source,target
 The Parkes radio telescope is part of the Australia Telescope.which is funded by the Conunomvealth of Australia for operation as a National Facility managed by CSIRO.," The Parkes radio telescope is part of the Australia Telescope,which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO."
"luminosity distance d;(z) depends on the geometry of the universe, i.e. the sign of Q,, and is given by where and Dark energy parameterization schemes enter through f(z).","luminosity distance $d_L(z)$ depends on the geometry of the universe, i.e. the sign of $\Omega_k$, and is given by where and Dark energy parameterization schemes enter through $f(z)$."
" For the case where EOS is piecewise constant in redshift, f(z) can be rewritten as (?) where w; is the EOS parameter in the i redshift bin defined by an upper boundary at z;, and the zeroth bin is defined as zo=0."," For the case where EOS is piecewise constant in redshift, $f(z)$ can be rewritten as \citep{Sullivan:2007pd}
 where $w_i$ is the EOS parameter in the $i^{\mathrm{th}}$ redshift bin defined by an upper boundary at $z_i$ , and the zeroth bin is defined as $z_0=0$."
" In order to compare with previous analysis (?),, we define the first three redshift bins to be the same as those used by ? by setting z;=0.2, 2=0.5, and z=1.8."," In order to compare with previous analysis \citep{Sullivan:2007pd}, we define the first three redshift bins to be the same as those used by \citet{Sullivan:2007pd} by setting $z_1=0.2$, $z_2=0.5$, and $z_3=1.8$."
 The fourth bin is defined by z4=7 to include GRBs., The fourth bin is defined by $z_4=7$ to include GRBs.
" We carry out our analyses under two different assumptions about the high redshift (redshift greater than zg=7 in our case) behavior of dark energy, i.e. the so-called (see?) “weak” prior, which makes no assumptions about w(z) at z>7 and the “strong” prior, which assumes w(z)=-1 at z> 7."," We carry out our analyses under two different assumptions about the high redshift (redshift greater than $z_4=7$ in our case) behavior of dark energy, i.e. the so-called \citep[see][]{Riess:2006fw}
 “weak” prior, which makes no assumptions about $w(z)$ at $z>7$ and the “strong” prior, which assumes $w(z)=-1$ at $z>7$ ."
 In this paper we adopt x? statistic to estimate parameters., In this paper we adopt $\chi^2$ statistic to estimate parameters.
" For a physical quantity € with experimentally measured value €,, standard deviation σε,and theoretically predicted value &,(0), where 0 is a collection of parameters needed to calculate the theoretical value, the Y? value is given by and the total y? is the sum of all X258. ie. The likelihood function is then proportional to expwhich produces the posterior probability when (2X6)multiplied2), by the prior probability of 0."," For a physical quantity $\xi$ with experimentally measured value $\xi_o$, standard deviation $\sigma_{\xi}$,and theoretically predicted value $\xi_t(\theta)$ , where $\theta$ is a collection of parameters needed to calculate the theoretical value, the $\chi^2$ value is given by and the total $\chi^2$ is the sum of all $\chi_{\xi}^2$ s, i.e. The likelihood function is then proportional to $\exp\left(-\chi^2(\theta)/2\right)$,which produces the posterior probability when multiplied by the prior probability of $\theta$."
" In the case of our analysis, the calculation of x?s for different observational data is described in section 3.."," In the case of our analysis, the calculation of $\chi^2$ s for different observational data is described in section \ref{sec:observational_data}."
" According to the posterior probability derived in this way, Markov chains are generated through the Monte-Carlo algorithm to study the statistical properties of the parameters."," According to the posterior probability derived in this way, Markov chains are generated through the Monte-Carlo algorithm to study the statistical properties of the parameters."
" In this paper, we focus on the EOS parameters by marginalizing the others."," In this paper, we focus on the EOS parameters by marginalizing the others."
" As mentioned above, in the process of constraining cosmological parameters, standard candles play this roleby providing the luminosity distances at certain redshifts."," As mentioned above, in the process of constraining cosmological parameters, standard candles play this roleby providing the luminosity distances at certain redshifts."
" However, the luminosity distance depends on the integration of the behavior of the dark energy over redshift, so the estimates of the dark energy EOS parameters w; at high redshift depend on those at low redshift."," However, the luminosity distance depends on the integration of the behavior of the dark energy over redshift, so the estimates of the dark energy EOS parameters $w_i$ at high redshift depend on those at low redshift."
" In other words, the EOS parameters w; are correlated in the sense thatthe covariance matrix, is not diagonal."," In other words, the EOS parameters $w_i$ are correlated in the sense thatthe covariance matrix, is not diagonal."
" In the above equation, the w is a vector with components w; and the average is calculated by letting w run over the Markov chain."," In the above equation, the $\boldsymbol{w}$ is a vector with components $w_i$ and the average is calculated by letting $\boldsymbol{w}$ run over the Markov chain."
 We can obtain a set of decorrelated parameters w; through diagonalization of the covariance matrix by choosing an appropriate transformation There can be different choices for T., We can obtain a set of decorrelated parameters $\widetilde{w}_i$ through diagonalization of the covariance matrix by choosing an appropriate transformation There can be different choices for $\boldsymbol{T}$.
 In this paper we use the transformation advocated by ? (see below)., In this paper we use the transformation advocated by \citet{Huterer:2004ch} (see below).
" First we define the Fisher matrix and then the transformation matrix T is given by except that the rows of the matrix T are normalized such that The advantage of this transformation is that the weights (rows of T) are positive almost everywhere and localized in redshift fairly well, so the uncorrelated EOS parameters w; are easy to interpret intuitively (?).."," First we define the Fisher matrix and then the transformation matrix $\boldsymbol{T}$ is given by except that the rows of the matrix $\boldsymbol{T}$ are normalized such that The advantage of this transformation is that the weights (rows of $\boldsymbol{T}$ ) are positive almost everywhere and localized in redshift fairly well, so the uncorrelated EOS parameters $\widetilde{w}_i$ are easy to interpret intuitively \citep{Huterer:2004ch}."
" To constrain the dark energy EOS, we have made useof observational data described below."," To constrain the dark energy EOS, we have made useof observational data described below."
" Recently compiled SN Ia data (???) include 45nearby supernovae (???),, 60 ESSENCE supernovae (?),, 57 SNLS supernovae (?),, and 30 HST supernovae (?).."," Recently compiled SN Ia data \citep{Riess:2006fw,WoodVasey:2007jb,Davis:2007na} include 45nearby supernovae \citep{Hamuy:1996su, Riess:1998dv, Jha:2005jg}, 60 ESSENCE supernovae \citep{WoodVasey:2007jb}, , 57 SNLS supernovae \citep{Astier:2005qq}, , and 30 HST supernovae \citep{Riess:2006fw}. ."
 Figure 1 shows the distribution of these SN Ia samples versus redshift., Figure \ref{fig:SNIa_distr} shows the distribution of these SN Ia samples versus redshift.
αἱ the inner edge of the eric begin to interact dynamically.,at the inner edge of the grid begin to interact dynamically.
 A wave of strong dvnamieal interactions then moves out through the grid., A wave of strong dynamical interactions then moves out through the grid.
 It takes ~ 1 Myr for the wave to move from ~ 0.85 AU to e 1.15 AU., It takes $\sim$ 1 Myr for the wave to move from $\sim$ 0.85 AU to $\sim$ 1.15 AU.
 During this period. some oligarchs merge.," During this period, some oligarchs merge."
 Others migrate through the grid on highly eccentricity orbits., Others migrate through the grid on highly eccentricity orbits.
" From ~ 1 Myr onward. mergers slowly reduce AN,."," From $\sim$ 1 Myr onward, mergers slowly reduce $N_o$."
 It takes ~ 1 Myr lor the first 2 mergers and another ~ 2 Alyy for the second 2 mergers., It takes $\sim$ 1 Myr for the first 2 mergers and another $\sim$ 2 Myr for the second 2 mergers.
 After LOO AIve. only 3 oligarchs remain.," After 100 Myr, only 3 oligarchs remain."
 One of these has m~ 0.42 m.2a ~ 0.9 AU. and e& 0.08.," One of these has $m \sim$ 0.43 $m_{\oplus}$, $a \sim$ 0.9 AU, and $e \sim$ 0.08."
 The other two oligarchs have m.e 0.05 mi. and e 0.1 (Figure 7)., The other two oligarchs have $m \sim$ 0.05 $m_{\oplus}$ and $e \sim$ 0.1 (Figure 7).
 Aside from the eccentricity of the more massive planet. the properties of (hese objects are reasonably close to those of the Earth ancl Mars.," Aside from the eccentricity of the more massive planet, the properties of these objects are reasonably close to those of the Earth and Mars."
 Fragmentation and interactions with the gas probably promote smaller eccentricities for the largest objects (e.g..Wetherill&Stewart1993:AenorWard2002 ).," Fragmentation and interactions with the gas probably promote smaller eccentricities for the largest objects \citep[e.g.,][]{ws93,agn02,kom02}."
".Figure 7 illustrates the evolution of the semimajor axes of the oligarchs for three calculations with Mj = 2 g 7 (lower panel). Xj = 4 g ? (middle panel). and. X, =S8eem ? (upper panel)."," Figure 7 illustrates the evolution of the semimajor axes of the oligarchs for three calculations with $\Sigma_0$ = 2 g $^{-2}$ (lower panel), $\Sigma_0$ = 4 g $^{-2}$ (middle panel), and $\Sigma_0$ = 8 g $^{-2}$ (upper panel)."
 As in Figure IL. the (racks change color when two oligarchs collide and merge.," As in Figure 1, the tracks change color when two oligarchs collide and merge."
 The labels indicate the final mass. in Earth masses. of the largest oligarchs at 100 Myr.," The labels indicate the final mass, in Earth masses, of the largest oligarchs at 100 Myr."
 The Gmescale for the onset of chaotic growth depends on (he initial surface density., The timescale for the onset of chaotic growth depends on the initial surface density.
 More massive disks reach the transition first. (see.forexample.Lissaner1987).," More massive disks reach the transition first. \citep[see, for example,][]{lis87}."
". For M, = Secm 7 the transition begins al ~ a lew x10? vr."," For $\Sigma_0$ = 8 g $^{-2}$, the transition begins at $\sim$ a few $\times ~ 10^5$ yr."
" The transition is delaved to ~ 1 Myr for. E ""T M22gcem2-.", The transition is delayed to $\sim$ 1 Myr for $\Sigma_0$ = 2 g $^{-2}$.
 The character of the transition to chaotic growth also depends on (he initial surface densitv., The character of the transition to chaotic growth also depends on the initial surface density.
 In relatively massive disks with Xj ~ 8 g 7. many oligarchs develop highly eccentric orbits and exhibit large variations in their semimajor axes.," In relatively massive disks with $\Sigma_0$ $\sim$ 8 g $^{-2}$ , many oligarchs develop highly eccentric orbits and exhibit large variations in their semimajor axes."
 These large excursions result in many mergers and a rapid reduction in AN., These large excursions result in many mergers and a rapid reduction in $N_o$.
" In less massive disks with X,< 24 ο em7. only I or 2 oligarchs develop highly eccentric orbits."," In less massive disks with $\Sigma_0 \lesssim$ 2–4 g $^{-2}$, only 1 or 2 oligarchs develop highly eccentric orbits."
 Most mergers are caused by two-body interactions. instead of large-scale dynamical interactions throughout the grid.," Most mergers are caused by two-body interactions, instead of large-scale dynamical interactions throughout the grid."
 Figures 8I0 illustrate (hese general conclusions., Figures 8–10 illustrate these general conclusions.
 In Figure 8. (he orbit crossing paraimeler rapidly approaches zero for caleulations with Xj = 8 g 7.," In Figure 8, the orbit crossing parameter rapidly approaches zero for calculations with $\Sigma_0$ = 8 g $^{-2}$."
" At 0.11 Myr. p; has a long plateau: close approaches between oligarchs cause p, lo fall below zero: mergers cause p, (o jump above zero."," At 0.1–1 Myr, $p_o$ has a long plateau; close approaches between oligarchs cause $p_o$ to fall below zero; mergers cause $p_o$ to jump above zero."
" During a series of 4 mergers αἱ 10 Myr. p, remains below 0 [or a long period."," During a series of 4 mergers at 10 Myr, $p_o$ remains below 0 for a long period."
" After the final merger. p, jumps to 40. where it remains for many Myr."," After the final merger, $p_o$ jumps to 40, where it remains for many Myr."
 For smaller Mua. Po Yeluains well above zero until one or (wo close pairwise interactions pushes it below zero.," For smaller $\Sigma_0$ , $p_o$ remains well above zero until one or two close pairwise interactions pushes it below zero."
" Once(hese interactions produce a merger. (he svstems stabilize and p, moves. well above zero."," Oncethese interactions produce a merger, the systems stabilize and $p_o$ moves well above zero."
"plane is populated with an array of fiber positioners, distributed in a hexagonal pattern, so that a single device is used to position each fiber head in the desired location within its patrol disc.","plane is populated with an array of fiber positioners, distributed in a hexagonal pattern, so that a single device is used to position each fiber head in the desired location within its patrol disc."
 Each positioner is therefore devoted to observing a single target., Each positioner is therefore devoted to observing a single target.
" In a few words, the fiber positioning robot is a collection of positioners, all identical, distributed over an array which covers the entire focal plane."," In a few words, the fiber positioning robot is a collection of positioners, all identical, distributed over an array which covers the entire focal plane."
 The focal plane is therefore covered by these patrol discs so that all possible positions can be reached by at least one positioner (see Fig. 1))., The focal plane is therefore covered by these patrol discs so that all possible positions can be reached by at least one positioner (see Fig. \ref{fig:focalplane}) ).
" In order to cover the whole focal plane, a certain degree of overlap between patrol discs is needed so some regions of the focal plane can be reached by more than one positioner (two or maximum three), hence rising the possibility of fiber collisions."," In order to cover the whole focal plane, a certain degree of overlap between patrol discs is needed so some regions of the focal plane can be reached by more than one positioner (two or maximum three), hence rising the possibility of fiber collisions."
 In Fig., In Fig.
" 2 we show a view of a real subset of a fiber positioner robot, with 19 positioners in hexagonal pattern (?).."," \ref{fig:19_positioners} we show a view of a real subset of a fiber positioner robot, with $19$ positioners in hexagonal pattern \citep{Azzaro2010}."
 This concept offers a number of advantages as compared to others., This concept offers a number of advantages as compared to others.
" It is robust, scalable and easy to service and maintain (failure of one positioner causes the loss of one target only)."," It is robust, scalable and easy to service and maintain (failure of one positioner causes the loss of one target only)."
" Operationally, it provides extremely short reconfiguration times and allows an efficient real-time correction of differential atmospheric dispersion."," Operationally, it provides extremely short reconfiguration times and allows an efficient real-time correction of differential atmospheric dispersion."
" It is, however, specifically conceived for wide-field surveys."," It is, however, specifically conceived for wide-field surveys."
 The reason is that positioners cannot be densely packed onto a small portion of the focal plane., The reason is that positioners cannot be densely packed onto a small portion of the focal plane.
" Consequently, the system is efficient for rather uniform distributions of targets or, alternatively, for large areas where any possible bias is smoothed."," Consequently, the system is efficient for rather uniform distributions of targets or, alternatively, for large areas where any possible bias is smoothed."
 Find a complete discussion on this fiber positioning concept in ?.., Find a complete discussion on this fiber positioning concept in \cite{Azzaro2010}.
" The results presented in this work on the optimization of the fiber assignment process are based on a complete simulation of the focal plane of the SIDE spectrograph, which adopted a fiber positioning robot as that described above."," The results presented in this work on the optimization of the fiber assignment process are based on a complete simulation of the focal plane of the SIDE spectrograph, which adopted a fiber positioning robot as that described above."
 SIDE is an example of a state-of-the-art fiber-fed instrument capable of efficiently undergoing next-generation large-scale spectroscopic surveys., SIDE is an example of a state-of-the-art fiber-fed instrument capable of efficiently undergoing next-generation large-scale spectroscopic surveys.
 The focal plane of the SIDE spectrograph was designed as an array of 1003 positioners covering the 20-arcmin field of view at GTC., The focal plane of the SIDE spectrograph was designed as an array of 1003 positioners covering the 20-arcmin field of view at GTC.
" Important for this work, the results obtained with this simulation are valid for any focal plane consisting in an array of positioners as that outlined in this section."," Important for this work, the results obtained with this simulation are valid for any focal plane consisting in an array of positioners as that outlined in this section."
" The key parameter to describe the efficiency of the fiber assignment process, as we will see below, is the target-to-positioner ratio, η (instead of other parameters such as the size of the focal plane or the number of positioners)."," The key parameter to describe the efficiency of the fiber assignment process, as we will see below, is the target-to-positioner ratio, $\eta$ (instead of other parameters such as the size of the focal plane or the number of positioners)."
 In order to better illustrate our results we will also discuss another real-life example: BigBOSS., In order to better illustrate our results we will also discuss another real-life example: BigBOSS.
 In Table 1 we list some of the relevant parameters for both SIDE and In this section we briefly describe the philosophy behind our optimized fiber positioning algorithm: the draining algorithm., In Table \ref{tab:BB_SIDE} we list some of the relevant parameters for both SIDE and In this section we briefly describe the philosophy behind our optimized fiber positioning algorithm: the draining algorithm.
 We also discuss its performance as compared to a simple random approach., We also discuss its performance as compared to a simple random approach.
 Let us consider a generic instrument with a fiber positioning robot like that described in the previous section covering the entire focal plane with N positioners., Let us consider a generic instrument with a fiber positioning robot like that described in the previous section covering the entire focal plane with $N$ positioners.
" A set of targets is used to populate the focal plane according to a given target-to-positioner ratio, 7."," A set of targets is used to populate the focal plane according to a given target-to-positioner ratio, $\eta$."
 We will first assume that targets are randomly distributed in the focal plane., We will first assume that targets are randomly distributed in the focal plane.
" The design of the system considered implies that each target is reachable by one, two or maximum three"," The design of the system considered implies that each target is reachable by one, two or maximum three"
Since the discovery of the high-redshift Lava forest over 25 vears ago. these abundant absorption features in the spectra of QSOs have been used as evolutionary probes of the intergalactic medimm (IGMD). galactic halos. and now larec-scale structure and chemical evolution.,"Since the discovery of the high-redshift $\alpha$ forest over 25 years ago, these abundant absorption features in the spectra of QSOs have been used as evolutionary probes of the intergalactic medium (IGM), galactic halos, and now large-scale structure and chemical evolution."
 The rapid evolution iu the distribution of lines per uuit redshift. ΑλάνX(1τὸ (552.5 for c> 1.6) was consistent with a picture of these features as highly ionized “clouds” whose munbers aud sizes were controlled by the evolution of the IGM pressure. the mctagalactic ionizing radiation field. aud galaxy formation.," The rapid evolution in the distribution of lines per unit redshift, $d{\cal N}/dz \propto (1+z)^{\gamma}$ $\gamma \approx 2.5$ for $z \geq 1.6$ ), was consistent with a picture of these features as highly ionized “clouds” whose numbers and sizes were controlled by the evolution of the IGM pressure, the metagalactic ionizing radiation field, and galaxy formation."
 Early observations also suggested that Lya clouds had characteristic sizes 10 kpe. were much more abundant than (£.) galaxies. aud showed Little clusteriug iu velocity space.," Early observations also suggested that $\alpha$ clouds had characteristic sizes $\sim10$ kpc, were much more abundant than $L_*$ ) galaxies, and showed little clustering in velocity space."
 They were interpreted as pristine. zeroauctallicitv eas left over frou the recombination cra.," They were interpreted as pristine, zero-metallicity gas left over from the recombination era."
 One therefore expected low-redshift (2< 1) absorption clouds to show only traces of IT 1. due to photoionization aud evaporation in a lower pressure IGAL," One therefore expected low-redshift $z < 1$ ) absorption clouds to show only traces of H I, due to photoionization and evaporation in a lower pressure IGM."
 All these ideas have now changed with new data., All these ideas have now changed with new data.
 One of the delightful spectroscopic surprises from the (UST) was the discovery of Lava absorption lines toward the quasar 3€ 273 at ten0458 by both the Faint Object Spectrograph (FOS. (Baheall et al.," One of the delightful spectroscopic surprises from the (HST) was the discovery of $\alpha$ absorption lines toward the quasar 3C 273 at $z_{\rm em} = 0.158$ by both the Faint Object Spectrograph (FOS, (Bahcall et al."
 1991) and the Goddard Tigh Resolution Spectrograph (GITRS. Morris et al.," 1991) and the Goddard High Resolution Spectrograph (GHRS, Morris et al."
 1991)., 1991).
 Iu this review. I will describe (822) the current status of our eroups program with the IIST aud VLA to define the parameters and nature of the low-redshift Lya forest.," In this review, I will describe 2) the current status of our group's long-term program with the HST and VLA to define the parameters and nature of the low-redshift $\alpha$ forest."
 In 8323. I discuss related theoretical work ou the," In 3, I discuss related theoretical work on the"
solution and is seen to agree very well with the established codes.,solution and is seen to agree very well with the established codes.
" In our 3D code, two points may be at the same distance from the center, but separated by a large angle and they may not be radiatively connected, especially not in high opacity models."," In our 3D code, two points may be at the same distance from the center, but separated by a large angle and they may not be radiatively connected, especially not in high opacity models."
 These grid points may not see exactly the same radiation field because of the random nature of the grid and photon transport and therefore the level populations may not necessarily be exactly the same., These grid points may not see exactly the same radiation field because of the random nature of the grid and photon transport and therefore the level populations may not necessarily be exactly the same.
 There are no fluctuations in the results of the 1D codes because only a single cell with a single solution exist at a given radius., There are no fluctuations in the results of the 1D codes because only a single cell with a single solution exist at a given radius.
" If we take the solution to be the expected solution we can calculate reduced X? values, =>for cach of the 6 levels“of Pesta) the solution which gives us X20.59(1.08,1.11,1.02,1.17,1.00,1.00] for the optically thin case and Xo.s=(1.06,3.12,1.03,2.08,1.28,1.15} for the optically thick case."," If we take the solution to be the expected solution we can calculate reduced $\chi^2$ values, for each of the 6 levels of the solution which gives us $\chi^2_{l=0...5}\approx\{1.08, 1.11, 1.02, 1.17, 1.00, 1.00\}$ for the optically thin case and $\chi^2_{l=0...5}\approx\{1.06, 3.12, 1.03, 2.08, 1.28, 1.15\}$ for the optically thick case."
" The comparison is slightly worse for the optically thick case, but here we also see greater variation between the established codes."," The comparison is slightly worse for the optically thick case, but here we also see greater variation between the established codes."
 The example we present is a typical 2D hydrostatic protoplanetary disk model with a cold and dense mid-plane., The example we present is a typical 2D hydrostatic protoplanetary disk model with a cold and dense mid-plane.
 Such models are numerously found in the literature but here we use a simple analytic toy model for illustrative purposes.," Such models are numerously found in the literature \citep[e.g.,][]{chiang1997, dullemond2004, robitaille2006} but here we use a simple analytic toy model for illustrative purposes."
" The density structure is given by where We consider HCO*, H5O, and CH30H gas ata fractional abundance of 2x10? with respect to the Η2 density."," The density structure is given by where We consider $^+$, $_2$ O, and $_3$ OH gas ata fractional abundance of $\times 10^{-9}$ with respect to the $_2$ density."
" With these three species we illustrate the possibility of utilizing a large dynamic range in scales (HCO*), very opaque models (H20), and multiple overlapping lines (CH3OH)."," With these three species we illustrate the possibility of utilizing a large dynamic range in scales $^+$ ), very opaque models $_2$ O), and multiple overlapping lines $_3$ OH)."
 The temperature is given by a power-law In a more realistic model the temperature would be calculated self-consistently based on the radiation properties of the central source and the temperature would drop toward the mid-plane because this region would be shielded from stellar radiation by the upper layers of the disk., The temperature is given by a power-law In a more realistic model the temperature would be calculated self-consistently based on the radiation properties of the central source and the temperature would drop toward the mid-plane because this region would be shielded from stellar radiation by the upper layers of the disk.
" In our example we mimic this effect by lowering the temperature in a wedge shaped region around the mid-plane to 20 K. By letting water freeze out at temperatures below 90 K, we can simulate a complex abundance structure often used in protoplanetary disks (??).."," In our example we mimic this effect by lowering the temperature in a wedge shaped region around the mid-plane to 20 K. By letting water freeze out at temperatures below 90 K, we can simulate a complex abundance structure often used in protoplanetary disks \citep{jonkheid2007,woitke2009}."
 The disk extends to 500 AU and the values for no and Τρ are 10$ cm? and 90 K at the radius of 100 AU., The disk extends to 500 AU and the values for $n_0$ and $T_0$ are $10^8$ $^{-3}$ and 90 K at the radius of 100 AU.
 In addition we have added a 2 AU wide gap around a radius of 5 AU from the center., In addition we have added a 2 AU wide gap around a radius of 5 AU from the center.
 The disk is in Keplerian rotation., The disk is in Keplerian rotation.
" Figure shows the density, temperature, and H2O density of our disk."," Figure \ref{diskmod} shows the density, temperature, and $_2$ O density of our disk."
" Of other parameters that describes the disk are the turbulent velocity dispersion set to 150 ms-!, stellar mass of 1 Mo, and a gas-to-dust ratio of 100."," Of other parameters that describes the disk are the turbulent velocity dispersion set to 150 $^{-1}$, stellar mass of 1 $_\odot$ , and a gas-to-dust ratio of 100."
 We use thin mantled grains with 107 years of coagulation and the resulting disk mass is 0.02 Mo., We use thin mantled grains with $^7$ years of coagulation and the resulting disk mass is 0.02 $_\odot$.
" To break the azimuthal symmetry and make the model fully 3D, we have placed a protoplanetary condensation in the gap."," To break the azimuthal symmetry and make the model fully 3D, we have placed a protoplanetary condensation in the gap."
 The protoplanet has the same qualitative properties as the one described in ?.., The protoplanet has the same qualitative properties as the one described in \citet{narayanan2006}. .
 The protoplanet has been modeled by placing a spherical distribution of gridpoints at the desired spot and, The protoplanet has been modeled by placing a spherical distribution of gridpoints at the desired spot and
aabundance pattern.,abundance pattern.
 NUV spectra of aand wwere obtained using the Space Telescope Imaging Spectrograph (STIS) on the (HST))., NUV spectra of and were obtained using the Space Telescope Imaging Spectrograph (STIS) on the ).
" These spectra cover a wavelength region from aat R=A/AA~ 30,000."," These spectra cover a wavelength region from at $R \equiv \lambda/\Delta\lambda \sim$ 30,000."
" The optical spectrum of wwas obtained using the High Resolution Echelle Spectrograph (HIRES; Vogtetal. 1994)) on Keck I, and this spectrum covers a wavelength region from aat R~ 45,000."," The optical spectrum of was obtained using the High Resolution Echelle Spectrograph (HIRES; \citealt{vogt94}) ) on Keck I, and this spectrum covers a wavelength region from at $R \sim$ 45,000."
 See Cowanetal.(2005) for further details., See \citet{cowan05} for further details.
" In Figure 1, we show segments of the STIS spectra surrounding the Os transition at aand the the Cd transition at iin aand122563,, as well as A strong absorption feature is clearly identified at these wavelengths in bbut not in122563."," In Figure \ref{overplot}, we show segments of the STIS spectra surrounding the Os transition at and the the Cd transition at in and, as well as A strong absorption feature is clearly identified at these wavelengths in but not in."
. iis warmer (Το= 5200 K) and more metal-rich ([Fe/H] = —2.1) than (Te= 4570 K and [Fe/H] = —2.7)., is warmer $T_{\rm eff} =$ 5200 K) and more metal-rich ([Fe/H] $= -$ 2.1) than $T_{\rm eff} =$ 4570 K and [Fe/H] $= -$ 2.7).
" has a temperature (Το= 4720 K), metallicity ([Fe/H] = —2.9), and overall light element abundance distribution (i.e., 6 €Z 40) that closely resembles citepwestin00.."," has a temperature $T_{\rm eff} =$ 4720 K), metallicity ([Fe/H] $= -$ 2.9), and overall light element abundance distribution (i.e., 6 $\leq Z \leq$ 40) that closely resembles \\citep{westin00}."
 is overabundant in the heavy eelements ([Eu/Fe] = +0.7) relative to (([Eu/Fe] = —0.5)., is overabundant in the heavy elements ([Eu/Fe] $= +$ 0.7) relative to ([Eu/Fe] $= -$ 0.5).
 Therefore the only significant difference between the spectra of and sshould be the stronger heavy aabsorption lines in115444., Therefore the only significant difference between the spectra of and should be the stronger heavy absorption lines in.
". In Figure 1, we see that115444,, like3248,, also exhibits strong absorption features at 2282.28 and2288.02A,, but ddoes not."," In Figure \ref{overplot}, we see that, like, also exhibits strong absorption features at 2282.28 and, but does not."
 Thus heavy sspecies must be producing this absorption., Thus heavy species must be producing this absorption.
 We find no transitions of heavy sspecies at these wavelengths—or the Lu line at 2615.41À-—in the Kurucz or NIST line databases that could plausibly account for this absorption other than the species of interest., We find no transitions of heavy species at these wavelengths—or the Lu line at —in the Kurucz or NIST line databases that could plausibly account for this absorption other than the species of interest.
 References for published transition probabilities of the lines used in this analysis are given in Table 1.., References for published transition probabilities of the lines used in this analysis are given in Table \ref{abundtab}.
 We determined the transition probability of the Lu rresonance line to be log(gf) = +0.11 + 0.04 based on a laser-induced fluorescence lifetime measurement of its upper level (Fedchaketal.2000) and a branching fraction calculation of 0.971 (Quinetetal.1999).. (, We determined the transition probability of the Lu resonance line to be $gf$ ) $ = +$ 0.11 $\pm$ 0.04 based on a laser-induced fluorescence lifetime measurement of its upper level \citep{fedchak00} and a branching fraction calculation of 0.971 \citep{quinet99}. (
See also Lawleretal. 2009..),See also \citealt{lawler09}. .)
 The isotope is dominant of S. LLu; Lodders2003))., The isotope is dominant of S. Lu; \citealt{lodders03}) ).
" The isotope is blocked from production by the stable isotope, so it is expected to be entirely absent from 3248."," The isotope is blocked from production by the stable isotope, so it is expected to be entirely absent from ."
. The odd-Z isotope!?Lu has nonzero nuclear spin I= 7/2., The $Z$ isotope has nonzero nuclear spin $I =$ 7/2.
" Hyperfine structure (hfs) and an accurate line position are based on new laboratory measurements of the 6s6p 1Ρ0 level energy, 38223.406(8) cm"", hfs A, —0.03731(10) em~!, and hfs B, 0.0811(15) απ’."," Hyperfine structure (hfs) and an accurate line position are based on new laboratory measurements of the 6s6p $^{1}$ $^{0}$ level energy, 38223.406(8) $^{-1}$, hfs A, $-$ 0.03731(10) $^{-1}$, and hfs B, 0.0811(15) $^{-1}$."
" The naturally occurring iisotopes of Cd and Os are predominantly even-Z N isotopes with zero nuclear spin, thus we are justified in ignoring the hfs from their minority isotopes."," The naturally occurring isotopes of Cd and Os are predominantly $Z$ $N$ isotopes with zero nuclear spin, thus we are justified in ignoring the hfs from their minority isotopes."
 We use the current version of the LTE spectral analysis code MOOG (Sneden1973) to perform the abundance analysis., We use the current version of the LTE spectral analysis code MOOG \citep{sneden73} to perform the abundance analysis.
" We adopt the atmospheric parameters for aand dderived by Cowanetal.(2002) and Simmereretal.(2004) (T.g/log g/[M/H]/w= 5200 aand 4570 K/1.80/—2.08/1.9K/1.35/—2.50/2.9s~1,, respectively) and interpolate model atmospheres from the Kurucz grids (Castellietal.1997)."," We adopt the atmospheric parameters for and derived by \citet{cowan02} and \citet{simmerer04}
 $T_{\rm eff}$ /log $g$ $v_{t} =$ 5200 $-$ 2.08/1.9 and 4570 $-$ 2.50/2.9, respectively) and interpolate model atmospheres from the Kurucz grids \citep{castelli97}."
. We compare our results to abundances of other species derived from lines in the optical spectral range., We compare our results to abundances of other species derived from lines in the optical spectral range.
" In the NUV, bound-free continuous opacity from metals may be comparable to or greater than the bound-free continuous opacity from H that dominates in the optical spectral range for metal-poor stars (e.g., Travis&Matsushima 1968))."," In the NUV, bound-free continuous opacity from metals may be comparable to or greater than the bound-free continuous opacity from $^{-}$ that dominates in the optical spectral range for metal-poor stars (e.g., \citealt{travis68}) )."
" To compensate for deficiencies in our ability to model the continuousopacity in this spectral range, we have derived abundances of relatively clean, unsaturated, and unblended Fe and Zr lines across the NUV."," To compensate for deficiencies in our ability to model the continuousopacity in this spectral range, we have derived abundances of relatively clean, unsaturated, and unblended Fe and Zr lines across the NUV."
 We require that these lines have reliable log(g/) values, We require that these lines have reliable $gf$ ) values
dusty circumstellar envelopes of evolved AGB stars may be the source of the bulk of M33's diffuse 8um and 24μπι emission.,dusty circumstellar envelopes of evolved AGB stars may be the source of the bulk of M33's diffuse $\mu$ m and $\mu$ m emission.
 The contribution of the TP-AGB to the K-band has been combined with with the mean IR colors of Galactic TP-AGB and stars in order to estimate the contributions of bothC youngM and old stellar populations to mid-IR observations of galaxies., The contribution of the TP-AGB to the $K$ -band has been combined with with the mean IR colors of Galactic TP-AGB C and M stars in order to estimate the contributions of both young and old stellar populations to mid-IR observations of galaxies.
" Without tuning, we find that the resulting mid-IR luminosities of the TP- can reproduce the MIPS 24m fluxes for galaxies back to at least 2= in a manner consistent with restframe optical colors."," Without tuning, we find that the resulting mid-IR luminosities of the TP-AGB can reproduce the MIPS $24\mu$ m fluxes for galaxies back to at least $z=2$ in a manner consistent with restframe optical colors."
 We have also tested the validity of the model on local scales in the galaxy M81 and find reasonable agreement., We have also tested the validity of the model on local scales in the galaxy M81 and find reasonable agreement.
" The origins of correlations between optical colors and mid-IR luminosities seen by others, such as Salimetal.(2009),, can now be understood."," The origins of correlations between optical colors and mid-IR luminosities seen by others, such as \cite{salim2009}, can now be understood."
" With careful modeling of SEDs from the UV through the mid-IR, more detailed histories of star formation should be possible."," With careful modeling of SEDs from the UV through the mid-IR, more detailed histories of star formation should be possible."
" Unfortunately, stellar spectral libraries and theoretical modeling are neither sufficient for verifying nor reducing the uncertainties our models (Conroyetal.2009)."," Unfortunately, stellar spectral libraries and theoretical modeling are neither sufficient for verifying nor reducing the uncertainties our models \citep{conroy2009}."
". This is largely due to the great difficulty in modeling post-main-sequence evolution, including the envelopes of TP-AGB stars, though the UV may provide further constraints2008)."," This is largely due to the great difficulty in modeling post-main-sequence evolution, including the envelopes of TP-AGB stars, though the UV may provide further constraints."
" We are optimistic that improved characterization of the mid-IR colors of the 'TP-AGB can be incorporated into SED fitting, though our calculations have uncertainties perhaps on the order of a factor of two due to uncertainties in the ensemble colors of the TP-AGB populations at different ages."," We are optimistic that improved characterization of the mid-IR colors of the TP-AGB can be incorporated into SED fitting, though our calculations have uncertainties perhaps on the order of a factor of two due to uncertainties in the ensemble colors of the TP-AGB populations at different ages."
 With refinement we anticipate that incorporating the mid-IR into multiwavelength analysis of SEDs will provide the strongest constraints on the star formation histories of galaxies., With refinement we anticipate that incorporating the mid-IR into multiwavelength analysis of SEDs will provide the strongest constraints on the star formation histories of galaxies.
" There is little doubt that star formation and the growth of stellar mass was occurring more rapidly in the distant universe than today, but the nature of that growth has remained largely unknown."," There is little doubt that star formation and the growth of stellar mass was occurring more rapidly in the distant universe than today, but the nature of that growth has remained largely unknown."
 Earlier results (e.g.LeFloc’hetal.2005) had implied that ~1/3 of the stellar mass at the present epoch was formed after z=] — a result that appears to be at odds with the evolution in the stellar mass function to z—1 (e.g.Cirasuoloetal. 2007)., Earlier results \citep[e.g.][]{lefloch2005} had implied that $\sim 1/3$ of the stellar mass at the present epoch was formed after $z=1$ — a result that appears to be at odds with the evolution in the stellar mass function to $z=1$ \citep[e.g.][]{cirasuolo2007}.
. But the model presented here implies that the mid-IR provides the total mass in stars formed in windows stretching back 1.5 Gyr in cosmic time., But the model presented here implies that the mid-IR provides the total mass in stars formed in windows stretching back 1.5 Gyr in cosmic time.
" As a result, such observations must be used with care when constraining the star formation rate density of the universe at z« 2, or when considering whether variations in the initial mass function are warranted by the data (e.g.Davé2008;Wilkinsetal.2008)."," As a result, such observations must be used with care when constraining the star formation rate density of the universe at $z < 2$ , or when considering whether variations in the initial mass function are warranted by the data \citep[e.g.][]{dave2008,wilkins2008}."
. 'The detection of galaxies in the mid-infrared over most of a Hubble time has helped changeour view of galaxy, The detection of galaxies in the mid-infrared over most of a Hubble time has helped changeour view of galaxy
Ow work and data sharine-parallel tree (WDSILEPT) code is principally aimed at ruuniug LSS cosmological simmlations with a umber of particles as high as possible using supercomputers sucli as ταν T3E svstems.,Our work and data sharing-parallel tree (WDSH-PT) code is principally aimed at running LSS cosmological simulations with a number of particles as high as possible using supercomputers such as Cray T3E systems.
 In order to increase the code efficiency. we adopt initially the erouping iiethod proposed by Barues aud introduce a modified implementation of lis grouping policy vielding very high gains in the code performances with the same accuracy.," In order to increase the code efficiency, we adopt initially the grouping method proposed by Barnes and introduce a modified implementation of his grouping policy yielding very high gains in the code performances with the same accuracy."
 To compute the force ou a body. the BIL algorithm needs to build au interaction list (£L) for cach particle p.," To compute the force on a body, the BH algorithm needs to build an interaction list $IL$ ) for each particle $p$."
 Starting from the root cell. a tree inspection is done aud the opening angle parameter Ó is used to evaluate whether a cell ust be opened or closed as meutioned above.," Starting from the root cell, a tree inspection is done and the opening angle parameter $\theta$ is used to evaluate whether a cell must be opened or closed as mentioned above."
 If a cell las dimension C; aud distance d from the particle p so that Eq. (1)), If a cell has dimension $C_l$ and distance $d$ from the particle $p$ so that Eq. \ref{eq:un}) )
 is verified. the cell is closed. it is added to the ££. aud its subcells are not investigated further.," is verified, the cell is closed, it is added to the $IL$, and its subcells are not investigated further."
 Otherwise the cell is opened aud its subeells are investigated in the same wav., Otherwise the cell is opened and its subcells are investigated in the same way.
 Bodies belonging to au opened cell are added to the ZZ. Next. the force ou the body is computed using the monopole and quadrupole momenta for all the cells in the The tree inspection phase represeuts a sizeable task to compute the force because the cell opening criterion is applied may times for each particle.," Bodies belonging to an opened cell are added to the $IL$ Next, the force on the body is computed using the monopole and quadrupole momenta for all the cells in the The tree inspection phase represents a sizeable task to compute the force because the cell opening criterion is applied many times for each particle."
" The CPU time 2, to compute the force im a time-step for all the N particles is where (5j is the average time to build au JL aud (Ty) is the average time to compute the force on cach particle using the interaction", The CPU time $T_o$ to compute the force in a time-step for all the $N$ particles is where $\langle T_{l} \rangle$ is the average time to build an $IL$ and $\langle T_f \rangle$ is the average time to compute the force on each particle using the interaction
just a few cycles.,just a few cycles.
 Ideally. an image should ouly © conrpressed once. aud then all the subsequeut data analysis should be performed directlv on he tile-compressed FITS file.," Ideally, an image should only be compressed once, and then all the subsequent data analysis should be performed directly on the tile-compressed FITS file."
 If the software cannot read the compressed format directly. then it should operate on an uncompressed version of he original compressed fle. which then should rot be reconirpressed.," If the software cannot read the compressed format directly, then it should operate on an uncompressed version of the original compressed file, which then should not be recompressed."
 Tn order to make the nuage quautization aud colmpression techuiques that ave described in the previous sections more widely available to the astronomical conuuuuity. we have developed a pair : eeneral purpose utility programs. called. xd (Scamanctal.2007).. which can be used to compress and uuconpress any FITS nuage in integer or floating-point format.," In order to make the image quantization and compression techniques that are described in the previous sections more widely available to the astronomical community, we have developed a pair of general purpose utility programs, called and \citep{seaman2007}, which can be used to compress and uncompress any FITS image in integer or floating-point format."
 These utilities rely «i the underlying CFITSIO ibrary (Pence1999) to perform the quantization and colupression operations., These utilities rely on the underlying CFITSIO library \citep{pence1999} to perform the quantization and compression operations.
 Thefpack and utility programs were used in the experiments that are described in the following sectious to quantize id compress the images., The and utility programs were used in the experiments that are described in the following sections to quantize and compress the images.
 Further information yout andfunpachk is available frou the HEASARCweb siteat, Further information about and is available from the HEASARC web site at.
 Iu this section we present the results of experiments designed to show how the measurements ofobjects in an image are affected as the image is quantized by varviug degrees., In this section we present the results of experiments designed to show how the measurements of objects in an image are affected as the image is quantized by varying degrees.
 In particular. we will verity that he noise iu the inaege5 mereases as a fiction of q by the amount predicted bw equation 10.. and more siguificautly. that the statistical errors on the magnitude aud position measurcments of faint objects in an nuage. which are hnuited mainly by the backeround noise. also increase by a simular factor.," In particular, we will verify that the noise in the image increases as a function of q by the amount predicted by equation \ref{eq:fractionalnoise}, and more significantly, that the statistical errors on the magnitude and position measurements of faint objects in an image, which are limited mainly by the background noise, also increase by a similar factor."
 These results will provide ecucral euidelimes Του achieving the ercatest aout of mage compression while still preserviug the required level of scientific precision in the age., These results will provide general guidelines for achieving the greatest amount of image compression while still preserving the required level of scientific precision in the image.
 Section 3.1 describes the method of constructingc» the simulated CCD images that are used du the first 2 experiments., Section \ref{s:setup} describes the method of constructing the simulated CCD images that are used in the first 2 experiments.
 The first experiment. ii 83.2.. examines how quantization affects the uncertainties of measurements of single star inages. and the second experiuenut. iu 3.3.. examines the case where many quantized nuages are added together to detect sources far below the detection threshold of a single nuage.," The first experiment, in \ref{s:exp1}, examines how quantization affects the uncertainties of measurements of single star images, and the second experiment, in \ref{s:exp2}, examines the case where many quantized images are added together to detect sources far below the detection threshold of a single image."
" Finally. the third experiment. in §3.L.. is performed ou a set of actual astronomical images to verity the results obtained from the svuthetic Huages,"," Finally, the third experiment, in \ref{s:exp3}, is performed on a set of actual astronomical images to verify the results obtained from the synthetic images."
 Tn order to determine how quautization affects the precision of measurements of objects in an nuage. we eenecrated a large sample of realistic CCD star images with kuown iuput positious and maeguitudes.," In order to determine how quantization affects the precision of measurements of objects in an image, we generated a large sample of realistic CCD star images with known input positions and magnitudes."
 This allows us to xeciselv calculate the errors ou the measured positions and magnitudes in the quantized images., This allows us to precisely calculate the errors on the measured positions and magnitudes in the quantized images.
 All the stars have circular Gaussian profiles with o=1.0 aud FWIIM = 2.35 pixels., All the stars have circular Gaussian profiles with $\sigma = 1.0$ and FWHM = 2.35 pixels.
 This is typical of the spatial resolution couuuonlv found in astronomical CCD nuages and is adequate to avoid he difficulties when analyzing spatially undersampled iuages., This is typical of the spatial resolution commonly found in astronomical CCD images and is adequate to avoid the difficulties when analyzing spatially undersampled images.
 The central location of the star images. relative to the pixel grid. was varied so as to average out any subtle biases iu the subsequent star detectiou and measurement steps that might depend ou the //heasarc.gsfc.nasa.gov/fiusiosepaicw.," The central location of the star images, relative to the pixel grid, was varied so as to average out any subtle biases in the subsequent star detection and measurement steps that might depend on the exact position."
 The total integrated flux in the stars covered a range of LO magnitudes (a factor of 10000 in intensity) in 0.5 maenituce increments., The total integrated flux in the stars covered a range of 10 magnitudes (a factor of 10000 in intensity) in 0.5 magnitude increments.
 Finally. the skv backeround was simulated by adding 1000 counts ο cach pixel.," Finally, the sky background was simulated by adding 1000 counts to each pixel."
" Poissomau-cistributed shot noise aud Cassia distributed ""remd-out noise was then added to cach of these star ages to simulate real CCD nuages.", Poissonian-distributed shot noise and Gaussian distributed “read-out” noise was then added to each of these star images to simulate real CCD images.
" The shot noise iu each pixel was ταςοτι] calculated using a a equal to the square root of that pixel value (Gwhich implicitly assumes that the ""exin of the simulated CCD has been set to l electron per analog-to-digital readout count). and the readout noise was calculated using σ = LO."," The shot noise in each pixel was randomly calculated using a $\sigma$ equal to the square root of that pixel value (which implicitly assumes that the “gain” of the simulated CCD has been set to 1 electron per analog-to-digital readout count), and the readout noise was calculated using $\sigma$ = 10."
 The read-out noise iu these diuages is relatively siuall compared to the shot noise iu he sky backeround.g which is usually the case or real astronomical CCD nuages that lave a uoderatelv xieht vackeround level.," The read-out noise in these images is relatively small compared to the shot noise in the sky background, which is usually the case for real astronomical CCD images that have a moderately bright background level."
 The total roise in the background areas of these images as 8=ντους|10233.2.," The total noise in the background areas of these images has $\sigma =
\sqrt{1000 + 10^2} = 33.2$."
 Differeut starting random seed values were used so that the actual roise distribution varics in every nuage., Different starting random seed values were used so that the actual noise distribution varies in every image.
 The widely used SExtractor source extraction, The widely used SExtractor source extraction
superlliicl to the normal matter is likely to be responsible for pulsar elitches ancl postelitch relaxation.,superfluid to the normal matter is likely to be responsible for pulsar glitches and postglitch relaxation.
 A rotating neutron superlluid is thireaded by quantized vortex lines., A rotating neutron superfluid is threaded by quantized vortex lines.
 The superíIuid can alter its angular velocity by the radial motion of vortices., The superfluid can alter its angular velocity by the radial motion of vortices.
 In the inner crust of a neutron star neutron rich nuclei (hat form the bee lattice coexist with neutron superlluid., In the inner crust of a neutron star neutron rich nuclei that form the bcc lattice coexist with neutron superfluid.
 The vortex lines in (he inner crust are normally pinnecl to the lattice nuclei., The vortex lines in the inner crust are normally pinned to the lattice nuclei.
 Difference in velocity between superfIuid ancl nuclear lattice builds up since magnetic braking slows clown the nuclear latlice and pinning prevents (he vortex lines from moving., Difference in velocity between superfluid and nuclear lattice builds up since magnetic braking slows down the nuclear lattice and pinning prevents the vortex lines from moving.
 Then. (he neutron star undergoes sudden unpinning of a large number of vortex lines lollowed by Che outward motion.," Then, the neutron star undergoes sudden unpinning of a large number of vortex lines followed by the outward motion."
 This catastrophic unpinning has long been considered as a promising cause for glitehes Epstein.&Link 1992).," This catastrophic unpinning has long been considered as a promising cause for glitches \citep{and75, rud76, ala84, pin85, elb92, bel92}."
. A vortex line is subjected to the Magnus force when it moves relative to the superíIuid., A vortex line is subjected to the Magnus force when it moves relative to the superfluid.
 The catastrophic unpiniing model assumes that the pinnine force is strong enough to sustain the vortices to the nuclear lattice against the Magnus force until the moment just. before elitches., The catastrophic unpinning model assumes that the pinning force is strong enough to sustain the vortices to the nuclear lattice against the Magnus force until the moment just before glitches.
 Dased on the condensational ancl kinetic energies. (he pinning energy is estimated. ranging approximately 1—10 MeV. per nucleus (Alparetal.1984:Epstein&Bayvin.1938:pizzochero.Viverit.&Broglia 1997).," Based on the condensational and kinetic energies, the pinning energy is estimated, ranging approximately $1-10$ MeV per nucleus \citep{ala84, eps88, piz97}."
. This magnitude itself is strong enough against the Magnus force expected just before elitches., This magnitude itself is strong enough against the Magnus force expected just before glitches.
 Jones (1992) mentions. however. that (he pinnine forces on a randomly oriented rigid vortex line largely cancel since there are nearly an equal number of pinning sites on either side of the vortex line.," Jones (1992) mentions, however, that the pinning forces on a randomly oriented rigid vortex line largely cancel since there are nearly an equal number of pinning sites on either side of the vortex line."
" Link. Epstein. Davi (1993) lind that for a vortex line of finite tension. pinning becomes much more efficient by slightly bending aud forming kinks,"," Link, Epstein, Baym (1993) find that for a vortex line of finite tension, pinning becomes much more efficient by slightly bending and forming kinks."
 Recently. Jones (1997. 1993. 1999) argues that vortex interaction wilh a polvervstalline structure does not provide pinning strong enough (o explain the large elitches observed in the Vela pulsar (see Section ?? lor detail).," Recently, Jones (1997, 1998, 1999) argues that vortex interaction with a polycrystalline structure does not provide pinning strong enough to explain the large glitches observed in the Vela pulsar (see Section \ref{pinning} for detail)."
 llere we study the vortex configurations. oscillations aud pinning in (he inner crust οἱ a neutron star.," Here we study the vortex configurations, oscillations and pinning in the inner crust of a neutron star."
 Ii Section ?? we derive the equation of motion of vortex lines., In Section \ref{equation} we derive the equation of motion of vortex lines.
 In Section TT we present the equilibrium configurations of vortex lines., In Section \ref{configuration} we present the equilibrium configurations of vortex lines.
 In. Section ?? we examine the stability of equilibrium configurations ancl (he oscillations excited on a vortex line., In Section \ref{oscillation} we examine the stability of equilibrium configurations and the oscillations excited on a vortex line.
 In section ?? we discuss the vortex pinning based on (he results of the previous sections., In Section \ref{pinning} we discuss the vortex pinning based on the results of the previous sections.
 In the last section we summarize the results and mention the conclusions., In the last section we summarize the results and mention the conclusions.
relation.,relation.
 For their sample of acio-Ioud UDs. Berecr find /og(Ly/Ljg)~LI for late-M cwarfs. and fog(Ly/Lg)~12 for cooler dwarfs.," For their sample of radio-loud UDs, \citet{bbf+10} find $log(L_{X}/L_{R})\sim14$ for late-M dwarfs, and $log(L_{X}/L_{R})\sim12$ for cooler dwarfs."
 No clear trends jiwe been identified between the radio hunünosities of UDs aud stellar properties. such as rotation aud imiagnuetic Ποια streneth (Berecretal.2010).," No clear trends have been identified between the radio luminosities of UDs and stellar properties, such as rotation and magnetic field strength \citep{bbf+10}."
 Radio cussion fron UDs is variable on timescales [oveurss hours auc minutes.," Radio emission from UDs is variable on timescales of years, hours and minutes."
 Some UDs have radio icehteurves that are periodic ou the rotation periods of afew hours (Jallinanetal.2006.2007.2008:Bereeral. 2009).," Some UDs have radio lightcurves that are periodic on the rotation periods of a few hours \citep{had+06,hbl+07,had+08,brp+09}."
". These lighteurves are either characterized by uodulatious (οιοι,Tallinanetal.2006) or by short evcle peaks lasting for a few minutes (c.¢..Hallinauetal.Ww 07)."," These lightcurves are either characterized by modulations \citep[e.g.,][]{had+06} or by short duty-cycle peaks lasting for a few minutes \citep[e.g.,][]{hbl+07}."
. Other UDs exhibit isolated flares when otherwise radio-loud. also ou fes-uinute timescales (e...Durgasser&Putinan2005.hereafter DP05)..," Other UDs exhibit isolated flares when otherwise radio-loud, also on few-minute timescales \citep[e.g.,][hereafter BP05]{bp05}."
 The quickly-varvine cluission is generally 10054 circnlarly-polarized (e...ITal- 2008).," The quickly-varying emission is generally $\%$ circularly-polarized \citep[e.g.,][]{had+08}."
. In addition. the tvpes of radio ciission observed from UDs changes ou timescales of vears (Ostenetal. 2009).. varving between undetectable. quicsceut and periodic.," In addition, the types of radio emission observed from UDs changes on timescales of years \citep{oph+09}, varying between undetectable, quiescent and periodic."
 The variability of UD radio emission characteristics makes it hard to identify mubiased oud samples for population studies., The variability of UD radio emission characteristics makes it hard to identify unbiased radio-loud samples for population studies.
 Radio observations of UDs provide sguificaut insight iuto conditions in UD maeuctospheres., Radio observations of UDs provide significant insight into conditions in UD magnetospheres.
 Iu this Letter. we xeseut the widest-banud radio observations vet reported or the UD 395601. (hereafter DENISIO18). using the new Compact Array. Droadbaud Backend (Ferris&Wilsou2002) at the Australia Telescope Compact Array (ATCA.Fraterctal.1992)..," In this Letter, we present the widest-band radio observations yet reported for the UD $-$ 395604 (hereafter DENIS1048), using the new Compact Array Broadband Backend \citep{fw02} at the Australia Telescope Compact Array \citep[ATCA,][]{fbw92}."
 We propose a magnetospheric model which accounts for he violation of the CaiddelBeuz relation., We propose a magnetospheric model which accounts for the violation of the Güddel-Benz relation.
 This model could provide interesting insights into the magnetic field and plasina euviromneuts of these cuigliatic stars., This model could provide interesting insights into the magnetic field and plasma environments of these enigmatic stars.
 The tarect source. DENTSLOLS. was oue of seven Southern late-Al aud L dvarfs observed by BPOS with the ATCA in the ccm and ccm bands.," The target source, DENIS1048, was one of seven Southern late-M and L dwarfs observed by BP05 with the ATCA in the cm and cm bands."
 BPO5 reported a quicscent fux density of 1250.0 Limdy at 601. as well as a [5 nüuute flare in each baud. separated by 10 nüuutes with a peal flux density of 30nunuJw at Sec.," BP05 reported a quiescent flux density of $\pm$ mJy at cm, as well as a $-$ 5 minute flare in each band, separated by $\sim$ 10 minutes with a peak flux density of mJy at cm."
 DENISIOLS (spectralclassificationADS8.5.Πανal.2001). was identified as à UD in the DENTS survey (Epchteiuetal.1997). by Doelfosseetal.(2001).. ancl. at a distance of L.002E0.03 ppe (Costaetal.2005)... is one of the closest known stars.," DENIS1048 \citep[spectral classification M8.5,][]{hsb+04} was identified as a UD in the DENIS survey \citep{edc+97} by \citet{dfm+01}, and, at a distance of $\pm$ pc \citep{cmj+05}, is one of the closest known stars."
 A recent spectroscopic study w Martinetal.(2010). shows that it is uulikelv to be a own cawart., A recent spectroscopic study by \citet{mpb+10} shows that it is unlikely to be a brown dwarf.
 Επιστ:&Schinitt(2001). reported a aree optical flare aud a fast projected rotation velocity of esin/=2542 kkinss+., \citet{fs04} reported a large optical flare and a fast projected rotation velocity of $v\sin i=25\pm2$ $^{-1}$.
 While Ho eission was detected x Delfosseetal.(2001).. Schnutt&Liefke(2001). found 10 N-vav cuiission with an upper limit of241079 ss.! yon the ROSAT ΑΠδν Survey catalogue.," While $\alpha$ emission was detected by \citet{dfm+01}, \citet{sl04} found no X-ray emission with an upper limit of $2\times10^{26}$ $^{-1}$ from the ROSAT All-Sky Survey catalogue."
 Reiners&Das(2010) found au average lince-of-sielt magnetic field streugth of 23004LOO GG using measurements of Zeca xoadeniue in Fell absorption lines., \citet{rb10} found an average line-of-sight magnetic field strength of $2300\pm400$ G using measurements of Zeeman broadening in FeH absorption lines.
 We observed DENISIOI8 with the ATCA on 2000 August 10 and 11 in the 1.2ece02 band. aud sauultzueouslv im the 23 and Geem hands on 2009 August 15.," We observed DENIS1048 with the ATCA on 2009 August 10 and 11 in the cm band, and simultaneously in the 3 and cm bands on 2009 August 15."
 The six 22-metre ATCA antennas were placed in au exteuded configuration in order to niaxinise point-source sensitivity., The six 22-metre ATCA antennas were placed in an extended configuration in order to maximise point-source sensitivity.
 Bascline leneths ranged between 300nui aud 600012. corresponding to resolutions between approximately and at οσα.," Baseline lengths ranged between m and m, corresponding to resolutions between approximately and at cm."
 Visibility nieasurenüents for all basclines were recorded in two CCIz bands per Stokes polarization with NMMITz frequency resolution., Visibility measurements for all baselines were recorded in two GHz bands per Stokes polarization with MHz frequency resolution.
 The visibilitics were iutegrated over LOss intervals., The visibilities were integrated over s intervals.
 Details of the observations are even iu Table 1., Details of the observations are given in Table 1.
 We reduced the data using the MIRIAD software package (Saultetal.1995)., We reduced the data using the MIRIAD software package \citep{stw95}.
. Staudard calibrations were performed using observations of the ATCA primary calibrator 638 on cach dav. and frequeut observations of a radio galaxy 115 4.separated. bv 67 from DENISI0I8.," Standard calibrations were performed using observations of the ATCA primary calibrator $-$ 638 on each day, and frequent observations of a radio galaxy $-$ $-$ 445 $-$ separated by $^{\circ}$ from DENIS1048."
 Multi-fequeucy svuthesis totaliutensitv nuages were produced in sub-bands of MMIIz for the Geom aud 3ecu observations. and iu cach 2€GGIIzsub-baud for the L2ccm observations.," Multi-frequency synthesis total-intensity images were produced in sub-bands of MHz for the cm and cm observations, and in each GHzsub-band for the cm observations."
 We detected DENISLOLS as a point source iu all images. except that formed frou the 21GCGIIz data.," We detected DENIS1048 as a point source in all images, except that formed from the GHz data."
 The measured position of right- LOh. [812. 13.588 (40.038). declination: -397. 56. (40.55) is offset from the 2MASS position of DENISIOLS (Cutrietal2003). bv15.67.. which corresponds to the kuown proper motion (Deaconctal.20053.," The measured position of right-ascension: 10h, 48m, 13.58s $\pm0.03$ s), declination: $^{\circ}$, 56', $\pm0.5$ ) is offset from the 2MASS position of DENIS1048 \citep{c+03} by, which corresponds to the known proper motion \citep{dhc05}."
. The flux cdeusity of DENISLOLS was measured iu cach sub-hand by fitting the restoring Gaussian beans to the images., The flux density of DENIS1048 was measured in each sub-band by fitting the restoring Gaussian beams to the images.
 The beams were at position angles of 19° for the Gecin and 2e data. and 2° for the cc data. The rius noise levels. 0. in images made from cach sub-baud ranged between 2050 jy for the ccm data. aud between 25.35 Jy for the 3ccn data.," The beams were at position angles of $19^{\circ}$ for the cm and cm data, and $2^{\circ}$ for the cm data, The rms noise levels, $\sigma$, in images made from each sub-band ranged between $30-50$ $\mu$ Jy for the cm data, and between $25-35$ $\mu$ Jy for the cm data."
 For both the GGIIz aud CGCGIIz. 0=8 yr Jy.," For both the GHz and GHz, $\sigma=8$ $\mu$ Jy."
 We present the resulting spectrmm of DENISLOLS in Figure 1., We present the resulting spectrum of DENIS1048 in Figure 1.
" The Stokes I iicasureimoeuts of the flux deusityv of DENISI01ISs. Sv). at various frequencies r are au excellent fif to a power-law. ο)x»r"". where l.rlx 0.09."," The Stokes I measurements of the flux density of DENIS1048, $S(\nu)$, at various frequencies $\nu$ are an excellent fit to a power-law, $S(\nu)\propto\nu^{-\alpha}$, where $\alpha=1.71\pm0.09$ ."
 A similar process was also applied to the Stokes Q. U and V data.," A similar process was also applied to the Stokes Q, U and V data."
 While DENISIOIS was not found to have any detectable Stokes Q or U cinission. we detected Stokes Vo cussion atf frequencies up to GGIIz bv combining data iu imultiple sub-bauds.," While DENIS1048 was not found to have any detectable Stokes Q or U emission, we detected Stokes V emission at frequencies up to GHz by combining data in multiple sub-bands."
 Circular polarization fractions rangiug between 0.25 and 0.1 were found iu the cci band. aud 206 upper lanits of 0.2 were placed on the linear polarization fractious.," Circular polarization fractions ranging between 0.25 and 0.4 were found in the cm band, and $\sigma$ upper limits of 0.2 were placed on the linear polarization fractions."
 The Stokes V flux clensity measurenieuts are also plotted iu Figure 1l., The Stokes V flux density measurements are also plotted in Figure 1.
 An nuage of the data recorded between GGIIz aud [988CGGIIz. with Stokes V. contours overlayed ou a Stokes I erevscale nuage. is shown in Figure 2.," An image of the data recorded between GHz and GHz, with Stokes V contours overlayed on a Stokes I greyscale image, is shown in Figure 2."
 No sieuificaut short-timescale amplitude excursions or periodicities were detected iu any παςαλά in either the Stokes Tor V data., No significant short-timescale amplitude excursions or periodicities were detected in any sub-band in either the Stokes I or V data.
 We consider two possible radio emission mechanisms for DENISI0LS: evrosvuchrotron emission aud clectrou-evclotron maser (ECAL) eiission., We consider two possible radio emission mechanisms for DENIS1048: gyrosynchrotron emission and electron-cyclotron maser (ECM) emission.
 The spectral shape aud auuplitude are clearly inconsistent with thermal emission., The spectral shape and amplitude are clearly inconsistent with thermal emission.
 Cyrosvuchrotron and ECAD imechanisiis are both associated with muldly relativistic. nou-thermal electron populations. with cnergics >~— 20kkeV. Whereas eyvrosvuchrotron clissiou ds caused by incohereutlv radiating uou-thermal electrons propagating along magnetic field lines. ΤΟΝΤ cinission is coherent. and requires these electrons to lave au anisotropic pitcli-anele distribution (Dulk 1985)..," Gyrosynchrotron and ECM mechanisms are both associated with mildly relativistic, non-thermal electron populations, with energies $>\sim20$ keV. Whereas gyrosynchrotron emission is caused by incoherently radiating non-thermal electrons propagating along magnetic field lines, ECM emission is coherent, and requires these electrons to have an anisotropic pitch-angle distribution \citep{d85}. ."
 Gvrosvuchrotron, Gyrosynchrotron
"due to the fact that Sandell(1994) used the G93 model in order to determine his absolute calibration, which we have found to overestimate the brightness of Uranus by ~ 7%)).","due to the fact that \citet{sandell94}
 used the G93 model in order to determine his absolute calibration, which we have found to overestimate the brightness of Uranus by $\simeq 7$ )."
" It is not clear why our measured peak flux densities are higher for (94.5 and K3-50A, although the known extended emission in both sources, coupled with the fact that Sandell(1994) made single-pixel chopped photometry measurements at 27 arcsec resolution, may be the cause."," It is not clear why our measured peak flux densities are higher for G34.3 and K3-50A, although the known extended emission in both sources, coupled with the fact that \citet{sandell94}
 made single-pixel chopped photometry measurements at 27 arcsec resolution, may be the cause."
" We find that Uranus and Neptune behave as ideal sources for flux calibration at 143 GHz, with no evidence for temporal brightness variations."," We find that Uranus and Neptune behave as ideal sources for flux calibration at 143 GHz, with no evidence for temporal brightness variations."
" For Uranus, these results are in contrast to the lower frequency measurements of Kl06 and Kr08, who find -0.5 percent/year variations in the brightness temperature of Uranus at 8.6 and 90 GHz."," For Uranus, these results are in contrast to the lower frequency measurements of Kl06 and Kr08, who find $\simeq 0.5$ percent/year variations in the brightness temperature of Uranus at 8.6 and 90 GHz."
" Our data, combined with the measurements of O86 and G93, place a confidence level upper limit of 0.19 on the magnitude of variations in the brightness percent/yeartemperature of Uranus at c150 GHz over the same period."," Our data, combined with the measurements of O86 and G93, place a confidence level upper limit of 0.19 percent/year on the magnitude of variations in the brightness temperature of Uranus at $\simeq 150$ GHz over the same period."
 See Figure 2.., See Figure \ref{fig:f2}.
" A physical interpretation of the temporal variations in the brightness of Uranus seen at lower frequencies by K106 and Kr08, in combination with our static 143 GHz results, is beyond the scope of this manuscript, which is intended to quantify the magnitude and stability of the brightness of Uranus for the purposes of using it as a calibrator at 143 GHz."," A physical interpretation of the temporal variations in the brightness of Uranus seen at lower frequencies by Kl06 and Kr08, in combination with our static 143 GHz results, is beyond the scope of this manuscript, which is intended to quantify the magnitude and stability of the brightness of Uranus for the purposes of using it as a calibrator at 143 GHz."
" However, we do note that the combined results are not necessarily inconsistent, given that higher frequency observations of Uranus probe higher altitudes in the atmosphere (Kr08)."," However, we do note that the combined results are not necessarily inconsistent, given that higher frequency observations of Uranus probe higher altitudes in the atmosphere (Kr08)."
" Using Bolocam data collected between 2003 and 2010 we have tightly constrained the 143 GHz brightness ratio of Uranus and Neptune (1.027+0.006), and we find no evidence for temporal variations in the 143 GHz brightness temperature of either planet over that period."," Using Bolocam data collected between 2003 and 2010 we have tightly constrained the 143 GHz brightness ratio of Uranus and Neptune $1.027 \pm 0.006$ ), and we find no evidence for temporal variations in the 143 GHz brightness temperature of either planet over that period."
" Combining our results with those of O86 and G93, we find no evidence for 143 GHz brightness variations in either planet over the period from 1983—2010, and place a confidence level upper limit of on the magnitude of brightness variations over the 28 year period from 1983 to 2010."," Combining our results with those of O86 and G93, we find no evidence for 143 GHz brightness variations in either planet over the period from $1983-2010$, and place a confidence level upper limit of on the magnitude of brightness variations over the 28 year period from 1983 to 2010."
" By extrapolating the WMAP 94 GHz results given in Weilandetal.(2011) to our observing band using the brightness models presented in G93, we are able to constrain the absolute 143 GHz brightness temperature of each planet to ~3%."," By extrapolating the WMAP 94 GHz results given in \citet{weiland11} to our observing band using the brightness models presented in G93, we are able to constrain the absolute 143 GHz brightness temperature of each planet to $\simeq 3$."
". Additionally, we determine ~3% absolute 143 GHz peak flux densities for the ultracompact HII regions G34.3 and K3-50A and the protostellar source NGC 2071IR."," Additionally, we determine $\simeq 3$ absolute 143 GHz peak flux densities for the ultracompact HII regions G34.3 and K3-50A and the protostellar source NGC 2071IR."
" We acknowledge the assistance of: the Bolocam instrument team: Peter Ade, James Aguirre, James Bock, Sam Edgington, Jason Glenn, Alexy Goldin, Sunil Golwala, Douglas Haig, Andrew Lange, Glenn Laurent, Phil Mauskopf, Hien Nguyen, Philippe Rossinot, and Jack Sayers; Matt Ferry, Matt Hollister, Patrick Koch, Kai-Yang Lin, Sandor Molnar, Seth Siegel, and Keiichi Umetsu who, in addition to the Bolocam instrument team, helped collect the data presented in this manuscript; the day crew and Hilo staff of the Caltech Submillimeter Observatory, who provided invaluable assistance during commissioning and data-taking for this data set; Kathy Deniston, Barbara Wertz, and Diana Bisel, who provided effective administrative support at Caltech and in Hilo; and the referee, who provided helpful comments and suggestions."," We acknowledge the assistance of: the Bolocam instrument team: Peter Ade, James Aguirre, James Bock, Sam Edgington, Jason Glenn, Alexy Goldin, Sunil Golwala, Douglas Haig, Andrew Lange, Glenn Laurent, Phil Mauskopf, Hien Nguyen, Philippe Rossinot, and Jack Sayers; Matt Ferry, Matt Hollister, Patrick Koch, Kai-Yang Lin, Sandor Molnar, Seth Siegel, and Keiichi Umetsu who, in addition to the Bolocam instrument team, helped collect the data presented in this manuscript; the day crew and Hilo staff of the Caltech Submillimeter Observatory, who provided invaluable assistance during commissioning and data-taking for this data set; Kathy Deniston, Barbara Wertz, and Diana Bisel, who provided effective administrative support at Caltech and in Hilo; and the referee, who provided helpful comments and suggestions."
" Bolocam was constructed and commissioned using funds from NSF/AST-0098737, NSF/AST-9980846, NSF/AST-9618798,NSF/AST-0229008, and NSF/AST-0206158."," Bolocam was constructed and commissioned using funds from NSF/AST-9618798, NSF/AST-0098737, NSF/AST-9980846, NSF/AST-0229008, and NSF/AST-0206158."
" JS was partially supported by a NASA Graduate Student Research Fellowship, a NASA Postdoctoral Program fellowship, NSF/AST-0838261, and NASA/NNXI1ABOT7G; NC was partially supported by NASA Graduate Student Research Fellowship; SG acknowledges an Alfred P. Sloan Foundation fellowship."," JS was partially supported by a NASA Graduate Student Research Fellowship, a NASA Postdoctoral Program fellowship, NSF/AST-0838261, and NASA/NNX11AB07G; NC was partially supported by NASA Graduate Student Research Fellowship; SG acknowledges an Alfred P. Sloan Foundation fellowship."
The class of stars stil preseuts poorlv defined characteristics. aud this more than 50 vears after the discovery of the prototype member by Morgan et al (1913) who noted the abnormally weak metal lines of this AO dwarf star.,"The class of stars still presents poorly defined characteristics, and this more than 50 years after the discovery of the prototype member by Morgan et al (1943) who noted the abnormally weak metal lines of this A0 dwarf star."
 The properties that should define a star are not clearly established: the proposed spectroscopic criteria are usually. based on the weakness of metal lines. especially of the Me II. List. compared with what is expectec from the lvdrogen line type. while C. N. O and S have nearly solar abundances.," The properties that should define a star are not clearly established; the proposed spectroscopic criteria are usually based on the weakness of metal lines, especially of the Mg II 4481, compared with what is expected from the hydrogen line type, while C, N, O and S have nearly solar abundances."
 The kincmatic behaviour shoul allow to distinguish these stars from the metal poor A-type IHorizoutal Branch stars., The kinematic behaviour should allow to distinguish these stars from the metal poor A-type Horizontal Branch stars.
 Moderate to high projectec rotational velocities are usually found απο stars. although some exceptions have been recently ideutifie (e.g. IID 61191 and TD 7£872 selected by Paunzen Gray L997).," Moderate to high projected rotational velocities are usually found among stars, although some exceptions have been recently identified (e.g. HD 64491 and HD 74873 selected by Paunzen Gray 1997)."
 The result of he vaeueOo definitions of these non-evolvec metal uucderabunudaut stars is well reflected by the variety of opinions existing at present about the members of this class., The result of the vague definitions of these non-evolved metal underabundant stars is well reflected by the variety of opinions existing at present about the members of this class.
 The metal abundances obtained up to now reveal a hieh scatter from star to star., The metal abundances obtained up to now reveal a high scatter from star to star.
 Details on the evolution with time of the definition are sununuarized in Farageiana Gerbalci (1998): the not clearly defined properties of these stars are. at least xuwtiall. responsible of the various hypotheses xoposed to explain the plienomenou as well as of he uncertainty on the age attributed to these objects. which spans from that of stars not vet on the Main Sequence to that of old objects descending from coutact inary svstenas.," Details on the evolution with time of the definition are summarized in Faraggiana Gerbaldi (1998); the not clearly defined properties of these stars are, at least partially, responsible of the various hypotheses proposed to explain the phenomenon as well as of the uncertainty on the age attributed to these objects, which spans from that of stars not yet on the Main Sequence to that of old objects descending from contact binary systems."
 The preseut paper reviews the characteristics of the uembers of this class according to recent compilations aud discusses the effect of duplicity ou a composite spectrum as source of nusclassification for some of these camucidatecs., The present paper reviews the characteristics of the members of this class according to recent compilations and discusses the effect of duplicity on a composite spectrum as source of misclassification for some of these candidates.
 Iu a moderu astrophysical perspective. age. positio- in the IIR. diagram aud chemical abuudances are the kev quantities which describe a class of stars.," In a modern astrophysical perspective, age, position in the HR diagram and chemical abundances are the key quantities which describe a class of stars."
 The purpose of introducing a class of stars is to help identify a comune- nuderling phenomenology., The purpose of introducing a class of stars is to help identify a common underlying phenomenology.
 For stars the ain is f find the common factor which can explain the observea chemical peculiarities: to be iieaniueful this iust explai- a statistically significant sample of stars., For stars the aim is to find the common factor which can explain the observed chemical peculiarities; to be meaningful this must explain a statistically significant sample of stars.
 Bearing thiρα in nind. it is clear that anv classification scheme whic[um does not rely on abundauce criteria is unlikely to be helpful.," Bearing this in mind, it is clear that any classification scheme which does not rely on abundance criteria is unlikely to be helpful."
 It is probable that as high accuracy abundance data acciunulate. we will have to revise our concept of stars and probably reach a more plivsical definition.," It is probable that as high accuracy abundance data accumulate, we will have to revise our concept of stars and probably reach a more physical definition."
 May stars were cassified as iu the past., Many stars were classified as in the past.
 The catalogue of Ποιοι ot al (1990) includes over 100 candidates;, The catalogue of Renson et al (1990) includes over 100 candidates.
 Mauv of these turned out to be misclassified and the whole sample results too heterogeneous., Many of these turned out to be misclassified and the whole sample results too heterogeneous.
 We selected. stars classified as iu recent papers based on modern data. loping to extract a more homogeneous sample.," We selected stars classified as in recent papers based on modern data, hoping to extract a more homogeneous sample."
 They should be considered candidates. since for many of them further analysis to check whether they match auv given definition is still required.," They should be considered candidates, since for many of them further analysis to check whether they match any given definition is still required."
 The caudidates we selected. with the exception of three of them. have been listed in at least oue of the following papers: Abt Morrell(1995: hereafter: AM). Paunzen ct al (1997: hereafter CC. Cray (1999: hereafter €).," The candidates we selected, with the exception of three of them, have been listed in at least one of the following papers: Abt Morrell(1995; hereafter AM), Paunzen et al (1997; hereafter CC), Gray (1999; hereafter G)."
 The exceptions are: TID 290192 aud TD 90821 which were classified as by Pauuzeu Cray (1997): ΠΟ 105759 for which the CG classification is unpublished., The exceptions are: HD 290492 and HD 90821 which were classified as by Paunzen Gray (1997); HD 105759 for which the G classification is unpublished.
 Both iethods aud scope differ :unong the three papers (ie. AALCCO.C).," Both methods and scope differ among the three papers (i.e. AM,CC,G)."
 However. the deeree of reliability of cach of them is difficult to clefine.," However, the degree of reliability of each of them is difficult to define."
" Promising candidates are found iun alb lists. although ταν is probably the most reliable source. because the author (ταν Carrison 1051, 1L989a.L989b: Carrison ααν 1991: CC im Table 1) has classified a large suuple of ποια aud “standard” stars using the same methods."," Promising candidates are found in all lists, although Gray is probably the most reliable source, because the author (Gray Garrison 1987, 1989a,1989b; Garrison Gray 1994; GG in Table 1) has classified a large sample of “normal” and “standard” stars using the same methods."
 AAD is a study of stellar v sn of 1700 A-type stars of the Bright Star Catalogue (IILoffiei Warren 1991) (BSC)., AM is a study of stellar v $ \sin i$ of 1700 A-type stars of the Bright Star Catalogue (Hoffleit Warren 1994) (BSC).
 Ou the basis of their available spectra (photographic spectra of dispersion 39 Amun1 ) they eive a classification for cach star., On the basis of their available spectra (photographic spectra of dispersion 39 $\rm mm^{-1}$ ) they give a classification for each star.
 Some are classified as A Doo., Some are classified as $\lambda$ Boo.
kinematics typical of a halo cluster.,kinematics typical of a halo cluster.
 It is also highly reddened. and its CMD is affected by some differential reddening.," It is also highly reddened, and its CMD is affected by some differential reddening."
 Alonso et al. (1997)), Alonso et al. \cite{alonso97}) )
 present the only other CCD 7 and T CMD existent for this cluster., present the only other CCD $B$ and $V$ CMD existent for this cluster.
 NGC 6366. together with NGC 5053. are the only two clusters that were observed under not exceptionally good seeing conditions.," NGC 6366, together with NGC 5053, are the only two clusters that were observed under not exceptionally good seeing conditions."
 Still. all the sequences in the CMD can be identified (apart from the upper RGB). including what seems to be a well populated blue straggler sequence.," Still, all the sequences in the CMD can be identified (apart from the upper RGB), including what seems to be a well populated blue straggler sequence."
 The HB is very red. as expected on the basis of the metallicity. and tilted.," The HB is very red, as expected on the basis of the metallicity, and tilted."
 We measured a total of ~5500 stars for this cluster. (, We measured a total of $\sim 5500$ stars for this cluster. (
Fig. 21) ,Fig. \ref{ngc6535}) )
To our knowledge. Sarajedini (1994)) has published the only previous CCD study of this cluster: a B and V. CMD down to V~21.," To our knowledge, Sarajedini \cite{sarajedini94}) ) has published the only previous CCD study of this cluster: a $B$ and $V$ CMD down to $V\sim21$."
 His stellar population is slightly smaller than ours for this range of magnitudes (we reach V ~ 23)., His stellar population is slightly smaller than ours for this range of magnitudes (we reach V $\sim23$ ).
 NGC 6535 is the least luminous object of our northern sample. and probably the one with the smallest number of stars.," NGC 6535 is the least luminous object of our northern sample, and probably the one with the smallest number of stars."
 We measured ~7500 stars for this cluster., We measured $\sim7800$ stars for this cluster.
 Its RGB is identifiable. but not clearly defined. due also to field star contamination.," Its RGB is identifiable, but not clearly defined, due also to field star contamination."
 Its CMD somehow resembles the CMD of NGC 6717 (Paper D). (, Its CMD somehow resembles the CMD of NGC 6717 (Paper I). (
Fig. 22) ,Fig. \ref{ngc6779}) )
We have not found any previous CCD study on this cluster., We have not found any previous CCD study on this cluster.
 Our CMD is well defined. though it is slightly contaminated by foreground/background stars.," Our CMD is well defined, though it is slightly contaminated by foreground/background stars."
 The broadening of the SGB-RGB might suggest the existence of some differential reddening., The broadening of the SGB-RGB might suggest the existence of some differential reddening.
 The distribution of the stars along the BHB seems to be not homogeneous. with the possible presence of a gap.," The distribution of the stars along the BHB seems to be not homogeneous, with the possible presence of a gap."
 The total of measured stars was of ~11300. (, The total of measured stars was of $\sim11300$. (
Fig. 23) ,Fig. \ref{ngc6838}) )
As suggested also by its CMD. M71 ts a metal rich cluster. similar to 47 Tue (Paper D.," As suggested also by its CMD, M71 is a metal rich cluster, similar to 47 Tuc (Paper I)."
 Our CMD is well defined and extends for more than 4 magnitudes below the TO. covering a total of ~12500 stars.," Our CMD is well defined and extends for more than 4 magnitudes below the TO, covering a total of $\sim12500$ stars."
 The cluster has only a RHB. and the upper part of the RGB is not very well defined.," The cluster has only a RHB, and the upper part of the RGB is not very well defined."
 This cluster is located close to the Galactic plane. and this explains the contamination by disk stars clearly visible in the CMD.," This cluster is located close to the Galactic plane, and this explains the contamination by disk stars clearly visible in the CMD."
 It is very bright and relatively nearby., It is very bright and relatively nearby.
 Despite this. there is no CMD in the literature after Hodder et al. (1992)).," Despite this, there is no CMD in the literature after Hodder et al. \cite{hodder92}) )."
 They present a good B and V diagram. less populated than ours. reaching V=22.," They present a good $B$ and $V$ diagram, less populated than ours, reaching $V=22$."
 Previous CCD studies are in Richer Fahlman (1988)). who present (.D.V. photometry for the main sequence. down to V—22 (0= 25).," Previous CCD studies are in Richer Fahlman \cite{richer88}) ), who present $U,B,V$ photometry for the main sequence, down to $V=22$ $U=25$ )."
 No evolved stars are present in this work. (, No evolved stars are present in this work. (
Fig. 24)),Fig. \ref{ngc7078}) )
 This cluster has been extensively studied in the past. both with groundbased facilities and a large number of HST observations.," This cluster has been extensively studied in the past, both with groundbased facilities and a large number of HST observations."
 HST studies include Stetson 1994 and Yanny et al 1994... were a CMD of the cluster center is presented.," HST studies include Stetson \cite{stetson94} and Yanny et al \cite{yanny94}, , were a CMD of the cluster center is presented."
 The CMD does not arrive to the MS TO. and is quite disperse.," The CMD does not arrive to the MS TO, and is quite disperse."
 Conversely. Sosin King 1997. and Piotto et al. 1997))," Conversely, Sosin King \cite{sosin97} and Piotto et al. \cite{piotto97}) )"
 present and extraordinarily well defined. MS. but no evolved stars are present.," present and extraordinarily well defined MS, but no evolved stars are present."
 The most recent ground-based study is the composite CMD of Durrell Harris (1993)) based on CCD data from two telescopes., The most recent ground-based study is the composite CMD of Durrell Harris \cite{durrell93}) ) based on CCD data from two telescopes.
 This is the kind of problem that we try to avoid with the present catalog., This is the kind of problem that we try to avoid with the present catalog.
 Our diagram is well populated (~27000 stars) from the RGB tip down to V=22.5., Our diagram is well populated $\sim27000$ stars) from the RGB tip down to $V=22.5$.
 The CMD features are better identifiable when a radial selection. avoiding the clusters center. is done.," The CMD features are better identifiable when a radial selection, avoiding the clusters center, is done."
 The CMD in Fig., The CMD in Fig.
 24 gives the visual impression that there are three distinct groups of stars in the HB., \ref{ngc7078} gives the visual impression that there are three distinct groups of stars in the HB.
 The third possible group. on the red side of the RR Lyrae gap is surely a statistical fluctuation in the distribution of the RR Lyrae magnitudes and colors at random phase.," The third possible group, on the red side of the RR Lyrae gap is surely a statistical fluctuation in the distribution of the RR Lyrae magnitudes and colors at random phase."
 It 1s present neither in the CMDs of M15 in the above quoted works nor in our CMD of a larger stellar sample. with more accurate photometry from our HSTdata base.," It is present neither in the CMDs of M15 in the above quoted works nor in our CMD of a larger stellar sample, with more accurate photometry from our HSTdata base."
the magnetic field is initialized to be purely azimutha in the x y plane at all radii such that r<0Mee.,the magnetic field is initialized to be purely azimuthal in the $x$ $y$ plane at all radii such that $r\le r_{max}$.
 Essentially. this confguration is a sphere of neste circular inaenetic feld loops of constant strength.," Essentially, this configuration is a sphere of nested circular magnetic field loops of constant strength."
 Muuevically this configuration is realized by utilizing the vector potential. where B—WVxA.," Numerically this configuration is realized by utilizing the vector potential, where $\boldsymbol{B} = \boldsymbol{\nabla}\times \boldsymbol{A}$."
 For a coustau magnetic field of streneth Bo defined as described. the vector poteutial is given as The vector potential is caleulated at cell corners aud then differenced to calculate the face-ceutered magnetic fields.," For a constant magnetic field of strength $B_0$ defined as described, the vector potential is given as The vector potential is calculated at cell corners and then differenced to calculate the face-centered magnetic fields."
 The advantage of this maeuetic field geometry is that the leat flux is zero in the initial configuration: thus. all subsequent evolution is due to the MTI.," The advantage of this magnetic field geometry is that the heat flux is zero in the initial configuration; thus, all subsequent evolution is due to the MTI."
 The fiducial magnetic field streugth is chosen to be 1 uc. possibly moderately higher than the poorly constrained primordial feld but substautially less than today's observed feld.," The fiducial magnetic field strength is chosen to be 1 nG, possibly moderately higher than the poorly constrained primordial field but substantially less than today's observed field."
 A second magnetic field geometry is chosen to be a inore realistic represcutation for the tangled fields observed in clusters today., A second magnetic field geometry is chosen to be a more realistic representation for the tangled fields observed in clusters today.
 There is little theoretical euidanuce for the magnetic field power spectrmm in the ICAL so we choose a I&oliuogorov power spectrum for the magnetic field. initialized in Fourier space as where is chosen as the waveunuber correspouding μαςto 21 times the grid scale.," There is little theoretical guidance for the magnetic field power spectrum in the ICM, so we choose a Kolmogorov power spectrum for the magnetic field, initialized in Fourier space as where $k_{\textrm{peak}}$ is chosen as the wavenumber corresponding to 2–4 times the grid scale."
| We utilize the Fast Fourier Transform (FFT) as was done iu ? to caleulate the vector potentials iu real space., We utilize the Fast Fourier Transform (FFT) as was done in \citet{rs99} to calculate the vector potentials in real space.
 We also raucdomize the phase to avoid correlating the modes., We also randomize the phase to avoid correlating the modes.
" The magnetic enerev scales as B2οςμασ),", The magnetic energy scales as $B^2 \propto k^{-2(\alpha-1)}$.
" We initialize cach Gaussian component separately. so for the componentwise [xoluosorov spectrum. the appropriate choice is @=—17/6 to give the familiar sealing for energv of &-11/2,"," We initialize each Gaussian component separately, so for the componentwise Kolmogorov spectrum, the appropriate choice is $\alpha= -17/6$ to give the familiar scaling for energy of $k^{-11/3}$."
 This Respace scaling for lohuogorov turbulence is appropriate for initializing the 1D power spectrum (as opposed to the 3D power spectruni) in each direction separately., This $k$ -space scaling for Kolmogorov turbulence is appropriate for initializing the 1D power spectrum (as opposed to the 3D power spectrum) in each direction separately.
 We numerically check that the divergence of the maguetic field) remains zero and renormalize the maguetic energev such that (B*)=(Bj)., We numerically check that the divergence of the magnetic field remains zero and renormalize the magnetic energy such that $\langle B^2\rangle = \langle B_0^2\rangle$.
 Iu this section we discuss several of the characteristic timescales for a cluster as was outlined in ?.., In this section we discuss several of the characteristic timescales for a cluster as was outlined in \citet{ps07b}.
 The Bruut- frequency can be written in a more useful form for the cluster problem as The iiaxinma erowth rate is given bv the isothermal Iuuit of the Drunt-Viuisallà frequency. iuncly Table 2 examines these timescales in the galaxy cluster at a fiducial radius of 150 kpc.," The Brunt-V\""aiis\""all\""a frequency can be written in a more useful form for the cluster problem as The maximum growth rate is given by the isothermal limit of the Brunt-Väiisällä frequency, namely Table \ref{tab:clust:timescales} examines these timescales in the galaxy cluster at a fiducial radius of 450 kpc."
 Several of these timescales are dependent on the leneth scale of interest., Several of these timescales are dependent on the length scale of interest.
 Thus. they are cousidered on elobal scales. roughly a waveleneth of l1 Alpe. and the scale of the mean free path. roughly 30 kpc.," Thus, they are considered on global scales, roughly a wavelength of 1 Mpc, and the scale of the mean free path, roughly 30 kpc."
 The maenetic field is assumed to be 1 nC for these calculations., The magnetic field is assumed to be 1 nG for these calculations.
 As can be secu by exiuuination. the MTI has teus of erowtl times during a IIubble time. allowing significant rearranecinent of the atimosphere.," As can be seen by examination, the MTI has tens of growth times during a Hubble time, allowing significant rearrangement of the atmosphere."
 The magnetic field estimated using primordial values clearly plays no role. even on the leusth scale of the mean free path.," The magnetic field estimated using primordial values clearly plays no role, even on the length scale of the mean free path."
 Ou mean free path timescales. the conduction time is faster than the sound crossing time.," On mean free path timescales, the conduction time is faster than the sound crossing time."
 The potential worry is due to the thought that the heat fiux is saturated in the sense of ?.., The potential worry is due to the thought that the heat flux is saturated in the sense of \citet{cm77}.
 The right comparison there is nof the couduction time to the mode sound crossing finie but the electron thermal velocity to the velocity needed for electrous to transport the heat., The right comparison there is not the conduction time to the mode sound crossing time but the electron thermal velocity to the velocity needed for electrons to transport the heat.
 For the atinosphliere considered here. the saturated heat fiux is several orders of magnitude larger than the actual leat fiux.," For the atmosphere considered here, the saturated heat flux is several orders of magnitude larger than the actual heat flux."
 We use the 3D version of the Athena ATID code (C?) to simulate the AITT far into the nonlinear regine.," We use the 3D version of the Athena MHD code \citep{gs08,sg08} to simulate the MTI far into the nonlinear regime."
 Both the MIID aud the heat transport methodology and tests have been described in these references aud T. respectively.," Both the MHD and the heat transport methodology and tests have been described in these references and \citet{ps05}, respectively."
 The thermal diffusivity is either set as a constant or pernutted to vary spatially according to the standard Spitzer prescription., The thermal diffusivity is either set as a constant or permitted to vary spatially according to the standard Spitzer prescription.
 Tere we adopt the adopt the method of ? for handling variable thermal conductivities., Here we adopt the adopt the method of \citet{sh07} for handling variable thermal conductivities.
" Namely. the product of deusity and thermal diffusivity is interpolated to the cell faces using a harmonic average. mm one dimension as This harmonic averaging preveuts the Couraut condition frou, becoming severe due to discoutiuuous diffusivities aud densities at interfaces. should they develop."," Namely, the product of density and thermal diffusivity is interpolated to the cell faces using a harmonic average, in one dimension as This harmonic averaging prevents the Courant condition from becoming severe due to discontinuous diffusivities and densities at interfaces, should they develop."
 The timestep is determined with respect to the maxim thermal diffusivity ou the erid and the conduction module is sub-cvcled., The timestep is determined with respect to the maximum thermal diffusivity on the grid and the conduction module is sub-cycled.
 All the runs described in this chapter are performed onu a uniform Cartesian threc-dineusional grid with the initial cluster atmosphere described iu refsecnmodel.., All the runs described in this chapter are performed on a uniform Cartesian three-dimensional grid with the initial cluster atmosphere described in \\ref{sec:model}.
 The domain extends frou. —3.0x1074 cii to +3.0x1074 cin (968 kpe) in cach direction., The domain extends from $-3.0\times 10^{24}$ cm to $+3.0\times 10^{24}$ cm (968 kpc) in each direction.
 Most of the rus presented in this paper are snulated at a resolution of (128)? or correspouding to a zone size of 15 kpe respectively., Most of the runs presented in this paper are simulated at a resolution of $(128)^3$ or corresponding to a zone size of 15 kpc respectively.
 The simulations are typically runi for 3x101 s or 9.5 Car. a substantial fraction of cosmic time.," The simulations are typically run for $3\times 10^{17}$ s or 9.5 Gyr, a substantial fraction of cosmic time."
 The magnetic field is initialized in a region Tmax Which is slightly less than the leneth of the cube., The magnetic field is initialized in a region $r_{max}$ which is slightly less than the length of the cube.
 Typically for our siuulatious rj44=2.5x1074 (806 kpc)., Typically for our simulations $r_{\textrm{max}} = 2.5\times 10^{24}$ (806 kpc).
 Thus. the initial magnetic field is coufined to a spherical region.," Thus, the initial magnetic field is confined to a spherical region."
 Since there is no magnetic field outside of Pax. there is initially no conduction in this region.," Since there is no magnetic field outside of $r_{\textrm{max}}$, there is initially no conduction in this region."
 We use modified reflecting boundary conditions for all the MIID variables. in which the pressure aud deusitv are extrapolated iu the ghost zones.," We use modified reflecting boundary conditions for all the MHD variables, in which the pressure and density are extrapolated in the ghost zones."
 In order to prevent any uceative values for pressure or density iu the ghost zones. we introduce pressure and deusitv floors applied oulv in the ghost zones.," In order to prevent any negative values for pressure or density in the ghost zones, we introduce pressure and density floors applied only in the ghost zones."
 The maguetic field aud velocity field componcuts are simply reflected at the boundary., The magnetic field and velocity field components are simply reflected at the boundary.
 The heat fluxes are forced to be aciabatic by setting —0ou the boundary., The heat fluxes are forced to be adiabatic by setting on the boundary.
region of 20 pixel radius.,region of 20 pixel radius.
 The channels in the source spectrum were then binned in groups of 20 or more photons., The channels in the source spectrum were then binned in groups of 20 or more photons.
 Spectral fitting was done in NSPEC 12.5.1 (see Arnaud 1996 for a description of an earlier version ofλ, Spectral fitting was done in XSPEC 12.5.1 (see Arnaud 1996 for a description of an earlier version of.
ος Bebinned channels including photons below 0.5 keV and above S keV are ignored. because the response matrix lor Chandra. is better calibrated. within this energv range than outside of it.," Rebinned channels including photons below 0.5 keV and above 8 keV are ignored, because the response matrix for Chandra is better calibrated within this energy range than outside of it."
 We report the Lo errors on source parameters., We report the $\sigma$ errors on source parameters.
 In observation 321. taken 12 June 2000. the cluster's X-ray spectrum was well fitted (Cvo= 4.74/4) with a disk blackbody model with foreground. neutral hydrogen column density of 1.6«107 7. &T—O88(415 keV and normalization in NSPEC of L2.10 corresponcding toa best-fitting inner disk racius of 2 km assuming a lace- disk and no spectral hardening correction. (Mitsuda. et al.," In observation 321, taken 12 June 2000, the cluster's X-ray spectrum was well fitted $\chi^2/\nu=4.74/4$ ) with a disk blackbody model with foreground neutral hydrogen column density of $1.6\times10^{20}$ $^{-2}$, $kT = 0.88^{+0.16}_{-0.13}$ keV and normalization in XSPEC of $^{+1.6}_{-0.9} \times10^{-3}$, corresponding to a best-fitting inner disk radius of 72 km assuming a face-on disk and no spectral hardening correction (Mitsuda et al."
 1984)., 1984).
 The source Dux from 0.5-8.0 keV is um10+! fem /sec., The source flux from 0.5-8.0 keV is $^{+0.1}_{-0.9}\times10^{-14}$ $^2$ /sec.
 Phe best fitting value corresponds to à luminosity of 6.5«1077 eres/sec using a distance of 16 \Ipe to NGC 4472. based on the distance to the Virgo Cluster in which it is contained (Macri οἱ al.," The best fitting value corresponds to a luminosity of $6.5\times10^{38}$ ergs/sec using a distance of 16 Mpc to NGC 4472, based on the distance to the Virgo Cluster in which it is contained (Macri et al."
 1999)., 1999).
 1n observation 11274. taken on 27 February 2010. the source spectrum was well fitted. (i.c. v v=lO.5/19) with AL=152008 keV and normalization in NSPEC of 300$.]0 corresponding to a best fitting inner disk radius of 34 km assuming a face-on disk and no spectral hardening correction.," In observation 11274, taken on 27 February 2010, the source spectrum was well fitted (i.e. $\chi^2/\nu$ =10.5/19) with $kT =
1.52^{+0.16}_{-0.13}$ keV and normalization in XSPEC of $^{+3.3}_{-2.5}\times10^{-4}$, corresponding to a best fitting inner disk radius of 34 km assuming a face-on disk and no spectral hardening correction."
 The source [lux from 0.5-S.0. keV is m10H7 ergs/em?/sec., The source flux from 0.5-8.0 keV is $^{+0.2}_{-1.4}\times10^{-14}$ $^2$ /sec.
 The best fitting. value corresponds to a luminosity of 2.7/510° ergs/scc., The best fitting value corresponds to a luminosity of $2.7\times10^{39}$ ergs/sec.
 The temperatures of the disk ave thus different at nearly. the 3a level. and both spectra are. consistent with standard phenomenology that the inner disk radius will vary little in high/solt states.," The temperatures of the disk are thus different at nearly the $3\sigma$ level, and both spectra are consistent with standard phenomenology that the inner disk radius will vary little in high/soft states."
 Phe Iuminosity. difference is significant at more than deo. and the 3e. lower limit to the luminosity dillerence is about 55.107 ergs/sec. above the Exddington luminosity for a single neutron star.," The luminosity difference is significant at more than $4\sigma$, and the $3\sigma$ lower limit to the luminosity difference is about $5\times10^{38}$ ergs/sec, above the Eddington luminosity for a single neutron star."
 The Chandra spectra are shown in figure 1.., The Chandra spectra are shown in figure \ref{spectra}. .
 We have also triedἱ to [fit power law models to. the ata., We have also tried to fit power law models to the data.
 For observation 321. a power law model with the foreground Ny gives an acceptable fit. with ασE= 4176/4. with a power law index of 2.004O23US). and the 1-0 confidence interval for the [lux ranging from 10Ll ergs/sec/em. Doa," For observation 321, a power law model with the foreground $N_H$ gives an acceptable fit, with $\chi^2/\nu=4.76/4$ , with a power law index of $2.00\pm^{+0.24}_{-0.23}$, and the $\sigma$ confidence interval for the flux ranging from $\times10^{-14}$ $^2$."
nThe spectral shape is: thus muweinallv consistent with expectations for à. ονπαν state. but the luminosity is well above the few percent of 1e Exdldington luminosity in which hard states are typically 'ound (Maccarone 2003).," The spectral shape is thus marginally consistent with expectations for a low/hard state, but the luminosity is well above the few percent of the Eddington luminosity in which hard states are typically found (Maccarone 2003)."
 We thus favor the diskbb mocel fit as providing parameter values more likely to be indicative ‘the real physical state of the system. but we do note hat the spectral fits do not distinguish between the two scenarios.," We thus favor the diskbb model fit as providing parameter values more likely to be indicative of the real physical state of the system, but we do note that the spectral fits do not distinguish between the two scenarios."
 For observation 11274. a power law mocdel with the orceround Ny is formally a good fit. with αν=23/19. out with a spectral index of 1.3023:0.07. considerably harder han is ever seen in à low hard state from a Galactic black role X-ray. binary.," For observation 11274, a power law model with the foreground $N_H$ is formally a good fit, with $\chi^2/\nu=23/19$, but with a spectral index of $1.30\pm0.07$, considerably harder than is ever seen in a low hard state from a Galactic black hole X-ray binary."
 Since in the former case. the power law nmocel provides a poor fit to the data. and in the latter case. he best fitting value of the power law index lies outside the range expected. from. phenomenology. there is a strong case o be mace that the data are genuinely better explained with a strong thermal component than a pure power law spectrum.," Since in the former case, the power law model provides a poor fit to the data, and in the latter case, the best fitting value of the power law index lies outside the range expected from phenomenology, there is a strong case to be made that the data are genuinely better explained with a strong thermal component than a pure power law spectrum."
 The two other Chandra observations of this field of view. observation 322 (made 19 March. 2000). ancl observation SO95 (made 23 February 2008). have much shorter integration times.," The two other Chandra observations of this field of view, observation 322 (made 19 March 2000), and observation 8095 (made 23 February 2008), have much shorter integration times."
 For CXOU 1229410|075744. observation 322 vields 40 counts in 10 kiloseconcds with ACLIS-L. and observation NOO5 vields 24 counts in 5 kiloseconds. with ACIS-S. Both observations viele [lux levels of 5. 107 ergs/sec/eni.," For CXOU 1229410+075744, observation 322 yields 40 counts in 10 kiloseconds with ACIS-I, and observation 8095 yields 24 counts in 5 kiloseconds with ACIS-S. Both observations yield flux levels of $\sim$ 5 $\times10^{38}$ $^2$."
 Because there are not enough. counts [or detailed spectral fitting. there is a considerable uncertainty on the counts-to-energy conversion.," Because there are not enough counts for detailed spectral fitting, there is a considerable uncertainty on the counts-to-energy conversion."
 The Poisson errors are also substantial., The Poisson errors are also substantial.
 As a result. it is cdillicult to determine whether the flux levels during the two short. observations were higher or lower than those curing the longer observations.," As a result, it is difficult to determine whether the flux levels during the two short observations were higher or lower than those during the longer observations."
 “The X-ray detections ancl upper limits are summarized in Table 1.., The X-ray detections and upper limits are summarized in Table \ref{xrays}.
 Two deep NMM-Nexwton observations of this source have been mace as well., Two deep XMM-Newton observations of this source have been made as well.
 Llowever. this source is close cnough to the center of NCC 4472 that the clilfuse gas emission significantly alfects NMM'S sensitivity.," However, this source is close enough to the center of NGC 4472 that the diffuse gas emission significantly affects XMM's sensitivity."
 Phe 2XMM catalog (Watson et al., The 2XMM catalog (Watson et al.
 2009) reports a source S away [rom CXOU 1229410|075744. with a positional error of 4477 at 12h29m40.40s. |1 57m4.Is on 5 June 2002.," 2009) reports a source 8” away from CXOU 1229410+075744, with a positional error of 4.47” at 12h29m40.49s, $+7^{\circ}57$ m47.1s on 5 June 2002."
 The source is given a quality Hag (the EELACG parameter value) of 4. indicating that it is located within a region where spurious detections are likely. and that the source itself may be a spurious source.," The source is given a quality flag (the FLAG parameter value) of 4, indicating that it is located within a region where spurious detections are likely, and that the source itself may be a spurious source."
 Formally. 4o upper limits can be obtained from the ELIX tool. using data corresponding to the 2XMMI-DIU data release.," Formally, $4\sigma$ upper limits can be obtained from the FLIX tool, using data corresponding to the 2XMMi-DR3 data release."
 ELIN finds that the source was no brighter than about τι107 ergs/sec on 5 June 2002. and 2Q7 cres/sce on 1 January 2004.," FLIX finds that the source was no brighter than about $7\times10^{38}$ ergs/sec on 5 June 2002, and $2\times10^{38}$ ergs/sec on 1 January 2004."
 While the upper limits from FLIN appear to indicate that the source faded sometime after 2001. and re-brightened sometime between 2004 and 2008. we have also looked. at the aperture photometry from the FLIX tool.," While the upper limits from FLIX appear to indicate that the source faded sometime after 2001, and re-brightened sometime between 2004 and 2008, we have also looked at the aperture photometry from the FLIX tool."
 We set the extraction region to 5... in order to limit the cllects of confusion from nearby eas emission and other point sources.," We set the extraction region to 5”, in order to limit the effects of confusion from nearby gas emission and other point sources."
 We find that in the obseravations made on | January 2004. all three NAIAL instruments show a flux more than 3.86 above background in the 0.2-12 keV band. with the most sensitive PN detection above 5e.," We find that in the obseravations made on 1 January 2004, all three XMM instruments show a flux more than $3.8\sigma$ above background in the 0.2-12 keV band, with the most sensitive PN detection above $5\sigma$."
 The flux within 5° is 19+0.3.101 eres in the EPIC-PN.2.140.6.10H ergs/sec in MOSI. and /see3.0E0.6«1044 orgs/sec in MOS2.," The flux within 5” is $1.9\pm0.3\times10^{-14}$ ergs/sec in the EPIC-PN, $2.1\pm0.6\times10^{-14}$ ergs/sec in MOS1, and $3.0\pm0.6\times10^{-14}$ ergs/sec in MOS2."
 The encircled energy fraction at 57 is about, The encircled energy fraction at 5” is about.
 Taking the aperture photometry at face value. we estimate that the source was at about L2«10° cres/sec.," Taking the aperture photometry at face value, we estimate that the source was at about $1-2\times10^{39}$ ergs/sec."
 The aperture photometry from. FLEX for the 5 June 2002 observation gives a Lux level similar to that in the 1January 2004 observation. but the source was only about 20 above the background on 5 June 2002.," The aperture photometry from FLIX for the 5 June 2002 observation gives a flux level similar to that in the 1January 2004 observation, but the source was only about $2\sigma$ above the background on 5 June 2002."
 We tentatively trust. the aperture photometry results. in. part because they indicate," We tentatively trust the aperture photometry results, in part because they indicate"
these features is that in this part of the profile the signal is dominated by more highly delayed. components. making the periodic correlation C'(ó.7) contain signal power at larger |r| values than are present at earlier phases.,"these features is that in this part of the profile the signal is dominated by more highly delayed components, making the periodic correlation $C(\phi,\tau)$ contain signal power at larger $|\tau|$ values than are present at earlier phases."
 When transformed to the periodic spectrum domain. this results in [iner frequeney structure appearing at later pulse phases.," When transformed to the periodic spectrum domain, this results in finer frequency structure appearing at later pulse phases."
 Given the signal model presented in I5qn. 11..," Given the signal model presented in Eqn. \ref{eqn:model},"
 it is possible to determine both the SM. response and intrinsic pulse profile. directly from a single evelic spectrum., it is possible to determine both the ISM response and intrinsic pulse profile directly from a single cyclic spectrum.
" Phe two-dimensional evelie spectrum σταν) contains NeierNL cata values. while {νο(7) and Z(n) ave described bv only Nous|NS, model parameters."," The two-dimensional cyclic spectrum $S(\nu;\alpha_n)$ contains $N_{chan} \times N_{lag}^\prime$ data values, while $H_{ISM}(\nu)$ and $I(n)$ are described by only $N_{chan}+N_{lag}^\prime$ model parameters."
 This provides sullicient constraints for both to be determined via iterative least-squares minimization., This provides sufficient constraints for both to be determined via iterative least-squares minimization.
 X detailed. analysis of this method will be presented. in a separate paper (7).., A detailed analysis of this method will be presented in a separate paper \citep{walker:cyc}.
 One previous measurement. method for ο) has been published (?).. based on a dynamic spectrum. phase retrieval. procedure.," One previous measurement method for $h_{ISM}(t)$ has been published \citep{walker:hol}, based on a dynamic spectrum phase retrieval procedure."
 The evelic spectrum method is much simpler since in this case the wave phases can be measured. directly. giving an estimate of hs; from a single. “snapshot” observation.," The cyclic spectrum method is much simpler since in this case the wave phases can be measured directly, giving an estimate of $h_{ISM}$ from a single “snapshot” observation."
 The evelic spectrum also incorporates pulse. profile shape information. which is lost in standard dynamic spectra.," The cyclic spectrum also incorporates pulse profile shape information, which is lost in standard dynamic spectra."
 ‘This naturally lacis. for the first time. to a true coherently descattered pulse profile shape (Figure 3)).," This naturally leads, for the first time, to a true coherently descattered pulse profile shape (Figure \ref{fig:profs}) )."
 In contrast with previous intensitv-based profile deconvolution methods (?).. this requires no assumption of a specific functional form for hist ond is not alfected by ambiguity between intrinsic and ISM-induced: profile features.," In contrast with previous intensity-based profile deconvolution methods \citep{bhat:pbf}, this requires no assumption of a specific functional form for $h_{ISM}$ and is not affected by ambiguity between intrinsic and ISM-induced profile features."
 “Phe ESAL response shown in ligure 3 has an initial exponential decay followed by a more slowlv-decaving tail., The ISM response shown in Figure \ref{fig:profs} has an initial exponential decay followed by a more slowly-decaying tail.
" This will be interesting to compare in detail with the predictions of the standard. Ixolmogorov scattering mocel (o.g..ο),"," This will be interesting to compare in detail with the predictions of the standard Kolmogorov scattering model \citep[e.g.,][]{rjt+09}."
 There are several degeneracies that the descattering process alone can not resolve., There are several degeneracies that the descattering process alone can not resolve.
 As is ‘lear from Eqn. 1...," As is clear from Eqn. \ref{eqn:model},"
 multiplving {say by a constant. phase factor will produce no change in the observed eveclic spectrum., multiplying $H_{ISM}$ by a constant phase factor will produce no change in the observed cyclic spectrum.
 Similarly. without additional assumptions. the pulsar's intrinsic [ux Sy is degenerate. with the magnitude of £4;53j..," Similarly, without additional assumptions, the pulsar's intrinsic flux $S_0$ is degenerate with the magnitude of $H_{ISM}$."
 Most critically for pulsar timing. an arbitrary rotation can be applied to Z(ó). and absorbed into £s.," Most critically for pulsar timing, an arbitrary rotation can be applied to $I(\phi)$, and absorbed into $H_{ISM}$."
 That is. at this level of analysis it is impossible to distinguish an LSAI-induced delay. from a pulsar spin deviation or other timing ellect.," That is, at this level of analysis it is impossible to distinguish an ISM-induced delay from a pulsar spin deviation or other timing effect."
 Resolving this situation to obtain properly scattering-corrected timing will require the development of additional analysis techniques., Resolving this situation to obtain properly scattering-corrected timing will require the development of additional analysis techniques.
 This could range from assuming a constrained form. or applying moment analvsis to. fysay to physical models of the spatial distribution of scattering material. and is an active topic for further study.," This could range from assuming a constrained form or applying moment analysis to $h_{ISM}$ to physical models of the spatial distribution of scattering material, and is an active topic for further study."
 Compared with previous methods. the evelic spectrum. provides a qualitatively new way to measure the ISM response. and this new information dramatically expands the possibilities [or scattering corrections to timing data.," Compared with previous methods, the cyclic spectrum provides a qualitatively new way to measure the ISM response, and this new information dramatically expands the possibilities for scattering corrections to timing data."
 In addition to the determination of /;s. Eqn.," In addition to the determination of $H_{ISM}$, Eqn."
 9 allows for the appleation of other phase-coherent filters to the final integrated evelie spectra.," \ref{eqn:inout}
 allows for the applcation of other phase-coherent filters to the final integrated cyclic spectra."
 This technique can be used (ο perform coherent. dispersion corrections. within the limits of the evelie spectrum resolution.," This technique can be used to perform coherent dispersion corrections, within the limits of the cyclic spectrum resolution."
 Phe high frequency resolution of the pulsar cvelic spectrum. enables. precise »ost-detection. removal of narrow-band. radio. frequency interference. without sacrificing pulse phase resolution.," The high frequency resolution of the pulsar cyclic spectrum enables precise post-detection removal of narrow-band radio frequency interference, without sacrificing pulse phase resolution."
 More sophisticated approaches may also incorporate information eained [rom the evelostationaritv of the interference (7).., More sophisticated approaches may also incorporate information gained from the cyclostationarity of the interference \citep{feliachi:phd}.
 Although the discussion in refsec:analysis focused on the analysis of a single stochastic signal. pairs of correlated. evclostationary signals can be analyzed via evelic erossespectra. in complete analogy with standard. cross-spectra (2)...," Although the discussion in \\ref{sec:analysis} focused on the analysis of a single stochastic signal, pairs of correlated cyclostationary signals can be analyzed via cyclic cross-spectra, in complete analogy with standard cross-spectra \citep{gardner:book}."
 For. dual-polarization radio data. this results in the creation of evelic Stokes parameters. and allows for the application of phase-coherent matrix convolution (7)— directly. to the evelie spectra.," For dual-polarization radio data, this results in the creation of cyclic Stokes parameters, and allows for the application of phase-coherent matrix convolution \citep{straten:phase} directly to the cyclic spectra."
 For radio interferometers. analvzing cata from antenna pairs will produce evelic visibilities.," For radio interferometers, analyzing data from antenna pairs will produce cyclic visibilities."
 Along with recently developed VLBI imaging techniques for investigating pulsar scintillation (?7).. this could. prove to be an extremely powerful tool for exploring the ΙΔ.," Along with recently developed VLBI imaging techniques for investigating pulsar scintillation \citep{brisken:vlbi_arcs}, this could prove to be an extremely powerful tool for exploring the ISM."
 Cyclic spectral analysis is a powerful new observational echnique for studying radio pulsars., Cyclic spectral analysis is a powerful new observational technique for studying radio pulsars.
 Lt provides a clata representation that simultaneously preserves both high pulse shase resolution and high frequency resolution information about the signal., It provides a data representation that simultaneously preserves both high pulse phase resolution and high frequency resolution information about the signal.
 With the accompanying preservation of signal phase content. this allows fundamentally new analysis echniques not possible with standard filterbank data.," With the accompanying preservation of signal phase content, this allows fundamentally new analysis techniques not possible with standard filterbank data."
 This olds promise both for increasing our understanding of the ionized ΔΙ. and eventually for removing ISM scattering as an obstacle to achieving the highest. possible pulsar timing oxrecision.," This holds promise both for increasing our understanding of the ionized ISM, and eventually for removing ISM scattering as an obstacle to achieving the highest possible pulsar timing precision."
Quasars often exhibit narrow heavy element absorption lines near their emission redshift.,Quasars often exhibit narrow heavy element absorption lines near their emission redshift.
 One possible explanation for the origin of these systems is that they arise in clouds of matter associated with galaxies in the clusters surrounding the quasars., One possible explanation for the origin of these systems is that they arise in clouds of matter associated with galaxies in the clusters surrounding the quasars.
 Alternate possibility is that they originate in the clouds that are physically associated with the quasars themselves., Alternate possibility is that they originate in the clouds that are physically associated with the quasars themselves.
 It has been shown that both these scenarios may be true EEllingson et citeell1994:; Hamann et citeham 19972)., It has been shown that both these scenarios may be true Ellingson et \\cite{ell1994}; Hamann et \\cite{ham1997a}) ).
 Clusters of absorbers of any type are of particular interest., Clusters of absorbers of any type are of particular interest.
 On one hand. clustering. properties. of intervening. systems depend strongly on the type of absorbers. while on the other hand complexes of associated absorbers give a unique opportunity to analyze the properties of their hosts and of the quasar emission.," On one hand, clustering properties of intervening systems depend strongly on the type of absorbers, while on the other hand complexes of associated absorbers give a unique opportunity to analyze the properties of their hosts and of the quasar emission."
 The stumbling block in such studies is the fact that bright high redshift quasars with rich absorption are rare (for examples of such systems see. e.g.. Morris et citemor1986:: Foltz et citefol 987:: Petitjean et citepet1994:;; Hamann et citeham1997a:; Lespine Petitjean 1997:: Petitjean Srianand 1999)).," The stumbling block in such studies is the fact that bright high redshift quasars with rich absorption are rare (for examples of such systems see, e.g., Morris et \\cite{mor1986}; ; Foltz et \\cite{fol1987}; Petitjean et \\cite{pet1994}; Hamann et \\cite{ham1997a}; Lespine Petitjean \cite{les1997}; Petitjean Srianand \cite{pet1999}) )."
 There are only a few quasars known with more than just a handful of associated absorption systems which are bright enough to perform high resolution spectral analysis., There are only a few quasars known with more than just a handful of associated absorption systems which are bright enough to perform high resolution spectral analysis.
 In this paper we present a bright τμ=2.51 quasar 1160343820 (eyosy=16:03:07.7.04193) +38:20:07) with a very rich metal absorption spectrum.," In this paper we present a bright $z_{\rm em}=2.51$ quasar 1603+3820 $\alpha_{\rm 1950} = \mbox{16:03:07.7}, \delta_{\rm
1950} = \mbox{+38:20:07}$ ) with a very rich metal absorption spectrum."
 It was discovered during the course of the Hamburg/CfA Bright Quasar Survey (Hagen et 1995;; Dobrzycki et citedob1996)).Quasar candidates in the survey are selected, It was discovered during the course of the Hamburg/CfA Bright Quasar Survey (Hagen et \\cite{hag1995}; ; Dobrzycki et \\cite{dob1996}) ).Quasar candidates in the survey are selected
The research work of ο. D. is supported by the University. Grants Comunission. Government of India Grant No.,"The research work of S. D. is supported by the University Grants Commission, Government of India Grant No."
 3432/2008 (SR)., 34-32/2008 (SR).
" 5. G. and ο, V. acknowledges (he financial support provided by Council for Scientific and Industrial Research (CSIR) and University Grants Commission (UGC). Government of India. respectively."," S. G. and S. V. acknowledges the financial support provided by Council for Scientific and Industrial Research (CSIR) and University Grants Commission (UGC), Government of India, respectively."
from the emergent fluxes computed with the SYNSPEC code. applying Eq.,"from the emergent fluxes computed with the SYNSPEC code, applying Eq."
 5 for individual rotational phases., \ref{velik} for individual rotational phases.
 To study the influence of individual elements separately. we first calculated the light variations with the abundance map of one element only (Fig. 4)).," To study the influence of individual elements separately, we first calculated the light variations with the abundance map of one element only (Fig. \ref{prv_hvvel}) ),"
 assuming a fixed abundance of other elements (eq.= —1.0. eg=-3.75. ος=-5.9. εις= —44)," assuming a fixed abundance of other elements $\varepsilon_\text{He}=-1.0$ , $\varepsilon_\text{Si}=-3.75$, $\varepsilon_\text{Cr}=-5.9$, $\varepsilon_\text{Fe}=-4.4$ )."
 From Fig., From Fig.
 4. it follows that iron. silicon. and chromium contribute most to the light variations. while the contribution of helium is only marginal.," \ref{prv_hvvel} it follows that iron, silicon, and chromium contribute most to the light variations, while the contribution of helium is only marginal."
 This ts because of the large overabundance of these elements in the spots and by their large abundance variations on the stellar surface., This is because of the large overabundance of these elements in the spots and by their large abundance variations on the stellar surface.
" The amplitude of the light variations increases with decreasing wavelength. as can be expected from the plot of the magnitude difference Aun, in Fig. 3.."," The amplitude of the light variations increases with decreasing wavelength, as can be expected from the plot of the magnitude difference $\Delta m_\lambda$ in Fig. \ref{magtoky}. ."
 Because the overabundant regions are brighter in the (ον colours. the predicted light variations. reflect the equivalent width variations1).," Because the overabundant regions are brighter in the $uvby$ colours, the predicted light variations reflect the equivalent width variations."
. The light maximum occurs at the same phase at which the equivalent widths of a given element are the largest., The light maximum occurs at the same phase at which the equivalent widths of a given element are the largest.
 Because this happens at slightly different phases for individual elements. the light curves in Fig.," Because this happens at slightly different phases for individual elements, the light curves in Fig."
 4+ are slightly shifted., \ref{prv_hvvel} are slightly shifted.
 Taking into account the surface distribution of helium. silicon. chromium. and iron m the calculation. of the light curves (Fig. 5)).," Taking into account the surface distribution of helium, silicon, chromium, and iron in the calculation of the light curves (Fig. \ref{cuvir_hvvel}) ),"
 we obtained a good agreement between the observed and predicted light curves in the v. 6 and y bands of the Strómmgren photometric system.," we obtained a good agreement between the observed and predicted light curves in the $v$, $b$ and $y$ bands of the Strömmgren photometric system."
 On the other hand. our models are able to explain only about half of the amplitude in the 4 filter.," On the other hand, our models are able to explain only about half of the amplitude in the $u$ filter."
 The disagreement between the predicted and observed light curves is mostly apparent around phase @=0.6., The disagreement between the predicted and observed light curves is mostly apparent around phase $\phi=0.6$.
 ote also that a similar disagreement visible in 4 can be also found in other filters. but to a much smaller extent.," Note also that a similar disagreement visible in $u$ can be also found in other filters, but to a much smaller extent."
 These differences clearly point to an existence of some additional. unknown mechanism working especially in the violet band that still needs to be investigated (Fig. 5..," These differences clearly point to an existence of some additional, unknown mechanism working especially in the violet band that still needs to be investigated (Fig. \ref{cuvir_hvvel},"
 and see also Sect. 7))., and see also Sect. \ref{kecame}) ).
 The discrepancies between the predicted ad observed light curves increase when comparing the predicted and observed colour indices (see Fig. 6))., The discrepancies between the predicted and observed light curves increase when comparing the predicted and observed colour indices (see Fig. \ref{cuvir_uvby}) ).
 While the (5—v) data agree reasonably well. the (v—5) curves are mutually shifted. and the predicted metallic index gj=(v—5)—(b—xy) shows a significantly lower amplitude than the observed one.," While the $(b-y)$ data agree reasonably well, the $(v-b)$ curves are mutually shifted, and the predicted metallic index $m_{\text{1}}=(v-b)-(b-y)$ shows a significantly lower amplitude than the observed one."
 The inhomogeneous surface distribution of individual elements causes bright spots on the stellar surface., The inhomogeneous surface distribution of individual elements causes bright spots on the stellar surface.
 The spots. whose surface distribution can be derived using abundance maps and model atmospheres (see Fig. 7)).," The spots, whose surface distribution can be derived using abundance maps and model atmospheres (see Fig. \ref{cuvir_povrch}) ),"
 cause the light variability., cause the light variability.
 We have shown that the light variability of iis caused by the redistribution of flux from the far UV to the near UV and visible regions., We have shown that the light variability of is caused by the redistribution of flux from the far UV to the near UV and visible regions.
 Consequently. the light variability in the farUV regionshould be in antiphase with the visual one.," Consequently, the light variability in the farUV regionshould be in antiphase with the visual one."
 This behaviour was indeed found in a detailed analysis of IUE, This behaviour was indeed found in a detailed analysis of IUE
disces are derived by 2.. assuming saturation docs not occur vet.,"discs are derived by \citet{pbck09}, assuming saturation does not occur yet."
 7. reexamined the corotation torque in acliabatic disces. taking into account the effects. of pressure.," \citet{mc09} reexamined the corotation torque in adiabatic discs, taking into account the effects of pressure."
 Γον showed that the. entropy-relatecl torque does. not arise. from. the overdense ancl underdense regions. as had. been previously thought.," They showed that the entropy-related torque does not arise from the overdense and underdense regions, as had been previously thought."
 Instead. they showed. that entropy. gradients make the horseshoe region considerably asymmetric. and this asymmetry. exerts the entropy-related torque by. the excitation of evanescent waves at the horseshoe sparatrices.," Instead, they showed that entropy gradients make the horseshoe region considerably asymmetric, and this asymmetry exerts the entropy-related torque by the excitation of evanescent waves at the horseshoe sparatrices."
 Since these evanescent waves are excited by pressure disturbance that are a result. of horseshoe orbits. the magnitude of the entropy-relatecl torque depends on the perturbed pressure.," Since these evanescent waves are excited by pressure disturbance that are a result of horseshoe orbits, the magnitude of the entropy-related torque depends on the perturbed pressure."
 This gives an explanation of the results of? that the corotation torque in a very cold. acliabatic disc is identical to that in an isothermal disc.," This gives an explanation of the results of \citet{bm08} that the corotation torque in a very cold, adiabatic disc is identical to that in an isothermal disc."
 Thus. the corotation torque or horseshoe drag can be important only for disces assumed to be adiabatic with high emperatures. that is. the radiative cooling timescale in disces is longer than the planet's orbital period.," Thus, the corotation torque or horseshoe drag can be important only for discs assumed to be adiabatic with high temperatures, that is, the radiative cooling timescale in discs is longer than the planet's orbital period."
 Otherwise. he direction of migration is determined by the Lindblad orque.," Otherwise, the direction of migration is determined by the Lindblad torque."
 The horseshoe drag. however. has some problems.," The horseshoe drag, however, has some problems."
 One is the width of the horseshoe region. and the other is saturation.," One is the width of the horseshoe region, and the other is saturation."
 The former is characterised by the mass of the janets. but it is parameterized in numerical simulations xuwily because a planet is treated: as a point mass object (77) and partly because any simulation cannot infinitely resolve the horseshoe region (??)..," The former is characterised by the mass of the planets, but it is parameterized in numerical simulations partly because a planet is treated as a point mass object \citep{dkh03,pbck09} and partly because any simulation cannot infinitely resolve the horseshoe region \citep{mdk06,pp09}."
 For the latter problem. he horseshoe drag can be saturated (ic. negligible) due to acdiabatie invariance.," For the latter problem, the horseshoe drag can be saturated (i.e. negligible) due to adiabatic invariance."
 We emphasise that the problem of saturation is essentially how the disc viscosity connects the horseshoe region to the rest of disc by transferring angular momentunm. between them (e.g.2).., We emphasise that the problem of saturation is essentially how the disc viscosity connects the horseshoe region to the rest of disc by transferring angular momentum between them \citep[e.g.][]{mc10}.
 This is crucial for understanding horseshoe drags., This is crucial for understanding horseshoe drags.
