increases, the reverse projectile-to-target mass ratio decreases."
 euce. the total interacting mass in the reverse ipact decreases with increasing nÓupact anele.," Hence, the total interacting mass in the reverse impact decreases with increasing impact angle."
 The velocity coutours 'rrespond to coustant remnant mass divided by total interacting mass., The velocity contours correspond to constant remnant mass divided by total interacting mass.
 The changing total nass aud mass ratio leads to the intersection of the catastrophic disruption contour (blue dot-dashed lunes in Figure 1)) aud onset of projectile erosion contour (blue dotted Hues} near bog aud divergence at larger inupact augles., The changing total mass and mass ratio leads to the intersection of the catastrophic disruption contour (blue dot-dashed lines in Figure \ref{fig:collmap}) ) and onset of projectile erosion contour (blue dotted lines) near $b_{\rm crit}$ and divergence at larger impact angles.
 Puthermore. there is a ΗΠΑ in the projectile erosion coutour at an οπα interacting mass fraction from the target.," Futhermore, there is a minimum in the projectile erosion contour at an optimum interacting mass fraction from the target."
 We exanmuned the colliious in two receut AN -bacly studies of the late stages of terrestrial planct formation., We examined the collisions in two recent $N$ -body studies of the late stages of terrestrial planet formation.
 xforiued 8 suimaulations of terrestrial planet formation beeimuing with 25 Mars-inass clubrvos and an equal mass of material iu a population of 1000 0.00233-A/ear plauetesimals ina zone from 0.3 to LAU., performed 8 simulations of terrestrial planet formation beginning with 25 Mars-mass embryos and an equal mass of material in a population of 1000 $M_{\rm Earth}$ planetesimals in a zone from 0.3 to 4 AU.
" performed 10 simulations beeiuniug with 85-90 planetary enmibrvos (0.005 to 0.1 Merah} and 1000 or 2000 AM, planuctesimals between 0.5 and £5 AU.", performed 40 simulations beginning with 85-90 planetary embryos (0.005 to 0.1 $M_{\rm Earth}$ ) and 1000 or 2000 $M_{\rm Earth}$ planetesimals between 0.5 and 4.5 AU.
 The beginning stage of cach study. approximates the end of oligarchic growth and the onset of stochastic erowth., The beginning stage of each study approximates the end of oligarchic growth and the onset of stochastic growth.
 When the total mass in planetary enübryos is equal to the total mass in smaller planctesimals. viscous stirring by the embryos caunot be damped by dvinuuical yiction from the planctesimals. which marks the eud of oligarchic growth2001).," When the total mass in planetary embryos is equal to the total mass in smaller planetesimals, viscous stirring by the embryos cannot be damped by dynamical friction from the planetesimals, which marks the end of oligarchic growth."
. It was assumed that the nebular gas had aissipated aud Jupiter aud Saturn were fully formed at re start of the simulations., It was assumed that the nebular gas had dissipated and Jupiter and Saturn were fully formed at the start of the simulations.
 The orbital configurations of Jupiter and Saturu were varied over a plausible range to consider their influence on the final state of auets in the terrestrial zone., The orbital configurations of Jupiter and Saturn were varied over a plausible range to consider their influence on the final state of planets in the terrestrial zone.
 Not all cases result iu errestrial plaucts m agreement with our Solar Syste: moreover. the dynamical historv of the eiat planets in our Solar System is still an active area of research with new ideas that have not vet been incorporated into detailed accretion studies of the terrestrial planets2010).," Not all cases result in terrestrial planets in agreement with our Solar System; moreover, the dynamical history of the giant planets in our Solar System is still an active area of research with new ideas that have not yet been incorporated into detailed accretion studies of the terrestrial planets."
". Ποσο, the set of simulations are representative of the eeneral αναος of terrestrial planet erowth in the presence of two outer gas ejaut plaucts."," Hence, the set of simulations are representative of the general dynamics of terrestrial planet growth in the presence of two outer gas giant planets."
 The study by used the SvAIBA N-hody code1998). aud. used the Mercury N-body code1999).," The study by used the SyMBA $N$ -body code, and used the Mercury $N$ -body code."
. Both codes are similar svuuplectic iteerators that calculate close encounters between planetary bodies., Both codes are similar symplectic integrators that calculate close encounters between planetary bodies.
 For every collision. the two bodies were merged aud linear momentum was conserved.," For every collision, the two bodies were merged and linear momentum was conserved."
 Iu these simulations. the embrvos eravitationally interacted with all other bodies.," In these simulations, the embryos gravitationally interacted with all other bodies."
 The gravitational influence of planetesinials upon clubrvos was calculated: however. planctesimals did not influence other planctesimals aud could not collide ith each other.," The gravitational influence of planetesimals upon embryos was calculated; however, planetesimals did not influence other planetesimals and could not collide with each other."
 In this work. we preseut a retrospective analysis of the sinnuulations to assess the range of true collision outcomes during the eud stage of terrestrial planet formation.," In this work, we present a retrospective analysis of the simulations to assess the range of true collision outcomes during the end stage of terrestrial planet formation."
 We divided the collision outcomes from the N-body studies iuto three groups. described iu Table 1..," We divided the collision outcomes from the $N$ -body studies into three groups, described in Table \ref{tab:outcomes}. ."
" Group l consists of all collisions leading to the erowth of 15 planets with final masses of O71 to 1.58 Mg, frou 8 different simulations iu(20063.", Group 1 consists of all collisions leading to the growth of 15 planets with final masses of 0.74 to 1.58 $M_{\rm Earth}$ from 8 different simulations in.
.. These 15 plauets were also studied by o investigate the evolution of the hafiun-tuugsteu isotopic svsteni curing plauet erowth., These 15 planets were also studied by to investigate the evolution of the hafnium-tungsten isotopic system during planet growth.
" Group 2 includes all collisious leading to the growth of 52 planets with fual misses between 0.70 and 1.15 Ag, from LO simulations by(2009).", Group 2 includes all collisions leading to the growth of 52 planets with final masses between 0.70 and 1.45 $M_{\rm Earth}$ from 40 simulations by.
. Group 3 considers oulv the eiaut impacts onto all 161 planets from the 10 siauulations imo(2009)., Group 3 considers only the giant impacts onto all 161 planets from the 40 simulations in.
. Cüant impacts are defiued as collisions between plauctary cubrvos., Giant impacts are defined as collisions between planetary embryos.
 A final planet expericuces at least one giant collision: hence. eroup 3 excludes surviving enibrvos that ouly accrete planctesimals (26 cuibrvos survived without a eiut mipact in LO snimlations).," A final planet experiences at least one giant collision; hence, group 3 excludes surviving embryos that only accrete planetesimals (26 embryos survived without a giant impact in 40 simulations)."
 Iu cach case. the simulation collision parameters were used to calculate the outcome based on our analytic model.," In each case, the simulation collision parameters were used to calculate the outcome based on our analytic model."
 The outcome depends ou the mass ratio of the two bodies. the impact angle. the impact velocity normalized to the autual escape velocity. and the catastrophic disruption criteria.," The outcome depends on the mass ratio of the two bodies, the impact angle, the impact velocity normalized to the mutual escape velocity, and the catastrophic disruption criteria."
 Here. we used values of &=1.9 and f=0.36 to calculate the catastrophic disruption criteria. which are appropriate for strenethless plauets as we asstuued that the planets are hot aud possibly partially molten during the late stage of planet formation.," Here, we used values of $c^*=1.9$ and $\bar \mu=0.36$ to calculate the catastrophic disruption criteria, which are appropriate for strengthless planets as we assumed that the planets are hot and possibly partially molten during the late stage of planet formation."
 There were a total of 1207 collisious by plauetesimials and embryos during the erowth of the 15 planets iu group 1l., There were a total of 1207 collisions by planetesimals and embryos during the growth of the 15 planets in group 1.
 Of these. 1110 collisions were bv planctesimals.," Of these, 1140 collisions were by planetesimals."
 The analytic model predicts that the majority of planctesimal collisions will lead to partial accretion (73%))., The analytic model predicts that the majority of planetesimal collisions will lead to partial accretion ).
 The donunance of accretionary events is foremost a reflection of the impact velocity distribution. which is peaked between Laud 2V.. (Figure 2A A).," The dominance of accretionary events is foremost a reflection of the impact velocity distribution, which is peaked between 1 and $2V_{\rm esc}$ (Figure \ref{fig:vimpact}A A)."
 Note that oulv half, Note that only half
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) ," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ "
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) ," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ $"
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) R," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ $R"
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) R," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ $R_"
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) Ry," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ $R_s"
 2=5.8 of :=6 ACDM (O4.09.01)(0.7.0.26.0.00. fy=70kaus|. Nu AR. ap T=10'R. (uj) Ry. ἐςx10) Ry.," $z=5.8$ $z\ge 6$ $\Lambda$ $(\Omega_\Lambda,\Omega_0,\Omega_{\rm b})=(0.7,0.26,0.04)$ $H_0=70~{\rm km~s^{-1}}$ $\dot N_{ph}$ $R_s$ $\alpha_B$ $T=10^4$ $\langle n_H^2 \rangle$ $R_s$ $z\lsim 10$ $R_s$"
asymmetries due to the ISM should be roughly independent of the source size if the density profile doesn’t lead to a large change in vz.,asymmetries due to the ISM should be roughly independent of the source size if the density profile doesn't lead to a large change in $v_h$.
" We have compared this to the observed asymmetries in radio galaxies, using the 3CRR sources with with FR II morphology and z<1 from ? for a ACDM cosmology with Q4=0.7, Qm=0.3 and h=0.7."," We have compared this to the observed asymmetries in radio galaxies, using the 3CRR sources with with FR II morphology and $z < 1$ from \citet{Mullin+2008} for a $\Lambda$ CDM cosmology with $\Omega_\Lambda = 0.7$, $\Omega_\text{m} = 0.3$ and $h = 0.7$."
" Of these, only sources with clearly identified hotspots on opposite sides are considered (88 sources) and projection effects are not accounted for here (differences should be less than 50 per cent for most radio galaxies)."," Of these, only sources with clearly identified hotspots on opposite sides are considered (88 sources) and projection effects are not accounted for here (differences should be less than 50 per cent for most radio galaxies)."
" Although the relative asymmetries (with respect to the total source size) decrease for larger sources (?),, the absolute arm length asymmetries increase much."," Although the relative asymmetries (with respect to the total source size) decrease for larger sources \citep{ArshakianLongair2000}, the absolute arm length asymmetries increase much."
" For the smaller sources (sum of LLS <100 kpc, 20 sources), however, the scatter does not vary strongly with size and we argue that asymmetries caused by a clumpy ISM cannot be larger than the scatter seen on these scales (mostly between 0 and ~10 kpc)."," For the smaller sources (sum of LLS $\le 100$ kpc, 20 sources), however, the scatter does not vary strongly with size and we argue that asymmetries caused by a clumpy ISM cannot be larger than the scatter seen on these scales (mostly between $0$ and $\sim 10$ kpc)."
" The corresponding percentiles are 7.6 kpc (50 per cent), 10.2 kpc (75 per cent) and 11.8 kpc (90 per cent)."," The corresponding percentiles are $7.6$ kpc (50 per cent), $10.2$ kpc (75 per cent) and $11.8$ kpc (90 per cent)."
" Based on a fiducial jet propagation speed of 0.05c, the corresponding percentiles for the propagation delay are 0.50, 0.66 and 0.77 Myr."," Based on a fiducial jet propagation speed of $0.05 \; c$, the corresponding percentiles for the propagation delay are $0.50$, $0.66$ and $0.77$ Myr."
" Comparison of these values with our Monte Carlo runs now rises on the question, how typical situations as in our hydrodynamical simulation with asymmetries larger than expected are."," Comparison of these values with our Monte Carlo runs now rises on the question, how typical situations as in our hydrodynamical simulation with asymmetries larger than expected are."
" If this is the rather typical case, and actual asymmetries may be factors of a few larger than the 1D estimates, the observed typical asymmetries could be described by asymmetries in the Monte Carlo runs of 0.1-0.2 Myr, suggesting disc densities are a factor of >10 smaller than in our chosen set of parameters (with other combinations of parameters possible, or course)."," If this is the rather typical case, and actual asymmetries may be factors of a few larger than the 1D estimates, the observed typical asymmetries could be described by asymmetries in the Monte Carlo runs of $0.1$ $0.2$ Myr, suggesting disc densities are a factor of $>10$ smaller than in our chosen set of parameters (with other combinations of parameters possible, or course)."
" Although a more detailed comparison with observed data is beyond the scope of this paper, the corresponding masses for a dense clumpy medium of 10° to 10'°Mo may be compatible with actually measured gas masses (ase.g.in??).."," Although a more detailed comparison with observed data is beyond the scope of this paper, the corresponding masses for a dense clumpy medium of $10^9$ to $10^{10}
M_\odot$ may be compatible with actually measured gas masses \citep[as e.g.
in][]{Catinella+2010,Emonts+2010}."
" However, if the asymmetric clearing of the central region by the initial blastwave and clumps remaining in the jet’s path are rather rare, the observed asymmetries require disc densities almost as high as in our hydrodynamical setup even for the local universe, with total masses of 101?M5 and more."," However, if the asymmetric clearing of the central region by the initial blastwave and clumps remaining in the jet's path are rather rare, the observed asymmetries require disc densities almost as high as in our hydrodynamical setup even for the local universe, with total masses of $10^{10} M_\odot$ and more."
" To us, the first case seems more probable since the asymmetric blastwave simply is caused by the asymmetric initial density and hence no exceptional behaviour."," To us, the first case seems more probable since the asymmetric blastwave simply is caused by the asymmetric initial density and hence no exceptional behaviour."
" While the asymmetries of small radio sources (below 100 kpc) may be explained by a clumpy ISM, this is not true for the larger sources with larger absolute length asymmetries."," While the asymmetries of small radio sources (below 100 kpc) may be explained by a clumpy ISM, this is not true for the larger sources with larger absolute length asymmetries."
" Although propagation of delayed jets through a declining density profile can result in increasing absolute asymmetries, it is hardly possible that they grow by a factor of 10 or more."," Although propagation of delayed jets through a declining density profile can result in increasing absolute asymmetries, it is hardly possible that they grow by a factor of 10 or more."
 These large sources might actually become more asymmetric by a strongly asymmetric ambient density profile at large scales (?) or due to an unstable jet propagation on one side possibly caused by instabilies or obstructing clumps in one jet., These large sources might actually become more asymmetric by a strongly asymmetric ambient density profile at large scales \citep{Jeyakumar+2005} or due to an unstable jet propagation on one side possibly caused by instabilies or obstructing clumps in one jet.
" For the largest sources with large propagation speeds caused by a very low density environment, light travel time effects may actually play a significant role even if it doesn't for the smaller sources."," For the largest sources with large propagation speeds caused by a very low density environment, light travel time effects may actually play a significant role even if it doesn't for the smaller sources."
" ? have found that in almost all cases of their sample, that the extended optical line emission in [OII] is brightest on the side of the shorter lobe, indicating that environmental effects cause the length asymmetries in powerful radio sources."," \citet{McCarthy+1991} have found that in almost all cases of their sample, that the extended optical line emission in [OII] is brightest on the side of the shorter lobe, indicating that environmental effects cause the length asymmetries in powerful radio sources."
 Our 3D hydrodynamical simulations are now able to provide theoretical support for this scenario., Our 3D hydrodynamical simulations are now able to provide theoretical support for this scenario.
" Dense clouds or atomic or molecular gas in the ISM are able to restrain a propagating jet for some time due to their large inertia, causing asymmetries in the observed radio source."," Dense clouds or atomic or molecular gas in the ISM are able to restrain a propagating jet for some time due to their large inertia, causing asymmetries in the observed radio source."
" At the same time, the impact of the jet has considerable effects on the clouds themselves: depending on the exact location and cloud properties, they are accelerated, shock-ionized and ablated by the jet's ram pressure and compressed by the high pressure in the jet cocoon."," At the same time, the impact of the jet has considerable effects on the clouds themselves: depending on the exact location and cloud properties, they are accelerated, shock-ionized and ablated by the jet's ram pressure and compressed by the high pressure in the jet cocoon."
 Cooling by line emission stabilizes them additionally (cf.?) and results in bright emission at the location of the strongest interaction with the jet., Cooling by line emission stabilizes them additionally \citep[cf.][]{Mellema+2002} and results in bright emission at the location of the strongest interaction with the jet.
 Fig., Fig.
 8 shows the density of the group of clumps responsible for the large asymmetry in the simulation and the strongly increased pressure (hence strongest expected shock ionization) at the impact location of the jet on the clumps., \ref{fig:denseclumps} shows the density of the group of clumps responsible for the large asymmetry in the simulation and the strongly increased pressure (hence strongest expected shock ionization) at the impact location of the jet on the clumps.
" The long-term survival of the clouds, however, does not only depend on their direct interaction with the jet and its bow shock, but also on their long exposure to the fast and turbulent cocoon plasma (?),, which may destroy but also create emission line clouds."," The long-term survival of the clouds, however, does not only depend on their direct interaction with the jet and its bow shock, but also on their long exposure to the fast and turbulent cocoon plasma \citep{KrauseAlexander2007}, which may destroy but also create emission line clouds."
" While radio sources in the local universe can grow more easily due to small gas fractions and deposit their energy also at larger distances (e.g. stopping cooling flows), radio galaxies at high redshift can be expected to show considerably more interaction with the gas-rich and clumpy environment and the cold gas phase."," While radio sources in the local universe can grow more easily due to small gas fractions and deposit their energy also at larger distances (e.g. stopping cooling flows), radio galaxies at high redshift can be expected to show considerably more interaction with the gas-rich and clumpy environment and the cold gas phase."
" In fact, the clumpy appearance of high redshift galaxies (7) and clumps formed by Toomre unstable discs in cosmological simulations"," In fact, the clumpy appearance of high redshift galaxies \citep{Elmegreen+2007} and clumps formed by Toomre unstable discs in cosmological simulations"
 AGN accretion dises are less well understood than disces in N-rav. binaries on comparable relative scales. because we do not have σους observational constraints on the origin of eas accreting on to the SMDLI," AGN accretion discs are less well understood than discs in X-ray binaries on comparable relative scales, because we do not have good observational constraints on the origin of gas accreting on to the SMBH."
IL lis becoming the only exception to this as observations improve., is becoming the only exception to this as observations improve.
" In this paper we made an attempt to realistically simulate the outer 0.1 10"" region. of the gas [low on to", In this paper we made an attempt to realistically simulate the outer $\sim 0.1$ $10''$ region of the gas flow on to.
 The resulting gas Low is far more complex than thought earlier. based on studies that. included: non-raciative fast stellar winds from stars either fixed in space or distributed in a sphericallv-svmuimetrie fashion., The resulting gas flow is far more complex than thought earlier based on studies that included non-radiative fast stellar winds from stars either fixed in space or distributed in a spherically-symmetric fashion.
 Phe presence of cool gas in the sub-aresecond region. as found. here. may considerably. complicate the interpretation of observational constraints on the accretion of," The presence of cool gas in the sub-arcsecond region, as found here, may considerably complicate the interpretation of observational constraints on the accretion of."
 representative is the current low luminosity state of.. if the feeding of the inner region is indeed so turbulent and time-variable as our simulation suggests?," representative is the current low luminosity state of, if the feeding of the inner region is indeed so turbulent and time-variable as our simulation suggests?"
 Another aspect of the same issue is that ‘acerction of a cool blob in our simulations is not vet a true acerction event., Another aspect of the same issue is that `accretion' of a cool blob in our simulations is not yet a true accretion event.
 I£ the blob manages to survive in the hot gas and settles to a disc or a ring at sav ~LORS. it may circle Που a long time without being noticed.," If the blob manages to survive in the hot gas and settles to a disc or a ring at say $\sim
10^3 R_{\rm S}$, it may circle for a long time without being noticed."
 Further uncertainty in these results is the interaction between the hot and the cold gas via thermal conduction., Further uncertainty in these results is the interaction between the hot and the cold gas via thermal conduction.
 I£ a cold blob enters the inner region of the hot How. and is evaporated there. how will this alfect the flow there?," If a cold blob enters the inner region of the hot flow, and is evaporated there, how will this affect the flow there?"
 These and other related questions are to be resolved in future work if we want to reach a full uncerstancding of the accretion process on to, These and other related questions are to be resolved in future work if we want to reach a full understanding of the accretion process on to
time for typical jet aud cnviromment parameters.,time for typical jet and environment parameters.
 Au FRIT radio source will therefore influence the evolution of the gas surrounding it far bevoud its own linited life time., An FRII radio source will therefore influence the evolution of the gas surrounding it far beyond its own limited life time.
 It is well known that simulations of the formation of galaxy eroups aud clusters 1- the hierarchical structure formation picture predict gas density distributions with cusppA at the ceutre of the distribution (c.e. Navarro. Frenk White 1995).," It is well known that simulations of the formation of galaxy groups and clusters in the hierarchical structure formation picture predict gas density distributions with cusps at the centre of the distribution (e.g. Navarro, Frenk White 1995)."
 N-rav observationy of the hot eas in clusters reveal flat density profiles at their centres (0.8. Jones FormaὋmt 1981)., X-ray observations of the hot gas in clusters reveal flat density profiles at their centres (e.g. Jones Forman 1984).
 To reconcile the simulations with the observations additional sources of heat i- he cluster centre are invoked such as super nova explosious resulting from carly sta oration in the cluster progenitors., To reconcile the simulations with the observations additional sources of heat in the cluster centre are invoked such as super nova explosions resulting from early star formation in the cluster progenitors.
 However. the energy of may super novae is need o flatten the density profiles in simulations and these super novae would produce hig[um values for the metalicity in the gas of galaxy eroups aud clusters which is not observed (Pomman in this volume).," However, the energy of many super novae is needed to flatten the density profiles in simulations and these super novae would produce high values for the metalicity in the gas of galaxy groups and clusters which is not observed (Ponman in this volume)."
 The enonuous amount of mechanical euergyv transtered by he jets in FRIT radio sources to the ICAL may explain the observed fattening towards he centre of the density distribution in these objects without producing any additional netalicitv., The enormous amount of mechanical energy transfered by the jets in FRII radio sources to the IGM may explain the observed flattening towards the centre of the density distribution in these objects without producing any additional metalicity.
 We have preseuted models for the intrinsic and cosmological evolutiou of radio galaxies of type FRIT., We have presented models for the intrinsic and cosmological evolution of radio galaxies of type FRII.
 The observed decrease of the wean linear size of these objects with increasing redshift is explained by two possible scenarios., The observed decrease of the mean linear size of these objects with increasing redshift is explained by two possible scenarios.
 Either the life time of sources depeuds on their jet power or the eas in the environments of sources with more powerful jets is deuser., Either the life time of sources depends on their jet power or the gas in the environments of sources with more powerful jets is denser.
 The second explanation coufirius observational results that ERIT radio sources seein to be located in rieher euvironmneuts at lieher redshift., The second explanation confirms observational results that FRII radio sources seem to be located in richer environments at higher redshift.
 This miplies that super nassive black holes iu galaxw clusters in the local universe must be starved of fuel jecause although they must exist. they do not produce powerful radio sources.," This implies that super massive black holes in galaxy clusters in the local universe must be starved of fuel because although they must exist, they do not produce powerful radio sources."
 We have also investigated the properties of the flow of shocked. gas of the ICM )tween the bow shock aud the cocoon of ΕΠΗ sources., We have also investigated the properties of the flow of shocked gas of the IGM between the bow shock and the cocoon of FRII sources.
 We have shown that the ieating of this material bv the bow shock leads to au cuhanced enmissiou. of. N-ravs., We have shown that the heating of this material by the bow shock leads to an enhanced emission of X-rays.
 The resulting distribution of the N-ray surface brightuess iu the flow reflects the density xofile of the material external to the radio source., The resulting distribution of the X-ray surface brightness in the flow reflects the density profile of the material external to the radio source.
 The expansion of powerful radio ealaxies coutributes to the euergv of the ICM iu clusters and eroups of galaxies aud nay coustitute the additional source of heat necessary to reconcile numerical sniulatious of the formation of clusters and eroups with the observed properties of the hot eas iu hese objects., The expansion of powerful radio galaxies contributes to the energy of the IGM in clusters and groups of galaxies and may constitute the additional source of heat necessary to reconcile numerical simulations of the formation of clusters and groups with the observed properties of the hot gas in these objects.
«quadrupole moment Qo is given bv where x and v are the position and velocity of the body. n= x/r.= neve hh=xvv. and J=J/|J| (see. eg. Will(1993))).,"quadrupole moment $Q_2$ is given by where $\bf x$ and $\bf v$ are the position and velocity of the body, ${\bf n} = {\bf x}/r$ , ${\dot r} = {\bf n}\cdot {\bf v}$ , ${\bf h}= {\bf x} \times {\bf v}$, and ${\bf {\hat J}} = {\bf J}/|J|$ (see, eg. \cite{tegp}) )."
 The first line of Eq. (1)), The first line of Eq. \ref{eom}) )
 correspouds to the Sclavarzsclild part of the aetric (at post-Neowtoniui order). the secoud line is the franmie-drageiug effect. and the third lune is the effect of the quadrupole moment (formally a Newtoman-order effect).," corresponds to the Schwarzschild part of the metric (at post-Newtonian order), the second line is the frame-dragging effect, and the third line is the effect of the quadrupole moment (formally a Newtonian-order effect)."
 For an axisvununetre black hole. the sviuumetry axis of the holes quadrupole moment coincides with its rotation axis. given by the unit vector J.," For an axisymmetric black hole, the symmetry axis of the hole's quadrupole moment coincides with its rotation axis, given by the unit vector ${\bf {\hat J}}$."
 The magnitude of the quadrupole moment will be left free., The magnitude of the quadrupole moment will be left free.
 Using standard orbital perturbation theory. we find that the precessions per orbit of the orientation variables are given by where where Aw=|cos/AQ is the precession of oxriceuter relative to the fixed reference direction. and p=etl€?) is the semilatus rectum.," Using standard orbital perturbation theory, we find that the precessions per orbit of the orientation variables are given by where where $\Delta {\varpi} = \Delta \omega + \cos i \,\Delta \Omega$ is the precession of pericenter relative to the fixed reference direction, and $p=a(1-e^2)$ is the semilatus rectum."
" The quantities à and are the polar angles of the black role’s angular momentum vector with respect the star's orbital plane defined by the line of nodes e,,. aud the vector in the orbital plane e, orthogonal oe, aud h."," The quantities $\alpha$ and $\beta$ are the polar angles of the black hole's angular momentum vector with respect the star's orbital plane defined by the line of nodes ${\bf e}_p$, and the vector in the orbital plane ${\bf e}_q$ orthogonal to ${\bf e}_p$ and ${\bf h}$."
 The structure of Eqs. (2b)), The structure of Eqs. \ref{dOmega}) )
 and (20)) can be understood as follows: Eq. (1)), and \ref{di}) ) can be understood as follows: Eq. \ref{eom}) )
" miplies that the orbital angular momentum h precesses according to dh/dt=w«bh. where the orbit-averaged w is given by w=JG,Ao,cosa) the orbit elemieut variations are givou by dijdt=ce, aud sin(dO/dt=w-e,."," implies that the orbital angular momentum ${\bf h}$ precesses according to $d{\bf h}/dt =
\fourvec{\omega} \times {\bf h}$, where the orbit-averaged $\fourvec{\omega}$ is given by $\fourvec{\omega} = {\bf {\hat J}} (A_J - A_{Q_2} \cos \alpha)$; the orbit element variations are given by $di/dt = \fourvec{\omega} \cdot {\bf e}_p$ and $\sin i d\Omega/dt =\fourvec{\omega} \cdot {\bf e}_q$."
 As a consequence. we have the purely ecometric relationship. To ect au idea of the astrometric size of these precessions. we define an angular precession rate amplitude Ó;=(ufDA;/P. where D is the distance to the ealactic center aud DaaSAL? ds the orbital period.," As a consequence, we have the purely geometric relationship, To get an idea of the astrometric size of these precessions, we define an angular precession rate amplitude ${\dot \Theta}_i = (a/D) A_i/P$, where $D$ is the distance to the galactic center and $P=2\pi (a^3/M)^{1/2}$ is the orbital period."
 Using M=3.6s109AL... D=Skpc. we obtain the rates. iu mnicroarcsecouds per vear where we lave assuiued Qo|=Αν.," Using $M=3.6 \times 10^6 \, M_\odot$ , $D = 8 \, {\rm
kpc}$, we obtain the rates, in microarcseconds per year where we have assumed $|Q_2|= M^3 \chi^2$ ."
 The observable precessious will be reduced. somewhat from these raw rates because the orbit must be projected onto the plane of the sky., The observable precessions will be reduced somewhat from these raw rates because the orbit must be projected onto the plane of the sky.
 For example. the coutributious to Af aud sinAO are reduced by a factor sin/: for an orbit in the plane of the skv. the plane precessious are unnieasurable.," For example, the contributions to $\Delta i$ and $\sin i \Delta \Omega$ are reduced by a factor $\sin
i$; for an orbit in the plane of the sky, the plane precessions are unmeasurable."
 Forthe quadrupole precessious to be observable. it is clear that the black hole 118st. have a deceut angular momentum (4> 0.5) aud that the star must be iu a short period hieh-ecceutricitv orit.," For the quadrupole precessions to be observable, it is clear that the black hole must have a decent angular momentum $\chi > 0.5$ ) and that the star must be in a short period high-eccentricity orbit."
 Figures l and 2 show the quautitive requirements. based on these rate aniplitudes.," Figures \ref{fig1} and \ref{fig2} show the quantitive requirements, based on these rate amplitudes."
 Although the pericenter advance is the larecst relativistic orbital effect. it isnet the most suitable effect for testing the uo-hair theorems.," Although the pericenter advance is the largest relativistic orbital effect, it is the most suitable effect for testing the no-hair theorems."
 The fiune-drageme aud quadiupole effects are siuall corrections of the leading Sclavarzschild periceuter precession. aud thus oue would need to know AL. « aud e to sufficient accuracy to be ableto subtract that dominant term to reveal the smaller effects of interest.," The frame-dragging and quadrupole effects are small corrections of the leading Schwarzschild pericenter precession, and thus one would need to know $M$, $a$ and $e$ to sufficient accuracy to be ableto subtract that dominant term to reveal the smaller effects of interest."
 Furthermore. the pericenter advance is affected by a umber ofcomplicating phenomena. ," Furthermore, the pericenter advance is affected by a number ofcomplicating phenomena. ("
G) For such relativistic orbits. Selawarzsclild contributions to thepericeuter precession at the,"i) For such relativistic orbits, Schwarzschild contributions to thepericenter precession at the"
review).,review).
 Since the variability timescale is also Π./2T?. this scenario would miplv a eap timescale comparable to the variability timescale. which is clearly not the case.," Since the variability timescale is also $R_\gamma/2\Gamma^2 c$, this scenario would imply a gap timescale comparable to the variability timescale, which is clearly not the case."
 Alorsouv et al. (, Morsony et al. (
2007) investigated the jet propagation through the star with an elaborate uunuerical simulation and ideutiBed three distinct phases during the evolution. ic. the precursor phase. the shocked jet phase aud the uushocked jet phase.,"2007) investigated the jet propagation through the star with an elaborate numerical simulation and identified three distinct phases during the evolution, i.e. the precursor phase, the shocked jet phase and the unshocked jet phase."
 They find that a high-pressure cocoon. formed as the sub-relativistic jet head makes its wav out of the star. is released when the head of the je reaches the stellar surface (which can produce a precursor. Ramurvez-Ruiz et al.," They find that a high-pressure cocoon, formed as the sub-relativistic jet head makes its way out of the star, is released when the head of the jet reaches the stellar surface (which can produce a precursor, Ramirez-Ruiz et al."
 20025)., 2002b).
 Within the framework of this model. an observer which is located at siuall or modes viewing angeles relative to the jet axis would be expected to see first a relatively bright precursor. tlen a gap plase during which there is little cussion. and finally a bright GRB phase when the uushocked jet reaches the radius of the stellar surface.," Within the framework of this model, an observer which is located at small or modest viewing angles relative to the jet axis would be expected to see first a relatively bright precursor, then a gap phase during which there is little emission, and finally a bright GRB phase when the unshocked jet reaches the radius of the stellar surface."
 Iu 82. we consider first a precursor model such as discussedk above. which is based on the time delays associated with the same jet eiviug rise both to the precursor aud to the main burst event.," In 2, we consider first a precursor model such as discussed above, which is based on the time delays associated with the same jet giving rise both to the precursor and to the main burst event."
 We show that the shocked jet phase could not last much longer than ~10 s. due to the fact that once the jet head reaches the stellar surface. a rarefaction wave will form which propagates back iuto the shocked jet component. cecreasing the pressure in the shocked jet siguificanuth. aud as a result. the jet attains its ultimate relativistic velocity.," We show that the shocked jet phase could not last much longer than $\sim 10$ s, due to the fact that once the jet head reaches the stellar surface, a rarefaction wave will form which propagates back into the shocked jet component, decreasing the pressure in the shocked jet significantly, and as a result, the jet attains its ultimate relativistic velocity."
" Hence. the propagation time taken by the unshocked jet to reach the stellar surface will be Πίος to ~Ryfe. which is ouly from a few seconds to ten seconds for Wolf-Bavet progenitors of long GRBs. where A, is the stellar radius of the progenitor."," Hence, the propagation time taken by the unshocked jet to reach the stellar surface will be limited to $\sim R_{\star}/c$, which is only from a few seconds to ten seconds for Wolf-Rayet progenitors of long GRBs, where $R_{\star}$ is the stellar radius of the progenitor."
 Thus it appears that this model has difficultics in explaining the ~100 s long gaps seen in some GRBs., Thus it appears that this model has difficulties in explaining the $\sim100$ s long gaps seen in some GRBs.
 Iu 83 we then sugeest that eaps hundreds of seconds long could arise in a fallback collapsar scenario. or in a “type II collapsar” scenario (MacFadyen ct al.," In 3 we then suggest that gaps hundreds of seconds long could arise in a fallback collapsar scenario, or in a “type II collapsar” scenario (MacFadyen et al."
 2001). out through the star. xoduces the precursor. while the main burst is produced X a subsequent more energetic jet. fed by accretion of the allback gas.," 2001), out through the star, produces the precursor, while the main burst is produced by a subsequent more energetic jet, fed by accretion of the fallback gas."
 Some possible formation niechanisnis for the precursor jet are considered iu 5., Some possible formation mechanisms for the precursor jet are considered in \ref{sec:jetmech}.
 A sunumary of the results is eiven in ον, A summary of the results is given in \ref{sec:discussion}.
 Iu the collapsar model (Woosley 1993: Paczvisski 1998: MacFacdven Woosley 1999) GRBs are caused hy relativistic jets expelled alone the rotation axis of a collapsing stellar core.," In the collapsar model (Woosley 1993; Paczyńsski 1998; MacFadyen Woosley 1999), GRBs are caused by relativistic jets expelled along the rotation axis of a collapsing stellar core."
 The relativistic jets are duc to a black hole or a neutron star accretion disk. after the iron core of the massive star progenitor has collapsed.," The relativistic jets are due to a black hole or a neutron star accretion disk, after the iron core of the massive star progenitor has collapsed."
 As the jet advances through the star. it drives a bow shock ahead of itself iuto the star. while the ram pressure of the shocked eas aliead of the jet drives a reverse shock into the head of the jet. slowing the jet head down to a sub- velocity.," As the jet advances through the star, it drives a bow shock ahead of itself into the star, while the ram pressure of the shocked gas ahead of the jet drives a reverse shock into the head of the jet, slowing the jet head down to a sub-relativistic velocity."
 Thus there are three distinct regions: 1} Tn frout of the contact discontinuity between the jet aud he stellar gas. there is a thin layer of shocked stellar gas noving ahead with a sub-relativistie velocity ~0j iuto the star: 2) behind the coutact ciscontimuty. there is a shocked jet] region. where the relativistic jet with D;L. is slowed down to a velocity ~ορ by the reverse shock. aud 3) aud low this is the uushocked jet. whose bulk Lorentz factor chaves as if it were a free jet.," Thus there are three distinct regions: 1) In front of the contact discontinuity between the jet and the stellar gas, there is a thin layer of shocked stellar gas moving ahead with a sub-relativistic velocity $\sim v_h$ into the star; 2) behind the contact discontinuity, there is a shocked jet region, where the relativistic jet with $\Gamma_j\gg1$, is slowed down to a velocity $\sim v_h$ by the reverse shock, and 3) and below this is the unshocked jet, whose bulk Lorentz factor behaves as if it were a free jet."
 Du this uushocked jet. at ower radi. the eradual conversion of its internal energv into kinetic energy results iu D;=Pod;/roGa). uutil a saturation radius at which it reaches its asviuptotic value.," In this unshocked jet, at lower radii, the gradual conversion of its internal energy into kinetic energy results in $\Gamma_j=\Gamma_0 (r\theta_{j}/r_0\theta_{0})$ , until a saturation radius at which it reaches its asymptotic value."
 Ileve 0; is the opening angle of the jet at radius r aud Dy aud Jy are. respectively. the initial Lorentz factor aud opening angle at the injection radius ry.," Here $\theta_j$ is the opening angle of the jet at radius $r$ and $\Gamma_0$ and $\theta_0$ are, respectively, the initial Lorentz factor and opening angle at the injection radius $r_0$."
" Let us first consider the scenario in which the precursor is related. to the jet breakout (οι, Raiirez-Riuiz ct al.", Let us first consider the scenario in which the precursor is related to the jet breakout (e.g. Ramirez-Ruiz et al.
 2002a.b: Wasinan 2003: Morsony et al.," 2002a,b; Waxman 2003; Morsony et al."
 2007)., 2007).
 Iu this scenario. the precursor is produced by the bow shock enisson or the cocoon emission when the jet head breaks out of the stellar surface.," In this scenario, the precursor is produced by the bow shock emission or the cocoon emission when the jet head breaks out of the stellar surface."
 After this. the shocked jet phase cimerges. which may have a relatively simall opening angle for ultra-crelativistic material duc to that the musing of the shocked jet with stellar material lowers its teriumal Lorentz factor. so that an observer located at a lareer viewing angle would see a dark phase.," After this, the shocked jet phase emerges, which may have a relatively small opening angle for ultra-relativistic material due to that the mixing of the shocked jet with stellar material lowers its terminal Lorentz factor, so that an observer located at a larger viewing angle would see a dark phase."
 The relativistic reverse shock may be located well below the stellar surface at the time when the jet head has just reached the surface., The relativistic reverse shock may be located well below the stellar surface at the time when the jet head has just reached the surface.
 One may think that this dark plase could last long enough. if the shocked jet material moves with a low velocity.," One may think that this dark phase could last long enough, if the shocked jet material moves with a low velocity."
 However. ounce the jet lead reaches the stellar surface. the pressure in frout of the jet head decreases sudadeulv and a rarefaction wave will form aud propagate back iuto the shocked jet material at the speed of sound.," However, once the jet head reaches the stellar surface, the pressure in front of the jet head decreases suddenly and a rarefaction wave will form and propagate back into the shocked jet material at the speed of sound."
" The speed of ποπ]. in the shocked jet plana is relativistic. e,=¢//3. even if the head. velocity ey<ο."," The speed of sound in the shocked jet plasma is relativistic, $c_s=c/\sqrt{3}$, even if the head velocity $v_h\ll c$."
 When this rarefaction wave arrives at the reverse shock. the pressure of the shocked jet material also drops aud it can no longer decelerate the fast uushocked jet.," When this rarefaction wave arrives at the reverse shock, the pressure of the shocked jet material also drops and it can no longer decelerate the fast unshocked jet."
" Supposing that the reverse shock is located at a position well below the stellar surface when the jet head reaches the stellar surface. the width ofthe shocked jet is AxRy. aud the time that the rarefaction wave takes to arrive at tle reverse shock is f4=Ase,<BR.je.GB."," Supposing that the reverse shock is located at a position well below the stellar surface when the jet head reaches the stellar surface, the width ofthe shocked jet is $\Delta\la R_{\star}$, and the time that the rarefaction wave takes to arrive at the reverse shock is $t_1=\Delta/c_s\la
R_{\star}/c_s=6R_{\star,11} \,{\rm s} $."
 A new system of forward aud reverse shocks will form. aud the rarefied VArocked jet plasima is accelerated to a relativistic velocity with a Lorentz factor where D54 is the Loreutz factor of the shocked jet before the rarefaction wave propagating back (see Eq.(15) of Waxaniadi2003).," A new system of forward and reverse shocks will form, and the rarefied shocked jet plasma is accelerated to a relativistic velocity with a Lorentz factor where $\Gamma_{h1}$ is the Lorentz factor of the shocked jet before the rarefaction wave propagating back (see Eq.(15) of Waxman2003)."
" Eveu for a sub-relativistic velocity Py,z 1. the rarefied shocked jet is accelerated"," Even for a sub-relativistic velocity $\Gamma_{h1}\simeq1$ , the rarefied shocked jet is accelerated"
"€,=| for dishes.",$\epsilon_{\rm g}=1$ for dishes.
" Explicitly, ,((55)?] for AASs, where 0 is the zenith-angle ofthe point-source, Agps is the observing wavelength, and Ag=c/vo is the Nyquist-sampling wavelength of the array."," Explicitly, ] for AASs, where $\theta$ is the zenith-angle ofthe point-source, $\lambda_{\rm obs}$ is the observing wavelength, and $\lambda_0\equiv c/\nu_0$ is the Nyquist-sampling wavelength of the array."
" e,=€1: is the product of two interpretable factors: εει=cos0 corrects€» the collecting area for the linear projection of the wavefront onto the horizontal array; e»=min[l,455,/40]min[1,Agps/(Aocos6)] ensures that the sensitivity is correctly reduced (c is increased) in the case of a sparse (i. e. sub-Nyquist) sampling of the wavefront."," $\epsilon_{\rm g}\equiv\epsilon_{\rm g1}\cdot\epsilon_{\rm g2}$ is the product of two interpretable factors: $\epsilon_{\rm g1}\equiv\cos\theta$ corrects the collecting area for the linear projection of the wavefront onto the horizontal array; $\epsilon_{\rm g2}\equiv\min[1,\lambda_{\rm obs}/\lambda_0]\min[1,\lambda_{\rm obs}/(\lambda_0\cos\theta)]$ ensures that the sensitivity is correctly reduced $\sigma$ is increased) in the case of a sparse (i. e. sub-Nyquist) sampling of the wavefront."
" The “correlator quantization efficiency” ει measures the noise level output by the correlator (software or hardware) compared to that of an ideal correlator; we here assume high-end correlators with e,=0.95.", The “correlator quantization efficiency” $\epsilon_{\rm q}$ measures the noise level output by the correlator (software or hardware) compared to that of an ideal correlator; we here assume high-end correlators with $\epsilon_{\rm q}=0.95$.
" The “array ει measures the losses due to the time needed to efficiency”reconfigure the array and due the differential weighting applied to the visibilities (i. e. tapering of the (u, v)-plane, see "," The “array efficiency” $\epsilon_{\rm x}$ measures the losses due to the time needed to reconfigure the array and due the differential weighting applied to the visibilities (i. e. tapering of the $(u,v)$ -plane, see )."
"Here we adopt the value of Holdaway|1998;e;[Yun=0.9& as we Kogan|1999)).consider fixed array optimisticconfigurations (the most compact configurationonly for ALMA and the permanent configuration for SKA), working in a low resolution mode close to the natural weighting of the visibilities (low tapering)."," Here we adopt the optimistic value of $\epsilon_{\rm x}=0.9$ as we only consider fixed array configurations (the most compact configuration for ALMA and the permanent configuration for SKA), working in a low resolution mode close to the natural weighting of the visibilities (low tapering)."
" Finally, the “antenna efficiency” (sometimes called “aperture efficiency”) ει is the fraction of the electromagnetic energy transmitted from the collector to the receiver."," Finally, the “antenna efficiency” (sometimes called “aperture efficiency”) $\epsilon_{\rm a}$ is the fraction of the electromagnetic energy transmitted from the collector to the receiver."
" For dishes, ει can be approximated by the equation i (3) where ερ«0.8 is the ο...long wavelength maximum efficiency, 6 is the RMS value of the surface error distribution (values given in Tab. B». "," For dishes, $\epsilon_{\rm a}$ can be approximated by the Ruze-equation = ], where $\epsilon_0\approx0.8$ is the long wavelength maximum efficiency, $\delta$ is the RMS value of the surface error distribution (values given in Tab. \ref{tab_telescope_properties}) ),"
and Aps is the observed wavelength., and $\lambda_{\rm obs}$ is the observed wavelength.
 We note that c in eq. (??)), We note that $\sigma$ in eq. \ref{eq_sigma}) )
" is the RMS of the random component of the observing noise (in units proportional to Jy), measured per frequency channel of width Ay and per synthesized beam, i. e. per pixel of the synthesized sky image."," is the RMS of the random component of the observing noise (in units proportional to Jy), measured per frequency channel of width $\Delta\nu$ and per synthesized beam, i. e. per pixel of the synthesized sky image."
 Hence o is the per-channel-noise of any source small enough to be fully contained within the synthesized beam., Hence $\sigma$ is the per-channel-noise of any source small enough to be fully contained within the synthesized beam.
 This feature applies in particular and always to point-sources., This feature applies in particular and always to point-sources.
 Therefore the sensitivity defined as the inverse of the noise σ is often referred to as “point-source sensitivity”., Therefore the sensitivity defined as the inverse of the noise $\sigma$ is often referred to as “point-source sensitivity”.
" For resolved sources, the sensitivity deteriorates, such as detailed in Section ??.."," For resolved sources, the sensitivity deteriorates, such as detailed in Section \ref{subsection_spatial_resolution}."
" The full-width-half-maximumyov (FWHM) of the primary beam of an AAS or a SFD with diameter D is approximately and lambda,therefore the field-of-view (FoV)) of the primary beam is AASs constantly (A,collect electro-magnetic radiation from a large fraction of the hemisphere, typically covering about 10*deg? (half the hemisphere)."," The full-width-half-maximum (FWHM) of the primary beam of an AAS or a SFD with diameter $D$ is approximately and therefore the field-of-view ) of the primary beam is AASs constantly collect electro-magnetic radiation from a large fraction of the hemisphere, typically covering about $10^4\rm\,deg^2$ (half the hemisphere)."
" The beams are “formed” through digital processing, and in principle the number of instantaneous beams Npeams is only limited by the processing power."," The beams are “formed” through digital processing, and in principle the number of instantaneous beams $N_{\rm beams}$ is only limited by the processing power."
" Given Npeams, the instantaneous of AASs reads eam."," Given $N_{\rm beams}$, the instantaneous of AASs reads ."
 Note that ZNpeamswe here assume that SKA-LF only uses digital beam forming., Note that we here assume that SKA-LF only uses digital beam forming.
" By contrast, the “pathfinder” instruments MWA and LOFAR also use analogue beam formers that cut down the FoV.."," By contrast, the “pathfinder” instruments MWA and LOFAR also use analogue beam formers that cut down the ."
2006).,.
.. The following analvses will highlieht the branching fraction in cach euvironnneut. as well as the relative importance of electron impact excitation vs. ionization | recombination using equation (158)).," The following analyses will highlight the branching fraction in each environment, as well as the relative importance of electron impact excitation vs. ionization + recombination using equation \ref{eqdeltavszeta}) )."
 Civeu that the analvsis in 822.1 did not account for the processes exiuniucd iu 855.1. we felt it prudeut to revisit the calculations for diffuse molecular clouds.," Given that the analysis in 2.1 did not account for the processes examined in 5.1, we felt it prudent to revisit the calculations for diffuse molecular clouds."
" We use the same values as before 0Τὸ=: Gye=23x1048 1h but now also assune fj,= ον αρ=ll100ὃν and reg=10 '."," We use the same values as before $E(B-V)=1$; $\zeta_{\rm He}=3\times10^{-16}$ $^{-1}$ ), but now also assume $f_{\rm H_2}=2/3$ , $x_e=1.4\times10^{-4}$, and $x_{\rm CO}=10^{-7}$ ."
" The general results for this environment (b=0.08: f,=11xsto P; N,=63«LOS 7: WV=031 114)) are simular to those for the specific diffuse molecular sight lune TD 18531123. with the differences due to the lower color excess."," The general results for this environment $b=0.08$; $f_m=1.1\times10^{-12}$ ; $N_m=6.3\times10^8$ $^{-2}$; $W_{\lambda}=0.31$ ) are similar to those for the specific diffuse molecular sight line HD 183143, with the differences due to the lower color excess."
 Assunniug that all of the material has the sale velocity. metastable helium absorption should be observable in diffuse molecular clouds at a 320 level with S/N~1500.," Assuming that all of the material has the same velocity, metastable helium absorption should be observable in diffuse molecular clouds at a $\sigma$ level with $\sim1500$."
" Caven the small branching fraction above. P(óg,s)=OS and we couclude that metastable helium is predominantly formed via electron impact excitation in diffuse molecular clouds."," Given the small branching fraction above, $P(\delta_{\rm He^*})=0.8$ and we conclude that metastable helium is predominantly formed via electron impact excitation in diffuse molecular clouds."
 Dense clouds. while providing a larger total heliua column. have several characteristics detrimental to the formation of inetastable helimm.," Dense clouds, while providing a larger total helium column, have several characteristics detrimental to the formation of metastable helium."
 The cosmic-ray ionization rate tends to be about l order of magnitude lower in dense clouds than iu diffuse clouds (DalearuoWw IOG)., The cosmic-ray ionization rate tends to be about 1 order of magnitude lower in dense clouds than in diffuse clouds \citep{dalgarno}.
". Also. the fractional abundance of electrons is much lower. ow,cτν1407. while the fractional abundance of CO is mmceh higher. ecozcινlo! (Woodalletal.2007)."," Also, the fractional abundance of electrons is much lower, $x_e\approx4\times10^{-8}$, while the fractional abundance of CO is much higher, $x_{\rm CO}\approx1.4\times10^{-4}$ \citep{woo07}."
. Because &45 is so much larger than any of the other rate coefficients. collisions with CO will dominate the destruction of Ile! aud equation (16)) can be simplified to Given the fractional abundances above and the relevant rate cocficicuts (65 aud Aew were computed for T= WOW). the branching fraction is b—10 9.," Because $k_{\ref{rHeCO}}$ is so much larger than any of the other rate coefficients, collisions with CO will dominate the destruction of $^+$ and equation \ref{eqfbranch}) ) can be simplified to Given the fractional abundances above and the relevant rate coefficients $\alpha_3$ and $k_{\rm CO}$ were computed for $T=40$ K), the branching fraction is $b\sim10^{-6}$ ."
 As a result. P(dye)21. meaning that metastable helium is formed exclusively by electron impact excitation im dense clouds.," As a result, $P(\delta_{\rm He^*})\approx1$, meaning that metastable helium is formed exclusively by electron impact excitation in dense clouds."
 Even with this formation mechanisia though. the expected equivalent width (M4=0.13 mÀ)) aud necessary S/N for a 3o detection (S/N~ 3100). coupled with the large atteuuation of the background stars flux at T μπα. male the detection of Ποῦ in deuse clouds highly uulikely.," Even with this formation mechanism though, the expected equivalent width $W_{\lambda}=0.13$ ) and necessary S/N for a $\sigma$ detection $\sim3700$ ), coupled with the large attenuation of the background star's flux at 1 $\mu$ m, make the detection of He* in dense clouds highly unlikely."
 Diffuse atomic clouds. on the other hand. have negligible concentrations of IT aud CO (Suow&McCall2006). and presuuably share the high ionization rate of diffuse molecular clouds.," Diffuse atomic clouds, on the other hand, have negligible concentrations of $_2$ and CO \citep{sno06} and presumably share the high ionization rate of diffuse molecular clouds."
 Iu purely atomic conditions. electron recombination only has to compete with reaction (10)) aud equation (16)) can be approximated as The simnipli&ed result for atomic clouds is then 5zx 0.10. with a corresponding Pay)=0.15. meaning that ionization and clectron inpact excitation plav roughly equal roles iu forming metastable helium in such cuviroumeuts.," In purely atomic conditions, electron recombination only has to compete with reaction \ref{rHeH}) ) and equation \ref{eqfbranch}) ) can be approximated as The simplified result for atomic clouds is then $b\approx0.40$ , with a corresponding $P(\delta_{\rm He^*})=0.45$, meaning that ionization and electron impact excitation play roughly equal roles in forming metastable helium in such environments."
 Despite this branching fraction being closer to the ideal case of 6=0.62. the low απο! of material along such a sight line (E(BV)—0.1) results ina predicted equivalent width ofWy0.0611À.," Despite this branching fraction being closer to the ideal case of $b=0.62$, the low amount of material along such a sight line $E(B-V)\sim0.1$ ) results in a predicted equivalent width of$W_{\lambda}\approx0.06$."
. However. there are some diffuse atomic sight lines witli nore favorable conditious.," However, there are some diffuse atomic sight lines with more favorable conditions."
 One such candidate. σ Sco. ws E(BWV)=0.10 (Clayton&Ihuisou1993). aud hus a predicted equivalent width of V2:0.22 musing equations (17)) (20)).," One such candidate, $\sigma$ Sco, has $E(B-V)=0.40$ \citep{cla93} and thus a predicted equivalent width of $W_{\lambda}\approx0.22$ using equations \ref{eqfmBZDA}) ) \ref{atobranch}) )."
" IIowever. σ Sco also has ueasured values of N(ID)=2.1.1023 ein3. ΑΠΟ}= cm2 (Savageetal.1977).. and N(CO)=6.5«1012 3 (Allenctal.1990)... which correspoud o fi,=0.019 and vag=2.610"," However, $\sigma$ Sco also has measured values of $N({\rm H})=2.4\times10^{21}$ $^{-2}$, $N({\rm H_2})=6.2\times10^{19}$ $^{-2}$ \citep{sav77}, and $N({\rm CO})=6.5\times10^{12}$ $^{-2}$ \citep{all90}, which correspond to $f_{\rm H_2}=0.049$ and $x_{\rm CO}=2.6\times10^{-9}$."
 Usine these values aud equation (16)). we cau test the accuracy of equation (20)) at small molecular fractious.," Using these values and equation \ref{eqfbranch}) ), we can test the accuracy of equation \ref{atobranch}) ) at small molecular fractions."
 The result is b—0.31. or about a error in the approximation.," The result is $b=0.31$, or about a error in the approximation."
" At fu,=0.10. equation (20)) overestimates P. by a factor of 2. so this approximation should oulv be applied for fu,&0.1."," At $f_{\rm H_2}=0.15$, equation \ref{atobranch}) ) overestimates $b$ by a factor of 2, so this approximation should only be applied for $f_{\rm H_2}\lesssim0.1$."
" Taking the brauching fraction from the full calculation, we predict an equivalent width of Wy=0.20 mA.. aud a correspondiug S/N ~2100 necessary for a 3e detection."," Taking the branching fraction from the full calculation, we predict an equivalent width of $W_{\lambda}\approx0.20$ , and a corresponding S/N $\sim2400$ necessary for a $\sigma$ detection."
 If such a detection. can be made. however. it will provide the exciting opportunity to probe the cosmic-ray ionization rate in au enviroment where oobservations cannot be made due to the low molecular fraction.," If such a detection can be made, however, it will provide the exciting opportunity to probe the cosmic-ray ionization rate in an environment where observations cannot be made due to the low molecular fraction."
 We lave analyzed the possibility of detecting absorption lines due to interstellar metastable helium at 10830Α., We have analyzed the possibility of detecting absorption lines due to interstellar metastable helium at 10830.
. Observations toward the diffuse cloud sieht line ΠΟ 183113 were taken. aud a spectrum with S/N~TOO was obtained. but no interstellar Πο 1*7. lines were detected.," Observations toward the diffuse cloud sight line HD 183143 were taken, and a spectrum with $\sim$ 700 was obtained, but no interstellar He * lines were detected."
" In examining the chemistry associated with metastable helium. we have identified important formation and destruction pathlswvavs. aud have derived new equations for the steady state aualvsis of Ποῦ,"," In examining the chemistry associated with metastable helium, we have identified important formation and destruction pathways, and have derived new equations for the steady state analysis of He*."
 While these reactions have been kuown for some tine. this is the first instance where they have been applied to iietastable οι chemistry.," While these reactions have been known for some time, this is the first instance where they have been applied to metastable helium chemistry."
 Using our observations aud the newly derived equations. we inferred an upper liuüt for the οδόταν ionization rate of helium which. although consistent with other studies. is about 5 times larger thui xeviouslv inferred. values.," Using our observations and the newly derived equations, we inferred an upper limit for the cosmic-ray ionization rate of helium which, although consistent with other studies, is about 5 times larger than previously inferred values."
 To determine if future observations of interstellar ITe* are warranted. we predicted the S/N ratios necessary or 3e detectious in various cuviromments.," To determine if future observations of interstellar He* are warranted, we predicted the S/N ratios necessary for $\sigma$ detections in various environments."
 Diffuse uolecular clouds are the most pronuüsing targets with S/N1500 required. while favorable diffuse atomic clouds wed S/N~2LOO.," Diffuse molecular clouds are the most promising targets with $\sim$ 1500 required, while favorable diffuse atomic clouds need $\sim$ 2400."
 While such observations are extremely challenging at preseut. advancements iu telescope aud jear-ufrared detector technology may oue dav make uetastable heliuni a widely applicable probe. ofthe cosmic-ray dPonization rate.," While such observations are extremely challenging at present, advancements in telescope and near-infrared detector technology may one day make metastable helium a widely applicable probe ofthe cosmic-ray ionization rate."
 Iu diffuse molecular clouds. Ποῦ will act as a cosmic-ray probe independent of » and together with it will also enable IL}determination of the absorption path leugth aud average cloud deusitv.," In diffuse molecular clouds, He* will act as a cosmic-ray probe independent of , and together with it will also enable determination of the absorption path length and average cloud density."
 Πο observatious will also be especially portant for diffuseatomic clouds. where there are no other reliable tracers of the ionization rate.," He* observations will also be especially important for diffuseatomic clouds, where there are no other reliable tracers of the ionization rate."
Massive clusters anc OB associations associated with eiant LIL regions such as 14136 in 30 Doradus (c.g.2??).. the central clusters in NGC 3603 (ος.77). and NGC 604 (eg7). and Trumpler 14. 15 and 16 and Collinder. 228 (c.g.77) in the Carina HIE region. each containing tens to hundreds of Otype stars. are ideal. places to test. our understanding of star formation and the effects of feedback from the high.mass end of the ΙΔΗΣ.,"Massive clusters and OB associations associated with giant HII regions such as R136 in 30 Doradus \citep[e.g.][]{1999A&A...347..532S,2006AJ....131.2140T,2009ApJ...694...84I}, the central clusters in NGC 3603 \citep[e.g.][]{2001RMxAA..37...39T,2006AJ....132..253S} and NGC 604 \citep[e.g][]{2008ApJ...685..919T}, and Trumpler 14, 15 and 16 and Collinder 228 \citep[e.g.][]{2003MNRAS.339...44T,2006MNRAS.367..513T} in the Carina HII region, each containing tens to hundreds of O–type stars, are ideal places to test our understanding of star formation and the effects of feedback from the high–mass end of the IMF."
 Star formation in such regions appears to be hierarchical. with structure extant over à wide range of length anc mass scales.," Star formation in such regions appears to be hierarchical, with structure extant over a wide range of length and mass scales."
 The dynamics of these regions. or at least of their remaining eas content. seem to be dominated: by feedback from Ostars in. the orm of giant or multiple LL regions. wind.blown bubbles and supernova shells.," The dynamics of these regions, or at least of their remaining gas content, seem to be dominated by feedback from O–stars in the form of giant or multiple HII regions, wind–blown bubbles and supernova shells."
 Phese phenomena drive powerful outllows. expelling mass from the embedded: clusters aud »haps unbinding them.," These phenomena drive powerful outflows, expelling mass from the embedded clusters and perhaps unbinding them."
 Several authors (e.gο) have concluded that the majority of star clusters do not survive heir embedded: phase ancl the loss of large quantities of gas via outllows olfers an attractive explanation for this The dispersal of clouds by the action. of. feedback iis been studied by many authors.," Several authors \citep[e.g][]{2003ARA&A..41...57L,2005ApJ...631L.133F} have concluded that the majority of star clusters do not survive their embedded phase and the loss of large quantities of gas via outflows offers an attractive explanation for this The dispersal of clouds by the action of feedback has been studied by many authors."
 ? and later ?.. ? ? and ? considered the clvnamical elfect on clusters of removing gas left over by the star formation process. while. ee. 7.2 7. 7. and 2? consider the selflimiting elfect. of Feedback on the starformation cllicicney in clouds.," \cite{1980ApJ...235..986H} and later \cite{1997MNRAS.284..785G}, \cite{2003MNRAS.338..673B}, \cite{2003MNRAS.338..665B} and \cite{2006MNRAS.373..752G} considered the dynamical effect on clusters of removing gas left over by the star formation process, while, e.g., \cite{1987sbge.proc..467L}, \cite{1988ARA&A..26..145T}, \cite{1994ApJ...436..795F} and \cite{2002ApJ...566..302M} consider the self–limiting effect of feedback on the star–formation efficiency in clouds."
 These authors did not. however. model the process of gas removal itself.," These authors did not, however, model the process of gas removal itself."
 2 performed. hybrid body{91Η calculations in which they modelled: the interaction of the eas ack stars ποconsistently. but the expulsion of the gas. by heating or by driving a shockwave through it. were still parameterized.," \cite{2001MNRAS.323..988G} performed hybrid N–body/SPH calculations in which they modelled the interaction of the gas ad stars self–consistently, but the expulsion of the gas, by heating or by driving a shockwave through it, were still parameterized."
 lt is clear that an understanding of the process by which stellar svstenmis lose gas is 7. introduced the concept to the champagne flow. in which an Ostar born near the edge of a cloud creates a cavity around. itself! through which eas erocdecl from the wall of the cloud Uows at. high. velocity into the ISM.," It is clear that an understanding of the process by which stellar systems lose gas is \cite{1979A&A....71...59T} introduced the concept to the champagne flow, in which an O–star born near the edge of a cloud creates a cavity around itself through which gas eroded from the wall of the cloud flows at high velocity into the ISM."
 Using an analytic model. ο found that this process would result in star formation elliciencies at. the scale of whole eint molecular clouds would be ~54.," Using an analytic model, \cite{1979MNRAS.186...59W} found that this process would result in star formation efficiencies at the scale of whole giant molecular clouds would be $\sim5\%$."
 2D numerical simulations by ? also showed that champagne llows could be an efficient dispersal mechanism and they clearly do play such a role in many svstems. such as Orion (7)..," 2–D numerical simulations by \cite{1979ApJ...233...85B} also showed that champagne flows could be an efficient dispersal mechanism and they clearly do play such a role in many systems, such as Orion \citep{2005ApJ...627..813H}."
 However. and ? found that the disruption of clouds by LILL regions is strongly impeded or prevented if the clouds are in freefall and if the ionizing sources are located near the centres of the clouds.," However, \cite{1980A&A....90...65M} and \cite{1989A&A...216..207Y} found that the disruption of clouds by HII regions is strongly impeded or prevented if the clouds are in freefall and if the ionizing sources are located near the centres of the clouds."
 As noted above. observations often indicate that massive stars are more likely to be found near the centres of starforming regions. or at any rate at the centres of subclusters. anc many simulations reproduce this result.," As noted above, observations often indicate that massive stars are more likely to be found near the centres of star–forming regions, or at any rate at the centres of subclusters, and many simulations reproduce this result."
 This can be the result of competitive accretion (e.gο) or rapid mass segregation (c.g?).., This can be the result of competitive accretion \citep[e.g][]{2003MNRAS.343..413B} or rapid mass segregation \citep[e.g][]{2007ApJ...655L..45M}.
 Additionally. the abovecited. mocels of champagne lows treat the eas as being initially uniform or at least smoothlyvarving.," Additionally, the above–cited models of champagne flows treat the gas as being initially uniform or at least smoothly–varying."
 In contrast. simulations and observations," In contrast, simulations and observations"
The entropy [1]. withthe ,reads where the polynomials $P(r)$ are given in the appendix.
charges (qu. jp!)repla," For $D_{ABC}=D_{333}$ and$D_A=D_3$: and $\xi_1(r),\xi_2(r)$ are irrelevant."
ced by (Qu.P3).," For $D_{ABC}=D_{123}$ and $D_A=D_3$: As discussed before,for $\mu>0$ our solutions for $\xi_A(r),\xi_0(r),\xi_T(r)$ diverge at $r=0$."
 which arefunctions oftheoriginal hu," Note also that for $\mu=0$ the radial derivatives of our solutions for $\xi_A(r),\xi_0(r),\xi_T(r)$ diverge at $r=0$."
 The temperatur," The curvature, however, is regular."
e and(iemass 2.2 Non-Extre," The entropy is given by \ref{genentropy}) ), where in our solutions $D$ does not contribute to first order in $\epsilon$ ."
mal Black , Note also that $G_N(\mu)\neq1$ .
Holeswith, The entropy reads the Hawking temperature is
2008).,.
. None of the kuown radio pulsars match the position (nor the characteristics) of NGC 6110 X-2., None of the known radio pulsars match the position (nor the characteristics) of NGC 6440 X-2.
 Although millisecond radio pulsus in binary systenis have been found in other elobular clusters (see.e.9..therein). if is an iutrieuine question why NGC 6110 is the only elobular cluster known today to host (two) AMNPs (SAN J1718.92021 αντetal.2007 and Altinuiranoetal.2008 and NGC GLLO X-2 this paper) while uo AMXPs have been detected in any other elobular cluster.," Although millisecond radio pulsars in binary systems have been found in other globular clusters \citep[see, e.g.,][and references
therein]{Ransom05, Freire08}, it is an intriguing question why NGC 6440 is the only globular cluster known today to host (two) AMXPs (SAX J1748.9–2021 – \citealt{Gavriil07} and \citealt{Altamirano08b}
 – and NGC 6440 X-2 – this paper), while no AMXPs have been detected in any other globular cluster."
 This müsht be only a selection effect. as current all-sky inonitors cannot detect short low-luuinosity outbursts.," This might be only a selection effect, as current all-sky monitors cannot detect short low-luminosity outbursts."
 Monitoring N-ray observations of differeut elobular clusters would be needed to further investigate this., Monitoring X-ray observations of different globular clusters would be needed to further investigate this.
Another important relation is Eqs. (,Another important relation is Eqs. (
5)-(12) ave exact and have been derived from Eqs. (,5)-(12) are exact and have been derived from Eqs. (
4).,4).
 These relations imply very interesting consequences when written approximately as Tavlor series in (he powers of 544 coming from the orthogonal mixing matrix O which can be written as where (he svinbols have their usual meaning., These relations imply very interesting consequences when written approximately as Taylor series in the powers of $s_{13}$ coming from the orthogonal mixing matrix $O$ which can be written as where the symbols have their usual meaning.
 We substitute (lese elements in equations and expand the results in the powers of sj4., We substitute these elements in equations (5)-(12) and expand the results in the powers of $s_{13}$.
 The mass ratios in Eqs. (, The mass ratios in Eqs. (
5) and (6) are given bv and which are consistent with our earlier results H.5].,"5) and (6) are given by and which are consistent with our earlier results \cite{a1a2 paper, 2t
paper}."
 The mass ratio 2 is nich snaller than one., The mass ratio $\frac{m_1}{m_2}$ is much smaller than one.
 Therefore. the neutrino mass matrix considered here has a normal hierarchy.," Therefore, the neutrino mass matrix considered here has a normal hierarchy."
 This fact is iniportant since (he neutrino oscillation parameters change very little in the RG evolution from the weak scale to GUT scale for the normal hierarchy., This fact is important since the neutrino oscillation parameters change very little in the RG evolution from the weak scale to GUT scale for the normal hierarchy.
 The matrix elements A. 2 and C are given by and Moreover. the element DD can be expressed as The ratios i and E can be written as and," The matrix elements $A$, $B$ and $C$ are given by and Moreover, the element $D$ can be expressed as The ratios $\frac{A}{C}$ and $\frac{B}{C}$ can be written as and"
the basic finding of NFW that CDM haloes are cuspy (e.g. ?;; ?;; 25 25; 23; 2)).,the basic finding of NFW that CDM haloes are cuspy (e.g. \citealt{1997ApJ...477L...9F}; ; \citealt{1998ApJ...499L...5M}; ; \citealt{2000ApJ...529L..69J}; ; \citealt{2000ApJ...535...30J}; \citealt{2001ApJ...557..533F}; \citealt{2002ApJ...574..538J}) ).
" These studies led to debate about the exact value of the logarithmic inner slope, which ranged from a~1 to 1.5 (e.g., ?,, ?))."," These studies led to debate about the exact value of the logarithmic inner slope, which ranged from $\alpha \sim 
1$ to $1.5$ (e.g., \citealt{1997ApJ...490..493N}, \citealt{1999MNRAS.310.1147M}) )."
" The study of ? provided convergence criteria that allowed simulators to understand the impact of numerical artifacts on the central structure of haloes, and to identify the innermost radius at which the mass profile could be considered reliably resolved."," The study of \citet{2003MNRAS.338...14P} provided convergence criteria that allowed simulators to understand the impact of numerical artifacts on the central structure of haloes, and to identify the innermost radius at which the mass profile could be considered reliably resolved."
" More recently, a great deal of effort has gone into even higher resolution simulations that have revealed density profiles of CDM haloes to well within 1% of the virial radius (?;; ?;; ?;; ?;; ?))."," More recently, a great deal of effort has gone into even higher resolution simulations that have revealed density profiles of CDM haloes to well within $1\%$ of the virial radius \citealt{2004ApJ...606..625F}; \citealt{2004ApJ...607..125T}; \citealt{2004MNRAS.349.1039N}; \citealt{2005MNRAS.357...82R}; \citealt{2005MNRAS.364..665D}) )."
 The highest resolved simulation to-date reached an effective mass resolution of about 130 million particles in a cluster sized dark matter halo still supporting the evidence for a central cusp with a logarithmic inner slope of about a~1.2 (?).., The highest resolved simulation to-date reached an effective mass resolution of about 130 million particles in a cluster sized dark matter halo still supporting the evidence for a central cusp with a logarithmic inner slope of about $\alpha \sim 1.2$ \citep{2005MNRAS.364..665D}.
" Cosmological simulations allow us to characterise the functional form of the density profile and to explore the important physical processes (e.g. merging, smooth accretion) that drive this form (cf.,??),, but a theoretical understanding of the origin of the mass profile is essential."," Cosmological simulations allow us to characterise the functional form of the density profile and to explore the important physical processes (e.g. merging, smooth accretion) that drive this form \citep[cf.,
][]{2006MNRAS.368.1931L, 2007ApJ...666..181S}, but a theoretical understanding of the origin of the mass profile is essential."
" Is the form of the profile set by non-linear processes during the virialisation of the halo, or is there an imprint of the primordial power spectrum P(k)?"," Is the form of the profile set by non-linear processes during the virialisation of the halo, or is there an imprint of the primordial power spectrum $P(k)$?"
 One must make strong assumptions about the connection between density and velocity dispersion to obtain analytical predictions about halo structure., One must make strong assumptions about the connection between density and velocity dispersion to obtain analytical predictions about halo structure.
" For example, under the assumption that the phase-space density is a power law in radius as suggested by ? one can solve the spherical Jeans equation to obtain the density profile (?;; ?;; ?))."," For example, under the assumption that the phase-space density is a power law in radius as suggested by \citet{2001ApJ...563..483T} one can solve the spherical Jeans equation to obtain the density profile \citealt{2004MNRAS.352L..41H}; ; \citealt{2005MNRAS.363.1057D}; \citealt{2005ApJ...634..756A}) )."
" These studies, guided by the results of the numerical simulations, confirm the central logarithmic slope to be in the range a~1 to 2, although ? have claimed that equilibrated haloes have central slopes of a~0.8."," These studies, guided by the results of the numerical simulations, confirm the central logarithmic slope to be in the range $\alpha \sim 1$ to $2$, although \citet{2006JCAP...05..014H} have claimed that equilibrated haloes have central slopes of $\alpha \sim 0.8$."
" However, it is interesting to ask whether or not there is a dependence of halo structure on the primordial power spectrum P(k)."," However, it is interesting to ask whether or not there is a dependence of halo structure on the primordial power spectrum $P(k)$."
" In particular, does the form of the profile depend on the (effective) spectral index n of P(k)?"," In particular, does the form of the profile depend on the (effective) spectral index $n$ of $P(k)$?"
" Oneof the key predictions of the NFW papers is that the shape of the “universal” profile should hold in any hierarchical cosmology, including scale-free ones."," Oneof the key predictions of the NFW papers is that the shape of the “universal” profile should hold in any hierarchical cosmology, including scale-free ones."
 This was confirmed by subsequent numerical simulations (e.g.?).., This was confirmed by subsequent numerical simulations \citep[e.g.][]{1996MNRAS.281..716C}.
" However, a number of analytical studies have claimed that "," However, a number of analytical studies have claimed that the density profile should depend on spectral index \citep[e.g., ][]{1985ApJ...297...16H,
 1998MNRAS.293..337S, 2000ApJ...538..528S, 2003MNRAS.340.1199H,
 2007ApJ...666..181S}, and these have been supported by numerical simulations providing similar evidence \citep[e.g.,
][]{1994ApJ...434..402C, 2001ApJ...554..114E, 2003MNRAS.344.1237R,
 2004astro.ph..3352C, 2005MNRAS.357...82R, 2007ApJ...663L..53R}."
Within this context it is interesting to consider the findings of ? and ?.., Within this context it is interesting to consider the findings of \citet{2003MNRAS.344.1237R} and \citet{2004astro.ph..3352C}.
" Both studies analysed high-resolution cosmological simulations and each argued that dark matter haloes at high redshifts have shallow central logarithmic slopes, with azz0.2—0.4."," Both studies analysed high-resolution cosmological simulations and each argued that dark matter haloes at high redshifts have shallow central logarithmic slopes, with $\alpha \approx 0.2-0.4$."
" In particular, ? claimed that the central logarithmic slope depends explicitly on the effective spectral index n, in agreement with the predictions of ?.."," In particular, \citet{2003MNRAS.344.1237R} claimed that the central logarithmic slope depends explicitly on the effective spectral index $n$, in agreement with the predictions of \citet{2000ApJ...538..528S}."
 We note that ? performed and analysed simulations comparable to those presented in ? and found no evidence for the shallow “cores” (a@~ 0.2); rather they found that their data favoured “cusps” (a& 1)., We note that \citet[][]{2004ApJ...612...50C} performed and analysed simulations comparable to those presented in \citet[][]{2003MNRAS.344.1237R} and found no evidence for the shallow “cores” $\alpha \sim 0.2$ ); rather they found that their data favoured “cusps” $\alpha \approx 1$ ).
" However, ? have recently revisited this topic using simulations with higher mass and force resolution, and they continue to argue in favour of shallow cores, in agreement with their earlier ? and ? sought to isolate the effect of spectral index n on halo structure by using series of simulations of the ACDM model with different box-sizesa and evolved for different numbers of expansion factors, to mimic a single n."," However, \citet{2007ApJ...663L..53R} have recently revisited this topic using simulations with higher mass and force resolution, and they continue to argue in favour of shallow cores, in agreement with their earlier \citet{2003MNRAS.344.1237R} and \citet{2007ApJ...663L..53R} sought to isolate the effect of spectral index $n$ on halo structure by using a series of simulations of the $\Lambda$ CDM model with different box-sizes and evolved for different numbers of expansion factors, to mimic a single $n$."
 In this short paper we revisit this topic and the claims of ? and ? using high resolution cosmological N-body simulations of scale-free models in which we vary systematically the spectral index n., In this short paper we revisit this topic and the claims of \citet{2003MNRAS.344.1237R} and \citet{2007ApJ...663L..53R} using high resolution cosmological $N$ -body simulations of scale-free models in which we vary systematically the spectral index $n$.
 This “clean” approach allows us to study whether the density profiles of dark matter haloes indeed show a dependence on the spectral index n., This “clean” approach allows us to study whether the density profiles of dark matter haloes indeed show a dependence on the spectral index $n$.
 In we give a detailed description of how we have set up and run our scale-free simulations., In \ref{sec:numerical_simulations} we give a detailed description of how we have set up and run our scale-free simulations.
 There are some important issues to be considered when deciding on a scale-free simulation and the simulation to compare halo properties., There are some important issues to be considered when deciding on a scale-free simulation and the simulation to compare halo properties.
 We encapsulate our findings in a set of well defined and physically motivated criteria., We encapsulate our findings in a set of well defined and physically motivated criteria.
" In [5] we present the results of our analysis of the halo mass profiles, and we summarise our results in Hl."," In \ref{sec:analysis} we present the results of our analysis of the halo mass profiles, and we summarise our results in \ref{sec:conclusions}."
" As we intend to perform scale-free cosmological simulations, we use a power law for the initial power spectrum of the simulation with A being the amplitude scaling factor and denoting the power of the white noise of a random distribution of N? particles in a box with size L and the Nyquist frequency, respectively."," As we intend to perform scale-free cosmological simulations, we use a power law for the initial power spectrum of the simulation with $A$ being the amplitude scaling factor and denoting the power of the white noise of a random distribution of $N^3$ particles in a box with size $L$ and the Nyquist frequency, respectively."
" The simple scaling with expansion |a is valid only for an Einstein-de Sitter universe, which is the cosmology of our choice."," The simple scaling with expansion $a$ is valid only for an Einstein–de Sitter universe, which is the cosmology of our choice."
" The box-size L is completely arbitrary because of the scale-free nature of the power spectra, and so we set it to 1 Mpc."," The box-size $L$ is completely arbitrary because of the scale-free nature of the power spectra, and so we set it to $1$ Mpc."
 N denotes the number of particles along one dimension., $N$ denotes the number of particles along one dimension.
" We run a sequence of simulations with the parallel N-body code Gadget2 (?) containing 512? particles that differ only in the value of the spectral index n; we use n=-0.50, -1.50, -2.25, -2.50 and -2.75."," We run a sequence of simulations with the parallel $N$ -body code Gadget2 \citep{2005MNRAS.364.1105S} containing $512^3$ particles that differ only in the value of the spectral index $n$; we use $n$ =-0.50, -1.50, -2.25, -2.50 and -2.75."
" In order to set-up and run the simulations, we still need to specify theamplitude scaling factor A for all models and to find a criterion for when to stop and compare objects from different runs."," In order to set-up and run the simulations, we still need to specify theamplitude scaling factor $A$ for all models and to find a criterion for when to stop and compare objects from different runs."
 These two choices will be presented and discussed in the following two subsections., These two choices will be presented and discussed in the following two subsections.
" For setting up the initial conditions of the simulations,only the amplitude scaling factor A in equation[] needs to be determined; all other factors are given by the specifics of the model under investigation, i.e. N and n."," For setting up the initial conditions of the simulations,only the amplitude scaling factor $A$ in equation \ref{eqn:definition_Pk} needs to be determined; all other factors are given by the specifics of the model under investigation, i.e. $N$ and $n$ ."
" The mass fluctuations o7,, within the computational domain can bewritten asfollows wherethe integration range in K contains all significant frequencies reproduced in the box, e.g.. kz,y,2€[2n/L, Nn/L]."," The mass fluctuations $\sigma^2_{\rmn{box}}$ within the computational domain can bewritten asfollows wherethe integration range in $\bmath{k}$ contains all significant frequencies reproduced in the box, e.g.. $k_{x,y,z} \in \left[2\upi/L,N\upi/L\right]$ ."
 With the definition of P(k) (cf., With the definition of $P(k)$ (cf.
 eq. BJ), eq. \ref{eqn:definition_Pk}) )
 this can be evaluated analytically to be, this can be evaluated analytically to be
»etter fits for a homogeneous medium than a wind.,better fits for a homogeneous medium than a wind.
 This discrepancy may be resolved if the afterglow does not arise ina [freely expanding wind. but in the environment resulting rom the interaction of the wind with the circumstellar gas (Wijers 2001) or with the winds blown by other stars (Scalo Wheeler 2001).," This discrepancy may be resolved if the afterglow does not arise in a freely expanding wind, but in the environment resulting from the interaction of the wind with the circumstellar gas (Wijers 2001) or with the winds blown by other stars (Scalo Wheeler 2001)."
 Ht is then possible that the GRB ejecta run into a CDM whose density. profile at smaller racii is the r£ expected for a uniform. free wind. and closer to uniformity at larger distances.," It is then possible that the GRB ejecta run into a CBM whose density profile at smaller radii is the $r^{-2}$ expected for a uniform, free wind, and closer to uniformity at larger distances."
 Then. if the ES cooling frequeney is above the optical domain. the optical afterglow light-curve index should. decrease by da=0.5 when the wind termination shock is reached.," Then, if the FS cooling frequency is above the optical domain, the optical afterglow light-curve index should decrease by $\delta \alpha = 0.5$ when the wind termination shock is reached."
" ""Phe resulting index decrease is slightly smaller than observed. but it is possible that deviations from uniformity of the environment outside the unperturbed wind account for the dillerence."," The resulting index decrease is slightly smaller than observed, but it is possible that deviations from uniformity of the environment outside the unperturbed wind account for the difference."
 One important. issue for this wind-bubble scenario is under what conditions the wind termination shock is located at the radius Ze. of the afterglow at the time ἐν when the light-curve transits from a steeper to a slower decay., One important issue for this wind-bubble scenario is under what conditions the wind termination shock is located at the radius $R_*$ of the afterglow at the time $t_*$ when the light-curve transits from a steeper to a slower decay.
" From equations (13)) and (38)). one obtains R, is higher by a factor of a few for the wind parameters ely~OL which we find for this scenario. and by an extra [actor z10 for the high ejecta kinetic energy obtained. for the afterglow 9090123."," From equations \ref{R2}) ) and \ref{time}) ), one obtains $R_*$ is higher by a factor of a few for the wind parameters $A_* \sim 0.1$ which we find for this scenario, and by an extra factor $\simg 10$ for the high ejecta kinetic energy obtained for the afterglow 990123."
" hus. we shall find that 2,~0.3 pe for the afterglow 990123 and /?,S0.02 pe for the afterglow 021211."," Thus, we shall find that $R_* \sim 0.3$ pc for the afterglow 990123 and $R_* \siml 0.02$ pc for the afterglow 021211."
" Because the afterglow raclius increases as Box(07 al 2oRy and because the slower decay of the afterglows 990123 and 021211 is seen from /=/, untill /~ few clays. the uniform: part of the (BAL must extend up to at [east 5p..."," Because the afterglow radius increases as $R \propto t^{1/4}$ at $R > R_*$ and because the slower decay of the afterglows 990123 and 021211 is seen from $t = t_*$ untill $t \sim$ few days, the uniform part of the CBM must extend up to at least $5\, R_*$."
 Castor. MeCray Weaver (1975) have derived. the major physical properties of a bubble resulting from the interaction of stellar winds with the interstellar gas. taking into account the cooling and the cilfusion of the interstellar gas into the shocked wind.," Castor, McCray Weaver (1975) have derived the major physical properties of a bubble resulting from the interaction of stellar winds with the interstellar gas, taking into account the cooling and the diffusion of the interstellar gas into the shocked wind."
" Phe radius of the wind termination shock A, can be estimated from the equality of the wind ram. pressure and that inside the bubble. leading to R8;=4AUSota»lamyO13Co401 pe. where ALs is: the mass-loss rate in LO7AZ.vrte ray ds the wind velocity in km/s. no is the interstellar gas density in emi7. and and ἐς is the duration of the wind measured in 107 vears."," The radius of the wind termination shock $R_t$ can be estimated from the equality of the wind ram pressure and that inside the bubble, leading to $R_t = 4\, \dot{M}_{-5}^{0.3} v_{w,3}^{0.1} n_0^{-0.3} t_5^{0.4}$ pc, where $\dot{M}_{-5}$ is the mass-loss rate in $10^{-5}\, \Msunyear$, $v_{w,3}$ is the wind velocity in km/s, $n_0$ is the interstellar gas density in $\cm3$, and and $t_5$ is the duration of the wind measured in $10^5$ years."
" From here. the ratio of the contact cliscontinuity radius Ze, to that of the wind termination shock is 2,,4//8=2.341DAOnHUS, "," From here, the ratio of the contact discontinuity radius $R_{cd}$ to that of the wind termination shock is $R_{cd}/R_t = 2.3\, \dot{M}_{-5}^{-0.1} v_{w,3}^{0.3} n_0^{0.1} t_5^{0.2}$."
"""Thus for a GRB occurring in a dense cloud (n>10en7). the termination shock radius could be at location recquire by the CBAL scenario (equation 64)) and the shocked. win shell could be sullicientlv thick."," Thus for a GRB occurring in a dense cloud $n > 10^5\, \cm3$ ), the termination shock radius could be at location required by the CBM scenario (equation \ref{Rtrans}) ) and the shocked wind shell could be sufficiently thick."
 However. WI winds do not interact with the interstellar medium. but with the wind. expelled. during the rec supergiant (RSC) phase. which collides with the main-|sequence phase wind. decelerated by the interaction with he interstellar medium.," However, WR winds do not interact with the interstellar medium but with the wind expelled during the red supergiant (RSG) phase, which collides with the main-sequence phase wind decelerated by the interaction with the interstellar medium."
" Phe numerical byedrodynamica calculations of Ramirez-Ruiz (2001) take into accoun he wind history and show that Z2;0.02 pe for η=lem and |=10"" vears."," The numerical hydrodynamical calculations of Ramirez-Ruiz (2001) take into account the wind history and show that $R_t \sim 0.02$ pc for $n = 1 \,\cm3$ and $t = 10^6$ years."
 Such a termination shock radius is suitable. for the wind-bubble. scenario anc the afterglow 1211. however the wind-bubble size (0.3. pe) shown by tamirez-Ruiz (2001) is surprisingly small. being 100 ines less than that expected from the analvtical results of Castor (1975).," Such a termination shock radius is suitable for the wind-bubble scenario and the afterglow 021211, however the wind-bubble size (0.3 pc) shown by Ramirez-Ruiz (2001) is surprisingly small, being 100 times less than that expected from the analytical results of Castor (1975)."
 Chevalier (2004) have considered he possibility that a high interstellar pressure may stall the rubble expansion., Chevalier (2004) have considered the possibility that a high interstellar pressure may stall the bubble expansion.
" For the external pressure expected in a intense starburst region. their numerical simulations lead to a wind shock termination radius /?;=0.4 pe and a contact discontinuity located at Z?,;=442). which is about right for the wind-bubble scenario and the afterglow 990123."," For the external pressure expected in a intense starburst region, their numerical simulations lead to a wind shock termination radius $R_t = 0.4$ pc and a contact discontinuity located at $R_{cd} = 4\, R_t$, which is about right for the wind-bubble scenario and the afterglow 990123."
" Alternatively. the uniformity of the CDM at £227ΠΠ, required. by the wind-bubble scenario might arise from a sudden increase in the wind speed. leading to a inner shock propagating into the incoming wind."," Alternatively, the uniformity of the CBM at $R > R_*$ required by the wind-bubble scenario might arise from a sudden increase in the wind speed, leading to a inner shock propagating into the incoming wind."
 The self-similar solutions derived. bv Chevalier Imamura (1983). for colliding winds show that a thick. uniform. censity shell forms behind the inner shock if the termination shock moves at less than of the unshocked wind speed. which requires the Uuetuation in the wind to consist of a decrease in the mass-loss rate by a factor 100 and an increase of the wind speed. increases by a factor LOO or larger.," The self-similar solutions derived by Chevalier Imamura (1983) for colliding winds show that a thick, uniform density shell forms behind the inner shock if the termination shock moves at less than of the unshocked wind speed, which requires the fluctuation in the wind to consist of a decrease in the mass-loss rate by a factor 100 and an increase of the wind speed increases by a factor 100 or larger."
 Such a dramatic, Such a dramatic
STFA in the non-relativistic limit behaves differently from highly relativistic STFA.,STFA in the non-relativistic limit behaves differently from highly relativistic STFA.
 Ai the core of these differences is the energy dependence of the electron. velocity at low energies., At the core of these differences is the energy dependence of the electron velocity at low energies.
 Thus. unlike the relativistic case. both the rate of reflections aud (he probability of escaping the acceleration region al an enerey ἐς vary.," Thus, unlike the relativistic case, both the rate of reflections and the probability of escaping the acceleration region at an energy $E$ vary."
 Using a lest particle approach. we have examined (his behavior and derived the spectrum of post-acceleration electrons in a plasma under impulsive solar (lare conditions.," Using a test particle approach, we have examined this behavior and derived the spectrum of post-acceleration electrons in a plasma under impulsive solar flare conditions."
 For traditional STFA. where there is a minimum pitch angle constraint which determines whether an individual encounter results in reflection. it is seen Chat the steady acceleration rate can dominate over (he diffusive acceleration rate.," For traditional STFA, where there is a minimum pitch angle constraint which determines whether an individual encounter results in reflection, it is seen that the steady acceleration rate can dominate over the diffusive acceleration rate."
 This arises [rom the averaging over pitch angles to evaluate (NI)., This arises from the averaging over pitch angles to evaluate $\left< \Delta E \right>$.
 Some previous treatments of the generalized Fermi acceleration problem do not have such reflection conditions. and thus do not retain factors of the turbulent field strength. 05/D. when averaging.," Some previous treatments of the generalized Fermi acceleration problem do not have such reflection conditions, and thus do not retain factors of the turbulent field strength, $\delta B/B$, when averaging."
 In those treatments. such as Longair(1915):Webb (1983).. the steady. and diffusive terms (vpically are seen to be of the same order.," In those treatments, such as \citet{Longair, Skilling, Webb}, the steady and diffusive terms typically are seen to be of the same order."
 For some processes this is appropriate. however non-resonant STFA is not one of them.," For some processes this is appropriate, however non-resonant STFA is not one of them."
 Thus. the phase space conditions for scattering bv the acceleration mechanism can play a very significant role. even in cases where pitch. angle isotropy is maintained.," Thus, the phase space conditions for scattering by the acceleration mechanism can play a very significant role, even in cases where pitch angle isotropy is maintained."
 The nature of (he pitch angle scattering turns out to be (he dominant factor in determining electron escape. and therefore (he shape of (he spectrum.," The nature of the pitch angle scattering turns out to be the dominant factor in determining electron escape, and therefore the shape of the spectrum."
 We find that whistler wave turbulence. which is well studied in solar flares (Melrose1974:Miller&Steinacker1992).. is an excellent source of piteh angle scattering which allows STFA to produce a cuasi-thermal electron distribution that peaks at ZZ 5keV. This matches the lowest energy portion of the observed X-ray emission very. well.," We find that whistler wave turbulence, which is well studied in solar flares \citep{melrose, millerstein}, is an excellent source of pitch angle scattering which allows STFA to produce a quasi-thermal electron distribution that peaks at $E \approx 5$ keV. This matches the lowest energy portion of the observed X-ray emission very well."
 Llowever. to produce the power law spectrum observed in (he range -10— 100keV bv STFA requires at least à second scattering mechanism.," However, to produce the power law spectrum observed in the range $\backsim 10-100$ keV by STFA requires at least a second scattering mechanism."
 Matching the spectral index and (he transition energy [rom quasi-thermal to power law spectrum recuires an undetermined scattering mechanism which satisfies Ac/Lj;=T/L with P=0.073/6V.. and naturally becomes the dominant pitch angle scatterer al roughly. 20keV. If the constrained pitch angle scattering mechanism is discovered. it implies (hat the acceleration of electrons in solar [lares is at least a two stage process.," Matching the spectral index and the transition energy from quasi-thermal to power law spectrum requires an undetermined scattering mechanism which satisfies $\lambda_C / L_F = \Gamma/E$ with $\Gamma = 0.073keV$, and naturally becomes the dominant pitch angle scatterer at roughly $20$ keV. If the constrained pitch angle scattering mechanism is discovered, it implies that the acceleration of electrons in solar flares is at least a two stage process."
 The first stage. STFA in the downflow region. produces both the quasi-thermal spectrum below νο10/eV. and the lower hall of the power law spectrum up to LOOkeV. To produce the highest energy electrons. as well as the spectral break at E= 100keV requires a second acceleration mechanism at the top ofthe soft X-ray loop.," The first stage, STFA in the downflow region, produces both the quasi-thermal spectrum below $\backsim 10keV$ and the lower half of the power law spectrum up to $100$ keV. To produce the highest energy electrons, as well as the spectral break at $E=100$ keV requires a second acceleration mechanism at the top of the soft X-ray loop."
 We are further exploring (he possibility that first order acceleration al a weak [ast shock. lormecl as (he downllow impacts the top of the closed flare loop. is responsible for electron acceleration to the highest observed energies.," We are further exploring the possibility that first order acceleration at a weak fast shock, formed as the downflow impacts the top of the closed flare loop, is responsible for electron acceleration to the highest observed energies."
 Acceleration at [ast shocks is known to have an injection energy of roughly I00keV. and varies with temperature.," Acceleration at fast shocks is known to have an injection energy of roughly $100$ keV, and varies with temperature."
While nearly all galaxies. ranging from giant ellipticals to compact dwarf ellipticals. appear to lie on the FP (alsoseeetal.2006:δυοοἱ2007) it is interesting to note that clilfuse chwarl ellipticals do not (Ixormendy1987): they seen to be fundamentally. dillerent objects.,"While nearly all galaxies, ranging from giant ellipticals to compact dwarf ellipticals, appear to lie on the FP \citep[also see e.g.][]{jorgensen95, 
bernardi03, cappellari06, bolton07} it is interesting to note that diffuse dwarf ellipticals do not \citep{kormendy87}: they seem to be fundamentally different objects."
 The observed. Fundamental Plane not. only. provides information on the dynamical state of the object. but. also on the evolution of its stellar content and. by implication. about its formation.," The observed Fundamental Plane not only provides information on the dynamical state of the object but also on the evolution of its stellar content and, by implication, about its formation."
" For a virialized object with effective radius #, and mass-to-light ratio L/L the FP relation will have the form in which J,=Lf/inh- is the mean surface brightness and Cl. a constant dependent on the structure of the object.", For a virialized object with effective radius $R_e$ and mass-to-light ratio $M/L$ the FP relation will have the form in which $I_e=L/4\pi R_e^{2}$ is the mean surface brightness and $C_{s}$ a constant dependent on the structure of the object.
 The observed parameter. values for elliptical. galaxy Lundamenal Plane (SCO Eqn. 9)), The observed parameter values for elliptical galaxy Fundamental Plane (see Eqn. \ref{eq:jorgensen}) )
 are clillerent from what might be expected for a plane that results simply from virialization ancl constant mass-Co-light ratio., are different from what might be expected for a plane that results simply from virialization and constant mass-to-light ratio.
 One explanation for this dillerence is that galaxies. may. be structurally equivalent while having a mass-dependent AZ/L ratio., One explanation for this difference is that galaxies may be structurally equivalent while having a mass-dependent $M/L$ ratio.
 That would imply a formation process involving a tight fine tuning of A/L., That would imply a formation process involving a tight fine tuning of $M/L$ .
 Nevertheless. pursuing this view. the parameters inferred by Jorgensenetal.(1996) (eqn. 9))," Nevertheless, pursuing this view, the parameters inferred by \cite{jorgensen96} (Eqn. \ref{eq:jorgensen}) )"
" would imply a mass-to-leht ratio dependence on mass: using ALxack, and £Lxddr (seeeg.Faber 1987).", would imply a mass-to-light ratio dependence on mass: using $M\propto \sigma_v^2 R_e$ and $L \propto I_e R_e^2$ \citep[see e.g.][]{faber87}.
. Recent semi-analvtical modelling of galaxy formation suggest à more complex relation between the mass-to-light ratio and luminosity. involving a minimum M£L for galaxies with AJzLott107. tM..," Recent semi-analytical modelling of galaxy formation suggest a more complex relation between the mass-to-light ratio and luminosity, involving a minimum $M/L$ for galaxies with $M\approx10^{11}-10^{12}h^{-1}$ $_{\odot}$."
. In the absence of any mass-to-light dependeney. the discerepaney between the planes would have to be due to variations in the structure parameters of the galaxies.," In the absence of any mass-to-light dependency, the discrepancy between the planes would have to be due to variations in the structure parameters of the galaxies."
 There is an intrinsic scatter of the FP that has been ound for elliptical galaxies: this has not been completely explained anc may be a manifestation of the formation LOCOSS., There is an intrinsic scatter of the FP that has been found for elliptical galaxies: this has not been completely explained and may be a manifestation of the formation process.
 A slightly dillerent approach is used in the gravitational ensing study of. Boltonet.al.(2007)., A slightly different approach is used in the gravitational lensing study of \cite{bolton07}.
. These authors oesented a new formulation of the FP using lensing data to replace surface brightness with surface mass density. arriving at the relationship of the form where a2 is the velocity dispersion. within half of the ellective radius ο. and Furthermore they suggest that the scatter about the Fundamental Plane. derived from their data. correlates with their derived. mass-to-light ratio for the galaxies in their sample.," These authors presented a new formulation of the FP using lensing data to replace surface brightness with surface mass density, arriving at the relationship of the form where $\sigma_{e2}$ is the velocity dispersion within half of the effective radius $R_{e}$, and Furthermore they suggest that the scatter about the Fundamental Plane, derived from their data, correlates with their derived mass-to-light ratio for the galaxies in their sample."
 The evidence is not strong though it is suggestive., The evidence is not strong though it is suggestive.
" They also present an interesting alternative. which they refer to as the ""Mass Plane? (AIP). in which they find the dependence of log(A.) on log(a,2) and surface mass density Noe within a radius 2)./2: with Using surface mass density X,» within a radius /2,/2 in place of surface brightness ἐν. removes one of the assumptions about the relationship between mass and light."," They also present an interesting alternative, which they refer to as the “Mass Plane” (MP), in which they find the dependence of $\log(R_e)$ on $\log(\sigma_{e2})$ and surface mass density $\Sigma_{e2}$ within a radius $R_e/2$: with Using surface mass density $\Sigma_{e2}$ within a radius $R_e/2$ in place of surface brightness $I_e$ removes one of the assumptions about the relationship between mass and light."
 If clusters. were fully virtalizecl objects with the same internal clvnamics. they would necessarily lie ona universal Fundamental Plane in the Mass-velocitv-radius space.," If clusters were fully virialized objects with the same internal dynamics, they would necessarily lie ona universal Fundamental Plane in the Mass-velocity-radius space."
 Εις, This
observation. an opaque object blocks (hie emission originating bevond it. so (hat the observed emission originates between the viewer and the object.,"observation, an opaque object blocks the emission originating beyond it, so that the observed emission originates between the viewer and the object."
 For the shadowing object. we have chosen a filament in (he Southern Galactic hemisphere (see Figure 2)).," For the shadowing object, we have chosen a filament in the Southern Galactic hemisphere (see Figure \ref{fig:diras}) )."
 estimated (he distance to (he filament as 280430 pe. which places (he filament between the Local Bubble and the Galactic halo.," \citet{penprase_etal} estimated the distance to the filament as $\pm$ 30 pc, which places the filament between the Local Bubble and the Galactic halo."
 Penpraseetal.(1998). also estimated the mean color excess (E(D— V)) of the filament as 0.170.05 magnitudes. implving an absorbing column densitv of Ny=8442.5x107 >7.," \citet{penprase_etal} also estimated the mean color excess $E(B-V)$ ) of the filament as $\pm$ 0.05 magnitudes, implying an absorbing column density of $N_H = 8.4 \pm 2.5 \times 10^{20}$ $^{-2}$."
" This is consistent with the column density implied by the Schlegel.Finkbeiner.&Davis(1998).//45 LOO jm measurement of e7.3 MJy. srt. which when scaled by the 100 yam to Nyy converstion relation for the southern hemisphere listed in Snowdenetal.(2000).. vields a column density of 9.9xLO?"" em7."," This is consistent with the column density implied by the \citet{schlegel_etal}
 100 $\mu$ m measurement of $\sim 7.3$ MJy $^{-1}$, which when scaled by the 100 $\mu$ m to $N_H$ converstion relation for the southern hemisphere listed in \citet{snowden_etal_00}, yields a column density of $9.9 \times 10^{20}$ $^{-2}$."
" For (his color excess aud (he extinction curve and parameterization presented in (1999).. 80.3,% of the pphotons originating bevond the filament should be blocked."," For this color excess and the extinction curve and parameterization presented in \citet{fitzpatrick}, $89^{+5}_{-11}\%$ of the photons originating beyond the filament should be blocked."
" As a demonstration of the filaments ""shadowing"" function. we note its ability to block κο N-ravs. ("," As a demonstration of the filament's “shadowing” function, we note it's ability to block soft X-rays. ("
The theoretical extinction of ~1 N-ravs is larger (han that of ultraviolet photons.),The theoretical extinction of $\sim\frac{1}{4}$ X-rays is larger than that of ultraviolet photons.)
" TheROSAL "" keV band image (see Figure 2)) reveals an obvious soft. X-ray depression coincident with the filament.", The $\frac{1}{4}$ keV band image (see Figure \ref{fig:diras}) ) reveals an obvious soft X-ray depression coincident with the filament.
 The surface brightness seen in the direction of the filament and attributed to the Local Bubble is 590x105 counts 1| 7. while the ~olf-lilament” surface brightness is ~1300x10.° counts >7 (x. D. Kuntz. private communication).," The surface brightness seen in the direction of the filament and attributed to the Local Bubble is $590 \times 10^{-6}$ counts $^{-1}$ $^{-2}$, while the “off-filament” surface brightness is $\sim 1300 \times 10^{-6}$ counts $^{-1}$ $^{-2}$ (K. D. Kuntz, private communication)."
 Not surprisingly. the filament has already been used successlully inROSAT soft X-ray shadowing analvses (Wang&Yu1995:Snowdenetal.2000).," Not surprisingly, the filament has already been used successfully in soft X-ray shadowing analyses \citep{wang_yu,snowden_etal_00}."
. One potential difficulty in using this region of the sky is posed by Penpraseetal. (1998)s sugeestion (hat (he filament may be part of a supernova remnant., One potential difficulty in using this region of the sky is posed by \citet{penprase_etal}' 's suggestion that the filament may be part of a supernova remnant.
 If this were (he case. then the foreground intensity should be attributed to both the Local Bubble and the supposed supernova remnant.," If this were the case, then the foreground intensity should be attributed to both the Local Bubble and the supposed supernova remnant."
 Because the results or our study are upper limits. (his point is unimportant.," Because the results or our study are upper limits, this point is unimportant."
" Observations of the targeted region. (he bulbous portion ofthe filament around —45.3"". are discussed in the following section."," Observations of the targeted region, the bulbous portion of the filament around $l = 278.6^{\rm{o}},b = -45.3^{\rm{o}}$ , are discussed in the following section."
 The ffoeal plane assembly contains four spectrograph entrance apertures., The focal plane assembly contains four spectrograph entrance apertures.
 The largest. the low resolution (LWRS) aperture measuring 30° x 30°. is used for observations of diffuse sources.," The largest, the low resolution (LWRS) aperture measuring 30” $\times$ 30”, is used for observations of diffuse sources."
 Furthermore. the instrument includes multiple approximately co-aligued channels.," Furthermore, the instrument includes multiple approximately co-aligned channels."
 Four of the channels (LiF, Four of the channels (LiF
we are aware of. the shape of the whole spatial distribution of the halo GCS has received. no explanation.,"we are aware of, the shape of the whole spatial distribution of the halo GCS has received no explanation."
 The aim of this paper is to present a possible moclel accounting for the distribution around the Galactic centre of the mass content of the halo GCS. that is. the variation with ealactocentric distance of the mass density. of the halo GCS.," The aim of this paper is to present a possible model accounting for the distribution around the Galactic centre of the mass content of the halo GCS, that is, the variation with galactocentric distance of the mass density of the halo GCS."
 We will consider. solely the Old. Lalo (OLD) GCs. excluding from our analysis the Younger Halo (YII) subsystem.," We will consider solely the Old Halo (OH) GCs, excluding from our analysis the Younger Halo (YH) subsystem."
 This one is made of GCs suspected of having been acereted and is thus of limited relevance to the earliest stages of the main body of our Galaxy (see. e.g.. Zinn 1993. van den Bereh 1993).," This one is made of GCs suspected of having been accreted and is thus of limited relevance to the earliest stages of the main body of our Galaxy (see, e.g., Zinn 1993, van den Bergh 1993)."
" A common trend. of dilferent scenarios for the formation of GC's is to assume that their gaseous progenitor clouds. whatever their size (~10""M.. e.g. Fall Rees 1985: —10M... eg. Harris DPudritz 1994). are embeddec in a hot and tenuous background. at the virial temperature."," A common trend of different scenarios for the formation of GCs is to assume that their gaseous progenitor clouds, whatever their size $\sim 10^6\,{\rm M}_{\odot}$, e.g., Fall Rees 1985; $\sim 10^9\,{\rm M}_{\odot}$, e.g., Harris Pudritz 1994), are embedded in a hot and tenuous background at the virial temperature."
 We build on this picture. splitting the protoCGalaxy in à set. of three components: a gaseous medium consisting of a hot and a cold phases (in the form of a collection of cold and dense clouds. the gaseous precursors of the halo GCs. pressure-bound. by à hot. medium). and a dark matter corona.," We build on this picture, splitting the protoGalaxy in a set of three components: a gaseous medium consisting of a hot and a cold phases (in the form of a collection of cold and dense clouds, the gaseous precursors of the halo GCs, pressure-bound by a hot medium), and a dark matter corona."
 We investigate whether the mass density. profile of the halo GCS may trace the profile of the cold phase. that is. of the cold barvonic matter which was available to star formation some GCvr ago.," We investigate whether the mass density profile of the halo GCS may trace the profile of the cold phase, that is, of the cold baryonic matter which was available to star formation some Gyr ago."
 The outline of the paper is as follows., The outline of the paper is as follows.
 In. Section. 2. we build the radial mass density. profile of the OLL and obtain new fits of a power-law with a core. with parameter values appropriate to this subsystem of GCs only.," In Section 2, we build the radial mass density profile of the OH and obtain new fits of a power-law with a core, with parameter values appropriate to this subsystem of GCs only."
 We also summarize the evidence from the literature following which mass-relatecl quantities may be better probes to the initial conditions than number related quantities., We also summarize the evidence from the literature following which mass-related quantities may be better probes to the initial conditions than number related quantities.
 In Section 3. we present our hypothesis regarding the shape of the initial mass clensity profile of the OLI GCS and we compare the OLI profile obtained in Section 2 with our suggested model. that is. with the radial density. profile of the cold. protogalactic material.," In Section 3, we present our hypothesis regarding the shape of the initial mass density profile of the OH GCS and we compare the OH profile obtained in Section 2 with our suggested model, that is, with the radial density profile of the cold protogalactic material."
 In Section 4. we simulate the evolution with time ofa GCS whose initial mass density profile mirrors the one of the cold protogalactic eas. and this for various initial GC mass spectra.," In Section 4, we simulate the evolution with time of a GCS whose initial mass density profile mirrors the one of the cold protogalactic gas, and this for various initial GC mass spectra."
 We compare the spatial mass distributions of these evolved systems with the presently. observed: spatial mass distribution of the OLI., We compare the spatial mass distributions of these evolved systems with the presently observed spatial mass distribution of the OH.
 Finally. our conclusions. are presented in Section 5.," Finally, our conclusions are presented in Section 5."
" The observed. racial distribution of the Galactic GCS (i.o.. the number of GC's per unit volume in space as a function of Galactocentric distance. 2) is often. parametrized by a simple power law with a core: Realizing a 7chi-bv-eve"". fitting of this type of curve on the observed spatial distribution of the GCS. Djoreovski Moevlan (1994) found. good matches Lory~ 3.5-4.0 and D.~ kkpe. the steepest. slope being associated. with the largest core."," The observed radial distribution of the Galactic GCS (i.e., the number of GCs per unit volume in space as a function of Galactocentric distance $D$ ) is often parametrized by a simple power law with a core: Realizing a “chi-by-eye” fitting of this type of curve on the observed spatial distribution of the GCS, Djorgovski Meylan (1994) found good matches for $\gamma \sim$ 3.5-4.0 and $D_c \sim$ kpc, the steepest slope being associated with the largest core."
 This approach is purely empirical however and is not meant to imply anv physical meaning of the distribution given by equation (1))., This approach is purely empirical however and is not meant to imply any physical meaning of the distribution given by equation \ref{eq:pl_core}) ).
 3oth the number and the mass density. profiles of the halo (Fe/1] « 0.8) GCS can be described by equation (1)). as both profiles are indistinguishable in shape.," Both the number and the mass density profiles of the halo ([Fe/H] $<$ –0.8) GCS can be described by equation \ref{eq:pl_core}) ), as both profiles are indistinguishable in shape."