 As a example. we summarise the work done bv ? who considered the saturation of the vortensitv-related and. entropy-related: horseshoc drags.," As a example, we summarise the work done by \citet{pbk10} who considered the saturation of the vortensity-related and entropy-related horseshoe drags."
 For the vortensity-related. one. the saturation is controlled. only bv. viscous cillusion (alsosee2?7).," For the vortensity-related one, the saturation is controlled only by viscous diffusion \citep[also see][]{m01,m02,ward07}."
. For the disces with a~LO he horseshoe drag becomes almost zero while it is unsaturated for the disc with a~0.01 (?)..," For the discs with $\alpha \sim 10^{-5}$, the horseshoe drag becomes almost zero while it is unsaturated for the disc with $\alpha \sim 0.01$ \citep{pp08}."
 ? (7)..," \citet{pbk10} \citep{pbk10},"
"tendency to overestimate the error as v becomes low; the ση, bias has no dependence on the pixel sampling.",tendency to overestimate the error as $\nu$ becomes low; the $\tilde{\sigma}_{\eta_i}$ bias has no dependence on the pixel sampling.
 The v dependence is approximately πω..., The $\nu$ dependence is approximately $\sqrt{\langle\Delta\eta_i^2/\tilde{\sigma}_{\eta_i}^2\rangle}\simeq $ $1-\frac{0.6}{\nu}$.
" Figure 7 shows the accuracy of a deconvolution fit when a symmetric, exponential galaxy is convolved with an Airy PSF."," Figure \ref{fig:dcvlshapeerror100} shows the accuracy of a deconvolution fit when a symmetric, exponential galaxy is convolved with an Airy PSF."
" We first discuss a high-S/N case, v=100."," We first discuss a $S/N$ case, $\nu=100$."
" The measurements were done at various minor axis resolutions, where rp=0.5, 1, 2, and 5 each correspond to the columns from left to right."," The measurements were done at various minor axis resolutions, where $r_b=0.5$, 1, 2, and 5 each correspond to the columns from left to right."
 The panels in the top two rows show the shape error (An;) as a function of the input galaxy ellipticity., The panels in the top two rows show the shape error $\langle\Delta\eta_i\rangle$ as a function of the input galaxy ellipticity.
" In the top row, the Airy PSF is circular (epsr= 0.0), while in the middle row the Airy PSF is anisotropic, with an ellipticity of"," In the top row, the Airy PSF is circular $e_{\rm PSF}=0.0$ ), while in the middle row the Airy PSF is anisotropic, with an ellipticity of"
he aperture used. to avoid confusion we do not give a ucasured excess value. oulv the plotospheric fux which can be subtracted from azuv later measurcieuts.,"the aperture used, to avoid confusion we do not give a measured excess value, only the photospheric flux which can be subtracted from any later measurements."
 The shotospheric flux given in Table 1 does not include the coutributiou from the C dwarf (90 aud 10τιν at 51 andl TOyan. respectively).," The photospheric flux given in Table \ref{tab:par} does not include the contribution from the G dwarf $90$ and $10 ~{\rm mJy}$ at $24$ and $70 ~\micron$, respectively)."
 The top left panel iu Figure 1 shows he sumuned iuaege from epochs 2 aud 3. to demoustrate he asviunietrv sueeested even before PSF subtraction.," The top left panel in Figure 1 shows the summed image from epochs 2 and 3, to demonstrate the asymmetry suggested even before PSF subtraction."
 For the fist epoch 21jan nuage. the refercuce star lage was subtracted from the image of 6 Velormu. with a scale factor chosen as the masxinuun value that would completely remove the nuage core without creating siguificant negative flux residuals.," For the first epoch $24 ~\micron$ image, the reference star image was subtracted from the image of $\delta$ Velorum, with a scale factor chosen as the maximum value that would completely remove the image core without creating significant negative flux residuals."
 The deeper exposures from the secoud and third epochs were designed to reveal faint structures far from the star. where the observed PSF is difficult to extract accurately.," The deeper exposures from the second and third epochs were designed to reveal faint structures far from the star, where the observed PSF is difficult to extract accurately."
 Therefore. we used simulated PSFs (from STinwTim 2002))) aud the AQPS simulator7.," Therefore, we used simulated PSFs (from STinyTim ) and the MIPS simulator."
. Because bright structures nearly iu he PSF contribute to the residuals at large distances. we oversubtracted the PSF to compensate.," Because bright structures nearly in the PSF contribute to the residuals at large distances, we oversubtracted the PSF to compensate."
 The first epoch PSF subtracted 21jan image is shown iu the bottom xuels of Figure 1. aud the composite from epochs 2 aud 3 in the upper right., The first epoch PSF subtracted $24 ~\micron$ image is shown in the bottom panels of Figure \ref{fig:im} and the composite from epochs 2 and 3 in the upper right.
 The PSF subtracted nuages in Figure l1. show that he asvuuuetrv is caused bv a bow shock., The PSF subtracted images in Figure \ref{fig:im} show that the asymmetry is caused by a bow shock.
 As shown in the lower left. the head of the bow shock points approximately toward the direction of the stellar proper notion.," As shown in the lower left, the head of the bow shock points approximately toward the direction of the stellar proper motion."
 The bottom right paucl shows the excess fiux contours and that it consists of incomplete spherical shells centered ou à. Velorzuu., The bottom right panel shows the excess flux contours and that it consists of incomplete spherical shells centered on $\delta$ Velorum.
 Combined with the upper right damage. there is also a parabolic cavity. as expected for a bow shock.," Combined with the upper right image, there is also a parabolic cavity, as expected for a bow shock."
 The stagnation points (where photon pressure equals gravitational force) of the grains in the bow shock are within ~200AU of the star. according to the observations.," The stagnation points (where photon pressure equals gravitational force) of the grains in the bow shock are within $\sim 200 ~{\rm AU}$ of the star, according to the observations."
 A notable feature in the upper right is the wines of the bow shock. which are detectable to 1500AU.," A notable feature in the upper right is the wings of the bow shock, which are detectable to $\sim 1500 ~{\rm AU}$."
 The 70ji observation is shown iu Figure 2.., The $70 ~\micron$ observation is shown in Figure \ref{fig:70}.
 The PSF subtraction (scaled to the point source flux of 125 αι) does uot reveal the bow shock structure at this wavelength. only that there is extended excess.," The PSF subtraction (scaled to the point source flux of $125 ~{\rm mJy}$ ) does not reveal the bow shock structure at this wavelength, only that there is extended excess."
 The total flux of the residual of the PSF subtracted inage is 119wy., The total flux of the residual of the PSF subtracted image is $119 ~{\rm mJy}$.
 The iuteusitv coutowurs panel) sugeest that the 70pin excess fades at the cavity behind the star. but the effect is small.," The intensity contours ) suggest that the $70 ~\micron$ excess fades at the cavity behind the star, but the effect is small."
 The ecometry aud direction of the bow shock are discussed in more detail iu 83.2., The geometry and direction of the bow shock are discussed in more detail in 3.2.
 Based on a previous sugeestion bv(1990).. proposed a physical model to explain the abundance— pattern of A Boottis stars through πανΔΙ interaction and the diffusion/accretion hvpothesis.," Based on a previous suggestion by, proposed a physical model to explain the abundance pattern of $\lambda$ Boöttis stars through star-ISM interaction and the diffusion/accretion hypothesis."
 Then imeocel is based on a lunimnous nmnaiu-sequeuce star passing through a diffuse ISM. cloud., Their model is based on a luminous main-sequence star passing through a diffuse ISM cloud.
 The star blows the interstellar dust eraius away by its radiation pressure. but accretes the interstellar gas onto its surface. thus establishing a thin surface laver with abundance anomalics.," The star blows the interstellar dust grains away by its radiation pressure, but accretes the interstellar gas onto its surface, thus establishing a thin surface layer with abundance anomalies."
 So long as the star is inside the cloud. the dust erains are heated to produce excess in the infrared above the photospheric radiation of the star.," So long as the star is inside the cloud, the dust grains are heated to produce excess in the infrared above the photospheric radiation of the star."
 Martfunez-CGalarza et ((2007. in prep.)," Martínnez-Galarza et (2007, in prep.)"
 have developed a model of this process aud show that the elobal spectral energy. distributions of a eroup of A Boottis type stars that have infrared) excesses are consistent with the emission from the hivpothesized ISM cloud., have developed a model of this process and show that the global spectral energy distributions of a group of $\lambda$ Boöttis type stars that have infrared excesses are consistent with the emission from the hypothesized ISM cloud.
 Details of the mocel can be found in their paper., Details of the model can be found in their paper.
" Tere we adapt their model anc improve its fidelity (c.e.. with higher resolution itceratious). aud also model the surface brightuess distribution to describe the observed bow shock seen around 6 ολοι,"," Here we adapt their model and improve its fidelity (e.g., with higher resolution integrations), and also model the surface brightness distribution to describe the observed bow shock seen around $\delta$ Velorum."
 The phenomenon of stzr-ISM interactions generating vow shocks was first studied by., The phenomenon of star-ISM interactions generating bow shocks was first studied by.
(1997)... They showed that the radiative pressure force on a subanicron dust erain can be many times that of he eravitational force as it approaches the star., They showed that the radiative pressure force on a sub-micron dust grain can be many times that of the gravitational force as it approaches the star.
 The scattering surface will be a parabola with the star at the focus point of the parabolic shaped dust cavity., The scattering surface will be a parabola with the star at the focus point of the parabolic shaped dust cavity.
 Since he star heats the erains outside of the cavity and close o the parabolic surface. an infrared-emitting bow shock cature is expected.," Since the star heats the grains outside of the cavity and close to the parabolic surface, an infrared-emitting bow shock feature is expected."
 The shape of the parabola (for cach erain size) cau ο given in terms of the distance between the star (focus) aud the vertex., The shape of the parabola (for each grain size) can be given in terms of the distance between the star (focus) and the vertex.
 This so-called avoidance radius (or the p/2 parameter of the scattering parabola) can be calculated from euerev. conservation to be1997): where 6 is the radius of the particle. AZ is the umass of the star ancl ey is the relative velocity between the star and the dust eraius.," This so-called avoidance radius (or the $p/2$ parameter of the scattering parabola) can be calculated from energy conservation to be: where $a$ is the radius of the particle, $M$ is the mass of the star and $v_{\rm rel}$ is the relative velocity between the star and the dust grains."
" “as the ratio of photon pressure to eravitatioual force on a erain and it is eiven by1979): where à is the bulk density of the erain material and QV, is the radiation pressure oficieucy averaged over tlie stellar spectrum.", $\beta^a$ is the ratio of photon pressure to gravitational force on a grain and it is given by: where $\delta$ is the bulk density of the grain material and $Q_{\rm pr}^a$ is the radiation pressure efficiency averaged over the stellar spectrum.
" QUU) can be expressed in terns of erain. properties. PRSEscattering. cocfiicicnt QU.[aan(A) and the scattering asviunietry.(Qu, factor"," $Q_{\rm pr}^a(\lambda)$ can be expressed in terms of grain properties )$, scattering coefficient $Q_{\rm sca}^a(\lambda)$ and the scattering asymmetry factor"
where the longitudinal and latitucinal components of j£ are proportional to the acceleration of the solar svstem projected on the celestial plane assumes that the acceleration of the solar svstem barvcenter has only dy = 4 component. (he equations (5)) (7)) for the elective proper motion caused by the secular aberration are simplified and reduced to Proper motion vectors j£ of a given number of objects represent a discrete vector field on the sphere which can be decomposed in a set of vector spherical harmonics (Thorne.1980)..,"where the longitudinal and latitudinal components of $\vec\mu$ are proportional to the acceleration of the solar system projected on the celestial plane If one assumes that the acceleration of the solar system barycenter has only $A_X=A$ component, the equations \ref{2a}) \ref{3a}) ) for the effective proper motion caused by the secular aberration are simplified and reduced to Proper motion vectors $\vec\mu$ of a given number of objects represent a discrete vector field on the sphere which can be decomposed in a set of vector spherical harmonics \citep{thorne}."
 The largest galactocentric component of (he secular aberration can be determined [rom global astromeltric observations as à svsteniatic dipole component of this vector field., The largest galactocentric component of the secular aberration can be determined from global astrometric observations as a systematic dipole component of this vector field.
 For quasars the problem of its determination is simpler (han for stars since {μον have negligible small proper motions caused by their peculiar velocities with respect to the Hubble flow., For quasars the problem of its determination is simpler than for stars since they have negligibly small proper motions caused by their peculiar velocities with respect to the Hubble flow.
 Therefore. the secular aberration can be directly measured Irom the observed proper motions of quasars.," Therefore, the secular aberration can be directly measured from the observed proper motions of quasars."
 The magnitude of the secular aberration effect in (he case givenby Eq. (8)), The magnitude of the secular aberration effect in the case givenby Eq. \ref{4}) )
 is where sin€=V1—cos?/b and ὁ is the angle between the direction towards the galactic center and (hat to the stir.," is \citep{gaia-report}
 where $\sin\zeta=\sqrt{1-\cos^2l\cos^2b}$ and $\zeta$ is the angle between the direction towards the galactic center and that to the star."
 In what follows. we investigate a more accurate approximation of Eq. (8))," In what follows, we investigate a more accurate approximation of Eq. \ref{4}) )"
 that includes all three components of the Sun's acceleration. ancl evaluate the effect of the secular aberration more adequately in terms of vector harmonics.," that includes all three components of the Sun's acceleration, and evaluate the effect of the secular aberration more adequately in terms of vector harmonics."
 The velocity vector of the Sun in the galaxy is commonly considered (o be the sum of two components (Dinnev&Merrifield1998)., The velocity vector of the Sun in the galaxy is commonly considered to be the sum of two components \citep{binney}.
. The first (and largest) component is the motion ol the so-called. Local Standard of Rest (LR).," The first (and largest) component is the motion of the so-called, Local Standard of Rest (LSR)."
 By definition (Dinnev&Merrifield1993).. the LSR. is involved in a cireular planar motion around the center of mass of the galaxy. at a constant rate wilh a period £7.," By definition \citep{binney}, the LSR is involved in a circular planar motion around the center of mass of the galaxy at a constant rate with a period $P_0$ ."
 The second component of the solar velocity is the differential, The second component of the solar velocity is the differential
he discrepauey. between the two colors is only at the 20 evel.,the discrepancy between the two colors is only at the $\sigma$ level.
 The colors predicted from a 0.2 keV. metallicity ISM are (C21.032 =0.51.0.22). whereas the colors for a 13 keV. motallicity ISM are (021.032 =1.17.0.16).," The colors predicted from a 0.2 keV, metallicity ISM are (C21,C32 $= 0.54, 0.22)$, whereas the colors for a 0.3 keV, metallicity ISM are (C21,C32 $= 1.17, 0.46)$."
" ""Thus. if any ISM is preseut in NGC 1697. its temperature uust be below 0.3 keV and at a low metallicity. or else he C21 color of the LAINBs|ISM would be higher than he LAINBs alone. which is not observed."," Thus, if any ISM is present in NGC 4697, its temperature must be below 0.3 keV and at a low metallicity, or else the C21 color of the LMXBs+ISM would be higher than the LMXBs alone, which is not observed."
 In conclusion. we cannot rule out the prescuce of some low temperature ISM in NGC L697. although it is certain that an ISAL cannot constitute a majority of the cussion.," In conclusion, we cannot rule out the presence of some low temperature ISM in NGC 4697, although it is certain that an ISM cannot constitute a majority of the emission."
 Lwiu Breeian (19995) found that Galactic and MOI elobular cluster LAINB ταν colors were correlated with the aetallicity of the globular cluster. in the sense that lugher metallicity globular clusters had LATINBs with softer N-vav colors.," Irwin Bregman (1999b) found that Galactic and M31 globular cluster LMXB X-ray colors were correlated with the metallicity of the globular cluster, in the sense that higher metallicity globular clusters had LMXBs with softer X-ray colors."
 If this correlation extended to all LAINBs. it would predict that the N-vav colors of NGC L697 should harden with increasing radius. since metallicity decreases with radius iu elliptical galaxies.," If this correlation extended to all LMXBs, it would predict that the X-ray colors of NGC 4697 should harden with increasing radius, since metallicity decreases with radius in elliptical galaxies."
 Furthermore. the metallicity of NCC 1697 is rather low.," Furthermore, the metallicity of NGC 4697 is rather low."
 Within half an effective radius. the average ietallicity is onlv solar (Trager et 22000).," Within half an effective radius, the average metallicity is only solar (Trager et 2000)."
 The metallicity-color relation of Irwin Bregman (1999b) would predict a C32 color of about 1.5 within half au effective radius. aud au increase with increasing radius.," The metallicity-color relation of Irwin Bregman (1999b) would predict a C32 color of about 1.5 within half an effective radius, and an increase with increasing radius."
 The colors of the four resolved sources as well as the unresolved cuiissiou are at odds with this inetallicitv-color relation., The colors of the four resolved sources as well as the unresolved emission are at odds with this metallicity-color relation.
 Appaveuthy. if such a metallicity-color relation truly exists for LAINBs. it oulv applies to LAINBs that reside iuglobular clusters.," Apparently, if such a metallicity-color relation truly exists for LMXBs, it only applies to LMXBs that reside inglobular clusters."
 The X-ray source in NGC 1697 associated with a globular cluster (Source 11) has a C32 color of 1.11250.30. which would be consistent with the metallicity-color relation ifthe elobular cluster has a high metallicity.," The X-ray source in NGC 4697 associated with a globular cluster (Source 11) has a C32 color of $1.14 \pm 0.30$, which would be consistent with the metallicity-color relation if the globular cluster has a high metallicity."
" We also investigated the possibility that LAINBs below the detection threshold of the IIRI could account for the ""resolved eimissiou eiven a reasonable LAINB Iuninosityv distribution function for NGC 1697.", We also investigated the possibility that LMXBs below the detection threshold of the HRI could account for the unresolved emission given a reasonable LMXB luminosity distribution function for NGC 4697.
 Wo assuued a Dhuunositv distribution function ΑςLy)xLU. which is consistent within the errors with the bhuuinositv distribution function of pointsources in MOI with huuinositics greater than 2«LO cress3| (Primini ct 11993).," We assumed a luminosity distribution function $N(>L_X) \propto L_X^{-1.3}$, which is consistent within the errors with the luminosity distribution function of pointsources in M31 with luminosities greater than $2 \times 10^{37}$ ergs $^{-1}$ (Primini et 1993)."
 The function was normalized to vield the ohservec N-rav luminosity of NGC 1697 when inteerated over al LMXD hiuuinosities., The function was normalized to yield the observed X-ray luminosity of NGC 4697 when integrated over all LMXB luminosities.
 This model predicted 11 sources with uuivositics over 3«LOPS eyes 1; which coutributed o the total N-rav enissiou from LAINBs.," This model predicted 11 sources with luminosities over $3 \times 10^{38}$ ergs $^{-1}$, which contributed to the total X-ray emission from LMXBs."
 This agrees wel with what was observed with the URI: neglecting the poiut source associated with au unidentified optical counterpart. he remaining 11 detected sources comprised of he total emission.," This agrees well with what was observed with the HRI; neglecting the point source associated with an unidentified optical counterpart, the remaining 11 detected sources comprised of the total emission."
 Thus. if the luminosity distribution muction of LAINBs of NGC. L697 is similar to that of he brighter LAINBs in M2. the integrated eimissiou frou LAINBs below the detection threshold of the IIRI cau account for most of the uuresolveck emission.," Thus, if the luminosity distribution function of LMXBs of NGC 4697 is similar to that of the brighter LMXBs in M31, the integrated emission from LMXBs below the detection threshold of the HRI can account for most of the unresolved emission."
 Tuterestingly. the detection limit of the IIRI observation of 3«1075 eres 1 Bes above the Eddinetou luminosity laut for a 1.1AZ. ueutrou star.," Interestingly, the detection limit of the HRI observation of $3 \times 10^{38}$ ergs $^{-1}$ lies above the Eddington luminosity limit for a $1.4~M_{\odot}$ neutron star."
 LAINBs of simular huninosities as the ones found here exist in our own Galaxy., LMXBs of similar luminosities as the ones found here exist in our own Galaxy.
"A compilation by Christian Swank (1997) found cight galactic LAINBs with Iuninosities ereater than Jos10"" ores + (we have converted their 0.71.5 keV huninosities to 0.25-10 keV. huninositics usine the spectral model of 3)).",A compilation by Christian Swank (1997) found eight galactic LMXBs with luminosities greater than $3 \times 10^{38}$ ergs $^{-1}$ (we have converted their 0.7–4.5 keV luminosities to 0.25-10 keV luminosities using the spectral model of \ref{sec:spectral}) ).
 These high Iuninosities imply either that he compact object within the binary is a black hole (with Aipyc6AL.. for the most huuiuous binaries) or that he huninositics truly exceed the Edcdiugton limit for a jeutron star., These high luminosities imply either that the compact object within the binary is a black hole (with $M_{BH} \ge 6~M_{\odot}$ for the most luminous binaries) or that the luminosities truly exceed the Eddington limit for a neutron star.
 The former would iuplv that active binaries with massive black holes are fairly couunon in galaxies., The former would imply that active binaries with massive black holes are fairly common in galaxies.
 It should be noted that the bulee of M31 lacks the very ugh huninosity LAINBs that NGC 1697 has: the brightest LMXDB in MO was oulv L8&1075 eres | (Supper et 11997)., It should be noted that the bulge of M31 lacks the very high luminosity LMXBs that NGC 4697 has; the brightest LMXB in M31 was only $1.8 \times 10^{38}$ ergs $^{-1}$ (Supper et 1997).
 Tlowever. this is likely the result of siuall πο statistics.," However, this is likely the result of small number statistics."
 Siniulatious of the bulge of M31 using a unnuimositv distribution fiction of the form INN(5Ly)x⊉∖⊳⋟∐↓≼∐↸⊳⋜↧↑↸∖≼↧↑∐⋜↧↑∪∐⋅↖↽⋅≩↴∖↴≺∏∐⋅↸⊳↸∖↴∖↴↖↖↽↕↑∐↕⋯⊔∐⋯∖↴↕⊓↸∖↴∖↴LBs ↽∙ ⋅ ⋅⋅⋅ ↸∖⊼↸⊳↸∖↸∖≼∐∐∶↴⋁∐∣⋮⋝↖↸∖↥⋅∶↴↜⋱∖↴↴∖↴↴∖↴↓∪∏↕≺∏⋝↸∖↕≯∪∏∐≼⊔∐⋀∖↕∶∐∙↕∐∐↖⇁↸, Simulations of the bulge of M31 using a luminosity distribution function of the form $N(>L_X) \propto L_X^{-1.3}$ indicated that only 1–3 sources with luminosities exceeding $10^{38}$ ergs $^{-1}$ should be found in M31.
∖ ↴∖↴↸∖↻⋜∐⋅⋜↧↑↸∖↴∖↴↕∐∐∏⋜↧↑↕∪∐↴∖↴∪↕⋟⋀∖↕∶≩↽∙↑∐↸∖↻↸∖⋜∐↘↽↕∏∐∏∐∪↴∖↴↕↑⋅↖↽↕⋟∪↥⋅⋜⋯ ∫⇀⋀∖↕⊸∖⊽↕≧≼∐≼∐∪↑↸∖⊼∩∖↸∖≼⇂∶≩∖↕∩⋮⋝⋉↸∖↥⋅∶↴∙∷∖↴↴∖↴↓∙↕∐⋜↧∶↴∙⊾↥⋅↸∖↸∖⋯↸∖∐↑ with observation.," In five separate simulations of M31, the peak luminosity for an LMXB did not exceed $3 \times 10^{38}$ ergs $^{-1}$, in agreement with observation."
 We cannot rule out the presence of at least some iutersteHar imuediuni in NCC 1697 aud X-rav faint type galaxies in general., We cannot rule out the presence of at least some interstellar medium in NGC 4697 and X-ray faint early-type galaxies in general.
 Using the X-ray temperatureoptical velocity. dispersion relation of Davis White (1996). anv ISAT present iun NCC L697 would be expected to have a temperature around 0.3 keV. This would be very difficult to distinguisli from the soft component from LAINBs on a spectroscopic basis alouc.," Using the X-ray temperature--optical velocity dispersion relation of Davis White (1996), any ISM present in NGC 4697 would be expected to have a temperature around 0.3 keV. This would be very difficult to distinguish from the soft component from LMXBs on a spectroscopic basis alone."
 What is needed to separate the ISAL component frou the LAINB cutissiou is the lieh spatial resolution that cau be afforded byChandra., What is needed to separate the ISM component from the LMXB emission is the high spatial resolution that can be afforded by.
 Delow. we preseut a simulation of what we expect the emission from NGC 1697 to look like in the event that the emission is composed solely of LAINBs.," Below, we present a simulation of what we expect the emission from NGC 4697 to look like in the event that the emission is composed solely of LMXBs."
 We have an approved Cwele 1 10.000. 8Chendre Qsorvation of NGC 1697: here we show that this observation should resolve the hard and soft N-raw Cluission iuto individual sources. assunüug that the wission ds frou LAINBs.," We have an approved Cycle 1 40,000 s observation of NGC 4697; here we show that this observation should resolve the hard and soft X-ray emission into individual sources, assuming that the emission is from LMXBs."
 Couversely. the observation should cleanly seurate a truly diffuse cussion from tla of LAINBs.," Conversely, the observation should cleanly separate a truly diffuse emission from that of LMXBs."
 Since the main goal is to resolve the issue of the very soft componcut. the soft N-ray sensitive backside-Uhuninated (BI) S3 chip of the ACIS-S array will be usec for the observation.," Since the main goal is to resolve the issue of the very soft component, the soft X-ray sensitive backside-illuminated (BI) S3 chip of the ACIS-S array will be used for the observation."
 We have used the MARX (Mode ofANVAF Respouse to N-ravs: Wise. IIeuenmoerder. Davis 1997) Simulator to generate a svuthetic image of NGC 1697.," We have used the MARX (Model of Response to X-rays; Wise, Huenemoerder, Davis 1997) Simulator to generate a synthetic image of NGC 4697."
 The MARX Simulator takes as input the desired. spectral model aud spatial distribution model of an N-ray source and creates an image of the source as it would appear ouce having passed through the optics ofChandra., The MARX Simulator takes as input the desired spectral model and spatial distribution model of an X-ray source and creates an image of the source as it would appear once having passed through the optics of.
 The spectral and spatial distribution models described below were fed into ATARN using the ACTIS-S BI response to produce an image of NCC 1697 for a 10.000 x observation.," The spectral and spatial distribution models described below were fed into MARX using the ACIS-S BI response to produce an image of NGC 4697 for a 40,000 s observation."
 For the spectra of the LAINBs. we assume a model that best fit the jointROSAT PSPC | spectiiii of NGC 1697 discussed in 23.," For the spectra of the LMXBs, we assume a model that best fit the joint PSPC + spectrum of NGC 4697 discussed in \ref{sec:spectral}."
 For the spatial distribution of the N-rav enussion. we assume that the LAINBs have the same spatial distribution as the stellaz light.," For the spatial distribution of the X-ray emission, we assume that the LMXBs have the same spatial distribution as the stellar light."
" We taxe the optical distribution to be a de Vaucouleurs profile (de Vaucouleurs et 11991) with a mean haltlieht radius of 72"". an effective senminnajor axis of 95"". an effective scluimuuor axis of 55"". resulting in an ellipticity of 0.12. and elougated at a position augle of 677. ("," We take the optical distribution to be a de Vaucouleurs profile (de Vaucouleurs et 1991) with a mean half-light radius of $72^{\prime\prime}$, an effective semimajor axis of $95^{\prime\prime}$ , an effective semiminor axis of $55^{\prime\prime}$ , resulting in an ellipticity of 0.42, and elongated at a position angle of $^\circ$ . ("
Jedrzejewsld et 11987: Faber et 11989: Peleticer et 11990).,Jedrzejewski et 1987; Faber et 1989; Peletier et 1990).
where p and e are respectively (he pressure and the macroscopic energy density measured in proper coordinates.,where $p$ and $\epsilon $ are respectively the pressure and the macroscopic energy density measured in proper coordinates.
 Einsteins field equations without the cosmological constant reduce to denote differentiation with respect (o r., Einstein's field equations without the cosmological constant reduce to where primes denote differentiation with respect to $r$.
" These three equations together with the equation of stateof the material e = p(e) determine the mechanical equilibrium of the matter distribution as well as the dependence of the metric g,,'s on r."," These three equations together with the equation of stateof the material $\epsilon $ = $
p(\epsilon )$ determine the mechanical equilibrium of the matter distribution as well as the dependence of the metric $g_{\mu \nu }$ 's on $r$."
 The boundary of the matter distribution is the value of 7=ry for which p= 0. aud such (hat for r«rg.p>0.," The boundary of the matter distribution is the value of $r=r_{b}$ for which $%
p= 0, and such that for $r<r_{b},p>0$."
 For r«ry the solution depends on the equation of state of the malerial connecting p aud e., For $r<r_{b}$ the solution depends on the equation of state of the material connecting $p$ and $\epsilon $.
 For many equations of state a sharp boundary. exists with a finite value of rj., For many equations of state a sharp boundary exists with a finite value of $r_{b}$.
 In ihe empty space. p=€ 0. surrounding the spherically svinnmetric distribution of matter. the Sehwarzschild’s exterior solution is obtained: where m. is the Newlonian mass of the matter as calculated by a distant observer.," In the empty space, $p = \epsilon = 0$ , surrounding the spherically symmetric distribution of matter, the Schwarzschild's exterior solution is obtained: where $m$ is the Newtonian mass of the matter as calculated by a distant observer."
 Inside the boundary. Eqs. (5)). (6)).," Inside the boundary, Eqs. \ref{fieldeq1}) ), \ref{fieldeq2}) ),"
 and (7)) may be rewritten as follows., and \ref{fieldeq3}) ) may be rewritten as follows.
 Using the equation of state e= e(p). Eq. (7))," Using the equation of state $\epsilon = \epsilon(p)$ , Eq. \ref{fieldeq3}) )"
" max be immediately integrated The constant e""!) is determinedby making e continuous across the boundary.", may be immediately integrated The constant $e^{\nu(r_b)}$ is determinedby making $e^\nu$ continuous across the boundary.
the New Luvytei Two-Tenths Catalogue (Luyteo1. 1980 - NLTT).,"the New Luyten Two-Tenths Catalogue (Luyteon, 1980 - NLTT)."
" Once correlated. we can use the Gu,— Ks) colo was a crude plotometric parallax estimator. with the long baseline compeusatiug lo sone extent or the uncertainties in the red 1magnitudes."," Once correlated, we can use the $m_r-K_S$ ) colour as a crude photometric parallax estimator, with the long baseline compensating to some extent for the uncertainties in the red magnitudes."
 Paper I describes the definitiou of au initial sample o. uearby-star candidates. drawu rom NLTT sources which have potential 2ALASS counterparts wihin a 10-arcsecoud search racius.," Paper I describes the definition of an initial sample of nearby-star candidates, drawn from NLTT sources which have potential 2MASS counterparts within a 10-arcsecond search radius."
 By applying a series of cuts in colour-maguituce ancl colour-colow planes. we reduced the list of 23795 optical/IR matches to 1215 sources with yhotometric pre)perties consistent. with their beiig late-type clwarls within 20 parsecs of the Suu.," By applying a series of cuts in colour-magnitude and colour-colour planes, we reduced the list of 23795 optical/IR matches to 1245 sources with photometric properties consistent with their being late-type dwarfs within 20 parsecs of the Sun."
 These stars coistitute NLTT Sample 1., These stars constitute NLTT Sample 1.
 Paper I compiles photometric data from the literature or 169 st:ars. and uses colour-maguitude relationsat (Ny. (V-Ix). (Na. (V-I)) and (Aly. (1-0) to estimate ¢istauces to those stars.," Paper I compiles photometric data from the literature for 469 stars, and uses colour-magnitude relationsat $_V$ , (V-K), $_V$ , (V-I)) and $_I$, (I-J)) to estimate distances to those stars."
 Three hundred of those stars. aud a further 39 ultracool (spectral ype >M6) cdwarls. have formal distauces of less than 20 parsecs. including 76 stars not previously included i1 nearby star catalogues.," Three hundred of those stars, and a further 39 ultracool (spectral type $>$ M6) dwarfs, have formal distances of less than 20 parsecs, including 76 stars not previously included in nearby star catalogues."
 The current paper coutinues analysis of the NLTT Sample 1. presenting optical photometry ol a sampe of 180 relatively-bright southeru stars.," The current paper continues analysis of the NLTT Sample 1, presenting optical photometry of a sample of 180 relatively-bright southern stars."
 The following section outlines the sample and p'esents the observations., The following section outlines the sample and presents the observations.
 Section 3 describes our procedures for estimating distauces to these stars. ud Sectiou f discusses some of the more interesting stars in the sample.," Section 3 describes our procedures for estimating distances to these stars, and Section 4 discusses some of the more interesting stars in the sample."
" Our results are πα, in the final section.", Our results are summarised in the final section.
 As descried iu Paper L tie 1215 stars in NLTT Sample 1 were selected ou he basis of their having locatious iu tlie Gn. Crp) and (J-H)/(H-Ix)) planes consistent with ukl- or late-type M dwar witlin 20 parsecs of he Suu.," As described in Paper I, the 1245 stars in NLTT Sample 1 were selected on the basis of their having locations in the $m_r$, $m_r$ $_S$ )) and ((J-H)/(H-K)) planes consistent with mid- or late-type M dwarfs within 20 parsecs of the Sun."
 Regious within —1¢ of he Galactic Plane were excludedpriori. since tle NLTT catalogte has :i significantly brighter linitiug maguitu« ea ilose latitudes.," Regions within $\pm10^o$ of the Galactic Plane were excluded, since the NLTT catalogue has a significantly brighter limiting magnitude at those latitudes."
 The selected stars have maguituces iu he range 8«n<2Q. wil hover Lyi 1g|jetween Lith aud 16th imagnituce.," The selected stars have magnitudes in the range $8 < m_r < 20$, with over lying between 11th and 16th magnitude."
 They span the full raee of Right Ascension. alhough the majOriv lie at northieru Decliuation. reflectiug both the areal coverage of the second iiicremental release of 2NLASS «ala auc incompleteness ii the NLTT sou rol dé=—30°.," They span the full range of Right Ascension, although the majority lie at northern Declination, reflecting both the areal coverage of the second incremental release of 2MASS data and incompleteness in the NLTT south of $\delta = -30^o$."
 Several huuclrecl stars. howeve'. lie sout rol the equator.," Several hundred stars, however, lie south of the equator."
 Southern hemisplere proper-1uojon stars have generally. received less attention than tjelr northern counterparts. aud. as a result. even relatively bright objects in the current. sample |ave uo previous detailed 1jeasureiments.," Southern hemisphere proper-motion stars have generally received less attention than their northern counterparts, and, as a result, even relatively bright objects in the current sample have no previous detailed measurements."
 Figure 1 shows the distribution ou tlie celestial sphere aud in the (ny. Qny-Ixs)) coour-magnitude plane of the 180 NLTT cwarls targeted here.," Figure 1 shows the distribution on the celestial sphere and in the $m_r$ , $m_r$$_S$)) colour-magnitude plane of the 180 NLTT dwarfs targeted here."
For an observer at X=(X.Y.Z). the condition IX- should be satisfied in order to detect a holonomy y in a shell region ofrj«rrs.,"For an observer at $\vec X=(X, Y, Z)$, the condition $|\vec X - \gamma \vec X| /2< r_2$ should be satisfied in order to detect a holonomy $\gamma$ in a shell region of $r_1<r<r_2$."
 The lefthand side is the distance from the observer to the face of his Dirichlet domain. which corresponds to y.," The lefthand side is the distance from the observer to the face of his Dirichlet domain, which corresponds to $\gamma$ ."
 ↑↴⋯⊲⋗∕⋮⊺⋮≺↕∠∕∖⋒⊺∖≺∠∕∖⋒∪⋮≺∕⊓⋅⋯⋯ for y= ⊺⋮≺↕∠∕∖∕⋮⋟⊺∖≼−∠∕∖∕≣⋟∪⋮≺∕⊓⋅∖∖⇁∣↴⊜∣⊲⊜∠⋮∣≺↴⊂↿∣⊃∁ and rs»Ξ8.2 Gpe.," for $\gamma= T_z(\pm L/\sqrt{2})T_x(L/\sqrt{2})O_z(\pi)$ , and for $\gamma=T_z(\pm L/\sqrt{2})T_x(-L/\sqrt{2})O_z(\pi) $, where $L=16$ Gpc and $r_2=8.2$ Gpc."
 An observer satisfying each condition can detect each par of holonomies., An observer satisfying each condition can detect each pair of holonomies.
 It can be seen that the Z- of the observer affects nothing., It can be seen that the $Z$ -location of the observer affects nothing.
 However. the bigger the Y-location becomes. the farther away all faces are located. hence the harder to detect all holonomies.," However, the bigger the $Y$ -location becomes, the farther away all faces are located, hence the harder to detect all holonomies."
 The X-location has an effect of pushing two faces away. while drawing the other two. which is due to the translational direction that does not accord with the rotational axis.," The $X$ -location has an effect of pushing two faces away, while drawing the other two, which is due to the translational direction that does not accord with the rotational axis."
 The last effect cannot be seen in spaces without half-turn corkscrew motion (type IL) or glide reflection (type ID., The last effect cannot be seen in spaces without half-turn corkscrew motion (type II) or glide reflection (type II).
 According to these conditions. we chose six locations of (X.Y.Z)= (0. 0. 0). (1. 0. 0). (3. 0. 0). (5. 0. 0). (0. 0.5. 0). and (0. I. 0). in units of Gpe.," According to these conditions, we chose six locations of $(X,Y,Z)=$ (0, 0, 0), (1, 0, 0), (3, 0, 0), (5, 0, 0), (0, 0.5, 0), and (0, 1, 0), in units of Gpc."
 We prepared catalogs of toy quasars seen from these observers. and applied our method to them.," We prepared catalogs of toy quasars seen from these observers, and applied our method to them."
 Thecoordinate axes were chosen correctly here., Thecoordinate axes were chosen correctly here.
 Results for these observers are given in Table 4. and Figure 6.., Results for these observers are given in Table \ref{table4} and Figure \ref{figure6}.
 In this table. it can be seen that the signal gets weaker às the observer moves along the y-axis. since the faces get farther and the ghosts decrease in number.," In this table, it can be seen that the signal gets weaker as the observer moves along the $y$ -axis, since the faces get farther and the ghosts decrease in number."
 This is also seen in the histograms. where the hills constituted by ghosts disappear.," This is also seen in the histograms, where the hills constituted by ghosts disappear."
 It is necessary to use a larger shell region. if possible. to detect the ghosts.," It is necessary to use a larger shell region, if possible, to detect the ghosts."
 As the observer moves along the x-axis. on the other hand. the signal and the hills remain like the initial one in which the observer is located at the center. since one pair of faces gets farther. but the others get closer.," As the observer moves along the $x$ -axis, on the other hand, the signal and the hills remain like the initial one in which the observer is located at the center, since one pair of faces gets farther, but the others get closer."
 As long as the coordinate axes are chosen correctly. our method can detect holonomies that are close enough to the observer.," As long as the coordinate axes are chosen correctly, our method can detect holonomies that are close enough to the observer."
 Our method ts suited to obtaining a lower limit to the size of the Universe., Our method is suited to obtaining a lower limit to the size of the .
 In this paper we have developed a cosmic crystallography method that significantly extends previous methods., In this paper we have developed a cosmic crystallography method that significantly extends previous methods.
 A thin. shell-Hke part (rj«r 7: of the full catalog is used. similar to the circles-in-the-sky method.," A thin, shell-like part $r_1<r<r_2$ ) of the full catalog is used, similar to the circles-in-the-sky method."
 This region should be as large às possible. but the comoving density of objects should be simultaneously high enough there.," This region should be as large as possible, but the comoving density of objects should be simultaneously high enough there."
 The quadruplets of these objects are filtered three times: separation. vectorial condition. and lifetime of objects.," The quadruplets of these objects are filtered three times; separation, vectorial condition, and lifetime of objects."
 These filters drop the false stochastic ones. while keeping the real topological ones.," These filters drop the false stochastic ones, while keeping the real topological ones."
 Flat spaces described by Euclidean geometry are assumed. and the second filter. vectorial condition. i$ specialized to detect their holonomies.," Flat spaces described by Euclidean geometry are assumed, and the second filter, vectorial condition, is specialized to detect their holonomies."
 This assumption ts not fundamental. since similar filters for the holonomies in spherical or hyperbolic spaces can also be constructed.," This assumption is not fundamental, since similar filters for the holonomies in spherical or hyperbolic spaces can also be constructed."
 The number of quadruplets having passed these filters is translated into an index of multiconnectednessof theuniverse. and then the objects are classifiedby 5;. the number of such," The number of quadruplets having passed these filters is translated into an index of multiconnectednessof theuniverse, and then the objects are classifiedby $s_i$ , the number of such"
ol dark matter clearing by black hole mergers of Merrittetal.(2002).,of dark matter clearing by black hole mergers of \citet{Meretal02}.
". To ealeulate the effect of gravitational focusing byΑι, a black hole mass of 3x105 is asstuned. and the velocily distribution is assigned to be isotropic wilh a dispersion of σι=155 km/s. The black hole mass. the assumption of an isotropic velocity distribution. andthe value of σι used here are all approximately. consistent will observed stellar kinematics in the (Ghezetal.1993:Genzel2000)."," To calculate the effect of gravitational focusing by, a black hole mass of $3\times 10^6$ is assumed, and the velocity distribution is assigned to be isotropic with a dispersion of $\sigma_v=155$ km/s. The black hole mass, the assumption of an isotropic velocity distribution, andthe value of $\sigma_v$ used here are all approximately consistent with observed stellar kinematics in the \citep{Gheetal98, Genetal00}."
". The observed dark matter sell-aunihilation flux depend on the local emissivity. where Pam/y; is the dark matter number density. and (0,,,0) gives the sell-annihilation rate per unit densitv."," The observed dark matter self-annihilation flux depend on the local emissivity, where $\rho_{\rm dm}/m_{\rm dm}$ is the dark matter number density, and $\left<\sigma_{ann} v\right>$ gives the self-annihilation rate per unit density."
" For the neutralino. (wpical values from the literature (e.g.DergstrómGondolo1996) are my=may100 GeV. and (0,,,0)=107"" cm/s. independent of pairwise closing speed v."," For the neutralino, typical values from the literature \citep[e.g.][]{BerGon96} are $m_{\chi}
\equiv m_{\rm dm} = 100$ GeV, and $\left<\sigma_{ann} v\right> =
10^{-26}$ $^3$ /s, independent of pairwise closing speed $v$."
 The quantity Y specifies the. vield of decay by-products: for example. the bolometric vield corresponds to Y—mic.," The quantity $Y$ specifies the yield of decay by-products; for example, the bolometric yield corresponds to $Y=m_\chi c^2$."
 The emissivity per unit frequency ol photons produced by electrons in a magnetic field depends on electron-positron production channels. as well as svnchrotron radiative efficiencies Tvler(e.g..2002).," The emissivity per unit frequency of photons produced by electrons in a magnetic field depends on electron-positron production channels, as well as synchrotron radiative efficiencies \citet[e.g.,][]{Tyl02}."
. In the case of certain neutralino decay products. namely neutrinos. the flux is a straightlorwarc line-o[-sight integral over (he emissivity. since sell-absorption and diffusion do not occur 1999).," In the case of certain neutralino decay products, namely neutrinos, the flux is a straightforward line-of-sight integral over the emissivity, since self-absorption and diffusion do not occur \citep{GonSil99}."
. The line of sight integral along some sky direction » is conveniently expressed in dimensionless form as (Bergstromοἱal.1998:Merritt2002) Figure 2 gives J. averaged inside a circular aperture centered onAx.. as a function of aperture radius.," The line of sight integral along some sky direction $\hat{n}$ is conveniently expressed in dimensionless form as \citep{BerUllBuc98, Meretal02}
 Figure 2 gives $J$, averaged inside a circular aperture centered on, as a function of aperture radius."
 The density profile is (he same as in Figure 1., The density profile is the same as in Figure 1.
 The enhancement from eravitational focusing is significant insile small apertures., The enhancement from gravitational focusing is significant inside small apertures.
 Even so. Bertoneetal.(2004) point out that (he neutrino flux from (the Galactic Center will be undetectable if (he current eamnin-ray constraints are anv indication of the annihilation rate.," Even so, \citet{Beretal04} point out that the neutrino flux from the Galactic Center will be undetectable if the current gamma-ray constraints are any indication of the annihilation rate."
 Erkocaetal.(2010) are more hopeful [rom a theoretical perspective. while (he observations are providing limits to the neutrino flux (e.g..fromIeeCubeAbbasietal. 2011).. but no Galactic Center signal at (his point.," \citet{Erketal10} are more hopeful from a theoretical perspective, while the observations are providing limits to the neutrino flux \citep[e.g., from IceCube][]{Abbetal11}, , but no Galactic Center signal at this point."
 The strength. of a gravitationallv focused. censitw profile around a compact object is, The strength of a gravitationally focused density profile around a compact object is
Previous ROSAT observations have shown that red. giants are not substantial X-ray emittors.,Previous ROSAT observations have shown that red giants are not substantial X-ray emittors.
 Only one late-type giant was deteced in the ROSAT all-skv survey (2:?:2). and pointed observations placed an extremely tight upper [init of 310aeeres ton the X-ray lux of the LELE red. giant Arcturus (2)..," Only one late-type giant was detected in the ROSAT all-sky survey \cite{Haisch91,Haisch92,Huensch96}, and pointed observations placed an extremely tight upper limit of $3\times10^{25}\rm\,erg\,s^{-1}$ on the X-ray flux of the III red giant Arcturus \cite{Ayers91}."
 Thus we can be confident that the X-ray emission from 4 Draconis reported in this paper originates on the ultraviolet companion. 4 DD. Our. ROSAT observations are consistent with this secondary containing an accreting white chwart.," Thus we can be confident that the X-ray emission from 4 Draconis reported in this paper originates on the ultraviolet companion, 4 B. Our ROSAT observations are consistent with this secondary containing an accreting white dwarf."
" The ~HkkeV temperature of the optically-thin X-ray spectrum is characteristic of non-magnetic cataclysmic variables (c.g.7) and of the ""bombardment solution"" for radial accretion onto a white chwarl (c.g.2)..", The $\sim$ keV temperature of the optically-thin X-ray spectrum is characteristic of non-magnetic cataclysmic variables \egcite{Wheatley96} and of the “bombardment solution” for radial accretion onto a white dwarf \egcite{Woelk95}.
 Phe bombardment solution applies when the mass accretion rate per unit area is too low for a stand-olI shock to form (im«]0+estem 7).," The bombardment solution applies when the mass accretion rate per unit area is too low for a stand-off shock to form $\rm\dot{m}<10^{-1}\,g\,s^{-1}\,cm^{-2}$ )."
 Our measured Luminosity of 6107ergs l-iniplies. an accretionoa rate of (24LS10bgs+ for white dwarf masses in the range 0.30LOALY.," Our measured luminosity of $6\times10^{31}\rm\,erg\,s^{-1}$ implies an accretion rate of $0.24-1.8\times10^{15}\rm\,g\,s^{-1}$ for white dwarf masses in the range $0.3-1.0\rm\,M_{\sun}$."
 For the bombardment solution to aplv his accretion rate must be spread over an area of at. least ηLs101em?. although this is a small fraction of the surface area of even a massive white ναι," For the bombardment solution to apply this accretion rate must be spread over an area of at least $0.24-1.8\times10^{16}\rm\,cm^2$, although this is a small fraction of the surface area of even a massive white dwarf."
 Although our observations are consistent with the yrescnee of an accreting white να they do not support the presence of an AAL Ller system.," Although our observations are consistent with the presence of an accreting white dwarf, they do not support the presence of an AM Her system."
 First. the τοΛΙ spectra of AAT ers are typically dominated: by intense optically-thick soft) emission. with characteristic temperatures of ~20ceV. We can rule out the presence of such a component in the 1993 spectrum of 4 BB reffig-spec)).," First, the ROSAT spectra of AM Hers are typically dominated by intense optically-thick soft emission, with characteristic temperatures of $\sim$ eV. We can rule out the presence of such a component in the 1993 spectrum of 4 B \\ref{fig-spec}) )."
 Second. it is clear from the LIBI lighteurve reffie-le}) that the X-ray emission is not strongly modulated abi a period of Shh. as it is for everv known hieh-state AM Ler system and most other magnetic cataclysmic variables.," Second, it is clear from the HRI lightcurve \\ref{fig-lc}) ) that the X-ray emission is not strongly modulated at a period of h, as it is for every known high-state AM Her system and most other magnetic cataclysmic variables."
 AM Her systems have shown spectra much like that of 4 Draconis during low accretion rate states (e.g.2).. but our measured Luminosity is rather high for a low-state ANI Ler. ancl we believe the lack of an A-ray orbital periodicity alone is sullicient evidence to rule out the presence of an AM Ler in the 4 Draconis system.," AM Her systems have shown spectra much like that of 4 Draconis during low accretion rate states \egcite{Ramsay95}, but our measured luminosity is rather high for a low-state AM Her, and we believe the lack of an X-ray orbital periodicity alone is sufficient evidence to rule out the presence of an AM Her in the 4 Draconis system."
 Non-magnetic cataclysmic variables chwarl novae) usually have no optically-thick component in the ROSAT bandpass (e.g.2).. have characteristic N-ray. temperatures lower than AM LHers. and do not exhibit strong orbital. X-rav modulation.," Non-magnetic cataclysmic variables dwarf novae) usually have no optically-thick component in the ROSAT bandpass \egcite{Wheatley96}, have characteristic X-ray temperatures lower than AM Hers, and do not exhibit strong orbital X-ray modulation."
 Pherefore we cannot rule out the presence of a non-magnetic cataclysmic variable., Therefore we cannot rule out the presence of a non-magnetic cataclysmic variable.
 However. the original case for the presence of a cataclysmic variable was based upon the claimed detection of a 4hh ultraviolet period (?)..," However, the original case for the presence of a cataclysmic variable was based upon the claimed detection of a h ultraviolet period \cite{Reimers88}."
 Reviewing the lighteurve in Fig.33 of Reimers ct we believe the case for a periodic moculation is not strong., Reviewing the lightcurve in 3 of Reimers et we believe the case for a periodic modulation is not strong.
 Also. more recent LIST. observations do not support the presence of a 4hh period Gaensicke. private communication).," Also, more recent HST observations do not support the presence of a h period Gaensicke, private communication)."
 ‘Thus. in the [ace [ni evidence clearly supporting the presence of an accreting white chwarl. but none requiring the," Thus, in the face of evidence clearly supporting the presence of an accreting white dwarf, but none requiring the"
deteriuuatiou of D4». since it relies ou cosmological siuulatious for inodeliug the temperature and density field.,"determination of $\Gamma_{-12}$, since it relies on cosmological simulations for modeling the temperature and density field."
"""Disks. Extrasolar Planets and Mown Dwarfs held at. the LAP in July. 2000 for useful discussions.","'Disks, Extrasolar Planets and Brown Dwarfs' held at the IAP in July 2000 for useful discussions."
"(109A7... (IKI&oriunendy kl~ (TTrinchiert. ZL,~LO 1 E03 (PPellegriui (BBlaudford (11952) DP-—0.61.5) (A (11996) 1) (SSlee (11999; ",$10^9 M_\odot$ \markcite{KoRi95}K $kT \sim$ \markcite{TrFa86}T $L_x \sim 10^{45}$ $^{-1}$ $< 10^{-3}$ \markcite{Pell99}P \markcite{NaYi95} \markcite{Abrm95} \markcite{DiMa00} \markcite{BlBg99}B \markcite{Bndi52}1 $\Gamma \sim 0.6 - 1.5$ \markcite{AlDF00}A \markcite{Reyn96}1 \markcite{Harr98}1 \markcite{Slee94}S \markcite{DiMa99}1 
"The basic requirement of the observed spectro-astrometry is that the line forming gas must be orbiting the central star with strongly sub-Keplerian azimuthal velocities in order to produce the single peak without requiring that the emission is extended at the spatial resolution of CRIRES (—0""115).",The basic requirement of the observed spectro-astrometry is that the line forming gas must be orbiting the central star with strongly sub-Keplerian azimuthal velocities in order to produce the single peak without requiring that the emission is extended at the spatial resolution of CRIRES $\sim$ 15).
" A wide angle wind provides a convenient physical way of accomplishing this through simple conservation of angular momentum — as a gas parcel is forced outwards due to the wind pressure, the azimuthal velocity decreases linearly with radius, in comparison with the underlying Keplerian disk in which the velocity experiences a shallower decrease as R-!/2."," A wide angle wind provides a convenient physical way of accomplishing this through simple conservation of angular momentum – as a gas parcel is forced outwards due to the wind pressure, the azimuthal velocity decreases linearly with radius, in comparison with the underlying Keplerian disk in which the velocity experiences a shallower decrease as $R^{-1/2}$."
 'This generates gas above the disk that is supported by wind pressure and orbits at low azimuthal velocities., This generates gas above the disk that is supported by wind pressure and orbits at low azimuthal velocities.
" Following?,, the wind is constructed as set of linear streamlines with a locus below the centrala star at a distance d in units of R,."," Following, the wind is constructed as a set of linear streamlines with a locus below the central star at a distance $d$ in units of $R_*$."
 This generates a conical wind with no flow along the disk axis., This generates a conical wind with no flow along the disk axis.
" Briefly, the wind is accelerated along the field lines as: where | is the coordinate alongthe stream line, c, is the sound speed, Όρες is the asymptotic velocity at the end of the stream line and Agcaie is the scale of the acceleration region of the wind."," Briefly, the wind is accelerated along the field lines as: where $l$ is the coordinate alongthe stream line, $c_s$ is the sound speed, $v_{\rm esc}$ is the asymptotic velocity at the end of the stream line and $A_{\rm scale}$ is the scale of the acceleration region of the wind."
 ϱ is the wind acceleration parameter., $\beta$ is the wind acceleration parameter.
" Requiring angular momentum conservation, the azimuthal velocity component is: where F is the radial disk coordinate."," Requiring angular momentum conservation, the azimuthal velocity component is: where $R$ is the radial disk coordinate."
" 'The density of the wind is calculated assuming mass conservation: Here, X(w)οςR? is the local mass-loss rate, ὃ is the angle between the stream line and the disk normal and S is the distance to the wind locus."," The density of the wind is calculated assuming mass conservation: Here, $\dot{\Sigma}(w) \propto R^{-p}$ is the local mass-loss rate, $\delta$ is the angle between the stream line and the disk normal and S is the distance to the wind locus."
 The exponent of the local mass loss rate is taken to be p=7/2(?)., The exponent of the local mass loss rate is taken to be $p=7/2$.
". The total wind mass loss rate can be calculated by integrating over the disk and multiplying by two to include the opposite surface: The raytracer RADLite is used to render model lines and spectro-astrometry (7)for the wind models, based on a generic model of a flared protoplanetary disk, and assuming level populations in LTE."," The total wind mass loss rate can be calculated by integrating over the disk and multiplying by two to include the opposite surface: The raytracer RADLite is used to render model lines and spectro-astrometry for the wind models, based on a generic model of a flared protoplanetary disk, and assuming level populations in LTE."
" Specifically, the temperature structure is assumed to be in equilibrium with the stellar radiation field and dominated by dust heating/cooling."," Specifically, the temperature structure is assumed to be in equilibrium with the stellar radiation field and dominated by dust heating/cooling."
" In reality, the heating of the wind is likely to be dominated by photo-electric heating similar to the heating of the disk atmosphere οι, perhaps, ambipolar diffusion(?)."," In reality, the heating of the wind is likely to be dominated by photo-electric heating similar to the heating of the disk atmosphere or, perhaps, ambipolar diffusion."
". The cooling(1173) may be dominated by adiabatic expansion and molecular cooling (e.g., partly via the observed CO and H20O lines)."," The cooling may be dominated by adiabatic expansion and molecular cooling (e.g., partly via the observed CO and $_2$ O lines)."
" However, we restrict ourselves to qualitative models in this paper (see also refCaveats)), since a detailed and appropriate physical treatment of the thermal wind structure required to match the observations will be likely be a significant study in its own right."," However, we restrict ourselves to qualitative models in this paper (see also \\ref{Caveats}) ), since a detailed and appropriate physical treatment of the thermal wind structure required to match the observations will be likely be a significant study in its own right."
" Figure 10 illustrates the wind geometry and compares the observables generated using the wind modelfor the spectro-astrometry of AS 205N. The total mass-loss rate is 9x107?Mo yr-!, assuming a CO abundance of 5x107? relative to H."," Figure \ref{Wind_sketch} illustrates the wind geometry and compares the observables generated using the wind modelfor the spectro-astrometry of AS 205N. The total mass-loss rate is $9\times 10^{-9}\,\rm M_{\odot}\,yr^{-1}$ , assuming a CO abundance of $5\times 10^{-5}$ relative to $\rm H$ ."
 This mass-loss rate is consistent, This mass-loss rate is consistent
fitting a gaussian function to their emission profile derived from the SH data.,fitting a gaussian function to their emission profile derived from the SH data.
" This is illustrated in reffig:hires,, which shows the SH IRS observations obtained for the [SIV], [NeII], [NeIII] and [SHI] ionic lines."," This is illustrated in \\ref{fig:hires}, which shows the SH IRS observations obtained for the [SIV], [NeII], [NeIII] and [SIII] ionic lines."
" Since no sky subtraction could be performed for these data though, the underlying continuum and the equivalent widths (EW) of these features were estimated from the continuum of the low-resolution spectrum as modeled with PAHFIT."," Since no sky subtraction could be performed for these data though, the underlying continuum and the equivalent widths (EW) of these features were estimated from the continuum of the low-resolution spectrum as modeled with PAHFIT."
 Our measurements are given in Table 2 along with the fluxes and the equivalent widths of the main PAHs and ionic lines measured in the low-resolution data., Our measurements are given in Table \ref{table:features} along with the fluxes and the equivalent widths of the main PAHs and ionic lines measured in the low-resolution data.
" For the strongest and isolated PAHs (i.e.,um,,uum,, and µπι)), we indicate the results obtained with the global PAHFIT decomposition but we also provide the measures that we derived with a local fit of the continuum underlying each individual feature using a spline function."," For the strongest and isolated PAHs (i.e., and ), we indicate the results obtained with the global PAHFIT decomposition but we also provide the measures that we derived with a local fit of the continuum underlying each individual feature using a spline function."
 The latter approach has been commonly used in the literature to characterize the mid-IR spectra of star-forming galaxies., The latter approach has been commonly used in the literature to characterize the mid-IR spectra of star-forming galaxies.
" It usually leads to lower values than obtained with PAHFIT, since PAHFIT accounts for the full extent of the PAH wings."," It usually leads to lower values than obtained with PAHFIT, since PAHFIT accounts for the full extent of the PAH wings."
" We constrained the spectral energy distributions of the GRB host galaxy and the WR region over the full infrared wavelength range by fitting the broad-band photometry with the empirical libraries of galaxy templates published by Chary&Elbaz(2001), Dale&Helou and Lagacheetal. as well as with the (2002)physical SEDs derived from (2004),radiative transfer modeling by Siebenmorgen&Kriigel(2007)."," We constrained the spectral energy distributions of the GRB host galaxy and the WR region over the full infrared wavelength range by fitting the broad-band photometry with the empirical libraries of galaxy templates published by \citet{Chary01}, \citet{Dale02} and \citet{Lagache04}, as well as with the physical SEDs derived from radiative transfer modeling by \citet{Siebenmorgen07}."
". Between these different libraries the SEDs mostly vary in the relative strength of the PAH features with respect to the hot dust continuum, as well as in the temperature and the emissivity of the cold dust component shaping the peak of the SED in the far-IR."," Between these different libraries the SEDs mostly vary in the relative strength of the PAH features with respect to the hot dust continuum, as well as in the temperature and the emissivity of the cold dust component shaping the peak of the SED in the far-IR."
" In the library of Siebenmorgen&Krügel the SEDs also depend on the size of the star-forming(2007) region responsible for the IR. emission, and they are given for radii of 0.35, 1, 3, 9 and kkpc."," In the library of \citet{Siebenmorgen07} the SEDs also depend on the size of the star-forming region responsible for the IR emission, and they are given for radii of 0.35, 1, 3, 9 and kpc."
" We only considered sizes of kkpc and kkpc for the WR region and the whole galaxy, respectively."," We only considered sizes of kpc and kpc for the WR region and the whole galaxy, respectively."
 'To obtain the best possible constraints we combined the MIPS fluxes presented in refsec:photo with the photometry already published by LeFloc’hetal., To obtain the best possible constraints we combined the MIPS fluxes presented in \\ref{sec:photo} with the photometry already published by \citet{LeFloch06}.
" The fitting was performed separately for each library,(2006).. using the code (Arnoutsetal.1999;Ibert2006)."," The fitting was performed separately for each library, using the code \citep{Arnouts99,Ilbert06}."
". Although most of the IR SED templates from the aforementioned libraries vary as a function of the total IR luminosity (but see Dale&Helou2002 for a dependence on dust temperature), their normalization was kept as a free parameter and the best templates were derived from a basic x? minimization of the fit."," Although most of the IR SED templates from the aforementioned libraries vary as a function of the total IR luminosity (but see \citealt{Dale02} for a dependence on dust temperature), their normalization was kept as a free parameter and the best templates were derived from a basic $\chi^2$ minimization of the fit."
" In the case of the WR region, we did not include the photometry at since at this wavelength we were unable to separate its contribution from the emission of the host (see refsec:mips160))."," In the case of the WR region, we did not include the photometry at since at this wavelength we were unable to separate its contribution from the emission of the host (see \\ref{sec:mips160}) )."
 We checked however that the best fits obtained for the WR region did not exceed the total flux measured for the GRB host galaxy atum., We checked however that the best fits obtained for the WR region did not exceed the total flux measured for the GRB host galaxy at.
". 'The results are illustrated in , whichshowsthemeasurements f romourbroad— bandphotometryandI RS spectroscopytogetherwiththeglobalrangeo; fittemplatesthatwereobtained f oreachoftheAlibraries."," The results are illustrated in \\ref{fig:ir_total_sed}, which shows the measurements from our broad-band photometry and IRS spectroscopy together with the global range of possible SED fits defined from the best-fit templates that were obtained for each of the 4 libraries."
 Asexpected f bandf luxesmeasuredwithI RACandMIP Swenotethatthemid— tofar—I Rspectralslopeo ftheW regionismuchsteeperthanobserve , As expected from the different broad-band fluxes measured with IRAC and MIPS we note that the mid- to far-IR spectral slope of the WR region is much steeper than observed for the whole GRB host.
"andpm,, we derivedR total IR luminosities of log(Lip/Lo) 88.6640.04 and log(Lirn/Leo) 99.0140.07 for the WR region and the whole GRB host galaxy, respectively."," By integrating the best fit SEDs between and, we derived total IR luminosities of $_{\rm IR}$ $_{\odot}$ $\pm$ 0.04 and $_{\rm IR}$ $_{\odot}$ $\pm$ 0.07 for the WR region and the whole GRB host galaxy, respectively."
 In these estimates the uncertainties were obtained by combining, In these estimates the uncertainties were obtained by combining
is ~3% of the total energy.,is only $\sim 3\%$ of the total magnetic energy.
 This value may increaseonly slightly on a much longer magnetictimescale., This value may increase slightly on a much longer timescale.
 Also in , Also reported in Fig.
2 as dashed lines are the corresponding reportedevolution Fig.of the magnetic energies when a smaller resistivity of ηο/Μο=0.06 is used., \ref{fig:fig2} as dashed lines are the corresponding evolution of the magnetic energies when a smaller resistivity of $\eta_0/M_{\odot}=0.06$ is used.
" Since the evolution of the instability in this case is qualitatively very similar the evolution of E, we have confidence that our prescription for the resistive tor),behaviour of the magnetic field near the stellar surface does not influence the dynamics of the instability."," Since the evolution of the instability in this case is qualitatively very similar the evolution of $E_{\mathrm{m,tor}}$ ), we have confidence that our prescription for the resistive behaviour of the magnetic field near the stellar surface does not influence the dynamics of the instability."
" At the same time, however, a smaller is also responsible for a smaller of the poloidal resistivitymagnetic field (see inset), which is decayconsiderably the end of the simulation."," At the same time, however, a smaller resistivity is also responsible for a smaller decay of the poloidal magnetic field (see inset), which is considerably dissipated by the end of the simulation."
" While this behaviour is dissipatedinevitable byin a resistive context and has been reported also by other authors (Braithwaite2007),, it an aspect of these evolutions which could be improved representswith a fully consistent resistive MHD approach (Palenzuelaetal.2009).."," While this behaviour is inevitable in a resistive context and has been reported also by other authors \citep{Braithwaite2007}, it represents an aspect of these evolutions which could be improved with a fully consistent resistive MHD approach \citep{Palenzuela:2008sf}."
" Another important confirmation of the perturbative analysis is offered in Fig. 3,,"," Another important confirmation of the perturbative analysis is offered in Fig. \ref{fig:fig3},"
" where we show the inverse of the growth- 7, defined through the exponential growth of the toroidal component, versus the initial magnetic-field strength (red empty circles)."," where we show the inverse of the growth-time $\tau$, defined through the exponential growth of the toroidal component, versus the initial magnetic-field strength (red empty circles)."
" Note that the scaling is essentially linear for Bo&€7x1019 G, deviating from this for higher values, because of the magnetic tension."," Note that the scaling is essentially linear for $B_0
\lesssim 7 \times 10^{16}\,$ G, deviating from this for higher values, because of the stronger magnetic tension."
" More specifically, the stronger Lorentz strongerforce will tend to oppose the fluid motions in the direction near the neutral line and which trigger the instability."," More specifically, the stronger Lorentz force will tend to oppose the fluid motions in the polar direction near the neutral line and which trigger the instability."
"polar The presence of a linear scaling is essential to extend our results to pulsar magnetic- strengths, thus estimating a growth-timetypical of ~10s for a neutron star with Bg=10!? G. Also marked in Fig."," The presence of a linear scaling is essential to extend our results to typical pulsar magnetic-field strengths, thus estimating a growth-time of $\sim 10\,$ s for a neutron star with $B_0=10^{12}\,$ G. Also marked in Fig."
" 3 (blue star) is the inverse growth-time for the fiducial star evolved with the smaller of jo/M;=0.06; again, the close similarity in the resistivitytimescales confirms our expectation that the is not influenced the choice of the The instability"," \ref{fig:fig3} (blue star) is the inverse growth-time for the fiducial star evolved with the smaller resistivity of $\eta_0/M_{\odot}=0.06$; again, the close similarity in the timescales confirms our expectation that the instability is not influenced by the choice of the resistivity."
final discussion is reservedby for the potential GW resistivity.signal emitted during the of the, The final discussion is reserved for the potential GW signal emitted during the development of the instability.
 In Fig., In Fig.
 we report the GW strain in developmentthe + and x instability.polarizations as computed from the Newtonian formula., \ref{fig:fig4} we report the GW strain in the $+$ and $\times$ polarizations as computed from the Newtonian quadrupole formula.
" It is quite apparent that the signal is not ofquadrupole a burst type but, rather, that the main effect of the is that of triggering large-amplitude oscillations ofinstability the star in its fundamental F-mode."," It is quite apparent that the signal is not of a burst type but, rather, that the main effect of the instability is that of triggering large-amplitude oscillations of the star in its fundamental $F$ -mode."
" These GWs start from the numerical noise already at ~3.5 ms, butemerging are associated to high-m oscillations and hence not efficient sources of GWs."," These GWs start emerging from the numerical noise already at $\sim
3.5\,$ ms, but are associated to $m$ oscillations and hence not efficient sources of GWs."
" However, as the magnetic field starts to approach the final m=2 configuration at ~ 7ms, the oscillations become more efficient in producing a GW signal (Note that a m=N pertubation in the magnetic field leads to am=2N perturbation in the density)."," However, as the magnetic field starts to approach the final $m=2$ configuration at $\sim 7\,$ ms, the oscillations become more efficient in producing a GW signal (Note that a $m=N$ pertubation in the magnetic field leads to a $m=2N$ perturbation in the density)."
" Because these oscillations will have a rather narrow spectral distribution peaked around the F'-mode frequency (which is not significantly affected by the presence of magnetic fields), they represent very good sources of a periodic signal, potentially detectable by future advanced detectors."," Because these oscillations will have a rather narrow spectral distribution peaked around the $F$ -mode frequency (which is not significantly affected by the presence of magnetic fields), they represent very good sources of a periodic signal, potentially detectable by future advanced detectors."
" Defining the root-sum-square amplitude of the cross polarization as h;,,=fredth2,1/2, and assuming that the oscillations will persist| undamped(| for ~0.1— 1s, we estimate 4,=(0.54—1.7)x107? for a source at 10 kpc."," Defining the root-sum-square amplitude of the cross polarization as $h_{\rm
 rss}=\left[\int_{-\infty}^{+\infty} dt \,
 h_{\times}^2(t)\right]^{1/2}$, and assuming that the oscillations will persist undamped for $\simeq 0.1-1\,$ s, we estimate $h_{\rm rss}
= (0.54-1.7)\times 10^{-22}$ for a source at $10\,$ kpc."
" The corresponding signal-to-noise ratio for a detector such as advanced-LIGO or advanced-Virgo is S/N~1.6—5, thus potentially observable."," The corresponding signal-to-noise ratio for a detector such as advanced-LIGO or advanced-Virgo is $S/N \simeq 1.6-5$, thus potentially observable."
 A more detailed analysis of the spectral properties of the GW signal will be in a future work., A more detailed analysis of the spectral properties of the GW signal will be presented in a future work.
 These waveforms represent the first presentedestimate of the conversion of the kinetic energy generated the instability into GWs., These waveforms represent the first estimate of the conversion of the kinetic energy generated through the instability into GWs.
" For weaker magnetic fields, throughperturbative analyses have suggested this coupling is much weaker (Levin&vanHoven2011),, but more work is needed to investigate nonlinearly this regime."," For weaker magnetic fields, perturbative analyses have suggested this coupling is much weaker \citep{Levin:2011}, but more work is needed to investigate nonlinearly this regime."
 We report on numerical evolutions of the instability of poloidal magnetic fields in relativistic stars and the subsequent of a mixed-field configuration in quasi- In generat, We report on numerical evolutions of the instability of poloidal magnetic fields in relativistic stars and the subsequent generation of a mixed-field configuration in quasi-equilibrium.
"ionagreement with the expectations from analytic studies (Markey&Tayler1973; 1973),, we show perturbativethat the instability appears after about an WrightAlfvénn"," In agreement with the expectations from analytic perturbative studies \citep{Markey1973,
 Wright1973}, , we show that the instability appears after about an Alfvénn"
budget for (he secondary. pairs is quite limited. unless a higher emission can be ellectively suppressed in the Fermi-LAT band.,"budget for the secondary pairs is quite limited, unless a higher emission can be effectively suppressed in the Fermi-LAT band."
 This could be achieved either by assuming a broad enerev distribution of target photons extending to X-ray. energies. so to provide a significant attenuation also in the GeV band. or by introducing a very high lower-energy eutoff in the proton distribution.," This could be achieved either by assuming a broad energy distribution of target photons extending to X-ray energies, so to provide a significant attenuation also in the GeV band, or by introducing a very high lower-energy cutoff in the proton distribution."
 In absence of (hese (wo conditions. the X-ray. svnchrotron flix of the secondary. pairs would be approximately an order of magnitude below the reported X-ray [luxes.," In absence of these two conditions, the X-ray synchrotron flux of the secondary pairs would be approximately an order of magnitude below the reported X-ray fluxes."
 Therefore. in (his specific case. the internal absorption scenario requires additional ad-hoc assumptions to provide a sell-consistent interpretation of the TeV and X-ray data.," Therefore, in this specific case, the internal absorption scenario requires additional ad-hoc assumptions to provide a self-consistent interpretation of the TeV and X-ray data."
 These additional assumptions mstead are not needed in (he case of a hard proton spectrum (p= —0.5)., These additional assumptions instead are not needed in the case of a hard proton spectrum $p=-0.5$ ).
 The latter can provide both the energv budget to explain the X-ray data and. GeV. fluxes below the Fermi-LAT limits. as shown in Fig.," The latter can provide both the energy budget to explain the X-ray data and GeV fluxes below the Fermi-LAT limits, as shown in Fig."
 3. (Fit 2. whose corresponding parameters are given in Table 1)).," \ref{fig:0229} (Fit 2, whose corresponding parameters are given in Table \ref{table:parameters}) )."
 In the case of high EBL flux (model F1.6). the de-absorbed VIE spectrum has a photon index close to Di21. ie. harder than the unabsorbed svnchrotron spectrum from a proton clistvibution with index p~2.," In the case of high EBL flux (model F1.6), the de-absorbed VHE spectrum has a photon index close to $\Gamma_{\rm int}\simeq1$, i.e. harder than the unabsorbed synchrotron spectrum from a proton distribution with index $p\sim2$."
 Internal absorption allows the hardening of the TeV spectrum to the required level. but in the case of a conventional proton distribution the diserepaney with the Fermi-LAT upper limits is very strong.," Internal absorption allows the hardening of the TeV spectrum to the required level, but in the case of a conventional proton distribution the discrepancy with the Fermi-LAT upper limits is very strong."
" To avoid the conllict with Fermi-LAT data we need to suppress the GeV emission. by introducing additional assumptions such as an effective absorption of GeV 5-ravs (e.g. by X-rays) or a very. high lower-energv cutolf (at. 10"" TeV in proton energv)."," To avoid the conflict with Fermi-LAT data we need to suppress the GeV emission, by introducing additional assumptions such as an effective absorption of GeV $\gamma$ -rays (e.g. by X-rays) or a very high lower-energy cutoff (at $10^{6}$ TeV in proton energy)."
 However. these assumptions can hardly be endorsed without an additional observational or theoretical justification.," However, these assumptions can hardly be endorsed without an additional observational or theoretical justification."
 , 
"There are two major mechanisms for gas-giant planet ormation: one is the core accretion mechanism in which a massive solic core forms first and the clisk gas acerctes onto he core (Saronov1969:Goldreich&Ware1973:Pollackο)αἱ, 1996). and the other is the gravitational instability (GI) mechanism in which the circumstellar disk. cirectly ragmoents ino gas-giant planets via GI (CameronLOTS).","There are two major mechanisms for gas-giant planet formation: one is the core accretion mechanism in which a massive solid core forms first and the disk gas accretes onto the core \citep{safronov69,goldreich_ward73,pollacketal96}, and the other is the gravitational instability (GI) mechanism in which the circumstellar disk directly fragments into gas-giant planets via GI \citep{cameron78}."
. tecent discovery. of extra-solar planets at a great distance rom the central star such as HIVSTOOb. c. d and e (Marolsοἱ2008.201) and (το CPhalmannefa£.2009). creates a new problem for the planet formation.," Recent discovery of extra-solar planets at a great distance from the central star such as HR8799b, c, d and e \citep{maroisetal08,maroisetal10} and GJ579b \citep{thalmannetal09} creates a new problem for the planet formation."
 Lt is dillicult to orm planets in the regions far from central stars according o the core accretion mechanism. because massive solid core ormation before the dissipation of gaseous disk seems to be caüllicult (Dodson-Robinsonefad.20090).," It is difficult to form planets in the regions far from central stars according to the core accretion mechanism, because massive solid core formation before the dissipation of gaseous disk seems to be difficult \citep{dodsonetal09}."
. ‘The gravitationally instability mechanism may be more plausible for the formation o ‘these planets., The gravitationally instability mechanism may be more plausible for the formation of these planets.
 Many studies of clisk fragment:uijon have been done using either an analytic approach (ltalikov2005) or numerical simulations (e.g..&Date 2010).," Many studies of disk fragmentation have been done using either an analytic approach \citep{rafikov05} or numerical simulations \citep[e.g.,][]{ stamatellos_whitworth08, caietal08, boleyetal06, mejiaetal05, pickettetal03,meru_bate10}."
". These elforts. however. μα... to build a Consensus tha the. planet ormation by Gl within ~50r AU is highly «illicult when the clisk-to-stellar mass ratio is MaafAda""Yo0.1 whose ratio is suggested by observations (see.e.g...Witamurae£αἱ.2)02)."," These efforts, however, seem to build a consensus that the planet formation by GI within $\sim 50$ AU is highly difficult when the disk-to-stellar mass ratio is $M_{\rm disk}/M_{\rm star}\lesssim 0.1$ whose ratio is suggested by observations \citep[see, e.g.,][]{kitamuraetal02}."
. On the otyer hand. IEnutsukaefαἱ.(2010). showed that the circumstelar disk is comparable to or more massive than the protostar. (AdagfA 1) during the (early) main accretior1 phase (i.e. Class 0 or Class | stages) and is hiehly σανίαionally unstable.," On the other hand, \citet{imm10} showed that the circumstellar disk is comparable to or more massive than the protostar $M_{\rm disk}/M_{\rm star}\gtrsim 1$ ) during the (early) main accretion phase (i.e., Class 0 or Class I stages) and is highly gravitationally unstable."
 Recently. such massive disks were observed around. very young protostars," Recently, such massive disks were observed around very young protostars"
proposed byDiStefano. Greiner. Garcia. Murray 2001.,"proposed by, Greiner, Garcia, Murray 2001."
 Given the expected rate of TDs. in a galaxy such as M3l. several of these remnants could be active at any given time.," Given the expected rate of TDs, in a galaxy such as M31, several of these remnants could be active at any given time."
 Some stripped cores are expected to be WDs or pre-WDs. and some are expected to be helium stars.," Some stripped cores are expected to be WDs or pre-WDs, and some are expected to be helium stars."
 The possibility that SSSs in the center of nearby galaxies could be signatures of TDs ts interesting. particularly because other signatures of TDs are so difficult to identify with confidence.," The possibility that SSSs in the center of nearby galaxies could be signatures of TDs is interesting, particularly because other signatures of TDs are so difficult to identify with confidence."
 The complementary signature most considered is an event due to the accretion of a portion of the disrupted star’s envelope by the BH (Hills 1975. Lidskit Ozernoi 1979. Gurzadyan Ozernoi 1980. Rees 1988).," The complementary signature most considered is an event due to the accretion of a portion of the disrupted star's envelope by the BH (Hills 1975, Lidskii Ozernoi 1979, Gurzadyan Ozernoi 1980, Rees 1988)."
 The associated accretion event can last for months or decades. with luminosities possibly as high as ~10—1075 erg/s. There is a growing body of data on UV and X-ray flares that may be consistent with these sorts of accretion events (see references in eet al.," The associated accretion event can last for months or decades, with luminosities possibly as high as $\sim 10^{44}-10^{46}$ erg/s. There is a growing body of data on UV and X-ray flares that may be consistent with these sorts of accretion events (see references in et al."
 2001)., 2001).
 It is nevertheless difficult to establish a definite link between observed flare events and accretion events. so information. about stripped cores in nearby galaxies would be important.," It is nevertheless difficult to establish a definite link between observed flare events and accretion events, so information about stripped cores in nearby galaxies would be important."
 The possibility of studying the stripped cores of disrupted stars is an important motivation of the search for SSSs in the central regions of galaxies., The possibility of studying the stripped cores of disrupted stars is an important motivation of the search for SSSs in the central regions of galaxies.
 In this section we have so far focused on models in which the SSSs we discover are luminous X-ray binaries., In this section we have so far focused on models in which the SSSs we discover are luminous X-ray binaries.
 We expect. however. that other types of objects will produce the same broadband X-ray signatures.," We expect, however, that other types of objects will produce the same broadband X-ray signatures."
" SNRs form the primary class of SSS ""contaminants"" that are luminous(Ly>1076 ere y. and which are actually members of the galaxy being observed."," SNRs form the primary class of SSS “contaminants"" that are luminous$L_X > 10^{36}$ erg $^{-1}$ ), and which are actually members of the galaxy being observed."
 In M31. 2 SSSs are SNRs.," In M31, $2$ SSSs are SNRs."
 Interestingly. one of these M31 SNRs is among the softest sources in M31.," Interestingly, one of these M31 SNRs is among the softest sources in M31."
 Most of the other 33 M31 SSSs we identified using the criteria presented in this paper. are highly variable: many are transients.," Most of the other $33$ M31 SSSs we identified using the criteria presented in this paper, are highly variable; many are transients."
 We therefore know that SNR contanimants form only à minor portion of the SSSs in M31., We therefore know that SNR contanimants form only a minor portion of the SSSs in M31.
 In Kong (2003 a). we studied the available data on the variability of SSSs in 4 more distant galaxies (MIOI. M83. M51. and NGC 4697; see also Kong 2003 b)," In Kong (2003 a), we studied the available data on the variability of SSSs in $4$ more distant galaxies (M101, M83, M51, and NGC 4697; see also Kong 2003 b)."
 Although the limited time coverage of the observations we studied allowed only the brightest sources to be checked for variability. we did find evidence of variability on time scales of a year.," Although the limited time coverage of the observations we studied allowed only the brightest sources to be checked for variability, we did find evidence of variability on time scales of a year."
 This is consistent with an X-ray binary nature for the majority of bright SSSs., This is consistent with an X-ray binary nature for the majority of bright SSSs.
 Knots in diffuse emission from the galaxy can also have very soft spectra. and they may be misidentified as SSSs when they cannot be spatially resolved.," Knots in diffuse emission from the galaxy can also have very soft spectra, and they may be misidentified as SSSs when they cannot be spatially resolved."
 This is most likely to occur near the centers of galaxies with a significant diffuse soft component. but can happen in any location in. which the X-ray emission appears to be dominated by diffuse emission.," This is most likely to occur near the centers of galaxies with a significant diffuse soft component, but can happen in any location in which the X-ray emission appears to be dominated by diffuse emission."
 If the sources are bright or the time sampling is good. time variability can help to identify which sources in regions of diffuse emission may be X-ray binaries: observations at other wavelengths may be helpful in finding counterparts to extended objects.," If the sources are bright or the time sampling is good, time variability can help to identify which sources in regions of diffuse emission may be X-ray binaries; observations at other wavelengths may be helpful in finding counterparts to extended objects."
 In the absence of such complementary information. however. SSSs discovered in regions of diffuse emission should not be assumed to be X-ray binaries.," In the absence of such complementary information, however, SSSs discovered in regions of diffuse emission should not be assumed to be X-ray binaries."
 Other systems identified by our algorithm are dim foreground objects or bright background objects., Other systems identified by our algorithm are dim foreground objects or bright background objects.
 Foreground stars can emit soft X-rays., Foreground stars can emit soft X-rays.
 In many cases such stars will have been identified by optical surveys and can be ruled out as luminous X-ray binaries., In many cases such stars will have been identified by optical surveys and can be ruled out as luminous X-ray binaries.
 In high surface brightness regions of the observed galaxy. however. the survey of foreground stars may be less complete. and we may not be able to identify which SSSs are foreground stars.," In high surface brightness regions of the observed galaxy, however, the survey of foreground stars may be less complete, and we may not be able to identify which SSSs are foreground stars."
 A further complication is that the soft X-ray emission from foreground stars can be highly variable. so variability cannot be taken as a signature that the SSS is an X-ray binary.," A further complication is that the soft X-ray emission from foreground stars can be highly variable, so variability cannot be taken as a signature that the SSS is an X-ray binary."
 Distant soft AGN can also be selected as SSSs: observations at other wavelengths can help to identify some. but probably not all of these.," Distant soft AGN can also be selected as SSSs; observations at other wavelengths can help to identify some, but probably not all of these."
 Further. some nearby magnetic CVs can also be selected as SSSs: it may be difficult to identify such sources at other wavelengths.," Further, some nearby magnetic CVs can also be selected as SSSs; it may be difficult to identify such sources at other wavelengths."
 The standard method to estimate the contribution of foreground and background sources is to use results derived from deep field surveys (Giaccont et 2001. Brandt et 2001).," The standard method to estimate the contribution of foreground and background sources is to use results derived from deep field surveys (Giacconi et 2001, Brandt et 2001)."
 Because. however. we are specifically interested 11 SSSs. which have not yet been studied in the deep fields. we have used another approach. sketched below. and discussed i more detail in Stefano et 2003).," Because, however, we are specifically interested in SSSs, which have not yet been studied in the deep fields, we have used another approach, sketched below, and discussed in more detail in Stefano et 2003)."
 Briefly. we have applied our algorithm to data from several fields analyzed by the ChAMP team.," Briefly, we have applied our algorithm to data from several fields analyzed by the ChAMP team."
 We consider only fields located away from the Galactic plane. and containing no clusters or galaxies.," We consider only fields located away from the Galactic plane, and containing no clusters or galaxies."
 [t such fields. we generally we find 1—3 VSSs in the 53 CCD.," In such fields, we generally we find $1-3$ VSSs in the S3 CCD."
 When. therefore. in observations of an external galaxy. we discover tens of VSSs in the S3 CCD. we can assume that the majority of them are associated with the galaxy.," When, therefore, in observations of an external galaxy, we discover tens of VSSs in the S3 CCD, we can assume that the majority of them are associated with the galaxy."
" Finally. we note that. although SNRs. foreground stars. and other ""contaminants"" do not dominate the VSSs we identify with galaxies. our algorithm does provide an efficient way to search for X-ray active SNRs and for a subset of foreground stars."," Finally, we note that, although SNRs, foreground stars, and other “contaminants"" do not dominate the VSSs we identify with galaxies, our algorithm does provide an efficient way to search for X-ray active SNRs and for a subset of foreground stars."
 Our phenomenological definition should. select. sources described by the physical models discussed above., Our phenomenological definition should select sources described by the physical models discussed above.
 The WD models alone define a broad range of temperatures. from 10 eV up to ~150 For example. while V751 Cyg had a best fit temperature with AT<10 eV. a L4M.. WD with Eddington-luminosity nuclear burning on its surface would have ΚΤ— 150eV. NBWD luminosities range from ~I0? erg s! up to the Eddington limit fora ΤΕΜ. object (~2«10? ere s! y.," The WD models alone define a broad range of temperatures, from $k\, T < 10$ eV up to $\sim 150$ For example, while V751 Cyg had a best fit temperature with $k\, T < 10$ eV, a $1.4\, M_\odot$ WD with Eddington-luminosity nuclear burning on its surface would have $k\, T \sim 150$ eV. NBWD luminosities range from $\sim 10^{35}$ erg $^{-1}$ up to the Eddington limit for a $1.4\, M_\odot$ object $\sim 2 \times 10^{38}$ erg $^{-1}$ )."
" The stripped core of à high-mass star might have a temperature near the low end of the temperature range. but a luminosity in excess of 10?? erg s!, Accreting BHs could have even higher luminosities. with temperatures in the SSS range or even higher."," The stripped core of a high-mass star might have a temperature near the low end of the temperature range, but a luminosity in excess of $10^{39}$ erg $^{-1}.$ Accreting BHs could have even higher luminosities, with temperatures in the SSS range or even higher."
 The sensitivities of the detectors used for X-ray astronomy tend to peak for photons with energies near or above | keV. Until the advent of and then ROSAT. it was difficult to study sources with energy distributions peaked significantly below | keV. It was also difficult to detect and study such," The sensitivities of the detectors used for X-ray astronomy tend to peak for photons with energies near or above $1$ keV. Until the advent of and then , it was difficult to study sources with energy distributions peaked significantly below $1$ keV. It was also difficult to detect and study such"
individually small contributions can be added together to produce a large overall result. if one has enough of them: and (hough Newtonian-evel perturbations weaken as ~1/7. the number of them in a spherical shell increases as 77? (easily overwhelming anv [factors of ο). creating a total perturbative effect that would formally be when integrated out to r=x. if not reined in by the finite causal horizon out to which an observer can ‘see clumped structure (hat has had sufficient time since the Die Bane to form: a situation reminiscent of Olbers: Paradox (Weinberg1972)..,"individually small contributions can be added together to produce a large overall result, if one has enough of them; and though Newtonian-level perturbations weaken as $\sim$$1/r$, the number of them in a spherical shell increases as $\sim$$r^{2}$ (easily overwhelming any factors of $v^{2}/c^{2}$ ), creating a total perturbative effect that would formally be when integrated out to $r = \infty$, if not reined in by the finite causal horizon out to which an observer can `see' clumped structure that has had sufficient time since the Big Bang to form; a situation reminiscent of Olbers' Paradox \citep{WeinbergGravCosmo}."
 For a causalitv-respecting approach. one must instead (as in electrodyvnanmics) use the full wave equation. lor special-relativistically consistent perturbation potential function $a: (Note that factors relating to the cosmic expansion are still neglected here. for simplicity.)," For a causality-respecting approach, one must instead (as in electrodynamics) use the full wave equation, for special-relativistically consistent perturbation potential function $\Phi _{\mathrm{SR}}$: (Note that factors relating to the cosmic expansion are still neglected here, for simplicity.)"
 Now. (he usual impulse is to immediately drop the extra term in Equation 1.. involving OpaΟΙ equivalent to dropping the eravilomagnetlic terms. as is done in the Buchert formalism — because of its resulting prefactor of 02/62: this factor would seem to make il verv small given (he assumption of nonrelativistic speeds for most matter flows. ancl thus (assumedlv) ensuring it to be negligible compared to the spatial variations (erm in any backreaction ealeulation.," Now, the usual impulse is to immediately drop the extra term in Equation \ref{EqnPoissonDynamic}, involving $\partial^2 \Phi_{\mathrm{SR}} / \partial t^2$ – equivalent to dropping the gravitomagnetic terms, as is done in the Buchert formalism – because of its resulting prefactor of $v^{2}/c^{2}$; this factor would seem to make it very small given the assumption of nonrelativistic speeds for most matter flows, and thus (assumedly) ensuring it to be negligible compared to the spatial variations term in any backreaction calculation."
 But this thinking is based only upon considerations of individual Fourier perturbation modes. not on the overall causal behavior of information flow in the siructure-forming universe.," But this thinking is based only upon considerations of individual Fourier perturbation modes, not on the overall causal behavior of information flow in the structure-forming universe."
 If we instead. all terms. ancl solve Equation 1. as-is. then one eels (adaptingfromJackson1915.eq. 6.69): where the bracketed numerator is always evaluated at theHime. l=1—|x—-x|/c.," If we instead all terms, and solve Equation \ref{EqnPoissonDynamic} as-is, then one gets \citep[adapting from][eq. 6.69]{JacksonEM}: : where the bracketed numerator is always evaluated at the, $t^{\prime} = 
t - \vert {\bf x} - {\bf x}^{\prime} \vert / c$."
 lt is Chis retarded-time condition which restores causalitv. allowing different regions of the universe (o communicate wilh (and gravitationally perturb) one another: and which provides (he escape route [rom the Buchert suppression of Newtonian-level backreaction. because such backreaction isnof (uly expressible as a total divergence.," It is this retarded-time condition which restores causality, allowing different regions of the universe to communicate with (and gravitationally perturb) one another; and which provides the escape route from the Buchert suppression of Newtonian-level backreaction, because such backreaction is truly expressible as a total divergence."
 We will refer to this propagation of gravitational perturbation information between distant (though communicating) regions as “Causal updating.," We will refer to this propagation of gravitational perturbation information between distant (though communicating) regions as “causal updating""."
 Given (he [act that the kev metric perturbation function. Φωνή). is predominantly affected by inhomogeneity information coming in from distant locations. the retarded-time condition of an integrated formula like Equation 2 (suitably modified for cosmological calculations) implicitly gives it the abilitv toexhibit relativistic behavior in what would," Given the fact that the key metric perturbation function, $\Phi _{\mathrm{SR}} (t)$, is predominantly affected by inhomogeneity information coming in from distant locations, the retarded-time condition of an integrated formula like Equation \ref{EqnSRpotential} (suitably modified for cosmological calculations) implicitly gives it the ability toexhibit relativistic behavior in what would"
overtone) for highest luminosities or smallest. &ravities in the figure (see Fig.,overtone) for highest luminosities or smallest gravities in the figure (see Fig.
 3 in Pamvatuykh 2000)., 3 in Pamyatnykh 2000).
 The Blue Edge for the radial fundamental mode lies approximately in the center of the 9 Scuti instability strip., The Blue Edge for the radial fundamental mode lies approximately in the center of the $\delta$ Scuti instability strip.
 An aclelitional study of the instability along the 2.5 M. evolutionary track shows that the best theoretical general Blue Edge for X=0.716. Y=0.26. Z=0.024 will be located. very. elose to the blue edge shown in Fig.," An additional study of the instability along the 2.5 $M_{\odot}$ evolutionary track shows that the best theoretical general Blue Edge for $X=0.716$, $Y=0.26$, $Z=0.024$ will be located very close to the blue edge shown in Fig."
 5. because the dillerences in the rotational velocity and in the overshooting eLlliclency do not inlluence the position of the Blue Eclees and because the dillerences in the helium abundance are small.," 5, because the differences in the rotational velocity and in the overshooting efficiency do not influence the position of the Blue Edges and because the differences in the helium abundance are small."
 Moreover. convection has only a minor influence on the position of this hot general Bluc Eclee (see Fig.," Moreover, convection has only a minor influence on the position of this hot general Blue Edge (see Fig."
 9 in Pamvatuykh 2000)., 9 in Pamyatnykh 2000).
 For the fundamental racial moodle the best Blue Edge will be hotter by 0.008—0.009 in logZ;47., For the fundamental radial mode the best Blue Edge will be hotter by $0.008-0.009$ in $\log T_{\rm{eff}}$.
 Phis is mainly due to a higher value of the mixing- parameter., This is mainly due to a higher value of the mixing-length parameter.
 From Fig., From Fig.
 5 we immediately obtain a strong constraint on the possible effective. temperature of the primary of 67 ‘Yau., 5 we immediately obtain a strong constraint on the possible effective temperature of the primary of $\theta^2$ Tau.
 All models with log(L/L.)>167 and logT;3.907 CHapZ7SOTO WIS) are stable in all modes., All models with $\log (L/L_{\odot})>1.67$ and $\log T_{\rm{eff}}>3.907$ $T_{\rm{eff}}>8070$ K) are stable in all modes.
 A AIS moclel of 2.5 AJ. on the Blue Edge (τμ=SOTO WIS) is marginally unstable in radial mode ps with the frequency. 18.74 1 which is well outside the observed frequency range.," A MS model of 2.5 $M_{\odot}$ on the Blue Edge $T_{\rm{eff}} = 8070$ K) is marginally unstable in radial mode $p_6$ with the frequency 18.74 $^{-1}$, which is well outside the observed frequency range."
 We can conclude that only significantly. cooler models can pulsate with the observed frequencies in the 10.8 to 16 ed.+ range., We can conclude that only significantly cooler models can pulsate with the observed frequencies in the 10.8 to 14.6 $^{-1}$ range.
 This conclusion. is confirmed by computation of oscillations of the selected test models for the primary of 67 ‘Tau., This conclusion is confirmed by computation of oscillations of the selected test models for the primary of $\theta^2$ Tau.
 In Fig., In Fig.
 6. the normalized. growth rates of. radial and. nonraclial modes are plotted: against frequency for. all nine higher-mass models which are marked in Fig.," 6, the normalized growth rates of radial and nonradial modes are plotted against frequency for all nine higher-mass models which are marked in Fig."
 5., 5.
 Only axisvmmetrie modes (i= 0) are shown., Only axisymmetric modes $m = 0$ ) are shown.
 The independence of the growth rate on the spherical harmonic degree. f£. is a tvpical feature of modes excited by the & mechanism.," The independence of the growth rate on the spherical harmonic degree, $\ell$, is a typical feature of modes excited by the $\kappa$ mechanism."
 The rotational velocities of the models are SI to 86 km/s. The rotational splitting of the modes can extend the frequency range by approximately 0.5 c/d on both sides., The rotational velocities of the models are 81 to 86 km/s. The rotational splitting of the modes can extend the frequency range by approximately 0.5 c/d on both sides.
 We can see that excited. frequencies of the 245 AL. model with dig=TSOO WH are in excellent agreement with the observed frequeney range., We can see that excited frequencies of the 2.45 $M_{\odot}$ model with $T_{\rm{eff}} = 7800$ K are in excellent agreement with the observed frequency range.
 The frequeney range of unstable modes spans three racial orders from py to ps for radial. modes (mode pj is marginally unstable)., The frequency range of unstable modes spans three radial orders from $p_4$ to $p_6$ for radial modes (mode $p_4$ is marginally unstable).
 As was noted already. thje results are sensitive to the treatment of convection.," As was noted already, the results are sensitive to the treatment of convection."
 For example. if we use à mixing-length parameter a=2.0 insead of à=1.6. the frequency range of unstable moces [ου 245 AJ. model with Zip TSOOIx. is extended by 1 cf on both sides.," For example, if we use a mixing-length parameter $\alpha=2.0$ instead of $\alpha=1.6$, the frequency range of unstable modes for 2.45 $M_{\odot}$ model with $T_{\rm{eff}} = 7800$ K is extended by 1 c/d on both sides."
 Moreover. our assumption about the unperurbed convective [ux during an oscillation cvwcle is. not fulfilled) inside the hydrogen convective zone and may result in artificial acdcditiona driving in this zone.," Moreover, our assumption about the unperturbed convective flux during an oscillation cycle is not fulfilled inside the hydrogen convective zone and may result in artificial additional driving in this zone."
 Pheree. these preliminary results must be considered with caution.," Therefore, these preliminary results must be considered with caution."
 Similar results were obt:uned for the models. withou overshooting. the best fitting is achieved. in this case for 2.50 AJ. model with Yup= TSOOWKK. Also. for slightly more massive ALS models with overshooting. we obtainec a good agreement between the observed and the theoretica frequency ranges.," Similar results were obtained for the models without overshooting, the best fitting is achieved in this case for 2.50 $M_{\odot}$ model with $T_{\rm{eff}} = 7800$ K. Also, for slightly more massive MS models with overshooting, we obtained a good agreement between the observed and the theoretical frequency ranges."
 The parameters of some mocels are given in ‘Table 4 below., The parameters of some models are given in Table 4 below.
 In Fig., In Fig.
 7 we show the normalized. growth rates in test models of the secondary. component., 7 we show the normalized growth rates in test models of the secondary component.
 These models are also nmiwked in Fig., These models are also marked in Fig.
 5., 5.
 As for the primary. we used mocdoels with elective. temperatures from. 7800. to KIN. The," As for the primary, we used models with effective temperatures from 7800 to K. The"
At this frequency the resolving power of the telescope is 9.6 aresee (Πα Power Beam Width) aud the 1 CIIz bandwidth corresponds to 11705.,At this frequency the resolving power of the telescope is 9.6 arcsec (Half Power Beam Width) and the 1 GHz bandwidth corresponds to 1170.
 The resulting spectral resolution and the noise iu the coadded and rebiuued spectrini were. respectively. 56 aand 0.3? mds (2.8 wv). leading to a accuracy of the flux density scale.," The resulting spectral resolution and the noise in the coadded and rebinned spectrum were, respectively, 56 and 0.3 mK (2.8 mJy), leading to a accuracy of the flux density scale."
" The i| line was detected at a siguificance level of Sa for the total exposure time of 12.1 h. The redshift and the peak intensity of the [C1] line are ig=6.11589+0.0006 and τος=11.5 ταν,", The ] line was detected at a significance level of $8\sigma$ for the total exposure time of 12.4 h. The redshift and the peak intensity of the ] line are $z_{\rm fs} = 6.4189 \pm 0.0006$ and $I_{158} = 11.8$ mJy.
 The reported error σ.=0.0006 corresponds to the uncertainty of the line position mcasurement of a κιν. whic[um is about one bin size iu the 11] spectrum: at the Nyquis+ iuit of 2 resolution clemeuts.," The reported error $\sigma_z = 0.0006$ corresponds to the uncertainty of the line position measurement of $\sigma_v \sim$ 24, which is about one bin size in the ] spectrum at the Nyquist limit of 2 resolution elements."
" Observations of the CO 3G) and 35) omission ines were obtained with the IRAAL Plateau de Bure interferometer at the frequencies 108.721 GIIz (the total integration tiuie Dig,=22 h) aud 93.206 GIIz (Lig,11 1). respectively (Bertoldi et al."," Observations of the CO $\rightarrow$ 6) and $\rightarrow$ 5) emission lines were obtained with the IRAM Plateau de Bure interferometer at the frequencies 108.724 GHz (the total integration time $T_{\rm exp} = 22$ h) and 93.206 GHz $T_{\rm exp} = 14$ h), respectively (Bertoldi et al."
 2003)., 2003).
 At about 5 arcsec angular resolution (5.77«LA” at 3.2 mim) the CO emission ine is unresolved aud colucides within the astrometric uncertainties of £0.3 arcsec with the optical position of he quasar eiven by Fan ct al. (, At about 5 arcsec angular resolution $5.7''\times4.1''$ at 3.2 mm) the CO emission line is unresolved and coincides within the astrometric uncertainties of $\pm0.3$ arcsec with the optical position of the quasar given by Fan et al. (
2003).,2003).
 The coadded 3 nuu data were rebiuned to GL (27 »6)andSo ((7—6 »5) resulting in the accuracy of the me position lüueasurenmieuts of a. ~36 aud 21 respectively.," The coadded 3 mm data were rebinned to 64 $J=7\rightarrow6$ ) and 55 $J=6\rightarrow5$ ) resulting in the accuracy of the line position measurements of $\sigma_v \sim$ 36 and 24, respectively."
 These uncertainties are again of a bin size in the reduced spectra., These uncertainties are again of a bin size in the reduced spectra.
 The redshifts and the peak intensities of the CO ⋅ : ⋖∣≻↭⋜⋯≼⊔∩≻⋅↱⊐⋝↕∐∐∖↴∖↴⋜∐⋅↸∖∙↥⋅↸∖↴∖↴↻↸∖↸⊳⊓↖⇁↸∖↕⋅↖↽∙−∙↕∴⊺⇂∶∩⋅⊔≝∟≻∶≓: (T6)⋅↽⊲ ∩∙∩∩∩∩∙∫∩−⋯∶⊇∙↕↕⊔⋅↧⋅↖⇁∙⋜⋯≼↧ 27-6.4189dcOLQUQG. fig3)=2.15 wwdy.," The redshifts and the peak intensities of the CO $\rightarrow$ 6) and $\rightarrow$ 5) lines are, respectively, $z^{(7-6)}_{\rm rot} = 6.4192 \pm 0.0009$ , $I_{(7-6)} = 2.14$ mJy, and $z^{(6-5)}_{\rm rot} = 6.4189 \pm 0.0006$, $I_{(6-5)} = 2.45$ mJy."
" Weighting the reported rotational redshifts with these peak iutensitics. one obtains the mean typo,=6.1190+ 0.0005."," Weighting the reported rotational redshifts with these peak intensities, one obtains the mean $z_{\rm rot} = 6.4190 \pm 0.0005$ ."
 We will take this value for the quasars svstenic redshift 7., We will take this value for the quasar's systemic redshift $z$.
 Using the reported redshift τε aud the averaged noe Eq.(9)) viclds ΔΕΕΞ(0.141.0)«103.," Using the reported redshift $z_{\rm fs}$ and the averaged $z_{\rm rot}$, \ref{EQ8}) ) yields ${\Delta F}/{F} = (0.1 \pm 1.0)\times10^{-4}$."
 The second [Cu] line was detected at τε=16908 towards the northern componcut of the quasar (lone et al., The second ] line was detected at $z_{\rm fs} = 4.6908$ towards the northern component of the quasar (Iono et al.
 2006)., 2006).
 The profile of this line is similar to the CO »1) and +6) lines seen at tor=LG6916 from the same component (Oment et al., The profile of this line is similar to the CO $\rightarrow$ 4) and $\rightarrow$ 6) lines seen at $z_{\rm rot} = 4.6916$ from the same component (Omont et al.
 1999)., 1999).
 The [Cu] 158 pau cinission was observed with the Subuullimeter Arrav interferometer (SMA. Πο oet al.," The ] 158 $\mu$ m emission was observed with the Submillimeter Array interferometer (SMA, Ho et al."
 2001)., 2004).
" The total exposure fine at a redshifted [C1] frequeney of 333.969 GIIz was Τον=19.6 h. and the angular resolution was 3.17«2.7""."," The total exposure time at a redshifted ] frequency of 333.969 GHz was $T_{\rm exp} = 19.6$ h, and the angular resolution was $3.4''\times2.7''$."
 The coadded spectrun was averaged using 120 bbin size resulting in the rs noise of 7.5 mJy. or the signal-to-noise ratio S/N~3 (the peak flux deuxitv ~23 mJy as shown inFig.," The coadded spectrum was averaged using 120 bin size resulting in the rms noise of 7.5 mJy, or the signal-to-noise ratio $\sim 3$ (the peak flux density $\sim$ 23 mJy as shown inFig."
 b iu Ione et al)., 1 in Iono et al.).
" Assiuuine the uncertainty of the | line position as —1/1 bin size. 61ο ects the error o,230 "," Assuming the uncertainty of the ] line position as $\sim$ 1/4 bin size, one gets the error $\sigma_v \simeq 30$ ."
"The CO J=5l1 line observed with the IRAM iuterferoimneter is detected at the ~56 confidence level (Ting,~16 b). and the CO πλ>6 line observed with the IRAM. 30-1 telescope at the 30 confidence level."," The CO $J=5\rightarrow4$ line observed with the IRAM interferometer is detected at the $\sim 5\sigma$ confidence level $T_{\rm exp} \sim 16$ h), and the CO $J=7\rightarrow6$ line observed with the IRAM 30-m telescope – at the $3\sigma$ confidence level."
 The aneularOo resolution im the interferometric observations was 5442.5 arcsec. and velocity resolution of about GOἘ," The angular resolution in the interferometric observations was $5.0\times2.5$ arcsec, and velocity resolution of about 60."
"ν, The redshift of the northern compouent is τα2=L6016.", The redshift of the northern component is $z_{5-4} = 4.6916$.
 TIje uncertaintv of this value is. probably. 25-30Woede approximately one resolution clement. cousidering rather noisy line profiles shown in Fig.," The uncertainty of this value is, probably, 25-30, i.e. approximately one resolution element, considering rather noisy line profiles shown in Fig."
 2 in Omout et al., 2 in Omont et al.
 The aneular resolution of the 30-12 telescope for the 2-uuu beam dis 17 arcsec., The angular resolution of the 30-m telescope for the 2-mm beam is 17 arcsec.
 The error of the reporte redshift i£[46=|6915d:0.001 corresponds to the radia velocity uncertainty of 53, The error of the reported redshift $z_{7-6} = 4.6915\pm0.001$ corresponds to the radial velocity uncertainty of 53.
" Taking mto account that the angular resolutions are similar in observations of the [Cul and CO f=5)> enisson lines. we| en use their redshifts τε=L6908+0.0006 and s=1.691643:0.0006 (both errors correspon to a,=30 Ly) to calculate ΑΕΕ=(1.1510 "," Taking into account that the angular resolutions are similar in observations of the ] and CO $J=5\rightarrow4$ emission lines, we can use their redshifts $z_{\rm fs} = 4.6908\pm0.0006$ and $z_{\rm rot} = 4.6916\pm0.0006$ (both errors correspond to $\sigma_v = 30$ ) to calculate ${\Delta F}/{F} = (1.4 \pm 1.5)\times10^{-4}$ ."
While comparing the redshifted. frequencies. of. to castre hvwpothetical variations of physical constants. one niust account for random Doppler shifts of the line positions caused by non-identical spatial distributions of s)ecies (referred to as the Doppler noise hereinafter) whicl1 can niuie non-zero signals in oor oor Ina combinaion of these quantities (0... Levshakoy 1991: Caxilli et al.," While comparing the redshifted frequencies of to measure hypothetical variations of physical constants, one must account for random Doppler shifts of the line positions caused by non-identical spatial distributions of species (referred to as the Doppler noise hereinafter) which can mimic non-zero signals in or or in a combination of these quantities (e.g., Levshakov 1994; Carilli et al."
 2000: Bahcall et al., 2000; Bahcall et al.
 2001)., 2004).
 To quantity Πο iudiwed by the Doppler noise a sample of (Aqfa)(Ai) measurements is to be collected., To quantify uncertainties induced by the Doppler noise a sample of $(\Delta\alpha/\alpha)/(\Delta\mu/\mu)$ measurements is to be collected.
 The man pr‘oblem here is how to cstimate the dispersion of random velocity shifts 0. for a given system of spectral lines., The main problem here is how to estimate the dispersion of random velocity shifts $\sigma_{\rm v}$ for a given system of spectral lines.
" In case of a laree sample size the value of ao, can be found from the scatter of »outs.", In case of a large sample size the value of $\sigma_{\rm v}$ can be found from the scatter of points.
 For a sinele measurement. a guess for σς comes roni the comparison with data on velocity differences vetwween spectral lines of similar species in nearby clouds.," For a single measurement, a guess for $\sigma_{\rm v}$ comes from the comparison with data on velocity differences between spectral lines of similar species in nearby clouds."
" Observations of k(al galaxies show that the inteusitv of Ci] is strongly correlated with the intensities of the low-vine rotational |ines of CO. the fine-structure dines of Ci] AASTO0.609. , πα and [OL AAG3.116. pan (Malhotra ( al."," Observations of local galaxies show that the intensity of ] is strongly correlated with the intensities of the low-lying rotational lines of CO, the fine-structure lines of ] $\lambda\lambda370, 609$ $\mu$ m and ] $\lambda\lambda63, 146$ $\mu$ m (Malhotra et al."
 2001). ane the fine-structure line of [ΠΠ A205 pau (Petuchowski Bennett 1993: Abel 2006).," 2001), and the fine-structure line of ] $\lambda205$ $\mu$ m (Petuchowski Bennett 1993; Abel 2006)."
 However. 1ο surface distribution of the [Ci] emission may not xeciselv. follow t1ο actual D 2CO- contours (Stacey.+ et al.," However, the surface distribution of the ] emission may not precisely follow the actual $^{12}$ CO contours (Stacey et al."
 19855)., 1985).
 The CO rotational ues. if optically thin. are (uitted throughout the whole molecular cloud.," The CO rotational lines, if optically thin, are emitted throughout the whole molecular cloud."
 As for jio. r1]. endissio1 it is usually enhanced at the edges of the molecular cloud in the photodissociation regions (PDRs).," As for the ] emission, it is usually enhanced at the edges of the molecular cloud in the photodissociation regions (PDRs)."
 Additionally. diffuse eas from the regions cau coutributeto the intensity of the ΡΟ lines (Ixaufuia et al.," Additionally, diffuse gas from the regions can contributeto the intensity of the `PDR' lines (Kaufman et al."
 1999)., 1999).
 ILowever. the impact from the diffuse gas decreases with increasing gas densities anddrops from YA at nyp~locuni ," However, the impact from the diffuse gas decreases with increasing gas densities anddrops from $\sim$ at $n_{\rm H} \sim 1$ "
the uncertainties ou these parameters. which lie between ~1050%.,"the uncertainties on these parameters, which lie between $\sim$ 10–50."
. Therefore. in the general study above. this effect is not crucial in the determination of the elobal characteristics of the flares.," Therefore, in the general study above, this effect is not crucial in the determination of the global characteristics of the flares."
 Since the refined wwodel also leads to lower \2 values. the main source of uucertaiuty that now remains is the level of the background radio flix.," Since the refined model also leads to lower $\chi_\nu^2$ values, the main source of uncertainty that now remains is the level of the background radio flux."
 However. in the case of a strong backeround. this level is poorly constrained.," However, in the case of a strong background, this level is poorly constrained."
 Indeed. there is a degeneracy between the offset level Avy aud the other parameters: if [y is fixed to lower values. the fitting routine will chauge the other parameters to increase the overlap between flares. which will lead to an acceptable ft.," Indeed, there is a degeneracy between the offset level $K_{0}$ and the other parameters: if $K_{0}$ is fixed to lower values, the fitting routine will change the other parameters to increase the overlap between flares, which will lead to an acceptable fit."
 This effect is particularly true in the case of strong overlap., This effect is particularly true in the case of strong overlap.
" Iu order to quantify this issue. we attributed a ""confidence index” to our data."," In order to quantify this issue, we attributed a “confidence index"" to our data."
 This index is based onu two criteria: the level of backeround fiux. aud the uorphologv of the observed flares.," This index is based on two criteria: the level of background flux, and the morphology of the observed flares."
 Indeed. when a radio oscillation is fully shaped. im particular with a clear exponential tail we have good confidence that the vackeround subtraction is accurate.," Indeed, when a radio oscillation is fully shaped, in particular with a clear exponential tail, we have good confidence that the background subtraction is accurate."
 Ou the other haud. in the case when only the “tip” of the flare is visible. the vackerouud level caunot be precisely constrained. which is asource of higher uncertainty for the determination of flare properties.," On the other hand, in the case when only the “tip"" of the flare is visible, the background level cannot be precisely constrained, which is a source of higher uncertainty for the determination of flare properties."
 We attributed a confidence iudex of 1 to the most reliable data: observations with fully shaped flares. either isolated or ou top of a low background enisiou (= 15 mJy. Fig. 1)).," We attributed a confidence index of 1 to the most reliable data: observations with fully shaped flares, either isolated or on top of a low background emission $\la$ 15 mJy, Fig. \ref{exemples1}) )."
 Au iudex of 2 correspouds to observations where the expoucutial decrease is still clearly visible. witli inoderate background emission (<30 mJy. Fig. 2..," An index of 2 corresponds to observations where the exponential decrease is still clearly visible, with moderate background emission $\la$ 30 mJy, Fig. \ref{exemples2},"
 left)., left).
 Finally. observations with almost sinusoidal oscillations ou top of a strong backgrouud (up to 120 indy. Fig. 2..," Finally, observations with almost sinusoidal oscillations on top of a strong background (up to 120 mJy, Fig. \ref{exemples2},"
 rieht) correspoud to iudex 3., right) correspond to index 3.
 Thus. parameters deduced roni iudex 3 observations should be considered with care. While iudex 1 observations would produce reliable »uwanmeters.," Thus, parameters deduced from index 3 observations should be considered with care, while index 1 observations would produce reliable parameters."
 Among the observations listed iun. Table 1.. four observations had to be excluded. from our data set: on lhree observatious. two successive flares are visible but rot distiuguishable. while ou one more observation the radio data are too noisy to ect any constraint on the Hare.," Among the observations listed in Table \ref{logg}, four observations had to be excluded from our data set: on three observations, two successive flares are visible but not distinguishable, while on one more observation the radio data are too noisy to get any constraint on the flare."
 To measure the characteristics of the N-rayv dips. we used the following definition.," To measure the characteristics of the X-ray dips, we used the following definition."
 Time 0 is defined as the time when the phase of highly variable N-ray flux euds., Time 0 is defined as the time when the phase of highly variable X-ray flux ends.
 This time is also the first point of spectral hardening (visible in the ITR)., This time is also the first point of spectral hardening (visible in the HR).
 We used the position of the masini flux of the N-rav spike to mark the end of the dip. whose duration will be noted Af.," We used the position of the maximum flux of the X-ray spike to mark the end of the dip, whose duration will be noted $\Delta t$."
" At this time. the IIR has gone down to values close to the pre-dip ράσο,"," At this time, the HR has gone down to values close to the pre-dip phase."
Furthermore. it has recently been suggested that θά of the stellar mass at 2c5 is missed by traditional drop-out selection techniques (Stark et al.,"Furthermore, it has recently been suggested that $\simeq60\%$ of the stellar mass at $z\simeq5$ is missed by traditional drop-out selection techniques (Stark et al."
 2006). which exclude high-redshift galaxies which are too red in the rest-frame optical to satisfy LBG selection criteria (see discussion in Section 6).," 2006), which exclude high-redshift galaxies which are too red in the rest-frame optical to satisfy LBG selection criteria (see discussion in Section 6)."
 However. even if we increase our estimated number density of massive galaxies at 2o5 by a factor of two. and assume ax=0.75. XCDM can still produce the required number of dark matter halos if the stellar to dark matter ratio is 10.," However, even if we increase our estimated number density of massive galaxies at $z\simeq5$ by a factor of two, and assume $\sigma_{8}=0.75$, $\Lambda$ CDM can still produce the required number of dark matter halos if the stellar to dark matter ratio is $\simeq 10$."
 In Fig 6 we also show the estimated number densities of ogML galaxies at 2—3 derived from α ἐν band selectec sample of galaxies in the GOODS CDFS (Caputi et al., In Fig 6 we also show the estimated number densities of $\geq10^{11}\Msolar$ galaxies at $z\leq3$ derived from a $K-$ band selected sample of galaxies in the GOODS CDFS (Caputi et al.
 2006)., 2006).
 The Caputi et al., The Caputi et al.
 sample has a magnitude limit of ἐν<23.3. and is c85% complete for stellar masses >1075M. (Salpeter IMP) a redshifts 2.—3.," sample has a magnitude limit of $K\leq23.3$, and is $\geq85$ complete for stellar masses $\geq10^{11}\Msolar$ (Salpeter IMF) at redshifts $z\leq3$."
 As can be seen from Fig 6. the conclusions of Caputi et al.," As can be seen from Fig 6, the conclusions of Caputi et al."
 were that 204€ of the local mass density comprised by galaxies with stellar masses2104M. was already in place by z&2. and that —the majority was in place by z—1.," were that $\simeq20$ of the local mass density comprised by galaxies with stellar masses$\geq10^{11}\Msolar$ was already in place by $z\simeq2$, and that the majority was in place by $z\simeq1$."
 Similar conclusions have been reached by numerous studies of deep. smal area. near-infrared surveys (e.g. Drory et al.," Similar conclusions have been reached by numerous studies of deep, small area, near-infrared surveys (e.g. Drory et al."
 2005: Fontana 2004)., 2005; Fontana 2004).
 The results presented here strongly suggest that the increase in number density of massive galaxies within the redshift interva 2.5«25.5 closely traces the build-up of suitable dark matter halos and that. as a consequence. only ::14 of the local density of 2104}AL. galaxies was in place by zc5.," The results presented here strongly suggest that the increase in number density of massive galaxies within the redshift interval $2.5<z<5.5$ closely traces the build-up of suitable dark matter halos and that, as a consequence, only $\ltsim\,1\%$ of the local density of $\geq10^{11}\Msolar$ galaxies was in place by $z\simeq5$."
 It has recently become apparent that the number density of massive. red galaxies observed at high redshift is much larger than would have been predicted by semi-analytic galaxy formation models five years ago (e.g. Cimatti et al.," It has recently become apparent that the number density of massive, red galaxies observed at high redshift is much larger than would have been predicted by semi-analytic galaxy formation models five years ago (e.g. Cimatti et al."
 2002: Glazebrook et al., 2002; Glazebrook et al.
 2004)., 2004).
 In essence this is simply a result of the fact that galaxy formation models based on hierarchical assembly naturally produce the most massive galaxies at late times., In essence this is simply a result of the fact that galaxy formation models based on hierarchical assembly naturally produce the most massive galaxies at late times.
" This apparent discrepancy between the models and observations has been described variously as ""anti-hierarchical” behaviour. or cosmic downsizing."," This apparent discrepancy between the models and observations has been described variously as ``anti-hierarchical'' behaviour, or cosmic downsizing."
 It is clear therefore that important constraints can be placed on the latest generation of galaxy formation models via comparison with the observed number density of massive galaxies already in place at 25., It is clear therefore that important constraints can be placed on the latest generation of galaxy formation models via comparison with the observed number density of massive galaxies already in place at $z\geq5$.
 In Fig 7 we show the predicted number density of galaxies as a function of stellar mass at 2=5.3 (median. redshift of our LBG candidates) from the latest generation of Durham semi-analytic galaxy formation models. which incorporate AGN feedback (Bower et al.," In Fig 7 we show the predicted number density of galaxies as a function of stellar mass at $z=5.3$ (median redshift of our LBG candidates) from the latest generation of Durham semi-analytic galaxy formation models, which incorporate AGN feedback (Bower et al."
 2006)., 2006).
 Also shown in Fig 7 are the predictions (G.L. Granato. private communication) from the latest version of the Granato et al. (," Also shown in Fig 7 are the predictions (G.L. Granato, private communication) from the latest version of the Granato et al. ("
2004) galaxy formation model. which is based on an anti-hierarchieal baryon collapse scenario.,"2004) galaxy formation model, which is based on an anti-hierarchical baryon collapse scenario."
 The filled circle is our estimate for the number density of galaxies within a bin centred on 104XL.. based on the results of this study.," The filled circle is our estimate for the number density of galaxies within a bin centred on $10^{11}\Msolar$, based on the results of this study."
 When plotting the data-point in Fig 7. we have shifted the centre ofthe bin to lower mass by 0.15 dex. to account for the difference between the Salpeter IMF adopted in this paper. and the IMFs adopted in the Bower et al.," When plotting the data-point in Fig 7, we have shifted the centre of the bin to lower mass by 0.15 dex, to account for the difference between the Salpeter IMF adopted in this paper, and the IMFs adopted in the Bower et al."
 and Granato et al., and Granato et al.
 models (Kennicutt and Romano et al., models (Kennicutt and Romano et al.
 2002 respectively)., 2002 respectively).
 As can be seen from Fig 7. our estimated number density is clearly in good agreement with the predictions of the Bower et al.," As can be seen from Fig 7, our estimated number density is clearly in good agreement with the predictions of the Bower et al."
 and Granato et al., and Granato et al.
 models., models.
 Interestingly. given that our number density is almost certainly a lower limit. both model predictions can accommodate a number density which is a factor of &2—3 higher than our estimate. as required if LBGs constitute <50% of the total stellar mass at >25 (e.g. Stark et al.," Interestingly, given that our number density is almost certainly a lower limit, both model predictions can accommodate a number density which is a factor of $\simeq2-3$ higher than our estimate, as required if LBGs constitute $\leq50\%$ of the total stellar mass at $z\geq5$ (e.g. Stark et al."
 2006)., 2006).
 Finally. although not included in Fig 7. we also note that our estimated number density of 2°<25 LBGs at 2>5 is fully consistent with the hydro-dynamical simulations of Night et al. (," Finally, although not included in Fig 7, we also note that our estimated number density of $z^{\prime}\leq25$ LBGs at $z\geq5$ is fully consistent with the hydro-dynamical simulations of Night et al. ("
2006).,2006).
 In this study we have exploited the large co-moving volume covered by the SXDS/UDS data-set to identify a sample of bright (x 25) LBGs at 2>5., In this study we have exploited the large co-moving volume covered by the SXDS/UDS data-set to identify a sample of bright $z^{\prime}\leq25$ ) LBGs at $z\geq5$.
 In this section we compare our results with those of three recent studies based on the extensive multi-wavelength data available in the GOODS CDFS (Grazian et al., In this section we compare our results with those of three recent studies based on the extensive multi-wavelength data available in the GOODS CDFS (Grazian et al.
 2006: Stark et al., 2006; Stark et al.
 2006: Yan et al., 2006; Yan et al.
 2006)., 2006).
 The GOODS-MUSIC sample (Grazian et al., The GOODS-MUSIC sample (Grazian et al.
 2006) consists ofz bandand A/ band selected samples in the southern GOODS field. and provides a photometric redshift for each object calculated from SED fits to the extensive. high-quality. HST+VLT+Spitzer imaging available in the field.," 2006) consists of $z-$ band and $K-$ band selected samples in the southern GOODS field, and provides a photometric redshift for each object calculated from SED fits to the extensive, high-quality, HST+VLT+Spitzer imaging available in the field."
 The + band catalogue is 100A complete to zs).=25 and. although it only covers 142. square aremin. it is obviously of some interest to compare the number of 25 galaxies found in the MUSIC sample to the results presented here.," The $z-$ band catalogue is $100\%$ complete to $z_{850}=25$ and, although it only covers 142 square arcmin, it is obviously of some interest to compare the number of $z\geq5$ galaxies found in the MUSIC sample to the results presented here."
 Based on the results of this study. and correcting for the difference in area. the number of za5o25 LBG-type galaxies within the GOODS-MUSIC catalogue should be consistent with 0.732:0.30.," Based on the results of this study, and correcting for the difference in area, the number of $z_{850}\leq25$ LBG-type galaxies within the GOODS-MUSIC catalogue should be consistent with $0.73\pm0.30$."
" Interestingly. the GOODS-MUSIC catalogue contains seven objects with 2.5525 and a photometric redshift estimate of 25, seemingly very inconsistent with the results presented here."," Interestingly, the GOODS-MUSIC catalogue contains seven objects with $z_{850}\leq25$ and a photometric redshift estimate of $z\geq5$, seemingly very inconsistent with the results presented here."
 However. our own SED fits to the MUSIC photometry for these seven objects suggest that only two are believable high-redshift candidates.," However, our own SED fits to the MUSIC photometry for these seven objects suggest that only two are believable high-redshift candidates."
 Three of the seven objects (MUSIC IDs 1133. 8316 12966) have SEDs which are clearly stellar in nature. and have SExtractor stellarity parameters of 0.98. 0.99 and 0.99 respectively.," Three of the seven objects (MUSIC IDs 1133, 8316 12966) have SEDs which are clearly stellar in nature, and have SExtractor stellarity parameters of 0.98, 0.99 and 0.99 respectively."
" In addition. MUSIC ID27004 has a clear V— band detection which is inconsistent with the best-fitting photometric redshift of 2,,,,,= 6.91."," In addition, MUSIC ID=7004 has a clear $V-$ band detection which is inconsistent with the best-fitting photometric redshift of $z_{phot}=6.91$ ."