 However. as argued by AleLaughlin (1999). the spatial distribution of the mass is likely to be a better. estimate of the initial conditions than its number counterpart.," However, as argued by McLaughlin (1999), the spatial distribution of the mass is likely to be a better estimate of the initial conditions than its number counterpart."
 Dynamical evolution targetting mostly low-mass clusters and these ones accounting for a limited fraction of the CCS mass (see below and Section 4)). the decrease. with time of the total GCS mass is much slower than the decrease of the total number of GCs.," Dynamical evolution targetting mostly low-mass clusters and these ones accounting for a limited fraction of the GCS mass (see below and Section \ref{sec:evol_rho_D}) ), the decrease with time of the total GCS mass is much slower than the decrease of the total number of GCs."
 This interesting property comes from how the shape of the initial mass spectrum of the halo GC's may have Iooked like., This interesting property comes from how the shape of the initial mass spectrum of the halo GCs may have looked like.
 In our Galaxy. the luminosity function of the halo GCs (the number of GCs per unit absolute magnitude. which is proportional to the number of objects per logarithmic mass interval) is bell-shaped and usually fitted: with a gaussian.," In our Galaxy, the luminosity function of the halo GCs (the number of GCs per unit absolute magnitude, which is proportional to the number of objects per logarithmic mass interval) is bell-shaped and usually fitted with a gaussian."
 However. the underlying mass spectrum (i.c.. the number of objects per linear mass interval) is well fitted by a Gvo-indesx power-law. with exponents ~2 and ~0.2 above and below ~1.510 AL... respectively (AleLaughlin 1994).," However, the underlying mass spectrum (i.e., the number of objects per linear mass interval) is well fitted by a two-index power-law, with exponents $\sim -2$ and $\sim -0.2$ above and below $\sim 1.5 \times 
10^5$ $_{\odot}$, respectively (McLaughlin 1994)."
 Phe peak of the gaussian magnitude function in fact coincides with the cluster mass at which the slope of the mass spectrum changes., The peak of the gaussian magnitude function in fact coincides with the cluster mass at which the slope of the mass spectrum changes.
 Ehe slope of the high mass regime is reminiscent of what is observed in interacting and merging galaxies (see. e.c... Whitmore Schweizer 1995. Whitmore et al.," The slope of the high mass regime is reminiscent of what is observed in interacting and merging galaxies (see, e.g., Whitmore Schweizer 1995, Whitmore et al."
 2002) where svstems of voung GC's show well defined power-law with slopes ranging between I.S and 2 for their luminosity spectrum (but see the discussion in Section 4))., 2002) where systems of young GCs show well defined power-law with slopes ranging between –1.8 and –2 for their luminosity spectrum (but see the discussion in Section \ref{sec:evol_rho_D}) ).
 ‘This thus suggests that the initial mass spectrum of the halo GCS παν have been itself a single-power law., This thus suggests that the initial mass spectrum of the halo GCS may have been itself a single-power law.
 Numerous studies of GCS dynamical evolution modclling have shown iu a Hubble time long evolution turns such an initial spectrum into the presently observed one (e.g.. Baumegarelt 1998. Vesperini 1998. Fall Zhang 2001).," Numerous studies of GCS dynamical evolution modelling have shown that a Hubble time long evolution turns such an initial spectrum into the presently observed one (e.g., Baumgardt 1998, Vesperini 1998, Fall Zhang 2001)."
 In. fact. low-=ass Clusters being the most vulnerable to evaporation and disruption. the GC€ mass spectrum gets severly depleted below a turnover of ~1.5«Lo’ M... leading to a much garallower mass spectrum (ie. slope c— 0.2) in the mass regime.," In fact, low-mass clusters being the most vulnerable to evaporation and disruption, the GC mass spectrum gets severly depleted below a turnover of $\sim 1.5 \times 10^5$ $_{\odot}$, leading to a much shallower mass spectrum (i.e., slope $\simeq-0.2$ ) in the low-mass regime."
 Pal 5 constitutes a striking exaniple of a low-mass GC currently dissolved. by the Galactic tidal [ields (Ocenkirchen et al..," Pal 5 constitutes a striking example of a low-mass GC currently dissolved by the Galactic tidal fields (Odenkirchen et al.,"
 2001: Dehnen et al..," 2001; Dehnen et al.,"
 2004)., 2004).
 Assuming that most of the GCs more massive than the turnover are spared by the dynamical evolution. AleLaughlin (1999) compares the GCS initial and final mass spectra (ic. the single power-law with the two-index power-law) and derives useful formulae to estimate the fraction of surviving clusters. both in term of mass ancl numbers (his equations 4-7).," Assuming that most of the GCs more massive than the turnover are spared by the dynamical evolution, McLaughlin (1999) compares the GCS initial and final mass spectra (i.e., the single power-law with the two-index power-law) and derives useful formulae to estimate the fraction of surviving clusters, both in term of mass and numbers (his equations 4-7)."
 His results show that mass-relatecd quantities are reasonably preserved by a Llubble time long evolution. even though low-mass GC's are disrupted in large numbers.," His results show that mass-related quantities are reasonably preserved by a Hubble time long evolution, even though low-mass GCs are disrupted in large numbers."
 Considering the specific case, Considering the specific case
1994).,.
. ESEs (vpically have cdurations that range from 0.25 to 1.2 yv and have an amplitude [rom to at 2.7 Gllz., ESEs typically have durations that range from 0.25 to 1.2 y and have an amplitude from to at 2.7 GHz.
 From a sample of flat spectrum objects. estimate [rom a Green Bank Interferometer (GBI) survev a rate of 0.008 event-vears per sonrce-vear.," From a sample of flat spectrum objects, \citet{1994ApJ...430..581F} estimate from a Green Bank Interferometer (GBI) survey a rate of 0.008 event-years per source-year."
 2 out of 10 events in the GBI study have amplitudes of ~10054. implving a rate of ~0.001 event-vears per source-vear al this large amplitude.," 2 out of 10 events in the GBI study have amplitudes of $\sim 100\%$, implying a rate of $\sim 0.001$ event-years per source-year at this large amplitude."
 ΕΠΗ sensitivity. is predominantly to events of duration less (han 0.2 vears. shorter than the shortest duration known ESE.," PiGSS-II sensitivity is predominantly to events of duration less than 0.2 years, shorter than the shortest duration known ESE."
 The large number of sources monitored. however. does permit us set lo upper limits to the ESE event rate on these (ime scales.," The large number of sources monitored, however, does permit us set to upper limits to the ESE event rate on these time scales."
 If. we consider the fractional modulation limits for monthly data. we can place an upper limit on the number of ESE events at. amplitude on 1 month time scales of of all PiGSS events for sources brighter than 10 mJv.," If we consider the fractional modulation limits for monthly data, we can place an upper limit on the number of ESE events at amplitude on 1 month time scales of of all PiGSS events for sources brighter than 10 mJy."
 This translates directly to an upper limit of 0.019 events-vear per source-vear., This translates directly to an upper limit of 0.019 events-year per source-year.
 Note that this is limit differs from the GBI limit. which is based on a sample of flat spectrum sources.," Note that this is limit differs from the GBI limit, which is based on a sample of flat spectrum sources."
 In Paper I. we estimated Chat of sources in Chis field are flat spectrum.," In Paper I, we estimated that of sources in this field are flat spectrum."
 Thus. our limit on ESEs with 1 month duration is 0.1 events-vear per source-vear.," Thus, our limit on ESEs with 1 month duration is $\sim 0.1$ events-year per source-year."
 Matched fillers can provide an improved method for searching lor ESEs on a range of time scales: Lazioetal.(2001) applied a wavelet analvsis to Green Bank Interferometer data in search of ESEs., Matched filters can provide an improved method for searching for ESEs on a range of time scales; \citet{2001ApJS..136..265L} applied a wavelet analysis to Green Bank Interferometer data in search of ESEs.
 Diffractive scintillation in the ISM can lead to flickering on timescales of ~1 clay in compact. [Iat-spectrum radio sources (Lovelletal.2008)..," Diffractive scintillation in the ISM can lead to flickering on timescales of $\sim 1$ day in compact, flat-spectrum radio sources \citep{2008ApJ...689..108L}."
 The MASIV survey found. that ol such sources exhibited fluctuations greater than over 2 days., The MASIV survey found that of such sources exhibited fluctuations greater than over 2 days.
 The larger amplitude [uctuations that PiGSS is sensitive to are more rare., The larger amplitude fluctuations that PiGSS is sensitive to are more rare.
 Fractional variations ~0.1 occur in approximately ofthe NLASIV sources., Fractional variations $\gsim 0.1$ occur in approximately of the MASIV sources.
 For the majority ol PiGSS sources. variations on a 1-day time scale at this level awe οΠο to detect in our data.," For the majority of PiGSS sources, variations on a 1-day time scale at this level are difficult to detect in our data."
 What is clear (hat very laree amplitude fluctuations such as (hose seen for J13194-3845 and PINS 0405-385 are rarely. observed (IXedziora-Chucdczeretal.1997:Dennett-ThorpedeDru," What is clear that very large amplitude fluctuations such as those seen for J1819+3845 and PKS 0405-385 are rarely observed \citep{1997ApJ...490L...9K,2000ApJ...529L..65D}."
vn 2000).. Lovelletal.(2008) [ound no objects with this level of variability out of over 400 Lat spectrum sources investigated., \citet{2008ApJ...689..108L} found no objects with this level of variability out of over 400 flat spectrum sources investigated.
 Could some of the faint sources with strong variations be IDV?, Could some of the faint sources with strong variations be IDV?
 The large aanplitdue. but low probability variations that are seen in Fig.," The large amplitdue, but low probability variations that are seen in Fig."
 10 imply rather large brightness temperatures.," \ref{fig:fluxhistdaily}
 imply rather large brightness temperatures."
 A variation of 10 mJy with a timescale of 1 day implies a brightness temperature for a source al 1 Gpe of eLOM I. IL real. brightness temperatures this large require [SS as an explanation.," A variation of 10 mJy with a timescale of 1 day implies a brightness temperature for a source at 1 Gpc of $\sim 10^{16}$ K. If real, brightness temperatures this large require ISS as an explanation."
 As Figure 16. shows. there are some sources that exhibit strong variability that is statistically significant.," As Figure \ref{fig:var3} shows, there are some sources that exhibit strong variability that is statistically significant."
 What remains to be seen [rom this list of highly variable objects is whether that, What remains to be seen from this list of highly variable objects is whether that
colunn Nyy aud a shell at s with deusitv A).,column $N_{\rm HI}$ and a shell at $r$ with density $\Delta$ ).
 In the previous section. we found that j|zL5 for optically thin systeuis in both the simulations aud iu observations.," In the previous section, we found that $\beta \approx 1.8$ for optically thin systems in both the simulations and in observations."
 Equation (1)) indicates that such a o> results iu a strong relationship between e aud I., Equation \ref{eqn:relationG}) ) indicates that such a $\beta$ results in a strong relationship between $\epsilon$ and $\Gamma$.
 The power-lav of the density PDF. 5. i$ more fundamental for determing this relationship than the power-law of FUN). 7.," The power-law of the density PDF, $\gamma$, is more fundamental for determining this relationship than the power-law of $f(N_{\rm HI})$, $\beta$."
 At high densities. the eas density PDF iu the simulations can be approximated with the power-law 2.5<>«X which also implies a strong scaling between e aud DP (equ. 1)).," At high densities, the gas density PDF in the simulations can be approximated with the power-law $2.5 < \gamma < 3$, which also implies a strong scaling between $\epsilon$ and $\Gamma$ (eqn. \ref{eqn:relationG}) )."
 The left. panels in Fiewe 23 show A?P(A) at 2| (top right panel) aud >=6 (bottoni right =The dashed red curve is the ft to P(A) in MIIR., The left panels in Figure \ref{fig:PDF} show $\Delta^3P(\Delta)$ at $z=4$ (top right panel) and $z=6$ (bottom right The dashed red curve is the fit to $P(\Delta)$ in MHR.
 The blue dotted curve is the fit to more recent snauulatious by ? (BB)., The blue dotted curve is the fit to more recent simulations by \citealt{bolton09b} (BB).
 The black solid curve is A?P(A) in the simulation without winds. and the magenta dot-dashed curve is the simulation with strong winds.," The black solid curve is $\Delta^3 P(\Delta)$ in the simulation without winds, and the magenta dot-dashed curve is the simulation with strong winds."
" Thesimulation with winds has more eas around galaxies. which increases APP(A) somewhat relative to the fiducial Tuterestingly, all of the P(A) vield +2 2.5.where 5 is the power-law iudex of P(A)."," Thesimulation with winds has more gas around galaxies, which increases $\Delta^3P(\Delta)$ somewhat relative to the fiducial Interestingly, all of the $P(\Delta)$ yield $\gamma\gtrsim2.5$, where $-\gamma$ is the power-law index of $P(\Delta)$."
 For the MIIR fit to P(A). 5c2.5 and equation (1)) miplies that DXεἰ where p—4 Thus. the intereaactic pphlotoiouization rate scales as the of the emissivity.," For the MHR fit to $P(\Delta)$, $\gamma\approx2.5$ and equation \ref{eqn:relationG}) ) implies that $\Gamma\propto\epsilon^n$ where $n=3$ Thus, the intergalactic photoionization rate scales as the of the emissivity."
 However. à is extremely scusitive to 5 in this equation.," However, $n$ is extremely sensitive to $\gamma$ in this equation."
 The P(A) in our simulations aud in those of BB show ~=BN3 at relevant A (with 5 increasing with redshift}. which formally amply a=23/—x given equation CD.," The $P(\Delta)$ in our simulations and in those of BB show $\gamma=2.5-3$ at relevant $\Delta$ (with $\gamma$ increasing with redshift), which formally imply $n=3-\infty$ given equation \ref{eqn:relationG}) )."
 Therefore. the flatness of APP(A) indicates a strong relationship between € aud IE.," Therefore, the flatness of $\Delta^3P(\Delta)$ indicates a strong relationship between $\epsilon$ and $\Gamma$."
 Vow justified is the MIIR assumption of a critical density at which eas becomes neutral?, How justified is the MHR assumption of a critical density at which gas becomes neutral?
 The curves labeled “RT in the right panels of Figure 3. are the PDF of ionized seas in our calculations. or more specifically A°P(A) multiplied by DoggNNii.," The curves labeled “RT"" in the right panels of Figure \ref{fig:PDF} are the PDF of ionized gas in our calculations, or more specifically $\Delta^3P(\Delta)$ multiplied by $\Gamma n_{\rm HI}/[\alpha_{\rm A}\,n_{H}^2]$."
 The latter factor is equal to the square of the ionized fraction iu the absence of collisional jionizatious., The latter factor is equal to the square of the ionized fraction in the absence of collisional ionizations.
 The recombination rate is proportional to the logarithuuc iuteeral over the RT curves., The recombination rate is proportional to the logarithmic integral over the RT curves.
 The RT curves follow the density PDF curves before au abrupt cutoff. which supports the MITIR model assumption of a characteristic A;.," The RT curves follow the density PDF curves before an abrupt cutoff, which supports the MHR model assumption of a characteristic $\Delta_i$ ."
 We can measure the power-law relationship between e and E directly in the simmlations bv calculating the recombination rate of the eas (which is in balance with, We can measure the power-law relationship between $\epsilon$ and $\Gamma$ directly in the simulations by calculating the recombination rate of the gas (which is in balance with
 ο used to estimate the BIT mass (App)., $z>5.7$ be used to estimate the BH mass ).
 From the line Hux ratios we can instead derive chemical abundanuces of he BLR eas that are fundamental to set constraiuts on he star formation history of the QSO lost galaxy., From the line flux ratios we can instead derive chemical abundances of the BLR gas that are fundamental to set constraints on the star formation history of the QSO host galaxy.
 Under the asstuuption that the dvuamics of the DER is dominated by the central eravitational field. it is possible to estimate bby using the velocity aud tle distance of the line-cuutting eas from the ceutral BI :AMpgxRoof.," Under the assumption that the dynamics of the BLR is dominated by the central gravitational field, it is possible to estimate by using the velocity and the distance of the line-emitting gas from the central BH: $M_{BH}\propto R \ v^2$."
 From reverberation mapping studies of οσα active galactic nuclei (AGNs) it has been found that Ris related to the coutimiuun huumositv £ ΣΑ , From reverberation mapping studies of local active galactic nuclei (AGNs) it has been found that $R$ is related to the continuum luminosity $L$: $R\propto L^{0.5}$.
Measurements of the huniuositv aud of the gas velocity. via Doppler-xoadened Line-width. cau thus be used to determine the from single epoch spectra.," Measurements of the luminosity and of the gas velocity, via Doppler-broadened line-width, can thus be used to determine the from single epoch spectra."
 Various strong emission ines can be used as cestimators:Ho.οι.Mei. [|Peterson2010.," Various strong emission lines can be used as estimators:, ."
. For objects in the local universe. see]the RL relation and its iutriusic scatter have been investigated in detail using the Hine aud the relative continu.," For objects in the local universe, the $R-L$ relation and its intrinsic scatter have been investigated in detail using the line and the relative continuum."
 These studies have shown that one cau obtain accurate eestinates via the Wine., These studies have shown that one can obtain accurate estimates via the line.
 For sources at hnieh-z a complication is that the eenuission liue is redshifted out of the visible window already. at modest redshifts., For sources at high-z a complication is that the emission line is redshifted out of the visible window already at modest redshifts.
 Whether or not a particular UV line cau be used to estimate ddepends ou how well the respective UV line widths inACN spectra are correlated., Whether or not a particular UV line can be used to estimate depends on how well the respective UV line widths inAGN spectra are correlated.
In. this case. the set of equations that describe a geometrically thin. optically thick. stationary. accretion-disk with a Keplerian profile is given by where a=O.5aq5 18 the disk viscosity. M=I3M4My. Ry=(ον. M=10Myy is the disk mass accretion. g= O.82goss. Ty 1s the disk temperature. ay its density. Hy its half-height. and Uy is the photon energy density emitted by the disk.,"In this case, the set of equations that describe a geometrically thin, optically thick, stationary accretion-disk with a Keplerian profile is given by where $\alpha = 0.5\alpha_{0.5}$ is the disk viscosity, $M = 14
M_{\odot} M_{14}$ , $R_{X} = 10^{7} R_{X,7}$, $\dot{M} = 10^{19}
\dot{M}_{19}$ is the disk mass accretion, $q =
[1-(R_{S}/R_{X})^{1/2}]^{1/4} =0.82 q_{0.82}$ , $T_d$ is the disk temperature, $n_d$ its density, $H_d$ its half-height, and $U_d$ is the photon energy density emitted by the disk."
 To determine the accretion rate immediately before an event of violent magnetic reconnection. we assume the equilibrium between the disk gas ram pressure and the magnetic pressure of the magnetosphere anchored at the event horizon of the black hole.," To determine the accretion rate immediately before an event of violent magnetic reconnection, we assume the equilibrium between the disk gas ram pressure and the magnetic pressure of the magnetosphere anchored at the event horizon of the black hole."
 Assuming spherical geometry. the radial accretion velocity can be approached by the free fall velocity.," Assuming spherical geometry, the radial accretion velocity can be approached by the free fall velocity."
 Also. assuming that the intensity of the field anchored in the BH horizon ts on the order of the inner disk magnetic field (MacDonald et al.," Also, assuming that the intensity of the field anchored in the BH horizon is on the order of the inner disk magnetic field (MacDonald et al."
 1986: de Gouveia Dal Pino Lazarian 2005). we find that On the other hand. the disk magnetic field can be parameterized by 8. here defined as the ratio between the gastradiation pressure (which is dominated by the radiation pressure) and the magnetic pressure.," 1986; de Gouveia Dal Pino Lazarian 2005), we find that On the other hand, the disk magnetic field can be parameterized by $\beta$, here defined as the ratio between the gas+radiation pressure (which is dominated by the radiation pressure) and the magnetic pressure."
" Using Eq.(4) to obtain the radiation pressure (py=U,;/3) and the equation above. we find that the magnetic field and the accretion rate at Ry are where 5=O.8fos."," Using Eq.(4) to obtain the radiation pressure $p_{d} = U_{d}/3$ ) and the equation above, we find that the magnetic field and the accretion rate at $R_X$ are where $\beta = 0.8 \beta_{0.8}$."
 Liu et al. (, Liu et al. (
2002) proposed a simple model to quantify the parameters of the corona of a magnetized disk system.,2002) proposed a simple model to quantify the parameters of the corona of a magnetized disk system.
 Assuming as in the solar corona that gas evaporation at the foot point of a magnetic flux tube quickly builds up the density of the corona to a certain value and that the tube radiates the heating due to magnetic reconnection through Compton scattering. the coronal temperature and density in terms of the disk parameters can be derived respectively as where {ο=100Νν ts the scale height of the Y neutral zone in the corona.," Assuming as in the solar corona that gas evaporation at the foot point of a magnetic flux tube quickly builds up the density of the corona to a certain value and that the tube radiates the heating due to magnetic reconnection through Compton scattering, the coronal temperature and density in terms of the disk parameters can be derived respectively as where $l_{100}= 100 R_X$ is the scale height of the Y neutral zone in the corona."
 In the equations above we also assumed that the magnetic field at the reconnection region in the corona is on the order of the field anchored at the disk inner radius (see Fig., In the equations above we also assumed that the magnetic field at the reconnection region in the corona is on the order of the field anchored at the disk inner radius (see Fig.
 1), 1).
" As described in de Gouveia Dal Pino Lazarian (2005). the rate of magnetic energy that can be extracted from the Y-zone in the corona (above and below the disk) through reconnection is where B is the magnetic field at the reconnection zone. v4 is the coronal Alfvénn speed. v4,=Bf(Aenm,2n ny the hydrogen mass. and ARy is the width of the current sheet."," As described in de Gouveia Dal Pino Lazarian (2005), the rate of magnetic energy that can be extracted from the Y-zone in the corona (above and below the disk) through reconnection is where $B$ is the magnetic field at the reconnection zone, $v_A$ is the coronal Alfvénn speed, $v_A = B/(4\pi n_c m_p)^{1/2}$, $m_p$ the hydrogen mass, and $\Delta R_{X}$ is the width of the current sheet."
 This last term can be estimated considering the condition for which the resistivity at thereconnection zone is anomalous. as in Lazarian Vishiniae (1999) and de Gouveia Dal Pino Lazarian (2005):," This last term can be estimated considering the condition for which the resistivity at thereconnection zone is anomalous, as in Lazarian Vishiniac (1999) and de Gouveia Dal Pino Lazarian (2005):"
he decrease in vertical shear. aud the cousequet increase dmn ostabilitv. brought about bv an increase in lk inetallicitv.,"the decrease in vertical shear, and the consequent increase in stability, brought about by an increase in bulk metallicity."
" However. these simple relations are not enough to quantify the super-linear trend. because. A appears to have cancelled. out of both Oc,/0: aud the Druut frequency."," However, these simple relations are not enough to quantify the super-linear trend because $\Delta z$ appears to have cancelled out of both $\p v_{\phi}/\p z$ and the Brunt frequency."
 This difficulty is avoided iu a more ormal derivation of the relation between gry aud Sy/Me uade under the assunption of constant A7. as described in Appendix C...," This difficulty is avoided in a more formal derivation of the relation between $\mu_0$ and $\Sigmad/\Sigmag$, made under the assumption of constant $Ri$ , as described in Appendix \ref{app:superlinear}."
 We note further that jy scales with the inverse of the radial pressure eracieut parameter Όμωςὃς (equivalently i) in the sane super-linear way as for X4/X.., We note further that $\mu_0$ scales with the inverse of the radial pressure gradient parameter $\vmax/\cs$ (equivalently$\eta$ ) in the same super-linear way as for $\Sigmad/\Sigmag$ .
 The sinaller Is μμος. the greater is the maxinmu jy attainable: the relation between these quantities is derived mucder the asstuption of constant Ri in Appendix C..," The smaller is $\vmax/\cs$, the greater is the maximum $\mu_0$ attainable; the relation between these quantities is derived under the assumption of constant $Ri$ in Appendix \ref{app:superlinear}."
 Thus we expect our numerical results for maxpy (2.9. 26.1) to depend scusitively on our assumed value of easος= 0.025.," Thus we expect our numerical results for $\max \mu_0$ (2.9, 26.4) to depend sensitively on our assumed value of $\vmax/\cs = 0.025$ ."
 (Bai&Stone(2010€) also reported that the degree of chumping caused by the streaming instability mereased strouely with decreasing Cua ὃς), \citet{baistone10b} also reported that the degree of clumping caused by the streaming instability increased strongly with decreasing $\vmax/\cs$ .)
 With each iteration of our standard procedure we allowed dust particles to settle at their full terminal volocities. regardless of gas notions evinced i previous iterations.," With each iteration of our standard procedure we allowed dust particles to settle at their full terminal velocities, regardless of gas motions evinced in previous iterations."
 We tried to account for these eas motious iu a inocdified procedure by reducing settling velocities at altitude where dust may have already attained marginal stability., We tried to account for these gas motions in a modified procedure by reducing settling velocities at altitude where dust may have already attained marginal stability.
 Settling velocities were reduced by weighting functions chosen by eve., Settling velocities were reduced by weighting functions chosen by eye.
 This modified procedure enabled us to extend the settling sequence by one iteration but uo inore., This modified procedure enabled us to extend the settling sequence by one iteration but no more.
 Other weighting functions might allow the sequence to be exteuded further., Other weighting functions might allow the sequence to be extended further.
 Introducing weighting functions carlicr in the sequence (rather than at the end of our standard procedure. as we have done). aud increasing the midplane density by a smaller increeut with cach iteration (less than the increment that we have adopted). would allow for a more gradual evolution and possibly periit the midplane to reach still ereater densitics.," Introducing weighting functions earlier in the sequence (rather than at the end of our standard procedure, as we have done), and increasing the midplane density by a smaller increment with each iteration (less than the increment that we have adopted), would allow for a more gradual evolution and possibly permit the midplane to reach still greater densities."
 Such a program would be straightforward to pursue but would be subject to arbitrariness im thle forms of the weighting fuuctious., Such a program would be straightforward to pursue but would be subject to arbitrariness in the forms of the weighting functions.
" A amore direct approach would be to abandon our hybrid 1D]38D scheme aud uperade the 3D code to allow for a non-zero aerodyvnuanic stopping fine fa, for dust.", A more direct approach would be to abandon our hybrid 1D+3D scheme and upgrade the 3D code to allow for a non-zero aerodynamic stopping time $t_{\rm stop}$ for dust.
 Then both settling aud stability could be tracked within a single 3D code., Then both settling and stability could be tracked within a single 3D code.
 Similar codes have been written (e.e..Johansenetal.2009:Bai&Stone2OL0b).. but their application has Όσοι ocussed ou the streaming instability. on particles having Onteop2OL aud Quodeldepencdent) sizes upwards of cecimeters.," Similar codes have been written \citep[e.g.,][]{johansenetal09,baistone10a}, but their application has been focussed on the streaming instability, on particles having $\OmegaK t_{\rm stop} \gtrsim 0.1$ and (model-dependent) sizes upwards of decimeters."
 By contrast. we are interested im the yossibility that even the smallest particles. for which P<Ogfags<1. undergo eravitational instability.," By contrast, we are interested in the possibility that even the smallest particles, for which $0 < \OmegaK t_{\rm stop} \ll 1$, undergo gravitational instability."
 The woblem of settliug small particles may be coupled to he problem of settling bie ones., The problem of settling small particles may be coupled to the problem of settling big ones.
 Even if mareinally coupled particles comprise only. a minority of the disks solid mass. the turbulence they induce by the streaming instability may prevent simaller particles from settliug iuto the thin lavers required for gravitational instability (Bai&Stone2010a).," Even if marginally coupled particles comprise only a minority of the disk's solid mass, the turbulence they induce by the streaming instability may prevent smaller particles from settling into the thin layers required for gravitational instability \citep{baistone10}."
". Quautifvine what is meant by ""nmnibnortv remains a forefrout issue.", Quantifying what is meant by “minority” remains a forefront issue.
 Aa efficieut. sclieme or muuericallv simulating this problem: would combine he anelastic inethods we have adopted (so that the code inestep is not Haunted by the sound-crossing time) with an mplcit particle integrator like the kind devised by Bai&Stone(201010) (so that the code timestep is uot nuited by , An efficient scheme for numerically simulating this problem would combine the anelastic methods we have adopted (so that the code timestep is not limited by the sound-crossing time) with an implicit particle integrator like the kind devised by \citet{baistone10a} (so that the code timestep is not limited by $t_{\rm stop}$ ).
Adding κοτομ).οταν]τν would be another improvement., Adding self-gravity would be another improvement.
 As roted at the beginning of refsecidissun.. vertical self-eravity is expected to increase he maxima dust-to-eas ratio bv of order for the case of bulk solar metallicity.," As noted at the beginning of \\ref{sec:dissum}, vertical self-gravity is expected to increase the maximum dust-to-gas ratio by of order for the case of bulk solar metallicity."
" For the case of a few « supersolar metallicity. the maenitucle of the correction is ""uncertain."," For the case of a few $\times$ supersolar metallicity, the magnitude of the correction is uncertain."
 It is probably at least of order unity. but might be nuch more. eiven the appearance of an iufinite density cusp iu those solutions of Sekiva(1998). aud. Youdiu&Shu(2002) that account for vertical ποοταν," It is probably at least of order unity, but might be much more, given the appearance of an infinite density cusp in those solutions of \citet{sekiya98} and \citet{youdinshu02} that account for vertical self-gravity."
" At the sale time. seclberavity Πο actually lint τν,maxiuuu dust-to-gas ratios if the fluid becomes eravito-turbuleut without producing collapsed objects (Camunic2001)."," At the same time, self-gravity might actually limit maximum dust-to-gas ratios if the fluid becomes gravito-turbulent without producing collapsed objects \citep{gammie01}."
. Observations have unveiled several trends between stellar properties aud the likelihood of planet occurrence., Observations have unveiled several trends between stellar properties and the likelihood of planet occurrence.
 Among the most well-known is the positive correlation between the occurrence rate of giaut planets and the host star metallicity [Fe/TI] (Couzalez1997:Santosetal. 2005)..," Among the most well-known is the positive correlation between the occurrence rate of giant planets and the host star metallicity [Fe/H] \citep{gonzalez97, santosetal04,
 fischervalenti05}. ."
 Johnsonetal.(2010) provided a comprehensiveanalysis. using a sample of 1266 localstars to ask whether the treud with metallicity persists across all stellar masses AY...," \citet{johnsonetal10} provided a comprehensiveanalysis, using a sample of 1266 localstars to ask whether the trend with metallicity persists across all stellar masses $M_\ast$ ."
 The answer is, The answer is
also mace use of the Jodrell Bank timing data on the Crab pulsar. in particular the published barycentric arrival times on 2003 June 15. July 15 and August 15.,"also made use of the Jodrell Bank timing data on the Crab pulsar, in particular the published barycentric arrival times on 2003 June 15, July 15 and August 15."
 The Jodrell Bank ephemeris for 2003. Jub 15 was initially used., The Jodrell Bank ephemeris for 2003 July 15 was initially used.
" This gives a rotation [frequency of 29.8044286490 Lz. a frequency. derivative of 3.7353779107"" and a DAL of 56.76 “pe."," This gives a rotation frequency of 29.8044286490 Hz, a frequency derivative of $-3.7353779 \times 10^{-10}$ and a DM of 56.76 $^{-3}$ pc."
 The standard. timing package. TEMPO. was usec with this ephemeris ancl the arrival times lor RAPE. Jodrell Bank and Parkes data as cleseribecl above.," The standard timing package, TEMPO, was used with this ephemeris and the arrival times for RXTE, Jodrell Bank and Parkes data as described above."
 Ehe resultant residual is shown in the top panel of Fig 1l., The resultant residual is shown in the top panel of Fig \ref{crab_fit}.
 We then fitted. for frequency. frequency derivative and. the frequency second: derivative and the residual from this fit is shown in the lower panel of the figure.," We then fitted for frequency, frequency derivative and the frequency second derivative and the residual from this fit is shown in the lower panel of the figure."
 lt can be seen that all 3 data sets agree within the errors and the radio giants have a relatively large jitter in their arrival times., It can be seen that all 3 data sets agree within the errors and the radio giants have a relatively large jitter in their arrival times.
 We therefore believe that the times-ol-arrival of the RATE data are correct within the quoted errors ancl that the Parkes data are correctly de-dispersed and time tagged., We therefore believe that the times-of-arrival of the RXTE data are correct within the quoted errors and that the Parkes data are correctly de-dispersed and time tagged.
 Each dataset on was searched for giant pulses and their topocentic time of arrival at 1390 ALLL was recorded with an accuracy of SO yes. As shown in Paper L the eiant pulses in occur in two groups separated by about 0.25 phase (12 ms).," Each dataset on was searched for giant pulses and their topocentic time of arrival at 1390 MHz was recorded with an accuracy of 80 $\mu$ s. As shown in Paper I, the giant pulses in occur in two groups separated by about 0.25 phase (12 ms)."
 Within each eroup the jitter is 0.1 phase (5 ms)., Within each group the jitter is 0.1 phase (5 ms).
 Simultaneous RAPE anc Parkes observations were mace on 2003 August 6., Simultaneous RXTE and Parkes observations were made on 2003 August 6.
 Phe arrival of the X-ray pulse at the barycentre occurred 74832.4986 seconds after ALJD 52857.0 and at this epoch the rotation frequency. was 19.775530 112., The arrival of the X-ray pulse at the barycentre occurred 74832.4986 seconds after MJD 52857.0 and at this epoch the rotation frequency was 19.775530 Hz.
 A second. IUNTIZ epoch was obtained. on 2003 August 17., A second RXTE epoch was obtained on 2003 August 17.
 Using the rotation frequency of 19.775350. Lz obtained on that cate. we computed. a Frequency derivative of LST10τον ? between the two dates.," Using the rotation frequency of 19.775350 Hz obtained on that date, we computed a frequency derivative of $-1.87\times 10^{-10}$ $^{-2}$ between the two dates."
 This vieldecl an initial timing solution for the pulsar., This yielded an initial timing solution for the pulsar.
 We then included the times of arrival of the giant. pulses detected. during the August session., We then included the times of arrival of the giant pulses detected during the August session.
 For timing purposes. we picked only the largest amplitude pulses so that the results would not be alfected by possible spurious giants at low signal to noise ratios.," For timing purposes, we picked only the largest amplitude pulses so that the results would not be affected by possible spurious giants at low signal to noise ratios."
 We split the giants into the two groupings and timed each, We split the giants into the two groupings and timed each
be à universal property of RRab Several promising models have been proposed to explain the Blazhko phenomenon. among those are the magnetic oblique pulsator-rotator model (e.g..Shiba-hashi2000) that works similarly to the mechanism that causes the typical patterns of rop. variation. as well as models involving resonances between the main pulsation ancl either higher-order racial modes or non-radial modes (e.g...Dziembowski&Alizerski2004.and.referencestherein)..,"be a universal property of RRab Several promising models have been proposed to explain the Blazhko phenomenon, among those are the magnetic oblique pulsator-rotator model \citep[e.g.,][]{shi} that works similarly to the mechanism that causes the typical patterns of roAp variation, as well as models involving resonances between the main pulsation and either higher-order radial modes or non-radial modes \citep[e.g.,][and references therein]{dzi}."
 None of these models. however. succeeds. in explainine the full spectrum. of observed features of Blazhko stars.," None of these models, however, succeeds in explaining the full spectrum of observed features of Blazhko stars."
 The repeated non-cetection of the required. strong dipole magnetic fields in Ri Lvrae stars in recent studies (Chaclicletal.2004:Schnerral.2009) poses a significant problem for the magnetic models. anc the changes that have been reported. to occur in the Blazhko phenomenon of several stars. especially variations of its period. are a big challenge for any model that links the Blazhko ellect directly to rotation and therefore predicts an almost ¢lock-work like Ao scenario. that explicitly favors irregular or stochastic Blazhko eveles was published by Stothers (2006).," The repeated non-detection of the required strong dipole magnetic fields in RR Lyrae stars in recent studies \citep{cha04, schne, kol09, gug09} poses a significant problem for the magnetic models, and the changes that have been reported to occur in the Blazhko phenomenon of several stars, especially variations of its period are a big challenge for any model that links the Blazhko effect directly to rotation and therefore predicts an almost clock-work like A scenario that explicitly favors irregular or stochastic Blazhko cycles was published by \citet{sto}."
. It connects the amplitude ancl phase modulations of Blazhko stars to a evelic weakening and strengthening of the turbulent convection inside the helium and hyelrogen ionisation zones due to the presence of local transient. magnetic Alost recentlv. the detection of period doubling in several RRO Lsrae stars in the high-precision data delivered. by the. Wepler mission (Ixolenbergctal.Oh:Szaboetal.2010) triggered. the exploration of racial resonances in Blazhko lili Lyrae stars.," It connects the amplitude and phase modulations of Blazhko stars to a cyclic weakening and strengthening of the turbulent convection inside the helium and hydrogen ionisation zones due to the presence of local transient magnetic Most recently, the detection of period doubling in several RR Lyrae stars in the high-precision data delivered by the Kepler mission \citep{kol10b, szabo10} triggered the exploration of radial resonances in Blazhko RR Lyrae stars."
 While hvdrodsnamical simulations successfully reproduced period doubling (Szabóetal.0:Ixolláthοἱ and found a 9:2 resonance between the Oth overtone which appears as à surface mode and the fundamental pulsation to be responsible for the phenomenon. they were not able to viel modulated. light curves.," While hydrodynamical simulations successfully reproduced period doubling \citep{szabo10, kollath11}, and found a 9:2 resonance between the 9th overtone which appears as a surface mode and the fundamental pulsation to be responsible for the phenomenon, they were not able to yield modulated light curves."
 It was an alternative approach by Buchler&Ixolláth(2011). using the amplitude equation formalism. that succeeded in producing amplitude modulation of both regular aud irregular type.," It was an alternative approach by \citet{buchler11}, using the amplitude equation formalism, that succeeded in producing amplitude modulation of both regular and irregular type."
 In their simulations. chaos occurs because of the presence of a strange attractor in the dynamics. causing irregular Changes of both the amplitude and/or the length of the Blazhko eveles. irregularities in. the Blazhko phenomenon. sometimes also accompanied by a change in the main pulsation period have been reported for a sample of RR Lyrac stars.," In their simulations, chaos occurs because of the presence of a strange attractor in the dynamics, causing irregular Changes of both the amplitude and/or the length of the Blazhko cycles, irregularities in the Blazhko phenomenon, sometimes also accompanied by a change in the main pulsation period have been reported for a sample of RR Lyrae stars."
 A detailed look at the known changes in Blazhko evcles of dillerent stars will be taken in Section 5.1.., A detailed look at the known changes in Blazhko cycles of different stars will be taken in Section \ref{changes}.
" One has to note. however. that. previous studies of changing Blazhko phenomena usually relied. on ground-based. data ον, sullering from small or sometimes large gaps due to daylight and/or weather. and therefore also often from. incomplete coverage of the pulsation zu especially the Blazhko period."," One has to note, however, that previous studies of changing Blazhko phenomena usually relied on ground-based data only, suffering from small or sometimes large gaps due to daylight and/or weather, and therefore also often from incomplete coverage of the pulsation and especially the Blazhko period."
 Reports on long-term variations of the Blazhko effect in specific stars also often compare publications of dillerent. authors using cdilferen methods with varying precisions., Reports on long-term variations of the Blazhko effect in specific stars also often compare publications of different authors using different methods with varying precisions.
 It was therefore often impossible to sav when the changes took place anc whether they happened abruptly or continuously., It was therefore often impossible to say when the changes took place and whether they happened abruptly or continuously.
 In this study. we have. for the [first time. investigate strong evele-to-cvele changes of the Blazhko effect in a continuous and homogeneous data set that covers or255 pulsation and more than 4 full Blazhko Section 3. will present the data used for analysis. as well as data processing methods.," In this study, we have, for the first time, investigated strong cycle-to-cycle changes of the Blazhko effect in a continuous and homogeneous data set that covers 255 pulsation and more than 4 full Blazhko Section \ref{data} will present the data used for analysis, as well as data processing methods."
 Section 4 explains the analvsis methods anc presents the results. while their implications are discussed in Section 5..," Section \ref{analysis} explains the analysis methods and presents the results, while their implications are discussed in Section \ref{disc}."
 t the final stages of preparing our manuscript. we were informed that another group had. analyzed the same data set and published their results in Chaclicletal.(2011).," At the final stages of preparing our manuscript, we were informed that another group had analyzed the same data set and published their results in \citet{cha11}."
 The main cillerences between the results of the two manuscripts are brielly summarized in appendix A.., The main differences between the results of the two manuscripts are briefly summarized in appendix \ref{app}.
" The star CoRoT 105288363 (a=18""39""30.87.08|772653.9"". 2000) is à 15.3 magnitude star (V) in the constellation Ophiuchus."," The star CoRoT 105288363 $(\alpha=18^{h} 39^{m} 30.8^{s}, \delta=+7\degr 26' 53.9'', J2000$ ) is a 15.3 magnitude star (V) in the constellation Ophiuchus."
 Before the Color mission. it was not known be variable.," Before the CoRoT mission, it was not known to be variable."
 C'oltoT 105288363.ihe was classified as an RR Lyrac variable with CoBnot Variability. Classifier. using two different automated supervised: classification methods. (Dehosscheretal.2009) ancl was then confirmed. by human. inspection.," CoRoT 105288363 was classified as an RR Lyrae variable with the 'CoRoT Variability Classifier', using two different automated supervised classification methods \citep{deb} and was then confirmed by human inspection."
 The ExoDat database (Deleuiletal.2009)... which provides important information on the parameters of the stars observed. in the Colto nM field. lists a contamination of the ColtoT 105288363.m data of 0.177. meaning that 17.7. per cent οἱ measurec llux might originate from background stars.," The ExoDat database \citep{del}, which provides important information on the parameters of the stars observed in the CoRoT exoplanet field, lists a contamination of the CoRoT 105288363 data of 0.177, meaning that 17.7 per cent of the measured flux might originate from background stars."
 The nearest MMstars also included in the photometric mask of ColtoT. 10288363 are also listed in ExoDat ane are all 2 or more magniluces fainter than the target The data: used in this study were obtained in the framework of the Additional Programmes of the exoplanctary field during. the second long run. in direction galactic center (LItc02)., The nearest background stars also included in the photometric mask of CoRoT 105288363 are also listed in ExoDat and are all 2 or more magnitudes fainter than the target The data used in this study were obtained in the framework of the Additional Programmes of the exoplanetary field during the second long run in direction galactic center (LRc02).
. Observations were ee out during a time span of 145 d from April 15. 2008 diasto September 7. 2008. or ColtoT JD 3027.47 to ," Observations were carried out during a time span of 145 d from April 15, 2008 to September 7, 2008, or CoRoT JD 3027.47 to 3172.46."
Note that the zero point. of Coltol JD corresponds to LJD 2451545.0. which is January 1. 2000 at 12:00:00 UT.," Note that the zero point of CoRoT JD corresponds to HJD 2451545.0, which is January 1, 2000 at 12:00:00 UT."
 Phe nominal exposure time in the exoplanet field is 512 s. as 16 measurements with a sampling of 32 s are averaged on board. (Debosscheret ," The nominal exposure time in the exoplanet field is 512 s, as 16 measurements with a sampling of 32 s are averaged on board \citep{deb}. ."
For this studs we used the calibrated light, For this study we used the calibrated light
ol sight also carries valuable knowledge of the matter distribution (Pen2006 ).,"of sight also carries valuable knowledge of the matter distribution \citep{pen04,cooray06}."
. Individual. strongly lensecl standardized candles. as well as their statistics. provide important probes of cosmology and galaxy cluster mass profiles ancl velocity dispersions through the amplification Gime variation. multiple image separations. image flux ratios. and time delavs (lolz2001:Goobaretal.2002:Lewis&IbataLinder2004).," Individual, strongly lensed standardized candles, as well as their statistics, provide important probes of cosmology and galaxy cluster mass profiles and velocity dispersions through the amplification time variation, multiple image separations, image flux ratios, and time delays \citep{holz01,goobar02,lewisibata,linsl}."
. The high equality. multiband. eadenced sample of tens of strongly lensed. very high redshilt supernovae from SNAP will contribute a rich science resource.," The high quality, multiband, cadenced sample of tens of strongly lensed, very high redshift supernovae from SNAP will contribute a rich science resource."
 Very hieh redshift supernovae open windows on several areas of astrophivsics., Very high redshift supernovae open windows on several areas of astrophysics.
 We examine here the use of such observations to learn about supernova plivsies and dust properties., We examine here the use of such observations to learn about supernova physics and dust properties.
form as well as the interstellarseparation?.. and is about 3 orders of magnitude larger than the harel-solt semi-major axis at that radius. shown by the upper dotted line.,"form as well as the interstellar, and is about 3 orders of magnitude larger than the hard-soft semi-major axis at that radius, shown by the upper dotted line."
 We show the freeze-out. radius at the 0.5 Lagrangian racius. because very few permanent soft binaries form inside the half-mass radius (figure 1)).," We show the freeze-out radius at the 0.5 Lagrangian radius, because very few permanent soft binaries form inside the half-mass radius (figure \ref{1024lagr}) )."
 This is shown as the lower dashed line. only about 1: order of magnitude greater than the hard-soft bouncary at that raclius(the lower dotted line).," This is shown as the lower dashed line, only about 1 order of magnitude greater than the hard-soft boundary at that radius(the lower dotted line)."
 VPhroughout the evolution of the cluster. at the hall-mass radius is smaller than «ων by roughly an order of magnitude.," Throughout the evolution of the cluster, at the half-mass radius is smaller than $a_{sep}$ by roughly an order of magnitude."
 The conditions for binaries to drop out of the statistical balance are not met. and thus very few permanent soft. binaries form interior to the the half-mass radius.," The conditions for binaries to drop out of the statistical balance are not met, and thus very few permanent soft binaries form interior to the the half-mass radius."
" In the outer reaches of the cluster es,«aps For the entirety of the clusters evolution. and the semi-major axes of the permanent soft binaries formed tracks the evolution of a."," In the outer reaches of the cluster $a_{sep} <$ for the entirety of the cluster's evolution, and the semi-major axes of the permanent soft binaries formed tracks the evolution of $a_{sep}$."
" In this picture. in regions where ei,«ape; most nearest neighbours that are. instantancously bound.— should stay bound permanently."," In this picture, in regions where $a_{sep} <$ most nearest neighbours that are instantaneously bound should stay bound permanently."
 In order to estimate the number of soft permanent binaries that form. we need. to determine the fraction of nearest neighbours that are bound.," In order to estimate the number of soft permanent binaries that form, we need to determine the fraction of nearest neighbours that are bound."
 We begin by estimating a characteristic interstellar separation at the virial radius 2. as au8ΠΑΝDU , We begin by estimating a characteristic interstellar separation at the virial radius $R_v$ as $a_{sep} \approx R_v N^{-1/3}$.
The velocity associated with this separation d$ C44m(Comf£aus)1 , The velocity associated with this separation is $v_{sep} \approx (G m / a_{sep})^{1/2}$ .
".Phe boundary semi-major. axis. between a hard. ancl soft binary is given by a,57PN and is related to the velocity dispersion by az(Cem,..2"," The boundary semi-major axis between a hard and soft binary is given by $a_{h-s} \approx R_v N^{-1}$, and is related to the velocity dispersion by $\sigma \approx (G m / a_{h-s})^{1/2}$."
 Ifthe nearest neighbour of a star is at something close to the interstellar separation. what is the fraction of stars in the cluster that have a relative velocity low enough for them to be bound?," If the nearest neighbour of a star is at something close to the interstellar separation, what is the fraction of stars in the cluster that have a relative velocity low enough for them to be bound?"
 Phe relative velocities are a Maxwellian with dispersion. V2e. and. we are interested in pairs with velocities below 5νοων.," The relative velocities are a Maxwellian with dispersion $\sqrt{2} \sigma$, and we are interested in pairs with velocities below $\sqrt{2} v_{sep}$."
 Phe fraction of bound. neighbours is the integral over the Maxwellian velocity distribution up to that maximum velocity. where we are integrating over the ratio of the velocity to the dispersion.," The fraction of bound neighbours is the integral over the Maxwellian velocity distribution up to that maximum velocity, where we are integrating over the ratio of the velocity to the dispersion."
 “Phe ratio e/o8N143. even for clusters as small as No~100 less than about 0.2.," The ratio $v_{sep} / \sigma \approx N^{-1/3}$, even for clusters as small as $N \sim 100$ less than about 0.2."
 In this limit the exponential term is very close to unity. and the bound fraction is well approximated hy As noted. that ratio of velocities is. approximately Nος κο the bound. fraction should be frownedFON D," In this limit the exponential term is very close to unity, and the bound fraction is well approximated by As noted, that ratio of velocities is approximately $N^{-1/3}$, so the bound fraction should be $f_{bound} \approx N^{-1}$."
OA point of concern is that we are calculating using a single value of these variables for the entire cluster. ancl taking those values at the virial radius rather than the outer regions of the cluster.," A point of concern is that we are calculating using a single value of these variables for the entire cluster, and taking those values at the virial radius rather than the outer regions of the cluster."
 However. when the expansion of the cluster is driven by relaxation and nearly homologous. the local velocity dispersion tracks with the virial velocity. offset by a factor of order unity (see figure Al)).," However, when the expansion of the cluster is driven by relaxation and nearly homologous, the local velocity dispersion tracks with the virial velocity, offset by a factor of order unity (see figure \ref{1024densdisp}) )."
" Also note that the final result boils down to the ratio of e,4 to o. which can be recas as à ratio of αν lO es."," Also note that the final result boils down to the ratio of $v_{sep}$ to $\sigma$, which can be recast as a ratio of $a_{h-s}$ to $a_{sep}$."
 The ratio of these two quantities is roughly constant over the entirety of the simulations a all radii. which can be seen in figure 3...," The ratio of these two quantities is roughly constant over the entirety of the simulations at all radii, which can be seen in figure \ref{1024freeze}."
 The correction to the bound fraction calculation due to variations at dilleren radii will be a factor of order unity. not alfecting the scaling.," The correction to the bound fraction calculation due to variations at different radii will be a factor of order unity, not affecting the scaling."
 This argument has implications for the final binary energy spectrum and semi-major axis distribution., This argument has implications for the final binary energy spectrum and semi-major axis distribution.
 Provide there is some region where e.«pei as the cluster expands and (c4 grows larger the permanent binary population is built up from small separations up to large ones.," Provided there is some region where $a_{sep} <$, as the cluster expands and $a_{sep}$ grows larger the permanent binary population is built up from small separations up to large ones."
 If we consider a range of semi-major axes around the critical separation al a given time. sav a factor of 2. the number of bound pairs will be roughly frou. or of order unity.," If we consider a range of semi-major axes around the critical separation at a given time, say a factor of 2, the number of bound pairs will be roughly $f_{bound} N$, or of order unity."
 Thus as the region where soft permanent binaries are created sweeps through larecr values. seen in figure 3. as the region between the black lines. the number of permanent binaries formed in any logarithmic separation bin should be of order unity.," Thus as the region where soft permanent binaries are created sweeps through larger values, seen in figure \ref{1024freeze} as the region between the black lines, the number of permanent binaries formed in any logarithmic separation bin should be of order unity."
 Note that this is independent. of the population of the cluster., Note that this is independent of the population of the cluster.
 As long as there is a region of the cluster producing soft permanent binaries. details of the cluster density structure and population do not matter.," As long as there is a region of the cluster producing soft permanent binaries, details of the cluster density structure and population do not matter."
 AC flat distribution in the logarithm of the semi-major axis means that the energy. spectrum should. follow Npfdex+., A flat distribution in the logarithm of the semi-major axis means that the energy spectrum should follow ${\rm d}N_B/{\rm d}\epsilon \propto \epsilon^{-1}$.
 Phese scalings are roughly born out by our simulations: the best fit to the permanent binary spectrum over the soft energies in ligure 2 is dNefdex©17. and the number of permanent soft binaries in logarithmic bins of senmi-major axis are within a factor of a few over four orders of magnitudo.," These scalings are roughly born out by our simulations; the best fit to the permanent binary spectrum over the soft energies in figure \ref{1024semidist} is ${\rm d}N_B/{\rm d}\epsilon \propto \epsilon^{-1.2}$, and the number of permanent soft binaries in logarithmic bins of semi-major axis are within a factor of a few over four orders of magnitude."
 The permanent soft. population is a fossil. record. of the widest. interstellar separation achieved. by the regions of the cluster from which soft. binaries are able to freeze out., The permanent soft population is a fossil record of the widest interstellar separation achieved by the regions of the cluster from which soft binaries are able to freeze out.
 The final population is independent of the cluster parameters. such as the detailed density structure.," The final population is independent of the cluster parameters, such as the detailed density structure."
 This is in marked contrast to the energy. spectra of the statistical and instantaneous populations. which are functions of the finite size and geometry. of the cluster.," This is in marked contrast to the energy spectra of the statistical and instantaneous populations, which are functions of the finite size and geometry of the cluster."
" “Phe steady-state statistical spectrum derived in a uniform. infinite cluster is λίραςxο""72 at soft «nergies (llegeie1975:Goodman&Lut 1993).."," The steady-state statistical spectrum derived in a uniform, infinite cluster is ${\rm d}N_B/{\rm d}\epsilon \propto \epsilon^{-5/2}$ at soft energies \citep{heggie75,goodman93a}."
 When the cluster is finite. this spectrum is truncated at the soft end by the size scale of the cluster. which defines the largest possible separation of two stars. and thus the lowest energy binary attainable.," When the cluster is finite, this spectrum is truncated at the soft end by the size scale of the cluster, which defines the largest possible separation of two stars, and thus the lowest energy binary attainable."
 When the density field is non-uniform. the slope of the statistical energy spectrum. changes.," When the density field is non-uniform, the slope of the statistical energy spectrum changes."
 For instance. a star sitting a je center of a cluster with a censity profile decreasing outwards will see fewer potential binary partners ab large separations compared to a uniform. distribution (sce appendix D)). which leads to a fattening of the energv spectrum relative to the uniform. case.," For instance, a star sitting at the center of a cluster with a density profile decreasing outwards will see fewer potential binary partners at large separations compared to a uniform distribution (see appendix \ref{DensityAppendix}) ), which leads to a flattening of the energy spectrum relative to the uniform case."
 Both of these ellects can be seen in figure 2.. where the statistical population has a slope at soft energies more like «UNg/dexc. 07. flattening further at the softest energies whore it is eventually truncated.," Both of these effects can be seen in figure \ref{1024semidist}, where the statistical population has a slope at soft energies more like ${\rm d}N_B/{\rm d}\epsilon \propto \epsilon^{-1.5}$ , flattening further at the softest energies where it is eventually truncated."
 The instantaneous spectrum. which is some subset of the statistical population. will likewise reflect the current density structure of the cluster.," The instantaneous spectrum, which is some subset of the statistical population, will likewise reflect the current density structure of the cluster."
 The permanent spectrum. built up from harder to softer energies over time. should) generically be cdgfeleκ«1 by the arguments presented in this section.," The permanent spectrum, built up from harder to softer energies over time, should generically be ${\rm d}N_B/{\rm d}\epsilon \propto \epsilon^{-1}$ by the arguments presented in this section."
sanaller than —0.1.,smaller than $\sim$ 0.1.
 Iu other words. the condeusate mist be transparent enouehl for the absorption to be neclieible relative to scattering.," In other words, the condensate must be transparent enough for the absorption to be negligible relative to scattering."
 Among the possible abundaut condensates. MgSiO; prescuts such a property (Dorsclucr et 11995: Fortuev 2005).," Among the possible abundant condensates, $_3$ presents such a property (Dorschner et 1995; Fortney 2005)."
 Tf MeSiO; contains uo Fe atoms. the dmaginary part of the refraction iudex is found to be k~2«10 in the cousidered wavelength range.," If $_3$ contains no Fe atoms, the imaginary part of the refraction index is found to be $k\sim 2\times 10^{-5}$ in the considered wavelength range."
" Using this value. we find 6,,;,/ÀA=8«10 5."," Using this value, we find $a_{min}/\lambda= 8\times 10^{-3}$ ."
 Therefore. we conclude that MeSiO; is the candidate species possibly responsible for the observed Ravleigh scattering iu the 118972335 spectrum. aud its size ust be in the rauge ? l nicrons (see upper paucl of Fie. 3)).," Therefore, we conclude that $_3$ is the candidate species possibly responsible for the observed Rayleigh scattering in the 189733b spectrum, and its size must be in the range $^{-2}$ $^{-1}$ microns (see upper panel of Fig. \ref{TP_vs_size}) )."
 Assunug an abundance for the MgSiO; eris aud using Eq. 3..," Assuming an abundance for the $_3$ grains and using Eq. \ref{xiP},"
 we can evaluate the pressure at the effective plauetarv radius if the Bavleigh scattering by these ervains donmüuates the transit spectrum., we can evaluate the pressure at the effective planetary radius if the Rayleigh scattering by these grains dominates the transit spectrum.
 For MgS1O;. the refraction iudex is taken to be n<1.6 iu the rauge unm (Dorschner oet 11995).," For $_3$, the refraction index is taken to be $n$$\sim$ 1.6 in the range nm (Dorschner et 1995)."
 This gives a cross section o&1525849/A!., This gives a cross section $\sigma\approx 1528 a^6/\lambda^4$.
 The erain abundance is obtained using solar abundance and assunüug that it is limited by the available umuber of magnes atoms., The grain abundance is obtained using solar abundance and assuming that it is limited by the available number of magnesium atoms.
 Thus the erains have an abundance £a Αμ). where OMe©bosyo 48 the magnesium ΠΟΠ Is about eeO.L fines the mass of the proton (my) Pan«ος 7ds the erain density. « the particle size. aud | Avogadro's umber.," Thus the grains have an abundance $\xi_{\rm grain}=2\xi_{\rm Mg} \mu_{\rm MgSiO_3}/(\rho_{\rm grain} 4\pi/3 a^3 N m_p)$ , where $\xi_{\rm Mg}\approx 4\times 10^{-5}$ is the magnesium abundance, $\mu_{\rm MgSiO_3}$ is about 100.4 times the mass of the proton $m_p$ ), $\rho_{\rm grain} =3.2$ $^{-3}$ is the grain density, $a$ the particle size, and $N$ Avogadro's number."
" Therefore we lave £444,=1.0« °."," Therefore we have $\xi_{\rm grain}=1.0\times 10^{-15}(a/1\,\mu{\rm m})^{-3}$ ."
 Finally. at 2=0 defined by the effective radius at Azc THO. with T21310TKIEK we obtain a pressure P=2410 αν if the size of MeSiOs erains is about 0.01712. and P=2«108 bbar if the size is about 0.150. These values obtained with Eq.," Finally, at $z=0$ defined by the effective radius at $\lambda\approx 750$ nm, with K we obtain a pressure $P=2\times 10^{-3}$ bar if the size of $_3$ grains is about $\mu$ m, and $P=2\times 10^{-6}$ bar if the size is about $\mu$ m. These values obtained with Eq."
 3. are similar to those obtained with a general fit to the data (Fie. 3)).," \ref{xiP}
 are similar to those obtained with a general fit to the data (Fig. \ref{TP_vs_size}) )."
 It is notescorthy that these values are consistent with the condensation pressure of MeSiO; which is ~10 Ibbar at IXIx (Lodders 1999)., It is noteworthy that these values are consistent with the condensation pressure of $_3$ which is $\sim$ $^{-4}$ bar at K (Lodders 1999).
 Finally. Ravleigh scattering bv MgSiO; is preferred to scattering bv II» to explain the observed spectrin.," Finally, Rayleigh scattering by $_3$ is preferred to scattering by $_2$ to explain the observed spectrum."
 Tudeed. molecular hydrogen requires higher pressure. at which the signature of abundant species likeNar.Ir. IIO. aud possibly TiO should overcome the Ravleie¢h-scattering signature. except when they have anomalously low abuudauces.," Indeed, molecular hydrogen requires higher pressure, at which the signature of abundant species like, $_2$ O, and possibly TiO should overcome the Rayleigh-scattering signature, except when they have anomalously low abundances."
 Because tle cross section varies as xa? in the Ravleieh reenne. the scattering is largely dominated by the largest particles in the size distribution.," Because the cross section varies as $\propto a^6$ in the Rayleigh regime, the scattering is largely dominated by the largest particles in the size distribution."
 Therefore. tle typical sizes quoted above iust be considered as the size of the largest particles in the distribution.," Therefore, the typical sizes quoted above must be considered as the size of the largest particles in the distribution."
 This work assumes that the whole transit spectrum frou 550 to 1050nunm can be interpreted by the absorption by a unique species., This work assumes that the whole transit spectrum from 550 to nm can be interpreted by the absorption by a unique species.
 Alternatively. there could be a combination of absorptious by various species(ce...Nal.Ki. and Πο) in different parts of the spectrum to winic a spectruni of Ravleigh scattering with the expected atmospheric temperature.," Alternatively, there could be a combination of absorptions by various species, and $_2$ O) in different parts of the spectrum to mimic a spectrum of Rayleigh scattering with the expected atmospheric temperature."
 This would be coicidental. but it cannot be excluded from the preseut data.," This would be coincidental, but it cannot be excluded from the present data."
 This question weeds higher resolution data to be solved., This question needs higher resolution data to be solved.
 The cluperature aud pressure found above are uean values iuteerated along the planctary nub. where eniperature is expectec to vary from the le to the equator and from one side to the other.," The temperature and pressure found above are mean values integrated along the planetary limb, where temperature is expected to vary from the pole to the equator and from one side to the other."
 A mnunuerical integration of the absorption through the planetary atimosphere assuming a variation in femiperature as a function of altitude of TK oer scale heielit (Burrows et 22007) or as a function of longitude of IKI& over 120 deerees (Ixuutson ct 22007) shows that teniperatures found by solving Eq., A numerical integration of the absorption through the planetary atmosphere assuming a variation in temperature as a function of altitude of K per scale height (Burrows et 2007) or as a function of longitude of K over 120 degrees (Knutson et 2007) shows that temperatures found by solving Eq.
 1 are sheltly overestimated by no more than about and2%... respectively.," \ref{z_lambda}
 are slightly overestimated by no more than about and, respectively."
 Tt the measurements of planetary radius in the uni waveleneth baud are extrapolated to the infrared. where Spitzer measurements are available. we can obtain a nüniuuni effective radius due to Ravleigh scattering.," If the measurements of planetary radius in the nm wavelength band are extrapolated to the infrared, where Spitzer measurements are available, we can obtain a minimum effective radius due to Rayleigh scattering."
" From &,/R.=0.156 1b at nna. we extrapolate that &,/R. iust. be larger than 0.1539. L1531. andl 0.1526. at pu. qnn. arc S. mu. respectively (with 0.0003 (stat.)"," From $R_p/R_*$ =0.1564 at nm, we extrapolate that $R_p/R_*$ must be larger than 0.1539, 0.1531, and 0.1526 at $\mu$ m, $\mu$ m, and $\mu$ m, respectively (with $\pm$ 0.0003 (stat.)"
 0.0006. (svst.), 0.0006 (syst.)
 error vars)., error bars).
 These values are consisteu with the Spitzer/IRAC ueasureiieuts eiven by EKkuutsou et ((2007) aud Ehrenreich et ((2007). aud with measurements bv Beaulicu et (2007) at the Iit of he upper error bars.," These values are consistent with the Spitzer/IRAC measurements given by Knutson et (2007) and Ehrenreich et (2007), and with measurements by Beaulieu et (2007) at the limit of the upper error bars."
 Ravleigh scattering has also been proposed ο explain he detection of polarized scattered leht (Berdyueina et 22007)., Rayleigh scattering has also been proposed to explain the detection of polarized scattered light (Berdyugina et 2007).
 ILoxcever. this detection coucerus the high upper atiuospliere aud canoe be directly compared to the xeseut work on scattering deeper iu the atiosphere.," However, this detection concerns the high upper atmosphere and cannot be directly compared to the present work on scattering deeper in the atmosphere."
 Ground-based. high-resolution spectra allowed the detection of sodiun iu 1ο afinosphere of 118973) Redficld et 22008).," Ground-based, high-resolution spectra allowed the detection of sodium in the atmosphere of 18973b (Redfield et 2008)."
 Assuming a pressure at a elvenogtitude. the measured absorption allows the determination of the sociu abundance.," Assuming a pressure at a given altitude, the measured absorption allows the determination of the sodium abundance."
 For that purpose. a fit of the sodiunu line shape is needed. and still ws to be developed.," For that purpose, a fit of the sodium line shape is needed, and still has to be developed."
" Alternatively, by asstuuine the soditn abuudance. moeasuriug sodium absorption should constraiu the pressureand allow for differcutiating vetween the several carriers ofthe Ravleigh scattering xoposed in the present paper."," Alternatively, by assuming the sodium abundance, measuring sodium absorption should constrain the pressureand allow for differentiating between the several carriers ofthe Rayleigh scattering proposed in the present paper."
 Preseutly. extinction high iu the atinosphere by MgSiO; with its low coudeusatiou xessure of —10 !bbar appears a uatural explanation or the abseuce of broad spectral signature aud is the xeferred scenario.," Presently, extinction high in the atmosphere by $_3$ with its low condensation pressure of $\sim$ $^{-4}$ bar appears a natural explanation for the absence of broad spectral signature and is the preferred scenario."
The results are shown in the right-hand panels of fieures 5. and 6..,The results are shown in the right-hand panels of figures \ref{IImage2} and \ref{VImage2}.
" Although the Stokes V image is larecly consistent with noise with peak values at +L700. a faint pattern of residual sidelobes is visible surrounding the position of the upper-left ""I1 C source."," Although the Stokes V image is largely consistent with noise with peak values at $\pm 4.7 \sigma$, a faint pattern of residual sidelobes is visible surrounding the position of the upper-left “4 C” source."
 Some residual sidelobes to the secoud-strongest source remain iu the Stokes IE inage as well., Some residual sidelobes to the second-strongest source remain in the Stokes I image as well.
 This lower-right source is located at a poiut of steep eradieut i the primary beam response aud is thus siguificautlv affected. by collimation aud pointing errors., This lower-right source is located at a point of steep gradient in the primary beam response and is thus significantly affected by collimation and pointing errors.
 We believe that such errors are likely to be responsible for our failure to correct this image in full., We believe that such errors are likely to be responsible for our failure to correct this image in full.
 Of course. auv uucorrected systematic effects will lead to errors in the seltcalibration solutions.," Of course, any uncorrected systematic effects will lead to errors in the self-calibration solutions."
 Despite the preseuce of such residual systematic errors. the Squiut algoritlin vielded au increase in dvuamic range by more than one order of magnitude iu Stokes V. and a decrease of the xius noise iu the Stokes I image of ~2," Despite the presence of such residual systematic errors, the Squint algorithm yielded an increase in dynamic range by more than one order of magnitude in Stokes V and a decrease of the rms noise in the Stokes I image of $\sim 27$."
 Taking advantage of the EVLA's. increased sensitivity at lower frequencies (15 GIIz and below) will eenerallv require iÀuagiue aud deconvolviug the cutive primary bean. or at least those portions containiug sources.," Taking advantage of the EVLA's increased sensitivity at lower frequencies (15 GHz and below) will generally require imaging and deconvolving the entire primary beam, or at least those portions containing sources."
 Beau squint can produce artifacts well above the noise level., Beam squint can produce artifacts well above the noise level.
 Other interferometers with off-axis feeds. including focal plane array feeds. will share this problem This paper describes a technique for correcting radio interferometric Observations for the effects of beam squint.," Other interferometers with off-axis feeds, including focal plane array feeds, will share this problem This paper describes a technique for correcting radio interferometric observations for the effects of beam squint."
 The technique is a modification of the visibilitv-based CLEAN in which the Stokes I image is made in the usual wav. but when the nuage model is subtracte roni the data. corrections are mace such that the mode subtracted includes the effects of beam squint.," The technique is a modification of the visibility-based CLEAN in which the Stokes I image is made in the usual way, but when the image model is subtracted from the data, corrections are made such that the model subtracted includes the effects of beam squint."
 Thus. any errors meurred in the initial dnagine are correcte hrough iterative duaeing aud accurate model subtraction.," Thus, any errors incurred in the initial imaging are corrected through iterative imaging and accurate model subtraction."
 Selfcalibration is incorporated iuto the procedure in wo steps with phasc-only self-calibration performice first. subsequently followed by. amplitude aud phase selt-calibration.," Self-calibration is incorporated into the procedure in two steps with phase-only self-calibration performed first, subsequently followed by amplitude and phase self-calibration."
 We have performed several tests of au iplementation of this technique in the Obit task Squint., We have performed several tests of an implementation of this technique in the Obit task Squint.
 In all cases. careful initial calibration is critical.," In all cases, careful initial calibration is critical."
 Observations of the strong source JC81 were mace with the source at various locations in the antenna beam pattern resulting in strong instrumental circular polarization., Observations of the strong source 3C84 were made with the source at various locations in the antenna beam pattern resulting in strong instrumental circular polarization.
 Both 1.1 aud 5 CGIIz test data sets were examined and we found that this technique corrects the instrumental circular volarization due to the beam squint to a level that is limited by other effects such as pointing errors and msufBcient knowledec of the ΠΑΝ beam., Both 1.4 and 5 GHz test data sets were examined and we found that this technique corrects the instrumental circular polarization due to the beam squint to a level that is limited by other effects such as pointing errors and insufficient knowledge of the primary beam.
 We have presented. detailed examples of imaging of several observations., We have presented detailed examples of imaging of several observations.
 applying the beam squint correction lowered residual artifacts by iore than aud led to very substantial improvements to the Stokes V inages., applying the beam squint correction lowered residual artifacts by more than and led to very substantial improvements to the Stokes V images.
 Our second example demonstrates the behavior of the algorithin on au observation that requires hieh dyaunic range., Our second example demonstrates the behavior of the algorithm on an observation that requires high dynamic range.
 Tere. artifacts remain that cau be," Here, artifacts remain that can be"
that WALAP appears fully cousisteut with the ACDM simulations.,that WMAP appears fully consistent with the $\Lambda$ CDM simulations.
 Iu this paper we search for concentric low-variance rugs in the T-vear WAIAP temperature sky maps. secking to reproduce the results recently preseuted by Chuzadyiui&Penrose(2010).," In this paper we search for concentric low-variance rings in the 7-year WMAP temperature sky maps, seeking to reproduce the results recently presented by \citet{gurzadyan:2010}."
. While our two analyses do agree in ternis of specific variance profiles. they clearly disagree in teris of statistical interpretation aud sjeuificauce.," While our two analyses do agree in terms of specific variance profiles, they clearly disagree in terms of statistical interpretation and significance."
 Specifically. we fud a substantially larecr variance in our ACDM simmlations than Courzadvan&Penrose(2010) do in theirs.," Specifically, we find a substantially larger variance in our $\Lambda$ CDM simulations than \citet{gurzadyan:2010} do in theirs."
 When taking iuto account this lareer variance. anc accounting for statistical selection effects. the evidence for concentric circles iu the WMAP data appears minimal.," When taking into account this larger variance, and accounting for statistical selection effects, the evidence for concentric circles in the WMAP data appears minimal."
 Rather. the WALAP data appears fully consistent with our ΠΠΟΛ.," Rather, the WMAP data appears fully consistent with our simulations."
 The main difference between the two analyses must lie in the constiuction of the simulations., The main difference between the two analyses must lie in the construction of the simulations.
 ILoxcever. we have good reason to believe that our simulations are correct.," However, we have good reason to believe that our simulations are correct."
 First. we note that in our simmlations the mean variance profile decreases towards small angular distances.," First, we note that in our simulations the mean variance profile decreases towards small angular distances."
 This is bound to happen for two reasons: The CMD anisotropics constitute a correlated feld with a characteristic scale of l. correspouding to the first peak im the CMD spectu.," This is bound to happen for two reasons: The CMB anisotropies constitute a correlated field with a characteristic scale of $1^{\circ}$, corresponding to the first peak in the CMB spectrum."
 Also. the instrumental beam of WALAP smooths out all siuall scale structure.," Also, the instrumental beam of WMAP smooths out all small scale structure."
 It is therefore surprising that this effect is not seen in Figure 2 of Cawrzadvan&Peu-rose(2010)., It is therefore surprising that this effect is not seen in Figure 2 of \citet{gurzadyan:2010}.
. Second. the fact that our simulations agree with WALIAP provides further confidence: it is difficult to iuagine an eror in the snmlation pipeline that would cause the simulations to become sila to the observed data.," Second, the fact that our simulations agree with WMAP provides further confidence; it is difficult to imagine an error in the simulation pipeline that would cause the simulations to become similar to the observed data."
 Third. as noted by Cawzadvan&Peu-rose(2010).. there are both low aud high peaks iu the reported variance profiles.," Third, as noted by \citet{gurzadyan:2010}, there are both low and high peaks in the reported variance profiles."
" While Gurzacvan aud Penrose assign no sigmificance to the high variance peaks (stating that ""the peaks of high variance are of no importance. as these can result from nunuerous irelevaut effects). they are clearly relevant in our interpretation. as they illustrate the substantial statistical variance prescut im these profiles."," While Gurzadyan and Penrose assign no significance to the high variance peaks (stating that “the peaks of high variance are of no importance, as these can result from numerous irrelevant effects”), they are clearly relevant in our interpretation, as they illustrate the substantial statistical variance present in these profiles."
 This large variauce is observed both in the real data aud the simulations., This large variance is observed both in the real data and the simulations.
 Thus. we conclude that there is no evidence for the CCC inodel in the current WAIAP data.," Thus, we conclude that there is no evidence for the CCC model in the current WMAP data."
 Of course. Planck (Tauberetal.2010) ταν provide new lieht ou this issue. having higher sensitivity aud resolution than WMADP. but one should probably not have too ligh expectations in this reeard.," Of course, Planck \citep{tauber:2010} may provide new light on this issue, having higher sensitivity and resolution than WMAP, but one should probably not have too high expectations in this regard."
 Even if the CCC model should tuu out to describe the real universe. it will quite Likely be difficult to ununubiguouslv identity such concentric circles due to the dominant background οσα Vallance.," Even if the CCC model should turn out to describe the real universe, it will quite likely be difficult to unambiguously identify such concentric circles due to the dominant background cosmic variance."
We focus ou the problem of the minimum period and the discrepancy between observations aud models (see e Ning 1988 and I&olb 2001 for à review ou the properties of CV systems).,We focus on the problem of the minimum period and the discrepancy between observations and models (see e.g King 1988 and Kolb 2001 for a review on the properties of CV systems).
 A discussion aud conclusions follow in 81., A discussion and conclusions follow in 4.
 We used a SPII code. originally developed aud. kindly provided bv Willy Benz (see details in Beng et al.," We used a SPH code, originally developed and kindly provided by Willy Benz (see details in Benz et al."
 1990) to perform nuuerical sinmulatious of a close binary svsteni conrposed of. a poit. mass (primary): aud a polvtropic: star (secondarv)., 1990) to perform numerical simulations of a close binary system composed of a point mass (primary) and a polytropic star (secondary).
 The↴ SPIT⊲ method has been described⋅ extensively. in. the literature. (see Monaghan --1992 aud ↥⋅↸∖↕⋟↸∖↥⋅↸∖∐↸⊳↸∖↴∖↴↑↕∐∖↥⋅↸∖↕∐⋟⋜⋯≼↧↕↴∖↴∪↕⋟↑↸∖∐⋜↧⋯≻∐↸∖≼↧↑∪↑∐↸∖↴∖↴↑↿ dv of ↸⊳↕∪↴∖↴↸∖↴⋝↕∐⋜∐⋅⋅↖↽↴∖↴∙↖↽↴∖↴↑↸∖⊔↴∖↴≺↸, The SPH method has been described extensively in the literature (see Monaghan 1992 and references therein) and is often applied to the study of close binary systems (e.g Benz et al.
∖∙∶↴∙⊾↕≧↸∖∐∑↸∖⋜↧↕, 1990; Lai et al.
∙↕∩∩∩∶∫⇀⋜↧↕↸∖↑⋜↧↕∙↕⋂≝⊔∶ ↕⊰⋜↧↴∖↴↕∪∙∖↽≋∐⋜⋯∐⋅∪⊽∩∩⋅, 1994; Rasio Shapiro 1995; Segréttain et al.
↱≻∶≋↸∖∶↴⋁↥⋅↸↗∖↑↑⋜↧↕∐↸∖↑⋜↧↕∙↕⋂∩⊤⋝ ↕∐⋜↕∐⋯∐⋅↴∖↴↕⋯∏↕⋜↧↑↕∪∐↴∖↴∙↑∐↸∖↻↥⋅↕↕⊔⋜∐⋅⋅↖↽↕↴∖↴⋜↧↕⋀∐⋅↻∪↕↕↑≓↕∐↘↽↸∖ mass.," 1997) In all our simulations, the primary is a 1 $\msol$ point-like mass."
" The secondary is described by a polytropic equation of state p=Wet! TAN, where p is the pressure and p the density."," The secondary is described by a polytropic equation of state $p = K \rho ^{1+1/N}$ , where $p$ is the pressure and $\rho$ the density."
" The polvtropic constant A is fixed for a given index, Nobby the mass AL and radius R of the spherical secondary.", The polytropic constant $K$ is fixed for a given index $N$ by the mass $M$ and radius $R$ of the spherical secondary.
 We adopt two polvtropic indices. ie. No = 3/2. which provides a good description of fully convective objects such as low mass stars. and |. — 3 characteristic of. solar type stars with. A~.LAL...," We adopt two polytropic indices, i.e. $N$ = 3/2, which provides a good description of fully convective objects such as low mass stars, and $N$ = 3 characteristic of solar type stars with $M \sim 1 \msol$."
" For the particular⋅ case of DuCVs. systems below the period⋅ gap are well described. by N= -.3/2 polvtropes. whereas IN — 203 applies. to svstenis "" . ⋅⋅ ⋅ ↖↖⇁↕↕⊓⋉∖↥⋅↕∪≼↧↴∖↴∩∐⋜⋯≼↧↑↖↴⋯⊳⋜↧↕↕⊔⋜↧↴∖∷∖↴↸∖↴∖↴⋜∐⋅∪∏∐≼↧∿↓⋀∐"," For the particular case of CVs, systems below the period gap are well described by $N$ = 3/2 polytropes, whereas $N$ = 3 applies to systems with periods $>$ 6 h and typical masses around $\sim$ 1 $\msol$."
∙∙ ⋅↽ two values of [IN ⋅thus represent luting cases. for the0.06. . CV⋅ secondaries., The two values of $N$ thus represent limiting cases for the description of CV secondaries.
 ⋅Asstming that- A. ycmains Dppolvtrope .with spaceü appliesIl well» to4 fullyfull μcouvective Dicctobjects /—case .ofFig. adiabatie⋅ structure. audu inplies: a chemically Ixolb-2000). ⋅⋅ . leculmoleculara2 weight)ieht) forf .and :gbounce =⋅↽ with Wo = 3.," Assuming that $K$ remains constant in space applies well to fully convective objects with a fully adiabatic structure, and implies a chemically homogeneous structure (constant molecular weight) for the standard models with $N$ = 3."
quisi This° is ahe reasonable period. - NM prescuthatiu study., This is a reasonable approximation for the present study.
the . ⇁⋅ ⋅ 15000 particles., The simulations use $\sim$ 15000 particles.
⋅surface ιν order valueto Dpo . . . ↸⊳∐↸∖↸⊳↨↘↽↑∐↸∖⋜↧↸⊳↸⊳↿∐⋅⋜↧↸⊳⋅↖↽∪↕≯≺∏∐⋅↥⋅↸∖↴∖↴∏↕↴∖↴∙↖↖↽↸∖↥⋅⋜⋯⋜↧∐∐∐↑↸∖≼⊔⊔⋯↴⋝↸∖↥⋅ of simulatious with 57000 particles.," In order to check the accuracy of our results, we ran a limited number of simulations with 57000 particles."
 We fiud that 15000 ouwticles is a eood compromise between conutationa demand aud accuracy., We find that 15000 particles is a good compromise between computational demand and accuracy.
 The↴ particles− are initially⋅⋅⋅ uniforilv» distributed⋅⋅ ou a hexagonal close-packed lattice., The particles are initially uniformly distributed on a hexagonal close-packed lattice.
"⋅ The μ.μ...initia πο density of particles is coustant throughout the voluue of the sphere] describingo the initial‘ configurationon of the secondary,", The initial number density of particles is constant throughout the volume of the sphere describing the initial configuration of the secondary.
 The particle masses are proportiona o the local mass deusitv., The particle masses are proportional to the local mass density.
 This provides a good spatia near. the stellar surface. which. is ⋅⋅crucial for culationsoo... of critical lobe .determination where surfacesinular The vesulcaleulatious effects are Me]predomulnanut.," This provides a good spatial resolution near the stellar surface, which is crucial for our problem of critical lobe determination where surface effects are predominant."
‘ The simulations‘ are |performic in a corotating reference frame with the origin at the center of mass of the system., The simulations are performed in a corotating reference frame with the origin at the center of mass of the system.
 The initial separation iuis the: two components is :arbitrarily fixed∙⋅ :at four times. theexpansion separation. required. for. the secondary to fill its ---Roche-Iobe Apgoenes estimated frou the Egeletouao (1983) fit.," The initial separation $A_{\rm init}$ of the two components is arbitrarily fixed at four times the separation required for the secondary to fill its Roche-lobe $A_{\rm Roche}$, estimated from the Eggleton (1983) fit."
 For such a separation. tidal and rotational effects on the secoudarv are negligible.," For such a separation, tidal and rotational effects on the secondary are negligible."
 The orbital separation is decreased with the arbitrary constant rate (Aga:πο)Τάμα. SO that the otal timescale of the simulation Ta Is 1000 times the vpical bydrodvuamiucal relaxation tie Tas&ao) of the secondary.," The orbital separation is decreased with the arbitrary constant rate $(A_{\rm init} - A_{\rm Roche})/\tau_{\rm simu}$, so that the total timescale of the simulation $\tau_{\rm simu}$ is $\sim$ 1000 times the typical hydrodynamical relaxation time $\tau_{\rm relax} \simeq \left(\frac{R^3}{GM}\right)^{1/2}$ of the secondary."
 The simulation is stopped when the secondary fills its critical lobe when the first particles roni the secondary reach the πιο saddle point of the yoteutial5., The simulation is stopped when the secondary fills its critical lobe when the first particles from the secondary reach the inner saddle point of the potential.
 This marks the ouset of mass transfer., This marks the onset of mass transfer.
 Ouce he critical separation is reached. we check that the model was reached an equilibrium configuration. starting frou such critical separation and letting it relax iu a non rotating reference frame.," Once the critical separation is reached, we check that the model has reached an equilibrium configuration, starting from such critical separation and letting it relax in a non rotating reference frame."
 Our outgoal is to estimate“ the deformationt effects ou the secondaryBn due to tidal⋛↙∙↙ aud rotational‘ forces oeas it fills its critical lobe., Our goal is to estimate the deformation effects on the secondary due to tidal and rotational forces as it fills its critical lobe.
 The deformation cam be measured m terms ∪↕≯↑∐↥⋅⋜↧↑↕∪∪↕≯↑∐↸∖∐∐⋜↧↕↑∪↕∐↕↑↕⋜↧↕↴∖↴↑↸∖↕⋜∐⋅↥⋅⋜⊔∐∏↴∖↴⊈⊃∶∫↿⋟↕∫↿⋟↕∙ ∫↿, The deformation can be measured in terms of the ratio of the final to initial stellar radius $D = R_{\rm f}/R_{\rm i}$.
⋟↕↕↴∖↴∐↸∖↥⋅⋜∥∐∏↴∖↴∪↕⋟↑↕∐∖∏∏⋉∖↥⋅⊓∐⋅↴⋝↸∖≺↧↴∖↴↻∐↸∖∏↸⊳⋜↧↕↻∪↕⋅↖⇁⊓⋅∪↻↸∖⋅, $R_{\rm i}$ is the radius of the unperturbed spherical polytrope.
 Re is an effective radius defined as the radius of the sphere with the volume V? of the secondary filliue its critical lobe., $R_{\rm f}$ is an effective radius defined as the radius of the sphere with the volume $V_{\rm f}$ of the secondary filling its critical lobe.
 Ve is provided by our SPIT simulation at the ouset of lass transfer., $V_{\rm f}$ is provided by our SPH simulation at the onset of mass transfer.
" The method to estimate Vg is described ii Appendix A. - ↖↖↸∖↥⋅⋜⋯⋜↧∶↴∙⊾↥⋅↕≼↧∪↕↴∖↴∐⊔∏↕⋜↧⊓∪∐↴∖↴↕∪↥⋅↖⇁⋜∐⋅↕∪∏↴∖↴∐↓⋜↧↴∖↴↴∖↴↥⋅⋜↧⊓∪↴∖↴ . TM . . . . q=MofM, between the secondary aud the primary.", The method to estimate $V_{\rm f}$ is described in Appendix A. We ran a grid of simulations for various mass ratios $q=M_2/M_1$ between the secondary and the primary.
". Typically, CV. systems with periods from ~ 10 h down ↑∪↑∐↸∖⋯∐∐∐⋯⋯↻↸∖∐∪≺↧↸⊳∪↖↽↸∖↕⋅⋜↧↕⋅⋜⋯∶↴∙⊾↸∖∪↕↙∣↴⋈∖↑↖↖↽↸∖↸∖∐↓⋜⋯≺↧⋅"," Typically, CV systems with periods from $\sim$ 10 h down to the minimum period cover a range of $q$ between 1 and 0.06."
⋅ . . ., Fig.
 Fie. 1 ⋅⋅↽displays the⋅ &nal coufiguratiou⋅ of⋅. a. | —- 3 The4 mass ratio. q =∖↴⋅⋅ (0.8., \ref{fig1} displays the final configuration of a $N$ = 3 polytrope with mass ratio $q$ = 0.8.
 This illustrates ⋅⋅the description of CV systems .with periods =. 6N h (see. Daraffe & tcons, This illustrates the case of CV systems with periods $\simgr$ 6 h (see Baraffe Kolb 2000).
tant⋅, Fig.
" 2 shows the⋅ results for the case Αν. 5 3/2 with| a fully 0.07. characteristic of secondaries: approaching. lolnogcncous1 structivetret (coustauttant £444, (Ikolb- & Daratfe 1999)."," \ref{fig2} shows the results for the case $N$ = 3/2 and $q$ = 0.07, characteristic of secondaries approaching the period bounce $\pturn$ (Kolb Baraffe 1999)."
B note .the standard. models case No⋅⊀ = 3/2 (Fig.⋅ 2..," We note that in the case $N$ = 3/2 (Fig. \ref{fig2},"
 lower⋅ panel) .the approximation for the is∙ not constant.," lower panel), the surface value of $\phi$ is not constant."
 We ∙did not fiud any ↽The simulations use⋅ ~ ↴∖↴⋜↧↑↕↴∖↴↕⋜↧↸⊳↑∪↥⋅⋅↖↽↸∖⊼↻⋜⋯⋜↕, We did not find any satisfactory explanation for such behavior.
⊓∪∐↕∪↥⋅↴∖↴⊓⊳∐↴⋝↸∖↕⋜∏↽↕∪↥⋅∙↽∕∏∐↴∖↴↕↸∖⋜∏↥⋅↸∖ jas already been noted in some cases by Rasio aud Shapiro (1995) aud interpreted in terius of umber deusitv of SPIT articles biug not exactly coustant around the surface faὲ star with large tidal deformation., This feature has already been noted in some cases by Rasio and Shapiro (1995) and interpreted in terms of number density of SPH particles being not exactly constant around the surface of a star with large tidal deformation.
 Tacreasing the iuuber of particles from 15000 to 57000 auc double-checking that the models have reached an equilibrium⋅⋅⋅ confieuration⋅ do uot solve the problem., Increasing the number of particles from 15000 to 57000 and double-checking that the models have reached an equilibrium configuration do not solve the problem.
 We- do not expect hat this affects the accuracy of our final results. since our deformation c:are in excellent agreciment with resolution bv: other⋅⋅ authors (seebelow}.," We do not expect that this affects the accuracy of our final results, since our deformation calculations are in excellent agreement with similar calculations by otherauthors (see below)."
 our problem πιο deformations JD as a function of 4 are stunumarized− in− Table↴ d n»for N- = 3. and N- = 3/2., The resulting deformations $D$ as a function of $q$ are summarized in Table 1 for $N$ = 3 and $N$ = 3/2.
ds As expected. tidal aud rotational distortion vields an of.n the. secondary s]volume Pwith respect⋅↴ to. the of unperturbed spherical configuration.," As expected, tidal and rotational distortion yields an expansion of the secondary's volume with respect to the unperturbed spherical configuration."
 In terms of effective, In terms of effective
"given that 875 sources are detected in the K band and that many of the fainter, redder sources will be detected only at longer wavelengths.","given that 875 sources are detected in the $K$ band and that many of the fainter, redder sources will be detected only at longer wavelengths."
" Nevertheless, the sample is statistically significant when comparing with evolutionary tracks and obtaining an age estimate for the low mass sources in this region."," Nevertheless, the sample is statistically significant when comparing with evolutionary tracks and obtaining an age estimate for the low mass sources in this region."
" As a next step to better understanding this region, we evaluate the mass function of the"," As a next step to better understanding this region, we evaluate the mass function of the"
The FIRST radio survey [1.0 was conducted at the VLA at 1.1 GIIz in the D configuration.,"The FIRST radio survey \cite{bec95,whi97} was conducted at the VLA at 1.4 GHz in the B configuration."
" Its 5o flux liwit is 0.75 την. with a restoring beamFWIAL of 5"".| and a pixel size of 1"".L."," Its $5\sigma$ flux limit is 0.75 mJy, with a restoring beamFWHM of $5''.4$ and a pixel size of $1''.4$."
 The survey currently coutains about [|&107 sources over AL{200 deg*. with a mean redshift of (2)~1.," The survey currently contains about $4\times 10^5$ sources over $A \simeq 4,200$ $^2$, with a mean redshift of $\langle z \rangle
\sim 1$."
" Observing time has been allocated to exteud is coverage to -.7.200 deez.9 whiledos its nominal. area is- 10.000 deer,JD"," Observing time has been allocated to extend its coverage to 7,200 $^2$, while its nominal area is 10,000 $^{2}$ ."
" We characterize cach source by its ellipticity. e;=--a{σοςδα,sin2n]. where 6 aud b are the decouvoved major aud minor axes. andUd o is the position mele. derived from elliptical gaussian fits."," We characterize each source by its ellipticity, $\epsilon_{i} \equiv
\frac{a^2-b^2}{a^2+b^2} \{\cos 2\alpha,\sin 2\alpha\}$ , where $a$ and $b$ are the deconvolved major and minor axes, and $\alpha$ is the position angle, derived from elliptical gaussian fits."
" For our weak-lensing search. we ouly seep resolved sources (o>2"", b> 0). which represent of tle total inuuber sources aud amount to a source density of 7z36 deg7."," For our weak-lensing search, we only keep resolved sources $a>2^{\prime
\prime}$, $b>0$ ), which represent of the total number of sources and amount to a source density of $n\simeq 36$ $^{-2}$."
 Theweak lensing shear +; is related to the source-averaged ellipticity by =~~ g; where g=21a7)2 is: the shear-cllipticityHm conversion- fac.Or. σeDoMO-(65) Is the variuice of the iutriusic source cllipticitics.," Theweak lensing shear $\gamma_{i}$ is related to the source-averaged ellipticity by $\langle \epsilon_{i} \rangle \simeq -g \gamma_{i}$ , where $g\equiv 2(1-\sigma_{\epsilon}^{2})$ is the shear-ellipticity conversion factor, and $\sigma_{\epsilon}^{2} = \langle
\epsilon_{1}^{2} \rangle = \langle \epsilon_{2}^{2} \rangle$ is the variance of the intrinsic source ellipticities."
 For our suuple. σε2ll and gz1.61.," For our sample, $\sigma_{\epsilon}\simeq 0.44$ and $g\simeq 1.61$."
 While the simall source deusitv in or aniple prohibits a mapping of the shear. the lensing effect cau be studied isticallv.," While the small source density in our sample prohibits a mapping of the shear, the lensing effect can be studied statistically."
" This can be achieved by 1ieasurug the shear correlation functions Ct0)=g?teqiet(0) aud Co(0)=g?test)es(0)). where the average is Ove rsource pairs with separation 0, aud the rotated ellipticities e are nieastred along the separation vector."," This can be achieved by measuring the shear correlation functions $C_{1}(\theta)=g^{-2}\langle
\epsilon^{r}_{1}(0)\epsilon^{r}_{1}(\theta) \rangle$ and $C_{2}(\theta)=g^{-2}\langle
\epsilon^{r}_{2}(0)\epsilon^{r}_{2}(\theta) \rangle$, where the average is over source pairs with separation $\theta$ and the rotated ellipticities $\epsilon^{r}$ are measured along the separation vector."
 To estimate the expected lensing signal. we consider the four CDM models listed in Table 1 |3]..," To estimate the expected lensing signal, we consider the four CDM models listed in Table 1 \cite{kam98}."
" While model 1 i$ COBE-normalized. models 2-1 are osscutially cluster-normalized (6,097=O.G40.1. see [0])) anc are thus more realistic."," While model 1 is COBE-normalized, models 2-4 are essentially cluster-normalized $\sigma_{8} \Omega^{0.53} = 0.6 \pm 0.1$, see \cite{via96}) ) and are thus more realistic."
" For cach model. we list thers shear a.(1°) in square cells of size 0,-- 1. aloug with the sigual-to-uoise ratio SNR(1)~2.1g?62(17]o,2ASO. for detecting thisexcess variancewith FIRST."," For each model, we list the shear $\sigma_{\gamma}(1^{\circ})$ in square cells of size $\theta_{c}=1^{\circ}$ , along with the signal-to-noise ratio $(1^{\circ}) \simeq 2^{-1} g^{2} \sigma_{\gamma}^{2}(1^{\circ})
\sigma_{\epsilon}^{-2} n A^{\frac{1}{2}} \theta_{c}$ for detecting thisexcess variancewith FIRST."
 For the eluster-nonnalized models. an shear ofabout is expected to be detectable at the ~Le level.in this fashion.," For the cluster-normalized models, an shear ofabout is expected to be detectable at the $\sim 4\sigma$ level,in this fashion."
The success rate for radial velocity measurements iu our sample is 1l out of 57. or aboute,"The success rate for radial velocity measurements in our sample is 41 out of 57, or about."
 This is somewhat lower than the success rate in the RCO2 study. but the difference cau be attributed to two factors: The metallicity of cach star is estimated from its position in the (V. £. 7) coloranaeuitude diagram Fig. 1..," This is somewhat lower than the success rate in the RG02 study, but the difference can be attributed to two factors: The metallicity of each star is estimated from its position in the $V-I$ , $I$ ) color-magnitude diagram Fig. \ref{vi_cmd},"
 by comparing it to model isochrones from the Padova group (Cirardietal.2000). with 23. LT. 13. OF. (Q1 —0.02. and [0.18 aud £f=12.6 Cir.," by comparing it to model isochrones from the Padova group \citep{gir00} with $\rm[Fe/H]=-2.3$ , $-1.7$ , $-1.3$, $-0.7$, $-0.4$, $-0.02$, and $+0.18$ and $t=12.6$ Gyr."
 The isochrones are translated iuto apparent/observed Lvs. V-Ispeccbascdonanadopted N31 distaneco F783 kpe(Stanck&Garnavieh 1998:Holland1998)..oratr 2017. aud a mean reddening of E(BV);=0.06 towards Cl derived froii the dust map.," The isochrones are translated into apparent/observed $I$ $V-I$ space based on an adopted M31 distance of 783 kpc \citep{sta98,hol98}, or a true distance modulus of $(m-M)_0=24.47$ , and a mean reddening of $\langle{E(B-V)}\rangle=0.06$ towards G1 derived from the \citet*{sch98} dust map."
 A standard slope of Ry=3.1 is assuned for the Calactic dust extinction law. which translates iuto A(WD/E(B.V)=LE (ανασα.Clavtou.&Mathis1989).," A standard slope of $R_V=3.1$ is assumed for the Galactic dust extinction law, which translates into $E(V-I)/E(B-V)=1.4$ \citep*{car89}."
. The resulting model isochrones are fit with a Legeudre polvuouiual of 6th order in VZ and 10th order in Z to interpolate between the isochrones., The resulting model isochrones are fit with a Legendre polynomial of 6th order in $V-I$ and 10th order in $I$ to interpolate between the isochrones.
 This viclds a photometric estimate of cach stars uctallicity. [Fe/T|pior," This yields a photometric estimate of each star's metallicity, $\rm[Fe/H]_{phot}$."
 1 the actual age of the stellar population is closer to [Cir instead of the value of 12.6 Car adopted in this paper 2003).. the metallicity estimates would be revised upwards by about |0.3 dex (see Fig. 1)).," If the actual age of the stellar population is closer to 4 Gyr instead of the value of 12.6 Gyr adopted in this paper \citep{ric03}, the metallicity estimates would be revised upwards by about $+0.3$ dex (see Fig. \ref{vi_cmd}) )."
 The errors in metallicity are dominated by svstematics in the method., The errors in metallicity are dominated by systematics in the method.
 The relative metallicities of the siuuple may be ranked to within 0.1 dex. but the true metallicity of cach star is uncertain by at least 0.25 dex due to svstemiatie errors such as differential reddening. age error/spread. variations in the degree of alpha enhancement. aud inaccuracies iu the models.," The relative metallicities of the sample may be ranked to within 0.1 dex, but the true metallicity of each star is uncertain by at least 0.25 dex due to systematic errors such as differential reddening, age error/spread, variations in the degree of alpha enhancement, and inaccuracies in the models."
 The systematic error of 0.25 dex is added im quadrature to a randoni error component of 0.1 dex: conservativelv. our metallicities have overall errors on the order of 0.27 dex.," The systematic error of 0.25 dex is added in quadrature to a random error component of 0.1 dex: conservatively, our metallicities have overall errors on the order of 0.27 dex."
 The above error estimates apply only to stars located within the rauge of the model isochrones in Fie. 1.., The above error estimates apply only to stars located within the range of the model isochrones in Fig. \ref{vi_cmd}.
 Tt is clear from the CAID though that a significant nunuber of stars lie above the tip of the RGB and/or are bluer than the most metal-poor isochrone., It is clear from the CMD though that a significant number of stars lie above the tip of the RGB and/or are bluer than the most metal-poor isochrone.
" As discussed in 33, most of these outlicrs ave foreground Galactic dif starsfor which the [Fo/U),ior estimate is inany case 1ieauineless."," As discussed in 3, most of these outliers are foreground Galactic dwarf starsfor which the $\rm[Fe/H]_{phot}$ estimate is inany case meaningless."
" Two of the outliers are probable members of MBLs disk (see below): we caution that their extrapolated [Fo/II],j,"" estimates are very uncertain.", Two of the outliers are probable members of M31's disk (see below); we caution that their extrapolated $\rm[Fe/H]_{phot}$ estimates are very uncertain.
rate (dA df).,rate $dM_{\rm HI}/dt$ ).
 For the iufall velocities we adopt the values for egg for IVCs aud. IIVCS listed in Table 2., For the infall velocities we adopt the values for $v_{\rm infall}$ for IVCs and HVCs listed in Table 2.
 The expected number densities (4A/dzYsinye as a function of the galaxy. mass are indicated with the ereeu-shaded area in the right paucl of 22., The expected number densities $(d{\cal N}/dz)_{\rm disk+HVC}$ as a function of the galaxy mass are indicated with the green-shaded area in the right panel of 2.
 All results are stumarized in Table 3., All results are summarized in Table 3.
" Based ou these results we derive the following relation between the disk mass of galaxies. My Gu solar units). aud the racius of the neutral gas halo. A, (nu [kpc]): If we integrate the values of (ANddicuc: listed in Table 23 over the cutire mass range. we derive a total umuber density of disk/lalo absorbers of GUNfdanasjvc:=0.212."," Based on these results we derive the following relation between the disk mass of galaxies, $M_{\rm HI}$ (in solar units), and the radius of the neutral gas halo, $R_{\rm halo}$ (in [kpc]): If we integrate the values of $(d{\cal N}/dz)_{\rm disk+HVC}$ listed in Table 3 over the entire mass range, we derive a total number density of disk/halo absorbers of $(d{\cal N}/dz)_{\rm disk+HVC}=0.212$."
 This value is ~5 times larger than the muuber deusitv of DLAs at «=0 (Zwaan et 22005). sugeesting that the absorption-cross section of IIVCs with log NUT17.5 exceeds that of DLAs by a factor of ~L on average.," This value is $\sim 5$ times larger than the number density of DLAs at $z=0$ (Zwaan et 2005), suggesting that the absorption-cross section of HVCs with log $N$ $)\geq 17.5$ exceeds that of DLAs by a factor of $\sim 4$, on average."
 As for DLAs. the total absorption cross section of optically thick iu disks and halos is dominated by galaxies in the mass range Myg=8.810.0.," As for DLAs, the total absorption cross section of optically thick in disks and halos is dominated by galaxies in the mass range $M_{\rm HI}=8.8-10.0$."
 As our model indicates. the mea (projected) covering fraction of IIVCs in galaxy. halos is small. νο)=0.2. typically.," As our model indicates, the mean (projected) covering fraction of HVCs in galaxy halos is small, $\langle f_{\rm HVC} \rangle=0.2$, typically."
 Using the mass accretion rates (AL df) listed in Table 3 together with the mass function of the local ealaxv population (Zwaan et 22005) we can estimate the neutral gas accretiou-rate denusitv o λος (nass accretion rate per unit volume) at low redsüft., Using the mass accretion rates $dM_{\rm HI}/dt$ ) listed in Table 3 together with the mass function of the local galaxy population (Zwaan et 2005) we can estimate the neutral gas accretion-rate density of HVCs (mass accretion rate per unit volume) at low redshift.
 We obtain πμ. ο»... 7.," We obtain $dM_{\rm HI}/dt/dV = 0.022\,M_{\sun}$ $^{-1}$ $^{-3}$."
 Note that this value is calculated under the assunptiou that all of the neutral gas 1ji the halos of ealaxies is beiug acercted outo their disks. inclependcutly of its origin inside or outside he host galaxies.," Note that this value is calculated under the assumption that all of the neutral gas in the halos of galaxies is being accreted onto their disks, independently of its origin inside or outside the host galaxies."
 The above estimate does not imelude the mass of tie ionized gas component of ITVCs. which nay contribute substantially o the total mass of multi-phase halo clouds (6.9... Fox et 22010: Winkel et 22011).," The above estimate does not include the mass of the ionized gas component of HVCs, which may contribute substantially to the total mass of multi-phase halo clouds (e.g., Fox et 2010; Winkel et 2011)."
 Also not included are xutlv neutral eas fragments with masses and angular sizes below the detection limit of 21e IWC survevs., Also not included are partly neutral gas fragments with masses and angular sizes below the detection limit of 21cm HVC surveys.
 Such structures are known to exist in the Milkv Way iilo (Richter et 22009). but their (total) neutral eas nass most likely is siiall conrpared to the large. extended 2]cn UVCs.," Such structures are known to exist in the Milky Way halo (Richter et 2009), but their (total) neutral gas mass most likely is small compared to the large, extended 21cm HVCs."
 The role of ionized gas is further discussed low., The role of ionized gas is further discussed below.
" The value of 0.022M | P is remarkably close to the star-formation rate deusity at +— 0(5,=0.010.02AZ ! 7. as derived from ultraviolet aud infrared observational data (ITopkius Deacon 2006)."," The value of $0.022\,M_{\sun}$ $^{-1}$ $^{-3}$ is remarkably close to the star-formation rate density at $z=0$ $\dot{\rho}_{\star}=0.01-0.02\,M_{\sun}$ $^{-1}$ $^{-3}$, as derived from ultraviolet and infrared observational data (Hopkins Beacom 2006)."
 Therefore. cold-gas accretion by Ηνος possibly plays au important Gf not dominating) role in feeding galaxies at 2%0 with eascous material to power star formation.," Therefore, cold-gas accretion by HVCs possibly plays an important (if not dominating) role in feeding galaxies at $z\approx0$ with gaseous material to power star formation."
 The above given value for the aceretion-rate deusity can also be compared with recent estinates of the ~coldanode” eas accretion-rate densities at +=0 from cosmolosical simulations., The above given value for the accretion-rate density can also be compared with recent estimates of the “cold-mode” gas accretion-rate densities at $z=0$ from cosmological simulations.
" Using an SPI code. I&eres et ((2009) find 4M/dt/dV.~0.03A, 1AIMpe: P? for cold eas that never exceeded a maxim teniperature of Tuas=2.54105 K. However. using SPI simulations with more realistic eas plivsics VVoort et ((2011) derive a iuch lower ""cold-auode gas accretion-rate deusity for at ;=0 of dA/dt/dV.—0.002AL. tAMAIpe 72 while for the superordinate DA halos the cold-mode accretion-rate is estimated to be αλ~0.01M. tAIMpe >. thus five-times higher."," Using an SPH code, $\check{s}$ et (2009) find $dM/dt/dV \sim 0.03\,M_{\sun}$ $^{-1}$ $^{-3}$ for cold gas that never exceeded a maximum temperature of $T_{\rm max}=2.5\times10^5$ K. However, using SPH simulations with more realistic gas physics Voort et (2011) derive a much lower “cold-mode” gas accretion-rate density for at $z=0$ of $dM/dt/dV \sim 0.002\,M_{\sun}$ $^{-1}$ $^{-3}$, while for the superordinate DM halos the cold-mode accretion-rate is estimated to be $dM/dt/dV \sim 0.01\,M_{\sun}$ $^{-1}$ $^{-3}$, thus five-times higher."
 Therefore. oulv 20 percent of the cold gas that euters the DAL halo in their simulation is actually beime accreted as cold gas by the central galaxy.," Therefore, only 20 percent of the cold gas that enters the DM halo in their simulation is actually being accreted as cold gas by the central galaxy."
 Unfortunately. these studies do not provide information on the absorption cross section of all t1e cold gas in the DM halos aud its radial distribution around the galaxies (independently of whether it is being accreted or not). so that a detailed courparisou between the simulation results and our UVC model is not possible at this point.," Unfortunately, these studies do not provide information on the absorption cross section of all the cold gas in the DM halos and its radial distribution around the galaxies (independently of whether it is being accreted or not), so that a detailed comparison between the simulation results and our HVC model is not possible at this point."
 It needs to be meutioned that gas that is considered as “cold” in the cosimological simulations docesnot necessarily cud up as high-velocity eax that is detectable via 2lcm observations., It needs to be mentioned that gas that is considered as “cold” in the cosmological simulations does necessarily end up as high-velocity gas that is detectable via 21cm observations.
 It is expected that a substantial fraction of the accreted eas that never was heated up to the virial temperature of the host halo remains diffuse aud “wari. hes at low densities (yp10? P) and intermediate teiiperatures (T—10410 K).," It is expected that a substantial fraction of the accreted gas that never was heated up to the virial temperature of the host halo remains diffuse and “warm”, i.e., at low densities $n_{\rm H}<10^{-2}$ $^{-3}$ ) and intermediate temperatures $T=10^4-10^5$ K)."
 The neutral eas fraction in such wu eas is expected to be low. so that if remains unuseen in 2lem cussion (“warm mode of gas accretion: Ποσο Putian 2009: Blaud-Uawthorm 2008).," The neutral gas fraction in such warm gas is expected to be low, so that it remains unseen in 21cm emission (“warm“ mode of gas accretion; Heitsch Putman 2009; Bland-Hawthorn 2008)."
 The existence of such a wari. jonized gas component m the halos of ealaxies is stronely supported by the detection of intermediate- aud hiehl-iou absorption (c.e.. fromSILL.Cin.Civ. and Si1v)) iu the halo of the Mills. Way (e.g... Fox et 22006: Semibach et 11995. 1999) aud in he ecircunegalactie environments of other galaxies (6.9.. Bibaudo et 22011).," The existence of such a warm, ionized gas component in the halos of galaxies is strongly supported by the detection of intermediate- and high-ion absorption (e.g., from, and ) in the halo of the Milky Way (e.g., Fox et 2006; Sembach et 1995, 1999) and in the circumgalactic environments of other galaxies (e.g., Ribaudo et 2011)."
 Also the ionized envelopes of 21014 IIVC complexes represent significant eas reservoirs that reed to be considered for a realistic estimate of thetoted (neutral and iouized) gas mass that is Όσιο accreted w galaxies (e.g... Winkel et 22011: Fox et 22010).," Also the ionized envelopes of 21cm HVC complexes represent significant gas reservoirs that need to be considered for a realistic estimate of the (neutral and ionized) gas mass that is being accreted by galaxies (e.g., Winkel et 2011; Fox et 2010)."
 The coutrbutiou of the ionized eas couponcut to the otal eas infall rate is difficult to deteriuuc. however. as the infall velocity ο: jonized eas nav be substaitially ower than for ucutral gas because of hvdrodyuauical effects that affect the ionized cloud cuvelopes. such as eas stripping. turbulent mixing. aud heat conduction.," The contribution of the ionized gas component to the total gas infall rate is difficult to determine, however, as the infall velocity of ionized gas may be substantially lower than for neutral gas because of hydrodynamical effects that affect the ionized cloud envelopes, such as gas stripping, turbulent mixing, and heat conduction."
 The june processes also affect the total cloud mass aud the neutral gas fraction in IWCs aud thus iufluence the voluue filling factor in these clouds., The same processes also affect the total cloud mass and the neutral gas fraction in HVCs and thus influence the volume filling factor in these clouds.
 These aspects clearly are best resolved through high-resolution lydrodvuamiical simulations (e... Ueitsch Putinan 2009: Vieser Ileusler 2007).," These aspects clearly are best resolved through high-resolution hydrodynamical simulations (e.g., Heitsch Putman 2009; Vieser Hensler 2007)."
 To estimate the contribution. of UVCs to the munber density of optically thick Lya absorbers at low 2. it Is necessary to know the CDDF for log N 17 Satlowredshi ftlequation2)," To estimate the contribution of HVCs to the number density of optically thick $\alpha$ absorbers at low $z$ , it is necessary to know the CDDF for log $N$ $)>17.5$ at low redshift (equation 2)."
 Asmentione umndensitill iabsorbersarcrarcandthattheamountoftheQsOal lincdataintheultracioletislinited," As mentioned above, the CDDF at $z=0$ is poorly constrained for this column density range owing to the fact that high-column density absorbers are rare and that the amount of the QSO absorption-line data in the ultraviolet is limited."
" CorbellieBandicra (2002 \haceco linedata forintermediatcredshifts from BandicrakCorbelli( 2001), ftabsor ptiondatafron cymannetal, (1998). and2lem iei linedatafromRyan Weberctal, ((2003)toconstructthe iC11 DDFin 21."," Corbelli Bandiera (2002) have combined absorption-line data for intermediate redshifts from Bandiera Corbelli (2001), low-redshift absorption data from Weymann et (1998), and 21cm emission-line data from Ryan-Weber et (2003) to construct the CDDF in the rangelog $N$ $) \approx 13-21$ ."
 The CDDF preseuted in Corbelli Daudiera, The CDDF presented in Corbelli Bandiera
The complex field seen in theHS'T images of the Antennae makes finding counterparts to X-ray sources difficult and necessitated a different method for defining counterparts than that used for the IR (seeaboveandClarketal.2007).,The complex field seen in the images of the Antennae makes finding counterparts to X-ray sources difficult and necessitated a different method for defining counterparts than that used for the IR \citep[see above and ][]{cla07}.
. Using our precise frame-tie we defined areas of positional uncertainty around each X-ray source., Using our precise frame-tie we defined areas of positional uncertainty around each X-ray source.
" Specifically, an inner aperture with a radius of 1 arcsec and an annular region from 2.0 — 3.0 arcsec."," Specifically, an inner aperture with a radius of 1 arcsec and an annular region from 2.0 – 3.0 arcsec."
" We then defined possible matches as those X-ray sources with two optical sources in the circular aperture and less than five optical sources in the annulus, and likely matches as those X-ray sources with one optical source in the circular aperture and less than five optical sources in the annulus."," We then defined possible matches as those X-ray sources with two optical sources in the circular aperture and less than five optical sources in the annulus, and likely matches as those X-ray sources with one optical source in the circular aperture and less than five optical sources in the annulus."
" If more than five sources lay in the annular region, we considered the region to be too complicated for a positive counterpart identification, regardless of how many sources lay in the inner aperture."," If more than five sources lay in the annular region, we considered the region to be too complicated for a positive counterpart identification, regardless of how many sources lay in the inner aperture."
" Using these criteria, we identified seven X-ray sources with likely matches to a single J-band source and one X-ray source, with possible matches to two I-band sources."," Using these criteria, we identified seven X-ray sources with likely matches to a single $I$ -band source and one X-ray source, with possible matches to two $I$ -band sources."
 We used theHST I-band image to search for counterparts because this filter covers the longest wavelength of the availableHST bands and so is least affected by extinction., We used the $I$ -band image to search for counterparts because this filter covers the longest wavelength of the available bands and so is least affected by extinction.
" Repeating the procedure discussed in Clarketal. (2007), we estimated the level of source contamination associated with our identified optical counterparts to X-ray sources."," Repeating the procedure discussed in \citet{cla07}, we estimated the level of source contamination associated with our identified optical counterparts to X-ray sources."
" We expect five with a lo uncertainty of +0.5/-0.3'] of the seven likely counterparts to be due to chance superpositions of unrelated objects, and seven with a lo uncertainty of +3.8/-5.4'] for the one possible counterpart to be chance superpositions."," We expect five with a $1\sigma$ uncertainty of ] of the seven likely counterparts to be due to chance superpositions of unrelated objects, and seven with a $1\sigma$ uncertainty of ] for the one possible counterpart to be chance superpositions."
 Clearly these statistics indicate the majority of our optical counterparts are chance superpositions and further demonstrate the difficulty of making such matches in the complex structure of theHST images of the Antennae., Clearly these statistics indicate the majority of our optical counterparts are chance superpositions and further demonstrate the difficulty of making such matches in the complex structure of the images of the Antennae.
" Therefore, we did not perform a photometric analysis on these source as we could not reliably identify the counterparts and so could not provide any statistically meaningful information on the X-ray source environments."," Therefore, we did not perform a photometric analysis on these source as we could not reliably identify the counterparts and so could not provide any statistically meaningful information on the X-ray source environments."
" Instead, we considered the optical equivalents to the 32 IR cluster counterparts identified in this work."," Instead, we considered the optical equivalents to the 32 IR cluster counterparts identified in this work."
 These optical matches were identified using the IR-to-optical astrometric frame-tie to match IR counterpart positions to positions., These optical matches were identified using the IR-to-optical astrometric frame-tie to match IR counterpart positions to positions.
" As we discuss below, in many cases a single IR counterpart split into multiple optical counterparts, and we labelled these conglomerations as a positive match."," As we discuss below, in many cases a single IR counterpart split into multiple optical counterparts, and we labelled these conglomerations as a positive match."
 We found optical counterparts to 27 IR cluster counterparts and Fig., We found optical counterparts to 27 IR cluster counterparts and Fig.
 2 displays subimages of those counterparts to X-ray sources seen across all six IR and optical bands., 2 displays subimages of those counterparts to X-ray sources seen across all six IR and optical bands.
 Fig., Fig.
 4 is an I-band image of the Antennae showing the positions of all counterpart candidates to X-ray sources., 4 is an $I$ -band image of the Antennae showing the positions of all counterpart candidates to X-ray sources.
 We made (J—Κε) versus Ks colour magnitude diagrams, We made $(J-K_s)$ versus $K_s$ colour magnitude diagrams
should not cause additional problems.,should not cause additional problems.
 However. due to the dominance of earlv-type. galaxies. this distinction may be unnecessary in many clusters.," However, due to the dominance of early-type galaxies, this distinction may be unnecessary in many clusters."
 We investigated methods to constrain the mass clistribution of cluster galaxies from the distortions of the images of faint background galaxies., We investigated methods to constrain the mass distribution of cluster galaxies from the distortions of the images of faint background galaxies.
 Ln this paper we restricted the treatment to non-critical clusters (or the non-critical regions of critical ones). ancl we did not discuss the observational clillicultics in measuring image ellipticities or identifving cluster galaxies.," In this paper we restricted the treatment to non-critical clusters (or the non-critical regions of critical ones), and we did not discuss the observational difficulties in measuring image ellipticities or identifying cluster galaxies."
 The ¢-statistic is a straightforward method [ου determining aperture masses., The $\zeta$ -statistic is a straightforward method for determining aperture masses.
 significant (aperture) mass estimates for an ensemble of cluster galaxies can be obtained bv adding the results for a large number of galaxies., Significant (aperture) mass estimates for an ensemble of cluster galaxies can be obtained by adding the results for a large number of galaxies.
 The method provides a direct. handle on the lensing signal of the cluster galaxies without the need to specify a model for their mass distribution., The method provides a direct handle on the lensing signal of the cluster galaxies without the need to specify a model for their mass distribution.
 The galaxy. lensing elfects. are amplified by an underlving cluster mass distribution., The galaxy lensing effects are amplified by an underlying cluster mass distribution.
 Hence. in regions with non-negligible surface mass density. a cluster mass reconstruction is necessary in order to take this cllect into account in the caleulation of the cCstatistic.," Hence, in regions with non-negligible surface mass density, a cluster mass reconstruction is necessary in order to take this effect into account in the calculation of the $\zeta$ -statistic."
 Due to geometrical limitations it is not possible to include. all available information into the method., Due to geometrical limitations it is not possible to include all available information into the method.
 Towards the cluster centre the increasing number density of. cluster. galaxies precludes a useful application of the ¢-statistic., Towards the cluster centre the increasing number density of cluster galaxies precludes a useful application of the $\zeta$ -statistic.
 In addition. the generalization into the non-linear regime also implies an increasing sensitivity το uncertainties in the description of the cluster mass distribution or the redshift distribution of the source galaxies.," In addition, the generalization into the non-linear regime also implies an increasing sensitivity to uncertainties in the description of the cluster mass distribution or the redshift distribution of the source galaxies."
 In the outskirts of clusters. however. the c-statistic is applicable without major technical dilliculties.," In the outskirts of clusters, however, the $\zeta$ -statistic is applicable without major technical difficulties."
 For a quantitative analvsis. a maximum: Dikelihoo method. is more appropriate.," For a quantitative analysis, a maximum likelihood method is more appropriate."
 We tried. to separate the treatment of cluster galaxies and a global cluster mass distribution by reconstructing the latter one using stanclare inversion methods. anc then adding paramctrized mass models for the galaxies on top of that., We tried to separate the treatment of cluster galaxies and a `global cluster mass distribution' by reconstructing the latter one using standard inversion methods and then adding parametrized mass models for the galaxies on top of that.
 Phe results of our simulations demonstrate that this method is reliable in 10 sense of correctly retrieving the input. parameters for 1ο galaxy mass models within their confidence regions as long as the mass in galaxies is small compared to the otal mass of the svstem., The results of our simulations demonstrate that this method is reliable – in the sense of correctly retrieving the input parameters for the galaxy mass models within their confidence regions -- as long as the mass in galaxies is small compared to the total mass of the system.
 However. if the cluster galaxies o have extended dark matter haloes. this is not the case.," However, if the cluster galaxies do have extended dark matter haloes, this is not the case."
 The potentially significantIn mass fraction contributed. by rem also shows up in the cluster mass reconstruction. and adding additional mass in the form of galaxy mocels would violate the total mass constraint given by the reconstruction.," The potentially significant mass fraction contributed by them also shows up in the cluster mass reconstruction, and adding additional mass in the form of galaxy models would violate the total mass constraint given by the reconstruction."
 We dealt with that problem by. applying empirical. and acimittediv inclegant mass compensation procedures., We dealt with that problem by applying empirical and admittedly inelegant mass compensation procedures.
" This approach turned out to be workable. though not completely satisfving. in the outskirts of clusters where the requirements on the accuracy of the description. of the cluster. mass component are moderate,"," This approach turned out to be workable, though not completely satisfying, in the outskirts of clusters where the requirements on the accuracy of the description of the cluster mass component are moderate."
 1n the highly non-linear region of the cluster centre. jowever. Lb is impossible to treat the image distortion ellects caused by a global mass component and those caused w individual cluster galaxies independently.," In the highly non-linear region of the cluster centre, however, it is impossible to treat the image distortion effects caused by a global mass component and those caused by individual cluster galaxies independently."
 Rather. the xinciple of maximum likelihood should be taken seriously and the method. of choice should allow to determine the vest description. of the cluster mass component for each given set of galaxy mocdel parameters by explicitly taking the xesence of the galaxies into account.," Rather, the principle of maximum likelihood should be taken seriously and the method of choice should allow to determine the best description of the cluster mass component for each given set of galaxy model parameters by explicitly taking the presence of the galaxies into account."
 In general. this cannot ος accomplished: by resorting to simple parametrized. mass models for the cluster component itself.," In general, this cannot be accomplished by resorting to simple parametrized mass models for the cluster component itself."
" ""μονο represent an unjustified restriction ancl could therefore severely bias the results.", These represent an unjustified restriction and could therefore severely bias the results.
 Observational as well as numerical work incicates that clusters of galaxies. cannot be regarded. as nicely Virialized) systems., Observational as well as numerical work indicates that clusters of galaxies cannot be regarded as nicely virialized systems.
 Instead. their mass distribution often exhibits complicated: morphologies anc hence a virtually parameter-free approach is warranted for describing them.," Instead, their mass distribution often exhibits complicated morphologies and hence a virtually parameter-free approach is warranted for describing them."
 We developed: a generalized maximum likelihood method which enables us to cope with the problems discussed above and we will report on our experience therewith elsewhere., We developed a generalized maximum likelihood method which enables us to cope with the problems discussed above and we will report on our experience therewith elsewhere.
 In those cases for which we classified. the likelihood method presented in this paper as reliable or applicable. we believe that the general picture provided by the confidence regions in the galaxy model parameter space is correct.," In those cases for which we classified the likelihood method presented in this paper as reliable or applicable, we believe that the general picture provided by the confidence regions in the galaxy model parameter space is correct."
 Nevertheless. introducing additional degrees of freedom by allowing the cluster component to adapt to changes of the galaxy model will tend to widen the confidence regions.," Nevertheless, introducing additional degrees of freedom by allowing the cluster component to adapt to changes of the galaxy model will tend to widen the confidence regions."
 Especially for the galaxy input model with extended. dark, Especially for the galaxy input model with extended dark
 (AXPs:see?. 10°-10° cC-10P6; —3—4) (KT~0.5 (e.g.?).. (e.g.?).. (e.g.?)..," \citep[AXPs; see][for a recent
review]{magnetarsSandro} $^3$ $^5$ \citep[$\sim$10$^{15}$ $\sim$ $kT\sim0.5$ \citep[e.g.][]{tmt05}, \citep[e.g.][]{durant06}. \citep[e.g.][]{hulleman04}."
 to match the low optical/NIR fluxes., to match the low optical/NIR fluxes.
 In some AXPs good spectral fits are obtained with the sum of two blackbody components with different temperatures., In some AXPs good spectral fits are obtained with the sum of two blackbody components with different temperatures.
 Since this model does not suffer of the problems described above. it is usually preferred to the power-law plus blackbody model (e.g.?)..," Since this model does not suffer of the problems described above, it is usually preferred to the power-law plus blackbody model \citep[e.g.][]{halpern05}."
 However. also this model is only phenomenological and it is inadequate to represent the non-thermal phenomena that are expected to occur in the highly magnetized magnetosphere of magnetars (e.g.?)..," However, also this model is only phenomenological and it is inadequate to represent the non-thermal phenomena that are expected to occur in the highly magnetized magnetosphere of magnetars \citep[e.g.][]{lyutikov06}."
 More physical models of the X-ray spectra. including the effects of the strong magnetic field and charged currents. have recently been developed and successfully applied to a sample of magnetar candidates (???)..," More physical models of the X–ray spectra, including the effects of the strong magnetic field and charged currents, have recently been developed and successfully applied to a sample of magnetar candidates \citep[][]{fernandez07,guver07,RCSnanda}."
 From a purely observational point of view. it has not been possible to discriminate between the different models reproducing the magnetar X-ray spectra.," From a purely observational point of view, it has not been possible to discriminate between the different models reproducing the magnetar X–ray spectra."
 This is mainly due to the low sensitivity of hard X-ray detectors above ~10 keV and to the large uncertainties in the fits introduced by the high interstellar absorption. that severely suppresses the flux below -—1 keV. Being young neutron stars born from massive progenitors. all the Galactic magnetars are located in highly absorbed regions of the Galactic plane.," This is mainly due to the low sensitivity of hard X–ray detectors above $\sim$ 10 keV and to the large uncertainties in the fits introduced by the high interstellar absorption, that severely suppresses the flux below $\sim$ 1 keV. Being young neutron stars born from massive progenitors, all the Galactic magnetars are located in highly absorbed regions of the Galactic plane."
 All of them have column densities Ny ranging from ~5«107! to ~107* cm., All of them have column densities $_{\rm{H}}$ ranging from $\sim$$5\times10^{21}$ to $\sim$$10^{23}$ $^{-2}$.
 The two known magnetars in the Magellanic Clouds. being considerably less absorbed. offer the possibility. to better constrain the spectra in the low energy range.," The two known magnetars in the Magellanic Clouds, being considerably less absorbed, offer the possibility to better constrain the spectra in the low energy range."
" The study of SGR 0526-66. located in the Large Magellanic Cloud. is complicated by the presence of the surrounding supernova remnant N49, which is particularly bright in soft X-rays (?).."," The study of SGR 0526–66, located in the Large Magellanic Cloud, is complicated by the presence of the surrounding supernova remnant N49, which is particularly bright in soft X–rays \citep{kulkarni03}."
 Here weconcentratetherefore on the spectral properties of theonlyknown AXP in the Small Magellanic Cloud (SMC).," Here weconcentratetherefore on the spectral properties of \\citep{lamb02,lamb03errata,mcgarry05}, ,theonlyknown AXP in the Small Magellanic Cloud (SMC)."
 The first term in the RIIS describes a shift along the eritical curve. and so the non-vanishing contribution to JJ=dJ—au+be comes from the second term in the RIS.,"v = u The first term in the RHS describes a shift along the critical curve, and so the non-vanishing contribution to $J = dJ = au+bv$ comes from the second term in the RHS."
 J=-- VINE We can rewrite it in terms of the original notations., J = b We can rewrite it in terms of the original notations.
 If we stare at the solutions in ()) through (23)) for a moment. a few things are clear.," If we stare at the solutions in \ref{eqLinear}) ) through \ref{eqJdJtwo}) ) for a moment, a few things are clear."
winds.,winds.
 The solution of the chemical evolution in the presence of galactic fountains ts given by: A comparison of this solution with the solution of eq. (12)), The solution of the chemical evolution in the presence of galactic fountains is given by: A comparison of this solution with the solution of eq. \ref{eq:diffwsol}) )
 with infall of pristine gas (Z4= 0) is shown in Fig. 6.., with infall of pristine gas $Z_A = 0$ ) is shown in Fig. \ref{fount}.
 For both models plotted in this figure we have assumed t=3. A=| and a=5.," For both models plotted in this figure we have assumed $\lambda = 3$, $\Lambda = 1$ and $\alpha=5$."
 As expected. the galactic fountain model predicts larger vales of Z.," As expected, the galactic fountain model predicts larger vales of $Z$."
 These values exceed also the metallicities attained by the models with instantaneous mixing of the ICM (Sect., These values exceed also the metallicities attained by the models with instantaneous mixing of the ICM (Sect.
 3.3) shown in Fig. 5.., 3.3) shown in Fig. \ref{fig:compl}.
 This result is expected because the galactic fountain model maximizes the enrichment in metallicity of the infalling gas. whereas in the models shown in Seet.," This result is expected because the galactic fountain model maximizes the enrichment in metallicity of the infalling gas, whereas in the models shown in Sect."
 3.3 the metals escaping from the galaxy are diluted in a large amount of ICM., 3.3 the metals escaping from the galaxy are diluted in a large amount of ICM.
 From eqs. (12)), From eqs. \ref{eq:diffwsol}) )
 and (20)) we can also notice that the metallicity ratio tends asymptotically to the value [ία—[).t+Λα-Av—11 which ts always larger than one (for the special choice of parameters it is equal to 13/8) but it tends to | for a>1.," and \ref{eq:fountsol}) ) we can also notice that the metallicity ratio tends asymptotically to the value $[(\alpha
- 1) \lambda + \Lambda] / [(\lambda - \Lambda) (\alpha - 1)]$ which is always larger than one (for the special choice of parameters it is equal to 13/8) but it tends to 1 for $\alpha \gg 1$."
 In our example. only an infall of pre-enriched gas. whose metallicity i$ larger than 5/8 yz can therefore produce a metallicity in the galaxy larger than the one attained by the galactic fountain model.," In our example, only an infall of pre-enriched gas, whose metallicity is larger than 5/8 $y_Z$ can therefore produce a metallicity in the galaxy larger than the one attained by the galactic fountain model."
 From eq. (20)), From eq. \ref{eq:fountsol}) )
 we can also see that. in the special ease in which t=A. Z/sz tends to the solution of the closed box model (eq. 3)).," we can also see that, in the special case in which $\lambda = \Lambda$, $Z/y_Z$ tends to the solution of the closed box model (eq. \ref{eq:simple}) )."
 This is due to the fact that. in the framework of the simple models of chemical evolution. having outflow and infall with the same rate and metallicity or not having gas flows at all is formally the same.," This is due to the fact that, in the framework of the simple models of chemical evolution, having outflow and infall with the same rate and metallicity or not having gas flows at all is formally the same."
 Indeed. the fountains take a finite and non-negligible time to orbit around and fall back to the galaxy (Spitoni et al. 2008)).," Indeed, the fountains take a finite and non-negligible time to orbit around and fall back to the galaxy (Spitoni et al. \cite{srm08}) )."
 This implies a delay in the mixing of metals in the ISM. which conflicts with the fourth assumption of the simple models of chemical evolution (Sect.," This implies a delay in the mixing of metals in the ISM, which conflicts with the fourth assumption of the simple models of chemical evolution (Sect."
 2). therefore only detailed numerical models can ascertain the effect of this delay on the chemical evolution of galaxies (Spitont et al.," 2), therefore only detailed numerical models can ascertain the effect of this delay on the chemical evolution of galaxies (Spitoni et al."
 2008. in preparation).," 2008, in preparation)."
 In the previous sections we have assumed that both outflow and infall rates are proportional to the SFR and we have seen that in this way we obtain solutions in which w(t) cancels out., In the previous sections we have assumed that both outflow and infall rates are proportional to the SFR and we have seen that in this way we obtain solutions in which $\psi (t)$ cancels out.
 In this section we analyze how reliable are these assumptions and what kind of results we obtain if we assume general infall and outflow laws (see also Edmunds 1990:;: Kópppen Edmunds 1999))., In this section we analyze how reliable are these assumptions and what kind of results we obtain if we assume general infall and outflow laws (see also Edmunds \cite{edm90}; Köpppen Edmunds \cite{ke99}) ).
 First of all we notice that a correlation between infall rate and SFR arises naturally because the larger is the amount of infalling gas. the higher is the reservoir of gas inside the galaxy available to form stars.," First of all we notice that a correlation between infall rate and SFR arises naturally because the larger is the amount of infalling gas, the higher is the reservoir of gas inside the galaxy available to form stars."
 An example is given by detailed models of the chemical evolution of the Milky Way (Chiappini et al. 1997:;, An example is given by detailed models of the chemical evolution of the Milky Way (Chiappini et al. \cite{cmg97};
 Cescutti et al. 2007:;, Cescutti et al. \cite{cescu07};
 Colavitti et al. 2008)), Colavitti et al. \cite{cmm08}) )
 in which two main phases of gas infall turn out to produce two distinet episodes of star formation (although the similar behavior between the two rates does not imply that their ratio is constant)., in which two main phases of gas infall turn out to produce two distinct episodes of star formation (although the similar behavior between the two rates does not imply that their ratio is constant).
 We will show in this section that. under reasonable assumptions. a constant ratio between SER and infall rate can be attained during the late evolution of the considered galaxies.," We will show in this section that, under reasonable assumptions, a constant ratio between SFR and infall rate can be attained during the late evolution of the considered galaxies."
 On the other hand. a proportionality between the outflow rate and the SFR is quite realistic and it has been shown both observationally (e.g. Heckman 2002)) and theoretically (e.g. Silk 2003)).," On the other hand, a proportionality between the outflow rate and the SFR is quite realistic and it has been shown both observationally (e.g. Heckman \cite{heck02}) ) and theoretically (e.g. Silk \cite{silk03}) )."
 Therefore. let us assume for simplicity that eq. (5))," Therefore, let us assume for simplicity that eq. \ref{eq:w}) )"
 still holds and that the infalling gas is pristine (e.g. Z4.=0)., still holds and that the infalling gas is pristine (e.g. $Z_A = 0$ ).
 The extension of our calculations to the case in which W(r) is a generic function is. straightforward., The extension of our calculations to the case in which $W (t)$ is a generic function is straightforward.
" If we assume a generic infall law A(t). the system of equations we need to solve ts: subject to the usual initial conditions Z(0)=0. M,(0)=M,,(0)= Mo."," If we assume a generic infall law $A (t)$, the system of equations we need to solve is: subject to the usual initial conditions $Z(0)=0$, $M_g (0) = M_{tot}
(0) = M_{g, 0}$ ."
 In this case. however. it is not possible to solve this system of equations canceling out (f).," In this case, however, it is not possible to solve this system of equations canceling out $\psi (t)$."
" Therefore. at variance with what we have done so far. we must assume some dependence of u(t) on M, (Schmidt law)."," Therefore, at variance with what we have done so far, we must assume some dependence of $\psi (t)$ on $M_g$ (Schmidt law)."
 We assume a linear Schmidt law (e.g. W(t)=S M.(r)). because it is the only formulation for which the results can be expressed analytically.," We assume a linear Schmidt law (e.g. $\psi (t) = S M_g (t)$ ), because it is the only formulation for which the results can be expressed analytically."
 For Schmidt laws with different exponents detailed numerical models are required., For Schmidt laws with different exponents detailed numerical models are required.
 The equatior for the evolution of the gas mass can be simply solved. yielding: Substituting this expression into the third equation ofthe system (21)) also the evolution of the metallicity as a function of time can be calculated.," The equation for the evolution of the gas mass can be simply solved, yielding: Substituting this expression into the third equation ofthe system \ref{eq:system_general}) ) also the evolution of the metallicity as a function of time can be calculated."
 The result is the following:, The result is the following:
luminosity difference between the tirst and second most luminous GNim 2) and the first and the third most luminous GN5) galaxies in our Millennium data within fooand within 500 /!Kkpe.,luminosity difference between the first and second most luminous $\Delta m_{12}$ ) and the first and the third most luminous $\Delta m_{13}$ ) galaxies in our Millennium data within $R_{200}$and within 500 $h^{-1}$ kpc.
 In Fig. 4.," In Fig. \ref{aadfig4},"
 we plot the /i-band luminosity gap distribution of the Millennium simulation for the same mass range as the models. together with the luminosity gap distribution of730 SDSS C4 clusters (Milleretal.2005).," we plot the $R$ -band luminosity gap distribution of the Millennium simulation for the same mass range as the models, together with the luminosity gap distribution of730 SDSS C4 clusters \citep{b110}."
. Figs., Figs.
 daa and 4bb compare the predicted gap statistics from Milosavljeviéetal.(2006).for two values of the Coulomb logarithm. lnA—1 and InA=2. within Royo.," \ref{aadfig4}a a and \ref{aadfig4}b b compare the predicted gap statistics from \citet{b115} for two values of the Coulomb logarithm, $\ln \Lambda = 1$ and $\ln \Lambda = 2$, within $R_{200}$."
 Since the parameter [n.X is proportional to the force of dynamical friction between the centres of subhalo and primary halo during the process of merging. a higher value of InA corresponds to a faster effective halo merger rate.," Since the parameter $\ln \Lambda$ is proportional to the force of dynamical friction between the centres of subhalo and primary halo during the process of merging, a higher value of $\ln
\Lambda$ corresponds to a faster effective halo merger rate."
" In numerical simulations. InX is approximated by by./b,,;,. where Όρων. and 5,,;, are the maximum and minimum impact parameters respectively. and [nV is expected to be ~1.4 (Velázquez&White1999:Fellhaueretal.2000:D'Onghia 2005)."," In numerical simulations, $\ln \Lambda$ is approximated by $b_{max}/b_{min}$, where $b_{max}$ and $b_{min}$ are the maximum and minimum impact parameters respectively, and $\ln \Lambda$ is expected to be $\sim 1-4$ \citep{b190,b57,b50}. ."
. However. in the semi-analytic galaxy catalogues (Crotonetal.2006).. based on the Millennium simulation. used in this work. the above relation is approximated by In.X=In(1|Mooo/maa). where m; is the halo mass of the satellite galaxy.," However, in the semi-analytic galaxy catalogues \citep{b40}, based on the Millennium simulation, used in this work, the above relation is approximated by $ \ln \Lambda=\ln
(1+M_{\rm 200}/m_{\rm sat})$, where $m_{sat}$ is the halo mass of the satellite galaxy."
 Within the mass range of the SDSS data there are 8842 haloes in the Millennium simulation catalogue., Within the mass range of the SDSS data there are 8842 haloes in the Millennium simulation catalogue.
 Accordingly. in Fig. 4..," Accordingly, in Fig. \ref{aadfig4},"
 our data have been normalised to be comparable with the SDSS data and the theoretical model of Milosavljeviéetal. (2006)., our data have been normalised to be comparable with the SDSS data and the theoretical model of \citet{b115}.
. However. the simulation data is. unlike the observations. complete and uncontaminated by spurious groups or foreground and background galaxies.," However, the simulation data is, unlike the observations, complete and uncontaminated by spurious groups or foreground and background galaxies."
 All these effects are likely to be heavily dependent on the number of galaxies residing in the halo., All these effects are likely to be heavily dependent on the number of galaxies residing in the halo.
 As such. the comparison with the SDSS data shown in Fig.," As such, the comparison with the SDSS data shown in Fig."
 4. should be treated with caution., \ref{aadfig4} should be treated with caution.
 Given this caveat. our analysis based on the Millennium simulation catalogues agrees remarkably well with the models of Tilosavljevióetal.(2006) based on the SDSS survey for the uminosity gap distribution of the two brightest galaxies in each of the dark matter haloes. particularly for In.A=2 (Fig.," Given this caveat, our analysis based on the Millennium simulation catalogues agrees remarkably well with the models of \citet{b115} based on the SDSS survey for the luminosity gap distribution of the two brightest galaxies in each of the dark matter haloes, particularly for $\ln \Lambda
\! =\! 2$ (Fig."
 dau)., \ref{aadfig4}a a).
 However. for the /7-band luminosity gap between the brightest and hird brightest galaxies in each system (Fig.," However, for the $R$ -band luminosity gap between the brightest and third brightest galaxies in each system (Fig."
 20). the simulations significantly. depart from the model.," \ref{aadfig4}b b), the simulations significantly depart from the model."
 When comparing with the SDSS data (Figs., When comparing with the SDSS data (Figs.
 4cc and. 4dd). the simulations overpredict the requency of groups.," \ref{aadfig4}c c and \ref{aadfig4}d d), the simulations overpredict the frequency of groups."
 The simulations and the SDSS data have similar shaped distributions for the luminosity gap 2x5. but with a shift of ~O.5 mag toward higher Ar); in the simulated haloes.," The simulations and the SDSS data have similar shaped distributions for the luminosity gap $\Delta m_{13}$, but with a shift of $\sim$ 0.5 mag toward higher $\Delta m_{13}$ in the simulated haloes."
 We emphasize that the Millennium predictions for the luminosity gap statistic are sensitive to the assumed mass range and search radius of dark matter haloes within which brightest halo members are identified., We emphasize that the Millennium predictions for the luminosity gap statistic are sensitive to the assumed mass range and search radius of dark matter haloes within which brightest halo members are identified.
 SDSS cluster masses have been estimated from total ;-band luminosities. so any inaccuracies in this procedure would affect the comparison with the Millennium data.," SDSS cluster masses have been estimated from total $r$ -band luminosities, so any inaccuracies in this procedure would affect the comparison with the Millennium data."
 Observationally there is an excess population of groups with a small luminosity gap between the first and second ranked galaxies. above what is predicted by the theoretical models or the simulations.," Observationally there is an excess population of groups with a small luminosity gap between the first and second ranked galaxies, above what is predicted by the theoretical models or the simulations."
 This excess population is likely to result from contamination of observed group samples by local structure alignments. and renormalising to a sample without these groups scales down the “Millennium” distribution in Fig.," This excess population is likely to result from contamination of observed group samples by local structure alignments, and renormalising to a sample without these groups scales down the “Millennium” distribution in Fig."
 Jec. bringing the simulation results and the observational measurements into better agreement.," \ref{aadfig4}c c, bringing the simulation results and the observational measurements into better agreement."
 Results are similar in the A -band., Results are similar in the $K$ -band.
 The probability of finding fossil systems is expected to increase with decreasing halo mass. as shown in previous studies based on theoretical models or hydrodynamical simulations (D'OnghiadenBoschetal.2007).," The probability of finding fossil systems is expected to increase with decreasing halo mass, as shown in previous studies based on theoretical models or hydrodynamical simulations \citep{b50,b115,b147,b187}."
. Unfortunately. it is difficult to compare the results from different studies (both theoretical and observational). since they have used a range of search radii (from //jso to £337 — see Table.," Unfortunately, it is difficult to compare the results from different studies (both theoretical and observational), since they have used a range of search radii (from $R_{180}$ to $R_{337}$ – see Table."
 1) within which the Ar>2mag criterion is imposed.," 1) within which the $\Delta m_{12} \geq~2\,$ mag criterion is imposed."
 Clearly. the larger the search radius. the more demanding is the requirement on the galaxy contents of the system. and the smaller the fraction of groups which will qualify as fossils.," Clearly, the larger the search radius, the more demanding is the requirement on the galaxy contents of the system, and the smaller the fraction of groups which will qualify as fossils."
 In Fig. 5..," In Fig. \ref{aadfig5},"
 the rates of incidence. Pr(M). of optical fossils and X-ray fossils (using our preferred search radius of 0.577500. following Jonesetal.(200335) are plotted. as a function of the mass M of the halo. together with the predicted values from the models of Milosavljeviéetal.(2006). for two values of A.," the rates of incidence, $P_f(M)$, of optical fossils and X-ray fossils (using our preferred search radius of $R_{200}$, following \citet{b65}) ) are plotted, as a function of the mass $M$ of the halo, together with the predicted values from the models of \citet{b115} for two values of $\Lambda$."
 The shape of our curve for optical fossils is quite similar to the theoretical models (which included no X-ray luminosity criterion). but the latter actually employed a search radius of ooo.," The shape of our curve for optical fossils is quite similar to the theoretical models (which included no X-ray luminosity criterion), but the latter actually employed a search radius of $R_{200}$."
 To see the effect of this. we also show our Millennium results for this larger search radius.," To see the effect of this, we also show our Millennium results for this larger search radius."
 The fraction of fossil systems falls by approximately a factor of 2. when this more demanding requirement is imposed. and so lies signiticantly below that predicted by Milosavljeviéetal.(2006).," The fraction of fossil systems falls by approximately a factor of 2, when this more demanding requirement is imposed, and so lies significantly below that predicted by \citet{b115}."
. On scales of A4—1077.10/5. ΠΜ. ~S@—I18% of groups are optical fossils.," On scales of $M \!\sim\!
10^{13}\!-\!10^{14}h^{-1}$ $_{\odot}$, $\sim$ of groups are optical fossils."
 This probability falls to ~3%—S% for more massive (AL10h. *M.} fossil systems., This probability falls to $\sim$ for more massive $M\geq 10^{14}h^{-1}$ $_{\odot}$ ) fossil systems.
 For halo masses >5.10h tM. all optical fossils in the simulation are also X-ray fossils., For halo masses $>5\times10^{13}h^{-1}$ $_{\odot}$ all optical fossils in the simulation are also X-ray fossils.
 However. at the lowest halo masses the fraction of X-ray fossils drops steeply. since many low mass haloes do not satisfy the Lx threshold criterion.," However, at the lowest halo masses the fraction of X-ray fossils drops steeply, since many low mass haloes do not satisfy the $L_X$ threshold criterion."
 In Table., In Table.
 |. we summarize the incidence rates of fossil systems from present study as well as those found in the literature.," 1, we summarize the incidence rates of fossil systems from present study as well as those found in the literature."
 Comparison between these different estimates is difficult. since both the search radius and the halo mass range varies considerably from study to study.," Comparison between these different estimates is difficult, since both the search radius and the halo mass range varies considerably from study to study."
 However. a direct comparison with the onlyobservational estimate (from Jonesetal. (2003))) is possible. since we have used the same definitions of fossil groups as these authors.," However, a direct comparison with the only estimate (from \citet{b65}) ) is possible, since we have used the same definitions of fossil groups as these authors."
 Based on a comparison with the integrated local X-ray luminosity function of Ebelingetal.(2001). Jonesetal.(2003). estimatec that X-ray fossil systems constitute of all systems of the same X-ray luminosity (Lyin)20.251075 “erg +}.," Based on a comparison with the integrated local X-ray luminosity function of \citet{b56}, \citet{b65} estimated that X-ray fossil systems constitute of all systems of the same X-ray luminosity $L_{X,bol} \geq
0.25\times 10^{42} h^{-2}$ erg $^{-1}$ )."
 The right panel histogram of Fig., The right panel histogram of Fig.
 2 represents the fraction of optica fossil systems in each bin of £x».," \ref{aadfig2} represents the fraction of optical fossil systems in each bin of $L_{X,bol}$."
 Integrating this over all X- luminosities above the threshold value for fossils. we find tha ~ο of haloes with Lx42:0.25«1077 erg s lure X-ray fossils. which is reasonably consistent with the lower limi of ~ 8%. derived by Tonesetal. (2003).," Integrating this over all X-ray luminosities above the threshold value for fossils, we find that $\sim 7.2\pm 0.2\%$ of haloes with $L_{X,bol} \geq 0.25\times 10^{42} h^{-2}$ erg $^{-1}$ are X-ray fossils, which is reasonably consistent with the lower limit of $\sim 8\%$ , derived by \citet{b65}. ."
. In comparison. detailed hydrodynamical simulations by D'Onghiaetal.(2005). and Sommer-Larsen(2006)of 12 galaxy groups. predict a larger fraction of 165c for fossil systems of mass 10/5. !M. or larger.," In comparison, detailed hydrodynamical simulations by \citet{b50} and \citet{b147} of 12 galaxy groups, predict a larger fraction of $\pm$ for fossil systems of mass $10^{14}h^{-1}$ $_{\odot}$ or larger."
 This may be because it is easy to overestimate the local viscosity in hydrodynamic simulations (Tittlevetal. 2001). a process that would lead to central overmerging in the models.," This may be because it is easy to overestimate the local viscosity in hydrodynamic simulations \citep{b166}, , a process that would lead to central overmerging in the models."
 So far. the integrated space density of X-ray fossil groups has been studied for small samples. each of three to five X-ray fossil systems.," So far, the integrated space density of X-ray fossil groups has been studied for small samples, each of three to five X-ray fossil systems,"
"We assume a minimum progenitor mass of M;=8Mo, but we also generated other tables using different values.","We assume a minimum progenitor mass of $M_i=8\msun$, but we also generated other tables using different values."
" The bottom panel of Figure 5 shows the ejected mass for minimum progenitor masses of M;=6Mo, Mi=8Mo (the value assumed in this paper), and M;=10Mo."," The bottom panel of Figure \ref{masseject_pop} shows the ejected mass for minimum progenitor masses of $M_i=6\msun$, $M_i=8\msun$ (the value assumed in this paper), and $M_i=10\msun$."
" The differences are of order50%,, with the ejected mass being larger for a smaller minimum progenitor mass."," The differences are of order, with the ejected mass being larger for a smaller minimum progenitor mass."
" This shows that the particular choice of minimum progenitor mass can have a impact on the results, and we intend to investigate this issue in more details in future work."," This shows that the particular choice of minimum progenitor mass can have a impact on the results, and we intend to investigate this issue in more details in future work."
 Here we focus on the case of a minimum progenitor mass of M;=8Mo., Here we focus on the case of a minimum progenitor mass of $M_i=8\msun$.
" In a recent paper, Horiuchietal.(2011) point to a serious “supernova rate problem"": the measured cosmic massive-star formation rate predicts a rate of core-collapse supernovae about twice as large as the observed rate, at least for redshifts between 0 and 1, where surveys are thought to be quite complete."," In a recent paper, \citet{horiuchi11} point to a serious “supernova rate problem”: the measured cosmic massive-star formation rate predicts a rate of core-collapse supernovae about twice as large as the observed rate, at least for redshifts between 0 and 1, where surveys are thought to be quite complete."
" Several explanations are proposed to explain this major discrepancy, including a large fraction of unusually faint (intrinsically or dust-attenuated), and thus unaccounted for, core-colapse SNe and a possible overestimate of the star formation rate based on the current estimators."," Several explanations are proposed to explain this major discrepancy, including a large fraction of unusually faint (intrinsically or dust-attenuated), and thus unaccounted for, core-collapse SNe and a possible overestimate of the star formation rate based on the current estimators."
" If indeed this supernova rate problem is real, the SFR (see 855.1) might have to be scaled accordingly."," If indeed this supernova rate problem is real, the SFR (see 5.1) might have to be scaled accordingly."
" However, all simulations presented in this paper start at redshift z—15, and terminate at redshifts between 6 and 9."," However, all simulations presented in this paper start at redshift $z=15$, and terminate at redshifts between 6 and 9."
 It is not clear that there is a supernova rate problem at these redshifts., It is not clear that there is a supernova rate problem at these redshifts.
" During the evolution of a galaxy, the ISM is constantly enriched by ejecta from stellar winds and SNe."," During the evolution of a galaxy, the ISM is constantly enriched by ejecta from stellar winds and SNe."
" Hence, every generation of stars provides an environment richer in metals for the future generations."," Hence, every generation of stars provides an environment richer in metals for the future generations."
" The level of this enrichment depends on the SFR, since the metal production increases with the number of stars formed."," The level of this enrichment depends on the SFR, since the metal production increases with the number of stars formed."
" To simulate this process, we designed an algorithm that combines the outputs of Starburst99 with the SNe tables of N06."," To simulate this process, we designed an algorithm that combines the outputs of Starburst99 with the SNe tables of N06."
 We consider a galaxy with a total mass Mga., We consider a galaxy with a total mass $M_{\rm gal}$.
" We assume that the ratio of baryons to dark matter in the galaxy is equal to the universal ratio, which is a valid assumption for the initial stages of the galaxy."," We assume that the ratio of baryons to dark matter in the galaxy is equal to the universal ratio, which is a valid assumption for the initial stages of the galaxy."
 The baryonic mass of the galaxy is then given by, The baryonic mass of the galaxy is then given by
lower gave again very sinular result. with low rratio.,"lower gave again very similar result, with low ratio."
 The last svstematic which we studied is the effect of the uucertainty ou the structure of the siehtline., The last systematic which we studied is the effect of the uncertainty on the structure of the sightline.
" Iudeed. we fix in the fitiug of the Hine the values: Zpe=3000 EK. Tij:=sooo Ix. Spem2, to ope=05band Actepo=5.9 Ll. found iu 3.2 by the study of metal lines."," Indeed, we fix in the fiting of the line the values: $T_{\mathrm{BC}}=3000$ K, $T_{\mathrm{LIC}}=8000$ K, $\sigma_{\mathrm{BC}}=2.7$ , $\sigma_{\mathrm{LIC}}=0.5$, and $\Delta v_{\mathrm{LIC-BC}}=5.9$ , found in \ref{Interstellar_structure_of_the_line_of_sight} by the study of metal lines."
 We used the error bars on FT. a and Acpie:pe reported iu Table 3. to perform extra fits with different constraints. wwith components more or less broad. or more or less slited from each other.," We used the error bars on $T$, $\sigma$ and $\Delta v_{\mathrm{LIC-BC}}$ reported in Table \ref{res_19raies} to perform extra fits with different constraints, with components more or less broad, or more or less shifted from each other."
 Once again. we found similar results and low Ira10.," Once again, we found similar results and low ratio."
" Whereas alb these tests allowed us tfo estinate SVSCluatic error bars. we evaluated statistical errors by the unmethod. fixing""M the tto a value. and looking for the best ffor this given value. aid iterating."," Whereas all these tests allowed us to estimate systematic error bars, we evaluated statistical errors by the method, fixing the to a value, and looking for the best for this given value, and iterating."
 The evolution of aas a function of lis reported ou Fie. 10., The evolution of as a function of is reported on Fig. \ref{detla_chi2}.
 Following the same criterion as Vidal-Alacjar et al. (1998)).," Following the same criterion as Vidal-Madjar et al. \cite{avm98}) ),"
 we obtain A\?2=10 for Wipe=l.6ςΤο., we obtain 2=10 for $=1.6\times10^{-5}$.
 This statistical error is rather lareo. due to the rvelativelly low S/N aud spectral resoliuticDI," This statistical error is rather large, due to the relativelly low $S/N$ and spectral resolution."
R Possible systematic effects discussed above are. tlMus 108Tieibe dmn colparison with this statistical uncertainty., Possible systematic effects discussed above are thus negligible in comparison with this statistical uncertainty.
" Ilowever ""owe were able to apply this. munethod ouly o the ""pure interstellar” spectrum. even though the blue wine of the Sirius A ceconutaiis some information. aud i particular aIET xolibits too high vvalues."," However, we were able to apply this method only to the “pure interstellar” spectrum, even though the blue wing of the Sirius A contains some information, and in particular also prohibits too high values."
 We note that comparing many lines of sight through he LIC. Linsky (1998)) recently estimates a mean value of pHi.5O10.£0.10.," We note that comparing many lines of sight through the LIC, Linsky \cite{linsky98}) ) recently estimates a mean value of $=1.50\times10^{-5} \pm0.10$."
 Th we asstune that value. we obtain Ay72=10 for (D/IDpe-1.7«10.7.," If we assume that value, we obtain 2=10 for $=1.7\times10^{-5}$."
" We finally completed another study by fitting t[ume ""plre interstellar” sspectrun by relaxing the coustraiuts onpre... and assunine that the Ira10 Is free but the same in the two components. in o to find which unique Iraio Gs compatible with our data."," We finally completed another study by fitting the “pure interstellar” spectrum by relaxing the constraints on, and assuming that the ratio is free but the same in the two components, in order to find which unique ratio is compatible with our data."
 While keeping a NL (IT)Νο 1) close to unity as above. we found tlat unique ratio to be D/II-21.2«10..," While keeping a $N_{\mathrm{LIC}}($ $) / N_{\mathrm{BC}}($ $)$ close to unity as above, we found that unique ratio to be $=1.2\times10^{-5}$."
 Althonel we caniot exelide this result. this fit is siguificantlv worse witl la sale iratio in both clouds. rather than with two different o as above.," Although we cannot exclude this result, this fit is significantly worse with a same ratio in both clouds, rather than with two different ones as above."
 Fits with higher couunon rratios (l.l or 1.6«10 7) degrade even more the quaitv of the fit (see Fie. 11)), Fits with higher common ratios $1.4$ or $1.6\times10^{-5}$ ) degrade even more the quality of the fit (see Fig. \ref{fit_id}) )
 aud could be rejected im tex of Q2., and could be rejected in term of 2.
 These data secis thas to reject the possibility of a unique irafio in both components although mareinally., These data seems thus to reject the possibility of a unique ratio in both components although marginally.
 Iu bref. the results which we obtained in terms of and column densities. aud irafios. for the DC and the LIC απο sununuurized in Table L.," In brief, the results which we obtained in terms of and column densities, and ratios, for the BC and the LIC are summarized in Table \ref{NH_ND_ISM}."
 The range which we finally obtain in the Blue Component for the deuterium abuudance ij (0)ο ΕΕο7., The range which we finally obtain in the Blue Component for the deuterium abundance is $0<$ $<1.6\times10^{-5}$.
 The upper lint (D/IDpejl.6s10ο comepouds to a A\y?2=10 in comparison with the lowest oobtained for (D/IDpce;0.5«10, The upper limit $<1.6\times10^{-5}$ correponds to a $=10$ in comparison with the lowest obtained for $<0.5\times10^{-5}$.
° Thus we found that the deuterimuu abundance could be equal to 1.6«10 in LIC and DC. but with a low probability according to our data.," Thus we found that the deuterium abundance could be equal to $1.6\times10^{-5}$ in LIC and BC, but with a low probability according to our data."
 Moreover our wwas obtainedM fromia the we“pure interstellar” spectrum., Moreover our was obtained from the “pure interstellar” spectrum.
 Although we were unable tofit, Although we were unable tofit
The measurements were done in the 1.52—1.74jan (effective central wavelength 1.65jn) wavelength region. similar to the astronomical // band.,"The measurements were done in the $1.52-1.74~\mu$ m (effective central wavelength $1.65~\mu$ m) wavelength region, similar to the astronomical $H$ band."
 Observations of calibration sources were rapidly (within less than LO minutes) interleaved with the Cepheid observations. aud alter each 130-seconcd integration (he apertures were pointed to dark sky and a 30-secondD measurement of the background light level was mace.," Observations of calibration sources were rapidly (within less than $\sim 10$ minutes) interleaved with the Cepheid observations, and after each 130-second integration the apertures were pointed to dark sky and a 30-second measurement of the background light level was made."
 The calibrators were selected to be located no more than 16 degrees from the primary target on the skv and to have similar //-band magnitudes., The calibrators were selected to be located no more than 16 degrees from the primary target on the sky and to have similar $H$ -band magnitudes.
 In choosing calibration sources we avoided known binary or highly variable stars., In choosing calibration sources we avoided known binary or highly variable stars.
 The calibrators used are listed in Table 2.., The calibrators used are listed in Table \ref{tab:calibs}.
 In (his paper we make use of previously published observations of the Cepheid ¢ Gem 2000)., In this paper we make use of previously published observations of the Cepheid $\zeta$ Gem \citep{lane00}.
. ILowever. in order to improve on the previously published results we carried out additional observations of this source on 2001 March 13.15.," However, in order to improve on the previously published results we carried out additional observations of this source on 2001 March 13–15."
 We also observed additional unresolved calibrators in order to reduce the level of svstematic uncertainty., We also observed additional unresolved calibrators in order to reduce the level of systematic uncertainty.
 The original data have been jointly re-reduced using the improved calibrator diameters and uncertainties., The original data have been jointly re-reduced using the improved calibrator diameters and uncertainties.
 llowever. note that the primary. calibrator diameter has not changed [rom the value used in Laneetal.(2000).," However, note that the primary calibrator diameter has not changed from the value used in \citet{lane00}."
. PTI uses either a 10 or 20 ms sample rate., PTI uses either a 10 or 20 ms sample rate.
 Each such sample provides a measure of (he instantaneous finge visibility ancl phase., Each such sample provides a measure of the instantaneous fringe visibility and phase.
 While the phase value is converted to distance and fed back to the active delav. line to provide active Iringe tracking. the measured fringe visibility is averaged over the entire 130-second integration.," While the phase value is converted to distance and fed back to the active delay line to provide active fringe tracking, the measured fringe visibility is averaged over the entire 130-second integration."
 The statistical uncertainty in each measurement is estimated by breaking the 130 second integration into five equal-time segments and measuring the standard deviation about the mean value., The statistical uncertainty in each measurement is estimated by breaking the 130 second integration into five equal-time segments and measuring the standard deviation about the mean value.
 The theoretical relation between source brightness distribution and fringe visibility is given by the van Cittert-Zernike theorem., The theoretical relation between source brightness distribution and fringe visibility is given by the van Cittert-Zernike theorem.
" For a uniform intensity disk model the normalized fringe visibility (squared) can be related to the apparent angular cliameter as where J, is (he first-order Bessel function. D is the projected aperture separation. 0,:, is (he apparent aneular diameter of (he star in (he uniform-disk model. and Ay is the wavelength of the observation."," For a uniform intensity disk model the normalized fringe visibility (squared) can be related to the apparent angular diameter as where $J_{1}$ is the first-order Bessel function, $B$ is the projected aperture separation, $\theta_{UD}$ is the apparent angular diameter of the star in the uniform-disk model, and $\lambda_0$ is the center-band wavelength of the observation."
 It follows that the Iringe visibility of a point source measured by an ideal interferometer should be unity., It follows that the fringe visibility of a point source measured by an ideal interferometer should be unity.
 For a more realistic model that includes, For a more realistic model that includes
would respond to flexion if it is present. and should therefore be treated as estimators of any second-order systematics. or of (real or systematic) twist on scales where flexion is negligible.,"would respond to flexion if it is present, and should therefore be treated as estimators of any second-order systematics, or of (real or systematic) twist on scales where flexion is negligible."
 In Section 2? we use these estimators to constrain twist observationally for the first time. using the STAGES HST survey.," In Section \ref{sect_measurement} we use these estimators to constrain twist observationally for the first time, using the STAGES HST survey."
 We find that our twist estimator has a larger variance. than flexion estimators. and that its mean value is consistent with zero in the STAGES data.," We find that our twist estimator has a larger variance than flexion estimators, and that its mean value is consistent with zero in the STAGES data."
 We measure correlation functions for twist estimators. again finding that they are consistent with zero systematic in STAGES.," We measure correlation functions for twist estimators, again finding that they are consistent with zero systematic in STAGES."
 We summarise our results and conclude in Section ??.., We summarise our results and conclude in Section \ref{sect_summary}.
 We begin by discussing image distortions in weak lensing to first order (formoredetails.seeή).," We begin by discussing image distortions in weak lensing to first order \citep[for more details, see][]{2001PhR...340..291B}."
" We can describe the effect of lensing as a mapping between the surface brightness fs of a galaxy at a position (:2,.7») in the source plane. and the surface brightness fi at a position (61.6») in the image plane: where we have set the origin of 6; and .; to the centre of light in the respective planes."," We can describe the effect of lensing as a mapping between the surface brightness $f_S$ of a galaxy at a position $(\beta_1,\beta_2)$ in the source plane, and the surface brightness $f_I$ at a position $(\theta_1,\theta_2)$ in the image plane: where we have set the origin of $\theta_i$ and $\beta_i$ to the centre of light in the respective planes."
 ;Y is the Jacobian matrix which maps image positions to source positions. For lensing with a single lens plane. and assuming the Born approximation. this is given by where cis the lensing potential. Le. the gravitational potential suitablyprojected into 2D. We can therefore write ;1 as with the convergence # given by and the shear 7; given by There is an alternative notation that is useful to us. introduced by ?..," $A$ is the Jacobian matrix which maps image positions to source positions, For lensing with a single lens plane, and assuming the Born approximation, this is given by where $\psi$ is the lensing potential, i.e. the gravitational potential suitablyprojected into 2D. We can therefore write $A$ as with the convergence $\kappa$ given by and the shear $\gamma_i$ given by There is an alternative notation that is useful to us, introduced by \citet{2006MNRAS.365..414B}."
" We define the complex derivative O=0,| zin cylindrical coordinates this is given by with radial coordinate @ and azimuthal coordinate ó.", We define the complex derivative $\partial\equiv\partial_1+i\partial_2$; in cylindrical coordinates this is given by with radial coordinate $\theta$ and azimuthal coordinate $\phi$.
" We also define —54|£5». and then Besides simplifying notation. this format elucidates the spins of the quantities: when à is applied. the e"" term in equation (7)) raises the spin by one."," We also define $\gamma\equiv\gamma_1+i\gamma_2$, and then Besides simplifying notation, this format elucidates the spins of the quantities; when $\partial$ is applied, the $^{i\phi}$ term in equation \ref{eq:spin}) ) raises the spin by one."
 Similarly. the application of O° lowers the spin by one.," Similarly, the application of $\partial^*$ lowers the spin by one."
 So since c is a scalar. so is 5. while  is spin 2.," So since $\psi$ is a scalar, so is $\kappa$, while $\gamma$ is spin 2."
 However. our study of -f is not complete.," However, our study of $A$ is not complete."
 We have specified three quantities in οἱ. i.e. 5.54. and 5».," We have specified three quantities in $A$, i.e. $\kappa, \gamma_1$ , and $\gamma_2$."
 But 21 is a four element object. so there is a further degree of freedom which we have missed.," But $A$ is a four element object, so there is a further degree of freedom which we have missed."
 We quickly realise that this is arotation p. i.e. for small rotation angles p.," We quickly realise that this is a $\rho$, i.e. for small rotation angles $\rho$."
 Whereas & and  can be written as second derivatives of the lensing potential. this is not possible for p.," Whereas $\kappa$ and $\gamma$ can be written as second derivatives of the lensing potential, this is not possible for $\rho$."
 It is not activated by gravity in our approximation (due to the interchangability of the second derivatives of the gravitational potential. Οι.=Όλι). but may be present in a real lensing survey as a systematic (seee.g.therotationcausedbytelescopeconstrainedby?)..," It is not activated by gravity in our approximation (due to the interchangability of the second derivatives of the gravitational potential, $\partial_i\partial_j\psi = \partial_j\partial_i\psi$ ), but may be present in a real lensing survey as a systematic \citep[see e.g. the rotation caused by the telescope constrained by][]{2000MNRAS.318..625B}."
 This rotation has been described previously: see eg. 2. , This rotation has been described previously; see e.g. \citet{2003PhRvD..68h3002H}. .
We will find it convenient to write tas a sum of Pauli matrices. as these provide an orthogonal basis for studying further degrees of freedom at the next order of weak lensing approximation.," We will find it convenient to write $A$ as a sum of Pauli matrices, as these provide an orthogonal basis for studying further degrees of freedom at the next order of weak lensing approximation."
 The Pauli matrices are given by (2) so We can write 1 as We will need one further concept: in a weak lensing context. it is usual to assume that the shear and convergence are small and constant across an object.," The Pauli matrices are given by \citep{2005mmp..book.....A}
 so we can write $A$ as We will need one further concept: in a weak lensing context, it is usual to assume that the shear and convergence are small and constant across an object."
 We canthen write the surface brightness mapping as We will now modify this to show how flexion and the new distortions enter., We canthen write the surface brightness mapping as We will now modify this to show how flexion and the new distortions enter.
 The further step taken by flexion studies is to note that in reality. shear will vary across an object.," The further step taken by flexion studies is to note that in reality, shear will vary across an object."
 If we keep Las a constant across the object. we need a further term in a Taylor expansion in the surface brightness map. as given by ?.. This introduces the £ tensor:if we suppose that its components are purely due to a variation of Y across the image. we can write λεν= Ότι.," If we keep $A$ as a constant across the object, we need a further term in a Taylor expansion in the surface brightness map, as given by \citet{2005ApJ...619..741G}, This introduces the $D$ tensor;if we suppose that its components are purely due to a variation of $A$ across the image, we can write $D_{ijk}=\partial_k A_{ij}$ ."
 Then by differentiating equation C11») we find We can rewrite much of this in terms offlexion., Then by differentiating equation \ref{eq:pauli}) ) we find We can rewrite much of this in terms offlexion.
" We define the I-flexion as f—£i| ffs. and the 3-flexion €—Ch,| s. where f is manifestly spin | and Co is spin3."," We define the 1-flexion as $F\equiv F_1+iF_2$ , and the 3-flexion $G\equiv G_1+iG_2$ , where $F$ is manifestly spin 1 and $G$ is spin3."
 Comparing with, Comparing with
The property of the VOCE of detecting overdeusities respective of their shape is probably the kev for the detection of V26. a verv clougated svstem.,"The property of the VGCF of detecting overdensities irrespective of their shape is probably the key for the detection of V26, a very elongated system."
 Iu Fig., In Fig.
 10 we show the galaxies of V26 as detected by the VOCE before the regularization processes (black triangles)., 10 we show the galaxies of V26 as detected by the VGCF before the regularization processes (black triangles).
 We also show as erev tessels those of galaxies added at the eud of the regularization processes and as white tessels those of backeround galaxies., We also show as grey tessels those of galaxies added at the end of the regularization processes and as white tessels those of background galaxies.
 The plot refers to the tessollation of the PDCS field in the magnitude bin of maxima contrast for V26., The plot refers to the tessellation of the PDCS field in the magnitude bin of maximum contrast for V26.
 As far as the nehuess Ny. of VOCE clusters is concerned. we compute it almost in the same wav as P96. the only difference being that we use a fixed augular radius of 0.1 deg within which to count cluster galaxies.," As far as the richness, $N_{R}$, of VGCF clusters is concerned, we compute it almost in the same way as P96, the only difference being that we use a fixed angular radius of 0.1 deg within which to count cluster galaxies."
 For systems within the redshift range 0.3-0.6. our angular radius roughly corresponds to a linear radius of 1 7! ," For systems within the redshift range 0.3-0.6, our angular radius roughly corresponds to a linear radius of 1 $\,h^{-1}$ "
candidate progenitor identifications. we have also included. iu parentheses. the limits on the absolute maguitude and color of a possible progenitor. if the candidate we have ideutified is not the actual progenitor.,"candidate progenitor identifications, we have also included, in parentheses, the limits on the absolute magnitude and color of a possible progenitor, if the candidate we have identified is not the actual progenitor."
 It should be noted that for all the magnitude and color estimates. we have assuned possibly inaccurate distance estimates and. im inmost cases. only the Galactic component to he extinction toward the SN.," It should be noted that for all the magnitude and color estimates, we have assumed possibly inaccurate distance estimates and, in most cases, only the Galactic component to the extinction toward the SN."
" Consequently, we lay ave either underestimated or overestimated the absolute naguitude. or limits on the absolute magnitude. of candidate progenitors."," Consequently, we may have either underestimated or overestimated the absolute magnitude, or limits on the absolute magnitude, of candidate progenitors."
" Extinction local to the SNe within he host galaxies themselves will only lead to higher absolute brigltuesses. and to bluer intrinsic colors. or color Πιτ, for all these objects;"," Extinction local to the SNe within the host galaxies themselves will only lead to higher absolute brightnesses, and to bluer intrinsic colors, or color limits, for all these objects."
" At the least. we provide the neasured inagnitudes and magnitude lits for the SN xoesenitors, based on the IISTphot output. so that. with additional information. the reader eau niale lis or her own estimations."," At the least, we provide the measured magnitudes and magnitude limits for the SN progenitors, based on the HSTphot output, so that, with additional information, the reader can make his or her own estimations."
 Below. we briefly iuterpret our results. but we eschew transforming the observed maguitudes and colors into intrinsic properties. such as bolometric hDmunuinositv and surface temperature. for lack of adequate iuformation about the stars.," Below, we briefly interpret our results, but we eschew transforming the observed magnitudes and colors into intrinsic properties, such as bolometric luminosity and surface temperature, for lack of adequate information about the stars."
" The candidate SNe II progenitors of SNe 1001, 19990v. aud 2001dn all have absolute maguitudes (AL=5.9 to 6.9) that are consistent with the known red supereiauts in the Calasy."," The candidate SNe II progenitors of SNe 1999br, 1999ev, and 2001du all have absolute magnitudes $M^0_V \approx -5.9$ to $-6.9$ ) that are consistent with the known red supergiants in the Galaxy."
 All of the magnitude limits for the other SNe II are also cousisteut with supergiaut stars., All of the magnitude limits for the other SNe II are also consistent with supergiant stars.
 The only candidate with intrinsic color information. the progenitor candidate for SN 2001du. has a (V.I) value more consistent with an early Is spectral type (e.g... the Viluius spectral colors iu Bessell 1990). rather than the M-tvpe supergiant that we would expect. based on theorctica models.," The only candidate with intrinsic color information, the progenitor candidate for SN 2001du, has a $(V-I)^0$ value more consistent with an early K spectral type (e.g., the Vilnius spectral colors in Bessell 1990), rather than the M-type supergiant that we would expect, based on theoretical models."
 In fact. even if this candidate is not the progenitor. the (VWD) color Bit for the SN 2001du progenitor. as well as the color limits for the SN 1999s progenitor [if we discount the ((V)! Init]. imply spectral types tha can ouly be as late as early M-tvpe.," In fact, even if this candidate is not the progenitor, the $(V-I)^0$ color limit for the SN 2001du progenitor, as well as the color limits for the SN 1999bx progenitor [if we discount the $(U-V)^0$ limit], imply spectral types that can only be as late as early M-type."
 The slightly. bluer color night imply a somewhat more compact morphology for the progenitorOo envelope. or possible contamination of its helt by a close. fainter aud bluer companion star ina possible binary svsteni.," The slightly bluer color might imply a somewhat more compact morphology for the progenitor envelope, or possible contamination of its light by a close, fainter and bluer companion star in a possible binary system."
 Models for SNe Ib include the explosion of isolated WolfRavet stars or of helium stars iu binary svstems. possibly with a wide orbit including a more massive main-sequence secoudary (6.9.. van den IHeuvel 1991).," Models for SNe Ib include the explosion of isolated Wolf-Rayet stars or of helium stars in binary systems, possibly with a wide orbit including a more massive main-sequence secondary (e.g., van den Heuvel 1994)."
 Both mechanisis could lead to SNe Ib., Both mechanisms could lead to SNe Ib.
 However. Brauch et al. (," However, Branch et al. ("
2002) find. from their analysis of SN Ib spectral data. that tle masses and kinetic cucreies among SNe Ib are similar. nuüplviug that progenitor masses ust be similar as well.,"2002) find, from their analysis of SN Ib spectral data, that the masses and kinetic energies among SNe Ib are similar, implying that progenitor masses must be similar as well."
 Wolt-Ravoet stars that have been stripped of much of thei helm could lead to SNe Ic: however. mocel light curves decline too slowly. compared to observations (Woosley. Langer. Weaver 1993).," Wolf-Rayet stars that have been stripped of much of their helium could lead to SNe Ic; however, model light curves decline too slowly, compared to observations (Woosley, Langer, Weaver 1993)."
 Lowanass οταν stars in binarics (6.8. Nomoto et al.," Low-mass helium stars in binaries (e.g., Nomoto et al."
 1990) end up with too much helium for SNeIc., 1990) end up with too much helium for SNeIc.
 Nomoto et al. (, Nomoto et al. (
1991) explored a ~23 AL. CLO star (which originally evolved from a 1918 AL. main-sequence star) in a close binary as the progenitor of the SN Ic 19091 in M51.,1994) explored a $\sim$ 2–3 $M_\odot$ C+O star (which originally evolved from a 13–18 $M_\odot$ main-sequence star) in a close binary as the progenitor of the SN Ic 1994I in M51.
 Their model. possibly inchicding a conumion-envelope phase. involves two episodes of niass transfer with a secondary. which eveutuallv evolves to be a low-mass main sequence star. a neutron star. or a white dwarf.," Their model, possibly including a common-envelope phase, involves two episodes of mass transfer with a secondary, which eventually evolves to be a low-mass main sequence star, a neutron star, or a white dwarf."
 All of these scenarios involve compact stars. which are likely not particularly huninous: Barth ct al. (," All of these scenarios involve compact stars, which are likely not particularly luminous; Barth et al. ("
1996) place an upper lait of Wy7.3 mag on the SN 1991I progenitor.,"1996) place an upper limit of $M_V
{\gtrsim} -7.3$ mag on the SN 1994I progenitor."
 As Podsiadlowski et al. (, As Podsiadlowski et al. (
1992) point out. mass transfer. in fact. could make the secoudary more nuüassive and more luminous when the primary explodes. meaning that a detected “progenitor” could actually be the companion star.,"1992) point out, mass transfer, in fact, could make the secondary more massive and more luminous when the primary explodes, meaning that a detected “progenitor” could actually be the companion star."
 The candidate progenitor for the SN Ic 1999bu is quite huninons. with AY7.5 mag. which is cousistent with the upper limit for the SN 19901 progenitor mentioned. above.," The candidate progenitor for the SN Ic 1999bu is quite luminous, with $M^0_V \approx -7.5$ mag, which is consistent with the upper limit for the SN 1994I progenitor mentioned above."
 The candidate progenitors for the SNe Th 2001D aud 2OOLIs are also very Dmuuimous. with ARc.A fo 9 imag.," The candidate progenitors for the SNe Ib 2001B and 2001is are also very luminous, with $M^0_V \approx -8$ to $-9$ mag."
 The known WolfRavet stars in the Galaxy have absolute magnitudes spread over a large range. Mpzz2 to. S mag (van der IHIucht. 2001).," The known Wolf-Rayet stars in the Galaxy have absolute magnitudes spread over a large range, $M^0_V
\approx -2$ to $-8$ mag (van der Hucht 2001)."
 The SN Ib progenitor candidate Iuuinosities are ucar or slightly above the upper end of this luminosity range., The SN Ib progenitor candidate luminosities are near or slightly above the upper end of this luminosity range.
 Therefore. it is possible that these two SNe Ib arose from WolfRavet stars. (," Therefore, it is possible that these two SNe Ib arose from Wolf-Rayet stars. ("
Tlowever. with the uncertainties in the distances to and reddening within the host ealaxies. these absolute magnitudes may actually fall outside the WolfRavet Iuninositv range. 1.6.. they would be too bright.),"However, with the uncertainties in the distances to and reddening within the host galaxies, these absolute magnitudes may actually fall outside the Wolf-Rayet luminosity range, i.e., they would be too bright.)"
 The luminosities for these SN Ib progenitor candidates are also consistent with those of other. less evolved. presumably blue or vollow supergiauts (hunuplrevs Davidson 1979).," The luminosities for these SN Ib progenitor candidates are also consistent with those of other, less evolved, presumably blue or yellow supergiants (Humphreys Davidson 1979)."
 Alternatively. it is possible that these candidates are not the progenitors. but imstead multiple star svsteunis or compact star clusters.," Alternatively, it is possible that these candidates are not the progenitors, but instead multiple star systems or compact star clusters."
 Generally. the absolute magnitude lits for all other SNe Ib/c (the brightuess Iuuits for SNe 2001ai aud 2001¢1 are not very restrictive) are consistent both with the rauge of WoltRavet magnitudes and also with expectations for iuteracting binary models.," Generally, the absolute magnitude limits for all other SNe Ib/c (the brightness limits for SNe 2001ai and 2001ci are not very restrictive) are consistent both with the range of Wolf-Rayet magnitudes and also with expectations for interacting binary models."
 The tutrinsic color limits. although also usually not very restrictive. are consistent with blue or vellow stars.," The intrinsic color limits, although also usually not very restrictive, are consistent with blue or yellow stars."
 The most restrictive color limits are for the progenitors of SNe 1999ec and 200168 Gf iu this case. the extinction estimate Ayz5 6 mae is. in fact. correct): taken together. these limits imply that the progenitors had spectral types of A-type or earlier (Besscll 1990) and are also consistent with the ranee of D.V. (about |(0.5 to OL mae) for Galactic WolfRavet stars (van der Hucht 2001).," The most restrictive color limits are for the progenitors of SNe 1999ec and 2001ci (if, in this case, the extinction estimate $A_V \approx 5$ –6 mag is, in fact, correct): taken together, these limits imply that the progenitors had spectral types of A-type or earlier (Bessell 1990) and are also consistent with the range of $B-V$ (about $-0.5$ to $-0.1$ mag) for Galactic Wolf-Rayet stars (van der Hucht 2001)."
 The host galaxy of SN 200101. NGC 3079. is seen nearly edge-on. so it is possible that the SN progenitor could have been a Wolt-Rayet star explodiug while obscured by or embedded im dust.," The host galaxy of SN 2001ci, NGC 3079, is seen nearly edge-on, so it is possible that the SN progenitor could have been a Wolf-Rayet star exploding while obscured by or embedded in dust."
 To some extent. our search was not fully satisfviug.," To some extent, our search was not fully satisfying."
 Although it is true that. compared with the case of Van Dyk et al. (," Although it is true that, compared with the case of Van Dyk et al. ("
19995). theHST archive is currently much richer in pre-SN host galaxy images. which may poteutiallv contain SN progenitors. aud more muportantlv. post-SN nuages m which the fading SNe iav be recovered. the quality of these data is such that the S/N or umber of filters used are ecnerally still not ideal.,"1999b), the archive is currently much richer in pre-SN host galaxy images, which may potentially contain SN progenitors, and more importantly, post-SN images in which the fading SNe may be recovered, the quality of these data is such that the S/N or number of filters used are generally still not ideal."
 The data iu our sample are not vet sensitive cuough for us to place more stringent constraints ou the competing models for SNe Ib/c. The archive will steadily grow. however. as observations coutinue after the recent roefurbishiuneut nussion.," The data in our sample are not yet sensitive enough for us to place more stringent constraints on the competing models for SNe Ib/c. The archive will steadily grow, however, as observations continue after the recent refurbishment mission."
 These new observations will also include images of ealaxies with the superior Advanced Camera for Surveys (ACS)., These new observations will also include images of galaxies with the superior Advanced Camera for Surveys (ACS).
 Additionally. uew nearby SNe will be discovered by LOSS/LOTOSS aud other SN searches. ereatly expanding the potential sample.," Additionally, new nearby SNe will be discovered by LOSS/LOTOSS and other SN searches, greatly expanding the potential sample."
 We intend to further exploit the HST archive to continue to search for core-collapse SN progenitors: the future looks bright for this subject., We intend to further exploit the archive to continue to search for core-collapse SN progenitors; the future looks bright for this subject.
onto a black hole with rapid spin. ancl similar emission processes: svuchrotvon aud possible inverse Compton process (see Zhang 2007 lor reviews: Urry Paclovani 1995).,"onto a black hole with rapid spin, and similar emission processes: synchrotron and possible inverse Compton process (see Zhang 2007 for reviews; Urry Padovani 1995)."
" In spite of these similarities. the (wo classes of the objects differ from each other in following several respects: central engine mass. bulk Lorentz factor ancl power-spectral energy. distribution sequence,"," In spite of these similarities, the two classes of the objects differ from each other in following several respects: central engine mass, bulk Lorentz factor and power-spectral energy distribution sequence."
 It is now well known that the relativity jets are launched from a supper massive black hole with mass ~105?A. [or Blazars according to their spectroscopic observations (e.g.. Lacy et al.," It is now well known that the relativity jets are launched from a supper massive black hole with mass $\sim10^{8-9}M_\odot$ for Blazars according to their spectroscopic observations (e.g., Lacy et al."
 2001)., 2001).
 Nevertheless. (he popular “collapser” model indicates that Long-GIDs are produced by the death of voung massive stars wilh masses >25.M. (see Wooslev Broom 2006 [or a review).," Nevertheless, the popular “collapser” model indicates that Long-GRBs are produced by the death of young massive stars with masses $\geq25M_\odot$ (see Woosley Broom 2006 for a review)."
 Direct measurements of bulk Lorentz factors (D) of jets are available lor some Blazars through the VLBI observations of the superhuminoal velocity., Direct measurements of bulk Lorentz factors $\Gamma$ ) of jets are available for some Blazars through the VLBI observations of the superluminoal velocity.
 The observations reveal a tvpical Lorentz factor DP10 for Blazars (e.g. Jorstad et al.," The observations reveal a typical Lorentz factor $\Gamma\sim10$ for Blazars (e.g., Jorstad et al."
 2001: Savolainen et al., 2001; Savolainen et al.
 2010)., 2010).
 llowever. (he GRB fireball model requires a larger initial D (2100) to ensure the 5-rav photons are transparent to the 25—e= process (e.g.. Piran 1999).," However, the GRB fireball model requires a larger initial $\Gamma$ $>100$ ) to ensure the $\gamma$ -ray photons are transparent to the $\gamma\gamma\rightarrow e^{\pm}$ process (e.g., Piran 1999)."
 The power-spectral sequence has been well established for Dlazars by Fossati οἱ al. (, The power-spectral sequence has been well established for Blazars by Fossati et al. (
1993). and was recently confirmed by the Fermi--detected Blazars (Sambruna et al.,"1998), and was recently confirmed by the -detected Blazars (Sambruna et al."
 2010). in which (he two peaks of spectral energy distribution (SED) from radio to 2-ravs shift towarel lower frequency for more luminous objects.," 2010), in which the two peaks of spectral energy distribution (SED) from radio to $\gamma$ -rays shift toward lower frequency for more luminous objects."
 This sequence can be quantitatively described bv the Geht correlations between the photon frequency. of the first peak of the SED and (he Iuminosities in different bands., This sequence can be quantitatively described by the tight correlations between the photon frequency of the first peak of the SED and the luminosities in different bands.
 Several correlations have been found for GRD prompt emission in recent vears (see Schaefer 2007 [or à summary for these correlations)., Several correlations have been found for GRB prompt emission in recent years (see Schaefer 2007 for a summary for these correlations).
 Generally speaking. (hese correlations suggest thal GRBs with more powerlul prompt enission (or total released οποιον)vj tend to have higher peaked photon energy in (their lime averaged -paw spectra (e.g.. Amati et al.," Generally speaking, these correlations suggest that GRBs with more powerful prompt emission (or total released energy) tend to have higher peaked photon energy in their time averaged $\gamma$ -ray spectra (e.g., Amati et al."
 2009)., 2009).
 In this letter. we compare GRD's radio-optical afterglow emission with the Dlazar sequence.," In this letter, we compare GRB's radio-optical afterglow emission with the Blazar sequence."
 The study is motivated bv the fact that the Lorentz factors D in GRBs decrease with both time and radius of (he jets as a powerlaw. which means (he values of E in the late lime alterglows could be comparable to Blazars.," The study is motivated by the fact that the Lorentz factors $\Gamma$ in GRBs decrease with both time and radius of the jets as a powerlaw, which means the values of $\Gamma$ in the late time afterglows could be comparable to Blazars."
" The A cold dark matter cosmology with parameter hj=0.73. Q,,=0.24 and O4=0.76 is assumed throughout our calculations."," The $\Lambda$ cold dark matter cosmology with parameter $h_0=0.73$, $\Omega_m=0.24$ and $\Omega_\Lambda=0.76$ is assumed throughout our calculations."
 Frail et al. (, Frail et al. (
2003a) presented a complete catalog of radio afterglows of τὸ GGRBs (between 1997 and 2001).,2003a) presented a complete catalog of radio afterglows of 75 GRBs (between 1997 and 2001).
 The catalog contains the detections in the frequencies, The catalog contains the detections in the frequencies
the abrupt drop of the rratio produced at early ages (¢=5x10° yr) in both the central core and western/eastern cores is due to desorption effects of some molecules.,the abrupt drop of the ratio produced at early ages $t\simeq5\times10^3$ yr) in both the central core and western/eastern cores is due to desorption effects of some molecules.
 Finally. we explored the fractional abundances of other molecular species and compared them with observations when available or made some predictions for future observations.," Finally, we explored the fractional abundances of other molecular species and compared them with observations when available or made some predictions for future observations."
 We found that the fractional abundance of oobtained from the chemical model is in the range ~8x1075ιο at ¢2(4.8—5.5)xIO? yr. in agreement withthe value reported by Zhangetal.(2007).. which is in the range (1—4)x107%.," We found that the fractional abundance of obtained from the chemical model is in the range $\sim8\times10^{-8}-10^{-7}$ at $t=(4.5-5.5)\times10^{5}$ yr, in agreement withthe value reported by \citet{zhang2007}, which is in the range $(1-4)\times10^{-8}$."
 Additionally. our model predicts a CO abundance of 107 indicating that CO is desorbed from grain mantles due to the relatively high temperature (around ~70 K) and the powerful molecular outflows detected in CO (Zhangetal. 2007).," Additionally, our model predicts a CO abundance of $10^{-4}$ indicating that CO is desorbed from grain mantles due to the relatively high temperature (around $\sim70$ K) and the powerful molecular outflows detected in CO \citep{zhang2007}."
. We found that molecules like HCiN. HCO. CH. and CS should be detectable toward the central core. since their fractional abundances are even higher than the oones.," We found that molecules like $_3$ N, $_2$ CO, $_2$ H, and CS should be detectable toward the central core, since their fractional abundances are even higher than the ones."
 Concerning the western and eastern cores. the CO fractional abundance. of 102. is one order of magnitude lower than that of the central core.," Concerning the western and eastern cores, the CO fractional abundance, of $10^{-5}$, is one order of magnitude lower than that of the central core."
 For these cores. molecules such as CS. C:H. and aare quite abundant and would be detectable but we would not expect to detect any H:CO and HC3N. In summary. the models that can reproduce the observed values of the aabundance ratio toward the central core as well as in the western and eastern cores. were obtained with a high depletion at the end of phase I. Hence. the differences between the central and the western/eastern cores seen in the abundance ratio seem to be mainly due to density and temperature effects.," For these cores, molecules such as CS, $_2$ H, and are quite abundant and would be detectable but we would not expect to detect any $_2$ CO and $_3$ N. In summary, the models that can reproduce the observed values of the abundance ratio toward the central core as well as in the western and eastern cores, were obtained with a high depletion at the end of phase I. Hence, the differences between the central and the western/eastern cores seen in the abundance ratio seem to be mainly due to density and temperature effects."
 In particular. as shown by the chemical modeling of the region. the temperature is à key parameter in determining the aabundance ratio. and hence the abundance of each molecule.," In particular, as shown by the chemical modeling of the region, the temperature is a key parameter in determining the abundance ratio, and hence the abundance of each molecule."
 As temperature rises the fraction of species that will evaporate increase. and consequently the chemistry evolves differently.," As temperature rises the fraction of species that will evaporate increase, and consequently the chemistry evolves differently."
 The results obtained from the oobservations. together with ddata from the literature (Zhangetal.2002) show that there are three dense cores associated with the high-mass star-forming region 55142.," The results obtained from the observations, together with data from the literature \citep{zhang2002} show that there are three dense cores associated with the high-mass star-forming region 5142."
 The central core. strong in bbut almost devoid of... harbors a cluster of massive stars in their making.," The central core, strong in but almost devoid of, harbors a cluster of massive stars in their making."
 On the other hand. the western and eastern cores are stronger in tthan in eemission.," On the other hand, the western and eastern cores are stronger in than in emission."
 In the following section we discuss the possible reasons for the observed variation of the abundance ratio among the cores found in 55142., In the following section we discuss the possible reasons for the observed variation of the abundance ratio among the cores found in 5142.
 The central dense core in 55142 is actively forming a cluster of massive stars. still in the accretion phase. which displays the typical signposts of star formation. (molecular outflow and maser emission).," The central dense core in 5142 is actively forming a cluster of massive stars, still in the accretion phase, which displays the typical signposts of star formation (molecular outflow and maser emission)."
 Concerning the western and eastern cores. the relatively high temperature. around 20 K. could be due to the presence of an embedded YSO and/or heating produced by the three molecular outflows associated with the central core. which are strongly affecting the surrounding dense gas (Zhangetal.2002.2007).," Concerning the western and eastern cores, the relatively high temperature, around 20 K, could be due to the presence of an embedded YSO and/or heating produced by the three molecular outflows associated with the central core, which are strongly affecting the surrounding dense gas \citep{zhang2002,zhang2007}."
. Thus. the association of the western and eastern cores with an infrared source Is not obvious.," Thus, the association of the western and eastern cores with an infrared source is not obvious."
 The aabundance ratio map presented in Fig., The abundance ratio map presented in Fig.
 8 shows significant variations. with a ratio around «50-100 toward the western and eastern cores. and a ratio. up to 1000. toward the central core. due to a significant drop in the aabundance.," \ref{fratio} shows significant variations, with a ratio around $\sim$ 50–100 toward the western and eastern cores, and a ratio, up to 1000, toward the central core, due to a significant drop in the abundance."
 The values found for the aabundance ratio 1n the western and eastern cores are similar to those found in previous studies for cores harboring YSOs. for both low- and high-mass star-forming regions (Caselli2010).," The values found for the abundance ratio in the western and eastern cores are similar to those found in previous studies for cores harboring YSOs, for both low- and high-mass star-forming regions \citep{caselli2002a,hotzel2004,palau2007,friesen2010}."
. These studies are all consistent with the fact that a high ratio (X300) seems to be associated with starless cores and a low ratio. around 60-90. is found toward the YSOs. suggesting an anticorrelation between the the aabundance ratio and the evolutionary stage.," These studies are all consistent with the fact that a high ratio $\leq$ 300) seems to be associated with starless cores and a low ratio, around 60–90, is found toward the YSOs, suggesting an anticorrelation between the the abundance ratio and the evolutionary stage."
 Thus. the high rratio toward the central core does not follow the anticorrelation between the rratio and the evolutionary stage of the core like m the studies mentioned above.," Thus, the high ratio toward the central core does not follow the anticorrelation between the ratio and the evolutionary stage of the core like in the studies mentioned above."
 The noticeable increase of the rratio in the central core suggests a strong differentiation of the aabundance between the central core and the western/eastern cores., The noticeable increase of the ratio in the central core suggests a strong differentiation of the abundance between the central core and the western/eastern cores.
 Below we briefly investigate the origin of such a differentiation., Below we briefly investigate the origin of such a differentiation.
 As suggested by Qiuetal.(2008).. UV photons from 0052744334 are not likely to affect the dense gas. and the effects of the UV field from the embedded protostar(s) do not seem to be a major issue in determining the aand aabundance of the central core. since the high visual extinction. Ayz40 mag or higher. prevents UV photons to penetrate the central core.," As suggested by \citet{qiu2008}, UV photons from 05274+334 are not likely to affect the dense gas, and the effects of the UV field from the embedded protostar(s) do not seem to be a major issue in determining the and abundance of the central core, since the high visual extinction, $A_{V}\simeq40$ mag or higher, prevents UV photons to penetrate the central core."
 Even though we took into account the effects of opacity and different iin the calculation of the column densities. we consider whether the different excitation conditions among the dense cores may be the cause for the lower abundance of NH.. tthe high rratio.," Even though we took into account the effects of opacity and different in the calculation of the column densities, we consider whether the different excitation conditions among the dense cores may be the cause for the lower abundance of , the high ratio."
 The critical density of iis ~10? , The critical density of is $\sim10^5$ 
weight lor primordial composition: my: proton nass: and ae: linc-of-sight velocity dispersion).,weight for primordial composition; $m_p$: proton mass; and $\sigma_v$: line-of-sight velocity dispersion).
 Numerical simulations that only include gravitational heating showed that 31 1.3 (c.g. Navarro. Erenk White 1995: Ivrard. Metzler Navarro 1996: Bryan Norman 1998: Eke ct al.," Numerical simulations that only include gravitational heating showed that $\beta\simeq
1$ --1.3 (e.g. Navarro, Frenk White 1995; Evrard, Metzler Navarro 1996; Bryan Norman 1998; Eke et al."
 1998b: Dorgani. Ciovernato. Wacsley et al.," 1998b; Borgani, Governato, Wadsley et al."
 2002. BOAWV hereafter).," 2002, BGW hereafter)."
 A number of observational facts demonstrate that this picture is too simplistic. thus calling for the consideration of extra physics in the description of the ICM.," A number of observational facts demonstrate that this picture is too simplistic, thus calling for the consideration of extra physics in the description of the ICM."
 The Ly T relation is found to be steeper than predicted. with Lxx Poa ty2 keV (cre. White. Jones Forman 1997: Alarkeviteh 1998: Arnaud Evrard 19909: πο. De Grandi Molendi: 2002).. possibly- ioproaching the selfsimilar scaling only for the hottest svstems with Z8 keV (Allen Fabian. 1998).," The $L_X$ $T$ relation is found to be steeper than predicted, with $L_X\propto T^{\sim 3}$ at $T_X> 2$ keV (e.g., White, Jones Forman 1997; Markevitch 1998; Arnaud Evrard 1999; Ettori, De Grandi Molendi 2002), possibly approaching the self--similar scaling only for the hottest systems with $T\magcir 8$ keV (Allen Fabian 1998)."
 Evidences also emerged. for this relation to further steepen for colder eroups. Z21 keV (ee. Ponman ct al.," Evidences also emerged for this relation to further steepen for colder groups, $T\mincir 1$ keV (e.g., Ponman et al."
 1996: Lelsclon Ponman 2000: Alulchaey 2000)., 1996; Helsdon Ponman 2000; Mulchaey 2000).
 Furthermore. no evidence for a strong positive evolution of the Ly ZY relation has been found. to date out to z~1 (e.g. Mushotzky Scharf 1997: Reichart et al.," Furthermore, no evidence for a strong positive evolution of the $L_X$ $T$ relation has been found to date out to $z\sim 1$ (e.g., Mushotzky Scharf 1997; Reichart et al."
 1999: Fairley et al., 1999; Fairley et al.
 2000: Borgani et al., 2000; Borgani et al.
 2001a: Holden et al., 2001a; Holden et al.
 2002: Novicki. Sornig Henry 2002: cf.," 2002; Novicki, Sornig Henry 2002; cf."
 also Vikhlinin et al., also Vikhlinin et al.
 2002)., 2002).
 As for the S T relation. Ponman. Cannon Navarro (1999) found. from. ROSAT ancl ASCA data an excess of entropy within the central regions of Z5;2 keV systems (see also LlovelDavis et al.," As for the $S$ $T$ relation, Ponman, Cannon Navarro (1999) found from ROSAT and ASCA data an excess of entropy within the central regions of $T\mincir 2$ keV systems (see also Lloyd–Davis et al."
 2000. Finoguenov οἱ al.," 2000, Finoguenov et al."
 20022). possibly approaching the value S100 keV enm? for the coldest. groups.," 2002a), possibly approaching the value $S\sim 100$ keV $^2$ for the coldest groups."
 Finally. a series of evidences. based on ASCA (e.g. Llorner. Alushotzky Scharf 1999: Nevalainen. Alarkeviteh Forman 2000: Finoguenov. Reiprich jiohhringer 2001b). BeppoSAN (Ettori et al.," Finally, a series of evidences, based on ASCA (e.g., Horner, Mushotzky Scharf 1999; Nevalainen, Markevitch Forman 2000; Finoguenov, Reiprich Böhhringer 2001b), Beppo–SAX (Ettori et al."
 2002) and Chandra (Allen. Sehmidt Fabian 2001) data. shows that the observed AL T relation has a ~40 per cent lower normalization than predicted by simulations that only inclucle gravitational heating.," 2002) and Chandra (Allen, Schmidt Fabian 2001) data, shows that the observed $M$ $T$ relation has a $\sim 40$ per cent lower normalization than predicted by simulations that only include gravitational heating."
 In the attempt of interpreting these data. theoreticians are currently following two alternative routes. based. either on introducing nongravitational heating of the ICM or on allucing to the ellects of radiative cooling.," In the attempt of interpreting these data, theoreticians are currently following two alternative routes, based either on introducing non–gravitational heating of the ICM or on alluding to the effects of radiative cooling."
 An episode of nongravitational heating. occurring before or during the gravitational collapse. has the effect of increasing the entropy of the gas. preventing it [rom reaching high densities in the central cluster regions. and suppressing its VY rav emissivity (c.g. Evrard Henry 1991. Ixaiser 1991: Bower 1997).," An episode of non–gravitational heating, occurring before or during the gravitational collapse, has the effect of increasing the entropy of the gas, preventing it from reaching high densities in the central cluster regions and suppressing its $X$ –ray emissivity (e.g., Evrard Henry 1991, Kaiser 1991; Bower 1997)."
 For à fixed amount of specific heating. the effect is larger lor poorer svstems. Le. when the extra energy. per gas particle is comparable to the halo virial temperature.," For a fixed amount of specific heating, the effect is larger for poorer systems, i.e. when the extra energy per gas particle is comparable to the halo virial temperature."
 This produces both an excess entropy and a steeper Ly T relation (e.g... Cavaliere. Menci “Tozzi 1998: Balogh. Babul Patton 1999: Tozzi Norman 2001).," This produces both an excess entropy and a steeper $L_X$ $T$ relation (e.g., Cavaliere, Menci Tozzi 1998; Balogh, Babul Patton 1999; Tozzi Norman 2001)."
 Arguments based on semianalytical work (e.g. Tozz Norman 2001)Ui and numerical simulations (Dialek. Evrare Mohr 2001:üt Brighenti Mathews 2001: Borgani ct al.," Arguments based on semi–analytical work (e.g., Tozzi Norman 2001) and numerical simulations (Bialek, Evrard Mohr 2001; Brighenti Mathews 2001; Borgani et al."
" 2001b. 2002) suggest that a specific heating energy of ££,~1 keVpart or. equivalently. a precollapse entropy. Hloor. of s—100 keV emo. can account for the observed. (X. ray properties of galaxy systems (cf."," 2001b, 2002) suggest that a specific heating energy of $E_h\sim 1$ keV/part or, equivalently, a pre–collapse entropy floor of $S\sim 100$ keV $^2$, can account for the observed $X$ –ray properties of galaxy systems (cf."
 also Babul et al., also Babul et al.
 2002. Finoeucnoy et al.," 2002, Finoguenov et al."
 2002a for arguments suggesting a stronger preheating)., 2002a for arguments suggesting a stronger pre–heating).
 Yet. the origin for this energy. has still to be determined.," Yet, the origin for this energy has still to be determined."
 Enerey release from. supernovae feedback. has been advocated. as a possibility (e.g... Bower ct al.," Energy release from supernovae feedback has been advocated as a possibility (e.g., Bower et al."
 2001: AMenei Cavaliere 2001)., 2001; Menci Cavaliere 2001).
 Using the abundance of heavy elements of the ICM as a diagnostic for the past. history of the star formation within clusters (e.g. Renzini 1997: Ixravtsov Yepes 2000: Pipino et al.," Using the abundance of heavy elements of the ICM as a diagnostic for the past history of the star formation within clusters (e.g., Renzini 1997; Kravtsov Yepes 2000; Pipino et al."
 2002: Valdarnini 2002). a number of studies concluded that SN may fall short in providing the required extra.energy budget (cf.," 2002; Valdarnini 2002), a number of studies concluded that SN may fall short in providing the required extra–energy budget (cf."
 also Finoguenov. Arnaud David 2001a).," also Finoguenov, Arnaud David 2001a)."
 The other obvious candidate is represented by energy from AGN (e.g... Valageas Silk 1990: Wu. Fabian Nulsen 2000: Ale Namara et al.," The other obvious candidate is represented by energy from AGN (e.g., Valageas Silk 1999; Wu, Fabian Nulsen 2000; Mc Namara et al."
 2000: Nath Rovehowehury 2002: Cavaliere. Lapi Alenei 2002).," 2000; Nath Roychowdhury 2002; Cavaliere, Lapi Menci 2002)."
 In this case. the large amount of energy that is available requires some degree of tuning of the mechanisms responsible for its conversion into thermal energy of the eas.," In this case, the large amount of energy that is available requires some degree of tuning of the mechanisms responsible for its conversion into thermal energy of the gas."
 While a suitable amount of nongravitational heating can account for the observed Ly T. relation and. entropy excess. the AZ T relation is only mareinally allected by extra heating (c.g. BOA). thus leaving the cliserepaney between observed ancl precictecd relation unresolved.," While a suitable amount of non–gravitational heating can account for the observed $L_X$ $T$ relation and entropy excess, the $M$ $T$ relation is only marginally affected by extra heating (e.g. BGW), thus leaving the discrepancy between observed and predicted relation unresolved."
 As for cooling. its ellect is to selectively remove those lowentropy particles from the diffuse No rav emitting phase which have cooling times shorter than the Llubble time (e.g.. Voit Bryan 2002: Wu Xue 2002).," As for cooling, its effect is to selectively remove those low–entropy particles from the diffuse $X$ –ray emitting phase which have cooling times shorter than the Hubble time (e.g., Voit Bryan 2002; Wu Xue 2002)."
 Conversion of cooled gas into collisionless stars decreases the central gas density and. at the same time. he resulting lack of pressure support causes higher.entropy shocked. gas to How in from the outskirts of the cluster or eroup.," Conversion of cooled gas into collisionless stars decreases the central gas density and, at the same time, the resulting lack of pressure support causes higher–entropy shocked gas to flow in from the outskirts of the cluster or group."
 As a result. the X. ray luminosity is suppressed. while he entropy increases. much like in a preheating scenario (Pearee ct al.," As a result, the $X$ –ray luminosity is suppressed, while the entropy increases, much like in a pre–heating scenario (Pearce et al."
 2001: Muanwong et al., 2001; Muanwong et al.
 2002: Davé.. Ixatz Weinberg 2002).," 2002; Davé,, Katz Weinberg 2002)."
 However. by its nature. cooling is known to v à runaway. process: cooling causes gas to be accumulated into dense structures. and the ellicieney of cooling increases with gas density.," However, by its nature, cooling is known to be a runaway process: cooling causes gas to be accumulated into dense structures, and the efficiency of cooling increases with gas density."
 As a result. most simulations consistently ποιοί a significant [fraction of gas to be converted. into cold. “stars”. fioc30 per cent (e.g.. Suginohara Ostriker 1908: Lewis et al.," As a result, most simulations consistently predict a significant fraction of gas to be converted into cold “stars”, $f_{\rm cold}\magcir 30$ per cent (e.g., Suginohara Ostriker 1998; Lewis et al."
 2000: Yoshida et al., 2000; Yoshida et al.
 2002: BOW). while observations indicate a considerably lower value of fosLO vcr cent (e.g.. Balogh et al.," 2002; BGW), while observations indicate a considerably lower value of $f_{\rm cold}\mincir 10$ per cent (e.g., Balogh et al."
 2001: Wu Xue 2002)., 2001; Wu Xue 2002).
 ‘This suggests that in real clusters some source of extra wating is increasing the entropy of the gas. preventing overcooling.," This suggests that in real clusters some source of extra heating is increasing the entropy of the gas, preventing overcooling."
 Voit et al (2002) have developed: a semianalytical approach to derive X. rav observable properties of he ICM in the presence of both cooling and extra heating., Voit et al (2002) have developed a semi--analytical approach to derive $X$ –ray observable properties of the ICM in the presence of both cooling and extra heating.
 Dased on this approach. these authors found that cooling and a modest amount of extra heating are able to account or basically all the Y rav ICM observables.," Based on this approach, these authors found that cooling and a modest amount of extra heating are able to account for basically all the $X$ –ray ICM observables."
 Oh Benson (2002) pointed out that preheating is needed to increase the cooling time anc prevent overcooling. by suppressing the gas supply to galaxies (see also Finoguenov et al.," Oh Benson (2002) pointed out that pre–heating is needed to increase the cooling time and prevent overcooling, by suppressing the gas supply to galaxies (see also Finoguenov et al."
 2002b)., 2002b).
 Lt is rowever Clear that. as for any analvtical approach. suitable assumptions and approximations are needed to choose criteria for removing cooled gas from the hot dilfuse phase.," It is however clear that, as for any analytical approach, suitable assumptions and approximations are needed to choose criteria for removing cooled gas from the hot diffuse phase,"
maximum.,maximum.
 Though it has been claimed that SSco does not develop forbidden transitions (e.g. Warner 1995) and that the 2010 outburst was the first time that the nova displayed a nebular spectrum (e.g. Diaz et al., Though it has been claimed that Sco does not develop forbidden transitions (e.g. Warner 1995) and that the 2010 outburst was the first time that the nova displayed a nebular spectrum (e.g. Diaz et al.
" 2010), neither statement is accurate."," 2010), neither statement is accurate."
" First, because the observations performed during the past outbursts were not sufficiently extended in time after the maximum; second, because the average spectrum of Thoroughgood et ((2001, their figure 1) clearly shows a broad composite emission, which should be identified with [Ont] 15007."," First, because the observations performed during the past outbursts were not sufficiently extended in time after the maximum; second, because the average spectrum of Thoroughgood et (2001, their figure 1) clearly shows a broad composite emission, which should be identified with ] $\lambda$ 5007."
 Its profile is very similar to that reported in this paper (see Fig.1 inset)., Its profile is very similar to that reported in this paper (see Fig.1 inset).
 The forbidden transitions appear when the USSco continuum has significantly dimmed and the nova is about 3 magnitudes fainter than during the first plateau phase., The forbidden transitions appear when the Sco continuum has significantly dimmed and the nova is about 3 magnitudes fainter than during the first plateau phase.
" At this epoch the continuum varies not only with the time since maximum, but also with the orbital phase (see 11)."," At this epoch the continuum varies not only with the time since maximum, but also with the orbital phase (see 1)."
 The April spectrum was taken close to the eclipse time (at orbital phase 0.01) and shows a flat continuum., The April spectrum was taken close to the eclipse time (at orbital phase 0.01) and shows a flat continuum.
" The March and May spectra (centered at orbital phase 0.07 and 0.16, respectively) are characterized by a blue continuum."," The March and May spectra (centered at orbital phase 0.07 and 0.16, respectively) are characterized by a blue continuum."
 This can be explained by the hot blue component (the white dwarf itself or an accretion hot-spot) being masked by the secondary star at the time of the April observation., This can be explained by the hot blue component (the white dwarf itself or an accretion hot-spot) being masked by the secondary star at the time of the April observation.
" The evolution of the broad emission lines from the ejecta is independent of the orbitalphase, but their intensity is maximum when the continuum strength decreases."," The evolution of the broad emission lines from the ejecta is independent of the orbital, but their intensity is maximum when the continuum strength decreases."
" The three nebular spectra also show that the resonant transitions constantly weaken in time relative to the forbidden transitions, until they almost completely disappear by 112."," The three nebular spectra also show that the resonant transitions constantly weaken in time relative to the forbidden transitions, until they almost completely disappear by 12."
" This is indicative of a progressively lower density in the ejecta, though this is always relatively high when compared to the densities in planetary nebulae."," This is indicative of a progressively lower density in the ejecta, though this is always relatively high when compared to the densities in planetary nebulae."
" The analysis of the line profiles shows that the Ha emission dominates the “6563 blend"" in the March and April spectra, and that it is significantly weaker than the [Nr]46584 emission only in the May spectrum."," The analysis of the line profiles shows that the $\alpha$ emission dominates the “6563 blend” in the March and April spectra, and that it is significantly weaker than the $\lambda$ 6584 emission only in the May spectrum."
" Hence, only in the latter spectrum it is possible to use the [Nu] lines ratio to constrain the ejecta density and temperature."," Hence, only in the latter spectrum it is possible to use the ] lines ratio to constrain the ejecta density and temperature."
" At this epoch the 2(6584+6548)/A5755 flux ratio is ~6, implying that collisions are contributing to the line formation and that the gas densities are higher than 10? ccm? (see e.g. Osterbrock and Ferland 2006)."," At this epoch the $\lambda$ $\lambda$ 5755 flux ratio is $\sim$ 6, implying that collisions are contributing to the line formation and that the gas densities are higher than $10^5$ $^{-3}$ (see e.g. Osterbrock and Ferland 2006)."
" High gas densities are suggested also by the 4(50074-4959)44363 fluxratio!,, which is 2.97, 4.79 and 9.37 in the March, April and May spectra, respectively, and indicates densities >5x106-107 ccm? for temperatures in the nominal range KK. Figure 2 plots the diagnostic diagram for the [Om] and [Nri] flux ratios."," High gas densities are suggested also by the $\lambda$ $\lambda$ 4363 flux, which is 2.97, 4.79 and 9.37 in the March, April and May spectra, respectively, and indicates densities $\geq5\times10^{6}$ $^7$ $^{-3}$ for temperatures in the nominal range K. Figure 2 plots the diagnostic diagram for the ] and ] flux ratios."
" Note that the lower temperatures and densities indicated by the [Nm]216584,6548/[Nu]A5755 flux ratio are consistent with the fact that the [Nu] transitions typically form in the outer and cooler shell of the expanding ejecta (e.g. Osterbrock and Ferland 2006).", Note that the lower temperatures and densities indicated by the $\lambda\lambda$ $\lambda$ 5755 flux ratio are consistent with the fact that the ] transitions typically form in the outer and cooler shell of the expanding ejecta (e.g. Osterbrock and Ferland 2006).
" Though accurate elemental abundance determination requires the combined modeling of UV and optical observations (e.g., Schwarz 2002), a first oder approximation of the relative abundances can be computed by using the flux ratios of emission lines from ions with similar ionization potential energies, similar critical densities, and the same excitation mechanism (Kingdon and Williams 1997)."," Though accurate elemental abundance determination requires the combined modeling of UV and optical observations (e.g., Schwarz 2002), a first oder approximation of the relative abundances can be computed by using the flux ratios of emission lines from ions with similar ionization potential energies, similar critical densities, and the same excitation mechanism (Kingdon and Williams 1997)."
 This method has the advantage of being fairly insensitive to temperature uncertainties (temperatures that differ by a factor of 2 imply uncertainties of ~20% in the abundance) and has been tested against models for a range of temperatures and, This method has the advantage of being fairly insensitive to temperature uncertainties (temperatures that differ by a factor of 2 imply uncertainties of $\sim$ in the abundance) and has been tested against models for a range of temperatures and
 , 1cm
Solar flares provide many challenges for crucial aspects of high energy astrophysies. including energy release. particle acceleration and transport in magnetized plasmas (e.g.??.asrecent reviews)..,"Solar flares provide many challenges for crucial aspects of high energy astrophysics, including energy release, particle acceleration and transport in magnetized plasmas \citep[e.g.][as recent reviews]{Aschwanden2002,Brown_etal2006}."
 The impulsive phase of a flare marks the rapid release and conversion of a large amount of magnetic energy. stored in the solar corona. into the kinetic energy of particles.," The impulsive phase of a flare marks the rapid release and conversion of a large amount of magnetic energy, stored in the solar corona, into the kinetic energy of particles."
 In the standard thick-target model. (???).. reviewed by (??).. the stream of fast electrons which emits bremsstrahlung hard X-rays heats the dense chromospheric plasma collisionally. is produced first in the tenuous corona by electron acceleration from thermal energies (<| keV) to deka-keV and MeV energies.," In the standard thick-target model, \citep{Brown1971,Syrovatskii1972,LinHudson1976}, , reviewed by \citep{Brown_etal2003,BrownKontar2005}, the stream of fast electrons which emits bremsstrahlung hard X-rays heats the dense chromospheric plasma collisionally, is produced first in the tenuous corona by electron acceleration from thermal energies $\lesssim 1$ keV) to deka-keV and MeV energies."
 This standard geometry of flare electron acceleration and transport is consistent with a variety of spatially resolved observations (2???) and by electron time of flight effects in Hard X-ray light curves (2)..," This standard geometry of flare electron acceleration and transport is consistent with a variety of spatially resolved observations \citep[]{Aschwanden_etal2002,Emslie_etal2003,Kontar_etal2008,KruckerLin2008} and by electron time of flight effects in Hard X-ray light curves \citep{Aschwanden2002}."
 However. an electron beam undergoing solely collisional energy loss. as in the standard thick target model. gives up around 10° times energy to heat than to bremsstrahlung and demands (?) a very high electron production rate to yield observed hard X-ray fluxes.," However, an electron beam undergoing solely collisional energy loss, as in the standard thick target model, gives up around $10^5$ times energy to heat than to bremsstrahlung and demands \citep{Brown1971} a very high electron production rate to yield observed hard X-ray fluxes."
 Furthermore the electron beam and hard X-ray source anisotropies in the standard thick target model (?) are much higher than inferred from the flare hard X-ray data (?).., Furthermore the electron beam and hard X-ray source anisotropies in the standard thick target model \citep{Brown1972} are much higher than inferred from the flare hard X-ray data \citep{KontarBrown2006}.
 ? have proposed that if fast electrons. on reaching the chromosphere. undergo re-acceleration by current sheets there. their enhanced lifetimes increase the hard X-ray yield per electron. so reducing the injection rate needed for hard X-ray production. while greatly reducing the fast electron anisotropy in the main hard X-ray source.," \citet{Brown_etal2009} have proposed that if fast electrons, on reaching the chromosphere, undergo re-acceleration by current sheets there, their enhanced lifetimes increase the hard X-ray yield per electron, so reducing the injection rate needed for hard X-ray production, while greatly reducing the fast electron anisotropy in the main hard X-ray source."
 Therefore. any mechanism that can re-accelerate electrons in the chromosphere ts also of interest.," Therefore, any mechanism that can re-accelerate electrons in the chromosphere is also of interest."
 Various acceleration mechanisms have been proposed for energetic solar particles (2).. including acceleration by a large scaleparallel electric field (?).. electric. fields inside current sheets (2222). collapsing trap acceleration (?) as well as turbulent non-resonant (?).. and resonant acceleration by waves (seethereviewsby??)..," Various acceleration mechanisms have been proposed for energetic solar particles \citep{Aschwanden2002}, including acceleration by a large scaleparallel electric field \citep{Holman1985}, electric fields inside current sheets \citep{Litv2003,WoodNeukirch2005,Bian2008,SiverskyZharkova2009}, , collapsing trap acceleration \citep{BogachevSomov2007}
 as well as turbulent non-resonant \citep[]{BykovFleishman2009}, and resonant acceleration by waves \citep[see the reviews by][]{Miller_etal1997,Petrosian1999}."