 Finally. MUSIC ID=10140 has a very unusual SED which would appear to be due to severe blending with bright nearby objects in the near-infrared and Spitzer bands.," Finally, MUSIC ID=10140 has a very unusual SED which would appear to be due to severe blending with bright nearby objects in the near-infrared and Spitzer bands."
 Of the original seven, Of the original seven
"characteristic of this region, in order to reproduce the triangular shape of the observed feature.","characteristic of this region, in order to reproduce the triangular shape of the observed feature."
 The two intense humps at both sides of the central maximum would come from the hollow shells., The two intense humps at both sides of the central maximum would come from the hollow shells.
" However, the high-velocity wings are severely underestimated by our standard model, and we would have to significantly increase the excitation conditions of the very fast bipolar outflow of 6618 to reproduce their intensity."," However, the high-velocity wings are severely underestimated by our standard model, and we would have to significantly increase the excitation conditions of the very fast bipolar outflow of 618 to reproduce their intensity."
" We can also see in 44 our predictions for a model similar to the previous one, but with Ty ~ 200 K in the regions that present expansion velocities  100Κπις-]."," We can also see in 4 our predictions for a model similar to the previous one, but with $T_{\rm k}$ $\sim$ 200 K in the regions that present expansion velocities $\sim$ 100."
". Other parameters of the fast outflow, particularly its velocity and density distributions do not change with respect to the original model."," Other parameters of the fast outflow, particularly its velocity and density distributions do not change with respect to the original model."
 The asymmetry between the red and blue line wings is not reproduced by our predictions also in this case., The asymmetry between the red and blue line wings is not reproduced by our predictions also in this case.
 It is remarkable that the high-velocity outflow obviously contributes to the emission at the profile central features., It is remarkable that the high-velocity outflow obviously contributes to the emission at the profile central features.
" Therefore, in this model the requirements to reproduce the secondary maxima are significantly weaker, and a temperature similar to or even lower than assumed in our original model for the empty shells would be compatible with the observations."," Therefore, in this model the requirements to reproduce the secondary maxima are significantly weaker, and a temperature similar to or even lower than assumed in our original model for the empty shells would be compatible with the observations."
" The general properties of the central, dense component mentioned before, in particular its low velocity, are required in this case too."," The general properties of the central, dense component mentioned before, in particular its low velocity, are required in this case too."
" The high velocity wings are also detected in emission from other molecules, such as H20, HCN, and CN 11), which must be significantly abundant in this recently shocked gas."," The high velocity wings are also detected in emission from other molecules, such as $_2$ O, HCN, and CN 1), which must be significantly abundant in this recently shocked gas."
 The relatively high temperatures deduced here for the fast bipolar flow relax the discrepancy usually found between the high excitation of the shocked gas predicted by theoretical models and the observational results (anintricatetheoretical 2009).," The relatively high temperatures deduced here for the fast bipolar flow relax the discrepancy usually found between the high excitation of the shocked gas predicted by theoretical models and the observational results \citep[an intricate theoretical problem not discussed in this
letter, see e.g.][]{lee09}."
" However, the discrepancy persists."," However, the discrepancy persists."
" Leeetal.(2009) predict temperatures of the high-velocity gas in 6618 over ~ 1000 K and too weak CO emission in all rotational lines, since shocks are expected to dissociate molecules."," \cite{lee09} predict temperatures of the high-velocity gas in 618 over $\sim$ 1000 K and too weak CO emission in all rotational lines, since shocks are expected to dissociate molecules."
" The low-excitation component of the nebula model by SC04, the extended halo, has apparently no counterpart in the observations, because the model predicts a very low intensity from such cool gas and the high-J line profiles do not seem to require any contribution from it."," The low-excitation component of the nebula model by SC04, the extended halo, has apparently no counterpart in the observations, because the model predicts a very low intensity from such cool gas and the $J$ line profiles do not seem to require any contribution from it."
 In 11 we also show our HIFI spectra of llines., In 1 we also show our HIFI spectra of lines.
" The oobservations are not very sensitive, so the line is not detected with a limit Timp 00.2 K. As we can see, the contrast between aand llines is high (mainly in the line wings, about a factor ten for the highest transitions)."," The observations are not very sensitive, so the line is not detected with a limit $T_{\rm mb}$ 0.2 K. As we can see, the contrast between and lines is high (mainly in the line wings, about a factor ten for the highest transitions)."
" This result is compatible with our calculations, which suggest moderate opacities in high-J llines from the main nebular components, in particular with 1(16-15) 11 for gas flowing at 1100s“!."," This result is compatible with our calculations, which suggest moderate opacities in $J$ lines from the main nebular components, in particular with $\tau$ $-$ 15) 1 for gas flowing at 100."
", Our results can therefore be summarized as follows 1.", Our results can therefore be summarized as follows 1.
 We detected high-J CO emission using Herschel/HIFI., We detected $J$ CO emission using Herschel/HIFI.
" The high-velocity line wings characteristic of this source become progressively dominant as the level energies increase, with sshowing a spectacular composite profile."," The high-velocity line wings characteristic of this source become progressively dominant as the level energies increase, with showing a spectacular composite profile."
 2., 2.
" The temperature of the very fast bipolar outflow in CRL6618 is high, significantly higher than the previously adopted values."," The temperature of the very fast bipolar outflow in 618 is high, significantly higher than the previously adopted values."
" SCO4 proposed a temperature for this component < 100 K, which, in view of the intense line wings seen in the ttransition, must be significantly increased."," SC04 proposed a temperature for this component $<$ 100 K, which, in view of the intense line wings seen in the transition, must be significantly increased."
" From our calculations, we estimate that gas flowing at about 100 mmust have a temperature ~ 200 K. We suggest that this very fast outflow, with a kinematic age < 100 yr, was accelerated by a shock and has not yet fully cooled down."," From our calculations, we estimate that gas flowing at about 100 must have a temperature $\sim$ 200 K. We suggest that this very fast outflow, with a kinematic age $<$ 100 yr, was accelerated by a shock and has not yet fully cooled down."
" The rest of the physical conditions are not significantly changed, therefore"," The rest of the physical conditions are not significantly changed, therefore"
the number of stars in the second bin. the 50 returned. “detections” should include 4-5 real planetary transits if 47 Tuc were like the Solar Neighbourhood.,"the number of stars in the second bin, the 50 returned “detections” should include 4-5 real planetary transits if 47 Tuc were like the Solar Neighbourhood."
 It is important to note that the proceedure used to weed out false positive detections could conceivably include clisreearcling real transits., It is important to note that the proceedure used to weed out false positive detections could conceivably include disregarding real transits.
 It was found by visual inspection of randomly selected model transits that the signature is clearly visible on the data and has an extremely high. detection significance compared to the svstematic false positives., It was found by visual inspection of randomly selected model transits that the signature is clearly visible on the data and has an extremely high detection significance compared to the systematic false positives.
 It is nol expected that the transit recoverability would be significantly inpinged by this visual inspection method., It is not expected that the transit recoverability would be significantly impinged by this visual inspection method.
 The majority of false detections were caused by erowcding and are immediately identified by plotüng the lighteurve. which displays systematic features occuring al the same times Lor most false detections.," The majority of false detections were caused by crowding and are immediately identified by plotting the lightcurve, which displays systematic features occuring at the same times for most false detections."
 The problem was less severe in (he uncrowcded outer regions of 47 Tuc. where the false detection rates were 1/3 the values presented above.," The problem was less severe in the uncrowded outer regions of 47 Tuc, where the false detection rates were 1/3 the values presented above."
 Fig.12. shows the period distribution of all lighteurves that pass the detection criteria and as such is the period distribution of the false cleteetions that were common in the dataset., \ref{fdhist} shows the period distribution of all lightcurves that pass the detection criteria and as such is the period distribution of the false detections that were common in the dataset.
 A few periods have a significant. excess of detections over (he general trend., A few periods have a significant excess of detections over the general trend.
 In particular {ρω= 1.5 days and Prod= 448 days show a large excess of “detections”., In particular $\it{P_{mod}}=$ 1.5 days and $\it{P_{mod}}=$ 4.48 days show a large excess of “detections”.
 As it is more difficult for svstematies to produce a strong detection when the number of in-(üransit data points is reduced. the nunbers of false detections decreases as period increases.," As it is more difficult for systematics to produce a strong detection when the number of in-transit data points is reduced, the numbers of false detections decreases as period increases."
 The code is quick and easy to apply., The code is quick and easy to apply.
 Application to our whole 47 Tue dataset was accomplished in 16 steps on four 3057MIILz 4096Mb RAAT. i86pe machines.," Application to our whole 47 Tuc dataset was accomplished in 16 steps on four 3057MHz 4096Mb RAM, i86pc machines."
 The code completed the task in 12 hours. and is easily modifiable to run on existing datasets.," The code completed the task in 12 hours, and is easily modifiable to run on existing datasets."
 We have presented and described a quick. efficient. and easy. to apply computational method for the detection of planetary transits in large photometric (me-series datasets.," We have presented and described a quick, efficient and easy to apply computational method for the detection of planetary transits in large photometric time-series datasets."
 Using a cross correlation Function (tlie code compares each sampled lishteurve wilh a database ol model transits of appropriate transit depth and duration., Using a cross correlation function the code compares each sampled lightcurve with a database of model transits of appropriate transit depth and duration.
 A detection is implied by a sienificantly high value of the correlation distribution., A detection is implied by a significantly high value of the correlation distribution.
 Monte Carlo simulations using the actual temporal sampling ancl photometric characteristics of the data superimposed. on appropriately modeled transits. show an excellent weighted mean recoverability rate over the whole of the sampled period range with a relatively low false detection probability.," Monte Carlo simulations using the actual temporal sampling and photometric characteristics of the data superimposed on appropriately modeled transits, show an excellent weighted mean recoverability rate over the whole of the sampled period range with a relatively low false detection probability."
 In parücular the code achieves à very good recoverability when searching lor transits at or just below (he photometric noise level of the data., In particular the code achieves a very good recoverability when searching for transits at or just below the photometric noise level of the data.
 The code is easily adaptable to run on existing datasets to search for the same photometric signals. and is capable of testing 10.000 stars in," The code is easily adaptable to run on existing datasets to search for the same photometric signals, and is capable of testing 10,000 stars in"
Bellaziuis surface brightuess estimates are expected to be slightly too faint in the outer parts 22119.,Bellazini's surface brightness estimates are expected to be slightly too faint in the outer parts 2419.
 The radial surface brightuess profiles of four exemplary moclels projected onto the sky aud converted to units⋅ of⋅ mag > are shown in⋅ Figure⊲⋅ ye13., The radial surface brightness profiles of four exemplary models projected onto the sky and converted to units of mag $^{-2}$ are shown in Figure \ref{surfbright}.
.The merger objects show a Ixing-like prolile out to radii of about, The merger objects show a King-like profile out to radii of about.
The observed profile from Bellazzini(2007) is acided to Figure 13 to allow for a direct comparison., The observed profile from \cite{bellazzini} is added to Figure \ref{surfbright} to allow for a direct comparison.
 The surface brightness profile of model 91060 agrees very well with the observed profile at all radii., The surface brightness profile of model 50 agrees very well with the observed profile at all radii.
 The other three models in Figre 13. illustrate how he profiles chauge when oue of the parameter mass. size and initial distribution of star clusters is inodified.," The other three models in Figure \ref{surfbright} illustrate how the profiles change when one of the parameter mass, size and initial distribution of star clusters is modified."
 Model M.11-11.5-5250 has a similar shape as 520.but is too bright at al adii due to the larger mass.," Model 50 has a similar shape as 50, but is too bright at all radii due to the larger mass."
" Model 1100. which is a more extencec| version of mocle 1.11.11.5.220. agrees well with the observations between 'and"".. but it is cousicerably wiehter in the center aud the outer parts."," Model 100, which is a more extended version of model 50, agrees well with the observations between and, but it is considerably brighter in the center and the outer parts."
 Model 1100. wh has a broader initia distribution of star clusters than mocel 1100. shows a smaller cdeviatic1 from the observec surface brightness profile than moclel 1100.," Model 100, which has a broader initial distribution of star clusters than model 100, shows a smaller deviation from the observed surface brightness profile than model 100."
 Baungardtetal.(2009) observed the radial velocities of {0 stars within a srojected radius of 100 pe of 22119 aud derived a velocity dispersion of o; = 1240. 15 kin ., \cite{baumgardt} observed the radial velocities of 40 stars within a projected radius of 100 pc of 2419 and derived a velocity dispersion of $\sigma$ = $\pm$ 0.48 km $^{-1}$.
 The liue-o[-sight velocity dispersious within a projected radius of 100 pe of the moclels are lised in Table 3.., The line-of-sight velocity dispersions within a projected radius of 100 pc of the models are listed in Table \ref{tbl-2}.
 A number of models with masses A5 = 1.0. 1.5. and 2.0 x 105 M.. have velociv dispersious that are within the one sigma error of the observed velocity cdispersio1.," A number of models with masses $M^{\rm CC}$ = 1.0, 1.5, and 2.0 $\times$ $^{6}$ $_{\odot}$ have velocity dispersions that are within the one sigma error of the observed velocity dispersion."
 Model 1.0.5250. which has au effective radius aud euclosed mass very close to tle newest observed values f'om aud a surface brightuess profile that is a good app'oximatiou of the observed profile. has a velocity dispersion of 6 = L13 kms |. Le. almost exactly the observed ole.," Model 50, which has an effective radius and enclosed mass very close to the newest observed values from \cite{baumgardt} and a surface brightness profile that is a good approximation of the observed profile, has a velocity dispersion of $\sigma$ = 4.13 km $^{-1}$, i.e. almost exactly the observed one."
 C'ouskleriug masses. effective radii. surface brightness profies. aud velocity dispersions. model NLILII.0.550 provides the best representation of 22119.," Considering masses, effective radii, surface brightness profiles, and velocity dispersions, model 50 provides the best representation of 2419."
 However. a uunber of models reproduce the observed structural parameters of 22119 cuite well with the observatioual uucertaiuties. demonstratiug that au object like NOC22119 can be formed from merged. CCs without the need of fine-tuning of the input. parameters.," However, a number of models reproduce the observed structural parameters of 2419 quite well within the observational uncertainties, demonstrating that an object like 2419 can be formed from merged CCs without the need of fine-tuning of the input parameters."
 The proposed formation scenario for. NCC22119 starts with newly. born complexes of star clusters in the Galactic halo with orbital parameters allowing for au highly eccentric orbit., The proposed formation scenario for 2419 starts with newly born complexes of star clusters in the Galactic halo with orbital parameters allowing for an highly eccentric orbit.
 We model the dynamical evolution of various CCs leading to merger objects., We model the dynamical evolution of various CCs leading to merger objects.
 We do not. however. consider the process which formed the CCs in the first place as this wouldiucrease the complexity ol the sunulatious and add more degrees of Ireecdoum makiug the interpretation of the results difficult.," We do not, however, consider the process which formed the CCs in the first place as this would increase the complexity of the simulations and add more degrees of freedom making the interpretation of the results difficult."
A starburst is an intense period of star formation within a galaxv that cannot be sustained over ils lifetime. due to the huge amount of gas needed to fuel the process.,"A starburst is an intense period of star formation within a galaxy that cannot be sustained over its lifetime, due to the huge amount of gas needed to fuel the process."
 Typical starburst lifetimes are 105 to LO” vears., Typical starburst lifetimes are $^8$ to $^9$ years.
 Starbursts can occur on (wo scales: centralized in the ealactic nucleus (a nuclear starburst) or throughout the entire galaxy (a global starburst)., Starbursts can occur on two scales: centralized in the galactic nucleus (a nuclear starburst) or throughout the entire galaxy (a global starburst).
 In order to (rigger a starburst. there must be a plentiful supply of eas to the centre of the galaxy. which occurs when a large-scale disturbance to the angular momentum of the central region causes the infall of enough material.," In order to trigger a starburst, there must be a plentiful supply of gas to the centre of the galaxy, which occurs when a large-scale disturbance to the angular momentum of the central region causes the infall of enough material."
 In a global starburst this disturbance is usually associated with the collision (and possible merger) of (wo galaxies., In a global starburst this disturbance is usually associated with the collision (and possible merger) of two galaxies.
 li a nuclear starburst (such as M32) the disturbance may be due to the effects of shock Ivonis causecl by a stellar bar. a tidal interaction wilh another galaxy. or perhaps an active galactic nucleus (AGN).," In a nuclear starburst (such as M82) the disturbance may be due to the effects of shock fronts caused by a stellar bar, a tidal interaction with another galaxy, or perhaps an active galactic nucleus (AGN)."
 The most luminous starbursts appear to all be triggered by interactions with other ealaxies., The most luminous starbursts appear to all be triggered by interactions with other galaxies.
 Smith. Herter and Haynes (1993) studied a sample of 20 radio-Iuminous starburst ealaxies.," Smith, Herter and Haynes (1998) studied a sample of 20 radio-luminous starburst galaxies."
 They found that all 20 galaxies were mergers. interacting pairs. or members of eroups or clusters. suggesting that all the starbursts in the sample were most likely triggered by interactions with other galaxies.," They found that all 20 galaxies were mergers, interacting pairs, or members of groups or clusters, suggesting that all the starbursts in the sample were most likely triggered by interactions with other galaxies."
 It has become clear that a “pan-spectval” approach to observations is necessary (o comprehensively study. starburst galaxies. combining observations taken over as large a wavelength range as possible. and supported by theoretical advances and modeling.," It has become clear that a “pan-spectral"" approach to observations is necessary to comprehensively study starburst galaxies, combining observations taken over as large a wavelength range as possible, and supported by theoretical advances and modeling."
 However. parüceularlv as the more compact and Iuminous nuclear starbursts are enshrouded in dust clouds which are optically thick at shorter wavelengths. long wavelength data are uniquely able to peer through the curtain of extinction and derive (he basic properties of the stellar population.," However, particularly as the more compact and luminous nuclear starbursts are enshrouded in dust clouds which are optically thick at shorter wavelengths, long wavelength data are uniquely able to peer through the curtain of extinction and derive the basic properties of the stellar population."
 In some cases. IR. data is sufficient. but. where even IR radiation is strongly absorbed. it is necessary to (turn to the mm and radio domains.," In some cases, IR data is sufficient, but where even IR radiation is strongly absorbed, it is necessary to turn to the mm and radio domains."
 The IR luminosity is a widely used diagnostic of starburst activity., The IR luminosity is a widely used diagnostic of starburst activity.
 This strong emission comes Irom cust eraius presumed {ο be heated by photons from voung stars Iormed in the, This strong emission comes from dust grains presumed to be heated by photons from young stars formed in the
0.3in 0.211 Figure 1.,0.3in 0.2in Figure 1.
 Iuteerated intensity maps of the six PO QSOs detected in CO(L>0)., Integrated intensity maps of the six PG QSOs detected in $1\to0$ ).
 a} PG. 0838|770 - coutours are plotted as lo«(.1.6.1.6.2.6.3.6.16.5.6.6.6).," a) PG 0838+770 - contours are plotted as $\sigma
\times (-1.6, 1.6, 2.6, 3.6, 4.6, 5.6, 6.6)$."
 The peal intensity is (017. Jy. beam1 and corresponds to the position RAH=Os:1115.22 dec|76:53:08.96. (72000.0)., The peak intensity is 0.017 Jy $^{-1}$ and corresponds to the position RA=08:44:45.22 dec=+76:53:08.96 (J2000.0).
 b) PG 11191120 - contours are plotted as lo«(2.3.2.3.3:3.1.3.5.3).," b) PG 1119+120 - contours are plotted as $\sigma \times
(-2.3, 2.3, 3.3, 4.3, 5.3)$."
 The peak intensity is 0.011 Iv beau1. and corresponds to the position RA-11:21:17.12 dec=|11:LET8.30. (12000.0).," The peak intensity is 0.014 Jy $^{-1}$, and corresponds to the position RA=11:21:47.12 dec=+11:44:18.30 (J2000.0)."
 c) PG 13511610 - contours are plotted as lo<(1.6.1.6.2.6.3.6.1.6): the peak intensity is 0.0055 Jy beamLand corresponds to the position RA=13:53:15.62 dec=|63:15:15.72 (J2000.0).," c) PG 1351+640 - contours are plotted as $\sigma \times
(-1.6, 1.6, 2.6, 3.6, 4.6)$; the peak intensity is 0.0055 Jy $^{-1}$, and corresponds to the position RA=13:53:15.62 dec=+63:45:45.72 (J2000.0)."
 d) PC 11151151 - coutours are plotted as lo.(2.2.2.2.5.2.1.2.5.2): the peal intebsity is 0.051 Jv 5. and corresponds to the position RA=LL17:00.76 dec-|LLESG6.50 (J2000.03.," d) PG 1415+451 - contours are plotted as $\sigma \times
(-2.2, 2.2, 3.2, 4.2, 5.2)$; the peak intensity is 0.051 Jy $^{-1}$, and corresponds to the position RA=14:17:00.76 dec=+44:56:06.50 (J2000.0)."
 0) PG 111012356the - contours are plotted as lao«(.2.3.2.3.ολοι1.3.5.3.6.3): the peak tensity is (016 Jy J|. and corresponds to position RA=11:12:07.18 dec=|35:26:22.33 (J2000.0).," e) PG 1440+356 - contours are plotted as $\sigma \times
(-2.3, 2.3, 3.3, 4.3, 5.3, 6.3)$; the peak intensity is 0.016 Jy $^{-1}$, and corresponds to the position RA=14:42:07.48 dec=+35:26:22.33 (J2000.0)."
" Ὁ PC 16131658 - contours are plotted as lo«(/—1.6.2.66.6.7.6.8.6): the peak intensity is 0.012 Jy 1 aud corresponds to the position RA=16:13:57.15 dec=|65:13:09.623.0,1.0. ooeed(J2000.0)."," f) PG 1613+658 - contours are plotted as $\sigma \times
(-1.6, 1.6, 2.6, 3.6, 4.6, 5.6, 6.6, 7.6, 8.6)$; the peak intensity is 0.012 Jy $^{-1}$, and corresponds to the position RA=16:13:57.15 dec=+65:43:09.62 (J2000.0)."
 Olin Figure 2., 0.1in Figure 2.
 COGL> 0) spectra of the SiN de PG QSOs., $1\to0$ ) spectra of the six detected PG QSOs.
 For PG 0838|770 aud PC 11151151. the data have been smoothed to a resolution of 16 MITIz with a 8 MIIz sampling.," For PG 0838+770 and PG 1415+451, the data have been smoothed to a resolution of 16 MHz with a 8 MHz sampling."
 For PC 11191120. the data have been siioothed. to a resolution of 32 MIIz with a 16 MITz sampling.," For PG 1119+120, the data have been smoothed to a resolution of 32 MHz with a 16 MHz sampling."
 For PG 123511610. the data have been smoothed to a resolutiou of LO AIIIz with a 20 MITz sampling.," For PG 1351+640, the data have been smoothed to a resolution of 40 MHz with a 20 MHz sampling."
 For PC 111012356 aud PG 1613|658. the data have been smoothed to a resolution of 21 Mz with a 12 MIIz sampling.," For PG 1440+356 and PG 1613+658, the data have been smoothed to a resolution of 24 MHz with a 12 MHz sampling."
 O.lin Figure 3., 0.1in Figure 3.
 A plot of the CO fiux vs. the 100 pan flux density for PG OSOs aud ULICs detected to date in CO., A plot of the CO flux vs. the 100 $\mu$ m flux density for PG QSOs and ULIGs detected to date in CO.
 The CO data for IZwl iud Mrk 1014 were obtained from Barvainis et al. (, The CO data for IZw1 and Mrk 1014 were obtained from Barvainis et al. (
1989) and Solomon et al. (,1989) and Solomon et al. (
1997). respectively.,"1997), respectively."
 The ULICs CO data were obtained from Sanders et al. (, The ULIGs CO data were obtained from Sanders et al. (
1989b). Sanders. Scoville. Soifer (1988. 1991). Solomon et al. (,"1989b), Sanders, Scoville, Soifer (1988, 1991), Solomon et al. ("
1997). and Evans et al. (,"1997), and Evans et al. ("
1999).,1999).
 The 100722 flux deusities were obtained frou Saucers et al. (, The $\mu$ m flux densities were obtained from Sanders et al. (
19592. 1991) and Solomon et al. (,"1989a, 1991) and Solomon et al. ("
1997).,1997).
 Arrows denote 36 upper limits on the CO luminosity of PC 1126-011. PG 1202|281. and PC 1102|261.," Arrows denote $\sigma$ upper limits on the CO luminosity of PG 1126-041, PG 1202+281, and PG 1402+261."
 Ouly upper limits on Zt4 aud figo curently exist for PC 0007|106. aud thus PC 0007|106 is not included on the plot.," Only upper limits on $L'_{\rm CO}$ and $f_{100}$ currently exist for PG 0007+106, and thus PG 0007+106 is not included on the plot."
 Adapted from Figure. lof Solomon et al. (, Adapted from Figure 4 of Solomon et al. (
1997).,1997).
 O.lin Figure L., 0.1in Figure 4.
 Α plot of logLog versus redshift (2) for the low-: PG QSO sample. a fiux-linited sample (1ου>5.21 Jv) of iufrared huninous galaxies aud a sample of ultrahuninous infrared galaxies.," A plot of $\log L'_{\rm CO}$ versus redshift $z$ ) for the $z$ PG QSO sample, a flux-limited sample $f_{60} > 5.24$ Jy) of infrared luminous galaxies and a sample of ultraluminous infrared galaxies."
 The vertical dashed lines represeut the upper and lower 2 boundaries of the PO QSO sample., The vertical dashed lines represent the upper and lower $z$ boundaries of the PG QSO sample.
 The LIC and ULICs data have been obtained from the same sources as in Fieure 3., The LIG and ULIGs data have been obtained from the same sources as in Figure 3.
 Arrows denote 36 upper lanits on the CO Lhnunuinositv of PC 1126-011. PC 1202|281. and PC 1102|261.," Arrows denote $\sigma$ upper limits on the CO luminosity of PG 1126-041, PG 1202+281, and PG 1402+261."
 Q.lin Figure 5., 0.1in Figure 5.
 à) A plot of Zi vs. Lt; for the low-z: QSO sample. a fux-Iimited sample 275.21 Jy) of infrared huninous galaxies and a sample of ultralumiuous infrared galaxies.," a) A plot of $L_{\rm IR}$ vs. $L'_{\rm CO}$ for the $z$ QSO sample, a flux-limited sample $f_{60 \mu{\rm m}} > 5.24$ Jy) of infrared luminous galaxies and a sample of ultraluminous infrared galaxies."
 Arrows denote 30 upper (foolimits on the CO huninosity of PG 1126-011. PC 1202|281. and PG ΙΟΣ|261.," Arrows denote $\sigma$ upper limits on the CO luminosity of PG 1126-041, PG 1202+281, and PG 1402+261."
 b) A plot of Lin/Log vs. Eqs for the low-z QSO sample. a flux-limited saluple (fion>5.21 Jy) of infrared Iuninous galaxies and a sample of ültraluuiuous infrared. galaxies.," b) A plot of $L_{\rm IR}/L'_{\rm CO}$ vs. $L_{\rm IR}$ for the $z$ QSO sample, a flux-limited sample $f_{60
\mu{\rm m}} > 5.24$ Jy) of infrared luminous galaxies and a sample of ultraluminous infrared galaxies."
 Arrowsdenote Jo lower limits on Lig[ο of PG 1126-011. PG 1202|281. and PG 1102|261.," Arrowsdenote $\sigma$ lower limits on $L_{\rm IR}/L'_{\rm CO}$ of PG 1126-041, PG 1202+281, and PG 1402+261."
 For simplicity. all of the cool infrared huninous galaxies are plotted as plus sigue.," For simplicity, all of the cool infrared luminous galaxies are plotted as plus signs."
 0.1iu Figure 6., 0.1in Figure 6.
" A plot of logLey, versus redshift (+) for the low-. PG QSO sample and the high-redshift QSOs tected iu CO to date.", A plot of $\log L'_{\rm CO}$ versus redshift $z$ ) for the $z$ PG QSO sample and the high-redshift QSOs detected in CO to date.
 The moderate and οντοdshift QSO data havebeen obtained from the following references: 3€ 18dct (2=0.37: Scoville et al., The moderate and high-redshift QSO data have been obtained from the following references: 3C 48 $z = 0.37$: Scoville et al.
 1993). T1113|117 (2=¢2.56:n Barvainis1900). et al.," 1993), H1413+117 $z =
2.56$: Barvainis et al."
 199D. ATC OLLEE)O531 (2=2.61: Barvainis et al.," 1994), MG 0414+0534 $z=2.64$: Barvainis et al."
 1998). APM 08279|5255 (1=3.91: Downes sot ," 1998), APM 08279+5255 $z=3.91$: Downes et al."
BRI 1335-0115 --Ll: Cuilloteau et al.," 1999), BRI 1335-0415 $z=4.41$: Guilloteau et al."
 1997). and BR 1202-0725 (2=L69: Omonut et al.," 1997), and BR 1202-0725 $z=4.69$: Omont et al."
 1996)., 1996).
 For gravitationally lensed QSOs. Li is plotted in terms of both the observed. value aud the iutrinsic value.," For gravitationally lensed QSOs, $L'_{\rm CO}$ is plotted in terms of both the observed value and the intrinsic value."
 For MG 0141110531. the amplification is unknown. thus MG O04L4LL110531 is plotted with a solid line extending downward from the observed Lig.," For MG 0414+0534, the amplification is unknown, thus MG 0414+0534 is plotted with a solid line extending downward from the observed $L'_{\rm CO}$ ."
 Adapted from Figure 3 of Fraver ct al. (, Adapted from Figure 3 of Frayer et al. (
1999).,1999).
where If the Iuminositv function defined in Eq.(12)) has slope a=—1 the total flux [rom resolved and unresolved PWNe divided over the HESS field of view if 2.5 per cent of radio loud pulsars enit 5-ravs is The total [lux from the Galactic SNR. population is For a=-1 the integral flux expected lor the Milagro field of view [rom IIESS-like sources assuming a pulsar shaped surface densitv if 2.5 per cent of radio loud pulsars emit -FAVs Is while the contribution Lom SNRs shaped surface density is The fluxes in Eq. (19)),where If the luminosity function defined in \ref{eqn:luminosity}) ) has slope $\alpha=-1$ the total flux from resolved and unresolved PWNe divided over the HESS field of view if 2.5 per cent of radio loud pulsars emit $\gamma$ -rays is The total flux from the Galactic SNR population is For $\alpha=-1$ the integral flux expected for the Milagro field of view from HESS-like sources assuming a pulsar shaped surface density if 2.5 per cent of radio loud pulsars emit $\gamma$ -rays is while the contribution from SNRs shaped surface density is The fluxes in Eq. \ref{eqn:terzabis}) )
 and (20)) are lower than the HESS fluxes from resolved aud unresolved sources., and \ref{eqn:quarta}) ) are lower than the HESS fluxes from resolved and unresolved sources.
 In fact. as shown in Fig.3.. ESS observes the inner region of the Galaxy. whereas Milagro field of view is more spread toward (he outer regions in (he Galaxy. where the number of sources is substantially lower. so a lower contribution from uiresolved sources is expected for Milagros region of the Galactic plane than for HESS.," In fact, as shown in \ref{fig3}, HESS observes the inner region of the Galaxy, whereas Milagro field of view is more spread toward the outer regions in the Galaxy, where the number of sources is substantially lower, so a lower contribution from unresolved sources is expected for Milagro's region of the Galactic plane than for HESS."
cylindrical radius alouc. D.=(5). but the axial iaenetic field D. is constant iu our model.,"cylindrical radius alone, $B_{\varphi}= B_{\varphi}(s)$, but the axial magnetic field $B_z$ is constant in our model."
 We study the behaviour of ΑΠΟ modes in the incompressible linut., We study the behaviour of MHD modes in the incompressible limit.
 This approximation is well justified for modes with the characeristic time-scale longer than the ooriod. of sound. waves àuid for subsonic notions (see. e.g.àY Landau Lifshitz 198]j.," This approximation is well justified for modes with the characteristic time-scale longer than the period of sound waves and for subsonic motions (see, e.g., Landau Lifshitz 1981)."
 Poerturbalous of the deusityv caused by these motions are ια. aud. cau be uceleced in MIID equatiois., Perturbations of the density caused by these motions are small and can be neglected in MHD equations.
 By making use of the incompressile lut iua magnIDsed eas; one can cosider slow modes with the erowth rate (or frequency) lower than the frequeney| of fast maeuetosoniecS waves.," By making use of the incompressible limit in a magnetised gas, one can consider slow modes with the growth rate (or frequency) lower than the frequency of fast magnetosonic waves."
 Since the typical time scale of nodes uuder study is of the order of the inverse Alfvénn frequency. our consideration applies if the Alfvéuu velocity is lower than the sound speed or. in terms of the plasma. ;-parameter. if.m1 )j is the ratio of the eas and maguctic pressures).," Since the typical time scale of modes under study is of the order of the inverse Alfvénn frequency, our consideration applies if the Alfvénn velocity is lower than the sound speed or, in terms of the plasma $\beta$ -parameter, if $\beta \gg 1$ $\beta$ is the ratio of the gas and magnetic pressures)."
 Note that the velocity of jet V can be much higher than the Alfvéóunu aud sound speed., Note that the velocity of jet $V$ can be much higher than the Alfvénn and sound speed.
 Iu the incompressible lait. the MIID equations read Iun the basic state. the eas is assumed to be iu hydrostatic equilibrium in the racial direction. theu Stability will VD-qANOBbe studied. by maine use of a linear perturbative analysis.," In the incompressible limit, the MHD equations read In the basic state, the gas is assumed to be in hydrostatic equilibrium in the radial direction, then Stability will be studied by making use of a linear perturbative analysis."
 Because the basic state is stationary and axisvunnetric. the dependence of perturbations on f. y. and + can be taken in the form exp(otthotung) where fk. is the wavevector in the axial direction aud m is the azimuthal wavemuuber.," Because the basic state is stationary and axisymmetric, the dependence of perturbations on $t$, $\varphi$ , and $z$ can be taken in the form $\exp{(\sigma t - i k_z z - i m \varphi)}$ where $k_z$ is the wavevector in the axial direction and $m$ is the azimuthal wavenumber."
 Small perturbations will be indicated by subscript 1. while unperturbed quautitics will have no subscript.," Small perturbations will be indicated by subscript 1, while unperturbed quantities will have no subscript."
 Then. the liearized Eqs. (," Then, the linearized Eqs. ("
1)-(1) read Eliminating all variables in favour of the radial velocity perturbation ¢y.. we obtain This eqation was first derived by Bonanno Urpin (20081) in treir analysis of the non-axisvuuuaetrie stability of stellar uaenetic configurations.,"1)-(4) read Eliminating all variables in favour of the radial velocity perturbation $v_{1s}$, we obtain where This equation was first derived by Bonanno Urpin (2008b) in their analysis of the non-axisymmetric stability of stellar magnetic configurations."
 For axisvuuuetric )orturbatiois (Q0=0). Eq. (," For axisymmetric perturbations $m=0$ ), Eq. ("
10) recovers Eq. (,10) recovers Eq. (
11) of the per by Bonanno Urpin (2008a).,11) of the paper by Bonanno Urpin (2008a).
 Tustahiliics of the magnetic configurations associated o the electric current are basically absolue Iustabilities. i.c. they erow but do not propagate.," Instabilities of the magnetic configurations associated to the electric current are basically absolute instabilities, i.e. they grow but do not propagate."
 We suppose tiat this is the case also in the rest frame of the jet. aud iustable )orturbations are therefore simply advectcc| with the flow att he jet velocity.," We suppose that this is the case also in the rest frame of the jet, and unstable perturbations are therefore simply advected with the flow at the jet velocity."
 Equation (10) represeuts a lol-ear eleeuvalue problem for c. which cau be xved oX‘© the )nmdary conuditious are given.," Equation (10) represents a non-linear eigenvalue problem for $\sigma$, which can be solved once the boundary conditions are given."
 We asse hat (44 s1o0uld o finite at the t ands., We assume that $v_{1s}$ should be finite at the jet axis.
" As far as the outer bouudarv ds concerned, it i newhat difficult to formuate ap ausible )onndary co1 because :vetuallv there is no bouidirv )otween the j id the ailvent medium."," As far as the outer boundary is concerned, it is somewhat difficult to formulate a plausible boundary condition because actually there is no boundary between the jet and the ambient medium."
 Likely. t1ο jet is separated he zuubieif plasma by he shear laver lia has a fi uckness.," Likely, the jet is separated from the ambient plasma by the shear layer that has a finite thickness."
 The effect of this thickness ou he growth rate «justabilities las been studied by BaY (2005) who fornd hat the results are only slightly affect«xl wea change of ιο thickness., The effect of this thickness on the growth rate of instabilities has been studied by Baty (2005) who found that the results are only slightly affected by a change of the thickness.
 For the sake of simplicitY. herefore. we assume that the shear laver is iufiuiteY hin (see aso Appl et al.," For the sake of simplicity, therefore, we assume that the shear layer is infinitely thin (see also Appl et al."
 200D., 2000).
 In asi perimagnuetoson jet. uo signal can propagate from the jet interior fo 1 sumroundings. aid we can expect that the iustabilitic )oliave as 1 the jet is bounded by a rig colleποπιο wa," In a supermagnetosonic jet, no signal can propagate from the jet interior to its surroundings, and we can expect that the instabilities behave as if the jet is bounded by a rigid conducting wall."
" ""Therefore. we ca απλής the outer boundary by supposing CLs=0) at the jet radius s=,."," Therefore, we can mimic the outer boundary by supposing $v_{1s}=0$ at the jet radius $s=s_1$."
 Note tthat we also ried other outer boundary conditions (or example. with ty. £0). but this docs not change the results qualitatively.," Note that we also tried other outer boundary conditions (for example, with $v_{1s} 
\neq 0$ ), but this does not change the results qualitatively."
 We can represent the azimuthal maeuetic field as where By is the characteristic field streugth aud c l., We can represent the azimuthal magnetic field as where $B_{\varphi 0}$ is the characteristic field strength and $\psi \sim 1$ .
 To calculate the erowth rate of the instability. it is convenieut to introduce dimensionless (quantities Then. Eq. (," To calculate the growth rate of the instability, it is convenient to introduce dimensionless quantities Then, Eq. ("
10) reads where We thus solve Eq. (,10) reads where We thus solve Eq. (
13)for a wide rauge of the pariuneters and different functional dependence eC).,13)for a wide range of the parameters and different functional dependence $\psi(x)$ .
racius of 0.2554. however. the and smooth matter clistributions are virtually identical. and for larger radii the smooth matter distribution is found to be narrower than the smooth matter cistribution.,"radius of $0.25\eta_0$, however, the and smooth matter distributions are virtually identical, and for larger radii the smooth matter distribution is found to be narrower than the smooth matter distribution."
 We next compare the observed. elefel Dux ratio for Ale: 041410534. with our model probability distributions and construct an a posteriori. probability distribution for characteristic source radius and smooth matter percentage., We next compare the observed $A_2/A_1$ flux ratio for MG 0414+0534 with our model probability distributions and construct an a posteriori probability distribution for characteristic source radius and smooth matter percentage.
 Following WMS95 and SWO2 we conduct. our analysis using an observed Dux ratio of Ron.=(Aofle.O45d0.06 (Schechter&Moore1993)., Following WMS95 and SW02 we conduct our analysis using an observed flux ratio of $R_{obs} = (A_2/A_1)_{obs} = 0.45 \pm 0.06$ \citep{sm93}.
 ὃν comparing this observed Hux ratio with conditional probability distributions for the Hux ratio. we constructed likelihoods for the observed. ratio elven varius source raclii j. in units of the Einstein Racius gj. and smooth matter percentages s=K/h.," By comparing this observed flux ratio with conditional probability distributions for the flux ratio, we constructed likelihoods for the observed ratio given varius source radii $\eta$, in units of the Einstein Radius $\eta_0$, and smooth matter percentages $s = \kappa_c/\kappa_{tot}$."
" Using Baves’ theorem. this likelihood LI,5.1) was converted to an a posteriori differential probability distribution for smooth matter percentage and source radius as a fuction of e."," Using Bayes' theorem, this likelihood $L(R_{obs}|s, \eta)$ was converted to an a posteriori differential probability distribution for smooth matter percentage and source radius as a fuction of $R_{obs}$."
 These distributions are then mareinalised over the observed distribution for Dux ratio. where the error. in the [lux ratio was treated as a Gaussian with characteristic radius equal to. the observational error of £0.06.," These distributions are then marginalised over the observed distribution for flux ratio, where the error in the flux ratio was treated as a Gaussian with characteristic radius equal to the observational error of $\pm 0.06$."
 We used a logarithmic Bayesian prior lor source radius. and a constant Bavesian prior for smooth matter percentage. Source size is à quantity with units (in this case. units of Einstein Iacius). and is therefore assumed to have à prior probability that is constant per unit logarithm.," We used a logarithmic Bayesian prior for source radius, and a constant Bayesian prior for smooth matter percentage, Source size is a quantity with units (in this case, units of Einstein Radius), and is therefore assumed to have a prior probability that is constant per unit logarithm."
 The choice of a prior that is Dat in the logarithm ensures that the ratio of prior probability for two values of source size does. not depend on the units chosen., The choice of a prior that is flat in the logarithm ensures that the ratio of prior probability for two values of source size does not depend on the units chosen.
 On the other hand. the value of the smooth matter fraction is a climensionless quantity and is therefore assumed to have a uniformi prior.," On the other hand, the value of the smooth matter fraction is a dimensionless quantity and is therefore assumed to have a uniform prior."
 Probability contours were then drawn. through the resulting distribution and are plotted in Fig. 5.., Probability contours were then drawn through the resulting distribution and are plotted in Fig. \ref{contour}.
 This shows hat our simulations do not constrain the smooth matter content of the lens., This shows that our simulations do not constrain the smooth matter content of the lens.
 On the other hand an upper limit on he size of the I-band emission region exists for all smooth matter percentages., On the other hand an upper limit on the size of the I-band emission region exists for all smooth matter percentages.
 We can therefore. place a limit on the size of the I- emission region in the quasar., We can therefore place a limit on the size of the I-band emission region in the quasar.
 To do so. we marginalise he dillerential probability distribution over smooth matter oercentage: We then find the probability that the source is smaller than a particular radius. given the observed [ux ratio: Fig.," To do so, we marginalise the differential probability distribution over smooth matter percentage: We then find the probability that the source is smaller than a particular radius, given the observed flux ratio: Fig."
 6 shows the results of this analysis for an observed lux ratio of (cloflu.=0.45+0.06. (solid. lino)., \ref{probeta} shows the results of this analysis for an observed flux ratio of $(A_2/A_1)_{obs} = 0.45\pm0.06$ (solid line).
 We find that the radius of the IL-band emission. region in ALC 041410534. is smaller than 0.7055. with a statistical confidence ofO5%., We find that the radius of the I-band emission region in MG 0414+0534 is smaller than $0.70\eta_0$ with a statistical confidence of.
. In. physical units. this limit is 2.621025.“(AlAL.) em.," In physical units, this limit is $2.62 \times 10^{16} h^{-1/2}_{70} (M/M_{\odot})^{1/2} cm$ ."
 Our limit on the IE-band emission region is smaller than the limit found. in WMS95., Our limit on the I-band emission region is smaller than the limit found in WMS95.
 The improvement is due to the inclusion of a variable smooth matter component in our lens., The improvement is due to the inclusion of a variable smooth matter component in our lens.
 ‘To test the sensitivity of our results to the assumed prior probability on source radius we have re-caleulated the source radius constraints assuming a Dat. rather than a logarithmic. prior.," To test the sensitivity of our results to the assumed prior probability on source radius we have re-calculated the source radius constraints assuming a flat, rather than a logarithmic, prior."
 These results are presented in Fig., These results are presented in Fig.
 6 (dashed line)., \ref{probeta} (dashed line).
 We find that the constraints are less stringent where the Jat prior is used. with the cata constraining the source radius to be smaller than about 1.375.," We find that the constraints are less stringent where the flat prior is used, with the data constraining the source radius to be smaller than about $1.3\eta_0$."
 Thus. while the data do constrain the upper limit on source radius. the precise Constraints are sensitive to the prior chosen. indicating that the range of source radii that are consistent with the data remains considerable.," Thus, while the data do constrain the upper limit on source radius, the precise constraints are sensitive to the prior chosen, indicating that the range of source radii that are consistent with the data remains considerable."
obtained from a sample of primordial binaries.,obtained from a sample of primordial binaries.
" Each binary is defined by at least five initial parameters: primary mass My, mass- q, orbital separation a, eccentricity e and metallicity Z."," Each binary is defined by at least five initial parameters: primary mass $M_{\rm p}$ , mass-ratio $q$, orbital separation $a$, eccentricity $e$ and metallicity $Z$."
" Primary masses M, are distributed assuming a power law (?) for the initial mass function (IMF).", Primary masses $M_{\rm p}$ are distributed assuming a power law \citep{Kroupa93} for the initial mass function (IMF).
 This is constrained by the observation of the local luminosity function and stellar density of ? and ?.., This is constrained by the observation of the local luminosity function and stellar density of \citet{Wielen83} and \citet{Popper80}. .
" A flat distribution is adopted for mass-ratio (0«q 1) and eccentricity (0«e 1), since these are not well constrained by observation."," A flat distribution is adopted for mass-ratio $0<q<1$ ) and eccentricity $0<e<1$ ), since these are not well constrained by observation."
 The distribution of orbital separation a is assumed to be constant in logarithm for wide binaries and falls off smoothly at close separations (?).., The distribution of orbital separation $a$ is assumed to be constant in logarithm for wide binaries and falls off smoothly at close separations \citep{Han98}.
 We have assumed Z—0.02 throughout., We have assumed $Z=0.02$ throughout.
 All other input parameters are as given by ?.., All other input parameters are as given by \citet{Yu10}. .
" The present population synthesis simulation started with a sample of 10’ primordial MS+MS binaries, with total mass ~1.05x10"" Mo, yielding a sample total of 4.93x10* DDs over all orbital periods of less than 100 yr during a sampling period of 15 Gyr."," The present population synthesis simulation started with a sample of $10^{7}$ primordial $+$ MS binaries, with total mass $\approx1.05\times10^{7}~\rm M_{\odot}$ , yielding a sample total of $4.93\times10^{4}$ DDs over all orbital periods of less than 100 yr during a sampling period of 15 Gyr."
" In order to evaluate the computation of our DD sample, shows(le reffig,rogenitor ft)theorbitalperiods(logPorb/day) of each new-born DD against primary mass (My) in the progenitors and (right) the time tis from binary-star formation to the birth of its descendant DD."," In order to evaluate the computation of our DD sample, \\ref{fig_progenitor} shows (left) the orbital periods (log $P_{\rm orb}$ /day) of each new-born DD against primary mass $M_{\rm p}$ ) in the progenitors and (right) the time $t_{\rm MS}$ from binary-star formation to the birth of its descendant DD."
 We define DDs in this sample as unevolved DDs., We define DDs in this sample as unevolved DDs.
 This figure shows the relation of new-born DDs and their progenitors., This figure shows the relation of new-born DDs and their progenitors.
" In this section, we investigate how the present number of DDs and the number of new-born DDs depends on the star formation history of the thin disc by examining the contribution functions."," In this section, we investigate how the present number of DDs and the number of new-born DDs depends on the star formation history of the thin disc by examining the contribution functions."
 We take the current age of the thin disc to be 10 Gyr., We take the current age of the thin disc to be 10 Gyr.
 Star formation time tsp runs from 0 to 10 Gyr., Star formation time $t_{\rm sf}$ runs from 0 to 10 Gyr.
 reffig.ddotand3illustratethevariationof (ratecontributionstotheprdsanbG yond§sulisihthebitthratisosioiN elapentnumber , \\ref{fig_cddot} and \ref{fig_cdot} illustrate the variation of $\ddot{C}$ (rate contributions to the present birth and merger rates) and $\dot{C}$ (number contributions to the present numbers and total merged numbers) with $t_{\rm sf}$.
"Equivalently, the figures show us the age distribution of present new born, alive and merged DDs."," Equivalently, the figures show us the age distribution of present new born, alive and merged DDs."
" Since the age of a DD is defined as Laisc—tst refsec,s)), theagedistributionisobtainedbytrans formingthex— scaletotaisc—tst."," Since the age of a DD is defined as $t_{\rm disc}-t_{\rm sf}$ \\ref{sec_ps}) ), the age distribution is obtained by transforming the x-scale to $t_{\rm disc}-t_{\rm sf}$."
 The top panels in reffig.ddotindicatesthatthepresentnew|—bornHe HeandCO--H eDDscomemainlyf romearlystar formationtse Gyr., The top panels in \\ref{fig_cddot} indicates that the present new-born and CO+He DDs come mainlyfrom early star formation $t_{\rm sf} < 8 $ Gyr.
 This is not the case for CO+CO and ONeMg+X DDs., This is not the case for CO+CO and ONeMg+X DDs.
 The top panels in reffig.ddotalsoshowthatthepresentnewbornCO+ COandONeMg Xcomealmostentirely f romrecentstar formation; 8itse<10 Gyr., The top panels in \\ref{fig_cddot} also show that the present new-born CO+CO and ONeMg+X come almost entirely from recent star formation; $8 < t_{\rm sf} < 10$ Gyr.
 This remarkable discrepancy is basically a result of tus., This remarkable discrepancy is basically a result of $t_{\rm MS}$.
" reffig, (rightpanel)illustratesthatamassiveMS rogenitor SbinarygenerallytakeslessthanafewMyrand1GyrtoformONeMg+ XandCO+CODDsrespectively, leadingtotheir formationmuchmorequickl hadgc? "," \\ref{fig_progenitor} (right panel) illustrates that a massive MS+MS binary generally takes less than a few Myr and 1 Gyr to form ONeMg+X and CO+CO DDs respectively, leading to their formation much more quickly than He+He and CO+He DDs."
Oath XandCO--COincreasingdramaticallyatanearlystageohiked f discevolution., This also results in the birth rates of ONeMg+X and CO+CO increasing dramatically at an early stage of disc evolution.
Only. s HeandHe4- HeD Dsemergeanddotheirbirthratesgrowtoreachthepresentval figuirnum.., Only after some time do CO+He and He+He DDsemerge and do their birth ratesgrow to reach the present values shown in the left panel of \\ref{fig_birnum}. .
"Duetothequasi exponentialSF thebirthratesofONeMg+ XandCO COD rate, Dsstarttodeclineafterreachingapeakvalue."," Due to the quasi-exponential SF rate, the birth rates of ONeMg+X and CO+CO DDs start to decline after reaching a peak value."
Thelongtms for single He whitedwarfs also results in a small contribution of star formation from 0—7.5 Gyr to the number of new-born, The long $t_{\rm MS}$ for single He whitedwarfs also results in a small contribution of star formation from $-$ 7.5 Gyr to the number of new-born
"In other words, for arbitrarily large h, the radio excess with respect to the z0 FRC asymptotes to a value of ~5—10, depending on the assumed Schmidt Law, and the radio spectral slope asymptotes to ~1.1 for p=2.2.","In other words, for arbitrarily large $h$, the radio excess with respect to the $z \approx 0$ FRC asymptotes to a value of $\sim 5 - 10$, depending on the assumed Schmidt Law, and the radio spectral slope asymptotes to $\sim 1.1$ for $p = 2.2$."
" Relying on the FRC, a number of studies have used the GHz radio emission as a tracer of star-formation (e.g.,Carillietal.2008;SeymourGarn 2009)."," Relying on the FRC, a number of studies have used the GHz radio emission as a tracer of star-formation \citep[e.g.,][]{Cram98,Mobasher99,Haarsma00,Carilli08,Seymour08,Garn09}."
". Radio emission has the advantage that it is unaffected by dust obscuration, making it potentially very useful in starbursts, and therefore for most of the star-formation at zZ1 (eg.Chary&Elbaz2001;LeFloc'hetal."," Radio emission has the advantage that it is unaffected by dust obscuration, making it potentially very useful in starbursts, and therefore for most of the star-formation at $z \ga 1$ \citep[e.g.,][]{Chary01,LeFloch05,Dole06,Magnelli09,Pascale09}."
 Our models let us evaluate the theoretical basis for 2009)..radio as a SFR indicator at all redshifts., Our models let us evaluate the theoretical basis for radio as a SFR indicator at all redshifts.
 We show the predicted radio emissivity as a functionof star formation in Figure 4.., We show the predicted radio emissivity as a functionof star formation in Figure \ref{fig:SFRRadio}.
" At low surface densities (Zj<0.01gcm?; XspnX0.06Mokpc? yr- synchrotron radio has a non-linear dependence on star-formation1), at all redshifts."," At low surface densities $\Sigma_g \la 0.01~\gcm2$; $\Sigma_{\rm SFR} \la 0.06~\Msun~\kpc^{-2}~\yr^{-1}$ ), synchrotron radio has a non-linear dependence on star-formation at all redshifts."
" The weak radio emission is caused by electrons escaping their host galaxies, as inferred by Bell and discussed in LTQ."," The weak radio emission is caused by electrons escaping their host galaxies, as inferred by \citet{Bell03} and discussed in LTQ."
" That is, normal galaxies are (2003)not perfect electron calorimeters, so the radio emission is not a reliable star-formation tracer at low Xgrn."," That is, normal galaxies are not perfect electron calorimeters, so the radio emission is not a reliable star-formation tracer at low $\Sigma_{\rm SFR}$."
" At higher redshift, synchrotron emission is diminished by Inverse Compton off the CMB."," At higher redshift, synchrotron emission is diminished by Inverse Compton off the CMB."
" For a Milky Way-like galaxy, we find that radio is a good star-formation tracer at z<1, but underestimates it significantly by z=2 (eq. 1))."," For a Milky Way-like galaxy, we find that radio is a good star-formation tracer at $z \la 1$, but underestimates it significantly by $z \ga 2$ (eq. \ref{eqn:B07zCrit}) )."
" Already galaxies with star formation rates similar to Galactic levels are beginning to be observed in the radio at high redshift (Garnetal.2009),, so that the IC suppression may soon be observed."," Already galaxies with star formation rates similar to Galactic levels are beginning to be observed in the radio at high redshift \citep{Garn09}, so that the IC suppression may soon be observed."
" However, IC losses off the CMB should not be important even in the weakest starbursts until zZ4, as is also visible by the redshift evolution of the FRC in Figure 2.."," However, IC losses off the CMB should not be important even in the weakest starbursts until $z \ga 4$, as is also visible by the redshift evolution of the FRC in Figure \ref{fig:FRCEvolution}."
" Radio emission does grow linearly with star-formation rate between normal galaxies with X,=0.01gcm~? (at zS2) and compact starbursts.", Radio emission does grow linearly with star-formation rate between normal galaxies with $\Sigma_g = 0.01~\gcm2$ (at $z \la 2$ ) and compact starbursts.
" Therefore, it serves as an acceptable star-formation indicator for these galaxies."," Therefore, it serves as an acceptable star-formation indicator for these galaxies."
" However, if BοςX0799, puffy starbursts like SMGs have about 2—4 times the radio emission at any given star-formation rate than compact starbursts."," However, if $B \propto \Sigma_g^{0.7-0.8}$, puffy starbursts like SMGs have about $2 - 4$ times the radio emission at any given star-formation rate than compact starbursts."
" Therefore, we expect that if BοςxQ7-08 , the usual radio emission estimate based on the z0 FRC will their star formation rates by a factor of ~2—4."," Therefore, we expect that if $B \propto \Sigma_g^{0.7-0.8}$ , the usual radio emission estimate based on the $z \approx 0$ FRC will their star formation rates by a factor of $\sim 2 - 4$."
" The excess is greatest at Ly~lgcm? corresponding to Xsgg240—200Mokpe ?yr-!, typical of observed SMGs."," The excess is greatest at $\Sigma_g \approx 1~\gcm2$ corresponding to $\Sigma_{\rm SFR} \approx 40 - 200~\Msun \kpc^{-2} \yr^{-1}$ , typical of observed SMGs."
" Among the puffy starbursts themselves, the radio emission grows linearly with star-formation rate."," Among the puffy starbursts themselves, the radio emission grows linearly with star-formation rate."
 If instead B«999-96. the radio emission will underestimate the star-formation rate.," If instead $B \propto \rho^{0.5 - 0.6}$ , the radio emission will underestimate the star-formation rate."
" However, because the SMGs lie on their own FRC, there is little real redshift evolution in the radio emissivity of puffy starbursts, because of the buffering provided by IC losses off starlight (see 4.1,, Appendix A))."," However, because the SMGs lie on their own FRC, there is little real redshift evolution in the radio emissivity of puffy starbursts, because of the buffering provided by IC losses off starlight (see \ref{sec:FRCEvolution}, Appendix \ref{sec:CMBRadioDim}) )."
" Assuming a spectral slope a=0.7 will also underestimate the radio emissivity, since these galaxies can have steep radio spectra."," Assuming a spectral slope $\alpha = 0.7$ will also underestimate the radio emissivity, since these galaxies can have steep radio spectra."
" This explains the apparent evolution with z of puffy starbursts in Figure 4:: we have applied a k-correction using a typically employed a=0.7 when, in fact, the true synchrotron spectra are steeper."," This explains the apparent evolution with $z$ of puffy starbursts in Figure \ref{fig:SFRRadio}: we have applied a k-correction using a typically employed $\alpha = 0.7$ when, in fact, the true synchrotron spectra are steeper."
" If the radio star-formation tracer could be calibrated to the special conditions in puffy starbursts like SMGs, taking into account their different scale height, radio emissivity, and spectral slopes, we predict that radio would be a more accurate star-formation tracer for them."," If the radio star-formation tracer could be calibrated to the special conditions in puffy starbursts like SMGs, taking into account their different scale height, radio emissivity, and spectral slopes, we predict that radio would be a more accurate star-formation tracer for them."
" We can also directly calculate the GHz radio flux density S, from synchrotron emission of star-forming galaxies.", We can also directly calculate the GHz radio flux density $S_{\nu}$ from synchrotron emission of star-forming galaxies.
 We show the predicted flux density per unit star-formation at observer-frame 1.4 GHz in Figure 5.., We show the predicted flux density per unit star-formation at observer-frame 1.4 GHz in Figure \ref{fig:GHzRadioFluxes}.
" Surveys with the Expanded Very Large Array (EVLA) will have a continuum sensitivity of ~1uJy at frequencies of 1 - 50 GHz, and it should be able to directly detect galaxies with X,=0.01gcm""? and star-formation rates of 1Moyr-! out past zc0.5."," Surveys with the Expanded Very Large Array (EVLA) will have a continuum sensitivity of $\sim 1\ \muJy$ at frequencies of 1 - 50 GHz, and it should be able to directly detect galaxies with $\Sigma_g \ga 0.01\ \gcm2$ and star-formation rates of $1\ \Msun\ \yr^{-1}$ out past $z \approx 0.5$."
" As stated in Murphy(2009),, a starburst like M82 with SFR z3Moyr-! will become undetectable past ze1."," As stated in \citet{Murphy09c}, a starburst like M82 with SFR $\approx 3\ \Msun\ \yr^{-1}$ will become undetectable past $z \approx 1$."
" However, the buffering effect we emphasize in this paper preserves the radio emission of dense starbursts at high z, so that bright starbursts will be detectable further: starbursts with SFR >100Moyr! will be detectable with EVLA at 1.4 GHz out to z=4—5 and the most intense starbursts >1000Μοyr-! and X,= 1gcm wil be (SFRdetectable out past z10 in synchrotron ?)emission."," However, the buffering effect we emphasize in this paper preserves the radio emission of dense starbursts at high $z$ , so that bright starbursts will be detectable further: starbursts with SFR $\ga 100\ \Msun\ \yr^{-1}$ will be detectable with EVLA at 1.4 GHz out to $z \approx 4 - 5$ and the most intense starbursts (SFR $\ga 1000\ \Msun\ \yr^{-1}$ and $\Sigma_g \ga 1~\gcm2$ ) will be detectable out past $z \approx 10$ in synchrotron emission."
 Murphy(2009) predicts the SquareKilometer Array (SKA) will be sensitive to, \citet{Murphy09c} predicts the SquareKilometer Array (SKA) will be sensitive to
The sinaller the explosion energy per mit mass £4/AG becomes. the more significant our results deviate from equation (20)) even in the hieh euerew tails (Fig. 2)),"The smaller the explosion energy per unit mass $E_{\rm ex}/M_{\rm ej}$ becomes, the more significant our results deviate from equation \ref{eqn-fields}) ) even in the high energy tails (Fig. \ref{fig-fieldsb}) )."
 Our caleulatious for all the mocels listed in Table 3 with a constant adiabatic mdex equal to L/3 always result in the cnerey distributions of ejecta in good agreement with their fitting forumla at high cucreyv tails inrespective of values of Evy , Our calculations for all the models listed in Table \ref{tbl-model} with a constant adiabatic index equal to 4/3 always result in the energy distributions of ejecta in good agreement with their fitting formula at high energy tails irrespective of values of $E_{\rm ex}/M_{\rm ej}$.
Therefore this deviation should be caused by variable λίωνadiabatie iudices., Therefore this deviation should be caused by variable adiabatic indices.
 At the same time. the agreement of these results with equation (20)) suggests that the simple deusitv distributions used in Matzuer&AlcIl&ee(1999). are good approxinatious of realistic stars in the outermost lavers (0.001 of the ejecta mass).," At the same time, the agreement of these results with equation \ref{eqn-fields}) ) suggests that the simple density distributions used in \citet{Matzner_99} are good approximations of realistic stars in the outermost layers (0.001 of the ejecta mass)."
 From our calculations with a realistic equation of state (Eq. (13))), From our calculations with a realistic equation of state (Eq. \ref{eqn-eos}) ))
 varving explosion energies for three SN models in Table 3.. we have plotted AC»ε).e? at e—100 MovA£uucleoun as a function of ΓήΛέο iu M4Figure L.," varying explosion energies for three SN models in Table \ref{tbl-model}, we have plotted $M(>\epsilon)\times\epsilon^{3.6} / M_{\rm ej}$ at $\epsilon=100$ Mev/nucleon as a function of $E_{\rm ex}/M_{\rm ej}$ in Figure \ref{fig-fit}."
 Por less energetic explosious EλαL6«10 cres/M... the lunes of the three models deviate from cach other.," For less energetic explosions $E_{\rm ex}/M_{\rm ej}\ltsim 6\times10^{50}$ $/\Msun$, the lines of the three models deviate from each other."
 Thus a single fitting formula such as equation (20)) caunot account for all the realistic explosions., Thus a single fitting formula such as equation \ref{eqn-fields}) ) cannot account for all the realistic explosions.
 We need three different piriuueters ο for these three SN iodels to express the energy distribution of ejecta as that takes into account variable adiabatic iudices originated from the equation of states (Eq. (13)))., We need three different parameters $A$ for these three SN models to express the energy distribution of ejecta as that takes into account variable adiabatic indices originated from the equation of states (Eq. \ref{eqn-eos}) )).
 The coustant A is equal to 1.9«10+ for SN 1998Vbw model. 2.]«10.! for SN 2002ap. aud 2.810+t for SN 199Π. To investigate the role of supernova ejecta in light clement uucleosvuthesis. the modification of the euergv distribution of ejecta when they trauster iu the ISAL ποσα to be considered. because the cross sections of spallation reactions are scusitive to energies of particles.," The constant $A$ is equal to $1.9 \times 10^{-4}$ for SN 1998bw model, $2.1 \times 10^{-4}$ for SN 2002ap, and $2.8 \times 10^{-4}$ for SN 1994I. To investigate the role of supernova ejecta in light element nucleosynthesis, the modification of the energy distribution of ejecta when they transfer in the ISM need to be considered because the cross sections of spallation reactions are sensitive to energies of particles."
 Encrectic ejecta accelerated by a supernova explosion lose energy when they collide with neutral atoms in the ISAL and ionize them., Energetic ejecta accelerated by a supernova explosion lose energy when they collide with neutral atoms in the ISM and ionize them.
 The ionization cucrey loss rate of clement / iu the ejecta through II gas. v; (MeV/s). is given by the formula (Sclilickeiser2002):: where Ημ is the umuberdeusitv of neutral IT in the ISM. >=fe and JIGe) denotes the Heaviside step function.," The ionization energy loss rate of element $i$ in the ejecta through H gas, $\omega_i$ (MeV/s), is given by the formula \citep{Schlickeiser_02}: where $n_{\rm H\,I}$ is the numberdensity of neutral H in the ISM, $\beta = v/c$ and $H(x)$ denotes the Heaviside step function."
 The effective charec Zi; Is expressed as where Z; is the atomic nmuuber of the clement ; im the ejecta.," The effective charge $Z_{\mathrm{eff},i}$ is expressed as where $Z_i$ is the atomic number of the element $i$ in the ejecta."
 We use the leaka-box model (Meneguzzi.Audouze.&Reeves1971) aud the trauster equation for the mass of the clement { with an energy per nucleon € at time f. Fyle.t). is expressed as where As are the loss leugtlis in ο eii.7. p denotes the lass density of the ISM.0;(6) the velocity of the elemoeut ‘with an energy per uucleon of e.," 	We use the leaky-box model \citep{Meneguzzi_71} and the transfer equation for the mass of the element $i$ with an energy per nucleon $\epsilon$ at time $t$, $F_i (\epsilon,t)$, is expressed as where $\Lambda$ 's are the loss lengths in g $\mathrm{cm}^{-2}$, $\rho$ denotes the mass density of the ISM,$v_i(\epsilon)$ the velocity of the element $i$ with an energy per nucleon of $\epsilon$ ."
" X denotes the range before escaping froma given svstei (ve asstuue A=100 ο 2 following Suzuki&Yoshii (2001))). and A,,.; due to spallation reactious."," $\Lambda_{\rm esc}$ denotes the range before escaping from a given system (we assume $\Lambda_{\rm esc}=100$ g $^{-2}$ following \citet{Suzuki_01}) ), and $\Lambda_{n,i}$ due to spallation reactions."
 The latter is expressed as, The latter is expressed as
increase with Ny or also with LxNg (with the caveat that excessive Ny may in some cases be due to the disk itself).,increase with $N_{\rm H}$ or also with $L_{\rm X}N_{\rm H}$ (with the caveat that excessive $N_{\rm H}$ may in some cases be due to the disk itself).
" Although such a trend is present, it is not significant (Table 6))."," Although such a trend is present, it is not significant (Table \ref{table6}) )."
" If X-ray and EUV absorption is important but [Ner]] is still predominantly produced by disk irradiation, then we would expect that Liver; correlates more closely with the attenuated Lx than with the intrinsic Lx, although we recall the caveat that the absorption along our line of sight may differ from the absorption between the star and the disk."," If X-ray and EUV absorption is important but ] is still predominantly produced by disk irradiation, then we would expect that $L_{\rm [Ne\,II]}$ correlates more closely with the attenuated $L_{\rm X}$ than with the intrinsic $L_{\rm X}$, although we recall the caveat that the absorption along our line of sight may differ from the absorption between the star and the disk."
" Furthermore, π]] production should with increasing Ny."," Furthermore, ] production should with increasing $N_{\rm H}$."
 These two effects have not been significantly measured (Table 6))., These two effects have not been significantly measured (Table \ref{table6}) ).
" In the most extreme cases, accretion flows shield the circumstellar environment from X-ray or EUV irradiation."," In the most extreme cases, accretion flows shield the circumstellar environment from X-ray or EUV irradiation."
 This is particularly evident in strongly accreting sources with X-ray jets as discussed above., This is particularly evident in strongly accreting sources with X-ray jets as discussed above.
" In these cases, it is unlikely that X-ray/EUV photons reach the disk in significant numbers."," In these cases, it is unlikely that X-ray/EUV photons reach the disk in significant numbers."
" The origin of the very strong [Neu]] emission in these sources remains ambiguous because they all eject jets that can be very strong Π]] emitters (vanBoekeletal.,2009),, but massive, low-density accretion flows attenuating the X-ray emission may contribute to π]] emission as well."," The origin of the very strong ] emission in these sources remains ambiguous because they all eject jets that can be very strong ] emitters \citep{boekel09}, but massive, low-density accretion flows attenuating the X-ray emission may contribute to ] emission as well."
" One of the principal results of the present study is the evident [Νεπ]] excess in stars with jets, as previously suggested by Giideletal.(20092) and exemplified by the study of the T Tau triplet by vanBoekeletal.(2009)."," One of the principal results of the present study is the evident ] excess in stars with jets, as previously suggested by \citet{guedel09a} and exemplified by the study of the T Tau triplet by \citet{boekel09}."
". We have been careful not to confuse our sample with strong jets from Class I sources in which other mechanisms (excitation of i]] in the envelope, stronger accretion shocks from material falling onto the disk, etc) may dominate."," We have been careful not to confuse our sample with strong jets from Class I sources in which other mechanisms (excitation of ] in the envelope, stronger accretion shocks from material falling onto the disk, etc) may dominate."
" On the other hand, jets may also contribute to the generally high level of [Νεπ]] emission seen in Class I sources reported by Flaccomioetal.(2009).."," On the other hand, jets may also contribute to the generally high level of ] emission seen in Class I sources reported by \citet{flaccomio09}."
" Most of our objects are ordinary CTTS although some extreme cases, such as the flat-spectrum source DG Tau or the strongly absorbed (by a near-edge-on thick disk) T Tau S have been included."," Most of our objects are ordinary CTTS although some extreme cases, such as the flat-spectrum source DG Tau or the strongly absorbed (by a near-edge-on thick disk) T Tau S have been included."
 Fig., Fig.
 6 shows that the distribution of Ny is very similar for the jet sources and the optically thick disks without jets (the same is also true for the transition disks)., \ref{fig6} shows that the distribution of $N_{\rm H}$ is very similar for the jet sources and the optically thick disks without jets (the same is also true for the transition disks).
 What [Nen]] emission can be expected from jets?, What ] emission can be expected from jets?
" We briefly discuss three principal π]] formation mechanisms, namely from jet shocks, from irradiation of jets by stellar X- or EUV flux, and from X-ray emission produced by the jets themselves."," We briefly discuss three principal ] formation mechanisms, namely from jet shocks, from irradiation of jets by stellar X-rays or EUV flux, and from X-ray emission produced by the jets themselves."
" Jet gas is typically heated to 10* K by shocks, shock velocities being a few tens of km s! (Lavalley-Fouquetetal."," Jet gas is typically heated to $10^4$ K by shocks, shock velocities being a few tens of km $^{-1}$ \citep{lavalley00}."
",2000).. Hollenbach&Gorti(2009) estimate Liver] from fast (z100 km s!) shocks based on results from Hollenbach&McKee (1989), to find a linear relation between Le] and Macc (the latter assumed to scale linearly with Moss} see Fig. 10))."," \citet{hollenbach09} estimate $L_{\rm [Ne\,II]}$ from fast $\ga 100$ km $^{-1}$ ) shocks based on results from \citet{hollenbach89}, to find a linear relation between $L_{\rm [Ne\,II]}$ and $\dot{M}_{\rm acc}$ (the latter assumed to scale linearly with $\dot{M}_{\rm loss}$; see Fig. \ref{fig10}) )."
" For typical wind/jet velocities, densities, and mass loss rates, they find much higher Ljnem than expected from irradiated disks, fully compatible with our findings of very high Liver] in almost all jet sources."," For typical wind/jet velocities, densities, and mass loss rates, they find much higher $L_{\rm [Ne\,II]}$ than expected from irradiated disks, fully compatible with our findings of very high $L_{\rm [Ne\,II]}$ in almost all jet sources."
" Jets may also be irradiated by stellar X-rays similar to disk surfaces, and may thus be ionized and heated to produce [Νεπ]] emission."," Jets may also be irradiated by stellar X-rays similar to disk surfaces, and may thus be ionized and heated to produce ] emission."
" Jet irradiation by stellar X-rays is relatively straightforward because jets move through wide polar cavities evacuated of much of the circumstellar gas (Momoseetal., 1996).", Jet irradiation by stellar X-rays is relatively straightforward because jets move through wide polar cavities evacuated of much of the circumstellar gas \citep{momose96}.
". Evidence for very low gas column densities around CTTS jets has been found from jets that are themselves X-ray sources (see below) and show very low X-ray attenuation despite the presence of appreciable amounts of circumstellar material in other directions (Güdeletal.,2007b).", Evidence for very low gas column densities around CTTS jets has been found from jets that are themselves X-ray sources (see below) and show very low X-ray attenuation despite the presence of appreciable amounts of circumstellar material in other directions \citep{guedel07b}.
". For the T Tauri system, a simple estimate of X-ray induced [Ner]] line excitation across a lightly absorbing gas column showed that the observed stellar Lx may indeed yield the observed ΠΠ] fluxes out to a few arcsec from the star (Güdeletal.,2009a)."," For the T Tauri system, a simple estimate of X-ray induced ] line excitation across a lightly absorbing gas column showed that the observed stellar $L_{\rm X}$ may indeed yield the observed ] fluxes out to a few arcsec from the star \citep{guedel09a}."
". A rather unexpected finding are CTTS jets that produce X-rays themselves (Güdeletal.,2007b,2008).."," A rather unexpected finding are CTTS jets that produce X-rays themselves \citep{guedel07b, guedel08}."
" Apart from direct X-ray imaging of jets (in particular the case of DG Tau), such jets have also been identified spectroscopically in X-rays."," Apart from direct X-ray imaging of jets (in particular the case of DG Tau), such jets have also been identified spectroscopically in X-rays."
" Their anomalous spectra show a highly absorbed, hard and variable coronal component together with a soft, very weakly absorbed and non-variable component apparently produced by the jets close to the star."," Their anomalous spectra show a highly absorbed, hard and variable coronal component together with a soft, very weakly absorbed and non-variable component apparently produced by the jets close to the star."
 The excessive absorption of the coronal component is an order of magnitude larger than expected from, The excessive absorption of the coronal component is an order of magnitude larger than expected from
each accretion event. we also need to calculate the rate at which the mass. as estimated. above. is accreted.,"each accretion event, we also need to calculate the rate at which the mass, as estimated above, is accreted."
 This is assumed to scale with the IEddington rate for the MDBII. and is based. on the results of merger simulations. which heuristically track accretion onto a central MIBLI (27)..," This is assumed to scale with the Eddington rate for the MBH, and is based on the results of merger simulations, which heuristically track accretion onto a central MBH \citep{dimatteo05,hopkins05}."
 Phe time spent by a given simulated AGN at a given bolometric per logarithmic interval is approximated by (7?) ast where fg=10 wr. and à=0.95|0.32logCLica:1072L. ).," The time spent by a given simulated AGN at a given bolometric per logarithmic interval is approximated by \citep{hopkins05b} as: where $t_Q\simeq10^9$ yr, and $\alpha=-0.95+0.32\log(L_{\rm
peak}/10^{12} L_\odot)$ ."
 Here Lycus is the luminosity of the AGN at the peak of its activity., Here $L_{\rm peak}$ is the luminosity of the AGN at the peak of its activity.
 Hopkins et al. (, Hopkins et al. (
2006) show that approximating Lye with the Ecclington luminosity of the MILI at its final mass (1.0.. when it sits onthe Adpuσι relation) compared to computing the peak luminosity with eqn. (,"2006) show that approximating $L_{\rm peak}$ with the Eddington luminosity of the MBH at its final mass (i.e., when it sits on the $M_{\rm BH}-\sigma_c$ relation) compared to computing the peak luminosity with eqn. ("
6) above gives the same result and. in fact. the dillerence between these 2 cases is negligible.,"6) above gives the same result and in fact, the difference between these 2 cases is negligible."
 Volonteri et al. (, Volonteri et al. (
2006) derive the following simple cillerential equation to express the instantaneous accretion rate (ναπα units of the Ecelineton rate) for a MDII of mass Alpy in a galaxy with velocity dispersion σι: where here fis the time elapsed. from the beginning of the aceretion event.,"2006) derive the following simple differential equation to express the instantaneous accretion rate $f_{\rm Edd}$ ,in units of the Eddington rate) for a MBH of mass $M_{\rm BH}$ in a galaxy with velocity dispersion $\sigma_c$: where here $t$ is the time elapsed from the beginning of the accretion event."
 Solving this equation gives us the instantaneous Iddington ratio for a given MIT at a specific time. and therefore we can sell-consistentlv erow the MILII mass.," Solving this equation gives us the instantaneous Eddington ratio for a given MBH at a specific time, and therefore we can self-consistently grow the MBH mass."
 We set the Edcineton ratio fei=105 ab f=0., We set the Eddington ratio $f_{\rm Edd}=10^{-3}$ at $t=0$.
 This same tvpe of accretion is assumed to occur. at z15. following a major merger in which a MBLLis not fed by disc instabilities.," This same type of accretion is assumed to occur, at $z>15$, following a major merger in which a MBH is not fed by disc instabilities."
 In à hierarchical Universe. where galaxies grow by mergers. MDBLII mergers are a natural consequence. ancl we race their contribution to the evolving MDBII. population (cfr.," In a hierarchical Universe, where galaxies grow by mergers, MBH mergers are a natural consequence, and we trace their contribution to the evolving MBH population (cfr."
 Sesana et al., Sesana et al.
 2007 for details on the. cvnamical modeling)., 2007 for details on the dynamical modeling).
 During the final phases of a SIBLE merger. emission of gravitational racliation drives the orbital decay of he binary.," During the final phases of a MBH merger, emission of gravitational radiation drives the orbital decay of the binary."
" Recent numerical relativity simulations suggest hat merging MDII binarics might be subject to a large ""eravitational recoil: a general-relativistic cllect (22). due o the non-zero net lincar momentum carried. away by gravitational waves in the coalescence of two unequal mass Mack holes."," Recent numerical relativity simulations suggest that merging MBH binaries might be subject to a large “gravitational recoil"": a general-relativistic effect \citep{fitchett83,redmount89} due to the non-zero net linear momentum carried away by gravitational waves in the coalescence of two unequal mass black holes."
 Racliation recoil is a strong field effect. that depends on the lack of svmmoetry in the system., Radiation recoil is a strong field effect that depends on the lack of symmetry in the system.
 For merging AIBUs with high spin. in particular orbital configurations. he recoil velocity can be as high. as a few thousands. of kilometers per second. (22?72?)..," For merging MBHs with high spin, in particular orbital configurations, the recoil velocity can be as high as a few thousands of kilometers per second \citep{campanelli2007a,campanelli2007b,gonzalez2007,Herrmann2007,schnittman07}."
 Here. we aim to determine he characteristic features of the AIBLE population deriving ron a specilic seed. scenario. and its signature in. galaxies. we study the case without gravitational recoil.," Here, we aim to determine the characteristic features of the MBH population deriving from a specific seed scenario, and its signature in galaxies, we study the case without gravitational recoil."
 We discuss this issue further in section 4., We discuss this issue further in section 4.
 Detection of gravitational waves from seeds merging at the redshift’ of formation (?) is probably one of the best ways ο cliseriminate among formation mechanisms., Detection of gravitational waves from seeds merging at the redshift of formation \citep{sesana07} is probably one of the best ways to discriminate among formation mechanisms.
 On the other iud. the imprint of dillerent formation scenarios can also x sought in observations at lower redshifts.," On the other hand, the imprint of different formation scenarios can also be sought in observations at lower redshifts."
 The various seed formation scenarios have distinct consequences for the woperties of the MBII population at 2=0., The various seed formation scenarios have distinct consequences for the properties of the MBH population at $z=0$.
 Below. we esent theoretical. predictions of the various seed mocdels or the properties of the local SALBLL population.," Below, we present theoretical predictions of the various seed models for the properties of the local SMBH population."
 The repercussions of clilferent initial clliciencies for seed ormation for the overall evolution of the AIBLL population stretch from high-redshift to the local Universe., The repercussions of different initial efficiencies for seed formation for the overall evolution of the MBH population stretch from high-redshift to the local Universe.
 Obviously. a higher density of AIBLL seeds implies a more numerous population of MBDBlIs at later times. which can produce observational signatures in statistical samples.," Obviously, a higher density of MBH seeds implies a more numerous population of MBHs at later times, which can produce observational signatures in statistical samples."
 More subthy. he formation of seeds in a ACDAL scenario follows the cosmological bias.," More subtly, the formation of seeds in a $\Lambda$ CDM scenario follows the cosmological bias."
 As a consequence. the progenitors of massive galaxies (or clusters of galaxies) have a higher xobabilitv of hosting MBLI seeds (etr. ?)).," As a consequence, the progenitors of massive galaxies (or clusters of galaxies) have a higher probability of hosting MBH seeds (cfr. \citealt{madau01}) )."
 In the case of low- systems. such as isolated dwarl galaxies. very [ew of the ugh-2 progenitors have the deep potential wells needed for gas retention and cooling. a prerequisite for MDII formation.," In the case of low-bias systems, such as isolated dwarf galaxies, very few of the $z$ progenitors have the deep potential wells needed for gas retention and cooling, a prerequisite for MBH formation."
 We can read. oll directly from Fig., We can read off directly from Fig.
 1. the average number of massive progenitors required. for a present. day. galaxy to host a MDIL., \ref{fig1} the average number of massive progenitors required for a present day galaxy to host a MBH.
" In model A. a galaxy needs of order. 25 massive progenitors (mass above ~10"" Al.) to ensure a high probability of seeding within the merger tree."," In model A, a galaxy needs of order 25 massive progenitors (mass above $\sim10^7\msun$ ) to ensure a high probability of seeding within the merger tree."
 In model C. instead. the requirement drops to 4 massive progenitors. increasing the probability of ALBLE formation in lower bias halos.," In model C, instead, the requirement drops to 4 massive progenitors, increasing the probability of MBH formation in lower bias halos."
 The signature of the ellicienev of the formation of AIBLL seeds will consequently be stronger in isolated. dwarf ealaxies., The signature of the efficiency of the formation of MBH seeds will consequently be stronger in isolated dwarf galaxies.
 Fig., Fig.
 3 (bottom panel) shows a comparison between the observed Ag—0 relation and the one predicted by our models (shown with circles). and in particular. from left to right. the three models based on the 2? seed. masses with Qe=1.5. 2 and 3. and a fourth model based on. Iower- Population LL star seeds.," \ref{fig3}
 (bottom panel) shows a comparison between the observed $M_{\rm
BH}-\sigma$ relation and the one predicted by our models (shown with circles), and in particular, from left to right, the three models based on the \citet{LN06,LN07} seed masses with $Q_{\rm c}=1.5$, 2 and 3, and a fourth model based on lower-mass Population III star seeds."
 The upper panel of Fig., The upper panel of Fig.
 3 shows the fraction of galaxies that host anv massive black holes for different velocity. dispersion bins., \ref{fig3} shows the fraction of galaxies that host any massive black holes for different velocity dispersion bins.
 This shows that the fraction of galaxies without a MDBII increases with decreasing halo masses at z=0., This shows that the fraction of galaxies without a MBH increases with decreasing halo masses at $z = 0$.
 A larger fraction of low mass halos are devoid of central black holes for lower seed. formation elliciencies., A larger fraction of low mass halos are devoid of central black holes for lower seed formation efficiencies.
 Note that this is one of the key discriminants between our models ancl those seeded with Population LL remnants., Note that this is one of the key discriminants between our models and those seeded with Population III remnants.
 As shown in Fig., As shown in Fig.
 3. there are practically no galaxies without central BlIs for the Population LLL seeds.," 3, there are practically no galaxies without central BHs for the Population III seeds."
 It is interesting to note that our mocoel predictions are in very good agreement with the recent LIST ACS census of black holes in low mass galaxies in the Virgo cluster., It is interesting to note that our model predictions are in very good agreement with the recent HST ACS census of black holes in low mass galaxies in the Virgo cluster.
 ?? suggest that below a transition galaxy mass (2107 M.) a central massive black hole seems to be replaced by a nuclear," \cite{ferrarese06,Wehner2006} suggest that below a transition galaxy mass $\simeq 10^{10}\msun$ ) a central massive black hole seems to be replaced by a nuclear"
Despite recent progress in stellar magnetic field measurements. spectropolarimetrie surveys of early-type stars indicate that photospheric magnetic fields can only be detected in a small fraction of these stars.,"Despite recent progress in stellar magnetic field measurements, spectropolarimetric surveys of early-type stars indicate that photospheric magnetic fields can only be detected in a small fraction of these stars."
 Without direct constraints on. the magnetic field of the vast majority of early-type stars. our understanding of the role of magnetic fields on the structure and evolution of intermediate mass and massive stars is necessarily limited.," Without direct constraints on the magnetic field of the vast majority of early-type stars, our understanding of the role of magnetic fields on the structure and evolution of intermediate mass and massive stars is necessarily limited."
 In this Letter. we report the detection of a magnetic field on Vega and argue that Vega is probably the first member of anew class of yet undetected magnetic A-type stars.," In this Letter, we report the detection of a magnetic field on Vega and argue that Vega is probably the first member of a new class of yet undetected magnetic A-type stars."
 The proportion of stars hosting a detectable magnetic field is more firmly established for main sequence stars of intermediate mass (late-B and A-type stars) than for massive stars (early B and O-type stars) or intermediate mass. pre-main-sequence stars (Herbig Ae/Be stars)., The proportion of stars hosting a detectable magnetic field is more firmly established for main sequence stars of intermediate mass (late-B and A-type stars) than for massive stars (early B and O-type stars) or intermediate mass pre-main-sequence stars (Herbig Ae/Be stars).
 Magnetic A-type stars are indeed identified with the group of Ap-Bp chemically peculiar stars (excluding the subgroup of HgMn stars) since all known magnetic A-type stars belong to this group and. when observed with sufficient precision. Ap/Bp stars always show photospheric magnetic fields (Landstreet.1992:Auriéreetal.. 2007).," Magnetic A-type stars are indeed identified with the group of Ap-Bp chemically peculiar stars (excluding the subgroup of HgMn stars) since all known magnetic A-type stars belong to this group and, when observed with sufficient precision, Ap/Bp stars always show photospheric magnetic fields \citep{Lan92,Au07}."
. The incidence of the Ap/Bp chemical peculiarity among A-type stars then leads to a 5—10% estimate of magnetic stars (Wolff.1968)., The incidence of the Ap/Bp chemical peculiarity among A-type stars then leads to a $5-10\%$ estimate of magnetic stars \citep{Wo68}.
. Note that magnetic field detections have been reported for a few Am and HgMn stars (Lanz&Mathys.1993:Mathys&Hubrig.1995) but remain debated because they could not be confirmed by further investigations (seethediscussioninShorlinetal.. 2002).," Note that magnetic field detections have been reported for a few Am and HgMn stars \citep{Ma93,Ma95} but remain debated because they could not be confirmed by further investigations \citep[see the discussion in][]{Shor02}."
. Thanks to new high- spectropolarimeters. magnetic fields are now also detected in pre-main-sequence stars and in massive stars.," Thanks to new high-resolution spectropolarimeters, magnetic fields are now also detected in pre-main-sequence stars and in massive stars."
 According to recent surveys. the fraction of magnetic. stars among Herbig Ae/Be stars is 7% (Wadeetal..2009)... while the rate of detection for early B and O-type stars is also small (Bouretetal..2008:Schnerr2005).," According to recent surveys, the fraction of magnetic stars among Herbig Ae/Be stars is $7 \%$ \citep{Wade09}, while the rate of detection for early B and O-type stars is also small \citep{Bou08,Schnerr08}."
 The magnetic fields of Ap/Bp stars are characterized by a strong dipolar component. a long-term stability and dipolar strengths ranging from a lower limit of about 300 Gauss to tens of kilo-Gauss (Landstreet.1992;Auriéreetal...2007).," The magnetic fields of Ap/Bp stars are characterized by a strong dipolar component, a long-term stability and dipolar strengths ranging from a lower limit of about 300 Gauss to tens of kilo-Gauss \citep{Lan92,Au07}."
. Thus. if à population of weak dipolar-like fields corresponding to a weak field continuation of Ap/Bp stars exists. a longitudinal component of the magnetic field in the range of 10 to 100 Gauss should have been detected by recent spectropolarmmetric surveys of non Ap/Bp stars (Shorlinetal..2002:Wade2006:Bagnuloetal..Auriére 2008).," Thus, if a population of weak dipolar-like fields corresponding to a weak field continuation of Ap/Bp stars exists, a longitudinal component of the magnetic field in the range of $10$ to $100$ Gauss should have been detected by recent spectropolarimetric surveys of non Ap/Bp stars \citep{Shor02,Wade06,Ba06,Au09}."
. Instead. these surveys suggest there is a dichotomy between the population of strong. stable and dipolar-like magnetic fields corresponding to the Ap/Bp stars and the rest of A-type stars. whose magnetic properties remain unknown. except that their surface longitudinal magnetic field should be very small.," Instead, these surveys suggest there is a dichotomy between the population of strong, stable and dipolar-like magnetic fields corresponding to the Ap/Bp stars and the rest of A-type stars, whose magnetic properties remain unknown, except that their surface longitudinal magnetic field should be very small."
 Vega is well suited for the search of magnetic fields among A-type non Ap/Bp stars., Vega is well suited for the search of magnetic fields among A-type non Ap/Bp stars.
 Its brightness and its low equatorial projected velocity ensure high signal-to-noise V spectra. while the number of spectral lines of an AO-type star is important enough to allow à very large multiplex gain by gathering the polarimetric signal of all the lines using a cross-correlation technique (Least-Squares Deconvolution. Donatietal.(1997).. LSD hereafter).," Its brightness and its low equatorial projected velocity ensure high signal-to-noise V spectra, while the number of spectral lines of an A0-type star is important enough to allow a very large multiplex gain by gathering the polarimetric signal of all the lines using a cross-correlation technique (Least-Squares Deconvolution, \citet{Do97}, LSD hereafter)."
 Another advantage of Vega’s brightness is that its fundamental parameters are well known relative to other more anonymous stars (Gray.2007)., Another advantage of Vega's brightness is that its fundamental parameters are well known relative to other more anonymous stars \citep{Gr07}.
. In particular. spectral analysis and interferometric observations have shown that Vega is a rapidly rotating star seen nearly pole-on (Aufdenbergetal..2006:Petersonetal..Takeda2008 ).," In particular, spectral analysis and interferometric observations have shown that Vega is a rapidly rotating star seen nearly pole-on \citep{Auf06,Pe06,Ta08}."
. Vega was already included in. à previous spectropolarimetric survey of A-type non Ap/Bp stars using NARVAL at the Telescope Bernard Lyot of Pie du Midi. but the analysis of its 11 Stokes V spectra was not conclusive.," Vega was already included in a previous spectropolarimetric survey of A-type non Ap/Bp stars using NARVAL at the Telescope Bernard Lyot of Pic du Midi, but the analysis of its 11 Stokes V spectra was not conclusive."
 Here we present the results of a four night observing run fully dedicated to Vega. during which more than 300 Stokes V spectra were obtained.," Here we present the results of a four night observing run fully dedicated to Vega, during which more than 300 Stokes V spectra were obtained."
 Summing the information over a large number of these spectra leads to an unambiguous detection of a polarized signal., Summing the information over a large number of these spectra leads to an unambiguous detection of a polarized signal.
 The observations are described and interpreted in the next section., The observations are described and interpreted in the next section.
 In section 3. the origin of a ~| G longitudinal magnetic field in an A-type non Ap/Bp star is discussed and some of the perspectives opened by this field detection are considered.," In section 3, the origin of a $\sim \!1$ G longitudinal magnetic field in an A-type non Ap/Bp star is discussed and some of the perspectives opened by this field detection are considered."
 Our conclusions are given in section 4., Our conclusions are given in section 4.
the lines begin to overlap each other.,the lines begin to overlap each other.
" At the final time of 200 Myrs after the end of the simulation, we can identify one primary clump with a mass over 6.0x10* Mo with two smaller clumps with masses of 4.0x104 Mo and 2.5x104 Mo respectively."," At the final time of 200 Myrs after the end of the simulation, we can identify one primary clump with a mass over $\times$ $^{4}$ $_{\odot}$ with two smaller clumps with masses of $\times$ $^{4}$ $_{\odot}$ and $\times$ $^{4}$ $_{\odot}$ respectively."
" The two largest masses are far outside the dark matter halo, and are no longer bound to it."," The two largest masses are far outside the dark matter halo, and are no longer bound to it."
 Comparing the solid (HWT) and dotted red line we conclude that regardless of the resolution level (MWT)the same general conclusions hold., Comparing the solid (HWT) and dotted red line (MWT) we conclude that regardless of the resolution level the same general conclusions hold.
" There are some differences between the two resolution levels, primarily in the speed and position of the final clumps formed, but these are minor."," There are some differences between the two resolution levels, primarily in the speed and position of the final clumps formed, but these are minor."
 In each case a nearly identical distribution of stellar clusters is formed: one large cluster with a few smaller neighbors., In each case a nearly identical distribution of stellar clusters is formed: one large cluster with a few smaller neighbors.
" As discussed in Paper I, shock-minihalo interactions could be a source of halo globular clusters, as the knots will continue to collapse into dense stellar clusters and the longest-lived of these stars will survive to the present day."," As discussed in Paper I, shock-minihalo interactions could be a source of halo globular clusters, as the knots will continue to collapse into dense stellar clusters and the longest-lived of these stars will survive to the present day."
 In fact the clusters in our simulations are very dense ~ 10? cm~) and expected to become gravitationally bound(n to larger structures that form over cosmological time., In fact the clusters in our simulations are very dense (n $\sim$ $^{2}$ $^{-3}$ ) and expected to become gravitationally bound to larger structures that form over cosmological time.
 There are several other properties of our simulated clusters that support this connection., There are several other properties of our simulated clusters that support this connection.
 Globular cluster masses are well defined by a Gaussian in logio(Mac/Mo) with a mean mass of 10? Mo and a dispersion of 0.5., Globular cluster masses are well defined by a Gaussian in $_{10}$ $_{\rm{GC}}$ $_{\odot}$ ) with a mean mass of $^{5}$ $_{\odot}$ and a dispersion of 0.5.
" This represents a spread in globular cluster masses of 3.0x 104 Mo to 3.0x 10° Mo, which spans the range of the stellar cluster formed in our simulations."," This represents a spread in globular cluster masses of $3.0 \times$ $^{4}$ $_{\odot}$ to $3.0 \times$ $^{5}$ $_{\odot}$, which spans the range of the stellar cluster formed in our simulations."
 However the final cluster masses may depend on the initial mass in the minihalo a parameter study is required to determine this dependence., However the final cluster masses may depend on the initial mass in the minihalo a parameter study is required to determine this dependence.
 This is underway and will be presented in a future paper., This is underway and will be presented in a future paper.
" The lower mass limit for globular clusters seems to be set by several destruction mechanisms, which include mechanical evaporation (eg.,"," The lower mass limit for globular clusters seems to be set by several destruction mechanisms, which include mechanical evaporation (eg.,"
" Spitzer Thuan 1972) and shocking as the cluster passes through the host galaxy (eg.,"," Spitzer Thuan 1972) and shocking as the cluster passes through the host galaxy (eg.,"
 Ostriker 1972)., Ostriker 1972).
" On the other hand, the upper mass limit seems to be a property of the initial population (eg.,"," On the other hand, the upper mass limit seems to be a property of the initial population (eg.,"
 Fall Rees 1985; Peng Weisheit 1991; Elmegreen 2010)., Fall Rees 1985; Peng Weisheit 1991; Elmegreen 2010).
" In fact, the upper limit of zz 10° Mo roughly coincides with the virial temperature of Τα-104 K which corresponds to the limit at which atomic cooling becomes inefficient."," In fact, the upper limit of $\approx$ $^{6}$ $_{\odot}$ roughly coincides with the virial temperature of $\approx$ $^{4}$ K which corresponds to the limit at which atomic cooling becomes inefficient."
 The metallicity of halo globular clusters provides another constraint., The metallicity of halo globular clusters provides another constraint.
 The intracluster metallicity distribution is well described by a Gaussian with a mean value of [££]z -1.6 and a dispersion of 0.3 (Zinn 1985; Ashman Bird 1993)., The intracluster metallicity distribution is well described by a Gaussian with a mean value of $\left[\frac{Fe}{H}\right] \approx$ -1.6 and a dispersion of 0.3 (Zinn 1985; Ashman Bird 1993).
" The metallicity dispersion within a given globular cluster is small, usually within 0.1 dex "," The metallicity dispersion within a given globular cluster is small, usually within 0.1 dex (eg.,"
"Suntzeff although in some cases additional (eg.,late-time star-formation1993), from reprocessed material may complicate the final observed distribution Piotto 2007; D'Ercole 2008; Bekki 2010)."," Suntzeff 1993), although in some cases additional late-time star-formation from reprocessed material may complicate the final observed distribution Piotto 2007; D'Ercole 2008; Bekki 2010)."
 Our model reproduces the expected mean abundance (Z ~ 107? Zo) with an extremely homogeneous distribution given our initial abundance in the shock., Our model reproduces the expected mean abundance (Z $\sim$ $^{-2}$ $_{\odot}$ ) with an extremely homogeneous distribution given our initial abundance in the shock.
" Note that our model keeps track of the velocity, /2K, and eddy turnover scale, L, of bouyancy-driven and shear-driven turbulence, and assumes that below these lengths scales the flow will behave as fully developed turbulence."," Note that our model keeps track of the velocity, $\sqrt{2 K},$ and eddy turnover scale, $L$, of bouyancy-driven and shear-driven turbulence, and assumes that below these lengths scales the flow will behave as fully developed turbulence."
" In this case, as studed in detail in Pan (2010), the mixing of metals is driven by a cascade"," In this case, as studed in detail in Pan (2010), the mixing of metals is driven by a cascade"
where the kernels can be written Separation of £/D modes will not be discussed further in this paper as this is extensively treated in the references 1n figure (3)) and (4)) we have plotted the As(£.07) and A3(.C) kernels for à tophat window covering the same area on the skv as the Gaussian windows in figure (1)) and (2)).,"where the kernels can be written Separation of $E/B$ modes will not be discussed further in this paper as this is extensively treated in the references In figure \ref{fig:k2th5}) ) and \ref{fig:k2th15}) ) we have plotted the $K_2(\ell,\ell')$ and $K_{-2}(\ell,\ell')$ kernels for a tophat window covering the same area on the sky as the Gaussian windows in figure \ref{fig:k2g5}) ) and \ref{fig:k2g15}) )."
" sPhe kernel Aveo⊳(4.0) ∕⋅for the cross polarisationo. power spectrum C7. ""Ais ga10wn in figure (5)) for a 5 and 15 degree Gaussian window and in figure (6)) for the corresponding tophat windows."," The kernel $K_{20}(\ell,\ell')$ for the cross polarisation power spectrum $C^C_\ell$ is shown in figure \ref{fig:k20g}) ) for a $5$ and $15$ degree Gaussian window and in figure \ref{fig:k20th}) ) for the corresponding tophat windows."
 As for the temperature kernels. all the polarisation kernels show the same behaviour when changing type anc size of the window.," As for the temperature kernels, all the polarisation kernels show the same behaviour when changing type and size of the window."
 When going from smaller to larger windows. the diagonals get sharper.," When going from smaller to larger windows, the diagonals get sharper."
 Also the tophat kernels have more long range correlations than the Gaussian kernels (note that all the plots have the same vertical scale and can be compared In figure (7)) we have plotted slices of the dilferent. kernels at (=200 for comparison., Also the tophat kernels have more long range correlations than the Gaussian kernels (note that all the plots have the same vertical scale and can be compared In figure \ref{fig:polcutg}) ) we have plotted slices of the different kernels at $\ell=200$ for comparison.
 The slices are made of the kernels for 5 and 15 degree PWM Gaussian Gabor windows., The slices are made of the kernels for $5$ and $15$ degree FWHM Gaussian Gabor windows.
 The first thing to note is that the temperature kernel A(44607). the £ and B kernel Ae.) and the temperature-polarisation cross spectrum kernel ου.) only diller for the far off-diagonal elements.," The first thing to note is that the temperature kernel $K(\ell,\ell')$, the $E$ and $B$ kernel $K_2(\ell,\ell')$ and the temperature-polarisation cross spectrum kernel $K_{20}(\ell,\ell')$ only differ for the far off-diagonal elements."
 At the diagonal their shape and size are the same., At the diagonal their shape and size are the same.
 For this reason the relation shown in ΕΑΠ between the width of the kernel and the width of the size of the window for the temperature power spectrum is also valid for polarisation., For this reason the relation shown in HGH between the width of the kernel and the width of the size of the window for the temperature power spectrum is also valid for polarisation.
 This is an important result to be used for the likelihood estimation of the polarisation power spectra in the next section., This is an important result to be used for the likelihood estimation of the polarisation power spectra in the next section.
 Lt shows ju the number of polarisation pseudo spectrum coellicients to be used in the likelihood analvsis should be the same as for 1e likelihood. estimation of the temperature power In figure (8)) a similar plot is shown for the corresponding tophat windows., It shows that the number of polarisation pseudo spectrum coefficients to be used in the likelihood analysis should be the same as for the likelihood estimation of the temperature power In figure \ref{fig:polcutth}) ) a similar plot is shown for the corresponding tophat windows.
 The plot shows that the conclusions made for 10 Gaussian windows are also valid in this case., The plot shows that the conclusions made for the Gaussian windows are also valid in this case.
 The shape and size of the three kernels are the same around the diagonal., The shape and size of the three kernels are the same around the diagonal.
 For us reason the results shown for the temperature kernel that the tophat window has larger long range correlations whereas, For this reason the results shown for the temperature kernel that the tophat window has larger long range correlations whereas
"where k is a unit vector in the direction of the incoming light ray. x,,=x,—X,. aud ρω=πρωι.","where ${\bf k}$ is a unit vector in the direction of the incoming light ray, ${\bf x}_{ra} = {\bf x}_r - {\bf x}_a$ , and $r_{ra} = |
{\bf x}_{ra}|$."
 HE the ray passes by the body a minimum distance d that is small compared to Peg (hen The one-way delay amounts to 70 microseconds for a rav thal grazes the Sun and 10 nanoseconds for a rav (hal grazes Jupiter.," If the ray passes by the body a minimum distance $d$ that is small compared to $r_{ra}$, then The one-way delay amounts to 70 microseconds for a ray that grazes the Sun and 10 nanoseconds for a ray that grazes Jupiter."
 In addition to tests of the time delay bv the sun (Reasenbereetal.1979).. the (me delay has also been studied in a number of binary pulsar svslenis (see lor example. Stairsοἱal. (1998))).," In addition to tests of the time delay by the sun \citep{reasenberg}, the time delay has also been studied in a number of binary pulsar systems (see for example, \citet{stairs}) )."
 Advances in precision timekeeping and in VLBI have motivated the study of the first relativistic corrections. of order efe. to the basic Shapiro Formula.," Advances in precision timekeeping and in VLBI have motivated the study of the first relativistic corrections, of order $v/c$, to the basic Shapiro formula."
 These corrections would be relevant lor signals passing near moving bodies. such as bodies in binary pulsar svstenis. or planets such as Jupiter.," These corrections would be relevant for signals passing near moving bodies, such as bodies in binary pulsar systems, or planets such as Jupiter."
 In a series of papers. Ixopeikin and colleagues have analvzed these correction effects in detail (see IxXopeikinandSchaler(1999) and references therein).," In a series of papers, Kopeikin and colleagues have analyzed these correction effects in detail (see \citet{KopSch99} and references therein)."
" They lind that. to first order in 0ο. where ce, is the velocity of body a. the corrected expression takes the form where where all «quantities are to be evaluated at (he same moment of (ime. sav. the Gime of reception of the ray."," They find that, to first order in $v_a/c$, where $v_a$ is the velocity of body $a$, the corrected expression takes the form where where all quantities are to be evaluated at the same moment of time, say, the time of reception of the ray."
 For a light rav passing close to Jupiter. these corrections are small. of orderpicoseconcds or less. but may be detectable with the latest VLBI techniques 2002).," For a light ray passing close to Jupiter, these corrections are small, of orderpicoseconds or less, but may be detectable with the latest VLBI techniques \citep{KopFom02}."
 Recently. however Nopeikin has argued that. because of the motion of a body such as Jupiter during the passage of the light rav. the fact that the gravitational interaction is nol instantaneous should have an effect on the (ime delay (Ixopeikin 2001).," Recently, however Kopeikin has argued that, because of the motion of a body such as Jupiter during the passage of the light ray, the fact that the gravitational interaction is not instantaneous should have an effect on the time delay \citep{Kop01}."
". To study this phenomenon. he allowed the speed of gravity to be ¢,. where e,zc: this would modify the retardation of the gravitational fields used to caleulate the time delay."," To study this phenomenon, he allowed the speed of gravity to be $c_g$, where $c_g \ne c$; this would modify the retardation of the gravitational fields used to calculate the time delay."
 He argued that Eq. (3)), He argued that Eq. \ref{eq2}) )
" would be modified by replacing cbv e, in the prefactor 1—Kk:v4/c in Eq. (3))."," would be modified by replacing $c$by $c_g$ in the prefactor $1- {\bf k} \cdot {\bf v_a}/c$ in Eq.\ref{eq2}) ),"
 and in the velocity-dependent term in Eq. (4)) (Ixopeikin 2002).. IXopeikin, and in the velocity-dependent term in Eq. \ref{eq3}) ) \citep{Kop02}. .
anclFomalont(2002) , \citet{KopFom02} 
"However, these authors excluded ffrom their work because the only available ddataset at that time suffered from serious pile-up effects because of a bright binary outburst in the field-of-view (FoV).","However, these authors excluded from their work because the only available dataset at that time suffered from serious pile-up effects because of a bright binary outburst in the field-of-view (FoV)."
 In this paper we analyzed data from a newer observation where such an event did not occur., In this paper we analyzed data from a newer observation where such an event did not occur.
" For the X-ray analysis we used the CIAO software version 4.1, supported by tools from the FTOOLS package and XSPEC version 12.5.0 for spectral modeling (?).."," For the X-ray analysis we used the CIAO software version 4.1, supported by tools from the FTOOLS package and XSPEC version 12.5.0 for spectral modeling \citep{1996ASPC..101...17A}."
" The data were reprocessed with the latest position and energy calibration (CTI correction, v4.1.3) using bad pixel files generated byacis_run_hotpix."," The data were reprocessed with the latest position and energy calibration (CTI correction, v4.1.3) using bad pixel files generated by."
". The good-time-interval (GTI) file supplied by the standard processing, which was used by H06, screens out a ~4.0 ks interval of strong background flaring at the end of the observation."," The good-time-interval (GTI) file supplied by the standard processing, which was used by H06, screens out a $\sim$ 4.0 ks interval of strong background flaring at the end of the observation."
" To remove an additional time period of 4.3 ks with a slightly increased background level, we used the light curve in the 0.5—7.0 keV energy band after the core region of the cluster and additional bright sources were removed from the data."," To remove an additional time period of 4.3 ks with a slightly increased background level, we used the light curve in the 0.5–7.0 keV energy band after the core region of the cluster and additional bright sources were removed from the data."
 A screening threshold of 1.0 cts/s yielded a net exposure of 31.0 ks., A screening threshold of 1.0 cts/s yielded a net exposure of 31.0 ks.
 We chose these stricter criteria with respect to H06 because understanding the background is crucial for analyzing faint extended sources., We chose these stricter criteria with respect to H06 because understanding the background is crucial for analyzing faint extended sources.
" To detect and remove point-like X-ray sources from the event-list, we ran on the GTI-screened dataset in three energy bands (0.5--2.0 keV, 2.0--7.0 keV and 0.5--7.0 keV)."," To detect and remove point-like X-ray sources from the event-list, we ran on the GTI-screened dataset in three energy bands (0.5–2.0 keV, 2.0–7.0 keV and 0.5–7.0 keV)."
 H06 used for the detection within ry and for outer regions., H06 used for the detection within $_{\rm h}$ and for outer regions.
" In this paper we only analyzed areas outside rg, so results should be comparable."," In this paper we only analyzed areas outside $_{\rm h}$, so results should be comparable."
 We estimated a point-source detection limit of »2x107P? in the 0.5-7.0 keV band., We estimated a point-source detection limit of $\sim$ in the 0.5–7.0 keV band.
" For the most part our results are compatible with the sources listed by H06, Table 2."," For the most part our results are compatible with the sources listed by H06, Table 2."
" However, the shorter exposure time compared to the analysis of H06 led to a higher point-source detection threshold."," However, the shorter exposure time compared to the analysis of H06 led to a higher point-source detection threshold."
 Therefore we did not detect the faintest seven sources from H06 that we introduced manually into our source list., Therefore we did not detect the faintest seven sources from H06 that we introduced manually into our source list.
 Sources were removed from the dataset using the 2σ radius of the point spread function., Sources were removed from the dataset using the $\sigma$ radius of the point spread function.
" Additionally, all events within ry were disregarded."," Additionally, all events within $_{\rm h}$ were disregarded."
" To measure the level of diffuse X-ray emission around5, we extracted spectra from eight concentric annular regions centered on the cluster core with radii from 1.1’ to 3.9” (Fig. 1))."," To measure the level of diffuse X-ray emission around, we extracted spectra from eight concentric annular regions centered on the cluster core with radii from 1.1' to 3.9' (Fig. \ref{fig-map}) )."
 Each ring has a width of 0.4’., Each ring has a width of 0.4'.
 We chose rings with equal width over rings with constant area to have comparable statistical quality in the spectra since the surface brightness decreases with distance from the GC., We chose rings with equal width over rings with constant area to have comparable statistical quality in the spectra since the surface brightness decreases with distance from the GC.
" For the spectral analysis, we chose the 1—7 keV energy band."," For the spectral analysis, we chose the 1–7 keV energy band."
 Widening the band in either direction lead to lower signal-to-noise ratios., Widening the band in either direction lead to lower signal-to-noise ratios.
 At lower energies an increased contribution to the signal from soft thermal Galactic diffuse emission is expected., At lower energies an increased contribution to the signal from soft thermal Galactic diffuse emission is expected.
 At energies above 7—8 keV the charged particle induced background component increases significantly for instruments onboardChandra., At energies above 7--8 keV the charged particle induced background component increases significantly for instruments onboard.
 The mean effective area and energy response for each spectrum was calculated by weighting the contribution from each pixel by its flux using a detector map in the same energy band., The mean effective area and energy response for each spectrum was calculated by weighting the contribution from each pixel by its flux using a detector map in the same energy band.
" To subtract the particle induced non-X-ray background (NXB), we used a background dataset provided by the calibration database, where the detector was operated in stowed position."," To subtract the particle induced non-X-ray background (NXB), we used a background dataset provided by the calibration database, where the detector was operated in stowed position."
 The background spectrum for each ring was extracted from the respective region in this background dataset., The background spectrum for each ring was extracted from the respective region in this background dataset.
" To account for the time dependence ofthe NXB, we scaled the background by the ratio of the source and background count rates in the 9-12 keV energy band for each spectrum (asdescribedby?).."," To account for the time dependence of the NXB, we scaled the background by the ratio of the source and background count rates in the 9–12 keV energy band for each spectrum \citep[as described by][]{2003ApJ...583...70M}."
" To produce an image of diffuse X-ray emission above the particle background from the direction of5, we extracted counts in the 1—7 keV energy band and refilled the excluded source regions and the region inside ry with using the photon distributions from rings around the excluded areas."," To produce an image of diffuse X-ray emission above the particle background from the direction of, we extracted counts in the 1–7 keV energy band and refilled the excluded source regions and the region inside $_{\rm h}$ with using the photon distributions from rings around the excluded areas."
 We subtracted the particle background using the respective image from the stowed dataset after correction for the different exposures., We subtracted the particle background using the respective image from the stowed dataset after correction for the different exposures.
 The resulting image was corrected for relative exposure and adaptively smoothed withasmooth., The resulting image was corrected for relative exposure and adaptively smoothed with.
. We required a minimum significance of 3c for the kernel size of the smoothing algorithm., We required a minimum significance of $\sigma$ for the kernel size of the smoothing algorithm.
" The resulting smoothing radii were a few arcminutes, so that no details smaller than that scale can be seen in the smoothed image."," The resulting smoothing radii were a few arcminutes, so that no details smaller than that scale can be seen in the smoothed image."
 Figure 1 shows the resulting image together with all extraction regions that we used in this work., Figure \ref{fig-map} shows the resulting image together with all extraction regions that we used in this work.
" Even though a significant contribution from thermal Galactic diffuse emission is expected, the spectra from the single rings were fit well enough by an absorbed power- model for a preliminary flux estimate."," Even though a significant contribution from thermal Galactic diffuse emission is expected, the spectra from the single rings were fit well enough by an absorbed power-law model for a preliminary flux estimate."
 The resulting fit, The resulting fit
"reaches the surface aud the interior becomes isothermal. T=const. The temperature deviation between pole aud equator is now mainky caused bv the smaller surface eravity ο at the equator. since Z5Xgl! for fixed internal eniperature,","reaches the surface and the interior becomes isothermal, $\tilde T={\rm
const.}$ The temperature deviation between pole and equator is now mainly caused by the smaller surface gravity $g_{\rm s}$ at the equator, since $T_{\rm s} \propto g_{\rm s}^{1/4}$ for fixed internal temperature."
 Whereas the temperature deviation is still Hel in the case of nearly Kepler rotation (~31 or the model with O=O50; (~| about 10 wr. the photon surface raciation dominates he cooliug.," Whereas the temperature deviation is still high in the case of nearly Kepler rotation $\sim 31$ for the model with $\Omega=0.5\,\Omega_{\rm K}$ $\sim 4$ about $10^5$ yr, the photon surface radiation dominates the cooling."
 The temperature distribution tends oa new equilibriuu with dZ()/df=coust.. on a timescale of ~Q0 vr.," The temperature distribution tends to a new equilibrium with $\df T_{\rm m}(\theta)/\df t={\rm const.}$, on a timescale of $\sim
10^7$ yr."
 TU) chotes the temperature at the inner soundary of the photosphere at ο=101ecm ° Since he heat capacity is only weakly teniperature depenudoeut or T€10? K iu the outer crust. the surface temperature ends to an isothermal state. whereas the tenmiperature in the outer crust varies with the surface eravitv.," $T_{\rm m}(\theta)$ denotes the temperature at the inner boundary of the photosphere at $e=10^{10}\gccm$ Since the heat capacity is only weakly temperature dependent for $T\lesssim 10^9$ K in the outer crust, the surface temperature tends to an isothermal state, whereas the temperature in the outer crust varies with the surface gravity."
 This behaviour is accompanied by the breakdown of the scaling Toxgl! of he surface tempcrature with surface eravitv for sinall surface temperatures., This behaviour is accompanied by the breakdown of the scaling $T_{\rm s}\propto g_{\rm s}^{1/4}$ of the surface temperature with surface gravity for small surface temperatures.
 However. as oue can see by colmparing. the thin. dashed curve. which. assumes T;Xgs1 over the whole temperature range. with the thick curve iu Fie. 2..," However, as one can see by comparing the thin dashed curve, which assumes $T_{\rm
s}\propto g_{\rm s}^{1/4}$ over the whole temperature range, with the thick curve in Fig. \ref{fig:deviation},"
 this is only a sinall effect and cannot explain the tendency of the surface temperature fraction to unity., this is only a small effect and cannot explain the tendency of the surface temperature fraction to unity.
 Besides these effects on the angular dependency of the temperature. rotation las also a uct effect on cooling in he intermediate epoch.," Besides these effects on the angular dependency of the temperature, rotation has also a net effect on cooling in the intermediate epoch."
 This effect is caused o» the reduction of the neutrine luminosity. which sensitively depends on the central density.," This effect is caused by the reduction of the neutrino luminosity, which sensitively depends on the central density."
 Ao further effect of rotation on cooling of neutron stars is the enethenimg of the thermal ciffusion time by several imndredo vears., A further effect of rotation on cooling of neutron stars is the lengthening of the thermal diffusion time by several hundred years.
 Additionally the drop of the surface cluperature is stucother iu the case of rotation (see also AM:irallesetal. 1993)). since the cooling wave reaches the volar region earlier than the equator.," Additionally the drop of the surface temperature is smoother in the case of rotation (see also \cite{Miralles93}) ), since the cooling wave reaches the polar region earlier than the equator."
 During the cooling wave is reaching the different surface regions. the fraction ΤοΤσ falls below unity (s. Fig. 2)).," During the cooling wave is reaching the different surface regions, the fraction $T_{\rm s}^{\rm p}/T_{\rm s}^{\rm eq}$ falls below unity (s. Fig. \ref{fig:deviation}) )."
 Iu this letter. we have studied the effect of non-spherical ecolnctry on the cooling of neutron stars.," In this letter, we have studied the effect of non-spherical geometry on the cooling of neutron stars."
 Our general finding is that rapid rotation plavs a significant role iu the thermal evolution., Our general finding is that rapid rotation plays a significant role in the thermal evolution.
 This role is particularly iurportaut in the carly epoch. wheu the stars interior ids not vot isothermal.," This role is particularly important in the early epoch, when the star's interior is not yet isothermal."
 It is precisely this epoch. when even isolated pulsars müeht rotate very rapidly.," It is precisely this epoch, when even isolated pulsars might rotate very rapidly."
 The augular (pendent radial and transverse heat flow cause azimuthal temperature evacdicuts in the interior of the star and thus also at the surface., The angular dependent radial and transverse heat flow cause azimuthal temperature gradients in the interior of the star and thus also at the surface.
 The polar surface temperature is bv up to temperature., The polar surface temperature is by up to temperature.
The simulation of this non-isothermal epoch,The simulation of this non-isothermal epoch
our IRAC coverage.,our IRAC coverage.
 The Masseyetal.(2006) data cover a 36x36' field of view. including our entire Spitzer coverage area.," The \citet{mas06} data cover a $\arcmin$$\times$ $\arcmin$ field of view, including our entire Spitzer coverage area."
 The magnitude offsets ancl color terms for sources will centroids malching those in the HST photometry were calculated. using least squares fitting., The magnitude offsets and color terms for sources with centroids matching those in the HST photometry were calculated using least squares fitting.
 The appropriate offsets were then applied to all the detected sources in the V aud I photometry., The appropriate offsets were then applied to all the detected sources in the V and I photometry.
" The optical and II photometric catalogs were combined bv matching point sources (hal have the same centroids within a tolerance of x1"".", The optical and IR photometric catalogs were combined by matching point sources that have the same centroids within a tolerance of $\pm$ $\arcsec$.
 Throughout this paper all magnitudes are stated with respect to a Lyr (Vega)., Throughout this paper all magnitudes are stated with respect to $\alpha$ Lyr (Vega).
 In 87? we examine (he properties of (he evolved stellar population in WLM., In \ref{photometry} we examine the properties of the evolved stellar population in WLM.
 Because these objects can have similar apparent magnitudes aud colors to Galactic late-tvpe dwarts. il is important to determine the extent (to which our data will be affected by contamination by Galactic foreground stars.," Because these objects can have similar apparent magnitudes and colors to Galactic late-type dwarfs, it is important to determine the extent to which our data will be affected by contamination by Galactic foreground stars."
 We estimated the number of foreground stars in our IR. data using the Milky Wav stellar population svuthesis model of Robinetal.(2003).., We estimated the number of foreground stars in our IR data using the Milky Way stellar population synthesis model of \citet{rob03}.
 We chose a field one square degree in size centered on the Galactic coordinates of WLM to provide robust statistics., We chose a field one square degree in size centered on the Galactic coordinates of WLM to provide robust statistics.
 This model provides magnitudes for modeled stars in L band. whose central wavelength is close to that of the 3.6 URAC band.," This model provides magnitudes for modeled stars in L band, whose central wavelength is close to that of the 3.6 IRAC band."
 From this model we expect only 9 foreground stars in (he area Irom which our IR. CMD was constructed with —13 « Ma; « —5., From this model we expect only 9 foreground stars in the area from which our IR CMD was constructed with $-$ 13 $<$ $_{3.6}$ $<$ $-$ 5.
 These are all expected to have [3.6]— 4.5] colors very near Zero., These are all expected to have $-$ [4.5] colors very near zero.
 WLM is a highl-inclined (; = ον disk galaxy. elongated almost exactly north-south.," WLM is a highly-inclined \citep[$\it{i}$ = $\degr$ disk galaxy, elongated almost exactly north-south."
 Hs overall appearance varies considerably from optical to IR wavelengths., Its overall appearance varies considerably from optical to IR wavelengths.
 Figure 2 shows the U (a). I (b). and contimuun-subtracted Ila (c) images of WLM.," Figure \ref{3color} shows the U (a), I (b), and continuum-subtracted $\alpha$ (c) images of WLM."
 In the © image (here is a prominent feature arcing to the north-west., In the U image there is a prominent feature arcing to the north-west.
 The rest ol the emission consists of four associations in the central and southern galaxy that are currently undergoing star formation. as is evident from the Ila emission.," The rest of the emission consists of four associations in the central and southern galaxy that are currently undergoing star formation, as is evident from the $\alpha$ emission."
 In the I image we see the galaxy morphology change from that of a well defined arc and distinct star forming regions (o a much smoother stellar distribution., In the I image we see the galaxy morphology change from that of a well defined arc and distinct star forming regions to a much smoother stellar distribution.
 The IIa. emission is confined to the central and southern parts of the galaxy. with no detected emission in (he northern are.," The $\alpha$ emission is confined to the central and southern parts of the galaxy, with no detected emission in the northern arc."
 There is a, There is a
redshift increasing f preserves (approximately) the number of galaxies predicted but the distribution favours more galaxies with a higher stellar mass and metallicity whilst preserving the trend which is a similar shape to the AMAZE calibration curve (equation 5)).,redshift increasing $\beta$ preserves (approximately) the number of galaxies predicted but the distribution favours more galaxies with a higher stellar mass and metallicity whilst preserving the trend which is a similar shape to the AMAZE calibration curve (equation \ref{eq:cal}) ).
 This follows from the fact that at constant redshift increasing f results in the term (14-2)? in equation 3 being larger and thus it acts in a similar manner to a., This follows from the fact that at constant redshift increasing $\beta$ results in the term $\left(1+z\right)^\beta$ in equation \ref{eq:SFR} being larger and thus it acts in a similar manner to $\alpha$.
 The same number of mergers are predicted so that the mass distribution is similar but not identical since the SFR does play a role in determining the mass of individual galaxies (?).., The same number of mergers are predicted so that the mass distribution is similar but not identical since the SFR does play a role in determining the mass of individual galaxies \citep{wei07}.
" As in the previous section a simple x? analysis would return lower results for increasing 6, whereas we believe that the values for 6 should not be higher than 1."," As in the previous section a simple $\chi^2$ analysis would return lower results for increasing $\beta$, whereas we believe that the values for $\beta$ should not be higher than 1."
 With a and f held constant at their fiducial values & was varied over the range 0.1€&<1.0., With $\alpha$ and $\beta$ held constant at their fiducial values $\varepsilon$ was varied over the range $0.1\le\varepsilon\le1.0$.
" Following the discussion in section 2.3,, this range is investigated in order to test the model however we do not use excessively large values in order to artificially fit relations hereafter."," Following the discussion in section \ref{sec:eps}, this range is investigated in order to test the model however we do not use excessively large values in order to artificially fit relations hereafter."
 The plots in Figs., The plots in Figs.
 5(a) and 5(b) show the mean mass and metallicity predicted in each of the six mass bins used by 7? at z=2.27 and z=3.54 respectively., \ref{fig:epsz2} and \ref{fig:epsz3} show the mean mass and metallicity predicted in each of the six mass bins used by \citet{erb06} at $z=2.27$ and $z=3.54$ respectively.
 Fig., Fig.
 5(a) shows that the effect of increasing epsilon at z—2.27 is to lower the average metallicity in each bin whilst preserving the overall shape of the relation., \ref{fig:epsz2} shows that the effect of increasing epsilon at $z=2.27$ is to lower the average metallicity in each bin whilst preserving the overall shape of the relation.
" At higher values of e, more gas is ejected from the galaxy thereby reducing the average metallicity in each bin."," At higher values of $\varepsilon$, more gas is ejected from the galaxy thereby reducing the average metallicity in each bin."
 Thus the effect of changing & is to alter the offset of the relation without altering the slope., Thus the effect of changing $\varepsilon$ is to alter the offset of the relation without altering the slope.
 This effect is comparable to the one predicted by ? with the difference that we have self consistent chemical evolution that includes the finite lifetimesa of both SNIa and SNII., This effect is comparable to the one predicted by \citet{findave08} with the difference that we have a self consistent chemical evolution that includes the finite lifetimes of both SNIa and SNII.
" At z=3.54, Fig."," At $z=3.54$, Fig."
" 5(b) shows that changing the value of ε has very little effect on the relation, especially in the low mass regime, and basically preserves the shape of the relation. ?,,"," \ref{fig:epsz3} shows that changing the value of $\varepsilon$ has very little effect on the relation, especially in the low mass regime, and basically preserves the shape of the relation. \citet{Mann},"
" whose sample of LBGs at z~3 (discussed in the introduction), have found that the effective yield (the amount of metals synthesised and retained within the ISM per unit stellar mass) decreases with increasing stellar mass for galaxies in their sample suggesting that galactic outflows cannot account for the shape of the mass-metallicity relation since their power is diminished in more massive galaxies and thus they cannot be responsible for the decreasing effective yields."," whose sample of LBGs at $z\sim3$ (discussed in the introduction), have found that the effective yield (the amount of metals synthesised and retained within the ISM per unit stellar mass) decreases with increasing stellar mass for galaxies in their sample suggesting that galactic outflows cannot account for the shape of the mass-metallicity relation since their power is diminished in more massive galaxies and thus they cannot be responsible for the decreasing effective yields."
" Using chemical evolution models for galaxies of varying morphological types ? have found that the relation arises naturally, regardless of the morphology, if the SSFR is larger in more massive galaxies and that galactic outflows are not needed to explain the relation."," Using chemical evolution models for galaxies of varying morphological types \citet{calura} have found that the relation arises naturally, regardless of the morphology, if the SSFR is larger in more massive galaxies and that galactic outflows are not needed to explain the relation."
" As noted in the introduction, none of the models that focus solely on different outflow processes only have been able to fit the observed relation at z—3.54 and, taken together, these plots imply that outflows are only important in determining the low redshift relation whereas at higher redshifts, another mechanism is responsible for generating this relation, which may explain this lack of predictive power at higher redshifts."," As noted in the introduction, none of the models that focus solely on different outflow processes only have been able to fit the observed relation at $z=3.54$ and, taken together, these plots imply that outflows are only important in determining the low redshift relation whereas at higher redshifts, another mechanism is responsible for generating this relation, which may explain this lack of predictive power at higher redshifts."
" Considering these recent results, the findings of this section imply that it is the SFR-mass relation that generates the observed mass-metallicity relation and determines the slope at high redshift with outflows being important only for the low redshift properties."," Considering these recent results, the findings of this section imply that it is the SFR-mass relation that generates the observed mass-metallicity relation and determines the slope at high redshift with outflows being important only for the low redshift properties."
peaks at lower frequeucies.,peaks at lower frequencies.
 However. it is also easy. to notice the infinence of the long-term periodicitics on short-term peaks in the graphs of the autocorrelation functions.," However, it is also easy to notice the influence of the long-term periodicities on short-term peaks in the graphs of the autocorrelation functions."
 This effect is observed for the time series of solar activity indexes which are limited by the Ll-vear cvele., This effect is observed for the time series of solar activity indexes which are limited by the 11-year cycle.
 To find statistically significant periodicities it is reasonable to use the autocorrelation fiction aud the power spectrum method with a high resolution., To find statistically significant periodicities it is reasonable to use the autocorrelation function and the power spectrum method with a high resolution.
 In the case of a stationary time series they eive simular results., In the case of a stationary time series they give similar results.
 Moreover. for a stationary time series with the mean zero the Fourier transform is equivalent to the cosine transform of an autocorrelation function (Andersou 1971).," Moreover, for a stationary time series with the mean zero the Fourier transform is equivalent to the cosine transform of an autocorrelation function \citep{and}."
. Thus. after a comparison of a periodogram with an appropriate autocorrelation function one cau detect peaks which axe in the eraph of the first function and do not exist iu the exaph of the second function.," Thus, after a comparison of a periodogram with an appropriate autocorrelation function one can detect peaks which are in the graph of the first function and do not exist in the graph of the second function."
 The reasous of their existence could be explained by the long-term periodicities aud the echo-cffect., The reasons of their existence could be explained by the long-term periodicities and the echo-effect.
 Below method enables one to detect these effects., Below method enables one to detect these effects.
 The method of the diagnosis of au echo-effect iu the yower spectimm (DE) consists iun an analysis of a seriodograin of a even time series computed usus he BT method., The method of the diagnosis of an echo-effect in the power spectrum (DE) consists in an analysis of a periodogram of a given time series computed using the BT method.
 The BT method bases on the cosine ranstorm of the autocorrelation fiction which creates oeaks Which are in the periodograim. but not iu the autocorrelation fiction.," The BT method bases on the cosine transform of the autocorrelation function which creates peaks which are in the periodogram, but not in the autocorrelation function."
 The DE method is used for peaks which are computed w the FFT method (with high resolution) aud are statistically sieuificant., The DE method is used for peaks which are computed by the FFT method (with high resolution) and are statistically significant.
 The time series of suuspot activity indexes with the spacing interval one rotation or one mouth contain a \arkov-type persistence. which means a tendency for the successive values of the time series to remember their autecendent values.," The time series of sunspot activity indexes with the spacing interval one rotation or one month contain a Markov-type persistence, which means a tendency for the successive values of the time series to 'remember' their antecendent values."
 Thus. I use a confidence level basing ou the red noise of Mazkov (Mitchelletal.L966) for the choice of the sjeuificaut peaks of the periocdogram computed by the FFT inethod.," Thus, I use a confidence level basing on the 'red noise' of Markov \citep{mit} for the choice of the significant peaks of the periodogram computed by the FFT method."
 When a time series does not coutain the Markov-tvpe persistence I applv the Fisher test and the IKohluogorov-Suiiruov test at the significance level a=0.05 (Brockwell&Davis1991) to verity a statistically significance of periodoerans peaks., When a time series does not contain the Markov-type persistence I apply the Fisher test and the Kolmogorov-Smirnov test at the significance level $\alpha =0.05$ \citep{broc} to verify a statistically significance of periodograms peaks.
 The Fisher test checks the null hypothesis that the time series is white noise agains the alternative hvpothesis that the time series contains an added deterministic periodic component of muspecified frequency., The Fisher test checks the null hypothesis that the time series is white noise agains the alternative hypothesis that the time series contains an added deterministic periodic component of unspecified frequency.
 Because the Fisher test teuds to be severe in rejecting peaks as insignificant the Ikolinogorov-Suirnov test is also used., Because the Fisher test tends to be severe in rejecting peaks as insignificant the Kolmogorov-Smirnov test is also used.
mmagnelic fields (C43) and relativistic electrons (U44) can be obtained.,magnetic fields $U_{\rm B}$ ) and relativistic electrons $U_{\rm rel}$ ) can be obtained.
 Since p£22 where Faq8£f is the monochromatic optically thin svnchrotron {lux ancl Fy is the corresponding N-rav flux., Since $p\approx 2$ where $F_{\rm radio}\approx \nu F_{\nu}$ is the monochromatic optically thin synchrotron flux and $F_{\rm X}$ is the corresponding X-ray flux.
 As it turns out. the deduced value of B is such that the same electrons. roughly. are producing both the radio anc X-ray [hixes.," As it turns out, the deduced value of $B$ is such that the same electrons, roughly, are producing both the radio and X-ray fluxes."
 Hence. equation (17)) is not sensitive to the exact value of p.," Hence, equation \ref{eq:1.16a}) ) is not sensitive to the exact value of $p$."
 Assuming no intrinsic absorption and a power law spectrum with a spectral index consistent. with that in theradio give al /26 davs a monochromatic X-rav [lux Fyz2(3.020.5)x10.DPeresem?s |.," Assuming no intrinsic absorption and a power law spectrum with a spectral index consistent with that in theradio give at $t\approx 6$ days a monochromatic X-ray flux $F_{\rm X}\approx
(3.0\pm0.5)\times 10^{-15} ~\rm ergs ~cm^{-2}~s^{-1}$ ."
" At the same time. Fradio&2.0x10Peresem7sF and one finds from equation (17)) Il now μμo/. equations (16)) and (18)) lead to Up~6x107D!7: hence. Bο»0.3G and Up,3x10erescm7."," At the same time, $F_{\rm radio}\approx 2.0
\times 10^{-17} \rm ergs~cm^{-2}~s^{-1}$ and one finds from equation \ref{eq:1.16a}) ) If now $t_{\rm comp}\sim t$, equations \ref{eq:1.16}) ) and \ref{eq:1.17}) ) lead to $U_{\rm B}\sim 6\times 10^{-3} B^{1/2}$; hence, $B\sim 0.3~\rm 
G$ and $U_{\rm B} \sim 3\times 10^{-3}~\rm ergs ~cm^{-3}$."
" Together with the observed value Ly.jo221.6 at |&6 davs. (his implies cy,/e0.2."," Together with the observed value $L_{\rm bol,42}\approx 1.6$ at $t\approx 6$ days, this implies $v_{\rm sh}/c \sim 0.2$."
" With a supernova distance 7.3 Mpc. the observed X-ray flux corresponds (to a monochromatic X-ray luminosity Lyz1.9xLO""ergs |. from which the οποιον densitv in relativistic electrons is obtained as (cf."," With a supernova distance $7.3$ Mpc, the observed X-ray flux corresponds to a monochromatic X-ray luminosity $L_{\rm X}\approx 1.9\times 10^{37}\ergs$ , from which the energy density in relativistic electrons is obtained as (cf."
 eq. |1]]), eq. \ref{eq:1.1}] ])
 where. again. the logarithmic [actor is due to p&2.0.," where, again, the logarithmic factor is due to $p\approx 2.0$."
 Furthermore. equation (19)) assunies fegmp~/ so that. roughly. half of the injected energy emerges as X-ray flux and that. in turn. half of this is emitted through the forward shock (the other half being absorbed by the supernova ejecta).," Furthermore, equation \ref{eq:1.18}) ) assumes $t_{\rm comp}\sim t$ so that, roughly, half of the injected energy emerges as X-ray flux and that, in turn, half of this is emitted through the forward shock (the other half being absorbed by the supernova ejecta)."
 Hence. al /=6 davs. Ung~1xLO(3e/c)Παςui)evesemoE," Hence, at $t = 6$ days, $U_{\rm rel}\sim 1\times 10^{-4}(3v_{\rm sh}/c)^{-3}
\ln(\gamma_{\rm max}/\gamma_{\rm min}) ~\rm ergs ~cm^{-3}$."
 With the use of v4/cc0.2. this leads to C44~5x10.!InGSgas/nin)eresemoE," With the use of $v_{\rm sh}/c \sim 0.2$, this leads to $U_{\rm rel}\sim 5\times 10^{-4}
\ln(\gamma_{\rm max}/\gamma_{\rm min}) ~\rm ergs ~cm^{-3}$."
" since the unknown values of 54,; and 5,44, enter only logarithmically in C4. this shows that in the Compton cooling scenario for SN 2002ap. where the relativistic electrons cool on the external photons from the supernova itself, Cj~U,4. i.e. there is rough equipartition between the energy densities in magnetic fields ancl relativistic electrons."," Since the unknown values of $\gamma_{\rm max}$ and $\gamma_{\rm min}$ enter only logarithmically in $U_{\rm rel}$, this shows that in the Compton cooling scenario for SN 2002ap, where the relativistic electrons cool on the external photons from the supernova itself, $U_{\rm B}\sim U_{\rm rel}$, i.e., there is rough equipartition between the energy densities in magnetic fields and relativistic electrons."
 However. both of these energy densities are considerably smaller (han (hat in thermal particles ‘unless the mass loss rate of the progenitor is small.," However, both of these energy densities are considerably smaller than that in thermal particles $\epsilon_{\rm B} (\sim \epsilon_{\rm rel}) \sim
1\times 10^{-3} (\dot{M}_{-5}/v_{\rm w,3})^{-1}$ , unless the mass loss rate of the progenitor is small."
 Theactual values ol Uy and C4 deduced above are roughly the same asthose derived by BIXC using radio, Theactual values of $U_{\rm B}$ and $U_{\rm rel}$ deduced above are roughly the same asthose derived by BKC using radio
IDEMIUCNCT96-0034. “CERES”.,ERBFMRXCT96-0034 “CERES”.
 The VLA is operated bv the National Raclio Astronomy Observatory which is supported. by the National Science. Foundation operated under cooperative agreement by Associated Universities. Inc. ADB acknowledges the receipt ofa PPARC studentship.," The VLA is operated by the National Radio Astronomy Observatory which is supported by the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. ADB acknowledges the receipt of a PPARC studentship."
disc to the pressure exerted by the accreted material (Lóppez-Corredoira et al.,disc to the pressure exerted by the accreted material (L\'oppez-Corredoira et al.
 2008). together with Eqs. (2))," 2008), together with Eqs. \ref{poisson}) )"
 and (9)). we again get the same differential equation (4)) but with constants Ky-=daG-HEARSAXUQtyRadyS7 A>pe=ROGM.Τη .," and \ref{derazz}) ), we again get the same differential equation \ref{diffeq}) ) but with constants $K_1=\frac{4\pi G+F_z(R,\phi )C^2}{\langle v_z^2\rangle (R,\phi)}$, $K_2=\frac{GM_{gal}}{R^3\langle v_z^2\rangle (R,\phi )}$ ."
 The total acceleration is null at zo. where the pressure acceleration is compensated by other gravitational forces to keep the warp static.," The total acceleration is null at $z_0$, where the pressure acceleration is compensated by other gravitational forces to keep the warp static."
 With C~107—10? m-/kg. we get values of FAR.Φ)Ο- of the order of 4xG. that is. an external pressure as significant as the self-gravity.," With $C\sim 10^2-10^3$ $^2$ /kg, we get values of $F_z(R,\phi )C^2$ of the order of $4\pi G$, that is, an external pressure as significant as the self-gravity."
 And. most important. HWHM will depend on & because F- depends on @ and also on the maximum amplitude of the density. A. and the dispersion of velocities depends on ¢ through its dependence on the pressure at z=zo P(à): This last proportionality of the pressure stems from the external pressure acting like an extra self-gravity. and the pressure is proportional to the total acceleration.," And, most important, HWHM will depend on $\phi $ because $F_z$ depends on $\phi $ and also on the maximum amplitude of the density, $A$, and the dispersion of velocities depends on $\phi $ through its dependence on the pressure at $z=z_0$ $P(\phi )$: This last proportionality of the pressure stems from the external pressure acting like an extra self-gravity, and the pressure is proportional to the total acceleration."
 For a monoatomie gas. y=5/3 for adiabatic compression. and y=| for isothermal one.," For a monoatomic gas, $\gamma =5/3$ for adiabatic compression, and $\gamma =1$ for isothermal one."
 This applies in the distribution of pressure as a function of &: for the vertical dependence. we have already assumed that it is isothermal.," This applies in the distribution of pressure as a function of $\phi $; for the vertical dependence, we have already assumed that it is isothermal."
 In Fig. 2..," In Fig. \ref{Fig:hwhm},"
 we see how the HWHM is reduced for a given c when Κι Is increased. re. when F- is increased.," we see how the HWHM is reduced for a given $\sigma $ when $K_1$ is increased, i.e. when $F_z$ is increased."
" The parameters are R=25 kpe. Ma]=2xI0! Ma. and e,=10 km/s. Voskes (1999, Fig."," The parameters are $R=25$ kpc, $M_{gal}=2\times 10^{11}$ $_\odot $, and $\sigma _{v_z}=10$ km/s. Voskes (1999, Fig."
 15) and Levine et al. (, 15) and Levine et al. (
2006. Fig.,"2006, Fig."
 5) have shown that the scaleheight of the outer disc (R>20 kpe) is 2—3 times higher on average for 0<@«180° than for 180°«6360°., 5) have shown that the scaleheight of the outer disc $R>20$ kpc) is $2-3$ times higher on average for $0<\phi <180^\circ$ than for $180^\circ <\phi <360^\circ $.
 A more accurate estimation of the maximum of the scaleheight is derived by Kalberla et al. (, A more accurate estimation of the maximum of the scaleheight is derived by Kalberla et al. (
2007. Figs.,"2007, Figs."
 18. 19). who place it for 90°«@1107. while the minimum for 250°«@270°.," 18, 19), who place it for $90^\circ <\phi <110^\circ $, while the minimum for $250^\circ <\phi <270^\circ $."
 Within the LBB scenario. two possible directions are possible to produce the observed S-warp. and this is one of them: the wind coming from the direction of the northern warp. although this solution could not explain the asymmetry of the southern/northern warp as a sum of S+U warp.," Within the LBB scenario, two possible directions are possible to produce the observed S-warp, and this is one of them: the wind coming from the direction of the northern warp, although this solution could not explain the asymmetry of the southern/northern warp as a sum of S+U warp."
 A higher pressure is expected for the region around the southern warp and consequently a lower thickness therein., A higher pressure is expected for the region around the southern warp and consequently a lower thickness therein.
" Not only is the pressure lower at ó=90°. but the surface density «c is also lower than for the average value of c&(R) (Voskes 1999, Fig."," Not only is the pressure lower at $\phi \approx 
90^\circ $, but the surface density $\sigma $ is also lower than for the average value of $\sigma (R)$ (Voskes 1999, Fig."
 13: Levine et al., 13; Levine et al.
 2006. Fig.," 2006, Fig."
 1: Kalberla Dedes 2008. Fig.," 1; Kalberla Dedes 2008, Fig."
 9) and the amplitude of the density A (Kalberla Dedes 2008. Fig.," 9) and the amplitude of the density $A$ (Kalberla Dedes 2008, Fig."
 8)., 8).
 This is another fact explained by our model by means of Eqs. (7)), This is another fact explained by our model by means of Eqs. \ref{sigma}) )
 and (11)): the lower the pressure the lower the density., and \ref{amppres}) ): the lower the pressure the lower the density.
 If we take the values observed by Kalberla et al. (, If we take the values observed by Kalberla et al. (
"2007. 2008) at R=25 Kpe. excluding the bin of 90°«@110°. which is possibly an outlier in a special region: PS&x—24 3, ποMommy Tobin)4Ημ HAVTAPUda} 2.5.","2007, 2008) at $R=25$ Kpc, excluding the bin of $90^\circ <\phi <110^\circ $, which is possibly an outlier in a special region: $A(\phi _0)= 1.5\times 10^{-24}$ $^3$; $\frac{A(\phi _0+\pi)}
{A(\phi _0)}\approx 7$, $\frac{\sigma(\phi _0+\pi)}{\sigma(\phi _0)}\approx 
4$, $\frac{HWHM(\phi _0)}{HWHM(\phi _0+\pi)}=2.5$ ."
 This last number is not independent of the other three., This last number is not independent of the other three.
 The parameters that better fit these numbers are: y=1.22. y=-3[E. pQC7=1.8x107? m/kg. giving an azimuthal dependence of HWHM. A and σ as plotted in Fig. 3.," The parameters that better fit these numbers are: $\gamma =1.22$, $\theta _0=-31^\circ $, $\rho _bC^2=1.8\times 10^{-19}$ m/kg, giving an azimuthal dependence of HWHM, $A$ and $\sigma $ as plotted in Fig. \ref{Fig:azdep}."
 The average accretion at R=25 kpe is 5x107(io) ke/m-/Gyr. which is around 2 times the average surface density per Gyr: note. however. that only a small ratio of its linear momentum ( Co) is transmitted to the Galactic disc.," The average accretion at $R$ =25 kpc is $5\times 10^{-4}\left(\frac{\rho _b}{10^{-25}\ kg/m^3}\right)$ $^2$ /Gyr, which is around 2 times the average surface density per Gyr; note, however, that only a small ratio of its linear momentum $\sim C\sigma $ ) is transmitted to the Galactic disc."
 For the shape of the scaleheight as a function of & for R=25 kpe (or any other value of the galactocentric distance 20<Rx40 κρο). we observe in Fig.," For the shape of the scaleheight as a function of $\phi $ for $R=25$ kpc (or any other value of the galactocentric distance $20\le R\le 40$ kpc), we observe in Fig."
 19 of Kalberla et al. (, 19 of Kalberla et al. (
2007) a strongest dependence of the scaleheight with ὁ near the maximum: however. the variation in amplitude is very slight around the minimum of flaring.,"2007) a strongest dependence of the scaleheight with $\phi $ near the maximum; however, the variation in amplitude is very slight around the minimum of flaring."
 This is not observed in the shape of Fig. 3.., This is not observed in the shape of Fig. \ref{Fig:azdep}.
 Therefore. at present with our simple model. we cannot explain the exact azimuthal dependence.," Therefore, at present with our simple model, we cannot explain the exact azimuthal dependence."
 Possibly. our rough assumptions inthe present and LBB calculations need to be improved to get a more accurate result. assuming that Kalberla et al. (," Possibly, our rough assumptions inthe present and LBB calculations need to be improved to get a more accurate result, assuming that Kalberla et al. ("
2007. 2008) are also correct with their assumptions on the kinematics of the Galaxy.,"2007, 2008) are also correct with their assumptions on the kinematics of the Galaxy."
 Indeed. the Kalberla et al. (," Indeed, the Kalberla et al. ("
2007. 2008) density distributions are derived by assuming a non-axisymmetric dise. using epicyelic corrections in. the rotation curve. consistent with their hypothesis to explain,"2007, 2008) density distributions are derived by assuming a non-axisymmetric disc using epicyclic corrections in the rotation curve, consistent with their hypothesis to explain"
the blue wing of the line shows the ereater extension at f=LOvr.,the blue wing of the line shows the greater extension at $t = 10 \yr$.
" This is expected since the trailing edge of the relmnaut is not decelerated as rapidly as the leading οσο,", This is expected since the trailing edge of the remnant is not decelerated as rapidly as the leading edge.
 However. at #=5vr. the cold clouds exist xedominautlv ou the leading edee (the density and cooling rate are highest here) aud it is the red edge of the line profile that is the most extended.," However, at $t= 5 \yr$, the cold clouds exist predominantly on the leading edge (the density and cooling rate are highest here) and it is the red edge of the line profile that is the most extended."
 This behaviour is also secu when the remmant expands mto a flow with e=5000 or TOOOis., This behaviour is also seen when the remnant expands into a flow with $v = 5000$ or $7000 \kmps$.
 Hence as the remmant expands. the resulting line profile flips from a red to a bluc-slüft. (aud vice-versa for OS 157).," Hence as the remnant expands, the resulting line profile flips from a red to a blue-shift (and vice-versa for $\theta \ltsimm 45^{\circ}$ )."
 For cach of the 3 distinct. cases of aibient media investigated in Fie. 10.," For each of the 3 distinct cases of ambient medium investigated in Fig. \ref{fig:lp1},"
". the tfinc-averaged Lue profile displaved in the bottom row has a EWIIM z5000kus anda ""ull width at zero iuteusitv of zz6000SOOOnis L."," the time-averaged line profile displayed in the bottom row has a FWHM $\approx 4500-5000 \kmps$ , and a full width at zero intensity of $\approx 6000-8000 \kmps$ ."
 This range lies ahnost m the middle of the distribution of PWIIM. measures of the broad component of1v A1519 for radio-quiet sources (Suleutic 2000) )., This range lies almost in the middle of the distribution of FWHM measures of the broad component of $\lambda1549$ for radio-quiet sources (Sulentic \cite{SMD2000}) ).
 Tn Table 3 we list various statistics for the time-averaged line profiles shown iu Fie. ll.., In Table \ref{tab:line_params} we list various statistics for the time-averaged line profiles shown in Fig. \ref{fig:lp2}.
 Radio quiet sources show a scatter iu the asvnuuuetry values for the broad component of the C1vA1519. with AT=+£0.2. and (AT)=|(OL (Marziuu 1996)).," Radio quiet sources show a scatter in the asymmetry values for the broad component of the $\lambda 1549$, with ${\rm A.I.} = \pm 0.2$, and $\langle {\rm A.I.} \rangle \approx +0.04$ (Marziani \cite{M1996}) )."
 This lack of a stroug preference for red or blue asviunetres Is currently πο] iu need of confirmation. especially when one considers the systematic blueshift that A1519 shows in RO sources (see Suleutic 2000 and references therein).," This lack of a strong preference for red or blue asymmetries is currently much in need of confirmation, especially when one considers the systematic blueshift that $\lambda 1549$ shows in RQ sources (see Sulentic \cite{SMD2000} and references therein)."
 It is interesting to note that our models produce values for the asvunuetry index which are compatible with the observationally cetercmined values., It is interesting to note that our models produce values for the asymmetry index which are compatible with the observationally deteremined values.
 Observatious lave revealed ereat diversity in the profiles of particular broad enmüssion lines. such as ALD19. whereas variations iu otler ines. such as ALLO2. ave nich reduced m comparison (see.eg... Francis 1992:: Wills 19933).," Observations have revealed great diversity in the profiles of particular broad emission lines, such as $\lambda1549$, whereas variations in other lines, such as $\lambda1402$, are much reduced in comparison (see, Francis \cite{FHFC1992}; Wills \cite{W1993}) )."
 The variation in ALS19 from object to object can be explaince if a two-componcut structure is invoked - a broad “base” which is relatively constant between objects. aud a narrow “core” whose contribution o the overall line streugth is variable.," The variation in $\lambda1549$ from object to object can be explained if a two-component structure is invoked - a broad “base” which is relatively constant between objects, and a narrow “core” whose contribution to the overall line strength is variable."
" With this moctel. ines with large equivalent widths teud to be narrow (or ""euspyv) aud lave larec peak fluxes. as observatious require."," With this model, lines with large equivalent widths tend to be narrow (or “cuspy”) and have large peak fluxes, as observations require."
 Iu contrast. lines suchas AT102. which show far less variability frou object to object.| are essentisIv composed of a single broad component.," In contrast, lines such as $\lambda1402$, which show far less variability from object to object, are essentially composed of a single broad component."
" Iu such cases, the contribution from ai variable marrow core is sunall."," In such cases, the contribution from a variable narrow core is small."
 The observational iuterpretation of broad Lue profiles µας advanced ercatly Over the las decade. partly due to a better understanding of sample biases aud Ore careful consideration of contaminating lines and superposed narrow components.," The observational interpretation of broad line profiles has advanced greatly over the last decade, partly due to a better understanding of sample biases and more careful consideration of contaminating lines and superposed narrow components."
 Sometimes an obvious inflection demonstrates a superposed narrow compoucut., Sometimes an obvious inflection demonstrates a superposed narrow component.
 Alternatively. if a line has a rounded top. oue can infer that the narrow component is largely abseut.," Alternatively, if a line has a rounded top, one can infer that the narrow component is largely absent."
" Tndections also support the interpretation that the bro lues are formed in several kinematically audor ecolmetiically distine chutting regions. as docs the frequeut ""pmndsniate[um in profile Wines (Romano al.1996))."," Inflections also support the interpretation that the broad lines are formed in several kinematically and/or geometrically distinct emitting regions, as does the frequent “mismatch” in profile wings (Romano \cite{RZCS1996}) )."
 One possibility is that the variable narrow component forms ou the outer edge of the BELR (this Is sonuetinies referred o as an “intermediate line region}. with the broad component formed at “αλλ: radii within the BELR.," One possibility is that the variable narrow component forms on the outer edge of the BELR (this is sometimes referred to as an “intermediate line region”), with the broad component formed at smaller radii within the BELR."
 Variations are then most likely explained as a changing covering factor Gf optically thick) or volue, Variations are then most likely explained as a changing covering factor (if optically thick) or volume
For typical pulsar parameters. sy100. &~1 (Libschmann Arons 2001). this radius satisfies the condition (9) therefore. MIID. description of the wave is justified.,"For typical pulsar parameters, $\gamma_0\sim 100$ , $\kappa\sim
1-10^3$ (Hibschmann Arons 2001), this radius satisfies the condition (9) therefore MHD description of the wave is justified."
 For the typical parameters. this radius. exceeds he upper limit on the termination shock radius (10) for all »ulsars with the exception of the millisecond ones.," For the typical parameters, this radius exceeds the upper limit on the termination shock radius (10) for all pulsars with the exception of the millisecond ones."
" However here is strong evidence to suggest that the multiplicity xuwameter in the Crab pulsar significantly. exceeds the vpical one and may be as high as 5~10"" (Shklovsky 1970: Rees Gunn. 1974).", However there is strong evidence to suggest that the multiplicity parameter in the Crab pulsar significantly exceeds the typical one and may be as high as $\kappa\sim 10^6$ (Shklovsky 1970; Rees Gunn 1974).
 Extra pairs may. be produced ogether with the observed. gamma. radiation in the upper magnetosphere (Cheng. Ho Ituderman 1986: Lvubarskii 1996).," Extra pairs may be produced together with the observed gamma radiation in the upper magnetosphere (Cheng, Ho Ruderman 1986; Lyubarskii 1996)."
 At such a plasma density. the multiple shocks arise »xXore the How. reaches the termination shock (observed in he Crab at ~1021 em from the pulsar).," At such a plasma density, the multiple shocks arise before the flow reaches the termination shock (observed in the Crab at $\sim
10^{17}$ cm from the pulsar)."
 So formation of the shocks in the PAIS waves may occur both in the free pulsar wind within the termination shock and in the pulsar wind nebula bevond the termination shock., So formation of the shocks in the FMS waves may occur both in the free pulsar wind within the termination shock and in the pulsar wind nebula beyond the termination shock.
 After the multiple shocks arise. the wave energy. clissipates.," After the multiple shocks arise, the wave energy dissipates."
 'l'his occurs at the nonlinear scale. (11). which now may change because the released energy. heats the plasma flow.," This occurs at the nonlinear scale (11), which now may change because the released energy heats the plasma flow."
 One can consider evolution of the How parameters in the course of the wave decay applying the conservation laws to the system., One can consider evolution of the flow parameters in the course of the wave decay applying the conservation laws to the system.
 Let us separate the average I[uxes of conserving values into the wave and the [ow parts., Let us separate the average fluxes of conserving values into the wave and the flow parts.
 Such a separation may be performed in general terms for small amplitude waves (see Appendix 2)., Such a separation may be performed in general terms for small amplitude waves (see Appendix 2).
 The average plasma density. 2. and velocity. 0. (and the corresponding Lorentz factor 5) are defined such that the wave does not contribute to the matter Ilux (in Appendix 2 the averaged. quantities are marked. by tilde: here we work only with averaged quantities and tilde is omitted).," The average plasma density, $n$, and velocity, $v$, (and the corresponding Lorentz factor $\gamma$ ) are defined such that the wave does not contribute to the matter flux (in Appendix 2 the averaged quantities are marked by tilde; here we work only with averaged quantities and tilde is omitted)."
 Therefore the continuity equation may be written as (the [low is considered as locally spherically svmimetric) where the subscript “O° is referred to the quantities at the shock formation radius (13).," Therefore the continuity equation may be written as (the flow is considered as locally spherically symmetric) where the subscript ""0"" is referred to the quantities at the shock formation radius (13)."
 Phe energy equation may be written as where Q is the energy transferred from the wave to unit plasma volume per unit time., The energy equation may be written as where $Q$ is the energy transferred from the wave to unit plasma volume per unit time.
" The magnetic field strength may be expressed. via the density making use of the frozen Hux condition (see IE2q.CVX1.16)) The entropyp equationi describes the entropyp"" 8growth as a result of the wave decay: where dr=dits is the proper time.", The magnetic field strength may be expressed via the density making use of the frozen flux condition (see Eq.(A1.16)) The entropy equation describes the entropy growth as a result of the wave decay: where $d\tau=dR/\gamma$ is the proper time.
 We assume that just. after the shock formation. the plasma is heated. to relativistic temperatures. w=4nd.," We assume that just after the shock formation, the plasma is heated to relativistic temperatures, $w=4nT$."
" Because the wave propagates in the proper plasma frame with the velocity sy,αι O(l/e). its energy. and momenttun are equal. in this frame. to within l/e (see Appendix 2)."," Because the wave propagates in the proper plasma frame with the velocity $s_M=1-O(1/\sigma)$ , its energy and momentum are equal, in this frame, to within $1/\sigma$ (see Appendix 2)."
 Pherefore if the energy d= per unit mass is absorbed in the proper plasma frame. then the momentum dz per unit mass is also transferred. from the wave to the plasma.," Therefore if the energy $d\varepsilon$ per unit mass is absorbed in the proper plasma frame, then the momentum $d\varepsilon$ per unit mass is also transferred from the wave to the plasma."
 Then in the pulsar frame. the absorbed energy. is dI= 25dz.," Then in the pulsar frame, the absorbed energy is $dE=2\gamma d\varepsilon$ ."
 Taking into account that dVd is invariant. one can write the energy release rate as Substituting dz=dS. one writes the entropy equation in the form Let us now turn to the energv equation (15).," Taking into account that $dVdt$ is invariant, one can write the energy release rate as Substituting $d\varepsilon=TdS$, one writes the entropy equation in the form Let us now turn to the energy equation (15)."
 Making use of Eqs.(14. 16). one can see that the Povntine Lux (the second term in the brackets in the lefi-hanel side) is nearlyindependent. of # in theultrarelativistie case.," Making use of Eqs.(14, 16), one can see that the Poynting flux (the second term in the brackets in the left-hand side) is nearlyindependent of $R$ in theultrarelativistic case."
Expanding,Expanding
Here we present the second section of the 6 cem survey for the outer Galaxy covering the region 129°<€2307.,Here we present the second section of the $\lambda$ cm survey for the outer Galaxy covering the region $129\degr \leq \ell \leq 230\degr$.
 In Sect., In Sect.
 2 observation and data processing details for this survey area are discussed., 2 observation and data processing details for this survey area are discussed.
 In Sect., In Sect.
 3 we present the total power and polarization maps (Sect., 3 we present the total power and polarization maps (Sect.
 3.1). followed by a brief discussion on the survey's potential to study and detect SNRs (Sect.," 3.1), followed by a brief discussion on the survey's potential to study and detect SNRs (Sect."
 3.2) and regions (Sect., 3.2) and regions (Sect.
 3.3). while in Sect.," 3.3), while in Sect."
 3.4 we focus on newly detected and prominent Faraday Sereens in the interstellar medium., 3.4 we focus on newly detected and prominent Faraday Screens in the interstellar medium.
 Results are summarized in Sect., Results are summarized in Sect.
 4., 4.
 The Sino-German /06 cem polarization survey of the Galactic plane was carried out with the 25-m Urumai telescope., The Sino-German $\lambda$ cm polarization survey of the Galactic plane was carried out with the 25-m Urumqi telescope.
 The 16 cem system is a copy of an Effelsberg single-channel receiver and has a system temperature of about 22 K when pointing to the zenith at clear sky., The $\lambda$ cm system is a copy of an Effelsberg single-channel receiver and has a system temperature of about 22 K when pointing to the zenith at clear sky.
 The half-power beam width (HPBW) of the telescope was 975., The half-power beam width (HPBW) of the telescope was $9\farcm5$.
 Survey observations were exclusively made during clear sky at night time., Survey observations were exclusively made during clear sky at night time.
" In “broad band mode"" the centre frequency was 4800 MHz with a bandwidth 600 MHz. while in ""narrow band mode"" the centre frequency was 4963 MHz with a bandwidth of 295 MHz. """," In “broad band mode” the centre frequency was 4800 MHz with a bandwidth 600 MHz, while in “narrow band mode” the centre frequency was 4963 MHz with a bandwidth of 295 MHz. “"
"Narrow band mode"" was used to avoid contamination by the geostationary Indian INSAT-satellites located at four positions in southern and western directions. which emit strong signals below frequencies of about 4810 MHz.","Narrow band mode” was used to avoid contamination by the geostationary Indian INSAT-satellites located at four positions in southern and western directions, which emit strong signals below frequencies of about 4810 MHz."
" Thus all observations close to the satellite positions were made in. “narrow band mode"". while the ""broad band mode"" was used for all other directions."," Thus all observations close to the satellite positions were made in “narrow band mode”, while the “broad band mode” was used for all other directions."
 The survey region was limited at £=230°. because regions with larger { have to be observed at very low elevations. so that the increased ground radiation can not be subtracted with sufficient accuracy.," The survey region was limited at $\ell = 230\degr$, because regions with larger $\ell$ have to be observed at very low elevations, so that the increased ground radiation can not be subtracted with sufficient accuracy."
 Measurements of the ground radiation properties of the Urumai 25-m telescope at 16 cem were already reported by ?.., Measurements of the ground radiation properties of the Urumqi 25-m telescope at $\lambda$ cm were already reported by \citet{WC07}.
 The main observational survey parameters are listed in Table |., The main observational survey parameters are listed in Table 1.
 Survey maps were observed in two orthogonal directions: along £ and 5., Survey maps were observed in two orthogonal directions: along $\ell$ and $b$ .
 The combined survey consists of à large number of individual 87x226 or 8&2x226 maps observed in € direction and of 2°x107 or 222x10° maps observed along 5.," The combined survey consists of a large number of individual $\degr \times 2\fdg6$ or $8\fdg2 \times 2\fdg6$ maps observed in $\ell$ direction and of $2\degr \times 10\degr$ or $2\fdg2 \times 
10\degr$ maps observed along $b$."
 Total intensity. Stokes 7. and the linearly polarized components. Stokes U and Q. were measured simultaneously.," Total intensity, Stokes $I$, and the linearly polarized components, Stokes $U$ and $Q$, were measured simultaneously."
 3C286 and 3C295 served as the main polarized and un-polarized calibration sources. while 3C48. 3C138 served as secondary polarized calibrators.," 3C286 and 3C295 served as the main polarized and un-polarized calibration sources, while 3C48, 3C138 served as secondary polarized calibrators."
 Calibration sources were always observed before starting a survey map in the same observation mode., Calibration sources were always observed before starting a survey map in the same observation mode.
 We increased the original scanning speed of the observations from 225/min to 4°/min after tests performed in 2006., We increased the original scanning speed of the observations from $2\fdg5$ /min to $4\degr$ /min after tests performed in 2006.
 The reason was to minimize the influence of system instabilities and also the contamination by changing ground radiation and low-level RFI., The reason was to minimize the influence of system instabilities and also the contamination by changing ground radiation and low-level RFI.
 To achieve the same S/N ratio we thus mapped the same region more often., To achieve the same S/N ratio we thus mapped the same region more often.
 The sensitivity is not unique throughout the entire survey section. since the coverages of( and b maps differ.," The sensitivity is not unique throughout the entire survey section, since the coverages of $\ell$ and $b$ maps differ."
" The effective integration time of each map pixel is at least 2.6 see for total intensity and 1.9 see for polarization. where the integration time of map pixel observed in ""narrow band mode"" were divided by a factor of 2 to be comparable with that of ""broad band mode""."," The effective integration time of each map pixel is at least 2.6 sec for total intensity and 1.9 sec for polarization, where the integration time of map pixel observed in “narrow band mode” were divided by a factor of 2 to be comparable with that of “broad band mode”."
 The effective integration time of each sub-region in Stokes 7. U and Q for 600 MHz bandwidth is shown in Fig. 1..," The effective integration time of each sub-region in Stokes $I$, $U$ and $Q$ for 600 MHz bandwidth is shown in Fig. \ref{integration_time}."
 Data reduction was done following the standard procedures. which were already described in Paper I. Subsequently the following steps are applied: For total intensity 7 maps. a baseline was appropriately fitted for each sub-scan. which implies that large-scale diffuse emission exceeding the length of the sub-scans of 8° or 10° ts not preserved.," Data reduction was done following the standard procedures, which were already described in Paper I. Subsequently the following steps are applied: For total intensity $I$ maps, a baseline was appropriately fitted for each sub-scan, which implies that large-scale diffuse emission exceeding the length of the sub-scans of $8\degr$ or $10\degr$ is not preserved."
 In addition. spiky pixels were removed. distorted sub-scan sections or entire sub-scans were set to dummy values or. for smooth regions. replaced by interpolation of the two neighboring sub-scans.," In addition, spiky pixels were removed, distorted sub-scan sections or entire sub-scans were set to dummy values or, for smooth regions, replaced by interpolation of the two neighboring sub-scans."
 The baselines of the Stokes LU and Q maps were usually not fitted in order to preserve extended polarized emission. unless strong ground radiation at low elevations clearly contaminates the data.," The baselines of the Stokes $U$ and $Q$ maps were usually not fitted in order to preserve extended polarized emission, unless strong ground radiation at low elevations clearly contaminates the data."
" Baseline distortion effects along scanning direction were suppressed by the ""unsharp masking"" method (?)..", Baseline distortion effects along scanning direction were suppressed by the “unsharp masking” method \citep{Sofue79}.
 Spiky pixels and bad sub-scans were corrected in the same way as the / maps., Spiky pixels and bad sub-scans were corrected in the same way as the $I$ maps.
 We noted that afterwards many maps show residual distortions visible as inclined stripes. which seem to be caused by RFI-sources of unknown origin.," We noted that afterwards many maps show residual distortions visible as inclined stripes, which seem to be caused by RFI-sources of unknown origin."
" They were well removed by rotating the map that the stripes align to rows or columns of the map to apply the ""unsharp masking"" procedure and then rotating the map back.", They were well removed by rotating the map that the stripes align to rows or columns of the map to apply the “unsharp masking” procedure and then rotating the map back.
 Total intensity and. polarization calibration was based on 3C286 (see Table 1)., Total intensity and polarization calibration was based on 3C286 (see Table 1).
" Instrumental polarization from strong sourceswas removed by the ""REBEAM"" procedure of the NOD?2 package as described in Paper I. This method reduces the ringlike instrumental response in polarized intensity P7 by", Instrumental polarization from strong sourceswas removed by the “REBEAM” procedure of the NOD2 package as described in Paper I. This method reduces the ringlike instrumental response in polarized intensity $PI$ by
dark halo out to at least LOOkpe.),dark halo out to at least $100\kpc$ .)
 A thick clisk distribution cannot produce an optical depth toward the LMC of more than about 1.5107., A thick disk distribution cannot produce an optical depth toward the LMC of more than about $1.5 \times 10^{-7}$.
 However. it can explain (wihin the experimental uncertainties) all or a significant fraction of the current optical depth estimates.," However, it can explain (within the experimental uncertainties) all or a significant fraction of the current optical depth estimates."
 As more events are detected. it lla be »ossible to distinguish between very thick disk and halo lens distributions.," As more events are detected, it may be possible to distinguish between very thick disk and halo lens distributions."
 The most promising avenue dor such a discriminan is the observation of parallax events., The most promising avenue for such a discriminant is the observation of parallax events.
 Decause (isκ lenses vvould be both closer and on average slower than halOo lenses we expect a higher rate of such evens [or a 15.κ populaion., Because disk lenses would be both closer and on average slower than halo lenses we expect a higher rate of such events for a disk population.
" Although the survey experiment ligM curve asurements can only mareinally cliscriminate yetween isk and halo distributions for reasonable numbers o ""events. a modest ex»nditure of telescope time to obtain one percent photometry on all the Magellanic cloud. events should. be capable of making the distinction very. clearly."," Although the survey experiment light curve measurements can only marginally discriminate between disk and halo distributions for reasonable numbers of events, a modest expenditure of telescope time to obtain one percent photometry on all the Magellanic cloud events should be capable of making the distinction very clearly."
The successful launch of the Gamma-Ray Space Telescope has led us into. a new era of high-energy⋅ astrophysics.,The successful launch of the Gamma-Ray Space Telescope has led us into a new era of high-energy astrophysics.
" The sensitivity of the Large Area Telescope (LAT) on the spacecraft is much higher than that of its⋅ predecessor, the Energetic⋅ Gamma-Ray Experiment⋅ Telescope on the Gamma-Ray Observatory."," The sensitivity of the Large Area Telescope (LAT) on the spacecraft is much higher than that of its predecessor, the Energetic Gamma-Ray Experiment Telescope on the Gamma-Ray Observatory."
 This enables very efficient. searches for y—ray pulsars., This enables very efficient searches for $\gamma-$ ray pulsars.
" Shortly after its⋅ launch, it⋅ has already expanded the population⋅ of γ--ταγ pulsars considerably. (Abdo et al."," Shortly after its launch, it has already expanded the population of $\gamma-$ ray pulsars considerably (Abdo et al."
" 2009a,b,c)."," 2009a,b,c)."
 Abdo et al. (, Abdo et al. (
"2009a) has further reported the detections⋅ of 16 pulsars with. high. significance⋅⋅ in⋅ a blind⋅ search, including⋅ J","2009a) has further reported the detections of 16 pulsars with high significance in a blind search, including ."
2021+4026.. The y—ray detection of first]rsty reported inthe Tight source list witwith » wwassignal-to-noise ratio >in100 the(Abdo FERMIet al., The $\gamma-$ ray detection of was firstly reported in the bright source list with a signal-to-noise ratio $>10\sigma$ (Abdo et al.
 brigh20094)., 2009d).
 The nominal H— ay miti Chef His &'ocated at d edgeof fththe supernova remnant GT8.2424are. (Abdo et al., The nominal $\gamma-$ ray position of is located at the edge of the supernova remnant G78.2+2.1 (Abdo et al.
 2009d;the Green 2009)., 2009d; Green 2009).
" Using the first 6 months of the LAT data, the timingS ephemeridescp of the Ppulsar were recently reported by Abdo et al. ("," Using the first 6 months of the LAT data, the timing ephemerides of the pulsar were recently reported by Abdo et al. ("
2009c).,2009c).
 It has a spin. period. of P.=-—1265 ms and a spin-down⋅ rate of P5=5.48x10—14 ss., It has a spin period of $P=265$ ms and a spin-down rate of $\dot{P}=5.48\times10^{-14}$ s $^{-1}$.
 These spin. parameters imply. a ⋅⋅ ∁≹↥∂↕∂∁↿⊐⊖∐≲↿⊐↕∁∂⊆⊖⊙≸⊤≤∁↕∼⊤⊤↕∢≦⊔∁≯∂≲∐↕≸∂∁⊖↕∐∂⊆↕↥⊖↿⊐↕∁↕∶↓⊖↕⊂↥⊙≸ ⋅ 12 ⋅ ∼∠↨⋗⋖↕⊖∁↾∂↕↥⊂↥∂⊟↕⊃∐↥−⊂↥⊙∇∇↕↥↕∐∐∐∐⊙⊟↕↿⊐≦∕⊙≸⊡∼↕⊖⊖↕⊆⊟∙⋅⋅ ⋅35 1," These spin parameters imply a characteristic age of $\tau_{\rm sd}\sim77$ kyr, a surface magnetic field of $\sim4\times10^{12}$ G and a spin-down luminosity of $\dot{E}\sim10^{35}$ erg $^{-1}$."
" Apart from studying the pulsar properties in the y—ray regime, the effort in searching for counterparts in other wavelengths is also very important."," Apart from studying the pulsar properties in the $\gamma-$ ray regime, the effort in searching for counterparts in other wavelengths is also very important."
" The broadbandemission properties of pulsars, from radio to y—ray, are crucial"," The broadbandemission properties of pulsars, from radio to $\gamma-$ ray, are crucial"
by are also excited. with maximum amplitude around 0.2 for both.,"$b_4$ are also excited, with maximum amplitude around 0.2 for both."
" One could. now obviously do endless more runs. for example to discover how large the initial bj must be to cause b» to oscillate. or whether a sullicienthy large initial 5» could cause b, to oscillate instead."," One could now obviously do endless more runs, for example to discover how large the initial $b_1$ must be to cause $b_2$ to oscillate, or whether a sufficiently large initial $b_2$ could cause $b_1$ to oscillate instead."
 However. given that there is no observational or theoretical reason to prefer anv of these linear combinations over any other. that seems rather pointless.," However, given that there is no observational or theoretical reason to prefer any of these linear combinations over any other, that seems rather pointless."
 Lt is already. evident in figure 11 that Llall cirift allects mixed. parity solutions in much the same way as pure parity solutions. and that is probably all we can expect to learn [from these runs.," It is already evident in figure 11 that Hall drift affects mixed parity solutions in much the same way as pure parity solutions, and that is probably all we can expect to learn from these runs."
 The results presented. here suggest. that Hall drift. could indeed have a significant. inlluence on the evolution of a neutron stars magnetic field., The results presented here suggest that Hall drift could indeed have a significant influence on the evolution of a neutron star's magnetic field.
 Particularly i£ the internal toroidal field is as strong or stronger than the poloidal field. Llall drift can excite some of the higher harmonics to amplitudes comparable to the original. mode.," Particularly if the internal toroidal field is as strong or stronger than the poloidal field, Hall drift can excite some of the higher harmonics to amplitudes comparable to the original mode."
 However. as substantial as some of these higher harmonics are. this still does not appear to be enough to cause the original mode o decay significantly Faster than it otherwise would have.," However, as substantial as some of these higher harmonics are, this still does not appear to be enough to cause the original mode to decay significantly faster than it otherwise would have."
 This conclusion must be qualified though by our inability to increase Z?g indelinitely., This conclusion must be qualified though by our inability to increase $R_B$ indefinitely.
 Indeed. the very feature that causec he code to fal bevond certain limits. namely the fact tha he spectra got [latter ancl Hatter. also indicates that this ransfer of energy to the higher harmonics gets more ane more ellicient as Z?gp is Increased.," Indeed, the very feature that caused the code to fail beyond certain limits, namely the fact that the spectra got flatter and flatter, also indicates that this transfer of energy to the higher harmonics gets more and more efficient as $R_B$ is increased."
 Lt is conceivable. therefore. hat the solutions for. sav. 2e=1000 would show a very rapid decay of the original mode.," It is conceivable, therefore, that the solutions for, say, $R_B=1000$ would show a very rapid decay of the original mode."
 Also. the cascade may wel ος very different in 3D than in 2D. just like ordinary. [Lui urbulence is very. different.," Also, the cascade may well be very different in 3D than in 2D, just like ordinary fluid turbulence is very different."
 Extending our model here from 2D to 3D is possible in principle. but will obviously. require considerable computational resources.," Extending our model here from 2D to 3D is possible in principle, but will obviously require considerable computational resources."
 Finally. even i£ it should turn out that Lall cirift alone. in either 2D or 3D. simply does not generate a sulliciently strong cascade at any value of Ag. the combination of Hall απ and stratification may still cdo so.," Finally, even if it should turn out that Hall drift alone, in either 2D or 3D, simply does not generate a sufficiently strong cascade at any value of $R_B$, the combination of Hall drift and stratification may still do so."
 We've already. noted in the introduction that the electron number density » in equation (2) is in [act not constant. but rather varies by several orders of magnitude over the depth of the crust.," We've already noted in the introduction that the electron number density $n$ in equation (2) is in fact not constant, but rather varies by several orders of magnitude over the depth of the crust."
 Vainshtein et ((2000) show that if one includes this ellect. one can obtain a very rapid decay of a toroida Ποιά at least.," Vainshtein et (2000) show that if one includes this effect, one can obtain a very rapid decay of a toroidal field at least."
 In their. highly. idealizec analytical mocle it was not possible to inelude poloidal fields though (ve recall from section 2.4 that one can indeed: consistently consider only toroidal fields)., In their highly idealized analytical model it was not possible to include poloidal fields though (we recall from section 2.4 that one can indeed consistently consider only toroidal fields).
 In contrast. our numerica model here already includes poloidal fields. ancl including radial variations in 7 is possible too.," In contrast, our numerical model here already includes poloidal fields, and including radial variations in $n$ is possible too."
 Calculations are therefore currently uncer wav to see if this Vainshtein e rresult applies to poloidal fields as well., Calculations are therefore currently under way to see if this Vainshtein et result applies to poloidal fields as well.
 Rs stay in Germany was mace possible by a Research Fellowship of the Alexander von Humboldt Foundation., RH's stay in Germany was made possible by a Research Fellowship of the Alexander von Humboldt Foundation.
Hierarchical assembly is the estaplished leading theory for the evolution of structure in the universe from the viewpoint of Cold Dark Matter (CDM) theory.,Hierarchical assembly is the established leading theory for the evolution of structure in the universe from the viewpoint of Cold Dark Matter (CDM) theory.
 This sates that larger structures form from the merging of smaller structures., This states that larger structures form from the merging of smaller structures.
 Thus CDM halos grow in size. with the largest structures fortning latest in the history of the universe.," Thus CDM halos grow in size, with the largest structures forming latest in the history of the universe."
 Galaxies are often though to form principally in line with halo mergers., Galaxies are often thought to form principally in line with halo mergers.
 If they do. it is likely that merging of smaller galaxies to create more massive ones is the major factor in the evolution of galaxies over cosmic time.," If they do, it is likely that merging of smaller galaxies to create more massive ones is the major factor in the evolution of galaxies over cosmic time."
 Alternatives to a merger history of massive galaxies include rapid collapse mechanisms. whereby galaxies form over very short time-scales in the early universe. and then do not significantly merge during the rest of their lifetime.," Alternatives to a merger history of massive galaxies include rapid collapse mechanisms, whereby galaxies form over very short time-scales in the early universe, and then do not significantly merge during the rest of their lifetime."
" The aim of this paper is to address the question: what mechanism drives galaxy evolution with regards to the most massive (AZ,21077 AZ.) galaxies in the universe?", The aim of this paper is to address the question: what mechanism drives galaxy evolution with regards to the most massive $M_{*}>10^{11}M_{\odot}$ ) galaxies in the universe?
 We can observationally test this by calculating the merger fraction of massive galaxies at different redshifts., We can observationally test this by calculating the merger fraction of massive galaxies at different redshifts.
 Previous work by Conselice et al. (, Previous work by Conselice et al. (
2007) explores this problem for similar mass galaxies out to z  14. using morphological techniques.,"2007) explores this problem for similar mass galaxies out to z $\sim$ 1.4, using morphological techniques."
 We extend this work using a close-pair method to z ~ 3. using data from the GOODS NICMOS Survey.," We extend this work using a close-pair method to z $\sim$ 3, using data from the GOODS NICMOS Survey."
 There are several different ways to locate merging galaxies which roughly relate to the stage of the merger., There are several different ways to locate merging galaxies which roughly relate to the stage of the merger.
 The most direct method is to look at morphological disturbances in galaxies. e.g. Conselice et al. (," The most direct method is to look at morphological disturbances in galaxies, e.g. Conselice et al. ("
2003. 2006 and 2008).,"2003, 2006 and 2008)."
 In this approach one selects galaxies with asymmetries. or distortions in their morphologies.," In this approach one selects galaxies with asymmetries, or distortions in their morphologies,"
solar to twice-solar iictallicity using the Salpeter IME and with around haltsolar to solar metallicityv using the Ixeuuicut TIF.,solar to twice-solar metallicity using the \citeauthor{Salp55} IMF and with around half-solar to solar metallicity using the \citeauthor{Kenn83} IMF.
 With j23. the best-fit models lave a decrease in SER prior to +=1 (2o limit of FOAL D).," With $\beta\ga3$, the best-fit models have a decrease in SFR prior to $z=1$ $\sigma$ limit of FOM B)."
 Figure 9. shows best-fit reelous 1 La versus r owith >=2 for Cl.," Figure \ref{fig:alpha-versus-r-2}
 shows best-fit regions in $\alpha$ versus $r$ with $\beta=2$ for $\cal
C$ 1."
 Hore. the best-fit models are consistent with a plateau in SFR prior to:=1 Or n nireinal increase or decrease.," Here, the best-fit models are consistent with a plateau in SFR prior to $z=1$ or a marginal increase or decrease."
 Au upper limit would hea1.5Γ (20). if ο)>2 as is suggested by most direct methods of tracing the cosiuc SER (Iloeeoo2002).," An upper limit would be $\alpha<1.5$ $\sigma$ ), if $\beta>2$ as is suggested by most direct methods of tracing the cosmic SFR \citep{Hogg02}."
. All spectroscopic iuformation is subject to the effect of aperture bias (c.g...seethediscussionofIKochauek.Pale.&Faleo 2002).," All spectroscopic information is subject to the effect of aperture bias \citep*[e.g., see the discussion of][]{KPF02}."
. In particular. the apertire nav be too small to euconipass a represeutaive fraction of a galaxies liebt.," In particular, the aperture may be too small to encompass a representative fraction of a galaxies light."
 This effect will obviously be greater at lower τοςματ., This effect will obviously be greater at lower redshift.
" Figure 10 shows the increase in the effective size of a 2dF 2""1-fiber aperture with recshift.", Figure \ref{fig:sel-ap} shows the increase in the effective size of a 2dF $2''\!.1$ -fiber aperture with redshift.
 At >=0.1 this is 27h Lkkpe which is comparabο to a tvvical large disk scale leugth of 3h. tkkpe (deJong&Lacey2000)., At $z=0.1$ this is $h^{-1}$ kpc which is comparable to a typical large disk scale length of $h^{-1}$ kpc \citep{JL00}.
". In practice. the effective aperture is more lice cklh bkkpe (276) as the median observatioji seeing was about 1""n"," In practice, the effective aperture is more like $h^{-1}$ kpc $2''\!.6$ ) as the median observation seeing was about $1''\!.5$."
 Thus it is reasonable that the effect of aperture bias will be much sualler for +>0.1 as we are sampling more than half the total Bieht of galaxies., Thus it is reasonable that the effect of aperture bias will be much smaller for $z>0.1$ as we are sampling more than half the total light of galaxies.
 The daa allow for a further test of this because of ifs own incrnal sccing variations., The data allow for a further test of this because of its own internal seeing variations.
 Spectra taken in bad atinosplieric ποσο are a rough proxy for spectra taken through a arecr aperture. as the object is s1ieared out over a disk abott the size of the seeing disk.," Spectra taken in bad atmospheric seeing are a rough proxy for spectra taken through a larger aperture, as the object is smeared out over a disk about the size of the seeing disk."
 As a test of this. we chose a sauple of about 1500 ealaxics 0.15) that had measured spectra taken both in relatively good seeing 17.5) aud in poor κοπο pU3MI ) such that the ciffereuce iu representaIve aperture was greater than a linear factor of 1.5 for eaci ealaxy with Q>3 for both spectra.," As a test of this, we chose a sample of about 1500 galaxies $z<0.15$ ) that had measured spectra taken both in relatively good seeing $\la1''\!.5$ ) and in poor seeing $\ga3''$ ) such that the difference in representative aperture was greater than a linear factor of 1.5 for each galaxy with $Q\ge3$ for both spectra."
 With this siuuple. we measured the chanec in equivalent width (EW) of à number of lines between the larger represeutative aperture and the smaller aperture.," With this sample, we measured the change in equivalent width (EW) of a number of lines between the larger representative aperture and the smaller aperture."
 Iu some iudividual spectra. the skv sultraction was inadequate for accurate EW measurenrent.," In some individual spectra, the sky subtraction was inadequate for accurate EW measurement."
 Therefore. 1ieasuremoents for which the reduced COUNTS ποὉ too low or coutamunated bv skv-enission lines were excluded.," Therefore, measurements for which the reduced counts were too low or contaminated by sky-emission lines were excluded."
 For further robustuess. the ealaxies were divided iuto subsamples of ten as a function of redshift iu the median chanee iu EW of each group was determiued.," For further robustness, the galaxies were divided into subsamples of ten as a function of redshift and the median change in EW of each group was determined."
 The results are shown iu Fieure 11.., The results are shown in Figure \ref{fig:change-ew-lines}.
 Similar results were obtained ifa weighted mean (ov counts) was used rather than a median., Similar results were obtained if a weighted mean (by counts) was used rather than a median.
 There isevidence for any aperture effect i terms of the average change of EW for the galaxies iu this salple eiven a difference in representativo aperture with a linear factor in the range 1.52.3., There is for any aperture effect in terms of the average change of EW for the galaxies in this sample given a difference in representative aperture with a linear factor in the range 1.5–2.3.
" We cannot rule out a stuall aperture effect ou the measured cosnüc spectra particularly for i«1,05 where the test sample is s1121l.", We cannot rule out a small aperture effect on the measured cosmic spectra particularly for $z<0.05$ where the test sample is small.
 Tow do the measured cosmic spectra vary as a function of redshift due to selection effects; aperture effects; if any. and evolution?," How do the measured cosmic spectra vary as a function of redshift due to selection effects, aperture effects, if any, and evolution?"
 Fieure 12. plots the equivalent width ofOL. IIo. CIT.OWLMel audNal as a fuuction of redshift for a complee sample aud for a volunue-Innited sample.," Figure \ref{fig:EW-lines} plots the equivalent width of, $\delta$, CH, and as a function of redshift for a complete sample and for a volume-limited sample."
 These measurements were made ou luminosity-weighted. average spectra determined from redshift bius of mostly 0.005 in extent.," These measurements were made on luminosity-weighted, averaged spectra determined from redshift bins of mostly 0.005 in extent."
 To interpret this figure. we first consider the volune-Inited sample (diamonds).," To interpret this figure, we first consider the volume-limited sample (diamonds)."
 (e.g..Felgelsouetal.1993:Casanova1995:GagnéFlaecomio2000).. 2000) Flaccomio Flacconuio(2002) a—cw ," \citep[e.g.,][]{fei93,cas95,gag95a,fla00a}, \citep[HRC, ][]{mur00} \citet[][ hereafter Paper~I]{papI} \citet{fla02} $\alpha-\omega$ "
"assumption that the neutralino is a Majorana particle, ie. it is its own anti-particle.","assumption that the neutralino is a Majorana particle, i.e. it is its own anti-particle."
" The coefficient f, has different values in the literature.", The coefficient $f_\chi$ has different values in the literature.
" Its former factor, which quantifies the energy that remains inside the star, could be underestimated in our work: following the recent simulations of ?,, the energy loss could be as low as of the total energy from DM annihilations."," Its former factor, which quantifies the energy that remains inside the star, could be underestimated in our work: following the recent simulations of \citet{art-Scottetal2009}, the energy loss could be as low as of the total energy from DM annihilations."
" Our choice, more conservative, is in agreement with other authors (???).."," Our choice, more conservative, is in agreement with other authors \citep{art-FreeseBSG08, art-Ioccoetal2008, art-YoonIoccoAkiyama2008}."
" In our simulations we assumed the annihilation cross section to be «σαυ>=3-10:36 cm? s~!,following a value that is fixed by the relic density through the approximation: QA?z3-107?"" em?s1/ <oqv> (e.g., ???))."," In our simulations we assumed the annihilation cross section to be $<\sigma_a v >=3\cdot10^{-26}\;$ $^3\;$ $^{-1}$, a value that is fixed by the relic density through the following approximation: $\Omega_{\chi}h^2\approx3\cdot10^{-27}\;$ $^3\;$ $^{-1}/<\sigma_a v >$ (e.g., \citet{art-ScherrerTurner1986, art-Srednickietal1988, rev-BertoneHS2005}) )."
 We have implemented the effects of the annihilation of DM particles in our stellar evolution code and followed the evolution of low-mass stars since their proto-star phase and throughout the main sequence phase., We have implemented the effects of the annihilation of DM particles in our stellar evolution code and followed the evolution of low-mass stars since their proto-star phase and throughout the main sequence phase.
 These stars may experience dramatic changes on their evolution depending upon the amount of DM the star accumulates in its interior., These stars may experience dramatic changes on their evolution depending upon the amount of DM the star accumulates in its interior.
" The accretion of DM depends mainly on the particle halo density and also on the WIMP-nucleus spin-dependent scatteringp,, cross section cy,sp."," The accretion of DM depends mainly on the particle halo density $\rho_{\chi}$, and also on the WIMP-nucleus spin-dependent scattering cross section $\sigma_{\chi,SD}$."
" The more accretion of DM particles happens inside the core of the star, the more energy is produced by WIMP pair annihilation."," The more accretion of DM particles happens inside the core of the star, the more energy is produced by WIMP pair annihilation."
 The existence of this new source of energy leads to significantly different scenarios of stellar evolution., The existence of this new source of energy leads to significantly different scenarios of stellar evolution.
" Figure 1 shows the contribution of the different energy sources to the total energy generation rate, &p, of a star of 1 "," Figure \ref{f_3reg} shows the contribution of the different energy sources to the total energy generation rate, $\displaystyle{\varepsilon_T}$, of a star of 1 $_{\odot}$."
"The evolution of the star depends on the balance betweenMo. DM energy rate, £y, the thermonuclear energy rate produced by the pp chain, Epp, the thermonuclear energy rate produced by the CNO cycle, €ono, and the gravitational energy rate, £grav, produced by the gravitational contraction of the star."," The evolution of the star depends on the balance between DM energy rate, $\displaystyle{\varepsilon}_\chi$ , the thermonuclear energy rate produced by the $pp$ chain, $\varepsilon_{pp}$, the thermonuclear energy rate produced by the $CNO$ cycle, $\varepsilon_{CNO}$, and the gravitational energy rate, $\varepsilon_{grav}$, produced by the gravitational contraction of the star."
" Depending upon the amount of DM present in the host halo, we found that stars can experiment quite different evolution paths, which we classified in three distinct cases: Weak, Intermediate and Strong case scenarios."," Depending upon the amount of DM present in the host halo, we found that stars can experiment quite different evolution paths, which we classified in three distinct cases: Weak, Intermediate and Strong case scenarios."
" Normal stars are self-gravitating systems that most of the time are experimenting a gravitational contraction, leading to an increase in the temperature inside their cores."," Normal stars are self-gravitating systems that most of the time are experimenting a gravitational contraction, leading to an increase in the temperature inside their cores."
" The gravitational collapse is stopped by an additional source of energy, such as thermonuclear energy produced by the pp chain or CNO cycle in stars on the main sequence phase."," The gravitational collapse is stopped by an additional source of energy, such as thermonuclear energy produced by the $pp$ chain or $CNO$ cycle in stars on the main sequence phase."
" Nevertheless, stars evolving in DM halos can experiment a quite different scenario of evolution."," Nevertheless, stars evolving in DM halos can experiment a quite different scenario of evolution."
" For stars evolving within halos with low DM density the energy from WIMPs’ annihilation is a complementaryp,, source to the thermonuclear energy (see Figure 1."," For stars evolving within halos with low DM density $\rho_\chi$, the energy from WIMPs' annihilation is a complementary source to the thermonuclear energy (see Figure \ref{f_3reg}."
".b), that slightly delays the gravitational collapse, slowing down the arrival of the Hydrogen burning phase."," .b), that slightly delays the gravitational collapse, slowing down the arrival of the Hydrogen burning phase."
"The equilibrium is reached at a lower central temperature than that of the classical evolution case, leading to a smaller rate of energy produced by thermonuclear reactions +€cwo will evolve in the weak scenario if their €p,thermonuclear (starsenergy accounts for more than of the total energy in the beginning of the MS).","The equilibrium is reached at a lower central temperature than that of the classical evolution case, leading to a smaller rate of energy produced by thermonuclear reactions $\varepsilon_{pp} + \varepsilon_{CNO}$ (stars will evolve in the weak scenario if their thermonuclear energy accounts for more than of the total energy in the beginning of the MS)."
" Therefore, the time that a star spends in the main sequence phase is enlarged respect to the classical evolution scenario (see Figure "," Therefore, the time that a star spends in the main sequence phase is enlarged respect to the classical evolution scenario (see Figure \ref{f_timeMS}) )."
"The more massive the star, the more DM will be necessary2)). to produce the same effects."," The more massive the star, the more DM will be necessary to produce the same effects."
" A star of 1Mo will stay in the MS for a time greater than the current age of the universe if it evolves in a DM halo of py=10? cm~® and Ox,SD=10735 cm?, while a star of Mo evolving in the same halo will not be affected."," A star of $_{\odot}$ will stay in the MS for a time greater than the current age of the universe if it evolves in a DM halo of $\rho_{\chi}= 10^{9}\;$ $\;$ $^{-3}$ and $\sigma_{\chi,SD}=10^{-38}\;$ $^{2}$, while a star of $\;$ $_{\odot}$ evolving in the same halo will not be affected."
" In the case of one solar mass stars, ? obtained the same extension in the main-sequence lifetime for almost identical DM densities on the host halo."," In the case of one solar mass stars, \citet{art-Scottetal2009} obtained the same extension in the main-sequence lifetime for almost identical DM densities on the host halo."
" On the other hand, for greater masses our results are more conservative, due to the lower WIMP capture rates obtained for M,>1 Mo."," On the other hand, for greater masses our results are more conservative, due to the lower WIMP capture rates obtained for $M_{\star}>1\;$ $_{\odot}$."
 This evolution scenario is qualitatively similar to that predicted for Pop III stars by ?.., This evolution scenario is qualitatively similar to that predicted for Pop III stars by \citet{art-Taosoetal2008}.
" To grasp the role of the metallicity, we computed models with metallicities from Z=0.0004 to Z=0.04 and found that the main differences in the stellar evolution are those already expected in the classical picture; stars with higher metallicities have lower thermonuclear energy production rates and, therefore, extendedmain sequence lifetimes (???).."," To grasp the role of the metallicity, we computed models with metallicities from Z=0.0004 to Z=0.04 and found that the main differences in the stellar evolution are those already expected in the classical picture; stars with higher metallicities have lower thermonuclear energy production rates and, therefore, extendedmain sequence lifetimes \citep{art-Schalleretal1992, art-Schaereretal1993, art-LejeuneShaerer2001}."
" Table 2 shows the energy rates and andεκ for stars with metallicities Z—0.0004,DM 0.001, £p,0.02, 0.04 that evolve in a halo with a"," Table \ref{tab_metall} shows the energy rates $\varepsilon_{pp}$ and $\varepsilon_{\chi}$ for stars with metallicities Z=0.0004, 0.001, 0.02, and 0.04 that evolve in a halo with a DM"
and hieh euergy optious require major changes in the accelerator infrastructure. such as a refurbished SPS (or even the LIC) at CERN. as well as bieecr storage riues.,"and high energy options require major changes in the accelerator infrastructure, such as a refurbished SPS (or even the LHC) at CERN, as well as bigger storage rings."
 To match the same oscillation frequencies. sucli scenarios uecd further locations for the far detector. such as the Caufrauc or the Cran Sasso Underground Laboratories.," To match the same oscillation frequencies, such scenarios need further locations for the far detector, such as the Canfranc or the Gran Sasso Underground Laboratories."
 The physics potential covers the third neutrino mixing angle. the CP violating phase. as well as the neutrino mass hierarchy.," The physics potential covers the third neutrino mixing angle, the $\cal{CP}$ violating phase, as well as the neutrino mass hierarchy."
 Some reduction of the degeneracy problems is also expected., Some reduction of the degeneracy problem is also expected.
 A specific feasibility sti vods still to be done iu order to determine e.g. the Ίο intensities (that drastically influence tje sensitivities) aud the storage ring characteristics., A specific feasibility study is still to be done in order to determine e.g. the ion intensities (that drastically influence the sensitivities) and the storage ring characteristics.
 Nonochromatic uettring beams produced by boosted ious decaving through elecroh capture are proposed in [30]., Monochromatic neutrino beams produced by boosted ions decaying through electron capture are proposed in \cite{ber05}.
 The baseline envisaged is the same as fex the original bea-beznn., The baseline envisaged is the same as for the original beta-beam.
" A comparison of νο»rj oscillations (ouly v, are available) at different neutrino euergies is necessary.", A comparison of $\nu_e \rightarrow \nu_{\mu}$ oscillations (only $\nu_e$ are available) at different neutrino energies is necessary.
 Such a configuration reeives the acceleration and storage of not fully stripped ions., Such a configuration requires the acceleration and storage of not fully stripped ions.
 The achievable ion rates need to be ceterminued., The achievable ion rates need to be determined.
 A heta-beam facility has a rich aud broad pliysies potential., A beta-beam facility has a rich and broad physics potential.
 The future aud ongoing feasibility studies as well as the curent physics investigation will furnish the necessary clements to assess the final CP violation discovery reach., The future and ongoing feasibility studies as well as the current physics investigation will furnish the necessary elements to assess the final CP violation discovery reach.
 Ou the other hand. the availability of low cnereyv beta-beams would opeu new research axis of interest for particle. nuclear aud core-collapse superuova physics.," On the other hand, the availability of low energy beta-beams would open new research axis of interest for particle, nuclear and core-collapse supernova physics."
 This option nüght require either a devoted storage ring or detector(s) at off-axis., This option might require either a devoted storage ring or detector(s) at off-axis.
Osservatorio Astronomico cdi Trieste. Via CG. B. Tiepolo 11. 31131 Trieste.,"Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste,"
covering the contaminating features and iteratively fills the background inside the masks by interpolating the background from the regions surrounding them.,covering the contaminating features and iteratively fills the background inside the masks by interpolating the background from the regions surrounding them.
 For each galaxy we generated one set of masks for all passbands (generally using the Rc image). ensuring that the analysis is restricted to the same portions of the images.," For each galaxy we generated one set of masks for all passbands (generally using the $R_{\rm \scriptstyle C}$ image), ensuring that the analysis is restricted to the same portions of the images."
 The cleaned frames were visually inspected to remove any remaining sources of contamination in all. passbands., The cleaned frames were visually inspected to remove any remaining sources of contamination in all passbands.
" Some of the defects — such as objects appearing with different brightnesses in the individual passbands (e.g.. too ""blueος), meteor or satellite trails. diffraction spikes. bleeding along columns. scattered light. ete. —"," Some of the defects – such as objects appearing with different brightnesses in the individual passbands (e.g., too “blue”/“red”), meteor or satellite trails, diffraction spikes, bleeding along columns, scattered light, etc. –"
 are unique for each passband/frame and demand individual approach., are unique for each passband/frame and demand individual approach.
 For instance. owing to a bright star in the field of 5564. ghost images of the telescope main mirror and bleeding along columns were produced.," For instance, owing to a bright star in the field of 564, ghost images of the telescope main mirror and bleeding along columns were produced."
 These defects were corrected with the help of a set of individual masks., These defects were corrected with the help of a set of individual masks.
 We applied this technique in cases of stellar object contamination. especially when superposed on galaxy regions with large gradients.," We applied this technique in cases of stellar object contamination, especially when superposed on galaxy regions with large gradients."
 The contaminating objects were cleaned out by aligning. sealing. and subtracting the frame PSF.," The contaminating objects were cleaned out by aligning, scaling, and subtracting the frame PSF."
 We replaced the contaminated region with the region that is symmetric with respect to the galaxy centre and free of contaminating features in case the contaminated region does not cover too large a part of the galaxy area and is far enough from the galaxy centre., We replaced the contaminated region with the region that is symmetric with respect to the galaxy centre and free of contaminating features in case the contaminated region does not cover too large a part of the galaxy area and is far enough from the galaxy centre.
 The galaxy in the two regions should be symmetric with respect to the galaxy centre., The galaxy in the two regions should be symmetric with respect to the galaxy centre.
"where 7, is the absorptlon Cross section at ο in units em-.",where $\sigma_{\nu}$ is the absorption cross section at $\nu$ in units $^2$.
 The absorbed Luminosity function at an observed wavelength vane redshift 2. SaTeale(2). can be caleulatect by integrating over the unabsorbed bolometric QLE. qur Phe convolution is identical owe want to consider the Iuminosity function in band. (6.05). except the change of variable. in: equation. (10)) becomes TogdoyLEEleypa=+L ," The absorbed luminosity function at an observed wavelength $\nu$ and redshift $z$, $\left.\frac{dn}{dlogL_{\nu}}\right|_{obs}(z)$, can be calculated by integrating over the unabsorbed bolometric QLF, $\frac{dn}{dlogL_{\nu}}$, The convolution is identical if we want to consider the luminosity function in band $(\nu_a,\nu_b)$ , except the change of variable in equation \ref{NH_distribution}) ) becomes $\frac{dlog_{10}N_H}{dlogL^{\prime}_{\rm band}} = \frac{1}{N_H
 <\sigma_{\nu}>}$."
"Llere «m,2 is the average absorption cross section in the band. weighted by the observed luminosity ο0,5NH The probability. distribution. of the absorbing hydrogen column density. given in equation (9)) will not be an adequate description when the luminosity is close to the »ealk Luminosity. as much of the gas is expected to be blown away by radiation pressure."," Here $<\sigma_{\nu}>$ is the average absorption cross section in the band, weighted by the observed luminosity $\nu
L_{\nu} e^{-\sigma_{\nu}N_H}$, The probability distribution of the absorbing hydrogen column density given in equation \ref{NH_dist}) ) will not be an adequate description when the luminosity is close to the peak luminosity, as much of the gas is expected to be blown away by radiation pressure."
 As discussed by ?/— the true column clensity distribution in the simulations is bi-moclal. with quasars in the last e-folding of growth having à much ower obscuring column density. distribution.," As discussed by \citet{hopkins2005b} the true column density distribution in the simulations is bi-modal, with quasars in the last e-folding of growth having a much lower obscuring column density distribution."
 This so called “blow-out” phase lasts approximately 10 per cent of the otal time the quasar spends accreting., This so called “blow-out” phase lasts approximately 10 per cent of the total time the quasar spends accreting.
 ? suggest. that his bi-modality can explain why optically selected. quasars are observed to have lower obscuring column densities [or xieghter quasars (e.g.2).. counter to the positive correlation tween L and Ny in equation (9)).," \citet{hopkins2005b} suggest that this bi-modality can explain why optically selected quasars are observed to have lower obscuring column densities for brighter quasars \citep[e.g.][]{ueda2003}, counter to the positive correlation between $L$ and $\bar{N}_H$ in equation \ref{NH_dist}) )."
 We have taken a simple approach to modelling such a owout. phase: we assume that a fraction fios=0.1. of quasars within a factor of e of their peak luminosity experience no intrinsic absorption., We have taken a simple approach to modelling such a blowout phase; we assume that a fraction $f_{\rm blowout} = 0.1$ of quasars within a factor of $e$ of their peak luminosity experience no intrinsic absorption.
" The resulting absorbed uminosity function is then larger than that. in equation (100) bv 20Aa termdor Wei""niLmn): Fasssuas where⇁ diLo ; . 204 -- n ↓≱∖↥∐∢≺≥∟↓∪⇂≱∖∪⊔↓∩≱∖∖∖↓↿↓↥⊳∖↓≻⊔↓∐≼⋅∙ ∏⊥⇖⋭⊽⊣ ⇂⇂↓↕↓↕↓↕⋖≱≻↕↿∙∖⇁∠∕∣↿↓⋯⇂↓⋯∖⇁⋖⋅↿∪⋯⇂∣⋯⇂∪⊔↓⋖⋅↿↓⋰⊔∼↓⇂⇂↓↥↓↕↓↥⋖≱≻↕↿∙∖⇁∖∖⋰↓↿↓↕⊲↓⊔ ce TNo their3r peak Luminosity.1Mv πανdnLeiL). increase"," The resulting absorbed luminosity function is then larger than that in equation \ref{abs_lf}) ) by a term $\frac{dn}{dlogL_{\nu}}(\frac{L}{L_{\rm peak}}> \frac{1}{e}) \times
f_{\rm blowout}$ , where $\frac{dn}{dlogL_{\nu}}(\frac{L}{L_{\rm
 peak}>} \frac{1}{e})$ is the QLF of sources with specific luminosity $L_{\nu}$ that have total bolometric luminosity within $e$ of their peak luminosity. $\frac{dn}{dlogL_{\nu}}(\frac{L}{L_{\rm
 peak}>\frac{1}{e}})$,"
sIneregse withd Lia. and approaches the original (without blow out phase) value of Gu [or large Livy.," increases with $L_{\rm bol}$, and approaches the original (without blow out phase) value of $\frac{dn}{dlogL_{\nu}}$ for large $L_{\rm bol}$."
" LPhis prescription for the blowout phaseTogL, essentially puts a lower limit on the ratio of the absorbed to unabsorbed luminosity function at high Iuminosities equal to fintewent", This prescription for the blowout phase essentially puts a lower limit on the ratio of the absorbed to unabsorbed luminosity function at high luminosities equal to $f_{\rm blowout}$.
 The parameters of the blow-out- phase allect the relative number of bright optical and N-ray luminous sources., The parameters of the blow-out phase affect the relative number of bright optical and X-ray luminous sources.
 In particular. if we didn't include a blow-out phase (ancl were therefore assuming that more of the bright optical sources are obseured) then we would. predict. more. X-ray bright sources.," In particular, if we didn't include a blow-out phase (and were therefore assuming that more of the bright optical sources are obscured) then we would predict more X-ray bright sources."
 However we find that the absorption in the soft X-ray band behaves similarly to that in the optical and therefore if we did not include the blow-out. phase it would be very dillicult to reproduce the space density of quasars that are bright in soft. X-ravs., However we find that the absorption in the soft X-ray band behaves similarly to that in the optical and therefore if we did not include the blow-out phase it would be very difficult to reproduce the space density of quasars that are bright in soft X-rays.
 We vary the parameters (£4.6o.Lyooaauin) in order to obtain an acceptable fit to the observed. Luminosity functions at rest-Erame 1450A. and in the soft and hard. X-ray. bancs.," We vary the parameters $(t_q, \epsilon_o, L_{\rm peak, min})$ in order to obtain an acceptable fit to the observed luminosity functions at rest-frame $1450$, and in the soft and hard X-ray bands."
" We determine the normalisation of our models (governed wf, and ἐν) by comparing to the observed optical QLE. as hese constraints span the broadest redshift range."," We determine the normalisation of our models (governed by $t_q$ and $\epsilon_o$ ) by comparing to the observed optical QLF, as these constraints span the broadest redshift range."
 Llowever. as we will discuss below. the optical data has little power to constraln Lyoadauin and constraints on this value come from ow-Iuminosity X-ray observations alone.," However, as we will discuss below, the optical data has little power to constrain $L_{\rm
peak,min}$ and constraints on this value come from low-luminosity X-ray observations alone."
" We find that assuming the luminosity independent adiing law in equation (7)). it is dillieult to accommocate values of a, much less than zero. due to the intrinsic steepness of the cosmological merger rate we are adopting or the quasar formation rate."," We find that assuming the luminosity independent fading law in equation \ref{constL_fading}) ), it is difficult to accommodate values of $\alpha_L$ much less than zero, due to the intrinsic steepness of the cosmological merger rate we are adopting for the quasar formation rate."
" However fora; =0.01. 5,=l4.I10' vears and ey=10.77 we recover a good fit to he optical QLE at 2—2.6 (see Figure 2)."," However for $\alpha_L = -0.01$, $t_q = 1.74
\times 10^{7}$ years and $\epsilon_0 = 10^{-5.05}$ we recover a good fit to the optical QLF at $z = 2 - 6$ (see Figure 2)."
" This value of ay corresponds to a light-curve for which the luminosity drops olf almost exponentially with time. we will therefore refer to his mocel as the “rapicl fading"" model."," This value of $\alpha_L$ corresponds to a light-curve for which the luminosity drops off almost exponentially with time, we will therefore refer to this model as the “rapid fading” model."
 The corresponding ight curve is compared to the ? light curve (vith some adjustment described below) in Figure 1., The corresponding light curve is compared to the \citet{hopkins2005b} light curve (with some adjustment described below) in Figure 1.
" ""Phe ? fading law. with appropriate εν. also provides a reasonable fit to the optical data at >—2/—6 as described by equation (5))."," The \citet{hopkins2005b} fading law, with appropriate $\epsilon_o$, also provides a reasonable fit to the optical data at $z = 2-6$ as described by equation \ref{hopkins_fading}) )."
 To out it on equal footing with what we have done for the fit with the rapid Facing law we allow the characteristic timo. fo. ovary.," To put it on equal footing with what we have done for the fit with the rapid fading law we allow the characteristic time, $t_9$, to vary."
 We find that the fit is improved when fo is increased ⋅ D. ⋡∙∖⇁⋜↧⋯∙↿∪↓⋅∪⇂−≽↿∪−≽↓∪∙∖⇁∢⋜⊔⋅⊳∖⊳∆∖, We find that the fit is improved when $t_9$ is increased by a factor of 2 to $2\times 10^9$ years.
"⊳∖↓↓⋏∙≟↓∐↓∙∖⇁↓⋜⊔⋅⋏∙≟⋖⊾↓⋅∖⇁⋜↧↓⋯⋅∪⇂."" . (,=10LOT than for. the rapid.. facingoq. model is. required. o olfset the smaller amount of time that bright. quasars spend at their Eddington luminosity.", A slightly larger value of $\epsilon_o = 10^{-4.97}$ than for the rapid fading model is required to offset the smaller amount of time that bright quasars spend at their Eddington luminosity.
" We refer to the model with this facing law as the “slow facing"" model.", We refer to the model with this fading law as the “slow fading” model.
 Since the wo models provide comparable fits to the optical data. the optical data alone appears to oller Little power to constrain he luminosity dependence of the facing law.," Since the two models provide comparable fits to the optical data, the optical data alone appears to offer little power to constrain the luminosity dependence of the fading law."
 Note that there is an excess in the predicted. number of optically bright quasars at 2= for cach facing Law., Note that there is an excess in the predicted number of optically bright quasars at $z = 2$ for each fading law.
 The most plausible explanation for this ciscrepaney between our model and the data is probably our neglect. of ACN foecdback., The most plausible explanation for this discrepancy between our model and the data is probably our neglect of AGN feedback.
 AGN inject: large amounts of heat into their surroundings (e.g.22) and should be capable ofsuppressing cooling flows in dark matter halos with masses above ~ M. - resulting in the formation of groups ancl clustersof galaxies rather than super-sized quasars in very large dark matter halos (sce.c.g. ???)..," AGN inject large amounts of heat into their surroundings \citep[e.g.][]{dunn2006,best2007} and should be capable ofsuppressing cooling flows in dark matter halos with masses above $\sim {\rm few} \times 10^{13}h^{-1}$ $_{\sun}$ - resulting in the formation of groups and clustersof galaxies rather than super-sized quasars in very large dark matter halos \citep[see,
e.g.][]{sijacki2006, sijacki2007, rines2007}. ."
 This elfect, This effect
"with magnitude on the basis of the relation log,=0.3sneg|const (Brainerd ct al.",with magnitude on the basis of the relation $A_\omega=-0.3\times mag+const$ (Brainerd et al.
 1991: Roche ct al., 1994; Roche et al.
 1996) we derived The umuber counts here derived in the F300W and F150W bands aud in the F6OGW aud FalWW bands are shown in Figures 3 and 1 together with those from the literature., 1996) we derived The number counts here derived in the F300W and F450W bands and in the F606W and F814W bands are shown in Figures \ref{countsVI} and \ref{countsBU} together with those from the literature.
 The relation between counts and magnitude lav be written aswith 54> 5»., The relation between counts and magnitude may be written aswith $\gamma_1 > \gamma_2$ .
 The knee i is at Dz25 (Lilly et al., The knee $m'$ is at $\approx$ 25 (Lilly et al.
 1991. Metcalfe et al.," 1991, Metcalfe et al."
 1995). and the value of 24. varies between 0.1 ancl 1.6 according to the baud aud analogously for >> it varies between0.2 aud 0.5.," 1995), and the value of $\gamma_1$ varies between 0.4 and 0.6 according to the band and analogously for $\gamma_2$ it varies between0.2 and 0.5."
" We estimator both 54 aud 7» dn 45. F606W45 and yp. obtaining for VTEyy,~LEO, “LLFOUGU45v0.31dE0.1 and σαΕνατν©0.62£0.1. aud for 5»: 5sE150~~0.19-Ε 0.01. οΕὐυσΗyy07OL9EOL aud τοExiyy,c019 Ε0.1."," We estimated both $\gamma_1$ and $\gamma_2$ in $_{AB}$ , $_{AB}$ and $_{AB}$, obtaining for $\gamma_1$: $\gamma_{1,F450W_{AB}}\sim0.4\pm0.1$, $\gamma_{1,F606W_{AB}}\sim0.34\pm0.1$ and $\gamma_{1, F814W_{AB}}\sim0.62\pm0.1$, and for $\gamma_2$ : $\gamma_{2,F450W_{AB}}\sim0.19\pm0.01$ , $\gamma_{2,F606W_{AB}}\sim0.19\pm0.1$ and $\gamma_{2, F814W_{AB}}\sim0.19\pm0.1$ ."
" The most notable feature appears in the F300W-baud counts: these are described by a slope 5E3004,0.05 which is much steeper than the value +Fs00370.15 derived by Williams et al. (", The most notable feature appears in the F300W-band counts: these are described by a slope $\gamma_{F300W_{AB}}=0.47\pm0.05$ which is much steeper than the value $\gamma_{F300W_{AB}}\sim0.15$ derived by Williams et al. (
1996) aud Pozzetti ct al. (,1996) and Pozzetti et al. (
1998) on the IIDE-N data in the same magnitude rauge.,1998) on the HDF-N data in the same magnitude range.
 Such a steep slope. which agrees with the fiudiues of Tove et al. σι~0.5:," Such a steep slope, which agrees with the findings of Hogg et al. $\gamma_U\sim0.5$;"
 1997) and. Fontana et al. σι~0.19:, 1997) and Fontana et al. $\gamma_U\sim0.49$;
 1999). does not depend on a possible over-estimate of the incompleteness iu he faintest maguitude bius: the sine slope is actually described by counts a Πλ][τοις Usoo:26 where the sample is 1005€ complete.," 1999), does not depend on a possible over-estimate of the incompleteness in the faintest magnitude bins: the same slope is actually described by counts at magnitudes $_{300}<26$ where the sample is $\%$ complete."
 Moreover the F300W-hband counts do not show evidence of any turnover or flattening down to 5227. coutrary to what is claimed bv Pozzetti et al. (," Moreover the F300W-band counts do not show evidence of any turnover or flattening down to $_{AB}$ =27, contrary to what is claimed by Pozzetti et al. ("
1998).,1998).
 We will discuss this issue in Section 5.1., We will discuss this issue in Section 5.1.
 The amplitude aud slope of the uuuber counts in the whole range of maguituces in the other optical bauds are in a good agreciment with those previously derived by other authors., The amplitude and slope of the number counts in the whole range of magnitudes in the other optical bands are in a good agreement with those previously derived by other authors.
 We estimated FEIS0Wyp0v0.35+ 0.02. F6061yp(0.28+0.01ad Ενιν7.28EOLUOT for the 4p. FOOGWyp aud το counts respectively.," We estimated $\gamma_{F450W_{AB}}\sim0.35\pm0.02$ , $\gamma_{F606W_{AB}}\sim0.28\pm0.01$and $\gamma_{
F814W_{AB}}\sim0.28\pm0.01$ for the $_{AB}$ , $_{AB}$ and $_{AB}$ counts respectively."
 Ini order to lueastue colors unbiased with respect to the selection. band. we created a Ὃν sumaundus alb fourframes. afternormalizing themto," In order to measure colors unbiased with respect to the selection band, we created a by summing all fourframes, afternormalizing themto"
fingerprint of the structural properties predicted by our models of SG star formation and dynamical evolution (D’Ercole et al.,fingerprint of the structural properties predicted by our models of SG star formation and dynamical evolution (D'Ercole et al.
 2008; further investigation of the long-term evolution of multiple population clusters will be presented in Vesperini et al., 2008; further investigation of the long-term evolution of multiple population clusters will be presented in Vesperini et al.
" 2011, in preparation)."," 2011, in preparation)."
" Specifically, we showed in our previous studies that SG stars forming from AGB ejecta tend to form in a strongly concentrated subsystem in the FG cluster inner regions (see also Bekki 2011); we have now shown in this paper that in a cluster with such a structure, SG binaries are preferentially disrupted and that, more generally, binary disruption is enhanced compared to a standard cluster with similar mass and size but without an inner SG subsystem."," Specifically, we showed in our previous studies that SG stars forming from AGB ejecta tend to form in a strongly concentrated subsystem in the FG cluster inner regions (see also Bekki 2011); we have now shown in this paper that in a cluster with such a structure, SG binaries are preferentially disrupted and that, more generally, binary disruption is enhanced compared to a standard cluster with similar mass and size but without an inner SG subsystem."
 Our calculation is based on analytical calculations combined with the results of N-body simulations of cluster structural and kinematical evolution., Our calculation is based on analytical calculations combined with the results of N-body simulations of cluster structural and kinematical evolution.
 Further refinement of the calculations presented in this paper will require simulations including full treatment of binary stars; simulations including the self-consistent treatment of binaries are very computationally expensive and are beyond the scope of this initial exploratory study., Further refinement of the calculations presented in this paper will require simulations including full treatment of binary stars; simulations including the self-consistent treatment of binaries are very computationally expensive and are beyond the scope of this initial exploratory study.
" Future studies based on simulations with binaries will allow us to incorporate additional effects (e.g. binary-binary interactions, binary segregation, binary heating) not included in our simple analytical treatment of binary disruption."," Future studies based on simulations with binaries will allow us to incorporate additional effects (e.g. binary-binary interactions, binary segregation, binary heating) not included in our simple analytical treatment of binary disruption."
" The first observational indication of the preferential disruption of SG binaries, as found in our analysis, comes from a recent study of Ba stars in globular clusters (D’Orazi et al."," The first observational indication of the preferential disruption of SG binaries, as found in our analysis, comes from a recent study of Ba stars in globular clusters (D'Orazi et al."
 2010)., 2010).
 Ba stars are thought to be the result of the accretion of matter processed by a thermally pulsing AGB onto the secondary component of a binary system., Ba stars are thought to be the result of the accretion of matter processed by a thermally pulsing AGB onto the secondary component of a binary system.
" The Ba-rich envelope of the AGB component contaminates the companion via wind accretion, possibly followed by stable Roche lobe overflow, or by common envelope evolution, depending on the mass ratio at the time the donor AGB fills its Roche lobe (see Han et al."," The Ba-rich envelope of the AGB component contaminates the companion via wind accretion, possibly followed by stable Roche lobe overflow, or by common envelope evolution, depending on the mass ratio at the time the donor AGB fills its Roche lobe (see Han et al."
 1995 for a detailed study of the binary channels for the formation of Ba stars; see also Jorissen et al., 1995 for a detailed study of the binary channels for the formation of Ba stars; see also Jorissen et al.
" 1998, McClure Woodsworth 1990 for two observational studies of the Ba stars orbital properties)."," 1998, McClure Woodsworth 1990 for two observational studies of the Ba stars orbital properties)."
" In order for this process to occur, the initial binary separation must be larger than approximately 1 AU (smaller separations would affect the primary component evolution before it reaches the AGB phase)."," In order for this process to occur, the initial binary separation must be larger than approximately 1 AU (smaller separations would affect the primary component evolution before it reaches the AGB phase)."
 D’Orazi et al., D'Orazi et al.
 find that Ba stars belong predominantly to the FG population., find that Ba stars belong predominantly to the FG population.
 This result is consistent with a dynamical history in which the SG Ba star binary progenitors are disrupted more efficiently than those of the FG population., This result is consistent with a dynamical history in which the SG Ba star binary progenitors are disrupted more efficiently than those of the FG population.
 We note that the larger binary interaction rate of SG binaries can also lead them to harden more rapidly., We note that the larger binary interaction rate of SG binaries can also lead them to harden more rapidly.
" By tightening a binary below the minimum separation for the formation of Ba stars, the more rapid hardening of SG binaries may represent an additional channel for the suppression of Ba stars in the SG population."," By tightening a binary below the minimum separation for the formation of Ba stars, the more rapid hardening of SG binaries may represent an additional channel for the suppression of Ba stars in the SG population."
" Another interesting possible consequence of an enhanced binary interaction rate is that a binary might be disrupted after the mass transfer episode that led to the formation of the Ba star, resulting in a single Ba star."," Another interesting possible consequence of an enhanced binary interaction rate is that a binary might be disrupted after the mass transfer episode that led to the formation of the Ba star, resulting in a single Ba star."
 The sample of Ba stars discussed in D’Orazi et al., The sample of Ba stars discussed in D'Orazi et al.
" is still very small, and further observational studies aimed at exploring the relative abundance of FG and SG binaries will be extremely important to test the predictions of our study"," is still very small, and further observational studies aimed at exploring the relative abundance of FG and SG binaries will be extremely important to test the predictions of our study"
WHT/ACAM setup.,WHT/ACAM setup.
 No pulsations were detected to a limit of mmmags over the frequency range of mmHz., No pulsations were detected to a limit of mmags over the frequency range of mHz.
 This object has a measured loge=6.34+0.20 and 300 KK with a derivedmodel mass of 0.18M (Callananetal.1998) and also logg=6.75£0.07 and Tey..=8.550+25 KK with a derived model mass of 0.21M.. (vanKerkwiJketal. 1996)..," This object has a measured $\log g = 6.34 \pm 0.20$ and $T_{\rm eff} = 8,670 \pm 300$ K with a derivedmodel mass of $M_{\odot}$ \citep{cal98.mnras298} and also $\log g = 6.75 \pm 0.07$ and $T_{\rm eff} = 8,550 \pm 25$ K with a derived model mass of $M_{\odot}$ \citep{van96.apj467}."
 Neither of these measurements ts obviously superior., Neither of these measurements is obviously superior.
 was observed one time using the HST/WFC3 setup over 4 orbits., was observed one time using the HST/WFC3 setup over 4 orbits.
 The photometric analysis for this object was uniquely different than all other objects., The photometric analysis for this object was uniquely different than all other objects.
 Due to crowding in the field (PSR 11911-5958A is in a globular cluster) as well as the unique PSF of HST. aperture photometry is not the most precise method.," Due to crowding in the field (PSR J1911-5958A is in a globular cluster) as well as the unique PSF of HST, aperture photometry is not the most precise method."
 PSF-fitting photometry is ideal since the PSF of the WFC3 instrument is well understood (Jay Anderson. private communication).," PSF-fitting photometry is ideal since the PSF of the WFC3 instrument is well understood (Jay Anderson, private communication)."
 We used the PSF-fitting software developed by Jay Anderson (similar to Anderson&King 2006)) to extract the photometry from our data., We used the PSF-fitting software developed by Jay Anderson (similar to \citealt{and06.tech06}) ) to extract the photometry from our data.
 Since most atmospheric and sky effects are nonexistent in space. variable aperture photometry was not required or used.," Since most atmospheric and sky effects are nonexistent in space, variable aperture photometry was not required or used."
 We used 36 comparison stars with magnitudes between 17.5-25.0 to ensure the quality of our photometry., We used 36 comparison stars with magnitudes between 17.5–25.0 to ensure the quality of our photometry.
 Due to a stray light artifact. our background was increased by ~30%..," Due to a stray light artifact, our background was increased by $\approx$."
 No pulsations were detected to a limit of 16mmmags over the frequency range of mmHz., No pulsations were detected to a limit of mmags over the frequency range of mHz.
 This object has a measured logg=6.44+0.20 and Tay=10.090+150 KK with a derived model mass of 0.18M.. (Bassaetal.2006a)..," This object has a measured $\log g = 6.44 \pm 0.20$ and $T_{\rm eff} = 10,090 \pm 150$ K with a derived model mass of $M_{\odot}$ \citep{bas06.aap456}."
 Of the 12 objects we observed in this paper. seven are likely very low mass (<0.2M..) He WDs.," Of the 12 objects we observed in this paper, seven are likely very low mass $<$ $M_{\odot}$ ) He WDs."
 Whether or not these observations offer strong constraints on theory is currently an open matter., Whether or not these observations offer strong constraints on theory is currently an open matter.
 First we must consider the accuracy of the logg and Τομ measurements that place these objects within the predicted pulsation parameter space., First we must consider the accuracy of the $\log g$ and $T_{\rm eff}$ measurements that place these objects within the predicted pulsation parameter space.
 Unfortunately. very low mass WD atmospheres are not well understood.," Unfortunately, very low mass WD atmospheres are not well understood."
 Due to their low surface temperatures (TeyX9.000 KK). the H atmospheres are not sufficiently tonized and neutral broadening of the H absorption lines plays an important role.," Due to their low surface temperatures $T_{\rm eff}\lesssim9$ K), the H atmospheres are not sufficiently ionized and neutral broadening of the H absorption lines plays an important role."
 The theory of neutral broadening is not well understood and may account for significant errors in. line widths (Barklemetal.2000;Allard2004:Tremblayetal.2010:: private communication. Detlev Koester).," The theory of neutral broadening is not well understood and may account for significant errors in line widths \citealt{bar00.aap363,all04.aap424,tre10.apj712}; private communication, Detlev Koester)."
 As such. the reported errors on loge and Ίω for these objects are always the statistical error of the fit to theoretical atmosphere grids and do not take into account the uncertainties of the theory itself which can increase the uncertainty by as much as a factor of two or more (private communication. Detlev Koester).," As such, the reported errors on $\log g$ and $T_{\rm eff}$ for these objects are always the statistical error of the fit to theoretical atmosphere grids and do not take into account the uncertainties of the theory itself which can increase the uncertainty by as much as a factor of two or more (private communication, Detlev Koester)."
 Further. the uncertainty of the atmosphere theory is likely not random but rather a shift in a specific direction in the 7;;-log plane. affecting the parameter space location of all very low gmass He WDs.," Further, the uncertainty of the atmosphere theory is likely not random but rather a shift in a specific direction in the $T_{\rm eff}$ $\log g$ plane, affecting the parameter space location of all very low mass He WDs."
 This is why NLTT 11748 is such an important eclipsing binary system (Steinfadtetal.2010b).., This is why NLTT 11748 is such an important eclipsing binary system \citep{ste10.apj716}.
 As a potential double-lined spectroscopic eclipsing binary. it could offer high precision determinations of both the mass and radius of the He WD component providing a high precision constraint on its gravity for which any atmospheric gravity measurement must match.," As a potential double-lined spectroscopic eclipsing binary, it could offer high precision determinations of both the mass and radius of the He WD component providing a high precision constraint on its gravity for which any atmospheric gravity measurement must match."
" Of added concern is the location of the instability strip ""blue"" edge itself."," Of added concern is the location of the instability strip “blue"" edge itself."
" Steinfadtetal.(20103). derived the ""blue"" edge to be where pulsation modes of eigenvalues (=| and a=| were driven."," \citet{ste10.apj718} derived the “blue"" edge to be where pulsation modes of eigenvalues $\ell=1$ and $n=1$ were driven."
" This offers a temperature upper limit to the (21 instability strip because the ""blue"" edge shifts redward when higher radial orders of n are considered."," This offers a temperature upper limit to the $\ell=1$ instability strip because the “blue"" edge shifts redward when higher radial orders of $n$ are considered."
 In the few cases where pulsation mode eigenvalues have been identified observationally (e.g. HL Tau 76. Pechetal.2006:; GI17-BI15A and R548. Bradley 1998)) the highest amplitude observed modes range in 5 from | to several 10s.," In the few cases where pulsation mode eigenvalues have been identified observationally (e.g. HL Tau 76, \citealt{pec06.aap446}; G117-B15A and R548, \citealt{bra98.apjs116}) ) the highest amplitude observed modes range in $n$ from 1 to several 10s."
 If very low mass He WDs preferentially only excite the higher radial order modes. then the blue edge could shift redward by a few KK potentially removing our three best candidates from the potential instability region.," If very low mass He WDs preferentially only excite the higher radial order modes, then the blue edge could shift redward by a few K potentially removing our three best candidates from the potential instability region."
 Uncertainties in the precise convective efficiency and the lack of a detailed non-adiabatic analysis could further shift this blue edge by another several KK in either direction (Wingetetal.1982a:Fontaine& 2008).," Uncertainties in the precise convective efficiency and the lack of a detailed non-adiabatic analysis could further shift this blue edge by another several K in either direction \citep{win82.apj262,fon08.pasp120}. ."
. An additional observational concern is whether our detection limits are truly meaningful., An additional observational concern is whether our detection limits are truly meaningful.
 Only NLTT 11748. LP 400-20. SDSS J0822+2743. and SDSS J143543733 met our fiducial pulsation limit of 1Ommmags and only NLTT 11748. SDSS J143543733. and SDSS J2240-0935," Only NLTT 11748, LP 400-20, SDSS J0822+2743, and SDSS J1435+3733 met our fiducial pulsation limit of mmags and only NLTT 11748, SDSS J1435+3733, and SDSS J2240-0935"
The light curves in different. wavelengths follow the standard flare model for energy propagation at different heights in the solar atmosphere (Ixane1974).,The light curves in different wavelengths follow the standard flare model for energy propagation at different heights in the solar atmosphere \citep{Kane1974}.
. The general understanding ol the flare physics is based on the concept of reconnection of magnetic fied lines al coronal jeiehts (Sturrock1966:Lliravama1974:Ixopp&Pueuman1976).," The general understanding of the flare physics is based on the concept of reconnection of magnetic field lines at coronal heights \citep{Sturrock1966, Hirayama1974,
Kopp1976}."
. Energy released during a flare covers a wide range of wavelengths. however. it is easier to observe in certain spectral ines as shown in Figure 3..," Energy released during a flare covers a wide range of wavelengths, however, it is easier to observe in certain spectral lines as shown in Figure \ref{LCurvs}."
 During the pre-flare stage. where the release of the stored nagnelic energv is triggered. (he chromospheric flare ribbons are seen easily (see. Figure lop).," During the pre-flare stage, where the release of the stored magnetic energy is triggered, the chromospheric flare ribbons are seen easily (see, Figure \ref{TimSeqImg} )."
 The increasing separation ol flare ribbon with time results from reconnection of nagnetic field lines al successively increasing coronal heights., The increasing separation of flare ribbon with time results from reconnection of magnetic field lines at successively increasing coronal heights.
 Further. the energetic particles released in the corona during a flare take increasingly longer time (to propagate through the denser lavers downwards to the photosphere.," Further, the energetic particles released in the corona during a flare take increasingly longer time to propagate through the denser layers downwards to the photosphere."
" This agrees with the observed flare light curves in which started rising at UUT and thereafter in L700 corresponding, to the photosphere and the temperature minimum region.", This agrees with the observed flare light curves in which started rising at UT and thereafter in 1700 corresponding to the photosphere and the temperature minimum region.
 As the flare progressed. (he temperature also increased making the flare ribbons visible in higher temperature plasmas in (he coronal regions corresponding to the emission.," As the flare progressed, the temperature also increased making the flare ribbons visible in higher temperature plasmas in the coronal regions corresponding to the emission."
" The observed ""mnagnetüc and “Doppler” TFs appeared during (hie peak phase of the N22 [lare of 2011 February 15 (cL."," The observed “magnetic” and “Doppler” TFs appeared during the peak phase of the X2.2 flare of 2011 February 15 (c.f.,"
 Figure 2))., Figure \ref{ImMoz}) ).
 Similar features were reported earlier during ihe more energetic N17/4D. and X10/2D flaves of October 28 and 29. 2003 (Maurya&2009. 2010a).. and the X5.6 flare of 2001 April 6 (Qiu&Gary2003).," Similar features were reported earlier during the more energetic X17/4B and X10/2B flares of October 28 and 29, 2003 \citep{Maurya2008, Maurya2009,Maurya2010d}, and the X5.6 flare of 2001 April 6 \citep{Qiu2003}."
. Venkatakrishnanetal.(2008) have also reported co-spatial Doppler ribbons associated with the Ho flare ribbons of the X17/4D flare., \citet{Venkatakrishnan2008} have also reported co-spatial Doppler ribbons associated with the $\alpha$ flare ribbons of the X17/4B flare.
 These TFs. usually located around cooler umbral boundary of (he sunspots. were lound to be largely co-spatial with the flare ribbons observed al different heights of (he solar atmosphere. viz. chromosphere. transition region and corona (see Figures 1.. 2)).," These TFs, usually located around cooler umbral boundary of the sunspots, were found to be largely co-spatial with the flare ribbons observed at different heights of the solar atmosphere, viz, chromosphere, transition region and corona (see Figures \ref{TimSeqImg}, \ref{ImMoz}) )."
 A lime sequence of the consecutive difference images of the WAIL magnetograms of AR NOAA 11153 in Figure 1. shows dark patches representing the magnetic transients along the curves L1 and L2., A time sequence of the consecutive difference images of the HMI magnetograms of AR NOAA 11158 in Figure \ref{TimSeqImg} shows dark patches representing the magnetic transients along the curves L1 and L2.
 These TFs appeared and faded in a few minutes. period UUT) during the impulsive phase of the fare., These TFs appeared and faded in a few minutes' period UT) during the impulsive phase of the flare.
 From Figure L.. it is evident that the (ransients were co-spatial will the observed I line fare ribbons.," From Figure \ref{TimSeqImg}, it is evident that the transients were co-spatial with the observed H line flare ribbons."
 However. while the H flare ribbons separated away. the TFs remained nearly stationary with time.," However, while the H flare ribbons separated away, the TFs remained nearly stationary with time."
 Using an automated method described in Maurva&Ambastha(2010b).. we determined that the HE flare ribbons separated out with an average velocity of 8.," Using an automated method described in \citet{Maurya2010b}, we determined that the H flare ribbons separated out with an average velocity of 8."
"τν, This is much smaller as compared to the earlier reported velocities in (he range of 50-75 for", This is much smaller as compared to the earlier reported velocities in the range of 50-75 for
ourselves with estimating baryonic effects or trying to correct for them. beyond not fitting for the concentration at radit. r<Ο.ΕΛη.,"ourselves with estimating baryonic effects or trying to correct for them, beyond not fitting for the concentration at radii, $r<0.1R_{vir}$ ."
 The fact that we have good agreement with observations for massive clusters (Section 6)) may be viewed as added support to the argument that baryonic effects do not influence cluster profiles away from the inner regions., The fact that we have good agreement with observations for massive clusters (Section \ref{sec:comp}) ) may be viewed as added support to the argument that baryonic effects do not influence cluster profiles away from the inner regions.
 A large number of numerical studies have been carried out investigating halo profiles and paying close attention to the behavior of the density cusp on the very smallest scales., A large number of numerical studies have been carried out investigating halo profiles and paying close attention to the behavior of the density cusp on the very smallest scales.
 We are. however. concerned not with these scales. but more with scales of order (0.1-DA. since our target halos have relatively modest concentrations.," We are, however, concerned not with these scales, but more with scales of order $\sim(0.1-1)R_{vir}$, since our target halos have relatively modest concentrations."
 Previous numerical simulations have found that in the region of interest to us. the concentration is a slowly varying function of mass. typically described by power laws with index à~-0.1 at z=0.," Previous numerical simulations have found that in the region of interest to us, the concentration is a slowly varying function of mass, typically described by power laws with index $\alpha\simeq-0.1$ at $z=0$."
 These simulations have varied widely in dynamic range. box size. and mass resolution.," These simulations have varied widely in dynamic range, box size, and mass resolution."
 Partly as a result of this. there have been some disagreements in the value of the slope and the normalization of the c—M relation. and also some lack of clarity regarding the reasons underlying the differences.," Partly as a result of this, there have been some disagreements in the value of the slope and the normalization of the $c-M$ relation, and also some lack of clarity regarding the reasons underlying the differences."
 Among the more recent studies are those involving the Millenium simulation (MS) (Springeletal.2005) with 2160? particles and a box of side 500 47! Mpe assuming à WMAPI cosmology (Netoetal.2007:Gao2008;Hayashi&White2008).," Among the more recent studies are those involving the Millenium simulation (MS) \citep{springel_ms} with $2160^3$ particles and a box of side 500 $h^{-1}$ Mpc assuming a WMAP1 cosmology \citep{neto07,
 gao07, hayashi07}."
. Halo profiles were investigated over a mass range of 10710/7! .. and it was found that à~—0.1., Halo profiles were investigated over a mass range of $10^{12}-10^{15} h^{-1}$ $_\odot$ and it was found that $\alpha\simeq-0.1$.
 These results were mostly in agreement with a simulation campaign conducted by Maceid.Dutton.&vandenBosch(2008) and Maccióetal.(2007) who covered a mass range 10?— 10/7!... although with a slight discrepancy (~ 10%)) in the normalization.," These results were mostly in agreement with a simulation campaign conducted by \cite{maccio08} and \cite{maccio07}
 who covered a mass range $10^9-10^{13}h^{-1}$ $_\odot$, although with a slight discrepancy $\sim$ ) in the normalization."
M Duffyetal.(2008) carried out another set of simulations with three different box sizes (25. 100 and 400 #7! Mpe). each with 512? particles covering a mass range of 10!!—1005/7! |. using the best-fit WMAPS5 cosmology.," \cite{duffy08} carried out another set of simulations with three different box sizes (25, 100 and 400 $h^{-1}$ Mpc), each with $512^3$ particles covering a mass range of $10^{11}-10^{15}
h^{-1}$ $_\odot$ using the best-fit WMAP5 cosmology."
 They concluded that the median c—M relation ts lower by about at the low mass end and at the high mass end compared to the MS results in the mass range of 10!!—1077/7! ..., They concluded that the median $c-M$ relation is lower by about at the low mass end and at the high mass end compared to the MS results in the mass range of $10^{11}-10^{14} h^{-1}$ $_\odot$.
 In yet another set of simulations. Klypin.Trujillo-Gomez.&Primack(2010) and Pradaetal.(201 1).. have claimed that the concentration. instead of fattening out at high mass. in fact rises.," In yet another set of simulations, \cite{klypin10} and \cite{prada11}, have claimed that the concentration, instead of flattening out at high mass, in fact rises."
 Given this context. our primary purpose is to improve the statistical power in determining the c—M relation and its scatter at high masses. while retaining good mass resolution. and second. to study the behavior as a function of redshift and cosmology.," Given this context, our primary purpose is to improve the statistical power in determining the $c-M$ relation and its scatter at high masses, while retaining good mass resolution, and second, to study the behavior as a function of redshift and cosmology."
 Finally. we note that the improved statistical power is important in comparing with observations of massive clusters as the numbers of well-observed clusters is expected to rise significantly in the near future (in the past. simulations may have contained only one cluster at the upper mass end. where we have hundreds).," Finally, we note that the improved statistical power is important in comparing with observations of massive clusters as the numbers of well-observed clusters is expected to rise significantly in the near future (in the past, simulations may have contained only one cluster at the upper mass end, where we have hundreds)."
" Throughout this paper. we use the following ACDM cosmology as a reference: w,,=0.1296 (Q,,= 0.25). wp=0.0224 (QO, 0.043). 1,20.97. σε=0.8. and fr=0.72 where ο=ΟΙ and ©,, represents the total (dark + baryon) matter density."," Throughout this paper, we use the following $\Lambda$ CDM cosmology as a reference: $\omega_m=0.1296$ $\Omega_m=0.25$ ), $\omega_b=0.0224$ $\Omega_b=0.043$ ), $n_s=0.97$, $\sigma_8=0.8$, and $h=0.72$ where $\omega=\Omega h^2$ and $\Omega_m$ represents the total (dark + baryon) matter density."
 We assume spatial flatness., We assume spatial flatness.
 This model ts in excellent agreement with the latest best-fit cosmological model provided by WMAP-7 measurements etal. 2011). , This model is in excellent agreement with the latest best-fit cosmological model provided by WMAP-7 measurements \citep{wmap7}. .
In order to cover a wide range of masses. we analyze three simulations with different volumes and number of particles.," In order to cover a wide range of masses, we analyze three simulations with different volumes and number of particles."
 A summary of the runs is given in Table 1.., A summary of the runs is given in Table \ref{tab1}.
 The mass resolution in the large-box run is sufficient for measuring the concentrations for halo masses >10/7! ... with a minimum of 2000 particles per halo.," The mass resolution in the large-box run is sufficient for measuring the concentrations for halo masses $>10^{14}h^{-1}$ $_\odot$, with a minimum of 2000 particles per halo."
 At z20. we have more than 100.000 such halos. therefore our statistical control may be considered to be more than satisfactory.," At $z=0$, we have more than 100,000 such halos, therefore our statistical control may be considered to be more than satisfactory."
 In the MS and Duffyetal.(2008) simulations. the largest boxes used are of size 50057! Mpe and 300/47! Mpe respectively. with limited statistics for cluster size halos in the mass range 10!—10/7! M...," In the MS and \cite{duffy08} simulations, the largest boxes used are of size $500h^{-1}$ Mpc and $400 h^{-1}$ Mpc respectively, with limited statistics for cluster size halos in the mass range $10^{14}-10^{15}
h^{-1}$ $_{\odot}$ ."
 We provide a large sample of cluster size halos. with roughly 64 times more volume than in the MS run and 125 times more than in the simulations by Duffyetal.(2008).," We provide a large sample of cluster size halos, with roughly 64 times more volume than in the MS run and 125 times more than in the simulations by \cite{duffy08}."
. The largest simulation (both with respect to volume and particle number) is carried out using our new Hardware/Hybrid Accelerated Cosmology Code (HACC) framework described in Habibetal.(2009) and Popeetal.(2010)., The largest simulation (both with respect to volume and particle number) is carried out using our new Hardware/Hybrid Accelerated Cosmology Code (HACC) framework described in \cite{habib09} and \cite{pope10}.
. This simulation covers a volume of (2 /r! Gpc)? and evolves 2048? particles and was run on the hybrid supercomputer Cerrillos at Los Alamos National Laboratory. (, This simulation covers a volume of (2 $h^{-1}$ $^3$ and evolves $^3$ particles and was run on the hybrid supercomputer Cerrillos at Los Alamos National Laboratory. (
Another 2048? particle run with a 512 47! Mpe box was used to test the results obtained at z22 from the run described below.),Another $^3$ particle run with a 512 $h^{-1}$ Mpc box was used to test the results obtained at $z=2$ from the run described below.)
 The HACC framework has been designed with flexibility as a prime requirement; it is meant to be easily portable between high-performance computing platforms based on different architectures., The HACC framework has been designed with flexibility as a prime requirement; it is meant to be easily portable between high-performance computing platforms based on different architectures.
 The first version of the code has been optimized to run on the Cell-hybrid architecture shared by Roadrunner (the first computer to break the Petaflop barrier) and Cerrillos., The first version of the code has been optimized to run on the Cell-hybrid architecture shared by Roadrunner (the first computer to break the Petaflop barrier) and Cerrillos.
 A first extension of this version of the code has been developed for hybrid CPU/GPU systems. written in OpenCL.," A first extension of this version of the code has been developed for hybrid CPU/GPU systems, written in OpenCL."
 HACC’s code structure is split into two components: a long-range force solver and a short range module., HACC's code structure is split into two components: a long-range force solver and a short range module.
 The long-range force solver uses a parallel Particle-Mesh (PM) algorithm with spectral filtering and super-Lanezos differentiation 1998).., The long-range force solver uses a parallel Particle-Mesh (PM) algorithm with spectral filtering and super-Lanczos differentiation \citep{hamming}.
 In this part of the code. the long-range force is calculated by depositing tracer particles onto a regular grid and using Fourier transform methods to solve the Poisson equation (with in effect a modified Green function) and then interpolating the force from the grid back onto the particles.," In this part of the code, the long-range force is calculated by depositing tracer particles onto a regular grid and using Fourier transform methods to solve the Poisson equation (with in effect a modified Green function) and then interpolating the force from the grid back onto the particles."
 The spectral component of the code is implemented in C++/MPI and can run on any standard parallel machine., The spectral component of the code is implemented in C++/MPI and can run on any standard parallel machine.
 The current 2-D domain-decomposed implementation of the FFT allows it scale to millions of MPI ranks., The current 2-D domain-decomposed implementation of the FFT allows it scale to millions of MPI ranks.
 The implementation of the particle deposition and force interpolation routines depends on the machine architecture., The implementation of the particle deposition and force interpolation routines depends on the machine architecture.
 On Roadrunner and Cerrillos. these routines were implemented on the Cell processor.," On Roadrunner and Cerrillos, these routines were implemented on the Cell processor."
 The short-range module adds the high-resolution force between particles and can be implemented in different ways and on different platforms., The short-range module adds the high-resolution force between particles and can be implemented in different ways and on different platforms.
 On Cell and GPU-based systems. an N7-algorithm is used to evaluate theshort range forces (in chaining mesh patches). leading to a ΡΜ implementation.," On Cell and GPU-based systems, an $N^2$ -algorithm is used to evaluate theshort range forces (in chaining mesh patches), leading to a $^3$ M implementation."
 This works well on hardware-accelerated machines since it iscomputationally intensive and uses a simple data structure., This works well on hardware-accelerated machines since it iscomputationally intensive and uses a simple data structure.
 The ΡΜ version of HACC has been extensively tested against the code comparison, The $^3$ M version of HACC has been extensively tested against the code comparison
sealec from the result. of Abt&Alorrell(1905).,scaled from the result of \citet{am95}.
.. We obtained οκαί=42 + and this is the value of the rotational velocity. we used for spectrum synthesis., We obtained $\vsini=42~$ $^{-1}$ and this is the value of the rotational velocity we used for spectrum synthesis.
 We used. the two different set. of orbital elements. given. hy Abt&Levy(1985). and Alareonictal.(1992). in order to check our radial velocities., We used the two different set of orbital elements given by \citet{al85} and \citet{margoni92} in order to check our radial velocities.
 Our results are in good agreement with the radial velocity curve obtained by using the orbital elements of the latter authors (sce Figure 2))., Our results are in good agreement with the radial velocity curve obtained by using the orbital elements of the latter authors (see Figure \ref{fnew}) ).
" They gave the following orbital elements - Pa,=38.034"". A—10.0kmsfo e220.03. V,=160kmstow -00”."," They gave the following orbital elements - $P_{\rm orb}=38.034^{d}$, $K=10.0~{\rm km\,s^{-1}}$, =0.03, $V_0=-16.0~{\rm km\,s^{-1}}$, $\omega={\rm 92^{\circ}}$."
 Our results of the abundances define the star as Am star., Our results of the abundances define the star as Am star.
 The line of ll A eis well identified ancl is relatively stronger comparing to the other stars in this investigation., The line of I $\lambda$ is well identified and is relatively stronger comparing to the other stars in this investigation.
 That is why the obtained abundance of Li is well determined., That is why the obtained abundance of Li is well determined.
 1196544 (7 Del. 77883. |10 4339. 1101800. 1106322) is an ΑΝ) spectroscopic binary star.," 196544 $\iota$ Del, 7883, +10 4339, 101800, 106322) is an A2V spectroscopic binary star."
 Acanis determined for the first time the stellar racial velocity. anc obtained that it was variable., \citet{adams12} determined for the first time the stellar radial velocity and obtained that it was variable.
 He classified the star as A2 spectral tvpe star., He classified the star as A2 spectral type star.
 Later Osawa(1959) determined. the spectral class as VV according to ALK system and as A+ from metallic lines., Later \citet{osawa59} determined the spectral class as V according to MK system and as A4 from metallic lines.
 Levato(1975) confirmed. the spectral class as VW and obtained. the projected rotational velocity esin/=55 kmss| but later revised the velocity to esing=60kmss. + (Gareia&Levato 1984))., \citet{Levato75} confirmed the spectral class as V and obtained the projected rotational velocity $\vsini=55~$ $^{-1}$ but later revised the velocity to $\vsini=60~$ $^{-1}$ \citealt{gl84}) ).
 On the other hand. Abt&Morrell(1995). classified the star as ALLY and gave à smaller value of the rotational velocity - esin£=30 ss.+.," On the other hand, \citet{am95}
 classified the star as IV and gave a smaller value of the rotational velocity - $\vsini=30~$ $^{-1}$."
 Roveretal.(2002). derived the projected rotational velocity. and after merging it with the data available obtained οsin?—41 ss.|., \citet{rgbgz02} derived the projected rotational velocity and after merging it with the data available obtained $\vsini=41~$ $^{-1}$.
" The orbital elements were derived by Harper(1935). - P=11.039"". A—260kms+. e22023. 1,=49kms tow=618."," The orbital elements were derived by \citet{Harper35} - $P_{\rm orb}=11.039^{d}$, $K=26.0~{\rm km\,s^{-1}}$, =0.23, $V_0=-4.9~{\rm km\,s^{-1}}$, $\omega={\rm 61^{\circ}.8}$."
 Again. as in the case of 1138213 the dilferences between our racial velocity measurements and the predicted velocity curve are due to a small phase shift accumulated over the vears.," Again, as in the case of 138213 the differences between our radial velocity measurements and the predicted velocity curve are due to a small phase shift accumulated over the years."
 There have been a few elements abundances published in the literature. Lemke(1989," There have been a few elements abundances published in the literature. \citet{lemke89},"
).. Lemke(1990) and ltentzsch-Llolm(1997). eave the abundances of Fe. Ti. €. Ba. N and S using the atmospheric parameters Z;; 29100Why and log g=4.8 which were very close to our values (see Table 2)).," \citet{lemke90} and \citet{rh97} gave the abundances of Fe, Ti, C, Ba, N and S using the atmospheric parameters $T_{\rm eff}$ K and $\log g$ =4.3 which were very close to our values (see Table \ref{t2}) )."
 According to the abundances obtained by us. 1196544 seems to be an Am star.," According to the abundances obtained by us, 196544 seems to be an Am star."
 The abuncances of Fe and Ca are very well determined as Ca is underabundant and Fe is overabundant., The abundances of Fe and Ca are very well determined as Ca is underabundant and Fe is overabundant.
 Li line of eds very weak and the abundance of Li is determined. as only an upper limit., Li line of is very weak and the abundance of Li is determined as only an upper limit.
 Other elements like €. O and Ti have weak lines in this spectral region. so their abundances should be scrutinized as upper limits.," Other elements like C, O and Ti have weak lines in this spectral region, so their abundances should be scrutinized as upper limits."
 The dillerences between the abundances of Fe. Ti aid € obtained by us and. published by Lemke(1989). are within the errors.," The differences between the abundances of Fe, Ti and C obtained by us and published by \citet{lemke89} are within the errors."
 220418s(Hx. Pee. 88210. 1105860. |18 4794. WD221241|191. ASm) is an interesting single-Iined spectroscopic binarv with a companion star which is a massive white να C," 204188(IK Peg, 8210, 105860, +18 4794, 2124+191, A8m) is an interesting single-lined spectroscopic binary with a companion star which is a massive white dwarf."
owleyetal(1969)— identified 552160 as à mareinal Am star and determined the spectral class as ASm: but Abt&Bidelman(1969). identified itas a definite Am star., \citet{ccjj69} identified 8210 as a marginal Am star and determined the spectral class as A8m: but \citet{abtbid69} identified it as a definite Am star.
 According to Bertaud(1970). the spectral class of HICSS210 wasbetween AS and FO., According to \citet{bertaud70} the spectral class of 8210 wasbetween A5 and F0.
 Later Guthrie(1987). in his study of the caleium abundances in metallic-line stars found that Ca was almost solar abundant., Later \citet{Guthrie87} in his study of the calcium abundances in metallic-line stars found that Ca was almost solar abundant.
 The most completed spectral identification was mace by Abt&Alorrell(19905). - AG/ZAO9/E0 from Ix/IL/moetallie lines., The most completed spectral identification was made by \citet{am95} - A6/A9/F0 from K/H/metallic lines.
 Wurtz(1978). obtained that the primary Am star was also ὁ Set star., \citet{kurtz78} obtained that the primary Am star was also $\delta$ Sct star.