 Parallel acceleration by resonant interaction between electrons and the parallel electric field produced by turbulent Alfven waves is the subject of the present study., Parallel acceleration by resonant interaction between electrons and the parallel electric field produced by turbulent Alfven waves is the subject of the present study.
" The resonant coupling between a given electromagneticmode characterized by its dispersion relation w(k) and an electron gyrating at the gyrofrequency «4,=gBo/im while streaming at the speed »j along the magnetic field. is given by the Doppler resonance condition. «o—swe/y=ΛΙ"," The resonant coupling between a given electromagneticmode characterized by its dispersion relation $\omega (\mathbf{k})$ and an electron gyrating at the gyrofrequency $\omega_{ce}=qB_{0}/m$ while streaming at the speed $v_{\parallel}$ along the magnetic field, is given by the Doppler resonance condition, $\omega-s\omega_{ce}/\gamma=k_{\parallel}v_{\parallel}$."
 In this expression. Aj is the parallel wavenumber of the wave. y is the Lorentz factor and s is the harmonic number of We.," In this expression, $k_{\parallel}$ is the parallel wavenumber of the wave, $\gamma$ is the Lorentz factor and $s$ is the harmonic number of $\omega_{ce}$."
 Basically. the resonance condition specifies under which condition this electron experiences an electromagnetic force which is stationary.," Basically, the resonance condition specifies under which condition this electron experiences an electromagnetic force which is stationary."
 Therefore. if a broad spectrum of the electromagnetic field fluctuations associated with a particular mode is present. and moreover. if the resonance condition with this mode is satisfied for thermal electrons. then it is possible for these electrons to achieve a large energy gain. only limited by the final energy which corresponds to the last resonance with this mode.," Therefore, if a broad spectrum of the electromagnetic field fluctuations associated with a particular mode is present, and moreover, if the resonance condition with this mode is satisfied for thermal electrons, then it is possible for these electrons to achieve a large energy gain, only limited by the final energy which corresponds to the last resonance with this mode."
" Within quasilinear theory. this resonant acceleration process is a diffusion in velocity space. from the thermal velocity Vj, up to the final velocity Vj."," Within quasilinear theory, this resonant acceleration process is a diffusion in velocity space, from the thermal velocity $V_{Te}$ up to the final velocity $V_{f}$."
 The most straightforward way of producing a stream of fast electrons accelerated along the magnetic field lines is through wave resonance satisfying the condition either by the parallel electric force F=qEj or the magnetic mirror force Fo=pV|B. µ=nn?/2Bo being the magnetic moment.," The most straightforward way of producing a stream of fast electrons accelerated along the magnetic field lines is through wave resonance satisfying the condition either by the parallel electric force $F=qE_{\parallel}$ or the magnetic mirror force $F=\mu \nabla_{\parallel} B$, $\mu= m v^{2}_{\perp}/2B_{0}$ being the magnetic moment."
 Many people starting from (?) considered. stochastic acceleration of particles., Many people starting from \citep{Fermi1949} considered stochastic acceleration of particles.
 ? have developed a model of thermal electron acceleration during flares based on the Landau resonance between these electrons and the fluctuating parallel mirror force produced by the compressive magnetic field component of turbulent magnetoacoustic waves., \citet{Miller_etal1996} have developed a model of thermal electron acceleration during flares based on the Landau resonance between these electrons and the fluctuating parallel mirror force produced by the compressive magnetic field component of turbulent magnetoacoustic waves.
 The mechanism being the magnetic analog of Landau damping is called transit-time damping., The mechanism being the magnetic analog of Landau damping is called transit-time damping.
" Since magnetoacoustic waves have similar speeds as Alfven waves. their frequency being given by w=kV, they indeed can resonate with a population of thermal electrons. Le. Vr,-V4."," Since magnetoacoustic waves have similar speeds as Alfven waves, their frequency being given by $\omega=kV_{a}$ they indeed can resonate with a population of thermal electrons, i.e. $V_{Te}\sim V_A$."
" Under typical plasma conditions in the solar corona (e.g.??).. Le. magnetic field By=100 G. plasma density 2=5x IO""czr. and electron temperature T,=10° Κ. the Alfven velocity em/s) is close to the electron thermalspeed cm/s)."," Under typical plasma conditions in the solar corona \citep[e.g.][]{Emslie_etal2003,Kontar_etal2008}, i.e. magnetic field $B_{0}\approx 100$ G, plasma density $n\approx 5\times 10^{9}cm^{-3}$ , and electron temperature $T_e\approx 10^{6}$ K, the Alfven velocity $V_{A}\sim 3\times 10^8$ cm/s) is close to the electron thermalspeed $V_{Te}\sim 4\times 10^{8}$ cm/s)."
 In the model by ?.. the broadspectrum of magnetic fluctuations is produced by isotropic MHD turbulence.," In the model by \citet{Miller_etal1996}, , the broadspectrum of magnetic fluctuations is produced by isotropic MHD turbulence."
about 2 AU from its host star by means of observing a few-per-cent deviation in a mierolensing light curve.,about 2 AU from its host star by means of observing a few-per-cent deviation in a microlensing light curve.
 However. such a discovery requires photometric measurements on a few hundred microlensing events. assuming that a fair fraction of the host stars are orbited by such planets.," However, such a discovery requires photometric measurements on a few hundred microlensing events, assuming that a fair fraction of the host stars are orbited by such planets."
 A sufficient number of events can only arise from monitoring dense fields of stars., A sufficient number of events can only arise from monitoring dense fields of stars.
 With a probability of ~10 fora star in the Galactic bulge being magnified by more than 34 per cent at any given time due to the bending of light caused by the gravitational field of an intervening foreground star (2).. and such a microlensing event lasting of the order of a month. one namely needs to monitor 10° to LO” stars.," With a probability of $\sim 10^{-6}$ for a star in the Galactic bulge being magnified by more than 34 per cent at any given time due to the bending of light caused by the gravitational field of an intervening foreground star \citep{KP94}, and such a microlensing event lasting of the order of a month, one namely needs to monitor $10^{7}$ to $10^{8}$ stars."
 This was achieved by microlensing surveys like OGLE (Optical Gravitational Lensing Experiment) (2).. MACHO (MAssive Compact Halo Objects) (2).. EROS (Expérrience de la Recherche d'Objets Sombres) (2). and MOA (Microlensing Observations in Astrophysics) (2). with a roughly daily sampling.," This was achieved by microlensing surveys like OGLE (Optical Gravitational Lensing Experiment) \citep{OGLE:first}, MACHO (MAssive Compact Halo Objects) \citep{MACHO:first}, EROS (Expérrience de la Recherche d'Objets Sombres) \citep{EROS:first} and MOA (Microlensing Observations in Astrophysics) \citep{MOA:first} with a roughly daily sampling."
 Moreover. all these surveys have been equipped with real-time alert systems (22222). that notify the scientific community about ongoing microlensing events.," Moreover, all these surveys have been equipped with real-time alert systems \citep{OGLE:alert,OGLE:alert2,
MACHO:alert,EROS:alert,MOA:alert} that notify the scientific community about ongoing microlensing events."
 This allows to schedule follow-up observations that provide an increased photometric accuracy. a denser event sampling. and/or coverage during epochs outside the arget visibility from the telescope site used by the respective survey campaign.," This allows to schedule follow-up observations that provide an increased photometric accuracy, a denser event sampling, and/or coverage during epochs outside the target visibility from the telescope site used by the respective survey campaign."
 The PLANET (Probing Lensing Anomalies NETwork) established the first telescope network capable of round-the-clock nearly-continuous high-precision monitoring of microlensing events (7)— with the goal to detect gas giant janets and to determine their abundance.," The PLANET (Probing Lensing Anomalies NETwork) established the first telescope network capable of round-the-clock nearly-continuous high-precision monitoring of microlensing events \citep{PLANET:first}
 with the goal to detect gas giant planets and to determine their abundance."
 For being able to detect deviations of 5 per cent. PLANET aims at a 1-2 per cent johotometrie accuracy.," For being able to detect deviations of 5 per cent, PLANET aims at a 1-2 per cent photometric accuracy."
 With a typical sampling interval of 1.5 to 2.5 hrs allowing a characterization of planetary anomalies on the basis of at least 10-15. data points taken while these last. the required exposure time then limits the number of events that can be monitored.," With a typical sampling interval of 1.5 to 2.5 hrs allowing a characterization of planetary anomalies on the basis of at least 10-15 data points taken while these last, the required exposure time then limits the number of events that can be monitored."
" For bright (giant) stars. exposure times of a few minutes are sufficient. so that PLANET can monitor about 20 events each night or 75 events per observing season. but this reduces to about 6 events each night or 20 events per season for ""inter stars. for which exposure times reach 20 min (2)."," For bright (giant) stars, exposure times of a few minutes are sufficient, so that PLANET can monitor about 20 events each night or 75 events per observing season, but this reduces to about 6 events each night or 20 events per season for fainter stars, for which exposure times reach 20 min \citep{PLANET:EGS}."
" In 1999, TACHO and OGLE-II together provided about 100 microlensing alerts. out of which only 7 were on giant source stars."," In 1999, MACHO and OGLE-II together provided about 100 microlensing alerts, out of which only 7 were on giant source stars."
 This severely imited PLANET in its planet detection capabilities: rather than 75 events. only about 25 could be monitored per season.," This severely limited PLANET in its planet detection capabilities: rather than 75 events, only about 25 could be monitored per season."
 The OGLE-III upgrade. in effect from 2002. had a major impact on the xotential of microlensing planet searches. paving he way towards he now nearly 1000 microlensing events per year provided by the alert systems of the and surveys.," The OGLE-III upgrade, in effect from 2002, had a major impact on the potential of microlensing planet searches, paving the way towards the now nearly 1000 microlensing events per year provided by the alert systems of the and surveys."
 The much larger number of events arising from this upgrade allowed OGLE itself © obtain meaningful constraints on planets of Jugiter mass (22).. while OGLE and MOA have even demonstrated tjit such planets can in fact be detected by their surveys (2)..," The much larger number of events arising from this upgrade allowed OGLE itself to obtain meaningful constraints on planets of Jupiter mass \citep{Tsapras:OGLElimits,Snodgrass:OGLElimits}, while OGLE and MOA have even demonstrated that such planets can in fact be detected by their surveys \citep{Bond:planet}."
 However. for studying ess massive planets. their sampling is insufficient.," However, for studying less massive planets, their sampling is insufficient."
 At the same ime. the OGLE-III upgrade enabled PLANET to exploit its full heoretical capability. and moreover. it gave PLANET a reliable chance to detect planets of a few Earth masses provided that these are not rare around the stars that cause the microlensing events.," At the same time, the OGLE-III upgrade enabled PLANET to exploit its full theoretical capability, and moreover, it gave PLANET a reliable chance to detect planets of a few Earth masses provided that these are not rare around the stars that cause the microlensing events."
 The discovery of OGLE 2005-BLG-390Lb (??) explicitly proved the sensitivity of the PLANET observations to planets in that mass range.," The discovery of OGLE 2005-BLG-390Lb \citep{PLANET:planet,Dominik:planet} explicitly proved the sensitivity of the PLANET observations to planets in that mass range."
 Tierolensing events are also. regularly monitored by the MicroFUN ¢Microlensing Follow-Up Network)team., Microlensing events are also regularly monitored by the MicroFUN (Microlensing Follow-Up Network).
 However. rather than exploiting a permanent network. MicroFUN concentrates on particularly promising events and activates target-of-opportunity observations should such an event be in progress.," However, rather than exploiting a permanent network, MicroFUN concentrates on particularly promising events and activates target-of-opportunity observations should such an event be in progress."
 Besides |m-elass telescopes. their stand-by network includes a arger number of small (down to 0.911. diameter) telescopes operated by amateur astronomers. which are well suited to observe he peaks of events over which the source star makes a bright target.," Besides 1m-class telescopes, their stand-by network includes a larger number of small (down to 0.3m diameter) telescopes operated by amateur astronomers, which are well suited to observe the peaks of events over which the source star makes a bright target."
 Since the PLANET network is restricted in its capabilities of monitoring ~ 25 per cent of the currently alerted events with he observational requirements. the planet detection rate could be boosted by using larger (2m) telescopes or clusters of |m-class elescopes.," Since the PLANET network is restricted in its capabilities of monitoring $\sim\,$ 25 per cent of the currently alerted events with the observational requirements, the planet detection rate could be boosted by using larger (2m) telescopes or clusters of 1m-class telescopes."
 In fact. such an upgrade is required in order to obtain a sample thatallows a reliable test of models of the formation and evolution of planets around K- and M-dwarfs.," In fact, such an upgrade is required in order to obtain a sample thatallows a reliable test of models of the formation and evolution of planets around K- and M-dwarfs."
 (2?) marks the prototype of a network of 2m robotic telescopes. not only allowing a fast response time. but also a flexible scheduling by means of the multi-agent contract model provided by the eSTAR (22).," \citep{RoboNet} marks the prototype of a network of 2m robotic telescopes, not only allowing a fast response time, but also a flexible scheduling by means of the multi-agent contract model provided by the eSTAR \citep*{eStar,eStar1}."
 eSTAR is a key player in the Heterogeneous Telescope Networks (HTN) consortium and involved in the IVOA (International Virtual Observatory Alliance) standards process., eSTAR is a key player in the Heterogeneous Telescope Networks (HTN) consortium and involved in the IVOA (International Virtual Observatory Alliance) standards process.
 If one aims at the discovery of Earth-mass planets. the standard follow-up sampling of 1.5 hrs usually does not produce the amount of data required to characterize the corresponding signals. and with less frequent sampling one even faces a significant risk of missing any hint for a deviation from an ordinary microlensing light curve.," If one aims at the discovery of Earth-mass planets, the standard follow-up sampling of 1.5 hrs usually does not produce the amount of data required to characterize the corresponding signals, and with less frequent sampling one even faces a significant risk of missing any hint for a deviation from an ordinary microlensing light curve."
 However. planets of Earth mass and even below can be discovered by shortening the sampling interval to  110 min once a regularly sampled point is suspected to depart from a model light curve that represents a system without planet.," However, planets of Earth mass and even below can be discovered by shortening the sampling interval to $\sim$ 10 min once a regularly sampled point is suspected to depart from a model light curve that represents a system without planet."
 In order to properly trigger such anomaly alerts. all incoming data need to be checked immediately. and prompt action needs to be taken within less than ~ 11S min.," In order to properly trigger such anomaly alerts, all incoming data need to be checked immediately, and prompt action needs to be taken within less than $\sim$ 15 min."
 The amount of data and the required response time for achieving a good detection efficiency for Earth-mass planets are however prohibitive for relying on human inspection., The amount of data and the required response time for achieving a good detection efficiency for Earth-mass planets are however prohibitive for relying on human inspection.
 Therefore. we here describe the implementation of an automated anomaly detector that exploits the opportunities of immediate response and flexible scheduling of a network of robotic telescopes.," Therefore, we here describe the implementation of an automated anomaly detector that exploits the opportunities of immediate response and flexible scheduling of a network of robotic telescopes."
 A first similar warning system. dubbed EEWS. had been installed by OGLE in 2003 (2).. which however involves further human inspection and operates with a single telescope.," A first similar warning system, dubbed EEWS, had been installed by OGLE in 2003 \citep{OGLE:alert2}, which however involves further human inspection and operates with a single telescope."
 In contrast. our design needs to succeed without any human intervention and take care of a heterogeneous telescope network.," In contrast, our design needs to succeed without any human intervention and take care of a heterogeneous telescope network."
 The underlying algorithm follows previous experience on the assessment of anomalies., The underlying algorithm follows previous experience on the assessment of anomalies.
 We explicitly aim at reaching a significant detection efficiency to Earth-mass planets with the current survey/follow-up strategy of microlensing planet searches., We explicitly aim at reaching a significant detection efficiency to Earth-mass planets with the current survey/follow-up strategy of microlensing planet searches.
 This paper is organized as follows., This paper is organized as follows.
 In Sect., In Sect.
 2. we describe the modelling of ordinary microlensing events with particular emphasis on the importance of robust parameter estimates. not confused by outliers. in order to properly identify real deviations.," \ref{sec:ordinary} we describe the modelling of ordinary microlensing events with particular emphasis on the importance of robust parameter estimates, not confused by outliers, in order to properly identify real deviations."
 While Sect., While Sect.
 3. deals with the general strategy for detecting low-mass planets by microlensing. we derive a suitable concept for an anomaly detector in Sect. 4.," \ref{sec:lowmass} deals with the general strategy for detecting low-mass planets by microlensing, we derive a suitable concept for an anomaly detector in Sect. \ref{sec:concept}. ."
 The embedding of the, The embedding of the
Given that the correlation extends over a large range in GC luminosity. and is not seen for red GC's. selection bias (choosing redder GCs at bright magnitudes aud bluer GC's αἱ faint magnitudes) seems unlikely (ο be a factor.,"Given that the correlation extends over a large range in GC luminosity, and is not seen for red GCs, selection bias (choosing redder GCs at bright magnitudes and bluer GCs at faint magnitudes) seems unlikely to be a factor."
 There is no significant. correlation between GC huninositv and ealactocentric radius. ruling out. a radial variation in any quantitv as a cause (e.g.. dust).," There is no significant correlation between GC luminosity and galactocentric radius, ruling out a radial variation in any quantity as a cause (e.g., dust)."
 Together these [acts also suggest that a svstematic photonietric error cannot be blamed., Together these facts also suggest that a systematic photometric error cannot be blamed.
 To physically produce the observed correlation. either more massive GCs must have formed [rom more enriched gas. or individual GC's must have sell-enriched.," To physically produce the observed correlation, either more massive GCs must have formed from more enriched gas, or individual GCs must have self-enriched."
 In the former picture. we could imagine blue GCs [forming in proto-dwarl galaxies with varving metal enrichment.," In the former picture, we could imagine blue GCs forming in proto-dwarf galaxies with varying metal enrichment."
 The essential problem is that there is no evidence that the GCLE varies strongly among dEs. as we would need the most metal-rich dEs to have few or no low-mass GCs to preserve (he relation.," The essential problem is that there is no evidence that the GCLF varies strongly among dEs, as we would need the most metal-rich dEs to have few or no low-mass GCs to preserve the relation."
" GC sell-enrichment might explain (he correlation. as more massive GCs could retain a larger fraction of supernovae (SNe) ejecta,"," GC self-enrichment might explain the correlation, as more massive GCs could retain a larger fraction of supernovae (SNe) ejecta."
 The sellenrichment of GCs has been studied in some detail as a possible origin to the chemical inhomogeneilies observed among stars in Galactic GCs (e.g.. Smith 1937).," The self-enrichment of GCs has been studied in some detail as a possible origin to the chemical inhomogeneities observed among stars in Galactic GCs (e.g., Smith 1987)."
 Early works (e.g.. Dopita Smith 1986) argued that only (he most massive GCs could retain enough gas to sell-enrich. but (his depends critically on (he assumed initial metal abundance of (he proto-GC cloud and on the details of the cooling curve.," Early works (e.g., Dopita Smith 1986) argued that only the most massive GCs could retain enough gas to self-enrich, but this depends critically on the assumed initial metal abundance of the proto-GC cloud and on the details of the cooling curve."
 Morgan Lake (1989) found that à more accurate cooling curve reduced the critical mass to >LOAL. in a wupershell model. as suggested by Cavrel (1986).," Morgan Lake (1989) found that a more accurate cooling curve reduced the critical mass to $\ge 10^5 M_{\odot}$ in a “supershell"" model, as suggested by Cayrel (1986)."
 In the model of Parmentier (1999). proto-GC clouds are confined by a hot protogalactic medium. and (his model in [act predicts an GC mass-metallicitv relation. in which (he most nassive GC's are the most metal-poor (Parmentier Gilmore 2001).," In the model of Parmentier (1999), proto-GC clouds are confined by a hot protogalactic medium, and this model in fact predicts an GC mass-metallicity relation, in which the most massive GCs are the most metal-poor (Parmentier Gilmore 2001)."
 Clearly a wide range of models exist. ancl it is possible (hat with the appropriate initial conditions and phlivsica nechanism a self-enrichment model of this sort can be made to work.," Clearly a wide range of models exist, and it is possible that with the appropriate initial conditions and physical mechanism a self-enrichment model of this sort can be made to work."
 Another possibility is that the blue GCs formed inside individual dark matter (DAD) alos., Another possibility is that the blue GCs formed inside individual dark matter (DM) halos.
 This scenario was first proposed by Peebles (1984). but fell into cislavor (Moore 1996) alter studies of Galactic GCs found low mass-to-lisht ratios (Prvor 1989) and. tida tails were observed. around several GC's (e.g. Pal 5: Odenkirehen 2003).," This scenario was first proposed by Peebles (1984), but fell into disfavor (Moore 1996) after studies of Galactic GCs found low mass-to-light ratios (Pryor 1989) and tidal tails were observed around several GCs (e.g., Pal 5; Odenkirchen 2003)."
 Recently. Dromm Clarke (2002) and \lashehenko Sills (2005a.b) have used numerical simulations to argue that GC's with primordial DM halos could lose the bulk of the DM through either violent relaxation al early times or subsequent tidal stripping.," Recently, Bromm Clarke (2002) and Mashchenko Sills (2005a,b) have used numerical simulations to argue that GCs with primordial DM halos could lose the bulk of the DM through either violent relaxation at early times or subsequent tidal stripping."
 If true. then a present-day lack of DM does not necessarily imply that GCs never had DM halos.," If true, then a present-day lack of DM does not necessarily imply that GCs never had DM halos."
 It seems qualitatively plausible to produce the correlation in this context. but whether it could be sustained in detail requires additional simulation.," It seems qualitatively plausible to produce the correlation in this context, but whether it could be sustained in detail requires additional simulation."
 Any such model need also be compared to the rather siringent set of other observations of blue GC's (some of which are not usually considered).," Any such model need also be compared to the rather stringent set of other observations of blue GCs (some of which are not usually considered),"
The striking alignment of the collimated flow delineated by the Hs emission and the central location of the radio jet implies that these phenomena are coupled.,The striking alignment of the collimated flow delineated by the $_2$ emission and the central location of the radio jet implies that these phenomena are coupled.
 It is reasonable to assume that the radio jet is the driving force of the collimated flow., It is reasonable to assume that the radio jet is the driving force of the collimated flow.
 No stellar counterpart (o the radio jet was detected in the narrow-bancl near-infrared images (e.g. see Fig., No stellar counterpart to the radio jet was detected in the narrow-band near-infrared images (e.g. see Fig.
 3bb)., \ref{plottwo}b b).
 IRAS 16547—4247 is reminiscent of another voung massive stellar object. Η150-51 aab ιτ kpc).," IRAS $-$ 4247 is reminiscent of another young massive stellar object, HH80-81 $\approx 1.7 \times 10^4$ at 1.7 kpc)."
 HHIISO-81 contains a thermal radio jel centred on a collimated HIE flow that extends over 5 pe (Martietal.1993)., HH80-81 contains a thermal radio jet centred on a collimated HH flow that extends over 5 pc \citep{Marti93}.
. Evidence lor non-thermal radio emission has also been reported towards one of the HII emission knots., Evidence for non-thermal radio emission has also been reported towards one of the HH emission knots.
 Up until now this was the most Iuminous voung stellar object known to have a collimated jet., Up until now this was the most luminous young stellar object known to have a collimated jet.
" The 11.9-j/ image obtained in this study reveals a single unresolved (< 0.6 "")) emission source with a flux of 0.28 Jv. albeit there may be Iess-Iuminous objects present (hat are below (he sensitivity limit of (he observations."," The $\mu$ m image obtained in this study reveals a single unresolved $<$ 0.6 ) emission source with a flux of 0.28 Jy, albeit there may be less-luminous objects present that are below the sensitivity limit of the observations."
 Within the positional uncertainty of the mid-inlrared data. this source is coincident. wilh (the radio jet.," Within the positional uncertainty of the mid-infrared data, this source is coincident with the radio jet."
 The flux is consistent with the spectral enerev distribution for IRAS 16547—4247 shown in Garayetal.(2003)., The flux is consistent with the spectral energy distribution for IRAS $-$ 4247 shown in \citet{Garay03}.
. According to the relationship between jet raclio-lnminosity and outflow momentum rate reported by Angladaetal.(1998).. extrapolated to the high-mass regime. the IAS outflow should have a momentum rate of 0.2 | dan ft.," According to the relationship between jet radio-luminosity and outflow momentum rate reported by \citet{Anglada98}, extrapolated to the high-mass regime, the IRAS 16547--4247 outflow should have a momentum rate of 0.2 $^{-1}$ km $^{-1}$."
 This mechanical force can only be supplied by a driving source with a Iuninositv of z10? citepBeut her02.., This mechanical force can only be supplied by a driving source with a luminosity of $ \approx 10^5$ \\citep{Beuther02}. .
 The measured luminosity for IRAS 16547.4247 is 6.2x10!..," The measured luminosity for IRAS 16547–4247 is $6.2
\times 10^4$."
 Therefore we argue that the radio jet and the IIS collimated flow are powered by (he same single Iuminous object., Therefore we argue that the radio jet and the $_2$ collimated flow are powered by the same single luminous object.
" Furthermore. it is reasonable to suppose that the detected 11.9-, emission source is associated with this luninous object."," Furthermore, it is reasonable to suppose that the detected $\mu$ m emission source is associated with this luminous object."
 IRAS 16547-4247 is the most luminous embedded: pre-main sequence source in the Galaxy known (o harbor a thermal radio jet., IRAS $-$ 4247 is the most luminous embedded pre-main sequence source in the Galaxy known to harbor a thermal radio jet.
 We have detected a chain of I 2.12 jm emission knots towards IRAS 16547—4247 that delineate a collimated [low extending; over 1.5 pe., We have detected a chain of $_2$ 2.12 $\mu$ m emission knots towards IRAS $-$ 4247 that delineate a collimated flow extending over 1.5 pc.
 The geometryof the flow implies that it is driven by the thermal jet., The geometryof the flow implies that it is driven by the thermal jet.
 We have also, We have also
clistance scale shows that gradients of a-elements across (he Galactic disk are moclerate. and depend on the age of the PN population considered.,"distance scale shows that gradients of $\alpha$ -elements across the Galactic disk are moderate, and depend on the age of the PN population considered."
 The amplitude of these gradients agree with the metallicity dispersion observed in the solar vicinity. which arises mainly from (he radial mixing of stars through the disk.," The amplitude of these gradients agree with the metallicity dispersion observed in the solar vicinity, which arises mainly from the radial mixing of stars through the disk."
 Planetary nebulae wilh voung progenitors show sleeper gradient slopes than in the old populations. indicating that a-element gradients are steepening with time.," Planetary nebulae with young progenitors show steeper gradient slopes than in the old populations, indicating that $\alpha$ -element gradients are steepening with time."
 The results are statistically sound. and do not depend very much on the distance scale. as long as it is Magellanic Cloud-calibratec.," The results are statistically sound, and do not depend very much on the distance scale, as long as it is Magellanic Cloud-calibrated."
 Gracients of oxvgen and iron abundance from voung (voung stars ancl I II regions) and intermediate-age (open clusters) populations agree with those of PNe derived here. eiving strength to the scenario of gradients steepening with Gime.," Gradients of oxygen and iron abundance from young (young stars and H II regions) and intermediate-age (open clusters) populations agree with those of PNe derived here, giving strength to the scenario of gradients steepening with time."
 The oxveen eraclient is found (o increase from near-Iat racial abundance distribution in Tvpe III PNe. those whose progenitors are in the lowest mass range for AGB stars. to -0.035 dex + for Type I PNe. those with the most massive progenitors.," The oxygen gradient is found to increase from near-flat radial abundance distribution in Type III PNe, those whose progenitors are in the lowest mass range for AGB stars, to -0.035 dex $^{-1}$ for Type I PNe, those with the most massive progenitors."
 These results contradiet recent claim that gradients are flattening with time. and strongly suggest that such constraints should be taken with some caution.," These results contradict recent claim that gradients are flattening with time, and strongly suggest that such constraints should be taken with some caution."
 The data ou PNe are still sparse and the new distance scale. although significantlv improved. could still be affected by uncertainties.," The data on PNe are still sparse and the new distance scale, although significantly improved, could still be affected by uncertainties."
 In addition. abundance gradients for older populations of PNe Gn particular the Tvpe HIE sample) might be affected by migration. which tends to flatten such gradients.," In addition, abundance gradients for older populations of PNe (in particular the Type III sample) might be affected by migration, which tends to flatten such gradients."
 However. we find it unlikely that eradients in the old PN population could reach values as high as those found in some recent studies (e.g Maciel Costa 2009). and (his is confirmed by (the old open cluster population with high resolution spectroscopic abundance determinations.," However, we find it unlikely that gradients in the old PN population could reach values as high as those found in some recent studies (e.g Maciel Costa 2009), and this is confirmed by the old open cluster population with high resolution spectroscopic abundance determinations."
 Letizia Stanghellini warmly thanks Drs., Letizia Stanghellini warmly thanks Drs.
 Francoise Combes and Francois Hammer for (heir hospitality at the Observatoire de Paris (Paris and Meudon). where (his work has been conceived and completed.," Francoise Combes and Francois Hammer for their hospitality at the Observatoire de Paris (Paris and Meudon), where this work has been conceived and completed."
 We acknowledge scientific discussions with Drs., We acknowledge scientific discussions with Drs.
 Bruce Dalick. Laura Magrini. Karen Ixvitter. Richard Henry. Angela Bragaglia. Monica Tosi. and Mark," Bruce Balick, Laura Magrini, Karen Kwitter, Richard Henry, Angela Bragaglia, Monica Tosi, and Mark"
were likely to be synthesized in supernovae originated from massive stars rather than SNe Ia. The Mn/Fe ratio is an important indicator to distinguish products of thermonuclear SNe (SNe Ia) from those of other core-collapse supernovae.,were likely to be synthesized in supernovae originated from massive stars rather than SNe Ia. The Mn/Fe ratio is an important indicator to distinguish products of thermonuclear SNe (SNe Ia) from those of other core-collapse supernovae.
" In fact, theoretical models of SNe Ia have predicted [Mn/Fe]~0 in the ejecta (e.g.,Nomoto,Thielemann,&Yokoi1984;Khokhlov 1991)."," In fact, theoretical models of SNe Ia have predicted $\sim0$ in the ejecta \citep[e.g.,][]{Nomoto_84, Khokhlov_91}."
". Hence, if SNe Ia contributed to Mn and Fe in a low-o star, the [Mn/Fe] ratio would become greater than —0.4."," Hence, if SNe Ia contributed to Mn and Fe in a $\alpha$ star, the [Mn/Fe] ratio would become greater than $-0.4$."
 An IMF different from that of Galactic halo stars would also result in [Mn/Fe] ratios different from ~—0.4., An IMF different from that of Galactic halo stars would also result in [Mn/Fe] ratios different from $\sim -0.4$.
" Furthermore, a short timescale of the star formation inferred from the observed s-/r-process element ratios strongly suggests that SNe Ia cannot supply heavy elements to dSph stars."," Furthermore, a short timescale of the star formation inferred from the observed $s$ $r$ -process element ratios strongly suggests that SNe Ia cannot supply heavy elements to dSph stars."
" As already discussed in Tsujimoto&Shigeyama(2002,2003),, the observed Ba/Eu (or La/Eu) ratios of dSph stars are very close to the pure r-process ratio (Shetroneetal.2001, 2003),, which implies that few of dSph stars had evolved through AGB or supplied s-process elements to other dSph stars till the end of the star formation epoch."," As already discussed in \citet{Tsujimoto_02, Tsujimoto_03}, the observed Ba/Eu (or La/Eu) ratios of dSph stars are very close to the pure $r$ -process ratio \citep{Shetrone_01b,Shetrone_03}, , which implies that few of dSph stars had evolved through AGB or supplied $s$ -process elements to other dSph stars till the end of the star formation epoch."
 Thus the timescale of the star formation in these dSph galaxies needs to be less than a few times 10° yr., Thus the timescale of the star formation in these dSph galaxies needs to be less than a few times $10^8$ yr.
" On the other hand, the progenitor of a SN Ia requires a longer time scale to accrete matter enough to reach the Chandrasekhar mass limit."," On the other hand, the progenitor of a SN Ia requires a longer time scale to accrete matter enough to reach the Chandrasekhar mass limit."
" In this way, the origin of stars with low a/Fe ratios in dSph galaxies is still controversial."," In this way, the origin of stars with low $\alpha$ /Fe ratios in dSph galaxies is still controversial."
" In addition, a detailed comparison of elemental abundances of stars in the Galactic halo with those in dSph galaxies casts a doubt on the argument that low-a stars in the Galactic halo are originated from low-a stars that have once belonged to dSph galaxies (Fulbright2002)."," In addition, a detailed comparison of elemental abundances of stars in the Galactic halo with those in dSph galaxies casts a doubt on the argument that $\alpha$ stars in the Galactic halo are originated from $\alpha$ stars that have once belonged to dSph galaxies \citep{Fulbright_02}."
". In thisletter, we will propose a mechanism to explain the origin of heavy elements in these low-o stars."," In this, we will propose a mechanism to explain the origin of heavy elements in these $\alpha$ stars."
" There are other low-a stars without information on Mn/Fe ratios in young globular clusters Pal 12 and Ruprecht 106 (Brown,Wallerstein,&Zucker1997).", There are other $\alpha$ stars without information on Mn/Fe ratios in young globular clusters Pal 12 and Ruprecht 106 \citep{Brown_97}.
". The proper motion pair HD 134439/40 also exhibit low a/Fe ratios (King1997),, though their Mn/Fe ratios have not been measured."," The proper motion pair HD 134439/40 also exhibit low $\alpha$ /Fe ratios \citep{King_97}, though their Mn/Fe ratios have not been measured."
 We will also imply the origin of these low-a stars based on our scenario., We will also imply the origin of these $\alpha$ stars based on our scenario.
" In the next section, the surface gravities and effective temperatures of nearby low-a stars are investigated."," In the next section, the surface gravities and effective temperatures of nearby $\alpha$ stars are investigated."
" In §3, we discuss the relation between stellar elemental abundances in dSph galaxies and those in damped Ly α (DLA) absorbers."," In 3, we discuss the relation between stellar elemental abundances in dSph galaxies and those in damped Ly $\alpha$ (DLA) absorbers."
" In §4, a mechanism is proposed to explain metal-poor stars with low a/Fe ratios both in the Galaxy and in dSph galaxies in a unified manner."," In 4, a mechanism is proposed to explain metal-poor stars with low $\alpha$ /Fe ratios both in the Galaxy and in dSph galaxies in a unified manner."
" In 85, conclusions are presented and we discuss some observations to test the proposed mechanism."," In 5, conclusions are presented and we discuss some observations to test the proposed mechanism."
 If the nearby stars with [Fe/H]« —1 observed by Grattonetal.(2003) are plotted in a logg—Teg plane (Fig., If the nearby stars with $<-1$ observed by \citet{Gratton_03} are plotted in a $\log g-T_{\rm eff}$ plane (Fig.
" 2a), all the metal-poor stars with [Mg/Fe]<0.3 are located in a region limited by logg>4.1 showing that these stars are on the main-sequence."," 2a), all the metal-poor stars with $<0.3$ are located in a region limited by $\log g>4.1$ showing that these stars are on the main-sequence."
 Thus we will refer subgiants to stars with logg«4.1 in the following., Thus we will refer subgiants to stars with $\log g<4.1$ in the following.
" On the contrary, stars with [Mg/Fe]>0.3 resides both in dwarf and subgiant (red giant) branches."," On the contrary, stars with $>0.3$ resides both in dwarf and subgiant (red giant) branches."
" As a result, the elemental abundance pattern of dwarfs in the [Mg/Fe]— [Fe/H] plane (open circles in Fig."," As a result, the elemental abundance pattern of dwarfs in the $-$ [Fe/H] plane (open circles in Fig."
 1) have a larger dispersion than that of subgiants., 1) have a larger dispersion than that of subgiants.
 The same feature is seen for other elements like Na and Zn (Fig., The same feature is seen for other elements like Na and Zn (Fig.
" 2b, c)."," 2b, c)."
 Stars with low Na/Fe and Zn/Fe ratios also reside only on the main-sequence., Stars with low Na/Fe and Zn/Fe ratios also reside only on the main-sequence.
 These results suggest that the abundance features observed in the low-o stars were not solely determined by heavy elements in the ISM from which these stars were formed., These results suggest that the abundance features observed in the $\alpha$ stars were not solely determined by heavy elements in the ISM from which these stars were formed.
 Hence some mechanisms in addition to SN nucleosynthesis are needed to explain the observed elemental abundances., Hence some mechanisms in addition to SN nucleosynthesis are needed to explain the observed elemental abundances.
" In fact, the low-a stars observed by Grattonetal.(2003) have Mn/Fe ratios similar to those of the other halo stars."," In fact, the $\alpha$ stars observed by \citet{Gratton_03} have Mn/Fe ratios similar to those of the other halo stars."
" Furthermore, old stars on the main-sequence cannot alter the surface abundances of Mn, Fe, and Zn by nuclear reactions operating inside them."," Furthermore, old stars on the main-sequence cannot alter the surface abundances of Mn, Fe, and Zn by nuclear reactions operating inside them."
 Therefore the only mechanism to explain the observed feature would be the external pollution that brings some heavy elements into the shallow surface convection zone of a dwarf to significantly alter its surface elemental abundances., Therefore the only mechanism to explain the observed feature would be the external pollution that brings some heavy elements into the shallow surface convection zone of a dwarf to significantly alter its surface elemental abundances.
" For example, the accretion of ~0.1Ma Fe would reduce the abundance ratio [Mg/Fe] on the surfaceof a 0.8 M dwarf with [Fe/H]——1.5 by ~0.3 dex."," For example, the accretion of $\sim0.1\,M_\oplus$ Fe would reduce the abundance ratio [Mg/Fe] on the surfaceof a 0.8 $\Msun$ dwarf with $=-1.5$ by $\sim0.3$ dex."
" As the star turns off the main-sequence, the mass of the surface convection zone will increase by a factor of more than 100 and reduce the"," As the star turns off the main-sequence, the mass of the surface convection zone will increase by a factor of more than 100 and reduce the"
"ay20.00255, The corresponding mass of the blob is where έως is the mass in the nebula. and in the first equality we assume that the blob density is about equal to the density in the nebula.","$a_b \ga 0.0025 r_0$ The corresponding mass of the blob is where $M_{\rm neb}$ is the mass in the nebula, and in the first equality we assume that the blob density is about equal to the density in the nebula."
 To survive. the blob must be thermally isolated from the surrounding (otherwise it will be evaporated).," To survive, the blob must be thermally isolated from the surrounding (otherwise it will be evaporated)."
 We assume that tangled magnetic fields within the blob isolate the surviving blobs., We assume that tangled magnetic fields within the blob isolate the surviving blobs.
 We cannot estimate the number of surviving blobs. bul (he requirements of (7) an initial perturbation that will form a blob with negative radial velocity of ej~10kms.!. GP) a large enough blobto maintain its speed. and (7/7) suppression of heat conduction bv magnetic fields. suggest that their number will be limited.," We cannot estimate the number of surviving blobs, but the requirements of $i$ ) an initial perturbation that will form a blob with negative radial velocity of $v_b \sim 10 \km \s^{-1}$, $ii$ ) a large enough blobto maintain its speed, and $iii$ ) suppression of heat conduction by magnetic fields, suggest that their number will be limited."
" We scale the number of blobs by AN,=1000.", We scale the number of blobs by $N_b = 1000$.
 As long as the dense blob flows inward inside the hot bubble it does not feel (he ram pressure of the fast wind., As long as the dense blob flows inward inside the hot bubble it does not feel the ram pressure of the fast wind.
 When it gets out of the hot bubble through the inner boundary (reverse shock). the fast wind hits the blob directly. exerting a force of PF=pregnas. where py is the density of the fast wind.," When it gets out of the hot bubble through the inner boundary (reverse shock), the fast wind hits the blob directly, exerting a force of $F_{\rm ram}= \rho_f v_f^2 \pi a_b^2$, where $\rho_f$ is the density of the fast wind."
" The deceleration is Cyan=Phu/M,.", The deceleration is $a_{\rm ram}= F_{\rm ram}/M_b$.
 Using this valuewe find the distance over which the blob will stop. rash(5/25. to be While inside the hot bubble the density in the blob is determined by pressure equilibrium with the hot bubble.," Using this valuewe find the distance over which the blob will stop, $r_{\rm stop} \simeq v_b^2/2 a_{\rm ram}$, to be While inside the hot bubble the density in the blob is determined by pressure equilibrium with the hot bubble."
 Close to the inner boundary of the hot bubble. riae. (e pressure is about equal to (he ram pressure of the last wind there. and so is the blob pressure.," Close to the inner boundary of the hot bubble, $r_{\rm bubble}$, the pressure is about equal to the ram pressure of the fast wind there, and so is the blob pressure."
 This eves ppcρα)”. where ej10kms.! is the sound speed in the blob.," This gives $\rho_b \simeq \rho_f (v_f/c_0)^2$, where $c_0 \simeq 10 \km
\s^{-1}$ is the sound speed in the blob."
 In our scenario eyC9ey. and we find from equation (6)) the condition for the blob to reach the center to be 052lue:," In our scenario $c_0 \simeq {v_b}$, and we find from equation \ref{rstop1}) ) the condition for the blob to reach the center to be $a_b \ga r_{\rm bubble}$."
 Namely. the blob must be large when it gets out of the hot bubble: we'll come back to (his point later.," Namely, the blob must be large when it gets out of the hot bubble; we'll come back to this point later."
" Equating the ram pressure (o the pressure in (he blob ""n~mez. and substituting for the fast wind density py=πμ). and for the density in the blob My /(4x07/3). we can isolate αν."," Equating the ram pressure to the pressure in the blob $\rho_f v_f^2
\simeq \rho_b c_0^2$, and substituting for the fast wind density $\rho_f = \dot M_f/(4 \pi r^2
v_f)$, and for the density in the blob $M_b/(4 \pi a_b^3/3)$ , we can isolate $a_b$ ."
 Inserting this expression for the blob radius αν in the condition ayZμις , Inserting this expression for the blob radius $a_b$ in the condition $a_b \ga r_{\rm bubble}$ 
solution.,solution.
 Thus the topology can be controlled via the signs and ratio of these currents., Thus the topology can be controlled via the signs and ratio of these currents.
 In inverse-topologv cases (he shear- and plasma-induced currents are flowing in the same axial direction., In inverse-topology cases the shear- and plasma-induced currents are flowing in the same axial direction.
 Normal-topologv cases have additional complexity because the axiallv-directed currents associated with the shear and the plasma forces are [lowing in opposite directions., Normal-topology cases have additional complexity because the axially-directed currents associated with the shear and the plasma forces are flowing in opposite directions.
 An example is shown in Figure 11.., An example is shown in Figure \ref{normalsole}.
 FINESSE is less suited to the ealeulation of normal prominences (han of inverse prominences because it is designed to find equilibria with e=0 al the magnetic axis and &>0 evervwhere else. with maximum on the boundary.," FINESSE is less suited to the calculation of normal prominences than of inverse prominences because it is designed to find equilibria with $\psi =0$ at the magnetic axis and $\psi >0$ everywhere else, with maximum on the boundary."
 The flux [function of a normal prominence has a local mininunm al the magnetic axis but. since the overlving bipolar arcade and (he lower half of the flux rope must have flux traveling in the same horizontal direction. the flux function must have a saddle point above the [lux rope. above which the [lux function must decrease with height (see Figure 1)).," The flux function of a normal prominence has a local minimum at the magnetic axis but, since the overlying bipolar arcade and the lower half of the flux rope must have flux traveling in the same horizontal direction, the flux function must have a saddle point above the flux rope, above which the flux function must decrease with height (see Figure \ref{topologies}) )."
 The example in Figure 11. has such a saddle point [ar above the flix rope outside the field of view of the plot., The example in Figure \ref{normalsole} has such a saddle point far above the flux rope outside the field of view of the plot.
 ]t is not vet clear how to incorporate this aud other topological complications in a controlled WM., It is not yet clear how to incorporate this and other topological complications in a controlled way.
 A major obstacle in the wav of understanding solar activity is the difficulty of capturing in models the complexity of the plasma dvnamics and of the magnetic field structure., A major obstacle in the way of understanding solar activity is the difficulty of capturing in models the complexity of the plasma dynamics and of the magnetic field structure.
 For (his reason. most recent efforts to model the solar atmosphere have attempted (o recreate as [ar as practically possible the full 3D geometrical complexity. of (he physical parameters (e.g. Amari et al.," For this reason, most recent efforts to model the solar atmosphere have attempted to recreate as far as practically possible the full 3D geometrical complexity of the physical parameters (e.g. Amari et al."
 2003a. 2003b. Roussey οἱ al.," 2003a, 2003b, Roussev et al."
 2003. Wiegelmann Neukireh 2006).," 2003, Wiegelmann Neukirch 2006)."
 Here we have adopted the alternative approach. following Low IHundhlausen (1995) and Low Zhang (2004). of studving a simple generic plivsical svstem: a single solar prominence plasma enhancement suspended in a near-potential coronal magnetic field.," Here we have adopted the alternative approach, following Low Hundhausen (1995) and Low Zhang (2004), of studying a simple generic physical system: a single solar prominence plasma enhancement suspended in a near-potential coronal magnetic field."
 We have given new numerical magnetohvdrostatie solutions describing the gravitationally stratified. bulk equilibrium of cool. dense prominence plasma embedded in the near-potential coronal field.," We have given new numerical magnetohydrostatic solutions describing the gravitationally stratified, bulk equilibrium of cool, dense prominence plasma embedded in the near-potential coronal field."
 These solutions are calculated: using the FINESSE magnetohyvdrodynamics equilibrium solver aud describe the morphologies of magnetic field distributions in and around prominences and the cool prominence plasma that these fields support., These solutions are calculated using the FINESSE magnetohydrodynamics equilibrium solver and describe the morphologies of magnetic field distributions in and around prominences and the cool prominence plasma that these fields support.
 The new solutions were not accessible by previous analytical techniques., The new solutions were not accessible by previous analytical techniques.
 The numerical method allows us to prescribe in a controlled wav the temperature or entropy as a function of the magnetic [lux funcüon. enabling flexibiliix of choice of the physical parameter distributions.," The numerical method allows us to prescribe in a controlled way the temperature or entropy as a function of the magnetic flux function, enabling flexibility of choice of the physical parameter distributions."
 We focussed on new solutions wilh a range of values of the temperature. (he magnetic shear. the polvtropic index aud with large temperature variations perpendicular to the magnetic field.," We focussed on new solutions with a range of values of the temperature, the magnetic shear, the polytropic index and with large temperature variations perpendicular to the magnetic field."
 The axial component of the magnetic field gave demonstrably increased structural integrity, The axial component of the magnetic field gave demonstrably increased structural integrity
Assundug recent eclipse durations of 107.5τε 6.0ss. we obtain the relationship shown in Fig. 1..,"Assuming recent eclipse durations of $497.5\pm6.0$ s, we obtain the relationship shown in Fig. \ref{QvsIncFig}."
 We can attempt to further constrain the available parameter space iu other wavs., We can attempt to further constrain the available parameter space in other ways.
 The fact that we see the sharp neutron star eclipse at all indicates that iis not an accretiou disk corona (ADC) source., The fact that we see the sharp neutron star eclipse at all indicates that is not an accretion disk corona (ADC) source.
 This neans the inclination cannot be too high as our line-ofsight must pass over the disk rim., This means the inclination cannot be too high as our line-of-sight must pass over the disk rim.
 The disk rim weight is uot known directly. but must be ereater than hat expected from lydrostatic support alone.," The disk rim height is not known directly, but must be greater than that expected from hydrostatic support alone."
 This is a very weak coustraint. however: for example. for a disk. iidf-thickuess of 0.03. we only require ὁSS.37.," This is a very weak constraint, however; for example, for a disk half-thickness of 0.03, we only require $i < 88.3^{\circ}$."
 Thisconstraint is shown in Fie. 1.., Thisconstraint is shown in Fig. \ref{QvsIncFig}.
 Other constraints are more modeldependeut., Other constraints are more model-dependent.
 We ca- uake plausible estimates of the range of mass ratio:να ikehv. although values outside of this range are stiLB xossible.," We can make plausible estimates of the range of mass ratios likely, although values outside of this range are still possible."
 The companion star to ls probably above the hydrogen burning lait aud , The companion star to is probably above the hydrogen burning limit and non-degenerate.
This implies fo20.07 MAL. (Chabrier&Daraffe 2000).., This implies $M_2 \ga 0.07$ $_{\odot}$ \citep{Chabrier:2000a}.
. Assuming a MM... neutron star (Thorsett&Chakrabarty1999). then vields a niin lass ratio of 0.05., Assuming a $_{\odot}$ neutron star \citep{Thorsett:1999a} then yields a minimum mass ratio of 0.05.
 This limit is soft. as a iore massive neutron star is certainly possible if it has accreted sjenificaut mass from the companion (as secus Likely in 28 0921630: Shahbazetal.2001: Jonkeroetal. 20053).," This limit is soft, as a more massive neutron star is certainly possible if it has accreted significant mass from the companion (as seems likely in 2S 0921–630; \citealt{Shahbaz:2004a}; \citealt{Jonker:2005a}) )."
 At the high mass-ratio eud. we can assume that he companion star is uuderdenuse compared to a miain-sequence star that would fill the Roche lobe.," At the high mass-ratio end, we can assume that the companion star is underdense compared to a main-sequence star that would fill the Roche lobe."
 Again assumniue a MAL. neutrou star this vields the upper iuit on the mass ratio shown., Again assuming a $_{\odot}$ neutron star this yields the upper limit on the mass ratio shown.
 This could be increased a ittle for a somewhat lower mass neutron star. aud further if the companion is actually overdeuse.," This could be increased a little for a somewhat lower mass neutron star, and further if the companion is actually overdense."
 This is possible if he companion had undergone nuclear evolution. before osing most of its cuvelope in mass transfer (Schenker&Wing 2002: Haswelletal. 2002)).," This is possible if the companion had undergone nuclear evolution, before losing most of its envelope in mass transfer \citealt{Schenker:2002a}; \citealt{Haswell:2002a}) )."
 In this case the jeutron star nüeht also be expected to be more massive., In this case the neutron star might also be expected to be more massive.
 Consequently. there is probably not much scope for a uass ratio hieher than 0. lim this svstem.," Consequently, there is probably not much scope for a mass ratio higher than 0.4 in this system."
 It should be noted that the coustraiuts considered so nr aro effectivelv the same as obtained by Parmaretal. (1986).. namely 7575«ob««cN27.," It should be noted that the constraints considered so far are effectively the same as obtained by \citet{Parmar:1986a}, namely $75^{\circ} < i < 82^{\circ}$."
 As discussed above. he lmits are rather soft. and a slightly larger range is possible with a companion star and/or neutron star with extreme properties.," As discussed above, the limits are rather soft, and a slightly larger range is possible with a companion star and/or neutron star with extreme properties."
 To obtain other parameters of interest. we svutlesize a population of possible binaries.," To obtain other parameters of interest, we synthesize a population of possible binaries."
 We assume the known orbital period. aud the relationship between mass ratio and inclination eiven in Fie. 1..," We assume the known orbital period, and the relationship between mass ratio and inclination given in Fig. \ref{QvsIncFig}."
" We consider neutron star nasses with an asvuuuetric Caussian distribution 1.3585, MM. ic. following (Thorsett&Chakrabarty1999).. but allowing for a higher mass tail due to mass rauster,"," We consider neutron star masses with an asymmetric Gaussian distribution $M_1 =
1.35^{+0.2}_{-0.04}$ $_{\odot}$, i.e., following \citep{Thorsett:1999a}, but allowing for a higher mass tail due to mass transfer."
 We asstune a wnifori distribution of coumpaniou star mnasses between MAL... aud the mass at which ualn-sequence density is reached.," We assume a uniform distribution of companion star masses between $_{\odot}$, and the mass at which main-sequence density is reached."
 We derive a relatively narrow range of binary separations. (1.0340.05)«1013 ec (at uuarv period is known aud there is not a larec uncertainty in the total svsteni mass.," We derive a relatively narrow range of binary separations, $(1.03\pm0.05)\times 10^{11}$ cm (at binary period is known and there is not a large uncertainty in the total system mass."
 Disk parameters are more uncertain: the tidal truncation racius is (0.50+105)«10Hσσ and the projected area of a flat dis- would be (1.5+0.2)οςIO een?," Disk parameters are more uncertain; the tidal truncation radius is $(0.50\pm0.05)\times 10^{11}$ cm and the projected area of a flat disk would be $(1.5\pm0.2)\times
10^{21}$ $^2$."
" The projected area of the companion star. with a spherical approximation. would be (2.020.9)«107 ceni,"," The projected area of the companion star, with a spherical approximation, would be $(2.0\pm0.9)\times 10^{21}$ $^2$."
 While in general. the conrpaiion is expected to subtend a larger projected area than the disk. oulv a plase-depeudeut fraction of this will be X-rav heated. so this should be considered au upper luit on the area of the huninous regious of the companion. which could be significantly less than that of the disk.," While in general, the companion is expected to subtend a larger projected area than the disk, only a phase-dependent fraction of this will be X-ray heated, so this should be considered an upper limit on the area of the luminous regions of the companion, which could be significantly less than that of the disk."
 We cau estimate light travel times in the same way., We can estimate light travel times in the same way.
 The maxima lag from the pole of the companion star would be (6.8+ 0.3)9x at phase 0.5. although most. of he heated inner face would of course be a little shorter han this.," The maximum lag from the pole of the companion star would be $(6.8\pm0.3)$ s at phase 0.5, although most of the heated inner face would of course be a little shorter than this."
" Laes from the disk would be expected to span a range from zero to (3.350,3) ss assiuniue it extends to he tidal txuncatiou radius.", Lags from the disk would be expected to span a range from zero to $(3.3\pm0.3)$ s assuming it extends to the tidal truncation radius.
 We define several test cases consistent with Fig. 1:, We define several test cases consistent with Fig. \ref{QvsIncFig}:
 uodel 1 has 4=0.08. ;=82.," model 1 has $q=0.08$, $i=82^{\circ}$."
" Model 2 has 4=0.2. i=7S"". and model 3 has g=(0.314. ;/=75.57."," Model 2 has $q=0.2$, $i=78^{\circ}$, and model 3 has $q=0.34$, $i=75.5^{\circ}$."
 Fie., Fig.
 2 shows a schematic view corresponding to modcl 2 at phases when bursts were observed., \ref{BinSimFig} shows a schematic view corresponding to model 2 at phases when bursts were observed.
 Au important factor in considering radiation of the colupalion star is the opening angle of the disk. 0.," An important factor in considering irradiation of the companion star is the opening angle of the disk, $\beta$."
 For our purposes. this defines the height of X-ray absorbing material which may be above the optical photosplere. and may not be in livdvrostatic equilibrimm (for example material thrown up from the stream impact point or local flares}.," For our purposes, this defines the height of X-ray absorbing material, which may be above the optical photosphere, and may not be in hydrostatic equilibrium (for example material thrown up from the stream impact point or local flares)."
 Values derived from other objects have generally been rather high., Values derived from other objects have generally been rather high.
" deJong.vanParadijs.&Augusteiju(1996) derived ;=12"" aud cite other authors who obtained a range of 117.", \citet{deJong:1996a} derived $\beta=12^{\circ}$ and cite other authors who obtained a range of $^{\circ}$.
 Iu our case. the highest values are ruled out iu some models. as iis nof an ADC source we see neutron star eclipses aud prominent bursts. hence we do observe the neutron star directly.," In our case, the highest values are ruled out in some models, as is not an ADC source – we see neutron star eclipses and prominent bursts, hence we do observe the neutron star directly."
 Thus the opening angle iust be less than 90./. lless than 12° for model 1 aud less than 8? for model 2.," Thus the opening angle must be less than $90-i$, less than $12^{\circ}$ for model 1 and less than $8^{\circ}$ for model 2."
 This is not a constraint for model 3., This is not a constraint for model 3.
 Note that the presence of eclipses also indicates that at least some of the companion star must be exposed to direct radiation from the neutron star: it caunot be fully sbhielded by the cixk., Note that the presence of eclipses also indicates that at least some of the companion star must be exposed to direct radiation from the neutron star; it cannot be fully shielded by the disk.
 A final important parameter is the distance to Vol., A final important parameter is the distance to .
 The best indicator of this is iu neutrou star LAINBs is the peak flux observed during radius expansion X-ray bursts as this is believed to be an approximate standard, The best indicator of this is in neutron star LMXBs is the peak flux observed during radius expansion X-ray bursts as this is believed to be an approximate standard
"For the entire sample of 75 galaxies. we find an increase in (he structure map rnis o, wilh the barstveneth Qy. although with substantial scatter ancl evidence (he relation appears to (urn over αἱ laree Qj.","For the entire sample of 75 galaxies, we find an increase in the structure map rms $\sigma_{\mbox{\scriptsize sm}}$ with the barstrength $Q_b$, although with substantial scatter and evidence the relation appears to turn over at large $Q_b$."
 The observed increase in dust structure may be due to increased star formation rates. which are correlated with the gas surface density via the global Schmidt law (Schmidt1959:IXennicutt.1993).," The observed increase in dust structure may be due to increased star formation rates, which are correlated with the gas surface density via the global Schmidt law \citep{schmidt59, kennicutt98}."
". The structure maps for the twelve most strongly. barred ealaxies in our sample (Q,> 0.4) are shown in Figure 11..", The structure maps for the twelve most strongly barred galaxies in our sample $Q_b \ge 0.4$ ) are shown in Figure \ref{fig:strong}.
 OF these twelve. five have LGD spirals. two of which end at a circumnuclear ring.," Of these twelve, five have LGD spirals, two of which end at a circumnuclear ring."
 The other seven have either chaotic or chaotic spiral nuclear dust morphology (5 C. 2 CS).," The other seven have either chaotic or chaotic spiral nuclear dust morphology (5 C, 2 CS)."
 As a cireumnuclear ring is associated with nuclear star formation. and the chaotic structures seen in these strongly barred galaxies could potentially be related to star formation. it would be interesting to investigate the relationship between nuclear star formationrates. circumuuclear dust morphology. dust structure oy). and barstreugth.," As a circumnuclear ring is associated with nuclear star formation, and the chaotic structures seen in these strongly barred galaxies could potentially be related to star formation, it would be interesting to investigate the relationship between nuclear star formationrates, circumnuclear dust morphology, dust structure $\sigma_{\mbox{\scriptsize
sm}}$ , and barstrength."
 , 
à scenario that the explosion ts less energetic than a canonical supernova (ie. E«IO?! ergs). which is consistent with the conclusion drawn by Mavromatakis et al. (,"a scenario that the explosion is less energetic than a canonical supernova (i.e. $E<10^{51}$ ergs), which is consistent with the conclusion drawn by Mavromatakis et al. ("
2001) from their optical study.,2001) from their optical study.
 Assuming that the remnant us the result of a low energy supernova explosion has interesting implications for the properties of its progenitor., Assuming that the remnant is the result of a low energy supernova explosion has interesting implications for the properties of its progenitor.
 In the context of the current understanding in stellar evolution. a supernova with kinetic energy of ~10°° ergs can be a result of two different evolutionary tracks.," In the context of the current understanding in stellar evolution, a supernova with kinetic energy of $\sim10^{50}$ ergs can be a result of two different evolutionary tracks."
 In the first scenario. a Oxygen-Neon-Magnesium (ONeMg) core can be formed before Neon and subsequent nuclear burning take place.," In the first scenario, a Oxygen-Neon-Magnesium (ONeMg) core can be formed before Neon and subsequent nuclear burning take place."
 If the neutrino cooling 1s efficient enough. the core temperature will be reduced and prevents further nuclear fusion.," If the neutrino cooling is efficient enough, the core temperature will be reduced and prevents further nuclear fusion."
 When the ONeMsg core reaches the Chandrasakar mass. the electron degenerate pressure is no longer able to support the core.," When the ONeMg core reaches the Chandrasakar mass, the electron degenerate pressure is no longer able to support the core."
" Furthermore. electron capture by Meg and ""Ne will further reduce the electron degenerate pressure in the core and trigger the core to collapse (Miyaji et al."," Furthermore, electron capture by $^{24}$ Mg and $^{20}$ Ne will further reduce the electron degenerate pressure in the core and trigger the core to collapse (Miyaji et al."
 1980: Gutiérrrez. Canal Garea-Berro 2005).," 1980; Gutiérrrez, Canal Garca-Berro 2005)."
 This ts known as the electron-capture supernova., This is known as the electron-capture supernova.
 Most simulations have shown that this type of explosion has a rather low energy (see Eldridge. Mattila. Smartt 2007).," Most simulations have shown that this type of explosion has a rather low energy (see Eldridge, Mattila, Smartt 2007)."
 The progenitor's Nass of an electron-capture supernova is limited in a narrow range of ~6—8 M. (Eldridge. Mattila. Smartt 2007).," The progenitor's mass of an electron-capture supernova is limited in a narrow range of $\sim6-8$ $_{\odot}$ (Eldridge, Mattila, Smartt 2007)."
 For nore massive stars. they will go through all stages to silicon burning.," For more massive stars, they will go through all stages to silicon burning."
 In less massive stars. ONeMe cores cannot be formed.," In less massive stars, ONeMg cores cannot be formed."
 There is another possibility to produce a low energy supernova., There is another possibility to produce a low energy supernova.
 The exact evolution of a collapsing star after neutrino re-heating depends on the rate of early infall of stellar material on the collapsed core and on the binding energy of the envelope., The exact evolution of a collapsing star after neutrino re-heating depends on the rate of early infall of stellar material on the collapsed core and on the binding energy of the envelope.
 If both are large. which is the case in high-mass stars. the energy required to accelerate and heat up the ejecta is not available. preventing a successful explosion and resulting in a supernova which appears to be under-eergetic (see Heger et al.," If both are large, which is the case in high-mass stars, the energy required to accelerate and heat up the ejecta is not available, preventing a successful explosion and resulting in a supernova which appears to be under-energetic (see Heger et al."
 2003: Eldridge Tout 2004)., 2003; Eldridge Tout 2004).
 The progenitor of this evolutionary track is likely to be z20M..., The progenitor of this evolutionary track is likely to be $\gtrsim20M_{\odot}$.
 We have also discovered emission line features in. the remnant spectrum., We have also discovered emission line features in the remnant spectrum.
 The feature at E=4.0+0.2 keV is detected only in the northern rim., The feature at $E=4.0\pm 0.2$ keV is detected only in the northern rim.
 The width of this feature (c=0.3 keV) is a little larger than the energy resolution of ACIS-I at 4 keV (re. c~0.1 keV)., The width of this feature $\sigma=0.3$ keV) is a little larger than the energy resolution of ACIS-I at 4 keV (i.e. $\sigma\sim0.1$ keV).
 This might indicate that the feature can be a blend of several lines., This might indicate that the feature can be a blend of several lines.
" Its energy centroid is close to a number of K emission lines from ""Ca and/or ""Sc (ef.", Its energy centroid is close to a number of K emission lines from $^{44}$ Ca and/or $^{44}$ Sc (cf.
 Table 5 in Lyudin et al., Table 5 in Iyudin et al.
 2005 and references therein)., 2005 and references therein).
 Therefore. we speculate that the feature at 4 keV can possibly comprises these lines.," Therefore, we speculate that the feature at 4 keV can possibly comprises these lines."
" If the identification is correct. if suggests a possible presence of Ti because both ""Ca and ""Se are produced in the decay chain "" Sc TiG""Ca."," If the identification is correct, it suggests a possible presence of $^{44}$ Ti because both $^{44}$ Ca and $^{44}$ Sc are produced in the decay chain $^{44}$ $\rightarrow$$^{44}$ $\rightarrow$$^{44}$ Ca."
 The half-life of Ti is ~60 yrs., The half-life of $^{44}$ Ti is $\sim60$ yrs.
" If the line feature at 4 keV is indeed from the decay of ΤΙ, its short half-life implies that the remnant should be rather young."," If the line feature at 4 keV is indeed from the decay of $^{44}$ Ti, its short half-life implies that the remnant should be rather young."
 Also. the production of Ti in the supernova is very sensitive to the explosion mechanism and the ejecta dynamics (see discussion in. [yudin et al.," Also, the production of $^{44}$ Ti in the supernova is very sensitive to the explosion mechanism and the ejecta dynamics (see discussion in Iyudin et al."
 2005)., 2005).
" Therefore. obtaining the yield and spatial distribution of ""Ti can help to further constrain the physical properties of the remnant as well as the nature of the progenitor."," Therefore, obtaining the yield and spatial distribution of $^{44}$ Ti can help to further constrain the physical properties of the remnant as well as the nature of the progenitor."
 On the other hand. the broadening of the feature can also result from the motion of the ejecta.," On the other hand, the broadening of the feature can also result from the motion of the ejecta."
" However. this would imply the ejecta to have a velocity of ~10000 km/s. This is not consistent with bbeing the result of a low energy supernova explosion as inferred from our X-ray data analysis as well from optical observation,"," However, this would imply the ejecta to have a velocity of $\sim10000$ km/s. This is not consistent with being the result of a low energy supernova explosion as inferred from our X-ray data analysis as well from optical observation."
 Furthermore. the limited energy resolution of imaging data precludes any accurate measurement of the line width.," Furthermore, the limited energy resolution of imaging data precludes any accurate measurement of the line width."
 High resolution grating spectroscopy is required to disentangle the possible blend of lines as well as determine their widths., High resolution grating spectroscopy is required to disentangle the possible blend of lines as well as determine their widths.
 Apart from the feature at + keV. we have also found a emission line feature at ~7 keV in both. the northern anc southern rims.," Apart from the feature at 4 keV, we have also found an emission line feature at $\sim7$ keV in both, the northern and southern rims."
 The large errors of the energy centroid and the width do not allow a firm identification., The large errors of the energy centroid and the width do not allow a firm identification.
 A deep observatio is required to better constrain these parameters., A deep observation is required to better constrain these parameters.
 We note that the approximate energy of the feature Is rather close to the Fe-K emission., We note that the approximate energy of the feature is rather close to the Fe-K emission.
" This leads us to speculate that the feature ca be a result from unresolved Fe K, and Kj lines.", This leads us to speculate that the feature can be a result from unresolved Fe $_\alpha$ and $_\beta$ lines.
" This also requires data with high spectroscopic resolution for further investigation,", This also requires data with high spectroscopic resolution for further investigation.
 The Chandra observation of aalso leads to the detection of X-ray point sources at the proximity of the remnant’s geometrical center., The Chandra observation of also leads to the detection of X-ray point sources at the proximity of the remnant's geometrical center.
 However. the limited photon. statistics do not allow a constraining spectral analysis of these sources.," However, the limited photon statistics do not allow a constraining spectral analysis of these sources."
 The non-detection of optical counterparts for παπά lleaves these two objects as possible candiates for a stellar compact remnant., The non-detection of optical counterparts for and leaves these two objects as possible candiates for a stellar compact remnant.
 A dedicated deep optical observation Is desirable to better constraining the nature of the point sources., A dedicated deep optical observation is desirable to better constraining the nature of the point sources.
Physical. properties of galaxies depend. on the formation conditions and evolution.,Physical properties of galaxies depend on the formation conditions and evolution.
 In addition to intrinsic evolution. ealaxics are exposed to environmental influence (among others Dressler 1980. Lewis et al.," In addition to intrinsic evolution, galaxies are exposed to environmental influence (among others Dressler 1980, Lewis et al."
 2002. Gomez et al.," 2002, Gomez et al."
 2003. Einasto et al.," 2003, Einasto et al."
 2003. Blanton ct al.," 2003, Blanton et al."
 2005. Weinmann ct al.," 2005, Weinmann et al."
 2006. Martinez et al.," 2006, Martinez et al."
 2006. Park et al.," 2006, Park et al."
 2007. 2008).," 2007, 2008)."
 The density of galaxies (number of galaxies per volume unit) or luminosity density as well as the number of galaxies in group/cluster or distance to the nearest galaxy is often implied. as regarding the environment., The density of galaxies (number of galaxies per volume unit) or luminosity density as well as the number of galaxies in group/cluster or distance to the nearest galaxy is often implied as regarding the environment.
 The inlluence of an environment can be found till. 1 Alpe and even. farther (Ixaulfimann et al., The influence of an environment can be found till 1 Mpc and even farther (Kauffmann et al.
 2004. Blanton et al.," 2004, Blanton et al."
 2005. Park et al.," 2005, Park et al."
 2007. 2008). where small galaxy groups are observed.," 2007, 2008), where small galaxy groups are observed."
 The study of “enviromental cllects” in such poor galaxy. groups is helpful for understanding the galaxy evolution on intermediate scales between isolated. galaxies and rich groupsclusters.," The study of ""enviromental effects"" in such poor galaxy groups is helpful for understanding the galaxy evolution on intermediate scales between isolated galaxies and rich groups/clusters."
 The isolated galaxies that have Πο sullicientlv undergone the inlluence of environment allow us to consider them as the “autonomous laboratories” [ου studying evolutionary processes in the galaxies.," The isolated galaxies that have not sufficiently undergone the influence of environment allow us to consider them as the ""autonomous laboratories"" for studying evolutionary processes in the galaxies."
 Individual properties of isolated. galaxies (mass. luminosity. morphology. colour-index etc.)," Individual properties of isolated galaxies (mass, luminosity, morphology, colour-index etc.)"
 can be served as the standard when studying galaxies in the different environment. (see. for. example. Ixarachentseva 1973. (sl). Prada et al.," can be served as the standard when studying galaxies in the different environment (see, for example, Karachentseva 1973 (KIG), Prada et al."
 2003. Beda οἱ al.," 2003, Reda et al."
 2004. Stocke et al.," 2004, Stocke et al."
 2004. Verlev ct al.," 2004, Verley et al."
 2007)., 2007).
 For studing of galaxies” properties in dilferent environment. it is also important to define the galaxy’s isolation degree which is suitable to deseribe by some parameter., For studing of galaxies' properties in different environment it is also important to define the galaxy's isolation degree which is suitable to describe by some parameter.
 For example. ]xarachentsev and Ixasparova (2005) used the tidal index for cach galaxy to study elobal properties of nearest galaxies in different environments.," For example, Karachentsev and Kasparova (2005) used the tidal index for each galaxy to study global properties of nearest galaxies in different environments."
 Verlev et al. (, Verley et al. (
2007) quantified. the isolation degree of WIG galaxies by two parameters: local number density ancl tical strength.,2007) quantified the isolation degree of KIG galaxies by two parameters: local number density and tidal strength.
 lt is known that with the increase of galaxy svstenis richness from individual galaxies to clusters. their. mass increases more quickly than bIuminosity (Ixarachentsev ct al.," It is known that with the increase of galaxy systems richness from individual galaxies to clusters, their mass increases more quickly than luminosity (Karachentsev et al."
 1966. Ciürardi et al.," 1966, Girardi et al."
 2002)., 2002).
 The dark matter in small groups seers to be distributed in the whole volume of svstem in the case of compact groups and to be concentrated in the halo of individual &alaxies in the case of loose groups (Alulchacy et al., The dark matter in small groups seems to be distributed in the whole volume of system in the case of compact groups and to be concentrated in the halo of individual galaxies in the case of loose groups (Mulchaey et al.
 2003. Melnyk Vavilova 2006. Da Rocha et al.," 2003, Melnyk Vavilova 2006, Da Rocha et al."
 2008)., 2008).
 At the same time the amount of dark matter in galaxy groups is not enough for standard cosmological model (Malarov Ixarachentsev. 2007)., At the same time the amount of dark matter in galaxy groups is not enough for standard cosmological model (Makarov Karachentsev 2007).
 As à rule. for identifving groups by different selection methods. the principle of overdensity in comparison with background. is used.," As a rule, for identifying groups by different selection methods, the principle of overdensity in comparison with background is used."
 The richer the group population. the overdensity is more strong and therefore more likely that such a group is physically bound.," The richer the group population, the overdensity is more strong and therefore more likely that such a group is physically bound."
 Poor groups identification depends strongly on the limiting parameters of the method., Poor groups identification depends strongly on the limiting parameters of the method.
 These systems can be casily confused with the random, These systems can be easily confused with the random
naxinuun contribution of low mass objects to the Talo of he Milky Wav (Renault et al.,maximum contribution of low mass objects to the Halo of the Milky Way (Renault et al.
 L997. see also Alcock et al.," 1997, see also Alcock et al."
 1996)., 1996).
 Given the importance of these results. it is iiperative o verity them by using other lines of sight. the most o»onisneg ones beiug the σα Magellanic Cloud (SAIC) and \I31.," Given the importance of these results, it is imperative to verify them by using other lines of sight, the most promising ones being the Small Magellanic Cloud (SMC) and M31."
 Tere. we present a first analysis of uuicrolcusine data in the direction of the SAIC by using 5.3 iilliou ieht curves collected by EROS2 during the first vear of the strvey.," Here, we present a first analysis of microlensing data in the direction of the SMC by using 5.3 million light curves collected by EROS2 during the first year of the survey."
 More details can be found in (Palauque-Delabrouille 1997)., More details can be found in (Palanque-Delabrouille 1997).
 Our results have been obtained with a completely redesigned setup., Our results have been obtained with a completely redesigned setup.
 The EROS program. uow uses exclusively the dedicated 1 meter MÁARLY telescope. specially refurbished aud fully automated for the EROS2 survey (Dauer ct al.," The EROS program now uses exclusively the dedicated 1 meter MARLY telescope, specially refurbished and fully automated for the EROS2 survey (Bauer et al."
 1997). now in operation at the European Southern Observatory at La Silla. Chile.," 1997), now in operation at the European Southern Observatory at La Silla, Chile."
" The clescope optics allows sumuultaucous muaeius iu ""blue (AinI20.720 nui peak at Az560 nmn) and ""red (Ain620920 num. peak at A--του iu) wide pass-xuids of a one-square-deeree field."," The telescope optics allows simultaneous imaging in “blue” $\lambda {\rm\;in\;}
420-720$ nm, peak at $\lambda \simeq 560$ nm) and “red” $\lambda {\rm\;in\;}
620-920$ nm, peak at $\lambda \simeq 760$ nm) wide pass-bands of a one-square-degree field."
 This is achieved by a vcaun-splitting dichroic cube with a CCD camera mounted ychind each channel., This is achieved by a beam-splitting dichroic cube with a CCD camera mounted behind each channel.
 Each camera coutaius a mosaic of 8 Loral 2018 x 2015 thick CCDs., Each camera contains a mosaic of 8 Loral 2048 x 2048 thick CCD's.
 The total field is 0.7 dee (right ascension) x 1.l dee (declination)., The total field is 0.7 deg (right ascension) x 1.4 deg (declination).
 The pixel size is 1.6 aresec. aud typical global image quality (atimospheric seeing | instrament) is 2 arcsec EWITM.," The pixel size is 0.6 arcsec, and typical global image quality (atmospheric seeing + instrument) is 2 arcsec FWHM."
 The read-out of the eutire mosaic is done iu parallel. controlled by Digital Signal Processors. and takes 50 seconds.," The read-out of the entire mosaic is done in parallel, controlled by Digital Signal Processors, and takes 50 seconds."
" The data are first transferred to two VME crates (one per color). which manage the realtime part of the acquisition svstem. and then to two Alpha workstations where a quality assessment is run (uonitoring CCD defects, sky background. seciug. ΙΟΥ of )) and flat-tield reduction is done."," The data are first transferred to two VME crates (one per color), which manage the real-time part of the acquisition system, and then to two Alpha workstations where a quality assessment is run (monitoring CCD defects, sky background, seeing, number of ) and flat-field reduction is done."
 The raw and reduced data are finally. saver ou DLT tapes., The raw and reduced data are finally saved on DLT tapes.
 Data taking with the new apparatus beean iu July. 1996.," Data taking with the new apparatus began in July, 1996."
 Microleusiug targets include fields ucar the ealactic center. in the disk of the Galaxy. aud in the LMC aud SMC.," Microlensing targets include fields near the galactic center, in the disk of the Galaxy, and in the LMC and SMC."
 The data discussed here concern LO fields covering the densest 10deg? of the SMC. as illustrated in figure |," The data discussed here concern 10 fields covering the densest $10\;{\rm deg}^{2}$ of the SMC, as illustrated in figure \ref{carteSMC}."
 The fields were observed from July. 1996 to February. 1997 and again starting in July. 1997.," The fields were observed from July, 1996 to February, 1997 and again starting in July, 1997."
 Diving the 1996-97 season. from 60 to 120 usable mages were taken of each field. ceiving a sample time of one poiut every 2-Ll davs on average.," During the 1996-97 season, from 60 to 120 usable images were taken of each field, giving a sampling time of one point every 2-4 days on average."
 Exposure times varied from 5 minu in the ceutral fields to 15 miu in the outermost fields., Exposure times varied from 5 min in the central fields to 15 min in the outermost fields.
 The DLT tapes produced in Chile are shipped to he CCPN (IN2P3 computing center. CNRS) in Lvons. France. where data processing occurs.," The DLT tapes produced in Chile are shipped to the CCPN (IN2P3 computing center, CNRS) in Lyons, France, where data processing occurs."
 For cach of the fields. a template image is first constructed by adding ogether 10 exposures of good quality. cach re-suupled by a factor of 0.7.," For each of the fields, a template image is first constructed by adding together 10 exposures of good quality, each re-sampled by a factor of 0.7."
 A reference star catalog is then built using the star funding algorithia (the stellar detection Is Ono Ol a correlation nuage. obtained as described in section ὃν page 5)).," A reference star catalog is then built using the star finding algorithm (the stellar detection is done on a correlation image, obtained as described in section 3, page )."
 For cach subsequent image. after ecolmetrical alizument to the template catalog. cach star identified on the reference catalog is fitted together with neighboring stars. using a PSF determined on bright isolated stars aud naposiug the position from the reference catalog.," For each subsequent image, after geometrical alignment to the template catalog, each star identified on the reference catalog is fitted together with neighboring stars, using a PSF determined on bright isolated stars and imposing the position from the reference catalog."
 A relative photometric aliguiment is then performed. assume most stars do not vary.," A relative photometric alignment is then performed, assuming most stars do not vary."
 Photometric errors are computed for cach measurement. assuniues again that most stars are stable. and parameterized as a function of star brightuess aud image sequence uunber.," Photometric errors are computed for each measurement, assuming again that most stars are stable, and parameterized as a function of star brightness and image sequence number."
 Photometric accuracy is inthe &20% range at magnitude Voe20 (depending ou image quality). and of the order of 2% for bright stars (V.—1734.2 The amber of reconstructed stars varies. frou. δν∖↽↣10deg. 2.in the deusest region (where errors are dominated by cerowdiug) to LsLO?deg ?in the outer regions (where errors are dominated by signal-to-noise).," Photometric accuracy is in the $8-20\%$ range at magnitude $V\sim 20$ (depending on image quality), and of the order of $2\%$ for bright stars $V\sim 17$ The number of reconstructed stars varies from $8\times 10^5 {\rm \: deg}^{-2}$ in the densest region (where errors are dominated by crowding) to $4\times 10^5 {\rm \: deg}^{-2}$ in the outer regions (where errors are dominated by signal-to-noise)."
 The photometry is described in more details in (AnsariB. 1996b))., The photometry is described in more details in \cite{Peida}) ).
 The 5.3 nullion light curves are subjected to a series of selection criteria aud rejection cuts (globally called “cuts”) to isolate muicrolensing candidates (Palauque-Doelabrouille, The 5.3 million light curves are subjected to a series of selection criteria and rejection cuts (globally called “cuts”) to isolate microlensing candidates (Palanque-Delabrouille
hole.,hole.
" Each model, of course, comes with its own set of assumptions, and in a late-stage merging system such as NGC 6240, we must think carefully about what such models can tell us."," Each model, of course, comes with its own set of assumptions, and in a late-stage merging system such as NGC 6240, we must think carefully about what such models can tell us."
" While the quality of these data is clear, understanding how to analyze them is not straightforward."," While the quality of these data is clear, understanding how to analyze them is not straightforward."
 Here we discuss two possible ways to measure the black hole mass from these data and compare the results of the two methods., Here we discuss two possible ways to measure the black hole mass from these data and compare the results of the two methods.
" We begin our analysis by utilizing the JAM modeling code AnisotropicMulti-Gaussianexpansiondy-namical(JeansmodelsCappellari2008), a technique based on the two-integral axisymmetric Jeans formalism but which has been expanded to allow for anisotropy via the parameter 6,=1—(oc;/og)."," We begin our analysis by utilizing the JAM modeling code \citep[Jeans Anisotropic Multi-Gaussian expansion dynamical models][]{JAM}, a technique based on the two-integral axisymmetric Jeans formalism but which has been expanded to allow for anisotropy via the parameter $\beta _{z} = 1 - (\sigma _{z} / \sigma _{R} )^{2}$."
" JAM modeling efficiently utilizes the axisymmetric dynamics seen near the south nucleus, and does not require higher-order Hermite moments."," JAM modeling efficiently utilizes the axisymmetric dynamics seen near the south nucleus, and does not require higher-order Hermite moments."
" This method, which fits vm,=Vv2+02, is likely to overestimate the black hole mass by assuming the dynamics measured belong to a relaxed system."," This method, which fits $v_{rms} = \sqrt{v^{2} + \sigma ^{2}}$, is likely to overestimate the black hole mass by assuming the dynamics measured belong to a relaxed system."
" In fact, an unknown fraction of the measured velocity dispersion is due to intervening material, such as tidal tails, that has not yet reached dynamical equilibrium."," In fact, an unknown fraction of the measured velocity dispersion is due to intervening material, such as tidal tails, that has not yet reached dynamical equilibrium."
" Additionally, this method assumes axisymmetric and smooth light and mass profiles."," Additionally, this method assumes axisymmetric and smooth light and mass profiles."
" Finally, we assume a constant mass-to-light ratio."," Finally, we assume a constant mass-to-light ratio."
" The JAM modeling code requires a high-resolution light profile, which we parametrize using the Multi-Gaussian Expansion code Cappellari2002) designed to work with the JAM(MGE code."," The JAM modeling code requires a high-resolution light profile, which we parametrize using the Multi-Gaussian Expansion code \citep[MGE][]{MGE} designed to work with the JAM code."
" To fit our light profile over a larger field of view than is available in our OSIRIS data, we use our K’ NIRC2 imaging and mirror it about the minor axis of the nucleus."," To fit our light profile over a larger field of view than is available in our OSIRIS data, we use our K' NIRC2 imaging and mirror it about the minor axis of the nucleus."
" We do this because the southeast side of the nucleus is considerably less extincted, so our signal-to-noise ratio is much improved."," We do this because the southeast side of the nucleus is considerably less extincted, so our signal-to-noise ratio is much improved."
" Once we have symmetrized the observed light profile, we then de-extinct this using the extinction map of Figure 9 in Engeletal.(2010)."," Once we have symmetrized the observed light profile, we then de-extinct this using the extinction map of Figure 9 in \citet{Hauke}."
". Using this extinction map, our recovered intrinsic brightness peaks at the same location as the kinematic center of our dynamical data, which means that in K-band the nucleus is only partially extincted. ("," Using this extinction map, our recovered intrinsic brightness peaks at the same location as the kinematic center of our dynamical data, which means that in K-band the nucleus is only partially extincted. ("
"In contrast, the extinction at visible wavelengths is so severe that the entire region surrounding the south black hole cannot even be seen (Maxetal. 2005).)","In contrast, the extinction at visible wavelengths is so severe that the entire region surrounding the south black hole cannot even be seen \citep{Max05}. .)"
" This is important, as most of the orbital information reported by JAM modeling is contained in the light profile."," This is important, as most of the orbital information reported by JAM modeling is contained in the light profile."
" In order to determine the appropriate mass-to-light ratio, anisotropy parameter f; and black hole mass, we compare the resulting dynamical models to those measured from our OSIRIS data in K-band."," In order to determine the appropriate mass-to-light ratio, anisotropy parameter $\beta _{z}$ and black hole mass, we compare the resulting dynamical models to those measured from our OSIRIS data in K-band."
" Our best-fit models for this method measure a black hole mass of 2.0+0.2x10? Mo, and are shown, along with the symmetrized Όμπις data for comparison, in Figure 7.."," Our best-fit models for this method measure a black hole mass of $2.0 \pm 0.2 \times 10^9 M_{\sun}$ , and are shown, along with the symmetrized $v_{rms}$ data for comparison, in Figure \ref{JAM}."
" The reduced x? statistic, fitting over 120 points, is 2.21."," The reduced $\chi^{2}$ statistic, fitting over 120 points, is 2.21."
" As a sanity check on the JAM model, and to provide a lower-limit to the black hole mass, we explore a simple model comparing the velocity field to that of a thin disk with a given enclosed mass profile exhibiting Keplerian rotation."," As a sanity check on the JAM model, and to provide a lower-limit to the black hole mass, we explore a simple model comparing the velocity field to that of a thin disk with a given enclosed mass profile exhibiting Keplerian rotation."
 In this method we do not include a dispersion component because intervening material may inflate that measurement., In this method we do not include a dispersion component because intervening material may inflate that measurement.
 Here we assume that the energy in intrinsic dispersion in the nuclear stellar disk is negligible compared to the energy in rotation., Here we assume that the energy in intrinsic dispersion in the nuclear stellar disk is negligible compared to the energy in rotation.
 This should give a lower limit to the black hole mass., This should give a lower limit to the black hole mass.
 We are measuring the dynamics of young stars in thevery nucleus of a gas-rich merger., We are measuring the dynamics of young stars in thevery nucleus of a gas-rich merger.
 A thin disk, A thin disk
"The alternate 72-noise"" model. on the other haud. can clearly explain (he excess velocity al the extrema (and anv other precessional phase) bx the changing jet velocity amplitude.","	The alternate $\beta$ -noise” model, on the other hand, can clearly explain the excess velocity at the extrema (and any other precessional phase) by the changing jet velocity amplitude."
 such a model also has a physical basis. given recent advances in the modeling of relativistic jet production.," Such a model also has a physical basis, given recent advances in the modeling of relativistic jet production."
 Meieretal.(2001) dicuss a scenario where such jets are launched by a magnetic accretion disk instability. around. a black hole (or other compact object)., \citet{meier} dicuss a scenario where such jets are launched by a magnetic accretion disk instability around a black hole (or other compact object).
 Variations in the accretion flow onto the compact object (1.6. M. intrinsic magnetic field. etc.)," Variations in the accretion flow onto the compact object (i.e. $\dot M$, intrinsic magnetic field, etc.)"
 can alter the radius at which the magnetic field saturates and the jet is launched. and thus the jet velocity.," can alter the radius at which the magnetic field saturates and the jet is launched, and thus the jet velocity."
" The relation between jet velocity ancl launch radius for à non-rotating black hole follows: where 9=©. and 2, is the gravitational radius of the black hole (one-half of the Schwarzschild radius)."," The relation between jet velocity and launch radius for a non-rotating black hole follows: where $\beta = {v \over{c}}$, and $R_g$ is the gravitational radius of the black hole (one-half of the Schwarzschild radius)."
 It is also interesüing (o view these model in light of the apparent lack of in the Doppler shift residuals noted above., 	It is also interesting to view these model in light of the apparent lack of phase-dependence in the Doppler shift residuals noted above.
 By cdifferentiating the equation for Doppler shifts in the kinematic model (eqn., By differentiating the equation for Doppler shifts in the kinematic model (eqn.
 1) with respect to the potentially time-varving model components (2. 7. 0. and o) we can see (he relative phase-dependence of Doppler shit residuals on deviations in each term.," 1) with respect to the potentially time-varying model components $\beta$, $i$, $\theta$, and $\phi$ ) we can see the relative phase-dependence of Doppler shift residuals on deviations in each term."
 In the phase noise model. we would expect (the following dependence: Thus. we would expect the amplitude of the Doppler shift residuals to be sinusoidally modulated with phase. in apparent contradiction with our analvses above.," In the phase noise model, we would expect the following dependence: Thus, we would expect the amplitude of the Doppler shift residuals to be sinusoidally modulated with phase, in apparent contradiction with our analyses above."
" For the 7zZ-noise"" model. we have:"," For the $\beta$ -noise” model, we have:"
The lowest-order interaction. between photons and electrons. namely Compton scattering. results in. momentum and. energy exchange.,"The lowest-order interaction between photons and electrons, namely Compton scattering, results in momentum and energy exchange."
 It is a common and important process in astrophysics., It is a common and important process in astrophysics.
 The momentum exchange regulates accreting gases to accrete only below a critical value. corresponding to the Eddington limit on the luminosity. £i: (for spherical accretion).," The momentum exchange regulates accreting gases to accrete only below a critical value, corresponding to the Eddington limit on the luminosity, $\ledd$ (for spherical accretion)."
 The importance of energy exchange manifests itself in two aspects., The importance of energy exchange manifests itself in two aspects.
 For photons. Compton up-seattering by energetic electrons is the main mechanism to produce X-ray emission in various astrophysical systems. and Compton down-scattering by low-energy electrons often leads to modification of X-ray spectra.," For photons, Compton up-scattering by energetic electrons is the main mechanism to produce X-ray emission in various astrophysical systems, and Compton down-scattering by low-energy electrons often leads to modification of X-ray spectra."
 For electrons. they either gain or lose energy. depending on the average photon energy.," For electrons, they either gain or lose energy, depending on the average photon energy."
 This process is important. in particular. in hot accretion flows.," This process is important, in particular, in hot accretion flows."
 Hot accretion flows such as advection-dominated accretion flows (ADAF. e.g.. Narayan Yi 1994: Abramowiez et 11995) are optically thin in both vertical and radial directions.," Hot accretion flows such as advection-dominated accretion flows (ADAF, e.g., Narayan Yi 1994; Abramowicz et 1995) are optically thin in both vertical and radial directions."
 Thus. a shoton ean travel a long distance before being absorbed or scattered (e.g. Narayan Yi 1994: Narayan. Mahadevan Quataert 1998).," Thus, a photon can travel a long distance before being absorbed or scattered (e.g., Narayan Yi 1994; Narayan, Mahadevan Quataert 1998)."
 Then. photons produced in one location can either cool or hea he flow in another location. and Compton effect is not local buelobal.," Then, photons produced in one location can either cool or heat the flow in another location, and Compton effect is not local but."
 The extension of ADAF to higher accretion rates (but stil below the Eddington limit). namely luminous hot accretion flows (LHAF. Yuan 2001 hereafter YOI: Yuan 2003). should be even more affected by the global Compton scattering. since its optica," The extension of ADAF to higher accretion rates (but still below the Eddington limit), namely luminous hot accretion flows (LHAF, Yuan 2001 hereafter Y01; Yuan 2003), should be even more affected by the global Compton scattering, since its optical"
The purpose of our work is to buikl modified ISEDs based on (he observations of open clusters. so the clusters as a whole will be treated as unresolvable stellar populations.,"The purpose of our work is to build modified ISEDs based on the observations of open clusters, so the clusters as a whole will be treated as unresolvable stellar populations."
 Most of the cluster member stars can be in principle confined in the single-star evolution regime. including the unresolved. binaries shown in photometric binary sequence in (he CMDs.," Most of the cluster member stars can be in principle confined in the single-star evolution regime, including the unresolved binaries shown in photometric binary sequence in the CMDs."
 As the SSP component is based on single-star evolution theory. we should emphasize here that the IME applied to conventional SSP model should account for both the single stars aud the photometric binary stars in (he observational CMDs.," As the SSP component is based on single-star evolution theory, we should emphasize here that the IMF applied to conventional SSP model should account for both the single stars and the photometric binary stars in the observational CMDs."
 For a given cluster of age { and metallidtv Z. assuming Salpeter MIF oC). the ISED of SSP component is. where /(À.m.1.Z) is the flix of a star of mass m. age { and metallicity Z.," For a given cluster of age $\it{t}$ and metallicity $\it{Z}$, assuming Salpeter IMF $\it{\phi(m)}$, the ISED of SSP component is, where $\it{f(\lambda,m,t,Z)}$ is the flux of a star of mass $\it{m}$ , age $\it{t}$ and metallicity $\it{Z}$."
 cl is a normalization constant which is fixed by the cluster richness parameter No., $\it{A}$ is a normalization constant which is fixed by the cluster richness parameter $_2$.
" 2, and my; are the upper ancl lower integration limits. in (hie current context. i, is the initial mass of the most massive living star at the age of the cluster. while my takes its regular meaning."," $m_u$ and $m_l$ are the upper and lower integration limits, in the current context, $m_u$ is the initial mass of the most massive living star at the age of the cluster, while $m_l$ takes its regular meaning."
" By using Salpeter IME. al is derived from the formula: where m, anc m, are the initial masses corresponding to the lwo limiting magnitudes defined by No. i.e. 22, is the initial mass of the very star in the turnoll. ancl my, is the initial mass ol star whose magnitude is (wo magnitudes lower than that of (he cluster turnolf point."," By using Salpeter IMF, $\it{A}$ is derived from the formula: where $\it{m_1}$ and $\it{m_2}$ are the initial masses corresponding to the two limiting magnitudes defined by $_2$, i.e. $\it{m_2}$ is the initial mass of the very star in the turnoff, and $\it{m_1}$ is the initial mass of star whose magnitude is two magnitudes lower than that of the cluster turnoff point."
 For the BSS component. the integrated spectra Εως(λ.1.Z) is given by directly summing up the individual spectrum. where fj). is the theoretical spectrum for a BSS. the index 7 runs from 1 to Nps.," For the BSS component, the integrated spectra $\it{F_{BS}(\lambda,t,Z)}$ is given by directly summing up the individual spectrum, where $\it{f^i_{BS}}$ is the theoretical spectrum for a BSS, the index $\it{i}$ runs from 1 to $N_{BS}$."
 Nes is the total number of BSSs in a cluster., $_{BS}$ is the total number of BSSs in a cluster.
"Finally. the ISED of a cluster in our workis the combination of the integrated spectrum of SSP component Fi,,(A.4.2) and that of BSS component. Pyy(A.1. Z). ","Finally, the ISED of a cluster in our workis the combination of the integrated spectrum of SSP component $\it{F_{iso}(\lambda,t,Z)}$ and that of BSS component $\it{F_{BS}(\lambda,t,Z)}$ "
Therefore. we check the inadequacy of the latter model to see if our statistical model is good enough.,"Therefore, we check the inadequacy of the latter model to see if our statistical model is good enough."
 The Bayes factor in Eq. (3)) h, The Bayes factor in Eq. \ref{MIC}) )
ichhas a value of2.0x10!° for the four-planet model At;4. w means that the probability of the HIRES and HARPS data sets being inadequately described by the model is 5.0x107!!. a value low enough to conclude that there is no need to revise the model.," has a value of $2.0 \times 10^{10}$ for the four-planet model $\mathcal{M}_{I,4}$, which means that the probability of the HIRES and HARPS data sets being inadequately described by the model is $5.0 \times 10^{-11}$, a value low enough to conclude that there is no need to revise the model."
" We note that this model. ar order of magnitude more probable than the previously used model Af, (Tuomi.2011).. does not result in à revision of the orbital parameters (Table 5))."," We note that this model, an order of magnitude more probable than the previously used model $\mathcal{M}_{4}$ \citep{tuomi2011}, does not result in a revision of the orbital parameters (Table \ref{Gliese_parameters}) )."
 However. the noise parameters of the two data sets do differ from one another slightly.," However, the noise parameters of the two data sets do differ from one another slightly."
 Denoting the HIRES data set with /21 and the HARPS data set with /=2. the parameters σι.)=1.2. have MAP estimates of 2.39 and 1.50 ms. respectively.," Denoting the HIRES data set with $l=1$ and the HARPS data set with $l=2$, the parameters $\sigma_{I,l}, l=1,2$, have MAP estimates of 2.39 and 1.50 $^{-1}$, respectively."
 The corresponding credibility sets are [1.77. 3.09] and |1.00. 2.01] ms7!. respectively.," The corresponding credibility sets are [1.77, 3.09] and [1.00, 2.01] $^{-1}$, respectively."
 Therefore. the noise in the HARPS measurements gives an upper limit for the jitter of Gliese 581 of 2.01 ms!. whereas there is likely a small amount of additional instrument noise in the HIRES data.," Therefore, the noise in the HARPS measurements gives an upper limit for the jitter of Gliese 581 of 2.01 $^{-1}$, whereas there is likely a small amount of additional instrument noise in the HIRES data."
 The RV's of v And have shown three strong Keplerian signals resulting from three massive planets orbiting the star (Butlertenmyeretal..2007;Wright 2009)..," The RV's of $\upsilon$ And have shown three strong Keplerian signals resulting from three massive planets orbiting the star \citep{butler1997,butler1999,fischer2003,naef2004,wittenmyer2007,wright2009}. ."
 The star has been a target of five RV surveys for several years. namely. Lick (Butleretal..1999;Fischer2003:Wright2009).. the Advanced Fiber-Optic Echelle spectrometer (AFOE) at the Whipple Observatory (Butleretal..1999).. HJS (Wittenmyer 2007).. ELODIE at the Haute-Provence Observatory (Naefetal..2004).. and the Hobby-Eberly Telescope (HET) (McArthuretal..2010).," The star has been a target of five RV surveys for several years, namely, Lick \citep{butler1999,fischer2003,wright2009}, the Advanced Fiber-Optic Echelle spectrometer (AFOE) at the Whipple Observatory \citep{butler1999}, HJS \citep{wittenmyer2007}, ELODIE at the Haute-Provence Observatory \citep{naef2004}, and the Hobby-Eberly Telescope (HET) \citep{mcarthur2010}."
. Recently. the combined data of Lick (Fischeretal..2003;Wright2009) and ELODIE (Naefetal.2004) has been reported to contain a fourth planetary signal (Curieletal..2011).," Recently, the combined data of Lick \citep{fischer2003,wright2009} and ELODIE \citep{naef2004} has been reported to contain a fourth planetary signal \citep{curiel2011}."
. We re-analyse the combined RV data of v And by using the model inadequacy criterion., We re-analyse the combined RV data of $\upsilon$ And by using the model inadequacy criterion.
 However. before we start. we check the consistency of the 248 Lick RVs published in Fischeretal.(2003) and the 284 Lick RV's published in Wrightetal.(2009) (we denote these data sets as Lick] and Lick2. respectively). because Curieletal.(2011) used Lick2 data and the additional 30 RV. points from Lick! that were not included in Lick2.," However, before we start, we check the consistency of the 248 Lick RV's published in \citet{fischer2003} and the 284 Lick RV's published in \citet{wright2009} (we denote these data sets as Lick1 and Lick2, respectively), because \citet{curiel2011} used Lick2 data and the additional 30 RV points from Lick1 that were not included in Lick2."
 The fact that these 30 measurements were not included in Lick? likely because of suspected biases or calibration errors suggests that there could be some biases within the combined Lick data analysed in Curieletal.(2011) as well., The fact that these 30 measurements were not included in Lick2 likely because of suspected biases or calibration errors suggests that there could be some biases within the combined Lick data analysed in \citet{curiel2011} as well.
 The Lick! and Lick? data sets appear to have one striking difference., The Lick1 and Lick2 data sets appear to have one striking difference.
 While they both imply that there are indeed four Keplerian signals in the v And RV's. as concluded by Curie (2011).. they do not agree on the orbital period of the proposed fourth signal.," While they both imply that there are indeed four Keplerian signals in the $\upsilon$ And RV's, as concluded by \citet{curiel2011}, they do not agree on the orbital period of the proposed fourth signal."
 The probability of the three companion model ts significantly lower than that of the four planet model — 107 and 10—7 timeslower for Lick! and Lick2. respectively.," The probability of the three companion model is significantly lower than that of the four planet model – $10^{-4}$ and $10^{-24}$ timeslower for Lick1 and Lick2, respectively."
 This implies that there is either a fourth Keplerian signal in, This implies that there is either a fourth Keplerian signal in
"Knezevic, Z.. Milani. A.. Farinella. Ρ.. Froeschle. C.. Froeschle. 11991, Icarus. 93. 316 Krasinsky, G. Α.. Pitjeva, E. V., Vasilyev, M. Ν.. Yagudina, E. 22002, Icarus, 158, 98 Kring, D. Α.. Cohen, B. 22002, Journal of Geophysical Research (Planets), 107, 5009 Levison. H. F.. Duncan. M. 11994. Icarus, 108. 18 Levison, Η. E.. Dones. L.. Chapman. C. R.. Stern, S. A.. Duncan. M. J.. Zahnle. 22001. Icarus. 151. 286 Levison, H. E.. Morbidelli, Α.. Vanlaerhoven, C.. Gomes. R., Tsiganis, Hcarus 196, 258-273.","Knezevic, Z., Milani, A., Farinella, P., Froeschle, C., Froeschle, 1991, Icarus, 93, 316 Krasinsky, G. A., Pitjeva, E. V., Vasilyev, M. V., Yagudina, E. 2002, Icarus, 158, 98 Kring, D. A., Cohen, B. 2002, Journal of Geophysical Research (Planets), 107, 5009 Levison, H. F., Duncan, M. 1994, Icarus, 108, 18 Levison, H. F., Dones, L., Chapman, C. R., Stern, S. A., Duncan, M. J., Zahnle, 2001, Icarus, 151, 286 Levison, H. F., Morbidelli, A., Vanlaerhoven, C., Gomes, R., Tsiganis, Icarus 196, 258-273."
" Lin, D. N. C., Papaloizou, The Astrophysical Journal 309, 846-857."," Lin, D. N. C., Papaloizou, The Astrophysical Journal 309, 846-857."
" Malhotra, 11993.Nature.. 365. 819 Malhotra, 11995.AJ.. 110. 420"," Malhotra, 1993, 365, 819 Malhotra, 1995, 110, 420"
Follow-up (quiescent) spectroscopic observations of novae. such as those initially reported in Surinaetal.(2012). can greatly aid in the classification of the secondary stars in these systems.,"Follow-up (quiescent) spectroscopic observations of novae, such as those initially reported in \citet{MomayConf}, can greatly aid in the classification of the secondary stars in these systems."
 This publication makes use of data products from the Two Micron All Sky Survey. which ts a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology. funded by the National Aeronauties and Space Administration and the National Science Foundation.," This publication makes use 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."
 This research has made use of NASA's Astrophysics Data System., This research has made use of NASA's Astrophysics Data System.
 This research has made use of the VizieR catalog access tool. CDS. Strasbourg. France.," This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France."
 VARMR was supported by an STFC PhD studentship and is currently supported by a South African SKA Fellowship., VARMR was supported by an STFC PhD studentship and is currently supported by a South African SKA Fellowship.
 RAH acknowledges PhD funding from STFC., RAH acknowledges PhD funding from STFC.
 The authors would like to thank the referee. Massimo Della Valle. for his very constructive comments.," The authors would like to thank the referee, Massimo Della Valle, for his very constructive comments."
disk can accelerate the evolution and cuhance he mass transfer rates. as already. noticed in the evolutionary study of CVs (Taam&Spruit2001).,"disk can accelerate the evolution and enhance the mass transfer rates, as already noticed in the evolutionary study of CVs \citep{taam01}."
. This sugeests a plausible explanation for the rapid nass transfer observed in a few Aleol binaries with very low mass ratios (Qianetal.2002).., This suggests a plausible explanation for the rapid mass transfer observed in a few Algol binaries with very low mass ratios \citep{qian02a}.
 Finally. we note that the magnitude of the mass ceding parameter 6 is highly uncertain. let alone its variation with the mass trauster rates.," Finally, we note that the magnitude of the mass feeding parameter $\delta$ is highly uncertain, let alone its variation with the mass transfer rates."
 These uncertainties make it difficult to xeseut direct colparison between observations aud theoretical predicatious for Algol biuaries., These uncertainties make it difficult to present direct comparison between observations and theoretical predications for Algol binaries.
 Tlowever. our analysis provides a reasonable iechanisin for aueular moment loss iu semi-detachied binaries iucludius Aleo binaries.," However, our analysis provides a reasonable mechanism for angular momentum loss in semi-detached binaries including Algol binaries."
 More detailed iuulti-wavelength observations can provide stringent tests for the CD disk model. and the theories of the evolution of Aleol binaries.," More detailed multi-wavelength observations can provide stringent tests for the CB disk model, and the theories of the evolution of Algol binaries."
ealaxy.,galaxy.
physical scenario of the evolution of QSOs/AGNs not as a speculation. but as a result of the mechanical process.,"physical scenario of the evolution of QSOs/AGNs not as a speculation, but as a result of the mechanical process."
" We have proposed a magnetohyelrocdyvnamic model for ""engine. of OSOs/ACGNs: the Kerr BLE Us-wheel model (see section 3 of this paper and Nitta et al.", We have proposed a magnetohydrodynamic model for `engine' of QSOs/AGNs: the Kerr BH fly-wheel model (see section 3 of this paper and Nitta et al.
 1991)., 1991).
 μις engine is driven by the rotation of DII., This engine is driven by the rotation of BH.
 The rotation οποιον of BL is extracted. by an electromagnetic process. (magnetic breaking)., The rotation energy of BH is extracted by an electromagnetic process (magnetic breaking).
 The extracted energy is once stored in the magnetosphere in the form of the Maxwell stress. and then it will produce the plasma outllows.," The extracted energy is once stored in the magnetosphere in the form of the Maxwell stress, and then it will produce the plasma outflows."
 One mighte mislead. that the [Iy-wheel engineC» is the mechanism only for the racio-loucl activity because the released energy. produces the outflow., One might mislead that the fly-wheel engine is the mechanism only for the radio-loud activity because the released energy produces the outflow.
 This might cause from. a strong impression that highly collimated bipolar jets make he double radio lobes., This might cause from a strong impression that highly collimated bipolar jets make the double radio lobes.
 However. from the observational »oint of view. the presence of out[ows are required for other kind of XGNs.," However, from the observational point of view, the presence of outflows are required for other kind of AGNs."
" For example. it has heen established that. DAL QSOs also have outllows (the ""disk wind"" nearly in he plane of the disk. see Murray. ct al."," For example, it has been established that, BAL QSOs also have outflows (the “disk wind” nearly in the plane of the disk, see Murray et al."
 1995)., 1995).
 From the heoretical point of view. mechanics of the global structure of outIlows is argued in many Literature.," From the theoretical point of view, mechanics of the global structure of outflows is argued in many literature."
 Lhe produced outLows will show a wide variation of global structures. e.g. the ripolar jets of radio-Ioud QSOs/AGNs. the equatorial wind of BAL QSOs. or more (see Nitta 1994).," The produced outflows will show a wide variation of global structures, e.g., the bipolar jets of radio-loud QSOs/AGNs, the equatorial wind of BAL QSOs, or more (see Nitta 1994)."
 Thus we can sav hat the radio-Ioud activity is simply one possibility of the ]v-wheel engine., Thus we can say that the radio-loud activity is simply one possibility of the fly-wheel engine.
 In the Εννους model. we can clarify the properties and the evolution of individual engine (see section 3) xwametrized. by DII mass m. initial νου parameter et. magnetic field. By at the. source. region. anc a small dimension-less parameter e.," In the fly-wheel model, we can clarify the properties and the evolution of individual engine (see section 3) parametrized by BH mass $m$, initial Kerr parameter $a$, magnetic field $B_0$ at the source region and a small dimension-less parameter $\epsilon$."
 These engines are assumed. to correspond. to. QSOS/AGNs., These engines are assumed to correspond to QSOs/AGNs.
 I we obtain the statistical properties for these parameters. we can diseuss the statistics of ensemble of QSOS/AGNs.," If we obtain the statistical properties for these parameters, we can discuss the statistics of ensemble of QSOs/AGNs."
 Hore. we adopt. the. Press-Sehechter formalism. for the mass. distribution., Here we adopt the Press-Schechter formalism for the mass distribution.
" In. the scenario of this work. Ixerr. Bills are supposed to form at 2o—iQ,=200 with nearly maximum angular momentum αcm a the formation epoch."," In the scenario of this work, Kerr BHs are supposed to form at $z=z_{vir}=200$ with nearly maximum angular momentum $a \sim m$ at the formation epoch."
 The BLL mass is assumed to be of the total barvonic mass of the proto-galactic cloud., The BH mass is assumed to be of the total baryonic mass of the proto-galactic cloud.
 Since the magnetic field. Di seems to be related with the BIT mass m. we set Byxm.," Since the magnetic field $B_0$ seems to be related with the BH mass $m$ , we set $B_0 \propto m^\zeta$."
 As a result. very weak dependence O2¢~1/2 is preferred for the consistency with observations.," As a result, very weak dependence $0 \geq \zeta > -1/2$ is preferred for the consistency with observations."
 We assume ὁ=0 and By=1 T] to obtain the figures., We assume $\zeta=0$ and $B_0=1$ [T] to obtain the figures.
 Phe small parameter c is determined by he physies of plasma injection process. e.g.. the pair plasma xoduction or the overllow from the disk halo.," The small parameter $\epsilon$ is determined by the physics of plasma injection process, e.g., the pair plasma production or the overflow from the disk halo."
 Since we clo not have widely accepted standard theory of it. we assume as c—0.1 (the distance of the source region is several times he horizon radius).," Since we do not have widely accepted standard theory of it, we assume as $\epsilon=0.1$ (the distance of the source region is several times the horizon radius)."
 Phus the evolution depends only on the DII mass m., Thus the evolution depends only on the BH mass $m$.
 We have discussed. the evolution. of the luminosity unction and the spatial number density in a period. Q2X 5.and mace a qualitative comparison with observations.," We have discussed the evolution of the luminosity function and the spatial number density in a period $0 \leq z \leq 5$ , and made a qualitative comparison with observations."
 In the typical case n=OS and &= OQ. we obtain he evolution of the luminosity function. ancl the spatial number density with a plausible behavior in the period )Xz5 consistent with observations.," In the typical case $n=-0.8$ and $\zeta=0$ , we obtain the evolution of the luminosity function and the spatial number density with a plausible behavior in the period $0 \leq z \leq 5$ consistent with observations."
 The brighter-end of the luminosity function is lifted up for z3. then it drops and the curve changes to be short and more steep for πο<3 as shown in ligure 5.. 6..," The brighter-end of the luminosity function is lifted up for $z \geq 3$, then it drops and the curve changes to be short and more steep for $0 \leq z \leq 3$ as shown in figure \ref{fig:LF1}, \ref{fig:LF2}."
 In accordance with this havior. the spatial number density evolves as shown in lgure y..," In accordance with this behavior, the spatial number density evolves as shown in figure \ref{fig:pop1}."
 We should. note that these characteristic evolutions obtained in this paper are derived. from the evolution of he individual magnetospheric structure in the vicinity. of he Ixerr. BLL., We should note that these characteristic evolutions obtained in this paper are derived from the evolution of the individual magnetospheric structure in the vicinity of the Kerr BH.
 Vhis individual evolution is not a speculation rut the result. based: on the MIID. picture., This individual evolution is not a speculation but the result based on the MHD picture.
 In. the previous works. e.g.. Pei (1995). the evolution of individual ACiNs is simply an assumption without any mechanical scenario.," In the previous works, e.g., Pei (1995), the evolution of individual AGNs is simply an assumption without any mechanical scenario."
 We have tried to join the intrinsic Kerr BLE magnetospheric phwsies. Le. the f[Iv-wheel model with observational facts. and we have succeed to present a mechanical model of the evolution. at least qualitatively.," We have tried to join the intrinsic Kerr BH magnetospheric physics, i.e., the fly-wheel model with observational facts, and we have succeed to present a mechanical model of the evolution, at least qualitatively."
 1n order to explain the observational facts of 0<2.x5. somewhat flat mass function of Dlls (η~0.5 in equation 7)) and a weak dependence of the magnetic field. at the source reglon on the BIT mass (¢1/2 in equation 6)) are preferred.," In order to explain the observational facts of $0 \leq z \leq 5$ , somewhat flat mass function of BHs $n \sim -0.8$ in equation \ref{eq:IMF}) ) and a weak dependence of the magnetic field at the source region on the BH mass $\zeta > -1/2$ in equation \ref{eq:B0}) ) are preferred."
 These values of à ancl & should be determined through an extra physics. however we do not have widely accepted. model of them. so we have treated them. as free parameters of our picture.," These values of $n$ and $\zeta$ should be determined through an extra physics, however we do not have widely accepted model of them, so we have treated them as free parameters of our picture."
 bor simplicity. we assumed the BIL formation epoch as ter=200 independent of BLL mass m.," For simplicity, we assumed the BH formation epoch as $z_{vir}=200$ independent of BH mass $m$."
 From the Compton drag model (see Sasaki Umenmura 1996). seed. DII can formed only at the epoch in which the background photon density is sulliciently high.," From the Compton drag model (see Sasaki Umemura 1996), seed BH can formed only at the epoch in which the background photon density is sufficiently high."
 The formation epoch should be > 1075., The formation epoch should be $z > 10^2$ .
 OF course. in the actual case. se; will depen on m.," Of course, in the actual case, $z_{vir}$ will depend on $m$."
" llowever. when we translate the red shift z to the cosmic time / by virtue of the Einstein-de Sitter mocel. the variation around. z200 corresponds to the order of IU"" vr]. and is negligible comparing with the epoch arounc L9 B(~10 vr] in which we are interested."," However, when we translate the red shift $z$ to the cosmic time $t$ by virtue of the Einstein-de Sitter model, the variation around $z \sim 200$ corresponds to the order of $\sim 10^6$ [yr], and is negligible comparing with the epoch around $z \sim 3$ $\sim 10^9$ [yr]) in which we are interested."
 Llence. it seenis reasonable to suppose that 25;const. independent of nm.," Hence, it seems reasonable to suppose that $z_{vir} \sim const.$ independent of $m$."
 We assumed that the dependence of the magnetic fiel Bo at the source region on the DII mass m as Byxm., We assumed that the dependence of the magnetic field $B_0$ at the source region on the BH mass $m$ as $B_0 \propto m^\zeta$.
 In the realistic case. By should depend not only on m but. also on the mass accretion rate.," In the realistic case, $B_0$ should depend not only on $m$ but also on the mass accretion rate."
 This problem is very cillicult anc still opened at the present time as discussed in. subsection 6.3. however. to discuss this problem as a whole is bevone the scope of thispaper.," This problem is very difficult and still opened at the present time as discussed in subsection 6.3, however, to discuss this problem as a whole is beyond the scope of thispaper."
 We assumed that the initial Ixerr parameter e as em~ 1., We assumed that the initial Kerr parameter $a$ as $a/m \sim 1$ .
 BieTakk Dvor (1980) showed that extreme Ixerr hole does not. possesthe magnetic field threading the horizon., Bi\u{c}\\'{a}kk Dvo\u{r}\\'{a}kk (1980) showed that extreme Kerr hole does not possesthe magnetic field threading the horizon.
 This meansthat the magnetic breaking process can not extract the rotation energy from extreme Ixerr holes., This meansthat the magnetic breaking process can not extract the rotation energy from extreme Kerr holes.
 Hencewe can not set the initial Kerr parameter as e= I., Hencewe can not set the initial Kerr parameter as $a/m = 1$ .
 However we should note thatexact value of the initial Ixerr parameter is not essential., However we should note thatexact value of the initial Kerr parameter is not essential.
A more careful derivation establishes that equation is nol missing a significant numerical constant.,A more careful derivation establishes that equation is not missing a significant numerical constant.
" With h/rzz0.04. e,220.2 is required Lor complete saturation. but ej220.05 sullices to tip the balance in favor of eccentricity driving by Lindblad resonances as opposed to eccentricity damping by corotation resonances."," With $h/r\approx 0.04$ , $e_p\approx 0.2$ is required for complete saturation, but $e_p\approx 0.05$ suffices to tip the balance in favor of eccentricity driving by Lindblad resonances as opposed to eccentricity damping by corotation resonances."
" Partial saturation of corotation resonances leading to eccentricily growth further requires that the initial value oL e, be able to survive damping until the torque is adequately saturated.", Partial saturation of corotation resonances leading to eccentricity growth further requires that the initial value of $e_p$ be able to survive damping until the torque is adequately saturated.
" To assess the condition under which this is satisfied. we compare the timescale lor eccentricity damping eiven by equation(19).. with that during which αλα] achieves a steady state. Applving equation vields For plausible parameters. w/r21 and h/r20.04. (his ratio is less (han unity except for very large values of Mr?/M,."," To assess the condition under which this is satisfied, we compare the timescale for eccentricity damping given by equation, with that during which $d\Sigma/dr|_{CR}$ achieves a steady state, Applying equation yields For plausible parameters, $\w/r\approx 1$ and $h/r\approx 0.04$, this ratio is less than unity except for very large values of $\Sigma
r^2/M_p$."
 Under the dual assumptions of a steady state gap and steady state saturation. eccentricitv growth is governed by Samplesolutions of (his equation are plotted in figure 2..," Under the dual assumptions of a steady state gap and steady state saturation, eccentricity growth is governed by Samplesolutions of this equation are plotted in figure \ref{fig2}."
 Resonant interactions between a planet ancl a protostellar disk cause the planets orbital eccentricitv (o evolve on a short timescale., Resonant interactions between a planet and a protostellar disk cause the planet's orbital eccentricity to evolve on a short timescale.
 We have investigated whether these interactions might be responsible lor the eccentric orbits (hat characterize recently discovered extrasolar planets., We have investigated whether these interactions might be responsible for the eccentric orbits that characterize recently discovered extrasolar planets.
 Our preliminary [imdings are as follows., Our preliminary findings are as follows.
 Co-orbital Lindblad resonances damp eccentricity., Co-orbital Lindblad resonances damp eccentricity.
 They dominate the eccentricity evolution ol planets that aretoo small to clear gaps (Word1988;Arivimowiez 1993a)..," They dominate the eccentricity evolution of planets that aretoo small to clear gaps \citep{WAR88, ART93b}. ."
 External, External
‘from Paper II.,from Paper II.
 Next the microturbulent parameter iis given. which was inferred by us for the most of the stars from aand lines.," Next the microturbulent parameter is given, which was inferred by us for the most of the stars from and lines."
 However. for 16 cool stars these lines are too weak and. herefore. unfit for the ddetermination by the standard. method. when an agreement in abundances derived from relatively strong and weak lines should ake place.," However, for 16 cool stars these lines are too weak and, therefore, unfit for the determination by the standard method, when an agreement in abundances derived from relatively strong and weak lines should take place."
 We present for these stars the vvalues obtained in Paper III from lines (marked by asterisks in Table |)., We present for these stars the values obtained in Paper III from lines (marked by asterisks in Table 1).
 The projected rotational velocities Trom Paper III are given next in Table 1., The projected rotational velocities from Paper III are given next in Table 1.
 We remark below on the equivalent widths ΤΕ GIS1) and magnesium abundances logz(Me) oresented in two last columns., We remark below on the equivalent widths $W$ (4481) and magnesium abundances $\log \varepsilon({\rm Mg})$ presented in two last columns.
 It should be noted that the distances of programme stars. according to Paper IL. are less than 800 pe. so the stars are really in he solar neighbourhood.," It should be noted that the distances of programme stars, according to Paper II, are less than 800 pc, so the stars are really in the solar neighbourhood."
 High-resolution spectra of programme stars have been acquired in 1996-1998 at two observatories: the McDonald Observatory (McDO) of the University of Texas and the Crimean Astrophysical Observatory CCrAO)., High-resolution spectra of programme stars have been acquired in 1996–1998 at two observatories: the McDonald Observatory (McDO) of the University of Texas and the Crimean Astrophysical Observatory (CrAO).
 At the McDO the 2.7 m telescope and coudé echelle spectrometer (Tull et al., At the McDO the 2.7 m telescope and coudé echelle spectrometer (Tull et al.
 1995) was used., 1995) was used.
 A resolving yower was /? = 60000 and the typical signal-to-noise ratio was between [00 and 300., A resolving power was $R$ = 60000 and the typical signal-to-noise ratio was between 100 and 300.
 At the CrAO we observed on the 2.6 m elescope with coudé spectrograph., At the CrAO we observed on the 2.6 m telescope with coudé spectrograph.
 In this case we had /? = 30000 and a signal-to-noise ratio between 50 and 200., In this case we had $R$ = 30000 and a signal-to-noise ratio between 50 and 200.
 A more detailed description of the observations and reductions of spectra can be ‘ound in Paper I. The equivalent width 11. of the 4481.2 line was measured by direct integration., A more detailed description of the observations and reductions of spectra can be found in Paper I. The equivalent width $W$ of the 4481.2 line was measured by direct integration.
 The measurements were effected independently by two of us (TMR and partially by DBP)., The measurements were effected independently by two of us (TMR and partially by DBP).
 A comparison of these two sets of measurements showed good agreement and an absence of a systematic difference., A comparison of these two sets of measurements showed good agreement and an absence of a systematic difference.
 The averaged VW. values were adopted., The averaged $W$ values were adopted.
 It should be noted that a similar approach has been used by us in Paper Tin measurements of hydrogen and helium lines., It should be noted that a similar approach has been used by us in Paper I in measurements of hydrogen and helium lines.
 The WV. values of the AHS1.2 lline are given in Table |., The $W$ values of the 4481.2 line are given in Table 1.
 According to our estimates. the error in the W determination is 3-5 per cent on average.," According to our estimates, the error in the W determination is $\pm5$ per cent on average."
 In our list there are 12 common stars. which have been observed both at the McDO and at the CrAO.," In our list there are 12 common stars, which have been observed both at the McDO and at the CrAO."
 A comparison of the VW values for two observatories showed good agreement: the mean difference is + per cent and the maximum discrepancy is 9 per cent., A comparison of the $W$ values for two observatories showed good agreement: the mean difference is $\pm4$ per cent and the maximum discrepancy is $\pm9$ per cent.
 Note that the very good agreement (a scatter within 3-5 per cent) has been obtained as well in Paper I for llines., Note that the very good agreement (a scatter within $\pm5$ per cent) has been obtained as well in Paper I for lines.
 It would be interesting to compare our IV. values for the AHS1.2 line with other published data., It would be interesting to compare our $W$ values for the 4481.2 line with other published data.
 Such a comparison with measurements of Kilian Nissen (1989) for [OQ common stars is shown in Fig.3., Such a comparison with measurements of Kilian Nissen (1989) for 10 common stars is shown in Fig.3.
 One sees that for all the stars excepting one a difference in VV lies within +4 per cent., One sees that for all the stars excepting one a difference in $W$ lies within $\pm4$ per cent.
 The only exception is the hot B star HR 2739. for which our equivalent width is greater by 15 per cent than Kilian Nissen’s value.," The only exception is the hot B star HR 2739, for which our equivalent width is greater by 15 per cent than Kilian Nissen's value."
 It should be noted in this connection that use of Kilian Nissen's equivalent, It should be noted in this connection that use of Kilian Nissen's equivalent
Galaxy groups are believed to play a key role in the formation and evolution of structure in the universe as. within a hierarchical framework. they span the regime between individual galaxies and massive clusters.,"Galaxy groups are believed to play a key role in the formation and evolution of structure in the universe as, within a hierarchical framework, they span the regime between individual galaxies and massive clusters."
 They are also more varied in their properties than galaxy clusters. as seen when various scaling relations are compared with those of galaxy clusters (Kaiser1991:Ponmanetdon&Ponman2000:Xueetal.2001:Helsdon 2003).," They are also more varied in their properties than galaxy clusters, as seen when various scaling relations are compared with those of galaxy clusters \citep{b91,b136,b171,b3,b121,b4,b178,b89,b177,b90}."
. For instance. the relation between the luminosity and temperature of the X-ray emitting hot intergalactic medium (the £7 relation) jas a larger scatter and a different slope for groups. when compared o similar properties of clusters.," For instance, the relation between the luminosity and temperature of the X-ray emitting hot intergalactic medium (the $L\!-\!T$ relation) has a larger scatter and a different slope for groups, when compared to similar properties of clusters."
 Various feedback mechanisms are often invoked to explain these differences., Various feedback mechanisms are often invoked to explain these differences.
 In addition. due to their ower Velocity dispersion. groups are rapidly evolving systems. and galaxy mergers within groups ean have a more significant effect on hese relations than in clusters.," In addition, due to their lower velocity dispersion, groups are rapidly evolving systems, and galaxy mergers within groups can have a more significant effect on these relations than in clusters."
 In principle. the presence of cool cores and active galactic nuclei (AGN). as well as the star formation story. are all affected by major interactions in the heart of a group or cluster.," In principle, the presence of cool cores and active galactic nuclei (AGN), as well as the star formation history, are all affected by major interactions in the heart of a group or cluster."
 It would therefore be useful to tind a class of groups or clusters with no major mergers in their recent history. to provide a baseline for the evolution of a passive system. with no major disruption.," It would therefore be useful to find a class of groups or clusters with no major mergers in their recent history, to provide a baseline for the evolution of a passive system, with no major disruption."
 Fossil groups are good candidates for such a class of objects., Fossil groups are good candidates for such a class of objects.
" They are distinguished by a large gap between the brightest galaxy and the fainter members. with an under-abundance of £, galaxies."," They are distinguished by a large gap between the brightest galaxy and the fainter members, with an under-abundance of $L_\ast$ galaxies."
 Zabludoff&Mulchaey(1998). suggest that. for an. X-ray detected group. the merging timescale for the most luminous group members GLx L4) is of order of a few tenths of an Hubble time. in agreement with the numerical simulations.," \citet{b300} suggest that, for an X-ray detected group, the merging timescale for the most luminous group members $L\approx L_\ast$ ) is of order of a few tenths of an Hubble time, in agreement with the numerical simulations."
 À single giant elliptical galaxy can form as a result ofmultiple mergers within a few Gyr (Barnes1989)., A single giant elliptical galaxy can form as a result ofmultiple mergers within a few Gyr \citep{b15}.
.. Thus. it is likely that one can find merged groups in the form of an isolated giant elliptical galaxy with an extended halo of hot gas. since the timescale for gas infall is longer than that on which galaxies merge (Ponman&Bertram1993)..," Thus, it is likely that one can find merged groups in the form of an isolated giant elliptical galaxy with an extended halo of hot gas, since the timescale for gas infall is longer than that on which galaxies merge \citep{b135}."
 In such systems. the brighter galaxies. which have a relatively shorter merging timescale. are expected to merge earlier leaving the fainter end of the luminosity function intact (Dubinski1998:Miles 2004).," In such systems, the brighter galaxies, which have a relatively shorter merging timescale, are expected to merge earlier leaving the fainter end of the luminosity function intact \citep{b55,b105}."
. Following the discovery of a fossil group having the above characteristics from ROSAT observations (Ponmanetal. 1994). more fossil systems have been identified," Following the discovery of a fossil group having the above characteristics from ROSAT observations \citep{b130}, , more fossil systems have been identified"
limits the region already in a steady state. receiving 1. 3. 2. aud 7 perturbations iu difIereut localities.,"limits the region already in a steady state, receiving 1, 3, 5, and 7 perturbations in different localities."
 The ares (or circles) in Figure 2bb are forinalized by equation (1))! with the sources at v of w-multiples in the plane of ο=0., The arcs (or circles) in Figure \ref{fig:num}b b are formalized by equation \ref{equ:sol}) with the sources at $\varphi^\prime$ of $\pi$ -multiples in the plane of $\varphi=0$.
" The perturbation launched every time the object returus back to the original position (sz being a multiple of 2x) propagates as a sound wave leaving the vestige on the spherical shell with the radius of multiple of 27M,1: the perturbation generated half an orbit Cx in angular phase) later is markecl on the sphere. smaller by πριPp1 with the center at the mirror point iu the same mericiional plane."," The perturbation launched every time the object returns back to the original position $\varphi^\prime$ being a multiple of $2\pi$ ) propagates as a sound wave leaving the vestige on the spherical shell with the radius of multiple of $2\pi\mach^{-1}$; the perturbation generated half an orbit $\pi$ in angular phase) later is marked on the sphere, smaller by $\pi\mach^{-1}$, with the center at the mirror point in the same meridional plane."
 Aud by extension. the spiral in the orbital plane (Fig.," And by extension, the spiral in the orbital plane (Fig."
 2aa) emerees as au aftermath of the phase cilference of the perturbation source., \ref{fig:num}a a) emerges as an aftermath of the phase difference of the perturbation source.
 The density enhancement. o. inthe pattern follows a complicated rule because of the accumulation of gravitational perturbatious launched [rom the object at different. positious ou the curvilinear orbit.," The density enhancement, $\alpha$, in the pattern follows a complicated rule because of the accumulation of gravitational perturbations launched from the object at different positions on the curvilinear orbit."
 This complication is particularly caused by the different contributious of the respective yerturbatious. uulike the case when the object is in a straight-line trajectory.," This complication is particularly caused by the different contributions of the respective perturbations, unlike the case when the object is in a straight-line trajectory."
 The density euliaucement orofiles are displayed in Figure lec as a function of radial distance in various directions along the spiral arum (the lines in red. vellow. green. aud blue colors) and aloug the orbital axis (the evan iue). iu which all the curves appear well located within the black lines (see below).," The density enhancement profiles are displayed in Figure \ref{fig:ptm}c c as a function of radial distance in various directions along the spiral arm (the lines in red, yellow, green, and blue colors) and along the orbital axis (the cyan line), in which all the curves appear well located within the black lines (see below)."
 The profiles iu he orbital plane reveal the highest density peaks at the object orbit. r/ry=1. aud the peak values decrease with distance from the orbit.," The profiles in the orbital plane reveal the highest density peaks at the object orbit, $r/r_p=1$, and the peak values decrease with distance from the orbit."
 The minimum deusity enhancement iu azimuthal directions. e.. the baseline of the group of profiles. gradually decreases followiugthe bottom dashed line (up o r/rg— 0.1) starting [rom à—rg/ry at the orbital center.," The minimum density enhancement in azimuthal directions, i.e., the baseline of the group of profiles, gradually decreases followingthe bottom dashed line (up to $r/r_p=0.4$ ) starting from $\alpha=r_B/r_p$ at the orbital center."
" At r/r,=0.1. however. the baseline jumps to. and follows. another dashed line. aud another jump occurs at r/ry=0.75."," At $r/r_p=0.4$, however, the baseline jumps to, and follows, another dashed line, and another jump occurs at $r/r_p=0.75$."
" In this example case of M,=10. the baseline moves its paths among the dashed lines through three steps before 'eachiug the orbital radius."," In this example case of $\mach=10$, the baseline moves its paths among the dashed lines through three steps before reaching the orbital radius."
 Beyond the orbital radius. it follows the third dashed liue from bottom util it abruptly drops at τρ2.5 apart Ποια the pat[u," Beyond the orbital radius, it follows the third dashed line from bottom until it abruptly drops at $r/r_p\sim2.5$ apart from the path."
n This last drop of miuimui deusity enhancement coincides with the sudder isappearance of the inner arm boundary. which is related o the orbital evolution time of the object.," This last drop of minimum density enhancement coincides with the sudden disappearance of the inner arm boundary, which is related to the orbital evolution time of the object."
 Using the spiral Functional forms deduced iu 'e[secispl.. it is shown that the outer aud inner ari bouudaries reach r/ry=£1 aud 2.L respectively. al the moment that the perturber completes 5 orbits (i.e.. 9— 10x).," Using the spiral functional forms deduced in \\ref{sec:spi}, it is shown that the outer and inner arm boundaries reach $r/r_p=4.1$ and 2.4, respectively, at the moment that the perturber completes 5 orbits (i.e., $\varphi=10\pi$ )."
" The inner ari boundary lags Pebiud by 2.7-turn since it starts from (Γρ.v)=CM,1.l- 0.7M,,). deeper iuside than the starting point of the outer boundary at (rry.ο)=(1. 0)."," The inner arm boundary lags behind by 2.7-turn since it starts from $(r/r_p,\,\varphi)=(\mach^{-1},\,1+0.7\mach)$ , deeper inside than the starting point of the outer boundary at $(r/r_p,\,\varphi)=(1,\,0)$ ."
row shows the differeuce images. the second oi1e including the loop contour as obtained from the TRACE data.,"row shows the difference images, the second one including the loop contour as obtained from the TRACE data."
 The coarser spatial resolution of CDS images makes the loop less defined than in the TRACE images., The coarser spatial resolution of CDS images makes the loop less defined than in the TRACE images.
 For the analysis of the cussion from the kop plasina. oeir order to match casily the TRACE data aux| to use the sale loop outline. the CDS images have bec31 rebinued o the pixels size of TRACE.," For the analysis of the emission from the loop plasma, in order to match easily the TRACE data and to use the same loop outline, the CDS images have been rebinned to the pixels size of TRACE."
 The loop has been divided oeito 123 sectors iu the rebinued difference 1nages. ad je average line intensities have been compted im cach sector.," The loop has been divided into 13 sectors in the rebinned difference images, and the average line intensities have been computed in each sector."
 The loop sectors in CDS images are cilferent from approximately twice as long — those chosen to analyze 16 loop in the TRACE images (Sec. 3.3))., The loop sectors in CDS images are different from – approximately twice as long – those chosen to analyze the loop in the TRACE images (Sec. \ref{sec:loop}) ).
 Few CDS sector jxels vield negative counts: they have been mut to zero., Few CDS sector pixels yield negative counts; they have been put to zero.
 Figure 1l shows the intensities in five lines along the oop., Figure \ref{fig:cds3} shows the intensities in five lines along the loop.
 The error bars have been computed as tje standard deviation of the photon counts within cach CDS sector., The error bars have been computed as the standard deviation of the photon counts within each CDS sector.
" The profiles show a well-defined trend in the lines where he loop is visible iu the difference images. bo. frou, Ca XN 558 to Fe NIT 361As: there is an emission peak around sectors 1 to 3H and then the emission decreases nore or less eradually toward the right lee «Xf the loop."," The profiles show a well-defined trend in the lines where the loop is visible in the difference images, i.e. from Ca X 558 to Fe XII 364: there is an emission peak around sectors 1 to 3 and then the emission decreases more or less gradually toward the right leg of the loop."
" Iu the cool O V 629 line. the oulv. sieuific""uf feature is a bunip at the left extreme."," In the cool O V 629 line, the only significant feature is a bump at the left extreme."
 There is no clear link of lis bump to the loop emission., There is no clear link of this bump to the loop emission.
 The profile in the Mg IN 368 line overall appears similar to the |vackeromud-subtracted profile in the TRACE 171 A filter ]ρα] at 7:30 UT (Fig. 5..," The profile in the Mg IX 368 line overall appears similar to the background-subtracted profile in the TRACE 171 A filter band at 7:39 UT (Fig. \ref{fig:profbk},"
 see also Fig. 133)., see also Fig. \ref{fig:trace_cds}) ).
 Iu the hottest lines (Si XII. Fe NIV and Fe XVI) the profiles show weak. features on the right side of the loop region. which may be evidence of some hot plasma there.," In the hottest lines (Si XII, Fe XIV and Fe XVI) the profiles show weak features on the right side of the loop region, which may be evidence of some hot plasma there."
 In the lues peaking arouud 1 ME. the profiles are consistent with a more hnuuinous loft Ίου.," In the lines peaking around 1 MK, the profiles are consistent with a more luminous left leg."
5 This appears to be consistent with the emissjou distribution along the loop observed on average in the 171 filter band of TRACE iu the corresxndiug time iuterval (lower two plots in Fig. 5))., This appears to be consistent with the emission distribution along the loop observed on average in the 171 filter band of TRACE in the corresponding time interval (lower two plots in Fig. \ref{fig:profbk}) ).
 Line cuuissivities were computed using CIITÀNTT V1.0.2 with ionization equilibrium fractious from Mazzotta et al. (, Line emissivities were computed using CHIANTI V4.0.2 with ionization equilibrium fractions from Mazzotta et al. (
1998) and phlotospheric abundances.,1998) and photospheric abundances.
 Figure 12. shows the enission measure loci diagrauis of five CDS xCors along 16 loop. namcly CDS sectors 2. LL. 7. 9 aud 10 (sce Fig.," Figure \ref{fig:cds4} shows the emission measure loci diagrams of five CDS sectors along the loop, namely CDS sectors 2, 4, 7, 9 and 10 (see Fig."
 11 or some of the liue intensities). roughly corresponding o TRACE sectors L ὃν LE. 18 and 20 (Sec. 3.3)).," \ref{fig:cds3} for some of the line intensities), roughly corresponding to TRACE sectors 4, 8, 14, 18 and 20 (Sec. \ref{sec:loop}) )."
 CDS sectors 2 and [ are in the left leg. CDS sectx d$ around 16 loop apex. and CDS sectors 9 and 10 in the right leg.," CDS sectors 2 and 4 are in the left leg, CDS sector 7 around the loop apex, and CDS sectors 9 and 10 in the right leg."
 The curves are shown oulv for those lines dm which the enission im the CDS sector is larger than zero., The curves are shown only for those lines in which the emission in the CDS sector is larger than zero.
 Aioue the Ines we used in Fig. 12..," Among the lines we used in Fig. \ref{fig:cds4},"
 Li-like (Me X. Si NII) aud. Na- (Ca N) lies are those with the largest τιicertainuties.," Li-like (Mg X, Si XII) and Na-like (Ca X) lines are those with the largest uncertainties."
 As shown bv Laudi et al. (, As shown by Landi et al. (
2002a.5). the emissiπι nieasures of Li-like lines are lower by a factor of 2 when compared o the values obtained with other spectral liies.,"2002a,b), the emission measures of Li-like lines are lower by a factor of 2 when compared to the values obtained with other spectral lines."
 For the Na-like cuuissivities the status is less clear., For the Na-like emissivities the status is less clear.
 Na-like lines enissivities have been fouud to be higher by a factor of 2 (Landi et al 2000a) when compared with SUMER spectra., Na-like lines emissivities have been found to be higher by a factor of 2 (Landi et al 2000a) when compared with SUMER spectra.
 A good agreement with the other ious has been found in colparison with CDS spectra (Laudi ct al 20025)., A good agreement with the other ions has been found in comparison with CDS spectra (Landi et al 2002b).
 We wave found that the MeN 625 line is clearly iucousisteut with all others iu all sectors (dashed line in Fie. 12))., We have found that the Mg X 625 line is clearly inconsistent with all others in all sectors (dashed line in Fig. \ref{fig:cds4}) ).
 Siuilu problems with the Me X 625 line has hee- »oiuted out in a specific spectral study made on solar data using the ADAS atomic aud spectral model (Lauzafiuxc et al., Similar problems with the Mg X 625 line has been pointed out in a specific spectral study made on solar data using the ADAS atomic and spectral model (Lanzafame et al.
 2005)., 2005).
 We have then decided to discuss the eumissio- neasure distributions without considering this line., We have then decided to discuss the emission measure distributions without considering this line.
 As a result. in Fig.," As a result, in Fig."
 12. CDS sector 9 appears to be he hottest. with a peak around logLTx6.25 and with a relatively broad distribution on the cool side down to ogTz6.0.," \ref{fig:cds4} CDS sector 9 appears to be the hottest, with a peak around $\log T \approx 6.25$ and with a relatively broad distribution on the cool side down to $\log T \approx 6.0$."
 CDS sector 10 is somewhat cooler. well oealked. around logT.2:6.15. and CDS sectors [aud 7 are even cooler with peaks at logTLz6.05. and again with a relatively broad distribution towaer the cool side.," CDS sector 10 is somewhat cooler, well peaked around $\log T \approx 6.15$, and CDS sectors 4 and 7 are even cooler with peaks at $\log T \approx
6.05$, and again with a relatively broad distribution towaer the cool side."
 The situation of CDS sector 2 is less clear., The situation of CDS sector 2 is less clear.
 This CDS sector is located very close to the loop left footpoiut and appears brielt in the Si NIT line probably because of other bright overlapping structures., This CDS sector is located very close to the loop left footpoint and appears bright in the Si XII line probably because of other bright overlapping structures.
 In the liebt of this. the panel for CDS sector 2 may be compatible with a relatively cool distribution at logTz6.1. not differcut from CDS sectors laud 7. aud the Ca X line may sugeest the presence of senificant cooler contributions.," In the light of this, the panel for CDS sector 2 may be compatible with a relatively cool distribution at $\log T \approx 6.1$, not different from CDS sectors 4 and 7, and the Ca X line may suggest the presence of significant cooler contributions."
 This may be consistent with the brieht loft lee of the loop in the TRACE 171 images (Fig. 7)), This may be consistent with the bright left leg of the loop in the TRACE 171 images (Fig. \ref{fig:fovhr}) )
 and in the cool lines. CDS. images (Fig. 9))., and in the cool lines CDS images (Fig. \ref{fig:cds1}) ).
 Overall. the figure suggests a trend of increasing teiiperature from the footpoiuts to CDS sector 9. located in the right leg of the loop.," Overall, the figure suggests a trend of increasing temperature from the footpoints to CDS sector 9, located in the right leg of the loop."
 Knowing that the raster took about 1 h to span au X distance of 2107. we obtain that the time difference to raster from sector [| to 10 ( 507) is about 12 minutes (0.7 ks).," Knowing that the raster took about 1 h to span an X distance of 240"", we obtain that the time difference to raster from sector 4 to 10 ( 50"") is about 12 minutes (0.7 ks)."
 This is certainly too small a time lapse to deteriiue senificaut variations of this loop. and we conclide that we are secing the spatial structure of the loop.," This is certainly too small a time lapse to determine significant variations of this loop, and we conclude that we are seeing the spatial structure of the loop."
 The enuüsson measure appears to be the highest in CDS sector 2 (~2«410277 Gin?) and to decrease progressively toward the right cud of the loop (5«10°° y ," The emission measure appears to be the highest in CDS sector 2 $\sim
2 \times 10^{27}$ $^{-5}$ ) and to decrease progressively toward the right end of the loop $\sim 5 \times 10^{26}$ $^{-5}$ )."
Iu this work we present the analvsis of a coronal loop iuaeged in inultiple filters aud spectral lines over part of its Lifetime., In this work we present the analysis of a coronal loop imaged in multiple filters and spectral lines over part of its lifetime.
 The loop has been selected on TRACE inages., The loop has been selected on TRACE images.
 Our analysis collects the information comine frou the time-evolition of the loop region iu three TRACE passbands. and in oue Yolkoli/SNT passband at overlapping times. and two SollO/CDS rasters in twelve relevant lines. one during the TRACE observation. the other soon after.," Our analysis collects the information coming from the time-evolution of the loop region in three TRACE passbands, and in one Yohkoh/SXT passband at overlapping times, and two SoHO/CDS rasters in twelve relevant lines, one during the TRACE observation, the other soon after."
 The selected loop is bright. lies on the disk aud part of it is well isolated from other," The selected loop is bright, lies on the disk and part of it is well isolated from other"
As noted above. if one planet in a two-planet svstem transits its host star as viewed rom Earth. the probability that the second. planet will also transit is higher if the nimtual inclination of the two planetary orbits is small (e.g..Ragozzine&Holman2010).,"As noted above, if one planet in a two-planet system transits its host star as viewed from Earth, the probability that the second planet will also transit is higher if the mutual inclination of the two planetary orbits is small \citep[e.g.,][]{rh10}."
. This argument suggests (hat (he numbers of 1-planet. 2-planet... ...N-planet svstems detected in a arge (ransil survey contain information about both the multiplicity function.the fraction of 1ost slars containing 0.1.2......N planetsand the inclination distribution.," This argument suggests that the numbers of 1-planet, $\ldots$ $N$ -planet systems detected in a large transit survey contain information about both the multiplicity function—the fraction of host stars containing $0,1,2,\ldots,N$ planets—and the inclination distribution."
 The challenge is (o disentangle the (wo distributions to distinguish thick svstems will many. planets [rom (hin svstems with few planets., The challenge is to disentangle the two distributions to distinguish thick systems with many planets from thin systems with few planets.
 The first attempt to do this was made by Lissaueretal.(2011b).. who modeled the number of multiple-planet svstems detected in the first four months of data from (he Ixepler survey (Doruckietal.2011)- 115 with (vo transiting planets. 45 with three. 8 with four. and," The first attempt to do this was made by \cite{liss11b}, who modeled the number of multiple-planet systems detected in the first four months of data from the Kepler survey \citep{bor11}- —115 with two transiting planets, 45 with three, 8 with four, and"
Alanw recent studies. [from observational ancl theoretical viewpoints. have established that stellar bars in disc galaxies can play an important role in galaxy evolution poviews).,"Many recent studies, from observational and theoretical viewpoints, have established that stellar bars in disc galaxies can play an important role in galaxy evolution ."
. Theoretical work indicates that the redistribution of angular momentum. induced by the bar. in the galaxy interstellar medium. as well as in the stellar and dark matter components. has a number of important consequences 22227).," Theoretical work indicates that the redistribution of angular momentum, induced by the bar, in the galaxy interstellar medium, as well as in the stellar and dark matter components, has a number of important consequences ."
 Gas line bevond the bar ends is driven outwarcs. whereas gas lving within the bar ends is driven to the central regions 777777).," Gas lying beyond the bar ends is driven outwards, whereas gas lying within the bar ends is driven to the central regions ."
 This secular evolution scenario has been partially confirmed. at least. qualitatively. with observational evidence that barred galaxies show Latter chemical abundance (O/LD) radial gracients find that the stronger the bar the [latter the) and hieher central concentrations of molecular gas (CO 7))," This secular evolution scenario has been partially confirmed, at least qualitatively, with observational evidence that barred galaxies show flatter chemical abundance (O/H) radial gradients find that the stronger the bar the flatter the and higher central concentrations of molecular gas (CO – )."
 This movement of gas to the centre might in principle help build a voung ancl kinematically cold stellar bulge component. Le. a disc-like bulge 2).," This movement of gas to the centre might in principle help build a young and kinematically cold stellar bulge component, i.e. a disc-like bulge ."
.. Indeed. observations suggest that clise-like bulecs exist and. have formation processes linked to dynamical cise instabilities. such as bars. as opposed. to the old ancl kinematically hot ‘lassical bulges therein).," Indeed, observations suggest that disc-like bulges exist and have formation processes linked to dynamical disc instabilities, such as bars, as opposed to the old and kinematically hot classical bulges ."
. Theory also suggests how bars evolve with time., Theory also suggests how bars evolve with time.
 Broadly speaking. bars slow down their pattern. rotation speed. and get longer ancl thinner (i.c. more eccentric ancl stronger) during the course of their evolution. capturing stars [rom the disc 2).," Broadly speaking, bars slow down their pattern rotation speed, and get longer and thinner (i.e. more eccentric and stronger) during the course of their evolution, capturing stars from the disc ."
. Observations suggest that the strong bar in NCC 4608 has increased in mass by a [actor of z1.7. through the capture ofz13% of the dise stars(?).," Observations suggest that the strong bar in NGC 4608 has increased in mass by a factor of $\approx1.7$, through the capture of $\approx13\%$ of the disc stars."
. In acidition. more evolved bars also show more rectangular-like face-on isophotal shapes. ie. they are more boxy?).," In addition, more evolved bars also show more rectangular-like face-on isophotal shapes, i.e. they are more boxy."
. In detail. however. simulated bars can become abruptly shorter ancl thicker a few. Giga-vears after their formation. due to the onset of dynamical vertical instabilities that originate box/peanut bulges. (," In detail, however, simulated bars can become abruptly shorter and thicker a few Giga-years after their formation, due to the onset of dynamical vertical instabilities that originate box/peanut bulges. ("
ποσο seem to be simply the inner parts of bars that buckle olf the disc,These seem to be simply the inner parts of bars that buckle off the disc
characteristics to be investigated with these observations. such as the velocity. pattern. the morphology. ancl the location of NIL;.,"characteristics to be investigated with these observations, such as the velocity pattern, the morphology, and the location of $_3$."
 If the interpretation given by Gómezetal.(1992). for the outflow. as motions along the walls of a cavity is correct. this drag of material should be seen in all molecular tracers.," If the interpretation given by \cite{Gomez-etal92} for the outflow, as motions along the walls of a cavity is correct, this drag of material should be seen in all molecular tracers."
 In particular. the spatial distribution of bluc- and redshifted velocities of the dense gas traced by NIL; should be similar to the one seen in CO.," In particular, the spatial distribution of blue- and redshifted velocities of the dense gas traced by $_3$ should be similar to the one seen in CO."
 Our results refchan)) are not conclusive to reject the Gomme ct al., Our results \\ref{chan}) ) are not conclusive to reject the Gómmez et al.
's hypothesis.,'s hypothesis.
 There is some hint of more redshifted gas to the north. and more blueshifted one to the south. but the low signal-to-noise ratio of the emission. specially that to the north does not allow firm conclusions.," There is some hint of more redshifted gas to the north, and more blueshifted one to the south, but the low signal-to-noise ratio of the emission, specially that to the north does not allow firm conclusions."
 On the other hand. the most intense ammonia emission (C1) seems to be related to a particular infrared. source (sll). whieh also emits in the submillimeter.," On the other hand, the most intense ammonia emission (C1) seems to be related to a particular infrared source (s11), which also emits in the submillimeter."
 The ammonia seems to trace individual chumps. well defined in velocity. rather than a continuous distribution with a velocity gradient. which one could expect from the model proposed by Gomezetal.(1992).," The ammonia seems to trace individual clumps, well defined in velocity, rather than a continuous distribution with a velocity gradient, which one could expect from the model proposed by \cite{Gomez-etal92}."
 Classical examples. of bipolar outllows show interstellar oroids of dense gas. perpencicular to molecular outLows and/or jets (e.g.. TForrelles et al.," Classical examples of bipolar outflows show interstellar toroids of dense gas, perpendicular to molecular outflows and/or jets (e.g., Torrelles et al."
 1983: Wiseman et al., 1983; Wiseman et al.
 2001)., 2001).
 In the past. these interstellar toroids have been proposed as he collimating agents of these outfows. although the actual collimators seem to be much. smaller. circumstellar disks.," In the past, these interstellar toroids have been proposed as the collimating agents of these outflows, although the actual collimators seem to be much smaller circumstellar disks."
 llowever. given the usual relationship outllow-interstellar oroid. the presence of a dense structure (traced with NIL) »erpendieular to the outflow. and located close to is center. would have favored a more “classical” interpretation of the outllow.," However, given the usual relationship outflow-interstellar toroid, the presence of a dense structure (traced with $_3$ ) perpendicular to the outflow, and located close to is center, would have favored a more “classical” interpretation of the outflow."
 Moreover. ammonia emission has been used. as a ool to identify the excitation source of bipolar outllows.," Moreover, ammonia emission has been used as a tool to identify the excitation source of bipolar outflows."
 Excitation source of outllows usually coincides with the maximum emission of ammonia (Angladaetal.1989)., Excitation source of outflows usually coincides with the maximum emission of ammonia \citep{Anglada-etal89}.
. Phis is usually confirmed with the presence of local enhancements of temperature. (with a higher ratio of the emission. of ammonia (2.2) to (1.1) transitions). and turbulence (wider ammonia lines).," This is usually confirmed with the presence of local enhancements of temperature (with a higher ratio of the emission of ammonia (2,2) to (1,1) transitions), and turbulence (wider ammonia lines)."
 Vhe overall distribution of NIL; does not show any preferential orientation with respect to the molecular outllow., The overall distribution of $_3$ does not show any preferential orientation with respect to the molecular outflow.
 Only clump 3 shows an E-W orientation. roughly perpendicular to the outflow.," Only clump 3 shows an E-W orientation, roughly perpendicular to the outflow."
 Llowever. it is located to the south. on the blueshifted. lobe of the CO emission. rather than towards the central cluster. and no infrared. source is located near its maximum.," However, it is located to the south, on the blueshifted lobe of the CO emission, rather than towards the central cluster, and no infrared source is located near its maximum."
 Using the maximum. of ammonia (clump Cl) as a criterium to search for the powering source of the outflow. source sli would be a good candidate.," Using the maximum of ammonia (clump C1) as a criterium to search for the powering source of the outflow, source s11 would be a good candidate."
 Its spectral energy clistribution (kumarDewangan&Anandarao2010) and its distinctive nature as a submillimeter source shows that sll isa YSO., Its spectral energy distribution \citep{Dewangan&Anandarao10} and its distinctive nature as a submillimeter source shows that s11 is a YSO.
 Nevertheless. source sll is clearly olfset. from the center of the outflow. and it is hard to imagine that it could be its main driving source.," Nevertheless, source s11 is clearly offset from the center of the outflow, and it is hard to imagine that it could be its main driving source."
 However. we note that both. the recshifted and blueshiftec CO lobes show extensions to the cast (Gomezetal.1992)...," However, we note that both, the redshifted and blueshifted CO lobes show extensions to the east \citep{Gomez-etal92}."
 We suggest that these extensions could in fact be part of an independent. outflow driven. by source sll. while the bulk ofthe CO outllow would be driven bv the sources in the central cluster.," We suggest that these extensions could in fact be part of an independent outflow driven by source s11, while the bulk of the CO outflow would be driven by the sources in the central cluster."
 There are several sources in APGL 437 that could be undergoing mass-losssimultaneously., There are several sources in AFGL 437 that could be undergoing mass-losssimultaneously.
 Source Wx 34. is associated with an infrared. polarized nebula (Weintraub&]xastner1996:Moeakinctal. 2005).. ancl has been suggested to be the dominant exciting source of the outflow.," Source WK 34 is associated with an infrared polarized nebula \citep{Weintraub&Kastner96,Meakin-etal05}, and has been suggested to be the dominant exciting source of the outflow."
 The infrared. nebula and. its association with a water maser (Lorrellesetal.1992:Weintraub&Ixastner1900) clearly indicate that this source is an active source of mass-loss.," The infrared nebula and its association with a water maser \citep{Torrelles-etal92,Weintraub&Kastner96} clearly indicate that this source is an active source of mass-loss."
 Source APGL 4378 also shows elongated. infrared. emission (Alvarezetal.2004).. which is also suggestive of a star undergoing mass-loss. although this extension is weak. and close to the resolution limit of the maps.," Source AFGL 437S also shows elongated infrared emission \citep{Alvarez-etal04}, which is also suggestive of a star undergoing mass-loss, although this extension is weak, and close to the resolution limit of the maps."
 Our radio continuum map at 2 em (Lig. 5)), Our radio continuum map at 2 cm (Fig. \ref{radio3}) )
 shows. for the first time. the presence of a collimated jot associated to source AGL 437W. The previous detection of both radio continuum and water maser emission (Lorrelles οἱ al.," shows, for the first time, the presence of a collimated jet associated to source AFGL 437W. The previous detection of both radio continuum and water maser emission (Torrelles et al."
 1992) alreaciy. signaled. this source as à voung object. but now we see that its mass loss is highly. collimated.," 1992) already signaled this source as a young object, but now we see that its mass loss is highly collimated."
" ""Therefore we have strong evidence that at least WIx 34 and APGL 437W (and possibly AEGL 4378) are undergoing collimated mass loss.", Therefore we have strong evidence that at least WK 34 and AFGL 437W (and possibly AFGL 437S) are undergoing collimated mass loss.
 “Phis seems not to support the model of Gomezetal.(1992)... which suggested that the mass loss could be isotropic (ancl the observed CO) hipolarity would be a projection ellect)," This seems not to support the model of \cite{Gomez-etal92}, which suggested that the mass loss could be isotropic (and the observed CO bipolarity would be a projection effect)."
 We now favor that the observed CO outllow is the superposition of several bipolar outllows. which would explain its low degree of collimation.," We now favor that the observed CO outflow is the superposition of several bipolar outflows, which would explain its low degree of collimation."
 Sources Wh 34. AFGL 437W (ancl possibly AGL 4378) could be responsible for the bulk of high-velocity CO emission close to the center.," Sources WK 34, AFGL 437W (and possibly AFGL 437S) could be responsible for the bulk of high-velocity CO emission close to the center."
 We also propose that source sll is à voung embedded: object that could. drive an additional outflow. traced by the eastern extensions of the €CO lobes.," We also propose that source s11 is a young embedded object that could drive an additional outflow, traced by the eastern extensions of the CO lobes."
 Weintraub&Wastner(1996) and WKumarDewangan&Anancarao(2010) noticed that the infrared. emission near Wily 34 is oriented in the N-8 direction next to the source. but it bends to the northeast away from it.," \cite{Weintraub&Kastner96} and \cite{Dewangan&Anandarao10} noticed that the infrared emission near WK 34 is oriented in the N-S direction next to the source, but it bends to the northeast away from it."
 IxumarDewangan&Anan-carao(2010) suggested that this bending may be due to the interaction of the outflow from Wily 34 with mass loss from source AFGL 437N. but we suggest that it could reflect the interactions between the outllows from WlIx 34 and ALCL 437\W. ‘This superposition of several individual outflows. giving rise to complex morphologies when observing at low angular resolution. is also found in other high-mass star forming regions (e.g.. Beuther et al.," \cite{Dewangan&Anandarao10} suggested that this bending may be due to the interaction of the outflow from WK 34 with mass loss from source AFGL 437N, but we suggest that it could reflect the interactions between the outflows from WK 34 and AFGL 437W. This superposition of several individual outflows, giving rise to complex morphologies when observing at low angular resolution, is also found in other high-mass star forming regions (e.g., Beuther et al."
 2002. 2006: Ginsburg et al.," 2002, 2006; Ginsburg et al."
 2009)., 2009).
 An alternative scenario would be that only one source is significantly. driving the (low-collimation) outflow. even when present evidence is of highly collimated jets. if both a collimated. jet anc a. low-collimation wind. are driven simultaneously by the same source.," An alternative scenario would be that only one source is significantly driving the (low-collimation) outflow, even when present evidence is of highly collimated jets, if both a collimated jet and a low-collimation wind are driven simultaneously by the same source."
 Evidence. for simultaneous presence of high- and low-collimation mass loss has been found for the first time in a high-mass voung star in water maser observations of Cepheus A (Vorrellesοἱal. 2011).., Evidence for simultaneous presence of high- and low-collimation mass loss has been found for the first time in a high-mass young star in water maser observations of Cepheus A \citep{Torrelles-etal11}. .
 To test these scenarios. we propose that the molecular," To test these scenarios, we propose that the molecular"
ranee from 53° FEWIIM at EK-baud to 13° FWIIM at W-baud.,range from 53' FWHM at K-band to 13' FWHM at W-band.
" Because of this large rauge in resolution. we specify the pixel resolution aud harmonic space range for cach case separately,"," Because of this large range in resolution, we specify the pixel resolution and harmonic space range for each case separately."
" For instance. Ik-baud is pixclized at Midge=un512. and inchicdes multipoles up to fas,=750 (the highest uniltipole present iu the transfer function provided by the WAIAP team). while the ἂνας is pixelized at ως=1021. and includes multipoles up to ο=L700."," For instance, K-band is pixelized at $N_{\textrm{side}}=512$, and includes multipoles up to $\ell_{\textrm{max}}=750$ (the highest multipole present in the transfer function provided by the WMAP team), while the W-band is pixelized at $N_{\textrm{side}}=1024$, and includes multipoles up to $\ell_{\textrm{max}}=1700$."
 A full summary of all relevant pariuneters for cach DA is given in Table 1.., A full summary of all relevant parameters for each DA is given in Table \ref{tab:summary}.
 Note that the listed noise RAIS values are ouly used for estimating the power spectra weights iu Section 6.., Note that the listed noise RMS values are only used for estimating the power spectrum weights in Section \ref{sec:cosmology}.
 For simplicity we have adopted the official RAIS values for the foregrouud-areduced: 5-vear WALAP maps here. but note that there is a 1 bias in some of these values (Croeneboometal.2009)..," For simplicity we have adopted the official RMS values for the foreground-reduced 5-year WMAP maps here, but note that there is a $\sim1$ bias in some of these values \citep{groeneboom:2009b}."
 However. this has no sijenificaut iipact on the results presented im this paper.," However, this has no significant impact on the results presented in this paper."
 The bein maps for each DA are provided in the form of pixelized maps. and separately for side A aud D. Each bea map contaius non-zero values inside a radius around the beam center which is specified foreach. DA.," The beam maps for each DA are provided in the form of pixelized maps, and separately for side A and B. Each beam map contains non-zero values inside a radius around the beam center which is specified foreach DA."
 For mstauce. the I-baud radius is 77. aud the W-baud," For instance, the K-band radius is $7^{\circ}$ , and the W-band"
the progenitor orbited about the host before the GRB event.,the progenitor orbited about the host before the GRB event.
 Indeed with (he inferred stellar mass —Tx10HM.hep> of. the putative. host. unless the progenitor- was born on the outskirts- of the host gravitational potential. the (rue vy would have to have been comparable to or ereater than dispersion velocity of the host.," Indeed with the inferred stellar mass $7 \times 10^{11}
M_{\sun}\, h_{71}^{-2}$ of the putative host, unless the progenitor was born on the outskirts of the host gravitational potential, the true $v_{\rm kick}$ would have to have been comparable to or greater than dispersion velocity of the host."
 If the progenitor remains gravitationallv bound to G* (then the svstemic orbital velocity of progenitor spends most time near zero velocity. with ils initial kinetic energy stored as eravitational potential.," If the progenitor remains gravitationally bound to $G^*$ then the systemic orbital velocity of progenitor spends most time near zero velocity, with its initial kinetic energy stored as gravitational potential."
 That is. we nominally expect an orbiting progenitor to produce a burst near the maximal distance from its host.," That is, we nominally expect an orbiting progenitor to produce a burst near the maximal distance from its host."
 Iideed if all the energy is stored as potential. then for SUB 060502D. the gravitational potential of the progenitor svsten is Upon birth. the kinetic energy per unit mass imparted to the progenitor must have been: llere we have taken the nominal velocity of the kick as the geometric mean of the dispersion velocity (22460 kam 1) and tiem mint Laat ds. we assume eju=160 km +t.," Indeed if all the energy is stored as potential, then for SHB 060502B, the gravitational potential of the progenitor system is Upon birth, the kinetic energy per unit mass imparted to the progenitor must have been: Here we have taken the nominal velocity of the kick as the geometric mean of the dispersion velocity $\approx 460$ km $^{-1}$ ) and $v_{\rm kick, min} $ ; that is, we assume $v_{\rm kick} = 160$ km $^{-1}$."
" That €jiy 1s even within an order of magnitude of ερ, is either a remarkable OF. we suggest. indicative of support on dynamical grounds for the ejection hypothesis."," That $\epsilon_{\rm kin}$ is even within an order of magnitude of $\epsilon_{\rm pot}$ is either a remarkable or, we suggest, indicative of support on dynamical grounds for the ejection hypothesis."
 We end by acknowledging the οσον of confirming. bevond reasonable doubt. our hypothesis that C hosted the birth of the progenitor of 0060205b.," We end by acknowledging the difficulty of confirming, beyond reasonable doubt, our hypothesis that $G^*$ hosted the birth of the progenitor of 060205b."
 The progenitors of most LSBs. owing to their connection with massive stars. allowed [or unambiguous associations with putative hosts most with probability of chance alignment P<10* (Bloomοἱ 2002).," The progenitors of most LSBs, owing to their connection with massive stars, allowed for unambiguous associations with putative hosts — most with probability of chance alignment $P \ale 10^{-3}$ \citep{bkd02}."
". With 0060502b we have estimated under mildly conservative assumptions wwithout regard (o host (wpe) that the chance of a spurious assignment wilh G"" is Px1054..", With 060502b we have estimated under mildly conservative assumptions without regard to host type) that the chance of a spurious assignment with $G^*$ is $P \ale$.
" The ej,&ey, argument and the similarity with 050509b likely strengthen this parücular association.", The $\epsilon_{\rm kin} \approx \epsilon_{\rm pot}$ argument and the similarity with 050509b likely strengthen this particular association.
 Yet with SIIDs. especially if the majority of progenitors are long-lived hieh-velocity degenerate mergers. (he community must accept that an appreciable Iraction of host assignments relative to LSBs will be spurious (Bloometal.1997).," Yet with SHBs, especially if the majority of progenitors are long-lived high-velocity degenerate mergers, the community must accept that an appreciable fraction of host assignments relative to LSBs will be spurious \citep{btw97}."
. Of course absorption line redshifts of SIIB afterglows. one of the remaining observational goals of the field. will help to significantlycull the number density of viable hosts on the sky.," Of course absorption line redshifts of SHB afterglows, one of the remaining observational goals of the field, will help to significantlycull the number density of viable hosts on the sky."
may explain the presence of burst oscillations during the rise. it is not sufficient to explain the continuis preseuce of large-scale asynuunetrics iu the burst tail ouce the entire stellar surface has ignited (Strolumaver&Bildsten 2006).,"may explain the presence of burst oscillations during the rise, it is not sufficient to explain the continuing presence of large-scale asymmetries in the burst tail once the entire stellar surface has ignited \citep{str06}."
". This has led to the cousideration of alternative models,", This has led to the consideration of alternative models.
 Nou-radial elobal oscillations iu the surface lavers of the star. excited bv the flame spread. real a promising possibility (IIev12001).," Non-radial global oscillations in the surface layers of the star, excited by the flame spread, remain a promising possibility \citep{hey04}."
. Iu. this case he brightness asvuunetry would be caused by variations in ocean height associated with the mode., In this case the brightness asymmetry would be caused by variations in ocean height associated with the mode.
 Inertial frame wattern speed can be verv close to the spin rate. aud cooling of the lavers in the aftermath of the burst would wturally lead to frequency drift.," Inertial frame pattern speed can be very close to the spin rate, and cooling of the layers in the aftermath of the burst would naturally lead to frequency drift."
 The major probleii of his model is that it overpredicts the size of the frequency dift compared to observations (Piro&Bildsten2005:Berkhout&Levin 2008).," The major problem of this model is that it overpredicts the size of the frequency drift compared to observations \citep{pir05, ber08}."
. Alternative possibilities like shotospheric miodes (Wevl20018) or shear oscillations (Cunning2005)also have shortcomings in their preseut orm (Berkhout&Levin2008).," Alternative possibilities like photospheric modes \citep{hey04} or shear oscillations \citep{cum05}
also have shortcomings in their present form \citep{ber08}."
". Current efforts to resolve hese problems are focusing ou the role of the magnetic field. which can dominate the cyvnamics in the surface avers and is expected to have a huge effect on surface uodes,"," Current efforts to resolve these problems are focusing on the role of the magnetic field, which can dominate the dynamics in the surface layers and is expected to have a large effect on surface modes."
 If the magnetic feld is the most important factor determining the properties of burst oscillations then this wieht lead to a natural explanation for the differences iu he properties of the burst oscillations of SAX 11505.I- aud NTE JI1811-338 (hereafter collectively referred ο as SN: Chakrabartyetal.20023:Strolunaver2003:Wattsetal.2005:&Strolunaver 2006)) compared o those of the noun-AMPSs (Muuoetal.2002a.b..2003.2001:Callowayetal. 2008a).," If the magnetic field is the most important factor determining the properties of burst oscillations then this might lead to a natural explanation for the differences in the properties of the burst oscillations of SAX J1808.4-3658 and XTE J1814-338 (hereafter collectively referred to as SX: \citealt{cha03, str03, wat05, wat06}) ) compared to those of the non-AMPs \citep{mun02, mun02b, mun03, mun04, gal08a}."
. These cüfferences can be sununuarized as follows. (, These differences can be summarized as follows. (
1) SN show oscillations iu all of their bursts. even in the hard state: the non-AMPs do not (oscillations are detected primarily although: not exclusively in the soft state). (,"1) SX show oscillations in all of their bursts, even in the hard state; the non-AMPs do not (oscillations are detected primarily although not exclusively in the soft state). ("
2) SN show oscillations throughout their bursts (except during PRE): the nou-ANMIPs. in most cases. do not. (,"2) SX show oscillations throughout their bursts (except during PRE); the non-AMPs, in most cases, do not. ("
3) SN burst oscillations have amplitudes that fall with cucrev: the uon-AMP oscillations have amplitudes that rise. (,3) SX burst oscillations have amplitudes that fall with energy; the non-AMP oscillations have amplitudes that rise. (
1) SX burst oscillations have detectable harmonic coutent: the non-AXIPs have none. (,4) SX burst oscillations have detectable harmonic content; the non-AMPs have none. (
5) Frequency drift in SN is either very fast or non-existent: iu the non-AAIPs it is much slower.,5) Frequency drift in SX is either very fast or non-existent; in the non-AMPs it is much slower.
 The mnmaguetie field also plavs an important role iu models for intermittency of accretion-powered pulsations., The magnetic field also plays an important role in models for intermittency of accretion-powered pulsations.
 Iu the obscuration aud accretion stream wander models. the field is always present at the level recessary to channel the flow: but the accretion lot spot either wauders out of the line of sight or is obscured by uaguetospheric material.," In the obscuration and accretion stream wander models, the field is always present at the level necessary to channel the flow: but the accretion hot spot either wanders out of the line of sight or is obscured by magnetospheric material."
 In the maguetic burial uodel he field streneth aud eeometry chanee as the feld is suppressed by accretion., In the magnetic burial model the field strength and geometry change as the field is suppressed by accretion.
 If magnetic field affects both intermittency and burst oscillations. then stucving the atter may enable us to pinpoint the cause of the former.," If magnetic field affects both intermittency and burst oscillations, then studying the latter may enable us to pinpoint the cause of the former."
 Tn Aql X-1 the burst oscillations are similar in sropertics to those of the non-AMPs: however this source has an exceptionally low cutyv cvcle κο its intermittent pulsation episode may have been triggered wean extremely rare event., In Aql X-1 the burst oscillations are similar in properties to those of the non-AMPs: however this source has an exceptionally low duty cycle so its intermittent pulsation episode may have been triggered by an extremely rare event.
 Iu ΠΤΙ J1900.1-2155 the accretion-powered pulsations lasted for wach longer., In HETE J1900.1-2455 the accretion-powered pulsations lasted for much longer.
 Its nrst oscillations. however. also behave like those of he non-AMPs.," Its burst oscillations, however, also behave like those of the non-AMPs."
 This has important implications., This has important implications.
 If hot spot wander or obscuration models for intermuttency are correct. then a field strong enough to channel iufalliug naterial cannot be the only factor causing the atvpical αντ oscillatious of SAX Π50δ.1-3658 aud NTE J1811-338.," If hot spot wander or obscuration models for intermittency are correct, then a field strong enough to channel infalling material cannot be the only factor causing the atypical burst oscillations of SAX J1808.4-3658 and XTE J1814-338."
 Some other factor. such as the presence of a strong eniperature gradient around the magnetic pole. must also plav a role iu the burst oscillation οςαπΙσ (Wattsetal.2008)..," Some other factor, such as the presence of a strong temperature gradient around the magnetic pole, must also play a role in the burst oscillation mechanism \citep{wat08c}."
 If ou the other haud the ficld has en buried in UETE J1900.1-2155. then it must be screened to a depth where it is unable to affect the mast oscillation mechanisim ou the timescale of the burst.," If on the other hand the field has been buried in HETE J1900.1-2455, then it must be screened to a depth where it is unable to affect the burst oscillation mechanism on the timescale of the burst."
 Detailed calculations will be required to resolve this isst mut if screening at the burning depth is not possible. hen this could point to plhotospheric rather than oceanic nodes as a cause of burst oscillations.," Detailed calculations will be required to resolve this issue, but if screening at the burning depth is not possible, then this could point to photospheric rather than oceanic modes as a cause of burst oscillations."
 One other point of note is that in both Aql N-1 aud IIETE J1900.1-2155. burst oscillation frequency remains yclow spin frequency.," One other point of note is that in both Aql X-1 and HETE J1900.1-2455, burst oscillation frequency remains below spin frequency."
 Caven the similarities in properties it seenas probable that this is the case for uon-AAIPs as well., Given the similarities in properties it seems probable that this is the case for non-AMPs as well.
 However it is not the case for SAN JLsds.I-3658 aud NTE Jia1-338., However it is not the case for SAX J1808.4-3658 and XTE J1814-338.
 In SAN JI808.1-3658 the burst oscillations are first detected below the spin frequency t rapidly overshoot it. settling ~ 0.1 ITz above the spin requency in the burst tail (Chakrabartyetal.2003).," In SAX J1808.4-3658 the burst oscillations are first detected below the spin frequency but rapidly overshoot it, settling $\sim$ 0.1 Hz above the spin frequency in the burst tail \citep{cha03}."
. Tn NATE J1511-335 the two frequencies are identical. aud in act burst oscillations and accretion-powered pulsations are coherent aud phase-locked (Strolumaveretal.2003: 2005]...," In XTE J1814-338 the two frequencies are identical, and in fact burst oscillations and accretion-powered pulsations are coherent and phase-locked \citep{str03, wat05, wat08c}. ."
 Any unified model of burst oscillations iust be able to explain this diversity in he relationship between burst oscillation frequency aud spin., Any unified model of burst oscillations must be able to explain this diversity in the relationship between burst oscillation frequency and spin.
"high energy cut-offs 54,443»Amine",high energy cut-offs $\gamma_{\rm max} \gg \gamma_{\rm min}$.
" Thus. (52/5)~5sInGyuuas/mii). and the svnchrotron Iuninositv is where coefficient & ean be found as 'The flux densitv of the svnchrotron emission is then where di,=1025 Mpe is the Iuninositv distance to ος 273. and Bc=B/G."," Thus, $\langle \gamma^2 \rangle / \langle \gamma \rangle \sim \gamma_{\rm min} \, \ln(\gamma_{\rm max} / \gamma_{min})$, and the synchrotron luminosity is where coefficient $k$ can be found as The flux density of the synchrotron emission is then where $d_{\rm L} = 1025$ Mpc is the luminosity distance to 3C 273, and $B_{\mu {\rm G}} \equiv B / \mu {\rm G}$ ."
" For the model parameters 2,4,c10. Bacc3. τος~1 and τοως~0.2 (referring to the enerev ecquipartition between the magnetic field and (he radiating electrons for the outer lobe radius Ds~ 1). one gets the L4 GlIlz flux ~4 mJy. which is ~10.1 of the total 3C 273 [lux al this frequency."," For the model parameters $\gamma_{\rm min} \sim 10$, $B_{\mu {\rm G}} \sim 3$, $W_{59.5} \sim 1$ and $\varepsilon_{\rm e, \, lobe} \sim 0.2$ (referring to the energy equipartition between the magnetic field and the radiating electrons for the outer lobe radius $D_{2} \sim 1$ ), one gets the $1.4$ GHz flux $\sim 4$ mJy, which is $\sim 10^{-4}$ of the total 3C 273 flux at this frequency."
 Obviously. (he above estimates are illustrative only.," Obviously, the above estimates are illustrative only."
 However. we believe (hat anv more sophisticated approach would be at the present stage as arbitrary as the present one.," However, we believe that any more sophisticated approach would be at the present stage as arbitrary as the present one."
 That is because the number of the unknown old lobe parameters would increase significantly in such a case., That is because the number of the unknown old lobe parameters would increase significantly in such a case.
 In particular. using more realistic spectrum Lor the old lobe electrons would not necessarily result in more realistic prediction about the expected radio flix.," In particular, using `more realistic' spectrum for the old lobe electrons would not necessarily result in `more realistic' prediction about the expected radio flux."
 We note many controversies regarding (the complicated issue of modeling the electron spectral evolution in the lobes of powerful radio sources (e.g..2000:IxaiserManolakou&Ixirk2002 ).," We note many controversies regarding the complicated issue of modeling the electron spectral evolution in the lobes of powerful radio sources \citep[e.g.,][]{blu00,ka00,man02}."
. The relativistic electrons deposited within the outer lobe during the eventual previous jel active period can be pronounced not only at radio frequencies. but also at N-ray photon energies due (o inverse-Complton scattering on the CAMB photon field 1979) or on the Eu-inlrared radiation produced by the 3C 273B quasar core 1997).," The relativistic electrons deposited within the outer lobe during the eventual previous jet active period can be pronounced not only at radio frequencies, but also at X-ray photon energies due to inverse-Compton scattering on the CMB photon field \citep{har79} or on the far-infrared radiation produced by the 3C 273 quasar core \citep{bru97}."
. Such a non-thermal X-ray. emission was already. detected from the number of lobes in FR I radio galaxies aud quasars (see.e.g..Brunet2002.andreferencestherein)..," Such a non-thermal X-ray emission was already detected from the number of lobes in FR II radio galaxies and quasars \citep[see, e.g.,][and references therein]{bru02}."
 In {his context. it is tempting to speculate if the X-ray halo detected by ROSAT around 3C 273 (Roserοἱal.2000) is not due to the intergalactic hot gas. but consists of (wo different components: the thermal one originating in the interstellar medium of the 3C 273 host galaxy (seeMulchaev&Zabludotf1993). and the extended. non-thermal high-energy. tail due to relativistic electrons of the outer lobes.," In this context, it is tempting to speculate if the X-ray halo detected by ROSAT around 3C 273 \citep{roe00} is not due to the intergalactic hot gas, but consists of two different components: the thermal one originating in the interstellar medium of the 3C 273 host galaxy \citep[see][]{mul98} and the extended, non-thermal high-energy tail due to relativistic electrons of the outer lobes."
 However. we estimate (he total X-ray luminosityof the outer lobe due to comptonization of the CMD radiation (in analogy to the radio," However, we estimate the total X-ray luminosityof the outer lobe due to comptonization of the CMB radiation (in analogy to the radio"
"light cylinder, suggested to be relevant in the production of giant pulses (Cognardetal.1996),, is approximately that of both the Crab pulsar and PSR B1937+21, and comparable to that of PSR B1821—24, all of which exhibit giant pulses.","light cylinder, suggested to be relevant in the production of giant pulses \citep{1996ApJ...457L..81C}, is approximately that of both the Crab pulsar and PSR B1937+21, and comparable to that of PSR $-$ 24, all of which exhibit giant pulses."
" Additional radio observations, also with the GUPPI system, were carried out at roughly 3-month intervals to constrain the pulsar’s long-term timing behavior."," Additional radio observations, also with the GUPPI system, were carried out at roughly 3-month intervals to constrain the pulsar's long-term timing behavior."
" Notably, the pulse periods measured during and after the confirmation observation differed substantially from those detected during the two discovery observations made 1.5 years earlier, implying that a spin “glitch” of magnitude AP/Pc1.9x10:65 had occurred at an unknown epoch in this interval."," Notably, the pulse periods measured during and after the confirmation observation differed substantially from those detected during the two discovery observations made 1.5 years earlier, implying that a spin “glitch” of magnitude $\Delta P/P \simeq 1.9\times 10^{-6}$ had occurred at an unknown epoch in this interval."
 The spacing of the radio timing observations together with apparent “timing noise” instability in the pulsar’s rotation on similar timescales precluded derivation of a phase-connected timing solution., The spacing of the radio timing observations together with apparent “timing noise” instability in the pulsar's rotation on similar timescales precluded derivation of a phase-connected timing solution.
" We therefore determined the long-term average spin-down rate, 4.3192(27)x10:34, through a least-squares fit to the multi-epoch period measurements (Figure 2)), a result consistent with the short-term ray-derived ephemeris shown in Table 1 (see 844.1)."," We therefore determined the long-term average spin-down rate, $4.3192(27)\times10^{-14}$, through a least-squares fit to the multi-epoch period measurements (Figure \ref{fig:radiotiming}) ), a result consistent with the short-term X-ray-derived ephemeris shown in Table \ref{tab:ephem}
 (see 4.1)."
" The pulsar’s flux density at 2 GHz, Soanz, is 60 uJy; its 4.8 GHz flux density of &45 pJy suggests that hhas an unusually flat spectrum, a—0.33."," The pulsar's flux density at 2 GHz, $S_{\rm 2\,GHz}$, is 60 $\mu$ Jy; its 4.8 GHz flux density of $\approx 45$ $\mu$ Jy suggests that has an unusually flat spectrum, $\alpha \simeq -0.33$."
" The implied radio pseudo-luminosity S;4Gmgz;d?~7D?) mJy kpc? is unremarkable, low in comparison to the majority of known pulsars, but an order of magnitude higher than the luminosities of other young, faint pulsars discovered in deep searches of SNRs (Camilo2004).."," The implied radio pseudo-luminosity $S_{\rm 1.4\,GHz}d^2 \simeq 7\,D^2_{10}$ mJy $^2$ is unremarkable, low in comparison to the majority of known pulsars, but an order of magnitude higher than the luminosities of other young, faint pulsars discovered in deep searches of SNRs \citep{2004IAUS..218...97C}."
" Even with a long cumulative exposure, our best average pulse profile (Figure 2)) retains significant statistical noise; despite this faintness, a number of relevant pulse shape and polarization results are available."," Even with a long cumulative exposure, our best average pulse profile (Figure \ref{fig:radiotiming}) ) retains significant statistical noise; despite this faintness, a number of relevant pulse shape and polarization results are available."
" The radio pulsations of aare significantly affected by dispersion and scattering due to propagation in the interstellar medium, which are typically important at frequencies <1 GHz, even in our 2 GHz observations."," The radio pulsations of are significantly affected by dispersion and scattering due to propagation in the interstellar medium, which are typically important at frequencies $\lesssim 1$ GHz, even in our 2 GHz observations."
" To estimate dispersion measure (DM) and the pulse broadening timescale 7?*5*, we formed a pulse-shape model assuming a gaussian-shaped intrinsic profile, a one-sided exponential-decay impulse response function for the scatter-broadening, and a v- frequency dependence for the width of the exponential."," To estimate dispersion measure (DM) and the pulse broadening timescale $\tau^{\rm scatt}$, we formed a pulse-shape model assuming a gaussian-shaped intrinsic profile, a one-sided exponential-decay impulse response function for the scatter-broadening, and a $\nu^{-4}$ frequency dependence for the width of the exponential."
" We fit the S-band (ie., 2GGHz) data to this model in four evenly-spaced frequency sub-bands, allowing the width of the intrinsic gaussian profile to vary and also accounting for a DM bias caused by the frequency-dependent pulse broadening due to scattering."," We fit the S-band (i.e., GHz) data to this model in four evenly-spaced frequency sub-bands, allowing the width of the intrinsic gaussian profile to vary and also accounting for a DM bias caused by the frequency-dependent pulse broadening due to scattering."
" This simple model fit the data well, but we caution that the assumptions inherent in the model may introduce significant systematic errors, perhaps as large as twice the statistical uncertainties quoted below."," This simple model fit the data well, but we caution that the assumptions inherent in the model may introduce significant systematic errors, perhaps as large as twice the statistical uncertainties quoted below."
" The NE2001 Galactic electron distribution model (Cordes&Lazio fails to accommodate the derived DM=429.12002)+0.5 pc cm""? in the direction of J2022--3842-—formally, the model suggests a lower bound on the distance to the pulsar of 50 kpc."," The NE2001 Galactic electron distribution model \citep{2002astro.ph..7156C} fails to accommodate the derived ${\rm DM} = 429.1\pm0.5$ pc $^{-3}$ in the direction of —formally, the model suggests a lower bound on the distance to the pulsar of 50 kpc."
" Instead, a likely over-density of free electrons in the Cygnus region, along the line of sight, accounts for the higher-than-expected dispersion—a similar explanation has been advanced for the unexpectedly large DM of the nearby PSR J2021--3651 (Robertsetal.2002).."," Instead, a likely over-density of free electrons in the Cygnus region, along the line of sight, accounts for the higher-than-expected dispersion—a similar explanation has been advanced for the unexpectedly large DM of the nearby PSR J2021+3651 \citep{2002ApJ...577L..19R}."
" In this direction, the Perseus Arm lies at a distance of approximately 6 kpc, and the Outer Arm at 210 kpc."," In this direction, the Perseus Arm lies at a distance of approximately 6 kpc, and the Outer Arm at $\gtrsim10$ kpc."
" For convenience in scaling distance-dependent parameters and because the larger distance brings X-ray efficiencies more approximately in line with those of other young pulsars (see refsec:discuss)), we adopt a distance d=10Dio kpc."," For convenience in scaling distance-dependent parameters and because the larger distance brings X-ray efficiencies more approximately in line with those of other young pulsars (see \\ref{sec:discuss}) ), we adopt a distance $d = 10\, D_{10}$ kpc."
" Independent supporting evidence for the large distance derives from absorption and X-ray studies of the PWN CTB 87 (Kothesetal.2003),, roughly 2° from oon the sky."," Independent supporting evidence for the large distance derives from absorption and X-ray studies of the PWN CTB 87 \citep{2003ApJ...588..852K}, roughly $2\degr$ from on the sky."
" At a distance of 6.1 kpc, CTB 87 lies in the Perseus arm and its X-ray-derived absorbing column is Ng=(1.4+0.2)x107? cm? at confidence (Safi- Matheson Kothes, in preparation); although their uncertainties are large, the nominal column for iis somewhat larger than that for CTB 87."," At a distance of 6.1 kpc, CTB 87 lies in the Perseus arm and its X-ray-derived absorbing column is $N_{\rm H} =
(1.4\pm0.2)\times10^{22}$ $^{-2}$ at confidence (Safi-Harb, Matheson Kothes, in preparation); although their uncertainties are large, the nominal column for is somewhat larger than that for CTB 87."
 A radio bright extragalactic point source adjacent to CTB 87 exhibits, A radio bright extragalactic point source adjacent to CTB 87 exhibits
"Table 1 shows the number of events photometrically classified as SNIa or ""not SNIa"" for events classified spectroscopicaly as SNIa, SNcc and ""ambiguous"", as well as for events for which no spectrum was obtained.","Table \ref{classificationtab} shows the number of events photometrically classified as SNIa or “not SNIa” for events classified spectroscopicaly as SNIa, SNcc and “ambiguous”, as well as for events for which no spectrum was obtained."
" The table contains only those events that will be used for rate measurements in the next section, i.e. those with 0.05«z0.4 and ms;o«24.1 (equation 2))."," The table contains only those events that will be used for rate measurements in the next section, i.e. those with $0.05<z<0.4$ and $m_{570}<24.1$ (equation \ref{m570def}) )."
 The reasonable performance of the photometric classification is demonstrated by the fact that only seven of the 46 spectroscopic SNIa were not selected and only one of the 24 spectroscopic SNcc was selected., The reasonable performance of the photometric classification is demonstrated by the fact that only seven of the 46 spectroscopic SNIa were not selected and only one of the 24 spectroscopic SNcc was selected.
 The photometric classification also selected 14 events that had not been classified spectroscopically as SNIa., The photometric classification also selected 14 events that had not been classified spectroscopically as SNIa.
" As detailed below, the lack of spectroscopic confirmation was generally due to an insufficient supernova signal over the galactic background or to lack of telescope time to obtain a spectrum."," As detailed below, the lack of spectroscopic confirmation was generally due to an insufficient supernova signal over the galactic background or to lack of telescope time to obtain a spectrum."
" As our nominal SNIa sample, we choose the 46 events that were spectroscopically identified as SNIa plus the 14 events photometrically identified as SNIa that were not spectroscopic SNcc."," As our nominal SNIa sample, we choose the 46 events that were spectroscopically identified as SNIa plus the 14 events photometrically identified as SNIa that were not spectroscopic SNcc."
 The nominal SNcc sample is the 117 remaining events., The nominal SNcc sample is the 117 remaining events.
 The distribution of AMs79 for these events are shown as the histograms in Figs., The distribution of $\Delta M_{570}$ for these events are shown as the histograms in Figs.
 11 and 12.., \ref{ratefig} and \ref{absratefig}.
 We have no evidence that the 60 SNIa candidates are contaminated with SNcc incorrectly identified as SNIa., We have no evidence that the 60 SNIa candidates are contaminated with SNcc incorrectly identified as SNIa.
 We first consider the 46 spectroscopically identified SNIa., We first consider the 46 spectroscopically identified SNIa.
 It is unlikely that these events are significantly contaminated with SNcc since for z«0.4 the Si(615nm) line is visible making the identification reliable., It is unlikely that these events are significantly contaminated with SNcc since for $z<0.4$ the Si(615nm) line is visible making the identification reliable.
" In fact, of the 46 events, 43 were classified spectroscopically as ""SNIa"" and only 3 as ""SNIa?""."," In fact, of the 46 events, 43 were classified spectroscopically as “SNIa” and only 3 as “SNIa?”."
" The three ""SNIa?""", The three “SNIa?”
 events are all selected photometrically making them good SNIa candidates., events are all selected photometrically making them good SNIa candidates.
" Of the 46 events, only seven were not photometrically accepted but for reasons that do not call into question their SNIa character: three had photometric redshifts significantly different from the spectroscopic redshifts causing the SALT fit to be very poor; one event had an extreme color parameter falling outside our cuts; three events had a small number of poor photometric points causing the fits to fail our y? cut."," Of the 46 events, only seven were not photometrically accepted but for reasons that do not call into question their SNIa character: three had photometric redshifts significantly different from the spectroscopic redshifts causing the SALT fit to be very poor; one event had an extreme color parameter falling outside our cuts; three events had a small number of poor photometric points causing the fits to fail our $\chi^2$ cut."
 We now consider contamination of the 14 SNIa that have only photometric confirmation., We now consider contamination of the 14 SNIa that have only photometric confirmation.
" Of these, four events have spectroscopy that was of insufficient signal-to-noise to determine the SN type."," Of these, four events have spectroscopy that was of insufficient signal-to-noise to determine the SN type."
 The remaining 10 events had no spectra either because the event was discovered too late or because the estimated signal-to-noise was insufficiently (local flux increase < 20%)., The remaining 10 events had no spectra either because the event was discovered too late or because the estimated signal-to-noise was insufficiently (local flux increase $<20\%$ ).
" Only one of the 14 events was judged “unlikely” to be a SNIa by the spectroscopy target selection group, but the full light curve indicates that it is consistent with being a normal SNIa."," Only one of the 14 events was judged “unlikely” to be a SNIa by the spectroscopy target selection group, but the full light curve indicates that it is consistent with being a normal SNIa."
 We therefore have no evidence that the 14 events are contaminated with SNcc., We therefore have no evidence that the 14 events are contaminated with SNcc.
" However, we have no good template catalog of bright SNcc to evaluate the probability that a bright SNcc passes our SNIa photometric selection."," However, we have no good template catalog of bright SNcc to evaluate the probability that a bright SNcc passes our SNIa photometric selection."
 We therefore conservatively assign a systematic one standard deviation upper limit of 7events to contamination of the SNIa sample with SNcc.," We therefore conservatively assign a systematic one standard deviation upper limit of $7\,{\rm events}$ to contamination of the SNIa sample with SNcc."
" While we have no evidence that the SNIa sample is contaminated with SNcc, it is certain that the SNcc sample is contaminated by sub-luminous SNIa."," While we have no evidence that the SNIa sample is contaminated with SNcc, it is certain that the SNcc sample is contaminated by sub-luminous SNIa."
 We will evaluate this contamination in the next section., We will evaluate this contamination in the next section.
" In thissection, we will derive the SNcc rate using events with 0.05<z«0.4 and ms79«24.1."," In thissection, we will derive the SNcc rate using events with $0.05<z<0.4$ and $m_{570}<24.1$."
 The cut on 71579 is used to ensure that only events with good detection efficiency are used., The cut on $m_{570}$ is used to ensure that only events with good detection efficiency are used.
 The requirement that z>0.05 eliminates one event at z= 0.04., The requirement that $z>0.05$ eliminates one event at $z=0.04$ .
 The uncertainty in AMs;o is &(AMszo)~2σ./ζ so the event, The uncertainty in $\Delta M_{570}$ is $\sigma(\Delta M_{570})\sim 2\sigma_z/z$ so the event
"r end is mainly determined by the distribution of particles within individual halos, we could conclude that the internal distribution of particles in a structure becomes denser as the resolution of the simulation is increased.","$r$ end is mainly determined by the distribution of particles within individual halos, we could conclude that the internal distribution of particles in a structure becomes denser as the resolution of the simulation is increased."
" The runs with adaptive softening produce a correlation function which is in full agreement with that of the “fixed” run at the same resolution down to roughly 100h~'kpc; at smaller separation the amplitude grows instead larger, approaching the results obtained at higher resolution when using fixed softening."," The runs with adaptive softening produce a correlation function which is in full agreement with that of the “fixed” run at the same resolution down to roughly $100\; h^{-1}\mathrm{kpc}$; at smaller separation the amplitude grows instead larger, approaching the results obtained at higher resolution when using fixed softening."
" This is particularly evident in the 64?-run using adaptive softening and the correction of the equation of motion (*Adapt--corr - 64°”, blue curve): not only is the amplitude at small separation (10 - 50h ρε) higher than the other two 64? runs, but the behaviour at scales between 50 and 200h~'kpc is indistinguishable from the reference 128?-run (black, dashed curve)."," This is particularly evident in the $64^3$ -run using adaptive softening and the correction of the equation of motion (“Adapt+corr - $64^3$ ”, blue curve): not only is the amplitude at small separation $10$ - $50\; h^{-1}\mathrm{kpc}$ ) higher than the other two $64^3$ runs, but the behaviour at scales between $50$ and $200\; h^{-1}\mathrm{kpc}$ is indistinguishable from the reference $128^3$ -run (black, dashed curve)."
" Both the ""adaptive"" runs at the 128? resolution level behave well in reproducing the correlation function of the 256? simulation, the one with correction (purple curve) even slightly exceeding the results for the 256? case on scales below 100A!kpc."," Both the “adaptive” runs at the $128^3$ resolution level behave well in reproducing the correlation function of the $256^3$ simulation, the one with correction (purple curve) even slightly exceeding the results for the $256^3$ case on scales below $100\; h^{-1}\mathrm{kpc}$."
 The search for structures in the simulations has been carried out with the algorithms (?)) and (?))., The search for structures in the simulations has been carried out with the algorithms \citealt{fof}) ) and \citealt{springel01a}) ).
 Structures are first identified as collections of N>Nmin particles separated by mutual distances smaller than some fraction b of the mean interparticle separation., Structures are first identified as collections of $N > N_{min}$ particles separated by mutual distances smaller than some fraction $b$ of the mean interparticle separation.
 These so-called “FOF halos” are later examined by for the identification of self-bound substructures and the removal of spurious background particles., These so-called “FOF halos” are later examined by for the identification of self-bound substructures and the removal of spurious background particles.
 In the simulations presented here the halos have been searched using a linking length b=0.16 and a minimum threshold of 32particles., In the simulations presented here the halos have been searched using a linking length $b=0.16$ and a minimum threshold of $32$particles.
" The internal structure of these candidate objects has then been probed in order to identify local, gravitationally-bound overdensities; those containing at least 20 particles were addressed to as “subhalos” leaving the others as part of the smooth halo component."," The internal structure of these candidate objects has then been probed in order to identify local, gravitationally-bound overdensities; those containing at least $20$ particles were addressed to as “subhalos” leaving the others as part of the smooth halo component."
" Finally, particles not gravitationally bound to any substructure of the parent FOF halo were dismissed."," Finally, particles not gravitationally bound to any substructure of the parent FOF halo were dismissed."
 Note that was modified in the unbinding part so that the evaluation of the gravitational potential takes into account the individual softening length of the particles., Note that was modified in the unbinding part so that the evaluation of the gravitational potential takes into account the individual softening length of the particles.
 Fig., Fig.
 14. shows the mass function of the halos at z= 0; the number of objects per logarithmic mass interval, \ref{conv_mfct} shows the mass function of the halos at $z=0$ ; the number of objects per logarithmic mass interval
" (?).. (?),,"," \citep{Volonteri:2003p11499}. \citep{DiMatteo:2005p5934},"
 («5 Lig»10!1L5) (?) A5007 (?)., $<$ $L_{\mathrm{IR}}$$>$$10^{11}$$L_{\sun}$ \citep{Komossa:2003p11219} $\lambda$ \citep{Liu:2010p7984}.
. narrow line region (??)..," narrow line region \citep{Smith:2010p7983,Fischer:2011p11696}."
" Unfortunately, these systems are at higher redshifts with extremely close separations where the resolution of Chandra is unable to resolve these objects to confirm their binary AGN nature."," Unfortunately, these systems are at higher redshifts with extremely close separations where the resolution of $\C$ is unable to resolve these objects to confirm their binary AGN nature."
" As part of our Chandra program of following up the close mergers detected by Swift BAT (?),, we have discovered a binary AGN in Mrk 739 with a 3.4 kpc separation at a distance of 130 Mpc."," 	 	As part of our $\C$ program of following up the close mergers detected by $Swift$ BAT \citep{Koss:2010p7366}, we have discovered a binary AGN in Mrk 739 with a 3.4 kpc separation at a distance of 130 Mpc."
" The binary AGN is particularly interesting because it shows no evidence of being an AGN in the optical, UV, or radio."," The binary AGN is particularly interesting because it shows no evidence of being an AGN in the optical, UV, or radio."
" Other than NGC 6240, this stands as the nearest case of a binary AGN discovered to date."," Other than NGC 6240, this stands as the nearest case of a binary AGN discovered to date."
" In the following subsections, we describe the observations and analysis of Mrk 739."," 	 In the following subsections, we describe the observations and analysis of Mrk 739."
" Throughout this work, we adopt (2,,— 0.3, Ωλ-- 0.7, and Hp = 70 km s! Mpc-! to determine distances."," Throughout this work, we adopt $\Omega_m$ = 0.3, $\Omega_\Lambda$ = 0.7, and $H_0$ = 70 km $^{-1}$ $^{-1}$ to determine distances."
" At the redshift of Mrk 139, 1"" corresponds to 580 pc."," At the redshift of Mrk 739, $\arcsec$ corresponds to 580 pc."
" Mrk 739 was imaged by the SDSS on March 10, 2005."," 	Mrk 739 was imaged by the SDSS on March 10, 2005."
" Using a Sérrsic profile with a fixed bulge (n—4), we fit the optical nuclei using two-dimensional surface brightness fitting (GALFIT;?).."," Using a Sérrsic profile with a fixed bulge $n$ =4), we fit the optical nuclei using two-dimensional surface brightness fitting \citep[GALFIT;][]{Peng:2002p5550}."
" In Mrk 739E, a point source component was used to measure the AGN light since it has a broad line region "," In Mrk 739E, a point source component was used to measure the AGN light since it has a broad line region (BLR)."
"|We observed Mrk 739 with Gemini on February 7, (BLR).2011."," 	 	We observed Mrk 739 with Gemini on February 7, 2011."
" Both nuclei were observed simultaneously in the B600-G5307 grating with a 1"" slit in the 4300-7300 A wavelength range.", Both nuclei were observed simultaneously in the B600-G5307 grating with a $\arcsec$ slit in the 4300–7300 $\mathrm{\AA}$ wavelength range.
 The exposure totaled 37 minutes., The exposure totaled 37 minutes.
" We follow ? for correcting Milky Way reddening, starlight continuumsubtraction, and fitting AGN diagnostic lines."," We follow \citet{Winter:2010p6825} for correcting Milky Way reddening, starlight continuumsubtraction, and fitting AGN diagnostic lines."
" To correct our line ratios for extinction, we use the narrowBalmer line ratio"," To correct our line ratios for extinction, we use the narrowBalmer line ratio"
"does not represent a realistic extrapolation of the magnetic field that would be seen on the Sun, since it starts from a uniform field at t9, and only takes into account photospheric motions at one end of the field lines.","does not represent a realistic extrapolation of the magnetic field that would be seen on the Sun, since it starts from a uniform field at $t_0$, and only takes into account photospheric motions at one end of the field lines."
" Rather, we envisage using it as the starting point for 3D MHD simulations investigating energy release, with the advantage of having determined accurately the change in field line mapping."," Rather, we envisage using it as the starting point for 3D MHD simulations investigating energy release, with the advantage of having determined accurately the change in field line mapping."
" To demonstrate the proposed method, we apply it to a 12 hour sequence of photospheric velocities derived by local correlation tracking in Hinode/SOT magnetograms."," To demonstrate the proposed method, we apply it to a 12 hour sequence of photospheric velocities derived by local correlation tracking in Hinode/SOT magnetograms."
" The observed velocities are described in Sect. 2,,"," The observed velocities are described in Sect. \ref{sec:data},"
 while the inferred magnetic field line mapping is presented in Sect. 3.., while the inferred magnetic field line mapping is presented in Sect. \ref{sec:map}.
" In addition to Q, we compute the (FTLE) field c."," In addition to $Q$, we compute the (FTLE) field $\sigma$."
 This measure is a popular method in fluid mechanics for identifying so-called Lagrangian Coherent Structures (LCSs) in velocity fields., This measure is a popular method in fluid mechanics for identifying so-called Lagrangian Coherent Structures (LCSs) in velocity fields.
" Like Q. σ measures the maximum separation rate of initially nearby trajectories, and we illustrate how QSLs in the field line mapping correspond to LCSs in the photospheric velocity field."," Like $Q$, $\sigma$ measures the maximum separation rate of initially nearby trajectories, and we illustrate how QSLs in the field line mapping correspond to LCSs in the photospheric velocity field."
 In Sect., In Sect.
 4 we explain the pattern observed in the Q or o fields using a simple analytical model of photospheric convection., \ref{sec:interp} we explain the pattern observed in the $Q$ or $\sigma$ fields using a simple analytical model of photospheric convection.
" By varying the model parameters, we predict how the field line mapping would be expected to change given observations at higher resolution of faster flows."," By varying the model parameters, we predict how the field line mapping would be expected to change given observations at higher resolution of faster flows."
 Conclusions are given in Sect. 5., Conclusions are given in Sect. \ref{sec:conclusions}.
" Our velocity data have been derived by local correlation tracking in magnetograms, although the method could be applied to velocity fields from any source."," Our velocity data have been derived by local correlation tracking in magnetograms, although the method could be applied to velocity fields from any source."
 Detailed analysis of the data reduction procedure is given by?., Detailed analysis of the data reduction procedure is given by.
". Briefly, we use Stokes V/I from Hinode/NFI (Narrowband Filter Imager) observations in Fe I 6302À of active region 10930."," Briefly, we use Stokes $V/I$ from Hinode/NFI (Narrowband Filter Imager) observations in Fe I $6302\AA$ of active region 10930."
" These were calibrated to gauss following Equation (1) of?,, and the noise level estimated at —17G by fitting the core of histogrammed field strengths(?)."," These were calibrated to gauss following Equation (1) of, and the noise level estimated at $\sim 17\,\textrm{G}$ by fitting the core of histogrammed field strengths."
". In view of the subsequent reduction of noise by averaging in the tracking procedure, a tracking threshold of 15G was chosen, with no velocities assigned to pixels below this threshold."," In view of the subsequent reduction of noise by averaging in the tracking procedure, a tracking threshold of $15\,\textrm{G}$ was chosen, with no velocities assigned to pixels below this threshold."
" The magnetogram pixels are binned (2x2) from 0.16"" to 0.32"", consistent with SOT's 0.3"" diffraction limit at this wavelength."," The magnetogram pixels are binned (2x2) from $0.16''$ to $0.32''$, consistent with SOT's $0.3''$ diffraction limit at this wavelength."
" The cadence of the images is ~121s, and the sequence runs from 14:00UT on 12 December to 02:58UT on 13 December 2006."," The cadence of the images is $\sim 121\,\textrm{s}$, and the sequence runs from 14:00UT on 12 December to 02:58UT on 13 December 2006."
 The velocity field is extracted from the magnetograms using the Fourier local correlation tracking (FLCT) method(??)., The velocity field is extracted from the magnetograms using the Fourier local correlation tracking (FLCT) method.
". The method has a number of parameters: optimum values have been determined by an autocorrelation analysis, aiming to maximise frame-to-frame correlations and ensure robustness in the velocity estimate?)."," The method has a number of parameters: optimum values have been determined by an autocorrelation analysis, aiming to maximise frame-to-frame correlations and ensure robustness in the velocity estimate."
". Here, the windowing/apodization parameter is set to4 to avoid too much spatial averaging of small-scale flows."," Here, the windowing/apodization parameter is set to4 to avoid too much spatial averaging of small-scale flows."
 The sampling time between subsequent frames is chosen as At=8mins.," The sampling time between subsequent frames is chosen as $\Delta t = 8\,\textrm{mins}$."
" This is small enough to avoid significant decorrelation, but large enough to allow for boxcar averaging of 5 magnetograms to produce each frame, which greatly reduces noise."," This is small enough to avoid significant decorrelation, but large enough to allow for boxcar averaging of 5 magnetograms to produce each frame, which greatly reduces noise."
 We have repeated the calculations with At=4mins with qualitatively similar results.," We have repeated the calculations with $\Delta t=4\,\textrm{mins}$ with qualitatively similar results."
" For the analysis in this paper, we select a unipolar plage region of size 12.4Mmx (approximately 17""x 17""), away from the main sunspots, as shown in Fig."," For the analysis in this paper, we select a unipolar plage region of size $12.4\,\textrm{Mm}\times 12.4\,\textrm{Mm}$ (approximately $17''\times 17''$ ), away from the main sunspots, as shown in Fig."
 2 (left)., \ref{fig:location} (left).
 This is to avoid the large-scale flow associated with emerging flux and rotation of the sunspots., This is to avoid the large-scale flow associated with emerging flux and rotation of the sunspots.
" Since the magnetic flux in our region is concentrated in the supergranular lanes, there are inevitably areas where the line-of-sight magnetic field is too weak for reliable estimation of the velocity."," Since the magnetic flux in our region is concentrated in the supergranular lanes, there are inevitably areas where the line-of-sight magnetic field is too weak for reliable estimation of the velocity."
" This particular region has been chosen to minimise this problem over the length of the time sequence, although there are several regions where the velocity suffers locally from high-frequency noise."," This particular region has been chosen to minimise this problem over the length of the time sequence, although there are several regions where the velocity suffers locally from high-frequency noise."
 We have removed this noise with minimal disturbance to the well-resolved regions by applying a low-pass (Butterworth) filter to the velocity fields in Fourier space., We have removed this noise with minimal disturbance to the well-resolved regions by applying a low-pass (Butterworth) filter to the velocity fields in Fourier space.
 Histograms of the velocities both with and without filtering are shown in Fig., Histograms of the velocities both with and without filtering are shown in Fig.
 2 (right)., \ref{fig:location} (right).
" The mean flow speed is of the order 0.1kms!, which is rather lower than reported speeds for granular flows"," The mean flow speed is of the order $0.1\,\textrm{km}\,\textrm{s}^{-1}$, which is rather lower than reported speeds for granular flows."
 J]rie, There are a number of possible reasons for this.
utord2010.," Firstly, there is a likely averaging effect due to the convective cells being close to our spatial resolution of $0.3''$."
Therea," In addition, comparative tests show that FLCT has a bias toward underestimating speeds."
reanumberof ," However, it should be noted that the FLCT method tracks coherent magneticfeatures, which are expected to move more slowly than surrounding plasma due to suppression of convection ."
possiblereasons f orthis.Firstl, The possible effect of faster flows is explored in Sect. \ref{sec:interp}. .
BL Lac objects are the extreme class of active galactic nuclei(AGN) with weak or no emission lines and are categorized along with flat spectrum radio euasars(ESI) as blazars.,BL Lac objects are the extreme class of active galactic nuclei(AGN) with weak or no emission lines and are categorized along with flat spectrum radio quasars(FSRQ) as blazars.
 Their spectra cover a broad. range of photon energies starting from radio to gamma ravs with a [ew of them detected. in TeV energies by ground. based Air Cerenkov experiments(xrawezvnski(2004):Katarzviski.Sol.&Ixus(2001):Sambruna (2000)..Costamante&Chis-ομα (2002))).," Their spectra cover a broad range of photon energies starting from radio to gamma rays with a few of them detected in TeV energies by ground based Air Cerenkov \cite{kraw04, katar01, samb00}, \cite{costa02}) )."
 These sources are [found to be strongly variable with [lare time scales ranging from days to less than an hour (Caicosetal.(1996):Coppi&Aharonian(1999):Sambruna(2000):IXrawczvnskietal. (2000))).," These sources are found to be strongly variable with flare time scales ranging from days to less than an hour \cite{gaidos96, coppi99, samb00, kraw00}) )."
 The short time variability ancl their detection at. very. high. energies demand that the emission region should be moving down a jet at relativistic velocities close to the line of sight. of the observer (Ghisellinietal.(1993):Dondi&Chisellini (1995))).," The short time variability and their detection at very high energies demand that the emission region should be moving down a jet at relativistic velocities close to the line of sight of the observer \cite{ghisellini93, dondi95}) )."
 The strong polarization detected. in racio/optical energies and the non-thermal photon spectra indicates the radio to x-ray spectra is due to svnchrotron radiation fron a non-thermal electron. distribution cooling in a magnetic field., The strong polarization detected in radio/optical energies and the non-thermal photon spectra indicates the radio to x-ray spectra is due to synchrotron radiation from a non-thermal electron distribution cooling in a magnetic field.
 However the gamma ray emission from these sources is still not well understood., However the gamma ray emission from these sources is still not well understood.
 Leptonic models explain the high enission as Inverse C'ompton scattered svynchrotron photons by the electron population responsible for the svynchrotron process itselfSS8C) (Maraschi.Chisellini.&Celotti(1992):Bloom&Marscher(1996):3ottcher. (2000))) where as in Παζτοῖς models it is due to the svnchrotron proton emission and proton-photon interactions involving an external photon field. (Svnchrotron. proton blazar model(SPD)) (Mannheim(1998):Mückeetal. (2003))).," Leptonic models explain the high emission as inverse Compton scattered synchrotron photons by the electron population responsible for the synchrotron process itself(SSC) \cite{maraschi92, bloom96, bottcher00}) ) where as in hadronic models it is due to the synchrotron proton emission and proton-photon interactions involving an external photon field (synchrotron proton blazar model(SPB)) \cite{mannheim98, mucke03}) )."
 Under unification hypothesis of radio-loud AGN. BL Lac objects are considered. to. be aligned. jet version of Fanaroll-Riles tvpe 1: (EIU) racio ealaxies (Urry&Padovani (1995))).," Under unification hypothesis of radio-loud AGN, BL Lac objects are considered to be aligned jet version of Fanaroff-Riley type I (FRI) radio galaxies \cite{urrypado95}) )."
 ALXNSOL is a nearby BL Lac object (220.034) ancl also he second extra galactic source. detected in Γον photon energies by ground. based. Cherenkov Telescopes(Quinnοἱal. (1996)))., MKN501 is a nearby BL Lac object (z=0.034) and also the second extra galactic source detected in TeV photon energies by ground based Cherenkov \cite{quinn96}) ).
 Ht was later detected in MeV. photon energies w the satellite based experiment EGRET (Ixataokaetal. 999)))., It was later detected in MeV photon energies by the satellite based experiment EGRET \cite{katoka99}) ).
 Phe radio images of AUNNSOL show a jet emerging rom a bright nucleus (Eclwardsetal.(2000):Ciovanninietal.(1999):AaronCGiroletti (2004))).," The radio images of MKN501 show a jet emerging from a bright nucleus \cite{edward00,
giovanni99, aaron99, giroletti04}) )."
" The veh resolution (milli are second) radio images show a ransverse jet structure with the edges being brighter than 1 central spine commonly referred. as. ""Iimb-brightened"" structure (Edwardsetal.(2000):Clovannini(1999):ο.ürolettietal. (2004)))."," The high resolution (milli arc second) radio images show a transverse jet structure with the edges being brighter than the central spine commonly referred as ""limb-brightened"" structure \cite{edward00, giovanni99, giroletti04}) )."
 Phis feature is usually explained w the spine-sheath model where the velocity at the jet spine is larger compared to the velocity at the boundary.," This feature is usually explained by the ""spine-sheath"" model where the velocity at the jet spine is larger compared to the velocity at the boundary."
 Such a radial stratification of velocity across the jet arises when jet moves through the ambient medium. anc the viscosity involved will cause a shear at the boundary., Such a radial stratification of velocity across the jet arises when jet moves through the ambient medium and the viscosity involved will cause a shear at the boundary.
 Phree- hyerodvnamic simulations of relativistic jets, Three-dimensional hydrodynamic simulations of relativistic jets
DD lines were masked out so that they did not allect the cross-correlation process.,D lines were masked out so that they did not affect the cross-correlation process.
 We use the comparison star as à template. since its spectrum contains features of à late-twpe Westar.," We use the comparison star as a template, since its spectrum contains features of a late-type K-star."
 The resulting racial velocity. curve was then. fitted with a. sinusoid. with the orbital period. fixed at {μις 2920104. We determine the racial velocity. semi- As to be 403.0£4.5+. the svstemic velocity -=104+2kms land the time at orbital phase 0.0. 1 to be 2452646.6365+0.0005 phase. 0.0. corresponds to the inferior conjunction of the dd:secondary star.," The resulting radial velocity curve was then fitted with a sinusoid with the orbital period fixed at $P_{\rm orb}$ d. We determine the radial velocity semi-amplitude $K_2$ to be $\pm$, the systemic velocity $\gamma$ $\pm$ and the time at orbital phase 0.0, $T_0$ to be $\pm$ d; phase 0.0 corresponds to the inferior conjunction of the secondary star."
 Lhe reduced. 47 of the fit was 2.7 and the uncertainties quoted are 1-7 and have been rescaled so that the reduced. X7 of the fit is l., The reduced $\chi^2$ of the fit was 2.7 and the uncertainties quoted are $\sigma$ and have been rescaled so that the reduced $\chi^2$ of the fit is 1.
 Ht should. be noted that since. we used. the position of the comparison star's Ho. absorption line to determine the velocity. zero point of the instrumental Hexure. the radial velocities are relative to the comparison star.," It should be noted that since we used the position of the comparison star's $\alpha$ absorption line to determine the velocity zero point of the instrumental flexure, the radial velocities are relative to the comparison star."
 Furthermore. eiven the uncertainties in wavelength calibration due to the large slit width. the value for = should not be taken at [ace value.," Furthermore, given the uncertainties in wavelength calibration due to the large slit width, the value for $\gamma$ should not be taken at face value."
 The radial velocity curve and sinusoidal fits are shown in retEGRNV CURVE., The radial velocity curve and sinusoidal fits are shown in \\ref{FIG:RVCURVE}.
 Phe scatter in the racial velocity curve is caused by the uncertain wavelength calibration. due to the use of a wide slit.," The scatter in the radial velocity curve is caused by the uncertain wavelength calibration, due to the use of a wide slit."
 We also used a template star spectrum. obtained by shifting all the spectra of iinto the rest [rame of the secondary star. using the racial velocity. solution derived. by Marsh.etal.(1994).," We also used a template star spectrum obtained by shifting all the spectra of into the rest frame of the secondary star, using the radial velocity solution derived by \citet{Marsh94}."
.. The results obtained are the same as those obtained. using the comparison star as a template., The results obtained are the same as those obtained using the comparison star as a template.
 The amplitude we obtain for A» is less than that obtained by Marshetal.(1994)., The amplitude we obtain for $K_2$ is less than that obtained by \citet{Marsh94}.
.. ‘This is because our coverage of the minimum in the radial velocity. curve at. phase 0.25 is not completeand so the clerivecl value for A» is biased., This is because our coverage of the minimum in the radial velocity curve at phase 0.25 is not completeand so the derived value for $K_2$ is biased.
" By fitting the radial velocity curve with A» fixedat ""(Marshetal.1994). we obtain 14 140.0005 dd. Lt should be noted that the Z5 we obtain is dillerent by 0.43 phase to that quoted by Gelinoetal.(2001).. even though the nominal definition of orbital phase 0.0 adopted. is the same."," By fitting the radial velocity curve with $K_2$ fixedat \citep{Marsh94} we obtain $T_0$ $\pm$ d. It should be noted that the $T_0$ we obtain is different by 0.43 phase to that quoted by \citet{Gelino01}, even though the nominal definition of orbital phase 0.0 adopted is the same."
 This may have arisen [rom the potential ambiguity of defining phase 0.0 photometrically. as the minima at phase 0.0 and 0.5 can be almost the same depth and hence can be confused.," This may have arisen from the potential ambiguity of defining phase 0.0 photometrically, as the minima at phase 0.0 and 0.5 can be almost the same depth and hence can be confused."
 No such ambiguity exists with our spectroscopic ephemoerides., No such ambiguity exists with our spectroscopic ephemerides.
 1n rotEG:VETLCUBVESandawepresenttheV L'Econtinuumandemissiontin, In \\ref{FIG:VLT_LCURVES} and \ref{FIG:BCURVES} we present the VLT continuum and emission line lightcurves as a function of orbital phase.
cl reaned5000 rregions., The continuum lightcurve was obtained by summing the flux across the and regions.
Lhecontinuumlighleurvecchibilsrapidshorl lermvearialionsasscenprecioustybyllas," The continuum lightcurve exhibits rapid short-term variations as seen previously by \citet{Haswell92}, , \citet{Zurita03} and \citet{Hynes03}."
well (1992).., To determine the flare lightcurve we subtract a fit to the lower envelope of the lightcurve.
 Zuritactat.(2003ands," We use an iterative rejection scheme to fit the lower envelope, similar to \citet{Zurita03} and \citet{Hynes03}."
 mabove the fit. then refit. repeating the procedure until no new points are rejected.," We reject points more than $\sigma $ above the fit, then refit, repeating the procedure until no new points are rejected."
 Most. noticeable are the brief Dares at orbital phase 1.15 and 1.2 which have a rise time of 15 mmin and amplitudes of 3 anc 12 percent respectively., Most noticeable are the brief flares at orbital phase 1.15 and 1.2 which have a rise time of $\sim$ min and amplitudes of 3 and 12 percent respectively.
 A larger Hare is also seen at phase 0.6 which has a rise time of ~30 mmin and an amplitude of ~20 percent., A larger flare is also seen at phase 0.6 which has a rise time of $\sim$ min and an amplitude of $\sim$ 20 percent.