 Till now there are only a few stars which combine in one and the same star such contradictory characteristics., Till now there are only a few stars which combine in one and the same star such contradictory characteristics.
 The first orbit determination was made by Llarper(1927) who found the period of about 27 days ancl almost. circular orbit., The first orbit determination was made by \citet{Harper27} who found the period of about 27 days and almost circular orbit.
 Later he clarified the period. (Harper (1935))) and Batten.Fletcher&Mann(1978). assumed the eccentricity as ¢==0., Later he clarified the period \citet{Harper35}) ) and \citet{bfm78} assumed the eccentricity as =0.
 We used the orbital parameters from the Ninth Catalogue of Spectroscopic Binary Orbits (SBO)(Pourbaixetal. (2004): Pan= 21.7247. Wo=415kms+. e220. Το=24kms tow=O0.," We used the orbital parameters from the Ninth Catalogue of Spectroscopic Binary Orbits \citet{Pourbaix04}: $P_{\rm orb}=21.724^{d}$ , $K=41.5~{\rm km\,s^{-1}}$, =0, $V_0=-12.4~{\rm km\,s^{-1}}$, $\omega={\rm 0^{\circ}}$."
 There have. been many evaluations of the projected. rotational velocity of Hx. Peg in the literature - from resins=SO kmss+ (Lovato (1975))) to esin/=31kmss 1 (Abt&Morrell (1995)))., There have been many evaluations of the projected rotational velocity of IK Peg in the literature - from $\vsini=80~$ $^{-1}$ \citet{Levato75}) ) to $\vsini=31~$ $^{-1}$ \citet{am95}) ).
 Roverοἱal.(2002). determined the projected rotational velocity as resin?=40 scaling the results of Abt&Alorrcll (1995).," \citet{rgbgz02}
 determined the projected rotational velocity as $\vsini=40~$ $^{-1}$ scaling the results of \citet{am95}."
. Phe projected. rotational velocity. obtained. by us resin?=36kmss Ljsin the range of Abt&Morrell(1995) and Roveretal.(2002). ancl very close to the values given by Roclriguez.Lopez-Gonzalez&LopezdeCoca (2000).., The projected rotational velocity obtained by us $\vsini=36~$ $^{-1}$ is in the range of \citet{am95} and \citet{rgbgz02} and very close to the values given by \citet{rll00}. .
 The iron-peak elements like Fe. Pi and Ni are sligthly overabundant and those of Ca ane O - underabundant.," The iron-peak elements like Fe, Ti and Ni are sligthly overabundant and those of Ca and O - underabundant."
 For Li we present only an upper limit., For Li we present only an upper limit.
 As for the other stars of this study. Ba is overabundant., As for the other stars of this study Ba is overabundant.
 These results as well as the atmospheric parameters are in good agreement with the, These results as well as the atmospheric parameters are in good agreement with the
"of f (for E,>E Hc. Fu.mHis2[y c9my) is derived in 2).","of $f$ (for $E_{\mu} >> m_{\mu} c^2$ , $E_{\pi} >> m_{\pi} c^2$, $E_{p} >> m_{p} c^2$) is derived in \citet{2005MNRAS.363.1173B}."
" The steady state spectrum of high energy electrons in the IGM is given by (e.g.23: where the relevant cooling processes involve synchrotron and inverse Compton losses: B is the local magnetic field strength and D,/ἅπ gives the energy density of the CMB expressed as an equivalent magnetic field.", The steady state spectrum of high energy electrons in the IGM is given by \citep[e.g.][]{2000A&A...362..151D}: where the relevant cooling processes involve synchrotron and inverse Compton losses: $B$ is the local magnetic field strength and $B^{2}_{\mathrm{CMB}}/8\pi$ gives the energy density of the CMB expressed as an equivalent magnetic field.
 We calculate the electron spectrum from Eqs. 2-, We calculate the electron spectrum from Eqs. \ref{qepm1}-
-4 and 6-—7:: this can be approximated by: is related to fin Eq., \ref{fpi} and \ref{Nstat}- \ref{CRloss}; this can be approximated by: where $g$ is related to $f$ in Eq.
 5 via: . 1 for £7zzfew GeV. Theradio emissivity is : Ray be 3⋅ where vo=(3προsind(mc) is the critical frequency and F the integral over the synchrotron kernel: Here /v denotes the modified Bessel function of order 5/3., \ref{qelectrons} via: and $\Delta \approx 0.2$ for $E \approx$ few GeV. The radio emissivity is: where $\nu_{\mathrm{c}} = (3/4\pi) p^{2} e B \sin \theta /(mc)^{3}$ is the critical frequency and F the integral over the synchrotron kernel: Here $K_{\frac{5}{3}}$ denotes the modified Bessel function of order 5/3.
" For a power law spectrum of CRp. Αμ)xE,"""". the resulting synchrotron emission from secondary electrons is Joxpoe A"," For a power law spectrum of CRp, $N_p(E_p) \propto E_p^{-\alpha_{\mathrm{p}}}$, the resulting synchrotron emission from secondary electrons is $j_{\nu} \propto \nu^{-(\alpha_{\mathrm{p}} -\Delta)/2}$ ."
 As already mentioned before. CRp - proton collisions produce neutral pions. which in turn decay to 2 photons.," As already mentioned before, CRp - proton collisions produce neutral pions, which in turn decay to 2 photons."
 + -rays are a direct measure of the CRp and provide a complementary constraint to the injection process of secondary electrons., $\gamma$ -rays are a direct measure of the CRp and provide a complementary constraint to the injection process of secondary electrons.
 In order to allow for a prompt comparison with recent results we follow the formalism described in ?) to estimate the + -ray flux from CR in our simulations., In order to allow for a prompt comparison with recent results we follow the formalism described in \citet{2004A&A...413...17P} to estimate the $\gamma$ -ray flux from CR in our simulations.
" The  -ray source function is: where a.ca, is the asymptotic slope of the + -ray spectrum. which resembles the slope of the proton spectrum (2).."," The $\gamma$ -ray source function is: where $\alpha_{\gamma} \simeq \alpha_{\mathrm{p}}$ is the asymptotic slope of the $\gamma$ -ray spectrum, which resembles the slope of the proton spectrum \citep{1986A&A...157..223D}."
 The shape parameter. which describes the semianalytic model near the pion threshold. is 6.=O.4a.*°|0.44 by using an effective section app=32(0.06|exp(442.40.))mbarn.," The shape parameter, which describes the semianalytic model near the pion threshold, is $\delta_{\gamma} = 0.14 \alpha_{\gamma}^{-1.6} + 0.44$ by using an effective cross-section $\sigma_{\mathrm{PP}} = 32 \times (0.96 +
\mathrm{exp}(4.4-2.4\alpha_{\gamma})) \,\mathrm{mbarn}$."
 The integrated -ray source density A. is then obtained by integrating the source function over energy (2) where B.(a.b) denotes the incomplete beta-function and JG=flayf(b).," The integrated $\gamma$ -ray source density $\lambda_{\gamma}$ is then obtained by integrating the source function over energy \citep{2004A&A...413...17P} : where $\mathcal{B}_{\mathrm{x}}(a,b)$ denotes the incomplete beta-function and $[f(x)]^{a}_{b} = f(a) - f(b)$."
 To investigate the dependence of the predicted properties of non thermal emission of clusters on theunderlying assumptions. we investigate 3 models for the distribution of magnetic fields and cosmic rays in clusters.," To investigate the dependence of the predicted properties of non thermal emission of clusters on theunderlying assumptions, we investigate 3 models for the distribution of magnetic fields and cosmic rays in clusters."
 They are chosen to encompass the reasonable range suggested by theoretical and observational findings., They are chosen to encompass the reasonable range suggested by theoretical and observational findings.
" We keep the spectral index fixed to aj,=2.6 in order to be able to match the typical spectrum of giant radio halos. a~1.21.3 te.g.2).. although a fraction of presently known halos has a steeper spectrum (e.g.22) Also. a spectral index a),=2.6 allows to fit the spectral shape of the Coma halo atv <1.4 GHz. although also in this case the spectrum steepens at higher frequencies 990 In our first model the energy density of the CR protons is taken as a constant fraction of the thermal energy density."," We keep the spectral index fixed to $\alpha_{\mathrm{p}}=2.6$ in order to be able to match the typical spectrum of giant radio halos, $\alpha \sim 1.2-1.3$ \citep[e.g.][]{2008SSRv..134...93F}, although a fraction of presently known halos has a steeper spectrum \citep[e.g.][]{2008Natur.455..944B,2009A&A...507.1257G}
 Also, a spectral index $\alpha_{\mathrm{p}}=2.6$ allows to fit the spectral shape of the Coma halo at $\nu \leq 1.4$ GHz, although also in this case the spectrum steepens at higher frequencies \citep[e.g.][]{2003A&A...397...53T,2010MNRAS.401...47D}
 In our first model the energy density of the CR protons is taken as a constant fraction of the thermal energy density."
 This is reasonable if a constant fraction of the energy that is channeled into the IGM to heat the gas goes into the acceleration of CRp., This is reasonable if a constant fraction of the energy that is channeled into the IGM to heat the gas goes into the acceleration of CRp.
" Therefore. in this model. the normalisation A, is chosen to have a constant fraction, VY),=const. of kinetic CRp energy density c, to thermal energy density ci of the IGM: For the magnetic field distribution within the IGM we take directly the magneticfield extracted from the simulations."," Therefore, in this model, the normalisation $K_{\mathrm{p}}$ is chosen to have a constant fraction, $X_{\mathrm{p}}=\mathrm{const}$, of kinetic CRp energy density $\epsilon_{\mathrm{p}}$ to thermal energy density $\epsilon_{\mathrm{th}}$ of the IGM: For the magnetic field distribution within the IGM we take directly the magneticfield extracted from the simulations."
 In a second model we adopt a radius dependent cosmic ray energy density fraction. Node). as obtained from. simulations of CR acceleration in structure formation shocks by 2).. ," In a second model we adopt a radius dependent cosmic ray energy density fraction, $X_{\mathrm{CR}}(r)$ , as obtained from simulations of CR acceleration in structure formation shocks by \citet{2007MNRAS.378..385P}. ."
"We also assume a constant CRp spectral index over the whole cluster volume. à,= 2.6."," We also assume a constant CRp spectral index over the whole cluster volume, $\alpha_{\mathrm{p}}=2.6$ ."
 assundune ano dustantancous aud coniplete isobaric ο burn between 105&cur2cy Hp.,assuming an instantaneous and complete isobaric $^{12}$ C burn between $10^8\cd < y <y_b$ .
 This gives (οπο&Macbeth20014:Cimunineal. 2006).. (," This gives \citep{Cumming:04b, Cumming:06}, ."
x) IIlere we instead use the results of our (inge)time-dependent detonation calculation to determine T4)., Here we instead use the results of our time-dependent detonation calculation to determine $T_f(y)$.
 The ej tera has coutributious from two regious of uuburned fuel: the ?C between gp.<<4gων aud the I/We at y<yy., The $\epsilon_{\rm nuc}$ term has contributions from two regions of unburned fuel: the $^{12}$ C between $y_{\rm He} < y < y_{\rm det}$ and the H/He at $y < y_{\rm He}$.
" As noted in διὰ, due to the sharp temperature gradient at gq4. the °C will likely buri in a convective deflaeration that will reach the II/IΊο laver a few as after passage of the shock."," As noted in \ref{sec:upward}, due to the sharp temperature gradient at $y_{\rm det}$, the $^{12}$ C will likely burn in a convective deflagration that will reach the H/He layer a few $\trm{ms}$ after passage of the shock."
 For snslicity. we assunie an instautancous isobaric το) burn (apxoximately given by equation H[) in the deflagration reelOll «πο<<μαι ," For simplicity, we assume an instantaneous isobaric $^{12}$ C burn (approximately given by equation \ref{eq:isobaric}] ]) in the deflagration region $y_{\rm He} < y < y_{\rm det}$."
We assunue| an eneresv release iu the deflagration of Ej=101eresο+. corresponding to ?C Inning to °° Fe with Nyoz0.1. the fraction of fue ποιαήλιο at the ouset of the runaway that follows the convective stage.," We assume an energy release in the deflagration of $E_{\rm nuc}=10^{17} \trm{ ergs g}^{-1}$, corresponding to $^{12}$ C burning to $^{56}$ Fe with $X_{12}\approx0.1$, the fraction of fuel remaining at the onset of the runaway that follows the convective stage."
 To account for IL and Πο burning. we adopt separate strateeics depending on whether the shock triggersao uustable ! Ie buruius.," To account for H and $^4$ He burning, we adopt separate strategies depending on whether the shock triggers unstable $^4$ He burning."
 If the shock triggersoo unstable Te, If the shock triggers unstable $^4$He
 The advection/diffusion of large-scale (poloidal) magnetic fields is described by wherepotential. and the vertical velocity v- of the flow is neglected.," The advection/diffusion of large-scale (poloidal) magnetic fields is described by where, and the vertical velocity $v_z$ of the flow is neglected."
 Assuming the azimuthal current distribution in the vertical direction to be homogeneous. we have where J(R) is the surface currentdensity at A in the disk.," Assuming the azimuthal current distribution in the vertical direction to be homogeneous, we have where $J_{\phi}^{\rm s}(R)$ is the surface currentdensity at $R$ in the disk."
 As the work by Lubowetal.(1994).. the magnetic field potential (Roz)=ca4(Rz)cS(R25). where (ΑΝ.z) is contributed by the currents 1n the accretion flow. and c4(R)=BoR/2 1s the external imposed homogeneous vertical field. which can be regarded as being contributed by the currents at infinity (seeLubowetal.1994.forthe details)..," As the work by \citet{1994MNRAS.267..235L}, the magnetic field potential $\psi(R,z)=\psi_{\rm d}(R,z)+\psi_{\infty}(R,z)$, where $\psi_{\rm d}(R,z)$ is contributed by the currents in the accretion flow, and $\psi_{\infty}(R)=B_0R/2$ is the external imposed homogeneous vertical field, which can be regarded as being contributed by the currents at infinity \citep*[see][for the
details]{1994MNRAS.267..235L}. ."
 The potential cy Is related to J(8) with Differentiate Eq. (41) )," The potential $\psi_{\rm d}$ is related to $J_{\phi}^{\rm s}(R)$ with Differentiate Eq. \ref{psi}) ),"
 we have For steady case. Le. O/Or=0. equation (39)) becomes where the magnetic Prandtl number is define as 74= 1/1.," we have For steady case, i.e., $\partial/\partial t=0$, equation \ref{indu_1}) ) becomes where the magnetic Prandtl number is define as ${\cal P}_{\rm
m}=\eta/\nu$ ."
 This equation can reduce to a setof linear algebraic equations. Le.," This equation can reduce to a setof linear algebraic equations, i.e.,"
As an example we consider the coutributiou to the autiprotou flux eiven bv a chunp of neutralino dark matter defined by the same choice of paranueters as in Deugtsson ct al. (,As an example we consider the contribution to the antiproton flux given by a clump of neutralino dark matter defined by the same choice of parameters as in Bengtsson et al. (
1990). where chunipiuess was introduced in connection with the ucutralino induced >-rav signal with contimmunu enerev spectrum.,"1990), where clumpiness was introduced in connection with the neutralino induced $\gamma$ -ray signal with continuum energy spectrum."
 We fx hence M~10AZ. and 6~10°: the prefactor 348 is then about 1.3.101pkpe?. where we assuned as local halo density py=O8CeVan7.," We fix hence $M_{cl} \sim 10^{8} M_\odot$ and $\delta \sim 10^3$; the prefactor $M_{cl} \delta$ is then about $1.3 \cdot 10^4 \rho_0\,\rm{kpc}^{3}$, where we assumed as local halo density $\rho_0 = 0.3 \,\rm{GeV}\,\rm{cm}^{-3}$."
 Comparing the cocffücieut C-— with the analogous quantitv iu a smooth halo scenario(with the same choice of propagation model paramcters Cut=1GeV)—107ciasr 13 we find that the antiprotou flux from this sinele dark matter clump cau be at the level (or much higher) than the stm of the contributions from the whole dark matter halo if this source is within about [.5 kpe.," Comparing the coefficient $C_{\rm prop}^{cl}$ with the analogous quantity in a smooth halo scenario(with the same choice of propagation model parameters $C_{\rm prop}(T=1\,\rm{GeV}) \sim 10^{25}\,\rm{cm}\,\rm{sr}^{-1}$ ) we find that the antiproton flux from this single dark matter clump can be at the level (or much higher) than the sum of the contributions from the whole dark matter halo if this source is within about 4.5 kpc."
 We night also cousider au opposite approach., We might also consider an opposite approach.
" It is well established that a dark mass of at least 2«10937, is concentrated within 0.015 pc at the ealactic ceutre (Eckart Couzel 1996). forming probably a 1iassive black hole. possibly the astroplivsical object which is called Sex A."," It is well established that a dark mass of at least $2 \cdot 10^{6} M_\odot$ is concentrated within 0.015 pc at the galactic centre (Eckart Genzel 1996), forming probably a massive black hole, possibly the astrophysical object which is called Sgr $^*$."
 Such accretion of matter müghnt be associated to a region where the density of neutraliuo dark matter is eulauced as well., Such accretion of matter might be associated to a region where the density of neutralino dark matter is enhanced as well.
 Iu au extreme scenario (Berezinsky et al., In an extreme scenario (Berezinsky et al.
 1992) the potential well of a very steep dark matter halo profile (~1 pL) as the seed for the formation of the black hole itself., 1992) the potential well of a very steep dark matter halo profile $\sim 1/r^{1.8}$ ) is the seed for the formation of the black hole itself.
 It is also intriguing that an excess in the high euergv y-ray flux from the ealactic ceutre region. which has been found from the analysis of EGRET ata (Alaver-Tasschwanucer et al.," It is also intriguing that an excess in the high energy $\gamma$ -ray flux from the galactic centre region, which has been found from the analysis of EGRET data (Mayer-Hasselwander et al."
 1998). cau be explained in terms of neutralino aunilhilatious if an appropriate chhancement of the neutralino density is preseut there (Ullio 1999).," 1998), can be explained in terms of neutralino annihilations if an appropriate enhancement of the neutralino density is present there (Ullio 1999)."
 Reeardless of its possible origin. we cau estimate how large he accretion of neutralinos at the ealactic ceutre should be to give a measurable primary antiproton flux.," Regardless of its possible origin, we can estimate how large the accretion of neutralinos at the galactic centre should be to give a measurable primary antiproton flux."
 Assuming that the ealactocentric distance is 8.5 kpc. we find tha the flux induced by a source at the ealactic centre is xoportional to CLuSkpe)~πμ”.kpe (at T=1 GeV ).," Assuming that the galactocentric distance is 8.5 kpc, we find that the flux induced by a source at the galactic centre is proportional to $C_{\rm prop}^{cl} (8.5\,\rm{kpc}) \sim 4.5 \cdot 10^{19}
\,\rm{cm}\,\rm{sr}^{-1}\,\rm{kpc}^{-3}$ (at T=1 GeV )."
 Tf we require for lustance that its coutribution should be at least oue half of the total flux in a smooth halo scenario. we find that AL76 should be at least of the order of 1012AL...," If we require for instance that its contribution should be at least one half of the total flux in a smooth halo scenario, we find that $M_{cl} \delta$ should be at least of the order of $10^{12} M_\odot$."
 There is the possibility that a large fraction of the dark uatter nass is iu clumps. in the extreme case all of it.," There is the possibility that a large fraction of the dark matter mass is in clumps, in the extreme case all of it."
 To avoid violating dynamical constraints. clumps should be ight. with masses probably less than M4~10t109AZ...," To avoid violating dynamical constraints, clumps should be light, with masses probably less than $M_{cl} \sim 10^{4} - 10^{6} M_\odot$."
 If one could deal with a model that gives some accurate xedietiou for the masses of clamps aud their distribution in the Calas. it would be possible to exploit the approach of the previous paragraph and estimate the autiprotou Hux by adding the contributions from individual sources.," If one could deal with a model that gives some accurate prediction for the masses of clumps and their distribution in the Galaxy, it would be possible to exploit the approach of the previous paragraph and estimate the antiproton flux by adding the contributions from individual sources."
 As very little is known about the inhereutlv nou linear woblem of generating dark matter chumps. it secs more reasonable to follow a probabilistic approach.," As very little is known about the inherently non linear problem of generating dark matter clumps, it seems more reasonable to follow a probabilistic approach."
 Let f he the fraction of dark matter m chnunps aud Ny the total uunuber of chimps. all roughly of about the sale lnass and overdensitv.," Let $f$ be the fraction of dark matter in clumps and $N_{cl}$ the total number of clumps, all roughly of about the same mass and overdensity."
 We can defiue a probability density distribution of the chips in the Galaxy which iu the limit of larec f. o fulfll dvuiuical coustraints. has to follow the mass distribution iu the halo.," We can define a probability density distribution of the clumps in the Galaxy which in the limit of large $f$, to fulfill dynamical constraints, has to follow the mass distribution in the halo."
 In a Cartesian coordinate svsteni with origin at the ealactic centre. the probability to fiud a given chuup iu the volume clement d? at position ad is: We introduced here Mj. the total mass of the halo. so that pa has the correct normalization |patagdy— 1.," In a Cartesian coordinate system with origin at the galactic centre, the probability to find a given clump in the volume element $d^{\,3}x$ at position $\vec{x}$ is: We introduced here $M_h$, the total mass of the halo, so that $p_{cl}$ has the correct normalization $\int p_{cl} (\vec{x}) d^{\,3}x = 1$ ."
 The autiproton source function in the volume clement d? at the ooOealactic position à: is thon: while the autiproton flux is:," The antiproton source function in the volume element $d^{\,3}x$ at the galactic position $\vec{x}$ is then: while the antiproton flux is:"
removal of 0743-6719 or 0302-2223 results in the (wo values of D that are well-defined and that are in reasonable agreement with the value ealeulated at high redshift in the constant threshold ease.,removal of 0743-6719 or 0302-2223 results in the two values of $\Gamma$ that are well-defined and that are in reasonable agreement with the value calculated at high redshift in the constant threshold case.
" Removing only the one line [rom 0743-6719 nearest the Ly-a emission line with τμ=1.5058 and observed equivalent width equal to 0.23 results in P=6.23x10P !;,", Removing only the one line from 0743-6719 nearest the $\alpha$ emission line with $z_{\rm abs}=1.5058$ and observed equivalent width equal to 0.23 results in $\Gamma = 6.23 \times 10^{-12}$ $^{-1}$.
 This object was part of the LIST Kev Project sample (Jannuzi et 11998) and they cite no evidence of associated aborption in its spectrum., This object was part of the HST Key Project sample (Jannuzi et 1998) and they cite no evidence of associated aborption in its spectrum.
 Removing only the one line from 0302-2223 nearest (he Lv-o. emission line with τμ=1.3886 and observed equivalent width equal to 0.27 .results in D=8.14x10.P |., Removing only the one line from 0302-2223 nearest the $\alpha$ emission line with $z_{\rm abs}= 1.3886$ and observed equivalent width equal to 0.27 results in $\Gamma = 8.14 \times 10^{-12}$ $^{-1}$.
" This object shows an absorption svstem at zap,=1.406 and is Classified as an associated absorber.", This object shows an absorption system at $z_{\rm abs}=1.406$ and is classified as an associated absorber.
" No metal absorption is seen al z44,,=1.3886. though this absorber is within 5000 km | of the QSO. the canonical associated absorber region."," No metal absorption is seen at $z_{\rm abs}= 1.3886$, though this absorber is within 5000 km $^{-1}$ of the QSO, the canonical associated absorber region."
 Removing both of these lines gives T=3.88x1012 +., Removing both of these lines gives $\Gamma = 3.88 \times 10^{-12}$ $^{-1}$.
 Due to the small equivalent widths of both of these lines thev are not inelucled in the constant threshold analvsis. and the solutions for (79) aud D for z>1 are well-defined.," Due to the small equivalent widths of both of these lines they are not included in the constant threshold analysis, and the solutions for $J(\nu_{0})$ and $\Gamma$ for $z > 1$ are well-defined."
 It appears that this method has some trouble reliably recovering the background from a sample of absorption lines above an equivalent width threshold allowed to vary with S/N. As the method works well for the constant threshold case. we contend that the photoionization model. expressed in Equ. 3..," It appears that this method has some trouble reliably recovering the background from a sample of absorption lines above an equivalent width threshold allowed to vary with S/N. As the method works well for the constant threshold case, we contend that the photoionization model, expressed in Equ. \ref{eq:dndx},"
 used to create the likelihood function must not be an adequate model for (he proximity effect when weak lines are included in the analysis., used to create the likelihood function must not be an adequate model for the proximity effect when weak lines are included in the analysis.
 Liske Williger (2001) introduce a method for extracting J(4) from QSO spectra based on flux statistics., Liske Williger (2001) introduce a method for extracting $J(\nu_{0})$ from QSO spectra based on flux statistics.
 We shall return to this topic in future work., We shall return to this topic in future work.
 As the results listed in Table 4. indicate. the inclusion of the four blazars and one BL Lac object. all at 2«1. in our sample does not change the result. significantly.," As the results listed in Table \ref{table-jnu} indicate, the inclusion of the four blazars and one BL Lac object, all at $z < 1$, in our sample does not change the result significantly."
 However. (here is much observational evidence that radio loud and radio quiet quasars inhabit different environments. namely (hat radio loud quasars reside in rich clusters while radio quiet quasars exist in galaxy environments consistent with the field (Stockton 1932. Yee Green 1984. 1987. Yee LOST. Yates. Miller. Peacock 1989. Ellingson. Yee. Green 1991. Yee Ellingson 1993. Wold et 22000. Smith. Bovle. Maddox 2000).," However, there is much observational evidence that radio loud and radio quiet quasars inhabit different environments, namely that radio loud quasars reside in rich clusters while radio quiet quasars exist in galaxy environments consistent with the field (Stockton 1982, Yee Green 1984, 1987, Yee 1987, Yates, Miller, Peacock 1989, Ellingson, Yee, Green 1991, Yee Ellingson 1993, Wold et 2000, Smith, Boyle, Maddox 2000)."
 If there is a corresponding increase in (he number of Lv-o. absorption lines in the spectra of radio loud objects. this could cause the proximity effect to be suppressed. and the measured log[J(245)] to be artificially large.," If there is a corresponding increase in the number of $\alpha$ absorption lines in the spectra of radio loud objects, this could cause the proximity effect to be suppressed, and the measured $J(\nu_{0})$ ] to be artificially large."
 We have therefore divided our sample into radio loud and radio quiet subsamples using the, We have therefore divided our sample into radio loud and radio quiet subsamples using the
In a rough manner of speaking. the lisht from all accreting black holes. whether those of stellar mass (Galactic Black Holes. or GDIIs) or those residing in galactic nuclei with masses,"In a rough manner of speaking, the light from all accreting black holes, whether those of stellar mass (Galactic Black Holes, or GBHs) or those residing in galactic nuclei with masses"
For ease of exposition we assume that the initial turbulence spectrum has the form (4.0)Ijk7. so that Eq. (67) ,"For ease of exposition we assume that the initial turbulence spectrum has the form $I(k,0)=I_0k^{-2}$, so that Eq. \ref{57}) )"
"becomes where A=(IoD/|Zu|Y"".", becomes where $\Delta \equiv (I_0/|Z_0|)^2$.
 According to quasilinear theory (e.g. Earl 1973. Schlickeiser 1989)) as a consequence of pitch-angle scattering the beam particles adjusts to the isotropic distribution (41)) on a length scale given by the scattering length with e=V4/e and To obtain Eq. (69))," According to quasilinear theory (e.g. Earl \cite{earl73}, Schlickeiser \cite{sch89}) ) as a consequence of pitch-angle scattering the beam particles adjusts to the isotropic distribution \ref{36}) ) on a length scale given by the scattering length, with $\epsilon =V_{\rm A}/v$ and ^2) To obtain Eq. \ref{59}) )"
 we have inserted Eqs. (66)), we have inserted Eqs. \ref{56}) )
 and (68))., and \ref{58}) ).
 After staightforward but tedious integration the value of the integral (??)) to lowest order in the small parameters e<<| and A<< Lis so that the scattering length (59) becomes with Eq. (44)), After staightforward but tedious integration the value of the integral \ref{60}) ) to lowest order in the small parameters $\epsilon <<1$ and $\Delta <<1$ is so that the scattering length (59) becomes with Eq. \ref{38}) )
 Inserting our typical parameter values we obtain Note that the ratio of initial to fully developed turbulence intensities enters only weakly via the logarithm., Inserting our typical parameter values we obtain Note that the ratio of initial to fully developed turbulence intensities enters only weakly via the logarithm.
" For turbulence intensity ratios from 10. to 10.? implying values of A from 10.2 to LO2 we find with jy~10 σα, varies between 5.9 and 27.3."," For turbulence intensity ratios from $10^{-1}$ to $10^{-5}$ implying values of $\Delta $ from $10^{-2}$ to $10^{-10}$ we find with $\beta_{\rm A}\simeq 
10^{-2}$ that $\ln [\sqrt {2}\beta_{\rm A}\Delta ]^{-1}$ varies between $8.9$ and $27.3$."
 Taking the larger value in Eq. (??)), Taking the larger value in Eq. \ref{63}) )
 yields for the scattering length in the blast wave plasma which. corresponds to an isotropisation. time. scale of λαος7 If the thickness ¢/ of the blast waveregion is larger than the scattering length (75). indeed an isotropic distribution of the inflowing interstellar protons and electrons with Lorentz factor (see Eq. (62))," yields for the scattering length in the blast wave plasma which corresponds to an isotropisation time scale of /c=2 If the thickness $d$ of the blast waveregion is larger than the scattering length (75), indeed an isotropic distribution of the inflowing interstellar protons and electrons with Lorentz factor (see Eq. \ref{52}) ))"
 <P>=τα42)~FE in the blast wave ame Is effectively generated., $<\Gamma >=\Gamma (1-\beta_{\rm A}\beta )\simeq \Gamma $ in the blast wave frame is effectively generated.
 In the following sections we Vestigate the radiation products resulting from the inelastic [nteractions of these primary particles with the cold blast wave plasma., In the following sections we investigate the radiation products resulting from the inelastic interactions of these primary particles with the cold blast wave plasma.
 This discussion of particle isotropization on. self-excited turbulence applies to both AGN and GRBs., This discussion of particle isotropization on self-excited turbulence applies to both AGN and GRBs.
 The radiation modellingof GRBs often requires energy equipartition between electrons and protons (Katz 1994)). based on detailed plasma physics considerations (e.g. Beloborodov JeeDRpiansski 1995:: Smolsky Usov 1996:: Smolsky Usov 1999)).," The radiation modellingof GRBs often requires energy equipartition between electrons and protons (Katz \cite{ka94}) ), based on detailed plasma physics considerations (e.g. Beloborodov Demiańsski \cite{be95}; Smolsky Usov \cite{su96}; Smolsky Usov \cite{su99}) )."
 However. the isotropization itself provides electrons with an energy roughly 2000 times smaller than that of the protons.," However, the isotropization itself provides electrons with an energy roughly 2000 times smaller than that of the protons."
 Therefore a reacceleration of electrons would be required to reach equipartition., Therefore a reacceleration of electrons would be required to reach equipartition.
 Since the energy density of the turbulence ts only a fraction (x 74) of the energy density of the incoming beam. the turbulence is not energetic enough to reaccelerate electrons for 4l. and further studies may be required to understand the production of radiation in GRBs.," Since the energy density of the turbulence is only a fraction $\propto \beta_{\rm A}$ ) of the energy density of the incoming beam, the turbulence is not energetic enough to reaccelerate electrons for $\beta_{\rm A} \ll 1$, and further studies may be required to understand the production of radiation in GRBs."
 The situation is different with AGN. for which equipartition is not required and for which the variability timescales are substantially longer.," The situation is different with AGN, for which equipartition is not required and for which the variability timescales are substantially longer."
 Here we will discuss the radiation modelling for AGN on the basis of the particle distributions resulting from the isotropization process alone., Here we will discuss the radiation modelling for AGN on the basis of the particle distributions resulting from the isotropization process alone.
 ow we deal with isotropic particle distribution functions in the blast wave frame. which itself is not stationary because the blast wave sweeps up matter and thus momentum.," Now we deal with isotropic particle distribution functions in the blast wave frame, which itself is not stationary because the blast wave sweeps up matter and thus momentum."
 Aomentum conservation then requires a deceleration of the blast wave depending on whether or not the swept-up particles naintai1 their initial kinetic energy. and depending on possible nomentum loss from anisotropic emission of electromagnetic radiation.," Momentum conservation then requires a deceleration of the blast wave depending on whether or not the swept-up particles maintain their initial kinetic energy, and depending on possible momentum loss from anisotropic emission of electromagnetic radiation."
 As we have sketched in Fig.l.. the blast wave is assumed to have adisk-like geometry with constant radius 7? and thickness d that moves with bulk Lorentz factor I.," As we have sketched in \ref{sketch}, the blast wave is assumed to have a disk-like geometry with constant radius $R$ and thickness $d$ that moves with bulk Lorentz factor $\Gamma$ ."
" The matter density in ‘that disk #7), is supposed to be orders of magnitude higher than that of the ambient medium 177.", The matter density in that disk $n_{\rm b}$ is supposed to be orders of magnitude higher than that of the ambient medium $n_{i}^\ast$ .
"By changing both p and ymin appropriately it may be possible to have a typically high injection index and predict reasonable values for the observable distribution (number density, CXB contribution, volume filling factor, especially after the quasar era) of double-lobed sources.","By changing both $p$ and $\gamma_{\rm min}$ appropriately it may be possible to have a typically high injection index and predict reasonable values for the observable distribution (number density, CXB contribution, volume filling factor, especially after the quasar era) of double-lobed sources."
" Such is the case when p=3 and ymin= 2000, where we are not underestimating radio luminosities as in the p=3 and ymin=1 case."," Such is the case when $p=3$ and $\gamma_{\rm min}=2000$ , where we are not underestimating radio luminosities as in the $p=3$ and $\gamma_{\rm min}=1$ case."
" The minimum injected Lorentz factor Ymin, whose typical value is not well known, appears to be an important parameter for understanding the luminosity evolution of powerful double-lobed sources."," The minimum injected Lorentz factor $\gamma_{\rm min}$, whose typical value is not well known, appears to be an important parameter for understanding the luminosity evolution of powerful double-lobed sources."
 Figure 14 shows the evolution of Lorentz factorssince the time of injection., Figure \ref{fig:gEvo} shows the evolution of Lorentz factorssince the time of injection.
" In correlating injection index p with jet power Qj, we have made the least powerful sources brighter and the most powerful sources dimmer."," In correlating injection index $p$ with jet power $Q_{\rm j}$, we have made the least powerful sources brighter and the most powerful sources dimmer."
" This could, in principle, alter the volume filling factor and number density in either direction."," This could, in principle, alter the volume filling factor and number density in either direction."
" For our correlation we described earlier in this section, the number density and volume filling factor areincreased somewhat from the original case, and double-lobed sources account for 27 per cent of the extended sources of the CDEN survey and per cent of the unresolved CXB."," For our correlation we described earlier in this section, the number density and volume filling factor areincreased somewhat from the original case, and double-lobed sources account for $27$ per cent of the extended sources of the CDFN survey and $6$ per cent of the unresolved CXB."
" The ambient density of galaxies6 and its evolution, which is still not well understood, could significantly affect the estimate for thevolume filling factor of filaments by radio lobes."," The ambient density of galaxies and its evolution, which is still not well understood, could significantly affect the estimate for thevolume filling factor of filaments by radio lobes."
" Decreasing the ambient density (reducing po by a factor of 10) allows for sources to grow larger and initially more luminous, but luminosity also falls more quickly due to increased adiabatic losses."," Decreasing the ambient density (reducing $\rho_0$ by a factor of $10$ ) allows for sources to grow larger and initially more luminous, but luminosity also falls more quickly due to increased adiabatic losses."
 Volume filling factors are increased from the original case to above unity., Volume filling factors are increased from the original case to above unity.
" The observable number density of sources is higher by a factor of 2, however, than observed by the CDEN survey."," The observable number density of sources is higher by a factor of $2$, however, than observed by the CDFN survey."
 The unresolved contribution tothe CXB is 45 per cent., The unresolved contribution tothe CXB is $45$ per cent.
 We also investigate the effect of a steeper density profile with 8=2., We also investigate the effect of a steeper density profile with $\beta=2$.
 The surrounding density is larger than the original case for distances and smaller at distances r>ao., The surrounding density is larger than the original case for distances and smaller at distances $r>a_0$.
 The lobes will end up growing much larger and radio luminosity falls much more quickly in the evolution of the source., The lobes will end up growing much larger and radio luminosity falls much more quickly in the evolution of the source.
 Volume filling factors are increased from case [A] to ~0.4., Volume filling factors are increased from case [A] to $\sim0.4$.
 The contribution to the unresolved CXB is 5 per cent., The contribution to the unresolved CXB is $5$ per cent.
" It may be the case that the typical density profile around FR II sources falls more steeply at higher radii, such as if the density profile is similar to that of relaxed clusters (?),, which follow the Navarro-Frenk-White halo profile (less steep than r? near the centre, more steep than r7? at large distances) (??).. "," It may be the case that the typical density profile around FR II sources falls more steeply at higher radii, such as if the density profile is similar to that of relaxed clusters \citep{2006ApJ...640..691V}, which follow the Navarro-Frenk-White halo profile (less steep than $r^{-2}$ near the centre, more steep than $r^{-2}$ at large distances) \citep{1996ApJ...462..563N, 1997ApJ...490..493N}."
"Since most sources at redshifts z>2 tend to fall below the radio flux limit early in their evolution before they reach Mpc scales (their fractional duration of visibility compared to the jet life time may be less less than 0.01-0.1) (?),, and the total density of double- sources depends on how quickly the sources fall below the flux limit, the density profile nearer the source rather than at large distances plays a more important role in determining the total population of double-lobed sources."," Since most sources at redshifts $z\geq 2$ tend to fall below the radio flux limit early in their evolution before they reach Mpc scales (their fractional duration of visibility compared to the jet life time may be less less than $0.01$ $0.1$ ) \citep{1999AJ....117..677B}, and the total density of double-lobed sources depends on how quickly the sources fall below the flux limit, the density profile nearer the source rather than at large distances plays a more important role in determining the total population of double-lobed sources."
" If most sources were born over a broader span of time, which we investigate by setting Az—1, the volume filling factor during the quasar era is slightly larger than estimated with our original parameter."," If most sources were born over a broader span of time, which we investigate by setting $\Delta z=1$, the volume filling factor during the quasar era is slightly larger than estimated with our original parameter."
 This is a result of the fraction of sources that would be observable above the radio flux limit decreasing due to a wider spread in ages of sources at each redshift., This is a result of the fraction of sources that would be observable above the radio flux limit decreasing due to a wider spread in ages of sources at each redshift.
" With Az—1, we find a volume filling factor of 0.07 at redshifts 2 and 3, assuming all the parameters are the same as in our original case [A], while the number density and unresolved CXB contribution are comparable to the population described by the original birth function with Az—0.6."," With $\Delta z=1$, we find a volume filling factor of $0.07$ at redshifts $2$ and $3$, assuming all the parameters are the same as in our original case [A], while the number density and unresolved CXB contribution are comparable to the population described by the original birth function with $\Delta z=0.6$."
 Steepening the power-law index of jet energies from —2.6 to —3 has the effect of a larger number of sources being undetected in the survey and flattening it has the opposite effect., Steepening the power-law index of jet energies from $-2.6$ to $-3$ has the effect of a larger number of sources being undetected in the survey and flattening it has the opposite effect.
" Compared to the original case [A] which predicts ~29 lobed-galaxies per square degree visible in the X-ray, of which ~4 are IC ghosts, above the X-ray flux limit of the CDFN survey, and predicts the radio sources contribute about 2 per cent of unresolved CXB and the volume filling factor of the lobes is ~0.09-0.02 at z=2-3, if we increase the power-law index of jet energies from —2.6 to —3 we find ~39 visible sources per square degree of which ~4 are IC ghosts, a 6 per cent contribution to the unresolved CXB, and a volume filling factor of the lobes is ~0.07-0.04 at z= 2-3."," Compared to the original case [A] which predicts $\sim29$ lobed-galaxies per square degree visible in the X-ray, of which $\sim4$ are IC ghosts, above the X-ray flux limit of the CDFN survey, and predicts the radio sources contribute about $2$ per cent of unresolved CXB and the volume filling factor of the lobes is $\sim0.03$ $0.02$ at $z=2$ $3$, if we increase the power-law index of jet energies from $-2.6$ to $-3$ we find $\sim 39$ visible sources per square degree of which $\sim4$ are IC ghosts, a $6$ per cent contribution to the unresolved CXB, and a volume filling factor of the lobes is $\sim0.07$ $0.04$ at $z=2$ $3$."
" And if we decrease the power-law index of the jet energies to —2, we find ~16 visible sources per square degree of which ~2 are IC ghosts, a 1 per cent contribution to the unresolved CXB, and a volume filling factor of the lobes is ~ 0.01-0.004at z= 2-3."," And if we decrease the power-law index of the jet energies to $-2$, we find $\sim 16$ visible sources per square degree of which $\sim2$ are IC ghosts, a $1$ per cent contribution to the unresolved CXB, and a volume filling factor of the lobes is $\sim0.01$ $0.004$ at $z=2$ $3$."
 We have developed an analytic model to study the evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the CMB) of FR II radio galaxies in order to quantify the abundance of actual and observable powerful double-lobed radio sources and IC ghosts (sources with jets turned off that still radiate in the X-, We have developed an analytic model to study the evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the CMB) of FR II radio galaxies in order to quantify the abundance of actual and observable powerful double-lobed radio sources and IC ghosts (sources with jets turned off that still radiate in the X-ray).
" For a set of model parameters inferred from observations of radio sources (case [A]), which had t;—108 yr, Ymin= 1, p= 2.14, po=1.67x107?kgm? and 6= 1.5, we predict ~29 lobed-galaxies per square degree visible in the X-ray, of which ~4 are IC ghosts, above the X-ray flux limit of the CDEN survey."," For a set of model parameters inferred from observations of radio sources (case [A]), which had $t_{\rm j}=10^8~{\rm yr}$ , $\gamma_{\rm min}=1$ , $p=2.14$ , $\rho_0= 1.67\times 10^{-23}~{\rm kg}~{\rm m}^{-3}$ and $\beta=1.5$ , we predict $\sim29$ lobed-galaxies per square degree visible in the X-ray, of which $\sim4$ are IC ghosts, above the X-ray flux limit of the CDFN survey."
" The CDEN survey found 167792 extended X-ray sources, which consist of both X-ray clusters and lobes."," The CDFN survey found $167^{+97}_{-67}$ extended X-ray sources, which consist of both X-ray clusters and lobes."
 Thus a considerable fraction of these objects may turn out to be in fact powerful radio, Thus a considerable fraction of these objects may turn out to be in fact powerful radio
'eglcyn are not considered in the gradient determiuation. as in CGC 6377.,"region are not considered in the gradient determination, as in UGC 6377."
 There are some reelous in UOC 6205. as UO05bl aud U05c3. which were cousicerecdl of Ligh metallicity despite the simal value of the log\/O) ratio (section 3.2 in paper I).," There are some regions in UGC 6205, as U05b4 and U05c3, which were considered of high metallicity despite the small value of the log(N/O) ratio (section 3.2 in paper I)."
 Nevertheless. there is not change in the slope beuse they are located at the intermediate part o‘the galaxy. and therefore their iuclusion Is LO cru cial.," Nevertheless, there is not change in the slope because they are located at the intermediate part of the galaxy, and therefore their inclusion is not cru cial."
 As cliseissecl iu j»aper L despite the uucertaiuties in the metallicity ceteriation. ois rot quite likely that a ligh metallicity i'eglon was nmlsclassified as of low metallicity one.," As discussed in paper I, despite the uncertainties in the metallicity determination, it is not quite likely that a high metallicity region was misclassified as of low metallicity one."
 Another source of uncertaity inielit be he low number of rneasureiments for the deteriilation ol the gradient., Another source of uncertainty might be the low number of measurements for the determination of the gradient.
 Dutil Roy (2001) said that iu order to obaiu a robust measurement of the eractient at least 16 clata-polnts are ueeed., Dutil Roy (2001) said that in order to obtain a robust measurement of the gradient at least $16$ data-points are needed.
 This is αι1 impossible :ichieveiuent for the dwarf spiral gaaxles. uainly because most of them «ο not have sich a large 1uuber of regions.," This is an impossible achievement for the dwarf spiral galaxies, mainly because most of them do not have such a large number of regions."
 From the st«ly of Reves-Pérrez (2009) and the Ha images obtalued Lor two dozens of d$ galaxies by Hicaleo-Ganinuez. it can be concluded that less tlall 10 dwarf spirals out of more than 100 have more than 15 'eelons.," From the study of Reyes-Pérrez (2009) and the $\alpha$ images obtained for two dozens of dS galaxies by Hidalgo-Gámmez, it can be concluded that less than $10$ dwarf spirals out of more than $100$ have more than $15$ regions."
 Iu particular. all the regions were sticdlied for UGC 6205 while ouly oue aud two more exist or LOC 5296 and LOC 5212. resyectively (Reves-Pérrez Hidalgo-Giámauez. iu. preparation1).," In particular, all the regions were studied for UGC 6205 while only one and two more exist for UGC 5296 and UGC 5242, respectively (Reyes-Pérrez Hidalgo-Gámmez, in preparation)."
 Therefore. the results here shoild be taken with care because of the small number of data-poiuS. nut it has to be understood t1at tlere are no 1uore regious to be used.," Therefore, the results here should be taken with care because of the small number of data-points, but it has to be understood that there are no more regions to be used."
 Finally. it has to be said hat the eracients determined for aiother 11. galaxies in the literature were determiued with oily jve measurements or less (see able Lin Vila-Costas Exluuuds 1992).," Finally, it has to be said that the gradients determined for another 11 galaxies in the literature were determined with only five measurements or less (see table 4 in Vila-Costas Edmunds 1992)."
 Duti| Roy (2001) also 5aicl tiit not ouly the slope is uncertain cdie to the poor sampli nut also the gradient melt clange when more data-poius are added.," Dutil Roy (2001) also said that not only the slope is uncertain due to the poor sampling, but also the gradient might change when more data-points are added."
 This can be studieLI comparitο the gradieuts deterulned with the Lo. or the DP iethocds and those cetermineclw he N> or Ns Ones. because the number of regio1s luvolved are differeut. being the latter lu ower.," This can be studied here comparing the gradients determined with the $R_{23}$ or the $P$ methods and those determined with the $N_2$ or $N_3$ ones, because the number of regions involved are different, being the latter much lower."
 Tlie best galaxy is UGC 6202 because the nuuber of abundance determinatious afe Lol even wit1i the No aud AN5 methods., The best galaxy is UGC 6205 because the number of abundance determinations are not low even with the $N_2$ and $N_3$ methods.
 In. Table 1 it €ould be seen that there ai'e differences in [n]oO'acieut if cletermined with 11 measurements or wil1 fou fut they are stall.," In Table 1 it could be seen that there are differences in the gradient if determined with $11$ measurements or with four, but they are small."
 One iiell think that this ls he situation or both UGC 5296 and UCC 5212 in the sense that here are iumXlait cli[Iereuces 1 ithe gradieus determined with the clieent methods., One might think that this is the situation for both UGC 5296 and UGC 5242 in the sense that there are important differences in the gradients determined with the different methods.
 For these galaxies the utunber : data-poitis are the saue with both methods aud it is a problem of false nitrogen dete‘{ious., For these galaxies the number of data-points are the same with both methods and it is a problem of false nitrogen detections.
 Therefo'el it can be coiclided that noue of the possibe 50urce of uucertainties have a real ifluence 1 the [n]οLaclent of the :ibLidances.," Therefore, it can be concluded that none of the possible source of uncertainties have a real influence on the gradient of the abundances."
 A [illa criticism tha cau be made to the data presented lere is tlat as the abuudauces ale determi1ος] with few lines. hey might be not very reliable.," A final criticism that can be made to the data presented here is that as the abundances are determined with few lines, they might be not very reliable."
 This should be always taken into acCount when woriug with these galaxies. as well as with other galaxies for wich the abundances have been cleerined Crom the [OILI]/[NII] or the [NII]/Ha ratios. in the local Uuiverse (e.g. Roy et al.," This should be always taken into account when working with these galaxies, as well as with other galaxies for which the abundances have been determined from the [OIII]/[NII] or the $\alpha$ ratios, in the local Universe (e.g. Roy et al."
 1996) or for high z galaxies (e.g. Schulte-Ladbeck et al., 1996) or for high $z$ galaxies (e.g. Schulte-Ladbeck et al.
 2001)., 2004).
 As can be seer from Table 1 the value ol the eradieuts are. in geleral. very similar for each galaxy. when the abutidances are determiued with cifereut methods.," As can be seen from Table 1 the value of the gradients are, in general, very similar for each galaxy when the abundances are determined with different methods."
 Moreover. the values determined with the less/most metallic regions or the internal/exerual regious are also very similar to those determined [rom tle least-squared fittiug.," Moreover, the values determined with the less/most metallic regions or the internal/external regions are also very similar to those determined from the least-squared fitting."
" Therelofe, we think that. although the abundauces for some particular regions can be somehow"," Therefore, we think that, although the abundances for some particular regions can be somehow"
l.,\ref{fig:dns}.
 The frequency of the BIL quasi-normal mode is 9.3kIIz., The frequency of the BH quasi-normal mode is $\sim 9.3$ kHz.
 In addition. à bar-mocle instabilitv might develop in the early stage of (he merger. or a similar instability may arise intermittently in the inner disk.," In addition, a bar-mode instability might develop in the early stage of the merger, or a similar instability may arise intermittently in the inner disk."
 To illustrate the maximum signal levels that could arise [from such instabilities. in equation (11)) we used arbitrary but. plausible parameters mosoam!=2488M..L 7=AGm/c? and assuming that the waves remain coherent [or V=10 cvcles. we have plotted in (he same figure the characteristic strain (circle). wilh an error bar due to the uncertainty in the formation rate.," To illustrate the maximum signal levels that could arise from such instabilities, in equation \ref{eq:bar}) ) we used arbitrary but plausible parameters $m=m^\prime=2.8M_\odot$, $r=4Gm/c^2$ and assuming that the waves remain coherent for $N=10$ cycles, we have plotted in the same figure the characteristic strain (circle), with an error bar due to the uncertainty in the formation rate."
 As discussed above. DII-NS binaries can form from neutron star binaries in which the neutron star of the primary undergoes (oo much accretion during the common envelope phase ancl collapses to a black hole.," As discussed above, BH-NS binaries can form from neutron star binaries in which the neutron star of the primary undergoes too much accretion during the common envelope phase and collapses to a black hole."
 This Formation scenario (e in Table 1) produces a binary consisting of a neutron star of m»~LAAL. and a low-mass black hole of mq~3A. (Frver et al., This formation scenario $a$ in Table 1) produces a binary consisting of a neutron star of $m_2 \sim 1.4M_\odot$ and a low-mass black hole of $m_1 \sim 3M_\odot$ (Fryer et al.
 1999b)., 1999b).
 The more standard formation scenario for DII-NS svstem (scenario 6 in Table 1) begins wilh (wo massive stars in which (he primary have a mass greater (han 20M..., The more standard formation scenario for BH-NS system (scenario $b$ in Table 1) begins with two massive stars in which the primary have a mass greater than $\sim 20M_\odot$.
 The primary evolves off the main sequence. and continues (o evolve.," The primary evolves off the main sequence, and continues to evolve."
 When it forms a black hole. the svstem consists of a black hole and a massive star.," When it forms a black hole, the system consists of a black hole and a massive star."
 This svstem evolves through a common envelope phase as the secondary. star expands., This system evolves through a common envelope phase as the secondary star expands.
 During this common envelope phase. the black hole spirals into (he massive secondary and ejects the hydrogen envelope.," During this common envelope phase, the black hole spirals into the massive secondary and ejects the hydrogen envelope."
 The supernova explosion ol the secondary results in the formation of a binary consisting of a neutron star and a higher mass black hole mi~12.U. (Frver et al., The supernova explosion of the secondary results in the formation of a binary consisting of a neutron star and a higher mass black hole $m_1 \sim 12M_\odot$ (Fryer et al.
 1999b)., 1999b).
 Fiver et al. (, Fryer et al. (
1999b) obtain the bimoclal distribution of black hole masses presented in their Fig 17. assumüng (hat a black hole mass is equal to 1/3 of the progenitor mass.,"1999b) obtain the bimodal distribution of black hole masses presented in their Fig 17, assuming that a black hole mass is equal to 1/3 of the progenitor mass."
 Though recent studies based on core collapse simulations show that the mass distribution is rather flat (Frver Ixalogera 2001: Belezvuski et al., Though recent studies based on core collapse simulations show that the mass distribution is rather flat (Fryer Kalogera 2001; Belczynski et al.
 2002b). we apply mni~12M. (o the typical value of hish mass black holes.," 2002b), we apply $m_1 \sim 12
M_\odot$ to the typical value of high mass black holes."
 We assume that the gravitational wave signal trom the in-spiral binary ends around the frequency. given. by eq. (4)), We assume that the gravitational wave signal from the in-spiral binary ends around the frequency given by eq. \ref{eq:fi}) )
 ancl hence (his signal shuts off nominally al f;~ 6401IIz (scenario a) or f;e 2101IIz (scenario 6)., and hence this signal shuts off nominally at $f_i \sim 640$ Hz (scenario $a$ ) or $f_i\sim 210$ Hz (scenario $b$ ).
 When the BII-NS binary merges. the neutron star is lidally disrupted.," When the BH-NS binary merges, the neutron star is tidally disrupted."
 Some of the material accretes onto the DII directly. while the remainder forms an accretion disk of 0.3—0.7... (Janka et al.," Some of the material accretes onto the BH directly, while the remainder forms an accretion disk of $0.3-0.7 M_\odot$ (Janka et al."
 1999)., 1999).
 The electromagnetic GRB signal from BII-NS is similar to that in DNS binaries. ancl of comparable but somewhat larger energv (Aléssvdrros Rees 1997).," The electromagnetic GRB signal from BH-NS is similar to that in DNS binaries, and of comparable but somewhat larger energy (Mésszárros Rees 1997)."
 The eravitational wave signals are also comparable. the differences being associated with the DII mass (or possibly its spin rate. related to the total accretion historv).," The gravitational wave signals are also comparable, the differences being associated with the BH mass (or possibly its spin rate, related to the total accretion history)."
 We show the amplitudes of the gravitational waves for the (wo DII-NS, We show the amplitudes of the gravitational waves for the two BH-NS
l:oratory. the assignienut of particular structures to longer svaveleugth bands has proved challenging (see Speight (1991))).,"laboratory, the assignment of particular structures to longer wavelength bands has proved challenging (see Speight \cite{spe}) )."
 In the preseut work. we take advantage of the prodigious progress made. in the last two decades. both in 'omputer technology and fundamental computational chemistry. to complement laboratory experiments withnumerical determination of their (nfrared) spectrum of several structures relevant to the kerogen aud coal models (see Carlson (199233).," In the present work, we take advantage of the prodigious progress made, in the last two decades, both in computer technology and fundamental computational chemistry, to complement laboratory experiments with numerical determination of the ir (infrared) spectrum of several structures relevant to the kerogen and coal models (see Carlson \cite{car92}) )."
 Calculations whichpreviously required comples dedicated programming xd long epu times on powerful machines cau now be performed iu a few hours with state-of-the-art desktops and general purpose software (ee. Uwperchem xd Monaec: see. for iustauce. Hypercube (1996))).," Calculations which previously required complex dedicated programming and long cpu times on powerful machines can now be performed in a few hours with state-of-the-art desktops and general purpose software (e.g. Hyperchem and Momec; see, for instance, Hypercube \cite{hyp}) )."
 ALoreover. such software delivers. for cach mode. the ir intensity aud eraplic illustration— of the movement of cach atom in the structure. together with the ryequency of vibration.," Moreover, such software delivers, for each mode, the ir intensity and graphic illustration of the movement of each atom in the structure, together with the frequency of vibration."
 This is of exeat help in selecting chemical elements aud nolecular structures of interest. and later estimating their relative abundances in IS dust.," This is of great help in selecting chemical elements and molecular structures of interest, and later estimating their relative abundances in IS dust."
 Based ou the availability of such new tools. the present worls is an attempt to determine a set of simple chemical structures whose combination can reproduce he observed interstellar spectra aud explain the variations of the relative van iuteusities from sight Lue to sight line.," Based on the availability of such new tools, the present work is an attempt to determine a set of simple chemical structures whose combination can reproduce the observed interstellar spectra and explain the variations of the relative band intensities from sight line to sight line."
 The choices are constrained o» the known relative abuudauces of elemieuts aud the (less well known) abundances of frec-fiviug molecules., The choices are constrained by the known relative abundances of elements and the (less well known) abundances of free-flying molecules.
 Another. self-imposed. constraint is to init the eleineutary structures to the minima in nunuber aud complexity.," Another, self-imposed, constraint is to limit the elementary structures to the minimum in number and complexity."
 The aim is to determine the quantitative contribution of cach structure to he various bands. aud. if possible. the type of molecular vibration which is activated.," The aim is to determine the quantitative contribution of each structure to the various bands, and, if possible, the type of molecular vibration which is activated."
 Section 2 describes a πο of types of clemeutary structures. or molecules. which contribute to oue or more of the main IS bands.," Section 2 describes a number of types of elementary structures, or molecules, which contribute to one or more of the main IS bands."
 Iu this respect. the recent of availabilityobservational data with increased spectral span. resolution id scusitivity from various celestial euvironiaents is a precious asset (Spitzer SINGS: see IKeunicutt(2003)3).," In this respect, the recent availability of observational data with increased spectral span, resolution and sensitivity from various celestial environments is a precious asset (Spitzer SINGS; see \cite{ken03}) )."
 For amy proposed dust component must nof ilv contribute to the observed spectrum. but also be proved not to contribute —LBies or bands that are not observed throughout the ir spectrin.," For any proposed dust component must not only contribute to the observed spectrum, but also be proved not to contribute lines or bands that are not observed throughout the ir spectrum."
 Tudividual all structures at low temperatures produce ouly narrow lines id cannot provide the observed band widths aud coutimmiun by themselves., Individual small structures at low temperatures produce only narrow lines and cannot provide the observed band widths and continuum by themselves.
 However. stuall changes in the anchoring poiuts of peripheral eroups of atoms slightly shift the original lines. thus coutributing to fillime the baud width without altering the topological character of the structure.," However, small changes in the anchoring points of peripheral groups of atoms slightly shift the original lines, thus contributing to filling the band width without altering the topological character of the structure."
 The latter defines the type. or class. of the clementary structure.," The latter defines the type, or class, of the elementary structure."
 Iu terms of M. Liouville's equation (2)) becomes: | jM= and the anisotropic stresses are given by: ,M In terms of $M$ Liouville's equation \ref{Liou}) ) becomes: + M= and the anisotropic stresses are given by: .
Equatious (5)).(2)).(2)) for perturbations aud equ. (2)), Equations \ref{hprime}) \ref{Liou.rel}) \ref{Pi.rel}) ) for perturbations and eqn. \ref{exp}) )
" for scale factor together with the usual equations determining pewpypy, and ps form the closed system of ordinary differential equation which we have solved."," for scale factor together with the usual equations determining $\rho_C,~\rho_H~\rho_{\nu_0}$ and $\rho_\gamma$ form the closed system of ordinary differential equation which we have solved."
 We assume standard inflation according to which the initial amplitude of gravitational waves is independent of scale Qh(tinbP)x&7.," We assume standard inflation according to which the initial amplitude of gravitational waves is independent of scale $\langle|h(t_{in},k)|^2\rangle \propto k^{-3}$."
 Each solution of Eqs. (5)).(2)), Each solution of Eqs. \ref{hprime}) \ref{Liou.rel}) )
 aud (2)) can be preseuted as a suni of erowiug auc cecaving modes aud an iufinite umber of modes corresponding to perturbations of the collisiou-less medi [0].., and \ref{Pi.rel}) ) can be presented as a sum of growing and decaying modes and an infinite number of modes corresponding to perturbations of the collision-less medium \cite{JETF}.
 We are oulv interested in the growing mode which is given by the initial condition —coust., We are only interested in the growing mode which is given by the initial condition $h^T_{i j}(t \rightarrow 0)=$ const.
 and γε>0)= 0., and $\dot{h}_{i j}(t \rightarrow 0)=0$ .
 If hij—0. Eq. (2))," If $\dot{h}_{ij}=0$, Eq. \ref{Liou.rel}) )"
 does not adiit a tensor contribution to AV., does not admit a tensor contribution to $M$.
 Iun this case. AZxexp(in-k) and all compoucuts of the iuduced. anisotropic stress normal to k vanish.," In this case, $M\propto \exp(i{\bf n}\cdot{\bf k})$ and all components of the induced anisotropic stress normal to ${\bf k}$ vanish."
 Therefore. the correct (tensorial) iitial condition for M is λα>0)—0 aud also Πα>0)— 0.," Therefore, the correct (tensorial) initial condition for $M$ is $M(t \rightarrow 0)=0$ and also $\Pi_{ij}(t \rightarrow 0)=0$ ."
 These initial values remain unuchauged as lone as At«1., These initial values remain unchanged as long as $kt\ll 1$.
 Assuniue. e.g. spherical polarization and a flat spectrum from inflation. at some carly time. At<1 for all waveleneths considered. we thus choose the initial conditions = = =ὃν YWeHy2e0 APHO. where Ais the amplitude of eravitational waves.," Assuming, e.g. spherical polarization and a flat spectrum from inflation, at some early time, $kt\ll 1$ for all wavelengths considered, we thus choose the initial conditions = = =, = = 0, M=0, where $A$ is the amplitude of gravitational waves."
 It is easy sec that ou superliorizou scales 1). h —coust.," It is easy see that on superhorizon scales $kt \ll 1$ ), $h=$ const."
 and the evolution of gravitational waves aud as a result AT/T are independent of the model parameters., and the evolution of gravitational waves and as a result $\Delta T/T$ are independent of the model parameters.
 For scales Afz1. the metric perturbations begin to oscillate aud eveutually (ktc91) damp away (see Fies.," For scales $kt \approx 1$, the metric perturbations begin to oscillate and eventually $kt\gg
1)$ damp away (see Figs."
 d and 2)., 1 and 2).
 The non-zero b then induces anisotropic stresses via Eqs.(2)) aud (2))., The non-zero $\dot{h}$ then induces anisotropic stresses via \ref{Liou.rel}) ) and \ref{Pi.rel}) ).
 Very often. these anisotropic stresses have been neglected iu the literature.," Very often, these anisotropic stresses have been neglected in the literature."
 Hore we find that their effect is indeed very πα]., Here we find that their effect is indeed very small.
" There is typically about additional dampingdue to the loss of somegravitational wave energy into anisotropic stresses,", There is typically about additional dampingdue to the loss of somegravitational wave energy into anisotropic stresses.
 The main model dependence isthe mocification of thedamping term (6o) in the differcut backerounds considered., The main model dependence isthe modification of thedamping term $(\dot{a}/a)$ in the different backgrounds considered.
the superorbital periods seen in X-ray. binaries might now be accountable by the same mocet.,the superorbital periods seen in X-ray binaries might now be accountable by the same model.
 The most pertinent of the ODOL results. for. this cliscussion is the classification of behaviour into modes of warping (see figure 7 of ODOL)., The most pertinent of the OD01 results for this discussion is the classification of behaviour into modes of warping (see figure 7 of OD01).
 Phe stability of the accretion disk to warping is predicted as a function of the mass ratio d and the binary separation rj. for two regimes of mass input.," The stability of the accretion disk to warping is predicted as a function of the mass ratio $q$ and the binary separation $r_b$, for two regimes of mass input."
 The first region boundary corresponds to matter input at the Lindblad: resonance radius rj. for which every source above this line for which matter is input in this way can sustain mode 1 and higher warps.," The first region boundary corresponds to matter input at the Lindblad resonance radius $r_o$, for which every source above this line for which matter is input in this way can sustain mode 1 and higher warps."
 Hf matter is input at the circularisation radius re. this border does not apply. and persistent warping is not possible.," If matter is input at the circularisation radius $r_c$, this border does not apply, and persistent warping is not possible."
 Between the upper border of this region and the dotted line. mode 0 warping persists.," Between the upper border of this region and the dotted line, mode 0 warping persists."
 Finally in the uppermost region. mode 1 and higher warping modes become possible.," Finally in the uppermost region, mode 1 and higher warping modes become possible."
 The location of the borders between stability regions in rp - g space depends strongly on the global clisk viscosity parameter. a. and the neutron star accretion elliciency 9.," The location of the borders between stability regions in $r_b$ - $q$ space depends strongly on the global disk viscosity parameter, $\alpha$ and the neutron star accretion efficiency $\eta$."
 Uneertainty in these values translates into uncertainty as to the location of the border between regions and thus the stability classification of a system., Uncertainty in these values translates into uncertainty as to the location of the border between regions and thus the stability classification of a system.
 However. the adopted values of a = 0.3 and η = 0.1 are usually assumed to be appropriate for neutron star NIB. (Frank. Wine Raine 1995. ODOL and references therein).," However, the adopted values of $\alpha$ = 0.3 and $\eta$ = 0.1 are usually assumed to be appropriate for neutron star XRB (Frank, King Raine 1995, OD01 and references therein)."
 Asa HMXD. the accretion disk in SAIC X-1 is unlikely to reach out to ων," As a HMXB, the accretion disk in SMC X-1 is unlikely to reach out to $r_o$."
 Moreover. that the spin period. has been decreasing in a steady way compared to most. other IIMXD's suggests that mass transfer from. donor to disk is also comparatively steacky. suggesting mass transfer is collimated in some wav. even i£ not by Roche overllow.," Moreover, that the spin period has been decreasing in a steady way compared to most other HMXB's suggests that mass transfer from donor to disk is also comparatively steady, suggesting mass transfer is collimated in some way, even if not by Roche overflow."
" Dhese considerations lead us to suggest that the true site of mass input is closer tor, than tor... so we use the stability scheme appropriate for mass input at ον"," These considerations lead us to suggest that the true site of mass input is closer to $r_c$ than to $r_{o}$, so we use the stability scheme appropriate for mass input at $r_c$."
 SMC N-1 is then placed near the border between the region supporting stable mode 0 warping and that supporting mode 1 and higher modes., SMC X-1 is then placed near the border between the region supporting stable mode 0 warping and that supporting mode 1 and higher modes.
 We would thus expect the disk to form a precessing warp. giving rise to a long periodicity.," We would thus expect the disk to form a precessing warp, giving rise to a long periodicity."
 Llowever. this may not bea stable monotonic warp: instead. there may be an interaction between modes by virtue of the unique location of SAIC l near the border between the two regions.," However, this may not be a stable monotonic warp; instead, there may be an interaction between modes by virtue of the unique location of SMC X-1 near the border between the two regions."
 As two or more noces compete. then. a longer term variation may be set up in which the sum of mocoes itself changes slowly with time.," As two or more modes compete, then, a longer term variation may be set up in which the sum of modes itself changes slowly with time."
 This may manifest. itself as the observed variation in the superorbital. period of SAIC) X-1. which must represent an iniportant constraint on future development of such niodels.," This may manifest itself as the observed variation in the superorbital period of SMC X-1, which must represent an important constraint on future development of such models."
 We have used the dynamic power spectrum to show that the superorbital period. of SAIC ΝΤ varies in a coherent. apparently almost. sinusoidal. way.," We have used the dynamic power spectrum to show that the superorbital period of SMC X-1 varies in a coherent, apparently almost sinusoidal, way."
 In conjunction with the spectral behaviour of this variation. we have seen that a precessing. warped accretion disk must be responsible. for the superorbital variation.," In conjunction with the spectral behaviour of this variation, we have seen that a precessing, warped accretion disk must be responsible for the superorbital variation."
 However the influence of the warp may be felt not only through varying occultation. as is supposed. for Her. N-1. but through varying accretion at the neutron star boundary laver. permitted because the isk precession is not steady but quasi-steadsy.," However the influence of the warp may be felt not only through varying occultation, as is supposed for Her X-1, but through varying accretion at the neutron star boundary layer, permitted because the disk precession is not steady but quasi-steady."
 Finally we saw that the variation of the superorbital period is fully 'onsistent with current stability theory of warps in accretion isks., Finally we saw that the variation of the superorbital period is fully consistent with current stability theory of warps in accretion disks.
 An interaction of warp mocles can give rise to the Pwrving superorbital period. allowing its variation to change irection several times in a few vears.," An interaction of warp modes can give rise to the varying superorbital period, allowing its variation to change direction several times in a few years."
 This remarkable result was only possible due to the gsuperb. lone time-base of the CORO and IUNTIS databases.," This remarkable result was only possible due to the superb, long time-base of the CGRO and RXTE databases."
 — heralds a new understanding of the structure and volution of accretion disks which may have implications for isks on all scales., It heralds a new understanding of the structure and evolution of accretion disks which may have implications for disks on all scales.
 A search for similar behaviour in other X-ray binaries in these datasets is under way and will be the subject of future papers., A search for similar behaviour in other X-ray binaries in these datasets is under way and will be the subject of future papers.
 SCTL and WIC were in receipt of PPARC research studentships., SGTL and WIC were in receipt of PPARC research studentships.
 WIC) thanks Professor Brian Warner. for interesting discussion on the observational consequences of tiltecl and warped disks. and Drs.," WIC thanks Professor Brian Warner for interesting discussion on the observational consequences of tilted and warped disks, and Drs."
 Phil Uttley and Guillaume Dubus for informative comments., Phil Uttley and Guillaume Dubus for informative comments.
 Fhis work was only made possible through the efforts of the SMΗΝΕς team at MET and GSEC. and the BATSE/CGRO team at AISEC.," This work was only made possible through the efforts of the ASM/RXTE team at MIT and GSFC, and the BATSE/CGRO team at MSFC."
YSOs [rom ield stars (o.8.. magnetically active M dwagtls or short-perioc pulsating giants).,"YSOs from field stars (e.g., magnetically active M dwarfs or short-period pulsating giants)."
 This selection will miss YSOs without measurable variability. for example the ones withou accretion and no detectable spot activity.," This selection will miss YSOs without measurable variability, for example the ones without accretion and no detectable spot activity."
 A combined. colour-variabilitv criterion can reliably establish a sample of. YSOs with little contamination. bu un will still not provide a complete census.," A combined colour-variability criterion can reliably establish a sample of YSOs with little contamination, but it will still not provide a complete census."
 Specifically it wil miss 1) deeply embedded: sources not visible in the near-infrared bands. 2) objects with small inner disk holes anc thus no near-infrared excess. 3) WETS without disk. 4) YSOs without measurable variability on the timescales o£ 1 observations.," Specifically it will miss 1) deeply embedded sources not visible in the near-infrared bands, 2) objects with small inner disk holes and thus no near-infrared excess, 3) WTTS without disk, 4) YSOs without measurable variability on the timescales of the observations."
 The irst two groups can be identified with further photometric observations at. longer wavelengths., The first two groups can be identified with further photometric observations at longer wavelengths.
 WEES can often. be found. based. on variability alone. as rev show periodic lighteurves on timescales of days and/or Ilare activity.," WTTS can often be found based on variability alone, as they show periodic lightcurves on timescales of days and/or flare activity."
 Croup 4 max be of major relevance for our study. as our observations only cover three cays: As discussed. in 7.. such relatively short runs might miss more than all of the variables in star forming regions.," Group 4 may be of major relevance for our study, as our observations only cover three days: As discussed in \citet{2009MNRAS.400..603P}, such relatively short runs might miss more than half of the variables in star forming regions."
 On timescales of several vears. however. almost of YSOs are found to be variable.," On timescales of several years, however, almost of YSOs are found to be variable."
 Εις applies to variability zumplitudes in the range of a lew percent or larger. which is comparable to our detection limit.," This applies to variability amplitudes in the range of a few percent or larger, which is comparable to our detection limit."
 By combining our observations with PALASS data we will look for missing objects with long-term variations (Sect. 3.4)), By combining our observations with 2MASS data we will look for missing objects with long-term variations (Sect. \ref{2mass}) ).
 On the other hand. the fact that our run covers only a [ow nights helps us to rule out some classes of objects that are common contaminants in. YSO surveys.," On the other hand, the fact that our run covers only a few nights helps us to rule out some classes of objects that are common contaminants in YSO surveys."
 For example. quasars may appear red. but their dominant variability mocles have characteristic timescales in the order of vears in the quasar rest frame. thus is unlikely to be found with the current dataset.," For example, quasars may appear red, but their dominant variability modes have characteristic timescales in the order of years in the quasar rest frame, thus is unlikely to be found with the current dataset."
 Phe same argument applies to long-periodic pulsating red. giants (e.g. Mira. variables)., The same argument applies to long-periodic pulsating red giants (e.g. Mira variables).
 1n summary. using colour or variability as observational indicators for vouth gives incomplete and contaminated samples.," In summary, using colour or variability as observational indicators for youth gives incomplete and contaminated samples."
 Combining the two can potentially provide a much cleaner sample o£ YSO candidates. but will not completely solve the incompleteness issue.," Combining the two can potentially provide a much cleaner sample of YSO candidates, but will not completely solve the incompleteness issue."
 From the calibrated photometry of the stacked images (see Sect. 2)), From the calibrated photometry of the stacked images (see Sect. \ref{data}) )
 à deep (LHl-Ix. J-11). colour-colour. diagram. was constructed. as commonly. used. to identify objects with disks.," a deep (H-K, J-H) colour-colour diagram was constructed, as commonly used to identify objects with disks."
 Phis was done for the field containing IC1396W in chip las well as for the field covered by chip 4 for comparison., This was done for the field containing IC1396W in chip 1 as well as for the field covered by chip 4 for comparison.
 The full source catalogue for the 1€1396N field has S211 entries from which 7965 have reliable photometry in all three bands., The full source catalogue for the IC1396W field has 8211 entries from which 7965 have reliable photometry in all three bands.
 Clearly the majority. of these objects will not. be young menibers of A further cut was mace by limiting the diagram. to objects for which useful variability information is available., Clearly the majority of these objects will not be young members of A further cut was made by limiting the diagram to objects for which useful variability information is available.
 We include only sources for which the mean photometric noise. as determined from the lighteurves. is <0.2 mmag in J- and Ix-band. (see Sect. 3.2)).," We include only sources for which the mean photometric noise, as determined from the lightcurves, is $<0.2$ mag in J- and K-band (see Sect. \ref{var}) )."
 This reduces the number of objects to 4397., This reduces the number of objects to 4397.
 Ehe second cut. imposes. essentially a magnitude limit: while the full. catalogue extends down to J=22 and A=195 mmae. these values change to J= 194mmag and A= 1S.0mmae after the variability information is taken into account.," The second cut imposes essentially a magnitude limit; while the full catalogue extends down to $J=22$ and $K=19.5$ mag, these values change to $J=19.4$ mag and $K=18.0$ mag after the variability information is taken into account."
 The comparison field has in total 7496 objects with photometry in all bands., The comparison field has in total 7496 objects with photometry in all bands.
 After applying the variability cut a catalogue of 4422 objects is obtained. with limiting magnitudes of J=19.3 and A=18.0 mmae.," After applying the variability cut a catalogue of 4422 objects is obtained, with limiting magnitudes of $J=19.3$ and $K=18.0$ mag."
 The resulting colour-colour diagrams are shown in Fig. 2.., The resulting colour-colour diagrams are shown in Fig. \ref{f1}.
 The comparison ficld shows a clump of objects around (0.2.0.8) with a faint tail of objects with (small) HiIN excess.," The comparison field shows a clump of objects around (0.2,0.8) with a faint tail of objects with (small) $H-K$ excess."
 Most. of the objects in this tail appear extended and may be τοῦ galaxies., Most of the objects in this tail appear extended and may be red galaxies.
 There is no indication of strong extinction in the comparison field., There is no indication of strong extinction in the comparison field.
 Phe field around 1C1396N. shows the same clump of objects. but here it is stretched out along a well-defined path towards red colours.," The field around IC1396W shows the same clump of objects, but here it is stretched out along a well-defined path towards red colours."
 This is best explained by strong and variable extinction in the elobule. which alfects the colours from all background SOULCCS.," This is best explained by strong and variable extinction in the globule, which affects the colours from all background sources."
 The dotted lines. in Fie., The dotted lines in Fig.
 2. shows the standard, \ref{f1} shows the standard
Red-sequence galaxies are an important population Του understanding galaxy formation and evolution in general.,Red-sequence galaxies are an important population for understanding galaxy formation and evolution in general.
 They represent systems with very little or no on-going star-formation and thus are a unique tracer of the past activity of galaxies., They represent systems with very little or no on-going star-formation and thus are a unique tracer of the past activity of galaxies.
 DeLuciaetal.(2004). found a defieit of faint red-sequence galaxies in clusters at z-0.8 relative to. local clusters., \citet{De-Lucia:2004xa} found a deficit of faint red-sequence galaxies in clusters at $\sim$ 0.8 relative to local clusters.
" This would suggest that star formation ended earlier for the most luminous/massive galaxies at high redshift and would support the ""down-sizing"" picture first proposed by Cowieetal.(1996). in which the termination of star-formation progresses from the most massive to the least massive galaxies as the universe ages."," This would suggest that star formation ended earlier for the most luminous/massive galaxies at high redshift and would support the “down-sizing” picture first proposed by \citet{Cowie:1996xw}, in which the termination of star-formation progresses from the most massive to the least massive galaxies as the universe ages."
 Similar results for clusters spanning a range of redshifts have been found by Tanakaetal.(2005).. deLuciaetal. (2007).. Stottetal. (2007).. Gilbanketal.(2007). and others.," Similar results for clusters spanning a range of redshifts have been found by \citet{Tanaka:2005mk}, \citet{de-Lucia:2007li}, \citet{Stott:2007wc}, \citet{Gilbank:2007rq} and others."
 Similarly. surveys of field galaxies have attempted to characterise the evolution of the red-sequence luminosity function.," Similarly, surveys of field galaxies have attempted to characterise the evolution of the red-sequence luminosity function."
 The relative contributions of passive evolution/termination of star-formation and. number density evolution/dry merging are still open questions (e.g.. etal. 2004.. Cimattietal. 200600.," The relative contributions of passive evolution/termination of star-formation and number density evolution/dry merging are still open questions (e.g., \citealt{Bell:2004lb}, \citealt{Cimatti:2006vz}) )."
 Red-sequence galaxies can thus place constraints on galaxy formation prescriptions in theoretical models., Red-sequence galaxies can thus place constraints on galaxy formation prescriptions in theoretical models.
 Recent observations in the local universe using SDSS data have found that the fractions of satellite galaxies which are red are too high in current semi-analytic models., Recent observations in the local universe using SDSS data have found that the fractions of satellite galaxies which are red are too high in current semi-analytic models.
 With the recent abundance of surveys targeting red-sequence galaxies both in the cluster and the field. the time is now ripe to draw together these works to build a picture of the build-up of galaxies on the red-sequence as a function of environment and to confront these with predictions of galaxy formation models.," With the recent abundance of surveys targeting red-sequence galaxies both in the cluster and the field, the time is now ripe to draw together these works to build a picture of the build-up of galaxies on the red-sequence as a function of environment and to confront these with predictions of galaxy formation models."
 We aim to construct the most uniform sample possible using colour-selected red-sequence galaxy data from the literature., We aim to construct the most uniform sample possible using colour-selected red-sequence galaxy data from the literature.
 To this end. we transform all our data onto the same system.," To this end, we transform all our data onto the same system."
 A simpler quantity than the luminosity function (LF). which has been employed in the past. is the red-sequence dwarf-to-giant ratio. hereafter DGR.," A simpler quantity than the luminosity function (LF), which has been employed in the past, is the red-sequence dwarf-to-giant ratio, hereafter DGR."
 This is essentially just a LF reduced to two bins and avoids the complications of having to fit an analytic function (usually with degeneracies between the fitted parameters) to the data., This is essentially just a LF reduced to two bins and avoids the complications of having to fit an analytic function (usually with degeneracies between the fitted parameters) to the data.
 Following DeLuciaetal.(2004)... we define luminous. or giant. galaxies as those brighter than A/y=20.0 and faint. or dwarfs. as those with 2O«Ady18.2 (K- and evolution-corrected).," Following \citet{De-Lucia:2004xa}, we define luminous, or giant, galaxies as those brighter than $M_{\rm V}=-20.0$ and faint, or dwarfs, as those with $-20<M_{\rm V}\le-18.2$ (k- and evolution-corrected)."
 Where data are presented on a different photometric system. we use Bruzual&Charlot(2003) stellar population models to calculate the transformation using à ο=8. Solar metallicity. single stellar population with a Chabrier IMF.," Where data are presented on a different photometric system, we use \citet{Bruzual:2003de} stellar population models to calculate the transformation using a $z_f=3$, Solar metallicity, single stellar population with a Chabrier IMF."
 Where DGRs have been given in the original paper using these limits (as, Where DGRs have been given in the original paper using these limits (as
can also emit soft A-ravs (see e.g. Oh2001:Venkatesan.Giroux.&Shull 2001)).,"can also emit soft X-rays (see e.g. \citealp{O01,VGS01}) )."
 Photons with energies as lowas 0.2 keV can propagate as [ar as 3 comoving Alpe over (he atonic intergalactic medium at z10 before they are absorbed by hydrogen or helium., Photons with energies as lowas $0.2$ keV can propagate as far as 3 comoving Mpc over the atomic intergalactic medium at $z\sim 10$ before they are absorbed by hydrogen or helium.
 There may still be some wavs in which certain regions of the intergalactic medium may be illuminated by photons trom the first stars. without receiving soft. N-ravs as well.," There may still be some ways in which certain regions of the intergalactic medium may be illuminated by photons from the first stars, without receiving soft X-rays as well."
 For example. il stars form in a region with a high column densitv of hydrogen and helium wilh very little cust. ancl the hydrogen aud/or helium is not fully ionized for a long tme. the photons between aud the Lyman limit [rom stars would escape. while the ionizing and soft X-ray photons might all be locally absorbed.," For example, if stars form in a region with a high column density of hydrogen and helium with very little dust, and the hydrogen and/or helium is not fully ionized for a long time, the photons between and the Lyman limit from stars would escape, while the ionizing and soft X-ray photons might all be locally absorbed."
 In particular. there is the possibility. (hat singlv ionized helium remains sell-shielded as massive stars ionize the gas around them.," In particular, there is the possibility that singly ionized helium remains self-shielded as massive stars ionize the gas around them."
 We note Lom Figure 6 Chat the time required to bring down the spin temperature can be very short (107 vears or less) for typical values of the background intensity. and it is possible that a complete absorption of soft N-rays [rom the first stu-Iorming regions would persist long enough to allow lor a strong 21cm absorption signal in local regions of the intergalactic medium. when thev are illuminated by the first. light from stars forming in their vicinity.," We note from Figure 6 that the time required to bring down the spin temperature can be very short $10^8$ years or less) for typical values of the background intensity, and it is possible that a complete absorption of soft X-rays from the first star-forming regions would persist long enough to allow for a strong 21cm absorption signal in local regions of the intergalactic medium, when they are illuminated by the first light from stars forming in their vicinity."
 Nevertheless. it seems likely (hat anv decrease of the spin temperature will be short-lived. and that X-ray. heating will cause the 21cm signal to switeh to emission a short time after the first stars are formed.," Nevertheless, it seems likely that any decrease of the spin temperature will be short-lived, and that X-ray heating will cause the 21cm signal to switch to emission a short time after the first stars are formed."
 Future observations of the 2lem signal in absorption ancl emission at high angular aud frequency resolution have an enormous potential for revealing the details of the reionization epoch., Future observations of the 21cm signal in absorption and emission at high angular and frequency resolution have an enormous potential for revealing the details of the reionization epoch.
 Fluctuations in the antenia temperature arise from bot gas densitv aud spin temperature variations., Fluctuations in the antenna temperature arise from both gas density and spin temperature variations.
 The density fluctuations will inform us of the state of gravitational evolution of primordial [actuations at the hiehest attainable redshifts alter recombination. while (he spin temperature [Iuctuations will reveal the spatial distribution of the first sources of ultraviolet and X-ray emission in the universe.," The density fluctuations will inform us of the state of gravitational evolution of primordial fluctuations at the highest attainable redshifts after recombination, while the spin temperature fluctuations will reveal the spatial distribution of the first sources of ultraviolet and X-ray emission in the universe."
 This work was supported in part by NSF grants NSE-0098515 and PIIY99-07949., This work was supported in part by NSF grants NSF-0098515 and PHY99-07949.
 MAIR assumed that the heating rate per unit volume of the hydrogen gas due to scallering is equal to the recoil energv given to a hvdrogen atom ab rest. (hi) /(mgc). limes the scattering rate:," MMR assumed that the heating rate per unit volume of the hydrogen gas due to scattering is equal to the recoil energy given to a hydrogen atom at rest, $(h\nu_{\alpha})^2/(m_Hc^2)$ , times the scattering rate:"
photons. with the rest of the tthen free to cool to lower temperatures.,"photons, with the rest of the then free to cool to lower temperatures."
 It is also. possible that sightlines with low Nyy are sampling gas at higher distances from the Galactic plane. with lower metallicity and pressure.," It is also possible that sightlines with low $\nhi$ are sampling gas at higher distances from the Galactic plane, with lower metallicity and pressure."
 Two-phase models that incorporate detailed balancing of heating and cooling rates obtain lower CNM fractions at lower pressures and metallicities (Wolfireetal. 1995).., Two-phase models that incorporate detailed balancing of heating and cooling rates obtain lower CNM fractions at lower pressures and metallicities \citep{wolfire95}. .
 Observationally. Kanekaretal.(2009) have found evidence for an anti-correlation between spin temperature and metallicity in high-:. DLAs. with low-metallicity DLAs having higher spin temperatures. probably because the paucity of metals yields fewer cooling routes (Kanekar&Chengalur2001)..," Observationally, \citet{kanekar09c} have found evidence for an anti-correlation between spin temperature and metallicity in $z$ DLAs, with low-metallicity DLAs having higher spin temperatures, probably because the paucity of metals yields fewer cooling routes \citep{kanekar01a}."
 If μι sightlines contain “clouds” with systematically lower metallicities (and/or pressures). these could have lower cooling rates and hence. lower CNM fractions.," If $\nhi$ sightlines contain “clouds” with systematically lower metallicities (and/or pressures), these could have lower cooling rates and hence, lower CNM fractions."
 Unfortunately. we do not have estimates of either pressure or metallicity along our sightlines and hence cannot test this possibility.," Unfortunately, we do not have estimates of either pressure or metallicity along our sightlines and hence cannot test this possibility."
 We note that all sightlines with high spin temperatures are at intermediate or high Galactic latitudes. 5—10 (see Fig. 2)).," We note that all sightlines with high spin temperatures are at intermediate or high Galactic latitudes, $b > 40^\circ$ (see Fig. \ref{fig:fig2}) ),"
 suggesting larger distances from the plane., suggesting larger distances from the plane.
 Conversely. the figure also shows that low spin temperatures (=LOO K) are obtained even for sightlines at high Galactic latitudes (5~LQ) 707).," Conversely, the figure also shows that low spin temperatures $\lesssim 400$ K) are obtained even for sightlines at high Galactic latitudes $b \sim 40-70^\circ$ )."
 Measurements of the metallicity and pressure along the Ni sightlines. through UV spectroscopy. would be of much interest.," Measurements of the metallicity and pressure along the $\nhi$ sightlines, through UV spectroscopy, would be of much interest."
 There have been earlier suggestions. based on semi-analytical or numerical treatments of self-shielding. that cclouds are predominantly neutral for Nyyz10? ((e.g. Viegas1995;Wolfeetal. 2005)).," There have been earlier suggestions, based on semi-analytical or numerical treatments of self-shielding, that clouds are predominantly neutral for $\nhi \gtrsim 10^{20}$ (e.g. \citealt{viegas95,wolfe05}) )."
 However. this 1s the first direct evidence for a change in physical conditions in eclouds at this column density.," However, this is the first direct evidence for a change in physical conditions in clouds at this column density."
" Note that this is a factor of several lower than the known threshold of Nyy~5«10?"" ffor the formation of molecular hydrogen in Galactic clouds. set by the requirement of self-shielding against UV photons at wavelengths in the H» Lyman band (Savageetal.1977)."," Note that this is a factor of several lower than the known threshold of $\nhi \sim 5 \times 10^{20}$ for the formation of molecular hydrogen in Galactic clouds, set by the requirement of self-shielding against UV photons at wavelengths in the $_2$ Lyman band \citep{savage77}."
. Thus. there appear to be three column densities at which phase transitions occur in ISM clouds. at Ng2«10? rresulting in the formation of coldHL. at δη—5ν1029 rresulting in the formation of molecular hydrogen. and finally. at Nyy>10777. when most of the atomic gas is converted into the molecular phase.," Thus, there appear to be three column densities at which phase transitions occur in ISM clouds, at $\nhi \sim 2 \times
10^{20}$ resulting in the formation of cold, at $\nhi \sim 5
\times 10^{20}$ resulting in the formation of molecular hydrogen, and finally, at $\nhi > 10^{22}$, when most of the atomic gas is converted into the molecular phase."
 In this context. it is vital to appreciate that the abscissa of Fig.," In this context, it is vital to appreciate that the abscissa of Fig."
 | refers to ccolumn density under the assumption of negligible opacity of the pprofile., \ref{fig:fig1} refers to column density under the assumption of negligible self-opacity of the profile.
 The saturation. column density. Nx. is an upper limit to fTpdV and does not represent a physical limit on INjj.," The saturation column density, $_\infty$ , is an upper limit to $\int T_B dV$ and does not represent a physical limit on $\nhi$."
 In fact. the widespread occurrence of the sself-absorption phenomenon within the Galaxy (Gibsonetal.2005) and the detailed modeling of high resolution extragalactic sspectra suggests that self-opacity is a common occurrence (Braunetal.2009) which can disguise neutral column densities that reach Nyy~107? ?..," In fact, the widespread occurrence of the self-absorption phenomenon within the Galaxy \citep{gibson05} and the detailed modeling of high resolution extragalactic spectra suggests that self-opacity is a common occurrence \citep{braun09} which can disguise neutral column densities that reach $\nhi \sim 10^{23}$ ."
 The original definition of a DLA as an absorber with δι=2.107 wwas an observational one. based on the requirement that the damping wings of the Lyman-a line be detectable in resolution optical spectra of moderate sensitivity (Wolfeetal.1986).," The original definition of a DLA as an absorber with $\nhi \ge 2
\times 10^{20}$ was an observational one, based on the requirement that the damping wings of the $\alpha$ line be detectable in low-resolution optical spectra of moderate sensitivity \citep{wolfe86}."
". With today’s 10-m class optical telescopes. it is easy to detect the damping wings at significantly lower ccolumn densities. ~107? ""ίδια, Pérouxetal.2003): such systems are referred to as “sub-DLAs”."," With today's 10-m class optical telescopes, it is easy to detect the damping wings at significantly lower column densities, $\sim 10^{19}$ (e.g. \citealt{peroux03}) ); such systems are referred to as “sub-DLAs”."
 There has been much debate in the literature on whether or not DLAs and sub- should be treated as a single class of absorber and on their relative importance in contributing to the cosmic budget of neutral hydrogen and metals (e.g. Pérouxetal.2003;Wolfeetal.2005;Kulkarni 2010).," There has been much debate in the literature on whether or not DLAs and sub-DLAs should be treated as a single class of absorber and on their relative importance in contributing to the cosmic budget of neutral hydrogen and metals (e.g. \citealt{peroux03,wolfe05,kulkarni10}) )."
 Wolfeetal.(2005). argue that DLAs and sub-DLAs are physically different. claiming that most of the iin sub-DLAs ts i0nized and at high temperature. while that in DLAs is mostly neutral: this is based on numerical estimates of self-shielding in DLAs and sub-DLAs against the high-- UV background (Viegas1995).," \citet{wolfe05} argue that DLAs and sub-DLAs are physically different, claiming that most of the in sub-DLAs is ionized and at high temperature, while that in DLAs is mostly neutral; this is based on numerical estimates of self-shielding in DLAs and sub-DLAs against the $z$ UV background \citep{viegas95}."
. Our detection of an ccolumn density threshold for CNM formation that matches the defining DLA column density indicates that DLAs and sub-DLAs are indeed physically different types of absorbers. with sub-DLAs likely to have significantly lower CNM fractions than DLAs. at a given metallicity.," Our detection of an column density threshold for CNM formation that matches the defining DLA column density indicates that DLAs and sub-DLAs are indeed physically different types of absorbers, with sub-DLAs likely to have significantly lower CNM fractions than DLAs, at a given metallicity."
 In summary. we report the discovery of a threshold ceolumn density. Nyy~2«10?9?.. for cold gas formation in clouds in the interstellar medium.," In summary, we report the discovery of a threshold column density, $\nhi \sim 2 \times 10^{20}$, for cold gas formation in clouds in the interstellar medium."
 Above this threshold. the majority of Galactic sightlines have low spin temperatures. T.=500 K. with a median value of ~210 K. Below this threshold. typical sightlines have far higher spin temperatures. >600 K. with a median value of ~1500 K. The threshold for CNM formation appears to arise naturally due to the need for self-shielding against ultraviolet photons. which penetrate into the cloud at lower ccolumns and heat and i0nize theHI.. inhibiting the formation of the cold neutral medium.," Above this threshold, the majority of Galactic sightlines have low spin temperatures, $\ts \lesssim 500$ K, with a median value of $\sim 240$ K. Below this threshold, typical sightlines have far higher spin temperatures, $> 600$ K, with a median value of $\sim 1800$ K. The threshold for CNM formation appears to arise naturally due to the need for self-shielding against ultraviolet photons, which penetrate into the cloud at lower columns and heat and ionize the, inhibiting the formation of the cold neutral medium."
 We thank the staff of the GMRT and WSRT for help during the observations., We thank the staff of the GMRT and WSRT for help during the observations.
 The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research., The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research.
 The WSRT is operated by ASTRON with support from the Netherlands Foundation for Scientific Research (NWO)., The WSRT is operated by ASTRON with support from the Netherlands Foundation for Scientific Research (NWO).
 NK acknowledges support from the Department of Science and Technology through a Ramanujan Fellowship., NK acknowledges support from the Department of Science and Technology through a Ramanujan Fellowship.
 The National Radio Astronomy Observatory is a facility of the National Science Foundation operatedunder cooperativeagreement byAssociated Universities. Inc.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operatedunder cooperativeagreement byAssociated Universities, Inc."
The determination. of the eas temperature ancl ionized fraction in the intergalactic medium (GAL) and interstellar mecium (18M) is fundamental for a number of astrophysical studies.,The determination of the gas temperature and ionized fraction in the intergalactic medium (IGM) and interstellar medium (ISM) is fundamental for a number of astrophysical studies.
 In. particular. it is essential for the investigation of the nearly. uniform. dark. neutral state of the Universe known as Dark Ages. which has become in the last decade one of the most studied Copies in cosmology.," In particular, it is essential for the investigation of the nearly uniform, dark, neutral state of the Universe known as Dark Ages, which has become in the last decade one of the most studied topics in cosmology."
 The cosmic yhase between hvdrogen recombination at 2~ 1000 and he so-called Epoch of Retonization (ok) at z 9 can be directly detected by the 21 em hyperline triplet-singlet level ransition of the ground state of neutral hydrogen., The cosmic phase between hydrogen recombination at $z\sim $ 1000 and the so-called Epoch of Reionization (EoR) at $z \sim $ 9 can be directly detected by the 21 cm hyperfine triplet-singlet level transition of the ground state of neutral hydrogen.
 A new generation of low frequency radio interferometers such as the Low frequency Array (LOIATU.. the 21 Centimeter Array (PICAIA). the Mileura Wicle-field Array (AINWWA) and. the Square Wilometer Array (SILA). are expected to reach the sensitivity required to map the LIE distribution at angular resolution ofthe order of a [ew arcminutes (e.g. Pen. Wi Peterson 2004: Bowman. Morales. Hewitt 2005:) Ixassim et al.," A new generation of low frequency radio interferometers such as the Low frequency Array (LOFAR), the 21 Centimeter Array (21CMA), the Mileura Wide-field Array (MWA) and the Square Kilometer Array (SKA), are expected to reach the sensitivity required to map the HI distribution at angular resolution of the order of a few arcminutes (e.g. Pen, Wu, Peterson 2004; Bowman, Morales, Hewitt 2005; Kassim et al."
" 2004: Ανπο, Loeb. Barnes 2005)."," 2004; Wyithe, Loeb, Barnes 2005)."
 Η α few issues such as foreground removal. interferences from human-generated signals and ionospheric corrections will be successfully taken care of these large radio-arravs will be able to perform a tomography of the Universe before and during the σοι. lt ds therefore crucial to be able. to. predict the magnitude of the signal.," If a few issues such as foreground removal, interferences from human-generated signals and ionospheric corrections will be successfully taken care of these large radio-arrays will be able to perform a tomography of the Universe before and during the EoR. It is therefore crucial to be able to predict the magnitude of the signal."
 The standard: scenario. predicts the gas temperature. Zig. to decouple from the Cosmic Microwave Background (CMD) temperature. ορ. at 27 300.," The standard scenario predicts the gas temperature, $T_K$, to decouple from the Cosmic Microwave Background (CMB) temperature, $T_{CMB}$, at $z\sim $ 300."
 Z4 then starts decreasing adiabatically until the first sources of light heat again the gas above τρ at zc 20., $T_K$ then starts decreasing adiabatically until the first sources of light heat again the gas above $T_{CMB}$ at $z \sim $ 20.
 In this case the 21 em radiation would be seen in absorption against the CAIB in the redshift interval 20 <z 300 as discussed in detail by many recent studies (e.g. Loch Zaldarriaga 2004)., In this case the 21 cm radiation would be seen in absorption against the CMB in the redshift interval 20 $<z<$ 300 as discussed in detail by many recent studies (e.g. Loeb Zaldarriaga 2004).
 A number of more complex theoretical scenarios have been investigated. recently., A number of more complex theoretical scenarios have been investigated recently.
 In. particular if there was a mechanism to heat the eas at zz 10. thus producing a thermal history cillerent Crom the standard. one. a direct imprint would be left on the 21 em radiation from the neutral eas. which could then be observable in emission rather than in absorption.," In particular if there was a mechanism to heat the gas at $z\geq $ 10, thus producing a thermal history different from the standard one, a direct imprint would be left on the 21 cm radiation from the neutral gas, which could then be observable in emission rather than in absorption."
 First stars (Cuardi Salvaterra 2007). intermediate mass black holes (Zaroubi et al.," First stars (Ciardi Salvaterra 2007), intermediate mass black holes (Zaroubi et al."
 2006: Büpamonti. private communication) and decaving or annihilating Warn and Cold Dark Matter (CDM) particles (Shehekinoy Vasiliev 2006: Furlanctto. Oh. Picrpaoli 2006: Valdes οἱ al.," 2006; Ripamonti, private communication) and decaying or annihilating Warm and Cold Dark Matter (CDM) particles (Shchekinov Vasiliev 2006; Furlanetto, Oh, Pierpaoli 2006; Valdes et al."
 2007) could be capable of leaving a significant trace in the evolution of the neutral intergalactic gas., 2007) could be capable of leaving a significant trace in the evolution of the neutral intergalactic gas.
 Future, Future
1.809 MeV. photon iscmitted!.,1.809 MeV photon is.
". Assuming that the fraction of positrons forming positronium is fi, (seo refsecispec)). the fluxes in the 511. keV and 1.8 MeV. lines per 1 positron produced via 7 Al decay. are: Llere we assume that i) the fraction of para-positronium is 1/4 and ii) all positrons annihilating without formation of positronium (fraction 1.— f.) produce a narrow 511 keV line."," Assuming that the fraction of positrons forming positronium is $f_{\rm ps}$ (see \\ref{sec:spec}) ), the fluxes in the 511 keV and 1.8 MeV lines per 1 positron produced via $^{26}$ Al decay are: Here we assume that i) the fraction of para-positronium is $1/4$ and ii) all positrons annihilating without formation of positronium (fraction $1-f_{\rm ps}$ ) produce a narrow 511 keV line."
 “Phe factor 2 in the above expression accounts for the 2 photons produced in two-photon annihilation., The factor $2$ in the above expression accounts for the 2 photons produced in two-photon annihilation.
" Therefore. fs),=0.409.0.471 and 1.6375Ps. for fi, —1. 0.95 and 0. respectively (see ro[fsecispec Lor details)."," Therefore, $\displaystyle F_{511}=0.409, 0.471$ and $1.637
\times F_{1.8}$, for $f_{\rm ps}=$ 1, 0.95 and 0, respectively (see \\ref{sec:spec} for details)."
 Lt is interesting to compare this relation with the Iluxes obtained from the lieht-bucket images in the 508514 keV and 18051813 keV energy. bands. which should contain most of the 511 keV. and. 1809 keV line Duxes. unless the lines are strongly. broadened.," It is interesting to compare this relation with the fluxes obtained from the light-bucket images in the 508–514 keV and 1805–1813 keV energy bands, which should contain most of the 511 keV and 1809 keV line fluxes, unless the lines are strongly broadened."
 Shown in Fig., Shown in Fig.
 7 is a light-bucket longitude scan of the Galactic plane over the region {5X60.., \ref{fig:alu} is a light-bucket longitude scan of the Galactic plane over the region $l=\pm60$.
 The blue thick crosses show the llux in the 508514 keV band. while the thin red crosses show the observed Dux in the 1505.1813 keV band scaled by a factor of 0.409.," The blue thick crosses show the flux in the 508–514 keV band, while the thin red crosses show the observed flux in the 1805–1813 keV band scaled by a factor of $0.409$."
" ""ποσο τοῦ crosses correspond to the expected 51 keVH lineH flux arisingnma fromB 27"" AI decay under the assumptionH that of positrons annihilate through the formation of positronium.", These red crosses correspond to the expected 511 keV line flux arising from $^{26}$ Al decay under the assumption that of positrons annihilate through the formation of positronium.
 It will be observed later refsecispec)) that this assumption is supported hy spectra data., It will be observed later \\ref{sec:spec}) ) that this assumption is supported by spectral data.
 Clearly. the high 511 keV line [ux from the GC region cannot be explained by 7 AL decay (unlessthepositronsregion:seee.g.Prantzos 2006)..," Clearly, the high 511 keV line flux from the GC region cannot be explained by $^{26}$ Al decay \citep[unless the positrons produced in
 the disk are somehow transported to the central region; see
 e.g.][]{2006A&A...449..869P}."
 One can use the same set of templates as in refsec:templates— and repeat the analysis for a πο of energies to obtain the spectrum associated with each spatia component., One can use the same set of templates as in \\ref{sec:templates} and repeat the analysis for a set of energies to obtain the spectrum associated with each spatial component.
 We did this using the Disk|Bulge model. which was applied to all observations with the pointing direction. within from GC.," We did this using the Disk+Bulge model, which was applied to all observations with the pointing direction within from GC."
 Since we do no explicitly. account for compact sources in this procedure. the low energv. parts of the spectra obtained may not. be reliable.," Since we do not explicitly account for compact sources in this procedure, the low energy parts of the spectra obtained may not be reliable."
 Llowever. near the 511 keV and 1.5 MeV lines the contribution of individual sources should) not be crucial.," However, near the 511 keV and 1.8 MeV lines the contribution of individual sources should not be crucial."
 Nevertheless. this simplifving assumption should be kept in mind when interpreting the resulting spectra. shown in lig. δ..," Nevertheless, this simplifying assumption should be kept in mind when interpreting the resulting spectra, shown in Fig. \ref{fig:aldb}."
 The upper row in Fig., The upper row in Fig.
 S. shows the spectrum of the juge component in the vicinity of the 511 keV and. 1.5 AeN lines., \ref{fig:aldb} shows the spectrum of the Bulge component in the vicinity of the 511 keV and 1.8 MeV lines.
 The red line in the top-left panel shows the best-fitting model (Gaussian at 511 keV ancl ortho-positronium continuum: see relsce:spec below for details)., The red line in the top-left panel shows the best-fitting model (Gaussian at 511 keV and ortho-positronium continuum; see \\ref{sec:spec} below for details).
 Phe Dux in the 511 keV line in this model is πι=(0.84E0.03)10phots!em>., The flux in the 511 keV line in this model is $F_{511}=(0.84\pm0.03)~10^{-3} \pscm2$.
 Note that this flux was obtained from the spectral analysis and it dillers slightly from the “Bulge” flux obtained. from the analvsis of the count rate in the 508514 keV bac. quoted in Table 1..," Note that this flux was obtained from the spectral analysis and it differs slightly from the “Bulge” flux obtained from the analysis of the count rate in the 508–514 keV band, quoted in Table \ref{tab:templates}."
 Phe value Z5; was then recaleulated into the expected Hux in the 1.5 MeV line using the relation Py£51./0-409. corresponding to the assumption that all positronss are produced. by “PAL decay. and. the fraction. of annihilations via positronium is (see eq.," The value $F_{511}$ was then recalculated into the expected flux in the 1.8 MeV line using the relation $F_{1.8}=F_{511}/0.409$, corresponding to the assumption that all positrons are produced by $^{26}$ Al decay and the fraction of annihilations via positronium is (see eq."
 4. and relsce:spec))., \ref{eq:1.8} and \\ref{sec:spec}) ).
 A line with the resulting Hux £i is plotted in the top-right panel as a Gaussian line centered at 1:800 MeV. Clearly such a strong lino at 1.8 MeV is in stark contrast to the data. which show no evidence for 1.8 MeV. emission in the Dulge spectrum.," A line with the resulting flux $\displaystyle F_{1.8}$ is plotted in the top-right panel as a Gaussian line centered at 1.809 MeV. Clearly such a strong line at 1.8 MeV is in stark contrast to the data, which show no evidence for 1.8 MeV emission in the Bulge spectrum."
 The bottom row in Fig., The bottom row in Fig.
 S. shows the Disk component spectrum in the vicinity of the 511 keV and 1.8 MeV. lines., \ref{fig:aldb} shows the Disk component spectrum in the vicinity of the 511 keV and 1.8 MeV lines.
 In contrast to the Bulge spectrum. the 1.5 MeV line is now very prominent in the data (bottom-right panel).," In contrast to the Bulge spectrum, the 1.8 MeV line is now very prominent in the data (bottom-right panel)."
 The red linc shows the best-fitting Gaussian at 1.800 MeV. with flux bys=(4.140.5)10!photstem7., The red line shows the best-fitting Gaussian at 1.809 MeV with flux $F_{1.8}=(4.1\pm0.5)~10^{-4} \pscm2$.
 The blue line in the bottom-left figure now shows a 511 keV line with flux 0.400...P1 s. , The blue line in the bottom-left figure now shows a 511 keV line with flux $\displaystyle F_{511}=0.409\times F_{1.8}$ .
The data do show the presence of a 511 keV line in the Disk component. although our experiments with the alternative background mocels and. various spatial patterns demonstrate that the parameters ofthe line near 511 keV are not determined reliably.," The data do show the presence of a 511 keV line in the Disk component, although our experiments with the alternative background models and various spatial patterns demonstrate that the parameters ofthe line near 511 keV are not determined reliably."
 Thus. Fig.," Thus, Fig."
 8. suggests that with the two-component spatial Bulee|Disk moclel:, \ref{fig:aldb} suggests that with the two-component spatial Bulge+Disk model:
unfortunately insullicient to generally. produce a strong flux enhancement above that from the background density.,unfortunately insufficient to generally produce a strong flux enhancement above that from the background density.
 In a uniform bath of dark matter the flux only grows logarithmically wilh decreasing radius. and is much weaker (han in (he case of the clensity spike envisioned bv Gondolo&Silk(1999).," In a uniform bath of dark matter the flux only grows logarithmically with decreasing radius, and is much weaker than in the case of the density spike envisioned by \citet{GonSil99}."
. Still. gravitational focusing may have astrophysical relevance if the flux is enhanced by any distinctive properties of the environment around the compact object.," Still, gravitational focusing may have astrophysical relevance if the flux is enhanced by any distinctive properties of the environment around the compact object."
 This situation may occur in (he case of svnchrotron radiation [rom a region around a black hole or neutron star., This situation may occur in the case of synchrotron radiation from a region around a black hole or neutron star.
 For supermassive black holes. magnetic field strengtlis can be orders of magnitude higher than in the interstellar medium.," For supermassive black holes, magnetic field strengths can be orders of magnitude higher than in the interstellar medium."
 Just as the gravitadional focusing is pinned to the black hole. so is the magnetic field. as it is likely (ed (o gas accreting on {ο the black hole.," Just as the gravitational focusing is pinned to the black hole, so is the magnetic field, as it is likely tied to gas accreting on to the black hole."
 An estimate of the svnchrotron flux from {follows [rom the density profile of Fieure 1 and an ecquipartition model lor (he magnetic field strength. (Melia1992).. in which B=(r/pe)'? mG. The value for electron-positron. vield may be obtained as in Tvler(2002):: in the low energy limit. the electron energy distribution per neutralino annihilation is dN/dEzzE|.," An estimate of the synchrotron flux from follows from the density profile of Figure 1 and an equipartition model for the magnetic field strength \citep{Mel92}, in which $B = (r/{\rm
pc})^{-1.2}$ mG. The value for electron-positron yield may be obtained as in \citet{Tyl02}; in the low energy limit, the electron energy distribution per neutralino annihilation is $dN/dE \approx
E^{-1.5}$."
 An integration of the radiative transler equation should include (he possible effects of synchrotron sell-absorption., An integration of the radiative transfer equation should include the possible effects of synchrotron self-absorption.
 Svuchrotron limits have been used by Bertoneetal.(2001). to place constraints on dark matter properties., Synchrotron limits have been used by \citet{BerSigSil01} to place constraints on dark matter properties.
 llowever. these limits depend on a strong flux generated in a density cusp and spike. along with a relatively strong magnetic field. all of which must be centered on Ax.," However, these limits depend on a strong flux generated in a density cusp and spike, along with a relatively strong magnetic field, all of which must be centered on ."
.. According to the results of Merrittetal.(2002).. even a relatively minor merger between the Milky Wav and a small galaxy can greatly reduce any annihilation signal.," According to the results of \citet{Meretal02}, even a relatively minor merger between the Milky Way and a small galaxy can greatly reduce any annihilation signal."
 For exaniple. if (he Milky Wav were to accrete a galaxy with a black hole whose mass is one tenth ofAx.. then a strong clensily enhancement near wwoulc be destroved.," For example, if the Milky Way were to accrete a galaxy with a black hole whose mass is one tenth of, then a strong density enhancement near would be destroyed."
 On the other hand. the more modest density peak produced by eravitational focusing will persist. even aller a merger event. presuming (hat dark matter particle orbits in the vicinitv of anre randomized.," On the other hand, the more modest density peak produced by gravitational focusing will persist, even after a merger event, presuming that dark matter particle orbits in the vicinity of are randomized."
 Gravitational focusing will also occur around other. smaller compact objects in Galaxy.," Gravitational focusing will also occur around other, smaller compact objects in Galaxy."
 Consider. lor example. a neutron star moving with considerable velocity through a thermal bath of dark matter.," Consider, for example, a neutron star moving with considerable velocity through a thermal bath of dark matter."
 Figure 3 shows the density enhancement along the stars direction of motion. and Figure 4 illustrates the intensity of annihilation radiation from material in a plane containing the path of the star.," Figure 3 shows the density enhancement along the star's direction of motion, and Figure 4 illustrates the intensity of annihilation radiation from material in a plane containing the path of the star."
 The signal is strongest behind the star. and weaker in front. but the angle-averaged signal strength is not greatly different from the case where the star is at rest in the bulk dark matter frame.," The signal is strongest behind the star, and weaker in front, but the angle-averaged signal strength is not greatly different from the case where the star is at rest in the bulk dark matter frame."
 A neutron star is an improbable source of annihilation radiation in the form of svnchrotron photons: the volume where there is significant gravitational locusing is too small to be, A neutron star is an improbable source of annihilation radiation in the form of synchrotron photons; the volume where there is significant gravitational focusing is too small to be
In 1995 Mrk 501 was detected as a source of TeV gamma-rays by the team (Quinn et al. 1996)),In 1995 Mrk 501 was detected as a source of TeV gamma-rays by the team (Quinn et al. \cite{Quinn}) )
 for the first time., for the first time.
 Its flux level corresponded to of that of the Crab Nebula., Its flux level corresponded to of that of the Crab Nebula.
 The detection was confirmed by the HEGRA collaboration (Bradbury et al. 1997))., The detection was confirmed by the HEGRA collaboration (Bradbury et al. \cite{Brad}) ).
 A recent compilation of TeV observations of Mrk 501 (Protheroe et al. 1997)), A recent compilation of TeV observations of Mrk 501 (Protheroe et al. \cite{Protheroe}) )
 shows the source at very high level with flares up to 10 Crab throughout the entire observing season of 1997 well into the July observations presented here., shows the source at very high level with flares up to 10 Crab throughout the entire observing season of 1997 well into the July observations presented here.
 A similar brightening of Mrk 501 during 1997 has been observed in X-rays by the RXTE All Sky Monitor (ASM). the peak brightness in June 1997 being ~ 40 mCrab (Fig. 1)).," A similar brightening of Mrk 501 during 1997 has been observed in X-rays by the RXTE All Sky Monitor (ASM), the peak brightness in June 1997 being $\sim$ 40 mCrab (Fig. \ref{ASM}) )."
" The TeV and ASM (2-10 keV) light curves show similar flaring activity during 1997, the correlated X-ray and VHE gamma-ray variability will be discussed in a forthcoming paper."," The TeV and ASM (2-10 keV) light curves show similar flaring activity during 1997, the correlated X-ray and VHE gamma-ray variability will be discussed in a forthcoming paper."
 At the onset of this high activity in April 1997 observations with the SAX satellite were carried out (Pian et al. 1997))., At the onset of this high activity in April 1997 observations with the SAX satellite were carried out (Pian et al. \cite{Pian}) ).
 They find Mrk 501 with an unusually hard X-ray spectrum. extending up to photon energies of 100 keV with the hardest spectrum observed on 16 April. when the source was brightest.," They find Mrk 501 with an unusually hard X-ray spectrum, extending up to photon energies of 100 keV with the hardest spectrum observed on 16 April, when the source was brightest."
 The bright X-ray state of Mrk 501 in June/July 1997 triggered intense multi-frequency observations from radio to VHE mma-rays., The bright X-ray state of Mrk 501 in June/July 1997 triggered intense multi-frequency observations from radio to VHE ma-rays.
 Here we report on RXTE observations between 11 July and 16 July 1997 resulting in 21300 seconds of good data in 10 pointings (Tab. 1))., Here we report on RXTE observations between 11 July and 16 July 1997 resulting in 21300 seconds of good data in 10 pointings (Tab. \ref{obs_log}) ).
 We have used for the reduction of the PCA and HEXTE data., We have used for the reduction of the PCA and HEXTE data.
" PCA good times have been selected from the standard 2 mode data sets using the following criteria: target elevation >10"". pointing offset <0.01"". and all 5 PCUs switched on."," PCA good times have been selected from the standard 2 mode data sets using the following criteria: target elevation $> 10^\circ$, pointing offset $<0.01^\circ$, and all 5 PCUs switched on."
 For the resulting intervals spectra and light curves were extracted using all Xenon layers., For the resulting intervals spectra and light curves were extracted using all Xenon layers.
 The corresponding PCA background spectra and light curves were derived with, The corresponding PCA background spectra and light curves were derived with.
 After applying the above elevation and offset criteria. TTE spectra and light curves have been binned and background subtracted using the off-source looking intervals.," After applying the above elevation and offset criteria, TE spectra and light curves have been binned and background subtracted using the off-source looking intervals."
 Spectral fitting was performed with using the latest detector response matrix from 26 August 1997 for PCA and the response files from 20 March 1997 for HEXTE., Spectral fitting was performed with using the latest detector response matrix from 26 August 1997 for PCA and the response files from 20 March 1997 for HEXTE.
 The PCA spectra in the PHA channel range 3-60 (2.5-27 keV) and the spectra from both HEXTE clusters in the channel range 15-100 (15-100 keV) were combined for each of the 10 pointings and then fitted with single and broken power law spectra., The PCA spectra in the PHA channel range 3-60 (2.5-27 keV) and the spectra from both HEXTE clusters in the channel range 15-100 (15-100 keV) were combined for each of the 10 pointings and then fitted with single and broken power law spectra.
 The uncertainty in the absolute flux calibration of the HEXTE instrument. mainly due to uncorrected dead-time effects (see Rothschild et al. 1997)).," The uncertainty in the absolute flux calibration of the HEXTE instrument, mainly due to uncorrected dead-time effects (see Rothschild et al. \cite{Roth}) ),"
 was accounted for by allowing for a scaling factor between the PCA and HEXTE spectra., was accounted for by allowing for a scaling factor between the PCA and HEXTE spectra.
 Setting PCA to 1.0. the mean best fit value for the HEXTE normalization was 0.65.," Setting PCA to 1.0, the mean best fit value for the HEXTE normalization was 0.65."
 The absorbing column density on the line of sight to Mrk 501 was fixed to 2.87-1(Pcii.? as derived from the ROSAT spectrum (Lamer et al. 1996))., The absorbing column density on the line of sight to Mrk 501 was fixed to $2.87 \cdot 10^{20} {\rm cm^{-2}}$ as derived from the ROSAT spectrum (Lamer et al. \cite{Lamer96}) ).
 This value is larger than the galactic value as derived from 21cm H I measurements (1.73-10?«10.7. Stark et al. 1992)).," This value is larger than the galactic value as derived from $21\;{\rm cm}$ H I measurements $1.73 \cdot 10^{20} {\rm cm^{-2}}$, Stark et al. \cite{Stark}) )."
 However. the effect of this difference on the spectral results in the RXTE energy range is negligible.," However, the effect of this difference on the spectral results in the RXTE energy range is negligible."
 Note that Pian et al., Note that Pian et al.
 1997 used the galactic H I column density 21.7310?!ci.?. for the spectral fits to the SAX data and that the uncertainty in the value towards the source may have a significant effect on the spectral indices measured with the LECS instrument at the softest X-ray energies., \cite{Pian} used the galactic H I column density $1.73\cdot 10^{20} {\rm cm^{-2}}$ for the spectral fits to the SAX data and that the uncertainty in the value towards the source may have a significant effect on the spectral indices measured with the LECS instrument at the softest X-ray energies.
" Single power law models with Nyy, fixed to any reasonable value do not yield acceptable fits to the data of any pointing. whereas broken power law models with break energies between 5.5 and 6.0 keV give excellent fits to the individual spectra (see Tab. 2))."," Single power law models with $N_H$ fixed to any reasonable value do not yield acceptable fits to the data of any pointing, whereas broken power law models with break energies between 5.5 and 6.0 keV give excellent fits to the individual spectra (see Tab. \ref{spec}) )."
 Below the break point the model spectra are exceptionally hard with energy indices ranging from 0.65 to 0.77., Below the break point the model spectra are exceptionally hard with energy indices ranging from 0.65 to 0.77.
 In fact an X-ray synchrotron spectrum of this hardness, In fact an X-ray synchrotron spectrum of this hardness
parameters used in their study.,parameters used in their study.
Some authors. as discussed below. adopt even larger mass transfer rates al the top of the period gap.,"	Some authors, as discussed below, adopt even larger mass transfer rates at the top of the period gap."
 Ifthe magnetic braking mechanism that drives evolution of the secondary star is suddenly turned olf al an orbital period of:3. then the secondary approaches thermal equilibrium on a Ixelvin-IHlelmholtz timescale.," If the magnetic braking mechanism that drives evolution of the secondary star is suddenly turned off at an orbital period of$3^{\rm h}$, then the secondary approaches thermal equilibrium on a Kelvin-Helmholtz timescale."
 Consequently. mass transfer continues at a decreasing rate for zzLO!vr (Ritter1988).," Consequently, mass transfer continues at a decreasing rate for ${\approx}10^4{\rm yr}$ \citep{r1988}."
". But the alternation between high and low states in VY Scl stars is on a much shorter Gimescale and requires a separate mechanism (o switch (he mass transfer on and olf,", But the alternation between high and low states in VY Scl stars is on a much shorter timescale and requires a separate mechanism to switch the mass transfer on and off.
 Livio&Pringle(1994) discuss the problem and propose stuspots on the secondary star. which pass across the Ll point and cause reduced mass (ransfer.," \citet*{lp94} discuss the problem and propose starspots on the secondary star, which pass across the L1 point and cause reduced mass transfer."
 This proposal has been further developed (Ning&Cannizzo1998) with application of a time-dependent code io model the variable accretion disk. (, This proposal has been further developed \citep{kc98} with application of a time-dependent code to model the variable accretion disk. (
See also Schreiber.Gansicke.&Cannizzo 2000)).,See also \citealt*{sgc2000}) ).
 Bul the Nine&Cannizzo(1998) model produced the uuwantec result of cdwarl-nova tvpe outbursts in the low state. alter mass transfer had been switched off.," But the \citet{kc98} model produced the unwanted result of dwarf-nova type outbursts in the low state, after mass transfer had been switched off."
 A suggested escape was maintenance of the inner accretion disk in a permanent high state through irradiation by the WD (Leach et al., A suggested escape was maintenance of the inner accretion disk in a permanent high state through irradiation by the WD (Leach et al.
 1999. hereafter L1999).," 1999, hereafter L1999)."
 L1999 concluded that the presence of a 40.0001x WD does suppress dwarf nova outbursts.," L1999 concluded that the presence of a 40,000K WD does suppress dwarf nova outbursts."
The L1999 study adopted a high state mass transfer rale of 1.1x10.Viva! that was chosen to guarantee that hydrogen is fully ionized at the outer accretion disk boundary.,	The L1999 study adopted a high state mass transfer rate of $1.1{\times}10^{-8}{\cal M}_{\odot}{\rm yr}^{-1}$ that was chosen to guarantee that hydrogen is fully ionized at the outer accretion disk boundary.
 According to L1999. cessation of mass transfer produces a rapid transition to a state of low but non-zero viscosity.," According to L1999, cessation of mass transfer produces a rapid transition to a state of low but non-zero viscosity."
 The accretion disk remains nearly intact during the low state. transferring only a few percent of the accretion disk mass to the WD.," The accretion disk remains nearly intact during the low state, transferring only a few percent of the accretion disk mass to the WD."
 Because of non-zero viscosity. (he accretion disk still radiates at a low level during the low state.," Because of non-zero viscosity, the accretion disk still radiates at a low level during the low state."
 Hameury Lasota (2002. hereafter ILLO2) show that the adopted WD mass in L1999 (04M. ) is important to the suppression of outbursts. and (hat a WD mass of O0.T.VL. would have produced outbursts.," Hameury Lasota (2002, hereafter HL02) show that the adopted WD mass in L1999 ${\cal M}_{\odot}$ ) is important to the suppression of outbursts, and that a WD mass of ${\cal M}_{\odot}$ would have produced outbursts."
 ILLO2 alternatively propose (hat VY Sel stus have magnetic WDs and that the magnetic field truncates theaccretion disk., HL02 alternatively propose that VY Scl stars have magnetic WDs and that the magnetic field truncates theaccretion disk.
" IILO2 show that. lor a. WD mass of 0.7.Vf... and a magnetic moment of yp=5x10""Gem. no outbursts occur and the change in the V. magnitude. from high state to low state. is 5 magnitudes."," HL02 show that, for a WD mass of ${\cal M}_{\odot}$ and a magnetic moment of ${\mu}=5{\times}10^{30}{\rm Gcm^3}$, no outbursts occur and the change in the $V$ magnitude, from high state to low state, is 5 magnitudes."
 Tloard et al. (, Hoard et al. (
2004. hereafter 122004) used the BINSYN suite (Linnell to calculate a svstem model and corresponding svnthetie spectrum for MV. Lyr in a recent low state.,"2004, hereafter H2004) used the BINSYN suite \citep{lin96} to calculate a system model and corresponding synthetic spectrum for MV Lyr in a recent low state."
 The synthetic spectrum accurately fitsFUSE spectra aud contemporaneous optical speclra. as well asUE spectra [rom a prior low state.," The synthetic spectrum accurately fits spectra and contemporaneous optical spectra, as well as spectra from a prior low state."
 The H2004 discussion considers the connection of the low state study to earlier investigations of MV Lvr and shows that the low state can be understood in terms of a naked hot WD with a temperature of 47.0001. a photosphere log g of 3.25. and a metallicity of 0.3 solar.," The H2004 discussion considers the connection of the low state study to earlier investigations of MV Lyr and shows that the low state can be understood in terms of a naked hot WD with a temperature of 47,000K, a photosphere log $g$ of 8.25, and a metallicity of 0.3 solar."
 The log g. together with the mass- relation lor zero-temperature carbon WD models (lamaca&Salpeter1961) selects a model with My=0.73M... estimatecl error of O.LM... and radius of 0.010672...," The log $g$, together with the mass-radius relation for zero-temperature carbon WD models \citep*{hs61} selects a model with ${\cal M}_{\rm wd}=0.73{\cal M}_{\odot}$, estimated error of $0.1{\cal M}_{\odot}$ , and radius of $0.01067R_{\odot}$ ."