 In reICELATUSPOS we have marked the beginning and end of the strongest. most significant. [lare events ancl also the periods when Lares are not seen., In \\ref{FIG:FLAREPOS} we have marked the beginning and end of the strongest most significant flare events and also the periods when flares are not seen.
 To extract the Balmer line. Hluxes. the continuum background was removed bv [fitting and subtracting a smooth polynomial fit to the continuum regions around the lines before the line [lux was integrated.," To extract the Balmer line fluxes, the continuum background was removed by fitting and subtracting a smooth polynomial fit to the continuum regions around the lines before the line flux was integrated."
 Phe Balmer line lighteurves show significant variations. scatters of 3.8 and 7.6 percent for the Lla and 11) lishteurves respectively.," The Balmer line lightcurves show significant variations, scatters of 3.8 and 7.6 percent for the $\alpha$ and $\beta$ lightcurves respectively."
 The 11.1 and Ho lighteurves are strongly correlated., The $\beta$ and $\alpha$ lightcurves are strongly correlated.
 τοοἱΔον shows the Ila and Lhe? emission line wings and core determined by integrating the line (ux., \\ref{FIG:BCURVES} shows the $\alpha$ and $\beta$ emission line wings and core determined by integrating the line flux.
 The blue. core. and red wing Huxes were calculated by integrating the emission line over the velocity ranges 2500 to.+. -500 to and 500 to 2000 'respectivelv.," The blue, core, and red wing fluxes were calculated by integrating the emission line over the velocity ranges –2500 to, -500 to and 500 to 2000 respectively."
 One can clearly see that the Ho. and 112 emission line wings and core are correlated with each other., One can clearly see that the $\alpha$ and $\beta$ emission line wings and core are correlated with each other.
 Phe Balmer line lighteurves show some correlations with the Uare lighteurve rotIG:ΜΕRV ES) T, The Balmer line lightcurves show some correlations with the flare lightcurve \\ref{FIG:VLT_LCURVES}) ).
 hisisclearestfortheflarecventatphasel.d5., This is clearest for the flare event at phase 1.15.
 hei although the correlation is quite strong in 1.1.," There is no noticeable participation from $\alpha$, although the correlation is quite strong in $\beta$."
 However. it could be that there is an underlying source of variable contamination in the lla lishteurves such as from the clise (sec re[DOPPLER)). that prevents a complete correlation with the continuum lighteurve.," However, it could be that there is an underlying source of variable contamination in the $\alpha$ lightcurves such as from the disc (see \\ref{DOPPLER}) ), that prevents a complete correlation with the continuum lightcurve."
 The fractional variability in 12 is à [actor of ~2 larger than in Lla (see retIC:VETECURVES) In, The fractional variability in $\beta$ is a factor of $\sim$ 2 larger than in $\alpha$ (see \\ref{FIG:VLT_LCURVES}) ).
V4046€ C'yglhecorrelationbebweendlo and the continuum is much stronger., In Cyg the correlation between $\alpha$ and the continuum is much stronger.
 Also in V404CCνο the Ho emission line varies considerably (LIyvnes bv a [actor of ~2 more than in00., Also in Cyg the $\alpha$ emission line varies considerably \citep{Hynes02} by a factor of $\sim$ 2 more than in.
.. Llowever. it could be that the optical depth in iis larger than that in (νο so the emission line [lares are generally weaker. and LL? is more pronounced.," However, it could be that the optical depth in is larger than that in Cyg, so the emission line flares are generally weaker, and $\beta$ is more pronounced."
 Also. the persistent lines could be stronger relative to the flaring component in 00.," Also, the persistent lines could be stronger relative to the flaring component in ."
. The Ho /1L3 ratio varies hy S percent around. a mean value of 2.7. ancl is inversely correlated with the line [uxes. consistent with there being a higher optical depth in Ila than in 1.," The $\alpha$ $\beta$ ratio varies by 8 percent around a mean value of 2.7, and is inversely correlated with the line fluxes, consistent with there being a higher optical depth in $\alpha$ than in $\beta$ ."
 The ratio Πα is consistent with case D recombination (2.85 for P=10t WIS Osterbrock 1987)) and so indicates that the Balmer emission. lines are optically, The ratio $\alpha$ $\beta$is consistent with case B recombination (2.85 for $^4$ K \citealt{Osterbrock87}) ) and so indicates that the Balmer emission lines are optically
"The S-(vwpe N-Estendecd Supersvininetry lor the [ree particle is introduced through the generators (55),4(0D?), (0d9LL...d). which satisfy the set of equations We have In the subcase SL at first we fix D and compute the maximal number of 5 matrices ΔΕΗ(ος. by the Schur lemma,","The $S$ -type ${N}$ -Extended Supersymmetry for the free particle is introduced through the generators $(\gamma^{i})_{\alpha\beta}, (\Gamma^{m})_{\alpha\beta}$ $\alpha,\beta=1,\ldots, d$ ), which satisfy the set of equations We have In the subcase $S1$ at first we fix $D$ and compute the maximal number of $\gamma^i$ matrices admitted by the Schur lemma."
" Conversely. in the subcase 52 we fix at first No ancl compute ihe maximal number of D"" matrices admitted by the Schur lemma."," Conversely, in the subcase $S2$ we fix at first $N$ and compute the maximal number of $\Gamma^n$ matrices admitted by the Schur lemma."
 The subeases 51 and 52 coincide lor D—d 1..N—2 and lor D—3. d—4. N—4.," The subcases $S1$ and $S2$ coincide for $D=d=1$, $N=2$ and for $D=3$, $d=4$, $N=4$."
 Let us fix D>1 given bv with r=0.1.2.....7.," Let us fix $D\geq 1$ given by with $r=0,1,2,\ldots, 7$."
 The minimal d corresponding to the irreducible representation ol the Clifford algebra is The maximal value ων of the extended supersvnuuelry is given by the A(r) function:, The minimal $d$ corresponding to the irreducible representation of the Clifford algebra is The maximal value $N_{max}$ of the extended supersymmetry is given by the $K(r)$ function:
sampling in our dataset (Hobbs.Lyne&Kramer2010).,sampling in our dataset \citep*{hobbs10}.
. We also note that the (long-term) timing noise of young radio pulsars (age 10°yr) ean be better understood as resulting from the recovery from previous glitch events (Hobbs.Lyne&Kramer2010).. making it unlikely that the frequency second derivative is actually due to random noise.," We also note that the (long-term) timing noise of young radio pulsars (age $<10^5$ yr) can be better understood as resulting from the recovery from previous glitch events \citep*{hobbs10}, making it unlikely that the frequency second derivative is actually due to random noise."
 A possibility is therefore that the higher-order frequency derivatives we observed are manifestations of a glitch recovery., A possibility is therefore that the higher-order frequency derivatives we observed are manifestations of a glitch recovery.
 In the AXP IRXSJJI708—4009. for instance. negative second Tequeney derivatives inthe —(0.01 : 1.3). °° ? range 145 been detected just after a glitches (Dib.Kaspi&Gavriil2008:: Israeletal. 20075).," In the AXP J1708–4009, for instance, negative second frequency derivatives in the $-($ $\div$ $)\times$ $^{-20}$ $^{-2}$ range has been detected just after a glitches \citealt*{dib08}; \citealt{israel07}) )."
 We found no evidence for glitches in the ime spanned by our observations. but this does not exclude the »ossibilitv that such events occurred before the first observation of qe outburst.," We found no evidence for glitches in the time spanned by our observations, but this does not exclude the possibility that such events occurred before the first observation of the outburst."
 Another possibility is that the frequency second derivative we measured (or at least a significant fraction of it) is linked to 1e Magnetospheric activity of1833-0832., Another possibility is that the frequency second derivative we measured (or at least a significant fraction of it) is linked to the magnetospheric activity of.
. In the magnetar Pdcenario the spin derivative is in fact expected to increase while le Magnetospheric twist is growing. Le. for instance in periods oreceding large outbursts. and to decrease in the aftermath (see e.g. Thompson.Lyutikov&Kulkarni2002:Beloborodov 2009)).," In the magnetar scenario the spin derivative is in fact expected to increase while the magnetospheric twist is growing, i.e. for instance in periods preceding large outbursts, and to decrease in the aftermath (see e.g. \citealt*{tlk02,beloborodov09}) )."
 On ye other hand. as pointed out by Beloborodov(2009).. à negative ὦ ollowing a period of bursting activity (as that detected here) can be still accounted for if a magnetospheric twist is suddenly implanted but its strength is moderate (twist angle less than 1 rad).," On the other hand, as pointed out by \citet{beloborodov09}, a negative $\ddot{\nu}$ following a period of bursting activity (as that detected here) can be still accounted for if a magnetospheric twist is suddenly implanted but its strength is moderate (twist angle less than $\sim$ 1 rad)."
 Then the wist may still grow for a while in spite of the luminosity released by dissipation monotonically decreases., Then the twist may still grow for a while in spite of the luminosity released by dissipation monotonically decreases.
 Only after the twist angle qas reached its maximum value. it will start to decay. together with he torque.," Only after the twist angle has reached its maximum value, it will start to decay, together with the torque."
 Nevertheless. the timing properties of the source appear consistent with those typically observed in the AXP/SGR class.," Nevertheless, the timing properties of the source appear consistent with those typically observed in the AXP/SGR class."
 The spectral characteristics of aare instead somewhat less usual., The spectral characteristics of are instead somewhat less usual.
 The X-ray spectrum is well described by a single blackbody with temperature AZ’~1.2 keV. definitely higher than what generally observed both in transient and ‘persistent’ magnetars (7=0.7 keV. with the exception of 0041845729: Espositoetal.2010a:Rea 20100).," The X-ray spectrum is well described by a single blackbody with temperature $kT\sim1.2$ keV, definitely higher than what generally observed both in transient and `persistent' magnetars $kT\la 0.7$ keV, with the exception of 0418+5729; \citealt{esposito10short,rea10short}) )."
 We cannot however exclude that the high temperature of ppartially results from a bias in the spectral fits that. given the paucity of counts below ~2—3 keV towing to the large absorption). acts in the direction of increasing the temperature. in order to account for a second spectral component which cannot be properly modelled (see Section ??)).," We cannot however exclude that the high temperature of partially results from a bias in the spectral fits that, given the paucity of counts below $\sim$ 2–3 keV (owing to the large absorption), acts in the direction of increasing the temperature, in order to account for a second spectral component which cannot be properly modelled (see Section \ref{xspectroscopy}) )."
 The large increase in flux. a factor 20 above the quiescent level. is indicative of a rather powerful event. not dissimilar from those observed in other transient sources.," The large increase in flux, a factor $\ga$ 20 above the quiescent level, is indicative of a rather powerful event, not dissimilar from those observed in other transient sources."
 This. however. seems to be in contrast with the low level of activity seen in0832.. from which only few bursts were detected (Gógüset 2010a)..," This, however, seems to be in contrast with the low level of activity seen in, from which only few bursts were detected \citep{gogus10short}."
 A scenario in which we are presently witnessing the later stages of an outburst which was caught during its decay rather than at its onset. could account for the low activity but seems difficult to reconcile with the current high value of the temperature tif the thermal component in the spectrum of iis indeed at AZ’~1.2 keV).," A scenario in which we are presently witnessing the later stages of an outburst which was caught during its decay rather than at its onset, could account for the low activity but seems difficult to reconcile with the current high value of the temperature (if the thermal component in the spectrum of is indeed at $kT\sim 1.2$ keV)."
 A further possibility might be that eexperienced a (crustal) heating episode which. however. was not accompanied by (or did not trigger) a twisting of the external field. as possibly suggested by the non-detection of a hard X-ray tail.," A further possibility might be that experienced a (crustal) heating episode which, however, was not accompanied by (or did not trigger) a twisting of the external field, as possibly suggested by the non-detection of a hard X-ray tail."
 In this ease. however. an alternative explanation. not related to the twist evolution. for the presence of a negative 7 must be sought (perhaps a long-term postgliteh recovery. see above).," In this case, however, an alternative explanation, not related to the twist evolution, for the presence of a negative $\ddot{\nu}$ must be sought (perhaps a long-term postglitch recovery, see above)."
 Immediately after the BAT trigger that led to the discovery of 1833-0832... its observed flux was of —3.810E+. and it decreased by 2755€ during the following 5 months (which is not unusual for magnetars: e.g. Rea&Esposito2011». to —1.10+.," Immediately after the BAT trigger that led to the discovery of , its observed flux was of $\sim$$3.8\times10^{-12}$, and it decreased by $\approx$ during the following 5 months (which is not unusual for magnetars; e.g. \citealt{rea11}) ), to $\sim$$1.1\times10^{-12}$."
 Although present data do not allow us to diseriminate among different decay patterns. the flux evolution can be satisfactorily described by a broken power law. similarly to the case of 0041845729.," Although present data do not allow us to discriminate among different decay patterns, the flux evolution can be satisfactorily described by a broken power law, similarly to the case of 0418+5729."
" The flux of rremained fairly constant for about 20 days (a,~0). when the decay index changed to à»~—0.5."," The flux of remained fairly constant for about 20 days $\alpha_1\sim0$ ), when the decay index changed to $\alpha_2\sim-0.5$."
 Interestingly. also the decay of 0041845729 exhibited a break at ~20 days (Espositoet2010a).," Interestingly, also the decay of 0418+5729 exhibited a break at $\sim$ 20 days \citep{esposito10short}."
. As in the case of 0041845729 (see the discussion in Espositoetal.20102). the presence of a break. together with the rather flat decay indices. might be difficult to reconcile with the predictions of the deep crustal heating scenario (Lyubarsky.Eich-ler&Thompson 2002). Fx£75 with »~2-3.," As in the case of 0418+5729 (see the discussion in \citealt{esposito10short}) ), the presence of a break, together with the rather flat decay indices, might be difficult to reconcile with the predictions of the deep crustal heating scenario \citep*{let02}, $F\propto t^{-n/3}$ with $n\sim 2$ –3."
 This model provides a satisfactory description of the flux decay in 11627—31 (Kouveliotouetal. 2003.. although subsequent analyses found no evidence for the plateau around ~400—800 d predicted by the model: Mereghettietal. 0060) and AXP 22259556 (Zhuetal. 2008).," This model provides a satisfactory description of the flux decay in 1627--41 \citealt{kouveliotou03short}, , although subsequent analyses found no evidence for the plateau around $\sim 400$ –800 d predicted by the model; \citealt{mereghetti06}) ) and AXP 2259+586 \citep{zhu08}."
. At the same time. however. it cannot explain the variety of decay patterns which emerged from recent observations of SGRs/AXPs (e.g. Reaetal. 20099).," At the same time, however, it cannot explain the variety of decay patterns which emerged from recent observations of SGRs/AXPs (e.g. \citealt{rea09short}) )."
 This may reflect the intrinsic limitations of the model (which relies an a simplified. one-dimensional treatment). or point towards the existence of different heating mechanisms which are at work during the outbursts of magnetars. like in the case of1833-0832.," This may reflect the intrinsic limitations of the model (which relies an a simplified, one-dimensional treatment), or point towards the existence of different heating mechanisms which are at work during the outbursts of magnetars, like in the case of."
 Prompted by previous detections of a transient (pulsed) radio emission following X-ray transient activity in other magnetars (Camiloetal.2006.2007:Burgay2009)... we observed wwith the ATCA and the 64-m Parkes radio telescope (Burgayal.2010:Wieringaet 2010).," Prompted by previous detections of a transient (pulsed) radio emission following X-ray transient activity in other magnetars \citep{camilo06,camilo07,burgay09}, we observed with the ATCA and the 64-m Parkes radio telescope \citep{burgay10short,wieringa10short}."
. No evidence for radio emission was found. down to flux densities of 0.9 mJy and 0.09 mJy for the continuum and pulsed emissions. respectivelv.," No evidence for radio emission was found, down to flux densities of 0.9 mJy and 0.09 mJy for the continuum and pulsed emissions, respectively."
 Similar upper limits on the pulsed radio emission. 0.1 mJy at 1.38 GHz and 0.2 mJy at 2.28 GHz for a duty cycle. were obtained with the Westerbork Radio Synthesis Telescope in the same days (but not simultaneously with our observations: Gésiisetal. 20102).," Similar upper limits on the pulsed radio emission, 0.1 mJy at 1.38 GHz and 0.2 mJy at 2.28 GHz for a duty cycle, were obtained with the Westerbork Radio Synthesis Telescope in the same days (but not simultaneously with our observations; \citealt{gogus10short}) )."
 Despite this rather intensive coverage. the negative results of radio searches performed so far on ccannofanyway be taken as conclusive because of the rapid variability of the pulsed flux shown by the known radio magnetars (see e.g. Burgayetal. 2009).," Despite this rather intensive coverage, the negative results of radio searches performed so far on cannotanyway be taken as conclusive because of the rapid variability of the pulsed flux shown by the known radio magnetars (see e.g. \citealt{burgay09}) )."
 Moreover. for a distance d=10 kpe these limitstranslates into a pseudo-luminosity L=Sd? mJy Kpc. which is significantly smaller than the 1.4. GHz luminosity of the other knownradio magnetars at their. peak (~ 100-400 mJy kpe: Camiloetal.2006.2007:Levin 20100) but still much larger than the luminosities of some known ordinary radio," Moreover, for a distance $d=10$ kpc these limitstranslates into a pseudo-luminosity $L=Sd^2\approx 10$ mJy $^2$ , which is significantly smaller than the 1.4 GHz luminosity of the other knownradio magnetars at their peak $\sim$ 100–400 mJy $^2$ ; \citealt{camilo06,camilo07,levin10short}) ) but still much larger than the luminosities of some known ordinary radio"
optimization problem at the two-point level. and very good agreement was found among the different methods.,"optimization problem at the two-point level, and very good agreement was found among the different methods."
 We adopt the simplified analytical approach as described in JSO8. and reformulate it for three-point statistics here.," We adopt the simplified analytical approach as described in JS08, and reformulate it for three-point statistics here."
" For convenience we introduce the following notations: the bispectrum covariance matrix CovB. whose elements are the covariance matrix. CovY of the nulled bispectra Y. whose elements are a vector B,,, whose elements are partial derivatives of the bispectrum with respect to the cosmological parameter py and a corresponding vector Y,,, for nulled bispectra Y. whose elements are Then the Fisher information matrix from the original bispectra can be written as (following TJO4) and that from the nulled bispectra can be written as Here the matrix multiplication is a summation of all possible angular frequency combinations (£1.65.£3) and redshift bin combinations. (/j&) for the original bispectra and (ij) for the nulled bispectra."," For convenience we introduce the following notations: the bispectrum covariance matrix ${\rm \textbf CovB}$, whose elements are the covariance matrix ${\rm \textbf CovY}$ of the nulled bispectra $Y$, whose elements are a vector ${\rm \textbf B_{\textbf ,\,{\mu} }}$ whose elements are partial derivatives of the bispectrum with respect to the cosmological parameter $p_{\mu}$ and a corresponding vector ${\rm \textbf Y_{\textbf ,\,\mu}}$ for nulled bispectra $Y$, whose elements are Then the Fisher information matrix from the original bispectra can be written as (following TJ04) and that from the nulled bispectra can be written as Here the matrix multiplication is a summation of all possible angular frequency combinations $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ and redshift bin combinations, ${(ijk)}$ for the original bispectra and ${(ij)}$ for the nulled bispectra."
 In (36) and (37). CovB! and CovY! indicate the inverse of the covariance matrix.," In ) and ), ${\rm \textbf CovB}^{-1}$ and ${\rm \textbf CovY}^{-1}$ indicate the inverse of the covariance matrix."
 When the covariance Is approximated by triples of power spectra. the covariance between two different angular. frequency combinations (£1.65.£3)¢(£4.fs.£4) is zero. see (24). which means that the covariance matrix is block diagonal.," When the covariance is approximated by triples of power spectra, the covariance between two different angular frequency combinations $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)\neq(\bar{\ell}_4,\bar{\ell}_5,\bar{\ell}_6)$ is zero, see ), which means that the covariance matrix is block diagonal."
 In this case the matrix inversion can be done separately for each block specified by an angular frequency combination (£4.£5.£1).," In this case the matrix inversion can be done separately for each block specified by an angular frequency combination $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$."
 According to the idea of the simplified analytical approach. we consider the Fisher information on one cosmological parameter contained in bispectrum measuresBueE.fs) with a single (a...£3)combination and with redshift bin (i.j.K) combinations having common (i.j) indices.," According to the idea of the simplified analytical approach, we consider the Fisher information on one cosmological parameter contained in bispectrum measures$B_{\rm{GGG}}^{(ijk)}(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ with a single $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$combination and with redshift bin $(i,j,k)$ combinations having common $(i,j)$ indices."
 For every G.jJ) combination we build nulling weights 7? which maximizes the nulled Fisher matrix using the method of Lagrange multipliers.," For every $(i,j)$ combination we build nulling weights $T^{(ij)}$ which maximizes the nulled Fisher matrix using the method of Lagrange multipliers."
" Since here the nulled Fisher matrix receives contribution only from certain angular frequency and redshift combinations. we denote it as FQ"" to avoid ambiguity."," Since here the nulled Fisher matrix receives contribution only from certain angular frequency and redshift combinations, we denote it as $F_{\rm o}^{(ij)}$ to avoid ambiguity."
 FO” has only one component since only one cosmological parameter is taken into consideration., $F_{\rm o}^{(ij)}$ has only one component since only one cosmological parameter is taken into consideration.
 As only a single (£4.P5.£1) combination is involved. we will omit the {- dependence in all variables in the rest of this subsection to keep à compact form.," As only a single $(\bar{\ell}_1, \bar{\ell}_2, \bar{\ell}_3)$ combination is involved, we will omit the $\bar{\ell}$ -dependence in all variables in the rest of this subsection to keep a compact form."
 Again for notational simplicity. we follow JSO8 and introduce a veetor notation as follows.," Again for notational simplicity, we follow JS08 and introduce a vector notation as follows."
" For each (@./) in consideration. let the values of the weights T(y,) form a vector T=Τι. and define another vector p and a matrix € with elements Thus pi can be expressed. according to (37). as We further define a vector f with elements to write the nulling condition (18) as The problem of finding nulling weights Z which maximize ΕΙ under the constraint given by the nullingcondition canbe solved with the method of Lagrange multipliers by defining a function with 4| being the Lagrange multiplier. and setting the gradient of G with respectto Τ to zero."," For each $(i,j)$ in consideration, let the values of the weights $T^{(ij)}(\chi_k)$ form a vector $\vek{T}=T_k$, and define another vector $\vek{\rho}$ and a matrix $\bar{\bf{C}}$ with elements Thus $F_{\textrm{o}}^{(ij)}$ can be expressed, according to ), as We further define a vector $\vek{f}$ with elements to write the nulling condition ) as The problem of finding nulling weights $\vek{T}$ which maximize $F^{(ij)}_o$ under the constraint given by the nullingcondition canbe solved with the method of Lagrange multipliers by defining a function with $\lambda$ being the Lagrange multiplier, and setting the gradient of $G$ with respectto $\vek{T}$ to zero,"
so that the sample is probably complete and the period distribution. periocd-luminosity relation ancl period-colour ooperties of Miras in Ser Ll may be regarded as known.,"so that the sample is probably complete and the period distribution, period-luminosity relation and period-colour properties of Miras in Sgr I may be regarded as known."
 The Sgrlb and 66522. windows formed. part. of he MACHO gravitational lens survey., The I and 6522 windows formed part of the MACHO gravitational lens survey.
 Alard et al. (, Alard et al. (
2001) yresent variability information for all 332 stars that iive been detected at both ISOGAL and both NLACTIO wavelengths: e ((~0.54yan). r (C0. 700m). jm ancl jun. yearly all of the 332 objects were found to be semi-regular variables (SRVs) with periods of from 10 to 230 days and amplitudes « 1 mag.,"2001) present variability information for all 332 stars that have been detected at both ISOGAL and both MACHO wavelengths: $v$ $\sim$ $\mu$ m), $r$ $\sim$ $\mu$ m), $\mu$ m and $\mu$ m. Nearly all of the 332 objects were found to be semi-regular variables (SRVs) with periods of from 10 to 230 days and amplitudes $<$ 1 mag."
 and will be referred to collectively here as the ISOGAL/MACTIO sample., and will be referred to collectively here as the ISOGAL/MACHO sample.
 The SHVs in the present ficlds outnumber the Miras by a factor of about 20., The SRVs in the present fields outnumber the Miras by a factor of about 20.
 Note that the area surveyed by NLACTIO omits about of each ISOGAL field., Note that the area surveyed by MACHO omits about of each ISOGAL field.
 We have assumed tha the interstellar absorption is ely =1-5 mae for both fields., We have assumed that the interstellar absorption is $A_V$ =1.5 mag for both fields.
" We take in addition οεν. A; m0.245.4.. ely Ες and ely —0.085.1,. based on the van de Llulst curve (Class. 1999)."," We take in addition $A_I$ $A_V$, $A_J$ $A_V$, $A_H$ $A_V$ and $A_K$ $A_V$, based on the van de Hulst curve (Glass, 1999)."
 All objects falling in the ISOCCAL fields have been extracted from the DENIS and 2ALASS databases as well as the EW work., All objects falling in the ISOGAL fields have been extracted from the DENIS and 2MASS databases as well as the FW work.
" A search. radius of 2"" was chosen to avoicl mis-identifications.", A search radius of $''$ was chosen to avoid mis-identifications.
 Phe DENIS observations form part of a dedicated survey of the Galactic Bulee (Simon et al.," The DENIS observations form part of a dedicated survey of the Galactic Bulge (Simon et al.,"
 in preparation)., in preparation).
 “Phe 2\LASS observations are limited to SerLb and a small part of 66522 with the consequence that only 225 of the 332 ISOCGAAL/NLACLIO stars fall within the common area., The 2MASS observations are limited to I and a small part of 6522 with the consequence that only 225 of the 332 ISOGAL/MACHO stars fall within the common area.
 In this and the following section we show by direct comparisons that the available information is consistent., In this and the following section we show by direct comparisons that the available information is consistent.
 Firstly. it is necessary to consider what cllect the different filter. systems may be expected. to have on the photometry.," Firstly, it is necessary to consider what effect the different filter systems may be expected to have on the photometry."
 Phe DENIS filters have been convolved with the tvpical atmospheric transmission at La Silla (roucjué et al., The DENIS filters have been convolved with the typical atmospheric transmission at La Silla (Fouqué et al.
 2000). where the survey was mace.," 2000), where the survey was made."
 A summary. of the available clata is given in table 1., A summary of the available data is given in table 1.
 For details of the filter transmissions ancl svstematic response curves. see. l'ouqué et al (2000) for DENIS: 2ALASS web pages for 2\LASS.," For details of the filter transmissions and systematic response curves, see Fouqué et al (2000) for DENIS; 2MASS web pages for 2MASS."
 Important. differences between systems occur in the J- and dv-bands., Important differences between systems occur in the $J$ - and $K$ -bands.
 Vhe Caltech-CTLO svstem as used. by FW has an effective J wavelength (see Joi. in 44 of Persson οἱ al., The Caltech-CTIO system as used by FW has an effective $J$ wavelength (see $J_{\rm old}$ in 4 of Persson et al.
 1998) of about 1.2554. considerably longer than that of DENIS (71.22 jm).," 1998) of about $\mu$ m, considerably longer than that of DENIS $\sim$ $\mu$ m)."
 The ££ and dy bands of the SAAO photometric svsten are very close to those of the ESO system (see Bouchet. Schmicer Alanfroicd. 1991).," The $H$ and $K$ bands of the SAAO photometric system are very close to those of the ESO system (see Bouchet, Schmider Manfroid, 1991)."
 The SAAQO Aira data for the Baade’s Window field. (Glass ct al., The SAAO Mira data for the Baade's Window field (Glass et al.
 1995). to which we refer later on. were taken with the MELLE photometer. whose cllective wavelength at J is ~1.22 yam (Glass. 1993).," 1995), to which we refer later on, were taken with the MkIII photometer, whose effective wavelength at $J$ is $\sim$ $\mu$ m (Glass, 1993)."
 Phis is essentially identical to J/DENIS., This is essentially identical to $J_{\rm DENIS}$.
 Fie 1 shows histograms of dillerences between DIZNIS and 2ALASS J and As data for NLACTIO variables identified in both data sets., Fig 1 shows histograms of differences between DENIS and 2MASS $J$ and $K_S$ data for MACHO variables identified in both data sets.
 His seen that the agreement ds satisfactory. both AY and Advs being less than 0.01 mag on average. with σ ~ 0.12 ancl 0.09 for the two bands respectively.," It is seen that the agreement is satisfactory, both $\Delta J$ and $\Delta K_S$ being less than 0.01 mag on average, with $\sigma$ $\sim$ 0.12 and 0.09 for the two bands respectively."
 “Phe two surveys were conducted. during the, The two surveys were conducted during the
The transformations we give in equations (1) (5) are consistent wilh the range of previously published transformations.,The transformations we give in equations (1) – (5) are consistent with the range of previously published transformations.
 Because our linear transformation equations are derived for a practical purpose of calibrating CBWRI photometry. and are available for each of the Johnson-Cousins filters individually. our transformations are different in nature from those previously published.," Because our linear transformation equations are derived for a practical purpose of calibrating $UBVRI$ photometry, and are available for each of the Johnson-Cousins filters individually, our transformations are different in nature from those previously published."
 We briefly summarize here previously published (transformations and discuss how they differ from the ones given above., We briefly summarize here previously published transformations and discuss how they differ from the ones given above.
 Fukugitaetal.(1996) give synthetic transformations from UDVRI to u'g'r!iz'., \cite{fukugita96} give synthetic transformations from $UBVRI$ to $u'g'r'i'z'$ .
 Smithetal.(2002) gave translormations between UDVRI and u'g'r'!/z magnitudes observed with the Photometric Telescope (PT) at Apache Point Observatory [or some filters and for colors., \cite{smith02} gave transformations between $UBVRI$ and $u'g'r'i'z'$ magnitudes observed with the Photometric Telescope (PT) at Apache Point Observatory for some filters and for colors.
 Rodgersetal.(2006). give improved color Gransformations between u'g'r/'z' and UDVRI for main-sequence stars.," \cite{rodgers06}
 give improved color transformations between $u'g'r'i'z'$ and $UBVRI$ for main-sequence stars."
 They also consider higher-order color terms., They also consider higher-order color terms.
 H is important to note the dillerence between u'g'r!/z' and ugriz., It is important to note the difference between $u'g'r'i'z'$ and $ugriz$.
 This is discussed in Smithetal.(2007)., This is discussed in \cite{smith07}.
. Additional technical details concerning the dilference between the (wo svstems as well as transformations between (hem are discussed in Tucker (2006)., Additional technical details concerning the difference between the two systems as well as transformations between them are discussed in \cite{tucker06}.
. Jordiοἱal.(2006). give color transformations between ugriz as observed with the SDSS 2.5-m telescope (rather than the PT) and UDVRI., \cite{jordi06} give color transformations between $ugriz$ as observed with the SDSS 2.5-m telescope (rather than the PT) and $UBVRI$.
 Additional transformations are given bv Jesteretal.(2005).. INXaraalietal. (2003)... Naraalietal.(2005)... Diliretal.(2005).. Davenportetal. (2007).. ancl Diliretal.(2007).," Additional transformations are given by \cite{jester05}, \cite{karaali03}, \cite{karaali05}, \cite{bilir05}, \cite{davenport07}, and \cite{bilir07}."
. Some of the transformations including etal.(2007) consider polynomials in the color terms. but we found no need for higher-oider terms for the restricted range of colors we consider.," Some of the transformations including \cite{ivezic07} consider polynomials in the color terms, but we found no need for higher-order terms for the restricted range of colors we consider."
 Note that the above cited transformations consider only colors. transform from UDVRI (o ugriz. are derived for the u'g'r!//Zz' system. or give transformations only [or select. Johnson-Cousins filters.," Note that the above cited transformations consider only colors, transform from $UBVRI$ to $ugriz$, are derived for the $u'g'r'i'z'$ system, or give transformations only for select Johnson-Cousins filters."
 In this note. our aim has been (o give a practical means of photometrically calibrating UDVRI CCD images.," In this note, our aim has been to give a practical means of photometrically calibrating $UBVRI$ CCD images."
 Researchers who are interested in astrophvsical applications of SDSS photometry (such as the determination of spectroscopic parallaxes or fitting theoretical isochrones to ILE. diagrams) are referred to the above mentioned papers because the ugriz to UDVRI transformations depend on the Iuminosity class and metallicity of (he stars., Researchers who are interested in astrophysical applications of SDSS photometry (such as the determination of spectroscopic parallaxes or fitting theoretical isochrones to HR diagrams) are referred to the above mentioned papers because the $ugriz$ to $UBVRI$ transformations depend on the luminosity class and metallicity of the stars.
 We have minimized these effects for zero-point setting by using a lairly tight color selection., We have minimized these effects for zero-point setting by using a fairly tight color selection.
 We are grateful (to Katrin Jordi lor supplving the data from Jordi et al. (, We are grateful to Katrin Jordi for supplying the data from Jordi et al. (
2006) in machine-readable format. to Robert Lupton for useful discussion of the SDSS handling of PSF saturation. and the referee for useful comments.,"2006) in machine-readable format, to Robert Lupton for useful discussion of the SDSS handling of PSF saturation, and the referee for useful comments."
 We wish to thankTom Miller for making the photometric observations possible., We wish to thankTom Miller for making the photometric observations possible.
 This research has been supported by National Science Foundation grant through AST 03-07912. and (the University of Nebraska UCARE program.," This research has been supported by National Science Foundation grant through AST 03-07912, and the University of Nebraska UCARE program."
components to provide a rough estimate of the frequencies expected for the secondary.,components to provide a rough estimate of the frequencies expected for the secondary.
" The magnitude. difference of 1.10 mae shifts the 11.15 "" range of the primary; to edto which. agrees with the band of power seen in the power spectrum."," The magnitude difference of 1.10 mag shifts the 11–15 $^{-1}$ range of the primary to 25--33 $^{-1}$, which agrees with the band of power seen in the power spectrum."
 The light. of the secondary is heavily diluted: by. the light from the primary. which is 1.1 mag brighter than the secondary.," The light of the secondary is heavily diluted by the light from the primary, which is 1.1 mag brighter than the secondary."
 Consequently. the amplitudes of pulsation of the secondary are reduced to one fourth of their intrinsic values.," Consequently, the amplitudes of pulsation of the secondary are reduced to one fourth of their intrinsic values."
 Η our interpretation is correct. then the secondary would have V amplitudes of about 0.5 mamag in combined light. or 2 mmag in the star alone.," If our interpretation is correct, then the secondary would have $V$ amplitudes of about 0.5 mmag in combined light, or 2 mmag in the star alone."
 The hypothesis that these modes come from the secondary can be tested: the orbital motions produce light-time shifts of several minutes., The hypothesis that these modes come from the secondary can be tested: the orbital motions produce light-time shifts of several minutes.
 Regrettably. the observed. amplitudes are too small to obtain the required accuracy in the phasing at cillerent orbital times.," Regrettably, the observed amplitudes are too small to obtain the required accuracy in the phasing at different orbital times."
" In order to examine the nature of the pulsations of 67 ""Tau in more detail. the physical parameters for the two stars forming the binary svstem need to be determined."," In order to examine the nature of the pulsations of $\theta^2$ Tau in more detail, the physical parameters for the two stars forming the binary system need to be determined."
" A recent summary of dilferent. determinations of global parameters of @ ""au can be found in ce Muijne et al. (", A recent summary of different determinations of global parameters of $\theta^2$ Tau can be found in de Bruijne et al. (
2001).,2001).
 ‘Torres ct al. (, Torres et al. (
1997). used. the orbital parallax to. clerive absolute visual magnitudes. A4. of 0.37 and 1.47 for the two components.,"1997) used the orbital parallax to derive absolute visual magnitudes, $M_{\rm{v}}$, of 0.37 and 1.47 for the two components."
 Similar values. OAS ancl 1.58. are obtained bv de Bruijne et al. (," Similar values, 0.48 and 1.58, are obtained by de Bruijne et al. ("
2001) and Lebreton at al. (,2001) and Lebreton at al. (
2001) from Llipparcos dynamical parallax.,2001) from Hipparcos dynamical parallax.
 Both stars have similar temperatures and its value can be obtained from the Moon Dworetsky (1985) calibration of ουμι photometry. viz..," Both stars have similar temperatures and its value can be obtained from the Moon Dworetsky (1985) calibration of $uvby\beta$ photometry, viz.,"
 dag = TODOWW. This value is lower than rw value. of KI adopted by Breger et al. (, $T_{\rm{eff}}$ = K. This value is lower than the value of K adopted by Breger et al. (
LOST) as well as others. since the older mocdel-atmosphere. calibrations of πο) tended to overestimate the temperatures of A stars.,"1987) as well as others, since the older model-atmosphere calibrations of $uvby\beta$ tended to overestimate the temperatures of A stars."
 Using a calibration of the CBV photometry. de Bruijne et al. (," Using a calibration of the $UBV$ photometry, de Bruijne et al. ("
2001) derive Zigg = νι for the primary and Yigg = Why [or the secondary. component The Moon Dworetsky (1985) calibration also allows us to derive a logg = 3.69 from the eg: photometry of the combined light of the two stars.,2001) derive $T_{\rm{eff}}$ = K for the primary and $T_{\rm{eff}}$ = K for the secondary component The Moon Dworetsky (1985) calibration also allows us to derive a $\log~g$ = 3.69 from the $uvby\beta$ photometry of the combined light of the two stars.
 Correction of the measured Balmer ciscontinuity. ο for the less evolved: secondary places our estimate for the primary near log.g = 3.55.," Correction of the measured Balmer discontinuity, $c_{\rm{1}}$, for the less evolved secondary places our estimate for the primary near $\log~g$ = 3.55."
 This implies a considerably higher evolutionary status than that deduced by Torres et al.," This implies a considerably higher evolutionary status than that deduced by Torres et al.,"
 who adopted logg = 4.0., who adopted $\log~g$ = 4.0.
 Llowever. our value is consistent with the position of the star in the LlertzsprungRussell Diagram for the Lyvades cluster as well as the known luminosity (see above).," However, our value is consistent with the position of the star in the Hertzsprung–Russell Diagram for the Hyades cluster as well as the known luminosity (see above)."
 We can also derive the logg value from the known mass. luminosity and temperature: for a mass of 2.42 solar masses for the primary Clorres et al.)," We can also derive the $\log~g$ value from the known mass, luminosity and temperature: for a mass of 2.42 solar masses for the primary (Torres et al.)"
 a logg value of 3.63 is derived. in agreement with the value found above from ieby:? photometry.," a $\log~g$ value of 3.63 is derived, in agreement with the value found above from $uvby\beta$ photometry."
 Finally. this as well as similar studies neglect the ellect of rotation and aspect. which alfect the choice of the appropriate values for temperature. Iuminosity ancl gravity (e... sce Pérrez Hernánndez et al.," Finally, this as well as similar studies neglect the effect of rotation and aspect, which affect the choice of the appropriate values for temperature, luminosity and gravity (e.g., see Pérrez Hernánndez et al."
 1999)., 1999).
 The method of computation of stellar evolution aud. pulsation was the same as in our other studies of 0 Scuti stars (see Pamyatnykh 2000 and references therein)., The method of computation of stellar evolution and pulsation was the same as in our other studies of $\delta$ Scuti stars (see Pamyatnykh 2000 and references therein).
 In particular. we used the latest version of the OPAL opacities (Lelesias Rogers 1996) supplemented with the lowtemperature data of Alexander Ferguson (1994).," In particular, we used the latest version of the OPAL opacities (Iglesias Rogers 1996) supplemented with the low–temperature data of Alexander Ferguson (1994)."
 Also. we used an updated version of the OPAL equation of state (Rogers et al.," Also, we used an updated version of the OPAL equation of state (Rogers et al."
 1996). viz..," 1996), viz.,"
 version 20582001. which was copied from the OPAL cata.," version EOS2001, which was copied from the OPAL data."
. The computations were performed starting with chemically uniform models on the ZAAIS. assuming an initial hyelrogen abundance VY=0.716. a helium abundance )=0.26 and a heavy element. abundance Z=0.024.," The computations were performed starting with chemically uniform models on the ZAMS, assuming an initial hydrogen abundance $X=0.716$, a helium abundance $Y=0.26$ and a heavy element abundance $Z=0.024$."
 These values correspond to recent estimates of the chemical composition of the LIvades (Perryman et al., These values correspond to recent estimates of the chemical composition of the Hyades (Perryman et al.
 1998. Lebreton et al.," 1998, Lebreton et al."
 2001)., 2001).
 We also tested models of somewhat cülferent chemical composition. with slightly higher metallicity or with higher helium content (VY=0.723. Y=0.25. .X=0.686. Y=0.29. Z=0.024)," We also tested models of somewhat different chemical composition, with slightly higher metallicity or with higher helium content $X=0.723$, $Y=0.25$ , $Z=0.027$ ; $X=0.686$, $Y=0.29$, $Z=0.024$ )."
 We computed. models with and. without. overshooting rom the convective core., We computed models with and without overshooting from the convective core.
" In the first. case. the overshooting distance. dover. was chosen to be 0.24/5. where £4, is the ocal pressure scale height at the edge of the convective core."," In the first case, the overshooting distance, $d_{\rm{over}}$, was chosen to be $0.2 \, H_{\rm{p}}$, where $H_{\rm{p}}$ is the local pressure scale height at the edge of the convective core."
 Examples of evolutionary tracks for 0. Scuti models computed. with and without overshooting are given hy Brewer Pamvatovkh (1998) and Pamyvatuvkh (2000)., Examples of evolutionary tracks for $\delta$ Scuti models computed with and without overshooting are given by Breger Pamyatnykh (1998) and Pamyatnykh (2000).
 In the stellar envelope. the standard. mixine-leneth theory of convection with the mixine-leneth parameter a = 1.6 was used., In the stellar envelope the standard mixing-length theory of convection with the mixing-length parameter $\alpha$ = 1.6 was used.
 This value was also used by Perryman et al. (, This value was also used by Perryman et al. (
1998) and Lebreton et al. (,1998) and Lebreton et al. (
2001). who derived à from the calibration of the solar-mocdel radius.,"2001), who derived $\alpha$ from the calibration of the solar-model radius."
 Uniform (solid-bodyv) stellar rotation and conservation of global angular momentum cluring evolution [fron the ZAAIS were assumed for all computations., Uniform (solid-body) stellar rotation and conservation of global angular momentum during evolution from the ZAMS were assumed for all computations.
 These assumptions were chosen due to their simplicity., These assumptions were chosen due to their simplicity.
 The influence of rotation on the evolutionary tracks of 0 Scuti models was demonstrated by Breger Pamyatuykh (1998) and Pamyatnvkh (2000)., The influence of rotation on the evolutionary tracks of $\delta$ Scuti models was demonstrated by Breger Pamyatnykh (1998) and Pamyatnykh (2000).
 In most cases the initial equatorial rotational velocity on the ZAAIS was chosen to be LOO kms. The linear nonadiabatic analysis of low-cegree oscillations (ές 22) was performed using the code developed bv Dziembowski (LOTT)., In most cases the initial equatorial rotational velocity on the ZAMS was chosen to be 100 km/s. The linear nonadiabatic analysis of low-degree oscillations $\ell$ $\leq$ 2) was performed using the code developed by Dziembowski (1977).
 The ellects of slow rotation on oscillation frequencies were treated up to third. order. in the rotational velocity (Dziembowski Goode 1992. Souli et al.," The effects of slow rotation on oscillation frequencies were treated up to third order in the rotational velocity (Dziembowski Goode 1992, Soufi et al."
 1998)., 1998).
 The main aim of the present theoretical study was to check the instability of models of both stellar components of 67 “Tau for the whole range of allowed values of mass or gravity. cllective temperature and Luminosity and to outline possible asteroscismological constraints tothe models.," The main aim of the present theoretical study was to check the instability of models of both stellar components of $\theta^2$ Tau for the whole range of allowed values of mass or gravity, effective temperature and luminosity and to outline possible asteroseismological constraints tothe models."
 We did not attempt to construct any model which fits, We did not attempt to construct any model which fits
and S44 04kkmss5 for star C. These differences are caused. by slight differences in centring of the source on the slit ?..,and $-8.4\pm0.4$ $^{-1}$ for star C. These differences are caused by slight differences in centring of the source on the slit \cite{bkkv06}.
 Jasecdl on the location of star A with respect to the centre of the slit. before ancl after cach exposure. we estimate an average olfset in radial velocity. of about S.6X34 + for the first epoch and 3.732.9 ss for the second. epoch.," Based on the location of star A with respect to the centre of the slit before and after each exposure, we estimate an average offset in radial velocity of about $-8.6\pm3.4$ $^{-1}$ for the first epoch and $3.7\pm2.9$ $^{-1}$ for the second epoch."
 This is comparable to the weighted average in lj.ο=21+O03kkmss + for stars A and C. Subtracting these racial velocity. olfsets from. the measured velocities of the counterpart. we obtain Vy=101.0dX 7kkmss| and 15=16.5£5.9kkmss +. and a velocity clillerence of 14Ve=S5+Il ," This is comparable to the weighted average in $V_1-V_2=-12.1\pm0.3$ $^{-1}$ for stars A and C. Subtracting these radial velocity offsets from the measured velocities of the counterpart, we obtain $V_1=101.0\pm8.7$ $^{-1}$ and $V_2=16.5\pm5.9$ $^{-1}$, and a velocity difference of $V_1-V_2=85\pm11$ $^{-1}$."
This is consistent with the V4i5= ss.72kkmss difference in radial velocity predicted from the pulsar timing ephemeris.," This is consistent with the $V_1-V_2\,=\,88.72$ $^{-1}$ difference in radial velocity predicted from the pulsar timing ephemeris."
 This confirms that the optical counterpart. to ds the object in the 95-day orbit around the pulsar., This confirms that the optical counterpart to is the object in the 95-day orbit around the pulsar.
 Fig., Fig.
 5 shows the radial velocity measurements of the companion and the radial velocity. predictions based. on the orbital parameters determined from pulsar timing., \ref{fig:radial} shows the radial velocity measurements of the companion and the radial velocity predictions based on the orbital parameters determined from pulsar timing.
 This provides an independent estimate of the mass ratio (2=1.55+ 0.20) and the svstemic racial velocity of the binary. «=44.3449kkmss to which cannot be derived from the radio timing.," This provides an independent estimate of the mass ratio $R\,=\,1.55 \pm 0.20$ ) and the systemic radial velocity of the binary, $\gamma\,=\,44.3\pm4.9$ $^{-1}$, which cannot be derived from the radio timing."
 Since the companion is a non-degenerate star. it could in principle have a strong stellar wind. which should. be detectable as a variation of DAL as a function. of orbital phase.," Since the companion is a non-degenerate star, it could in principle have a strong stellar wind, which should be detectable as a variation of DM as a function of orbital phase."
 Such a signal would) produce a distortion in our measurement. of the Shapiro delav., Such a signal would produce a distortion in our measurement of the Shapiro delay.
 In. Fie., In Fig.
 6G we display the DAL averaged over 36. bins. of the pulsars mean anomaly. after correction of the long-term. DAL variations.," \ref{fig:DMs} we display the DM averaged over 36 bins of the pulsar's mean anomaly, after correction of the long-term DM variations."
 For some of these intervals we have smaller aniounts of data or a small rangeof frequencies., For some of these intervals we have smaller amounts of data or a small rangeof frequencies.
 Lf these result in DAL determinations with uncertainties greater than Q.01cmὌρο they are not depicted.," If these result in DM determinations with uncertainties greater than $ 0.01\,\rm cm^{-3}\,pc$, they are not depicted."
 We detect no DM variations greater than 0.001cni.pe.," We detect no DM variations greater than $0.001\,\rm cm^{-3}\,pc$."
 This means that the miss estimates derived from the Shapiro delay are accurate. within their uncertainties.," This means that the mass estimates derived from the Shapiro delay are accurate, within their uncertainties."
 The better timing precision. larger number of TOXs. longer data span ancl optimised. orbital. coverage of our new dataset not only improve previous measurements of relativistic effects (namely the observed. apsidal motion a. and the s parameter of the Shapiro delay. sce Champion et al.," The better timing precision, larger number of TOAs, longer data span and optimised orbital coverage of our new dataset not only improve previous measurements of relativistic effects (namely the observed apsidal motion $\dot{\omega}_o$ and the $s$ parameter of the Shapiro delay, see Champion et al."
.. 2008) but. also allow a precise. measurement of the r parameter of the Shapiro delay. in addition to a measurement of the proper motion fj and the variation it causes on the apparent size of the orbit (κου Table 1).," 2008) but also allow a precise measurement of the $r$ parameter of the Shapiro delay, in addition to a measurement of the proper motion $\mu$ and the variation it causes on the apparent size of the orbit $\dot{x}$ (see Table 1)."
 We now discuss the relevance of these parameters., We now discuss the relevance of these parameters.
 With the previously available timing data it was not possible to measure the companion mass m. [from the Shapiro delay. alone., With the previously available timing data it was not possible to measure the companion mass $m_c$ from the Shapiro delay alone.
 The precise (and frequent) Arecibo timing has completely changed. this situation. providing a very clear Shapiro delay signal (see Fig. 7)).," The precise (and frequent) Arecibo timing has completely changed this situation, providing a very clear Shapiro delay signal (see Fig. \ref{fig:residuals_orbit}) )."
 Assuming that general relativity (GR) is the correct theory of gravity. we obtainwhere 2.=GAL.fe? 4925490047;5 is the solar mass A. in time units.," Assuming that general relativity (GR) is the correct theory of gravity, we obtainwhere $T_{\odot} = G M_{\odot} / c^3 = 4.925490947 \mu$ s is the solar mass $M_{\odot}$ in time units."
 As usual € is Newton's gravitational constant and e is the velocity of light., As usual $G$ is Newton's gravitational constant and $c$ is the velocity of light.
" Phe orbital inclination derivedfrom q is /=(77.4240)"" or (102.60.4)."," The orbital inclination derivedfrom $\varsigma$ is $i = (77.4 \pm
0.4)^\circ$ or $(102.6 \pm 0.4)^\circ$."
" Given the mass function f. these values imply a pulsar mass mj,= α total binary mass AJ;=(2.200.11)4M. and a mass ratio /?,=1.62+ 0.03."," Given the mass function $f$, these values imply a pulsar mass $m_p = (1.67 \pm 0.08) M_{\odot}$ , a total binary mass $M_t = (2.70 \pm 0.11) M_{\odot}$ and a mass ratio $R_s = 1.62 \pm 0.03$ ."
 The uncertainties quoted above were estimated. using the Bavesian technique described by 2.., The uncertainties quoted above were estimated using the Bayesian technique described by \cite{sna+02}. .
" We assume that m, aud cos? have constant probability."," We assume that $m_c$ and $\cos
i$ have constant probability."
 For cach point in a, For each point in a
eain are a function. of temperature. anc accordingly the temperature of the receiver enclosure is regulated for field operation.,gain are a function of temperature and accordingly the temperature of the receiver enclosure is regulated for field operation.
 The RE components are fitted with insulation to prevent convective cooling and are thermally anchored to à common aluminium mounting plate., The RF components are fitted with insulation to prevent convective cooling and are thermally anchored to a common aluminium mounting plate.
 Athermally controlled noise diode radiates a calibration signal of  2.0 Ix directly into the corrugatecl horn for 1 second. before and alter cach 30. seconds of observations., A thermally controlled noise diode radiates a calibration signal of $\sim$ 2.0 K directly into the corrugated horn for 1 second before and after each 30 seconds of observations.
 These calibration data are then used to correct the eain Huetuations of the amplifiers., These calibration data are then used to correct the gain fluctuations of the amplifiers.
 Phe calibration data are then obtained by subtracting the signals withcaf-off from the those withcalon., The calibration data are then obtained by subtracting the signals with from the those with.
 The output voltage signal from the three channel detectors are read. with VTI converters which are connected to the detectors with shielded pairs to minimize earthing problems., The output voltage signal from the three channel detectors are read with VTF converters which are connected to the detectors with shielded pairs to minimize earthing problems.
 Along with the receiver channels. the spin encoder is read once per revolution. giving a total of four digital signals fed into the WEE converters.," Along with the receiver channels, the spin encoder is read once per revolution, giving a total of four digital signals fed into the VTF converters."
 The output signals from the VETE converters are read. by a counter card in a PC computer situated in an adjacent building., The output signals from the VTF converters are read by a counter card in a PC computer situated in an adjacent building.
 This computer also controls he square wave used to drive the calibration diode on and olf., This computer also controls the square wave used to drive the calibration diode on and off.
 The computer is connected to the VTE converters and he calibration diode via a fast link which consists of two 'T'EL-EXC'L converters. one at each of the connecting points.," The computer is connected to the VTF converters and the calibration diode via a fast link which consists of two TTL-ECL converters, one at each of the connecting points."
 The data are sampled. cach 4000 ys with a blanking ime (no recording) of 4005/5. This is equivalent to have three samples per beam ancl a total of ~220 samples per turn of he mirror., The data are sampled each 4000 $\mu$ s with a blanking time (no recording) of $400 \mu$ s. This is equivalent to have three samples per beam and a total of $\sim 220$ samples per turn of the mirror.
 “Phe computer temporally stores 30. seconds of data (about 30 turns of the mirror)., The computer temporally stores 30 seconds of data (about 30 turns of the mirror).
 For cach turn of the mirror a lock-in at multiples of the spin evele is performec N ecomposition into a Fourier series., For each turn of the mirror a lock-in at multiples of the spin cycle is performed by decomposition into a Fourier series.
 The first 106 Fourier cocllicients (harmonics hereafter) which correspond to 212 samples per turn are kept and stacked across the 30 seconc »xeriod., The first 106 Fourier coefficients (harmonics hereafter) which correspond to 212 samples per turn are kept and stacked across the 30 second period.
 Phe stacked harmonics are then stored in a FILS file., The stacked harmonics are then stored in a FITS file.
 This procedure does not only saves hard-cisk space on the XC but also accelerates the data reduction. because the 212 samples represent fixed. positions on the sky.," This procedure does not only saves hard-disk space on the PC but also accelerates the data reduction, because the 212 samples represent fixed positions on the sky."
 Εις is possible cause the change in LWA caused by the earth rotation in 30 seconds 07.12 is negligible with respect to the beamo-wicdth Ml , This is possible because the change in RA caused by the earth rotation in 30 seconds $\sim 0^{\circ}.12$ is negligible with respect to the beam-width $\sim 1^{\circ}$.
Phe instrument is installed at the Teide Observatory. which has been shown to be a good site for centimetre and millimetre CAIB observations (Davies et al.," The instrument is installed at the Teide Observatory, which has been shown to be a good site for centimetre and millimetre CMB observations (Davies et al."
 L996: Dicker et al., 1996; Dicker et al.
 1999)., 1999).
 Phe instrument started operation on 1990 September 1 and has remained operational until 2000 September. with interruptions due to instrumental tests. aclverse atmospheric conditions and technical failure.," The instrument started operation on 1999 September 1 and has remained operational until 2000 September, with interruptions due to instrumental tests, adverse atmospheric conditions and technical failure."
 During this period we have observed three overlapping regions of the skv between and in declination., During this period we have observed three overlapping regions of the sky between and in declination.
 About 100 days of, About 100 days of
Figue 2 shows the svstem at 2~19. briefle after turnaround.,"Figure 2 shows the system at $z\sim 13$, briefly after turnaround."
 The DAT component has developed a marked substructure iu response to the imprinted perturbations. and the barvous have begun to fall into the deepest DAL potential wells.," The DM component has developed a marked substructure in response to the imprinted perturbations, and the baryons have begun to fall into the deepest DM potential wells."
" Eveutuallv. close to the redshift of virialization. ti,c]10. the DAL is undergoing violet relaxation (Lyucen-Bell 1967). resulting in au approximate balauce between kiuetic aud gravitational potential cucrey."," Eventually, close to the redshift of virialization, $z_{\rm vir}\simeq 10$, the DM is undergoing violent relaxation (Lynden-Bell 1967), resulting in an approximate balance between kinetic and gravitational potential energy."
 T16 barvons. on the other haud. dissipatively settle iuto he center of the DAL halo (see Figure 3).," The baryons, on the other hand, dissipatively settle into the center of the DM halo (see Figure 3)."
 Focusing ou he innermost 200 pe of the simmlation box. Figure | dispavs the ceutral distribution of the eas density.," Focusing on the innermost $\sim 200$ pc of the simulation box, Figure 4 displays the central distribution of the gas density."
 At lus stage in the simulation. a high-density siuk particle of mass ~3<LOPAL. and radius zod pe has been creaed.," At this stage in the simulation, a high-density sink particle of mass $\sim 3\times 10^{6}M_{\odot}$ and radius $\la 1$ pc has been created."
 Subsequently the sink particle grows in mass by continuous accretion from the surrounding diffuse gas.," Subsequently, the sink particle grows in mass by continuous accretion from the surrounding diffuse gas."
"the 1.3 mm flux is emitted, namely between ~15 and 50 AU.","the 1.3 mm flux is emitted, namely between $\sim$ 15 and 50 AU."
" In this region, the surface density in RY Tau disk is almost constant with the radius, while it decreases roughly as 1/R in the case of DG Tau."," In this region, the surface density in RY Tau disk is almost constant with the radius, while it decreases roughly as $1/R$ in the case of DG Tau."
" Inside 15 AU and outside 50 AU, the observations lack both the angular resolution and the sensitivity required to directly constrain the surface density."," Inside 15 AU and outside 50 AU, the observations lack both the angular resolution and the sensitivity required to directly constrain the surface density."
" As a consequence, the values of X(R) strongly depend on the assumed model and can differ by one order of magnitude at the disk inner radius."," As a consequence, the values of $\Sigma(R)$ strongly depend on the assumed model and can differ by one order of magnitude at the disk inner radius."
 In this section we discuss the implications of the inferred surface density on the presence of planets., In this section we discuss the implications of the inferred surface density on the presence of planets.
There is little discussion possible about the coincidence between the recorded laboratory spectrum and the (5450 DIB.,There is little discussion possible about the coincidence between the recorded laboratory spectrum and the $\lambda$ 5450 DIB.
 Both bands have a central peak position. of 545 nm and a FWHM of 1.03 (0.1) nm (laboratory spectrum) and 0.953 nm (observational spectrum) (Tuairisgetal..2000)., Both bands have a central peak position of 545 nm and a FWHM of 1.03 (0.1) nm (laboratory spectrum) and 0.953 nm (observational spectrum) \citep{Tuairisg:2000}.
. The uncertainty in the first value is due to the overlap of the many individual transitions that prohibits a clear view on the broad feature., The uncertainty in the first value is due to the overlap of the many individual transitions that prohibits a clear view on the broad feature.
 The question is more whether this actually represents a DIB match and for this complementary information is needed., The question is more whether this actually represents a DIB match and for this complementary information is needed.
 Additional laboratory work has been performed. where it should be noted that scans as shown 11 Figs.," Additional laboratory work has been performed, where it should be noted that scans as shown in Figs."
 2 and 3 typically last 4IS minutes to an hour. in order to achieve the required sensitivity and to cover a frequency domain large enough to discriminate band profile and base line. t.e. fast optimizations are ot possible.," 2 and 3 typically last 45 minutes to an hour, in order to achieve the required sensitivity and to cover a frequency domain large enough to discriminate band profile and base line, i.e. fast optimizations are not possible."
 The laboratory band does not show any structure that can be related to unresolved P. Q and R-branches.," The laboratory band does not show any structure that can be related to unresolved P, Q and R-branches."
 With 1.03 (0.1) nm the band is also much broader than the unresolved rotational profile of a larger carbon chain radical., With 1.03 (0.1) nm the band is also much broader than the unresolved rotational profile of a larger carbon chain radical.
" For comparison. at 15 K. the band profile of the linear C,H radical (at 525 nm) is about five times narrower (Linnartzetal.. 1999)."," For comparison, at 15 K, the band profile of the linear $_6$ H radical (at 525 nm) is about five times narrower \citep{Linnartz:1999}."
. It should also be noted that such a broad feature actually represents a large absorption compared to many of the sharper DIBs., It should also be noted that such a broad feature actually represents a large absorption compared to many of the sharper DIBs.
 Changing the experimental settings to vary the final temperature in the expansion by measuring close (~ ‘warm’) and far (~ 'cold) downstream. does not substantially change the FWHM of the spectral contour.," Changing the experimental settings to vary the final temperature in the expansion by measuring close $\sim$ $^{\prime}$ $^{\prime}$ ) and far $\sim$ $^{\prime}$ $^{\prime}$ ) downstream, does not substantially change the FWHM of the spectral contour."
 As the narrow overlapping transitions have FWHMs close to the laser bandwidth. experimental broadening artifacts such as residual Doppler broadening in the expansion or amplified spontaneous emission. can be excluded.," As the narrow overlapping transitions have FWHMs close to the laser bandwidth, experimental broadening artifacts such as residual Doppler broadening in the expansion or amplified spontaneous emission, can be excluded."
 It is clear that the band profile is due to a temperature independent and carrier specific broadening effect. presumably life time broadening.," It is clear that the band profile is due to a temperature independent and carrier specific broadening effect, presumably life time broadening."
 The observed bandwidth of 1.0 nm (~ eem around 545 nm) corresponds to a lifetime of roughly 0.15 ps., The observed bandwidth of 1.0 nm $\sim$ $^{-1}$ around 545 nm) corresponds to a lifetime of roughly 0.15 ps.
 The bandwidth profile does not allow concluding on the nature of the laboratory carrier., The bandwidth profile does not allow concluding on the nature of the laboratory carrier.
 The carrier must be à transient species (a molecular radical. a cation or anion. a weakly bound radical complex. possibly charged. or a vibrationally or electronically excited species) as no comparable spectra are recorded without plasma (1.9. with a regular C4 H»/He expansion).," The carrier must be a transient species (a molecular radical, a cation or anion, a weakly bound radical complex, possibly charged, or a vibrationally or electronically excited species) as no comparable spectra are recorded without plasma (i.e. with a regular $_2$ $_2$ /He expansion)."
 The use of a C;D;/He expansion results in a red-shifted spectrum (Fig., The use of a $_2$ $_2$ /He expansion results in a red–shifted spectrum (Fig.
 3) and from this it can be concluded that the laboratory carrier must contain both carbon and hydrogen., 3) and from this it can be concluded that the laboratory carrier must contain both carbon and hydrogen.
 In order to check whether there are equivalent H-atoms in this carrier a C5H2/C:Ds 1:1 mixture in He has been used as an expansion gas. but this only results in a very broad absorption feature covering the whole region between results obtained from pure CsH> and pure CsD» expansions.," In order to check whether there are equivalent H-atoms in this carrier a $_2$ $_2$ $_2$ $_2$ 1:1 mixture in He has been used as an expansion gas, but this only results in a very broad absorption feature covering the whole region between results obtained from pure $_2$ $_2$ and pure $_2$ $_2$ expansions."
 It is not possible. as demonstrated for HC4H or HCH (Sinclairetal...1999;Balletal..2000a:Khoroshev 2004).. to conclude on the actual number of equivalent H-atoms in the carrier by. determining the number of bands that shows up.," It is not possible, as demonstrated for $_6$ $^+$ or $_7$ H \citep{Sinclair:1999, Ball:2000a, Khoroshev:2004}, to conclude on the actual number of equivalent H-atoms in the carrier by determining the number of bands that shows up."
 Also the use of another precursor (e.g. allene) did not provide conclusive information., Also the use of another precursor (e.g. allene) did not provide conclusive information.
 Additional experiments have been performed., Additional experiments have been performed.
 The 543-545 nm region has been scanned using a two-photon REMPI-TOF experiment with the aim to determine the mass of the carrier (Pinoetal..2001)., The 543-545 nm region has been scanned using a two-photon REMPI-TOF experiment with the aim to determine the mass of the carrier \citep{Pino:2001}.
. No spectrum could be recorded. which may be related to the short lifetime of the excited state or with the fact that the carrier is an ton.," No spectrum could be recorded, which may be related to the short lifetime of the excited state or with the fact that the carrier is an ion."
 [ons are indeed formed in this planar plasma source (Witkowiezetal..2004)., Ions are indeed formed in this planar plasma source \citep{Witkowicz:2004}.
. Both smaller and larger species have been observed. with optimum production. rates. depending. among other things. or the backing pressure.," Both smaller and larger species have been observed, with optimum production rates depending, among other things, on the backing pressure."
 The production of larger species is generally more critical. e.g. higher backing pressures are needed but this also may destabilize the plasma which is unfortunate. particularly. during long scan. procedures.," The production of larger species is generally more critical, e.g. higher backing pressures are needed but this also may destabilize the plasma which is unfortunate, particularly during long scan procedures."
 More complex species are generally found further downstream. but in this specific case we did not observe large differences as function of the distance from the laser beam to the nozzle orifice.," More complex species are generally found further downstream, but in this specific case we did not observe large differences as function of the distance from the laser beam to the nozzle orifice."
 This is the typical behaviour for a smaller constituent in the gas expansion., This is the typical behaviour for a smaller constituent in the gas expansion.
 We have tried to study systematically the voltage dependence of the signal: for a positive ton an increase in voltage should go along with a decrease in signal for distances further downstream. as the jaws carry a negative voltage.," We have tried to study systematically the voltage dependence of the signal; for a positive ion an increase in voltage should go along with a decrease in signal for distances further downstream, as the jaws carry a negative voltage."
 For anions it is the opposite. but 10 years of experience with this source have shown that negative tons are rather hard to produce.," For anions it is the opposite, but 10 years of experience with this source have shown that negative ions are rather hard to produce."
 Again. the changes we recorded were small and did not allow drawing hard conclusions.," Again, the changes we recorded were small and did not allow drawing hard conclusions."
 Following condition 2 mentioned in the introduction. we have also searched in other wavelength regions blue shifted by values typical for an excited C-C. C=C. C=C or CH stretch in the upper electronic state.," Following condition 2 mentioned in the introduction, we have also searched in other wavelength regions blue shifted by values typical for an excited C–C, $=$ C, $\equiv$ C or CH stretch in the upper electronic state."
 Such excited bands have not been observed here. but it should be noted that these bands can be intrinsically weak.," Such excited bands have not been observed here, but it should be noted that these bands can be intrinsically weak."
 In summary. we are left with à laboratory spectrum that coincides both in band maximum and band width with a known DIB band at 545 nm.," In summary, we are left with a laboratory spectrum that coincides both in band maximum and band width with a known DIB band at 545 nm."
 Our measurements show that the absorption spectrum of a transient molecule containing hydrogen and carbon reproduces the astronomical spectrum., Our measurements show that the absorption spectrum of a transient molecule containing hydrogen and carbon reproduces the astronomical spectrum.
 The profile can be explained with life time broadening and this is consistent with the observation that the laboratory and astronomical spectrum are identical. te. without temperature constraints.," The profile can be explained with life time broadening and this is consistent with the observation that the laboratory and astronomical spectrum are identical, i.e. without temperature constraints."
 [In addition. it explains why the large bandwidth of this DIB does not vary along different lines of sight.," In addition, it explains why the large bandwidth of this DIB does not vary along different lines of sight."
" The large effective absorption also may be indicative. for an abundant carrier,", The large effective absorption also may be indicative for an abundant carrier.
 The exact carrier. as such. remains an open question.," The exact carrier, as such, remains an open question."
 The present result. however. may be useful to stimulate upcoming DIB work.," The present result, however, may be useful to stimulate upcoming DIB work."
For the periodic fBm structure we find a very close agreement of the A-variance using the truncated filter with the theoretical value given by a slope α=1.,For the periodic fBm structure we find a very close agreement of the $\Delta$ -variance using the truncated filter with the theoretical value given by a slope $\alpha=1$.
 The mirror continuation results in an apparent reduction of the amount of large-scale structures in the map as they are partially assigned to larger modes only present in the map extended by mirroring., The mirror continuation results in an apparent reduction of the amount of large-scale structures in the map as they are partially assigned to larger modes only present in the map extended by mirroring.
 Thus the A-variance slope is systematically underestimated., Thus the $\Delta$ -variance slope is systematically underestimated.
 For the non-periodic structure. the assumption of periodicity and only the use of the truncated filters results in a good reproduction of the expected value for the slope.," For the non-periodic structure, the assumption of periodicity and only the use of the truncated filters results in a good reproduction of the expected value for the slope."
 Analogously to the statistical treatment by Benschetal.(2001) we vary the spectral index of the fBm structures and chose randomly 30 different fBms or fBm maps and determine their A-variance spectra., Analogously to the statistical treatment by \citet{Bensch} we vary the spectral index of the fBm structures and chose randomly 30 different fBms or fBm sub-maps and determine their $\Delta$ -variance spectra.
 as a function of the spectral index Z using the three different edge treatments., as a function of the spectral index $\zeta$ using the three different edge treatments.
 An optimum treatment should reproduce the relation «*=¢—2 indicated by the dotted line in Fig. 4.., An optimum treatment should reproduce the relation $\alpha=\zeta-2$ indicated by the dotted line in Fig. \ref{fig_edgesystem}.
 For the periodic fBms we find that the A-variance spectra from the truneated filter show about the same spectral indices as the periodic treatment., For the periodic fBms we find that the $\Delta$ -variance spectra from the truncated filter show about the same spectral indices as the periodic treatment.
 The error bars in the periodic treatmer= are zero because the A-variance spectrum is independent of the exact phase distribution and thus identical for each map of the sample., The error bars in the periodic treatment are zero because the $\Delta$ -variance spectrum is independent of the exact phase distribution and thus identical for each map of the sample.
 The standard deviation of the slopes in the truncatedfilter treatment is always about 0.08 here., The standard deviation of the slopes in the truncated-filter treatment is always about 0.08 here.
 The A-variance spectrum underestimates the power spectral index by 0.03 at €=3.6 and by 0.08 at €=4 because the theoretical value is only reached for infinitely large maps and the deviations grow wher approaching the asymptotic limit of a=j (see Stutzki et al., The $\Delta$ -variance spectrum underestimates the power spectral index by 0.03 at $\zeta=3.6$ and by 0.08 at $\zeta=4$ because the theoretical value is only reached for infinitely large maps and the deviations grow when approaching the asymptotic limit of $\alpha=4$ (see Stutzki et al.
 1998)., 1998).
 The A-variance spectrum computed for the mirror-continuation of the map always underestimates the spectral index by about 0.1., The $\Delta$ -variance spectrum computed for the mirror-continuation of the map always underestimates the spectral index by about 0.1.
 In the case of non-periodic fBm. sub-structures the periodicity assumption clearly fails., In the case of non-periodic fBm sub-structures the periodicity assumption clearly fails.
 The use of the simple A-variance without filter truncation or mirror continuation provides wrong results at power spectral indices above about Z=2.9., The use of the simple $\Delta$ -variance without filter truncation or mirror continuation provides wrong results at power spectral indices above about $\zeta=2.9$.
 In contrast. both the mirror-continuation and the filter truncation provide a reasonable measure for the actual map structure for all spectral indices.," In contrast, both the mirror-continuation and the filter truncation provide a reasonable measure for the actual map structure for all spectral indices."
 The mirror-continuation always underestimates the spectral index by about 0.1 (except at ¢= 4.0)., The mirror-continuation always underestimates the spectral index by about 0.1 (except at $\zeta=4.0$ ).
 The filter truncation method reveals the correct spectral index for €x3.0 and overestimates it by 0.05 at ¢=4.0., The filter truncation method reveals the correct spectral index for $\zeta \le 3.0$ and overestimates it by 0.05 at $\zeta=4.0$.
 Regarding the typical error bars of 0.15. the systematic errors are. however. lower than the scatter between different fBm realizations with the same spectral index.," Regarding the typical error bars of 0.15, the systematic errors are, however, lower than the scatter between different fBm realizations with the same spectral index."
 The same tests were repeated for map sizes ranging from 32° to 2567 pixels., The same tests were repeated for map sizes ranging from $32^2$ to $256^2$ pixels.
 In agreement with the studies by Benschetal.(2001) we found no systematic changes in the A-variance slopes exceeding 0.03 when changing the map size but an increase of the error bars from 0.15 at map sizes of 128 to, In agreement with the studies by \citet{Bensch} we found no systematic changes in the $\Delta$-variance slopes exceeding 0.03 when changing the map size but an increase of the error bars from 0.15 at map sizes of $128^2$ to
The upper left corner of the Lertzsprung-Russell diagram is populated by a handful of rapidly variable stars. the so-called GA Vir stars.,"The upper left corner of the Hertzsprung-Russell diagram is populated by a handful of rapidly variable stars, the so-called GW Vir stars."
 They are very hot. and. luminous. hyerogen-delicicnt pre-white dwarf stars characterized by surface lavers rich in helium. carbon and oxvgen (Werner Llerwig 2006) that exhibit nonracial g(gravitv)-mocdes with periods between 5 and 50 min see. c.g. Winget Ixepler (2008) and Althaus ct al. (," They are very hot and luminous, hydrogen-deficient pre-white dwarf stars characterized by surface layers rich in helium, carbon and oxygen (Werner Herwig 2006) that exhibit nonradial $g$ (gravity)-modes with periods between 5 and 50 min — see, e.g., Winget Kepler (2008) and Althaus et al. ("
2010).,2010).
 In recent vears. accurate asteroseismology of CAV Vir stars has started to vield details of the internal structure and evolutionary status of these stars.," In recent years, accurate asteroseismology of GW Vir stars has started to yield details of the internal structure and evolutionary status of these stars."
 On the observational side. the works of Vauclair et al. (," On the observational side, the works of Vauclair et al. ("
2002) on13412... Fu et al. (,"2002) on, Fu et al. ("
2007) On200.. ancl Costa οἱ al. (,"2007) on, and Costa et al. ("
2008) on are particularly noteworthy.,2008) on are particularly noteworthy.
 On the theoretical front. important progress in the modeling of the internal structure of P1159 stars (Althaus et al.," On the theoretical front, important progress in the modeling of the internal structure of PG1159 stars (Althaus et al."
 2005: Miller Bertolami Althaus 2006) has made it possible. unprecedented asteroseismological inferences for CN Vir stars. (Córrsico et al., 2005; Miller Bertolami Althaus 2006) has made it possible unprecedented asteroseismological inferences for GW Vir stars (Córrsico et al.
 2007ab. 2008. 2009).," 2007ab, 2008, 2009)."
 Asteroseismologv of GAY Vir stars provides information about the stellar mass. the chemical stratification. the luminosity. ancl clistance. and several other relevant properties such as stellar rotation rate ancl the presence and strength of magnetic fields.," Asteroseismology of GW Vir stars provides information about the stellar mass, the chemical stratification, the luminosity and distance, and several other relevant properties such as stellar rotation rate and the presence and strength of magnetic fields."
 Of particular interest in the present investigation is the potential of asteroscismology to place constraints on stellar rotation. an important aspect that has been proved to be very. dillieult. of assessing hy means of traditional techniques mostly spectroscopy.," Of particular interest in the present investigation is the potential of asteroseismology to place constraints on stellar rotation, an important aspect that has been proved to be very difficult of assessing by means of traditional techniques — mostly spectroscopy."
 Specifically. rotation removes the intrinsic mode degeneracy ofa nonracdial g-moce characterized by an harmonic degree f and a racial order A.," Specifically, rotation removes the intrinsic mode degeneracy of a nonradial $g$ -mode characterized by an harmonic degree $\ell$ and a radial order $k$."
 s à result. cach pulsation frequency ds split into multiplets ofδέ|1 frequencies specified by cillerent values of the azimuthal index m. ΕΠ... (Unno et al.," As a result, each pulsation frequency is split into multiplets of $2\ell+1$ frequencies specified by different values of the azimuthal index $m$, with $m= 0, \pm 1, \ldots, \pm \ell$ (Unno et al."
 1989)., 1989).
 Rotational splittines in the power μαrectrum of a compact pulsator were first discovered in yw white cwarl 15 548 (Robinson et al., Rotational splittings in the power spectrum of a compact pulsator were first discovered in the white dwarf R 548 (Robinson et al.
 1976)., 1976).
 Since then. [requeney splittings induced by rotation have been detected in à number of pulsating white cwarl and pre-white dwarl stars.," Since then, frequency splittings induced by rotation have been detected in a number of pulsating white dwarf and pre-white dwarf stars."
 If the rate of rotation is slow compared. with the pulsation frequencies. the Lrequency separation between cach component of the multiplet is proportional to the rotation velocity of the star.," If the rate of rotation is slow compared with the pulsation frequencies, the frequency separation between each component of the multiplet is proportional to the rotation velocity of the star."
 This has enabled to derive the rotation period of a number of white dwarf ancl pre-white dwarf stars., This has enabled to derive the rotation period of a number of white dwarf and pre-white dwarf stars.
 Interestingly. enough. this approach provides rotation velocities much more precise than those inferred [rom spectroscopy (Ixoester et al.," Interestingly enough, this approach provides rotation velocities much more precise than those inferred from spectroscopy (Koester et al."
 1998: Ixawaler 2004)., 1998; Kawaler 2004).
uncertainty for total GC populations.,uncertainty for total GC populations.
 It is tempting to argue that these groups represent different formation channels for dEs. e.g.. the facline/quenching of diris. harassment of low-mass spirals. or simply a continuation of the E sequence to [anter magnitudes.," It is tempting to argue that these groups represent different formation channels for dEs, e.g., the fading/quenching of dIrrs, harassment of low-mass spirals, or simply a continuation of the E sequence to fainter magnitudes."
 In some scenarios [ον blue GC formation (e.g... Sirader 2005: Rhode 2005). galaxies with roughly similar masses in a given environment would be expected to have similar numbers of blue GCs per unit mass of their DAI halos.," In some scenarios for blue GC formation (e.g., Strader 2005; Rhode 2005), galaxies with roughly similar masses in a given environment would be expected to have similar numbers of blue GCs per unit mass of their DM halos."
 Variations in Sa at fixed. luminosity would then be due to differences in the efficiency of converting barvons to starseither early in the galaxys history (due to feedback) or later. due to galaxy (ranslormation processes as described above.," Variations in $S_{N}$ at fixed luminosity would then be due to differences in the efficiency of converting baryons to stars—either early in the galaxy's history (due to feedback) or later, due to galaxy transformation processes as described above."
 Two pieces of observational evidence should help to differentiate among the possibilities., Two pieces of observational evidence should help to differentiate among the possibilities.
 First. GC kinematies can be used directly to constrain CE mass-to-light ratios (e.g.. Beasley 2005).," First, GC kinematics can be used directly to constrain dE mass-to-light ratios (e.g., Beasley 2005)."
 It will be interesting to see whether GC kinematics are connected to the apparent dichotomy of rotating; vs. non-rotating dEs (Pedraz 2002. Geha 2002. 2003. van Zee 2004).," It will be interesting to see whether GC kinematics are connected to the apparent dichotomy of rotating vs. non-rotating dEs (Pedraz 2002, Geha 2002, 2003, van Zee 2004)."
 Second. more detailed stellar population studies of dEs are needed. especially anv method which (unlike integrated light spectroscopy) can break (he burst strengt(li:age degeneracy.," Second, more detailed stellar population studies of dEs are needed, especially any method which (unlike integrated light spectroscopy) can break the burst strength–age degeneracy."
 A rather ad hoe alternative is that the efficienev of blue GC formation varies substantially among Virgo dEs. but this cannot be constrained al present.," A rather ad hoc alternative is that the efficiency of blue GC formation varies substantially among Virgo dEs, but this cannot be constrained at present."
 It is interesting that the fraction of blue GCs appears unrelated both to the nucleation of the dE aud the Sx variations: (his suggests that whatever process leads (to red GC formation in dEs is independent of these other factors., It is interesting that the fraction of blue GCs appears unrelated both to the nucleation of the dE and the $S_N$ variations; this suggests that whatever process leads to red GC formation in dEs is independent of these other factors.
 We have presented a detailed analvsis of the GC color and bIuminositw distributions of several ος and of the colors. specilic frequencies. luminositv functions. and nuclei of a large sample of dEs.," We have presented a detailed analysis of the GC color and luminosity distributions of several gEs and of the colors, specific frequencies, luminosity functions, and nuclei of a large sample of dEs."
 The most interesting feature in the eFs M87 and NGC 4649 is a correlation between mass and metallicity [or individual blue GCs., The most interesting feature in the gEs M87 and NGC 4649 is a correlation between mass and metallicity for individual blue GCs.
 Self-enrichment is a plausible interpretation of this observation. ancl could suggest Chat these GCs once possessed dark matter halos (whieh may have been subsequently stripped).," Self-enrichment is a plausible interpretation of this observation, and could suggest that these GCs once possessed dark matter halos (which may have been subsequently stripped)."
 Among the other new features observed are very luminous (22 20) GCs with intermediate to red colors., Among the other new features observed are very luminous $z \ga 20$ ) GCs with intermediate to red colors.
 These objects are slightly larger than (vpical GC's and may be remnants of sipped dwarf galaxies., These objects are slightly larger than typical GCs and may be remnants of stripped dwarf galaxies.
 Next. we see an intermediate-color group of GCs which lies near the GCLF turnover and in the gap between the blue and red GC's.," Next, we see an intermediate-color group of GCs which lies near the GCLF turnover and in the gap between the blue and red GCs."
 Also. the color spread. among the red. GCs is nearly twice that of the blue GCs. but because the relation between g—z and metallicity appears to be nonlinear. the lo dispersion in metallicity (~0.6 dex) max be the same for both subpopulations.," Also, the color spread among the red GCs is nearly twice that of the blue GCs, but because the relation between $g-z$ and metallicity appears to be nonlinear, the $1 \sigma$ dispersion in metallicity $\sim 0.6$ dex) may be the same for both subpopulations."
V69: in agreement with the positive parabolic shape of the O-C curve. the period that best fits to our data is slightly longer than in S65.,": in agreement with the positive parabolic shape of the O-C curve, the period that best fits to our data is slightly longer than in S65."
 Phe variable could. be resolved from its close companion in our photometry. and the light curves are very well defined with small scatter.V'TO:," The variable could be resolved from its close companion in our photometry, and the light curves are very well defined with small scatter.:"
 the old data for this variable have been recently reanalysecl by NCSO9. who derived. a period 0.486085. and suegeested this is a fundamental pulsator with unusually small amplitucle.," the old data for this variable have been recently reanalysed by NC89, who derived a period 0.486085 and suggested this is a fundamental pulsator with unusually small amplitude."
 Our data do not provide a good light curve with NCSO's period: we have derived a slightly longer period (0.486554) and the shape of the light curve is. sinusoidal with a V amplitude about 0.35 mag. rather tvpical of a," Our data do not provide a good light curve with NC89's period; we have derived a slightly longer period (0.486554) and the shape of the light curve is sinusoidal with a V amplitude about 0.35 mag, rather typical of a"
as reviewed by Eeeleton (1996).,as reviewed by Eggleton \shortcite{egg96}.
. One can only note that Sarna Fecorova (1950). who considered formation of solar-type contact binaries through the Case A mass-exchange mechanism. pointed out the importance of the initial mass-ratio: For mass-ratio sullicicntly close to unity. the rapid. (hydrodynamical) mass exchange can be avoided and the system may evolve in the thermal time-scale.," One can only note that Sarna Fedorova \shortcite{SF89}, who considered formation of solar-type contact binaries through the Case A mass-exchange mechanism, pointed out the importance of the initial mass-ratio: For mass-ratio sufficiently close to unity, the rapid (hydrodynamical) mass exchange can be avoided and the system may evolve in the thermal time-scale."
 Although the mass-reversal has not been mocoeled. it is likely that W Cry is the product of such a process.," Although the mass-reversal has not been modeled, it is likely that W Crv is the product of such a process."
 We thank AXndy Odell for providing the light curve ancl time-of-minima data and for extensive correspondence. numerous advices and suggestions and BBohdan Paczvisski and Janusz Ixaluμην for a critical reacing of the original version of the paper and several suggestions that improved. the presentation of the paper.," We thank Andy Odell for providing the light curve and time-of-minima data and for extensive correspondence, numerous advices and suggestions and Bohdan Paczyńsski and Janusz Ka\l{u}\\.znny for a critical reading of the original version of the paper and several suggestions that improved the presentation of the paper."
 (see?).. (see?).. (?.henceforthGS95).., \citep[see][]{Schlickeiser02}. \citep[see][]{Longairbook}. \citep[][henceforth GS95]{GS95}.
 B=PeasΌμως. (?).., $\beta\equiv P_{gas}/P_{mag}$ \citep{LG01}.
 compressible modes 1s weak and that the Alfvénnic modes follow the GS95 spectrum in compressible medium., \cite[][henceforth CL02]{CL02_PRL} compressible modes is weak and that the Alfvénnic modes follow the GS95 spectrum in compressible medium.
 This is consistent with the analysis of observational data (??)..," This is consistent with the analysis of observational data \citep[]{LP00,SL01}."
 The turbulence injected on large scales may correspond to GS95 model and its extensions to compressible medium is less efficient in scattering of CRs compared to the estimates made assuming that magnetic turbulence consists of plane waves moving parallel to magnetic field., The turbulence injected on large scales may correspond to GS95 model and its extensions to compressible medium is less efficient in scattering of CRs compared to the estimates made assuming that magnetic turbulence consists of plane waves moving parallel to magnetic field.
 A cascade of Alfvenie perturbations initiated at large injection scales is shown to be really inefficient for the CR scattering (?2).," A cascade of Alfvenic perturbations initiated at large injection scales is shown to be really inefficient for the CR scattering \citep[]{Chandran00, YL02}."
. At the same time. one should not disregard the possibilities of generation of additional perturbations by CR themselves.," At the same time, one should not disregard the possibilities of generation of additional perturbations by CR themselves."
 For instance. the slab Alfvénnic perturbation can be created. e.g.. vla streaming instability (see22)..," For instance, the slab Alfvénnic perturbation can be created, e.g., via streaming instability \citep[see][]{Wentzel74, Cesarsky80}."
 These perturbations are present for a range of CRs energies (e.g.. =I00GeV in interstellar medium for the streaming instability) owing to non-linear damping arising from ambient. turbulence (??.henceforthYLO2.YLO4.. ?)).," These perturbations are present for a range of CRs energies (e.g., $\lesssim 100$ GeV in interstellar medium for the streaming instability) owing to non-linear damping arising from ambient turbulence \citealp[][henceforth YL02, YL04]{YL02, YL04}, \citealp{FG04}) )."
 Instabilities induced by anisotropic distribution of CRs were also suggested as a possibility to scatter CRs (??)..," Instabilities induced by anisotropic distribution of CRs were also suggested as a possibility to scatter CRs \citep[]{Lerche, Melrose74}."
 Recent work by ?.henceforthLBOG proposed that compressible turbulence can induce gyroresonance— instability. which is an important feedback processes that can create slab modes to efficiently scatter CRs.," Recent work by \citet[][henceforth LB06]{LB06} proposed that compressible turbulence can induce gyroresonance instability, which is an important feedback processes that can create slab modes to efficiently scatter CRs."
 This process ts claimed to be more efficient in scattering CRs compared to direct action of turbulent fluctuations., This process is claimed to be more efficient in scattering CRs compared to direct action of turbulent fluctuations.
 This gyro-kinetic instability is induced by the anisotropic distribution of CRs. which is caused by the compression arising from large scale turbulence.," This gyro-kinetic instability is induced by the anisotropic distribution of CRs, which is caused by the compression arising from large scale turbulence."
 The degree of anisotropy. is determined by the compression on the scale of CR mean free path in LBO6.," The degree of anisotropy, is determined by the compression on the scale of CR mean free path in LB06."
 In their treatment the growth of CRs needs to be balanced with steepening in order to prevent the diffusion from approaching the Bohm limit. where the mean free path of particles becomes comparable to the Larmor radius.," In their treatment the growth of CRs needs to be balanced with steepening in order to prevent the diffusion from approaching the Bohm limit, where the mean free path of particles becomes comparable to the Larmor radius."
 In this paper. we shall investigate the nonlinear suppression of the instability by considering the self-adjustment of anisotropy due to scattering with the magnetic perturbations.," In this paper, we shall investigate the nonlinear suppression of the instability by considering the self-adjustment of anisotropy due to scattering with the magnetic perturbations."
 The instability reaches a stabilized growth rate due to the feedback of the increased perturbations on the anisotropy of CRs., The instability reaches a stabilized growth rate due to the feedback of the increased perturbations on the anisotropy of CRs.
 In what follows. in $22 we give a brief background on turbulence and CR scattering.in $33 weintroducethegyroresonance instability of CRs. in $4 we formulate our," In what follows, in 2 we give a brief background on turbulence and CR scattering,in 3 weintroducethegyroresonance instability of CRs, in 4 we formulate our"
vs confined ones aud therefore allow us to discriminate the confining role of the magnetic field. aud if observed stellar flares preseut such signatures.,"vs confined ones and therefore allow us to discriminate the confining role of the magnetic field, and if observed stellar flares present such signatures."
 The study that we illustrate here presents also interesting results ou the theoretical poiu of view: we describe the evolution of the nou-coufinec plasina in a stratified. corona atmosphere. ie. which is hot and where thermal couduction is fully efficient.," The study that we illustrate here presents also interesting results on the theoretical point of view: we describe the evolution of the non-confined plasma in a stratified coronal atmosphere, i.e. which is hot and where thermal conduction is fully efficient."
 This aspect makes this work quite different roni typica models of bursts. like supernovac. which instead propagate in conducting and cooler media.," This aspect makes this work quite different from typical models of bursts, like supernovae, which instead propagate in non-conducting and cooler media."
 Our approach is to set up anu initial stratified atimosplicre. simular to a confined one. inclhudiug chromosphere. transition region and corona. and where the plasma is not confiued to move along one spatial direction. and then to nipart a localized energy iupulse.," Our approach is to set up an initial stratified atmosphere, similar to a confined one, including chromosphere, transition region and corona, and where the plasma is not confined to move along one spatial direction, and then to impart a localized energy impulse."
 Plasina dvnamics aud heat conduction cau occur isotropically., Plasma dynamics and heat conduction can occur isotropically.
 The evolutiou of such svsteni needs to be described by a muuerical 2-D lydrodvuamiuc iaodel. with cnhauced spatial resolution iu the low corona aud in the transition region and including plasma thermal conduction: therefore it is also a demaucding uunucerical problems.," The evolution of such system needs to be described by a numerical 2-D hydrodynamic model, with enhanced spatial resolution in the low corona and in the transition region and including plasma thermal conduction; therefore it is also a demanding numerical problem."
 Iu order to compare our results with observations and to obtain diagnostical feedbacks. we svuthesize ποια our model results the expected evolution of the integrated. N-rav flare DIuuimositv. 1.6. by siauulatiug a fhuiug unresolved source. such as a star.," In order to compare our results with observations and to obtain diagnostical feedbacks, we synthesize from our model results the expected evolution of the integrated X-ray flare luminosity, i.e. by simulating a flaring unresolved source, such as a star."
 To have a realistic scenario. represcutative of real flare observations. we have chosen to svuthesize the cussion 1n a wide X-rav band such as at he focal plane of the ASCA/SIS (sensitive iu the rauge. approximately. 0.3 - LO keV). aud in two iutenuse X-rav lines.," To have a realistic scenario, representative of real flare observations, we have chosen to synthesize the emission in a wide X-ray band such as at the focal plane of the ASCA/SIS (sensitive in the range, approximately, 0.3 - 10 keV), and in two intense X-ray lines."
 Similar results can be expected for other wide band CCD instruments such as Chaudra/ACIS aud NMM/EDPIC. while the lines may be detectable bv instruments with good spectral resolutiou such as Chandra aud NMMNM-Newtou erating detectors.," Similar results can be expected for other wide band CCD instruments such as Chandra/ACIS and XMM/EPIC, while the lines may be detectable by instruments with good spectral resolution such as Chandra and XMM-Newton grating detectors."
 Tn Sect., In Sect.
 2 we describe our iiodeliug approach in detail. in Sect. 3..," \ref{sec:model} we describe our modeling approach in detail, in Sect. \ref{sec:simul},"
 the simulations performed and the results obtained are presented. in Sect.," the simulations performed and the results obtained are presented, in Sect."
 | the results are discussed and in Sect., \ref{sec:discuss} the results are discussed and in Sect.
 5 conclusions are drawn., \ref{sec:conclu} conclusions are drawn.
 The general concept of our modeling nou-confined coronal Hares is similar to modeling coufined fares (e.g. Peres et al., The general concept of our modeling non-confined coronal flares is similar to modeling confined flares (e.g. Peres et al.
 1982): the flare is triggered by an impulsive reating injected ina stratified plane-parallel static corona., 1982): the flare is triggered by an impulsive heating injected in a stratified plane-parallel static corona.
" The basic difference is that the unperturbed atinosphiere is not a senücirceular coronal loop aud hat the heat ransport. as well as auv plasima motion. is allowed in aux direction. iustead of beiug huited onlv along magnetic Ποια, ines parallel to the loop flux tube."," The basic difference is that the unperturbed atmosphere is not a semicircular coronal loop and that the heat transport, as well as any plasma motion, is allowed in any direction, instead of being limited only along magnetic field lines parallel to the loop flux tube."
 The evolution of a jieat perturbation propagating m auv direction in a stratified atfinosphnere can be properly described with a 2-D cylindrical geometry. (GI.Z).," The evolution of a heat perturbation propagating in any direction in a stratified atmosphere can be properly described with a 2-D cylindrical geometry $R, Z$ )."
. This description is adequate for our purposes of deriving the elobal properties of the plasina evolution aud X-ray emission as it would be detected at stellar distances., This description is adequate for our purposes of deriving the global properties of the plasma evolution and X-ray emission as it would be detected at stellar distances.
" The solar template of confined coronal flares has euided us iu configuring the initial uuperturbed atmosphere and in tuning the plana aud heating parameters,", The solar template of confined coronal flares has guided us in configuring the initial unperturbed atmosphere and in tuning the plasma and heating parameters.
 As shown in Fig. l..," As shown in Fig. \ref{fig:model},"
 the initia atinospliere consists of a stratified plane-parallel coroua exteudiusg vertically from. he stella surface., the initial atmosphere consists of a stratified plane-parallel corona extending vertically from the stellar surface.
 The nuit of our οςuputational clomain isjs at 10015 ocn from the stellar surface., The limit of our computational domain is at $10^{11}$ cm from the stellar surface.
 The corolla Is naintained steady at coronal οςvditions bv a wuitormly distribute heating., The corona is maintained steady at coronal conditions by a uniformly distributed heating.
 As our reference starting conditions we rave taken an atinosp1ος withi a pressure at the vase of the corona of 0.1 dvne 27. typical of coronal quiet regious. which may reasonably approxiuate non-confined coronal conditions.," As our reference starting conditions we have taken an atmosphere with a pressure at the base of the corona of 0.1 dyne $^{-2}$, typical of coronal quiet regions, which may reasonably approximate non-confined coronal conditions."
 Iu these conditions the temperature of the upper lavers of the nou-flaring corona of our computational domain is below 3 ADI., In these conditions the temperature of the upper layers of the non-flaring corona of our computational domain is below 3 MK.
" We have nude some simulations also with a hase pressure ↽1 due 2ον a οσο and hotter (x6 ME) initial atmosphere. to check the effec of changiug the initial conditious to rather extreme cases of very active ""non-confued coronae."," We have made some simulations also with a base pressure 1 dyne $^{-2}$, a denser and hotter $\le 6$ MK) initial atmosphere, to check the effect of changing the initial conditions to rather extreme cases of very active ""non-confined"" coronae."
 The bottom of the corona is matched to a much cooler chromosphere through a steep transition region., The bottom of the corona is matched to a much cooler chromosphere through a steep transition region.
 All this setting is similar to that for modclng confined coronal flares (c.g. Peres ct al., All this setting is similar to that for modeling confined coronal flares (e.g. Peres et al.
 1982. Cheng et al.," 1982, Cheng et al."
 1983. AleClvimout Canfield 1983).," 1983, McClymont Canfield 1983)."
 The chromosphere is required as nass reservoir for the flare evolution: our choice has been to consider an isothermal (2«104 K) and nowradiating chromosphere (Cheng et al., The chromosphere is required as mass reservoir for the flare evolution; our choice has been to consider an isothermal $2 \times 10^4$ K) and non-radiating chromosphere (Cheng et al.
 1983)., 1983).
 While the detailed structure of the chromosphere is dmportaut for the fue details of the evaporation aud coronal evolution. a coarse chromospheric model like the oue used here suffices to show the general characteristics ofthe evolution addressed here.," While the detailed structure of the chromosphere is important for the fine details of the evaporation and coronal evolution, a coarse chromospheric model like the one used here suffices to show the general characteristics of the evolution addressed here."
 We have verified that the unperturbed atinosphere is steady and stable for tines much lounger than the flare evolution times considered for this study., We have verified that the unperturbed atmosphere is steady and stable for times much longer than the flare evolution times considered for this study.
" The plasma evolution is described by solving the 2-D plasina bydrodvuamic equatious of conservation of lass, MolMentiun aud cherev with the ecometry described above: where s particle density per uuit volume. f time. v the plasina bulk velocity. p pressure. n average lass per particle. (650=qo2.11027! ο for solar abundance). g eravity acceleration. 1} radiative losses por unit chussion neasure. H heating per unit volume (uuiform and coustant in transition region). £ is the iuternal energy"," The plasma evolution is described by solving the 2-D plasma hydrodynamic equations of conservation of mass, momentum and energy with the geometry described above: where $n$ particle density per unit volume, $t$ time, $\vvec$ the plasma bulk velocity, $p$ pressure, $m$ average mass per particle $m =
2.1 ~ 10^{-24}$ g for solar abundance), $\gvec$ gravity acceleration, $P(T)$ radiative losses per unit emission measure, ${\cal H}$ heating per unit volume (uniform and constant in transition region), $\cal E$ is the internal energy"
After excluding all possible alternative scenarios we conclude that 222018— 1916 is (he first single sdD star which is rapidly rotating.,After excluding all possible alternative scenarios we conclude that $-$ 1916 is the first single sdB star which is rapidly rotating.
 Furthermore. the logg of 222018—1916 is (he lowest one ever measured for an sdD (see Figure 3)).," Furthermore, the $\log{g}$ of $-$ 1916 is the lowest one ever measured for an sdB (see Figure \ref{tefflogg}) )."
 arenec that the low gravity of the pulsating sdD J20163-+0928 (logg=5.15) mav be due to a rather thick laver of hvdrogen., argued that the low gravity of the pulsating sdB J20163+0928 $\log{g}=5.15$ ) may be due to a rather thick layer of hydrogen.
 In the model of even the merger remnants with the highest masses would need a hvdrogen laver of ~0.01AL. to reach at such low surface eravilies.," In the model of even the merger remnants with the highest masses would need a hydrogen layer of $\simeq0.01\,M_{\rm \odot}$ to reach at such low surface gravities."
 The formation of such an object through single star evolution is very hard to explain., The formation of such an object through single star evolution is very hard to explain.
 222018—1916 thus might have been formed by. a merger event., $-$ 1916 thus might have been formed by a merger event.
 Three merger scenarios wave been proposed to explain the origin of hot subdwarls., Three merger scenarios have been proposed to explain the origin of hot subdwarfs.
 and proposed the merger of two IHe-WDs as possible formation channel. which iis been further explored by(2002).," and proposed the merger of two He-WDs as possible formation channel, which has been further explored by."
. included (his channel in their binary evolution calculations and were able to model both the UV-excess in elliptical galaxies and the IM close binary. fractions of sdDs in populations of different age in a consistent wav2008)., included this channel in their binary evolution calculations and were able to model both the UV-excess in elliptical galaxies and the different close binary fractions of sdBs in populations of different age in a consistent way.
". He-WD mergers are believed {ο wave very small envelope masses and are expected to , situated at the verv blue end of the ENB.", He-WD mergers are believed to have very small envelope masses and are expected to be situated at the very blue end of the EHB.
 Bothis at variance with the position of 222013—1916 in the (Zar—logq)-diagram see Figure 3))., Both is at variance with the position of $-$ 1916 in the $T_{\rm eff}-\log{g}$ )-diagram (see Figure \ref{tefflogg}) ).
 proposed that the merger of a close binary system consisting of au sdD and a IHe-WD max form a single helium enriched sdO. 222013— 1916. jowever. is helium-cleficient.," proposed that the merger of a close binary system consisting of an sdB and a He-WD may form a single helium enriched sdO. $-$ 1916, however, is helium-deficient."
 222018—1916 most likely belongs to an old stellar population. either thick disk or 1alo.," $-$ 1916 most likely belongs to an old stellar population, either thick disk or halo."
 Its position in the (Z&r-log g)-diagram (see Figure 3)) may indicate a mass higher (han canonical. which would be consistent with the predictions bv2003).," Its position in the $T_{\rm eff}$ $\log{g}$ )-diagram (see Figure \ref{tefflogg}) ) may indicate a mass higher than canonical, which would be consistent with the predictions by."
.. IE il should be the remnant of a He-WD merger. this would imply important constraints on the merger process itself.," If it should be the remnant of a He-WD merger, this would imply important constraints on the merger process itself."
 Since the helium abundance of 222018— 1916 is ten (mes below the solar value. enough hydrogen must have survived the merger and must have been enriched in the atmosphere by diffusion processes.," Since the helium abundance of $-$ 1916 is ten times below the solar value, enough hydrogen must have survived the merger and must have been enriched in the atmosphere by diffusion processes."
 The third channel was suggested bv and further explored by2007)., The third channel was suggested by and further explored by.
. followed (his idea ancl focused on the formation of hot subclwarls., followed this idea and focused on the formation of hot subdwarfs.
 The merger of a red-giant. core and a low-mass. main-sequence star or substellar object during a common envelope phase max lead to the formation of a rapidly rotating hot subclwarl star.," The merger of a red-giant core and a low-mass, main-sequence star or substellar object during a common envelope phase may lead to the formation of a rapidly rotating hot subdwarf star."
 This scenario fits particularly well with observations for several reasols., This scenario fits particularly well with observations for several reasons.
 First. the helium core of a red giant merges with an unevolved low-mass star or a," First, the helium core of a red giant merges with an unevolved low-mass star or a"
1915|105.,1915+105.
 The first four of these are preseuted im Fie., The first four of these are presented in Fig.
 2. revealing the clear expansion of the source on daily timescales.," 2, revealing the clear expansion of the source on daily timescales."
 The jet sideduess is consistent with that reported im MB91. aud we are able to track the proper motions of three approaching aud oue receding components over the eutire set of images.," The jet sidedness is consistent with that reported in MR94, and we are able to track the proper motions of three approaching and one receding components over the entire set of images."
 The position angle of the ejections. approximately 115 deerees. is also very simular to that reported iu MBO9I.," The position angle of the ejections, approximately 145 degrees, is also very similar to that reported in MR94."
 All ejections are consistent with ballistic motions to better than104.. alcLowe find best-fits to the proper notions of: aud mas. di.," All ejections are consistent with ballistic motions to better than, and we find best-fits to the proper motions of: and mas. $^{-1}$,"
 deuifieanlv ereater than those reporte oe1i MROL, significantly greater than those reported in MR94.
 All fits are οood. with -<1.," All fits are good, with $\chi^2_{\rm red} \leq 1$."
 The proper motion of 17.640. Linas., The proper motion of $17.6 \pm 0.4$ mas.
 d.1 repored by MB91 for the approaching component can be ruled out for this ejection: fixing the proper nioion to this valuc loes not eive an acceptable fit to the data., $^{-1}$ reported by MR94 for the approaching component can be ruled out for this ejection; fixing the proper motion to this value does not give an acceptable fit to the data.
 luitial analysis of the proper motions. 1uder the standard assunnption of an iutrimsicallv svuuuetric ejection. suggests that we are measurjue sienificautly ereater velocities (bv >10543) than MR9L at a shuuilar angle to the line of sight (1108 likolv in the range GO — 70 degrees).," Initial analysis of the proper motions, under the standard assumption of an intrinsically symmetric ejection, suggests that we are measuring significantly greater velocities (by $\geq 10$ ) than MR94, at a similar angle to the line of sight (most likely in the range 60 – 70 degrees)."
 Again assundug a svuuuetric ejectioLh. we can use the xoper motions to placc lits on the distance to GRS 1915|105.," Again assuming a symmetric ejection, we can use the proper motions to place limits on the distance to GRS 1915+105."
 At the most extreme. eiven the measurement mucertaintics. the distance iust be <13.6 kpe.," At the most extreme, given the measurement uncertainties, the distance must be $\leq 13.6$ kpc."
 A more likev upper limüt is <11.2 kpc. ic. siguificautlv closer (although within their estimated errors) than the best estimate of 12.5 kpe used by ΔΠΘ.," A more likely upper limit is $\leq 11.2$ kpc, i.e. significantly closer (although within their estimated errors) than the best estimate of 12.5 kpc used by MR94."
 We lave preseuted preliminary results from a major set of MERLIN observatious of CBS 1915|105 sinultaueous with multiwvaveleugth radio aud X-rav monitoring., We have presented preliminary results from a major set of MERLIN observations of GRS 1915+105 simultaneous with multiwavelength radio and X-ray monitoring.
 While the nature of the plateau state itself remains unclear. it is now cert.un hat the radio flaring associated witi the eud of the state associated with relativistic ejections.," While the nature of the plateau state itself remains unclear, it is now certain that the radio flaring associated with the end of the state associated with relativistic ejections."
 These ejections. in particular the appr‘coaching componcut. have siguificautv ligher proper motions tha1i those recorded by MB91. most sniv interpreted as higher intrinsic veocitics at a similar anele tothe line of sight.," These ejections, in particular the approaching component, have significantly higher proper motions than those recorded by MR94, most simply interpreted as higher intrinsic velocities at a similar angle to the line of sight."
 We also find that GRS 1915|105 is likely to be siguificautly closer than the best extinate of 12.5 kpc of MB91., We also find that GRS 1915+105 is likely to be significantly closer than the best estimate of 12.5 kpc of MR94.
 Aore details of the observations. incluci1ο spatially resolved lincar polarisatio Linaps. aud their interpretation. will be found im a paper to be subnütted to AINRAS.," More details of the observations, including spatially resolved linear polarisation maps, and their interpretation, will be found in a paper to be submitted to MNRAS."
 We acknowledge ereat efforts bv many people. mostly at Jodrell Baws. which helped to make these observations a success.," We acknowledge great efforts by many people, mostly at Jodrell Bank, which helped to make these observations a success."
 Iu particular we would like to thank Peter Thomasson. Shane \chie and Richare Oeclev.," In particular we would like to thank Peter Thomasson, Shane McKie and Richard Ogley."
 MERLIN is operated by the University of Manchester at the Nuffield Radio Astronomy Laboratories. Jodrell Bauk. on behalfof the Particle Plivsics aud Astronomy Research Council.," MERLIN is operated by the University of Manchester at the Nuffield Radio Astronomy Laboratories, Jodrell Bank, on behalf of the Particle Physics and Astronomy Research Council."
 We acknowledge also the use of public data from NTE ASM and CBI., We acknowledge also the use of public data from XTE ASM and GBI.
 RPF acknowledges support from EC Marie Curie Fellowship ERDFMDICT 972136. aud DJAL frou EC TAIR-LESF coutract No.," RPF acknowledges support from EC Marie Curie Fellowship ERBFMBICT 972436, and DJM from EC TMR-LSF contract No."
 ERBFAIGECT 950012., ERBFMGECT 950012.
 Ly/Lp. vyxLy1.3.0 (~10' Ly/Lp Ly/Lp Ly/Lp) (—5 Ly/Lp ~5 ~0.3 , $L_X/L_B$ $L_X \propto L_B^{1.7-3.0}$ $\sim10^7$ $L_X/L_B$ $L_X/L_B$ $L_X/L_B$ $\sim$ $L_X/L_B$ $\sim$ $\sim$ 
in this plot is the overdcusity of stars uear the plane of the A\filky Way.,in this plot is the overdensity of stars near the plane of the Milky Way.
 In that region oue can notice relatively less populated areas due to dust lanes., In that region one can notice relatively less populated areas due to dust lanes.
 An cuipty spot near the Galactic Ceuter (field d) is an artifact., An empty spot near the Galactic Center (field ) is an artifact.
 The region is basically lost from the survey due to the very low nuuber of available frames., The region is basically lost from the survey due to the very low number of available frames.
 Each dot in Figure 2 represents a time series of typically a few hundred points spread over a total time bascline of 1 wear.," Each dot in Figure \ref{fig:sky}
 represents a time series of typically a few hundred points spread over a total time baseline of 1 year."
 Temporal coverage is subject to vearly visibility patterus., Temporal coverage is subject to yearly visibility patterns.