 The secondary star fills its Roche lobe and is cooler than 3500lN:35 it contributes nothing to the, The secondary star fills its Roche lobe and is cooler than 3500K; it contributes nothing to the
"For two galactic N-rav binary systems. GIU 1915|105 and GRO 1655-40. fig, and foo have been measured. for multiple ejection events.","For two galactic X-ray binary systems, GRS 1915+105 and GRO J1655-40, $\mu_{\rm app}$ and $\mu_{\rm rec}$ have been measured for multiple ejection events."
 The data are summarised in table 1., The data are summarised in table 1.
 Both sources have fairly accurate independent distance estimates., Both sources have fairly accurate independent distance estimates.
 For GRS 1915|105. Mirabel Iocdriguez (1994) estimate a distance. of 12.541.5 kpc based on lll measurements.," For GRS 1915+105, Mirabel Rodriguez (1994) estimate a distance of $12.5
\pm 1.5$ kpc based on HI measurements."
 Dhawan. Goss Rodriguez (2000) revise this distance estimate to 1231 kpe.," Dhawan, Goss Rodriguez (2000) revise this distance estimate to $12 \pm 1$ kpc."
 The large X-ray column and optical extinction to the source are in agreement with this relatively large clistance., The large X-ray column and optical extinction to the source are in agreement with this relatively large distance.
 For GRO J1655-40. Moelxav Westeven (1994) estimated. a distance of 3.5 kpe. ancl Tingayv et al. (," For GRO J1655-40, McKay Kesteven (1994) estimated a distance of 3.5 kpc, and Tingay et al. ("
1995) estimated: a distance of 35 kpe.,1995) estimated a distance of 3–5 kpc.
 The kinematic model fit »erformed. by Hjellming and Rupen (1995) resulted. in a distance estimated of 3.2+0.2 kpe., The kinematic model fit performed by Hjellming and Rupen (1995) resulted in a distance estimated of $3.2 \pm 0.2$ kpc.
 Most recently Greene. Dailvn Orosz (2001) derive d=3.79x0.69 kpe based on mocelling of optical data.," Most recently, Greene, Bailyn Orosz (2001) derive $d = 3.79 \pm 0.69$ kpc based on modelling of optical data."
 Comparison of these distance estimates with the values Or daas listed in table 1 reveals. immediately that all he distance estimates place the sources very close το (or even bevond!) di.," Comparison of these distance estimates with the values for $d_{\rm
max}$ listed in table 1 reveals immediately that all the distance estimates place the sources very close to (or even beyond!) $d_{\rm
max}$."
 Phe result. of this is that. from such observations we can only place a on the Lorentz actor of the jets., The result of this is that from such observations we can only place a on the Lorentz factor of the jets.
 ‘This is illustrated in Figs 1(20).(b).," This is illustrated in Figs 1(a),(b)."
 In these figures the solutions for 3 and 6. based on the observed proper motions. are plotted. as a function of distance to the sources.," In these figures the solutions for $\beta$ and $\theta$, based on the observed proper motions, are plotted as a function of distance to the sources."
 Also indicated. are the best. distance estimates. as well as the Lorentz and relativistic Doppler factors resulting from the solutions to αμα 9.," Also indicated are the best distance estimates, as well as the Lorentz and relativistic Doppler factors resulting from the solutions to $\beta$ and $\theta$."
 What is clear. for both sources. is that the distance estimates already fairly accurate cannot do more than place a lower limit of 23 on the Lorentz factors of the ejections.," What is clear, for both sources, is that the distance estimates – already fairly accurate – cannot do more than place a lower limit of 2–3 on the Lorentz factors of the ejections."
 No upper limit is possible as the range of possible distances includes dias.," No upper limit is possible as the range of possible distances includes $d_{\rm
max}$."
 Consequently we can only place upper limits on the Doppler shifts associated with the jets., Consequently we can only place upper limits on the Doppler shifts associated with the jets.
 These figures clearlv illustrate. that for these two celebrated sources. the measured. proper motions combined with the distance uncertainties do allow us to measure how relativistic the jets are.," These figures clearly illustrate that for these two celebrated sources, the measured proper motions combined with the distance uncertainties do allow us to measure how relativistic the jets are."
 In this paper we shall show that this will almost always be the case., In this paper we shall show that this will almost always be the case.
 A further misunderstanding propagating in the literature is that the [lux ratio observed between the approaching ancl receding knots is somehow an independent confirmation of any distance or velocity measurement already. derived. from the proper motions., A further misunderstanding propagating in the literature is that the flux ratio observed between the approaching and receding knots is somehow an independent confirmation of any distance or velocity measurement already derived from the proper motions.
" This asymmetry in brightness between the approaching and receding knots is due to a combination of classical Doppler and relativistic aberration effects. both contained in the relativistic Dopplerfactor An object moving at angle 8 to the line of sight with velocity 3 (ane resultant Lorentz factor D). will have an observed. surface brightness 9"" brighter. where 2<&3 (A=2 corresponds to the average of multiple events in e.g. a continuous jet. A=3 corresponds to emission dominated ον a singularly evolving event)."," This asymmetry in brightness between the approaching and receding knots is due to a combination of classical Doppler and relativistic aberration effects, both contained in the relativistic Dopplerfactor An object moving at angle $\theta$ to the line of sight with velocity $\beta$ (and resultant Lorentz factor $\Gamma$ ) will have an observed surface brightness $\delta^k$ brighter, where $2 < k < 3$ $k=2$ corresponds to the average of multiple events in e.g. a continuous jet, $k=3$ corresponds to emission dominated by a singularly evolving event)."
" Therefore the ratio of tux densities from approaching and receding knots — measured al the same angular separation [roni the core. so as to sample he knots at the same age in their evolution will be given Ds where à is the spectral index. of the. emitting region. defined such that S,cxον "," Therefore the ratio of flux densities from approaching and receding knots – measured at the same angular separation from the core, so as to sample the knots at the same age in their evolution – will be given by: where $\alpha$ is the spectral index of the emitting region, defined such that $S_{\nu} \propto \nu^{\alpha}$."
“This additional term compensates for the Doppler shifted: spectrum. when observing at a single frequency., This additional term compensates for the Doppler shifted spectrum when observing at a single frequency.
 The ratio of the proper motions is simply the ratio of the Doppler factors. so Thus once nop and face have been measured. the only additional information obtained by measuring the Εαν ratio between approaching and receding jet relates to the xwameter &.," The ratio of the proper motions is simply the ratio of the Doppler factors, so Thus once $\mu_{\rm app}$ and $\mu_{\rm rec}$ have been measured, the only additional information obtained by measuring the flux ratio between approaching and receding jet relates to the parameter $k$."
 Although it may seem. counter-intuitive that he Hux ratio should remain constant as : increases. this is recause at the same time @ is also increasing.," Although it may seem counter-intuitive that the flux ratio should remain constant as $\beta$ increases, this is because at the same time $\theta$ is also increasing."
 The meaning of ko will not be explored. in detail here: however a small rol is worth making: in observations in which we can be zirlv confident that we have resolved. a single radio knot. hen & should have the value 3.," The meaning of $k$ will not be explored in detail here; however a small point is worth making: in observations in which we can be fairly confident that we have resolved a single radio knot, then $k$ should have the value 3."
 LP we measure a value less han this it may indicate that the bulk velocity of the Low is significantly less than the velocity which we are observing (for further discussion see e.g. Blandford et al., If we measure a value less than this it may indicate that the bulk velocity of the flow is significantly less than the velocity which we are observing (for further discussion see e.g. Blandford et al.
 1971)., 1977).
"and GSO (50-100 keV), with a time bin of 10 ks.","and GSO (50–100 keV), with a time bin of 10 ks."
" The background was subtracted for the PIN and GSO, while the XIS background rate is <1% of the signal, and thus is negligible."," The background was subtracted for the PIN and GSO, while the XIS background rate is $<1$ of the signal, and thus is negligible."
" Note that the background rate of the PIN and GSO is around 0.3 and 8-10 count s, respectively."," Note that the background rate of the PIN and GSO is around 0.3 and 8–10 count $^{-1}$, respectively."
 All the observations clearly exhibit time variability in the XIS and PIN light curves with an amplitude of up to and a time scale of 10-20 ks., All the observations clearly exhibit time variability in the XIS and PIN light curves with an amplitude of up to and a time scale of 10–20 ks.
 This time scale is reasonable for the black hole mass of (0.5—1)~105M; (Silge et al., This time scale is reasonable for the black hole mass of $(0.5-1)\sim10^8 M_{\odot}$ (Silge et al.
 2005; Krajnovuie et al., 2005; Krajnovuie et al.
 2007; Neumayer et al., 2007; Neumayer et al.
 2007)., 2007).
 The largest variability occurred during the 2009-1st observation., The largest variability occurred during the 2009-1st observation.
" Looking at the light curves, there is a different variability pattern between the XIS and PIN."," Looking at the light curves, there is a different variability pattern between the XIS and PIN."
" For example, at 0—50000 sec (1-5th bin) in the 2009-1st observation, the rising trend of the count rate is linear for the PIN and concave for the XIS."," For example, at 0–50000 sec (1–5th bin) in the 2009-1st observation, the rising trend of the count rate is linear for the PIN and concave for the XIS."
" At 0-70000 (29-35th bin) sec in the 2009-3rd observation, the variability pattern is also different between the XIS and PIN."," At 0–70000 (29–35th bin) sec in the 2009-3rd observation, the variability pattern is also different between the XIS and PIN."
" For the GSO light curve, the error is somewhat large, but a similar trend of variability is clearly seen."," For the GSO light curve, the error is somewhat large, but a similar trend of variability is clearly seen."
 Figure 3 shows a correlation of the count rate among different energy bands., Figure \ref{correlation} shows a correlation of the count rate among different energy bands.
" We do not treat the 2005 data, since the XIS to PIN effective area ratio is different between 2005"," We do not treat the 2005 data, since the XIS to PIN effective area ratio is different between 2005"
aat an inter-order separation = 450J|.,at an inter-order separation $\equiv$ 450.
 This whole inter-order range can be covered with the pressure of nitrogen as the scanning gas being increased to 5.36 atmos., This whole inter-order range can be covered with the pressure of nitrogen as the scanning gas being increased to 5.36 atmos.
 above atmospheric pressure., above atmospheric pressure.
 One particular merit. of the pressurestepped FabryPerot is its operational simplicity., One particular merit of the pressure–stepped Fabry–Perot is its operational simplicity.
 JOC and JAL acknowledge the excellent assistance of the stall at the Nordic Optical telescope (NOT — La Palma) where these initial observations were mace., JOC and JM acknowledge the excellent assistance of the staff at the Nordic Optical telescope (NOT – La Palma) where these initial observations were made.
 In particular we are erateful to Hugo Schwartz for his assistance., In particular we are grateful to Hugo Schwartz for his assistance.
 We thank the technical stall in our department for manufacturing the device and PPARC for funding its construction., We thank the technical staff in our department for manufacturing the device and PPARC for funding its construction.
 JOC also thanks PPARC for à Research Studentship., JOC also thanks PPARC for a Research Studentship.
 The optical lavout of NOMI., The optical layout of MOMI.
 The δ.Ε S4avemin? image of the environs of P Cvgni in the light ofA., The 8.4 $\times$ 8.4 $^{2}$ image of the environs of P Cygni in the light of.
.. The outer shell o£P €vgni in the light ofΑ., The outer shell of P Cygni in the light of.
. The bright feature to the NW. of the star is a ‘ghost’ eencrated within the lavers of the interference filter., The bright feature to the NW of the star is a `ghost' generated within the layers of the interference filter.
 The inner shell in the light ofΑ., The inner shell in the light of.
. The residual scattered stellar continuum has been subtracted by modelling that around. a similarly bright star., The residual scattered stellar continuum has been subtracted by modelling that around a similarly bright star.
 No attempt has been made to remove the prominent dilfraction spikes., No attempt has been made to remove the prominent diffraction spikes.
"agreement with Gaoetal.(2004),, substructure is nearly independent of mass (Rs= 0.09), but strongly anti-correlated with concentration (Rs= —0.57).","agreement with \citet{Gao2004}, substructure is nearly independent of mass $\rank=0.09$ ), but strongly anti-correlated with concentration $\rank=-0.57$ )."
" It thus appears that concentration, and the very closely related parameter age, may in some sense be more fundamental than mass."," It thus appears that concentration, and the very closely related parameter age, may in some sense be more fundamental than mass."
" A better way to judge which (combinations of) parameters are most fundamental, is to carry out a PCA, which we will do next."," A better way to judge which (combinations of) parameters are most fundamental, is to carry out a PCA, which we will do next."
 PCA is a statistical technique to find the number of independent parameters which are needed to account for the variance in a data set., PCA is a statistical technique to find the number of independent parameters which are needed to account for the variance in a data set.
 Most of the variance in the data set can be represented by a subset of all eigenvectors of the covariance matrix., Most of the variance in the data set can be represented by a subset of all eigenvectors of the covariance matrix.
" These eigenvectors are known as the principal components (i.e., PC1, PC2, etc.)."," These eigenvectors are known as the principal components (i.e., $1$, $2$, etc.)."
 The eigenvalues corresponding to the eigenvectors indicate whether or not that PC is important., The eigenvalues corresponding to the eigenvectors indicate whether or not that PC is important.
" If the variables are standardized ttransformed to have mean zero and variance one), then the fraction of the total variance in the data set due to a given PC is equal to its eigenvalue divided by the total number of parameters."," If the variables are standardized transformed to have mean zero and variance one), then the fraction of the total variance in the data set due to a given PC is equal to its eigenvalue divided by the total number of parameters."
" Except for καν, which can be zero, we use the logarithm of the parameters."," Except for $\MR$, which can be zero, we use the logarithm of the parameters."
" Before running the PCA, we standardize the halo properties by subtracting the means and dividing"," Before running the PCA, we standardize the halo properties by subtracting the means and dividing"
Once the best Fe II broadening and scaling were identified. a Fe IH-subüracted spectrum was generated and the continuum was fit and removed between tlie emission lines over the range AA4200— 6000.,"Once the best Fe II broadening and scaling were identified, a Fe II-subtracted spectrum was generated and the continuum was fit and removed between the emission lines over the range $\lambda\lambda4200-6000$ ."
 IL2 ancl A5007 widths were measured [rom (hese normalized spectra., $\beta$ and $\lambda5007$ widths were measured from these normalized spectra.
 These widihs are not derived from fits to funcüons. but are actual measured widths of the two lines at half of their maximum intensity.," These widths are not derived from fits to functions, but are actual measured widths of the two lines at half of their maximum intensity."
 Six of the objects had no detectable (or very weak) ο III] emission. and so they were removed from the sample.," Six of the objects had no detectable (or very weak) [O III] emission, and so they were removed from the sample."
 The remaining 115 objects. together with Ibe PWHA and σοι CEWIIM/2.35: corrected for instrumental resolution: see below) are listed in table 1.," The remaining 115 objects, together with $\beta$ FWHM and $\sigma_{\rm [O III]}$ (FWHM/2.35; corrected for instrumental resolution; see below) are listed in table 1."
 Note that x {wo sels of measurements for the object observed (and. analyzed) twice. SDSS J032205.01201.4. differ bx or less.," Note that the two sets of measurements for the object observed (and analyzed) twice, SDSS J032205.05+001201.4, differ by or less."
 In the case of the [O IH] widths. the instrumental resolution. 166 km s| (or 2.8À al A5OOT). has been subtracted in quadrature from the measured widths.," In the case of the [O III] widths, the instrumental resolution, 166 km ${\rm s}^{-1}$ (or 2.8A at $\lambda5007$ ), has been subtracted in quadrature from the measured widths."
 Note (hat this correction only changes the line width by as much as in 12 of the 115 objects., Note that this correction only changes the line width by as much as in 12 of the 115 objects.
 For the IL? line widths an additional caveat is required., For the $\beta$ line widths an additional caveat is required.
 In approxinately one-fourth of the spectra. a narrow IL? spike is seen on top of the broad [Lo line.," In approximately one-fourth of the spectra, a narrow $\beta$ spike is seen on top of the broad $\beta$ line."
 We have ignored this spike in measuring the EWIIM of the IL2 line., We have ignored this spike in measuring the FWHM of the $\beta$ line.
 Although such spikes include only a small fraction of the flix in the line. they can dramatically change the FWIIM value measured.," Although such spikes include only a small fraction of the flux in the line, they can dramatically change the FWHM value measured."
" Recently Vestergaard(2002) has discussed at length the correct method for measuring ihe DLE. line width for the caleulation of M,.", Recently \citet{vestergaard02} has discussed at length the correct method for measuring the BLR line width for the calculation of $_{\bullet}$.
" As she points out. the appropriate DLR velocily dispersion is that measured [rom (he ""rms. spectrum. which represents (he varving part of the line profile."," As she points out, the appropriate BLR velocity dispersion is that measured from the `rms' spectrum, which represents the varying part of the line profile."
 She goes on to compare the EWIIM IL? values from the rms spectra of Ixaspietal.(2000). with mean and single-epoch measurements of the same objects., She goes on to compare the FWHM $\beta$ values from the rms spectra of \citet{kaspietal00} with mean and single-epoch measurements of the same objects.
 She concludes (hat. in general. (he best wav (o substitute a single-epoch spectrum [ον the rms spectrum is to remove the Fe II emission. but leave the narrow component of IL? to be included in the measurement.," She concludes that, in general, the best way to substitute a single-epoch spectrum for the rms spectrum is to remove the Fe II emission, but leave the narrow component of $\beta$ to be included in the measurement."
 The conclusion that (he narrow component should not be removed is motivated. primarily by the single object PGIT044-608 (3C 351). which has a strong. narrow spike on lop of a very broad IL? lime.," The conclusion that the narrow component should not be removed is motivated primarily by the single object PG1704+608 (3C 351), which has a strong, narrow spike on top of a very broad $\beta$ line."
 Measurements of the width of the broad lines in this object include 6560 kan s! (IL9: DG92). 13.000 km s! (la: (1994))). 10.000 kmsJ| (IL: Netzeretal. (1982))).," Measurements of the width of the broad lines in this object include 6560 km ${\rm s}^{-1}$ $\beta$; BG92), 13,000 km ${\rm s}^{-1}$ $\alpha$; \citet{eracleousandhalpern94}) ), 10,000 km ${\rm s}^{-1}$ $\beta$; \citet{netzeretal82}) )."
 However. quote 890 km s.! [or the mean spectrum and 400 km s.| [or the rms spectrum.," However, \citet{kaspietal00} quote 890 km ${\rm s}^{-1}$ for the mean spectrum and 400 km ${\rm s}^{-1}$ for the rms spectrum."
 Is it really the narrow component of 1L2 (hat is varving?, Is it really the narrow component of $\beta$ that is varying?
 There are several reasons to think that the idea that it is the narrow part of the line varving is in error., There are several reasons to think that the idea that it is the narrow part of the line varying is in error.
 First. (he narrow component only accounts for a small fraction of the line flix. around in this object.," First, the narrow component only accounts for a small fraction of the line flux – around in this object."
 Thus. to produce a change in total line f[Inx of a [factor of (wo. as is seen in (he Ilxaspietal.(2000). data. it would need (o vary bya factor of 20.," Thus, to produce a change in total line flux of a factor of two, as is seen in the \citet{kaspietal00} data, it would need to vary bya factor of 20."
 This is inconsistent with published spectra in Naspietal.(2000) and DG92. and the 5D55 EDR spectrum of this object. all of which show the narrow IL? at similar strength," This is inconsistent with published spectra in \citet{kaspietal00} and BG92, and the SDSS EDR spectrum of this object, all of which show the narrow $\beta$ at similar strength"
From Eqs. C,From Eqs. (
I) and (8) we have Performing integration to both sides we obtain where ᾧ is the phase of the pulsar. aud. 2 is a provisional timiug residual.,"4) and (8) we have Performing integration to both sides we obtain where $\Phi$ is the phase of the pulsar, and $R$ is a provisional timing residual."
 Thus oue lias {πι aud £) are the period aud its first derivative at begiuniug time., Thus one has $P_0$ and $\dot{P_0}$ are the period and its first derivative at beginning time.
 Equation (11) reflects the relationship between the fluctuation aud timing residual., Equation (11) reflects the relationship between the fluctuation and timing residual.
 We can obtain the real timine residual R by performing least-squares-litting to 2., We can obtain the real timing residual $\Re$ by performing least-squares-fitting to $R$.
 To understand more clearly about Eq. (, To understand more clearly about Eq. (
11). we try to provide a simple example.,"11), we try to provide a simple example."
 Let siu(22//19). one has From Eq. (," Let $\delta(t)=a\sin(2\pi t/t_0)$ , one has From Eq. ("
12) we can see that longer timescale variation will cause stronger noise because Rxf.,12) we can see that longer timescale variation will cause stronger noise because $\Re\propto {t_0}^2$.
" For a normal pulsar with £4,=0.1 s aud atuΓι. 10"" sandr=I. we obtain RK=0.013(xiPly) s. Π dis a very strong uoise a the timescale of years."," For a normal pulsar with $P_0=0.1$ s and $\dot{P_0}=1\times 10^{-14}$, when $a=0.01$, $t_0=y\times3.15\times10^{7}$ s and $n=1$, we obtain $\Re \cong 0.013 \times y^2 \times \sin(2\pi t/t_0)$ s. It is a very strong noise at the timescale of years."
 We further do a simulaloh Wih Eq. (, We further do a simulation with Eq. (
11).,11).
 Three sets of raudoii data. with different. Hurst pa‘ameter H. which reflects he time cependeuce of a time series NE are proclucec to simulate th‘ee types of 1regular f[Iuctialious in Ey.," Three sets of random data with different Hurst parameter $H$, which reflects the time dependence of a time series $^{[15]}$ are produced to simulate three types of irregular fluctuations in $\dot{E_u}$."
 As is shown in Fig., As is shown in Fig.
 L. each set of daa iis 10000 poluts.," 1, each set of data has 10000 points."
 Tle first set has more shor period componeuts. with H= 0.1: he second se is approximate wlΠο nolse. wih Η=0.6: 1ie third one lias more long »eriod Com»)0nelnts. with H—0«δν," The first set has more short period components, with $H=0.4$ ; the second set is approximate white noise, with $H=0.6$; the third one has more long period components, with $H=0.8$."
 In this sltutlation we take (Ga+1+ou)P= 0.lsaud 4)—]x10ll, In this simulation we take $(n+1+\delta_0)P_0=0.1$ s and $\dot{P_0}=1\times 10^{-14}$.
 Τιe correspoicine timing noises aσ'e shown in Fig, The corresponding timing noises are shown in Fig.
 2., 2.
 The fierres indicate that if tlie particle emission las a laldom variatiou with exent of abou 1% in daily timescale. the flux density from the most disali pulsars varies less than 5561 it will lead to a timiο noise with rauge of dozeus of iillisecoi di1 2000 «avs (shown on the left of Fi2.," The figures indicate that if the particle emission has a random variation with extent of about $1\%$ in daily timescale, the flux density from the most distant pulsars varies less than $5\%$ $^{[14]}$ it will lead to a timing noise with range of dozens of millisecond in 2000 days (shown on the left of Fig."
€ 2). aud several huudreds of millisecoud in. 10000 days (shown on the right of Fig.," 2), and several hundreds of millisecond in 10000 days (shown on the right of Fig."
 2)., 2).
 These curves also show the flicluation with more long period comporents {ο catse slronger noise. which accords with Eq. (," These curves also show the fluctuation with more long period components to cause stronger noise, which accords with Eq. ("
12 very well.,12) very well.
 Compared Fie, Compared Fig.
 So2 with the observations. Fig.," 2 with the observations, Fig."
 Lin Ref. [, 1 in Ref. [
11] and Figs.,11] and Figs.
 1 atd 2 in Ret. [, 1 and 2 in Ref. [
12]. we find that they have some common feaures. (,"12], we find that they have some common features. ("
1) Theinajority time curves have about one period-like,1) Themajority time curves have about one period-like
of supernova remnant shocks.,of supernova remnant shocks.
 In section 3... we report on the numerical code used to investigate the instability. and present simulation results.," In section \ref{sims_sect}, we report on the numerical code used to investigate the instability, and present simulation results."
 The relevant time ancl length scales inferred from theory and observations are accdressed in section 4.., The relevant time and length scales inferred from theory and observations are addressed in section \ref{compare_sect}.
 We conclude with a discussion of the implications for cosmic rav acceleration ancl escape of cosmic rays upstream of the shock in supernova remnants in the context of filamentation., We conclude with a discussion of the implications for cosmic ray acceleration and escape of cosmic rays upstream of the shock in supernova remnants in the context of filamentation.
 Within the dillusion approximation of shock acceleration theory. ai first order anisotropy ds. introduced. in. the Upstream: particle distribution as à result of the gradient in the isotropic part of the distribution.," Within the diffusion approximation of shock acceleration theory, a first order anisotropy is introduced in the upstream particle distribution as a result of the gradient in the isotropic part of the distribution."
 For a shock front propagating in the positive .r direction. with velocity ty. the resulting steady state Cest-particle solution is (c.gDrury1983) where für.p) is the isotropic part of the spectrum as measured in the upstream rest-frame. and @ is the particle pitch angle with respect to the shock normal.," For a shock front propagating in the positive $x$ direction, with velocity $u_{\rm sh}$, the resulting steady state test-particle solution is \cite[e.g][]{drury83}
 where $f_0(x,p)$ is the isotropic part of the spectrum as measured in the upstream rest-frame, and $\theta$ is the particle pitch angle with respect to the shock normal."
 Lt is generally unelerstooc that the current associated with the anisotropic part of the upstream particle distribution drives the growth of MILD. instabilities., It is generally understood that the current associated with the anisotropic part of the upstream particle distribution drives the growth of MHD instabilities.
 The resulting turbulent magnetic fields mediate the scattering that maintain the cosmic rays quasi-isotropic distribution. ensuring a high probability that particles repeatedly cross the shock before escaping.," The resulting turbulent magnetic fields mediate the scattering that maintain the cosmic rays' quasi-isotropic distribution, ensuring a high probability that particles repeatedly cross the shock before escaping."
 ‘To investigate the behaviour in higher dimensions. it is convenient to use the Vlasov equation. which for relativistic particles can be written in the form (4," To investigate the behaviour in higher dimensions, it is convenient to use the Vlasov equation, which for ultra-relativistic particles can be written in the form +."
) Ina reference25 frame in which the upstream cosmic rays are isotropic. the distribution function f(a.p./) is dependent only on the length of the momentum vector. not its direction. and it is straightforward to show that the magnetic field term makes no contribution.," In a reference frame in which the upstream cosmic rays are isotropic, the distribution function $f(\bm{x},p,t)$ is dependent only on the length of the momentum vector, not its direction, and it is straightforward to show that the magnetic field term makes no contribution."
 Lt follows that the only force relevant for calculating the particle distribution is that due to the local electric. field., It follows that the only force relevant for calculating the particle distribution is that due to the local electric field.
 On average. the upstream cosmic-ray distribution is isotropic in the rest frame of the shock (MeClemoentsctal. 1996)...," On average, the upstream cosmic-ray distribution is isotropic in the rest frame of the shock \citep{mcclementsetal96}. ."
 Neglecting the bulk deceleration of the incoming plasma due to the cosmic-rav pressure gradient. the background. plasma in this frame moves towards the shock with velocity wτα|ou. where ὅτι are the superimposed. background. [uid motions due to the cosmic-ray current. and d is the unit vector along the direction of the shock normal.," Neglecting the bulk deceleration of the incoming plasma due to the cosmic-ray pressure gradient, the background plasma in this frame moves towards the shock with velocity $\bm{u}= -u_{\rm sh}\bm{\hat{x}}+\delta{\bm{u}}$, where $\delta\bm{u}$ are the superimposed background fluid motions due to the cosmic-ray current, and $\bm{\hat{x}}$ is the unit vector along the direction of the shock normal."
 Conservation of momentuni dictates that these motions are small compared to the shock velocity. [ὅτι]my. ane to lowest order the local electric [eld is. in the ideal MED limit. B=πμ Di.," Conservation of momentum dictates that these motions are small compared to the shock velocity $|\delta{\bm u}|\ll u_{\rm sh}$, and to lowest order the local electric field is, in the ideal MHD limit, $\bm{E}=u_{\rm sh}\bm{\hat{x}}\times\bm{B_\bot}$ ."
 While this analysis is valid for all shock obliquities. we focus here on self-generated: magnetic fields δι due to current-driven instabilities.," While this analysis is valid for all shock obliquities, we focus here on self-generated magnetic fields $B_\bot$ due to current-driven instabilities."
 To investigate the role. of filamentation in the plane normal to the direction of the cosmic-ray streaming. we neglect the cosmic-ray pressure gradient in the precursor. and restrict the analysis to the case of slab svimetry in the + direction.," To investigate the role of filamentation in the plane normal to the direction of the cosmic-ray streaming, we neglect the cosmic-ray pressure gradient in the precursor, and restrict the analysis to the case of slab symmetry in the $x$ direction."
 Introducing the vector potential B=V.A. the local electric field is..(5) where the scalar potential is lL)—A-d.," Introducing the vector potential $\bm{B}=\bm{\nabla}\times\bm{A}$, the local electric field is, where the scalar potential is $A_\|=\bm{A}\cdot\bm{\hat{x}}$."
 Inserting into (2)). the distribution function. when observed in a reference [rame in which the shock is at rest. evolves according to where ued)54pm plays the role of the effective electric Ποια potential (e.g.Ixrall&Trivelpiece1973.sectionS.17).," Inserting into \ref{vlasov}) ), the distribution function, when observed in a reference frame in which the shock is at rest, evolves according to + where $u_{\rm sh}A_\|$ plays the role of the effective electric field potential \cite[e.g.][section 8.17]{kralltrivelpiece}."
. On the slowly evolving MILD. timescales. the cosmic-ray distribution will progress through equilibrium states)h," On the slowly evolving MHD timescales, the cosmic-ray distribution will progress through equilibrium states,."
m——— lt follows that. the. phase-space distribution. of the cosmic ravs consists of surfaces of equal density on the momentum iso-surfaces c., It follows that the phase-space distribution of the cosmic rays consists of surfaces of equal density on the momentum iso-surfaces $\epsilon$.
 Hence. if Of/üp«0. as is almost certainly the case. the cosmic-ray number density will be locally larger (smaller) in regions of positive (negative) sy.," Hence, if $\partial f/\partial p <0$, as is almost certainly the case, the cosmic-ray number density will be locally larger (smaller) in regions of positive (negative) $A_\|$."
 Specifically. if p>eyedic. making à Taylor expansion. the number density as a function of position is Sapfodp where we have performed an integration by parts.," Specifically, if $p\gg eu_{\rm sh}|A_\||/c$, making a Taylor expansion, the number density as a function of position is p f_0 p where we have performed an integration by parts."
 Here fo is the unperturbed part. of the spectrum. and ny.={απfodp the associated. uniform. number density.," Here $f_0$ is the unperturbed part of the spectrum, and $n_0=\int4\pi p^2f_0\diff p$ the associated uniform number density."
 Note that the correlation. with 24) is dependent on the choice of orientation., Note that the correlation with $A_\|$ is dependent on the choice of orientation.
 Lf the upstream: instead. was chosen to lie in the half plane αν«Q0. the density and. vector potential would anti-correlate.," If the upstream instead was chosen to lie in the half plane $x<0$, the density and vector potential would anti-correlate."
 In. addition. the correlation is charge dependent. such that in the precursor. the electrons. and protons will anti-correlate.," In addition, the correlation is charge dependent, such that in the precursor, the electrons and protons will anti-correlate."
 Since the number density. of non-thermal particles is very. much. less than that of the background. plasma. on the length scales of interest. charge neutrality is always maintained.," Since the number density of non-thermal particles is very much less than that of the background plasma, on the length scales of interest, charge neutrality is always maintained."
 The growth. of the magnetic field. is driven. by. the resulting cosmic-ray current., The growth of the magnetic field is driven by the resulting cosmic-ray current.
 Transforming back to the upstream frame. from (10)). it follows that the cosmic-raycurrent isalso a function of position," Transforming back to the upstream frame, from \ref{crdensity}) ), it follows that the cosmic-raycurrent isalso a function of position"
From observations of spirals and/or ares around stars. one may search for the possible existence of unseen companions. which are difficult to be directly. detected either due to high obscuratiou by the dense environment or due to the bright glare of the ceutral object.,"From observations of spirals and/or arcs around stars, one may search for the possible existence of unseen companions, which are difficult to be directly detected either due to high obscuration by the dense environment or due to the bright glare of the central object."
 The preseuce of the companions may be inferred by their imprints ou the enviroument at large distances [rom the star., The presence of the companions may be inferred by their imprints on the environment at large distances from the star.
 For example. spiral structures have been observed around AB Aur revealed in near-infrared scattered emission (Fukagawaetαἱ.2001).. arouncd AFCGL 3068 in cust scattered ealactic light (Matron&Hueeinsoo2006).. and around CIT 6 in molecular line emission 2009 ).," For example, spiral structures have been observed around AB Aur revealed in near-infrared scattered emission \citep{fuk04}, around AFGL 3068 in dust scattered galactic light \citep{mau06}, and around CIT 6 in molecular line emission \citep{din09}."
. According to the result in this paper. the deusity contrast of a gravitational deusity wake due toa 10 Jupiter mass planet.AU.. is expected to be of the order of hundreds AU from the central star. where the spiral arms are located in the circumstellar clisk of the Herbig Ae star AB Aur (Fukagawaetal.2001).," According to the result in this paper, the density contrast of a gravitational density wake due to a 10 Jupiter mass planet, is expected to be of the order of hundreds AU from the central star, where the spiral arms are located in the circumstellar disk of the Herbig Ae star AB Aur \citep{fuk04}."
. Although the density contrast of the order of disk (rather than spherical) system., Although the density contrast of the order of disk (rather than spherical) system.
 Whether such structures cau be observed for low mass objects remains to be ascertained., Whether such structures can be observed for low mass objects remains to be ascertained.
 Aud whether the deusity contrast due to the gravitational inlluence of planets las a similar order of magnitude in a disk system also needs to be checked., And whether the density contrast due to the gravitational influence of planets has a similar order of magnitude in a disk system also needs to be checked.
 To clarify the claim of Linetal.(2006) of formingm ODgiant planets as the orieiue of the observed spiral arms arouncl AB Aur. it is necessary to carefully examine the deusity prolile of the structure.," To clarify the claim of \citet{lin06} of forming giant planets as the origin of the observed spiral arms around AB Aur, it is necessary to carefully examine the density profile of the structure."
 lu the cases of AFCL 3068 and CIT 6. spiral structures are detected on the scale of 1-10 thousand &U (Maurou&Hugeius2006:Dinli-V.-TruugLim2009).. which exclude the possibility of planet wakes since the density contrast decreases with distance (E1 cireuumistellar envelopes are likely to be caused by reflex motion of the mass losing star in comparable uias binary system (Soker1991:Mastrodemos&Morris1999:He2007:Edgaretal.2008).," In the cases of AFGL 3068 and CIT 6, spiral structures are detected on the scale of 1–10 thousand AU \citep{mau06,din09}, which exclude the possibility of planet wakes since the density contrast decreases with distance $\lesssim1$ circumstellar envelopes are likely to be caused by reflex motion of the mass losing star in comparable mass binary system \citep{sok94,mas99,he07,
edg08}."
. Recently. Ragaetal.(2011). estimated approximately 1 solar mass for the companion of AFCL 3068 [rom the spiral shape.," Recently, \citet{rag11} estimated approximately 1 solar mass for the companion of AFGL 3068 from the spiral shape."
 With this companion mass. the gravitational wake is expected to contribute as much as distauce of a thousand AU. doubling the deusity iu the arm structure.," With this companion mass, the gravitational wake is expected to contribute as much as distance of a thousand AU, doubling the density in the arm structure."
 This density contrast ofthe coupanion wake may be comparable to the density enliaucement due to tlie reflex motion of the pritlary star., This density contrast of the companion wake may be comparable to the density enhancement due to the reflex motion of the primary star.
 Hence. in the central region (<< by adoptiug tje distance of Lkkpc to AFCL 3068). which will be soon resolved by the Atacama Large Millimeter/subinillimeter Array (ALMA). there could exist two separated arms caused by two clifferent meclanisims. ie.. oue structure due to the reflex motion of the mass losing star aud one gravitational density wake of the companion star.," Hence, in the central region $\lesssim$ by adopting the distance of kpc to AFGL 3068), which will be soon resolved by the Atacama Large Millimeter/submillimeter Array (ALMA), there could exist two separated arms caused by two different mechanisms, i.e., one structure due to the reflex motion of the mass losing star and one gravitational density wake of the companion star."
 A comparison between the two mechanisms is neeced in a range of parameter space relevant to the object aud backgrouud properties., A comparison between the two mechanisms is needed in a range of parameter space relevant to the object and background properties.
"(he upper limit values obtained from the data) ancl 0. is (he critical subsolar angle. such that sublimation integrated over all regions with 9>0, equals «M/dl.","the upper limit values obtained from the data) and $\theta_c$ is the critical subsolar angle, such that sublimation integrated over all regions with $\theta \ge \theta_c$ equals $dM/dt$."
" The asteroid radius. r,. is taken [rom Table (3))."," The asteroid radius, $r_n$, is taken from Table \ref{physical}) )."
 Figure (2)) shows the sublimation constraints eraphically in terms of the fraction of the surface occupied by ice as a function of the albedo of the ice., Figure \ref{model}) ) shows the sublimation constraints graphically in terms of the fraction of the surface occupied by ice as a function of the albedo of the ice.
 Red and blue curves show the constraints imposed by the non-cletection of sublimated molecules for Themis and Cybele. as determined by Equations (4)) and (5)).," Red and blue curves show the constraints imposed by the non-detection of sublimated molecules for Themis and Cybele, as determined by Equations \ref{sublimation}) ) and \ref{total}) )."
 Acceptable solutions must lie on or below the plotted red and blue curves. otherwise gas production by sublimation would have been large enough to be detected.," Acceptable solutions must lie on or below the plotted red and blue curves, otherwise gas production by sublimation would have been large enough to be detected."
 The region satislving both constraints is shown shaded., The region satisfying both constraints is shown shaded.
 Figure (2)) shows that models in which ice is globally distributed (f = 1) on Themis and Cybele are excluded., Figure \ref{model}) ) shows that models in which ice is globally distributed $f$ = 1) on Themis and Cybele are excluded.
 At one extreme. (his is because [ull-surface clean ice would violate the (low) average albedos.," At one extreme, this is because full-surface clean ice would violate the (low) average albedos."
 At the other. [ull-surface clirty ice would be warm enough to strongly sublimate ancl would violate the spectroscopic constraint on sublimated gas.," At the other, full-surface dirty ice would be warm enough to strongly sublimate and would violate the spectroscopic constraint on sublimated gas."
 No intermediate albedo solution with f olds found., No intermediate albedo solution with $f \sim$ 1 is found.
 Instead. the allowed solutions for both asteroids are those with ice albedos pi;= 0.3 and coverage fractions f.S 0.1.," Instead, the allowed solutions for both asteroids are those with ice albedos $p_i \gtrsim$ 0.3 and coverage fractions $f \lesssim$ 0.1."
 Ice on these bodies. if it is present. must be relatively clean and spatially localized.," Ice on these bodies, if it is present, must be relatively clean and spatially localized."
 Measurements from a single rotation show that the ice band on Thenis is approximately constant in depth (Campins et al., Measurements from a single rotation show that the ice band on Themis is approximately constant in depth (Campins et al.
 2010). consistent with a small angle between (he line of sight and (he spin vector.," 2010), consistent with a small angle between the line of sight and the spin vector."
 Independent observations dispersed over a five vear interval show a larger variation (e.g. using spectra reported in the Supplement to Rivkin and Emery 2010 we measured the fractional band depth in 2005 to be ~40% deeper than in 2003 (continuum linearly interpolated between 2.7 and 3.5 jm)., Independent observations dispersed over a five year interval show a larger variation (e.g. using spectra reported in the Supplement to Rivkin and Emery 2010 we measured the fractional band depth in 2005 to be $\sim$ deeper than in 2003 (continuum linearly interpolated between 2.7 and 3.5 $\mu$ m).
 Some of this variation is no doubt instrumental. but the data are consistent with a substantial variation).," Some of this variation is no doubt instrumental, but the data are consistent with a substantial variation)."
 In the future. a determination of the spin vector of Themis will be of great. value in further localizing the ice on this bocly.," In the future, a determination of the spin vector of Themis will be of great value in further localizing the ice on this body."
 Spin vector solutions have been published [or Cybele (Muller ancl Blommaert 2004) but 3 jan spectra have been reported from only two nights (UT 2009 Sep. 9: Licandro et al., Spin vector solutions have been published for Cybele (Muller and Blommaert 2004) but 3 $\mu$ m spectra have been reported from only two nights (UT 2009 Sep. 9; Licandro et al.
 2011). insullicient to determine (he spatial distribution.," 2011), insufficient to determine the spatial distribution."
 It is interesting to note that the 3.1 jn band appears in Themis and Cybele at only e of the local continuum depth., It is interesting to note that the 3.1 $\mu$ m band appears in Themis and Cybele at only $\sim$ of the local continuum depth.
" This band is intrinsically very strong. (absorption coellicient fk~ 10"" !: Irvine and Pollack 1968) and frequently appears saturated. in astronomical spectra.", This band is intrinsically very strong (absorption coefficient $k \sim$ $^{6}$ $^{-1}$; Irvine and Pollack 1968) and frequently appears saturated in astronomical spectra.
 The subdued band depth is consistent with a 10:1 dilution of the ice spectrum with bland (dust) continuum and so matches the inference drawn above. that the ice surface coverage fraction is fS 0.1.," The subdued band depth is consistent with a 10:1 dilution of the ice spectrum with bland (dust) continuum and so matches the inference drawn above, that the ice surface coverage fraction is $f \lesssim$ 0.1."
 Rivkin and Emery (2010) took a different approach. arguing (hat the unsaturated band results from a very limited optical path length through the ice.," Rivkin and Emery (2010) took a different approach, arguing that the unsaturated band results from a very limited optical path length through the ice."
 They used ice coatings only 7245 nm in thickness to model (he spectrum of Themis. apparently assuming / = 1l. anc were able to match the band depth aud shape in detail.," They used ice coatings only $\sim$ 45 nm in thickness to model the spectrum of Themis, apparently assuming $f$ = 1, and were able to match the band depth and shape in detail."
effeclive temperatures correspond {ο lower masses. so the sense of the variation of rotation with mass in Fig.,"effective temperatures correspond to lower masses, so the sense of the variation of rotation with mass in Fig."
 1 is model independent., 1 is model independent.
 H is evident in (he figure that the range of rotation rates is very large. regardless of the mass range considered.," It is evident in the figure that the range of rotation rates is very large, regardless of the mass range considered."
 While (he extreme values on both the high and low period ends may be questionable (due to possible effects of aliasing; aud harmonics) it is fair (ο sav (hat rotation periods in this cluster span al least a range of 0.8 to 12 davs. independent of mass.," While the extreme values on both the high and low period ends may be questionable (due to possible effects of aliasing and harmonics) it is fair to say that rotation periods in this cluster span at least a range of 0.8 to 12 days, independent of mass."
 What may be less obvious at first inspection. on account of that wide range. is (hat there is a definite change in the nature of the rotation period distribution with mass.," What may be less obvious at first inspection, on account of that wide range, is that there is a definite change in the nature of the rotation period distribution with mass."
 Part of that trend is indicated by the heavy solid line which shows (he median period within a sliding sample defined by a mass range +£0.05 M. al 8 central values from 0.1 to 0.4 M..., Part of that trend is indicated by the heavy solid line which shows the median period within a sliding sample defined by a mass range $\pm$ 0.05 $_\odot$ at 8 central values from 0.1 to 0.4 $_\odot$.
 This stastie and sampling interval were chosen for their robustness in the range M « 0.4 M... the focus of this paper.," This stastic and sampling interval were chosen for their robustness in the range M $<$ 0.4 $_\odot$, the focus of this paper."
 To make the trends clearer anc assess their statistical significance we show. in Figure 2. histograms of the rotation period distribution in three mass ranges.," To make the trends clearer and assess their statistical significance we show, in Figure 2, histograms of the rotation period distribution in three mass ranges."
 A double-sided ]xolmogorov-Suirnof test indicates that the probability that the high mass sample was drawn rom the same parent population as the low mass sample is less than 3x10.?.," A double-sided Kolmogorov-Smirnof test indicates that the probability that the high mass sample was drawn from the same parent population as the low mass sample is less than $3
\times 10^{-9}$."
 This result is independent of (he binning chosen to displav the histograms., This result is independent of the binning chosen to display the histograms.
 Clearly. the higher mass ranges show a bimodal distribution. as first. discovered by Attridge&Ilerbst(1992). and ater confirmed by Choi&Herbst(1996).," Clearly, the higher mass ranges show a bimodal distribution, as first discovered by \citet{ah92} and later confirmed by \citet{ch96}."
. Dimodality can be crudely quantified using the Double Root Residual test (Gebhardt&Beers1991) which. in this case. indicates for the ighest mass range that the distribution differs from unilormitv at greater than the 36 level.," Bimodality can be crudely quantified using the Double Root Residual test \citep{gb91}
 which, in this case, indicates for the highest mass range that the distribution differs from uniformity at greater than the $\sigma$ level."
" Clearly, (the middle sample shows a mixture of attributes."," Clearly, the middle sample shows a mixture of attributes."
 We conclude that the rotation period distribution in the ONC is bimodal for stars with M > 0.25 AL. and unimodal for lower mass stars. confirming the results of Herbstetal. (2000)..," We conclude that the rotation period distribution in the ONC is bimodal for stars with M $\geq$ 0.25 $_\odot$ and unimodal for lower mass stars, confirming the results of \citet{her00}. ."
 The interesting new result is that the majority of stars with M«0.3 AL. clearly rotate faster than the majority of higher Mass stars and we turn now to a discussion of this issue., The interesting new result is that the majority of stars with $<$ 0.3 $_\odot$ clearly rotate faster than the majority of higher mass stars and we turn now to a discussion of this issue.
 In an attempt to better understaxd (hese results. we first translate the observed quantity. rotation period (DP). into the fundamental physical quantity. specifie angular momentum (1).," In an attempt to better understand these results, we first translate the observed quantity, rotation period (P), into the fundamental physical quantity, specific angular momentum (j)."
 Assuming that convection enlorces rigid rotation in low mass stars. even al 1 My. the specific angular momentum of such a star with mass M. and radius I. is where J is (he total angular momentum. Iis the moment of inertia. w is the angular velocity and kis the radius of gvration in units of the stellarradius.," Assuming that convection enforces rigid rotation in low mass stars, even at 1 My, the specific angular momentum of such a star with mass M, and radius R, is where J is the total angular momentum, I is the moment of inertia, $\omega$ is the angular velocity and k is the radius of gyration in units of the stellarradius."
 We assume homologous stars, We assume homologous stars
of plasma blobs ejected in different epochs by the driving source and concluded that this mechanism is unlikely.,of plasma blobs ejected in different epochs by the driving source and concluded that this mechanism is unlikely.
 In addition these authors suggested that the most likely mechanism leading to a standing shock over a period >5 yrs might be a diamond shock forming near the launching/collimation site of the jet., In addition these authors suggested that the most likely mechanism leading to a standing shock over a period $>5$ yrs might be a diamond shock forming near the launching/collimation site of the jet.
 This idea is expanded here by developing a model of jet outflowing through a nozzle., This idea is expanded here by developing a model of jet outflowing through a nozzle.
" We found that, in such a configuration, a standing diamond shock forms just past the nozzle exit at the base of the jet."," We found that, in such a configuration, a standing diamond shock forms just past the nozzle exit at the base of the jet."
 The shock is stabilized under the action of the thermal conduction which damps the hydrodynamic instability developing within the cocoon and heavily perturbing the flow structure., The shock is stabilized under the action of the thermal conduction which damps the hydrodynamic instability developing within the cocoon and heavily perturbing the flow structure.
 We found that the X-ray emission arising from the diamond shock has morphology and spectral, We found that the X-ray emission arising from the diamond shock has morphology and spectral
Llere. ἐν is the kinetic energy. given by equation (72)).,"Here, $K$ is the kinetic energy given by equation \ref{en:kinetic}) )."
 lteaders may. wonder why the thermal inertial term appears., Readers may wonder why the thermal inertial term appears.
 Actually. the kinetic. thermal. and thermal inertial energies should not be considered separately because they depend on the frame of reference.," Actually, the kinetic, thermal, and thermal inertial energies should not be considered separately because they depend on the frame of reference."
 Even so. we used this definition through the paper to make clear the dilference between the non-relativistic and relativistic expansions.," Even so, we used this definition through the paper to make clear the difference between the non-relativistic and relativistic expansions."
 We can casily figure out that the total plasma energy can be described as the sum of these energies. as," We can easily figure out that the total plasma energy can be described as the sum of these energies, as"
fixed width in colour leads to significantly different numbers of spectra in cach bin.,fixed width in colour leads to significantly different numbers of spectra in each bin.
 Spectra resulting from such binning are not readily comparable since their signal-to-noise (S/N) varies as a function of the number of spectra per bin., Spectra resulting from such binning are not readily comparable since their signal-to-noise (S/N) varies as a function of the number of spectra per bin.
 The bins were therefore constructed by assigning approximately equal numbers of spectra to each bin. vielding final spectra of similar S/N. but with dillerent widths in colour.," The bins were therefore constructed by assigning approximately equal numbers of spectra to each bin, yielding final spectra of similar S/N, but with different widths in colour."
 In order to determine the number of spectra per bin acceptable for reliably measuring line-streneths. the following procedure was adopted.," In order to determine the number of spectra per bin acceptable for reliably measuring line-strengths, the following procedure was adopted."
 The Spectral Energy Distributions (SEDs) of Worthey (1904) (see $5.2) a a lixed age and range of metallicities were degraded: to the tvpical S/N of the NGC 4472 globular cluster spectra., The Spectral Energy Distributions (SEDs) of Worthey (1994) (see $\S5.2$ ) at a fixed age and range of metallicities were degraded to the typical S/N of the NGC 4472 globular cluster spectra.
 This was achieved. by adding random. noise to the spectra until they possessed a distribution in S/N equivalent to that of the NGC 4472 globular cluster data., This was achieved by adding random noise to the spectra until they possessed a distribution in S/N equivalent to that of the NGC 4472 globular cluster data.
 Subsequent spectra were then. co-added: ane their line-streneth indices measured (see 94.3 for discussion of index measurements)., Subsequent spectra were then co-added and their line-strength indices measured (see $\S4.3$ for discussion of index measurements).
 This process was reiterated until a sullicient number of realisations produced stable measurements in all indices. that were consistent with the indices measured for the original. undegraded spectrum.," This process was reiterated until a sufficient number of realisations produced stable measurements in all indices, that were consistent with the indices measured for the original, undegraded spectrum."
 An example of the results of this exercise is shown in Fig., An example of the results of this exercise is shown in Fig.
 2 for the «Lec and Ales indices., \ref{fig:dispersion} for the $<$ $>$ and $_{2}$ indices.
 Each filled. circle represents a set of realisations. with their associated statistical errors. derived. [rom the S/N of cach spectrum obtained by summing over pixels along the slit within a fixed wavelength range (ο 4545 5500 AY).," Each filled circle represents a set of realisations, with their associated statistical errors, derived from the S/N of each spectrum obtained by summing over pixels along the slit within a fixed wavelength range $\sim$ 4545 – 5500 )."
 The shaded column denotes where the number of co-acdded spectra were found to » sullicient to produce a stable index measurement., The shaded column denotes where the number of co-added spectra were found to be sufficient to produce a stable index measurement.
 In this case. the degraded: SED is that predicted by the Worthey (1994) models for a 17 Gyr stellar population with Fe/1] =-1.7 dex.," In this case, the degraded SED is that predicted by the Worthey (1994) models for a 17 Gyr stellar population with [Fe/H] = -1.7 dex."
 The indices measured from the co-added spectra (al = 32) in Fig., The indices measured from the co-added spectra (at = 32) in Fig.
 2. are 0.065 + 0.011 mae for Mg». and hss d 0.30 for «Lec. in excellent agreement with the models which ποιοί 0.06 mag for and 0.79for «be.," \ref{fig:dispersion} are 0.065 $\pm$ 0.011 mag for $_{2}$, and 0.85 $\pm$ 0.30 for $<$ $>$ , in excellent agreement with the models which predict 0.06 mag for and 0.79for $<$ $>$ ."
kin/s. and a temperature of ΤΟΝ. Such a column density is consistent. with the reddening value we adopted (e.g. Bohlinetal.(1978))).,"km/s, and a temperature of 170K. Such a column density is consistent with the reddening value we adopted (e.g. \citet{boh78}) )."
 These more realistic WD fitis to theHST STIS spectrum of V442 Cen with E(D-V) = 0.10 vielded a best-litting model consisting of a 4T.000IX. white clwarl with Log gy=8.3 for a distance of only 328 pe.," These more realistic WD fits to the STIS spectrum of V442 Cen with E(B-V) = 0.10 yielded a best-fitting model consisting of a 47,000K white dwarf with Log $g= 8.3$ for a distance of only 328 pc."
 This distance is well below even the value of G37 pc obtained from the Warner relation., This distance is well below even the value of 637 pc obtained from the Warner relation.
 This model. seen in figure 5. had a 42=2.95.," This model, seen in figure 5, had a $\chi^2_{\nu}=2.95$."
 Using the ISM model. we also tried a disk alone and disk+WD models but thev cid not lead to any improvement in the fit.," Using the ISM model, we also tried a disk alone and disk+WD models but they did not lead to any improvement in the fit."
 The disk alone models all had avery large A7 and the least 47 that could be obtained with a disk model was 8.7. while ie disk-+WD models had at best 42=5.5.," The disk alone models all had a very large $\chi^2_{\nu}$ and the least $\chi^2_{\nu}$ that could be obtained with a disk model was 8.7, while the disk+WD models had at best $\chi^2_{\nu}=5.5$."
 We also tried (wo-temperature WD models., We also tried two-temperature WD models.
 The »est-Fitting 2-T WD model had a best 4Z=2.67. comparable to. but not significantly better ian. the best single temperature WD moclel.," The best-fitting 2-T WD model had a best $\chi^2_{\nu}=2.67$, comparable to, but not significantly better than, the best single temperature WD model."
 It is important to note that by our fixing the metal abundances at their solar value rather wan allowing for metal abundance variations in the synthetic spectral filling. svstematic errors are introduced that carry through to other parameters.," It is important to note that by our fixing the metal abundances at their solar value rather than allowing for metal abundance variations in the synthetic spectral fitting, systematic errors are introduced that carry through to other parameters."
 There are two kinds of errors. )ose that drive the 47 up and those that increase the errors in all the other parameters.," There are two kinds of errors, those that drive the $\chi^{2}$ up and those that increase the errors in all the other parameters."
" The error in (4;sin? affects the abundances and 47 but not the other parameters. while 1e error in (he abundances affects. ¢,,;sin/ and 47 but not the other parameters."," The error in $v_{rot} \sin{i}$ affects the abundances and $\chi^{2}$ but not the other parameters, while the error in the abundances affects $v_{rot} \sin{i}$ and $\chi^{2}$ but not the other parameters."
 The (emperature error affects 47. the distance and gravity while the error in log g affects \7. the distance and temperature.," The temperature error affects $\chi^{2}$, the distance and gravity while the error in log g affects $\chi^{2}$, the distance and temperature."
 The error in distance affects 47. log ο and temperature.," The error in distance affects $\chi^{2}$, log g and temperature."
 Of these parameters. the distance. mass and temperature are more fundamental than the abundances and rotation since they affect the whole continuum while Ὁsin? and abunclances allect only the absorption line fits.," Of these parameters, the distance, mass and temperature are more fundamental than the abundances and rotation since they affect the whole continuum while $v_{rot} \sin{i}$ and abundances affect only the absorption line fits."
 Finally. the reader should be aware that none of the fits Chat we have obtained for the five svstems are formally acceptable fits [rom a strict mathematical point of view and thus one must use them with caution.," Finally, the reader should be aware that none of the fits that we have obtained for the five systems are formally acceptable fits from a strict mathematical point of view and thus one must use them with caution."
 Indeed. [rom a mathematical perspective. the probability that we have the correct model with a 42=2.0 being our best value. is essentially zero.," Indeed, from a mathematical perspective, the probability that we have the correct model with a $\chi^2_{\nu}=2.0$ being our best value, is essentially zero."
 ]lence. from (his standpoint it is very dillieult to argue that one model is really better (han another.," Hence, from this standpoint it is very difficult to argue that one model is really better than another."
 The five long period dwarl nova svstenis analvzed here. together with previously analvzed svslenms. now coniprise a sample of 13 svstems lor which we have estimates of the white dwarl surface teniperatures and their rotational velocities.," The five long period dwarf nova systems analyzed here, together with previously analyzed systems, now comprise a sample of 13 systems for which we have estimates of the white dwarf surface temperatures and their rotational velocities."
 This helps to remove the disparity between the sample of CV. WDs with known temperatures below the period gap and the number above the gap., This helps to remove the disparity between the sample of CV WDs with known temperatures below the period gap and the number above the gap.
 The white dwarf temperatures are typically uncertain by A+ 20001, The white dwarf temperatures are typically uncertain by ± 2000K
 The white dwarf temperatures are typically uncertain by A+ 20001I, The white dwarf temperatures are typically uncertain by ± 2000K
 The white dwarf temperatures are typically uncertain by A+ 20001Ix, The white dwarf temperatures are typically uncertain by ± 2000K
"of the best fit line increases [rom the ""calibrating set"" Cepheids to the LAIC Cepheids.",of the best fit line increases from the “calibrating set” Cepheids to the LMC Cepheids.
 The difference in slope between. “calibrating set” axl LMC. Cepheids found in the intrarelations plots is real ancl is probably attributable to the metallicity dillerences., The difference in slope between “calibrating set” and LMC Cepheids found in the intrarelations plots is real and is probably attributable to the metallicity differences.
 Due to the possible of non-lnearity and netallicitv dependence on the parent galaxy. the Fourier intrarelations are less preferable 1iu (he Fourier interrelations (Section +) for reconstructing the I band light curves with onv few data points available.," Due to the possible of non-linearity and metallicity dependence on the parent galaxy, the Fourier intrarelations are less preferable than the Fourier interrelations (Section 4) for reconstructing the I band light curves with only few data points available."
pattern in light of the SN-nduced star formation scenario proposed by ST98.,pattern in light of the SN-induced star formation scenario proposed by ST98.
 Subsequently in 82. uucleosvuthesis for Fe-eroup eleiieuts is diseussed based on the implicatious of the |Cr. Min. Co/Fo| ratios observed in these two stars. Which is surprisinely at variance with the prescut theoretical expectations from splerically svuuuetric SN models.," Subsequently in 3, nucleosynthesis for Fe-group elements is discussed based on the implications of the [Cr, Mn, Co/Fe] ratios observed in these two stars, which is surprisingly at variance with the present theoretical expectations from spherically symmetric SN models."
 The subliuminous SNe discovered so far are less energetic varieties of SNe. although theoretically some energetic SNe with high masses suchas 35 could also be subhuninous (Woosley&Weaver1995).," The subluminous SNe discovered so far are less energetic varieties of SNe, although theoretically some energetic SNe with high masses such as 35 could also be subluminous \citep{Woosley_95}."
. Such low energy reduces the mass Afey of ISM (1nostlv bydrogen) eventually swept up by a subhuninous SN. obeving the relation MiaXE77 (ST98).," Such low energy reduces the mass $M_{\rm SW}$ of ISM (mostly hydrogen) eventually swept up by a subluminous SN, obeying the relation $M_{\rm SW} \propto
E^{0.97}$ (ST98)."
 Since the metallicity [N/TII| of extremely poor stars born from the ISAL swept up by a SN remnanut (SNB) is inversely proportional to Vey. stars that inherit the ejecta of a sublininous SN should have larger [N/T] as long as the other conditions are the same.," Since the metallicity [X/H] of extremely metal-poor stars born from the ISM swept up by a SN remnant (SNR) is inversely proportional to $M_{\rm SW}$, stars that inherit the ejecta of a subluminous SN should have larger [X/H] as long as the other conditions are the same."
 As discussed in ST98. the abundance ratios [Mg/TI] in metal-poor stars can be used as au indicator of the progenitor mass of the SN inducing the formation of the stars. since theoretical models for massive stars predict that the mass of Me inside a star iucreases with iucreasing stellar mass (e.g...Woosley&Weaver1995:TineaNomoto 2002).," As discussed in ST98, the abundance ratios [Mg/H] in metal-poor stars can be used as an indicator of the progenitor mass of the SN inducing the formation of the stars, since theoretical models for massive stars predict that the mass of Mg inside a star increases with increasing stellar mass \citep[e.g.,][]{Woosley_95, Umeda_02}."
". Tn addition. the amount of ejected lighter elements such as Me cau be predicted more preciselv thu that of heavier elements such as Fe because the ejection of the outer laver is less affected by theoretical uncertainty concerning the SN explosion miechanisui (see,however.modelZ20AofWoosley&Weaver1995.for example)."," In addition, the amount of ejected lighter elements such as Mg can be predicted more precisely than that of heavier elements such as Fe because the ejection of the outer layer is less affected by theoretical uncertainty concerning the SN explosion mechanism \citep[see, however,
model Z20A of][ for example]{Woosley_95}."
" The relatiouships between the metallicity [Mg/II|] of stars aud the mass AM, of the SN progenitor thus obtained are shown in Figure 1 for E=E«10°"" cre Hine) aud E=1.10° erg Hine). assuming the metallicity [Mg/TII| of stars born from the shell formed by au SNR is approximated well by the average [Mg/II| inside the ISAL swept up by the SNR."," The relationships between the metallicity [Mg/H] of stars and the mass $M_{\rm ms}$ of the SN progenitor thus obtained are shown in Figure 1 for $E=4\times 10^{50}$ erg ) and $E=1\times10^{51}$ erg ), assuming the metallicity [Mg/H] of stars born from the shell formed by an SNR is approximated well by the average [Mg/H] inside the ISM swept up by the SNR."
 If CS29198-013 inherited the ejecta of a subluminous SN with explosion cucrey equal ο that of SN 1997D. the SN progenitor mass becoues 25M... which intriguinely agrees with that interred frou he lisht curve analyses of SN 1997D. The SN progenitor uass for CS22919-037 estimated in the same manner is Min.8 20M..," If CS29498-043 inherited the ejecta of a subluminous SN with explosion energy equal to that of SN 1997D, the SN progenitor mass becomes 25, which intriguingly agrees with that inferred from the light curve analyses of SN 1997D. The SN progenitor mass for CS22949-037 estimated in the same manner is $M_{\rm ms}\approx20$ ."
. The masses of ejected Fe are. estimated o be 0.006 (C'S29198-013) and 0.003 (C'S22919-EX) using the observed |Fe/II| ratios for the two stars and asstunine E=b<10° eve., The masses of ejected Fe are estimated to be 0.006 (CS29498-043) and 0.003 (CS22949-037) using the observed [Fe/H] ratios for the two stars and assuming $E=4\times 10^{50}$ erg.
 Both of the estimated Fe nasses indicate sublumiuous SNe such as SNe L997D aud 1999br., Both of the estimated Fe masses indicate subluminous SNe such as SNe 1997D and 1999br.
 Figure 2 shows the enhancement factors of cach clement defined by the abundance ratios of the element with respect to Fe in the iietal-poor stars discussed in this letter relative to those ratios in the ejecta of normal SNe with the corresponding progenitor masses., Figure 2 shows the enhancement factors of each element defined by the abundance ratios of the element with respect to Fe in the metal-poor stars discussed in this letter relative to those ratios in the ejecta of normal SNe with the corresponding progenitor masses.
 The abundauces of normal SNe have been interred from the elemental abuudance pattern observed for metal-poor stars im the manner described i Tsujimoto&Shigevama(1995)., The abundances of normal SNe have been inferred from the elemental abundance pattern observed for metal-poor stars in the manner described in \citet{Tsujimoto_98}.
" Thus derived abundance ratios correspond to the average values of imietal-poor stars observed bv McWilliamet.al.(1995) at the metallicity of [Mg/II|z2.3 and 39.8, respectively (see Fig."," Thus derived abundance ratios correspond to the average values of metal-poor stars observed by \citet{McWilliam_95} at the metallicity of $\approx -2.3$ and $-2.8$, respectively (see Fig."
 1)., 1).
" That is. an SN with E=1«LO ere and A4,=25 will imprint a iuetallicity /MJ=—2.3 on the desceudant stars. while au SN with the same cuerey but with AZ,20 corresponds to |Mg/II]|2.—2."," That is, an SN with $E=1\times10^{51}$ erg and $M_{\rm ms}=25$ will imprint a metallicity $=-2.3$ on the descendant stars, while an SN with the same energy but with $M_{\rm ms}=20$ corresponds to $=-2.8$."
8. As seen iu Figure 2. the abundance of clements heavier than Si in these stars is at least a factor of 5 sinaller than the average value of metal-poor stars. which is attributed to fallback outo the reumant in subluminous SNe.," As seen in Figure 2, the abundance of elements heavier than Si in these stars is at least a factor of 5 smaller than the average value of metal-poor stars, which is attributed to fallback onto the remnant in subluminous SNe."
 A moderate cuhanucement factor for Si in coluparison with Fe-eroup clements nüsght imply that fallback occurred inside the Si laver., A moderate enhancement factor for Si in comparison with Fe-group elements might imply that fallback occurred inside the Si layer.
 The euhbhaucemeut factors for Ca through Co have simular values in CS22919-037. while Cy through Fe are similar in CS29198-013.," The enhancement factors for Ca through Co have similar values in CS22949-037, while Cr through Fe are simlar in CS29498-043."
 A good coincidence in the cnulauccuent factors is secu especially in CS2299-037. probably due to more accurate abuudance deteriimatious.," A good coincidence in the enhancement factors is seen especially in CS22949-037, probably due to more accurate abundance determinations."
 This result sugeests that there is little difference in the ratios of Ca. Cr. Alu. or Co to Fe between subhuninous SNe auduormal SNe with the same progenitor mass. with iutrieuimg duplications for," This result suggests that there is little difference in the ratios of Ca, Cr, Mn, or Co to Fe between subluminous SNe andnormal SNe with the same progenitor mass, with intriguing implications for"
"and also from more reliable analysis by using both diagrams (Figs. 3,,","and also from more reliable analysis by using both diagrams (Figs. \ref{hr},"
 and 5)) in deriving extinction amounts., and \ref{cmd}) ) in deriving extinction amounts.
" For decades, the most reliable method in optical astronomy used to determine the age of a cluster is using the HR diagram (HRD), comparing the positions of member stars with theoretical evolutionary tracks on the HRD."," For decades, the most reliable method in optical astronomy used to determine the age of a cluster is using the HR diagram (HRD), comparing the positions of member stars with theoretical evolutionary tracks on the HRD."
" For embedded young cluster, this method is not validated because most of the members are not in the main sequence stage and can be observed only in longer wavelengths than optical."," For embedded young cluster, this method is not validated because most of the members are not in the main sequence stage and can be observed only in longer wavelengths than optical."
 The K-band luminosity function (KLF) is a simple tool to study the properties and estimate the age of an embedded cluster (Lada&Lada2003;Yasuietal.2006).," The K-band luminosity function (KLF) is a simple tool to study the properties and estimate the age of an embedded cluster \citep{lada03,yasui06}."
. Definition of the KLF can be expressed by the following equation: where πει is the K-band luminosity and M. is the stellar mass (Lada&Lada2003)., Definition of the KLF can be expressed by the following equation: where $m_k$ is the K-band luminosity and $M_*$ is the stellar mass \citep{lada03}.
. The first term in the right hand side is the underlying stellar mass function and the second term is the mass-luminosity relation (MLR)., The first term in the right hand side is the underlying stellar mass function and the second term is the mass-luminosity relation (MLR).
" It is noticed that the KLF of clusters peak at different magnitude, depending on the difference between their ages and star formation history (Muenchetal.2000).."," It is noticed that the KLF of clusters peak at different magnitude, depending on the difference between their ages and star formation history \citep{muench00}."
 Simple Monte Carlo simulations were carried out to construct the model KLFs., Simple Monte Carlo simulations were carried out to construct the model KLFs.
 The simulation was done in three step., The simulation was done in three step.
 The first step is to assume an initial mass function (IMF)., The first step is to assume an initial mass function (IMF).
" Two IMFs were used in our simulation, they are Trapezium IMF (Muenchetal.2000) and the IMF from (1979,hereafter MS79).."," Two IMFs were used in our simulation, they are Trapezium IMF \citep{muench00} and the IMF from \citet[][hereafter MS79]{ms79}."
" Then, we convert the mass function to the luminosity function using a mass-to-luminosity relation (MLR) from the isochrones of the PMS models(D'Antona& 2000)."," Then, we convert the mass function to the luminosity function using a mass-to-luminosity relation (MLR) from the isochrones of the PMS \citep{dm94,dm97,dm98,siess00}."
". The stellar luminosities were finally converted to the K-band luminosity, mx with bolometric correction (Flower1996) and stellar intrinsic color correction (Bessell&Brett1988)."," The stellar luminosities were finally converted to the K-band luminosity, $m_K$ with bolometric correction \citep{flower96} and stellar intrinsic color correction \citep{bb88}."
". By repeating this procedure with different age inputs, we fit model KLFs to observed KLFs and estimate the ages of clusters."," By repeating this procedure with different age inputs, we fit model KLFs to observed KLFs and estimate the ages of clusters."
" In Fig. 6,,"," In Fig. \ref{clusterage},"
" we show a result derived for embedded clusters in S233IR, tp be discussed in the following section."," we show a result derived for embedded clusters in S233IR, tp be discussed in the following section."
 Ages of the clusters embedded in the S233IR cloud were estimated by comparing the observed and model KLFs (Yasuietal.2006)., Ages of the clusters embedded in the S233IR cloud were estimated by comparing the observed and model KLFs \citep{yasui06}.
". Using the method mentioned in §??,, we constructed model KLFs for ages from 0.07 to 50 Myrs."," Using the method mentioned in \ref{klfmodel}, we constructed model KLFs for ages from 0.07 to 50 Myrs."
" By comparing the model and observed KLFs (Fig. 6)),"," By comparing the model and observed KLFs (Fig. \ref{clusterage}) ),"
" we derived the ages of~0.5+0.1, ~0.25+0.1, and ~1.5-£0.3 Myrs for the SW, NE, and the distributed stars, respectively."," we derived the ages of $\sim0.5\pm0.1$, $\sim0.25\pm0.1$, and $\sim1.5\pm0.3$ Myrs for the SW, NE, and the distributed stars, respectively."
 Although the MLR for the age younger than 1 Myr is uncertain between different, Although the MLR for the age younger than 1 Myr is uncertain between different
and period of rotation of the Earth we obtain the predicted value For the dipole moment of the Earth. The actual value of the Earth dipole moment is 77-1077.,"and period of rotation of the Earth we obtain the predicted value for the dipole moment of the Earth, The actual value of the Earth dipole moment is 7."
Am?.. We can see that the value predicted by (he model is of the same order of magnitude as the actual value., We can see that the value predicted by the model is of the same order of magnitude as the actual value.
 This is in contradiction will (he previous results that stated that this mechanism couldn't eive a value close to the experiment., This is in contradiction with the previous results that stated that this mechanism couldn't give a value close to the experiment.
 A remarkable thing that nist. be noted is that the model obtains directly. the wide known relation about magnetic dipole moment and (he moment of inertia of the object dd). Returning to the subject of ohnmie dissipation we could make an approach to the value of the power dissipated by a shell moving respect to the Earth., A remarkable thing that must be noted is that the model obtains directly the wide known relation about magnetic dipole moment and the moment of inertia of the object d. Returning to the subject of ohmic dissipation we could make an approach to the value of the power dissipated by a shell moving respect to the Earth.
 The less favorable case would be ihe one in which the outer shell rotates in opposite sense of the Earth rotation., The less favorable case would be the one in which the outer shell rotates in opposite sense of the Earth rotation.
 In. this case (he heat generated bv olimic dissipation would be where Vsthecurrentdensitg., In this case the heat generated by ohmic dissipation would be where is the current density.
Inthelastrelationweassumedaconstantdistribulionofacheargec(Q over a sphere of radius spinning at an angular velocity of 44x )respecttothe Rarth, In the last relation we assumed a constant distribution of a charge over a sphere of radius spinning at an angular velocity of 4 respect to the Earth.
 Substituting 29a nd3intlosiveoblainto In the case of the Earth. this value is 1129.," Substituting \ref{Q1} and \ref{lambda1} into \ref{pomega} we obtain In the case of the Earth, this value is 129."
MW... This value is far lower than the values of actual heat dissipation of the Earth that are of the order ofTT., This value is far lower than the values of actual heat dissipation of the Earth that are of the order of.
.. For the extension of (his result to the rest of the planets we need (he values of the conductivity and the [ree electron. density. for all of them., For the extension of this result to the rest of the planets we need the values of the conductivity and the free electron density for all of them.
 Even though there has been progresses in calculating the thermodynamical properties of the Earth core and mantle (Stevenson(1981):Voeadlo&Dobson(1999):Alleetal.(2002.2001):al. (1993))). we have not vel the detailed values of the transport coefficients," Even though there has been progresses in calculating the thermodynamical properties of the Earth core and mantle \cite{STEVE,LIDUNKA, ALFE1,ALFE2, SHAN, XU}) ), we have not yet the detailed values of the transport coefficients"
as long as the modes can be excited. the evolution. looks the same.,"as long as the modes can be excited, the evolution looks the same."
 The dominant. modes are low frequency and low harmonic order (dipoles) and can be driven by a wide variety of transient noise sources., The dominant modes are low frequency and low harmonic order (dipoles) and can be driven by a wide variety of transient noise sources.
 The outer power [aw exponent. 3. ds due to the repetitive excitation and. response of the halo to the outer /21 multipole.," The outer power law exponent, $-3$, is due to the repetitive excitation and response of the halo to the outer $l=1$ multipole."
 Phe common appearance of the r. profile in n-body. simulations suggests a noisce-driven origin., The common appearance of the $r^{-3}$ profile in n-body simulations suggests a noise-driven origin.
 This noise driven evolution provides a natural explanation for the near universality of the halo. profiles found in CDM simulations and may provide an explanation for a spread of inner power law exponents., This noise driven evolution provides a natural explanation for the near universality of the halo profiles found in CDM simulations and may provide an explanation for a spread of inner power law exponents.
 Variation in the substructure at dillerent scales (either due to the CDM power spectrum or dynamic range of the simulation) and differences in the initial halo profile will produce. cilferent exponents at the same point in time., Variation in the substructure at different scales (either due to the CDM power spectrum or dynamic range of the simulation) and differences in the initial halo profile will produce different exponents at the same point in time.
 Additional work will » required to make precise predictions for these trends., Additional work will be required to make precise predictions for these trends.
 onetheless. this work shows that noise naturally crives halo evolution with near-universal form.," Nonetheless, this work shows that noise naturally drives halo evolution with near-universal form."
 ] thank Neal Watz for stimulating discussions απ sugeestions and Enrico Vesperini for valuable comments on the manuscript., I thank Neal Katz for stimulating discussions and suggestions and Enrico Vesperini for valuable comments on the manuscript.
 This work was support in part by by NSE AST-9529328., This work was support in part by by NSF AST-9529328.
contributions of these dual components varies widely among the four stellar halos.,contributions of these dual components varies widely among the four stellar halos.
" The fractional contributions of these stellar populations to the simulated stellar halos, as well as their total masses, are summarized in Table 2."," The fractional contributions of these stellar populations to the simulated stellar halos, as well as their total masses, are summarized in Table 2."
" The fraction of accreted halo stars ranges from ~30— 85%, while the fraction of in-situ halo stars ranges from less than 10% to more than 50%."," The fraction of accreted halo stars ranges from $\sim 30 - 85\%$ , while the fraction of in-situ halo stars ranges from less than $\%$ to more than $\%$."
 The high and low ends of these ranges do not sum to 100% because of the small presence of the ambigious stars., The high and low ends of these ranges do not sum to $100\%$ because of the small presence of the ambigious stars.
" Although the fractional contribution of in-situ stars covers a wide range, the total mass of these stars in all four simulations is substantial."," Although the fractional contribution of in-situ stars covers a wide range, the total mass of these stars in all four simulations is substantial."
" The mass of in-situ stars in both the stellar halos of H277 and Gall is ~4x10?Mc, and ~1x10?M for MW1hr and H285."," The mass of in-situ stars in both the stellar halos of H277 and Gal1 is $\sim 4
\times 10^9 M_{\odot}$, and $\sim 1 \times 10^9 M_{\odot}$ for MW1hr and H285."
" All four of these simulated galaxies have similar total masses, however they span a range of merger histories."," All four of these simulated galaxies have similar total masses, however they span a range of merger histories."
" Three of the galaxies, MW H277, and H285 each host a stellar disk with a mass of lLhr,~2x101?M5, while the mass of Gall’s stellar disk is ~6x10!°Mo."," Three of the galaxies, MW1hr, H277, and H285 each host a stellar disk with a mass of $\sim 2 \times
10^{10} M_{\odot}$, while the mass of Gal1's stellar disk is $\sim 6
\times 10^{10} M_{\odot}$."
 The total halo mass of H277 and MWihr is 6—9x10? and ~3x10!°Mo for Gall and H285.," The total halo mass of H277 and MW1hr is $6-9 \times 10^9 M_{\odot}$, and $\sim 3 \times 10^{10} M_{\odot}$ for Gal1 and H285."
" The bulge to disk Mo,ratio (B/D) of each simulated galaxy was obtained using a two component Sersic + exponential fit to the one dimensional radial profile of the I band surface brightness maps made with the SUNRISE software package (Jonssonetal", The bulge to disk ratio (B/D) of each simulated galaxy was obtained using a two component Sersic $+$ exponential fit to the one dimensional radial profile of the I band surface brightness maps made with the SUNRISE software package \citep{Jonsson2006}.
" The for MWlhr, Gall, H277, and H285 are 2006)..0.37, 0.66, B/D0.29, and 1.2, respectively (Brooks et al, in prep)."," The B/D for MW1hr, Gal1, H277, and H285 are 0.37, 0.66, 0.29, and 1.2, respectively (Brooks et al, in prep)."
 What role might merger history play in the range of accreted/in-situ fractions observed in these four simulations?, What role might merger history play in the range of accreted/in-situ fractions observed in these four simulations?
 There is not an obvious trend between epoch of last major merger and either in-situ fraction or average assembly time of the accreted component; Gall, There is not an obvious trend between epoch of last major merger and either in-situ fraction or average assembly time of the accreted component; Gal1
scattering lensing.,scattering lensing.
 Within (he coherence scale. the probability for the photon path to weave through the (wo lenses can be ignored (RhieandBennett2010) (1110 from here on).," Within the coherence scale, the probability for the photon path to weave through the two lenses can be ignored \citep{RCB} (RB10 from here on)."
 Thus it is most reasonable to assume in general (hat the two gravitationally unbound microlens svslenis are at different distances. and they would be best considered as a double scattering lensing svstem.," Thus it is most reasonable to assume in general that the two gravitationally unbound microlens systems are at different distances, and they would be best considered as a double scattering lensing system."
" [ere it is assumed that the (wo lens elements are widely separated in the sky based on (he argument in (he previous paragraph and calculate the effects of the ""rogue"" svslem on the main lens."," Here it is assumed that the two lens elements are widely separated in the sky based on the argument in the previous paragraph and calculate the effects of the “rogue"" system on the main lens."
" The double scattering lensing is a time-sequential process. ancl 1 matters whether the ""rogue"" svstem is farther away than the main lens from (he observer or closer."," The double scattering lensing is a time-sequential process, and it matters whether the “rogue"" system is farther away than the main lens from the observer or closer."
 The two cases are schematically shown in figure 1.., The two cases are schematically shown in figure \ref{fig_twocases}.
 By wide separation it is implied that (he separation (is much larger (han the Einstein ring radius of the main lens., By wide separation it is implied that the separation $\ell$ is much larger than the Einstein ring radius of the main lens.
" We assume (hat (he ""rogue"" perturbing svstem is a single point mass."," We assume that the “rogue"" perturbing system is a single point mass."
 The main lens of interest will be a single star. a multiple star. a planet system with one or (wo host stars. or a Wide binary stars one of which hosts planets.," The main lens of interest will be a single star, a multiple star, a planet system with one or two host stars, or a wide binary stars one of which hosts planets."
 Ποιο we consider the most common ancl simplest case of a signle star ancl study Che wide separation approximation of the double scattering lwo point mass (DSTI!) lens., Here we consider the most common and simplest case of a signle star and study the wide separation approximation of the double scattering two point mass (DSTP) lens.
 Then the most important effect of Che perturbation is to break (he degeneracy of (he point caustic of the single lens to an extended caustic curve. and the size of the caustic will be the indicator of the influence of the perturber.," Then the most important effect of the perturbation is to break the degeneracy of the point caustic of the single lens to an extended caustic curve, and the size of the caustic will be the indicator of the influence of the perturber."
 It will be shown that the caustic size depends on the distances of the lenses and whether the perturber is in the front or in the back., It will be shown that the caustic size depends on the distances of the lenses and whether the perturber is in the front or in the back.
 When the perturber is the first scatterer. (he caustic is smaller than that of the binary lens. and it is similar in size when the main lens is perturbed by a “rogue” system in front.," When the perturber is the first scatterer, the caustic is smaller than that of the binary lens, and it is similar in size when the main lens is perturbed by a “rogue"" system in front."
 A binary lens forms when the two lenses have the same distance or within the coherence length., A binary lens forms when the two lenses have the same distance – or within the coherence length.
 The binary lens al large separation is made of a point mass and a constant shear (and plus (he source shift). aud it is briefly discussed in the appendix.," The binary lens at large separation is made of a point mass and a constant shear (and plus the source shift), and it is briefly discussed in the appendix."
 A multiple-point mass lens perturbing a single point mass main lens is approximated bv the same form of the approximate DSTP lens equation (with ellective coefficients) and can be concluded to behave in the similar manner to the single point mass perturber., A multiple-point mass lens perturbing a single point mass main lens is approximated by the same form of the approximate DSTP lens equation (with effective coefficients) and can be concluded to behave in the similar manner to the single point mass perturber.
 In lensing bv a galaxy. modelling is done customarily by assuming an elliptic mass (sometimes replaced by an elliptic potential) and a constant shear.," In lensing by a galaxy, modelling is done customarily by assuming an elliptic mass (sometimes replaced by an elliptic potential) and a constant shear."
 The galaxy. lensing is ol order 1 aresecond. and there are often other galaxies in the angular vicinity of the main lens svstem.," The galaxy lensing is of order $1$ arcsecond, and there are often other galaxies in the angular vicinity of the main lens system."
 The perturbers can be group memebers of the main lens or galaxies al clifferent distances., The perturbers can be group memebers of the main lens or galaxies at different distances.
 If there is a perturbing galaxy. al the same clistance. ils monopole will add an external shear as is (he case with the binary lens.," If there is a perturbing galaxy at the same distance, its monopole will add an external shear as is the case with the binary lens."
 However. if the perturbing masses are al different distances. the perturbation should include deflection terms other than (he constant external shear.," However, if the perturbing masses are at different distances, the perturbation should include deflection terms other than the constant external shear."
 We consider (he wide separation approximation of the double scattering two distributed mass (DSTD) lens., We consider the wide separation approximation of the double scattering two distributed mass (DSTD) lens.
 The other teris depend on the double scattering parameter ixl vanish when the perturbers are at the same distance as the main lens because the double, The other terms depend on the double scattering parameter and vanish when the perturbers are at the same distance as the main lens because the double
26? (see the bottom-center of 1)),$26^\circ$ (see the bottom-center panel of Figure \ref{fig:Vobs}) ).
" While this is insufficient to generate an panelimage Figuredirectly, the coverage is sufficient to address the structure of Sgr A*'s image."," While this is insufficient to generate an image directly, the coverage is sufficient to address the gross angular structure of Sgr A*'s image."
" Where the symmetricgross angulargaussian provides a in which to estimate the size of Sgr A*'s phenomenologicalemitting wayregion, an asymmetric gaussian can typicalbegin to probe its symmetry."," Where the symmetric gaussian provides a phenomenological way in which to estimate the typical size of Sgr A*'s emitting region, an asymmetric gaussian can begin to probe its symmetry."
" Figure 5 shows the minimum χ (or equivalently, the maximum likelihood) as a function of the average size, c, and anisotropy parameter, A."," Figure \ref{fig:agchi2} shows the minimum $\chi^2$ (or equivalently, the maximum likelihood) as a function of the average size, $\sigma$, and anisotropy parameter, $A$."
" The four left panels show this for the individual epochs, while the large right panel shows this for the combined data set."," The four left panels show this for the individual epochs, while the large right panel shows this for the combined data set."
" Unlike the symmetric gaussian model, the likely regions have somewhat different morphologies."," Unlike the symmetric gaussian model, the likely regions have somewhat different morphologies."
" This is due to the different of the u—v the various epochs (for example, the coveragelikely regions for planeepochs during2007 and 2009.95 are similar because the u—v these epochs is similar)."," This is due to the different coverage of the $u$ $v$ plane during the various epochs (for example, the likely regions for epochs 2007 and 2009.95 are similar because the $u$ $v$ coverage during these epochs is similar)."
" Nevertheless, the region coveragepreferred duringby the combined data sets is in all cases, implying that as with the symmetric gaussian presentall epochs are consistent with a underlying "," Nevertheless, the region preferred by the combined data sets is present in all cases, implying that as with the symmetric gaussian all epochs are consistent with a single underlying image morphology."
this time the flux normalizationsingle of the imagecompact morphology.component Duringvaried from 2.23Jy (2009.96) to 3.06 (2009.97).," During this time the flux normalization of the compact component varied from $2.23\,\Jy$ (2009.96) to $3.06\,\Jy$ (2009.97)."
" For all epochs theJy reduced-x? is nearly unity, ranging from 0.45 (2007) to 1.34 (2009.95)."," For all epochs the $\chi^2$ is nearly unity, ranging from $0.45$ (2007) to $1.34$ (2009.95)."
" The most likely configuration is highly asymmetric, g=20.579343uas, A=0.70700910,05, and €= —19?*2,'$,, withcorresponding to a major-minor axis ratio of more than 0.240.3 with symmetric models highly disfavored."," The most likely configuration is highly asymmetric, with $\sigma=20.5^{+0.3+0.5}_{-0.8-1.3}\,\muas$, $A=0.70^{+0.03+0.05}_{-0.1-0.18}$, and $\xi={-19^\circ}^{+3^\circ+6^\circ}_{-1^\circ-2^\circ}$ corresponding to a major–minor axis ratio of more than $2.4^{+0.2+0.3}_{-0.4-0.6}$, with symmetric models highly disfavored."
" The resulting 2.4*57*55. FWHMs of the minor and major axes are then 3741µας and 88+9yas, though these are significantly correlated due to the substantially larger fractional error on A in comparison to that on c."," The resulting ${\rm FWHM}$ s of the minor and major axes are then $37\pm1\,\muas$ and $88\pm9\,\muas$, though these are significantly correlated due to the substantially larger fractional error on $A$ in comparison to that on $\sigma$ ."
" The intrinsic image, scatter-broadened and associated visibilities of the most likely configuration is imageshown in the middle row of Figure 3.."," The intrinsic image, scatter-broadened image and associated visibilities of the most likely configuration is shown in the middle row of Figure \ref{fig:bestfit}."
" The x for the combined data set is 61.5, and much lower than that found for the symmetric case."," The $\chi^2$ for the combined data set is $61.5$, and much lower than that found for the symmetric case."
" As described in Section 4, a decrease in X? is expected given the two additional addition of two parameters."," As described in Section \ref{sec:BDA}, a decrease in $\chi^2$ is expected given the two additional addition of two parameters."
" However, the various ICs, given in Table 1,, a means for identifying significantly lower 7."," However, the various $\IC$ s, given in Table \ref{tab:results}, provide a means for identifying significantly lower $\chi^2$."
" The best fit provideasymmetric model has a BIC that is 6.8 lower than the best fit symmetric model, and an AIC that is 10.4 lower than the best fit symmetric model."," The best fit asymmetric model has a $\BIC$ that is 6.8 lower than the best fit symmetric model, and an $\AIC$ that is 10.4 lower than the best fit symmetric model."
" These provide “strong” evidence symmetric models for the image of Sgr A*, ruling these againstout at 2.60 (BIC) and 3.20 (AIC) levels, in terms of the relative significance."," These provide “strong” evidence against symmetric models for the image of Sgr A*, ruling these out at $2.6\sigma$ $\BIC$ ) and $3.2\sigma$ $\AIC$ ) levels, in terms of the relative significance."
" That is, the limited visibility coveragein the u—v plane, the existing despitemm-VLBI observations can conclusively detect asymmetric structure in Sgr A*."," That is,despite the limited visibility coveragein the $u$ $v$ plane, the existing mm-VLBI observations can conclusively detect asymmetric structure in Sgr A*."
MaeGregor 1992.. 1993:: Spruit 2002:: Maeder Meynet 2003.. 2004 )). itis still an open question.,"MacGregor \cite{Charbonneau92}, , \cite{Charbonneau93}; ; Spruit \cite{Spruit02}; ; Maeder Meynet \cite{Maeder03}, \cite{Maeder04}) ), it is still an open question."
 In this paper. we focus mainly on magnetic angular momentum transport and the mixing of elements associated with angular momentum redistribution.," In this paper, we focus mainly on magnetic angular momentum transport and the mixing of elements associated with angular momentum redistribution."
 In Sect., In Sect.
 2 we give the equations of stellar structure of a shellular rotation star., 2 we give the equations of stellar structure of a shellular rotation star.
 In Sect., In Sect.
 3 we deduce the diffusion coefficient for magnetic angular momentum transport and material mixing that is due to angular momentum redistribution., 3 we deduce the diffusion coefficient for magnetic angular momentum transport and material mixing that is due to angular momentum redistribution.
 Then. in Sect.," Then, in Sect."
 + we give the results of the numerical calculation., 4 we give the results of the numerical calculation.
 We then discuss our results and conclude in Sect., We then discuss our results and conclude in Sect.
 5., 5.
 The stars whose angular velocity is constant on their isobars are called shellular rotation stars (Meynet Maeder 1997)); the isobar surfaces are given by (Meynet Maeder 1997)) where Φ is the minus gravitational potential. O the angular velocity. r the radius. and @ the colatitude.," The stars whose angular velocity is constant on their isobars are called shellular rotation stars (Meynet Maeder \cite{Meynet}) ); the isobar surfaces are given by (Meynet Maeder \cite{Meynet}) ) where $\Phi$ is the minus gravitational potential, $\Omega$ the angular velocity, $r$ the radius, and $\theta$ the colatitude."
" The area of such an isobar surface is denoted by S. and the volume enclosed by the isobar surface by V,,."," The area of such an isobar surface is denoted by $S_{p}$, and the volume enclosed by the isobar surface by $V_{p}$."
 For any quantity q. which is not constant over an isobar surface. a mean value is defined by where dir is an element of the isobar surface.," For any quantity $q$, which is not constant over an isobar surface, a mean value is defined by where $d\sigma$ is an element of the isobar surface."
" The equations of stellar structure of a shellular rotation star. which were developed by Kippenhahn Thomas (1970)) and Meynet Maeder (1997)). are as follows: where— r,, is the radius of a sphere enclosing the volume V,. Le. The M, is. the mass inside. the isobar.. and 5, Is the effective gravity."," The equations of stellar structure of a shellular rotation star, which were developed by Kippenhahn Thomas \cite{Kippenhahn70}) ) and Meynet Maeder \cite{Meynet}) ), are as follows: where $r_{p}$ is the radius of a sphere enclosing the volume $V_{p}$, i.e., The $M_{p}$ is the mass inside the isobar, and Here $g_{e}$ is the effective gravity."
 The « in Eq. (9)), The $\alpha$ in Eq. \ref{rhobar}) )
 is à scalar πα , is a scalar $\frac{d\Omega}{d \Psi}$.
Equation (3)) is the hydrostatic equilibrium equation including centrifugal force. while Eq. (6))," Equation \ref{hyeq}) ) is the hydrostatic equilibrium equation including centrifugal force, while Eq. \ref{treq}) )"
 Is the equation of energy transport under the effects of rotation., is the equation of energy transport under the effects of rotation.
" The nondimensional rotating corrective factors fj, and fy depend on the shape of the isobars.", The nondimensional rotating corrective factors $f_{p}$ and $f_{T}$ depend on the shape of the isobars.
" Assuming that the shapes of isobars are spheroids with semi-major axis c and semi-minor axis 5. and given the angular velocity distribution. using definitions (7)) and (1)). Le. we can get the values of « and b for any given M, and r,: Le.. the surface of the isobar is determined."," Assuming that the shapes of isobars are spheroids with semi-major axis $a$ and semi-minor axis $b$, and given the angular velocity distribution, using definitions \ref{volume}) ) and \ref{isobar}) ), i.e., we can get the values of $a$ and $b$ for any given $M_{p}$ and $r_{p}$; i.e., the surface of the isobar is determined."
" Thus. the average values of the effective gravity and its inverse (€g,> and gll>) can be obtained."," Thus, the average values of the effective gravity and its inverse $<g_{e}>$ and $<g^{-1}_{e}>$ ) can be obtained."
" Then the £j, and fy are also obtained.", Then the $f_{p}$ and $f_{T}$ are also obtained.
 In the computation. the Roche mode (Kippenhahn Thomas 1990)) was used to compute the gravitational potential.," In the computation, the Roche mode (Kippenhahn Thomas \cite{Kippenhahn90}) ) was used to compute the gravitational potential."
 The mechanisms that redistribute angular momentum and the chemical elements in a rotating star can be divided into two categories according to the time scale involved., The mechanisms that redistribute angular momentum and the chemical elements in a rotating star can be divided into two categories according to the time scale involved.
 The first category is that of the dynamical instabilities. occurring on the dynamical timescale.," The first category is that of the dynamical instabilities, occurring on the dynamical timescale."
" If the dynamical unstable gradient occurs in star, if can be instantaneously smoothed (Endal Sofia 1978))."," If the dynamical unstable gradient occurs in star, it can be instantaneously smoothed (Endal Sofia \cite{Endal78}) )."
 One of the dynamical instabilities is the convective instability., One of the dynamical instabilities is the convective instability.
 We suppose that solid-body rotation was enforced in all convective regions., We suppose that solid-body rotation was enforced in all convective regions.
 Another much more important is dynamical shear instabilities., Another much more important is dynamical shear instabilities.
 These instabilities can ensure that the rotation velocity is constant on equipotential surfaces ( Pinsonneault et al. 1989))., These instabilities can ensure that the rotation velocity is constant on equipotential surfaces ( Pinsonneault et al. \cite{Pinsonneault}) ).
 The second category. with a time scale that is comparable to the Kelvin-Helmholtz time scale or the time scale for the evolution of the star. is that of secular instabilities.," The second category, with a time scale that is comparable to the Kelvin-Helmholtz time scale or the time scale for the evolution of the star, is that of secular instabilities."
 For secular instabilities. the transport process of angular momentum and chemical composition was treated as a diffusion process (Endal Sofia 1978:; Pinsonneault et al. 1989)).," For secular instabilities, the transport process of angular momentum and chemical composition was treated as a diffusion process (Endal Sofia \cite{Endal78}; ; Pinsonneault et al. \cite{Pinsonneault}) ),"
" so the radial equations for the redistribution of angular momentum and for the mass fraction X; are where D, is theac diffusion coefficient.", so the radial equations for the redistribution of angular momentum and for the mass fraction $X_{i}$ are where $D_{d}$ is the diffusion coefficient.
 Because of some inherent uncertainties in the diffusion equation. the adjustable parameter fo is introduced to represent these uncertainties.," Because of some inherent uncertainties in the diffusion equation, the adjustable parameter $f_{\Omega}$ is introduced to represent these uncertainties."
 Another adjustable parameter fi. is used to account for how the instabilities mix material less efficiently than they transport angular momentum (Pinsonneault et al. 1989))., Another adjustable parameter $f_{c}$ is used to account for how the instabilities mix material less efficiently than they transport angular momentum (Pinsonneault et al. \cite{Pinsonneault}) ).
 The second term on the right-side of Eq. (13)), The second term on the right-side of Eq. \ref{diffu1}) )
 is due to the secular contraction and/or expansion (Maeder Zahn 1998)). which can be dominant to induce differential rotation in a rotating star with a weak wind or without any wind.," is due to the secular contraction and/or expansion (Maeder Zahn \cite{Maeder98}) ), which can be dominant to induce differential rotation in a rotating star with a weak wind or without any wind."
 The second term on the right-side of Eq. (14)), The second term on the right-side of Eq. \ref{diffu2}) )
 1s the change inthe nuclear reaction., is the change inthe nuclear reaction.
 The V; in the Eq. (14)), The $V_{i}$ in the Eq. \ref{diffu2}) )
 15thevelocityof microscopic diffusion given by Thoul et al. (1994))., isthevelocityof microscopic diffusion given by Thoul et al. \cite{Thoul}) ).
 In our model. we use the diffusion," In our model, we use the diffusion"
constraints on the origin and evolution of dust-obscured activity in distant clusters.,constraints on the origin and evolution of dust-obscured activity in distant clusters.
 The SSTs sensitive mid-infrared imaging capabilities provide an unique opportunity to undertake complete and representative surveys of the obscured. active populations in distant clusters.," The 's sensitive mid-infrared imaging capabilities provide an unique opportunity to undertake complete and representative surveys of the obscured, active populations in distant clusters."
 To search for a population of mid-infrared sources 1n rich clusters environments. we have therefore used the Multiband Imaging Photometer forSpitzer (MIPS) to detect 24-um emission from galaxies in two clusters at z~0.5 covering a very wide range in environment from | MMpe out to the turn-around radius (~5 MMpc) where the clusters merge into the surrounding field.," To search for a population of mid-infrared sources in rich clusters environments, we have therefore used the Multiband Imaging Photometer for (MIPS) to detect $\mu$ m emission from galaxies in two clusters at $z\sim0.5$ covering a very wide range in environment from $\sim1$ Mpc out to the turn-around radius $\sim5$ Mpc) where the clusters merge into the surrounding field."
 These observations will. provide measures of the level of obscured star-formation in these clusters. and so allow us to build up a reliable picture of the evolution of dust-obseured activity in clusters over the past SGGyrs.," These observations will provide measures of the level of obscured star-formation in these clusters, and so allow us to build up a reliable picture of the evolution of dust-obscured activity in clusters over the past Gyrs."
 This paper presents a statistical analysis of the 24;:m populations in two z~0.5 clusters., This paper presents a statistical analysis of the $\mu$ m populations in two $z\sim 0.5$ clusters.
 A subsequent paper (Geach et iin prep) will discuss the properties of these sources in more detail using the available spectroscopic. and morphological surveys of the clusters (Moran et 22006)., A subsequent paper (Geach et in prep) will discuss the properties of these sources in more detail using the available spectroscopic and morphological surveys of the clusters (Moran et 2006).
 The paper is organised as follows: we describe our observations and their reduction in $22. analyse these in $33 and discuss our results and present our conclusions in $44 and $55. respectively.," The paper is organised as follows: we describe our observations and their reduction in 2, analyse these in 3 and discuss our results and present our conclusions in 4 and 5, respectively."
" Throughout. we adopt a geometry with ©,,20.3. O420.7 and Ha2TOkkm ss! ΜΜροΙ."," Throughout, we adopt a geometry with $\Omega_m=0.3$, $\Omega_\Lambda=0.7$ and $H_0 = 70$ $^{-1}$ $^{-1}$."
 The two clusters chosen for this study are unique in having panoramieHST imaging covering ~25'-diameter fields — extending from the cores out to the tum-around radii of the clusters (Treu et 22003: Kneib et 22003: Moran et 22005)., The two clusters chosen for this study are unique in having panoramic imaging covering $\sim 25'$ -diameter fields -- extending from the cores out to the turn-around radii of the clusters (Treu et 2003; Kneib et 2003; Moran et 2005).
 These data have been used for weak-lensing analysis of these clusters. yielding 2-D maps of the dark matter distributions on ~ 5-Mpe scales in the structures (Kneib et 22003).," These data have been used for weak-lensing analysis of these clusters, yielding 2-D maps of the dark matter distributions on $\sim 5$ -Mpc scales in the structures (Kneib et 2003)."
 Panoramic studies of the galaxy populations in these clusters also benefit from extensive deep. ground-based optical and near-infrared imaging and spectroscopy (Moran et 22006 in prep).," Panoramic studies of the galaxy populations in these clusters also benefit from extensive deep, ground-based optical and near-infrared imaging and spectroscopy (Moran et 2006 in prep)."
 Although both clusters are relatively rich. they differ in their X-ray luminosities: 0002416 (220.39) has a relatively modest X-ray luminosity. Ly~3.2«I0 ss7! (Treu et 22003). while 00451—03 (z= 0.55) Is some 84 more luminous.," Although both clusters are relatively rich, they differ in their X-ray luminosities: 0024+16 $z = 0.39$ ) has a relatively modest X-ray luminosity, $L_X\sim 3.2\times10^{44}$ $^{-1}$ (Treu et 2003), while $-$ 03 $z = 0.55$ ) is some $\times$ more luminous."
 This distinction may lead to differences in the effectiveness of the various processes influencing star formation (Treu et 22003). as traced by the distribution of the mid-infrared population.," This distinction may lead to differences in the effectiveness of the various processes influencing star formation (Treu et 2003), as traced by the distribution of the mid-infrared population."
 This will be useful in our subsequent detailed study to disentangle the potential mechanisms. for triggering and suppressing star formation., This will be useful in our subsequent detailed study to disentangle the potential mechanisms for triggering and suppressing star formation.
 MIPS 244m observations of the fields of 61000216 (ς= 0.39) and 00451-03 (z= 0.55) were obtained withSST in fixed-cluster offset mode on 2004 December 24-25., MIPS $\mu$ m observations of the fields of 0024+16 $z=0.39$ ) and $-$ 03 $z=0.55$ ) were obtained with in fixed-cluster offset mode on 2004 December 24–25.
 The observations of CIO00024-16 are centered on 335.70. 417009445 2000: while those for 00451]—03 are centered on: 110.80. —03 000557," The observations of 0024+16 are centered on 35.70, $+$ 45 (J2000); while those for $-$ 03 are centered on: 10.80, $-$ 57"
norphologically peculiar galaxy HC: τοῦ (Rubin et al.,morphologically peculiar galaxy HCG 79b (Rubin et al.
 1991: Williams et al., 1991; Williams et al.
 1991: Mendes de Oliveira Ticksou 1991: Villchez Iglesias-Párrano 1998)., 1991; Mendes de Oliveira Hickson 1994; lchez Iglesias-Párramo 1998).
 Chuveut X-ray observations are not sensitive enough o detect any X-ray cluission that may originate frou intragroup gas that nüeht be present in SS) (Pilclis. Breeman. Evrard 1995: Pouman ct al.," Current X-ray observations are not sensitive enough to detect any X-ray emission that may originate from intragroup gas that might be present in SS (Pildis, Bregman, Evrard 1995; Ponman et al."
 1996)., 1996).
 ITowever. Suleutic Lorre (1983) and Nishiura et al. (," However, Sulentic Lorre (1983) and Nishiura et al. ("
20000) detected a faint optical euvelope around SS that is dlausibly composed of stars tidally liberated from the ealaxies iu SS. plus Williams. McMahon van Corkous (1991) found. extended emission.,"2000b) detected a faint optical envelope around SS that is plausibly composed of stars tidally liberated from the galaxies in SS, plus Williams, McMahon van Gorkom (1991) found extended emission."
 These observatious Sugeest that SS is a plivsically real compact eroup., These observations suggest that SS is a physically real compact group.
 Iu this paper. we present results of our photometric study of TDSS.," In this paper, we present results of our photometric study of TDSS."
 Since this tidal debris system in SS (hereafter TDSS) is uxneogically ή to other tidal debris. such as Arp LO5S and Arp 215N (Braine et al.," Since this tidal debris system in SS (hereafter TDSS) is morphologically similar to other tidal debris, such as Arp 105S and Arp 245N (Braine et al."
 2000). we will also compare the photometric properties of TDSS with these two tidal otdebris.," 2000), we will also compare the photometric properties of TDSS with these two tidal debris."
" Throughout this paper we adopt a distance to SS Li Alpe determined using the mean recession velocity of TCC 79a. 79b. του, aud του referenced to the galactic standard of rest. Veg = LLL9 kim (de Vaucouleurs et al."," Throughout this paper we adopt a distance to SS of 44 Mpc determined using the mean recession velocity of HCG 79a, 79b, 79c, and 79d referenced to the galactic standard of rest, $V_{\rm GSR}$ = 4449 km $^{-1}$ (de Vaucouleurs et al."
 1991). aud a IInbble constaut. Ty = 100 1u | |.," 1991), and a Hubble constant, $H_{0}$ = 100 km $^{-1}$ $^{-1}$."
 We obtained the archival HST/WEDPC F13901 images of SS (PI: Suleutic. J. W.).," We obtained the archival HST/WFPC $F439W$ images of SS (PI: Sulentic, J. W.)."
 The total exposure time was SLOO seconds (Wi Rabacaa Suleutic 1991: Rabacaa 1997).," The total exposure time was 8100 seconds (Wu, Rabaçaa Sulentic 1994; Rabaçaa 1997)."
 We used to reject cosumic-ravs aud to conibine inages., We used to reject cosmic-rays and to combine images.
 We also obtained the flus-calibrated archival IST/WFPC? P336W. FBOW. Poss. and £SIIWH- inages of SS (PE: IIuusberger. S. D.).," We also obtained the flux-calibrated archival HST/WFPC2 $F336W$, $F439W$, $F555W$, and $F814W$ images of SS (PI: Hunsberger, S. D.)."
 The total exposure times were 5200 seconds for £336]. 5200 secouds for FI39W. 2000 secouds for ΕΡΤ. aud. 2000 seconds for FSILIW.," The total exposure times were 5200 seconds for $F336W$, 5200 seconds for $F439W$, 2000 seconds for $F555W$, and 2000 seconds for $F814W$."
 We compute a Johnson B magnitude assunniug that the filter function of ΕΟΟ is the same as that of JoliusonD., We compute a Johnson $B$ magnitude assuming that the filter function of $F439W$ is the same as that of Johnson.
 We also do a JohnsonV magnitude assumniug that the filter function of F555W is the same as that of οποια.V., We also do a Johnson magnitude assuming that the filter function of $F555W$ is the same as that of Johnson.
 According to Fig 11 iu Ποια et al (1995). Johnson ~DB(FA39W) - 0.1 for JohusouD - JohusouV of about 1.," According to Fig 11 in Holtzman et al (1995), Johnson $\sim$ - 0.1 for Johnson - Johnson of about 1."
 Jolusou — - 0.05 for Johuson - Zof about l., Johnson $\sim$ - 0.05 for Johnson - of about 1.
 Apparent Johusou£ and JohusonV maguitudes of TDSS nav be 0.1 and 0.05 mae brighter. respectively.," Apparent Johnson and Johnson magnitudes of TDSS may be 0.1 and 0.05 mag brighter, respectively."
 But. our results usingB-V and V-7 colors do not significantly change.," But, our results using and colors do not significantly change."
 V- and A-baud deep images of SS were obtained with the Ly (1021 « 1021) COD camera attached to the 105 cni Sclunidt telescope of the University of Tokvo at KISO Observatory. ou 20 April 1996 (H-band) aud 21 April. 1996 (V-band).," $V$ - and $R$ -band deep images of SS were obtained with the 1K (1024 $\times$ 1024) CCD camera attached to the 105 cm Schmidt telescope of the University of Tokyo at KISO Observatory, on 20 April, 1996 $R$ -band) and 21 April, 1996 $V$ -band)."
 Thecamera provided a z12/5«1275 field of view., The camera provided a $\approx 12\farcm 5\times 12\farcm 5$ field of view.
 The spatial resolution was 0/75 per pixel., The spatial resolution was 75 per pixel.
 The integration time for each exposure was set to 900 seconds for V-baud aud600 seconds for R-baucd., The integration time for each exposure was set to 900 seconds for $V$ -band and 600 seconds for $R$ -band.
 Four exposures for the V-baud aud five exposures for the A-baud weretakeu: thus. the total integration time was 3.600 seconds in the V-banud tage aud 3.000 seconds in the Παπ image.," Four exposures for the $V$ -band and five exposures for the $R$ -band were taken; thus, the total integration time was 3,600 seconds in the $V$ -band image and 3,000 seconds in the $R$ -band image."
 The seeing was ~1/6 for V-baud aud 2572 for B-baud diving the observations., The seeing was $\simeq$ 6 for $V$ -band and $\simeq$ 2 for $R$ -band during the observations.
 Data reduction was performed in a standard wav using IRAF., Data reduction was performed in a standard way using IRAF.
 Flux calibration for the R-baud nuages was made usimg the data of photometric standard stars iu the fold of PC. | 029 (Landolt 1992)., Flux calibration for the $R$ -band images was made using the data of photometric standard stars in the field of PG $+$ 029 (Landolt 1992).
 The V-baud observations were carried out uuder non-photometric coucditious., The $V$ -band observations were carried out under non-photometric conditions.
 V-band image calibration was performed simply by using the measured magnitude of a star in the same frame of SS. AC2000-73822| (Urban et al.," $V$ -band image calibration was performed simply by using the measured magnitude of a star in the same frame of SS, AC2000-738224 (Urban et al."
 1997: Kislvuk et al., 1997; Kislyuk et al.
 1999)., 1999).
 The photometric errors were estimated to be £0.27 mae for the V-banud and £0.01 mag for the A-baud., The photometric errors were estimated to be $\pm 0.27$ mag for the $V$ -band and $\pm 0.04$ mag for the $R$ -band.
 We used VR- aud f-baud iuages taken from our previous studies (Muraviiua et al., We used $VR$ - and $I$ -band images taken from our previous studies (Murayama et al.
 2000: Nishiura ct al., 2000; Nishiura et al.
 20005)., 2000b).
 Since the VA-baud is uot a standard photometric band (Jewitt. Luu Chen 1996). we adopted an AB magnitude scale for this baudpass.," Since the $VR$ -band is not a standard photometric band (Jewitt, Luu Chen 1996), we adopted an AB magnitude scale for this bandpass."
 Near-intraredd J- and /7- nuages of SS were obtained using the 105 cm Schinidt telescope at the KISO Observatory during the period between 1 July 2001 aud 1 July 2001., Near-infrared $J$ - and $H$ - images of SS were obtained using the 105 cm Schmidt telescope at the KISO Observatory during the period between 1 July 2001 and 4 July 2001.
 The telescope was equipped with a larec-format ucar-intrared camera called. the IXiso Observatory Near-lifrared Camera (ISONIC) Utoh et al., The telescope was equipped with a large-format near-infrared camera called the Kiso Observatory Near-Infrared Camera (KONIC) (Itoh et al.
 1995)., 1995).
 KONIC' have 1010. « 1010 pixels providing a zc18!«I8! field of view.," KONIC have 1040 $\times$ 1040 pixels providing a $\approx 18\farcm 
\times 18\farcm$ field of view."
 Tle spatial resolution was 1./06 aresec per pixel., The spatial resolution was $\farcm$ 06 arcsec per pixel.
 We use the images further binned iuto 520 &« 520 pixels. hence a pixel scale is 2712 per the 242 biuued pixels.," We use the images further binned into 520 $\times$ 520 pixels, hence a pixel scale is $\farcs$ 12 per the $\times$ 2 binned pixels."
 The integration time for cach exposure was set to 150 seconds., The integration time for each exposure was set to 180 seconds.
 Tweuty five exposures for J-boaud aud thirty two exposures for /f-band were taken., Twenty five exposures for $J$ -band and thirty two exposures for $H$ -band were taken.
" Therefore the total integration times were 1500 seconds for J-band aud ES5760 seconds for Z[-baud. respectively,"," Therefore the total integration times were 4500 seconds for $J$ -band and 5760 seconds for $H$ -band, respectively."
 The secing was ~ duriug the observation., The seeing was $\sim$ $\farcs$ 5 during the observation.
 Data reduction was performed in a standard wav using ΠΑΕ., Data reduction was performed in a standard way using IRAF.
 Flux calibration was made usine the measured maenitudes of stars by 2MÁÀSS in the same frame of SS. | 203915. | 205019. and | 201805.," Flux calibration was made using the measured magnitudes of stars by 2MASS in the same frame of SS, $+$ 203915, $+$ 205049, and $+$ 204805."
 The photometric errors were estimated tobe —E0.0 mag for J-baud and to be £0.00 mae for ZT-baud. respectively.," The photometric errors were estimated to be $\pm 0.0x$ mag for $J$ -band and to be $\pm 0.0x$ mag for $H$ -band, respectively."
 Near-infrared ας tages of SS were obtained with the 256 --« Iufared Camera attached to the f/153.5 € focus of the University of Hawaii 0.6 ii Planctary Patrol telescope at Manna Kea Observatory. on 9 Mav 1991.," Near-infrared -band images of SS were obtained with the 256 $\times$ 256 Infrared Camera attached to the f/13.5 Cassegrain focus of the University of Hawaii 0.6 m Planetary Patrol telescope at Mauna Kea Observatory, on 9 May 1994."
 The camera provided a zzSÍ5.8!5 field of view., The camera provided a $\approx 8\farcm 5 \times 8\farcm 5$ field of view.
 The spatial resolution was 2/0 arcsec per pixel., The spatial resolution was $\farcm$ 0 arcsec per pixel.
 The μαinteeration time for cach exposure was setto 120 seconds., The integration time for each exposure was setto 120 seconds.
 Light exposures were takeu: thus. the total iuteeration time amounted 960 seconds.," Eight exposures were taken; thus, the total integration time amounted to 960 seconds."
 The secius was ~ 271 uring the observation., The seeing was $\sim$ $\farcs$ 4 during the observation.
 Data reduction was performed in a standard wav using IRAF., Data reduction was performed in a standard way using IRAF.
 Flux calibration was made using the data of the UIKIRTbright staudard stars IIDsL800. ITDIODGOT. and IIDI36751. trauslated into," Flux calibration was made using the data of the UKIRT bright standard stars HD84800, HD105601, and HD136754, translated into"
to Nap=3.n i a simple model (68.3 per cent confidence).,to $\Neff=3.4_{-0.5}^{+0.6}$ in a simple model (68.3 per cent confidence).
 iniFor the more general model. including Curvature. tensors neutrino mass. only a marginal improvement is observed.," For the more general model, including curvature, tensors and neutrino mass, only a marginal improvement is observed."
 The results obtained. here are compatible with other recent estimates based on galaxy clusters2009).. rellecting the σους agreement in recent ex constraints based on X-ray and optically selected clusters," The results obtained here are compatible with other recent estimates based on galaxy clusters, reflecting the good agreement in recent $\sigma_8$ constraints based on X-ray and optically selected clusters."
 Although current cosmological data are not sullicient to rule out the existence of sterile neutrino species or distinguish between the normal and inverted mass hierarchies. they continue to. provide. some of the tightest constraints available. in particular on the mass scale.," Although current cosmological data are not sufficient to rule out the existence of sterile neutrino species or distinguish between the normal and inverted mass hierarchies, they continue to provide some of the tightest constraints available, in particular on the mass scale."
 We also consider the prospects for further improvement. finding that a few per cent level measurement of. the Llubble parameter will significantly improve the constraints on models where ds. free.," We also consider the prospects for further improvement, finding that a few per cent level measurement of the Hubble parameter will significantly improve the constraints on models where is free."
 X similarly improved determination of ax. combined with improved. CMD data fromPlanck will farther tighten limits on the neutrino ⊔↓⋜↧⊳∖⊳∖⊳∖≼∼⋜↧↓⋖⋅⊳⋟↓≻∢⊾↓⋅⇂↥⋜↧↓≻⊳∖↓≻↓⋅∪∖⇁⊔⊔⊔⋏∙≟↿⇂⊔⊾∐↓⋅⊳∖↿↓⊔⊔↿⊳∖∪⇂⊔∪⊔−∠∢⊾↓⋅∪ M ⋅ . ⋅ niass [rom cosmological data.," A similarly improved determination of $\sigma_8$, combined with improved CMB data from, will further tighten limits on the neutrino mass perhaps providing the first hints of non-zero mass from cosmological data."
 More precise measurenients of the growth of structure at late times. and the extension of such data to higher redshifts. will provide a powerful. new mechanism to constrain neutrino mass.," More precise measurements of the growth of structure at late times, and the extension of such data to higher redshifts, will provide a powerful, new mechanism to constrain neutrino mass."
 We are grateful to Harald Ebeling and Alex Drlica-M'agner or their contributions to this series of papers. and to Glenn Alorris. Stuart. Marshall and the SLAC unix support team or technical support.," We are grateful to Harald Ebeling and Alex Drlica-Wagner for their contributions to this series of papers, and to Glenn Morris, Stuart Marshall and the SLAC unix support team for technical support."
 We also thank Giorgio Cratta and oko Ixurahashi for useful discussions., We also thank Giorgio Gratta and Naoko Kurahashi for useful discussions.
 Calculations were carried out using the KIPAC NOC anc Orange compute clusters at the SLAC National Accelerator Laboratory and he SLAC Unix compute farm., Calculations were carried out using the KIPAC XOC and Orange compute clusters at the SLAC National Accelerator Laboratory and the SLAC Unix compute farm.
 We acknowledge support rom the National Acronautics and Space Administration (NASA) through Chandra: Award. Numbers DD5-6031X. GOT-8125X and COS-9118X. issued by the Chandra. X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and. on. behalf of NASA under contract’ NASS-03060," We acknowledge support from the National Aeronautics and Space Administration (NASA) through Chandra Award Numbers DD5-6031X, GO7-8125X and GO8-9118X, issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060."
 This work was supported. in part by the U.S. Department of Enerey under contract number DE-ACO2-76SF00515., This work was supported in part by the U.S. Department of Energy under contract number DE-AC02-76SF00515.
 AM. was supported. by a Stanford. Ciracduate Fellowship and an appointment to the NASA Postdoctoral Program. administered by Oak Ricdec Associated Universities through a contract with NASA.," AM was supported by a Stanford Graduate Fellowship and an appointment to the NASA Postdoctoral Program, administered by Oak Ridge Associated Universities through a contract with NASA."
"To impose also the continuity of the second derivative of 5,(7,) at all the dividing points can remove the foregoing instabilities.",To impose also the continuity of the second derivative of $S_{\nu}(\tau_{\nu})$ at all the dividing points can remove the foregoing instabilities.
 Consequently we propose here a cubic spline model lor each specific source Dunction., Consequently we propose here a cubic spline model for each specific source function.
 In some wav (his model constitutes a regularization of the process to computing the values of the source functions., In some way this model constitutes a regularization of the process to computing the values of the source functions.
 The formalism of the cubic spline approximation (namely a two-point boundary. value problem developed to interpolate among the explicitly known values of a given function) can be emploved in the present case although the values of (τη) are vet unknown., The formalism of the cubic spline approximation (namely a two-point boundary value problem developed to interpolate among the explicitly known values of a given function) can be employed in the present case although the values of $S_{\nu}(\tau_{\nu})$ are yet unknown.
 To emplov the cubic spline approach in order to describe the behaviour of the source unctüon in tvpical RT problems. where a scattering term appears in the source function. is the best (may be (he unique) correct choice for both theoretical and numerical reasons.," To employ the cubic spline approach in order to describe the behaviour of the source function in typical RT problems, where a scattering term appears in the source function, is the best (may be the unique) correct choice for both theoretical and numerical reasons."
 A theoretical reason is brought about by the non-local nature of the problem: the specific intensities aud consequently the source function al a eiven depth point depend via the RT process on (he values of the source function at all the other points of the svstem., A theoretical reason is brought about by the non-local nature of the problem: the specific intensities and consequently the source function at a given depth point depend via the RT process on the values of the source function at all the other points of the system.
 Thus the iunerical values of (he source function must be computed simultaneously at all the depth points., Thus the numerical values of the source function must be computed simultaneously at all the depth points.
 Therefore such a non-local character of the physical problem must be represented by neans of a non-local mathematical structure., Therefore such a non-local character of the physical problem must be represented by means of a non-local mathematical structure.
 Also the derivatives of the source function at anv depth point must be formulated as a linear relation including the implicit values of the source function at all the depth points. not only as a linear relation of (he implicit values of the source function al each triad of consecutive depth points.," Also the derivatives of the source function at any depth point must be formulated as a linear relation including the implicit values of the source function at all the depth points, not only as a linear relation of the implicit values of the source function at each triad of consecutive depth points."
 The pratical reason is lor the sake of the stability of the computational algorithm., The pratical reason is for the sake of the stability of the computational algorithm.
 The cubic spline model minimizes the strain enerey integral. (hat is the integral of the scquared values of the values of the second derivative of the protagonist function. namely of the variation of its curvature - the oscillations. (," The cubic spline model minimizes the strain energy integral, that is the integral of the squared values of the values of the second derivative of the protagonist function, namely of the variation of its curvature - the oscillations. ("
See.e.g.. Rivlin. 1931.),"See, Rivlin, 1981.)"
 That is. the use of the cubic spline approximation to the source function minimizes the risk of destabilizing oscillations.," That is, the use of the cubic spline approximation to the source function minimizes the risk of destabilizing oscillations."
" The cubic spline representation constitutes by itself another (wo-points boundary problem: we must know the values of S(7) at all the depth points in order to compute S'(7) and 5""(7) at each depth point.", The cubic spline representation constitutes by itself another two-points boundary problem: we must know the values of $S(\tau)$ at all the depth points in order to compute $S^{\prime}(\tau)$ and $S^{\prime\prime}(\tau)$ at each depth point.
 Nevertheless this apparent drawback turns out to be on the contrary an advantage. because we can carry on simultaneously both two-points boundary problems: the RT problem and the cubic spline interpolation.," Nevertheless this apparent drawback turns out to be on the contrary an advantage, because we can carry on simultaneously both two-points boundary problems: the RT problem and the cubic spline interpolation."
 From the aleorithmical stand point. (he kernel of the original LEM is a forward-elimination scheme that links the so [ar unknown values of the source function at each pair of consecutive optical depth points (75.751) by mean of a linear relation with known coefficients.," From the algorithmical stand point, the kernel of the original IIM is a forward-elimination scheme that links the so far unknown values of the source function at each pair of consecutive optical depth points $(\tau_{L}, \tau_{L+1})$ by mean of a linear relation with known coefficients."
 The latter are determined by taking into account the RT equations that describe laver by laver the propagation of both the downgoing and the upgoing specific intensities., The latter are determined by taking into account the RT equations that describe layer by layer the propagation of both the downgoing and the upgoing specific intensities.
 Now we realized that. by using (he cubic spline formalism the same forward-elimination scheme can also be enmploved to link the unknown values of the second derivatives of (he source functions. again," Now we realized that, by using the cubic spline formalism the same forward-elimination scheme can also be employed to link the unknown values of the second derivatives of the source functions, again"
Linkage International schemes) and the Victorian Partnership for Advanced Computing (through its Expertise Cuants scheme) is acknowledged.,Linkage International schemes) and the Victorian Partnership for Advanced Computing (through its Expertise Grants scheme) is acknowledged.
 Alibes. A. Labay. J. Canal. I. 2001. AAA. 370. 1103 r) CGoswami. X. Prantzos. N.. 2000. AA. 359. 191 Imbriani. C. Limongi. M.. Gialanella. L.. Ferrasi. Fe. Straniero. O. Chielfi. A. 2001. ApJ. 558. 903 Iwamoto. Ix.. Drachwitz. E.. Nomoto. Ix.. lxishimoto. N.. Umeda. HL. Hix. W. E. Thielemann. E.-Ix.. 1999. ApJS. 125. 439 ]xarakas. X. Ll. Lattanzio. J. ο. 2003a. Carnegie Observatories Astrophysies Series. Vol.," Alibes, A., Labay, J. Canal, R., 2001, A, 370, 1103 Gay, P. L. Lambert, D. L., 2000, ApJ, 533, 260 Goswami, A. Prantzos, N., 2000, A, 359, 191 Imbriani, G., Limongi, M., Gialanella, L., Terrasi, F., Straniero, O. Chieffi, A., 2001, ApJ, 558, 903 Iwamoto, K., Brachwitz, F., Nomoto, K., Kishimoto, N., Umeda, H., Hix, W. R. Thielemann, F.-K., 1999, ApJS, 125, 439 Karakas, A. I. Lattanzio, J. C., 2003a, Carnegie Observatories Astrophysics Series, Vol."
 4: Origin and Evolution of the Elements. ed.," 4: Origin and Evolution of the Elements, ed."
 A. MeWilliam anc M. Bauch (Pasadena: Carnegie, A. McWilliam and M. Rauch (Pasadena: Carnegie
Epstein regime.,Epstein regime.
" We show in how the collision time-scale can be easily calculated from the friction time-scale, useful ffor simulations of gas and particles in protoplanetary discs."," We show in how the collision time-scale can be easily calculated from the friction time-scale, useful for simulations of gas and particles in protoplanetary discs."
 Consider now a grid cell containing N superparticles., Consider now a grid cell containing $N$ superparticles.
 For particle i the collision probability for a representative from superparticle i to collide with the particle swarms j=i1 to j= Nis calculated., For particle $i$ the collision probability for a representative from superparticle $i$ to collide with the particle swarms $j=i+1$ to $j=N$ is calculated.
" The collision occurs if a random number, drawn for each collision partner, is smaller than P from(3)."," The collision occurs if a random number, drawn for each collision partner, is smaller than $P$ from."
. The collision instantaneously changes the velocity vectors of both particles i and j., The collision instantaneously changes the velocity vectors of both particles $i$ and $j$.
" This way the correct collision frequency is obtained for both particles, even though the algorithm only considers the possible collision i with j, but not j with ;."," This way the correct collision frequency is obtained for both particles, even though the algorithm only considers the possible collision $i$ with $j$, but not $j$ with $i$."
" In we describe how to consistently limit the number of collision partners, and thus save computation time, in grid cells which contain many (>> 100) particles."," In we describe how to consistently limit the number of collision partners, and thus save computation time, in grid cells which contain many $\gg$ 100) particles."
 There are several advantages to using such a probabilistic swarm approach to particle collisions., There are several advantages to using such a probabilistic swarm approach to particle collisions.
" We mention here a few: (i) it is fast because we do not have to track when particles touch or overlap within the grid cells, (ii) it allows us to freely choose the relative speed that enters the collision frequency, useful ffor subtracting off the Keplerian shear (see refs:shear)), and (iii) the algorithm is easily generalisable to also include a probabilistic approach to particle coagulation and shattering."," We mention here a few: (i) it is fast because we do not have to track when particles touch or overlap within the grid cells, (ii) it allows us to freely choose the relative speed that enters the collision frequency, useful for subtracting off the Keplerian shear (see \\ref{s:shear}) ), and (iii) the algorithm is easily generalisable to also include a probabilistic approach to particle coagulation and shattering."
 In we show the collision path length of test particles injected into a medium with 10 superparticles per grid cell and a mean free path of A=0.1., In we show the collision path length of test particles injected into a medium with 10 superparticles per grid cell and a mean free path of $\lambda=0.1$.
 Collisions are tracked through the Monte Carlo method described above., Collisions are tracked through the Monte Carlo method described above.
 The collision algorithm makes some particles collide after a short flight path and others after a longer., The collision algorithm makes some particles collide after a short flight path and others after a longer.
 The distribution plotted in follows closely the expectation N=Noexp(—€/A).," The distribution plotted in follows closely the expectation $N=N_0
\exp(-\ell/\lambda)$."
 The Monte Carlo approach to collisions is very similar to the physical particle approach in the distribution of free flight paths., The Monte Carlo approach to collisions is very similar to the physical particle approach in the distribution of free flight paths.
" The main technical difference between using inflated particles (see introduction) and our newly developed collision algorithm for superparticles is that inflated particles always collide when they overlap physically (the particle size can be associated with the grid cell size), while superparticles sharing the same grid cell collide with a certain probability which guarantees that collisions occur on the average after a collisional time-scale."," The main technical difference between using inflated particles (see introduction) and our newly developed collision algorithm for superparticles is that inflated particles always collide when they overlap physically (the particle size can be associated with the grid cell size), while superparticles sharing the same grid cell collide with a certain probability which guarantees that collisions occur on the average after a collisional time-scale."
" Another difference is that superparticles which do not approach must still be allowed to collide, as otherwise the mean free path will be too long."," Another difference is that superparticles which do not approach must still be allowed to collide, as otherwise the mean free path will be too long."
 Non-approaching particles are collided by flipping the relative velocity vector before collision and reflipping afterwards., Non-approaching particles are collided by flipping the relative velocity vector before collision and reflipping afterwards.
" The main issue with approaching collisions is that collisions occur in fixed grid cells which are not centred on the superparticle in question, and thus a superparticle at the edge of a grid cell will have too few collision partners if only approaching collisions are allowed."," The main issue with approaching collisions is that collisions occur in fixed grid cells which are not centred on the superparticle in question, and thus a superparticle at the edge of a grid cell will have too few collision partners if only approaching collisions are allowed."
 We show in how the superparticle approach transforms smoothly to the inflated particle approach when the number of superparticles is reduced., We show in how the superparticle approach transforms smoothly to the inflated particle approach when the number of superparticles is reduced.
" The Monte Carlo collision scheme presented here could equally well be formulated in terms of inflated particles, by constructing inflated particles smaller than a grid cell."," The Monte Carlo collision scheme presented here could equally well be formulated in terms of inflated particles, by constructing inflated particles smaller than a grid cell."
" Solving statistically for the collision outcome of these ""sub-grid"" particles is mathematically equivalent to the interpretation, chosen for this paper, of the numerical particles as swarms."," Solving statistically for the collision outcome of these “sub-grid” particles is mathematically equivalent to the interpretation, chosen for this paper, of the numerical particles as swarms."
 We have implemented the Monte Carlo superparticle collision scheme described in into the open source code PencilCode?., We have implemented the Monte Carlo superparticle collision scheme described in into the open source code Pencil.
". The Pencil Code evolves gas on a fixed grid and has fully parallelised modules for an additional solid component represented by superparticles (Johansenetal.,2007;Youdin&Johansen, 2007)."," The Pencil Code evolves gas on a fixed grid and has fully parallelised modules for an additional solid component represented by superparticles \citep{Johansen+etal2007,YoudinJohansen2007}."
". We first validate the collision algorithm in the limit of inflated particles wwhere two particles occupying the same grid cell always collide and only approaching collisions are considered), to compare our results directly to those of Lithwick&Chiang(2007)."," We first validate the collision algorithm in the limit of inflated particles where two particles occupying the same grid cell always collide and only approaching collisions are considered), to compare our results directly to those of \cite{LithwickChiang2007}."
. The 2-D algorithm of Lithwick&Chiang(2007) has a probabilistic approach to determine whether two particles are in the same vertical zone when they overlap in the plane., The 2-D algorithm of \cite{LithwickChiang2007} has a probabilistic approach to determine whether two particles are in the same vertical zone when they overlap in the plane.
 Their algorithm can thus be seen as ahybrid of the inflated particle approach and a Monte Carlo scheme., Their algorithm can thus be seen as ahybrid of the inflated particle approach and a Monte Carlo scheme.
 We set up a test problem similar to the one presented in Lithwick&Chiang (2007).., We set up a test problem similar to the one presented in \cite{LithwickChiang2007}. .
 We define a 2-D simulation box, We define a 2-D simulation box
The fit to the AVG star with the set L (Figure4)) shows a better agreement because in (his case both $i and Ca are very. well reproduced by almost all stellar models.,The fit to the AVG star with the set L (Figure\ref{fig04}) ) shows a better agreement because in this case both Si and Ca are very well reproduced by almost all stellar models.
" By the way. note that the 25M. does not produce enough Ni to fit the observed [Mg/Fe]: therefore in (his case we simply fixed the mass cut at the border of the Fe core. choice which corresponds to the largest possible amount of ""Ni."," By the way, note that the $25~M_\odot$ does not produce enough $\rm ^{56}Ni$ to fit the observed [Mg/Fe]; therefore in this case we simply fixed the mass cut at the border of the Fe core, choice which corresponds to the largest possible amount of $\rm ^{56}Ni$."
 Conversely. [Al/Fe]. which was fitted by all tbe masses of set LL. now is fitted only by our most massive stellar model. i.e. the 80M...," Conversely, [Al/Fe], which was fitted by all the masses of set H, now is fitted only by our most massive stellar model, i.e. the $80 M_\odot$."
 A detailed discussion of the dependence of the vields of the various elements on the carbon abundance left bv Che He burning may be found in lnbrianietal.(2001) and hence here we simply remind that Mg ancl Al seale directly. with the Carbon abundance left bv the He burning because are both direct products of the Carbon burning., A detailed discussion of the dependence of the yields of the various elements on the carbon abundance left by the He burning may be found in \cite{ietal01} and hence here we simply remind that Mg and Al scale directly with the Carbon abundance left by the He burning because are both direct products of the Carbon burning.
 The vields of Mg and Al produced bv the two sets (HE and L) of models are shown in (he (wo upper panels of Figure 5.. while the trend of [AL/Mg] with the initial mass for the two sets of models is shown in the lowest panel of the same figure.," The yields of Mg and Al produced by the two sets (H and L) of models are shown in the two upper panels of Figure \ref{fig05}, while the trend of [Al/Mg] with the initial mass for the two sets of models is shown in the lowest panel of the same figure."
 The value of [AI/Mg] for the AVG star (-1.27 dex) (solid horizontal line) as well as its error bar (dotted lines) are also shown in Figure 5.. lowest panel.," The value of [Al/Mg] for the AVG star (-1.27 dex) (solid horizontal line) as well as its error bar (dotted lines) are also shown in Figure \ref{fig05}, lowest panel."
 It is readily evident that while all the models of set HE fall within the error bar of the observed |M/Mg]. most of the models of set L lie well above the range of compatibility.," It is readily evident that while all the models of set H fall within the error bar of the observed [Al/Mg], most of the models of set L lie well above the range of compatibility."
 The adoption of set L changes also the fit to the heaviest elements (Se through Ni) without leading anvwayv to an acceptable fit., The adoption of set L changes also the fit to the heaviest elements (Sc through Ni) without leading anyway to an acceptable fit.
 More specifically: [Sc/Fe] remains systematically at least 1 dex below the observed value for all the masses in our grid. [Ti/Fe] (which was always well reproduced in the set ID) is now underestimated by 0.4-0.6 dex. [Cr/Fe] and |Mn/Fe] are both overproduced (by 0.6 and 0.3 dex respectively) by all masses. [Co/Fe] shows a trend with the initial mass (in particular it lowers as the initial mass increases) ancl a good fit is obtained for a mass of the order of 20 M. while [Ni/Fe] is always underestimated by a factor ranging between 0.6 and 1 dex.," More specifically: [Sc/Fe] remains systematically at least 1 dex below the observed value for all the masses in our grid, [Ti/Fe] (which was always well reproduced in the set H) is now underestimated by 0.4-0.6 dex, [Cr/Fe] and [Mn/Fe] are both overproduced (by 0.6 and 0.3 dex respectively) by all masses, [Co/Fe] shows a trend with the initial mass (in particular it lowers as the initial mass increases) and a good fit is obtained for a mass of the order of 20 $\rm M_{\odot}$ while [Ni/Fe] is always underestimated by a factor ranging between 0.6 and 1 dex."
 One could argue al this point that there is a contradiction between (he present results and those reported by Inbrianietal.(2001) where il is stated that a low C abundance (ie. sel ID) is necessary (o preserve a scaled solar abundances., One could argue at this point that there is a contradiction between the present results and those reported by \cite{ietal01} where it is stated that a low C abundance (i.e. set H) is necessary to preserve a scaled solar abundances.
 To clarifv this apparent contrasting results. we show in Figure 6 a comparison between the [N/Mg] obtained with set L (open squares) and set IL (filled squares). where each panel refers to a specific mass.," To clarify this apparent contrasting results, we show in Figure \ref{fignew} a comparison between the [X/Mg] obtained with set L (open squares) and set H (filled squares), where each panel refers to a specific mass."
 The comparison refers to the elements which are not significantly affected by (the mass cut (provided that the fall back is not exceedinglv strong)., The comparison refers to the elements which are not significantly affected by the mass cut (provided that the fall back is not exceedingly strong).
 The crosses mark the values obtained for the AVG star., The crosses mark the values obtained for the AVG star.
 Imbrianietal.(2001). computed the evolution of one star (the 25 M. ) of solar chemical composition aud found (among other things) that: a) the abundances of ihe light elements (up to Al and exeluding O) scale directly with the C abundance while the heaviest ones (up (o Ca) scale inversely with C (see fig.16 in (Imbrianietal. 2001))) and b) ifa 25 M. would be the main representative of a generation of massive stus. as suggested also by Weaver&Woosley. (1993).. then a rather low C abundance should be," \cite{ietal01} computed the evolution of one star (the 25 $\rm M_\odot$ ) of solar chemical composition and found (among other things) that: a) the abundances of the light elements (up to Al and excluding O) scale directly with the C abundance while the heaviest ones (up to Ca) scale inversely with C (see fig.16 in \citep{ietal01}) ) and b) if a 25 $\rm M_\odot$ would be the main representative of a generation of massive stars, as suggested also by \cite{ww93}, , then a rather low C abundance should be"
The ESO Imaging Survey ts being carried out to help the selection of targets for the first year of operation of VLT.,The ESO Imaging Survey is being carried out to help the selection of targets for the first year of operation of VLT.
 This paper presents some examples of possible candidates of interest. giving special emphasis to stellar populations and quasars.," This paper presents some examples of possible candidates of interest, giving special emphasis to stellar populations and quasars."
 Using the area covered by the survey one ts able to find candidate WDs and red objects likely to be associated with very low mass stars or brown dwarts., Using the area covered by the survey one is able to find candidate WDs and red objects likely to be associated with very low mass stars or brown dwarfs.
 A preliminary list is also presented for quasars., A preliminary list is also presented for quasars.
" These lists and image postage stamps in all three passbands are also available in the ESO Science Archive server which allows the examination of the candidates (“http://www.eso.org/eis/"").", These lists and image postage stamps in all three passbands are also available in the ESO Science Archive server which allows the examination of the candidates (“http://www.eso.org/eis/”).
 Finding charts can also be easily extracted., Finding charts can also be easily extracted.
 Also available 1s the parent color sample from which these candidates have been defined., Also available is the parent color sample from which these candidates have been defined.
 It ts important to emphasize that in addition to providing these preliminary lists. the present work has been an essential part in understanding the characteristics of the color catalogs being produced and for the verification of their reliability.," It is important to emphasize that in addition to providing these preliminary lists, the present work has been an essential part in understanding the characteristics of the color catalogs being produced and for the verification of their reliability."
 Improvements in the sample selection are. certainly possible., Improvements in the sample selection are certainly possible.
 Since the data are publicly available. interested groups may refine the selection criteria and produce their own samples.," Since the data are publicly available, interested groups may refine the selection criteria and produce their own samples."
 The present results lead to samples that are of the order of 50 to 100 candidates each., The present results lead to samples that are of the order of 50 to 100 candidates each.
 The yield will only be defined by follow-up spectroscopic observations., The yield will only be defined by follow-up spectroscopic observations.
 Much larger samples will be available from the Pilot Survey to be carried out with the new wide-field camera (mecWIDE) on the 2.2 m telescope at La Silla., Much larger samples will be available from the Pilot Survey to be carried out with the new wide-field camera (mecWIDE) on the 2.2 m telescope at La Silla.
 The present exploratory work has been done on à relatively small sample with preliminary selection. criteria and by handling the data in a standard way., The present exploratory work has been done on a relatively small sample with preliminary selection criteria and by handling the data in a standard way.
 Nevertheless. it has already demonstrated the need for providing users with more information than possible with traditional catalogs. as emphasized by several other groups.," Nevertheless, it has already demonstrated the need for providing users with more information than possible with traditional catalogs, as emphasized by several other groups."
 The exercise points out the need for the development of an objectoriented database and tools to inspect the multi-dimensional space of magnitudes. colors and extraction parameters.," The exercise points out the need for the development of an object-oriented database and tools to inspect the multi-dimensional space of magnitudes, colors and extraction parameters."
 In addition. full exploration of the data also requires tools to facilitate the cross-identification of detected objects with available databases in other wavelengths and with spectral information. and to handle time-dependent information obtained in the course of deep surveys.," In addition, full exploration of the data also requires tools to facilitate the cross-identification of detected objects with available databases in other wavelengths and with spectral information, and to handle time-dependent information obtained in the course of deep surveys."
 The integration of EIS and the program being developed by the ESO Science Archive Group ts an essential step in the process of translating results from multicolor deep (co-added) imaging surveys into target lists for the VLT., The integration of EIS and the program being developed by the ESO Science Archive Group is an essential step in the process of translating results from multicolor deep (co-added) imaging surveys into target lists for the VLT.
 The Pilot Survey to be conducted on the 2.2m telescope early next year offers the ideal test case to define the basic science-driven requirements for data mining the associated database., The Pilot Survey to be conducted on the 2.2m telescope early next year offers the ideal test case to define the basic science-driven requirements for data mining the associated database.
 However. in order to take full advantage of the new opportunities in a timely fashion. as required to support VLT-science. a significant effort must be made well beyond what has been done for EIS.," However, in order to take full advantage of the new opportunities in a timely fashion, as required to support VLT-science, a significant effort must be made well beyond what has been done for EIS."
 As generally recognized. the coming of age of large. digital. multicolor imaging surveys creates new demands for nore efficient ways of extracting information.," As generally recognized, the coming of age of large, digital, multicolor imaging surveys creates new demands for more efficient ways of extracting information."
 The development of these tools and of efficient unsupervised pipelines is currently the major challenge for the optimal extraction of valuable scientific results., The development of these tools and of efficient unsupervised pipelines is currently the major challenge for the optimal extraction of valuable scientific results.
"the limiting radius, and the effective radius “measured” from the truncated profile (seeTrujillo,Graham&Caon2001,fortherel-evant expressions)...","the limiting radius, and the effective radius “measured” from the truncated profile \citep*[see][for the relevant expressions]{TGC01}."
 We thus obtained for each model the values of isophotal magnitude and mean effective surface brightness that would be measured from truncated profile., We thus obtained for each model the values of isophotal magnitude and mean effective surface brightness that would be measured from a truncated profile.
" We show the results ain Figurerefmueff.sferoides, , wherethedottedline f ollowstheisophotalma THM refmueff,eroides,eatier., te e brightngasrelatien, Sérrsicmodelst < "," We show the results in \\ref{mueff_esferoides}, where the dotted line follows the isophotal magnitude versus mean effective surface brightness relations for Sérrsic models truncated at isophotal radii corresponding to 26.0 mag $^{-2}$."
"While profile truncation always leads to a magnitude dimming and a lower measured reg, low n (i.e., fainter) galaxies are more strongly affected than galaxies with n>1."," While profile truncation always leads to a magnitude dimming and a lower measured $r_\mathrm{eff}$, low $n$ (i.e., fainter) galaxies are more strongly affected than galaxies with $n\ge 1$."
" This gives a curved relation in the observed magnitude vs. mean effective surface brightness plane, which should be a straight line for galaxies with the same effective radius."," This gives a curved relation in the observed magnitude vs. mean effective surface brightness plane, which should be a straight line for galaxies with the same effective radius."
" Then, the downturn of the relation for our dwarfs at faint galaxy magnitudes may be attributed to this effect, corresponding to our limiting isophote of about 26.0 magaarcsec?."," Then, the downturn of the relation for our dwarfs at faint galaxy magnitudes may be attributed to this effect, corresponding to our limiting isophote of about 26.0 $^{-2}$."
" The same departure towards fainter magnitudes of the dwarfs at the faint end of this relation, with respect to the general trend, is present in the compilation from different environments by DeRijckeetal.(2009)."," The same departure towards fainter magnitudes of the dwarfs at the faint end of this relation, with respect to the general trend, is present in the compilation from different environments by \citet{deRij09}."
". Both cE galaxies clearly depart from the locus of constant effective radius but, at first glance, in a different manner."," Both cE galaxies clearly depart from the locus of constant effective radius but, at first glance, in a different manner."
" 1110 seems to extend the break defined by the brightest galaxies towards fainter magnitudes, but 1192 is located with the bulk of early-type dwarf galaxies defining what could be their low limiting reg."," 110 seems to extend the break defined by the brightest galaxies towards fainter magnitudes, but 192 is located with the bulk of early-type dwarf galaxies defining what could be their low limiting $r_{\rm eff}$ ."
" If we calculate for their luminosities the corresponding (μοβ) on the locus of reg=1 kkpc, we obtain that they differ from the measured values in Ἀίμοα)=2.9 mag arcsec~? for FS901110, and A(Heg)=2.7 mag arcsec? for 1192."," If we calculate for their luminosities the corresponding $\langle\mu_{\rm eff}\rangle$ on the locus of $r_{\rm eff} = 1$ kpc, we obtain that they differ from the measured values in $\Delta\langle\mu_{\rm eff}\rangle=2.9$ mag $^{-2}$ for 110, and $\Delta\langle\mu_{\rm eff}\rangle=2.7$ mag $^{-2}$ for 192."
" Therefore both cE galaxies depart from the trend defined by early-type dwarf galaxies in a similar manner, defining what could be a photometric criterion to identify candidate cE galaxies."," Therefore both cE galaxies depart from the trend defined by early-type dwarf galaxies in a similar manner, defining what could be a photometric criterion to identify candidate cE galaxies."
" Alternatively, the location of the cEs with respect to the surface brightness-luminosity relation can be judged as consistent with a stripping scenario."," Alternatively, the location of the cEs with respect to the surface brightness-luminosity relation can be judged as consistent with a stripping scenario."
 The luminosity-effective radius diagram presented by Barazzaetal.(2009) in Abell 901/902 (their fig., The luminosity–effective radius diagram presented by \citet{Barazza09} in Abell 901/902 (their fig.
" 2a), shows that their galaxies scatter about a mean constant effective radius."," 2a), shows that their galaxies scatter about a mean constant effective radius."
 In ségnf dtd thegalaxieslocatedbelowthedashedlinehavetegtine," In \\ref{mueff_esferoides}, the galaxies located below the dashed line have $r_{\rm eff} < 1$ kpc and those found above the line, $r_{\rm eff} > 1$."
"a SAGE dwarfs in the central region of Antlia, either redder or bluer than the colour of the mean CMR, show similar effective radii, in agreement with Barazza et al."," We see that early-type dwarfs in the central region of Antlia, either redder or bluer than the colour of the mean CMR, show similar effective radii, in agreement with Barazza et al."
’s findings.,'s findings.
" In particular, red dwarfs (excluding the two cEs, 16 galaxies) display a mean effective radius (rog)=0.74 (rms 0.34) kpc, while blue dwarfs (33 systems), (reg)=0.79 (rms 0.30) kpc."," In particular, red dwarfs (excluding the two cEs, 16 galaxies) display a mean effective radius $\langle r_{\rm eff} \rangle = 0.74$ (rms 0.34) kpc, while blue dwarfs (33 systems), $\langle r_{\rm eff} \rangle = 0.79$ (rms 0.30) kpc."
" We have also plotted, with green squares, the data corresponding to the study of the early-type galaxy population in poor groups performed by Annibalietal.(2011)."," We have also plotted, with green squares, the data corresponding to the study of the early-type galaxy population in poor groups performed by \citet{An11}."
". The bright and faint early-type systems in these groups,follow the same luminosity—(e) relation as Antlia galaxies with a similar scatter."," The bright and faint early-type systems in these groups,follow the same $\langle\mu_{\rm eff}\rangle$ relation as Antlia galaxies with a similar scatter."
 In we show the location of our galaxy sample in the, In \\ref{posiciones} we show the location of our galaxy sample in the
Astrometry independently measures the first four of these. as well as Z.,"Astrometry independently measures the first four of these, as well as $I$."
 Astrometric observatious also involve six other parameters: the position and proper motion of the Calactic center on the sla. the distauce to the Galactic center. aud Q.," Astrometric observations also involve six other parameters: the position and proper motion of the Galactic center on the sky, the distance to the Galactic center, and $\Omega$."
 The mass of the black hole is not an independent parameter. since it is a fiction of P aud «a.," The mass of the black hole is not an independent parameter, since it is a function of $P$ and $a$."
 For our purposes. ouly Z from astrometry is essential.," For our purposes, only $I$ from astrometry is essential."
 Iu testing the EEP. while we shall argue that observation of the star over a short time around periceuter suffices for spectroscopy. recovery of the inclination via astrometiy can be done anywhere ou the orbit.," In testing the EEP, while we shall argue that observation of the star over a short time around pericenter suffices for spectroscopy, recovery of the inclination via astrometry can be done anywhere on the orbit."
 It is nuportaut to note vy and ν΄ need not refer to a single spectral line., It is important to note $\nu_0$ and $\nu$ need not refer to a single spectral line.
 The spectra of S stars (seee$.Alartiusetal.2008). contain iuultiple features.," The spectra of S stars \citep[see e.g.,][]{martins}
 contain multiple features."
 Most are early-type stars with II aud Ie features. while about are late-type stars with molecular aud metal bauds/lines and little or no II or He.," Most are early-type stars with H and He features, while about are late-type stars with molecular and metal bands/lines and little or no H or He."
" Ποσο, S-star spectra could. in principle. test the equivalence principle for multiple atomic processes."," Hence, S-star spectra could, in principle, test the equivalence principle for multiple atomic processes."
 If the stellar atinosphere does not change appreciably over au orbit. au observed spectrum can be cross-correlated on a logaxithlinic waveleneth scale with a spectruii observed at some other epoch. aud the cross-correlatioun peak would directly give the redshift lu(ngf/r) with my an unknown coustaut.," If the stellar atmosphere does not change appreciably over an orbit, an observed spectrum can be cross-correlated on a logarithmic wavelength scale with a spectrum observed at some other epoch, and the cross-correlation peak would directly give the redshift $\ln(\nu_0/\nu)$ with $\nu_0$ an unknown constant."
 If different atomic/molecular species behave differently iu a frecly-falling frame. the shape of the cross-correlation curve would chanec.," If different atomic/molecular species behave differently in a freely-falling frame, the shape of the cross-correlation curve would change."
 Alternatively. inultiple spectral features could be fitted simultaucouslv with variable redshift.," Alternatively, multiple spectral features could be fitted simultaneously with variable redshift."
 We do not. however. attempt to model the observable spectra explicitly in this paper.," We do not, however, attempt to model the observable spectra explicitly in this paper."
 We now simulate the recovery of à as follows., We now simulate the recovery of $\alpha$ as follows.
 We generate 10 mock redshift data points of $2 taken over two nouths at periceuter. plus four additional data points. at cl.c2xr around periccuter.," We generate 10 mock redshift data points of S2 taken over two months at pericenter, plus four additional data points, at $\pm 1,\pm2$ yr around pericenter."
 The data are generated with a=2. aud orbital parameters taken from Callessenetal.(2009a).," The data are generated with $\alpha = 2$, and orbital parameters taken from \cite{gillessen}."
. To them we add gaussian rvaudom noise at a dispersion of 1θκι . and then fit via the seven parameters.," To them we add gaussian random noise at a dispersion of $10\kms$ , and then fit via the seven parameters."
 We then assume { has beeu measured by astromoetrv auc use (8)) to recover o., We then assume $I$ has been measured by astrometry and use \ref{strategy}) ) to recover $\alpha$.
 Figure (13) shows an example for a few mock data realizations at a fixed accuracy. aud figure (2)) shows the dependency of the recovered value of alpha with the data accuracy.," Figure \ref{fig:getting_alpha}) ) shows an example for a few mock data realizations at a fixed accuracy, and figure \ref{fig:recovering_alpha}) ) shows the dependency of the recovered value of alpha with the data accuracy."
 Testing the equivalence principle using a combination of spectroscopy and astrometry seenis possible in the near future., Testing the equivalence principle using a combination of spectroscopy and astrometry seems possible in the near future.
 Iu comparing the spread iu ARAg from mock data to the recovered value for J from real astrometric data (illustrated in Fig. 1)).," In comparing the spread in $A_C^2/A_R$ from mock data to the recovered value for $I$ from real astrometric data (illustrated in Fig. \ref{fig:getting_alpha}) ),"
 iu testingthe Equivalence Principle using S2. the current accuracy," in testingthe Equivalence Principle using S2, the current accuracy"
scatter in the resulting values of Tig provides an estimate of the observational uncertainty in the parameter. to whicji we add in quadrature the estimate of svstenatic CLrOLr described. above.,"scatter in the resulting values of $T_{\rm eff}$ provides an estimate of the observational uncertainty in the parameter, to which we add in quadrature the estimate of systematic error described above."
 The resulting uucertaiuties nre Listec in Table 1., The resulting uncertainties are listed in Table 1.
 These uncertainties should be courred to the uncertainties in T.y (aso listed in Table 1). whicji are computed using the uncertainty in the star's properties aud the palret’s orbit.," These uncertainties should be compared to the uncertainties in $T_{\varepsilon=0}$ (also listed in Table 1), which are computed using the uncertainty in the star's properties and the planet's orbit."
 There are two πιοσα] issues with the lnear iuterxlation tempcrature estimation technique., There are two practical issues with the linear interpolation temperature estimation technique.
" Iu ποιο cases. onlv upper τν have been obtaimec. therefore oue could set ο=0, with the appropriate 1-sigma uncertaiuty."," In some cases, only upper limits have been obtained, therefore one could set $\psi=0$, with the appropriate 1-sigma uncertainty."
 But this approach leads to huge uncertainties dn Tog for planets with a secouday eclipse upper-lanit near their blackbody peak., But this approach leads to huge uncertainties in $T_{\rm eff}$ for planets with a secondary eclipse upper-limit near their blackbody peak.
 Iustead of “punishing” these planets. we opt to uot use wpper-luts (though for completeness we include them in Table 1).," Instead of “punishing” these planets, we opt to not use upper-limits (though for completeness we include them in Table 1)."
" Secondly. whem mutiple measurements of an eclipse depth have been pullished for a given wavebanud. we use the most recent observation. iudicated with a superscript ""c7 in Table 1."," Secondly, when multiple measurements of an eclipse depth have been published for a given waveband, we use the most recent observation, indicated with a superscript ” in Table 1."
 In a] cases these observations either explicitly agree with heir older counterpart. or agree with the re-analvzed oder data.," In all cases these observations either explicitly agree with their older counterpart, or agree with the re-analyzed older data."
 For cach plauct. we use thermal observations (essentially those in tie J. IL. Ky. and lauds) to estimate the plauet?s effective day-side temperature. Ty. aud when plase variations are available Ty.," For each planet, we use thermal observations (essentially those in the J, H, $_{s}$, and bands) to estimate the planet's effective day-side temperature, $T_{\rm d}$, and —when phase variations are available— $T_{\rm n}$."
 These ναues are lised in Table 1., These values are listed in Table 1.
 Iun five cases (CoRoT-1». ColoT-2b. ΠΑΤΕ». TD 209Lash. TrES-2h). secondary eclipses and/or phase variations lave con obtained at optic:d svaveleugths.," In five cases (CoRoT-1b, CoRoT-2b, HAT-P-7b, HD 209458b, TrES-2b), secondary eclipses and/or phase variations have been obtained at optical wavelengths."
 Such observations iwe the potential to directly constrain the albedo of τοσο planets., Such observations have the potential to directly constrain the albedo of these planets.
 One approach is o adopt the T4 from jerinal observations alxd calculate the expected coutrast ratio at optical wavekneths. under the assumption of dackhody cuission («οalsoINippiug&Bakos2010).," One approach is to adopt the $T_{\rm d}$ from thermal observations and calculate the expected contrast ratio at optical wavelengths, under the assumption of blackbody emission \citep[see also][]{Kipping_2010}."
. Tusofar as the observeL eclipse depths are deeper than us calculated depth. one can iuvoke the contribution ft reflected liebt. aud «onmpute a geometric albedo. Ay.," Insofar as the observed eclipse depths are deeper than this calculated depth, one can invoke the contribution of reflected light and compute a geometric albedo, $A_{g}$."
 If oue treats the plux toas a muiform Lambert sphere. 16 geometric albedo is related to the spherical albedo at iat waveleneth by Ay=2d.," If one treats the planet as a uniform Lambert sphere, the geometric albedo is related to the spherical albedo at that wavelength by $A_{\lambda} = \frac{3}{2}A_{g}$."
 These values are listed iu Table 1., These values are listed in Table 1.
 But reflected ποτ is not the only explanation for al unexpecedly deep optical eclipse., But reflected light is not the only explanation for an unexpectedly deep optical eclipse.
 Alternatively. the cluissivity of the plauets may simply be greater at optical waveloneths than at mid-IR wavelengths. in agrecineut with realistic spectral models of hot Jupiters. which predict bightuess teu]veratures ercater than Z;g on the Wien tail (sec. for ex:uuple. the Fortney et al.," Alternatively, the emissivity of the planets may simply be greater at optical wavelengths than at mid-IR wavelengths, in agreement with realistic spectral models of hot Jupiters, which predict brightness temperatures greater than $T_{\rm eff}$ on the Wien tail (see, for example, the Fortney et al."
 model shown in Figure 2.. which does not include reflected light).," model shown in Figure \ref{tres3_2pi_TiO.flx}, which does not include reflected light)."
 Note that this increase in cuussivity should occur regardless of whether or not the planct MUS a stratosphere: by definition. the depth at which the ortical thermal emission is enütted is the depth at which incident starlight is absorbed. which will necessarily be a lot laver assunune the incident stellar spectrum peaks 1i the optical.," Note that this increase in emissivity should occur regardless of whether or not the planet has a stratosphere: by definition, the depth at which the optical thermal emission is emitted is the depth at which incident starlight is absorbed, which will necessarily be a hot layer —assuming the incident stellar spectrum peaks in the optical."
 Determining the allolo directly (Ge: by observiug reflected light) cam be difficult for short period. plaucts. because there is no way to distinguish between reflected and re-racliated photous.," Determining the albedo directly (ie: by observing reflected light) can be difficult for short period planets, because there is no way to distinguish between reflected and re-radiated photons."
 The blackbody peaks of the star and planet often differ by less than a micron., The blackbody peaks of the star and planet often differ by less than a micron.
 Therefore. πικο Solar System planets. these worlds do not exhibit a ninmiun in their spectral energy distribution between the reflected and thermal peaks.," Therefore, unlike Solar System planets, these worlds do not exhibit a minimum in their spectral energy distribution between the reflected and thermal peaks."
 The hottest ancl therefore most ambiguous case of the five transiting planets with optical constraints is ILAT-P-7b., The hottest —and therefore most ambiguous case— of the five transiting planets with optical constraints is HAT-P-7b.
 If one takes the mid-IR eclipse depths at face value. the planet has a cdlav-side effective teuperature of ~2000 In. When combined with the Ixeer observatious. one computes an albedo «ft ereater than," If one takes the mid-IR eclipse depths at face value, the planet has a day-side effective temperature of $\sim 2000$ K. When combined with the Kepler observations, one computes an albedo of greater than."
 The large day-night auplitude soen in the Ihepler bandpass is then. simply due to the act that the planet's wielt-side reflects no starlielht. and the cool dax-side can be attributed to high Ap aud/or z.," The large day-night amplitude seen in the Kepler bandpass is then simply due to the fact that the planet's night-side reflects no starlight, and the cool day-side can be attributed to high $A_{B}$ and/or $\varepsilon$."
 If. on the other haud. oue takes the optical flux to be eitirely therual iu origin (Ay=0). the dav-side effective teurperature is 2800 Is. This is very close to tha planct’s T.y. leaving very little power left or tιο night-ide. agaiji explaining the huge day-night contrast observed by EKepler.," If, on the other hand, one takes the optical flux to be entirely thermal in origin $A_{\lambda}=0$ ), the day-side effective temperature is $\sim 2800$ K. This is very close to that planet's $T_{\varepsilon=0}$, leaving very little power left for the night-side, again explaining the large day-night contrast observed by Kepler."
" The truth probably lies somewhere )etwoeen these two extremes. but in any case his degeneracy will be neatly broken with observations: the two scenarios outlined above will lead ο πια]. ane laree thermal phase variations. respectively,"," The truth probably lies somewhere between these two extremes, but in any case this degeneracy will be neatly broken with observations: the two scenarios outlined above will lead to small and large thermal phase variations, respectively."
 It is telling hat the only optical measurement in Table 1 hat is uuainiouslv cousicdered to coustrain albedo aud not thertmal cimission is the MOST observatious of IID 20915851» (Roweetal.2008).. the coolest of the five ransitine panets with optical photometric coustraiuts.," It is telling that the only optical measurement in Table 1 that is unanimously considered to constrain albedo ---and not thermal emission— is the MOST observations of HD 209458b \citep{Rowe_2008}, the coolest of the five transiting planets with optical photometric constraints."
 The bott1u line is that extracting a coustraimt on reflected lielit frou optical measurements of hot Jupiters is best cdoje with a detailed spectral iocel., The bottom line is that extracting a constraint on reflected light from optical measurements of hot Jupiters is best done with a detailed spectral model.
 But evel owien reflected Light cau be directly. coustraimed. converting this constraint on ly into a constraint on Ap also requires detailed knowledge of both t1ο star and the planets spectral energy distributions. making for a modeldeperardent exercise.," But even when reflected light can be directly constrained, converting this constraint on $A_{\lambda}$ into a constraint on $A_{B}$ also requires detailed knowledge of both the star and the planet's spectral energy distributions, making for a model-dependent exercise."
 Setting aside optical eclipses aud direct 1icasuremoenuts of albedo. we quay use the rich uear- aud mua-IR data fo consrain the Bond albedo and redistributiono cficieucy of short-period eiut plancts.," Setting aside optical eclipses and direct measurements of albedo, we may use the rich near- and mid-IR data to constrain the Bond albedo and redistribution efficiency of short-period giant planets."
 We define a 20« exid in Ap and os and use Equations | 5 to calculate thi' normalized day-side aud night-side effective temperatures. Z4/70 aud TiTog. at each grid poiit ἐν).," We define a $20\times20$ grid in $A_{B}$ and $\varepsilon$ and use Equations 4 5 to calculate the normalized day-side and night-side effective temperatures, $T_{\rm d}/T_{0}$ and $T_{\rm n}/T_{0}$, at each grid point, $(i,j)$."
 For each plauct. we have an observational/ estimate of the cdav-side effective temperature. and in three cases we also have an estimate of the might-side effective teniperature (as well as associated uncertainties).," For each planet, we have an observational estimate of the day-side effective temperature, and in three cases we also have an estimate of the night-side effective temperature (as well as associated uncertainties)."
 We first verify whether or rot the observations are consistent with a single Ap aux e., We first verify whether or not the observations are consistent with a single $A_{B}$ and $\varepsilon$.
" To evaluate this ""null hypothesis. we compute the usnal 42=$5214dnodeldata)?P/errorT at cach evid point."," To evaluate this “null hypothesis”, we compute the usual $\chi^{2} = \sum_{i=1}^{24} ({\rm model}-{\rm data})^{2}/{\rm error}^{2}$ at each grid point."
 We use onlv the estimates of cav-side and (swren available) uieht-side effective. teluperatures to calculate the X7. e¢ivine us η. degrees of freedom.," We use only the estimates of day-side and (when available) night-side effective temperatures to calculate the $\chi^{2}$, giving us 27-2=25 degrees of freedom."
 The “best-fit” has 4= (reduced yrD=. 5.3). sO he current observations- y.ronglv ruk yout a sinele Boud albedo aud redistribution ficiency for all 21 plaucts.," The “best-fit” has $\chi^{2}=132$ (reduced $\chi^{2}=5.3$ ), so the current observations strongly rule out a single Bond albedo and redistribution efficiency for all 24 planets."
 For 21 of the 21 planets considered here. we construct a two-dimensional distribution function for cach plauet," For 21 of the 24 planets considered here, we construct a two-dimensional distribution function for each planet"
"with and Then. as X can be expressed in terms of a in the form the relation between X» ancl We, is Now. by using eq. (12)).","with and Then, as $\Sigma$ can be expressed in terms of $\eta$ in the form the relation between $\Sigma_{2}$ and $\Psi_{2r}$ is Now, by using eq. \ref{metkal2}) ),"
 we obtain and the result in the original frame is Obviously. this DF is the same as (34)) when the 17)) ," we obtain and the result in the original frame is Obviously, this DF is the same as \ref{DFm2A1}) ) when the condition \ref{omega1}) ) is satisfied."
DE ," Finally, by eq. \ref{DFgen1}) ),"
with maximum entropy is given by We can see the behavior of these DEs in figures 4. and 5.., the resulting DF with maximum entropy is given by We can see the behavior of these DFs in figures \ref{fig:DFm2A} and \ref{fig:DFm2B}.
 In figures 4((a) and 4((b) we show the contours of fo for the two rotational states given by (29))., In figures \ref{fig:DFm2A}( (a) and \ref{fig:DFm2A}( (b) we show the contours of $f_{2}^{(A)}$ for the two rotational states given by \ref{omega1}) ).
 Such DE. is maximum over a narrow diagonal strep. near to the zero probability region and. similarly to the case showed in figure 3.. the probability decreases as ¢ increases.," Such DF is maximum over a narrow diagonal strep, near to the zero probability region and, similarly to the case showed in figure \ref{fig:DFm1B}, , the probability decreases as $\varepsilon$ increases."
 Stellar svstenis characterized by different € ave shown in figures 5((a) and 5((b). where we plot the contours of By (this equals to foalli when © is∢⊀ given by (29))).," Stellar systems characterized by different $\Omega$ are shown in figures \ref{fig:DFm2B}( (a) and \ref{fig:DFm2B}( (b), where we plot the contours of $f_{2}^{(B)}$ (this equals to $f_{2}^{(A)}$ when $\Omega$ is given by \ref{omega1}) ))."
 In this. case the DE.. varies. moreops rapidlv as © decreases. originating narrower banIs.," In this case the DF varies more rapidly as $\Omega$ decreases, originating narrower bands."
" un ⋅ ⋅∖↵↲↴ ∐↥∢⋅↓⋅∢⋅⊔↓⋜⊔⊔↓⊔⋏∙≟∐⋏∙≟⊔↓⋅⋖⋅⊳∖⊳∖↓↕∪∖∖⊽⇂↓↕∢⊾≼∼∪⊔⋯⊔↓⋅⊳∖∪⇂⇠∕⊐⋜⋯∠⇂ ⇂⋅∪↓⋅∠⇂⊀↓∐⋅∢⊾↓⋅⋖⋅⊔↿∖⇁⋜↧↓⋯⋅⊳∖∪⇂⋅↿↓↕∢⊾↓≻⋜⊔⋅⋜⋯↓⋖⋅↿⋖⋅↓⋅⋂⊳⊳∖↓↕∪∖∖⋰↓⊔⋏∙≟⋜↧≻↕↓↥↓↕↓⋜↧↓⋅ behavior: than f,pHn"," The remaining figures show the contours of $\tilde{f}_{2}^{(A)}$ and $\tilde{f}_{2}^{(B)}$ for different values of the parameter $\alpha$, showing a similar behavior than $\tilde{f}_{1}^{(B)}$."
" Once again. if we want to use Ixalnajs method. it is necessary to derive the relation X5(V5,) and. according to (42)). it is posible if we can invert the equation of the relative potencial. which in this case is given by in order to obtain g(V3,)."," Once again, if we want to use Kalnajs method, it is necessary to derive the relation $\Sigma_3(\Psi_{3r})$ and, according to \ref{denseta}) ), it is posible if we can invert the equation of the relative potencial, which in this case is given by in order to obtain $\eta(\Psi_{3r})$."
 To solve it. we must deal with a cubic equation and with its non-trivial solutions: fortunately. we still have O as a free parameter.," To solve it, we must deal with a cubic equation and with its non-trivial solutions; fortunately, we still have $\Omega$ as a free parameter."
 One can casily note that it is possible to write (47)) as with Now. by replacing (42)) into (48)). we obtain ," One can easily note that it is possible to write \ref{psi3}) ) as with and $\Omega$ has be chosen as Now, by replacing \ref{denseta}) ) into \ref{psi32}) ), we obtain and, by using eq. \ref{metkal2}) ),"
Coming back to the original frame. the result is whilethe respective DE with maximum entropy is," Coming back to the original frame, the result is whilethe respective DF with maximum entropy is"
bv 2.,by \citet{2000MNRAS.315..543H}.
 To calculate the instantaneous rates of secular evolution of the orbital clements. we follow the evohitiou of the orbital senui-nuajor axis and eccentricity of eccentric. effective Roche lobe overflowing binarics for 100 consecutive orbits.," To calculate the instantaneous rates of secular evolution of the orbital elements, we follow the evolution of the orbital semi-major axis and eccentricity of eccentric, effective Roche lobe overflowing binaries for 100 consecutive orbits."
 During this evolution. trausitions may take place from direct impact accretion to selfaccretion or vice versa.," During this evolution, transitions may take place from direct impact accretion to self-accretion or vice versa."
" Svstenis for which this happens within LOO orbits from the start of mass overflow are confined to a fairvy restricted reeion of the parameter space and are shown iu black iu Figures 5- ὃν,", Systems for which this happens within 100 orbits from the start of mass overflow are confined to a fairly restricted region of the parameter space and are shown in black in Figures \ref{fig-dadtDI}- \ref{fig-dedtSA}.
 Iu addition. for simall initial mass ratios q;=0.0L0.02. the radius of star 2 is so large relative to the size of the orbit that the binary becomes a coutact binary rather than a senu-detached binary.," In addition, for small initial mass ratios $q_i \la 0.01-0.02$, the radius of star 2 is so large relative to the size of the orbit that the binary becomes a contact binary rather than a semi-detached binary."
 These binarics are also left out of consideration in Figures 5- 8.., These binaries are also left out of consideration in Figures \ref{fig-dadtDI}- \ref{fig-dedtSA}.
 For binaries that do not transition between direct inipact and sclbaccretion aud that do not form contact binaries. timescales of orbital evolution are calculated by averaging the changes in the orbital elements over one orbital period.," For binaries that do not transition between direct impact and self-accretion and that do not form contact binaries, timescales of orbital evolution are calculated by averaging the changes in the orbital elements over one orbital period."
parameter lower than ~100-200kpe. the contribution from. this halo will be negligible.,"parameter lower than $\sim$ 100-200kpc, the contribution from this halo will be negligible."
 We have in this work determined the O VIE column clensity of hot halo gas along various lines-of-5ight in three simulated cise galaxies., We have in this work determined the O VII column density of hot halo gas along various lines-of-sight in three simulated disc galaxies.
 In. order to emulate. observations »erformed. at the solar position in the Milky Way. we have. in each galaxy. chosen a position in the midplane of disc. ocated S kpe from the centre of the galaxy.," In order to emulate observations performed at the solar position in the Milky Way, we have, in each galaxy, chosen a position in the midplane of disc, located 8 kpc from the centre of the galaxy."
 From. this »osition we have drawn lines-ol-siehts cmiulating all sky COVELARC., From this position we have drawn lines-of-sights emulating all sky coverage.
 We have tested. that the results obtained. do not in any significant way depend. on where. along the 2=8 kpe midplane circle. the observer is assumed to be located.," We have tested that the results obtained do not in any significant way depend on where, along the $R=8$ kpc midplane circle, the observer is assumed to be located."
 Aloreover. we have for galaxy W838 tested that the results obtained do not in any significant wav epencd on. the numerical resolution of the galaxy formation simulation.," Moreover, we have for galaxy K33 tested that the results obtained do not in any significant way depend on the numerical resolution of the galaxy formation simulation."
 For the two Alilky Way sized. galaxies. of V;=207 and 245 km/sec. respectively. we find median halo gas O VIL column densities of 1.5-2.5:107* 7. with a dispersion in loe(N(O VIL) of about 0.2.," For the two Milky Way sized galaxies, of $V_c=207$ and 245 km/sec, respectively, we find median halo gas O VII column densities of $\cdot10^{14}$ $^{-2}$ , with a dispersion in $N$ (O VII)) of about 0.2."
 For the somewhat smaller disc galaxy 1x33. of V;=180 km/s. we find à median halo gas O VIL column density of 3-104? 7. also with a dispersion in log(O VID) of about 0.2.," For the somewhat smaller disc galaxy K33, of $V_c=180$ km/s, we find a median halo gas O VII column density of $\cdot10^{13}$ $^{-2}$, also with a dispersion in $N$ (O VII)) of about 0.2."
 The lower value for this galaxy is primarilyN due to the somewhat lower (virial) temperature of the hot gas (by about a factor of two). which. cf," The lower value for this galaxy is primarily due to the somewhat lower (virial) temperature of the hot gas (by about a factor of two), which, cf."
 Fig. L..," Fig. \ref{fractions},"
" leads to a significant reduction of the number of oxvgen ions in the sixth ionization stage for the relevant density range. ng~10"".—H7 "," leads to a significant reduction of the number of oxygen ions in the sixth ionization stage for the relevant density range, $n_H \sim 10^{-6}-10^{-3.5}$ $^{-3}$."
The main result of the paper is hence that for the two AMlilky Way sized. galaxies. the median. predicted: halo O VIE column density lies about a factor of 20 below the observational; upper limit Tof 5-10715 cm2 reported by. ? (anc is comparable to the upper limits of logN14.2.Leas set by 2. but these limits are based on halo sight- in general. passing far away from the galactic centres a Comparison is less straightforward see also. below).," The main result of the paper is hence that for the two Milky Way sized galaxies, the median predicted halo O VII column density lies about a factor of 20 below the observational upper limit of $5\cdot10^{15}$ $^{-2}$ reported by \cite{yao2008} (and is comparable to the upper limits of $log(N(OVII))<14.2-14.8$ set by \citet{yao2010}, but these limits are based on halo sight-lines, in general, passing far away from the galactic centres a comparison is less straightforward — see also below)."
 Moreover. not a single line-of-sight was found in any of the ealaxies with a halo O VII column density exceeding the ? limit.," Moreover, not a single line-of-sight was found in any of the galaxies with a halo O VII column density exceeding the \cite{yao2008} limit."
 When the dise gas. as well as gas in satellites: aud LIL clouds. is not excluded in the O VIE column density estimates. the median V(O VIL) increases by about a factor of two.," When the disc gas, as well as gas in satellites and HI clouds, is not excluded in the O VII column density estimates, the median $N$ (O VII) increases by about a factor of two."
 Moreover. the N(O VIL) distributions display. tails towards significantly larger values with a few lines-of-sight exceeding the ?/— limit this highlights the importance of excluding “contamination” from the disc and other components. as discussed by the same authors.," Moreover, the $N$ (O VII) distributions display tails towards significantly larger values with a few lines-of-sight exceeding the \cite{yao2008} limit — this highlights the importance of excluding “contamination” from the disc and other components, as discussed by the same authors."
 Lt also strongly suggests that the routinely. reported. ionic column densities of NCOV1)~Loom 7 at zero redshift originate in gas located near or inside the galactic disc. while the extended: gaseous. corona has a much lower contribution.," It also strongly suggests that the routinely reported ionic column densities of $N(O VII)\sim 10^{16}$ $^{-2}$ at zero redshift originate in gas located near or inside the galactic disc, while the extended gaseous corona has a much lower contribution."
 The largest values of ΑΟ VID) along a few lines-of-ight are mainly caused by either hot. super-nova driven bubbles in the disc gas or (in the case of N33) an outer. partly photo- warp. originating from gas stripped olf a previously accreted satellite.," The largest values of $N$ (O VII) along a few lines-of-sight are mainly caused by either hot, super-nova driven bubbles in the disc gas or (in the case of K33) an outer, partly photo-ionized warp, originating from gas stripped off a previously accreted satellite."
 To test the sensitivity. of our results on the assumed UVB and (simplified) radiative transfer scheme. we repeated he calculations assuming no UVB.," To test the sensitivity of our results on the assumed UVB and (simplified) radiative transfer scheme, we repeated the calculations assuming no UVB."
 For the two Milky Wav like galaxies. this loads to mareinally larger. median ΑΟ VID) values.," For the two Milky Way like galaxies, this leads to marginally larger median $N$ (O VII) values."
 The reason for this is that at the (virial) emperatures of the halo gas. O VIE is the most abundant oxvgen state. and with the UVB switched on. some of the O VILE ions are photo-ionized to (mainlv) the O VILL stage. owering the population of O VIL ions.," The reason for this is that at the (virial) temperatures of the halo gas, O VII is the most abundant oxygen state, and with the UVB switched on, some of the O VII ions are photo-ionized to (mainly) the O VIII stage, lowering the population of O VII ions."
 For the lower mass ealaxy W33. on the other hand. the cllect of the UVB is o boost the O VIE ion population.," For the lower mass galaxy K33, on the other hand, the effect of the UVB is to boost the O VII ion population."
 This is confirmed. by calculations (not. presented. in this paper) of the O VI and O VILE column densities for the same lines of sight., This is confirmed by calculations (not presented in this paper) of the O VI and O VIII column densities for the same lines of sight.
" Finally, we have tried το quantify the effect. a neighbouring galactic halo might have on the O VIL column density for a random line of sight."," Finally, we have tried to quantify the effect a neighbouring galactic halo might have on the O VII column density for a random line of sight."
 “Phe probability of that happening and the relative elect this might have on the fina result depends. of course. on the sizes of the two galaxies anc on the distance between them.," The probability of that happening and the relative effect this might have on the final result depends, of course, on the sizes of the two galaxies and on the distance between them."
 In a simple caleulation. we have randomly chosen the starting and ending coordinates of 10000 Lines of sight outside a certain halo and calculate their O VIL column densities.," In a simple calculation, we have randomly chosen the starting and ending coordinates of 10000 lines of sight outside a certain halo and calculated their O VII column densities."
 We find that the contribution is very small unless the impact parameter of the line of sight to the centre of the galaxy is lower than 100-200kpe., We find that the contribution is very small unless the impact parameter of the line of sight to the centre of the galaxy is lower than 100-200kpc.
 Including the disc gas and satellites in. this case. does not alter the results. presented. above unless the. impac parameter is very small (smaller than 50kpe)., Including the disc gas and satellites in this case does not alter the results presented above unless the impact parameter is very small (smaller than 50kpc).
 This is in agreement with what ? find for their line of sight. passing closest to M31. at a distance of 380kpc. giving no substantial contribution to the absorption.," This is in agreement with what \citet{bregmanlloyd07} find for their line of sight passing closest to M31, at a distance of 380kpc, giving no substantial contribution to the absorption."
 Considering this result. possible contamination to the lines of sight that probe the Milkv. Way halo could. likely only come from M31. (more. distant. galaxies would have their O VIL line redshifted. so it would be relatively casy to distinguish their halo gas contribution [rom the one coming [rom local gas: this is beyond the scope of this paper. and will be the topic of a forthcoming paper see also below).," Considering this result, possible contamination to the lines of sight that probe the Milky Way halo could likely only come from M31 (more distant galaxies would have their O VII line redshifted, so it would be relatively easy to distinguish their halo gas contribution from the one coming from local gas; this is beyond the scope of this paper, and will be the topic of a forthcoming paper — see also below)."
 ΑΙΟ1 is located at a distance of approximately TOOkpe from our galaxy. which would cause it to contribute to the O VII column density. with more than 1Ottem 2 or only about 0.5% of the sky area (56τς LOOkpe see Fig. 6)).," M31 is located at a distance of approximately 700kpc from our galaxy, which would cause it to contribute to the O VII column density with more than $10^{14}$ $^{-2}$ for only about $0.5\%$ of the sky area $b\la 100$ kpc — see Fig. \ref{monte_carlo}) )."
 Excluding bx 200kpe would reduce the M31 contribution to less than about 210 7. and still only exelude about of the sky area.," Excluding $b\le 200$ kpc would reduce the M31 contribution to less than about $2\times10^{13}$ $^{-2}$, and still only exclude about of the sky area."
 As mentioned above. it will be the topic of a forthcoming paper to investigate the contribution from the haloes of other. more distant. galaxies.," As mentioned above, it will be the topic of a forthcoming paper to investigate the contribution from the haloes of other, more distant galaxies."
 This studywill be based on the proper statistical descriptors at the large-scale ealaxy distribution., This studywill be based on the proper statistical descriptors at the large-scale galaxy distribution.
 In conclusion. the present. observational upper limit is perfectly consistent with the results of. state-of-the- galaxy formation models. based on fully cosmological," In conclusion, the present observational upper limit is perfectly consistent with the results of state-of-the-art galaxy formation models, based on fully cosmological"
"the shock velocity. and related to the outflow age by e;=Ry/t. ancl ος is the ambient density. and related to the ambient number density by the mass of molecular hydrogen (p;=qumgn,).","the shock velocity, and related to the outflow age by $v_s=R_s/t$, and $\rho_o$ is the ambient density, and related to the ambient number density by the mass of molecular hydrogen $\rho_o=\mu m_H n_o$ )."
 While much of this wind luminosity goes into accelerating the ambient medium. some of it is also transferred into thermal energv.," While much of this wind luminosity goes into accelerating the ambient medium, some of it is also transferred into thermal energy."
" From Basuetal.(1999).. the thermal energy can be expressed as Fy,=(5/11)£,/. or. eiven the value for / above. Ly,=(5/11).v."," From \citet{Basu99}, the thermal energy can be expressed as $E_{\rm th}=(5/11)L_o t$, or, given the value for $t$ above, $E_{\rm th}=(5/11)L_o R_s/v_s$."
 Both the calculated. wind luminosity and thermal energv required to power (hese wind driven shocks awe listed in Table 1.., Both the calculated wind luminosity and thermal energy required to power these wind driven shocks are listed in Table \ref{tab:sio_prop}.
 These thermal energies are of approximately (he same order of magnitude as the kinetic energies calculated for the CO outflows in à number of massive star forming regions (seeforinstanceWuοἱal.2004:Klaassen&Wilson2007b):: similarly the wind luminosities are comparable to the Iuminosites of their HII regions Wood&Churchwell 19359).," These thermal energies are of approximately the same order of magnitude as the kinetic energies calculated for the CO outflows in a number of massive star forming regions \citep[see for instance][]{Wu04,KW07b}; similarly the wind luminosities are comparable to the luminosities of their HII regions \citep[see for instance][]{WC89}."
. Many authors suggest (hat an asvimanmetrie self absorbed line profile of an optically thick line (racer in which (he blue emission peak is brighter than the red. and the optically thin tracer has a single line peak. can be indicative of infall G.e.Mlardonesetal.1997;Gregersen1997:Fulleretal. 2005).," Many authors suggest that an asymmetric self absorbed line profile of an optically thick line tracer in which the blue emission peak is brighter than the red, and the optically thin tracer has a single line peak, can be indicative of infall \citep[i.e.][]{Mardones97,Gregersen97,Fuller05}."
. Herve. our optically thick line is — (J—4-2) ancl the optically thin isotopologue is IP — (J24-3).," Here, our optically thick line is $^+$ (J=4-3) and the optically thin isotopologue is $^{13}$ $^+$ (J=4-3)."
 From Paper 1. we expected to observe infall signatures in GIO.47 and CG19.61.," From Paper 1, we expected to observe infall signatures in G10.47 and G19.61."
 Infall is detected towards these (wo sources. as well as towards G20.08 [rom our original study.," Infall is detected towards these two sources, as well as towards G20.08 from our original study."
 In our single pointing observations. G20.08 was shown to have a double peaked line profile in both and HECO . which was suggested to be due to two overlapping sources.," In our single pointing observations, G20.08 was shown to have a double peaked line profile in both $^+$ and $^{13}$ $^+$, which was suggested to be due to two overlapping sources."
 However. in the more extended map. we see that IICO — becomes single peaked. suggesting that perhaps it is optically Chick towards the center of the source and that mapping is required to resolve the ambiguity with respect to the chance super-position of line of sieht. clouds and self absorption of multiple isotopologues.," However, in the more extended map, we see that $^{13}$ $^+$ becomes single peaked, suggesting that perhaps it is optically thick towards the center of the source and that mapping is required to resolve the ambiguity with respect to the chance super-position of line of sight clouds and self absorption of multiple isotopologues."
 G10.6 was not in our original sample. but was added because it was known to have small scale infall motions.," G10.6 was not in our original sample, but was added because it was known to have small scale infall motions."
 It too is seen to have a large scale infall signature., It too is seen to have a large scale infall signature.
 In Paper 1. we suggested that beam dilution may have been a contributing factor as to why we did not detect infall in a number of sources.," In Paper 1, we suggested that beam dilution may have been a contributing factor as to why we did not detect infall in a number of sources."
 That we have detected extended infall in (wo distant ( 6 kpe) sources in this study suggests that if beam dilution of the signal is a problem. it only affects in(rinsically smaller sources. aud not intrinsically more distant ones. since our unresolved detections are for 19.61 and G20.08 at 4.5 and 4.1 kpe.," That we have detected extended infall in two distant $\sim$ 6 kpc) sources in this study suggests that if beam dilution of the signal is a problem, it only affects intrinsically smaller sources, and not intrinsically more distant ones, since our unresolved detections are for G19.61 and G20.08 at 4.5 and 4.1 kpc."
 Infall velocities were calculated for each self absorbed | spectrum towards G10.47.," Infall velocities were calculated for each self absorbed $^+$ spectrum towards G10.47,"
abundance profile in run Dl.,abundance profile in run D1.
 Figure 8 shows radial profiles of emission-weighted spherically averaged metallicity Z at various time epochs in this simulation., Figure \ref{plot8} shows radial profiles of emission-weighted spherically averaged metallicity $Z$ at various time epochs in this simulation.
" Clearly during the early times dotted and short-dashed as the low-density (thecavity is created at the cluster lines)center, the abundance profile is shifted toward larger radii, while the metallicity within the cavity is nearly constant."," Clearly during the early times (the dotted and short-dashed lines) as the low-density cavity is created at the cluster center, the abundance profile is shifted toward larger radii, while the metallicity within the cavity is nearly constant."
" As the cavity breaks up and the cluster relaxes to the NCC state, high-metallicity gas moves back to the cluster core."," As the cavity breaks up and the cluster relaxes to the NCC state, high-metallicity gas moves back to the cluster core."
" As clearly seen in Figure 8 (the dot-short dashed and dot-long dashed lines), the gas abundance within the central ~50 kpc in the NCC state is efficiently diluted by mixing, while the abundance profile at large radii remains similar to that in the original CC state."," As clearly seen in Figure \ref{plot8} (the dot-short dashed and dot-long dashed lines), the gas abundance within the central $\sim 50$ kpc in the NCC state is efficiently diluted by mixing, while the abundance profile at large radii remains similar to that in the original CC state."
" However, since the size of abundance peak in the original CC abundance profile is very broad (‘metal=160 kpc), the abundance profile in the final NCC state still has a central peak, with a maximum abundance value of around 0.6—0.65, which is roughly the abundance value of the initial CC profile at a cluster-centric radius of 50 kpc."," However, since the size of abundance peak in the original CC abundance profile is very broad $r_{\rm metal}=160$ kpc), the abundance profile in the final NCC state still has a central peak, with a maximum abundance value of around $0.6-0.65$, which is roughly the abundance value of the initial CC profile at a cluster-centric radius of $50$ kpc."
" Thus we find that in this run, though the abundance peak value does decrease, the central abundance peak is not removed during the CC to NCC transformation, which is consistent with recent observations by ? and ?,, while not explaining NCC clusters with relatively flat abundance profiles observed by ? and ?.."," Thus we find that in this run, though the abundance peak value does decrease, the central abundance peak is not removed during the CC to NCC transformation, which is consistent with recent observations by \citet{leccardi08} and \citet{sanderson09}, , while not explaining NCC clusters with relatively flat abundance profiles observed by \citet{degrandi01} and \citet{degrandi04}."
" Figure shows radial profiles of emission-weighted spherically 9((a)averaged metallicity at t=0.5 Gyr in our runs D1, D1-A, D1-B, and D1-C. Clearly the central abundance peak is not removed in any of these runs, suggesting that it is very difficult to remove it by varying the energy or location of the CR injection."," Figure \ref{plot9}( (a) shows radial profiles of emission-weighted spherically averaged metallicity at $t=0.5$ Gyr in our runs D1, D1-A, D1-B, and D1-C. Clearly the central abundance peak is not removed in any of these runs, suggesting that it is very difficult to remove it by varying the energy or location of the CR injection."
" X-ray observations indicate that some clusters and elliptical galaxies exhibit a dip in abundance in their very centers, e.g., Abell 2199 the long-dashed line in Figure 2))."," X-ray observations indicate that some clusters and elliptical galaxies exhibit a dip in abundance in their very centers, e.g., Abell 2199 (see the long-dashed line in Figure \ref{plot2}) )."
 We performed (seeanother run D1-D to study if such a CC abundanceprofile may result in a final NCC, We performed another run D1-D to study if such a CC abundanceprofile may result in a final NCC
From this point of view. to lind a Be-type star in this cluster should. not. be odd.,"From this point of view, to find a Be-type star in this cluster should not be odd."
 However. the distance of LSS 440 disagrees with the cluster distance and it is placed a bit far from the cluster center.," However, the distance of LSS 440 disagrees with the cluster distance and it is placed a bit far from the cluster center."
 Likewise. the mass of LSS 440 is extremely high if compared. to the mass of nex bright member star onto the cluster MS (see Sect.," Likewise, the mass of LSS 440 is extremely high if compared to the mass of next bright member star onto the cluster MS (see Sect."
 3.3. ane Sect.," \ref{sec:parameters}
 and Sect."
 5 in advance) which is 22meg fainter., \ref{sec:LFIMF} in advance) which is $\approx 2 mag$ fainter.
 Certainly. the location of LSS 440 onto the Ady vs. D.V and C.D vs. D.V diagrams> are in agreement> with the usual location of other Be stars in open clusters (see Figs.," Certainly, the location of LSS 440 onto the $M_V$ vs. $B-V$ and $U-B$ vs. $B-V$ diagrams are in agreement with the usual location of other Be stars in open clusters (see Figs."
 Ga and 7 given by Moermilliod 1982) but the available elements at the momen preclude any kind of clear physical relationship between the cluster and this star., 6a and 7 given by Mermilliod 1982) but the available elements at the moment preclude any kind of clear physical relationship between the cluster and this star.
 Racial velocities would be a very useful tool to settle this question., Radial velocities would be a very useful tool to settle this question.
" For the construction of the cluster. luminosity function. defined as the distribution of stars over the magnitude range in bins 1"" wide. we applied the procedure already described in Baume et al. ("," For the construction of the cluster luminosity function, defined as the distribution of stars over the magnitude range in bins $1^m$ wide, we applied the procedure already described in Baume et al. ("
2004).,2004).
 Phat is. we first. computed. the apparent magnitude distribution of /m ancl par stars for," That is, we first computed the apparent magnitude distribution of $lm$ and $pm$ stars for"
accurately weighted and calibrated signal and noise measurements for each pixel. each measurement being wholly independent of values for its neighbouring pixels. with [3.d-aresec resolution at yim. These signal and noise values reflect the stream of data collected when bolometers are centred within the region of sky corresponding to a particular pixel.,"accurately weighted and calibrated signal and noise measurements for each pixel, each measurement being wholly independent of values for its neighbouring pixels, with 13.4-arcsec resolution at $\mu$ m. These signal and noise values reflect the stream of data collected when bolometers are centred within the region of sky corresponding to a particular pixel."
 These unsmoothed images were used for source detection (see refextraction))., These unsmoothed images were used for source detection (see \\ref{extraction}) ).
 The submm images of each of the three quasar fields — jim contours superposed on greyscale representations of the pm data — are shown in Fig. 1..," The submm images of each of the three quasar fields – $\mu$ m contours superposed on greyscale representations of the $\mu$ m data – are shown in Fig. \ref{scuba},"
 where we have smoothed with 6- and 3-aresec Gaussians and the resulting 850- and 450-j/m maps have typical noise levels of 1.5 and +., where we have smoothed with 6- and 3-arcsec Gaussians and the resulting 850- and $\mu$ m maps have typical noise levels of 1.5 and $^{-1}$.
 For comparison. the Sa 850-j/m confusion limit for the JCMT is zl— I.5mmly. so we have reached close to the depth at which confusion is likely to begin posing problems.," For comparison, the $\sigma$ $\mu$ m confusion limit for the JCMT is $\approx$ mJy, so we have reached close to the depth at which confusion is likely to begin posing problems."
 Source detection at j/m was accomplished using the algorithm described in detail by ?.. utilising the signal and noise maps and a PSF (measured for the blazar. 3345) to perform a simultaneous maximum-likelihood fit to all the potentially significant peaks in each map.," Source detection at $\mu$ m was accomplished using the algorithm described in detail by \citet{scott02}, utilising the signal and noise maps and a PSF (measured for the blazar, 345) to perform a simultaneous maximum-likelihood fit to all the potentially significant peaks in each map."
 Sources down to a signiticance level of 3c are listed in Table 2.., Sources down to a significance level of $\sigma$ are listed in Table \ref{tab2}.
 Adopting a 3¢ detection threshold. at jim jim) a total of I4 (7) sources are detected: 2 (1) QSOs and 12 (6) companions in the three fields. with flux densities between 4.4(16) and mm]y (S6mmJy).," Adopting a $\sigma$ detection threshold, at $\mu$ m $\mu$ m) a total of 14 (7) sources are detected: 2 (1) QSOs and 12 (6) companions in the three fields, with flux densities between 4.4 (16) and mJy mJy)."
 Five sources. including one QSO. are detected at both wavelengths (Table 21).," Five sources, including one QSO, are detected at both wavelengths (Table \ref{tab2}) )."
 Discussing each of the fields in turn:, Discussing each of the fields in turn:
The overall evolution of the 256 and Sk clusters is similar to he Ik case.,The overall evolution of the 256 and 8k clusters is similar to the 1k case.
 In figure 4 we show the Lagrangian racii anc ormation sites of binaries. analogous to figure 1..," In figure \ref{8192lagr} we show the Lagrangian radii and formation sites of binaries, analogous to figure \ref{1024lagr}."
 Recall tha he Sk runs are analysed at f=5107.lo, Recall that the 8k runs are analysed at $t=5\times10^4$.
cp The expansion. o he clusters is. as expected. similar to the Ik case modulo a shift of the time of core collapse related to the I dependence of the initial relaxation time. and the formation sites of »rmanent. soft. binaries are similarly concentrated: exterior o the half-mass radius.. Extending the Sk runs severa orders of magnitude in time would have perhaps been ideal. out. physical arguments. about the relevance of extending he runs (see the discussion below) made the computationa expense of that route seem a questionable investment," The expansion of the clusters is, as expected, similar to the 1k case modulo a shift of the time of core collapse related to the $N$ dependence of the initial relaxation time, and the formation sites of permanent soft binaries are similarly concentrated exterior to the half-mass radius.. Extending the 8k runs several orders of magnitude in time would have perhaps been ideal, but physical arguments about the relevance of extending the runs (see the discussion below) made the computational expense of that route seem a questionable investment."
 In figuree 5. we show the semi-major axis distributions. or the 256 and Sk runs., In figure \ref{8192semidist} we show the semi-major axis distributions for the 256 and 8k runs.
 The number of binaries forme at large separations. about one per cluster. are consistent across all the clusters.," The number of binaries formed at large separations, about one per cluster, are consistent across all the clusters."
 The truncation of the distribution for he Sk run is because of the shorter length of (logarithmic) ime those clusters were integrated post core-collapse. and »ecause the amount of cluster expansion necessary for the interstellar separation to reach a given value increases with NU.," The truncation of the distribution for the 8k run is because of the shorter length of (logarithmic) time those clusters were integrated post core-collapse, and because the amount of cluster expansion necessary for the interstellar separation to reach a given value increases with $N^{1/3}$."
 We have been dealing with dimensionless units up to this point., We have been dealing with dimensionless units up to this point.
 When applying these results to a cluster in a galaxy. were are two limiting length scales to take into account.," When applying these results to a cluster in a galaxy, there are two limiting length scales to take into account."
 First. there is the largest binary that we are interested in ooducing.," First, there is the largest binary that we are interested in producing."
 As discussed in the introduction. this is about 101 AU.," As discussed in the introduction, this is about $10^5$ AU."
 Binaries produced above that size scale are not of »wticular interest. because their numbers are depleted. by disruption in the galactic field., Binaries produced above that size scale are not of particular interest because their numbers are depleted by disruption in the galactic field.
 Second is the tidal radius of 16 cluster., Second is the tidal radius of the cluster.
 Dinaries are produced in the outer regions of the cluster. and as seen in figure 1. these reach radii of the order 100 units.," Binaries are produced in the outer regions of the cluster, and as seen in figure \ref{1024lagr} these reach radii of the order 100 units."
 HE this is larger than the tidal radius. these xnaries will not form. at least not in the relaxation-driven expansion scenario we have ciscussed.," If this is larger than the tidal radius, these binaries will not form, at least not in the relaxation-driven expansion scenario we have discussed."
 The first constraint. the upper limit of the binaries we are interested in. means that we are only concerned with binaries with semi-major axes of a less than a few units. thus cutting olf the final two bins of figure 2..," The first constraint, the upper limit of the binaries we are interested in, means that we are only concerned with binaries with semi-major axes of a less than a few units, thus cutting off the final two bins of figure \ref{1024semidist}."
 This means that cach cluster can be expected to. produce slightlv less than a single. binarv in the range we are interested in., This means that each cluster can be expected to produce slightly less than a single binary in the range we are interested in.
 The second constraint is that the binary is not formecl bevond the tidal radius of the cluster., The second constraint is that the binary is not formed beyond the tidal radius of the cluster.
 With a tidal racidus of order 10 pe. our choice of initial virial radius means that the eutolf is of order 100 units.," With a tidal radius of order 10 pc, our choice of initial virial radius means that the cutoff is of order 100 units."
 Inspecting figure l.. we see that binaries continue to be produced closer to the hall-mass radius through to the end of the simulation inside of 100 units. but the production in the outskirts will only continue in a truly ancl unrealistically isolated cluster.," Inspecting figure \ref{1024lagr}, we see that binaries continue to be produced closer to the half-mass radius through to the end of the simulation inside of 100 units, but the production in the outskirts will only continue in a truly and unrealistically isolated cluster."
 These two constraints both cut olf approximately the same binaries from consideration. however.," These two constraints both cut off approximately the same binaries from consideration, however."
 This is to be expected. to order of magnitude.," This is to be expected, to order of magnitude."
 Roughly speaking. the cluster becomes tidally limited as its mean density reaches some critical value. and a binary in the field can be thought of as limited by a similar density condition.," Roughly speaking, the cluster becomes tidally limited as its mean density reaches some critical value, and a binary in the field can be thought of as limited by a similar density condition."
 Since the binaries are formed. at about the interstellar separation. it follows that the two constraints allect the same binaries.," Since the binaries are formed at about the interstellar separation, it follows that the two constraints affect the same binaries."
 As is clear [from figure 3.. after the outer Lagrangian radii are outside a realistic tidal limit at a few thousand time units. the bulk of the binaries with separations less than 10 units have already been created. and the story is the same for the 256 runs.," As is clear from figure \ref{1024freeze}, after the outer Lagrangian radii are outside a realistic tidal limit at a few thousand time units, the bulk of the binaries with separations less than 10 units have already been created, and the story is the same for the 256 runs."
 Looking to the Sk runs. the situation is somewhat erimmer on the solt-binary production front.," Looking to the 8k runs, the situation is somewhat grimmer on the soft-binary production front."
" Phe formation site of nearly all the binaries are at radii bevoud several hundred: units. Hlirting with the tidal radius with the same initial scaling of 2,=0.1 pe."," The formation site of nearly all the binaries are at radii beyond several hundred units, flirting with the tidal radius with the same initial scaling of $R_v=0.1$ pc."
 A perhaps more-reasonable initial virial raclius for this larger cluster οἱ. sav. 0.25 pc exacerbates the problem: more populous clusters need to be ina tically unrestricted setting in order to expauxd sulliciently to. produce the soft. binaries we are interested in.," A perhaps more-reasonable initial virial radius for this larger cluster of, say, 0.25 pc exacerbates the problem; more populous clusters need to be in a tidally unrestricted setting in order to expand sufficiently to produce the soft binaries we are interested in."
 lt appears that when the constraints of the galaxy are inclucled. it is the less-populous clusters that are more likely to contribute to the population of wide binaries. for two reasons.," It appears that when the constraints of the galaxy are included, it is the less-populous clusters that are more likely to contribute to the population of wide binaries, for two reasons."
 First. with each cluster producing of order a single wide binary. 10 dispersed clusters of 200 stars will vield more wide field binaries than a single ONC of about 2000.," First, with each cluster producing of order a single wide binary, 10 dispersed clusters of 200 stars will yield more wide field binaries than a single ONC of about 2000."
 Second. the tidal limitation restricts the ability of larger clusters to produce even their single wide binary.," Second, the tidal limitation restricts the ability of larger clusters to produce even their single wide binary."
 In the most recent comprehensive survey of multiplicity in the Solar neighbourhood. encompassing 454. solar-tvpe stars within 25 pc. Raghavanetal.(2010). find. 10 binaries with estimated semimajor axes greater than 107 AU.," In the most recent comprehensive survey of multiplicity in the Solar neighbourhood, encompassing 454 solar-type stars within 25 pc, \citet{raghavan10} find 10 binaries with estimated semimajor axes greater than $10^4$ AU."
" ""Thus ocallv. ~2% of field stars are in the very wide svstems that we have explored here."," Thus locally, $\sim 2$ of field stars are in the very wide systems that we have explored here."
 With approximately one such binary ing created from each dissolving cluster. a field populated ον Ik clusters would have a wide binary population. while in a field populated by our 256 star clusters it would » more like154.," With approximately one such binary being created from each dissolving cluster, a field populated by 1k clusters would have a wide binary population, while in a field populated by our 256 star clusters it would be more like."
. The statistics of the local ficld are hus broadly consistent with the field being svnthesized by clusters of a few hundred stars. rather than a few thousand.," The statistics of the local field are thus broadly consistent with the field being synthesized by clusters of a few hundred stars, rather than a few thousand."
 This matches the statistics of clustered star formation sites (Lada&Lada2003:Porrasctal.2003).. which appear to jwe a median eluster membership of ~300 (Adamsctal. 2006).," This matches the statistics of clustered star formation sites \citep{lada03,porras03}, which appear to have a median cluster membership of $\sim 300$ \citep{adams06}."
. We emphasize that the clustered formation scenario should be thought of in terms of a hierarchical structure rather than as clustered versus isolated. modes (Dresseretal. 2010)., We emphasize that the clustered formation scenario should be thought of in terms of a hierarchical structure rather than as clustered versus isolated modes \citep{bressert10}.
. This formation process relics upon relaxation-driven expansion., This formation process relies upon relaxation-driven expansion.
 Before this point of a clusters life. there shoulc not be any wide binaries.," Before this point of a cluster's life, there should not be any wide binaries."
 This is consistent with the lack of observed wide binaries in the ONC (Seallyetal.1999).. ane -- is possible that a small number of wide binaries might be [ormed subsequently. during the dissolution of the ONC.," This is consistent with the lack of observed wide binaries in the ONC \citep{scally99}, and it is possible that a small number of wide binaries might be formed subsequently during the dissolution of the ONC."
 I has often been noted that the observed. binary statistics in 10 ONC are similar to that of the field. (thus encouraging 1e notion that the field. might be comprised. of. dissolve ONC-tvpe clusters). with the notable exception of the fac wt the ONC is lacking in wide binaries.," It has often been noted that the observed binary statistics in the ONC are similar to that of the field (thus encouraging the notion that the field might be comprised of dissolved ONC-type clusters), with the notable exception of the fact that the ONC is lacking in wide binaries."
 Conceivably. rerclore. this problem could. be solved if the wide binaries are vet to form.," Conceivably, therefore, this problem could be solved if the wide binaries are yet to form."
 Lt is however worth emphasizing that the current dvnamical status of the ONC is not well known observationallv anc that. strictly speaking. our present analysis should. not. be quantitatively applied: to clusters that expand from super-virial conditions as a result. of gas expulsion.," It is however worth emphasizing that the current dynamical status of the ONC is not well known observationally and that, strictly speaking, our present analysis should not be quantitatively applied to clusters that expand from super-virial conditions as a result of gas expulsion."
 We have not included any primordial binarics in these simulations., We have not included any primordial binaries in these simulations.
 As Kouwenhovenetal.(2010). point out. the," As \citet{kouwenhoven10} point out, the"
Ionized (Hm) regions are known to trigger the formation of stars by means of various physical mechanisms (see Elmegreen1998 and Deharveng etal.,Ionized ) regions are known to trigger the formation of stars by means of various physical mechanisms (see Elmegreen\cite{elm98} and Deharveng etal.
 2005. for a review)., \cite{deh05} for a review).
 Several regions have been studied individually in. the context of triggered star formation. focusing on the associated neutral material and the young stellar population (Zavagno et al. 2006::," Several regions have been studied individually in the context of triggered star formation, focusing on the associated neutral material and the young stellar population (Zavagno et al. \cite{zav06};"
Deharveng et al. 2009:; ,Deharveng et al. \cite{deh09}; ;
Pomaréss et al. 2009::, Pomarèss et al. \cite{pom09};
 Bieging et al. 2009))., Bieging et al. \cite{bie09}) ).
 These studies have shown that the expansion of regions can trigger the formation of new stars of all masses., These studies have shown that the expansion of regions can trigger the formation of new stars of all masses.
 The Spitzer-GLIMPSE survey of the Galactic plane (Benjamin et al. 2003)), The $\it{Spitzer}$ -GLIMPSE survey of the Galactic plane (Benjamin et al. \cite{ben03}) )
 detected nearly 600 bubbles (Churchwell et al. 2006))., detected nearly 600 bubbles (Churchwell et al. \cite{chu06}) ).
 Deharveng et al. (2010)), Deharveng et al. \cite{deh10}) )
 selected a series of 102 ronized bubbles and studied the star formation in their surroundings using Spitzer-GLIMPSE and MIPSGAL (Carey et al. 2009)).," selected a series of 102 ionized bubbles and studied the star formation in their surroundings using $\it{Spitzer}$ -GLIMPSE and MIPSGAL (Carey et al. \cite{car09}) ),"
 radio (MAGPIS: Helfand et al., radio (MAGPIS; Helfand et al.
 2006 and VGPS: Stil et al. 2006).," \cite{hel06} and VGPS; Stil et al. \cite{sti06}) ),"
 and ATLASGAL (Schuller et al. 2009)), and ATLASGAL (Schuller et al. \cite{sch09}) )
 data., data.
 They show that of these bubbles enclose regions. and that more than of 64 bubbles (for which the ATLASGAL angular resolution ts sufficient to resolve the spatial distribution of cold dust) show massive star formation on their borders.," They show that of these bubbles enclose regions, and that more than of 64 bubbles (for which the ATLASGAL angular resolution is sufficient to resolve the spatial distribution of cold dust) show massive star formation on their borders."
 This indicates that triggering 15 important in the creation of massive stars and that hot photodissociation regions (PDRs) are a good place to study the earliest phases of massive-star formation., This indicates that triggering is important in the creation of massive stars and that hot photodissociation regions (PDRs) are a good place to study the earliest phases of massive-star formation.
 Our long-term aim is to use Hi-GAL (Molinari et al. 2010)).," Our long-term aim is to use Hi-GAL (Molinari et al. \cite{mol10}) ),"
 combined with existing infrared. submillimeter. and radio surveys. to study the influence of regions on triggering the formation of stars in our Galaxy.," combined with existing infrared, submillimeter, and radio surveys, to study the influence of regions on triggering the formation of stars in our Galaxy."
 Hi-GAL’s extended wavelength coverage towards the far-infrared and its unprecedented sensitivity offer a unique opportunity to detect an embedded population of young sources that are not detected at shorter wavelengths., Hi-GAL's extended wavelength coverage towards the far-infrared and its unprecedented sensitivity offer a unique opportunity to detect an embedded population of young sources that are not detected at shorter wavelengths.
 This allows us to observe intermediate and high-mass YSOs over the complete range of evolutionary stages., This allows us to observe intermediate and high-mass YSOs over the complete range of evolutionary stages.
 The unprecedented resolution of Hi-GAL also offers the opportunity to accurately characterize the physical nature of the sources by means of a detailed fit to their spectral energy distribution (SED)., The unprecedented resolution of Hi-GAL also offers the opportunity to accurately characterize the physical nature of the sources by means of a detailed fit to their spectral energy distribution (SED).
 In this Letter we study the bubble-shaped tonized region. N49. from the Churchwell et al. (2006))," In this Letter we study the bubble-shaped ionized region, N49, from the Churchwell et al. \cite{chu06}) )"
 catalogue to illustrate the purpose of our project., catalogue to illustrate the purpose of our project.
 The N49 bubble was studied by Watson et al. (2008)), The N49 bubble was studied by Watson et al. \cite{wat08}) )
 and by Deharveng et al. (2010))., and by Deharveng et al. \cite{deh10}) ).
 However. these studies had no information in the jum range.," However, these studies had no information in the $\mu$ m range."
 This information. obtained with the PACS and SPIRE data presented here. allows us to discuss the star formation ofthis region in detail.," This information, obtained with the PACS and SPIRE data presented here, allows us to discuss the star formation ofthis region in detail."
" We use PACS and SPIRE images obtained in parallel mode at 70. 160. 250. 350 and um (at resolutions of δν 11.4"".. 17.9""... and 35.7"".. respectively)to determine the influence of rregions on their surroundings using the N49"," We use PACS and SPIRE images obtained in parallel mode at 70, 160, 250, 350 and $\mu$ m (at resolutions of , , , and , respectively)to determine the influence of regions on their surroundings using the N49"
The most important difference between subkeplerian dises and Keplerian dises. as far as dise-planet interactions are concerned. is the change in position of the Lindblad and corotation resonances.,"The most important difference between subkeplerian discs and Keplerian discs, as far as disc-planet interactions are concerned, is the change in position of the Lindblad and corotation resonances."
 It was shown in?. that a embedded object can exchange angular momentum with the dise only at the location of a resonance., It was shown in\cite{gt79} that an embedded object can exchange angular momentum with the disc only at the location of a resonance.
 Corotation resonances occur where the dise corotates with the planet. and inner (outer) Lindblad resonances are located inside (outside) corotation.," Corotation resonances occur where the disc corotates with the planet, and inner (outer) Lindblad resonances are located inside (outside) corotation."
 The strongest Lindblad resonances occur at a distance ~Η of the planet ?.., The strongest Lindblad resonances occur at a distance $\sim H$ of the planet \cite{ward97}.
 In Keplerian disces. a planet o a circular orbit is located close to corotation. with Lindblac resonances on either side of its orbit.," In Keplerian discs, a planet on a circular orbit is located close to corotation, with Lindblad resonances on either side of its orbit."
 In strongly subkeplerian dises. the distance of the planet to corotation is large enough so that we can safely neglect any nonbarotropic effects associatec with the corotation torque (?)..," In strongly subkeplerian discs, the distance of the planet to corotation is large enough so that we can safely neglect any nonbarotropic effects associated with the corotation torque \citep{paardpap08}."
 In this sense. subkeplerian dises are easier to handle. since we only have to deal with Lindblad resonances.," In this sense, subkeplerian discs are easier to handle, since we only have to deal with Lindblad resonances."
 The approximate position of the Lindblad resonances up to 10th order are shown in Fig., The approximate position of the Lindblad resonances up to 10th order are shown in Fig.
 | for different values of f., \ref{fig1} for different values of $f$.
 Pressure effects have been ignored in calculating these positions., Pressure effects have been ignored in calculating these positions.
 In a purely Keplerian disc (f= 1). the planet interacts with both inner and outer resonances.," In a purely Keplerian disc $f=1$ ), the planet interacts with both inner and outer resonances."
 For f£<1. the resonance positions move inward. with the result that the planet now mainly interacts with the outer Lindblad resonances.," For $f<1$, the resonance positions move inward, with the result that the planet now mainly interacts with the outer Lindblad resonances."
 This has consequences for both migration and gap formation., This has consequences for both migration and gap formation.
 We first consider the torque I on low-mass planets. not massive enough to open up a gap.," We first consider the torque $\Gamma$ on low-mass planets, not massive enough to open up a gap."
 We compare results from linear calculations to hydrodynamical simulations for different values of f in Fig. 2.., We compare results from linear calculations to hydrodynamical simulations for different values of $f$ in Fig. \ref{fig2}.
" The torque is normalised by Γρ=qXysQstr. where g=M,/M. and Q, is the planets angular velocity."," The torque is normalised by $\Gamma_0=q^2\sigp\rp^4\op^2/h^2$, where $q=\mpl/M_*$ and $\op$ is the planet's angular velocity."
 We plot the absolute value of the torque: it is negative for all values of f., We plot the absolute value of the torque; it is negative for all values of $f$.
 It is immediately clear from Fig., It is immediately clear from Fig.
 2. that the torque very strongly depends on f., \ref{fig2} that the torque very strongly depends on $f$.
 This can be understood in terms of a change in the position of the resonances with respect to the planet., This can be understood in terms of a change in the position of the resonances with respect to the planet.
 For f=| we find the classical Type I torque. modified by nonlinear effects at corotation (2)..," For $f=1$ we find the classical Type I torque, modified by nonlinear effects at corotation \citep{drag}."
 Around |—fοὐh. the planet mainly interacts with the strongest outer Lindblad resonances. yielding a very strong negative torque.," Around $1-f\approx h$, the planet mainly interacts with the strongest outer Lindblad resonances, yielding a very strong negative torque."
 The total torque approaches the one-sided Lindblad torque (?).. which would be obtained when considering only outer Lindblac resonances and which 15 a factor of ~1//1 stronger than the differential Lindblad torque.," The total torque approaches the one-sided Lindblad torque \citep{ward97}, which would be obtained when considering only outer Lindblad resonances and which is a factor of $\sim 1/h$ stronger than the differential Lindblad torque."
 The maximum torque depends or the adopted smoothing. with higher values for lower values of b.," The maximum torque depends on the adopted smoothing, with higher values for lower values of $b$ ."
 For 1—f>fh. the torque decreases. since the resonaces It interacts with become weaker as the planet moves further away from corotation.," For $1-f \gg h$, the torque decreases, since the resonances it interacts with become weaker as the planet moves further away from corotation."
 For /;=0.05 and f=0.6. the resulting torque is comparable ir magnitude to the classical Type | torque.," For $h=0.05$ and $f=0.6$, the resulting torque is comparable in magnitude to the classical Type I torque."
 Linear calculations and nonlinear simulations agree very well. which again indicates that nonlinear effects at corotation do not play an important role.," Linear calculations and nonlinear simulations agree very well, which again indicates that nonlinear effects at corotation do not play an important role."
 The results depicted in Fig., The results depicted in Fig.
 2. indicate that the crucial parameter determining the total torque on the planet is (1— ΕΠ., \ref{fig2} indicate that the crucial parameter determining the total torque on the planet is $p=(1-f)/h$ .
 The maxima of the curves occur factors of 2 apart in Fig. 2..," The maxima of the curves occur factors of 2 apart in Fig. \ref{fig2},"
 confirming this picture., confirming this picture.
 The scaling of the torque with I; ensures that for £=|. the curves fall on topof each other.," The scaling of the torque with $\Gamma_0$ ensures that for $f=1$, the curves fall on topof each other."
 When p=1. a sizeable fraction of the one-sided Lindblad torque can be exerted on the planet.," When $p\approx1$, a sizeable fraction of the one-sided Lindblad torque can be exerted on the planet."
 The one-sided torque scales as 7. while the differential Lindblad torque scales as 77.," The one-sided torque scales as $h^{-3}$ , while the differential Lindblad torque scales as $h^{-2}$."
 This is the reason for the different maxima for differentvalues of /i., This is the reason for the different maxima for differentvalues of $h$.
 This scaling holds for all f<I: only for f=| do we get the 177 scaling of the differential Lindblad torque., This scaling holds for all $f<1$; only for $f=1$ do we get the $h^{-2}$ scaling of the differential Lindblad torque.
 Therefore. in subkeplerian dises. fora fixed value of p. the torque scales as 47.," Therefore, in subkeplerian discs, fora fixed value of $p$ , the torque scales as$h^{-3}$ ."
 For a fixed value of f. the situation can be different.," For a fixed value of $f$ , the situation can be different."
 For, For
we note that consideration of the distribution of observed masses will lead to stricter constraints than consideration of just the observed rates.,we note that consideration of the distribution of observed masses will lead to stricter constraints than consideration of just the observed rates.
 The theoretical calculation of rates involves estimating a mumber selection effects and calibrating with other sources which leads to several uncertainties., The theoretical calculation of rates involves estimating a number selection effects and calibrating with other sources which leads to several uncertainties.
 The calculation of the observed clistvibution of chirp masses is [ree from such uncertainties because a distributions essentially equivalent to consiclering the ratios of the number of mergers of different (wpe. and all the normaliztüon factors (hat enter the rate estimates do cancel out.," The calculation of the observed distribution of chirp masses is free from such uncertainties because a distributions essentially equivalent to considering the ratios of the number of mergers of different type, and all the normaliztion factors that enter the rate estimates do cancel out."
 Finally. we have to mention several effects not taken info account in this paper.," Finally, we have to mention several effects not taken into account in this paper."
 A more detailed calculation must include the consideration of the effects of lifetimes of binaries of different (wpe., A more detailed calculation must include the consideration of the effects of lifetimes of binaries of different type.
 Belezvuski. INalogera ancl Bulik (2002) have shown that the tvpical lifetimes of double neutron star binaries are much smaller (han the black hole binaries.," Belczynski, Kalogera and Bulik (2002) have shown that the typical lifetimes of double neutron star binaries are much smaller than the black hole binaries."
 The effects due to changing of the star formation rate with the redshift will affect (he observed population of merging binaries., The effects due to changing of the star formation rate with the redshift will affect the observed population of merging binaries.
 When considering the advanced detectors sensitive to mergers al Cosmological distances one also needs to (ake into account cosmological effects: the fact that (the true measure quantitv is the redshilted mass (1+:).Vf. and also the change of the observed volume with the redshift (here we have assiuned (he Euclidean geometry).," When considering the advanced detectors sensitive to mergers at cosmological distances one also needs to take into account cosmological effects: the fact that the true measure quantity is the redshifted mass $(1+z)\chirp$, and also the change of the observed volume with the redshift (here we have assumed the Euclidean geometry)."
 These issues will be considered in a separate paper., These issues will be considered in a separate paper.
 We thank Vicky Ixalogera for comments on this project., We thank Vicky Kalogera for comments on this project.
 TB thanks the hospitality. of the Theoretical Astrophysics Group at Northwestern University., TB thanks the hospitality of the Theoretical Astrophysics Group at Northwestern University.
 We acknowledge support from IXDN through grant 5PO3D01120., We acknowledge support from KBN through grant 5P03D01120.
"where r, and 5 are the correlation length and the power law index respectively.",where $r_o$ and $\gamma$ are the correlation length and the power law index respectively.
 For galaxies. rà; is of the order 5.4 ht Alpe (Davis Peebles. 1983) with 5~L.7L8.," For galaxies, $r_o$ is of the order 5.4 $^{-1}$ Mpc (Davis Peebles, 1983) with $\gamma \sim 1.7-1.8$."
 Fhis correlation length has been found to increase as the scale of the system increases (ic., This correlation length has been found to increase as the scale of the system increases (ie.
 a larger value ofr is found for rich clusters and even a larger value is found for superclusters)., a larger value of $r_o$ is found for rich clusters and even a larger value is found for superclusters).
" Baheall Soneira (1983) found i,—25 + Mpe and 5~1.7 for Abell clusters.", Bahcall Soneira (1983) found $r_o \sim 25$ $^{-1}$ Mpc and $\gamma \sim 1.7$ for Abell clusters.
 To find the best. power law Lit. we have used the method of 4? minimisation.," To find the best power law fit, we have used the method of $\chi^{2}$ minimisation."
 and the errors on cach parameter correspond to 0X7=1., and the errors on each parameter correspond to $\delta \chi^{2}=1$.
 Note that this method is valid only if the errors of the correlation function at a fixed separation are Gaussian distributed and if the values at different separations are uncorrelated., Note that this method is valid only if the errors of the correlation function at a fixed separation are Gaussian distributed and if the values at different separations are uncorrelated.
 The power law model is usually fitted to the data [or ο 1 Alpe and since these separations are typically much smaller than the size of the sample. the οςntral [limit theorem ensures that the cistribution of errors will be Gaussian.," The power law model is usually fitted to the data for r $\leq$ 20 $^{-1}$ Mpc and since these separations are typically much smaller than the size of the sample, the central limit theorem ensures that the distribution of errors will be Gaussian."
" According to the linear biasing theory (Ixzdser. 1984). the (wo point correlation function between populations ‘a’ and ∕∕b can be approximated⋠ by: where 6, and b, are the bias parameters (ie."," According to the linear biasing theory (Kaiser, 1984), the two point correlation function between populations $'a'$ and $'b'$ can be approximated by: where $b_a$ and $b_b$ are the bias parameters (ie."
" the contrast enhancement factor of the distribution of tracers compared to the underlying mass distribution) for populations 'a ane ""b respectively and νο) is the correlation function of the uncerlving mass density.", the contrast enhancement factor of the distribution of tracers compared to the underlying mass distribution) for populations $'a'$ and $'b'$ respectively and $\xi_m(r)$ is the correlation function of the underlying mass density.
 b is defined as: Calculating the correlation function of various. tracers indicates the relative bias parameters. of these tracers (Lahav. Nemiroll ct al..," b is defined as: Calculating the correlation function of various tracers indicates the relative bias parameters of these tracers (Lahav, Nemiroff et al.,"
. 1990)., 1990).
 Also. comparing a cross-correlation function. (£ix(r)) with απ auto-correlation function (ει). gives extra relative biasing between two types of mass (racers: Llaving described the calculation of the spatial correlation function. let us now have a brief. review of the angular correlation function.," Also, comparing a cross-correlation function $(\xi_{IX}(r))$ with an auto-correlation function $(\xi_{II}(r))$, gives extra relative biasing between two types of mass tracers: Having described the calculation of the spatial correlation function, let us now have a brief review of the angular correlation function."
 The angular correlation function can be expressed in terms of probability in a similar way as the spatial correlation function., The angular correlation function can be expressed in terms of probability in a similar way as the spatial correlation function.
" If one considers two differential elements of solid angle on the skv. dO, and dO». then the joint probalitv. dP. that galaxies will occupy. the two elements with an angular separation of 6 can be written as: where n is the mean surface density of galaxies."," If one considers two differential elements of solid angle on the sky, $\Omega_1$ and $\Omega_2$, then the joint probality, dP, that galaxies will occupy the two elements with an angular separation of $\theta$ can be written as: where n is the mean surface density of galaxies."
 Note that a random (Poisson) distribution of galaxies vields (0) = 0 for all 6., Note that a random (Poisson) distribution of galaxies yields $\theta$ ) = 0 for all $\theta$.
 Also: Op: Again. the errors are calculated as Poissonian errors.," Also: or: Again, the errors are calculated as Poissonian errors."
 Finally. w(8) can be approximated by a power law of the form: As before the best fit. can be found using the methods of 47 minimisation. and the errors on cach parameter correspond to 047 —1 The results of the various angular ancl spatial auto and cross correlation functions are shown in figures S-15.," Finally, $\theta$ ) can be approximated by a power law of the form: As before the best fit, can be found using the methods of $\chi^{2}$ minimisation, and the errors on each parameter correspond to $\delta \chi^2$ =1 The results of the various angular and spatial auto and cross correlation functions are shown in figures 8-15."
 The best power law fit to all the cata analvsed in this work are shown in solid lines., The best power law fit to all the data analysed in this work are shown in solid lines.
 For further comparisons. we have also plotted power law fits from. previous work.," For further comparisons, we have also plotted power law fits from previous work."
 For, For
We start from the local LE at 00 saa from Saunders et al. (,We start from the local LF at 60 $\mu$ m from Saunders et al. (
1990) (Fig. 5)).,1990) (Fig. \ref{LF_60}) ).
" We convert the GO yam LE in a bolometric LE (L=1-1000 jim) using our template spectra: at the ‘low-luminosity’ and “high-luminosity’ part. we assign the ""normal ancl starburst template spectra Although the number of parametres is quite low. idt is too much time consuming to do a blind search through the whole parametre space."," We convert the 60 $\mu$ m LF in a bolometric LF (L=1-1000 $\mu$ m) using our template spectra: at the 'low-luminosity' and 'high-luminosity' part, we assign the 'normal' and starburst template spectra Although the number of parametres is quite low, it is too much time consuming to do a blind search through the whole parametre space."
 We therefore search. the best solution for the parametres near values expected from clirect observationnal evidences: The best evolution of the LE that reproduces Ht number, We therefore search the best solution for the parametres near values expected from direct observationnal evidences: The best evolution of the LF that reproduces IR number
Next we tried a combination of a WD plus an oplically thick disk.,Next we tried a combination of a WD plus an optically thick disk.
 We created a grid in WD temperature 7;;; from 16.000Ix to 35.000Ix in steps of 1000lx. with each time a mass Mig Wa agreement with a white dwarf mass the same as each one assumed in the grid of disk models of Wade&IInbeny(1993).," We created a grid in WD temperature $T_{eff}$ from 16,000K to 35,000K in steps of 1000K, with each time a mass $M_{wd}$ in agreement with a white dwarf mass the same as each one assumed in the grid of disk models of \citet{wad98}."
.. The disk fIux is divided by LOO to normalize it at 1000pc to match the WD fIux. then both fluxes are added [ον comparison with the observed flux.," The disk flux is divided by 100 to normalize it at 1000pc to match the WD flux, then both fluxes are added for comparison with the observed flux."
" Ii that cases one has: where £,, is the observed FUSE (lux (integrated over the entire FUSE wavelength range). Fig is the theoretical (integrated) flux of the WD. £55; is the theoretical (integrated) [lux of the disk. and d=1000/VS’ pe."," In that cases one has: where $F_{obs}$ is the observed FUSE flux (integrated over the entire FUSE wavelength range), $F_{wd}$ is the theoretical (integrated) flux of the WD, $F_{disk}$ is the theoretical (integrated) flux of the disk, and $d=1000/\sqrt{S}$ pc."
 llere (oo. we started by fixing Yd=65 pc.," Here too, we started by fixing $d=65$ pc."
" The best-fittàng disk plus WD combination. vielded Tipp=23.000. V,sin/= 400km 1S1 — 0.5 x solar. C = 0.1 x solar. 1.21.4... with a disk model having an accretion rate 10.1M, t and 7=81 degrees."," The best-fitting disk plus WD combination, yielded $T_{eff} =
23,000K$, $_{rot}\sin{i} 
= 400$ km $^{-1}$ , Si = 0.5 x solar, C = 0.1 x solar, $M_{wd}=1.21 M_{\odot}$ , with a disk model having an accretion rate $10^{-10.5} M_{\odot}$ $^{-1}$ and $i=81$ degrees."
 The combination fit had a 472 = 11.03., The combination fit had a $\chi^2_{\nu}$ = 11.03.
 In this fit. the WD contributed of the flix and the accretion disk of the flux.," In this fit, the WD contributed of the flux and the accretion disk of the flux."
 This composite model is shown in Figure 4 and is listed in Table 2 (model 10)., This composite model is shown in Figure 4 and is listed in Table 2 (model 10).
" We then (ried a model in which we fixed both d-65pc and the radius H,,4; of the WD.", We then tried a model in which we fixed both d=65pc and the radius $R_{wd}$ of the WD.
 The disk models (from the ον] of models of Wade&IInbeny (1998))) with parameters in best agreement with the parameters of the VW IIvi systems are (he disk models with (corresponding to logy= 8.23) and /=60 degrees.," The disk models (from the grid of models of \citet{wad98}) ) with parameters in best agreement with the parameters of the VW Hyi systems are the disk models with $M_{wd}=
0.8 M_{\odot}$ (corresponding to $\log{g}=8.23$ ) and $i=60$ degrees."
" The best such composite WD plus disk fit model is presented in Table 2 (model 11). with Z,,;=21. 00019. M=10“OAL yy4 Vysin?= 400kans ft witha VL=32.9."," The best such composite WD plus disk fit model is presented in Table 2 (model 11), with $T_{wd}=21,000$ K, $\dot{M}=10^{-10.5} M_{\odot}$ $^{-1}$, $V_{rot}\sin{i}=400$ km $^{-1}$ with a $\chi^2_{\nu}=32.9$."
 ere too we assumed solar abundances for simplicity., Here too we assumed solar abundances for simplicity.
 The WD contributes of the Πιν while the disk contributes of the fIux., The WD contributes of the flux while the disk contributes of the flux.
 Lastly. we tried a combination of a WD plus an accretion belt.," Lastly, we tried a combination of a WD plus an accretion belt."
 The accretion belt moclel is really a stellar atmosphere model but with only a fractional area of the WD and parameters consistent wilh a fast rotating hot accretion belt., The accretion belt model is really a stellar atmosphere model but with only a fractional area of the WD and parameters consistent with a fast rotating hot accretion belt.
 Since the belt is [ast rotating its effective eravily is reciuced to a fraction of the gravity of thestar as follows:, Since the belt is fast rotating its effective gravity is reduced to a fraction of the gravity of thestar as follows:
"As a third approach, these considerations lead us to evaluate the significant contribution to the total N-band flux, but located interior to the dust rim, of: (1) the star itself and (2) a gaseous disk.","As a third approach, these considerations lead us to evaluate the significant contribution to the total $N$ -band flux, but located interior to the dust rim, of: (1) the star itself and (2) a gaseous disk."
 The best examples of these two types of model are presented alongside the observations in refspec.., The best examples of these two types of model are presented alongside the observations in \\ref{spec}.
" First, we construct a dust envelope illuminated by a ZAMS star (but without disk component)."," First, we construct a dust envelope illuminated by a ZAMS star (but without disk component)."
" As a starting point, we use the Murakawa et al. ("," As a starting point, we use the Murakawa et al. ("
"2008) geometry, which has a parabolic cavity geometry and a cavity density that is roughly a thousand times lower than that of the envelope.","2008) geometry, which has a parabolic cavity geometry and a cavity density that is roughly a thousand times lower than that of the envelope."
" High mid-IR fluxes are now achieved by extending the inner boundary of the envelope in the z-direction, rather than emission from the disk as previously."," High mid-IR fluxes are now achieved by extending the inner boundary of the envelope in the z-direction, rather than emission from the disk as previously."
" This gives rise to a torus-like dust structure refdens)), a geometry previously suggested based on far-IR data by Harvey et al. (2000))."," This gives rise to a torus-like dust structure \\ref{dens}) ), a geometry previously suggested based on far-IR data by Harvey et al. \nocite{2000ApJ...534..846H}) )."
" The inner dust rim is constrained to be at a distance of ~170 AAU from the star, required to fit the short baselines of the Keck observations (black full and dashed lines in refste))."," The inner dust rim is constrained to be at a distance of $\sim 170$ AU from the star, required to fit the short baselines of the Keck observations (black full and dashed lines in \\ref{ste}) )."
 We ran a total of about 150 RT models and iterated to an optimal model envelope (see refmodpar))., We ran a total of about 150 RT models and iterated to an optimal model envelope (see \\ref{modpar}) ).
 We kept the same cavity opening angle as in the Murakawa et al. (, We kept the same cavity opening angle as in the Murakawa et al. (
2008) model.,2008) model.
 The “envelope-only” model is also presented in refspec by the green dash-dotted line., The “envelope-only” model is also presented in \\ref{spec} by the green dash-dotted line.
 We note that the addition of a gaseous disk (see below) does not substantially alter the total model flux., We note that the addition of a gaseous disk (see below) does not substantially alter the total model flux.
" The “envelope-only” model also reproduces the azimuthally averaged profile of a spatially resolved image, taken with the 8m SUBARU telescope (de Wit et al."," The “envelope-only” model also reproduces the azimuthally averaged profile of a spatially resolved image, taken with the 8m SUBARU telescope (de Wit et al."
 2009) (see refnorm24))., 2009) (see \\ref{norm24}) ).
" With these envelope parameters at hand, we verified that, indeed, a (hot) ZAMS object as a central illuminating source is too faint at N-band to have a significant effect on the visibilities."," With these envelope parameters at hand, we verified that, indeed, a (hot) ZAMS object as a central illuminating source is too faint at $N$ -band to have a significant effect on the visibilities."
" On the other hand, an equally luminous, cool star bright enough in N-band to have a significant contribution."," On the other hand, an equally luminous, cool star bright enough in $N$ -band to have a significant contribution."
 The exchange of a hot for a cool star is motivated by work by Hosokawa Omukai (2009)) and Hosokawa et al. (2010))., The exchange of a hot for a cool star is motivated by work by Hosokawa Omukai \nocite{2009ApJ...691..823H}) ) and Hosokawa et al. \nocite{2010ApJ...721..478H}) ).
" These authors illustrate that, during the main accretion phase, the central object undergoes a period of significant swelling (100 Ro) and has a relatively cool Teg~6000K."," These authors illustrate that, during the main accretion phase, the central object undergoes a period of significant swelling $\sim 100\,\Rsun$ ) and has a relatively cool $T_{\rm
 eff}\sim 6000\,{\rm K}$."
 A cool star with the luminosity of 22136 (the red dashed line in refspec)) has an intrinsic flux of a few percent of the total N-band flux., A cool star with the luminosity of 2136 (the red dashed line in \\ref{spec}) ) has an intrinsic flux of a few percent of the total $N$ -band flux.
" However, since an envelope illuminated by a cool star generates less flux at the short end of the mid-IR wavelength range, the fit to the SED is somewhat poorer, although the MIDI visibility spectrum is accurately reproduced."," However, since an envelope illuminated by a cool star generates less flux at the short end of the mid-IR wavelength range, the fit to the SED is somewhat poorer, although the MIDI visibility spectrum is accurately reproduced."
information not only on the motions of the stars. but also the gravitational potential responsible for the motions.,"information not only on the motions of the stars, but also the gravitational potential responsible for the motions."
 For S0 galaxies. one important piece. of stellar-dvnamica evidence would. be provided by an analysis of the Tullv-Fisher relation.," For S0 galaxies, one important piece of stellar-dynamical evidence would be provided by an analysis of the Tully-Fisher relation."
" In later-tvpe disc galaxies. there is a strong correlation. between circular rotation speed and. optica uminositv (Pully Fisher. 1977). and this relationship comes even tighter when one looks in the near infrarec λογος ""Tulle 1992)."," In later-type disc galaxies, there is a strong correlation between circular rotation speed and optical luminosity (Tully Fisher 1977), and this relationship becomes even tighter when one looks in the near infrared (Pierce Tully 1992)."
 LE SO galaxies formed in a relatively »nign wav from spiral galaxies. one would expect tha rely optical luminosities and circular rotation speeds wou »e Little affected by the process. so a Tullv-Fisher relation ga1ould still be apparent: the only significant cilference wou »r that the stripping of their gas would switch olf the star ormation process. so the optical luminosities of the SOs ga1ould fade over time. shifting the zero-point of the relation.," If S0 galaxies formed in a relatively benign way from spiral galaxies, one would expect that their optical luminosities and circular rotation speeds would be little affected by the process, so a Tully-Fisher relation should still be apparent; the only significant difference would be that the stripping of their gas would switch off the star formation process, so the optical luminosities of the S0s should fade over time, shifting the zero-point of the relation."
 'To-date. the most thorough search for a Tullv-Fisher relation in SO galaxies was that made by Neistein ((1999).," To-date, the most thorough search for a Tully-Fisher relation in S0 galaxies was that made by Neistein (1999)."
" ""Ehis analysis is complicated by the fact that there is no simple measure of the circular speed in an SO galax, there is no eas at large radii moving on circular orbits. ancl the stars follow significantly elliptical orbits. so their mean streaming velocity at any racius is lower than the local circular velocity."," This analysis is complicated by the fact that there is no simple measure of the circular speed in an S0 galaxy: there is no gas at large radii moving on circular orbits, and the stars follow significantly elliptical orbits, so their mean streaming velocity at any radius is lower than the local circular velocity."
 Neistein overcame the problem by appealing to the equations of ealactic dynamics: by making a few simplifying assumptions. they were able to use the asvmumetric drift equation (Binney Tremaine LOST) to combine the mean streaming velocity ancl velocity dispersion. of the stars in order to estimate the circular velocity at each radius.," Neistein overcame the problem by appealing to the equations of galactic dynamics: by making a few simplifying assumptions, they were able to use the asymmetric drift equation (Binney Tremaine 1987) to combine the mean streaming velocity and velocity dispersion of the stars in order to estimate the circular velocity at each radius."
 Although this analysis revealed. some evidence for a trend between L-band luminosity and circular speed. Neisten found a huge scatter in the relation. and that there was very Little olfset in the mean from the Tullv-Fisher relation of later-tvpe galaxies.," Although this analysis revealed some evidence for a trend between I-band luminosity and circular speed, Neisten found a huge scatter in the relation, and that there was very little offset in the mean from the Tully-Fisher relation of later-type galaxies."
 They therefore concluded that jese systems could. not all have formed from the simple garipping of spiral galaxies., They therefore concluded that these systems could not all have formed from the simple stripping of spiral galaxies.
 Instead. they suggested that the ul0 classification actually represents a rather heterogeneous ‘lass of galaxies. which formed through a rather wide variety of processes.," Instead, they suggested that the S0 classification actually represents a rather heterogeneous class of galaxies, which formed through a rather wide variety of processes."
 They further suggested that the absence of an olfset in the Tullv-Fisher relation could be understood if the SO galaxies have more massive disces. so any fading in their luminosities is olfset by the larger number of stars.," They further suggested that the absence of an offset in the Tully-Fisher relation could be understood if the S0 galaxies have more massive discs, so any fading in their luminosities is offset by the larger number of stars."
 1n order to explore these conclusions a little further. this paper presents a detailed. dynamical. analysis of six. SO ealaxies.," In order to explore these conclusions a little further, this paper presents a detailed dynamical analysis of six S0 galaxies."
 These galaxies have been selected to contain relatively small central bulges., These galaxies have been selected to contain relatively small central bulges.
 IP any SOs formed [rom simple stripping processes. one would expect their bulges to be little: alfected.," If any S0s formed from simple stripping processes, one would expect their bulges to be little affected."
 Thus. by. selecting SOs with the small bulges characteristic of later-tvpe spirals. one might hope to pick out a relatively. homogeneous. subsample of systems that formed via this route.," Thus, by selecting S0s with the small bulges characteristic of later-type spirals, one might hope to pick out a relatively homogeneous subsample of systems that formed via this route."
 Unfortunately. it is only when SO galaxies are very close to edge on that one can reliably determine that their bulges are small.," Unfortunately, it is only when S0 galaxies are very close to edge on that one can reliably determine that their bulges are small."
 As Neistein ((1999) demonstrated. the line-of-sight. integration of starlicht. through such an edge-on disc means that there is quite a large correction to convert the observable mean line-of-sight velocity into the circular streaming velocity of the stars.," As Neistein (1999) demonstrated, the line-of-sight integration of starlight through such an edge-on disc means that there is quite a large correction to convert the observable mean line-of-sight velocity into the circular streaming velocity of the stars."
 As a further complication. the observed velocity distribution for any line of sight through an edge-on disc will be highly non-Ciaussian. due to the contribution from stars at large radii with small line-oFsieht velocities.," As a further complication, the observed velocity distribution for any line of sight through an edge-on disc will be highly non-Gaussian, due to the contribution from stars at large radii with small line-of-sight velocities."
 A dynamical analysis based. on moments derived. [rom a Gaussian fit to the line-of-sight velocity distribution is therefore. prone to systematic error., A dynamical analysis based on moments derived from a Gaussian fit to the line-of-sight velocity distribution is therefore prone to systematic error.
 “Lo obviate these clilliculties. the current analysis uses data with a high enough signal-to-noise ratio for the complete line-of-sight. velocity distribution to be derived. ancl these data are then fitted to a complete dynamical model in order to derive both the stellar distribution function and the gravitational potential needed for the Tullv-Eisher relation.," To obviate these difficulties, the current analysis uses data with a high enough signal-to-noise ratio for the complete line-of-sight velocity distribution to be derived, and these data are then fitted to a complete dynamical model in order to derive both the stellar distribution function and the gravitational potential needed for the Tully-Fisher relation."
 The remainder of the paper is laid out as follows., The remainder of the paper is laid out as follows.
 Section ?? describes the sample. the data analysis. the mocel fitting. and the resulting distribution functions and rotation curves.," Section \ref{datasec} describes the sample, the data analysis, the model fitting, and the resulting distribution functions and rotation curves."
 Section ??. discusses the correlations in derived. quantities. with particular reference to. the Tullv-Fisher. relation.," Section \ref{discussionsec} discusses the correlations in derived quantities, with particular reference to the Tully-Fisher relation."
 Section ??— presents the conclusions that can be drawn from this analysis., Section \ref{conclusionsec} presents the conclusions that can be drawn from this analysis.
 The galaxies chosen for this study were selected. from the sample presented in Exuijken. Fisher Alerrificlel (1996).," The galaxies chosen for this study were selected from the sample presented in Kuijken, Fisher Merrifield (1996)."
 This galaxy sample contains 28 early-type disce: galaxies. and was originally observed to search. for counter-rotating populations. so high signal-to-noise ratio spectra were obtained.," This galaxy sample contains 28 early-type disc galaxies, and was originally observed to search for counter-rotating populations, so high signal-to-noise ratio spectra were obtained."
 Details of the spectroscopic observations and stancare data reduction can be found in Ixuijken. Fisher Merrifield. (1996).," Details of the spectroscopic observations and standard data reduction can be found in Kuijken, Fisher Merrifield (1996)."
 From this sample we selected the six ul0 galaxies of with similar mean rotation speeds. so that there is some chance that the svstems are comparable in their dynamics.," From this sample we selected the six S0 galaxies of with similar mean rotation speeds, so that there is some chance that the systems are comparable in their dynamics."
 We also selected. galaxies that are close nough to edge-on for it to be apparent that the systems are isc-dominated. with relatively small bulges (and thus that a simple evolutionary. path [rom later-type spiral galaxies is plausible).," We also selected galaxies that are close enough to edge-on for it to be apparent that the systems are disc-dominated, with relatively small bulges (and thus that a simple evolutionary path from later-type spiral galaxies is plausible)."
 Images of the sample galaxies are shown in Vig. 1.., Images of the sample galaxies are shown in Fig. \ref{sampleimages}.
 LOSVDs were extracted from the reduced. spectra using the unresolved: gaussian decomposition (UGD) algorithm (Ixuijken Morrifield 0903)., LOSVDs were extracted from the reduced spectra using the unresolved gaussian decomposition (UGD) algorithm (Kuijken Merrifield 1993).
 This method. models. each LOSVD as the sum of a set of unresolved gaussians with fixed means ancl dispersions., This method models each LOSVD as the sum of a set of unresolved gaussians with fixed means and dispersions.
 The amplitudes of the eaussians are varied so as to minimize the dillerence between the galaxy spectrum and. the mocel derived by convolving the LOSVD with a suitable template star spectrum., The amplitudes of the gaussians are varied so as to minimize the difference between the galaxy spectrum and the model derived by convolving the LOSVD with a suitable template star spectrum.
 This approach has the advantage that it does not force any particular. functional form. on the LOSVD. beyond. the," This approach has the advantage that it does not force any particular functional form on the LOSVD, beyond the"
Another spectrum of the star obtained with VLE UVES was significantly cifferent from the FEROS spectrum with much less intense spectral lines of the rare earth. elements (ονhammeretal. 20082).,Another spectrum of the star obtained with VLT UVES was significantly different from the FEROS spectrum with much less intense spectral lines of the rare earth elements \citealt{Freyhammer08b}) ).
 The similarity of the spectra and chemical abundances of 096237 to those of 1101065. which was the first. detected: rapidly oscillating Ap star. increases the interest of this star.," The similarity of the spectra and chemical abundances of 96237 to those of 101065, which was the first detected rapidly oscillating Ap star, increases the interest of this star."
 Lt is not known what determines the pulsation amplitude of the roAp stars., It is not known what determines the pulsation amplitude of the roAp stars.
 While the principal periods of 996237 and 1101065 are similar mmin ancl mmin. respectively). their photometric ancl spectroscopic radial velocity amplitudes are very clillerent.," While the principal periods of 96237 and 101065 are similar min and min, respectively), their photometric and spectroscopic radial velocity amplitudes are very different."
 Our results for 669013 demonstrate clearly that this is à new roAp star with a low pulsation amplitude., Our results for 69013 demonstrate clearly that this is a new roAp star with a low pulsation amplitude.
 This star shows possible rotation modulation anc may. be a useful target to study pulsation behaviour over rotation period., This star shows possible rotation modulation and may be a useful target to study pulsation behaviour over rotation period.
 DWI and VG acknowledge support for this work from the Science and Technology. Facilities Council (SPEC) of the Ulx., DWK and VGE acknowledge support for this work from the Science and Technology Facilities Council (STFC) of the UK.
 This paper uses observations made at the South African Astronomical Observatory (SAO)., This paper uses observations made at the South African Astronomical Observatory (SAAO).
aare scaled from those of ICT and helium (Neuleld&Green.1994).,are scaled from those of HCl and helium \citep{neufeld1994}.
. The average Galactic background radiation field adopted in RADEX consists of the cosmic microwave background. average Galactic starlight in (he solar neighborhood in ultraviolet/visible/near-inlrared part of the spectrum. ancl single-temperature fit to the Galactic thermal dust. emission Lor the far-infrared and submillimeter part of the spectrum.," The average Galactic background radiation field adopted in RADEX consists of the cosmic microwave background, average Galactic starlight in the solar neighborhood in ultraviolet/visible/near-infrared part of the spectrum, and single-temperature fit to the Galactic thermal dust emission for the far-infrared and submillimeter part of the spectrum."
 Contributions from non-thermal radiation in the Galaxy are also included for low frequency part of the spectrum (<30 Gllz)., Contributions from non-thermal radiation in the Galaxy are also included for low frequency part of the spectrum $\le$ 30 GHz).
 This composite interstellar radiation field and any additional continuum background [rom user input provide radiative excitation in the RADEX formulism., This composite interstellar radiation field and any additional continuum background from user input provide radiative excitation in the RADEX formulism.
 For the subset of our sample where ILC] emission is observed. no significant. continuum is seen in anv of these sources.," For the subset of our sample where HCl emission is observed, no significant continuum is seen in any of these sources."
 We therefore use the default composite interstellar radiation field in RADEN simulations., We therefore use the default composite interstellar radiation field in RADEX simulations.
 Simulations were run in off-line mode to cover a large parameter space. and relative |? was sought between the observed line temperatures ancl the model results relative to the observed line temperature.," Simulations were run in off-line mode to cover a large parameter space, and relative $\chi^2$ was sought between the observed line temperatures and the model results relative to the observed line temperature."
 Under the assumption that the observed ILC] emission suffers no sienilicant beam dilution. this process vields [or a given gas temperature (he most likely combination of eas density and HC] column density to reproduce the observed line strength ol the hyperfine components.," Under the assumption that the observed HCl emission suffers no significant beam dilution, this process yields for a given gas temperature the most likely combination of gas density and HCl column density to reproduce the observed line strength of the hyperfine components."
 Figure 5. shows a RADEX simulation run for OMC-I (0. -60) with a gas temperature of 45 IX. Contours are the relative 4? starting [rom 0.5 wilh a step of -Q.1: blue and red curves mark (he hyperfine component ratios under optically (hin limit (3 between F=5/23/2 and F=1/23/2 (transitions in blue. 1.5 between F=5/23/2 and F—3/2/3/2 transitions in red).," Figure \ref{fig:radex} shows a RADEX simulation run for OMC-1 (0, -60) with a gas temperature of 45 K. Contours are the relative $\chi^2$ starting from 0.5 with a step of -0.1; blue and red curves mark the hyperfine component ratios under optically thin limit (3 between F=5/2–3/2 and F=1/2–3/2 transitions in blue, 1.5 between F=5/2–3/2 and F=3/2–3/2 transitions in red)."
 The solid smooth line denotes (he observed optical cept for the ICI line ancl the two dotted lines its zo error bar., The solid smooth line denotes the observed optical depth for the HCl line and the two dotted lines its $\pm1\sigma$ error bar.
 In cases where the quoted errors for LICL optical depth in Table 2. exceed30%.. we generally use to set the error bar for the optical depth.," In cases where the quoted errors for HCl optical depth in Table \ref{tab:line-fit} exceed, we generally use to set the error bar for the optical depth."
 The cross-section between the 4? contours and the optical depth curves Clearly confines gas density and HCl column density in an often tight range., The cross-section between the $\chi^2$ contours and the optical depth curves clearly confines gas density and HCl column density in an often tight range.
obtain information on galactic structure through the use of variables such as RR Lyrac as standard candles. ancl is the Κον to determining extra-galactic clistances through the use of standard candles such as Cepheids and supernovae “Pvpe I Most of our knowledge of variability is based. on the study of apparently bright sources. which naturally selects members of.σα. bright populations.,"obtain information on galactic structure through the use of variables such as RR Lyrae as standard candles, and is the key to determining extra-galactic distances through the use of standard candles such as Cepheids and supernovae Type Ia. Most of our knowledge of variability is based on the study of apparently bright sources, which naturally selects members of bright populations."
 t. present ittle is known about variability of intrinsically fainter populations because in bright samples they are. lacking altogether. or are. only represented. by a few members., At present little is known about variability of intrinsically fainter populations because in bright samples they are lacking altogether or are only represented by a few members.
 The Faint Sky Variability Survey (οσι Groot et. al. (2003))), The Faint Sky Variability Survey (FSVS; Groot et al. \shortcite{groot03}) )
 was designed to account for this deficit by studying wo unexplored regions of the variability space: the short imescale variability region (down to tens of minutes) and he intrinsically faint variable sources (down to V — 24 mag) at mid and high Galactic [atitudes., was designed to account for this deficit by studying two unexplored regions of the variability space: the short timescale variability region (down to tens of minutes) and the intrinsically faint variable sources (down to V = 24 mag) at mid and high Galactic latitudes.
 The FSVS also contains colour information for all targets. giving us the option of positioning objects in the colour-colour. diagram as well as finding the variability timescales and. amplitudes that characterise them.," The FSVS also contains colour information for all targets, giving us the option of positioning objects in the colour-colour diagram as well as finding the variability timescales and amplitudes that characterise them."