 The trade-off between this cuormous monitoring coverage on one side. and on the other. relatively low resolution couipounded x coniplexities of very wide field photometry. shaped the final data quality.," The trade-off between this enormous monitoring coverage on one side, and on the other, relatively low resolution compounded by complexities of very wide field photometry, shaped the final data quality."
 The faintest objects recorded in the survey have 1.5 mag. however the icompletcue..S starts increasing sharply at 15th maguitude.," The faintest objects recorded in the survey have $V\sim$ 15.5 mag, however the incompleteness starts increasing sharply at 15th magnitude."
 Saturation nay occur in stars as faint as 10.5 mae on some nights. mit mostly affects stars brighter than 10 mae.," Saturation may occur in stars as faint as 10.5 mag on some nights, but mostly affects stars brighter than 10 mag."
 Due to exposure times shortened by a factor of L duriug bright lie. sonie stars as bright as 8.0 mag still have a number ofunsaturated measurements sufficient for analysis.," Due to exposure times shortened by a factor of 4 during bright time, some stars as bright as 8.0 mag still have a number of unsaturated measurements sufficient for analysis."
 Figure 3 sununuarizes dportant statistics of the NSVS., Figure \ref{fig:stats} summarizes important statistics of the NSVS.
 NMuucrous survey parameters strongly correlate with the Galactic latitude aud declination., Numerous survey parameters strongly correlate with the Galactic latitude and declination.
 Several artifacts due to the low volume and quality of available data near the Galactic plane at low declinatious are visible., Several artifacts due to the low volume and quality of available data near the Galactic plane at low declinations are visible.
 The bright spot in the plots of ΠΙΟ of available frames is duc to a special data run in Ποια (schoe ct al., The bright spot in the plots of number of available frames is due to a special data run in field (Kehoe et al.
 2002)., 2002).
 The darker areas near the Galactic plane are a result of a lower success rate iu imnatcehing frames to the Tycho catalog., The darker areas near the Galactic plane are a result of a lower success rate in matching frames to the Tycho catalog.
" Strong differences ucar the celestial pole between panels ο) and d) are caused by exclusion of flagMOUNTFLIP iu the definition of a ""good nieasureieut.", Strong differences near the celestial pole between panels c) and d) are caused by exclusion of flag in the definition of a “good” measurement.
 Lower than average performance of camera is evident from aperiodic pattern in the map of photometric scatter (panel b)., Lower than average performance of camera is evident from a periodic pattern in the map of photometric scatter (panel b).
 The field pattern iu the προ of database frames reveals that calera was not collecting data for about 3 mouths. when it had to be serviced after an clectronics failure.," The field pattern in the number of database frames reveals that camera was not collecting data for about 3 months, when it had to be serviced after an electronics failure."
 Although the uunber of useful iieasureinents below the equator drops dramatically to fewer than 100. this is still sufficieut to detect variables aud the NSVS remains useful over a large section of the southern hemisphere.," Although the number of useful measurements below the equator drops dramatically to fewer than 100, this is still sufficient to detect variables and the NSVS remains useful over a large section of the southern hemisphere."
 Statistical scatter of object positions im individual frames can be better than 0.1 pixel (1.17) within a sinele field (lower part of Figure ))., Statistical scatter of object positions in individual frames can be better than 0.1 pixel $\arcsec$ ) within a single field (lower part of Figure \ref{fig:scatter}) ).
 Median positious from a laree number of measurements should be mach more accurate than that. however that ignores svsteniatic errors of the coordinate svstenà derived separately in each field.," Median positions from a large number of measurements should be much more accurate than that, however that ignores systematic errors of the coordinate system derived separately in each field."
 A better measure for overall positional accuracy is the difference of median positious Gu 2-D this time) for the same bright unsaturated stars observed in overlapping warts of adjacent fields., A better measure for overall positional accuracy is the difference of median positions (in 2-D this time) for the same bright unsaturated stars observed in overlapping parts of adjacent fields.
 Such differences should he dominated by asystematic contribution and are shown in Figure 7.., Such differences should be dominated by asystematic contribution and are shown in Figure \ref{fig:systematics}.
 The distribution of these offsets turus out to © conrparable to that from Figure and fits well within a single nuage pixel., The distribution of these offsets turns out to be comparable to that from Figure \ref{fig:scatter} and fits well within a single image pixel.
 Figure 7 also shows how typical »ositiou uncertainties are affected by the hieh density of stars in the vicinity of the Galactic plane., Figure \ref{fig:systematics} also shows how typical position uncertainties are affected by the high density of stars in the vicinity of the Galactic plane.
 The distribution )eaks at a higher value for the error aud develops a much longer tail due to strong bleudiug., The distribution peaks at a higher value for the error and develops a much longer tail due to strong blending.
 Figure — (upper pancl) preseuts magnitude scatter as a function of median object magnitude iu a random field away from the Galactic equator., Figure \ref{fig:scatter} (upper panel) presents magnitude scatter as a function of median object magnitude in a random field away from the Galactic equator.
" Plotometric scatter is estimated using ""eood' photometric points (Section 3.2.3)) corresponding to about of the best data.", Photometric scatter is estimated using “good” photometric points (Section \ref{sec:compilation}) ) corresponding to about of the best data.
 We consider magnitude scatter for a median star between 11 and 12 mag in each field to be the “lamiting scatter. that is the best attaimable for a significant fraction of bright stars in a eiven field.," We consider magnitude scatter for a median star between 11 and 12 mag in each field to be the “limiting scatter”, that is the best attainable for a significant fraction of bright stars in a given field."
 Observatious in this magnuitude range are lanited bv various systematics of photometric coucditious aud data reductions rather than the statistics of the backeround., Observations in this magnitude range are limited by various systematics of photometric conditions and data reductions rather than the statistics of the background.
 There is a strong correlation between limiting scatter and Calactic latitude which is evident in Figure &.., There is a strong correlation between limiting scatter and Galactic latitude which is evident in Figure \ref{fig:galb}.
 The median lnitiug scatter over the total πιάνο area is 0.02 mae., The median limiting scatter over the total survey area is 0.02 mag.
 Towever the Galactic plane region. where photometric accuracy suffers sienificant degradation. has a higher number density of objects.," However the Galactic plane region, where photometric accuracy suffers significant degradation, has a higher number density of objects."
 Averaged over aa 87«8? field. spatial deusity of he NSVS objects can vary between 150 and 1000 7.," Averaged over an $8\arcdeg\times8\arcdeg$ field, spatial density of the NSVS objects can vary between 150 and 1000 $^{-2}$."
 Similar to astrometry. svstematies of photometry can be investigated by examining the offsets between magnitudes ucasured for stars in overlapping parts of adjacent fields.," Similar to astrometry, systematics of photometry can be investigated by examining the offsets between magnitudes measured for stars in overlapping parts of adjacent fields."
 Ilstogranus of these differences for two random overlap regions at low aud high Galactic latitudes are dominated w constant stars. and are shown in Figure 7..," Histograms of these differences for two random overlap regions at low and high Galactic latitudes are dominated by constant stars, and are shown in Figure \ref{fig:systematics}."
 Πα of he stars in the fleure differ by 0.01 mae or less iu their uedian magnitude obtained from light curves constructed independenutle i neighbormg fields., Half of the stars in the figure differ by 0.04 mag or less in their median magnitude obtained from light curves constructed independently in neighboring fields.
 In individual cases. rowever. such differences can reach 0.10.2 mag.," In individual cases, however, such differences can reach 0.1–0.2 mag."
 Thev result primarily from residual shutter problems that xopaesated to the construction. of feld templates. but also from ireducible atinospherie color effects in sinele xoad baud photometry.," They result primarily from residual shutter problems that propagated to the construction of field templates, but also from irreducible atmospheric color effects in single broad band photometry."
 The fact that the histogram width does not change iu a siguificant wav iu the proximity of the Calactic equator agrees with our assessinent that he differences arise due to systematics assoclated with a particular set of field images aud uot because of high jiuuber density of stars or bleudiug., The fact that the histogram width does not change in a significant way in the proximity of the Galactic equator agrees with our assessment that the differences arise due to systematics associated with a particular set of field images and not because of high number density of stars or blending.
 Ht must be stressed hat the overlap regious between the fellis provide the upper bound on the systematic errors., It must be stressed that the overlap regions between the fields provide the upper bound on the systematic errors.
 This is where nanny instrumental effects (Section 2)) manifest themselves stronecst., This is where many instrumental effects (Section \ref{sec:instruments}) ) manifest themselves strongest.
 The internal consisteucv over the remaining area is certainly iiuchli better. although not casily studied without a suitable external comparison catalog.," The internal consistency over the remaining area is certainly much better, although not easily studied without a suitable external comparison catalog."
 All photometric time series data in the NSVS is available or public access., All photometric time series data in the NSVS is available for public access.
 The primary mcans to search aud extract he data is Sky Database for Objects in Time-Domain5., The primary means to search and extract the data is Sky Database for Objects in Time-Domain.
. The colunus are explained in Tables 6 and 7.., The columns are explained in Tables \ref{tab:columns1} and \ref{tab:columns2}. .
 Five of those ables represeut major eutities m temporal work: F," Five of those tables represent major entities in temporal work: ,"
 Five of those ables represeut major eutities m temporal work: Fi," Five of those tables represent major entities in temporal work: ,"
 Five of those ables represeut major eutities m temporal work: Fie," Five of those tables represent major entities in temporal work: ,"
 Five of those ables represeut major eutities m temporal work: Fiel," Five of those tables represent major entities in temporal work: ,"
 Five of those ables represeut major eutities m temporal work: Field," Five of those tables represent major entities in temporal work: ,"
 Five of those ables represeut major eutities m temporal work: Field.," Five of those tables represent major entities in temporal work: ,"
"SMC-type extinction to the SED (dashed lines in Figure 10)), assuming Ay=0.3, which is the average determined extinction value in the V band (Schadyetal.2010;Greiner2011).","SMC-type extinction to the SED (dashed lines in Figure \ref{fig10}) ), assuming $A_{\rm V} = 0.3$, which is the average determined extinction value in the $V$ band \citep{schady, greiner}."
". The extinction in the host-galaxy rest frame has been calculated for an average observed GRB redshift z=2.2 and for redshift z=0.7, which is the average redshift of detected OAs in our simulation."," The extinction in the host-galaxy rest frame has been calculated for an average observed GRB redshift $z = 2.2$ and for redshift $z = 0.7$, which is the average redshift of detected OAs in our simulation."
 There is also a contribution to extinction by our Galaxy., There is also a contribution to extinction by our Galaxy.
" We left the contribution of Galactic extinction to vary between 0€ΑναX0.3 and, using Cardellietal.(1989),, added Galactic contribution to the SED."," We left the contribution of Galactic extinction to vary between $0 \leq A_{\rm V,GA} \leq 0.3$ and, using \citet{cardelli}, added Galactic contribution to the SED."
" In Figure 10,, shaded areas mark the possible range of SED curves depending on the Ayqa value."," In Figure \ref{fig10}, shaded areas mark the possible range of SED curves depending on the $A_{\rm V,GA}$ value."
 Vertical lines correspond to the central wavelengths of the Gaia photometric instrument’s three wide passbands (Jordietal.2010).., Vertical lines correspond to the central wavelengths of the $\textit{Gaia}$ photometric instrument's three wide passbands \citep{jordi}.
" Since Gaia photometry will be obtained by means of two low-resolution spectra (so-called red photometer (RP) and blue photometer (BP) spectra with central frequencies shown in Figure 10 as Grp and Gpp vertical lines), these spectra could provide us with enough information to determine the SED shape."," Since $\textit{Gaia}$ photometry will be obtained by means of two low-resolution spectra (so-called red photometer (RP) and blue photometer (BP) spectra with central frequencies shown in Figure \ref{fig10} as $G_{\rm RP}$ and $G_{\rm BP}$ vertical lines), these spectra could provide us with enough information to determine the SED shape."
" In the case of bright sources, integrated flux from the radial velocity instrument (Gmys) can also be"," In the case of bright sources, integrated flux from the radial velocity instrument $G_{\rm RVS}$ ) can also be"
Usiug our indicatrices. one cau see in Fie.,"Using our indicatrices, one can see in Fig."
 3. that the north-south geodesic is straight. but that the east-west geodesi€ 1s bent downward.," \ref{fg:us_mercator} that the north-south geodesic is straight, but that the east-west geodesic is bent downward."
 This shows dramatically the flexion in this region of t Mercaor map., This shows dramatically the flexion in this region of the Mercator map.
 One cau even read o[the average value of the flexion by παπα., One can even read off the average value of the flexion by hand.
 Take a protract and measttre the tarcent to the east-west geodesic at the two ends of the cross bar., Take a protractor and measure the tangent to the east-west geodesic at the two ends of the cross bar.
 Measure t cifTereice in the anele orientation o‘the two., Measure the difference in the angle orientation of the two.
 That gives the integrated flexiou aloug 21° of t elobe., That gives the integrated flexion along $24^\circ$ of the globe.
 Divide the doaigle difference by 21° aud you will have the average value of the flexion alo that cve., Divide that angle difference by $24^\circ$ and you will have the average value of the flexion along that curve.
 The skewuess ls also visible in lal the center o“the cross is below the center of the circ 10wll& the lopsidehess to the nor1.," The skewness is also visible in that the center of the cross is below the center of the circle, showing the lopsidedness to the north."
 In fact. oue can observe the sτονμον iu any direcion [rom le center wv seelug how far olf center the center of he cross is wit1 respec to the center of the ‘ircle in clifferent di‘ectious.," In fact, one can observe the skewness in any direction from the center by seeing how far off center the center of the cross is with respect to the center of the circle in different directions."
 For coparison. we have in Figure L shown tle continental United tates in a obliqi ehercator projection where the east-wesl geodesic hrougl 1e geograpuc center “the contilienta Luuitecl States is 1ow the equator o‘the Mercator »rojectio=," For comparison, we have in Figure \ref{fg:us_oblique_mercator} shown the continental United States in a oblique Mercator projection where the east-west geodesic through the geographic center of the continental United States is now the equator of the Mercator projection."
 The flexiou aid skewness aong he equaor ofa Νlercator map a'e judeec Zero. so the arms of the cross aὁ now stralelit. aud the circle is now nealv a perlect circle centeος on the center of the cross.," The flexion and skewness along the equator of a Mercator map are indeed zero, so the arms of the cross are now straight, and the circle is now nearly a perfect circle centered on the center of the cross."
" This gives a ""straight on” view of the coninental Uuitecd States. lal more accurately portrays its appearauce on the elobe."," This gives a ""straight on"" view of the continental United States, that more accurately portrays its appearance on the globe."
 One can place the Coldbere-Gott iudicarices eveΝ 607 in longitude aud every 30° iu atitucle on the globe to siow how the fexion aud skewness vary over the map., One can place the Goldberg-Gott indicatrices every $60^\circ$ in longitude and every $30^\circ$ in latitude on the globe to show how the flexion and skewness vary over the map.
 In Figs. 5-- 27..," In Figs. \ref{fg:indmap_first}- - \ref{fg:indmap_last},"
 we provide G-G indicatrix iuaps fo: a tuber of well-known ojectlolis., we provide G-G indicatrix maps for a number of well-known projections.
 Iu Lact. the Coldel'g-Gott almost iudicatrices Cal ijtst replace the Tissot indicatrices yeECaAUSeE the shape aud size of the oval in the Coldbere-Got itclic‘alvin is approximately the size aud shape ol the Tissot ellipse.," In fact, the Goldberg-Gott almost indicatrices can just replace the Tissot indicatrices because the shape and size of the oval in the Goldberg-Gott indicatrix is approximately the size and shape of the Tissot ellipse."
 Tie Tissot ellipse shows the [1iagnilied shape aud size of an infinitesiimal circle on the globe. tje oval in the Coldbere-CGott indIcaLx shows the shape απ size of a finite circle (radius 12°) οι iue ια itself at correct scae.," The Tissot ellipse shows the [magnified] shape and size of an infinitesimal circle on the globe, the oval in the Goldberg-Gott indicatrix $\oplus$ shows the shape and size of a finite circle (radius $12^\circ$ ) on the map itself at correct scale."
 Thi>. i tle ap is equal area. the indicatrices. wi lall have equal area ou the 1jap.," Thus, if the map is equal area, the Goldberg-Gott indicatrices, will all have equal area on the map."
 If the ujap is conformal the Coldbere-Cott iudicatrices will all be 1early perfectly circular., If the map is conformal the Goldberg-Gott indicatrices will all be nearly perfectly circular.
" If there 1 a ""| anisotropy in the Tissot ellipses in a given reglon the Coldbere-Gott inclicatrices ovals will lave tlat same 2:1 axis ratio.", If there is a 2:1 anisotropy in the Tissot ellipses in a given region the Goldberg-Gott indicatrices ovals will have that same 2:1 axis ratio.
 Thus far. we have defined the geueral properties of skewness aud flexion. given a few analytic results for particular map projections. aud given a eraplic approach for describiug aud interpreting flexiou auc skewuess ou maps.," Thus far, we have defined the general properties of skewness and flexion, given a few analytic results for particular map projections, and given a graphic approach for describing and interpreting flexion and skewness on maps."
 Iu this sectiou. we approach the matter somewhat differently. and. produce eeneral analytic results for all projectious as well as a prescription for measuring tlie [lexion aud skewness analytically.," In this section, we approach the matter somewhat differently, and produce general analytic results for all projections as well as a prescription for measuring the flexion and skewness analytically."
 Let's consider a spherical globe with coordinates: Note that here and throughout. we will use a to refer to coordinates in the globe frame. aud απ το refer to coordinates iu tlie map frame.," Let's consider a spherical globe with coordinates: Note that here and throughout, we will use $x^{\ol{a}}$ to refer to coordinates in the globe frame, and $x^a$ to refer to coordinates in the map frame."
 On the globe. the metric is:," On the globe, the metric is:"
For the forward shock. we obtain Therefore. the resulting svachrotron photons emitted by the two shocks are expected to peak at two dilferent energy bands and thus two clistinet spectral. nents’...Phe peak of reverse shock spectrum will be at hard A-ray. but peak of the forward shock will be at FER.,"For the forward shock, we obtain Therefore, the resulting synchrotron photons emitted by the two shocks are expected to peak at two different energy bands and thus two distinct spectral .The peak of reverse shock spectrum will be at hard X-ray, but peak of the forward shock will be at FIR."
 The synchrotron self-absorption must be taken into account., The synchrotron self-absorption must be taken into account.
 In Mua<Maoveg Case. the syncehrotron. self-absorption frequeney in region 2 reads (Panaitescu Ixumar 2000) ln £a<MeacFuss Case. the svnchrotron. self-absorption frequency in region 3 can be calculated. by (Panaitescu Ixumar 2000) The maximum Lorentz factor is limited. by the svnchrotron losses and is given by (Cheng Wei 1996) Another mechanism to restrict the maximum energy of an electron is cilfusion.," In $\nu_{m,2}<\nu_{a,2}<\nu_{c,2}$ case, the synchrotron self-absorption frequency in region 2 reads (Panaitescu Kumar 2000) In $\nu_{a,3}<\nu_{c,3}<\nu_{m,3}$ case, the synchrotron self-absorption frequency in region 3 can be calculated by (Panaitescu Kumar 2000) The maximum Lorentz factor is limited by the synchrotron losses and is given by (Cheng Wei 1996) Another mechanism to restrict the maximum energy of an electron is diffusion."
 Ht turns out that maximum Lorentz factor restricted by dilfusion is much Larger than that in equation (10))., It turns out that maximum Lorentz factor restricted by diffusion is much larger than that in equation \ref{gammaM}) ).
 S0 The maximal svnehrotron photon energy can beestimated (Fan Piran 2008) where fis the Planck constant. E equals to σοι or 534.," So The maximal synchrotron photon energy can beestimated (Fan Piran 2008) where $h$ is the Planck constant, $\Gamma$ equals to $\gamma_{21}$ or $\gamma_{34}$."
 The spectrum. of internal shock model is shown in ligure 2. using above parameters during a high state., The spectrum of internal shock model is shown in Figure \ref{spectrum} using above parameters during a high state.
 The X-ray spectrum of Swift J1644157 can be generated in our model., The X-ray spectrum of Swift J1644+57 can be generated in our model.
 A moderate extinction. (ely—3 5) is required to explain the spectrum., A moderate extinction $A_V\sim 3-5$ ) is required to explain the spectrum.
 This value of extinction is reasonable in this case. because of this event is arising in the nucleus of host galaxy.," This value of extinction is reasonable in this case, because of this event is arising in the nucleus of host galaxy."
 This value is also consistent with that determined by Bloom ct al. (, This value is also consistent with that determined by Bloom et al. (
2011) and Burrows et al. (,2011) and Burrows et al. (
2011).,2011).
 Because of large value of svnchrotron self-absorption frequeney. the radio emission of internal shock is suppressed.," Because of large value of synchrotron self-absorption frequency, the radio emission of internal shock is suppressed."
 From observations. the radio emission is from Lager radius comparing with X-ray emission (Bloom et al.," From observations, the radio emission is from larger radius comparing with X-ray emission (Bloom et al."
 2011: Burrows et al., 2011; Burrows et al.
 2011)., 2011).
 The interaction between the first shell ejected bv central engine and the ISM results in an external shock., The interaction between the first shell ejected by central engine and the ISM results in an external shock.
 The radio emission is from large racius and can be moceled by this external shock. similar as CRB afterglow.," The radio emission is from large radius and can be modeled by this external shock, similar as GRB afterglow."
" The total energy. release. during this initial period. is about i,~10 ere (Bloom et al."," The total energy release during this initial period is about $E_{\rm
iso}\sim 10^{53}$ erg (Bloom et al."
 2011)., 2011).
 The ISM density is about n10cm. 7., The ISM density is about $n\sim 10$ $^{-3}$.
 Following Sari et al. (, Following Sari et al. (
1998) and Bloom et al. (,1998) and Bloom et al. (
2011). we obtain the svnchrotron frequencies and peak Hux of external shock as follow The expression of £s is a little dillerent from that of Sarl et al. (,"2011), we obtain the synchrotron frequencies and peak flux of external shock as follow The expression of $F_{\nu,\max}$ is a little different from that of Sari et al. ("
1998). because the observer has already observed the edges of the jet. as discussed in Bloom et al. (,"1998), because the observer has already observed the edges of the jet, as discussed in Bloom et al. ("
2011).,2011).
 The spectrum of the external shock is shown as dashed line in figure 2.. which can only produce a simple power law in X-ray region.," The spectrum of the external shock is shown as dashed line in figure \ref{spectrum}, which can only produce a simple power law in X-ray region."
 The radio light curve is different from /aes. behavior observed the late N-rav light. curve (Ciannios Metzger 2011: Metzger et al., The radio light curve is different from $t^{-5/3}$ behavior observed the late X-ray light curve (Giannios Metzger 2011; Metzger et al.
 2011) because the racio light curve should be determined by the evolution of the external shock and has nothing to do with the accretion rate in the clisk., 2011) because the radio light curve should be determined by the evolution of the external shock and has nothing to do with the accretion rate in the disk.
 So our model predicates that. during the high state (Llaring). the emission of internal shock will dominate at X-rav band and a broken power-law spectrum is shown.," So our model predicates that, during the high state (flaring), the emission of internal shock will dominate at X-ray band and a broken power-law spectrum is shown."
 During the low state (no ares). there is no internal shocks and the emission is from the external shock.," During the low state (no flares), there is no internal shocks and the emission is from the external shock."
 Because the tvpical frequencies of external shock is low at the first few clays (see equation. (12))). the spectrum at X-ray band. exhibits as a single power-law if no energy injection happens.," Because the typical frequencies of external shock is low at the first few days (see equation \ref{exter}) )), the spectrum at X-ray band exhibits as a single power-law if no energy injection happens."
 In both states. the radio emission is from the external shock.," In both states, the radio emission is from the external shock."
 In Figure 3.. we fit the spectrum cata from. Burrows et al. (," In Figure \ref{Burrows}, , we fit the spectrum data from Burrows et al. ("
2011) detected at the same period.,2011) detected at the same period.
 We adopt the, We adopt the
one model than another). then the quantity Pr(d|4/;) may be used in comparing the relative probailities of each mocel under consideration.,"one model than another), then the quantity $\pr(\datav|\model_j)$ may be used in comparing the relative probailities of each model under consideration."
 For more details on the use of this quantity. known as the “eviclenee” (seee.g.2?2).," For more details on the use of this quantity, known as the “evidence” \citep[see \eg][]{Jaynes,ST/Mac92}."
. Calculation of the evidence is in principle straightforward: marginalising out the N; parameters of the model gives Llowever. for the purposes of this work it is useful to note hat the evidence is sensitive both to the parameter prior and the likelihood.," Calculation of the evidence is in principle straightforward; marginalising out the $N_i$ parameters of the model gives However, for the purposes of this work it is useful to note that the evidence is sensitive both to the parameter prior and the likelihood."
 Models providing a better fit to the data. and so a higher value at the peak of the likelihood function. ive higher evidence associated with them.," Models providing a better fit to the data, and so a higher value at the peak of the likelihood function, have higher evidence associated with them."
 Conversely. nmiocdels whose priors define large volumes of low likelihood »wameter space will give. lower evidence values —- overly complex mocdoels are penalised.," Conversely, models whose priors define large volumes of low likelihood parameter space will give lower evidence values – overly complex models are penalised."
 We now turn to the practical problems associated with he caleulation of the posterior probability Pr(8|d.12; and he associated evidence. Pr(d[|//;).," We now turn to the practical problems associated with the calculation of the posterior probability $\pr(\parsv|\datav,\model_j)$ and the associated evidence $\pr(\datav|\model_j)$."
 One approach. )much used. in the field of cosmological parameter. estimation. is to calculate. the prior density and. likelihood on a discrete parameter eric.," One approach, much used in the field of cosmological parameter estimation, is to calculate the prior density and likelihood on a discrete parameter grid."
 However. as the models considered become more complex. this task becomes. exponentially more computationally intensive.," However, as the models considered become more complex, this task becomes exponentially more computationally intensive."
 As an illustration. if a likelihood cvaluation for a 19 parameter model takes just. 1 second. the time to produce a eric of posterior probability densities. ten. pixels in each dimension. is of order 104I seconds. or 300. νους.," As an illustration, if a likelihood evaluation for a 10 parameter model takes just 1 second, the time to produce a grid of posterior probability densities, ten pixels in each dimension, is of order $10^{10}$ seconds, or 300 years."
 Clearly4 this.. procedure is neither practical nor accurate., Clearly this procedure is neither practical nor accurate.
" Instead. we use an exploratory Markov-Clhain Monte-Carlo (AICAIC) algorithm ο draw. samples from the multidimensional. unnormalised xsterior. Pr(d|0.11,)Pr(0|H;). (2)..."," Instead, we use an exploratory Markov-Chain Monte-Carlo (MCMC) algorithm to draw samples from the multidimensional unnormalised posterior $\pr(\datav|\parsv,\model_j)\pr(\parsv|\model_j)$ \citep{MCMC}."
 The output of the AICMC. algorithm is a ist. of samples whose number density in parameter space is proportional to the posterior obabilitv density., The output of the MCMC algorithm is a list of samples whose number density in parameter space is proportional to the posterior probability density.
 This. allows a representation. of the desired. posterior to be constructed which is both ellicienthy calculated (computation time is twpically of the order of a ew hours) and convenient to use., This allows a representation of the desired posterior to be constructed which is both efficiently calculated (computation time is typically of the order of a few hours) and convenient to use.
 For example. the sample xvwameter values may be combined to calculate predictions or other properties of the mocol.," For example, the sample parameter values may be combined to calculate predictions for other properties of the model."
 Calculating the evidence by performing the integral of equation. (7)) numerically by ordinary means would of course involve a similar. number of operations as that outlined. above., Calculating the evidence by performing the integral of equation \ref{eq:evint}) ) numerically by ordinary means would of course involve a similar number of operations as that outlined above.
" We instead make use of the technique of ""thermodynamic integration"" to calculate the evidence cdnamically during an initial ""burn-in phase of the MCMC algorithm. (7)...", We instead make use of the technique of “thermodynamic integration” to calculate the evidence dynamically during an initial “burn-in” phase of the MCMC algorithm \citep{MCMC}.
" Ehis process results in evidence values precise to a fraction of a unit in log,Pr(d|//;).", This process results in evidence values precise to a fraction of a unit in $\log_e{\pr(\datav|\model_j)}$.
" This corresponds to a probability ratio between two mocdels of less than 3. well below the 7belief threshold"" of a sensible analyst."," This corresponds to a probability ratio between two models' of less than 3, well below the “belief threshold” of a sensible analyst."
 A major benefit of working with samples drawn from the posterior rather than a grid of posterior values is that the process of marginalisation becomes trivial., A major benefit of working with samples drawn from the posterior rather than a grid of posterior values is that the process of marginalisation becomes trivial.
 When estimating a single parameter 6; of a model £2; the distribution. of interest is where the integral is over all other parameters., When estimating a single parameter $\theta_i$ of a model $\model_j$ the distribution of interest is where the integral is over all other parameters.
 This projection takes into account all the parameter degeneracies of the model. as well as the priors on all of the parameters.," This projection takes into account all the parameter degeneracies of the model, as well as the priors on all of the parameters."
 An ensemble of sample O-vectors. drawn: [rom the ful posterior can be projected onto the 8; direction. just by extracting the 6; values from the ensemble., An ensemble of sample $\parsv$ -vectors drawn from the full posterior can be projected onto the $\param_i$ direction just by extracting the $\param_i$ values from the ensemble.
 Although computing n-point statistics [rom à se of samples is very easy. reconstructing the marginalisec posterior pdf is not so straightforward.," Although computing $n$ -point statistics from a set of samples is very easy, reconstructing the marginalised posterior pdf is not so straightforward."
 To do this we provide as estimators for these distributions histograms of sample values smoothed to some arbitrary length scale. such tha we err on the side of caution ancl never underestimate the distribution. widths.," To do this we provide as estimators for these distributions histograms of sample values smoothed to some arbitrary length scale, such that we err on the side of caution and never underestimate the distribution widths."
" This is in keeping with our general approach: the marginalised posterior probability distribution. Pr(6,]d) is in general broader than. those conditional on other parameters being fixed at. for instance. the maximum. likelihood. point."," This is in keeping with our general approach: the marginalised posterior probability distribution $\pr(\param_k|\datav)$ is in general broader than those conditional on other parameters being fixed at, for instance, the maximum likelihood point."
 The resulting estimators are therefore as accurate as possible. since the maximum amount of information has been included. and as precise as allowed. by the quality of the data. since the errors on the observed: quantities have been rigorously propagated in a self-consistent. way.," The resulting estimators are therefore as accurate as possible, since the maximum amount of information has been included, and as precise as allowed by the quality of the data, since the errors on the observed quantities have been rigorously propagated in a self-consistent way."
 By taking this process one step further we can answer question (ii). by marginalising over model space.," By taking this process one step further we can answer question (iii), by marginalising over model space."
 This procedure ijs important in the context of cluster data analysis: we want to be able to make robust. mocdel-independent statements about cosmological parameters [rom cluster. data.," This procedure is important in the context of cluster data analysis: we want to be able to make robust, model-independent statements about cosmological parameters from cluster data."
" To this end. and. clenoting the cosmological parameterες of interest 6,. one should calculate The last) proportionality is as such because we have discarded. the normalising constant of equation (6))."," To this end, and denoting the cosmological parameter of interest $\param_k$ , one should calculate The last proportionality is as such because we have discarded the normalising constant of equation \ref{eq:bayes2}) )."
 Equation (10)) is now a relationship between quantities that we can calculate. and represents à model-averaging process.," Equation \ref{eq:marg_models2}) ) is now a relationship between quantities that we can calculate, and represents a model-averaging process."
 We might hope that one particular model would be many ines more probable given the data. in which case we have earnt something about the astrophysies of the cluster and he sum will be dominated by this model.," We might hope that one particular model would be many times more probable given the data, in which case we have learnt something about the astrophysics of the cluster and the sum will be dominated by this model."
 On the other hand. it is always possible to construct à range of models whose xwameter priors all match the data's likelihood equally well. and so give similar evidences.," On the other hand, it is always possible to construct a range of models whose parameter priors all match the data's likelihood equally well, and so give similar evidences."
" In this case the averaging »pocess serves CO increase the width of the posterior density of interest. that of the interesting parameter 6, given the data only. by an amount appropriate to the uncertainty over he range of models."," In this case the averaging process serves to increase the width of the posterior density of interest, that of the interesting parameter $\param_k$ given the data only, by an amount appropriate to the uncertainty over the range of models."
 In this wav. (quasi)-mocel independent statements can be made about cosmological parameters. such as the cluster gas fraction. from the cluster data.," In this way, (quasi)-model independent statements can be made about cosmological parameters, such as the cluster gas fraction, from the cluster data."
 In this section we give a brief introduction. to. weak lensing and interferometric Sunvaev-Zel'dovich. clleet data. demonstrating the construction of thelikelihood function in cach case.," In this section we give a brief introduction to weak lensing and interferometric Sunyaev-Zel'dovich effect data, demonstrating the construction of thelikelihood function in each case."
and halo kinematies (such as. e.g.. Carollo et al. 2010),"and halo kinematics (such as, e.g., Carollo et al. )"
) will be important ways to explore this question of inner/outer halo origins further: all of them expand the effective search space. either by surveying to larger distances or by focusing on stars with large apogalactic distances.," will be important ways to explore this question of inner/outer halo origins further: all of them expand the effective search space, either by surveying to larger distances or by focusing on stars with large apogalactic distances."
 The homogeneity of metallicity in present-day globular clusters seems to favor massive models of globular cluster formation. while the observed range in oxygen and sodium abundances (see. e.g.. Carretta et al. 2009)," The homogeneity of metallicity in present-day globular clusters seems to favor massive models of globular cluster formation, while the observed range in oxygen and sodium abundances (see, e.g., Carretta et al. )"
) indicates that dilution of feedback material and incomplete mixit¢ of the gas that makes up the second stellar generation play a central role in setting final light-element abundances for incividual stars., indicates that dilution of feedback material and incomplete mixing of the gas that makes up the second stellar generation play a central role in setting final light-element abundances for individual stars.
 In order to evaluate the veracity of various globular cluster formation models. it is necessary to explore their implications for the formation of the Galactic stellar halo.," In order to evaluate the veracity of various globular cluster formation models, it is necessary to explore their implications for the formation of the Galactic stellar halo."
 Massive models. which require a large fraction of first-generation stars to be lost to the halo field at early times. will produce a large enhancement between 5e and fi.," Massive models, which require a large fraction of first-generation stars to be lost to the halo field at early times, will produce a large enhancement between $f_{h}^{2G}$ and $f_{h}^{GC}$."
 The recent paper of considers this question from ⋅≏↧↾∣↴⊜⋯⋪⊖⊓∁∐∣⋋↾⋅≏⋯∐∣⊃⋂⋯↾⋅∐⋋∩∶↔⊺⋔⊜⊱↾∣∪⇂⋯∣⋯⋪∁∣∐⋋↾⊜∣⋪⋋⊖∦↴− enrichment model of to calculate the mass in first-generation stars needed to produce a significant second generation.," The recent paper of considers this question from a theoretical standpoint, using the globular cluster self-enrichment model of to calculate the mass in first-generation stars needed to produce a significant second generation."
 In the model. rapidly rotating massive stars provide chemical feedback between the first and second generations. and explore the effects of varying the slope of the high-mass end of the stellar initial mass funetion (IMF) on the resulting second-generation population.," In the model, rapidly rotating massive stars provide chemical feedback between the first and second generations, and explore the effects of varying the slope of the high-mass end of the stellar initial mass function (IMF) on the resulting second-generation population."
 Requiring that the present-day ratio of first- to second-generation stars be 1:2. the authors calculate that initial globular cluster masses must have been 8 to 10 times their present-day values for a Salpeter IMF.," Requiring that the present-day ratio of first- to second-generation stars be 1:2, the authors calculate that initial globular cluster masses must have been 8 to 10 times their present-day values for a Salpeter IMF."
 They then compare the mass im first-generation stars that was lost from globular clusters at early times to the mass of the present-day Galactic stellar halo., They then compare the mass in first-generation stars that was lost from globular clusters at early times to the mass of the present-day Galactic stellar halo.
 Since roughly 35% of the mass in a Salpeter IMF is in low-mass. long-lived stars. and the present-day Galactic globular cluster system comprises 2% of the mass of the halo. they estimate that escaped first-generation globular cluster stars make up 5—8% of the mass of the halo.," Since roughly $35\%$ of the mass in a Salpeter IMF is in low-mass, long-lived stars, and the present-day Galactic globular cluster system comprises $2\%$ of the mass of the halo, they estimate that escaped first-generation globular cluster stars make up $5-8\%$ of the mass of the halo."
 then consider the origin of the second-generation stars found in the halo by MGIO and by?.. specifically whether they can reasonably be understood as havi5 been lost to the halo during the strong early mass loss that removed roughly 90% of the first-generation stars or whether they were transferred during later episodes of globular cluster tidal disruption.," then consider the origin of the second-generation stars found in the halo by MG10 and by, specifically whether they can reasonably be understood as having been lost to the halo during the strong early mass loss that removed roughly $90\%$ of the first-generation stars or whether they were transferred during later episodes of globular cluster tidal disruption."
 Folding in some assumptions involving the initial cluster mass function (ICMF). they conclude that all second-generation stars in the halo were lost at early tines.," Folding in some assumptions involving the initial cluster mass function (ICMF), they conclude that all second-generation stars in the halo were lost at early times."
 This raises the fraction of cluster mass that was lost in this early phase. which necessarily increases the initial cluster mass to 15 to 25 times the present-day mass and also raises the fraction of halo stars that originally formed in globular clusters to as much as 20%.," This raises the fraction of cluster mass that was lost in this early phase, which necessarily increases the initial cluster mass to 15 to 25 times the present-day mass and also raises the fraction of halo stars that originally formed in globular clusters to as much as $20\%$."
 However. given the observed examples of globular cluster dissolution in progress. e.g.. Palomar 5 (Rockost et al.2," However, given the observed examples of globular cluster dissolution in progress, e.g., Palomar 5 (Rockosi et al.;"
002:: Odenkirchen et al. 2003))," Odenkirchen et al. ),"
". NGC 5466 and the GD-1 stellar stream(?).. as well as the relative emptiness of the more inhospitable regions of the ""vital diagram"". we expect cluster dissolution to be the dominant source of halo field stars with"," NGC 5466 and the GD-1 stellar stream, as well as the relative emptiness of the more inhospitable regions of the “vital diagram”, we expect cluster dissolution to be the dominant source of halo field stars with"
and. multitude. of detected: periods. the Whole Earth Telescope. (WEP). employed. either. the prewhiteningor svnthesis methods in their analysis (Ixepler.. 1993).,"and multitude of detected periods, the Whole Earth Telescope (WET), employed either the prewhitening synthesis methods in their analysis (Kepler, 1993)."
 From the statistical point of view the two methods correspond to CGauss-Seidel (G-S) and. Newton-Raphson (N-18) solutions of the least squares problem (LSQ)., From the statistical point of view the two methods correspond to Gauss-Seidel (G-S) and Newton-Raphson (N-R) solutions of the least squares problem (LSQ).
 On one hand. a current astronomical practice favors the synthesis. (N-R) method. emploving the covariance matrix with large extra-diagonal cocllicients.," On one hand, a current astronomical practice favors the synthesis (N-R) method, employing the covariance matrix with large extra-diagonal coefficients."
 Presence of close frequencies and/or heir combinations in the svnthesis method. vielcls near singular normal equations and may produce large near cancelling terms in the solution. creating the x »oblem and vielding solutions with excess amplitudes.," Presence of close frequencies and/or their combinations in the synthesis method yields near singular normal equations and may produce large near cancelling terms in the solution, creating the $\infty-\infty$ problem and yielding solutions with excess amplitudes."
 On he other hand. the method. recommenced to deal. with singularity in least squares fitting (LSQ) is by means of he singular value decomposition (SYD. c.g. Press ct al..," On the other hand, the method recommended to deal with singularity in least squares fitting (LSQ) is by means of the singular value decomposition (SVD, e.g. Press et al.,"
 1986)., 1986).
 In the SYD procedure the near singular terms of the covariance matrix are set small. resulting in choice of the solution with minimum norm (minimum amplitudes in the present context).," In the SVD procedure the near singular terms of the covariance matrix are set small, resulting in choice of the solution with minimum norm (minimum amplitudes in the present context)."
 This resembles somewhat the prewhitening method. where impΙον all extra-diagonal terms are set zero (Cray Desikachary. 1973).," This resembles somewhat the prewhitening method, where implicitly all extra-diagonal terms are set zero (Gray Desikachary, 1973)."
 We are unaware of any paper Comparing merits of he prewhitening ancl svnthesis methods in rigid matheniaticeub (statistical) terms., We are unaware of any paper comparing merits of the prewhitening and synthesis methods in rigid mathematical (statistical) terms.
 We employ the oxewhitening and svuthesis methods in xwallel to analyze our SX Phe light curves., We employ the prewhitening and synthesis methods in parallel to analyze our SX Phe light curves.
 We emploved no more than 6 harmonies in prewhitening and in most cases just 2 or 3 harmonies for the fy mode and onc juwnmonic for other modes., We employed no more than 6 harmonics in prewhitening and in most cases just 2 or 3 harmonics for the $f_0$ mode and one harmonic for other modes.
 The values of. (fundamental) requencies were adjusted. by nonlinear iterations. their jwmonics/combinations were tied to the base frequencies.," The values of (fundamental) frequencies were adjusted by nonlinear iterations, their harmonics/combinations were tied to the base frequencies."
 The resulting. frequencies are. listed in. Table. 2., The resulting frequencies are listed in Table 2.
 The hi. methods vielcleck consistent. frequencies for all strong detections. corresponding to the AoW statistics O715.," The both methods yielded consistent frequencies for all strong detections, corresponding to the AoV statistics $\Theta>15$."
 We observed no adverse effect of reappearance of the frequencies once prewhitened., We observed no adverse effect of reappearance of the frequencies once prewhitened.
 Ambiguity. if any. arose occasionally due to aliasing and it manifested with equal strength in both the prewhitening and synthesis methods.," Ambiguity, if any, arose occasionally due to aliasing and it manifested with equal strength in both the prewhitening and synthesis methods."
 Such cases are marked in Table 2 with superscript , Such cases are marked in Table 2 with superscript $^1$.
The novelty in our approach. as compared with WET. is in use of the multi-harmonic AoW periodosram (Schwarzenberg-C'erny. 1996).," The novelty in our approach, as compared with WET, is in use of the multi-harmonic AoV periodogram (Schwarzenberg-Czerny, 1996)."
 Lt emplovs orthogona unctions and is able to combine power from. harmonics (NII—2 harmonies were combined in practice)., It employs orthogonal functions and is able to combine power from harmonics (NH=2 harmonics were combined in practice).
 Importance of use of orthogonal functions in period search was argue w Lomb (1976). Ferraz-Mello (1981). Scargle (1982). anc Foster (1994).," Importance of use of orthogonal functions in period search was argued by Lomb (1976), Ferraz-Mello (1981), Scargle (1982) and Foster (1994)."
 Advantage in combining harmonics is two-old: they contribute extra power for the base frequency ane at the same time reduce power in the residuals., Advantage in combining harmonics is two-fold: they contribute extra power for the base frequency and at the same time reduce power in the residuals.
 Any methoc sensitive to the harmonies (e.g. phase folding and. binning and the present case of Fourier fit) is prone to. produce sub-harmonics in the periodogram., Any method sensitive to the harmonics (e.g. phase folding and binning and the present case of Fourier fit) is prone to produce sub-harmonics in the periodogram.
 The subharmonic pose little problem in practice as they are easily. identified. by tight packing of aliases., The subharmonic pose little problem in practice as they are easily identified by tight packing of aliases.
 Phere exist exact relations between power in the data. root-mean square (rms) of the residuals and the oV statistics O emploved in the present case (e.g. Sechwarzenberg-C'erny. 1999).," There exist exact relations between power in the data, root-mean square (rms) of the residuals and the AoV statistics $\Theta$ employed in the present case (e.g. Schwarzenberg-Czerny, 1999)."
 Detection of frequencies poses special case of hypothesis testing in statistics., Detection of frequencies poses special case of hypothesis testing in statistics.
" In our case the detection criterion O7©,=SN roughly: corresponced to mode amplitude exceeding 4 times its standard deviation socdeoa.", In our case the detection criterion $\Theta>\Theta_c\equiv 8$ roughly corresponded to mode amplitude exceeding 4 times its standard deviation $A>4\sigma_A$.
 Any frequencies near/below that detection limit are deemed. unsafe. and. indicated. with superscript  in ‘Table 2., Any frequencies near/below that detection limit are deemed unsafe and indicated with superscript $^2$ in Table 2.
 The purpose of listing these marginal detections (15>0 S) is solely to indicate deviations of residuals [rom pure noise and not to ponder on frequencies., The purpose of listing these marginal detections $15>\Theta>8$ ) is solely to indicate deviations of residuals from pure noise and not to ponder on frequencies.
 An example of our results for NV324 is shown in Fig., An example of our results for NV324 is shown in Fig.
 2., 2.
 The panels show ANOVA periodograms (Schwarzenberg-Czermy 1996)., The panels show ANOVA periodograms (Schwarzenberg-Czerny 1996).
 The uppermost panel is computed. for the original data and reveals. the dominant peak with its aliases., The uppermost panel is computed for the original data and reveals the dominant peak with its aliases.
 The remaining ones are computed for the data after subtraction of all so far identified frequencies and significant combinations of thereof., The remaining ones are computed for the data after subtraction of all so far identified frequencies and significant combinations of thereof.
 Fig., Fig.
 3 gashows the light curves of NV324 associated with all six periods found., 3 shows the light curves of NV324 associated with all six periods found.
 Each light curve. phasec with the particular period. was prewhitened with five remaining periods and their harmonics.," Each light curve, phased with the particular period, was prewhitened with five remaining periods and their harmonics."
 Note, Note
the relationship between the abundances of 22 chemical clements and the ratio.,the relationship between the abundances of 22 chemical elements and the ratio.
 Lt is clear form their Fig., It is clear form their Fig.
 12 that the ratio is higher for the thick disc than the thin disc by almost 0.15 until the metallicity reaches Fe/H]-0.3., 12 that the ratio is higher for the thick disc than the thin disc by almost 0.15 until the metallicity reaches $\rm[Fe/H]=-0.3$.
 At larger metallicities. the ratios of the two disces becomes similar.," At larger metallicities, the ratios of the two discs becomes similar."
 Phe authors explain this fact bv invoking an extended: period. of enrichment in iron by Type Ia SNe. an explanation that is supported by our work.," The authors explain this fact by invoking an extended period of enrichment in iron by Type Ia SNe, an explanation that is supported by our work."
 Fig., Fig.
 16 in the same article shows that chemical elements other than the a-elements do not follow the same pattern. which is further evidence of the important role of Typo 11 SNe in the formation of the Milkv Way. ancl support the scenario that a major collision took place in the history of the Milky Way.," 16 in the same article shows that chemical elements other than the $\alpha$ -elements do not follow the same pattern, which is further evidence of the important role of Type II SNe in the formation of the Milky Way, and support the scenario that a major collision took place in the history of the Milky Way."
 Another similar study was cone hy )ensbvοἱal. (2005)., Another similar study was done by \citet{bensbyetal05}.
.. “Phat study presents abuncances for 102. dwarf E and €i stars. ancl uses their kinematics to determine if they belong to the thin or thick disc.," That study presents abundances for 102 dwarf F and G stars, and uses their kinematics to determine if they belong to the thin or thick disc."
 Their Fig., Their Fig.
 δ shows the abundances of oxvgen. magnesium. and silicon as functions of metallicity. which indicates that that stars in the thick and thin cise have cillerent abundances for a metallicity Vefl]«0.5.," 8 shows the abundances of oxygen, magnesium, and silicon as functions of metallicity, which indicates that that stars in the thick and thin disc have different abundances for a metallicity $\rm[Fe/H]<-0.5$."
 The Fig., Their Fig.
 10 is particularly. interesting and shows that the abundance of oxveen decreases. with increasing metallicity in the interval 1.0ο«0.0., 10 is particularly interesting and shows that the abundance of oxygen decreases with increasing metallicity in the interval $\rm-1.0<[Fe/H]<0.0$.
 This is all in agreement with the results. presented. here., This is all in agreement with the results presented here.
 These authors suggest the existence of several observational constraints related to the formation and chemical evolution of the thick disc: Our results mostly agree with these constraints. which supports the gas-rich. major-collision scenario. for the formation of the thick disc of the Alilky Wa. a scenario in which a collision leads to an intense starburst accompanied by à very large number of Type LE SNe.," These authors suggest the existence of several observational constraints related to the formation and chemical evolution of the thick disc: Our results mostly agree with these constraints, which supports the gas-rich, major-collision scenario for the formation of the thick disc of the Milky Way, a scenario in which a collision leads to an intense starburst accompanied by a very large number of Type II SNe."
" ""μονο SNe enrich the gas supply in a-clements. allowing the formation of stars with a high ratio."," These SNe enrich the gas supply in $\alpha$ -elements, allowing the formation of stars with a high ratio."
 The starburst also leads to a progressive enrichment in iron caused hy “Pype la SNe., The starburst also leads to a progressive enrichment in iron caused by Type Ia SNe.
 Stars formed after the collision will therefore have a smaller for the same metallicity., Stars formed after the collision will therefore have a smaller for the same metallicity.
 These stars will form a thin disc with a smaller velocity dispersion than the stars formed, These stars will form a thin disc with a smaller velocity dispersion than the stars formed
the question of what and. where the NLACTIO lenses are remains unanswered.,the question of what and where the MACHO lenses are remains unanswered.
 From the observed. events we can construct theobserved clistribution function of time seales. vf).," From the observed events we can construct the distribution function of time scales, $\nu(\hat{t})$."
 The true distribution will then be ph)=μη)ες]{pOfetdi.," The true distribution will then be $\rho(\hat{t})=\nu(\hat{t})/\epsilon(\hat{t})/\int
\nu(\hat{t})/\epsilon(\hat{t}) d\hat{t}$."
 We want to calculate which requires knowing the function v(/)., We want to calculate which requires knowing the function $\nu(\hat{t})$.
 Our best euess for this will be to Let N , Our best guess for this will be to let _i _i - ).
Substituting in gives , Substituting in gives =.
Using the events and efficiencies. towards the LMC (Alcocketal.1996) we obtain f=61 davs. (Binney&“Tremaine198," Using the events and efficiencies towards the LMC \cite{MACHOmass} we obtain $\bar{\hat{t}}= 61$ days. \cite{binney},"
Using the events and efficiencies. towards the LMC (Alcocketal.1996) we obtain f=61 davs. (Binney&“Tremaine1987," Using the events and efficiencies towards the LMC \cite{MACHOmass} we obtain $\bar{\hat{t}}= 61$ days. \cite{binney},"
Using the events and efficiencies. towards the LMC (Alcocketal.1996) we obtain f=61 davs. (Binney&“Tremaine1987)," Using the events and efficiencies towards the LMC \cite{MACHOmass} we obtain $\bar{\hat{t}}= 61$ days. \cite{binney},"
Using the events and efficiencies. towards the LMC (Alcocketal.1996) we obtain f=61 davs. (Binney&“Tremaine1987).," Using the events and efficiencies towards the LMC \cite{MACHOmass} we obtain $\bar{\hat{t}}= 61$ days. \cite{binney},"
Using the events and efficiencies. towards the LMC (Alcocketal.1996) we obtain f=61 davs. (Binney&“Tremaine1987)..," Using the events and efficiencies towards the LMC \cite{MACHOmass} we obtain $\bar{\hat{t}}= 61$ days. \cite{binney},"
assuming a flat prior on axial ratios and random orientations.,assuming a flat prior on axial ratios and random orientations.
 Forcing the shape to follow results from ;V-body simulations and the orientation to be biased. dispersion is comparable with the spherical symmetric case. but the estimated concentration is significantly lower (ουςLO vs. e200~19).," Forcing the shape to follow results from $N$ -body simulations and the orientation to be biased, dispersion is comparable with the spherical symmetric case, but the estimated concentration is significantly lower $c_{200} \sim 10$ vs. $c_{200} \sim 13$ )."
 The most meaningful comparison can be made with Corless(2009).. who first employed a Bayesian analysis to deproject weak lensing data ofAI6897.," The most meaningful comparison can be made with \citet{cor+al09}, who first employed a Bayesian analysis to deproject weak lensing data of."
. Even if they used a different data set obtained with the ESO/MPG Wide Field Imager. the obtained posterior distributions for c»oo are in agreement with ours for both location and dispersion.," Even if they used a different data set obtained with the ESO/MPG Wide Field Imager, the obtained posterior distributions for $c_{200}$ are in agreement with ours for both location and dispersion."
 Orientation and shape biases can be very sizable when estimating halo concentrations from lensing but are less effective in X-ray analyses (COguri&Blandford2009:Meneghettietal. 2010). which usually provide lesser values for συ in Al689 (Coeetal.2010).," Orientation and shape biases can be very sizable when estimating halo concentrations from lensing but are less effective in X-ray analyses \citep{og+bl09,men+al10}, which usually provide lesser values for $c_{200}$ in A1689 \citep{coe+al10}."
 A proper statistical modelling of triaxiality is then mandatory for reliable estimates., A proper statistical modelling of triaxiality is then mandatory for reliable estimates.
 This deserves attention since an unbiased lensing estimate can provide concentration values without assuming hydrostatic equilibrium. which ean plague X-ray methods (Molnaretal.2010).," This deserves attention since an unbiased lensing estimate can provide concentration values without assuming hydrostatic equilibrium, which can plague X-ray methods \citep{mol+al10}."
. Combined X-ray and SZ methods are interesting foo. since they can directly infer the elongation of the intra-cluster medium distribution without the hydrostatic equilibrium hypothesis (DeFilippisetal.2005:Sereno2006:Sereno 2007).," Combined X-ray and SZ methods are interesting too, since they can directly infer the elongation of the intra-cluster medium distribution without the hydrostatic equilibrium hypothesis \citep{def+al05,ser+al06,ser07}."
. However. the gas density is expected to differ from the dark matter profile.," However, the gas density is expected to differ from the dark matter profile."
 Some further hypotheses have to be used to link the gas to the dark matter distribution., Some further hypotheses have to be used to link the gas to the dark matter distribution.
 MS thanks M. Limousin for making available some tabulated results of the strong lensing analysis in Limousinetal.(2007)., MS thanks M. Limousin for making available some tabulated results of the strong lensing analysis in \citet{lim+al07}.
 KU acknowledges support from the Academia Sinica Career Development Award and the National Science Council of Taiwan under the grant NSC97- 2112-M-001-020-MY3., KU acknowledges support from the Academia Sinica Career Development Award and the National Science Council of Taiwan under the grant NSC97- 2112-M-001-020-MY3.
contributions from individual sources as a function of their flux density.,contributions from individual sources as a function of their flux density.
 In Figure 3. we present this comparison to observations for 24. 70. 160. 250. 350. 500. 850. and data.," In Figure \ref{fig:resolved.cirb} we present this comparison to observations for 24, 70, 160, 250, 350, 500, 850, and data."
 It is clear that the model ean account for the vast majority of the CDIRB: at 24. 70. 160. and we find good agreement with the fraction of emission at those wavelength above a given flux density down to =10% of the total emission.," It is clear that the model can account for the vast majority of the CDIRB; at 24, 70, 160, and we find good agreement with the fraction of emission at those wavelength above a given flux density down to $\approx 10\%$ of the total emission."
 At the same time. however. we find that the model cannot account for the =10.15'4 of the CDIRB owing to the brightest sources at Aw.zz250jm.," At the same time, however, we find that the model cannot account for the $\approx 10-15\%$ of the CDIRB owing to the brightest sources at $\lambda_{obs} \gsim 250$."
. This is a well-known problem. exemplitied by the difficulty analytic. models have found in reproducing the bright counts (22)..," This is a well-known problem, exemplified by the difficulty semi-analytic models have found in reproducing the bright counts \citep{baugh2005,swinbank2008}."
 There are a number of potential solutions have been proposed in the literature. including cosmological gas accretion and a more sophisticated calculation of the IR SED including full radiative transfer ¢e.g..2) combined with the well-known effects of cosmic variance in these rather small-area surveys (seediscussionine.g.. 22)..," There are a number of potential solutions have been proposed in the literature, including cosmological gas accretion \citep{dave2009} and a more sophisticated calculation of the IR SED including full radiative transfer \citep[e.g.,][]{narayanan2009.smg} combined with the well-known effects of cosmic variance in these rather small-area surveys \citep[see discussion in e.g.,][]{weiss2009,austermann2010}."
 However. because the model agrees with observations over =90'4 of the CDIRB emission. we do not believe this diserepaney materially affects our results.," However, because the model agrees with observations over $\gsim 90\%$ of the CDIRB emission, we do not believe this discrepancy materially affects our results."
 Modeling the bright end of the luminosity function and the number counts more generally is. however. clearly a very interesting problem in its own right," Modeling the bright end of the luminosity function and the number counts more generally is, however, clearly a very interesting problem in its own right"
They can also reproduce the effect of dillering brightness distributions between the irradiated and un-irradiated faces of the stream. and this elfect is not reproduced in the mocel of Llarrop-Allin ((1999a ancl 1999b).,"They can also reproduce the effect of differing brightness distributions between the irradiated and un-irradiated faces of the stream, and this effect is not reproduced in the model of Harrop-Allin (1999a and 1999b)."
 However. the Llarrop-Allin (technique has the benefit. of being sensitive to the total emission from the stream (not just the line emission).," However, the Harrop-Allin technique has the benefit of being sensitive to the total emission from the stream (not just the line emission)."
 The technique also has the advantage of access to high signal-to-noise ratio data. which is crucial in producing robust fits.," The technique also has the advantage of access to high signal-to-noise ratio data, which is crucial in producing robust fits."
 The lighte curves presented here were obtained usinge the S-Cam2 Superconducting Tunnel Junction (ST) camera. developed: by the ESA Astrophysics. Division at ENTEC.," The light curves presented here were obtained using the S-Cam2 Superconducting Tunnel Junction (STJ) camera, developed by the ESA Astrophysics Division at ESTEC."
 The camera is the second. prootvpe of a new generation of detectors that record the energy as well as the position and time of arrival (to within ~5frs for this particular detector) of the incident photons (Rando 22000)., The camera is the second prototype of a new generation of detectors that record the energy as well as the position and time of arrival (to within $\sim5\ \mu$ s for this particular detector) of the incident photons (Rando 2000).
 Phe application of S'TJs to optical photon counting was first. proposed by Perryman. Foden Peacock (1993). ancl has since been applied to observations of the Crab Pulsar (Perryvman 11999). the magnetic cataclysmic variable UZ For (Derrvman 22001) and to quasar spectroscopy (de Bruijne 22002).," The application of STJs to optical photon counting was first proposed by Perryman, Foden Peacock (1993), and has since been applied to observations of the Crab Pulsar (Perryman 1999), the magnetic cataclysmic variable UZ For (Perryman 2001) and to quasar spectroscopy (de Bruijne 2002)."
 The detector itself consists of a liquid. helium: cooled array of 6« pixels. cach being 25« pini. corresponding ο 0.60:60 aresec? per pixel ancl a field-of-view of about 4d aresec?.," The detector itself consists of a liquid helium cooled array of $6\times 6$ pixels, each being $25\times 25$ $\mu$ $^2$, corresponding to $0.6 \times 0.6$ $^{2}$ per pixel and a field-of-view of about $4 \times 4$ $^2$."
" The pixels are sandwiches of superconducting antalum with a thin insulating laver in the micelle and he whole device is cooled well below the superconductor's critical temperature (about 0.1T,).", The pixels are sandwiches of superconducting tantalum with a thin insulating layer in the middle and the whole device is cooled well below the superconductor's critical temperature (about $_{c}$ ).
 An incident photon then »erturbs. the device equilibrium ancl as the energy. gap o*ween the ground. state and the excited state is only a few meV. a large. number of free electrons. is. created » each photon. this number being proportional to the οποίο energy.," An incident photon then perturbs the device equilibrium and as the energy gap between the ground state and the excited state is only a few meV, a large number of free electrons is created by each photon, this number being proportional to the photon energy."
 This is in contrast to normal optical CCD semiconductors where the band gap is 1 eV. and photon absorption results in typically only one free electron being created.," This is in contrast to normal optical CCD semiconductors where the band gap is $\sim1$ eV, and photon absorption results in typically only one free electron being created."
 The S-Cam2 instrument ἰ particulary suited to observations of cataclysmic variables., The S-Cam2 instrument is particularly suited to observations of cataclysmic variables.
 The high-time resolution ancl simultaneous. observations of spectral and intensity variations is ideal for eclipsing svstems with orbital periods of the order of those in cataclysmic variables., The high-time resolution and simultaneous observations of spectral and intensity variations is ideal for eclipsing systems with orbital periods of the order of those in cataclysmic variables.
 The intensity variations over the rapid ingress and egress can be probed. directly. and the rapid. variations of the intensity of the accretion stream can be used to provide information on the possible mechanisms of emission along the stream.," The intensity variations over the rapid ingress and egress can be probed directly, and the rapid variations of the intensity of the accretion stream can be used to provide information on the possible mechanisms of emission along the stream."
 S-Cam2 was mounted at the Nasmyth focus of the William llerschel. Telescope. curing 2000 October 2/3 and 3/4., S-Cam2 was mounted at the Nasmyth focus of the William Herschel Telescope during 2000 October 2/3 and 3/4.
 ‘Table 1 gives the evele numbers (relative to the ephemeris of Schwope 22001). start time in UTC. time of mid. egress ancl the observation length in seconds.," Table \ref{tab:obslog} gives the cycle numbers (relative to the ephemeris of Schwope 2001), start time in UTC, time of mid egress and the observation length in seconds."
 A total of live eclipses of MIU. Aqr were. recorded., A total of five eclipses of HU Aqr were recorded.
 The ingress was missed [or eclipse 20982 (ephemeris of Schwope 22001). and only just recorded for 29993.," The ingress was missed for eclipse 29982 (ephemeris of Schwope 2001), and only just recorded for 29993."
 The relatively high count rate of LIU Aqr caused. some clillicultics for the data acquisition svstem. limiting the duration of the runs.," The relatively high count rate of HU Aqr caused some difficulties for the data acquisition system, limiting the duration of the runs."
 The first three eclipses exceeded the data acquisition svsteni limits. resulting in loss of absolute time reference.," The first three eclipses exceeded the data acquisition system limits, resulting in loss of absolute time reference."
 Eclipse 29994 was therefore taken with a neutral density filter witha throughput reduction factor of 10., Eclipse 29994 was therefore taken with a neutral density filter with a throughput reduction factor of 10.
 “Phis is the most complete of the eclipses. but sullers from reduced signal-to-noise ratio.," This is the most complete of the eclipses, but suffers from reduced signal-to-noise ratio."
 The data gap in cycle 29982 was caused. by the problems with the data acquisition system noted above., The data gap in cycle 29982 was caused by the problems with the data acquisition system noted above.
 The seeing, The seeing
the same age.,the same age.
 As seen in Figure | and Table l.. increasing the convective core overshoot increases both the effective temperature and luminosity slightly.," As seen in Figure \ref{fig:HR} and Table \ref{tab:models}, increasing the convective core overshoot increases both the effective temperature and luminosity slightly."
 Increased rotation does the opposite. causing a slight decrease in temperature and luminosity.," Increased rotation does the opposite, causing a slight decrease in temperature and luminosity."
 This decrease is small except for the most rapidly rotating model considered here (200 ))., This decrease is small except for the most rapidly rotating model considered here (200 ).
 These changes in temperature and luminosity can be related to the change in the radius of the star., These changes in temperature and luminosity can be related to the change in the radius of the star.
 As the rotation rate increases. the equatorial radius increases. while the polar radius decreases.," As the rotation rate increases, the equatorial radius increases, while the polar radius decreases."
 This effect is well known. and has been demonstrated by many other authors (see.forexample???)..," This effect is well known, and has been demonstrated by many other authors \cite[see, for example][]{bodenheimer70,mm97,bob01}."
 We have also found that for a given rotation rate. increasing the convective core overshoot decreases the radius by up to 0.8 R for models at the same age and velocity. despite the corresponding increase in both temperature and luminosity (see Table 1..)," We have also found that for a given rotation rate, increasing the convective core overshoot decreases the radius by up to 0.8 $_{\odot}$ for models at the same age and velocity, despite the corresponding increase in both temperature and luminosity (see Table \ref{tab:models}. .)"
 To help us assess the effect of changing core overshoot on the structure. and hence the frequencies. we have calculated the Viiaisiialiia frequency. defined as for each of our models.," To help us assess the effect of changing core overshoot on the structure, and hence the frequencies, we have calculated the a frequency, defined as for each of our models."
 In Figure 3.. we show Njg for a non-rotating model and a rapidly rotating model (200 )) with no convective core overshooting.," In Figure \ref{bv1}, we show $N^2/g$ for a non-rotating model and a rapidly rotating model (200 ) with no convective core overshooting."
 The small wiggles visible. particularly in. the outer sections of the star. are purely. numerical effects. resulting from the finite difference calculation of the derivative.," The small wiggles visible, particularly in the outer sections of the star, are purely numerical effects, resulting from the finite difference calculation of the derivative."
 The main peak at the boundary of the convective core has approximately the same size and shape in both models., The main peak at the boundary of the convective core has approximately the same size and shape in both models.
 Clearly. changing the rotation rate does not produce much change in the shape of the normalized Brunt-Viatsiialiia frequency.," Clearly, changing the rotation rate does not produce much change in the shape of the normalized a frequency."
 Although increased rotation increases the absolute size of the convective core. in terms of fractional radius. this size remains roughly constant.," Although increased rotation increases the absolute size of the convective core, in terms of fractional radius, this size remains roughly constant."
 In these models. local conservation of momentum means there is little radial mixing. so the composition gradient does not change significantly with rotation rate.," In these models, local conservation of momentum means there is little radial mixing, so the composition gradient does not change significantly with rotation rate."
 Although there are slight differences throughout the envelope of the star. they are small and unlikely to cause large shifts in the frequencies.," Although there are slight differences throughout the envelope of the star, they are small and unlikely to cause large shifts in the frequencies."
 On the other hand. the overshoot has a much larger effect on the Brunt-Váaisáalüa frequency.," On the other hand, the overshoot has a much larger effect on the a frequency."
 Figure 4. shows the Viiaisiialéia frequency for two non-rotating models with core overshoot parameters of 0 and 0.38., Figure \ref{bv2} shows the a frequency for two non-rotating models with core overshoot parameters of 0 and 0.38.
 As expected. the peak at the boundary of the convective core has shifted outwards in radius.," As expected, the peak at the boundary of the convective core has shifted outwards in radius."
 This region is really the only significant difference. and the Brunt-Viiaisialiia frequencies are similar throughout the envelopes of the models.," This region is really the only significant difference, and the a frequencies are similar throughout the envelopes of the models."
 Using the 2D stellar evolution and pulsation calculations described in Section 2.. we have calculated pulsation frequencies for models with rotational velocities from 0-200 aand overshoot parameters of 0-0.38.," Using the 2D stellar evolution and pulsation calculations described in Section \ref{method}, we have calculated pulsation frequencies for models with rotational velocities from 0-200 and overshoot parameters of 0-0.38."
 Each model was evolved to an age of 15.6 Myr., Each model was evolved to an age of 15.6 Myr.
" As the overshoot and rotation change the evolution slightly. all of these models have slightly different radii and core hydrogen fraction (X,.). as discussed in section (see also Table | and Figure 1))."," As the overshoot and rotation change the evolution slightly, all of these models have slightly different radii and core hydrogen fraction $_c$ ), as discussed in section (see also Table \ref{tab:models} and Figure \ref{fig:HR}) )."
 In order to offset the effects of this difference. we have scaled the frequencies by a factor of ViGM/R(40°*) when looking for the effects of rotation and convective core overshoot.," In order to offset the effects of this difference, we have scaled the frequencies by a factor of $\sqrt(GM/R(40^{\circ})^3)$ when looking for the effects of rotation and convective core overshoot."
 We have chosen the radius at this colatitude as it has been found to produce the best pulsation, We have chosen the radius at this colatitude as it has been found to produce the best pulsation
Figure 5 shows (his test results. which confirm the two verification items: The left plot Clearly shows there is no artificial pattern caused by digital processing. and for the right plot it can be clearly seen that the noise level decreases in proportion to L/integrationlime.,"Figure \ref{fig:3} shows this test results, which confirm the two verification items; The left plot clearly shows there is no artificial pattern caused by digital processing, and for the right plot it can be clearly seen that the noise level decreases in proportion to $1/\sqrt{\rm integration~ time}$."
 We also conducted the test of receiving signals from ALMA antennas and data processing ab Array Operation Site (AOS). and verified that the ACA Correlator successfully received the sienals and processed the digitized data without anv problems (Figure 6)).," We also conducted the test of receiving signals from ALMA antennas and data processing at Array Operation Site (AOS), and verified that the ACA Correlator successfully received the signals and processed the digitized data without any problems (Figure \ref{fig:4}) )."
rather Uattenecd within 3.5 Gar.,rather flattened within 3.5 Gyr.
 This is mainly because stellar. populations that are located at different. |z]. and thas have dillerent/ Fe/1l] can be mixed. well during the bar instability and the evolution of the bar., This is mainly because stellar populations that are located at different $|z|$ and thus have different [Fe/H] can be mixed well during the bar instability and the evolution of the bar.
 The simulated vertical metallicity gradients do not. Lt well with the observational results. in particular. for |z|1.7 kpe. which suggests that the bulge can not be simply formed from a pure thin one-component stellar clisk through bar instability.," The simulated vertical metallicity gradients do not fit well with the observational results, in particular, for $|z| \sim 1.7$ kpc, which suggests that the bulge can not be simply formed from a pure thin one-component stellar disk through bar instability."
 As shown in Fig., As shown in Fig.
 l. a stellar bar can be developed in the two-component disk within 2 CGvr in the mocel TCDS and it looks like a (boxy) bulge in edge-on view.," 1, a stellar bar can be developed in the two-component disk within $\sim 2$ Gyr in the model TCDS1 and it looks like a (boxy) bulge in edge-on view."
 Although the thick disk can not become a bar for itself owing o the smaller mass fraction of the disk. it can become a xr when the thin disk is transformed. into a bar through xw instability.," Although the thick disk can not become a bar for itself owing to the smaller mass fraction of the disk, it can become a bar when the thin disk is transformed into a bar through bar instability."
 Fie., Fig.
" 4 clearly shows that both the thin and hick disks show the maximum. Vi, of ~100 km + and jwe cvlindrical rotation with the amplitudes ancl profiles similar to each other in the central 3 kpe.", 4 clearly shows that both the thin and thick disks show the maximum $V_{\phi}$ of $\sim 100$ km $^{-1}$ and have cylindrical rotation with the amplitudes and profiles similar to each other in the central 3 kpc.
 The simulated maximum: value of σ and e-profiles dependent on |z| in he thin and thick disks are in good agreement with the observed ones., The simulated maximum value of $\sigma$ and $\sigma$ -profiles dependent on $|z|$ in the thin and thick disks are in good agreement with the observed ones.
 Although the thick disk initially has higher velocity clispersions and a smaller amplitude of rotation than he thin disk. the two components can finally have similar sinematical properties: the thick disk has @ at |z|=Likpe and 2.1 kpe higher than those of the thin disk.," Although the thick disk initially has higher velocity dispersions and a smaller amplitude of rotation than the thin disk, the two components can finally have similar kinematical properties: the thick disk has $\sigma$ at $|z|=1.4$ kpc and 2.1 kpc higher than those of the thin disk."
 Fig., Fig.
 5 shows that although the initial vertical metallicity eracdient of the bulge region in the thin disk can be significantly Dlattened. the simulated. profile for the whole disk can fit much better with the observational data in comparison with those derived in the PDSI.," 5 shows that although the initial vertical metallicity gradient of the bulge region in the thin disk can be significantly flattened, the simulated profile for the whole disk can fit much better with the observational data in comparison with those derived in the PDS1."
 The most important reason for this is that the mean metallicity at ;|=1.7 προ in this model can be as low as 0.2 owing o the presence of metal-poor stars of ED there: these metal-poor stars originate [rom J?3 kpe of ED., The most important reason for this is that the mean metallicity at $|z|=1.7$ kpc in this model can be as low as $-0.2$ owing to the presence of metal-poor stars of FD there: these metal-poor stars originate from $R>3$ kpc of FD.
 Since rese stars initially stay at higher |z| in the dynamically jotter thick disk. they can not be stronely inlluenced. by 10 bar and consequently they can stay longer at. higher ;| and thus can keep the lower mean miectallicity there.," Since these stars initially stay at higher $|z|$ in the dynamically hotter thick disk, they can not be strongly influenced by the bar and consequently they can stay longer at higher $|z|$ and thus can keep the lower mean metallicity there."
 As a result of this. the mean metallicity of the whole disk axulee) at higher | can keep lower.," As a result of this, the mean metallicity of the whole disk (bulge) at higher $|z|$ can keep lower."
 1n addition. the bar n this model does not mix so well stellar populations with ilferent metallicities in the thin disk in comparison with the DS1.," In addition, the bar in this model does not mix so well stellar populations with different metallicities in the thin disk in comparison with the PDS1."
 This less ellicient mixing of stellar populations with ilerent initial [ο] and Fe/LH] also contribute to the steeper Pertieal metallicity gradient to some extent., This less efficient mixing of stellar populations with different initial $|z|$ and [Fe/H] also contribute to the steeper vertical metallicity gradient to some extent.
 The results for wee different models in Fig., The results for three different models in Fig.
 5 show that steeper vertical metallicity eracdicnts can be seen in models with steeper Anieds In TCDS.," 5 show that steeper vertical metallicity gradients can be seen in models with steeper ${\alpha}_{\rm b, tcds}$ in TCDS."
 Thus PCDS can reproduce. reasonably well the evlindrical rotation and vertical metallicity gradient observed in the Galactic bulge in a self-consistent manner., Thus TCDS can reproduce reasonably well the cylindrical rotation and vertical metallicity gradient observed in the Galactic bulge in a self-consistent manner.
Recent measurements of cosmic ravs [rom energies of one GeV to one TeV have shown a spectrum. (77) and abundance of positrons (7) that are. dillicult. to reconcile with astrophysical sources.,"Recent measurements of cosmic rays from energies of one GeV to one TeV have shown a spectrum \citep{2008Natur.456..362C,2008PhRvL.101z1104A}
 and abundance of positrons \citep{2009Natur.458..607A} that are difficult to reconcile with astrophysical sources."
 “These observations have naturally stirred up great interest among the particle physics community ancl especially people who study. dark matter (e.g.2).., These observations have naturally stirred up great interest among the particle physics community and especially people who study dark matter \citep[e.g.][]{2009NatPh...5..176H}.
 Essentially the problem is that the observec spectrum is much harder than that expected to be produces by astrophysical sources such as supernova shocks or pulsars. so it is quite natural to look at more exotic possibilities. including clecaving dark matter.," Essentially the problem is that the observed spectrum is much harder than that expected to be produced by astrophysical sources such as supernova shocks or pulsars, so it is quite natural to look at more exotic possibilities, including decaying dark matter."
 On the other hand. severa works have also examined the question of whether or no astrophysical sources can account for the observed spectrum and positron abundance by including a reasonable moce or the diffusion of cosmic ravs through the Galaxy.," On the other hand, several works have also examined the question of whether or not astrophysical sources can account for the observed spectrum and positron abundance by including a reasonable model for the diffusion of cosmic rays through the Galaxy."
 In this Letter we consider the expected abundance of cosmic-ray electrons ancl positrons (hereafter referred to as cosmic rays) ooduced by magnetars and. pulsars., In this Letter we consider the expected abundance of cosmic-ray electrons and positrons (hereafter referred to as cosmic rays) produced by magnetars and pulsars.
" Alagnetars (??) are ultramagnetized neutron stars with ields B,~Lot!101 GG. fueled by either magnetic field decay (22). or residual thermal energy (??).."," Magnetars \citep{Dunc92,Thom95} are ultramagnetized neutron stars with fields $B_* \sim 10^{14} - 10^{16}$ G, fueled by either magnetic field decay \citep{Thom96,Heyl98decay} or residual thermal energy \citep{Heyl97kes,Heyl97magnetar}."
 Magnetars are hought to produce copious numbers of electron-positron xrs both in bursts (2?) and in quiescence (??)..," Magnetars are thought to produce copious numbers of electron-positron pairs both in bursts \citep{Thom95,Heyl03sgr} and in quiescence \citep{Heyl05sgr,2007ApJ...657..967B}."
 Moreover. he local radiation from these pairs is thought to power he bursts from. soft-eamma repeaters (2) as well as the recently discovered. non-thermal emission from soft-gamma repeaters and anomalous x-ray pulsars in quiescence (?2)..," Moreover, the local radiation from these pairs is thought to power the bursts from soft-gamma repeaters \citep{Thom95} as well as the recently discovered non-thermal emission from soft-gamma repeaters and anomalous x-ray pulsars in quiescence \citep{2005A&A...433L...9M,2006ApJ...645..556K}."
 Consequently. magnetars seem a natural candidate to make an important contribution to the observed. abundance of electrons and. positrons observed at Earth.," Consequently, magnetars seem a natural candidate to make an important contribution to the observed abundance of electrons and positrons observed at Earth."
 7. presented. a detailed caleulation of the expected spectrum of cosmic ravs in various models for their production from pulsars., \citet{2008arXiv0812.4457P} presented a detailed calculation of the expected spectrum of cosmic rays in various models for their production from pulsars.
 Llis calculation. focused. on the population of gamma-ray pulsars., His calculation focused on the population of gamma-ray pulsars.
 The situation for magnetars is somewhat different because these objects are much rarer than ganuna-rav pulsars: the birth rate for magnetars is roughly ten times smaller than that of pulsars., The situation for magnetars is somewhat different because these objects are much rarer than gamma-ray pulsars; the birth rate for magnetars is roughly ten times smaller than that of pulsars.
 Consequently. the cosmic ray Dux that we observe can come both from the magnetars that are active today as well as from more ordinary looking objects that may. have been active magnetars in the past such as RAJ 07204-3125 (??)..," Consequently, the cosmic ray flux that we observe can come both from the magnetars that are active today as well as from more ordinary looking objects that may have been active magnetars in the past such as RXJ 0720.4-3125 \citep{Heyl98rxj,Heyl98decay}."
 ‘To caleulate the expected abuncances of cosmic ravs from maenctars. we generate a Monte. Carlo simulation of the magnetar population over the past ten million vears ancl compare it with a similar simulation of the pulsar population over the past million vears.," To calculate the expected abundances of cosmic rays from magnetars, we generate a Monte Carlo simulation of the magnetar population over the past ten million years and compare it with a similar simulation of the pulsar population over the past million years."
 'To model the cosmic ray emission from pulsars we assume a production rate always proportional to the spin-down power by magnetic dipole emission., To model the cosmic ray emission from pulsars we assume a production rate always proportional to the spin-down power by magnetic dipole emission.
 In contrast to 2... we do not make any distinction between objects that we expect to be ganima-ray pulsars versus the rest of the pulsar population.," In contrast to \citet{2008arXiv0812.4457P}, we do not make any distinction between objects that we expect to be gamma-ray pulsars versus the rest of the pulsar population."
 ‘To specify the model. we assume that all the pulsars are born with a period of 49 milliseconds and spin down to one second by the time we observe them.," To specify the model, we assume that all the pulsars are born with a period of 49 milliseconds and spin down to one second by the time we observe them."
 For the magnetars. we take the cosmic rav emission to be proportional to the magnetic field decay power.," For the magnetars, we take the cosmic ray emission to be proportional to the magnetic field decay power."
 We use the calculations of ? to follow the evolution of the magnetic field starting at 1075 G, We use the calculations of \citet{Heyl98decay} to follow the evolution of the magnetic field starting at $10^{16}$ G
performed using standard routines.,performed using standard routines.
 Spectra distortion due to the optics were corrected using data reduction package within the environment., Spectra distortion due to the optics were corrected using data reduction package within the environment.
 Cosmic rays were detected and removed using (?).., Cosmic rays were detected and removed using \citep{vanDokkum01}.
 Residual cosmic rays were removed by manually editing the spectrum., Residual cosmic rays were removed by manually editing the spectrum.
 Wavelength calibration was performed using standard [RAF routines., Wavelength calibration was performed using standard IRAF routines.
 Comparison Th+Ar spectra were obtained during the night close in time to the scientific spectra., Comparison Th+Ar spectra were obtained during the night close in time to the scientific spectra.
 Because two different grisms were used for the two runs. we optimized the wavelength calibration in. different spectral ranges: 4545A«2« 56654. for run I. and 4700A<259004. for run 2.," Because two different grisms were used for the two runs, we optimized the wavelength calibration in different spectral ranges: $4545 \AA < \lambda < 5665 \AA$ , for run 1, and $4700 \AA < \lambda < 5900 \AA$, for run 2."
 With this choice. we were able to minimize the errors in the wavelength calibration. which are about +10 aas measured from the calibrated comparison spectra. and from the sky line emission Ines.," With this choice, we were able to minimize the errors in the wavelength calibration, which are about $\pm 10$ as measured from the calibrated comparison spectra and from the sky line emission lines."
 Absorption lines asHf... ttriplet and ffall inside the two selected wavelength ranges.," Absorption lines as, triplet and fall inside the two selected wavelength ranges."
 Finally. the spectra were corrected for change in the slit illumination along the slit direction using the spectra obtained on sky blank fields.," Finally, the spectra were corrected for change in the slit illumination along the slit direction using the spectra obtained on sky blank fields."
 Sky subtraction may introduce errors in the measurements from spectra of low surface brightness regions., Sky subtraction may introduce errors in the measurements from spectra of low surface brightness regions.
 To limit systematic effects as much as possible. we account for the sky subtraction in two ways.," To limit systematic effects as much as possible, we account for the sky subtraction in two ways."
 The first method is to obtain sky spectra from blank fields., The first method is to obtain sky spectra from blank fields.
 The sky spectrum is then free of contamination either from the galaxy halos or intracluster light. but the spectra are not taken simultaneously with the scientific exposures.," The sky spectrum is then free of contamination either from the galaxy halos or intracluster light, but the spectra are not taken simultaneously with the scientific exposures."
 Therefore. if the relative intensities of the sky continuum. emission or absorption lines change with time. sky residuals are present in the galaxy spectra.," Therefore, if the relative intensities of the sky continuum, emission or absorption lines change with time, sky residuals are present in the galaxy spectra."
 The second method is to extract the sky spectrum from a region of the slit where the galaxy light is negligible (central part of the slit for run |. outer borders of the slit for run 2)," The second method is to extract the sky spectrum from a region of the slit where the galaxy light is negligible (central part of the slit for run 1, outer borders of the slit for run 2)."
 The sky is now observed simultaneously to the galaxy observations but the disadvantage is that it might contain a residual contribution from the galaxy halo and/or intracluster light., The sky is now observed simultaneously to the galaxy observations but the disadvantage is that it might contain a residual contribution from the galaxy halo and/or intracluster light.
 We then may subtract spectral features. which belong to the galaxy and which we are. in fact. interested in measuring.," We then may subtract spectral features, which belong to the galaxy and which we are, in fact, interested in measuring."
 In the upper panel of Fig., In the upper panel of Fig.
 2. we compare the sky spectra extracted using the two different methods., \ref{fig:sky_comparison} we compare the sky spectra extracted using the two different methods.
 If the sky spectrum extracted at the slit center (run. 1) or at the slit edges (run 2) contains a small residual contribution from the galaxy (stellar continuum and/or absorption line features) it should become visible when comparing with the sky spectrum extracted at the offset position., If the sky spectrum extracted at the slit center (run 1) or at the slit edges (run 2) contains a small residual contribution from the galaxy (stellar continuum and/or absorption line features) it should become visible when comparing with the sky spectrum extracted at the offset position.
 Residuals are approximately +0.5 counts (i.e. ~2% of the average sky level at 5100 A))., Residuals are approximately $\pm 0.5$ counts (i.e. $\sim 2$ of the average sky level at 5100 ).
 This means that, This means that
Lilly 1991: Miller and appear to favour galaxy groups and weak clusters: they tend to avoid the densest environments except in the few cases where they are in the special location of being hosted by the central dominant galaxy of a cluster.,"Lilly 1991; Miller \nocite{pre88,hil91,mil02b} and appear to favour galaxy groups and weak clusters; they tend to avoid the densest environments except in the few cases where they are in the special location of being hosted by the central dominant galaxy of a cluster."
 To date. though. these studies have been both limited to the most powerful radio sources and. generally. based upon galaxy number count statistics or cross—correlation analyses. with little or no spectroscopic redshift information (the Miller sstudy is the exception to this. providing redshifts for a handful of galaxies in the ~20 aremin radius region around each of 25 low redshift radio sources).," To date, though, these studies have been both limited to the most powerful radio sources and, generally, based upon galaxy number count statistics or cross–correlation analyses, with little or no spectroscopic redshift information (the Miller study is the exception to this, providing redshifts for a handful of galaxies in the $\sim 20$ arcmin radius region around each of 25 low redshift radio sources)."
" By comparing the 2dFGRS with a deep large-area radio survey such as the NRAO VLA Sky Survey (NVSS: Condon it is possible to overcome both of these deficiencies. studying the spectroscopically—determined large-scale environments of ""typical radio-loud AGN within the 2dFGRS. and comparing these to those of the galaxy population in general."," By comparing the 2dFGRS with a deep large–area radio survey such as the NRAO VLA Sky Survey (NVSS; Condon \nocite{con98} it is possible to overcome both of these deficiencies, studying the spectroscopically–determined large–scale environments of `typical' radio–loud AGN within the 2dFGRS, and comparing these to those of the galaxy population in general."
 This is the goal of the current paper., This is the goal of the current paper.
 In Section 2.. the galaxy and radio source samples used in the analysis are defined.," In Section \ref{samples}, the galaxy and radio source samples used in the analysis are defined."
 The methods used to derive the properties of these galaxies are described in Section 3.., The methods used to derive the properties of these galaxies are described in Section \ref{methods}.
 The results of the environmental analysis are described in Section 4.. and these are discussed in Section 5..," The results of the environmental analysis are described in Section \ref{results}, and these are discussed in Section \ref{discuss}."
 Section 6— summarises the results., Section \ref{concs} summarises the results.
" Throughout the paper. the values adopted for the cosmological parameters are ,,,=0.3. O4.=0.7. and 65kkmss !Mpe !."," Throughout the paper, the values adopted for the cosmological parameters are $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0 =
65$ $^{-1}$ $^{-1}$."
 The primary galaxy sample for this study is drawn from the 2dF Galaxy Redshift Survey. described by Colless shorteitecolOl..," The primary galaxy sample for this study is drawn from the 2dF Galaxy Redshift Survey, described by Colless \\shortcite{col01}."
" The 2HFGRS obtained spectra through —2.1 arcsec diameter tibres for nearly a quarter of a million galaxies brighter han a nominal extinetion-corrected magnitude limit of 6, 19.45. in two declination strips (one equatorial and the other close o the south galactic pole: these are hereafter referred to as the GP and SGP strips respectively) and a number of random 2—degree diameter fields."," The 2dFGRS obtained spectra through $\sim$ 2.1 arcsec diameter fibres for nearly a quarter of a million galaxies brighter than a nominal extinction-corrected magnitude limit of $b_J=19.45$ , in two declination strips (one equatorial and the other close to the south galactic pole; these are hereafter referred to as the NGP and SGP strips respectively) and a number of random 2--degree diameter fields."
 For this paper. analysis was restricted to hose galaxies with reliable redshifts (quality =3: cf.," For this paper, analysis was restricted to those galaxies with reliable redshifts (quality $\ge 3$; cf."
 Colless 22001) which lie within the NGP or SGP strip., Colless 2001) which lie within the NGP or SGP strip.
 A cut in redshift was made to select those galaxies which ay in the redshift range 0.02<2.0.1., A cut in redshift was made to select those galaxies which lay in the redshift range $0.02 < z < 0.1$.
 At redshifts below >~0.02 the physical size of the 2dFGRS survey region is too small to investigate the large-scale galaxy environments. whilst he upper redshift cut was set by the depth of the 2dFGRS survey. as discussed below.," At redshifts below $z \sim 0.02$ the physical size of the 2dFGRS survey region is too small to investigate the large–scale galaxy environments, whilst the upper redshift cut was set by the depth of the 2dFGRS survey, as discussed below."
 The absolute B-band magnitudes of hese galaxies were calculated. using the average K-correction for 2dFGRS galaxies derived by Madgwick shorteitemad02:: Ag(z)z1.92| 2.727.," The absolute B–band magnitudes of these galaxies were calculated, using the average K–correction for 2dFGRS galaxies derived by Madgwick \\shortcite{mad02}; $K_B(z) \approx 1.9z + 2.7z^2$ ."
 Only those galaxies with absolute magnitudes Alp<19 (that is. Lg2O.25Lp: cf Norberg et al were retained for subsequent analysis: this absolute magnitude limit corresponds roughly to the apparent magnitude limit of the survey at a redshift 2~O.1.," Only those galaxies with absolute magnitudes $M_{B} < -19$ (that is, $L_{B} \gta 0.25 L_{B}^*$; cf Norberg et al \nocite{nor02} were retained for subsequent analysis; this absolute magnitude limit corresponds roughly to the apparent magnitude limit of the survey at a redshift $z \sim 0.1$."
 Thus. the combination of absolute magnitude and redshift cuts largely removes any redshift biases from the sample.," Thus, the combination of absolute magnitude and redshift cuts largely removes any redshift biases from the sample."
 This produced a sample of 56143 galaxies., This produced a sample of 56143 galaxies.
 However. not all of these galaxies are appropriate for environmental analysis. for example because they lie close to the boundaries ofthe survey. or in regions of low spectroscopic completeness.," However, not all of these galaxies are appropriate for environmental analysis, for example because they lie close to the boundaries of the survey, or in regions of low spectroscopic completeness."
 This was assessed for each galaxy individually during the process of local environment estimation through the [Oth nearest neighbour method. as discussed in Section 3.1: about of the galaxies were rejected from the sample during this analysis. due to their locations.," This was assessed for each galaxy individually during the process of local environment estimation through the 10th nearest neighbour method, as discussed in Section \ref{10near}: about of the galaxies were rejected from the sample during this analysis, due to their locations."
 Note that removal of these galaxies will not bias any of the results of the paper. firstly because these are largely a random subset of galaxies which happen to lie near the boundaries of the survey. and secondly because in any case these same cuts are applied to all of the samples under study.," Note that removal of these galaxies will not bias any of the results of the paper, firstly because these are largely a random subset of galaxies which happen to lie near the boundaries of the survey, and secondly because in any case these same cuts are applied to all of the samples under study."
 By this process. a basis catalogue of 50684 galaxies with redshifts 0.02—z<0.10 and absolute magnitudes 1g<19 was derived. for each of which good estimates of the local galaxy density can be made.," By this process, a basis catalogue of 50684 galaxies with redshifts $0.02
\le z \le 0.10$ and absolute magnitudes $M_B < -19$ was derived, for each of which good estimates of the local galaxy density can be made."
 From this basis catalogue. subsamples of radio galaxies are constructed using the radio source sample of Sadler (2002: hereafter Sad02).," From this basis catalogue, subsamples of radio galaxies are constructed using the radio source sample of Sadler (2002; hereafter \nocite{sad02}."
. These authors cross-correlated an earlier version of the 2dFGRS. which contained almost of the final 2dFGRS catalogue. with the radio sources in he NRAO VLA Sky Survey (2)... which is a GGHz survey to a limiting flux density of about mmJy covering the entirety of the sky north of 360 degrees declination.," These authors cross-correlated an earlier version of the 2dFGRS, which contained almost of the final 2dFGRS catalogue, with the radio sources in the NRAO VLA Sky Survey \cite{con98}, which is a GHz survey to a limiting flux density of about mJy covering the entirety of the sky north of $-$ 40 degrees declination."
 SadQ2 identified all of the single component radio sources which lay within 15 areseconds of a galaxy with a redshift in the 2dFGRS catalogue. and also added to this sample a small number of double or multiple comyonent radio sources for which an examination of a radio—optica overlay indicated a host galaxy within the 2udFGRS catalogue.," Sad02 identified all of the single component radio sources which lay within 15 arcseconds of a galaxy with a redshift in the 2dFGRS catalogue, and also added to this sample a small number of double or multiple component radio sources for which an examination of a radio–optical overlay indicated a host galaxy within the 2dFGRS catalogue."
 For each of the 912 candidate radio source matches. they examined the optical emission and absorption line spectrum of the host galaxy. to classify the source as: (i) “star-forming” galaxies(SEX... where the spectrum is dominated by strong narrow Balmer emission lines. (," For each of the 912 candidate radio source matches, they examined the optical emission and absorption line spectrum of the host galaxy, to classify the source as: (i) `star-forming' galaxies, where the spectrum is dominated by strong narrow Balmer emission lines. ("
i) AGN. separated into three subclasses: absorption-line ellipticals galaxies (Aa). absorption line galaxies with weak LINER-like emission lines (Aae). and. galaxies with spectra dominated by nebular emission lines such as [OII] or [ONT] (Ae). G,"ii) AGN, separated into three subclasses: absorption–line ellipticals galaxies (Aa), absorption line galaxies with weak LINER–like emission lines (Aae), and galaxies with spectra dominated by nebular emission lines such as [OII] or [OIII] (Ae). ("
il) sources whose classifications are likely (SF?.,"iii) sources whose classifications are likely (SF?,"
 Aa?.," Aa?,"
 Ae?.," Ae?,"
 Aue?), Aae?)
 or completely uncertain η., or completely uncertain (???).
 These classifications were made by visual examination of the spectra. and their reliability was checked against Principle," These classifications were made by visual examination of the spectra, and their reliability was checked against Principle"
"value of w could then be equal to —1/3 only once in the entire history of the universe, and that would have to happen right now.","value of $w$ could then be equal to $-1/3$ only once in the entire history of the universe, and that would have to happen right now."
" The distinction between our proposed cosmology with Ry,=ct (for all t, not just 15), and other FRW models with past epochs of deceleration, is quite pronounced at redshifts larger than the current limits (~1.5— 2) of study."," The distinction between our proposed cosmology with $R_{\rm h}=ct$ (for all $t$, not just $t_0$ ), and other FRW models with past epochs of deceleration, is quite pronounced at redshifts larger than the current limits $\sim 1.5-2$ ) of study."
" This happens because the application of Birkhoff’s theorem, together with the Weyl postulate and the Cosmological Principle, suggests that w——1/3 for all t, whereas (w) in ACDM changes with cosmic time (see figure 2)."," This happens because the application of Birkhoff's theorem, together with the Weyl postulate and the Cosmological Principle, suggests that $w=-1/3$ for all $t$, whereas $\langle w\rangle$ in $\Lambda$ CDM changes with cosmic time (see figure 2)."
" Based on current Type Ia supernova measurements, the use of ACDM as the standard evolutionary model seems to provide an adequate fit to the data."," Based on current Type Ia supernova measurements, the use of $\Lambda$ CDM as the standard evolutionary model seems to provide an adequate fit to the data."
" This could present a problem for our proposal because our explanation for the observed equality Αι)=cto would suggest that the ACDM version of the luminosity distance dj, used to fit the Type Ia supernova data (e.g., the *gold sample"" in Riess et al."," This could present a problem for our proposal because our explanation for the observed equality $R_{\rm h}(t_0)=ct_0$ would suggest that the $\Lambda$ CDM version of the luminosity distance $d_{\rm L}$ used to fit the Type Ia supernova data (e.g., the “gold sample"" in Riess et al."
 2004) is not correct in a flat spacetime (see also Riess et al., 2004) is not correct in a flat spacetime (see also Riess et al.
" 1998, and Perlmutter et al."," 1998, and Perlmutter et al."
 1999)., 1999).
" However, the disparity between this version of dj, and that required by a flat cosmology with w=—1/3, increases with redshift, so in principle we should be able to distinguish between the two by observing events at sufficiently early times."," However, the disparity between this version of $d_{\rm L}$ and that required by a flat cosmology with $w=-1/3$, increases with redshift, so in principle we should be able to distinguish between the two by observing events at sufficiently early times."
"radius (r=L.7R, where R,=20.5 R.). then the EMy is zzL&xLO”? (using dar?AP Me) which is comparable tothe lowest energv line EMy (&5x10? for vi)) derived. fromHETGS observations (e.g.. Wojdowski Schulz 2005).","radius $r = 1.7\Rstar$ where $\Rstar =
20.5\Rsun$ ), then the $EM_V$ is $\approx 1.8 \times 10^{55}$ (using $4 \pi r^2 ~ \DEMC$ ) which is comparable tothe lowest energy line $EM_V$ $\approx 5 \times 10^{55}$ for ) derived from observations (e.g., Wojdowski Schulz 2005)."
" since (he EM, is expected to be > theobserved EMy: (optical depth effects). the XUV-X-ray flux required (o reduce iis well within the observational limits."," Since the $EM_V$ is expected to be $>$ the $EM_V$ (optical depth effects), the XUV+X-ray flux required to reduce is well within the observational limits."
 Now we examine (he effects of NUV--X-ray radiation on bby considering the ratio q(P.v)/q(Sv)., Now we examine the effects of XUV+X-ray radiation on by considering the ratio $\QPV / \QSV$.
 As shown in Figure 5. for the case when Fy=0. (his ratio is z1 lor a large range in wwhich supports the FOG ssurrogale argument.," As shown in Figure 5, for the case when $\FX= 0$, this ratio is $\approx 1$ for a large range in which supports the F06 surrogate argument."
 However. as iincreases. q(Pv)/q(Sv) decreases which means that is significantly less sensitive to the NUV4X-ray radiation as compared to the dependence olv).," However, as increases, $\QPV / \QSV$ decreases which means that is significantly less sensitive to the XUV+X-ray radiation as compared to the dependence of."
. This is a direct consequence of the difference in the and pphotoionization rates shown in Figure 3 (see 82). and invalidates the sulfur surrogate argument.," This is a direct consequence of the difference in the and photoionization rates shown in Figure 3 (see 2), and invalidates the sulfur surrogate argument."
 In general. for all luminosity classes. q(P.v)/q(Sv) reaches a minimum value of zz0.14 over most of the O-star spectral range.," In general, for all luminosity classes, $\QPV / \QSV$ reaches a minimum value of $\approx 0.14$ over most of the O-star spectral range."
 The required (to produce this minimum value is dependent on Iuminosity class as shown in Figure 5., The required to produce this minimum value is dependent on luminosity class as shown in Figure 5.
 These results imply that the dderivedfrom FUSE observations could be uuderestimatedbv alinost an order of magnitude., These results imply that the derivedfrom observations could be underestimatedby almost an order of magnitude.
The οιποιο star (IID 37179: D2Vpe: V— 6.66) has long been known to harbor a circumstellar maeuetosphere iu which plasuia is trapped and forced iuto co-rotation bv the stars strong ( 10kC) dipolar magnetic feld (see.coe.Landstrect&Borra1978:CrooteIIuuser 1982).,"The helium-strong star (HD 37479; B2Vpe; $V=6.66$ ) has long been known to harbor a circumstellar magnetosphere in which plasma is trapped and forced into co-rotation by the star's strong $\sim
10\,{\rm kG}$ ) dipolar magnetic field \citep[see,
e.g.,][]{LanBor1978,GroHun1982}."
 This magnetosphere is larecly responsible for the stir distinctive eclipse-like dimuuines. which occur when plasma clouds transit across the stellar disk twice every LELLO rotation evele (Townsend&Owocld2005).," This magnetosphere is largely responsible for the star's distinctive eclipse-like dimmings, which occur when plasma clouds transit across the stellar disk twice every 19 rotation cycle \citep{TowOwo2005}."
. Some fraction of the stars photometric variations likely also arise from its photospheric abundance imhomoecucitics. asin other chemically peculiar stars (e.g.Milkuláseketal. 2009): but for tthe magnetospheric contribution to the variations is dominant (Townsend2008).," Some fraction of the star's photometric variations likely also arise from its photospheric abundance inhomogeneities, as in other chemically peculiar stars \citep[e.g,][]{Mik2009}; but for the magnetospheric contribution to the variations is dominant \citep{Tow2008}."
. This paper presents new C-baud photometry of the stins primary lightiuiniuuunl. obtained over four seasons spannime 20012009 using the STARTS 00πι elescope at Cerro Tololo Tuter-American Observatory (CTIO).," This paper presents new $U$ -band photometry of the star's primary light, obtained over four seasons spanning 2004–2009 using the SMARTS 0.9-m telescope at Cerro Tololo Inter-American Observatory (CTIO)."
 When combined with historical measurements x Lesseretal.(1977).. these new data allow a precise ucasureineut of the stars rotation period. and its evolution. over the past three decades.," When combined with historical measurements by \citet{Hes1977}, these new data allow a precise measurement of the star's rotation period, and its evolution, over the past three decades."
 A description of the observations. both archival aud jew. is provided iu the following section.," A description of the observations, both archival and new, is provided in the following section."
 Iu retsec:analysis.. we discuss a procedure for accurately neasurme the times oof primary light aim. and then use these ucasureieuts to construct a standard C) diagram for the star. allowing us to assess the evolution of the stars rotation period.," In \\ref{sec:analysis}, we discuss a procedure for accurately measuring the times of primary light minimum, and then use these measurements to construct a standard ) diagram for the star, allowing us to assess the evolution of the star's rotation period."
 We discuss aud summarize our findines in refsecidiscuss.., We discuss and summarize our findings in \\ref{sec:discuss}.
 Tesseretal. (1977).observed a primary light minium ofc oon the night of 1977 January 26/27. as part of their lone-term Strónuueren weby monitoring of the star using the uunber P 0.1 telescope at CTIO.," \citet{Hes1977} observed a primary light minimum of on the night of 1977 January 26/27, as part of their long-term Strömmgren $uvby$ monitoring of the star using the number 1 0.4-m telescope at CTIO."
 Their photometric data were kindlv provided to us iu electronic form bv Prof. C. T. Bolton., Their photometric data were kindly provided to us in electronic form by Prof. C. T. Bolton.
 No error estimates were supplied. πο a lncasurement error Aw=τις is assunied for all data poiuts the value quoted by esseretal.(L976) as an upper limit on their photometric uucertaimties.," No error estimates were supplied, so a measurement error $\Delta u = 7\,{\rm mmag}$ is assumed for all data points — the value quoted by \citet{Hes1976} as an upper limit on their photometric uncertainties."
 We do not correct for the apparent seasou-to-season brightening noted by Tesseretal.(1977)(1977)... ince this has no effect on the ddetermunations.," We do not correct for the apparent season-to-season brightening noted by \citet{Hes1977}, since this has no effect on the determinations."
 The «band light curve is plotted iu Fie. 1:, The $u$ -band light curve is plotted in Fig. \ref{fig:minima};
 the accompanving οὐ data are not shown. since they play no direct role iu the period determination (however. see refssecianalvsis-svs)).," the accompanying $vby$ data are not shown, since they play no direct role in the period determination (however, see \\ref{ssec:analysis-sys}) )."
 We observed a primary light minima on the nieht of 2001 November 26/27. during Johnson (BVRI monitoring of musing the Casseerain-focus Tek 2018 CCD on the SMARTS 0.9-11 telescope," We observed a primary light minimum on the night of 2004 November 26/27, during Johnson $UBVRI$ monitoring of using the Cassegrain-focus Tek 2048 CCD on the SMARTS 0.9-m telescope"
flat-tield response.,flat-field response.
 The reseau marks were removed using neighboring pixels., The reseau marks were removed using neighboring pixels.
 The three nuages with three polarizers are known to be slightly shifted relative to one another., The three images with three polarizers are known to be slightly shifted relative to one another.
 In our FOC images of Mix 3. there are no poiut sources we can use for the nuage registration.," In our FOC images of Mrk 3, there are no point sources we can use for the image registration."
 Therefore. we used the mage shift calibration results frou: Hodge(1993.1995) which are accurate to £0.3 pixel.," Therefore, we used the image shift calibration results from Hodge(1993,1995) which are accurate to $\pm
0.3$ pixel."
" The background was subtracted using the outer region of the nuages,", The background was subtracted using the outer region of the images.
 Before combining the three nuages. cach huage was scaled in order to allow for the different ranshuttances of the three polarizers.," Before combining the three images, each image was scaled in order to allow for the different transmittances of the three polarizers."
" We have estimated the effective transmittances of cach volarizer plus filter, using large-aperture spectra το the IIST/FOS data (Cohen et al."," We have estimated the effective transmittances of each polarizer plus filter, using large-aperture spectra from the HST/FOS data (Cohen et al."
 2001) and erounud-based data (Nav 199, 2001) and the ground-based data (Kay 1994).
 Then the hice theimages through the three polarizersH were scaled accordingly. aud combined to produce the Stokes £.Q.0° nuages," Then the three images through the three polarizers were scaled accordingly, and combined to produce the Stokes $I, Q, U$ images."
 The polarized flux and )olarizatiou⋅⋅ are caleulated as \/Q?=|U? aud YQ?fon)0|C?T)/T. respectively.. and debiased+ .following+ Sinuuous and Stewart (1985).," The polarized flux and polarization are calculated as $\sqrt{Q^2 + U^2}$ and $\sqrt{Q^2 + U^2} /I$, respectively, and debiased following Simmons and Stewart (1985)."
 Usiug the same larec-aperture spectra. we also estimated the narrow emission line coutamination in these filters to he ~30% for both of the filters.," Using the same large-aperture spectra, we also estimated the narrow emission line contamination in these filters to be $\sim 30$ for both of the filters."
 The F275W filter is primarily affected by the Mel AP line and the F312W filter by [OIT| A372T7À.. INeVIA3126. and [NeV]A3316 lines.," The F275W filter is primarily affected by the MgII $\lambda$ line and the F342W filter by [OII] $\lambda$, $\lambda$ 3426, and $\lambda$ 3346 lines."
 This affects the absolute flux measurement of the coutiunua accordingly., This affects the absolute flux measurement of the continuum accordingly.
 For small spatial bius. the line contanunation could be cifferent from this estimation.," For small spatial bins, the line contamination could be different from this estimation."
 Tn terms of P measurement. the line contamination siuplv results im diluting P. since the narrow lines are not strongly. polarized. [essentially only contaiuiug the foreground iuterstellay polarization in omB Galaxy5.spwy {seeOQ below:DMJ SchnüdtCH MillerHIu 1985.. GoodrichMTe 11992).* althoughn theyAX could hxD slightlyVo- polarizedqvo intrinsically1⋅⋅- (Trany. 10471995]].," In terms of $P$ measurement, the line contamination simply results in diluting $P$, since the narrow lines are not strongly polarized [essentially only containing the foreground interstellar polarization in our Galaxy (see below; Schmidt Miller 1985, Goodrich 1992), although they could be slightly polarized intrinsically (Tran 1995)]."
 TheIE coutauuiiuation by uupolkuized Bues esseutiallv will iof affect the ϐ aud © ineasurociuents (though he λα]. spatial scale variation of the effective ranstnittance would slightly affect the ( aud { neasurements: the resulting uncertaiutv im 2 is estimated to be less than ~ ))., The contamination by unpolarized lines essentially will not affect the $Q$ and $U$ measurements (though the small spatial scale variation of the effective transmittance would slightly affect the $Q$ and $U$ measurements: the resulting uncertainty in $P$ is estimated to be less than $\sim$ ).
 However. our two filters are on the so-called bbunp. which cousists of broad Fell lines aud Bahuer continua plus high-order Baluier emission lines.," However, our two filters are on the so-called bump, which consists of broad FeII lines and Balmer continuum plus high-order Balmer emission lines."
" The relative polarized fiux color nicasuremoenut between different locations would not be affected by these contanunations. since the incident spectrum frou, the hidden nucleus is the same. but the absolute color measurement will be slieltly affected."," The relative polarized flux color measurement between different locations would not be affected by these contaminations, since the incident spectrum from the hidden nucleus is the same, but the absolute color measurement will be slightly affected."
 We will discuss this in refsoc-disc.., We will discuss this in \\ref{sec-disc}.
 The optical interstellar polarization in our Galaxy toward Mk 3 has been estimated to be ~ at PA =132°. from the polarization of the jcarby foreground stars (Seluuidt Miller 1985).," The optical interstellar polarization in our Galaxy toward Mrk 3 has been estimated to be $\sim$ at PA =, from the polarization of the nearby foreground stars (Schmidt Miller 1985)."
 We have corrected our polarization maps for this oreeround polarization. using the Serkowski curve (Sorkowskd. Mathewson. Ford 1975) with the owuneters adopted by Tran (1995) which are sed ou the measurement of Schiuidt Miller.," We have corrected our polarization maps for this foreground polarization, using the Serkowski curve (Serkowski, Mathewson, Ford 1975) with the parameters adopted by Tran (1995) which are based on the measurement of Schmidt Miller."
 The iuases theonel the F275NV and F312W filters are also shifted to cach other., The images through the F275W and F342W filters are also shifted to each other.
 We lave revistored thou by taking cross-correlation of the ceutral ~L” region of the I images produced above. since both images are dominated by the sale chuupy structure in the central region.," We have registered them by taking cross-correlation of the central $\sim 4''$ region of the $I$ images produced above, since both images are dominated by the same clumpy structure in the central region."
 The uncertaintv in this registration is estimated be -E0.5 pixel., The uncertainty in this registration is estimated be $\pm 0.5$ pixel.
 There are various error sources d the FOC oenaging polariuetry., There are various error sources in the FOC imaging polarimetry.
 These are described in detail 1 Nishimoto (1999)., These are described in detail in Kishimoto (1999).
 Briefly. there are four major yomources: (1) statistical error (2) uncertainty in the oenage registrations of the three polarizer images 3) uuncertaintv in the polarizer axes direction (1) ucertaiutv in the relative inteusities throueh each polarizer. mainly frou the differences in the shape of the poiut spread function (PSF) through each polarizer.," Briefly, there are four major sources: (1) statistical error (2) uncertainty in the image registrations of the three polarizer images (3) uncertainty in the polarizer axes direction (4) uncertainty in the relative intensities through each polarizer, mainly from the differences in the shape of the point spread function (PSF) through each polarizer."
 The source (1) becomes a major error source when the svuthetic aperure or binning size for measuring polarization is sniall., The source (4) becomes a major error source when the synthetic aperture or binning size for measuring polarization is small.
" For niuiv cases, the error sources (1) and (1) are larger han others."," For many cases, the error sources (1) and (4) are larger than others."
 For (1).4 PoissonH noiseH isH assumed.," For (1), Poisson noise is assumed."
 The source (1) depends ou the binningH sizeH inH the »olarization: calculations., The source (4) depends on the binning size in the polarization calculations.
": In this: paper. we mainly: use a 10 pixel biu (~ 0,711) and a 10 pixel bin (~ 1757). and adopt uncertainties of aud for he error source (1) iu these bins. respectively (the orlucr is the samme value as iu Nishimoto 1999. aud he latter is an extrapolation from the value for he 10 pixel bin aud the 20 pixel bin)."," In this paper, we mainly use a 10 pixel bin $\sim 0.''14$ ) and a 40 pixel bin $\sim 0.''57$ ), and adopt uncertainties of and for the error source (4) in these bins, respectively (the former is the same value as in Kishimoto 1999, and the latter is an extrapolation from the value for the 10 pixel bin and the 20 pixel bin)."
 In addition ο these error sources. we also added in quadrature of the background. subtraction amount as an error in the counts iu each biuued image. iu order to evaluate the polarization measurement uncertaintv in the diffuse outer regions.," In addition to these error sources, we also added in quadrature of the background subtraction amount as an error in the counts in each binned image, in order to evaluate the polarization measurement uncertainty in the diffuse outer regions."
"Poseἔφη cifectively deteriunes the minimal erain size UTE The next section discusses the dependence of dust properties on μμ. aud eives corresponding values of ""ErFign- ","$f_{esc}f_{igm}$ effectively determines the minimal grain size $a_{min}$ The next section discusses the dependence of dust properties on $a_{min}$, and gives corresponding values of $f_{esc}f_{igm}$ ."
The abscuce of àzz0.1pau gradus would have iuportaut inuplications for the properties of iuterealactic dust., The absence of $a \la 0.1\mic$ grains would have important implications for the properties of intergalactic dust.
 The most commonly used model for Calactic dust is the two component Draine Lee (198bt DL) model consisting of silicate and graphite spheres with a distribution iu radius (as proposed bv Mathis. Bunipl aud. Nordsieck 1977: MRN) of N(ajdaxa77.Q05;un.<aXO25 ym.," The most commonly used model for Galactic dust is the two component Draine Lee (1984; DL) model consisting of silicate and graphite spheres with a distribution in radius (as proposed by Mathis, Rumpl and Nordsieck 1977; MRN) of $N(a)da \propto a^{-3.5},\ 0.005\mic \le a \le
0.25\mic$ ."
" After svuthesizine diclectric fuuctious for both eraphite aud astrouonical silicate’ and assuniug a silicate/eraphite mass ratio ~1. DL demoustrated that the resulting model fits both the observed opacity aud polarization over a wide wavelength range (OLyanziAzz 1000,42). most notable fitting the observed features at 0.2175son and Ἱθμια."," After synthesizing dielectric functions for both graphite and `astronomical silicate' and assuming a silicate/graphite mass ratio $\sim 1$, DL demonstrated that the resulting model fits both the observed opacity and polarization over a wide wavelength range $0.1\mic \la \lambda \la 1000\mic$ ), most notably fitting the observed features at $0.2175\mic$ and $10\mic$."
 This paia cluplovs the DL model not because it is most likely to be correct. but because there is little agreement as to what the correct erain model mieht de.," This paper employs the DL model not because it is most likely to be correct, but because there is little agreement as to what the correct grain model might be."
 The DL model is widely used and familiar. and hopefully (but bx no meaus certainly) captures the esseutial features of the dust.," The DL model is widely used and familiar, and hopefully (but by no means certainly) captures the essential features of the dust."
 Other models are cliscussed briefly. below., Other models are discussed briefly below.
 Au interesting aspect of the AIRN distribution is that while the geometrical cross section (X 607) is dominated by unallaadius erains. the mass (X 47) is dominated by erains of large radii.," An interesting aspect of the MRN distribution is that while the geometrical cross section $\propto a^2$ ) is dominated by small-radius grains, the mass $\propto a^3$ ) is dominated by grains of large radii."
 Thus. removing the very small eraius can affect the opacity curve dramatically. without radically changing the total dust mass.," Thus, removing the very small grains can affect the opacity curve dramatically, without radically changing the total dust mass."
" Figue 2. shows the extinction curve for silicate and eraplüte with the MBN size distribution over e;,iuOCTGg for Ginin=0.005.naeUJ aud Ginin=0.1.0,= 0.25."," Figure \ref{fig-opacs} shows the extinction curve for silicate and graphite with the MRN size distribution over $a_{min} \le a \le a_{max}$ for $a_{min} = 0.005,
a_{max}=0.1$ and $a_{min} = 0.1, a_{max}=0.25$ ."
 These curves use publiclv available extinction data calculated using the method of Laor Draine (1993)., These curves use publicly available extinction data calculated using the method of Laor Draine (1993).
 With the very small erains gone. the eraplite absorption curve becomes quite flat out to A~Lynn. Figures 3. and 1. show the extinction. reddening and mass fraction (relative to the full MBN distribution) of dust distributions with various value of νι," With the very small grains gone, the graphite absorption curve becomes quite flat out to $\lambda \sim 1\mic.$ Figures \ref{fig-props} and \ref{fig-reds} show the extinction, reddening and mass fraction (relative to the full MRN distribution) of dust distributions with various value of $a_{min}$."
 Curves are eiven both for (rest-frame) LOBV)/V reddening concentrated at one redshift. aud for a cosmological dust distribution (as described iu refsec-snace)).," Curves are given both for (rest-frame) $E(B-V)/V$ reddening concentrated at one redshift, and for a cosmological dust distribution (as described in \\ref{sec-snae}) )."
" These show that even iu the (more reddening) integrated extiuction. for e,,;,20.06pau. eraplite erains give very littl (D.Ἐν reddening."," These show that even in the (more reddening) integrated extinction, for $a_{min} \ga 0.06\mic$, graphite grains give very little $(B-V)/V$ reddening."
" Silicate grains do uot become grew for e,,;,<0.2. but the combined silicate|graphite reddening falls bv for Gyi,z0.09110."," Silicate grains do not become grey for $a_{min} \la 0.2$, but the combined silicate+graphite reddening falls by for $a_{min} \ga 0.09\mic$."
 Moreover. this large chauge in the reddening behavior of the dust docs not require a large change im the mass: these -erew dust distributions contain LO554 of the mass of the MBN distribution.," Moreover, this large change in the reddening behavior of the dust does not require a large change in the mass: these `grey' dust distributions contain $40-55\%$ of the mass of the MRN distribution."
 The above conclusions. based on the assumption that dust is characterized by the DL model. may not hold for other dust models.," The above conclusions, based on the assumption that dust is characterized by the DL model, may not hold for other dust models."
 Mathis Whiffen (1989) lave proposed that ealactic eraius are composites of very siuall (a<<0.005jan) silicate. graphite aud amorphous carbou particles.," Mathis Whiffen (1989) have proposed that galactic grains are composites of very small $a \la 0.005\mic$ ) silicate, graphite and amorphous carbon particles."
 These composite erains have a filline factor of (.2.Land correspouding maximal size ~0.90.23qna.," These composite grains have a filling factor of $\sim 0.2-1$ and corresponding maximal size $\sim
0.9 - 0.23\mic$."
 Sputtering would be effective at destroving all sizes of low flliung-factor composite graius. since both gas drag (slowing the graius) and sputtering would be much mere effective than in comparably sizes solid spheres.," Sputtering would be effective at destroying all sizes of low filling-factor composite grains, since both gas drag (slowing the grains) and sputtering would be much more effective than in comparably sizes solid spheres."
 Also. sputtering might teud to ‘cleave’ large. flameutary gradus into simaller ones.," Also, sputtering might tend to `cleave' large, filamentary grains into smaller ones."
 Large flliug-factor particles in this model would be much like the Draine Lee model. although the optical properties of the composite materials would differ from those of pure graphite or silicate.," Large filling-factor particles in this model would be much like the Draine Lee model, although the optical properties of the composite materials would differ from those of pure graphite or silicate."
 Several coreauautle erain imodecls have also been proposed: see e.g. Duley. Jones Williams (1989) and Li Creeubere (1997).," Several core-mantle grain models have also been proposed; see e.g., Duley, Jones Williams (1989) and Li Greenberg (1997)."
 The latter model assuies a three-component imo0del: large silicate core-orgauic refractory imautle dust. verv small carbonaceous egraius. and polvaromatic hivdrocarbous (PATIs).," The latter model assumes a three-component model: large silicate core-organic refractory mantle dust, very small carbonaceous grains, and polyaromatic hydrocarbons (PAHs)."
 The latter two components would presumably be destroved as dust leaves the ealaxy. leaviug the laree core/nmautle erains.," The latter two components would presumably be destroyed as dust leaves the galaxy, leaving the large core/mantle grains."
 Li Greenberg take the size distribution of these grains as Gaussian. stronglv dominated by ~0.142 grams. with piruneters chosen to ft the observed extinction. curve.," Li Greenberg take the size distribution of these grains as Gaussian, strongly dominated by $\sim 0.1\mic$ grains, with parameters chosen to fit the observed extinction curve."
 Such a distribution would be insienificautly affected by. removal of the small or larec-size portions. so intergalactic dust would have properties exemplified by the large core/nanutle erains (these erains will reddenu less than the full three-component model. but only slightly).," Such a distribution would be insignificantly affected by removal of the small or large-size portions, so intergalactic dust would have properties exemplified by the large core/mantle grains (these grains will redden less than the full three-component model, but only slightly)."
 Ou the other haud. it secis that there are good reasous to expect a power-law erain size distribution (Diermaun ILuwit 1979: Mathis Whiffen 1989).," On the other hand, it seems that there are good reasons to expect a power-law grain size distribution (Biermann Harwit 1979; Mathis Whiffen 1989)."
 It would be interesting to investigate whether the model of Li Creeuberg could accommodate a power law distribution (as they assume for the ΡΑΣ aud the very siuiall grains)., It would be interesting to investigate whether the model of Li Greenberg could accommodate a power law distribution (as they assume for the PAHs and the very small grains).
 The Duley. Joucs Williams (1989) model assunes a bimodal erain-size distribution: small silicate core/eraphite coated graius provide UV extinction and the 0.2175jan bump. whereas an MBN distribution of evlindrical silicate grains provides extinction in the IR. with ervey extinction iu UV aud optical.," The Duley, Jones Williams (1989) model assumes a bimodal grain-size distribution: small silicate core/graphite coated grains provide UV extinction and the $0.2175\mic$ bump, whereas an MRN distribution of cylindrical silicate grains provides extinction in the IR, with grey extinction in UV and optical."
 In this model. intergalactic dust (composed of the large silicate grains) would be significantly more erev than ealactic dust. assiuniueg that it can escape.," In this model, intergalactic dust (composed of the large silicate grains) would be significantly more grey than galactic dust, assuming that it can escape."
 Fractal grains (e.g. Wiieht 1987) and needles (e.g. A99 and refereuces therein) provide another possible dust component., Fractal grains (e.g. Wright 1987) and needles (e.g. A99 and references therein) provide another possible dust component.
 Needles aud platelets have been observed im Catured dust (Bradley. Brownlee Veblen 1983). aud might explain very cold’ dust in the ISM. (Reach et al.," Needles and platelets have been observed in captured dust (Bradley, Brownlee Veblen 1983), and might explain `very cold' dust in the ISM (Reach et al."
 1995)., 1995).
 As argued in ΑΘ these erains redden very little (especially if eraphitic) aud absorb with lugh efficiency. hence would be prefereutially ejected by radiation pressure.," As argued in A99 these grains redden very little (especially if graphitic) and absorb with high efficiency, hence would be preferentially ejected by radiation pressure."
 Alone the same lines. DL erains iust be at least somewhat elongated iu order to correctly predict polarization.," Along the same lines, DL grains must be at least somewhat elongated in order to correctly predict polarization."
 Elougated grains are somewhat more erey than spherical eraius of the same mass. ceiving sonie additional support to the ecueral assuniption that there is a sigmificant erevsub-component to interstellar dust.," Elongated grains are somewhat more grey than spherical grains of the same mass, giving some additional support to the general assumption that there is a significant greysub-component to interstellar dust."
 While a different erain mocel nught predict a differcut effect of destroving simall erains. if is also true that any viable erain mniodel must be capable of accommodating," While a different grain model might predict a different effect of destroying small grains, it is also true that any viable grain model must be capable of accommodating"
"where Sops is the observed flux density, Mest is the rest frequency, &a(Lesc) is the rest-frequency dust mass absorption coefficient, T; is the dust temperature, and Ῥήνιοςι, is the Planck blackbody function (Hughesetal. 1997).","where $S_{\rm obs}$ is the observed flux density, $\nu_{\rm rest}$ is the rest frequency, $\kappa_d(\nu_{\rm rest})$ is the rest-frequency dust mass absorption coefficient, $T_d$ is the dust temperature, and $B(\nu_{\rm rest}, T_d)$ is the Planck blackbody function \citep{hugh97}."
". Τα)It is believed that the absorption coefficient varies with frequency as καοςv?, where B lies between 1 and 2 (e.g,Hildebrand1983)."," It is believed that the absorption coefficient varies with frequency as $\kappa_d \propto \nu^{\beta}$, where $\beta$ lies between 1 and 2 \citep[e.g,][]{hild83}."
. We assume &4(125jum)=1.875 m? kg-! (Hildebrand1983)., We assume $\kappa_d(125{\rm \mu m}) = 1.875$ $^2$ $^{-1}$ \citep{hild83}.
" Ty and 6 depend on the properties of the dust, and hence, on the type of galaxy being considered."," $T_d$ and $\beta$ depend on the properties of the dust, and hence, on the type of galaxy being considered."
" Becausethe submm flux is detected only at 850 um (Bergeretal.2003),, Τα and 8 cannot be uniquely determined."," Becausethe submm flux is detected only at 850 $\mu$ m \citep{berg03}, $T_d$ and $\beta$ cannot be uniquely determined."
" We adopt Ty= 30-50 K and 8=1.5, the typical values for local ULIRGs and SMGs (e.g.,Yangetal.2007;Kovacs2006;Coppinetal.2008;Michalowski 2010)."," We adopt $T_d = 30$ –50 K and $\beta = 1.5$, the typical values for local ULIRGs and SMGs \citep[e.g.,][]{yang07, kova06, copp08, mich10}."
. The dust mass is calculated to be M4= (4-10)x105 Mo., The dust mass is calculated to be $M_d = (4$ $10) \times 10^8$ $M_{\odot}$ .
" This is consistent with M4=8.2x10° Mo derived from SED model fit of Michalowskietal.(2008),, where they assume Τα=50 K. From the 2c upper limit of molecular gas mass derived in ??,, the 2e upper limit of molecular gas-to-dust mass ratio is estimated to be 10-20."," This is consistent with $M_d = 8.2 \times 10^8$ $M_{\odot}$ derived from SED model fit of \cite{mich08}, where they assume $T_d = 50$ K. From the $\sigma$ upper limit of molecular gas mass derived in \ref{sec:gas-mass}, the $\sigma$ upper limit of molecular gas-to-dust mass ratio is estimated to be $\sim$ 10–20."
" This is lower than that of other galaxy samples, such as 100-200 of our Galaxy (e.g.,Hildebrand1983) and ~50-a few 100 for spiral galaxies and star-forming galaxies at local to high-redshift (e.g.,Dunneetal.2000;Stevens2005;Kovácsetal.2006;Michalowski 2010).."," This is lower than that of other galaxy samples, such as 100–200 of our Galaxy \citep[e.g.,][]{hild83} and $\sim$ 50–a few 100 for spiral galaxies and star-forming galaxies at local to high-redshift \citep[e.g.,][]{dunn00, stev05, kova06, mich10}."
 We note that the derived molecular gas-to-dust ratio relies on the estimates of both gas mass and dust mass that are themselves quite uncertain., We note that the derived molecular gas-to-dust ratio relies on the estimates of both gas mass and dust mass that are themselves quite uncertain.
" If we adopt a Galactic H» conversion factor for deriving molecular gas mass, the upper limit on molecular gas-to-dust ratio would increase by about a factor of 6."," If we adopt a Galactic $_2$ conversion factor for deriving molecular gas mass, the upper limit on molecular gas-to-dust ratio would increase by about a factor of 6."
" The CO luminosity and the far-infrared (FIR) luminosity are measures of the molecular gas mass and SFR, respectively."," The CO luminosity and the far-infrared (FIR) luminosity are measures of the molecular gas mass and SFR, respectively."
" Therefore, the ratio of indicates how efficiently stars are formed fromLrir/Loo molecular gas and is used as an indicator of star-formation efficiency (SFE;Youngetal.1986)."," Therefore, the ratio of $L_{\rm{FIR}}/L'_{\rm{CO}}$ indicates how efficiently stars are formed from molecular gas and is used as an indicator of star-formation efficiency \citep[SFE;][]{youn86}."
 The 2σ lower limit is Lemg/Loo>6.7x10? Lo (K km s! pc?) ! and is obtained using the FIR luminosity derived by Michalowskietal.(2008)., The $\sigma$ lower limit is $L_{\rm{FIR}}/L'_{\rm{CO}} > 6.7 \times 10^2$ $L_{\odot}$ (K km $^{-1}$ $^2$ $^{-1}$ and is obtained using the FIR luminosity derived by \cite{mich08}.
". This is higher than that of local spiral galaxies (710—100;Youngetal.1996),, LIRGs, and ULIRGs (~afewhundred;Sandersetal.1991;Solomonetal. and is located at the higher end of SMGs and QSOs 1997)(seeSolomon&VandenBout2005,andreferences therein),, indicating that active star formation occurs in the host galaxy."," This is higher than that of local spiral galaxies \citep[$\sim$10--100;][]{youn96}, LIRGs, and ULIRGs \citep[$\sim$a few hundred;][]{sand91, solo97} and is located at the higher end of SMGs and QSOs \citep[see][and references therein]{solo05}, , indicating that active star formation occurs in the host galaxy."
 This is shown in terms of a specific star formation rate (SSFR; SFR per unit stellar , This is shown in terms of a specific star formation rate (SSFR; SFR per unit stellar mass).
"SSFR is considered to be an indicator of current star-formingmass). activity, and its inverse is related to the mass doubling time."," SSFR is considered to be an indicator of current star-forming activity, and its inverse is related to the mass doubling time."
" The SSFR of 12-15 Gyr7! derived in previous studies (Christensenetal.2004;Michalowskietal.2008;Svensson2010) is higher than that of other galaxy populations in the local to high-redshift universe (e.g.,CastroCerónetal.2006)."," The SSFR of 12–15 $^{-1}$ derived in previous studies \citep{chri04, mich08, sven10} is higher than that of other galaxy populations in the local to high-redshift universe \citep[e.g.,][]{cast06}."
". It is known that GRB hosts have higher SSFRs compared to field galaxies (e.g.,Charyetal.2002;Christensen 2009).."," It is known that GRB hosts have higher SSFRs compared to field galaxies \citep[e.g.,][]{char02, chri04, cast06, sava09}. ."
 'The high SFE of this host galaxy is consistentwith the typical properties of GRB hosts., The high SFE of this host galaxy is consistentwith the typical properties of GRB hosts.
" The high SFE could be due to the uncertainty of the CO luminosity derived in this work and/or the FIR luminosity derived from submm emission, and we discuss this issue inthe next section."," The high SFE could be due to the uncertainty of the CO luminosity derived in this work and/or the FIR luminosity derived from submm emission, and we discuss this issue inthe next section."
this paper.. we are interested in. qualifving. theeach — differences between different statistical methods which exist in the literature. and comparing them with a new method we present in Section ??..,"In this paper, we are interested in qualifying the differences between different statistical methods which exist in the literature, and comparing them with a new method we present in Section \ref{sec:saclaymethod}."
 By statistical method. we nean the method which is used to quantifv the sieuificauce of a signal. not the space in which the signal is mcasured.," By statistical method, we mean the method which is used to quantify the significance of a signal, not the space in which the signal is measured."
 Therefore. aud without loss of generality. the review preseuted in Section ??7. sunnuarises methods usine spherical harmonics.," Therefore, and without loss of generality, the review presented in Section \ref{sec:method:review} summarises methods using spherical harmonics."
 We compare the pros and cous of method in Section ??.., We compare the pros and cons of each method in Section \ref{sec:method:vs}.
 We begin by describing how theIu ISW signal— 207cau be measured in spherical ⋅⋅harmonicsMEN iu Sectionoy ?? ," We begin by describing how the ISW signal can be measured in spherical harmonics in Section \ref{sec:method:isw}
 "
spe (as ineasured iu the 1-D decomposition).,kpc (as measured in the 1-D decomposition).
 However. infrared Πασάς of IC 2522 (see Figure 10) reveals that his galaxwv has a bar with a major axis leneth ~2 kpc tthe radius within which the model overcstimates he observed rotational velocities) aud a major-to-munlo0r axis ratio of —2. (," However, infrared imaging of IC 2522 (see Figure 10) reveals that this galaxy has a bar with a major axis length $\sim$ 2 kpc the radius within which the model overestimates the observed rotational velocities) and a major-to-minor axis ratio of $\sim$ 2. ("
It is conunon for new-IB iacine o reveal bars that niv have been hidden due to dust extinction iu an optical image. SSeigar James 1998a: Exkridge et al.,"It is common for near-IR imaging to reveal bars that may have been hidden due to dust extinction in an optical image, Seigar James 1998a; Eskridge et al."
 2000: Seigar 2002: Scigar et al., 2000; Seigar 2002; Seigar et al.
 2003)., 2003).
 The spectroscopic data taken by Matliesvson ct ((1992) were observed with a slit aligned along the major axis of cach galaxy. aud in the case of IC 2522. the major axis of the bar is well aligned with the galaxy major axis.," The spectroscopic data taken by Mathewson et (1992) were observed with a slit aligned along the major axis of each galaxy, and in the case of IC 2522, the major axis of the bar is well aligned with the galaxy major axis."
 The stellar orbits witlin a bar are such that tle dominant motion is parallel to its major-axis AAthanassoula 1992). aud so this will account (to some extent) for the low values of the measured rotation velocities (compared to the modeled values) within a few kpc.," The stellar orbits within a bar are such that the dominant motion is parallel to its major-axis Athanassoula 1992), and so this will account (to some extent) for the low values of the measured rotation velocities (compared to the modeled values) within a few kpc."
 Furthermore. if we double the effective radius of the modeled bulec. the resulting rotation curve is the dashed line in Figure 9.," Furthermore, if we double the effective radius of the modeled bulge, the resulting rotation curve is the dashed line in Figure 9."
 This still fits the outer part of the galaxy rotation curve extremely well. aud the central velocities are not as badly overestimated.," This still fits the outer part of the galaxy rotation curve extremely well, and the central velocities are not as badly overestimated."
 Mocdifviug the mass models iu this way does not affect the trends displayed in Figures G and S. it just affects how well the model reproduces the inner part of the observed rotation curve.," Modifying the mass models in this way does not affect the trends displayed in Figures 6 and 8, it just affects how well the model reproduces the inner part of the observed rotation curve."
 This is probably because the main coustraits we are using to model these galaxies are at a 10 kpe radius. well outside the region where the bulge or bar is dominating the rotational velocities.," This is probably because the main constraints we are using to model these galaxies are at a 10 kpc radius, well outside the region where the bulge or bar is dominating the rotational velocities."
 As a result. the concentrations we determine from our modeling do not depend on the mass distribution asstuucd for the bulee tthe mass distribution within the central few kpc).," As a result, the concentrations we determine from our modeling do not depend on the mass distribution assumed for the bulge the mass distribution within the central few kpc)."
 This approach is. therefore. a powerful aud robust method. because its constraints are relatively iuseusitive to the details of bars versus bulges in the ceutral regions.," This approach is, therefore, a powerful and robust method, because its constraints are relatively insensitive to the details of bars versus bulges in the central regions."
 Tn this paper we have shown that near-intrared aud optical spiral avin pitch augles axe the same. on average. and απ a result we have strenethened the correlation οποσα spiral avin pitch angle aud shear rate originally shown in Seigar et ((2005) and expanded here using optical data.," In this paper we have shown that near-infrared and optical spiral arm pitch angles are the same, on average, and as a result we have strengthened the correlation between spiral arm pitch angle and shear rate originally shown in Seigar et (2005) and expanded here using optical data."
 Using an infall model. we have shown that he use of rates of shear Gvlich can now be derived from spiral aria pitch aneles) allow us to put constraints on he total ceutral mass concentration. the dark matter concentration and the imitial NEW concentration.," Using an infall model, we have shown that the use of rates of shear (which can now be derived from spiral arm pitch angles) allow us to put constraints on the total central mass concentration, the dark matter concentration and the initial NFW concentration."
 Iu sole cases it may be possible to determine if the iufall its to occur adiabatically or non-adiabaticallv. aud this is demonstrated by IC 2522 which has to uuderego nou-adiabatic infall.," In some cases it may be possible to determine if the infall has to occur adiabatically or non-adiabatically, and this is demonstrated by IC 2522 which has to undergo non-adiabatic infall."
 This method can be used to determine the ceutral concentrations of galaxies aud to constrain galaxy formation models in any galaxy that has detectable spiral structure., This method can be used to determine the central concentrations of galaxies and to constrain galaxy formation models in any galaxy that has detectable spiral structure.
 In future papers we will apply our techuique to a large sample of galaxies., In future papers we will apply our technique to a large sample of galaxies.
 Furthermore. suce spiral structure can clearly be secu in disk galaxies out to 2—1 (Ehucercen et 22001). the evolution of ceutral mass concentrations in disk galaxies can be estimated ax a function of look-back time. and we plan to investieate this as well.," Furthermore, since spiral structure can clearly be seen in disk galaxies out to $z\sim 1$ (Elmegreen et 2004), the evolution of central mass concentrations in disk galaxies can be estimated as a function of look-back time, and we plan to investigate this as well."
 Support for this work was provided by NASA through evant nuuber HST-AR-10685.01-À from) the Space Telescope Science. Tustitute. which is operated by the Association of Universities for Researcli in Astrouoniv. Iuc.. under NASA contract NAS5-26555.," Support for this work was provided by NASA through grant number HST-AR-10685.01-A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555."
 This research has macle use of the NASA/TPAC Extragalactic Database (NED) which is) operated by the Jet Propulsion Laboratory. California Institute of Technology. uuder contract with the National Acronautics and Space Achninistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
" This work alko made use of data from the Ohio State University Bright Spiral Calaxy Survey, which was funded by eranuts AST-9217716 aud AST-9617006 frou the United States National Science Foundation. with additional support from the Ohio State University."," This work also made use of data from the Ohio State University Bright Spiral Galaxy Survey, which was funded by grants AST-9217716 and AST-9617006 from the United States National Science Foundation, with additional support from the Ohio State University."
 The authors wish to thank Paolo Salucci for supplving the rotation curve data frou which shear aud he Y5» velocities were derived., The authors wish to thank Paolo Salucci for supplying the rotation curve data from which shear and the $V_{2.2}$ velocities were derived.
 We also wish to show our appreciation to the referee. GGroshbol. for js nanny useful coments.," We also wish to show our appreciation to the referee, Grosbol, for his many useful comments."
often present in these sources. and au appareit increase dn ust rate (mdicated by arrows) when t1e source becomes zduter.,"often present in these sources, and an apparent increase in burst rate (indicated by arrows) when the source becomes fainter."
 Iu coutrast. the lehtcurves of 110 2d 30 show strong variations. axd irsts are onlv observed when the fiux is low.," In contrast, the lightcurves of $-$ 440 and $-$ 30 show strong variations, and bursts are only observed when the flux is low."
 Note that burss would have con easilv detected at the highest obserVOC )orsisteut flux evels of all sources. because those leve sare presumed to o still significantly below the Eddiugtc11 int.," Note that bursts would have been easily detected at the highest observed persistent flux levels of all sources, because those levels are presumed to be still significantly below the Eddington limit."
 To study the burst rate as a functio iof versistent flux we assigned to eaci burst the average WEC-anucasured fiux over the coni]ete observation in which the burst occurred., To study the burst rate as a function of persistent flux we assigned to each burst the average WFC-measured flux over the complete observation in which the burst occurred.
 We also cheesed tie average persistent flux iun a 5-1te tine interva prkx to each burst. but the difference with the aforeimetioned flux is within the errors.," We also checked the average persistent flux in a 5-minute time interval prior to each burst, but the difference with the aforementioned flux is within the errors."
 The persistent flux range was divided iu 5 Or 10 iutervals of equal size., The persistent flux range was divided in 5 or 10 intervals of equal size.
 Oilv the flux rauge of 260. the sole transient source mm our sample. was divided in LO bins with different biu sizes.," Only the flux range of $-$ 260, the sole transient source in our sample, was divided in 10 bins with different bin sizes."
 For cach flux interval we determuue the total exposure time and the number of bursts: the latter with an error equal to the square root of this muuber Gt uo bursts are within au interval upper Πές of confideuce were esinated)., For each flux interval we determined the total exposure time and the number of bursts; the latter with an error equal to the square root of this number (if no bursts are within an interval upper limits of confidence were estimated).
 In rofburstflux we show for cach source the burst rate as a function of observed οποίοι flux (bottom axis) and the derived enerey flix (fyp axis)., In \\ref{burstflux} we show for each source the burst rate as a function of observed photon flux (bottom axis) and the derived energy flux (top axis).
 To get an indication of the conversion of pioton flux to energy flux we eencrated for cach source a Spectruu for each canaleji, To get an indication of the conversion of photon flux to energy flux we generated for each source a spectrum for each campaign.
", We fitted the sSpectrun. asswine a1 absorbe thermal breunisstraliluug inodel. aud we derived a Weal, conversio1 factor over all canupaieus (corrected for absorption). see roftop.."," We fitted the spectrum, assuming an absorbed thermal bremsstrahlung model, and we derived a mean conversion factor over all campaigns (corrected for absorption), see \\ref{top}."
 The smead in the coiversion Actors over all calnpaigns is about for ceich source., The spread in the conversion factors over all campaigns is about for each source.
 In the WEC passband the asstuption of a |xyenisstraihe spectrum is good enough to derive fiuxes: Huxes derived using other models give comparable results., In the WFC passband the assumption of a bremsstrahlung spectrum is good enough to derive fluxes; fluxes derived using other models give comparable results.
conditions JecRe or fay<Ry ds met. the Ejector stage ceases.,"conditions $\R{sh} < \R{G}$ or $\R{sh} < \R{l}$ is met, the Ejector stage ceases."
 After that. matter falls down till its pressure is counterbalancecl by the magnetic field pressure.," After that, matter falls down till its pressure is counterbalanced by the magnetic field pressure."
 The radius at which these pressures are equalized is called the Alfven radius: for the case Ray<fee: and for the opposite., The radius at which these pressures are equalized is called the Alfven radius: for the case $\R{A} < \R{G}$ and for the opposite.
 AL is the accretion rate., $\dot M$ is the accretion rate.
 The Propeller stage begins if ἐν2Ro. where is the corotation radius at whieh the solid. body. rotational velocity. equals the escape velocity.," The Propeller stage begins if $\R{A} > \R{c}$, where is the corotation radius at which the solid body rotational velocity equals the escape velocity."
 At this stage matter is “propelled” away [rom a star. because of its interaction with the magnetosphere.," At this stage matter is “propelled” away from a star, because of its interaction with the magnetosphere."
 For the propeller stage we use the model proposed by2., For the propeller stage we use the model proposed by.
. Phe same approach was also used in PaperLL., The same approach was also used in Paper.
" Phe period derivative can be written as: For a=1 we obtain: where ου is a magnetic dipole moment in units of 10°? € cm7. n is the ISAL number density. epg is the total velocity \a2|στη in units of 10 km toa,—I0kms.| is the sound speed."," The period derivative can be written as: For $\alpha = 1$ we obtain: where $\mu_{30}$ is a magnetic dipole moment in units of $10^{30}$ G $^{-3}$, $n$ is the ISM number density, $v_{10}$ is the total velocity $\sqrt{ a_\mr{s}^2 + v_\mr{rel}^2 }$ 	in units of 10 km $^{-1}$ , $a_\mr{s} = 10\ \kmps$ is the sound speed."
 When a NS spin-downs enough for the condition £2.cRy to be met. a star leaves the Propeller stage and switches to the next stage. depending on the relation between Ay ancl Jic.," When a NS spin-downs enough for the condition $\R{c} > \R{A}$ to be met, a star leaves the Propeller stage and switches to the next stage, depending on the relation between $\R{A}$ and $\R{G}$."
 Note. that in our scenario this can also happen because of changes in the ISM density or in the velocity of a Ns.," Note, that in our scenario this can also happen because of changes in the ISM density or in the velocity of a NS."
 IU BR00Re. then a NS enters. the Ceorotator stage. which is called. so because of similarity of the NS magnetosphere structure to the Earth magnetosphere in the fast solar wind.," If $\R{A} > \R{G}$, then a NS enters the Georotator stage, which is called so because of similarity of the NS magnetosphere structure to the Earth magnetosphere in the fast solar wind."
 At this stage in our model no spin-up/spin-clown mechanisms are taken into account., At this stage in our model no spin-up/spin-down mechanisms are taken into account.
" Otherwise. i£ 24<Re then a star at [irst enters the subsonic Propeller stage. where the main accretion mechanism — the IHavleigh-Tavlor instability. is supressed by high. temperature of an envelope (ie. the gas is “too light"")."," Otherwise, if $\R{A} < \R{G}$ then a star at first enters the subsonic Propeller stage, where the main accretion mechanism – the Rayleigh-Taylor instability – is supressed by high temperature of an envelope (i.e., the gas is “too light”)."
" ""Temperature increases because of heating (a NS loses angular momentum to the envelope and heats it). and decreases because of radiative losses (mainly. bremsstrahlung)."," Temperature increases because of heating (a NS loses angular momentum to the envelope and heats it), and decreases because of radiative losses (mainly bremsstrahlung)."
 Phe spin-down rate at this stage is taken in the following form(7): Note. that P is constant if the field. is not decaving.," The spin-down rate at this stage is taken in the following form: Note, that $\dot P$ is constant if the field is not decaying."
 ANS starts to accrete from the ISM ancl enters the Accretor stage when heating of an envelope due to rotational energv losses by a NS becomes less elfective than bremsstrahlung cooling. and so the matter at the magnetospheric boundary becomes so heavy that the Havleigh-Taylor instability. develops.," A NS starts to accrete from the ISM and enters the Accretor stage when heating of an envelope due to rotational energy losses by a NS becomes less effective than bremsstrahlung cooling, and so the matter at the magnetospheric boundary becomes so heavy that the Rayleigh-Taylor instability develops."
" This occurs at. the critical period.(?):: where £24,i is the Alfven radius in units of 10/7 em."," This occurs at the critical period: where $R_\mr{A,\,10}$ is the Alfven radius in units of $10^{10}$ cm."
 At the Aceretor stage the spin-down is calculated as at the subsonic Propeller stage (eq. 9)).," At the Accretor stage the spin-down is calculated as at the subsonic Propeller stage (eq. \ref{ssP_spindown}) ),"
 and. we neglect. possible quasi equilibrium at this stage., and we neglect possible quasi equilibrium at this stage.
 This is an oversimplification(?).. but as here we are not interested in details of spin properties of Aceretors we neglect some details.," This is an oversimplification, but as here we are not interested in details of spin properties of Accretors we neglect some details."
 We consider two different field distributions., We consider two different field distributions.
 The first is a delta-function., The first is a delta-function.
 As à standard. value we use ου=1. which gives us Bo=1072 €. according to p=DIU.," As a standard value we use $\mu_{30} = 1$, which gives us $B_\mr{eq} = 10^{12}$ G, according to $\mu = B_\mr{eq}R^3$."
 Vhis distribution is chosen to make comparison with the results from Paper L.. The second distribution is a result of the magnetic field. ἄοσαν starting with the soptimal” one from the paper ?., This distribution is chosen to make comparison with the results from Paper I. The second distribution is a result of the magnetic field decay starting with the “optimal” one from the paper.
". ""This ""optimal distribution is the lognormal one with log(Byoe/G])=13.25 and egpel=0.6. where Dye is the value of the poloidal field on the magnetic pole (Di= 2544)."," This “optimal” distribution is the lognormal one with $\langle \log (B_\mr{pole}/[G])\rangle\ = 13.25$ and $\sigma_{\log B_\mr{pole}} = 0.6$, where $B_\mr{pole}$ is the value of the poloidal field on the magnetic pole $B_\mr{pole} = 2 B_\mr{eq}$ )."
 Till the magnetic field reaches some saturation value Bain dHundergoes decay according to where Toman ls the Ohmic characteristic tine. and τη is the typical timescale of the fast.," Till the magnetic field reaches some saturation value $B_\mathrm{min}$ itundergoes decay according to where $\tau_\mr{Ohm}$ is the Ohmic characteristic time, and $\tau_\mr{Hall}$ is the typical timescale of the fast,"
 ~ (7>1000 2009: Rauscher Menou 2010).," $\sim$ $T
\gsim 1000$ 2009; Rauscher Menou 2010)."
 Atmospheric. motions are driven. by. pressure-gradient forces arising from differential heating of the atmosphere., Atmospheric motions are driven by pressure-gradient forces arising from differential heating of the atmosphere.
" A small fraction of the atmospheric. ""available"" enthalpy 15 continuously converted into kinetic energy of the atmospheric motions. which is itself continuously dissipated by (Lorenz 1955. Pearce 1978. Marquet 1991. Goodman 2009)."," A small fraction of the atmospheric ""available"" enthalpy is continuously converted into kinetic energy of the atmospheric motions, which is itself continuously dissipated by (Lorenz 1955, Pearce 1978, Marquet 1991, Goodman 2009)."
 In steady-state. asymptotic. wind speeds are thus reached through a detailed balance between continuous thermal forcing and sustained friction.," In steady-state, asymptotic wind speeds are thus reached through a detailed balance between continuous thermal forcing and sustained friction."
 While the source of wind friction on the Earth. and other Solar System terrestrial planets by extension. is understood to be largely associated with surface drag. the origin of friction in the atmospheres of gaseous giant planets remains a major open question in atmospheric science. even in the Solar System (e.g.. Schneider Liu 2009; Liu et al.," While the source of wind friction on the Earth, and other Solar System terrestrial planets by extension, is understood to be largely associated with surface drag, the origin of friction in the atmospheres of gaseous giant planets remains a major open question in atmospheric science, even in the Solar System (e.g., Schneider Liu 2009; Liu et al."
 2008; Showman et al., 2008; Showman et al.
 2010)., 2010).
 Identifying dominant sources of internal friction in gaseous giant planet atmospheres can thus be as important as adequately modeling their sources of thermal foreing., Identifying dominant sources of internal friction in gaseous giant planet atmospheres can thus be as important as adequately modeling their sources of thermal forcing.
 We show here that magnetic drag on weakly-ionized winds in the predominantly neutral atmospheres of hot Jupiters. which arises from wind interaction with the magnetic field generated in the planet’s bulk interior. is a plausible source of sizable friction. that may need to be accounted for in atmospheric circulation models of hot Jupiters.," We show here that magnetic drag on weakly-ionized winds in the predominantly neutral atmospheres of hot Jupiters, which arises from wind interaction with the magnetic field generated in the planet's bulk interior, is a plausible source of sizable friction, that may need to be accounted for in atmospheric circulation models of hot Jupiters."
 We note that. while this manuscript was being prepared. Batygin Stevenson (2010) completed a study of the closely related ohmie dissipation process associated with the currents induced by magnetic drag.," We note that, while this manuscript was being prepared, Batygin Stevenson (2010) completed a study of the closely related ohmic dissipation process associated with the currents induced by magnetic drag."
 Here. we focus on the role of magnetic drag on atmospheric winds and defer a study of ohmie dissipation to future work.," Here, we focus on the role of magnetic drag on atmospheric winds and defer a study of ohmic dissipation to future work."
 Our study is based on the three dimensional hot Jupiter atmospheric circulation model of HD 209458b_ presented by Rauscher Menou (2010)., Our study is based on the three dimensional hot Jupiter atmospheric circulation model of HD 209458b presented by Rauscher Menou (2010).
 The model provides. at each point in the 3D atmosphere. values for the pressure.," The model provides, at each point in the 3D atmosphere, values for the pressure,"
well as the completeness for individual colours.,well as the completeness for individual colours.
 In all cases we obtained. similar. results for the turnover magnitudes ancl clistribution width within about 0.10 mag. independent of the type of function used.," In all cases we obtained similar results for the turn–over magnitudes and distribution width within about 0.10 mag, independent of the type of function used."
 This gives us confidence in the results ancl provides a measure of the overall error of Less man 0.10 mag., This gives us confidence in the results and provides a measure of the overall error of less than 0.10 mag.
 The results are tabulated in Tab., The results are tabulated in Tab.
 2., 2.
 Foreing a broad function (σον= 1.35) to our data. as oposed by Whitmore (1997) for bright ellipticals. pushes je turnover values to zz0.15 magnitudes fainter but results in unaccetable fits.," Forcing a broad function $\sigma_{Gauss}=1.35$ ) to our data, as proposed by Whitmore (1997) for bright ellipticals, pushes the turn–over values to $\approx 0.15$ magnitudes fainter but results in unaccetable fits."
 Phe width of the GOCLE of NGC 1380 (an ul0 galaxy) is in much better agreement with values found for 1e Milky Wav and M31 (ο. Secker 1992) and fainter carlyvpe galaxies (Ixissler et al., The width of the GCLF of NGC 1380 (an S0 galaxy) is in much better agreement with values found for the Milky Way and M31 (e.g. Secker 1992) and fainter early--type galaxies (Kissler et al.
 1994. Wissler-Patig. Richtler. —ilker 1996). supporting the result from our free fits.," 1994, Kissler-Patig, Richtler, Hilker 1996), supporting the result from our free fits."
 A previous determination ofthe V turn.over magnitude or NGC 1380. was made by Blakeslee Tonry (1996). who clerived. a value of eomy.=.24.05£0.25 or:in disagreement. with our results.," A previous determination of the $V$ turn–over magnitude for NGC 1380 was made by Blakeslee Tonry (1996), who derived a value of $m_V^0=24.05\pm0.25$ in disagreement with our results."
 However. it seems (Blakeslee priv.," However, it seems (Blakeslee priv."
 com. ), com. )
 hat from their V. data alone. they could not correct for à ickground: cluster located. about 30 arcesec. Last of NGC 1380 (see Wissler-Patig et al.," that from their $V$ data alone, they could not correct for a background cluster located about 30 arcsec East of NGC 1380 (see Kissler-Patig et al."
 L997)., 1997).
 Lowe include these xickeround. galaxies (having V. magnitudes between 21 ancl 24 mag). and compute the fit to their magnitude limit. we can reproduce their result in the sense that our peak appears o be shifted by almost half a magnitude fainter.," If we include these background galaxies (having $V$ magnitudes between 21 and 24 mag), and compute the fit to their magnitude limit, we can reproduce their result in the sense that our peak appears to be shifted by almost half a magnitude fainter."
 lt is now well established. that. excluding some small metallicity ancl perhaps some galaxyἵνρο cllects. the absolute turnover of the GCLE is constant for the old clusters in all galaxies (c.g. Whitmore 1997. Harris. 1997).," It is now well established that, excluding some small metallicity and perhaps some galaxy–type effects, the absolute turn–over of the GCLF is constant for the old clusters in all galaxies (e.g. Whitmore 1997, Harris 1997)."
 The absolute peak luminosity can be derived. from. “local” calibrators such as the globular cluster svstems of the Milky Was or M31., The absolute peak luminosity can be derived from “local” calibrators such as the globular cluster systems of the Milky Way or M31.
" While comparing globular clusters in. the Alilky Way and. M31 to those in bright ellipticals is often quoted. as comparing “apples with oranges”. because of 1yossible iglobular cluster polpopulation cillerences. (""galaxy5 ↿∙∖⇁↓≻⋖⋅↼↼⋖⋅∐∎∢⋅≼∙≱∖⊐⋡↿↓↥⋖⋅≼⇍∪⊔↓↓≻⋜⊔⋰↓⊳∖∪⊔⊔↓⋜↧↳∢⋅⊳∖⊔↓∪↓⋅⋖⋅⊳∖∢⊾⊔⊳∖⋖⋅⊲↓⊔↿↓↥⋖⊾ case of NGC€ 1380. classified as an S0 galaxy."," While comparing globular clusters in the Milky Way and M31 to those in bright ellipticals is often quoted as comparing “apples with oranges”, because of possible globular cluster population differences (``galaxy--type'' effects), the comparison makes more sense in the case of NGC 1380 classified as an S0 galaxy."
 The colour distribution of the NGC 1380. elobular clusters is similar to that of the Milkv Way elobular clusters (Ixisslor-Datig et al., The colour distribution of the NGC 1380 globular clusters is similar to that of the Milky Way globular clusters (Kissler-Patig et al.
" 1997). including old blue halo clusters. and. old. red ""ίσο clusters. with only the colour distribution in NGC 1380 extending further to the red."," 1997), including old blue halo clusters, and old red ""bulge"" clusters, with only the colour distribution in NGC 1380 extending further to the red."
 We shall shortly discuss the implications. but. shall first review the absolute turnover luminosities for the Alilkyw Way ancl M31: GCLEs.," We shall shortly discuss the implications, but shall first review the absolute turn--over luminosities for the Milky Way and M31 GCLF's."
 Secker (1992) and Sancage Temumann (1995) recently determined. the turnover values AjI and ALYI forJ M31. and the Milkv. Way., Secker (1992) and Sandage Tammann (1995) recently determined the turn–over values $M_V^0$ and $M_B^0$ for M31 and the Milky Way.
 They respectively found Ady=7.5140.15 and Ay!=7.2040.13. and AJ=7.70+0.20 and Ad=7.604011 for M31 and the Milky Way.," They respectively found $M_V^0=-7.51\pm0.15$ and $M_V^0=-7.29\pm0.13$, and $M_V^0=-7.70\pm0.20$ and $M_V^0=-7.60\pm0.11$ for M31 and the Milky Way."
" While the peak of the GCLE in M31. depends: ""only on the adopted. distance for Ancromeca. the peak of the GCLE in the Alilky Way depends on the clistance moduli adopted for the individual clusters. ic. for our purpose on the absolute magnitude of the horizontal branch and. its metallicity dependence."," While the peak of the GCLF in M31 depends “only” on the adopted distance for Andromeda, the peak of the GCLF in the Milky Way depends on the distance moduli adopted for the individual clusters, i.e. for our purpose on the absolute magnitude of the horizontal branch and its metallicity dependence."
 “Phe former large uncertainties are rellected. in the discrepant. values of Seeker ancl Sandage Tammann., The former large uncertainties are reflected in the discrepant values of Secker and Sandage Tammann.
 However. recently Reid (1997) and Gratton et al. (," However, recently Reid (1997) and Gratton et al. ("
1997). derived distances to several globular clusters » attaching their main sequences to nearby subcwarls whose parallaxes had been measured. with high precision wHIPPARBCOS.,1997) derived distances to several globular clusters by attaching their main sequences to nearby subdwarfs whose parallaxes had been measured with high precision by.
 Their results support à. dependence. of he absolute horizontal branch luminosity on the metallicity of the type: Ady(LB)=0.29(+0.09)-(be1I]|.1.5)|).43(+40.04)., Their results support a dependence of the absolute horizontal branch luminosity on the metallicity of the type: $M_V(HB)=0.29(\pm0.09)\cdot({\rm [Fe/H]} + 1.5) + 0.43(\pm 0.04)$ .
 We therefore decided to re-fit the GCLE of the Alilky Way in D. V. and 2 using the new distance implied w this relation.," We therefore decided to re-fit the GCLF of the Milky Way in $B$, $V$, and $R$ using the new distance implied by this relation."
 We used. the MeMaster: globular cluster. database (Llarris 1996) compiling data for 146 elobular clusters in he Milkv Way., We used the McMaster globular cluster database (Harris 1996) compiling data for 146 globular clusters in the Milky Way.
 We corrected. for reddening according to ueke Lebolsky (1985). ancl derived. distances using the relation mentioned above to derive absolute D. V anc IH magnitudes for all clusters.," We corrected for reddening according to Rieke Lebofsky (1985), and derived distances using the relation mentioned above to derive absolute $B$, $V$ and $R$ magnitudes for all clusters."
 The. resulting. luminosity. unctions are. shown in Fig., The resulting luminosity functions are shown in Fig.
 5. together with the bes Gaussian [its.," 5, together with the best Gaussian fits."
 The mean [from various fits to cilleren xnnings with both Gaussian and ἐς functions. and. various subsamples (excluding the most. reddened: clusters). are isted in Tab. 3..," The mean from various fits to different binnings with both Gaussian and $t_5$ functions, and various subsamples (excluding the most reddened clusters), are listed in Tab. \ref{tab.mw_turnover},"
 the errors are given as clispersions arounmc he mean. without considering any systematic error.," the errors are given as dispersions around the mean, without considering any systematic error."
 The errors in the individual determinations are twpically of the order 0.07 mag. as shown in the table.," The errors in the individual determinations are typically of the order 0.07 mag, as shown in the table."
 Varving the binning ancl subsamples results in tvpical errors of the same order. eading to a total random error of 0.10 mag.," Varying the binning and subsamples results in typical errors of the same order, leading to a total random error of 0.10 mag."
 Llowever we ive to account for any systematic error introduced. by our Alc οΕΕ relation., However we have to account for any systematic error introduced by our $M_V(HB)$ –[Fe/H] relation.
 We therefore recomputed all distances for FusiPecci's ct al. (, We therefore recomputed all distances for Fusi–Pecci's et al. (
"1996) relation. derived rowever from M31. clusters. and implving a much weaker metallicity dependence Af,(10)=0.13(£0.07)-Cke/1)| ).95(£0.09)] (sce also Carney et al.","1996) relation, derived however from M31 clusters, and implying a much weaker metallicity dependence $M_V(HB)=0.13(\pm0.07)
\cdot({\rm [Fe/H]}) + 0.95(\pm 0.09)$ ] (see also Carney et al."
 1992)., 1992).
 We then derive mean turnover values svstematicallyfazer by about 0.2 mag., We then derive mean turn–over values systematically by about 0.2 mag.
 The above two relations span the range currently under debate., The above two relations span the range currently under debate.
 In the following we will adopt the relation derived or the Alilky Way clusters using the Cuatton et al. (, In the following we will adopt the relation derived for the Milky Way clusters using the Gratton et al. (
1997) relation. and keep in mind a possible systematic error of the urnover values of up to. 0.2 mag.,"1997) relation, and keep in mind a possible systematic error of the turn–over values of up to –0.2 mag."
 Our final result for the Milky Wav AJ= 7.6240.10] compares well with the average of the values derived for M31 ov Secker (1992) and Sandage Tammann (1995) (418= 7.614£0.13)., Our final result for the Milky Way $M_V^0=-7.62\pm0.10$ ] compares well with the average of the values derived for M31 by Secker (1992) and Sandage Tammann (1995) $M_V^0=-7.61\pm0.13$ ).
 By combining our Milky Way results with the urnover magnitudes of Tab., By combining our Milky Way results with the turn–over magnitudes of Tab.
 2. we find," 2, we find"
with probabilities 4.4D?N and 2.Nrespectively. Themomenta of the recombined hadrons ar,"mass shell, we multiply the momenta of all produced hadrons by a common factor so that"
with probabilities 4.4D?N and 2.Nrespectively. Themomenta of the recombined hadrons are,"mass shell, we multiply the momenta of all produced hadrons by a common factor so that"
where N4(£) is the number of different. baselines corresponding to multipole £.,where $N_\neq(\ell)$ is the number of different baselines corresponding to multipole $\ell$.
" The variance of this estimator is (C, is the power spectrum): where we used Wick's theorem to caleulate the fourth order moments and the fact that each of the ΑΛ) different baselines contributing to C; is measured independantly so that their variances add linearly.", The variance of this estimator is $\mathsf{C}_\ell$ is the power spectrum): where we used Wick's theorem to calculate the fourth order moments and the fact that each of the $N_\neq(\ell)$ different baselines contributing to $C_\ell$ is measured independantly so that their variances add linearly.
 If one makes the additional assumption that all of these different baselines have the same noise variance Nij=σηó;;. the error on the power spectrum reads: which is the equivalent for interferometry of the well known imaging-oriented. Knox formula (Knox. 1997)).," If one makes the additional assumption that all of these different baselines have the same noise variance $\mathcal{N}_{ij}=\sigma_\mathsf{V}^2~\delta_{ij}$, the error on the power spectrum reads: which is the equivalent for interferometry of the well known imaging-oriented Knox formula \cite{knox}) )."
 The expression for N(£) is the number of different modes one can have access to at a given f., The expression for $N_\neq(\ell)$ is the number of different modes one can have access to at a given $\ell$.
 We assume that we are considering à bin in visibility space Au=A£/27 centered at u: the number of modes is the ratio between the available surface of the bin zuAu (we only consider the top part of the Fourier plane as the modes in the bottom part are the same) to the effective surface of the beam in Fourier space 2zo;: we thereforeποπ find the same formula as for an imager. except for the noise part of course: where the noise on the visibilities is taken from (Charlassieretal.. 2008)).," We assume that we are considering a bin in visibility space $\Delta\mathrm{u}=\Delta\ell /2\pi$ centered at $\mathrm{u}$; the number of modes is the ratio between the available surface of the bin $\pi \mathrm{u}\Delta\mathrm{u}$ (we only consider the top part of the Fourier plane as the modes in the bottom part are the same) to the effective surface of the beam in Fourier space $2\pi \sigma_\mathrm{u}^2$: we therefore find the same formula as for an imager, except for the noise part of course: where the noise on the visibilities is taken from \cite{coherentsummation}) )."
 The above expression. is the same for both heterodyne interferometry and direct imaging. only the expression of σν changes.," The above expression is the same for both heterodyne interferometry and direct imaging, only the expression of $\sigma_\mathsf{V}$ changes."
" For heterodyne interferometry. if the noise equivalent temperature of one of the two input channels of the correlator is NETy). the noise on the reconstructed Stokes parameter visibility calculated with NV, time samples and averaged over Nog equivalent baselines is given by: The first factor 2 comes from the multiplication of the two sine waves. a factor V2 from the fact that two correlators are involved when calculating Stokes parameters visibilities. another factor V2 appears because we are talking about the noise on the complex visibility instead of its real or imaginary part."," For heterodyne interferometry, if the noise equivalent temperature of one of the two input channels of the correlator is $\mathrm{NET_{HI}}$ , the noise on the reconstructed Stokes parameter visibility calculated with $N_t$ time samples and averaged over $N_\mathrm{eq}$ equivalent baselines is given by: The first factor 2 comes from the multiplication of the two sine waves, a factor $\sqrt{2}$ from the fact that two correlators are involved when calculating Stokes parameters visibilities, another factor $\sqrt{2}$ appears because we are talking about the noise on the complex visibility instead of its real or imaginary part."
 Finally a factor 1/V2 is regained because two sets of independent measurements of the Stokes parameters visibilities can be simultaneously obtained if one forms all the possible complex correlations., Finally a factor $1/\sqrt{2}$ is regained because two sets of independent measurements of the Stokes parameters visibilities can be simultaneously obtained if one forms all the possible complex correlations.
 The expression we find is in agreement with (HobsonandMaguetjo.1996)) and (Whiteetal..1999))., The expression we find is in agreement with \cite{hobson}) ) and \cite{white}) ).
 In the direct imaging case. the error on the power spectrum is taken from (Knox.1997)) and adapted to partial sky polarized measurements: where B;=exp(-Cos.i/2) is the imager’s beam transfer function.," In the direct imaging case, the error on the power spectrum is taken from \cite{knox}) ) and adapted to partial sky polarized measurements: where $B_\ell=\exp(-\ell^2\sigma_\mathrm{beam}^2/2)$ is the imager's beam transfer function."
" In the imaging case Q is of course defined as the solid angle covered on the sky Q=df, (the fact that the integral of the primary beam is the total solid angle covered on the sky is specific to interferometry).", In the imaging case $\Omega$ is of course defined as the solid angle covered on the sky $\Omega=4\pi f_\mathrm{sky}$ (the fact that the integral of the primary beam is the total solid angle covered on the sky is specific to interferometry).
 Note that the factor of 4 is obtained by a factor of 2 on the polarized NET for polarization sensitive bolometers and another factor of 2 due. as before. to the fact that Q and U cannot be obtained at the same time.," Note that the factor of 4 is obtained by a factor of 2 on the polarized NET for polarization sensitive bolometers and another factor of 2 due, as before, to the fact that $Q$ and $U$ cannot be obtained at the same time."
 As the sample variance term is exactly the same whatever technique is used (as expected). we are only interested in comparing the noise terms.," As the sample variance term is exactly the same whatever technique is used (as expected), we are only interested in comparing the noise terms."
 We assume in the following that we are comparing three instruments observing the same fraction of the sky fy from the ground for the same duration: The choice of 90GHz ts motivated by the fact that a packed array of 20 degrees FWHM primary horns interferometer operating at these frequencies would cover the multipole range relevant for primordial B-mode signals (25<€ 200)., We assume in the following that we are comparing three instruments observing the same fraction of the sky $f_\mathrm{sky}$ from the ground for the same duration: The choice of 90GHz is motivated by the fact that a packed array of $~20$ degrees FWHM primary horns interferometer operating at these frequencies would cover the multipole range relevant for primordial B-mode signals $25<\ell<200$ ).
 It is also at these frequencies that coherent and bolometric detectors can operate simultaneously., It is also at these frequencies that coherent and bolometric detectors can operate simultaneously.
 We will use the direct imager as à reference and calculate the ratio of the direct imager’s noise error to that of the interferometers., We will use the direct imager as a reference and calculate the ratio of the direct imager's noise error to that of the interferometers.
 This ratio therefore should be less than one if the direct imager is more sensitive from the strict noise point of For the bolometric interferometer. onegets: as the NET are the same for the bolometers used for imaging or for bolometric interferometry.," This ratio therefore should be less than one if the direct imager is more sensitive from the strict noise point of For the bolometric interferometer, onegets: as the $\mathrm{NET}$ are the same for the bolometers used for imaging or for bolometric interferometry."
larger) are prescut elsewhere iu the spectrum.,larger) are present elsewhere in the spectrum.
 The claim that the sidereal aud solar diurnal waves are real is based upon its occurrence at a frequency of “a prio interest aud on the stability of its amplitude aud phase with tine., The claim that the sidereal and solar diurnal waves are real is based upon its occurrence at a frequency of “a priori” interest and on the stability of its amplitude and phase with time.
" We fud that the amplitudes aud the probabilities for the null lbypothesis computed by the two methods are in fair agreement with the oues obtained using a staudard ""folding"" iiethod |9]..", We find that the amplitudes and the probabilities for the null hypothesis computed by the two methods are in fair agreement with the ones obtained using a standard “folding” method \cite{MACanis}.
 The first method used in searching for correlations iu the arrival times was the study of the time iuterval distribution., The first method used in searching for correlations in the arrival times was the study of the time interval distribution.
 For cach 10non arriving at time ty we calculated the distribution of the time iuterval elapsed vetween the first mon ty and the next five mmons: t;-ty. i21.....5. see Fig. 3..," For each muon arriving at time ${_0}$ we calculated the distribution of the time interval elapsed between the first muon ${_0}$ and the next five muons: ${_i}$ ${_0}$, i=1,...,5, see Fig. \ref{fig:3}."
. À complete analysis was nblished in [ü0].., A complete analysis was published in \cite{erlangen}.
" Tere we report the results for the direction bands with 07< RA<360° and 25« decl «DO"" that include the Οτο X-3 region.", Here we report the results for the direction bands with $0^\circ <$ $< 360^\circ$ and $<$ decl $<50^\circ$ that include the Cyg X-3 region.
 The experimental distributions show some deviations frou the uuon random arrival expectation., The experimental distributions show some deviations from the muon random arrival expectation.
 The probability computed using the Noluoeorov-Suurnoy test shows some disagreement (prob=0.38) but the available statistics is too poor to reach clear conclusions., The probability computed using the Kolmogorov-Smirnov test shows some disagreement (prob=0.38) but the available statistics is too poor to reach clear conclusions.
 Scan statistics is a powerful method to search for bursts of events., Scan statistics is a powerful method to search for bursts of events.
 It is a bin-free method aud it provides unbiased results when data are analysed (sce [0| and references therein}., It is a bin-free method and it provides unbiased results when data are analysed (see \cite{scan} and references therein).
 We used scan statistics in the following way: for cach run 7. let [.4;.B;| be the time interval ranging from the start aud the cud of the iun.," We used scan statistics in the following way: for each run $i$, let $[A_i,B_i]$ be the time interval ranging from the start and the end of the run."
 We open a “time window” of fixed length ο and scau the interval [A;.Bj] counting the απο of events falling inside a.," We open a “time window” of fixed length $w$ and scan the interval $[A_i,B_i]$ counting the number of events falling inside $w$."
 Ay is the maxinuun nuuber of events recorded during the scan., $k_i$ is the maximum number of events recorded during the scan.
 Finally. for each rum. we compute the probability P; that a statistical fluctuation would produce a burst of eveuts as large as &;.," Finally, for each run, we compute the probability $P_i$ that a statistical fluctuation would produce a burst of events as large as $k_i$."
 The ouly choice is the size of w., The only choice is the size of $w$ .
" We tried different sizes («= 3008. 5 unin and 15 miu) aud for each of them we analysed the probability distribution Z5. i21. N,4,."," We tried different sizes $w=30$ s, 5 min and 15 min) and for each of them we analysed the probability distribution $P_i$, i=1, $_{run}$."
 Iu Fig., In Fig.
 | we show the probability distribution for the 6113 ruus surviving our cuts: ο=30 8 above. 5 min at the ceutre and 15 min below.," \ref{fig:4} we show the probability distribution for the 6113 runs surviving our cuts: $w=30$ s above, 5 min at the centre and 15 min below."
 No significant deviations from the null hypothesis is found: we also inspected πιστα. uus with probabilities μπαλα: thui 5.10 aud we found that the “burps” of events were coucentratednear the beeimuine or eud of the runs., No significant deviations from the null hypothesis is found; we also inspected unusual runs with probabilities smaller than $5\cdot 10^{-4}$ and we found that the “bumps” of events were concentratednear the beginning or end of the runs.
"is the effective Landé factor, e is the electron charge, 4 is the wavelength, m, the electron mass, c the speed of light, d//dA is the derivative of Stokes 7, and (B;) is the mean longitudinal magnetic field.","is the effective Landé factor, $e$ is the electron charge, $\lambda$ is the wavelength, $m_e$ the electron mass, $c$ the speed of light, ${{\rm d}I/{\rm d}\lambda}$ is the derivative of Stokes $I$, and $\left<B_{\rm z}\right>$ is the mean longitudinal magnetic field."
 An initial frequency analysis was performed on the longitudinal magnetic field measurements using a non-linear least-squares fit of the multiple harmonics utilizing the Levenberg-Marquardt method (Press et citePress92)) with an optional possibility of pre-whitening of the trial harmonics., An initial frequency analysis was performed on the longitudinal magnetic field measurements using a non-linear least-squares fit of the multiple harmonics utilizing the Levenberg-Marquardt method (Press et \\cite{Press92}) ) with an optional possibility of pre-whitening of the trial harmonics.
 To detect the most probable period we calculated the frequency spectrum for the same harmonic with a number of trial frequencies by solving the linear least-squares problem., To detect the most probable period we calculated the frequency spectrum for the same harmonic with a number of trial frequencies by solving the linear least-squares problem.
" At each trial frequency we performed a statistical test of the null hypothesis for the absence of periodicity (Seber 1977)), ttesting that all harmonic amplitudes are at zero."," At each trial frequency we performed a statistical test of the null hypothesis for the absence of periodicity (Seber \cite{Seber77}) ), testing that all harmonic amplitudes are at zero."
" The resulting amplitude spectrum clearly showed a dominant peak with an equivalent period of dd. To increase the accuracy of the rotation period determination and to exclude the presence of other periods, we used photometric data that include 920 V-band and 539 I-band observations from ASAS (Pojmafisski 2002)) and 1426 R-band observations from the robotic telescope Pi of the Sky (Burd et al. 2005;;"," The resulting amplitude spectrum clearly showed a dominant peak with an equivalent period of d. To increase the accuracy of the rotation period determination and to exclude the presence of other periods, we used photometric data that include 920 $V$ -band and 539 $I$ -band observations from ASAS (Pojmańsski \cite{pojm02}) ) and 1426 $R$ -band observations from the robotic telescope Pi of the Sky (Burd et al. \cite{burd05};"
 Malek et al. 2010))., Malek et al. \cite{malek10}) ).
" Further, 78 triads of measurements (UBV bands) over eight nights with internal accuracy of 9.4, 6.4, and mmmag were obtained in South Africa Astrophysical Observatory (SAAO) in April 2010."," Further, 78 triads of measurements $\mathit{UBV}$ bands) over eight nights with internal accuracy of 9.4, 6.4, and mmag were obtained in South Africa Astrophysical Observatory (SAAO) in April 2010."
" Combining the magnetic and photometric data, and using the method of Mikulá et al. (2010)),"," Combining the magnetic and photometric data, and using the method of Mikul\'{a}\\v{s}eek et al. \cite{zdenek10}) ),"
" we obtain The corresponding periodogram and the light curve variations in the U, B, V, R, and J bands are presented in Figs."," we obtain The corresponding periodogram and the light curve variations in the $U$, $B$, $V$, $R$, and $I$ bands are presented in Figs."
 1 and 2.., \ref{fig:period} and \ref{fig:krivky}.
" The full description of the photometric analysis is given in Appendices A and B. A very asymmetrical shape of the R-band light curve, with a deeper minimum at phases 0.15—0.30 and large scatter at the phase 0.85 is probably related to a specific wavelength range covered by this band, which includes the Ho emission line."," The full description of the photometric analysis is given in Appendices A and B. A very asymmetrical shape of the $R$ -band light curve, with a deeper minimum at phases 0.15–0.30 and large scatter at the phase 0.85 is probably related to a specific wavelength range covered by this band, which includes the $\alpha$ emission line."
" As we showed in our previous work, this line is doubled-peaked and strongly variable (see FFig."," As we showed in our previous work, this line is doubled-peaked and strongly variable (see Fig."
 1 in Hubrig et citeHubrig10)), 1 in Hubrig et \\cite{Hubrig10}) ).
" The radial velocity of the blue component changes from --33.6 to —67.5kkmss! whereas the red component, which actually appears triple in the phase 0.17, is shifted by 25.5 to ss~'."," The radial velocity of the blue component changes from $-$ 33.6 to $-$ $^{-1}$ whereas the red component, which actually appears triple in the phase 0.17, is shifted by 25.5 to $^{-1}$."
 Our measurements of the Ha emission line flux over the rotation cycle on available HARPS and UVES spectra presented in Fig., Our measurements of the $\alpha$ emission line flux over the rotation cycle on available HARPS and UVES spectra presented in Fig.
 3 do not contradict this proposition., \ref{fig:phaseEW} do not contradict this proposition.
" However, the secondary minimum in the emission flux appears at phase 0.74."," However, the secondary minimum in the emission flux appears at phase 0.74."
" The phases of the minima in the measured values roughly coincide with the phases where the longitudinal field approaches zero value, cclose to the magnetic equator."," The phases of the minima in the measured values roughly coincide with the phases where the longitudinal field approaches zero value, close to the magnetic equator."
Local helioseismology has become an important tool to study solar interior structures and dynamics.,Local helioseismology has become an important tool to study solar interior structures and dynamics.
" Significant progress has been made recently. na deriving subsurface structures and flow fields of sunspots (Kosovichev,Duvall.&ScherrerMetal. 2002).. inferring large scale subsurface flows (Haberetal.2002;004;Kommetal. 2004)., and imaging solar far side active regions (Lindsey&Braun2000:Braun&Lindsey 2001).. by use of different local helioseismological techniques, including time- helioseismology. ring-diagram analysis. acoustic imaging and helioseismic holography."," Significant progress has been made recently, e.g., deriving subsurface structures and flow fields of sunspots \citep{kos00, zha01, sun02}, inferring large scale subsurface flows \citep{hab02, zha04, kom04}, and imaging solar far side active regions \citep{lin00, bra01}, by use of different local helioseismological techniques, including time-distance helioseismology, ring-diagram analysis, acoustic imaging and helioseismic holography."
" Meanwhile, with the advancement of scientific investigations, specific cautions are also taken on interpreting local helioseismology observations, which include etforts to refine time-distance measurement (Gizon&Birch 2004),, to improve accuracy of modeling and interpreting observations (Birch&Felder2004;Hindmanetal.2005).. and to address some potential systematic effects in measurements, such as ""inclined magnetic field effect"" (Schunkeretal.2005).. “showerglass effect"" (Lindsey&Braun2005a,b).. and “masking effect"" caused by acoustic power deficit in sunspots (Rajaguru,Zhao.&Duvall2005)."," Meanwhile, with the advancement of scientific investigations, specific cautions are also taken on interpreting local helioseismology observations, which include efforts to refine time-distance measurement \citep{giz04}, , to improve accuracy of modeling and interpreting observations \citep{bir04,
hin05}, and to address some potential systematic effects in measurements, such as “inclined magnetic field effect” \citep{sch05}, “showerglass effect” \citep{lin05a,lin05b}, and “masking effect” caused by acoustic power deficit in sunspots \citep{raj05}."
. Both the inclined magnetic field effect and showerelass effect were first observed by use of the helioseismic holography technique., Both the inclined magnetic field effect and showerglass effect were first observed by use of the helioseismic holography technique.
" By measuring phase shifts obtained from the so-called “local control correlation"" phase-sensitive holography (Lindsey&Braun2005b) inside sunspot penumbra when the sunspot was at different locations on the solar disk, Schunkeretal.(2005) found that ingression acoustic phase shifts, which correspond to the ingoing travel times in measurement, vary with different viewing angles."," By measuring phase shifts obtained from the so-called “local control correlation” phase-sensitive holography \citep{lin05b} inside sunspot penumbra when the sunspot was at different locations on the solar disk, \citet{sch05} found that ingression acoustic phase shifts, which correspond to the ingoing travel times in time-distance measurement, vary with different viewing angles."
 They suggested that these phase shifts might be due to the inclination of magnetic field lines relative to the line-of-sight direction., They suggested that these phase shifts might be due to the inclination of magnetic field lines relative to the line-of-sight direction.
" They argued that the inclined magnetic field might cause an elliptic photospherie motion, resulting in variations of the observed magnetoacoustic wave with the viewing angle with respect to the field direction."," They argued that the inclined magnetic field might cause an elliptic photospheric motion, resulting in variations of the observed magnetoacoustic wave with the viewing angle with respect to the field direction."
" The other, showerglass effect, has been introduced by Lindsey&Braun(2004,2005a.b)."," The other, showerglass effect, has been introduced by \citet{lin04, lin05a, lin05b}."
". The authors argued that the surface magnetic field may shift the phases of acoustic waves, and that the phase shifts function as a sort of acoustic showerglass that impairs the coherence of seismic waves and degrades images of subsurface anomalies."," The authors argued that the surface magnetic field may shift the phases of acoustic waves, and that the phase shifts function as a sort of acoustic showerglass that impairs the coherence of seismic waves and degrades images of subsurface anomalies."
" Unlike the inclined magnetic field effect, which is caused by the inclination of magnetic field and most noticeable in sunspot penumbra close to the solar limb, the showerglass effect exists in wherever magnetic field is present at solar surface."," Unlike the inclined magnetic field effect, which is caused by the inclination of magnetic field and most noticeable in sunspot penumbra close to the solar limb, the showerglass effect exists in wherever magnetic field is present at solar surface."
" Although these observational etfects were found by the helioseismic holography technique, we are interested to know whether the similar effects exist in time-distancee measurements, and how they affect the inversion results from time-distance helioseismology."," Although these observational effects were found by the helioseismic holography technique, we are interested to know whether the similar effects exist in time-distance measurements, and how they affect the inversion results from time-distance helioseismology."
" In this paper, we measure the inclined magnetic field effect by the use of thetime-distance technique on different types of observations of solar oscillations, including MDI Dopplergrams, intensitygrams and line-depth"," In this paper, we measure the inclined magnetic field effect by the use of thetime-distance technique on different types of observations of solar oscillations, including MDI Dopplergrams, intensitygrams and line-depth"
D|V colour index is used here as a suitable indicator or dividing the sample into two subsets. as explained. in Section 6..,"$B-V$ colour index is used here as a suitable indicator for dividing the sample into two subsets, as explained in Section \ref{analysis}."
" There are 12520 ""survey! stars with parallaxes ereater han 10 mas. out of 1182158 entries found in the LHipparcos Catalogue."," There are 12520 `survey' stars with parallaxes greater than 10 mas, out of 118218 entries found in the Hipparcos Catalogue."
 However. only 11009. of these stars have their xwallax uncertainties less than 10 per cent.," However, only 11009 of these stars have their parallax uncertainties less than 10 per cent."
 Finally. for 1007 of them the 5Y colours are known.," Finally, for 11007 of them the $B-V$ colours are known."
 On the other 1and. we find 19467 stars with known radial velocities. out of 18209 entries in the Llipparcos Input Catalogue.," On the other hand, we find 19467 stars with known radial velocities, out of 118209 entries in the Hipparcos Input Catalogue."
 Only 4597 stars are found in both subsets. if the catalogue running numbers are used as a matching criterion (HIP= LIC).," Only 4597 stars are found in both subsets, if the catalogue running numbers are used as a matching criterion $\mbox{HIP}=\mbox{HIC}$ )."
 Before we proceed with our analysis of the velocity distribution. some important points have to be emphasized here concerning the problem of bias.," Before we proceed with our analysis of the velocity distribution, some important points have to be emphasized here concerning the problem of bias."
 First of all. not all spectral classes are equally. represented. in our sample.," First of all, not all spectral classes are equally represented in our sample."
 ThePhe 11Hipparcos cataloguetalogu is essentiallytiall magnitudeenitude |Imited.l which means that we shall have a significant celicieney of ped dwarfs. compared. to the voung earlv-tvpe stars.," The Hipparcos catalogue is essentially magnitude limited, which means that we shall have a significant deficiency of red dwarfs, compared to the young early-type stars."
 The situation is illustrated in Figure L.., The situation is illustrated in Figure \ref{hrdata}.
 A great majority of stars are concentrated around BV—0.5. corresponding to the main-sequence E stars.," A great majority of stars are concentrated around $B-V=0.5$, corresponding to the main-sequence F stars."
 Phere is also a possible concentration of earlier-tvpe stars around AQ. as well as a clistinet peak of Ix giants (red-clump stars on the horizontal branch. to be more precise) around £3|—LO.," There is also a possible concentration of earlier-type stars around A0, as well as a distinct peak of K giants (red-clump stars on the horizontal branch, to be more precise) around $B-V=1.0$."
 This should be kept in mind when drawing any conclusions regarding the stellar ages (see Section 6)). but it will essentially not allect our results.," This should be kept in mind when drawing any conclusions regarding the stellar ages (see Section \ref{analysis}) ), but it will essentially not affect our results."
 Ao possibly more. serious problem. concerning our stellar sample is abias. Dinney ct al. (, A possibly more serious problem concerning our stellar sample is a. Binney et al. (
1997) demonstrated that racial velocities are. predominantIv known for high-proper-motion stars.,1997) demonstrated that radial velocities are predominantly known for high-proper-motion stars.
 I only the stars with known radial velocities are used. then any velocity distribution derived. from such a biased. saniple might. give a false picture and. lead to some wrong conclusions about the local stellar kinematics.," If only the stars with known radial velocities are used, then any velocity distribution derived from such a biased sample might give a false picture and lead to some wrong conclusions about the local stellar kinematics."
 Phat is the reason why many authors today choose not to include the measured racial velocities at all (sec also Dehnen Binney 1998. Dehnen 1998. Crézzé οἱ al.," That is the reason why many authors today choose not to include the measured radial velocities at all (see also Dehnen Binney 1998, Dehnen 1998, Crézzé et al."
 1998. Chereul et al.," 1998, Chereul et al."
" L998.1999),"," 1998,1999)."
 We have checked. for potential kinematic bias in our case. and the result is presented. in Figure 2..," We have checked for potential kinematic bias in our case, and the result is presented in Figure \ref{rvbias}."
" Two istributions are shown as functions of the transverse Pvlocity οἱ=44 px). one for the total sample of 11007 ""Uurvevo stars within LOO pc (V). and the other for the μαas with known radial velocities only (η)."," Two distributions are shown as functions of the transverse velocity $\vtran=4.74\,\mu/\pi$ ), one for the total sample of 11007 `survey' stars within 100 pc $\nbig$ ), and the other for the stars with known radial velocities only $\nsmall$ )."
 The (axis was been divided into 4-kms bins and the stars have en counted in each bin., The $\vtran$ -axis has been divided into $\kms$ bins and the stars have been counted in each bin.
 Wo there was no kinematic bias. ren the probability that a star has a radial velocity should »' constant from bin to bin. and the ratio niΝο would appear as a [lat line.," If there was no kinematic bias, then the probability that a star has a radial velocity should be constant from bin to bin, and the ratio $\nsmall/\nbig$ would appear as a flat line."
 Lt is obvious from Figure 2. that this is not the case for our sample., It is obvious from Figure \ref{rvbias} that this is not the case for our sample.
 While the radial velocities are known for about 40 per cent of the stars at ο=20kms he ratio reaches SO per cent at ej=120kms|.," While the radial velocities are known for about 40 per cent of the stars at $\vtran=20\ \kms$, the ratio reaches 80 per cent at $\vtran=120\ \kms$."
 However. he effect. becomes a real problem only atvelocities. above TO SO kms.4+. as easily seen from the ciagram.," However, the effect becomes a real problem only at, above 70 – 80 $\kms$, as easily seen from the diagram."
 Below his limit. the ratio stavs more or less flat. so that we can expect no significant distortions in the inner parts of the velocity distribution. where we shall primarily concentrate our attention.," Below this limit, the ratio stays more or less flat, so that we can expect no significant distortions in the inner parts of the velocity distribution, where we shall primarily concentrate our attention."
 We shall return to this problem again when we, We shall return to this problem again when we
we have shown. the slowing of neutrons within the jet also gives rise to an interesting and potentially detectable neutrino signal.,"we have shown, the slowing of neutrons within the jet also gives rise to an interesting and potentially detectable neutrino signal."
 Neutrinos produced during the slowing of the jet can precede GRB photons by tens to several tens of seconds. depending on the jet dynamics aud stellar progenitor.," Neutrinos produced during the slowing of the jet can precede GRB photons by tens to several tens of seconds, depending on the jet dynamics and stellar progenitor."
 By contrast. neuürinos produced in a jet that is not subsequently. cramatically slowed arrive within 7) seconds of the GRB photons. where i; is the radius where (he jet shocks and produces observed photons.," By contrast, neutrinos produced in a jet that is not subsequently dramatically slowed arrive within $\sim
0.3 (r_{\gamma}/10^{12}{\rm cm})(100/\Gamma_{j}^{(L)})$ seconds of the GRB photons, where $r_{\gamma}$ is the radius where the jet shocks and produces observed photons."
 The observation of GeV neutrinos preceding a GRB flash by ~20 seconds would be an indication that a relativistic jet had been slowed while oplically thick., The observation of GeV neutrinos preceding a GRB flash by $\sim 20$ seconds would be an indication that a relativistic jet had been slowed while optically thick.
 In turn. this could imply that the jet had punched Chrough a stellar envelope.," In turn, this could imply that the jet had punched through a stellar envelope."
 Slowing of the jet within the star also has an impact on the jel composition., Slowing of the jet within the star also has an impact on the jet composition.
 This is because neutron-neutron collisions. whieh dominate the slowing of neutrons if the jet is neutron rich. preferentiallv produce protons.," This is because neutron-neutron collisions, which dominate the slowing of neutrons if the jet is neutron rich, preferentially produce protons."
 Near threshold. for example. roughly 75% of (he inelastic nn(pp) cross section goes toward the production of a p(n) (MeGilletal.1984).," Near threshold, for example, roughly $75\%$ of the inelastic nn(pp) cross section goes toward the production of a p(n) \citep{mcg}."
 A jet born near the central black hole with a very low electron fraction will arrive at large radii with Y.1/2., A jet born near the central black hole with a very low electron fraction will arrive at large radii with $Y_e\sim 1/2$.
 This will influence subsequent nucleosvnthesis in the jet (Pruet.2002:Lemoine 2002).. as well as (he production of neutrinos by inelastic nuclear processes at large radii.," This will influence subsequent nucleosynthesis in the jet \citep{pgf02,lem02}, as well as the production of neutrinos by inelastic nuclear processes at large radii."
 Apart [rom composition effects. (though. the source of GeV neutrinos we have discussed arises independently of other proposed sources of GeV neutrinos in relativistic fireballs.," Apart from composition effects, though, the source of GeV neutrinos we have discussed arises independently of other proposed sources of GeV neutrinos in relativistic fireballs."
 For example. neutron diffusion in internal shocks at r>10!em or the transverse diffusion of neutrons into the jet at larger radii (Mészáros&Rees2000).. and inelastie nuclear collisions during neutron decoupling (Dalicall&Alészaros2000).. can sill occur and produce neutrinos.," For example, neutron diffusion in internal shocks at $r > 10^{11}{\rm cm}$ or the transverse diffusion of neutrons into the jet at larger radii \citep{mes00}, and inelastic nuclear collisions during neutron decoupling \citep{bah00}, can still occur and produce neutrinos."
 In the most optimistic case where all of these various processes occur. the detection rate of neutrinos in a kin-scale detector could be as high as 30 per vear.," In the most optimistic case where all of these various processes occur, the detection rate of neutrinos in a km-scale detector could be as high as 30 per year."
 The author acknowledges helpful correspondence with Weiqua Zhang regarding the conditions in collapsar jets and several useful suggestions from the referee John. Deacom., The author acknowledges helpful correspondence with Weiqun Zhang regarding the conditions in collapsar jets and several useful suggestions from the referee John Beacom.
 This research. has been supported bx the DOE Program [or Scientific Discovery through Advanced Computing (ΡΟΛΟ DE-FCO2-01ERATITG)., This research has been supported by the DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DE-FC02-01ER41176).
 This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore Laboratory under contract W-7405-ENG-43., This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore Laboratory under contract W-7405-ENG-48.
The methylidyne ton CH was among the first molecules to be detected in the interstellar medium (ISM) Douglas&Herzberg (1941).,The methylidyne ion $^+$ was among the first molecules to be detected in the interstellar medium (ISM) \cite{douglas41}.
.. This reactive ton is prevalent in the diffuse ISM with column densities several orders of magnitude above the predictions of UV-driven equilibrium models (seereferencesinGodardetal. 2009)., This reactive ion is prevalent in the diffuse ISM with column densities several orders of magnitude above the predictions of UV-driven equilibrium models \citep[see references in][]{godard09}.
. Apart from the strong emission lines of CH™ detected in both the envelope of the Red Rectangle Hobbsetal.(2004) and NGC 7027 Cernicharoetal.(1997).. all other observations are absorption lines detected at visible wavelengths in the spectra of nearby stars.," Apart from the strong emission lines of $^+$ detected in both the envelope of the Red Rectangle \cite{hobbs04} and NGC 7027 \cite{cernicharo}, all other observations are absorption lines detected at visible wavelengths in the spectra of nearby stars."
 iis à light molecule and its rotational lines lie at submillimeter and far infrared. wavelengths., is a light molecule and its rotational lines lie at submillimeter and far infrared wavelengths.
 The exact frequencies of the rotational transitions of CH. have remained elusive for a long time because of the extreme reactivity of CH™ and the difficulty in isolating it in the laboratory Pearson&Drouin (2006)., The exact frequencies of the rotational transitions of $^+$ have remained elusive for a long time because of the extreme reactivity of $^+$ and the difficulty in isolating it in the laboratory \cite{pearson06}.
. Recent laboratory measurements have led to v=835.137498(20) GHz for the ground-state transition (Amano. 2010).," Recent laboratory measurements have led to $\nu=835.137498(20)$ GHz for the ground-state transition (Amano, 2010)."
 Ground-based astronomical detection of CH-((1-0) is prevented by its proximity to a strong atmospheric line of water vapor., Ground-based astronomical detection of (1-0) is prevented by its proximity to a strong atmospheric line of water vapor.
 The ground-state frequency of the isotopologueCH-.. redshifted by ~5 GHz. has superior sky transmission.," The ground-state frequency of the isotopologue, redshifted by $\sim 5$ GHz, has superior sky transmission."
 It has been detected at the Caltech Submillimeter Observatory towards several massive forming regions of the inner Galaxy (Falgaroneetal.inprep..Falgaroneetal. 2005).," It has been detected at the Caltech Submillimeter Observatory towards several massive star-forming regions of the inner Galaxy \citep[Falgarone et al. in prep., ][]{falgarone05}."
. The abundances averaged along these long lines-of-sight (/os). confirm the high abundances of this species inferred from visible observations in the local ISM. [CH7]]/[H]~ 8x107? on average.," The abundances averaged along these long lines-of-sight ), confirm the high abundances of this species inferred from visible observations in the local ISM, $\sim$ $\times 10^{-9}$ on average."
 In this paper. we report the detection of the ttransition towards the massive star-forming region. DR21I. presented in Sect.," In this paper, we report the detection of the transition towards the massive star-forming region DR21, presented in Sect."
 2., 2.
 The HIFI observations are described in Sect., The HIFI observations are described in Sect.
 3., 3.
 The results. given in Sect.," The results, given in Sect."
 4. are compared to models in Sect.," 4, are compared to models in Sect."
 5., 5.
 The massive star-forming region DR 21 is located in. the Cygnus X complex at an average distance of 1.7 kpe. that of the Cvg OB? stellar association," The massive star-forming region DR 21 is located in the Cygnus X complex at an average distance of 1.7 kpc, that of the Cyg OB2 stellar association"
IIuchtineier et al. C,Huchtmeier et al. (
1980. hereafter ΠΟΛΟ) measured the distribution across NGC 3109 with the Effelsberg radio telescope and a beam size of9'.,"1980, hereafter HSM80) measured the distribution across NGC 3109 with the Effelsberg radio telescope and a beam size of."
. We apply the procedure used for the N-vay detections in the field of the SAIC to the N-rav detectious iu the field of NCC 3109., We apply the procedure used for the X-ray detections in the field of the SMC to the X-ray detections in the field of NGC 3109.
" First we make use of the map of IISMSO which las an extent of «30"".", First we make use of the map of HSM80 which has an extent of $\times$.
 We convert the intensity iuto hydrogen column densities with the equation given iu Dickey Lockman (1990). c£.," We convert the intensity into hydrogen column densities with the equation given in Dickey Lockman (1990), cf."
 Ikaliabka (1999) aud we derive a peak of δι~1.3«1073cm 7., Kahabka (1999) and we derive a peak of $N_{\rm H}\sim1.3\times10^{21}\ {\rm cm}^{-2}$ .
 IISMSO have found that NGC 3109 has a large extent inIT. with an extension (distortion) of the in the SW.," HSM80 have found that NGC 3109 has a large extent in, with an extension (distortion) of the in the SW."
 With our X-ray catalog we cover the whole extent of the of NCC 3109., With our X-ray catalog we cover the whole extent of the of NGC 3109.
" If we restrict the analysis to the inner oof this field aud to sotreos with well coustraied bharduess ratios ÓZIR2 <0.2 then we cau classify 7 sources as ACN,", If we restrict the analysis to the inner of this field and to sources with well constrained hardness ratios $\delta H\!R2\le$ 0.2 then we can classify 7 sources as AGN.
 Aanuch higher resolution map of NCC 3109 with a lean size of hhas been derived by Jobin Carignan (1990. hereafter JC90) with the VLA.," A much higher resolution map of NGC 3109 with a beam size of has been derived by Jobin Carignan (1990, hereafter JC90) with the VLA."
 We now make use of this hieh-resolution inage which we take from plate 67 of JC9O., We now make use of this high-resolution image which we take from plate 67 of JC90.
" The distribution of NGC 3109 has an extent of « 12"".", The distribution of NGC 3109 has an extent of $\times$ .
" The peak lvdrogen column deusitv is ~2.3mehONaqu»10275απD 2; aud the lowest coblunm density: is ""D101?cD7."," The peak hydrogen column density is $\rm \sim2.3\times10^{21}\ {\rm cm}^{-2}$ , and the lowest column density is $\rm 10^{19}\ {\rm cm}^{-2}$."
 Iun Fig., In Fig.
 we show the positious of the catalogedROSATPSPC sources overlaid on the οταν scale image of NGC 3109 aud taken from JC90., we show the positions of the cataloged sources overlaid on the gray scale image of NGC 3109 and taken from JC90.
 We fiud 26ROSATPSPC sources within the contours of JCO90., We find 26 sources within the contours of JC90.
 If we restrict the analvsis to the inner oof this field and to sources with well coustraimed harciucss ratios ο <0.2. then we can classify 3 sotgees (Qumanboer 336. llaid 63) as ACN and 2 sources (anuuber 53 and το) as N-ray binaries.," If we restrict the analysis to the inner of this field and to sources with well constrained hardness ratios $\delta H\!R2\le$ 0.2, then we can classify 3 sources (number 36, 41 and 63) as AGN and 2 sources (number 53 and 73) as X-ray binaries."
 Source 53 may be seen through lugher gas columus while source ην73 is secu hrough lower eas columns (see Fie., Source 53 may be seen through higher gas columns while source 73 is seen through lower gas columns (see Fig.
 | and Equation 11), \ref{ps:hihr2jc} and Equation 11).
 One source (απο 82) can be either class., One source (number 82) can be either class.
 The two sources 52 aud 92 cinnot be classified as AGN or N-vav bilaries., The two sources 52 and 92 cannot be classified as AGN or X-ray binaries.
 Source 92 ay © a foreeround object (cf., Source 92 may be a foreground object (cf.
 Fie. L.," Fig. \ref{ps:hihr2jc},"
 Fig., Fig.
 5 aud Table 2))., \ref{ps:hr1hr2} and Table \ref{tab:classjc}) ).
 Source 52 has sinular larcduess ratios as the LMC SNB 0518-70.1 (Haberl Pietsch 1999)., Source 52 has similar hardness ratios as the LMC SNR 0548-70.4 (Haberl Pietsch 1999).
 It could be a (voung) SNB iu NGC 3109., It could be a (young) SNR in NGC 3109.
 NGC 3109 has a 11a simaller tiu.or Comparable to. the LAIC aud 2 ταν binaries with bhuuinuosities above a few times ~1phergst would be in agreement with extrapolations froinROSAT findigsoe or the EMC (cf.," NGC 3109 has a mass smaller than,or comparable to, the LMC and 2 X-ray binaries with luminosities above a few times $\sim 10^{36}\ {\rm erg\ s}^{-1}$ would be in agreement with extrapolations from findings for the LMC (cf."
 Taber] Pietsch 1999)., Haberl Pietsch 1999).
 There are LlPSPC sources which are projected onto NCC 3109 intrinsic liverogen cohuuus of NW1023an? (tef., There are 14 sources which are projected onto NGC 3109 intrinsic hydrogen columns of $N_{\rm H}\ge 10^{21}\ {\rm cm}^{-2}$ (cf.
 Fie. 3))., Fig. \ref{ps:hijc}) ).
 The largest coluun is derived for source 86 (Nj=2.31021€nP 7), The largest column is derived for source 86 $N_{\rm H} = 2.3\ 10^{21}\ {\rm cm}^{-2}$ ).
 Thisdoc source could be associated with a spiral arii or an region of NGC 3109., This source could be associated with a spiral arm or an region of NGC 3109.
 Tsvo further sources. 53 aud 59. are closeto," Two further sources, 53 and 59, are closeto"
then when fitting the mixing width using ((20)) k will equal the expected mixing layer widths divided by the expected width as a function of Mach numbers as given by Papamoschou Roshko (1988) in their 116.,then when fitting the mixing width using \ref{deltaeqn}) ) $k$ will equal the expected mixing layer widths divided by the expected width as a function of Mach numbers as given by Papamoschou Roshko (1988) in their 16.
" As refLGfig shows, our model reproduces the expect linear growth extremely well across a range of Mach numbers."," As \\ref{LGfig} shows, our model reproduces the expect linear growth extremely well across a range of Mach numbers."
" This range is much larger that seen our simulations, which have typical Mach numbers between 0.3-0.7."," This range is much larger that seen our simulations, which have typical Mach numbers between 0.3-0.7."
 Table 2 summarizes the initial setup parameters for the results in refLGfig as well as the final mixing widths and values for k., Table \ref{c2table} summarizes the initial setup parameters for the results in \\ref{LGfig} as well as the final mixing widths and values for $k$.
 'The growth rate of a shear layer is dependent primarily on the velocity and density ratio on either side of the shear discontinuity., The growth rate of a shear layer is dependent primarily on the velocity and density ratio on either side of the shear discontinuity.
" This dependence has been studied by numerous authors Brown Roshko Slessor (2000) and references(e.g. and as (1974),shown by Soteriou Ghoniem (1995) is within)small and for a given velocity ratio does not alter the growth rate very much."," This dependence has been studied by numerous authors (e.g. Brown Roshko (1974), Slessor (2000) and references within) and as shown by Soteriou Ghoniem (1995) is small and for a given velocity ratio does not alter the growth rate very much."
" Above 104 K the cooling function is primarily controlled by atomic radiation and, at very high temperatures, bremsstrahlung radiation."," 		 	Above $10^4$ K the cooling function is primarily controlled by atomic radiation and, at very high temperatures, bremsstrahlung radiation."
 These contributions are calculated from a table lookup using values calculated using CLOUDY 1998)., These contributions are calculated from a table lookup using values calculated using CLOUDY (Ferland 1998).
 Here we assume Case B recombination (Ferlandand consider only collisional ionization by use of the “coronal equilibrium” command of a metal free gas., Here we assume Case B recombination and consider only collisional ionization by use of the “coronal equilibrium” command of a metal free gas.
 Below 104 K the cooling is dominated by molecular line cooling and metal-line cooling., Below $^{4}$ K the cooling is dominated by molecular line cooling and metal-line cooling.
" Molecular cooling is described in Paper I, but now in addition, we have included"," 	 	Molecular cooling is described in Paper I, but now in addition, we have included"
it is. Claus. requirecl (ο study how Chis flow matches the inner boundary conditions set bv the parameters of (he star.,"it is, thus, required to study how this flow matches the inner boundary conditions set by the parameters of the star."
 The study of the inner boundary laver is presented in (his paper., The study of the inner boundary layer is presented in this paper.
 We present an analvtical sell-similar solution and confirm it numerically., We present an analytical self-similar solution and confirm it numerically.
 Our results are in agreement with other studies (Tilarchuk.Lapidus&Muslimov 1999).. aud max be important for the interpretation of kIIz quasi-perioclic oscillations.," Our results are in agreement with other studies \citep{TLM98,TO99}, and may be important for the interpretation of kHz quasi-periodic oscillations."
 We critically examine the limitations of our model as well., We critically examine the limitations of our model as well.
 We consider viscous hydroclvnamic accretion. onto a compact spinning object with a surface., We consider viscous hydrodynamic accretion onto a compact spinning object with a surface.
" The central object has a radius A,=rR, (where R,=26M,/c2.8x10i em is the Sehwarzehild radius). à mass AL,— mL... and an angular velocity O,=sOjy,. where Ok(R)=(CM,RY? is the Keplerian angular velocity at radius 2 and Oy;=O&(HR,)."," The central object has a radius $R_*=r_* R_g$ (where $R_g=2GM_*/c^2=2.8\times10^5 m$ cm is the Schwarzchild radius), a mass $M_*=m M_{\sun}$ , and an angular velocity $\Omega_*=s \Omega_{K*}$, where $\Omega_K(R)=(GM_*/R^3)^{1/2}$ is the Keplerian angular velocity at radius $R$ and $\Omega_{K*}=\Omega_K(R_*)$ ."
 The mass accretion rate is A=iMygaa. where Maa=1.39x107m g | (corresponding to a radiative efficiency of 1055)).," The mass accretion rate is $\dot M=\dot m\dot M_{\rm Edd}$, where $\dot M_{\rm Edd}=1.39\times10^{18}m$ g $^{-1}$ (corresponding to a radiative efficiency of )."
 We use the height-integrated form of the viscous hydrodynamic equations (Iehimaru1977:Abramowicz.etal.19383:Paczviiski1991:Naravan&Yi1994).," We use the height-integrated form of the viscous hydrodynamic equations \citep{I77,A+88,Paczynski91,NY94}."
 In standard accretion problems (he radial coordinate. 2. varies ürough a large range.," In standard accretion problems the radial coordinate, $R$, varies through a large range."
 Tlence an analytical self-similar solution. in which the gas parameters (density. temperature. and such) scale as power-laws of A. is usually possible in (he region far [rom the boundaries.," Hence an analytical self-similar solution, in which the gas parameters (density, temperature, and such) scale as power-laws of $R$, is usually possible in the region far from the boundaries."
 Unlike the bulk of the flow. the solution to the boundary laver (BL) cannot be obtained in a sell-similar form in terms of the radial coordinate f.," Unlike the bulk of the flow, the solution to the boundary layer (BL) cannot be obtained in a self-similar form in terms of the radial coordinate $R$."
 Ixdeed. the structure of the BL is intvinsically non-sell-similar in 2 because all the gas parameters (e.g.. the temperature. gas density. etc.)," Indeed, the structure of the BL is intrinsically non-self-similar in $R$ because all the gas parameters (e.g., the temperature, gas density, etc.)"
" change very dramatically over a relatively short radial region: Ry,<RS2R,.", change very dramatically over a relatively short radial region: $R_*\le R \la 2 R_*$.
 For instance. the clensity nearly cliverges as one gets close (ο the star surface whereas the temperature decreases to the values well below the virial temperature.," For instance, the density nearly diverges as one gets close to the star surface whereas the temperature decreases to the values well below the virial temperature."
 Such a behavior. however. suggests to look for a self-similar solution in terms of (he distance from the stellar surface. 1.e.. in ternis of D-RB-R..," Such a behavior, however, suggests to look for a self-similar solution in terms of the distance from the stellar surface, i.e., in terms of D=R-R_*."
(1)In our calculation we neglect the effects of radiation transfer and Comptonization., In our calculation we neglect the effects of radiation transfer and Comptonization.
 Thev max be important in hot regions. but will unlikely stronely affect the flow closer to the star. where the temperature of the gas falls below [ewx10? Ix or so (see discussion in Section 1)).," They may be important in hot regions, but will unlikely strongly affect the flow closer to the star, where the temperature of the gas falls below $\times10^{9}$ K or so (see discussion in Section \ref{s:discuss}) )."
 Unlike the hot settling flow case. here we cannotneglect the radial (infall) velocity.," Unlike the hot settling flow case, here we cannotneglect the radial (infall) velocity."
 Weuse the heieht-integrated (6wo-temperature hydrodvnanmic equations. written in (he approximation," Weuse the height-integrated two-temperature hydrodynamic equations, written in the approximation"
close to the total of 1564 entries given in reftconst.. but spuriously so since Hevelius gives no own measurements for 18 of the 1564 entries.,"close to the total of 1564 entries given in \\ref{t:const}, but spuriously so since Hevelius gives no own measurements for 18 of the 1564 entries."
 Hevelius indicates. through an OT number or a position from Tycho. for 915 entries that they are from reft:const)).," Hevelius indicates, through an OT number or a position from Tycho, for 915 entries that they are from \\ref{t:const}) )."
 For 905 of these gglves his own measurements (see refs:brahe))., For 905 of these gives his own measurements (see \\ref{s:brahe}) ).
 To obtain the higher number of 946 stars from the note. we have two options.," To obtain the higher number of 946 stars from the note, we have two options."
 One is to add the 28 stars from theClassis. (, One is to add the 28 stars from the. (
These were also measured by Brahe. according to Kepler. albeit with less accuracy.),"These were also measured by Brahe, according to Kepler, albeit with less accuracy.)"
 This option leaves us with too small a number., This option leaves us with too small a number.
 The other option is to add the 47 entries for which our identification corresponds to an identification inKeplerE., The other option is to add the 47 entries for which our identification corresponds to an identification in.
. This would imply that Hevelius was aware that more stars from his catalogue corresponded to stars in tthan the 915 entries marked by him às such through OT or Tycho position., This would imply that Hevelius was aware that more stars from his catalogue corresponded to stars in than the 915 entries marked by him as such through OT or Tycho position.
 If we subtract from the total number of 1564 entries in aall 962 that have a counterpart in aand further subtract the 28 entries thàt have a counterpart inClassis. we find a number of 574 entries first measured by Hevelius.," If we subtract from the total number of 1564 entries in all 962 that have a counterpart in and further subtract the 28 entries that have a counterpart in, we find a number of 574 entries first measured by Hevelius."
 573 of these are stars. the other one is 331.," 573 of these are stars, the other one is 31."
 Cerberus. Lacerta. Seutum. Sextans and Triangulum Minus. the truly new constellations by Hevelius. contain a total of 36 stars. of which only one possibly corresponds to a star in ((H11328 / K959: the position error of 9959. Is 2755. so à chance coincidence 1s possible).," Cerberus, Lacerta, Scutum, Sextans and Triangulum Minus, the truly new constellations by Hevelius, contain a total of 36 stars, of which only one possibly corresponds to a star in 1328 / K959: the position error of 959 is 5, so a chance coincidence is possible)."
 Monoceros and Camelopardalis. two constellations retained by Hevelius from Planeius. contain twelve and up to fourteen stars fromKeplerE.. respectively reftconst).," Monoceros and Camelopardalis, two constellations retained by Hevelius from Plancius, contain twelve and up to fourteen stars from, respectively \\ref{t:const}) )."
 The four constellations fashioned. by Hevelius from two constellations by Planctus contain up to sixteen stars fromKeplerE., The four constellations fashioned by Hevelius from two constellations by Plancius contain up to sixteen stars from.
. We use the qualification “up to for the stars listed under Ny in reft:const because some of the correspondences between aand mmay be chance comeidences., We use the qualification `up to' for the stars listed under $N_K$ in \\ref{t:const} because some of the correspondences between and may be chance coincidences.
 The six constellations retained of refashioned from Planeius by Hevelius contain 138 stars. so even accepting all 42 correspondences as real. we still find that a large majority of stars in these constellations was first observed by Hevelius.," The six constellations retained of refashioned from Plancius by Hevelius contain 138 stars, so even accepting all 42 correspondences as real, we still find that a large majority of stars in these constellations was first observed by Hevelius."
assumed to be constant in time.,assumed to be constant in time.
 We discuss the validity of this assumption in Section 5., We discuss the validity of this assumption in Section 5.
" Figure 8 shows Tgas as a function of the coremass for Ty= 1000K, f—1, and Zy=0.1,0.3,0.6,and0.8 (solid lines)."," Figure \ref{fig8} shows $\tau_\mathrm{gas}$ as a function of the coremass for $T_\mathrm{h} = 1000\mathrm{K}$ , $f = 1$, and $Z_\mathrm{h} = 0.1,~0.3,~0.6,~\mathrm{and}~0.8$ (solid lines)."
" For comparison, we plot the results for envelopes with the solar abundances: f=0.01 (dashed line) and grain-free (f= 0) envelopes (dotted one)."," For comparison, we plot the results for envelopes with the solar abundances: $f = 0.01$ (dashed line) and grain-free $f = 0$ ) envelopes (dotted one)."
 This figure demonstrates that envelope pollution by icy planetesimals accelerates gas accretion on to the protoplanet significantly., This figure demonstrates that envelope pollution by icy planetesimals accelerates gas accretion on to the protoplanet significantly.
 The acceleration is more effective compared to that by reduction of grain opacities in the envelope., The acceleration is more effective compared to that by reduction of grain opacities in the envelope.
 We do not suppose reduction of grain opacities in the upper envelope in those simulations., We do not suppose reduction of grain opacities in the upper envelope in those simulations.
" In addition to envelope pollution, if we take into account reduction of grain opacities, it gives positive feedback to shorten Tgas (see Table 3))."," In addition to envelope pollution, if we take into account reduction of grain opacities, it gives positive feedback to shorten $\tau_\mathrm{gas}$ (see Table \ref{tbl4}) )."
 Gas giant formation must be finished before disc gas disappears., Gas giant formation must be finished before disc gas disappears.
" The disc lifetime is believed to be 1-10 Myrs based on the disc frequency estimated from near-IR excess (JHK L-band) observations of stars in young clusters (Haisch,Lada,&Lada2001;Hernándezetal.2007)."," The disc lifetime is believed to be 1-10 Myrs based on the disc frequency estimated from near-IR excess $JHKL$ -band) observations of stars in young clusters \citep{Haisch+01,Hernandez+07}."
. We now consider the core masses with Tgas<1Myr as allowable for gas giant formation., We now consider the core masses with $\tau_\mathrm{gas} \leq1\mathrm{Myr}$ as allowable for gas giant formation.
 Minimum core masses (M22) that satisfy the criterion (rg.= 1Myr) are listed in Table 3 for f—1 and f—0.01., Minimum core masses $M^\mathrm{min}_\mathrm{core}$ ) that satisfy the criterion $\tau_\mathrm{gas} = 1\mathrm{Myr}$ ) are listed in Table \ref{tbl4} for $f = 1$ and $f = 0.01$.
 We cannot simulate quasi-static evolution of the protoplanet’senvelope with smaller cores than 0.1Mg because of numerical difficulty., We cannot simulate quasi-static evolution of the protoplanet'senvelope with smaller cores than $0.1M_\oplus$ because of numerical difficulty.
" In such a case, we show M25—0.1Mg@ in Table 3.."," In such a case, we show $M^\mathrm{min}_\mathrm{core} < 0.1M_\oplus$ in Table \ref{tbl4}. ."
" In Fig.9,, we also plot min as a function of Z, for three 71, 1000K (solid), 500K (dashed), and 300K (dotted)."," In \ref{fig9}, , we also plot $M^\mathrm{min}_\mathrm{core}$ as a function of $Z_\mathrm{h}$ for three $T_\mathrm{h}$, $1000\mathrm{K}$ (solid), $500\mathrm{K}$ (dashed), and $300\mathrm{K}$ (dotted)."
" The behaviours of M22 with respect of Z, are quite similar to those of Mc.", The behaviours of $M^\mathrm{min}_\mathrm{core}$ with respect of $Z_\mathrm{h}$ are quite similar to those of $M_\mathrm{crit}$.
 We find that envelope pollution has contributions to hasten Τρας in the similar manner to the lowering of Merit., We find that envelope pollution has contributions to hasten $\tau_\mathrm{gas}$ in the similar manner to the lowering of $M_\mathrm{crit}$.