 The main aims ofthe FSVS are thus to obtain a map of a region of the Galaxy (1 ddeg?) in variability ancl colour space. to determine the population density of the different variable objects that reside in the Galaxy and to find the photometric signature of up-to-now unknown intrinsically faint variable populations.," The main aims of the FSVS are thus to obtain a map of a region of the Galaxy $\sim$ $^2$ ) in variability and colour space, to determine the population density of the different variable objects that reside in the Galaxy and to find the photometric signature of up-to-now unknown intrinsically faint variable populations."
 In this paper we explore these three goals., In this paper we explore these three goals.
 There are other surveys that study the variable optical sky. cach emphasising one aspect or one particular region of this parameter space.," There are other surveys that study the variable optical sky, each emphasising one aspect or one particular region of this parameter space."
 The timescales sampled. depth and sky coverage of dilferent variability surveys varies depending on the astronomical objects they are designed to study.," The timescales sampled, depth and sky coverage of different variability surveys varies depending on the astronomical objects they are designed to study."
 For example. with a brightness limit similar to the PSVS. Street et al.," For example, with a brightness limit similar to the FSVS, Street et al."
 (2005). study the variability around an open cluster with timescales longer than a few hours. and Itansay JlHlakala (2005) study the rapid variability (down to 2 minutes) of objects as faint as 722.5.," \shortcite{s05} study the variability around an open cluster with timescales longer than a few hours, and Ramsay Hakala \shortcite{rh05} study the rapid variability (down to 2 minutes) of objects as faint as $\sim$ 22.5."
 OF great interest is the Deep Lens Survey (DLS) that. in a similar wav to 10 FSVS. combines colour ane variability information and explores similar variability timescales (Beckeretal.2004).," Of great interest is the Deep Lens Survey (DLS) that, in a similar way to the FSVS, combines colour and variability information and explores similar variability timescales \cite{dls}."
. Becker ct al., Becker et al.
 (2004) also provide a comprehensive review of vast and on-going variability surveys., \shortcite{dls} also provide a comprehensive review of past and on-going variability surveys.
 The future of optical variability surveys looks quite omising with the advent of large aperture telescopes such as the Larec-aperture Synoptic Survey S.43mim Telescope (Lvson2002).. the 4nim telescope VISTA and the nim ΝΕΤ Survey Telescope.," The future of optical variability surveys looks quite promising with the advent of large aperture telescopes such as the Large-aperture Synoptic Survey m Telescope \cite{tyson02}, the m telescope VISTA and the m VLT Survey Telescope."
 Vhe full Faint Sky Variability Survey (FESVS) data set consists of 78 Wide Field Camera (WEC) fields taken with the Isaac Newton telescope (INT) at La Palma., The full Faint Sky Variability Survey (FSVS) data set consists of 78 Wide Field Camera (WFC) fields taken with the Isaac Newton telescope (INT) at La Palma.
 The SVS covers an area in the sky of —21ddeg located at mid and high Galactic latitudes 40<b< 21. 15«b «50. SO«b «90).," The FSVS covers an area in the sky of $\sim$ $^2$ located at mid and high Galactic latitudes $-$ $<b<$$-$ 21, $<b<$ 50, $<b<$ 90)."
 The WEC is a moisac of four 2kxtk CCDs., The WFC is a moisac of four 2kx4k CCDs.
 For cach field. we took one set of D. Ll and V band observations on a given photometric night.," For each field, we took one set of B, I and V band observations on a given photometric night."
 Photometric variability observations were taken with the V filter on several consecutive nights., Photometric variability observations were taken with the V filter on several consecutive nights.
 On average. fields were observed 10 20 times within one week in the V band.," On average, fields were observed 10 – 20 times within one week in the V band."
 Exposure times were LO min with a dead. time between observations of 2 min., Exposure times were 10 min with a dead time between observations of 2 min.
 This observing pattern allows us to sample perioclicity imescales [rom (observing time | dead time) (Le. 24 min) to twice the maximum time separation of observations (which ranges [rom 3 davs to 13 davs)., This observing pattern allows us to sample periodicity timescales from $\times$ (observing time + dead time) (i.e. 24 min) to twice the maximum time separation of observations (which ranges from 3 days to 13 days).
 See for more details Groot et al. (2003)., See for more details Groot et al. \shortcite{groot03}.
. ALL Gelels were re-observed: vears later to. cletermine oper motions., All fields were re-observed years later to determine proper motions.
 In this paper we concentrate on the shorter imescale variability. (from 0.4 hours to a few days) of the argets and we do not include those observations., In this paper we concentrate on the shorter timescale variability (from 0.4 hours to a few days) of the targets and we do not include those observations.
 Of the 78 fields. LO were only observed in the V. band on two or three occasions due to bac weather. making it impossible to use these for precise variability studies.," Of the 78 fields, 10 were only observed in the V band on two or three occasions due to bad weather, making it impossible to use these for precise variability studies."
 We also encountered cata accquisition/reduction problems in several occasions which resulted. in. parts of fields being lost., We also encountered data acquisition/reduction problems in several occasions which resulted in parts of fields being lost.
 Initially 79 fields were defined but one. 67. was never observed.," Initially 79 fields were defined but one, 67, was never observed."
 For data handling consistency we have kept the original numbering., For data handling consistency we have kept the original numbering.
 A complimentary analysis on the variability at. short and long timescales (including vear-Iong timescales) of the ESVS has been carried out by Huber et al. (2006)., A complimentary analysis on the variability at short and long timescales (including year-long timescales) of the FSVS has been carried out by Huber et al. \shortcite{h06}.
.. They make use of a variability test similar to that described in Section 3.1 to find signatures of the presence of variability with some indication of its timescale and amplitude.," They make use of a variability test similar to that described in Section \ref{an:chisq}
 to find signatures of the presence of variability with some indication of its timescale and amplitude."
 By using the vearly re-observations they find a variability fraction of 5 to s percent in two survey regions., By using the yearly re-observations they find a variability fraction of 5 to 8 percent in two survey regions.
 This number is larger than that found in Section 4.1 due to several factors: in our analysis we are only considering shor period variables and thus do not make use of the vearly re- we determine the variability [fraction using the entire area of the survey instead of two separate regions. anc we use a reduced weighted X7 to establish variability insteac of the reduced. un-weighted 47 found in the public release IFSVS data products.," This number is larger than that found in Section \ref{res:varnovar} due to several factors: in our analysis we are only considering short period variables and thus do not make use of the yearly re-observations, we determine the variability fraction using the entire area of the survey instead of two separate regions, and we use a reduced weighted $\chi^2$ to establish variability instead of the reduced un-weighted $\chi^2$ found in the public release FSVS data products."
 Most. of the variable. sources. fou by Huber et al., Most of the variable sources found by Huber et al.
 (2006). are lone period variables classifie as such thanks to the V brightness of the re-observation a vear later., \shortcite{h06} are long period variables classified as such thanks to the V brightness of the re-observation a year later.
 Phe number of possible periodicities in the data when the sampling is sparse and the time span long is very large and their analysis is devised to find possible variable systems more than to find their actual variability timescale ancl amplitude. which is one of the main goals of the work presented here.," The number of possible periodicities in the data when the sampling is sparse and the time span long is very large and their analysis is devised to find possible variable systems more than to find their actual variability timescale and amplitude, which is one of the main goals of the work presented here."
 ‘Table 1. gives a list of the number of times cach field was observed in V and the maximum time span of the data in each case., Table \ref{obs:jo} gives a list of the number of times each field was observed in V and the maximum time span of the data in each case.
 In summary. we have photometric data that can be used for variability analvsis for —17.5ddeg out of the 21ddeg? that constitute the ESVS.," In summary, we have photometric data that can be used for variability analysis for $\sim$ $^2$ out of the $^2$ that constitute the FSVS."
 For ~9.2 ddeg? the number of measurements is equal or more than 15 whereas for the other 78.3 ddeg? the number is between 5 and. 15., For $\sim$ $^2$ the number of measurements is equal or more than 15 whereas for the other $\sim$ $^2$ the number is between 5 and 15.
 Vhis makes a dilferenee in the accuracy with which we can measure the variability timescale of cach object., This makes a difference in the accuracy with which we can measure the variability timescale of each object.
 Phe methods. used. to study. the variability in the, The methods used to study the variability in the
frequency Sy~6.,frequency $S_N \sim 6$.
 This relatively high value suggests that we have not missed a significant number of IGC's. and that the properties of these flour [GC's may be representative of the 1GC population in Virgo.," This relatively high value suggests that we have not missed a significant number of IGCs, and that the properties of these four IGCs may be representative of the IGC population in Virgo."
 Our value of Sy~6 can be used to place a constraint on the origins of the Virgo intracluster population., Our value of $S_N \sim 6$ can be used to place a constraint on the origins of the Virgo intracluster population.
 If most of (he stars in Virgos intergalactic space originated in (vpical spirals (i.e..wereliberatedvia(hegalaxy.harassment 1999).. (hen we would expect to measure a much lower value for the globular cluster specific frequency. wilh Sy~1 (e.g..Goudfrooi]etal.2003:Chandar.Whitmore.&Lee2004).," If most of the stars in Virgo's intergalactic space originated in typical spirals \citep[\ie\
were liberated via the galaxy harassment scenario of][]{moore96,
moore99}, then we would expect to measure a much lower value for the globular cluster specific frequency, with $S_N \sim 1$ \citep[\eg][]{goudfrooij03, chandar04}."
. This argument may apply to low surface brightness spirals as well (JIL. Ixim et al..," This argument may apply to low surface brightness spirals as well (J.H. Kim et al.,"
 in preparation)., in preparation).
 Alternatively. if intracluster stars are the disrupted remains of low-luminosity cwarfs. then Sx should be ~20 (Qrebel.Dolphin.&Guhathakurta2000;Straderetal.2003).," Alternatively, if intracluster stars are the disrupted remains of low-luminosity dwarfs, then $S_N$ should be $\sim 20$ \citep{grebel00, strader03}."
. Our value for the specific frequency. of globular clusters lies between (hese (wo extremes. in the range normally associated with ο) galaxies (Westοἱal.1995:Forbes.Drodie.&Grilimair1997) and dwarf ellipticals (Durrelletal.1996:Miller1998:Beasley2006).," Our value for the specific frequency of globular clusters lies between these two extremes, in the range normally associated with cD galaxies \citep{west95, forbes97} and dwarf ellipticals \citep{durrell96, miller98, beasley06}."
. In fact. dwarf elliptical galaxies are the most common morphological (wpe in galaxy. clusters (Dinggeli.Sandage.&Tammann1933).. and the Virgo core currently contains about 900 of these objects.," In fact, dwarf elliptical galaxies are the most common morphological type in galaxy clusters \citep{binggeli88}, and the Virgo core currently contains about 900 of these objects."
 This is a significant number of galaxies: Durrelletal.(2002) estimate that if two-thirds of all dwarl ellipicals are destroved through gravitational interactions over a IIubble time. then their remnants could account for Virgos entire intracluster population.," This is a significant number of galaxies: \citet{durrell02} estimate that if two-thirds of all dwarf ellipticals are destroyed through gravitational interactions over a Hubble time, then their remnants could account for Virgo's entire intracluster population."
 The preceding has (wo caveats., The preceding has two caveats.
 First. (he low metallicities ancl high specific frequency of 1GCs could be due to prelerential stripping of elobular clusters during tidal encounters.," First, the low metallicities and high specific frequency of IGCs could be due to preferential stripping of globular clusters during tidal encounters."
 The racial distribution of clusters within a galaxy is often flatter than that of the galaxys light (e.g..Puziaetal.2004:Forbes2006): this fact is consistent with the idea that such svstems are often formed curing galactic mergers and interactions (Ashman&Zepf1992).," The radial distribution of clusters within a galaxy is often flatter than that of the galaxy's light \citep[\eg][]{puzia2004, forbes2006}; this fact is consistent with the idea that such systems are often formed during galactic mergers and interactions \citep{ashman1992}."
. since clusters (and stus) in Che outskirts of galaxies are more susceptible to tidal forces (han interior objects. (his mismatch can lead to the increased stripping of globular clusters with respect to the stars.," Since clusters (and stars) in the outskirts of galaxies are more susceptible to tidal forces than interior objects, this mismatch can lead to the increased stripping of globular clusters with respect to the stars."
 The result is (hat in rich clusters. where tidal encounters are important. the specific frequency. of clusters in intergalactic space can be enhanced at (hie expense of galactic values.," The result is that in rich clusters, where tidal encounters are important, the specific frequency of clusters in intergalactic space can be enhanced at the expense of galactic values."
 There is some evidence for just this ellect: in Virgo. some galaxies have lower values of Sy (han (heir field counterparts (seeElueereen1999.andreferences. therein). ," There is some evidence for just this effect: in Virgo, some galaxies have lower values of $S_N$ than their field counterparts \citep[see][and references
therein]{elmegreen1999}. ."
Aloreover. since svstems of blue globular clusters often have flatter racial distributions (han those of red clusters (e.g.Dassino.Richtler.&Dirsch2006:Forbes 2006).. this process can explain why the four LGC! candidates found in our survey are all metal-poor.," Moreover, since systems of blue globular clusters often have flatter radial distributions than those of red clusters \citep[\eg][]{bassino2006, forbes2006, harris06}, this process can explain why the four IGC candidates found in our survey are all metal-poor."
 A second caveat to our measurement of Sa concerns the survival of clusters in the galactic and extragalactic environments., A second caveat to our measurement of $S_N$ concerns the survival of clusters in the galactic and extragalactic environments.
 In large galaxies. bulge shocks. disk shocks.and," In large galaxies, bulge shocks, disk shocks,and"
Astrophysical fluids are magnetized and therefore. the astrophysical turbulence is magnetohydrodynamic (MHD) in its nature.,Astrophysical fluids are magnetized and therefore the astrophysical turbulence is magnetohydrodynamic (MHD) in its nature.
 Compressible MHD turbulence ts a key element for understanding star formation and velocity fluctuations. determine many of its properties., Compressible MHD turbulence is a key element for understanding star formation and velocity fluctuations determine many of its properties.
 For instance. in the modern paradigm of star formation that turbulent velocity sweep up the matter from large expands of the interstellar space to create molecular clouds.," For instance, in the modern paradigm of star formation that turbulent velocity sweep up the matter from large expands of the interstellar space to create molecular clouds."
 Thus. it is important to know the statistical properties of the velocity field. e.g. its spectrum that reflects how much energy Is associated with the motions at a particular scale (see below).," Thus, it is important to know the statistical properties of the velocity field, e.g. its spectrum that reflects how much energy is associated with the motions at a particular scale (see below)."
 A further insight into the properties of turbulence. including its generation. consequences and dissipation calls for the use of more sophisticated measures.," A further insight into the properties of turbulence, including its generation, consequences and dissipation calls for the use of more sophisticated measures."
 For example. the processes of magnetic field generation depend on the velocity field vorticity associated with the solenoidal motions. while the processes of compressing gas are determined by the compressible motions.," For example, the processes of magnetic field generation depend on the velocity field vorticity associated with the solenoidal motions, while the processes of compressing gas are determined by the compressible motions."
 In approaching the problem of decomposing velocity field into solenoidal and dilatational put following the Helmholtz-Hodge decomposition i5 frequently attempted 2009)., In approaching the problem of decomposing velocity field into solenoidal and dilatational part following the Helmholtz-Hodge decomposition is frequently attempted .
 Another approach ts the decomposition of the turbulent field in MHD case into basic modes. re.. Alfvénn. slow and fast waves.," Another approach is the decomposition of the turbulent field in MHD case into basic modes, i.e., Alfvénn, slow and fast waves."
 While this approach ts trivial for the case of the strong magnetic field with infinitesimal fluctuations 1980).. proposed astatistical decomposition of modes in the Fourier space.," While this approach is trivial for the case of the strong magnetic field with infinitesimal fluctuations , proposed a decomposition of modes in the Fourier space."
 The statistical nature of the procedure is clear when one considers its application to strongly perturbed magnetic fields., The statistical nature of the procedure is clear when one considers its application to strongly perturbed magnetic fields.
 As the Fourier transform 1s defined in the reference frame related to the mean magnetic field. while the MHD motions happen in respect to the local magnetic field. there is an inevitable contribution of all types of motion to the decomposed modes.," As the Fourier transform is defined in the reference frame related to the mean magnetic field, while the MHD motions happen in respect to the local magnetic field, there is an inevitable contribution of all types of motion to the decomposed modes."
 However. studying the cases when the real space decomposition was possible in real space. showed that the cross-talk between the modes is small for subAlfvénnie turbulence.," However, studying the cases when the real space decomposition was possible in real space, showed that the cross-talk between the modes is small for subAlfvénnic turbulence."
 Testing of the results in CLO3 and increasing the accuracy of the MHD mode decomposition of turbulence Is one of the key goals of the present study., Testing of the results in CL03 and increasing the accuracy of the MHD mode decomposition of turbulence is one of the key goals of the present study.
 In doing so in the present paper we make use of the wavelet transformations in addition to the Fourier transformations., In doing so in the present paper we make use of the wavelet transformations in addition to the Fourier transformations.
 Wavelets present a natural way of describing MHD turbulence., Wavelets present a natural way of describing MHD turbulence.
" Indeed. while in the representation of the model of turbulence the anisotropy is frequently described in terms of eddies with parallel «| and perpendicular Kj, wave vectors. the actual description calls for choosing for | and L in respect to the/oca/ magneticfield'."," Indeed, while in the representation of the model of turbulence the anisotropy is frequently described in terms of eddies with parallel $k_{\|}$ and perpendicular $k_{\bot}$ wave vectors, the actual description calls for choosing for $\|$ and $\bot$ in respect to the magnetic."
. The latter is really easy to understand. as it is only local magnetic field that influences fluid motions at à given point.," The latter is really easy to understand, as it is only local magnetic field that influences fluid motions at a given point."
 Wavelets allow for a local description of the magnetized, Wavelets allow for a local description of the magnetized
 Ruderman&Sutherland(1975.hereafterRS75) ExDB Q-B«0. 3?Fe (lorreviewseeAbrahams&Melros," \citet[][ hereafter RS75]{rs75} ${\bf E}\times{\bf B}$ ${\bf\Omega}\cdot{\bf B}<0$ $^{56}_{26}$ \citep[for review see][]{as91,um95,xqz99}."
e1995:Xuetal.1999).. 2; R~105 2;=5D. 629Lin , $^{56}_{26}$ ${\cal R}\sim 10^6$ $B_s=bB_d$ $b \gg 1$ 
cells where the thermal gas deusity drops below 1079ecu iuxideὉ,cells where the thermal gas density drops below $10^{-30}$g $^{-3}$.
",This restriction ouly affects some suall reeious deep the bubbles. aud does not appreciably affect thebubbleevolution."," This restriction only affects some small regions deep inside the bubbles, and does not appreciably affect the bubble evolution."
 Tere we present tho results of our numerical calculations. which are compared directly with the eanuua-rayv observations of the bubbles.," Here we present the results of our numerical calculations, which are compared directly with the gamma-ray observations of the bubbles."
 Our mai purpose is not to perfectly| reproduce the bubbles. but rather we aimi to identity poreutia phivsical niechanisnis relevant for the bubble eveut.," Our main purpose is not to perfectly reproduce the bubbles, but rather we aim to identity potential physical mechanisms relevant for the bubble event."
 Iu particular. we investigate the poteutial roles of viscosity and CR diffusion on thebubble evolution aud the CR distribution within the bubbles.," In particular, we investigate the potential roles of viscosity and CR diffusion on the bubble evolution and the CR distribution within the bubbles."
 To study if viscosity. can indeed suppress the development of NIT iustabilities. we performed a series of simulations with different levels of viscosity.," To study if viscosity can indeed suppress the development of KH instabilities, we performed a series of simulations with different levels of viscosity."
" These rus are denoted as ""run Vg. where the viscosity coefficient for our six runs are chosen to be pq,=0. 0.5. 1. 3. 10. aud © Lou D (see Table 1)."," These runs are denoted as “run $\mu$ ”, where the viscosity coefficient for our six runs are chosen to be $\mu_{\rm visc} = 0$, 0.5, 1, 3, 10, and 30 g $^{-1}$ $^{-1}$ (see Table 1)."
 In these runs. CR diffusion plavs a uceleible role. as CR. diffusivity is always chosen to be a small constant &=3«1075 c? 1 (see equation 7).," In these runs, CR diffusion plays a negligible role, as CR diffusivity is always chosen to be a small constant $\kappa=3\times10^{26}$ $^{2}$ $^{-1}$ (see equation 7)."
 Fiewre 2. shows central slices of CR energy. density distribution iu these ruus at f=fgg. when the resulting CR bubble reaches a distance of τ=10.5 kpe along the jet direction.," Figure \ref{plot2} shows central slices of CR energy density distribution in these runs at $t=t_{\rm Fermi}$, when the resulting CR bubble reaches a distance of $z=10.5$ kpc along the jet direction."
 Iu the uon-viscous run VO. regularities clearly develop at the surface of the jetanduced CR bubble. indicating the significance of KII instabilities.," In the non-viscous run V0, irregularities clearly develop at the surface of the jet-induced CR bubble, indicating the significance of KH instabilities."
 As the viscosity cocficient iucreases in ruus VO.5 and Vi. the magnitude of surface nreenlaritics becomes s2aller.," As the viscosity coefficient increases in runs V0.5 and V1, the magnitude of surface irregularities becomes smaller."
 Iu vin V3. VIO. and V30. surface irregularities disappear.," In run V3, V10, and V30, surface irregularities disappear."
 Thus viscosity effectivolv suppresses RT aud WO instabilities when jeZ9 οTEM tootNoc. us ThisisIs , Thus viscosity effectively suppresses RT and KH instabilities when $\mu_{\rm visc}\gtrsim 3$ g $^{-1}$ $^{-1}$.
exactlyexacth: whatwhi: weο expected: As the viscosity coefficient. iucreases; the viscous stress at thebubble surfacebecomes more significant. effectively suppressing the erowth of small perturbations. which would otherwise erow into large vortices.," This is exactly what we expected: As the viscosity coefficient increases, the viscous stress at the bubble surface becomes more significant, effectively suppressing the growth of small perturbations, which would otherwise grow into large vortices."
 As discussed in Section2.2. the true value of viscosity in and out the bubbles is very unclear. particularly due to the uncertain role of magnetic fieldsiu transport processes.," As discussed in Section 2.2, the true value of viscosity in and out the bubbles is very unclear, particularly due to the uncertain role of magnetic fields in transport processes."
 The values of viscosity adopted in successful ruus V3. VIO. and VW30. respectively faa.=3. 10. 3080mbs tare mech less than the Spitzer viscosity of hot eas sumroundiug thebubbles.," The values of viscosity adopted in successful runs V3, V10, and V30, respectively $\mu_{\rm visc}=3$, $10$, $30\text{ g cm}^{-1}\text{ s}^{-1}$, are much less than the Spitzer viscosity of hot gas surrounding the bubbles."
 This hot gas is strouglv heated by the jet-nduced shock. aud currently has temperatures of ~0.6 «IO K (even higher at earlier times).," This hot gas is strongly heated by the jet-induced shock, and currently has temperatures of $\sim 0.6$ – $4\times 10^{8}$ K (even higher at earlier times)."
 For comparison. the temperature 10? lk correspouds to the Spitzer viscosity (eq.," For comparison, the temperature $10^{8}$ K corresponds to the Spitzer viscosity (eq."
" 5) of ~6000&en.ts 1, ", 5) of $\sim 6000\text{ g cm}^{-1}\text{ s}^{-1}$ .
Thus the adopted viscosities in these ruus are onlv around 0.1 l'4 of the Spitzer value in the surrounding eas., Thus the adopted viscosities in these runs are only around $0.1\%$ - $1\%$ of the Spitzer value in the surrounding gas.
 Such a low viscosity level max represent the true level of momentum transport rate across bubble edges., Such a low viscosity level may represent the true level of momentum transport rate across bubble edges.
 This is due to the suppression of transpor across nearlv-parallel maguctic field lines at thebubble processessurface. as discussed in Section2.2.," This is due to the suppression of transport processes across nearly-parallel magnetic field lines at the bubble surface, as discussed in Section 2.2."
 It is likely that near thebubble surface. the magnetic field lues are not completely taugeutial aud a simall level of field taugliug allows a low level of momentum transport across the bubble surface. which is strong enough to suppress the instabilities as shown in our calculations.," It is likely that near the bubble surface, the magnetic field lines are not completely tangential and a small level of field tangling allows a low level of momentum transport across the bubble surface, which is strong enough to suppress the instabilities as shown in our calculations."
 The nuportanee of viscous transport inside but near the bubble surface can be seen bv small values of the Revuolds uuuber in the jet backflow: where p—107)@anP and Lo0.1 kpe are rouelily the thermal gas deusitv aud thickuess of the jet backflow laver., The importance of viscous transport inside but near the bubble surface can be seen by small values of the Reynolds number in the jet backflow: where $\rho\sim 10^{-29}\text{ g cm}^{-3}$ and $L\sim 0.1$ kpc are roughly the thermal gas density and thickness of the jet backflow layer.
 In contrast. the Reynolds uunuber in the aimbieut shock-heated gas is much larecr: where p~LOecmP aud £~10 kpe are roughly the thermal gas density aud. velocity leugth scale in the shocked halo eas. indicating that viscosity at this level is dynamically unimportant there.," In contrast, the Reynolds number in the ambient shock-heated gas is much larger: where $\rho\sim 10^{-28}\text{ g cm}^{-3}$ and $L\sim 10 $ kpc are roughly the thermal gas density and velocity length scale in the shocked halo gas, indicating that viscosity at this level is dynamically unimportant there."
 Viscosity also helps dissipate gas notions in the bubble interior. reclucing the level of CR advection. as clearly seen iu Figure 2..," Viscosity also helps dissipate gas motions in the bubble interior, reducing the level of CR advection, as clearly seen in Figure \ref{plot2}."
 When viscosity is not importaut (e.g. in πας VO and V0.5). CR advection driven by circulating σας motions transports aud mixes CRs within thebubble. producing a volume-filune CR bubble.," When viscosity is not important (e.g., in runs V0 and V0.5), CR advection driven by circulating gas motions transports and mixes CRs within the bubble, producing a volume-filling CR bubble."
 Iu contrast. when viscosity becomes inportaut (in ruus V3. VIO aud V30). eas motions are significantly reduced. and CRs are mainly located iu the jet backflow near bubble edees.," In contrast, when viscosity becomes important (in runs V3, V10 and V30), gas motions are significantly reduced, and CRs are mainly located in the jet backflow near bubble edges."
 Tn the runs with low viscosity. the iejet backflow forms a large scale circulating flow in the bub interior. as better seen in run V1 (the right-top panel). which advect CRs. producime a volume-filling CR bubble.," In the runs with low viscosity, the jet backflow forms a large scale circulating flow in the bubble interior, as better seen in run V1 (the right-top panel), which advect CRs, producing a volume-filling CR bubble."
" ILlowever. iu ruus V3. V1O. and 30. viscosity the shear motions imduced by the backflow uearisipates bubble οσος, preveutius the formation of circulating motions in thebubble interior."," However, in runs V3, V10, and 30, viscosity dissipates the shear motions induced by the backflow near bubble edges, preventing the formation of circulating motions in the bubble interior."
 This viscosity effect can be better secu in Figure 3.. which compares the early-stage jet evolution iu ruus VO and V3.," This viscosity effect can be better seen in Figure \ref{plot3}, which compares the early-stage jet evolution in runs V0 and V3."
 Here the velocity field is over-plotted on the distribution of CR euerev deusity., Here the velocity field is over-plotted on the distribution of CR energy density.
 As clearly secu. in the ion-viscous tun VO. the hiejet backflow induces significant circulating motions. whn advect CRs to thebubble interior.," As clearly seen, in the non-viscous run V0, the jet backflow induces significant circulating motions, which advect CRs to the bubble interior."
 In contrast. m the viscous run V3. circulating notions are only seen at the very early time f=0.1 Abvr. and at later times. the expandsjet backtlow stops flowing ραασ and mainly into the Calactic halo.," In contrast, in the viscous run V3, circulating motions are only seen at the very early time $t=0.1$ Myr, and at later times, the jet backflow stops flowing backward and mainly expands into the Galactic halo."
 One consequence of this viscosity effect is the reduction of shear motions at thebubble surface. which helps suppress he erowth of IKIT instabilitics.," One consequence of this viscosity effect is the reduction of shear motions at the bubble surface, which helps suppress the growth of KH instabilities."
" Au important feature of the observed. bubbles is the approximately uniform, sanuni-rayv surface brightness. particularly at high latitude (Jb,2 30°: see Suetal. 2010))."," An important feature of the observed bubbles is the approximately uniform gamma-ray surface brightness, particularly at high latitude $|b|\gtrsim 30^{\circ}$ ; see \citealt{su10}) )."
 It is uot trivial to form such a flat surface brightness distribution., It is not trivial to form such a flat surface brightness distribution.
 The top paucl of Fieure Lo shows the liuc-otsieht projected CR enerev deusitv distribution iu Calactic coordinates in, The top panel of Figure \ref{plot4} shows the line-of-sight projected CR energy density distribution in Galactic coordinates in
As determined by measurements from the Automated Plate Machine (APM) ancl Sloan Digital Sky Survey (SDSS). the distribution of spiral galaxy ellipticities in the local neighborhood is basically flat. wilh e=1—5/e ranging trom ~0.2 (to 0.8 (?22)..,"As determined by measurements from the Automated Plate Machine (APM) and Sloan Digital Sky Survey (SDSS), the distribution of spiral galaxy ellipticities in the local neighborhood is basically flat, with $\epsilon = 1 - b/a$ ranging from $\sim 0.2$ to 0.8 \citep{lambas,padilla}."
 We can compare this result to the ellipticities ofresolved 2=3.1 LAEs with S/N>30 bv using the values produced by ihe PSF-convolvecl 2-dimensional elliptical models of This is done in Figure &.., We can compare this result to the ellipticities ofresolved $z = 3.1$ LAEs with $S/N > 30$ by using the values produced by the PSF-convolved 2-dimensional elliptical models of This is done in Figure \ref{fig:ellipticities}.
 As (he figure illustrates. the distribution of ellipticiües is not flat: it is skewed towards Lieher values and peaks αἱ ον0.55.," As the figure illustrates, the distribution of ellipticities is not flat: it is skewed towards higher values and peaks at $\epsilon \sim 0.55$."
 In a similar study using the same technique. ? found the same result [or LBG galaxies at z>2.5: in contrast. star-forming galaxies al 2~1.2 had the same flat elliplcity distribution seen in the local universe.," In a similar study using the same technique, \citet{Ravindranath06} found the same result for LBG galaxies at $z > 2.5$; in contrast, star-forming galaxies at $z \sim 1.2$ had the same flat ellipticity distribution seen in the local universe."
 The distribution of ellipticities hints that at z~3. the majority of LBGs and LAEs are elongated and prolate.," The distribution of ellipticities hints that at $z \sim 3$, the majority of LBGs and LAEs are elongated and prolate."
 Some mar even be similar to the “chain” galaxies identified in other survevs (e.g..?)..," Some may even be similar to the “chain"" galaxies identified in other surveys \citep[e.g.,][]{elmegreen}. ."
 To test the robustness of (his result. we again used the ?— sample of field stars (o determine the ellipticity distribution of point sources on the GEMS images.," To test the robustness of this result, we again used the \citet{MartinStars}
 sample of field stars to determine the ellipticity distribution of point sources on the GEMS images."
 Using IMEXAM in IRAF vielded values near zero (tvpicallv less than 0.05) as expected., Using IMEXAM in IRAF yielded values near zero (typically less than 0.05) as expected.
 However. as Figure 8 illustrates. when fitting (ο a Sérrsic profile as was used lor the galaxies. finds that the vast majority of stars have hieh values for ellipticitv (e> 0.7). rather than values near zero.," However, as Figure \ref{fig:ellipticities} illustrates, when fitting to a Sérrsic profile as was used for the galaxies, finds that the vast majority of stars have high values for ellipticity $\epsilon > 0.7$ ), rather than values near zero."
 We have cliecked that the position angles reported by GALFIT for the stars are randomly distributed. so we do not believe there is a svstematic issue wilh the measured axis ratios.," We have checked that the position angles reported by GALFIT for the stars are randomly distributed, so we do not believe there is a systematic issue with the measured axis ratios."
 We note that ? found a similar result of unusually high ellipticities measured in a sample ol bulges of SDSS galaxies using a different program (GALACTICA:72)., We note that \citet{benson07} found a similar result of unusually high ellipticities measured in a sample of bulges of SDSS galaxies using a different program \citep[GALACTICA;][]{benson02}.
. 7. attributed this discrepancy. (o not imcluding a needed a necessary component to the fit. in their case the presence of an elongated bar.," \citet{benson07} attributed this discrepancy to not including a needed a necessary component to the fit, in their case the presence of an elongated bar."
 The PSF has known thermal variations and aliasing produced by the drizzling process (?) which we have not accounted for in our analvsis which mav be increasing the difliculiv in measuring the ellipticitv of an unresolved source., The PSF has known thermal variations and aliasing produced by the drizzling process \citep{rhodes} which we have not accounted for in our analysis which may be increasing the difficulty in measuring the ellipticity of an unresolved source.
 The main source of this odd result is the inherent clifficulty associated with fitting unresolved sources using PSF convolution., The main source of this odd result is the inherent difficulty associated with fitting unresolved sources using PSF convolution.
 When the angular size of an object is close to that of a point-source a hieh-ellipticity model of its light profile will be as good a fit as a low-ellipticitv model alter PSF convolution., When the angular size of an object is close to that of a point-source a high-ellipticity model of its light profile will be as good a fit as a low-ellipticity model after PSF convolution.
 Thus. the best-fit ellipticity as reported by is reflecting the underlying noise in the image ancl anv errors in our model of the PSF.," Thus, the best-fit ellipticity as reported by is reflecting the underlying noise in the image and any errors in our model of the PSF."
 Nevertheless. the experiment does prove that the observed ellipticity distribution of resolved LAEs is not an artifact produced bx the program.," Nevertheless, the experiment does prove that the observed ellipticity distribution of resolved LAEs is not an artifact produced by the program."
 This confirms the results obtained by ?/— using Monte Carlo simulations: the algorithms are not responsible for the skewness seen in the figure., This confirms the results obtained by \citet{Ravindranath06} using Monte Carlo simulations: the algorithms are not responsible for the skewness seen in the figure.
 In addition to using the measurements of e. we also directly measured the second-ordermoments of each resolved. LAEs luminosityprofile using the ellipse parameters," In addition to using the measurements of $\epsilon$ , we also directly measured the second-ordermoments of each resolved, LAE's luminosityprofile using the ellipse parameters"
(Aumann )).,\citep{aum84}. ).
 Since the imaging of the j| Pie system (Smith&Ter-rile 1984).. nearly two dozen nearby debris disks have been spatially resolved.," Since the imaging of the $\beta$ Pic system \citep{smi84}, nearly two dozen nearby debris disks have been spatially resolved."
 The morphological appearance of resolved debris disks is predicted to be influenced by interactions between dust in the disk and nearby planets (Ozernoyetal.2000:Kuchner&Holman 2003).. the local interstellar medium (Manessetal.2009).. recent stellar flybys and binary companions (Wyattetal.1999). mutual grain collisions (Thébault&Wu2008).. and interaction of dust with residual gas (Klahr&Lin2005).," The morphological appearance of resolved debris disks is predicted to be influenced by interactions between dust in the disk and nearby planets \citep{oze00,kuc03}, the local interstellar medium \citep{man09}, recent stellar flybys and binary companions \citep{wya99}, mutual grain collisions \citep{thebault08}, and interaction of dust with residual gas \citep{klahr05}."
. Many resolved systems exhibit all morphological structures predicted by these mechanisms (Schneideretal.1999;Kalas2005:Golimowskial.2006:Kalaset 2008).," Many resolved systems exhibit all morphological structures predicted by these mechanisms \citep{sch99,kalas05,gol06,kal08}."
. The observable morphology of resolved. optically thin debris disks is also wavelength dependent. as different bandpasses sample different grain size distributions (Wyatt2006).," The observable morphology of resolved, optically thin debris disks is also wavelength dependent, as different bandpasses sample different grain size distributions \citep{wya06}."
 is a young (~8-10Myr:Staufferetal.1995).. nearby (72.8+1.7pe:vanLeeuwen2007).. AOV-type star first identified as a debris disk system from an IR excess observed with IRAS (Jura1991).," is a young \citep[$\sim$8--10\,Myr;][]{stauffer95}, nearby \citep[72.8\,$\pm$\,1.7\,pc;][]{vanleeuwen07}, A0V-type star first identified as a debris disk system from an IR excess observed with IRAS \citep{jur91}."
. It has a co-moving M-type stellar companion at a separation of 7777 (Juraetal. 1993).., It has a co-moving M-type stellar companion at a separation of 7 \citep{jur93}. .
 The HR 4796 A debris disk has been spatially resolved at numerous optical. infrared. and sub-millimeter wavelengths (e.g..Koerneretal.1998:Jayawardhana1998;Schnei-deretal. 2009).. appearing às a narrow. highly inclined belt with a radius of 17005.," The HR 4796 A debris disk has been spatially resolved at numerous optical, infrared, and sub-millimeter wavelengths \citep[e.g.,][]{koe98,jay98,sch99,sheret04,hinkley09,schneider09}, appearing as a narrow, highly inclined belt with a radius of 05."
" Models suggest a dual dust population including gravitationally confined. grains at —9—10 AAU in addition to those imaged at ~70 AAU (Augereauetal. 1999)., possibly involving radiationally evolved organicmaterials"," Models suggest a dual dust population including gravitationally confined grains at $\sim$ AU in addition to those imaged at $\sim$ AU \citep{augereau99}, , possibly involving radiationally evolved organicmaterials"
for minor companions. so their η 1s a lower limit.,"for minor companions, so their $f_{m/M}$ is a lower limit."
 On the other hand. study the different properties of major (Am-<2. pE 1/7) and minor (Am->2. iix 1/7) close pairs in SDSS.," On the other hand, study the different properties of major $\Delta m_{z} < 2$, $\mu \gtrsim 1/7$ ) and minor $\Delta m_{z} > 2$, $\mu \lesssim 1/7$ ) close pairs in SDSS."
 Unfortunately. they do not attempt to derive merger fractions. but the influence of close companions on galaxy properties (see also ??)).," Unfortunately, they do not attempt to derive merger fractions, but the influence of close companions on galaxy properties (see also )."
 Therefore. to our knowledge. there does not seem to be any local estimation of the minor merger fraction of bright galaxies in the literature.," Therefore, to our knowledge, there does not seem to be any local estimation of the minor merger fraction of bright galaxies in the literature."
 As a close proxy. we estimate the local merger fraction as finn=fin(uz1/10)-fM," As a close proxy, we estimate the local merger fraction as $f_{\rm mm} = f_{\rm m}\,(\mu\,\geq 1/10) - f_{\rm MM}$."
 We follow the methodology in Sect., We follow the methodology in Sect.
" ?? to measure the major (2 1/4) merger fraction of Myx-20 galaxies at ς=0.09 from the Millennium Galaxy Catalogue(MGC"".. 2)."," \ref{ncs} to measure the major $\mu\,\geq 1/4$ ) merger fraction of $M_{B}^{\rm e} \leq -20$ galaxies at $z = 0.09$ from the Millennium Galaxy Catalogue, )."
 This survey comprises 10095 galaxies with βμως<20 over 37.5 deg. with à spectroscopic completeness of(?:: see also ??)).," This survey comprises 10095 galaxies with $B_{MGC} < 20$ over 37.5 $\deg^2$ , with a spectroscopic completeness of; see also )."
 We obtain INC=0.139zx0.009 for m=10057! kpe., We obtain $f_{\rm MM}^{\rm MGC} = 0.139\pm0.009$ for $r_{\rm p}^{\rm max} = 100h^{-1}$ kpc.
 We then assume two different types of evolution for the major + minor merger fraction: (1) a constant evolution with redshift. fnQe=1/10)0.461 for me=1007! kpe. which implies. finn(0.09)=0.322: and (2) an evolution which evolves with redshift as a=0.8 (fit of a power-law function to our observational major + minor merger fractions). which implies. fin(0.09)=0.187.," We then assume two different types of evolution for the major + minor merger fraction: (1) a constant evolution with redshift, $f_{\rm m}\,(\mu\,\geq 1/10) = 0.461$ for $r_{\rm p}^{\rm max} = 100h^{-1}$ kpc, which implies $f_{\rm mm}(0.09) = 0.322$; and (2) an evolution which evolves with redshift as $m = 0.8$ (fit of a power-law function to our observational major + minor merger fractions), which implies $f_{\rm mm}(0.09) = 0.187$."
 Finally. we fit Eq. (12))," Finally, we fit Eq. \ref{fmz}) )"
 to our minor merger fraction data and both local estimates. defining a confidence area for the minor merger fraction between z=0 and z=| (Fig. 5)).," to our minor merger fraction data and both local estimates, defining a confidence area for the minor merger fraction between $z = 0$ and $z = 1$ (Fig. \ref{ffmmfig}) )."
 This area is limited by the following curves. The power law-index from the fits is a=—0.4+ 0.7.," This area is limited by the following curves, The power law-index from the fits is $m = -0.4 \pm 0.7$ ."
 The negative value implies that the minor merger fraction decreases with increasing redshift., The negative value implies that the minor merger fraction decreases with increasing redshift.
 We note that our results are compatible with a constant fij since z=| (Le. mm= 0).," We note that our results are compatible with a constant $f_{\rm mm}$ since $z = 1$ (i.e., $m = 0$ )."
 Even in that case. the minor merger fraction does not evolve in the same way as the major one. that increases with redshift Gn>0. see below).," Even in that case, the minor merger fraction does not evolve in the same way as the major one, that increases with redshift $m > 0$, see below)."
 use Halo Occupation Distribution (HOD) models to interpret the evolution since z| of the correlation function from VVDS-Deep and SDSS., use Halo Occupation Distribution (HOD) models to interpret the evolution since $z \sim 1$ of the correlation function from VVDS-Deep and SDSS.
 Their results suggest that the average number of satellite galaxies per dark matter halo increases with cosmic time. which could be related with our suggested increase in the minor merger fraction.," Their results suggest that the average number of satellite galaxies per dark matter halo increases with cosmic time, which could be related with our suggested increase in the minor merger fraction."
 Specifically. we expect the minor merger fraction in the local universe to be two to three times the major merger one.," Specifically, we expect the minor merger fraction in the local universe to be two to three times the major merger one."
 Direct measurements of the minor merger fraction at low redshift will be needed to better constrain the minor merger fraction evolution with z., Direct measurements of the minor merger fraction at low redshift will be needed to better constrain the minor merger fraction evolution with $z$.
 The least-squares fit to the major merger data yields (Fig. 5)), The least-squares fit to the major merger data yields (Fig. \ref{ffmmfig}) )
 Ina previous work in VVDS-Deep. measured the major merger fraction (i>1/4) of less luminous galaxies than those reported in present paper.," In a previous work in VVDS-Deep, measured the major merger fraction $\mu \geq 1/4$ ) of less luminous galaxies than those reported in present paper."
" They find that the major merger fraction evolves faster with z for fainter samples. with a power-law index a=4.7 for Mi,€—-18 galaxies and n=3.1 for My,€—18.77 galaxies."," They find that the major merger fraction evolves faster with $z$ for fainter samples, with a power-law index $m = 4.7$ for $M_B^{\rm e} \leq-18$ galaxies and $m = 3.1$ for $M_B^{\rm e} \leq-18.77$ galaxies."
" The evolution of #1=1.3 for the major merger fraction of My,€—20 galaxies confirms the trend found by and extends it to brighter galaxies.", The evolution of $m = 1.3$ for the major merger fraction of $M_B^{\rm e} \leq-20$ galaxies confirms the trend found by and extends it to brighter galaxies.
 In a previous study. have attempted to measure the power-law index s.," In a previous study, have attempted to measure the power-law index $s$ ."
" They find *~—0.6 at z€[0.2.1.1) for principal galaxies with M,=10!""Mo."," They find $s \sim -0.6$ at $z \in [0.2,1.1)$ for principal galaxies with $M_{\star} \gtrsim 10^{10}\ M_{\sun}$."
 This value is similar to ours at zo0.8. but at z~0.5 the discrepancy between both studies ts important (> 207).," This value is similar to ours at $z = 0.8$, but at $z \sim 0.5$ the discrepancy between both studies is important $>2\sigma$ )."
 This suggests that s depends not only on both redshift and colour. but also on stellar mass.," This suggests that $s$ depends not only on both redshift and colour, but also on stellar mass."
" Because the B- luminosities of red galaxies are only slightly affected by star formation. our red merger fraction Is a proxy of the merger fraction of log(M,/M.)~10.8 galaxies."," Because the $B$ -band luminosities of red galaxies are only slightly affected by star formation, our red merger fraction is a proxy of the merger fraction of $\log\, (M_{\star}/M_{\odot}) \sim 10.8$ galaxies."
 We therefore find that the power-law index does not evolve for massive galaxies. 5=—-0.79+0.12.," We therefore find that the power-law index does not evolve for massive galaxies, $s = -0.79\pm0.12$."
 This. combining with results. suggests that (1) s does not evolve with z in mass-selected samples: that is. the evolution of the total (major + minor) merger fraction is similar to that of the major merger one. as predicted by the cosmological models of?.. and (11) the power-law index is lower for massive galaxies indicating that massive galaxies have a higher minor-to-major merger ratio than less massive ones.," This, combining with results, suggests that (i) $s$ does not evolve with $z$ in mass-selected samples; that is, the evolution of the total (major + minor) merger fraction is similar to that of the major merger one, as predicted by the cosmological models of, and (ii) the power-law index is lower for massive galaxies indicating that massive galaxies have a higher minor-to-major merger ratio than less massive ones."
 The minor merger fraction in. different. mass-selected samples will be the subject of a future work to expand on resultspresented here., The minor merger fraction in different mass-selected samples will be the subject of a future work to expand on resultspresented here.
 Similarly to the minor merger fraction. there doesnot seem to exist any published reference in the refereed literature for the local minor merger rate.," Similarly to the minor merger fraction, there doesnot seem to exist any published reference in the refereed literature for the local minor merger rate."
 We follow the same steps as in Sect., We follow the same steps as in Sect.
 to estimate a confidence area for theminor merger rate in the, \ref{ffmmevol} to estimate a confidence area for theminor merger rate in the
acceleration (Fy= Ve).,acceleration $\b F_{\rm t}=-\nabla\Phi_{\rm t}$ ).
 Then if the trial potential is correct. we have 8= Fy. and e|=$&v4 so 6|=Pdvwedsfealt where £) is the component of Fy along the line of sieht.," Then if the trial potential is correct, we have $\ddot\b s=\b F_{\rm t}$ , and $\vlos=\hat\b s.\b
v=\dot s$ so $\dot\vlos=\Flos+\b v.\d\hat\b s/\d t$ , where $\Flos$ is the component of $\b F_{\rm t}$ along the line of sight."
" Also SO Aloreover. the component of v in the plane of the sky Va satisfies where we have now fixed the meaning of the parameter ""odo be the angular distance along the trajectory."," Also so Moreover, the component of $\b v$ in the plane of the sky $\b v_\perp$ satisfies where we have now fixed the meaning of the parameter $u$ to be the angular distance along the trajectory."
 Eliminating PL[ between equations (2)) and (3)). we obtain a quadratic equation for dé that has solution Thus if we guess s at some point on the trajectory. we can solve for dé between observations. and calculate ££.We get a new value of [ος each pair of data points.," Eliminating $|\vperp|^2$ between equations \ref{eq:2}) ) and \ref{eq:3}) ), we obtain a quadratic equation for $\d t$ that has solution Thus if we guess $s$ at some point on the trajectory, we can solve for $\d
t$ between observations, and calculate $E$ .We get a new value of $E$ for each pair of data points."
 We can also update s [rom ds=ed., We can also update $s$ from $\d s=\vlos\d t$.
 To obtain a robust numerical scheme we divide and equation (4)) by the differential of 8 to obtain the set of coupled ordinary cillerential equations The sign ambiguity in the first equation is resolved such that / increases along the trajectory., To obtain a robust numerical scheme we divide $\d s=\vlos \d t$ and equation \ref{basicdt}) ) by the differential of $ u$ to obtain the set of coupled ordinary differential equations The sign ambiguity in the first equation is resolved such that $t$ increases along the trajectory.
 The algorithm was tested. by reconstructing orbits from pseudodata obtaineclk by projecting orbits in a mioclel potential., The algorithm was tested by reconstructing orbits from pseudodata obtained by projecting orbits in a model potential.
 The tests showed that it is important to determine accurately the distance s along the trajectory to each data point., The tests showed that it is important to determine accurately the distance $ u$ along the trajectory to each data point.
 This can be determined in a two-step process: we first obtain a crude estimate Then we fit cubic splines in A to the values 6;=5(A;) and /;= /(A;). and use the resulting functions of A to evaluate numerically the integrals where a prime denotes dillerentiation. with respect to lambda.," This can be determined in a two-step process: we first obtain a crude estimate Then we fit cubic splines in $\lambda$ to the values $b_i=b(\lambda_i)$ and $l_i=l(\lambda_i)$ , and use the resulting functions of $\lambda$ to evaluate numerically the integrals where a prime denotes differentiation with respect to lambda."
Finally we fit cubic splines to the values 6;=b(u;). ete.,"Finally we fit cubic splines to the values $b_i=b( u_i)$, etc.,"
 and use these functions of & and the fourth-orcer Runge-hutta algorithm to solve equations , and use these functions of $ u$ and the fourth-order Runge-Kutta algorithm to solve equations \ref{basicde}) ).
At each integration step we re-evaluate Lo=i60|57d$., At each integration step we re-evaluate $E=\frac12(\vlos^2+s^2\dot u^2)+\Phi_{\rm t}$.
 Orbits were integrated. in the MiyamotoNagai »»ential that has θα=0.2 and GAL/a=1jmainBodyCitationEnd751]Mivam., Orbits were integrated in the Miyamoto–Nagai potential that has $b/a=0.2$ and $GM/a=1$.
 They were then reconstructed: using either this potential or a Alivamotovagal potential with different parameters., They were then reconstructed using either this potential or a Miyamoto--Nagai potential with different parameters.
 The 42 dots in he right panel of Fig., The 42 dots in the right panel of Fig.
 1. show the input coordinates on the sky of the model orbit when it is viewed from a point. in he svmmetry plane anc Se from the centre. while the left xul shows the linbe-of-ight. velocities along the orbit.," \ref{onsky1} show the input coordinates on the sky of the model orbit when it is viewed from a point in the symmetry plane and $8a$ from the centre, while the left panel shows the linbe-of-sight velocities along the orbit."
 The orbit has energy O.0322CAlfa., The orbit has energy $-0.0322GM/a$.
 Hostarts at b=5deg and a distance Ίσα from the point of observation. and moves out ο a distance 22.60 as it rises to b=68.9deg.," It starts at $b=-5\deg$ and a distance $15a$ from the point of observation, and moves out to a distance $22.6a$ as it rises to $b=68.9\deg$."
 The triangles in Fig., The triangles in Fig.
 2 show the rms variation Ad? in the output energy E along the reconstructed orbit when the true potential is used to integrate equations (5)) from these data points and an initialdistance s that is the stated multiple of its true value. sy. Phere is à sharp minimum in AZ whens= sy. ‘The squares and pentagons in Fig.," \ref{erms1} show the rms variation $\Delta E$ in the output energy $E$ along the reconstructed orbit when the true potential is used to integrate equations \ref{basicde}) ) from these data points and an initialdistance $s$ that is the stated multiple of its true value, $s_0$ There is a sharp minimum in $\Delta E$ when$s=s_0$ The squares and pentagons in Fig."
 2 show the corresponding results when the wrong potential is used to reconstruct the orbit lareer values of b/a generate rounder potentials., \ref{erms1} show the corresponding results when the wrong potential is used to reconstruct the orbit – larger values of $b/a$ generate rounder potentials.
In (his paper. we use triangulation to localise CALE apexes in 3D. From (his. we derive the CME apex trajectory and kinematics.,"In this paper, we use triangulation to localise CME apexes in 3D. From this, we derive the CME apex trajectory and kinematics."
 These kinematics are (hen used to investigate the effects of drag on the CALE., These kinematics are then used to investigate the effects of drag on the CME.
 We present the reconstructed CME (apex) kinematics for three events. one acceleration. one clecelerating. and one with constant velocity.," We present the reconstructed CME (apex) kinematics for three events, one acceleration, one decelerating, and one with constant velocity."
 In Section 2 we describe the observations. data reduction. and the reconstruction and fitting techuicque.," In Section 2 we describe the observations, data reduction, and the reconstruction and fitting technique."
 section 3 includes a discussion of each event in detail and presents the reconstructed kinematicV. themselves., Section 3 includes a discussion of each event in detail and presents the reconstructed kinematics themselves.
 The implications of our results aud our final conclusions are given in Section 4., The implications of our results and our final conclusions are given in Section 4.
 The trajectories of three CMESs were reconstructed using observations [rom STEREO SECCIIL, The trajectories of three CMEs were reconstructed using observations from STEREO SECCHI.
 SECCHI consists of five telescopes. the Extreme Ultraviolet hnager (EUVI). the inner and outer coronagraphs (CORT and CODBR2). and finally the IHeliosphereic Luager (III and Τσ).," SECCHI consists of five telescopes, the Extreme Ultraviolet Imager (EUVI), the inner and outer coronagraphs (COR1 and COR2), and finally the Heliosphereic Imager (HI1 and HI2)."
 CORL images the corona from 1.44.0 E... while COR2 images the corona from 2.515 R..," COR1 images the corona from 1.4–4.0 $_{\odot}$, while COR2 images the corona from 2.5–15 $_{\odot}$."
 Both of the coronagraphs take sequences of three polarised images which can be combined to give total brightness (D) or polarised brightness (pD) images (LlowarclThompsonetal. 2003).," Both of the coronagraphs take sequences of three polarised images which can be combined to give total brightness (B) or polarised brightness (pB) images \citep{Howard:2008p4742,Thompson:2003p1587}."
. The ILE instrument is a combination of (wo refractive optical telescopes with multi-vein. nulti-stage light rejection svstem which images the inner ]leliosphere from 489 degrees (Evlesetal.2008)..," The HI instrument is a combination of two refractive optical telescopes with multi-vein, multi-stage light rejection system which images the inner Heliosphere from 4–89 degrees \citep{Eyles:2008p3861}."
" HL images the inner Heliosphere from 23.98"" (degrees elongation) in white light with a cadence of 40 minutes while ILI2 images the IHeliosphere from 83.68"" in white Bght with a cadence of 2 hours.", HI1 images the inner Heliosphere from $^{\circ}$ (degrees elongation) in white light with a cadence of 40 minutes while HI2 images the Heliosphere from $^{\circ}$ in white light with a cadence of 2 hours.
 The three CAIEs considered here were observed during: 2007 October 813 (CME 1). 2008 March 2527 (CME 2). and 2008 April 912 (CME 3).," The three CMEs considered here were observed during: 2007 October 8–13 (CME 1), 2008 March 25–27 (CME 2), and 2008 April 9–12 (CME 3)."
 The observations were reduced using trom theSOLARSOFT Library (Freelance&Handy1905)., The observations were reduced using from the library \citep{Freeland:1998p3546}.
 This consisted of debasing and flat-fielding for all images., This consisted of debasing and flat-fielding for all images.
 The CORI and COR? images were also corrected for vignelling. exposure (ime. and an optical distortion.," The COR1 and COR2 images were also corrected for vignetting, exposure time, and an optical distortion."
 The CORI observations had a model background subtracted to remove static coronal features., The COR1 observations had a model background subtracted to remove static coronal features.
 The III instrument has no shutter. and as such. these observations needed. additional corrections for smearing and pixel bleeding.," The HI instrument has no shutter, and as such, these observations needed additional corrections for smearing and pixel bleeding."
 The pointing of the IHE observations were updated using known star positions within the filed-o[-view (Brownetal.2008).., The pointing of the HI observations were updated using known star positions within the filed-of-view \citep{Brown:2008p3595}.
 Standard running difference images were created from the CORIL/2 observations while a specialised running difference technique was used to suppress the stars for the III observations (Maloneyetal.2009).., Standard running difference images were created from the COR1/2 observations while a specialised running difference technique was used to suppress the stars for the HI observations \citep{Maloney:2009p6617}.
 The relative drift. due to satellite motion. of the star field between (wo successive HI images is caleulated and (then the earlier image is shilted to account for this motion removing a large part of the background signal.," The relative drift, due to satellite motion, of the star field between two successive HI images is calculated and then the earlier image is shifted to account for this motion removing a large part of the background signal."
 shows reduced observations from the 2008 March 28 event where the CME is, shows reduced observations from the 2008 March 28 event where the CME is
"From the parallax distances, if available, and otherwise the spectroscopic distances provided by ?,, we calculate the projected separation in astronomical units.","From the parallax distances, if available, and otherwise the spectroscopic distances provided by \citet{Riaz2006}, we calculate the projected separation in astronomical units."
 The uncertainty in spectroscopic distance according to ? is 37%., The uncertainty in spectroscopic distance according to \citet{Riaz2006} is $37\%$.
 Figure 8 shows the distribution of projected separation of all binaries and triples in our M dwarf sample compared to that of all known VLMS/BD binaries from the Very Low Mass Binaries Archive., Figure 8 shows the distribution of projected separation of all binaries and triples in our M dwarf sample compared to that of all known VLMS/BD binaries from the Very Low Mass Binaries Archive.
" As for the mass-ratio distribution, we divide the observed systems into two groups, containing approximately equal number of systems, to see if the separation distribution is the same for ’early M’ and ’late M’ type binaries divided at M950.3Mo."," As for the mass-ratio distribution, we divide the observed systems into two groups, containing approximately equal number of systems, to see if the separation distribution is the same for 'early M' and 'late M' type binaries divided at $M\approx0.3M_{\sun}$."
" Figure 9 shows the respective mean semi-major axis distributions, where the projected separation has been multiplied with 1.26 to account for random orbital elements (?).."," Figure 9 shows the respective mean semi-major axis distributions, where the projected separation has been multiplied with 1.26 to account for random orbital elements \citep{FischerMarcy1992}."
" We performed a K-S test, which yielded a probability that the distributions are alike."," We performed a K-S test, which yielded a probability that the distributions are alike."
" We note that the distributions may peak at close systems in the 'late M subsample, however more data is necessary to determine whether this is a real property or not."," We note that the distributions may peak at close systems in the 'late M' subsample, however more data is necessary to determine whether this is a real property or not."
 M dwarfs comprise a transitional region within which the multiplicity properties change from being similar to those of solar-type stars to the very different characteristics of very low mass stars and brown dwarfs., M dwarfs comprise a transitional region within which the multiplicity properties change from being similar to those of solar-type stars to the very different characteristics of very low mass stars and brown dwarfs.
 Smaller surveys of different mass ranges have provided some insight into the transitional behaviour., Smaller surveys of different mass ranges have provided some insight into the transitional behaviour.
 We observed 124 nearby M dwarfs from the ? catalogue., We observed 124 nearby M dwarfs from the \citet{Riaz2006} catalogue.
" Forty-four of our targets were observed to have potential binary/multiple companions within 0.1""—9.5"" of the primary star.", Forty-four of our targets were observed to have potential binary/multiple companions within $0.1\arcsec-9.5\arcsec$ of the primary star.
 Most of these companions were previously unknown., Most of these companions were previously unknown.
" We have estimated the multiplicity fraction for M0-M6 young (5600 MMyr) dwarfs with angular separations 0.1""— 6"", corresponding to projected separation AA.U. at median distance 30ppc, in this largest sample to date to be 32+6%."," We have estimated the multiplicity fraction for M0-M6 young $\la600$ Myr) dwarfs with angular separations $0.1\arcsec-6\arcsec$ , corresponding to projected separation A.U. at median distance pc, in this largest sample to date to be $32\pm6\%$."
" While differences in the binary fraction have been found in various nearby star-forming regions (????),, observations of the MMyr old a Persei and the MMyr old Praesepe clusters suggest that the companion star fraction does not significantly decline over an age range from MMyr to GGyr (?).."," While differences in the binary fraction have been found in various nearby star-forming regions \citep{Leinert1993, Ghez1993, BrandnerKoehler1998, Koehler2006}, observations of the Myr old $\alpha$ Persei and the Myr old Praesepe clusters suggest that the companion star fraction does not significantly decline over an age range from Myr to Gyr \citep{Patience2002}."
 We therefore did not expect there to be a strong evolution in binary properties from ages ~100 MMyr to a few Gyr., We therefore did not expect there to be a strong evolution in binary properties from ages $\sim100$ Myr to a few Gyr.
 Our derived /Μωι is consistent with previous surveys in, Our derived $f_\mathrm{Mult}$ is consistent with previous surveys in
index n.,index $n$.
 We often average density profiles of halos for some range of Μι., We often average density profiles of halos for some range of $\Mvir$.
" When doing so, we scale the radii to units of the virial radius of each halo and then average the densities."," When doing so, we scale the radii to units of the virial radius of each halo and then average the densities."
 The averaged density profile is then fit again., The averaged density profile is then fit again.
" In some cases, before we do the fitting, we also split the halo population of a given mass range into 3-4 sub-samples with a narrow range of concentrations."," In some cases, before we do the fitting, we also split the halo population of a given mass range into 3-4 sub-samples with a narrow range of concentrations."
 The parameters of the density fits together with some other properties of the halos are given in Table 2.., The parameters of the density fits together with some other properties of the halos are given in Table \ref{tab:tab2}.
 The halos in our catalogs come from different environments., The halos in our catalogs come from different environments.
" Some of them are inside the virial radii of larger halos; some have strong interactions with smaller, but still massive neighbors."," Some of them are inside the virial radii of larger halos; some have strong interactions with smaller, but still massive neighbors."
 We call a halo “distinct” if it does not belong to a larger halo., We call a halo “distinct” if it does not belong to a larger halo.
" Most of the time we are interested in isolated halos: distinct halos, which do not have large companions."," Most of the time we are interested in isolated halos: distinct halos, which do not have large companions."
 We search for halos around the given halo., We search for halos around the given halo.
" If within the distance dxRy;the largest companion is smaller than Myi,/r, then the halo is called isolated."," If within the distance $d\times\Rvir$the largest companion is smaller than $\Mvir/m$, then the halo is called isolated."
" When doing the pair-wise comparisons of the halos, we use the largest virial radius of the two halos, but we use My, of the given halo for the test of the masses."," When doing the pair-wise comparisons of the halos, we use the largest virial radius of the two halos, but we use $\Mvir$ of the given halo for the test of the masses."
 Different isolation criteria are used., Different isolation criteria are used.
" We typically use the d=2 and m=5 combination (no massive companion within 2R,4,)", We typically use the $d=2$ and $m=5$ combination (no massive companion within $\Rvir$ ).
" For Milky-Way size halos with My,z1012Μα this condition typically gives of all distinct halos of this mass.", For Milky-Way size halos with $\Mvir \approx 10^{12}\Msunh$ this condition typically gives of all distinct halos of this mass.
 Figure 1 gives examples of density profiles of two halos with virial masses 1.4x1025-1Mg (left panel) and 2.6x1011471Mo (right panel) in the simulation Box20., Figure \ref{fig:fig1} gives examples of density profiles of two halos with virial masses $1.4\times 10^{12}\Msunh$ (left panel) and $2.6\times 10^{11}\Msunh$ (right panel) in the simulation Box20.
 The halos have the virial radii of 230h-!kpc and 1901kpc respectively., The halos have the virial radii of $230\kpch$ and $130\kpch$ respectively.
" The halos were done with very high resolution, which allows us to track the density profile below 0.01Ryir"," The halos were done with very high resolution, which allows us to track the density profile below $0.01\Rvir$."
 The larger halo is isolated with its nearest companion being at 3.5Ryir., The larger halo is isolated with its nearest companion being at $3.5\Rvir$.
" The density profile of the halo has some spikes due to substructure, but otherwise it clearly extends up to 3Ryir where we see large fluctuations due to its companion."," The density profile of the halo has some spikes due to substructure, but otherwise it clearly extends up to $3\Rvir$ where we see large fluctuations due to its companion."
" The smaller halo on the right panel has a neighbor at 2R4,.", The smaller halo on the right panel has a neighbor at $2\Rvir$.
" So, it is not isolated."," So, it is not isolated."
 Eq.( 2)), Eq.( \ref{eq:Sersic}) )
 gives very good approximations for both halos., gives very good approximations for both halos.
 Figure 2 gives more information on the structure of these two halos., Figure \ref{fig:fig2} gives more information on the structure of these two halos.
 The 3D rms velocities are what one would naively expect for “normal” halos., The 3D rms velocities are what one would naively expect for “normal” halos.
 The rms velocity first increases when we go from the center and reaches a maximum at some distance., The rms velocity first increases when we go from the center and reaches a maximum at some distance.
 The radius of the maximum rms velocity is smaller for the halo on the right panel., The radius of the maximum rms velocity is smaller for the halo on the right panel.
 This is because it has larger concentration., This is because it has larger concentration.
 At larger radii the rms velocity first declines relatively smoothly., At larger radii the rms velocity first declines relatively smoothly.
 It has some fluctuations due to substructure., It has some fluctuations due to substructure.
 At radii larger than Ry; the decline stops., At radii larger than $\Rvir$ the decline stops.
 The average radial velocity is more interesting and to some degree is surprising., The average radial velocity is more interesting and to some degree is surprising.
 Nothing unusual inside Ry: it is practically zero with tiny (zzbkm s!) variations due to substructure., Nothing unusual inside $\Rvir$ : it is practically zero with tiny $\approx 5\kms$ ) variations due to substructure.
 This is a clear sign of a virialized object., This is a clear sign of a virialized object.
 At larger distances, At larger distances
"all spectra are dominated by the object’s shot-noise, the precision of the instrumental magnitudes is of the order of or better.","all spectra are dominated by the object's shot-noise, the precision of the instrumental magnitudes is of the order of or better."
" Above this wavelength the dominant source of uncertainty is fringing, which reaches peak-to-peak amplitudes of ~20%.."," Above this wavelength the dominant source of uncertainty is fringing, which reaches peak-to-peak amplitudes of $\sim$."
 This limits the usable range to wavelengths shorter than 8100A., This limits the usable range to wavelengths shorter than 8100.
. The instrumental magnitudes were computed within adjacent bins up to 6800A., The instrumental magnitudes were computed within adjacent bins up to 6800.
". To mitigate the effect of fringing, at larger wavelengths we have selected three bins (having widths of 160, 200, and 200 A)), centred at 7060, 7450, and 7940 respectively, in order to avoid the O? and H2O bands (Fig. 1))."," To mitigate the effect of fringing, at larger wavelengths we have selected three bins (having widths of 160, 200, and 200 ), centred at 7060, 7450, and 7940 respectively, in order to avoid the $_2$ and $_2$ O bands (Fig. \ref{fig:trans}) )."
" Once the instrumental magnitudes are corrected for the efficiency degradation (see previous section) and slit losses due to bad seeing (see Appendix Appendix A:)), they can be used to finally derive the extinction curve."," Once the instrumental magnitudes are corrected for the efficiency degradation (see previous section) and slit losses due to bad seeing (see Appendix \ref{sec:seeing}) ), they can be used to finally derive the extinction curve."
" Among all possible algorithms for combining data obtained for different programme stars, we opted for the global solution proposed by Hayes Schmidtke (1987))."," Among all possible algorithms for combining data obtained for different programme stars, we opted for the global solution proposed by Hayes Schmidtke \cite{hs}) )."
" This method is applicable to spectro-photometry and narrow-band photometry, i.e. when the passbands are nearly monochromatic, as is our case."," This method is applicable to spectro-photometry and narrow-band photometry, i.e. when the passbands are nearly monochromatic, as is our case."
" Under these circumstances there are no colour-terms to be taken into account, and each wavelength bin can be treated independently from the others."," Under these circumstances there are no colour-terms to be taken into account, and each wavelength bin can be treated independently from the others."
" One issue with this method is that, by construction, one cannot also solve for the zero-point of the linear relation at the same time that the slope (i.e. the extinction coefficient) is being determined."," One issue with this method is that, by construction, one cannot also solve for the zero-point of the linear relation at the same time that the slope (i.e. the extinction coefficient) is being determined."
" However, for our purposes this is not a problem, since we are only interested in the extinction term."," However, for our purposes this is not a problem, since we are only interested in the extinction term."
 The result is presented in Fig. 2.., The result is presented in Fig. \ref{fig:ext}.
" As the values derived from the two settings in the intersection region (4400-6075 A)) are fully consistent within the estimated uncertainties, we averaged them."," As the values derived from the two settings in the intersection region (4400–6075 ) are fully consistent within the estimated uncertainties, we averaged them."
" Also, we replaced the values corresponding to the strong Balmer lines with a linear interpolation between the adjacent bins."," Also, we replaced the values corresponding to the strong Balmer lines with a linear interpolation between the adjacent bins."
 In Fig., In Fig.
 2 we also included the confidence level deduced from the distribution of k(A) derived from each single observation (the extinction variations are discussed in more detail in Sect. 6))., \ref{fig:ext} we also included the confidence level deduced from the distribution of $k(\lambda)$ derived from each single observation (the extinction variations are discussed in more detail in Sect. \ref{sec:var}) ).
 To derive the basic physical parameters related to the extinction curve of Paranal we used the Line By Line Radiation Transfer Model (LBLRTM; Clough et al. 2005))., To derive the basic physical parameters related to the extinction curve of Paranal we used the Line By Line Radiation Transfer Model (LBLRTM; Clough et al. \cite{clough}) ).
" Thiscode®,, based on the HITRAN database (Rothman et al. 2009)),"," This, based on the HITRAN database (Rothman et al. \cite{rothman}) ),"
" has been validated against real spectra from the UV to the sub-millimeter, and is widely used for the retrieval of atmospheric constituents."," has been validated against real spectra from the UV to the sub-millimeter, and is widely used for the retrieval of atmospheric constituents."
" LBLRTM solves the radiative transfer using an input atmospheric profile, which contains the height profiles for temperature, pressure, and chemical composition."," LBLRTM solves the radiative transfer using an input atmospheric profile, which contains the height profiles for temperature, pressure, and chemical composition."
" The code also includes the treatment of continuum scattering, and has an internal model for tropospheric aerosols (based on LOWTRAN)."," The code also includes the treatment of continuum scattering, and has an internal model for tropospheric aerosols (based on LOWTRAN)."
 For the atmospheric profiles we adopted a standard equatorial profile as a basis for all calculations., For the atmospheric profiles we adopted a standard equatorial profile as a basis for all calculations.
" To make the simulations more realistic we then replaced the standard profiles of pressure, temperature, and water content with an average vertical profile derived from the Global Data Assimilation (GDAS)."," To make the simulations more realistic we then replaced the standard profiles of pressure, temperature, and water content with an average vertical profile derived from the Global Data Assimilation (GDAS)."
" The average profile, provided to us by W. Kausch and M. Barden (Kausch Barden 2010, private communication), was obtained averaging GDAS data over the last 6 years for the Paranal site."," The average profile, provided to us by W. Kausch and M. Barden (Kausch Barden 2010, private communication), was obtained averaging GDAS data over the last 6 years for the Paranal site."
" The corresponding amount of precipitable water vapor (PWV) is 2.0 mm, while the ozone column density is 238.8 Dobson Units (DU)®."," The corresponding amount of precipitable water vapor (PWV) is 2.0 mm, while the ozone column density is 238.8 Dobson Units ."
. Vacuum wavelengths were converted into air wavelengths using the relation derived by Morton (1991))., Vacuum wavelengths were converted into air wavelengths using the relation derived by Morton \cite{morton}) ).
" Following Hayes Latham (1975)), rather than assuming an aerosol model, we derived it from the data."," Following Hayes Latham \cite{hayes}) ), rather than assuming an aerosol model, we derived it from the data."
" For doing this we disabled the aerosol calculation in LBLRTM, and we computed the aerosol term K44(A4) as the difference between the data and the resulting model."," For doing this we disabled the aerosol calculation in LBLRTM, and we computed the aerosol term $k_{\rm{aer}}(\lambda)$ as the difference between the data and the resulting model."
 The outcome is displayed in Fig. 3.., The outcome is displayed in Fig. \ref{fig:aer}.
" As first suggested by Anngstrom (1929, 1964)), the aerosol extinction can be described as Κωοι(λ)=Κολ. where ko and α depend on the column density and size distribution of the aerosol mixture."," As first suggested by Ånngstrom \cite{angstrom29,angstrom64}) ), the aerosol extinction can be described as $k_{\rm{aer}}(\lambda)=k_o
\lambda^{-\alpha}$, where $k_0$ and $\alpha$ depend on the column density and size distribution of the aerosol mixture."
 This analytical formulation has been used in a numberof extinction studies (Hayes, This analytical formulation has been used in a numberof extinction studies (Hayes
"First, we concentrated on calibration of Monte Carlo models for which the influence of the tidal field of a parent galaxy is characterised by the tidal energy cutoff - all stars which have energy larger than E;,,=—GM/r; are immediately removed from the system — M is the total mass and Τε is the tidal radius.","First, we concentrated on calibration of Monte Carlo models for which the influence of the tidal field of a parent galaxy is characterised by the tidal energy cutoff - all stars which have energy larger than $E_{t_c} = -GM/r_{t}$ are immediately removed from the system – $M$ is the total mass and $r_{t}$ is the tidal radius."
 The comparison of the evolution of the mass with time (Fig. 1)), The comparison of the evolution of the mass with time (Fig. \ref{fig:mass_tc_comparison}) )
" suggests that a value just about 7=0.02 is an appropriate choice (especially for an age of order a few Gyr, as in M67)."," suggests that a value just about $\gamma = 0.02$ is an appropriate choice (especially for an age of order a few Gyr, as in M67)."
" Apart from mass, the other fundamental measure of a cluster is its radius, and the same comparison for the radius (rj) is presented in Fig. 2.."," Apart from mass, the other fundamental measure of a cluster is its radius, and the same comparison for the half-mass radius $r_h$ ) is presented in Fig. \ref{fig:rh_tc_comparison}."
" It is however, much less discriminating of the appropriate value of y, particularly for N=2500."," It is however, much less discriminating of the appropriate value of $\gamma$, particularly for $N=2500$."
" A comparison of the two panels also suggests caution in applying the Monte Carlo method to a single system with N<10%, because of the increasing role of statistical fluctuations."," A comparison of the two panels also suggests caution in applying the Monte Carlo method to a single system with $N\ltorder10^3$, because of the increasing role of statistical fluctuations."
 To properly assess the inferred values of the free parameters of the Monte Carlo code it is important to check the intrinsic statistical fluctuation of the code., To properly assess the inferred values of the free parameters of the Monte Carlo code it is important to check the intrinsic statistical fluctuation of the code.
 As can be seen from Fig., As can be seen from Fig.
" 3 the spread between models with exactly the same parameters, but with different initial random number sequence (iseed), is substantial, even for N=15000."," \ref{fig:tc_iseed_comparison} the spread between models with exactly the same parameters, but with different initial random number sequence (iseed), is substantial, even for $N = 15000$."
" This spread is even larger for N=2500, as can be expected from theory."," This spread is even larger for $N=2500$, as can be expected from theory."
" The spread between results with different 8,,:n and τ is well inside the spread connected with different iseed.", The spread between results with different $\beta_{min}$ and $\tau$ is well inside the spread connected with different iseed.
 Only the spread between models with different » is larger that the one connected with different iseed., Only the spread between models with different $\gamma$ is larger that the one connected with different iseed.
" The best values of the free code parameters are: 0.2, 8=0.03 and 7=0.01."," The best values of the free code parameters are: $\gamma = 0.2$ , $\beta = 0.03$ and $\tau = 0.01$."
 The process of escape from a cluster in a steady tidal field is extremely complicated., The process of escape from a cluster in a steady tidal field is extremely complicated.
" Some stars which fulfil the energy criterion (binding energy of the star greater than the critical energy E,=—1.5(GM/rt), see Spitzer (1987)) can still be trapped inside the potential well."," Some stars which fulfil the energy criterion (binding energy of the star greater than the critical energy $E_{t_f} =
-1.5(GM/r_{t})$, see Spitzer (1987)) can still be trapped inside the potential well."
 Those stars can be scattered back to lower energy before they escape from the system., Those stars can be scattered back to lower energy before they escape from the system.
" As was pointed out by Baumgardt(2001) these mechanisms cause the cluster lifetime to scale nonlinearly with relaxation time, in contrast with what would be expected from the standard theory."," As was pointed out by \citet{baum2001} these mechanisms cause the cluster lifetime to scale nonlinearly with relaxation time, in contrast with what would be expected from the standard theory."
 The efficiency of these effects decreases as the number of stars increases., The efficiency of these effects decreases as the number of stars increases.
 To account for this in the Monte Carlo code an additional free parameter was introduced according to the theory presented by Baumgardt(2001)., To account for this in the Monte Carlo code an additional free parameter was introduced according to the theory presented by \citet{baum2001}.
". The critical energy for escaping stars was approximated by: Ex,=—a(GM/rt), where a=1.5—a(In(yN)/N)*/4."," The critical energy for escaping stars was approximated by: $E_{t_f} = -\alpha (GM/r_{t})$, where $\alpha = 1.5 - a (ln(\gamma N)/N)^{1/4}$."
" Thus the effective tidal radius for Monte Carlo simulations is r;,,,=Τε/α and it is smaller than r;.", Thus the effective tidal radius for Monte Carlo simulations is $r_{t_{eff}} = r_{t}/\alpha$ and it is smaller than $r_{t}$.
" This leads to the result that for Monte Carlo simulations a system is slightly too concentrated compared to N-body simulations, but the evolution of the total mass is well reproduced, as well as the scaling of the dissolution time with N."," This leads to the result that for Monte Carlo simulations a system is slightly too concentrated compared to $N$ -body simulations, but the evolution of the total mass is well reproduced, as well as the scaling of the dissolution time with $N$."
 Fig., Fig.
 4 shows the evolution of the total mass and the half-mass radius for different a for N= 10000., \ref{fig:tf_alfa_comparison} shows the evolution of the total mass and the half-mass radius for different $\alpha$ for $N = 10000$ .
" The other free parameters for the case of a full tidal field are the same as for the tidal cutoff case: y=0.02, 7=0.01 and Bmin=0.03."," The other free parameters for the case of a full tidal field are the same as for the tidal cutoff case: $\gamma = 0.02$, $\tau = 0.01$ and $\beta_{min} = 0.03$."
" As can be seen by comparing Fig.5 (lower two panels) with Fig.3 (top panel), again the spread between models with different Bmin and 7 is well inside the spread connected with different iseed."," As can be seen by comparing \ref{fig:tf_gamma_beta_tau_comparison} (lower two panels) with \ref{fig:tc_iseed_comparison} (top panel), again the spread between models with different $\beta_{min}$ and $\tau$ is well inside the spread connected with different iseed."
 The statistical spread also does not substantially interfere with the determination of a andy (see Fig.5 (top panel) for Υ)., The statistical spread also does not substantially interfere with the determination of $\alpha$ and$\gamma$ (see \ref{fig:tf_gamma_beta_tau_comparison} (top panel) for $\gamma$ ).
AMG7 is probably the most thoroughly studied old open cluster in (he Galaxy. (hanks to its small distance from us.,"M67 is probably the most thoroughly studied old open cluster in the Galaxy, thanks to its small distance from us."
 Typically quoted values for the clusters age (4270.5 Gyr: Dinescu el, Typically quoted values for the cluster's age $4 \pm 0.5$ Gyr; Dinescu et
procedure. and do not include errors in the luminosity normalizations.,"procedure, and do not include errors in the luminosity normalizations."
 This additional term is likely to be small. ~105.," This additional term is likely to be small, $\sim 10\%$."
 The greatest uncertainty in the normalizations probably comes from the bolometric corrections. which were computed [rom (he galaxies. spectral energy distributions. as defined by broadband optical ancl infrared colors.," The greatest uncertainty in the normalizations probably comes from the bolometric corrections, which were computed from the galaxies' spectral energy distributions, as defined by broadband optical and infrared colors."
 Since (hese photometric measuremeni(s are not always homogeneous or complete. errors of up to 0.1 mag are possible.," Since these photometric measurements are not always homogeneous or complete, errors of up to $\sim 0.1$ mag are possible."
 Fortunately in all cases. the derived bolometric corrections are within 0.1 mag of those predicted for old stellar svstems by population synthesis models (1.e..Worthey.1994).," Fortunately in all cases, the derived bolometric corrections are within 0.1 mag of those predicted for old stellar systems by population synthesis models \citep[\ie][]{worthey}."
 Figure 1. shows (he behavior of ας as a function of several galactic parameters., Figure \ref{fig1} shows the behavior of $\alpha_{0.5}$ as a function of several galactic parameters.
 For two of the variables. the elobular cluster specific frequency. 2004) and the [MgFe] composite absorption line index (González 2004).. ays shows no strong trend.," For two of the variables, the globular cluster specific frequency \citep{kisslerpatig, rhode} and the [MgFe] composite absorption line index \citep{gonzalez, tantalo}, $\alpha_{0.5}$ shows no strong trend."
 However. the other four plots show correlations which are significant al greater than the confidence level.," However, the other four plots show correlations which are significant at greater than the confidence level."
 Galaxies wilh absolute magnitudes fainter than My.~—19 and colors bluer than (V.—7)<L1 have ~1 [O III|-bright PN [or everv 4x105L. of bolometric light., Galaxies with absolute magnitudes fainter than $M_B \sim -19$ and colors bluer than $(V-I) < 1.1$ have $\sim 1$ [O III]-bright PN for every $4 \times 10^8 L_{\odot}$ of bolometric light.
 In larger and redder galaxies. the luminosity specific number of PNs declines as the galaxys UV upturn. as measured by the satellite (Bursteinοἱal.1988).. increases.," In larger and redder galaxies, the luminosity specific number of PNs declines as the galaxy's UV upturn, as measured by the satellite \citep{burstein}, increases."
 This effect is dramatic. so that in the most extreme cases. αμ. is almost an order of magnitude smaller than in low-Tuminosityv objects.," This effect is dramatic, so that in the most extreme cases, $\alpha_{0.5}$ is almost an order of magnitude smaller than in low-luminosity objects."
" The last panel of Figure 1. shows the behavior of 65,5 as a Iunction of the strength οἱ the ealaxw’s IL? absorption line.", The last panel of Figure \ref{fig1} shows the behavior of $\alpha_{0.5}$ as a function of the strength of the galaxy's $\beta$ absorption line.
 Although the equivalent. width of this feature depends on a number of [actors. such as the svstem's metallicity and the a-element (o iron ratio. the index is generally considered to be a good indicator of population age (e...González1993:Worthev1994:Tantalo&Chiosi 2004).," Although the equivalent width of this feature depends on a number of factors, such as the system's metallicity and the $\alpha$ -element to iron ratio, the index is generally considered to be a good indicator of population age \citep[\eg][]{gonzalez, worthey, tantalo}."
. Thus. the direct correlation between 0545 and 13 strength suggests that vounger populations are more efficient at producing [O.III|-bright planetaries (han older. lower-turnoff mass svstenis.," Thus, the direct correlation between $\alpha_{0.5}$ and $\beta$ strength suggests that younger populations are more efficient at producing [O III]-bright planetaries than older, lower-turnoff mass systems."
 To translate a into stellar fractions. we need an estimate of the time that a tvpical PN remains in the top 0.5 mag of luminosity function.," To translate $\alpha$ into stellar fractions, we need an estimate of the time that a typical PN remains in the top 0.5 mag of luminosity function."
 This is not difficult to derive., This is not difficult to derive.
 If ~10% of a PN's energy comes out in [O III] A5007. then the exciting star of an object in this stage of evolution must have L>3900L. and T=50.000 Ix.," If $\sim 10\%$ of a PN's energy comes out in [O III] $\lambda 5007$ , then the exciting star of an object in this stage of evolution must have $L > 3900 L_{\odot}$ and $T \gtrsim 50,000$ ."
 Using these numbers. one can simply use stellar evolutionary (racks (i.e..Vassiliadis&Wood1994:Blocker1995). to estimate how long a particular central star satisfies these conditions.," Using these numbers, one can simply use stellar evolutionary tracks \citep[\ie][]
{vw94, blocker} to estimate how long a particular central star satisfies these conditions."
 Alternatively. one can take the approach of Marigoetal.(2004) and place evolving post-AGD stars within dvnamically evolving nebular models. and track the evolution of all the PNs emission lines as a function of time.," Alternatively, one can take the approach of \citet{marigo} and place evolving post-AGB stars within dynamically evolving nebular models, and track the evolution of all the PN's emission lines as a function of time."
 Such an analysis shows that. although the precise timescale for |O HI] evolution depends on a number of parameters. such as central star mass. post-AGD transition time. and the composition of the energy producing shell. a value of /500 vr is appropriateforthe brightest PNs in a galaxy.," Such an analysis shows that, although the precise timescale for [O III] evolution depends on a number of parameters, such as central star mass, post-AGB transition time, and the composition of the energy producing shell, a value of $t \sim 500$ yr is appropriateforthe brightest PNs in a galaxy."
"across the current sheet, a likely scenario for this case considering the complex morphology of the underlying field and the occurrence of low-altitude disconnection events, can also result in sub-Alfvénnic outflow speeds BOLO: (Murphy, Sovinec,2010; &Cas- 003).","across the current sheet, a likely scenario for this case considering the complex morphology of the underlying field and the occurrence of low-altitude disconnection events, can also result in sub-Alfvénnic outflow speeds \citeauthor{murphy-sovinec-cassak_2010} \citeyear{murphy-sovinec-cassak_2010}; \citeauthor{reevesEA_2010} \citeyear{reevesEA_2010}; \citeauthor{seaton_2008} \citeyear{seaton_2008}) )."
" While it is possible that these inflowing and outflowing motions are independent, the timing, position, and appearance of these features provide support for the case of magnetic reconnection being directly observed in the wake of an erupting flux rope (within the constraints of not having coronal magnetic field measurements)."," While it is possible that these inflowing and outflowing motions are independent, the timing, position, and appearance of these features provide support for the case of magnetic reconnection being directly observed in the wake of an erupting flux rope (within the constraints of not having coronal magnetic field measurements)."
 8. L. Savage is supported by an appointment to the NASA Postdoctoral Program at Goddard Space Flight Center administered by Oakridge Associated Universities through a contract with NASA and under the mentorship of G. Holman., S. L. Savage is supported by an appointment to the NASA Postdoctoral Program at Goddard Space Flight Center administered by Oakridge Associated Universities through a contract with NASA and under the mentorship of G. Holman.
 G. Holman is supported by a NASA HGI Grant and the RHESSI program., G. Holman is supported by a NASA HGI Grant and the RHESSI program.
 K. K. Reeves is supported under contract SP02H1701R from Lockheed-Martin to SAO., K. K. Reeves is supported under contract SP02H1701R from Lockheed-Martin to SAO.
 Support for DBS's contribution to this paper came from PRODEX grant no., Support for DBS's contribution to this paper came from PRODEX grant no.
" C90345 managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office (BELSPO) in support of the PROBA2/SWAP mission, and from the European CommissionOs Seventh Framework Programme (FP7/ 2007-2013) under the grant agreement no."," C90345 managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office (BELSPO) in support of the PROBA2/SWAP mission, and from the European CommissionÕs Seventh Framework Programme (FP7/ 2007-2013) under the grant agreement no."
" 218816 (SOTERIA project, www.soteria-"," 218816 (SOTERIA project, www.soteria-space.eu)."
 D.E. McKenzie is supported under contract SP02H3901R from Lockheed-Martin to MSU., D.E. McKenzie is supported under contract SP02H3901R from Lockheed-Martin to MSU.
 The authors would like to thank Dr. Nicholas Murphy for valuable discussions and the anonymous referee for enhancing the manuscript., The authors would like to thank Dr. Nicholas Murphy for valuable discussions and the anonymous referee for enhancing the manuscript.
stellar interior conditions.,stellar interior conditions.
 We can. however. estimate the conditions for generation of a dynamo in LMS or BD interiors.," We can, however, estimate the conditions for generation of a dynamo in LMS or BD interiors."
 The nücroscopic magnetic diffusivity of metallic ivdrosen is- ogcE 100-107PIE3 οςD|, The microscopic magnetic diffusivity of metallic hydrogen is $\eta \approx 10^2$ $10^3$ $\cm2s$.
 According. to Olun’s aw and Maxwell's equations (Bivdromagnetic induction equation). a magnetic fleld will decay unless a velocity field can counteract or balance the diffusive effects.," According to Ohm's law and Maxwell's equations (hydromagnetic induction equation), a magnetic field will decay unless a velocity field can counteract or balance the diffusive effects."
" For ypical values of the convective velocity (see above). the characteristic magnetic Revuolds uuuboer over a star-size conducting region is Ry,—CoaneRefy29100."," For typical values of the convective velocity (see above), the characteristic magnetic Reynolds number over a star-size conducting region is $R_m=v_{conv} \,R_\star/\eta \gg 100$."
" According o dvnamo theory. &,, iu LMS aud BD iuteriors is thus aree enough for dynamo to occur. providing both rotation and convection are present."," According to dynamo theory, $R_m$ in LMS and BD interiors is thus large enough for dynamo to occur, providing both rotation and convection are present."
 Once the criterion for αναο ouset js satisfied. the field will grow and is supposed o equilibrate when the Loreutz aud the Coriolis forces vecolme conrpiurable (Elsasser number of order τήτν). reaching the aforcieutioned MAC balance.," Once the criterion for dynamo onset is satisfied, the field will grow and is supposed to equilibrate when the Lorentz and the Coriolis forces become comparable (Elsasser number of order unity), reaching the aforementioned MAC balance."
" This vields an amplitude for the internal field. Bu,z(προ)>LOG. cov fast rotators (vi;ο. Ly, "," This yields an amplitude for the internal field, $B_{eq} \approx (8\pi \bar{\rho} \eta \Omega)^{1/2}\ga 10\,{\rm G}$, for fast rotators $\vrot \ga 10\kms$ )."
"At large R,,. ic. in the clissipationless rceie. however. uaenetic diffusion is mainly due to turbulent rather than uolecular diffusion. μυ ion"," At large $R_m$, i.e. in the dissipationless regime, however, magnetic diffusion is mainly due to turbulent rather than molecular diffusion, with $\eta \equiv \eta_t\sim l\,v_{conv}$."
"-linear saturation occurs when turbulence. enlianciug he diffusive processes. is strong enough to reduce Z7, down to the critical value for dynamo action. Πο>50."," In that case, non-linear saturation occurs when turbulence, enhancing the diffusive processes, is strong enough to reduce $R_m$ down to the critical value for dynamo action, $R_{m}\ga 50$."
" This vields typical maecneticC» leonethc» scales 7R,/50. aud hus D.=~afew10+ C for LMS average conditions. in eood agreement with Seld determinatious of a ew kCG (Donatietal.2006: Reimers&Bai 2007))."," This yields typical magnetic length scales $l\la R_\star/50$, and thus $B_{eq}\approx {\rm a\, few}\,10^4$ G for LMS average conditions, in good agreement with field determinations of a few kG \cite{Donati06}; \cite{ReinersBasri}) )."
 This corresponds to Alfven velocities ey=ELZNeones SO hat for such strong fields the Loreutz force wil inpede he convection bv reducing the flow speed.," This corresponds to Alfven velocities $v_A={B\over \sqrt{4\pi \rho}} \ga \vconv$, so that for such strong fields the Lorentz force will impede the convection by reducing the flow speed."
 The main effect of a strong magnetic field is to inhibit motions across if in comparison with motions along it., The main effect of a strong magnetic field is to inhibit motions across it in comparison with motions along it.
 An ideally conducting fluid is tied to the fluid lines., An ideally conducting fluid is tied to the fluid lines.
 In a fluid of Πιο conductivity. motion across the field is possible at a rate eoverned by the conductivity.," In a fluid of finite conductivity, motion across the field is possible at a rate governed by the conductivity."
 Ina Bbiglly couductive ποαι with a strong magnetic field. the motion will be slow.," In a highly conductive medium with a strong magnetic field, the motion will be slow."
 Steveusou's (1979) stabilitv analysis shows that the conibinatiou of fast rotation (Ro 50.1) aud a maguetic field with finite diffusivity couvection. because of he reduction by the Lorentz force of the flow anisotropy due to the Proudimau-Tavlor coustraint.," Stevenson's (1979) stability analysis shows that the combination of fast rotation $Ro\la 0.1$ ) and a magnetic field with finite diffusivity convection, because of the reduction by the Lorentz force of the flow anisotropy due to the Proudman-Taylor constraint."
 Steveusou's approach. however. applies to planar geometry. ie. thin convection zones. and to uniforin density and magnetic fields and is likely to break down for huge (star-size) convective zoues aud strong fields.," Stevenson's approach, however, applies to planar geometry, i.e. thin convection zones, and to uniform density and magnetic fields and is likely to break down for large (star-size) convective zones and strong fields."
 Magueto-convection 3D simulations iudeed show that the magnetic field inhibits he magnitude of the velocity fluctuations and reduces he heat flux (Steinetal. 19923)., Magneto-convection 3D simulations indeed show that the magnetic field inhibits the magnitude of the velocity fluctuations and reduces the heat flux \cite{Stein92}) ).
 Ou the wis of the aforementioned feld streneth values. if seems unavoidable o suppose that. even though the magnetic field will rot necessarily stabilise the fluid against convection iua fluid of finite clectrical resistivity. it will cause a serious reduction of convective efficiency.," On the basis of the aforementioned field strength values, it seems unavoidable to suppose that, even though the magnetic field will not necessarily stabilise the fluid against convection in a fluid of finite electrical resistivity, it will cause a serious reduction of convective efficiency."
" These estimates. on the other Laud. show that he iaenetic pressure in LMS or BD interiors. p?Sirzd0'dvuen↽−⋅≻⋅7 is orders of. magnitude. lower than he gas pressure. 2,GAR>>1022-1016 dvacui? (CD00)). aud it can be safely ignored in the mterual structure equations."," These estimates, on the other hand, show that the magnetic pressure in LMS or BD interiors, ${B^2\over 8\pi}\la 10^7\dyn$, is orders of magnitude lower than the gas pressure, $P_{g}\ga 10^{12}$ $10^{16}\dyn$ \cite{CB00}) ), and it can be safely ignored in the internal structure equations."
 Tudeed. if the fluid is couvectively unstable. the ratio of the magnetic pressure inside the flux tube over the surrounding nean gas pressure is expected to be of the order of the superaciabaticity. SEV22]Vir)<-107 (Cough&Tavler1966: Meyer1991)).," Indeed, if the fluid is convectively unstable, the ratio of the magnetic pressure inside the flux tube over the surrounding mean gas pressure is expected to be of the order of the superadiabaticity, ${(B^2/8\pi)\over P_{g}}\la (\nabla - \nabla_{ad})\la 10^{-7}$ \cite{GoughTayler66}; ; \cite{Meyer}) )."
 An estimate for colplete inhibition of convection is obtained when the Loreutz force is strong chough to balance the buovancy force: where 7R.ods the aforementioncd characteristic magnetic leneth scale im a dvuamo turbulent mediun., An estimate for complete inhibition of convection is obtained when the Lorentz force is strong enough to balance the buoyancy force: where $l\ll R_\star$ is the aforementioned characteristic magnetic length scale in a dynamo turbulent medium.
 This viclds field amplitudes of the order of 104 C. colparable to the value of Brq»," This yields field amplitudes of the order of $10^4$ G, comparable to the value of $B_{eq}$."
 Magnetic fields ean thus in principle severely inhibit convection i the interior of active LAIS aud DDs., Magnetic fields can thus in principle severely inhibit convection in the interior of active LMS and BDs.
" The criterion (2)) for stability against convection in the presence of a magnetic field is sHudar to the oue derived by Stevenson iu the dissipationless regimüe and by Cough Tavler (their Eq.(1.2)). except for the reducing factor ~IR, for the gas pressure torii (assuunug VP,— Πιν)."," The criterion \ref{crit}) ) for stability against convection in the presence of a magnetic field is similar to the one derived by Stevenson in the dissipationless regime and by Gough Tayler (their Eq.(1.2)), except for the reducing factor $\sim l/R_\star$ for the gas pressure term (assuming $\nabla P_g\sim P_g/R_\star$ )."
" The Cough and Tavler approach. however. is primarily devoted to the stucky of surface spots. where the magnetic and eas pressures are comparable,"," The Gough and Tayler approach, however, is primarily devoted to the study of surface spots, where the magnetic and gas pressures are comparable."
 Applvine this criterion to LMS interiors yields field streugths >10* G for the inhibition of convection in the core of a 0.3 A. star (Mullaun&MacDonald 2001))., Applying this criterion to LMS interiors yields field strengths $\ga 10^7$ G for the inhibition of convection in the core of a 0.3 $\msol$ star \cite{Mullan}) ).
 It seems rather dificult to eenerate such strong fields., It seems rather difficult to generate such strong fields.
 Together. uear-equipartition Qvithin a factor ~10) between turbulent aud maguetic enorgv. D/8&Dd~per. aud the factJ hat L(r)xLm(pw) ds a slowly varvius quantity. vield au wuplification factor -—10-100 from the surface to the central regions.," Together, near-equipartition (within a factor $\sim$ 10) between turbulent and magnetic energy, $B^2/8\pi \sim \rho v^2_{conv}$, and the fact that $L(r)\propto 4\pi r^2(\rho \vconv^3)$ is a slowly varying quantity, yield an amplification factor $\sim$ 10-100 from the surface to the central regions."
 A full field of several megaCiauss would lus be in super-equipartition aud. if confined to the interior. would be unstable (Elsasser παρουν c 1) (Tavler1973: Markey&Tavler 19733).," A full field of several megaGauss would thus be in super-equipartition and, if confined to the interior, would be unstable (Elsasser numbers $\gg 1$ ) \cite{Tayler73}; \cite{MarkeyTayler73}) )."
 Therefore. it does rot seen realistic to apply he Cough-Tavler criterion to he eutie stellar structure. iu particular or unifornilv dense objects like LMS aud BDs.," Therefore, it does not seem realistic to apply the Gough-Tayler criterion to the entire stellar structure, in particular for uniformly dense objects like LMS and BDs."
 A veal picture of à maeuetised. convectivelv uustable uediun is cooling flows along the magnetic flux tubes massing through the couvective mediuu.," A real picture of a magnetised, convectively unstable medium is cooling flows along the magnetic flux tubes passing through the convective medium."
 Part of the hermal flux. confined to the tubes. is thus carried * diffuxou.," Part of the thermal flux, confined to the tubes, is thus carried by diffusion."
 This coutraiut on the flow patterus eads to a substautialreduction in the transport of CLOITSM and reduces the asin possible heat fux., This contraint on the flow patterns leads to a substantialreduction in the transport of energy and reduces the maximum possible heat flux.
 Caiven the absence of a proper freatment of heat, Given the absence of a proper treatment of heat
review).,.
.. Measurements of the anisotropies allow constraints to be placed on the rate of growth of clustering., Measurements of the anisotropies allow constraints to be placed on the rate of growth of clustering.
 On large scales. where linear perturbation theory is valid. i is natural to work in a Fourier basis because the symmetries of he background solution imply that k-modes evolve independently.," On large scales, where linear perturbation theory is valid, it is natural to work in a Fourier basis because the symmetries of the background solution imply that $\mathbf{k}$ -modes evolve independently."
 On smaller scales. and especially once survey non-idealities and tingers-of-god become important. the choice is not so clear.," On smaller scales, and especially once survey non-idealities and fingers-of-god become important, the choice is not so clear."
 Because the velocity field departs from its linear theory prediction on extremely large scales (k<0.037Mpe. |). models beyond inear theory must be used to extract cosmological information Tom redshift surveys.," Because the velocity field departs from its linear theory prediction on extremely large scales $k \lesssim 0.03\,h\,{\rm Mpc}^{-1}$ ), models beyond linear theory must be used to extract cosmological information from redshift surveys."
 This has been long recognised and a variety of methods have been attempted to model the distortions., This has been long recognised and a variety of methods have been attempted to model the distortions.
 Severa recent studies of redshift space distortions have provided non-inear descriptions of the matter density field in Fourier space which agree well with direct N-body calculations of the effect., Several recent studies of redshift space distortions have provided non-linear descriptions of the matter density field in Fourier space which agree well with direct N-body calculations of the effect.
 However. we do not generally observe the matter density but rather tracers which tend to live in dark matter halos.," However, we do not generally observe the matter density but rather tracers which tend to live in dark matter halos."
 This introduces further effects which must be carefully modelled if we are to achieve the desired accuracy., This introduces further effects which must be carefully modelled if we are to achieve the desired accuracy.
 In this paper we find a strong dependence on halo bias in the shape of the redshift space correlation function. indicating the need for more sophisticated theoretical modelsapproach).," In this paper we find a strong dependence on halo bias in the shape of the redshift space correlation function, indicating the need for more sophisticated theoretical models."
.. We trace this strong bias dependence primarily to the non-linear mapping between real and redshift space., We trace this strong bias dependence primarily to the non-linear mapping between real and redshift space.
 While more slowly varying with bias. non-linear evolution of the pairwise velocity distribution also substantially changes the redshift space clustering in comparison to linear theory.," While more slowly varying with bias, non-linear evolution of the pairwise velocity distribution also substantially changes the redshift space clustering in comparison to linear theory."
 and(2007).. building on the work of(1999).. combined the streaming and halo models to describe the redshift space correlation function on scales of r«204 'Mpc.," and, building on the work of, combined the streaming and halo models to describe the redshift space correlation function on scales of $r<20\,h^{-1}$ Mpc."
 While we take a similar approach here. we focus on larger scales and only on halos and ignore the contributions from satellite galaxies for now.," While we take a similar approach here, we focus on larger scales and only on halos and ignore the contributions from satellite galaxies for now."
 This greatly simplifies our modelling compared with(2007): however. as we will see. there is still a rich phenomenology compared to dark matter clustering.," This greatly simplifies our modelling compared with; however, as we will see, there is still a rich phenomenology compared to dark matter clustering."
 The outline of the paper is as follows., The outline of the paper is as follows.
 We first review linear and quasilinear descriptions of redshift space distortions in both Fourier and contiguration space. and introduce the scale-dependent Gaussian streaming model that we study in detail in this paper.," We first review linear and quasilinear descriptions of redshift space distortions in both Fourier and configuration space, and introduce the scale-dependent Gaussian streaming model that we study in detail in this paper."
 In Section 3. we present a simplitied Fisher matrix calculation of the expected constraint on the peculiar velocity field from the ongoing Baryon Oscillation Spectroscopic Survey2011)., In Section \ref{fisher} we present a simplified Fisher matrix calculation of the expected constraint on the peculiar velocity field from the ongoing Baryon Oscillation Spectroscopic Survey.
. This calculation sets the target for the accuracy of our model., This calculation sets the target for the accuracy of our model.
 In Section + we compare the streaming model ansatz as a transformation between real space clustering and velocity statistics and clustering in redshift space for halo mass bins. finding very good agreement.," In Section \ref{simxis} we compare the streaming model ansatz as a transformation between real space clustering and velocity statistics and clustering in redshift space for halo mass bins, finding very good agreement."
 Then Section 5 examines the ability of perturbation theory to describe the four ingredients of the streaming model ansatz for tracers of the matter density field: the real space correlation function. the mean tracer pairwise velocity. and the tracer velocity dispersions along and perpendicular to the line-of-sight (LOS).," Then Section \ref{ptsec} examines the ability of perturbation theory to describe the four ingredients of the streaming model ansatz for tracers of the matter density field: the real space correlation function, the mean tracer pairwise velocity, and the tracer velocity dispersions along and perpendicular to the line-of-sight (LOS)."
 We show in Section 6 that using our perturbation theory description as input into the scale-dependent Gaussian streaming model. we have an analytic model accurate at the 2 per cent level on scales s>40/7' Mpc.," We show in Section \ref{combinesec} that using our perturbation theory description as input into the scale-dependent Gaussian streaming model, we have an analytic model accurate at the 2 per cent level on scales $s > 40\,h^{-1}$ Mpc."
 Sections 7 and 8 identify the dominant non-linear terms. elucidating how our model depends on redshift and halo bias.," Sections \ref{zdep} and \ref{biasdep} identify the dominant non-linear terms, elucidating how our model depends on redshift and halo bias."
 We begin by reviewing the effect of redshift space distortions in linear theory both in Fourier space and contiguration space., We begin by reviewing the effect of redshift space distortions in linear theory both in Fourier space and configuration space.
 While Fourier space is usually preferred for theoretical investigations. configuration space is simpler when dealing with wide-angle effects and often preferred in observational analyses.," While Fourier space is usually preferred for theoretical investigations, configuration space is simpler when dealing with wide-angle effects and often preferred in observational analyses."
 The redshift-space position of a galaxy differs from its real-space position due to its peculiar velocity. where vx)=uitxd/(aH) is the. line-of-sight (LOS) component of the galaxy velocity (assumed non-relativistic) in units of the Hubble velocity. and we have taken the LOS to be the cuxis.," The redshift-space position of a galaxy differs from its real-space position due to its peculiar velocity, where $v_z({\bf x}) \equiv u_z({\bf x})/(aH)$ is the line-of-sight (LOS) component of the galaxy velocity (assumed non-relativistic) in units of the Hubble velocity, and we have taken the LOS to be the $z$ -axis."
 We shall adopt the “plane-parallel” approximation. so this direction is fixed for all tracers (halos. galaxies. ete.).," We shall adopt the “plane-parallel” approximation, so this direction is fixed for all tracers (halos, galaxies, etc.)."
" The galaxy over-density field in redshift-space can be obtained by imposing mass conservation. (1+0;kPs=(I0,XPr."," The galaxy over-density field in redshift-space can be obtained by imposing mass conservation, $(1+\delta_g^s)d^3s=(1+\delta_g)d^3r$."
 For a uniform. z-independent mean galaxy density. 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. v./z is small and it is only the second term that is important1987:: but see 20051). If we assume an irrotational velocity field we can write v.=-Üj/ÓzN 8. where Ξ-V-v. and V7 is the inverse Laplacian operator.," For a uniform, $z$ -independent mean galaxy density, 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, $v_z/z$ is small and it is only the second term that is important; but see ), If we assume an irrotational velocity field we can write $v_z= -\partial/\partial z\,\nabla^{-2}\theta$ , where $\theta\equiv-\nabla\cdot{\bf v}$, and $\nabla^{-2}$ is the inverse Laplacian operator."
 In Fourier space. (ζ/0V=th.[krpe. where je is the cosine of the LOS angle. so we have that to linear order.," In Fourier space, $(\partial/\partial z)^2\nabla^{-2}=(k_z/k)^2=\mu^2$, where $\mu$ is the cosine of the LOS angle, so we have that to linear order."
 Often it is further assumed that the velocity field comes from linear perturbation theory., Often it is further assumed that the velocity field comes from linear perturbation theory.
 Then where f=dInD/dIna= 1980)., Then where $f\equiv d\ln D/d\ln a \approx \Omega_m^{0.6}$ .
" For a population of galaxies. which we denote with a subscript 2. the linear. redshift-space power spectrum is then proportional to the linear. real-space matter power spectrum. P5,(4) first showed in detail the relation between the Kaiser formula in Fourier space. Eq. 6.."," For a population of galaxies, which we denote with a subscript $g$, the linear, redshift-space power spectrum is then proportional to the linear, real-space matter power spectrum, $P_m^r(k)$ first showed in detail the relation between the Kaiser formula in Fourier space, Eq. \ref{pkkaiser},"
 and the redshift space correlation function: we rely heavily on that work for this section., and the redshift space correlation function; we rely heavily on that work for this section.
 In linear theory. the correlation between ó(x) and v(x) gives rise to a mean infall vistr) between pairs of matter tracers.," In linear theory, the correlation between $\delta({\bf x})$ and ${\bf v}({\bf x'})$ gives rise to a mean infall $v_{12}({\bf r})$ between pairs of matter tracers."
 The velocity dispersion along the LOS. cuin-(ivivx). depends both on scale and the orientation of thepair separation vector with respect to the LOS.," The velocity dispersion along the LOS, $\sigma_{12}^2(r) = \left\langle ({\bf v}_{z}({\bf x}) - {\bf v}_{z}({\bf x'})^2\right\rangle$, depends both on scale and the orientation of thepair separation vector with respect to the LOS."
 These scale dependencies give rise to linear redshift- distortions in configuration space. apparent in Fig.," These scale dependencies give rise to linear redshift-space distortions in configuration space, apparent in Fig."
 |. as the squashing of contours along the Z axis., \ref{fig:butterfly} as the squashing of contours along the $Z$ axis.
"In the optical (UBVR), the source is again too faint to correspond to a massive (> 10M.) evolved star, with limits on its brightness similar to those for the progenitor (see right panel in Fig. 2)).","In the optical $UBVR$ ), the source is again too faint to correspond to a massive $>10 \,M_\odot$ ) evolved star, with limits on its brightness similar to those for the progenitor (see right panel in Fig. \ref{fig:sed}) )."
 The extinction would have to be increased from the Ay~2.1 mag estimated to be present post-explosion (Botticellaetal. 2009)) to Ay~3.6—5.8 in order to obscure the models shown in Fig. 2.., The extinction would have to be increased from the $A_V\simeq 2.1$ mag estimated to be present post-explosion \citealt{Botticella2009}) ) to $A_V\sim 3.6-5.8$ mag in order to obscure the models shown in Fig. \ref{fig:sed}.
" The magtransient is still detectable in the near-IR, but it is fading rapidly with a slope of approximately 6+1 mag/year at K band that is significantly steeper than the mean slope of 2.3+0.1 mag/year between the late phases of the Botticellaetal.(2009) light curve and our first LBT observation."," The transient is still detectable in the near-IR, but it is fading rapidly with a slope of approximately $6 \pm 1$ mag/year at $K$ band that is significantly steeper than the mean slope of $2.3 \pm 0.1$ mag/year between the late phases of the \cite{Botticella2009} light curve and our first LBT observation."
 The SED is rising to the red with H—K>2.2 mag., The SED is rising to the red with $H-K > 2.2$ mag.
" If we extrapolate the H-band flux from December 2009 to March 2010 using the slope of the K-band light curve, we estimate H~21.9 mag and thus H—K~2.7 mag, which is significantly redder than the H—K~1.4 mag color in the late phases of Botticellaetal. (2009)."," If we extrapolate the H-band flux from December 2009 to March 2010 using the slope of the $K$ -band light curve, we estimate $H \simeq 21.9$ mag and thus $H-K \simeq 2.7$ mag, which is significantly redder than the $H-K \simeq 1.4$ mag color in the late phases of \cite{Botticella2009}."
. We can roughly estimate a temperature and luminosity for the March 2010 epoch., We can roughly estimate a temperature and luminosity for the March 2010 epoch.
" Fitting a blackbody to the measured K-band flux and either the H-band magnitude limit (20.4 mag) or the extrapolated estimate (20.9 mag), we get temperatures of T~900 K and 750 K and luminosities of L~68000L;; and 130000 respectively."," Fitting a blackbody to the measured $K$ -band flux and either the $H$ -band magnitude limit $20.4$ mag) or the extrapolated estimate $20.9$ mag), we get temperatures of $T \simeq 900$ K and 750 K and luminosities of $L\simeq 68000\,L_\odot$ and $130000\,L_\odot$, respectively."
" With a A7! emissivity law, the estimated temperaturesL;, and luminosities are lower, with T~800 K and 700 K and L~50000Lo and 9500010."," With a $\lambda^{-1}$ emissivity law, the estimated temperatures and luminosities are lower, with $T
\simeq 800$ K and $700$ K and $L \simeq 50000\,L_\odot$ and $95000\,
L_\odot$."
" With the further fading between March and May 2010, the source luminosity is now comparable to the estimated luminosity L—4000010 of the progenitor star (Prietoetal.2008;; Botticellaetal. 2009;; Wessonetal. 2010))."," With the further fading between March and May 2010, the source luminosity is now comparable to the estimated luminosity $L
\simeq 40000\,L_\odot$ of the progenitor star \citealt{Prieto2008}; \citealt{Botticella2009}; \citealt{Wesson2010}) )."
" Thompsonetal.(2009) proposed that SN 2008S and the NGC 300 transient were the archetypes of a new class of transients potentially including the M85 OT-1 transient (Kulkarnietal.2007;; Pastorelloetal. 2007)), SN 1999bw (Lietal.2002 and references therein), and now PTF10fgs (Kasliwaletal. 2010))."," \cite{Thompson2009} proposed that SN 2008S and the NGC 300 transient were the archetypes of a new class of transients potentially including the M85 OT-1 transient \citealt{Kulkarni2007}; \citealt{Pastorello2007}) ), SN 1999bw \citealt{Li2002} and references therein), and now PTF10fqs \citealt{Kasliwal2010}) )."
" The initial defining characteristics were (1) a dust-enshrouded progenitor without optical counterpart and mid-IR magnitudes that places them at the tip of the AGB sequence in a mid-IR CMD, and (2) a"," The initial defining characteristics were (1) a dust-enshrouded progenitor without optical counterpart and mid-IR magnitudes that places them at the tip of the AGB sequence in a mid-IR CMD, and (2) a"
"estimate that g,=0.2 is appropriate for proper motions.",estimate that $g_*=0.2$ is appropriate for proper motions.
" In this case VG),=2 stars.", In this case $N_{\rm M15}^L=2$ stars.
 HE this Alp—7 conjecture is correct. the top three clusters should contain of order 10 high-velocity stars between them with the balance of the 12 clusters in Table 1 contributing another 5 or so in total.," If this $M_{\rm BH}-\sigma$ conjecture is correct, the top three clusters should contain of order 10 high-velocity stars between them with the balance of the 12 clusters in Table \ref{T:top choices} contributing another 5 or so in total."
 In addition. their radial range is double that for radial velocities.," In addition, their radial range is double that for radial velocities."
 On the other hand. NE.=0.08 stars. and the black holes will be undetectable by this method.," On the other hand, $N_{\rm M15}^H=0.08$ stars, and the black holes will be undetectable by this method."
 Proper motions have the feature that their uncertainty is inversely proportional to the lime baseline and proportional to the distance., Proper motions have the feature that their uncertainty is inversely proportional to the time baseline and proportional to the distance.
 Nonetheless. the top three clusters. all with distances between. 10 and 12 kpe. should be close enough that. given sufficient data. the black hole hypothesis can be tested. assuming a value of 9 at the lower end of its range.," Nonetheless, the top three clusters, all with distances between 10 and 12 kpc, should be close enough that, given sufficient data, the black hole hypothesis can be tested, assuming a value of $\beta$ at the lower end of its range."
 The main limitation at (his distance will be the increase in elleclive crowcding. proportional to the distance sequared.," The main limitation at this distance will be the increase in effective crowding, proportional to the distance squared."
 For the top three clusters in Table 1.. croweling will be 10 to 16 times higher than in the NGC 6752 observations of Drukieretal.(2003).," For the top three clusters in Table \ref{T:top
choices}, crowding will be 10 to 16 times higher than in the NGC 6752 observations of \citet{dbvg}."
". In the absence of a black hole. the flat extrapolation would lead us to expect to see one or lwo fast-moving stars within 7, in each of our top three candidates."," In the absence of a black hole, the flat extrapolation would lead us to expect to see one or two fast-moving stars within $r_h$ in each of our top three candidates."
 These stars will, These stars will
enission has not been measured directly. but the average electron deusitv has been determined over the cutire Northern Arima by Scovilleetal.(2003) by comparing the Pao aud T1920 fluxes.,"emission has not been measured directly, but the average electron density has been determined over the entire Northern Arm by \citet{sco03} by comparing the $\alpha$ and $\alpha$ fluxes."
 We use their value of ως~104 ciiP to estimate the optical depth to electron scattering., We use their value of $n_{\rm e} \sim 10^{4}$ $^{-3}$ to estimate the optical depth to electron scattering.
 Asstuuing that the depth of the scattering region is simular to its major axis length. 7zz0.2 pe. the column density is No—nd2:6«1073 7.," Assuming that the depth of the scattering region is similar to its major axis length, $l \approx 0.2$ pc, the column density is $N_{\rm e} = n_{\rm e} l \approx 6\times10^{21}$ $^{-2}$."
 The optical depth to Thompson scattering is then rpστιλzz0.001., The optical depth to Thompson scattering is then $\tau_{\rm T} = \sigma_{\rm T} N_{\rm e} \approx 0.004$.
 We have measured the scattered flux. ρω10Poecm (958 keV: Table 3)). so we cau solve for the intrinsic huninosity of musing Equation νι," We have measured the scattered flux, $L_{\rm scat} = 1.6\times10^{-13}$ (2–8 keV; Table \ref{tab:diff}) ), so we can solve for the intrinsic luminosity of using Equation \ref{eq:scat}."
 If we assune 0=907. we find Lxm2<109LÍ.," If we assume $\theta = 90$, we find $L_{\rm X} \approx 2\times10^{36}$."
" We cousider this to be a conservative estimate of the intrinsic Inninositv. because choosing a smaller value for 0 or assuming a sinaller depth aud projected area for the scattering region would result in au inferred bpuuünositv that is a factor of several higher. up to Ly~10°""1."," We consider this to be a conservative estimate of the intrinsic luminosity, because choosing a smaller value for $\theta$ or assuming a smaller depth and projected area for the scattering region would result in an inferred luminosity that is a factor of several higher, up to $L_{\rm X} \sim 10^{37}$."
 Therefore. the peak luninosity of nuuust have been at least ~100 times lareer than the values observed with (Table 2. and Figure 5)).," Therefore, the peak luminosity of must have been at least $\sim 100$ times larger than the values observed with (Table \ref{tab:spectra} and Figure \ref{fig:hist}) )."
 As mentioned above.TE PCA obscrvations would lave detected an outburst larger than 23«1079Ἐν and therefore conceivably could have missed aat its peak Lunimositv.," As mentioned above, PCA observations would have detected an outburst larger than $3\times10^{36}$, and therefore conceivably could have missed at its peak luminosity."
 Ilowever. the timine and morphology of the diffuse enmission argue that the peak. of the outburst should have been detected withNewton.," However, the timing and morphology of the diffuse emission argue that the peak of the outburst should have been detected with."
.. The region of diffuse X-ray cussion remained bright for at least two mouths between 200L July 5 and Aueust 28 (822.2). so the luminous portion of the outburst must have lasted at least this loug.," The region of diffuse X-ray emission remained bright for at least two months between 2004 July 5 and August 28 2.2), so the luminous portion of the outburst must have lasted at least this long."
 The peals of the outbirst had to have ocenrred d/ezLsin+4 mouths prior to the oobservatious., The peak of the outburst had to have occurred $d/c \approx 4\sin^{-1}\theta$ months prior to the observations.
 This places the peak of the outburst during 2001 Nuch and April. when oobserved the source.," This places the peak of the outburst during 2004 March and April, when observed the source."
 At that time the flux was similar to that in our oobservations (Bélangeretal.2005.D.Porquetin prep.)..," At that time the flux was similar to that in our observations \citep[][D. Porquet \etal, in prep.]{bel05}."
 Therefore. it seems Likely that the flux measured frou the location of bby aand is onlv a sinall fraction of its total output.," Therefore, it seems likely that the flux measured from the location of by and is only a small fraction of its total output."
 LIudeed. observations of edge-on LAINBs often suggest that their intrinsic bhuninosities are sienificantlv larecr than would be inferred from their observed X-ray fluxes.," Indeed, observations of edge-on LMXBs often suggest that their intrinsic luminosities are significantly larger than would be inferred from their observed X-ray fluxes."
 For instance. based on the streneth of oxvecu cluission lines in the Reflection Grating Spectrometer and Whigh-Encreyv Transmission Crating spectra of 25 0921-63. αναetal.(2003). Suggest that ouly ~30% of its total N-rav flux is transmitted toward the observer.," For instance, based on the strength of oxygen emission lines in the Reflection Grating Spectrometer and High-Energy Transmission Grating spectra of 2S 0921-63, \citet{kal03} suggest that only $\sim 30$ of its total X-ray flux is transmitted toward the observer."
 Similarly. based ou the low observed N-rav to optical fix of the accretion disk corona source X 1822731. Parmaretal.(2000) sueeest that we observe only of its total flux.," Similarly, based on the low observed X-ray to optical flux of the accretion disk corona source X 1822–731, \citet{par00} suggest that we observe only of its total flux."
 Our measurements of ssugecst that an even sinaller fraction. ~1%.. of the total flux is observed.," Our measurements of suggest that an even smaller fraction, $\sim$ , of the total flux is observed."
 If indeed the vast majority of the flux from lis obscured by the accretion disk. then it could help explain the fact noted by Naravan&MeCliutock(2001) that no confined black hole LAINB is known with au inclination larger than If oulv of the total flux can be detected. frou a black hole LAINB observed edge-on. then almost all of the black hole transients in Fender&Iuulkers(2001) would have apparent Lx<1079JL. and would have been alinost uudetectable bv the all-sky αποτους ou aand citeplev96.jae97..," If indeed the vast majority of the flux from is obscured by the accretion disk, then it could help explain the fact noted by \citet{nm04} that no confirmed black hole LMXB is known with an inclination larger than If only of the total flux can be detected from a black hole LMXB observed edge-on, then almost all of the black hole transients in \citet{fk01} would have apparent $L_{\rm X} \la 10^{36}$, and would have been almost undetectable by the all-sky monitors on and \\citep{lev96,jag97}."
 I£ ccoutains a black hole primary. then it could be the first such system observed edge-on.," If contains a black hole primary, then it could be the first such system observed edge-on."
 VLA observations by Boweretal.(2005) revealed two new radio sources that appeared coicident with the N-rav outburst of290031.," VLA observations by \citet{bow05}
 revealed two new radio sources that appeared coincident with the X-ray outburst of."
.. The N-rav source was located on the line between the two radio features. which sugeests that they are produced by svuchrotron cussion from a jet launched by the Nav source.," The X-ray source was located on the line between the two radio features, which suggests that they are produced by synchrotron emission from a jet launched by the X-ray source."
" The peak intensity was observed iu 2001 March. with 5,=90 uiv. or Lg&IxD?rS,=2«107 at [3 CGIIz."," The peak intensity was observed in 2004 March, with $S_{\nu} = 90$ mJy, or $L_{\rm R} \approx 4\pi D^2 \nu S_{\nu} \approx 2\times10^{32}$ at 43 GHz."
 Iu 2001 July. oulv the eastern feature was detected. with a flux density of z15 ιν at 13 CIIz. or Lgcd«107Ll.," In 2004 July, only the eastern feature was detected, with a flux density of $\approx 45$ mJy at 43 GHz, or $L_{\rm R} \approx 1\times10^{32}$."
 The intensity varied by zz20% from day-to-day., The intensity varied by $\approx 20$ from day-to-day.
 The spectrum of the emission is uncertain. because even when measurements were made at iultiple frequencies. VLBI observations revealed that he sources were resolved. aud therefore cach frequeney sanrples a different spatial scale from the jet.," The spectrum of the emission is uncertain, because even when measurements were made at multiple frequencies, VLBI observations revealed that the sources were resolved, and therefore each frequency samples a different spatial scale from the jet."
 It is also roteworthy that. unlike the relativistically-cxpaucding jets often seen from LMXDs (Feuder2001).. there was 10 proper motion of the radio sources aloug the jet axis (although there was some perpendicular to that axis: see Bower 22005 for further discussion).," It is also noteworthy that, unlike the relativistically-expanding jets often seen from LMXBs \citep{fen04}, there was no proper motion of the radio sources along the jet axis (although there was some perpendicular to that axis; see Bower 2005 for further discussion)."
 Therefore. the radio eatures probably formed where the jet impacted the interstellar meditu.," Therefore, the radio features probably formed where the jet impacted the interstellar medium."
 Indeed. the mud-intrared tage m Figure 9 reveals a significant amount of dust that is near iu projection to290031... particularly at the location of the brighter. casteru radio feature.," Indeed, the mid-infrared image in Figure \ref{fig:midir} reveals a significant amount of dust that is near in projection to, particularly at the location of the brighter, eastern radio feature."
 The radio Iuninositv of Hs unusually large compared to the Nav hunuinositv that we infer from the light echo. Exτε2«1076 sol.," The radio luminosity of is unusually large compared to the X-ray luminosity that we infer from the light echo, $L_{\rm X} \approx 2\times10^{36}$ ."
 First. LAINBs typically are observed to produce extended radio jets only during outburstswith peak luminosities of Lx>107 ," First, LMXBs typically are observed to produce extended radio jets only during outburstswith peak luminosities of $L_{\rm X} \ga 10^{37}$ "
> and evidence of dark matter haloes having a constant Cuna~3.5 dad zcl1 have been found by ?..,$z$ and evidence of dark matter haloes having a constant $c_{\rm dm}\sim 3.5-4$ at $z>1$ have been found by \citet{Gao-2008}.
 Comparing the mock-cluster values of ὃν measured here with the ones of the dark matter haloes predicted bv theoretical studies (7). at cliflerent 2 (see Section 6)). the results seem to show that galaxies have à simular concentration to dark matter at 2~1 but. subsequently they become more concentrated with decreasing redshift.," Comparing the mock-cluster values of $c_{\rm g}$ measured here with the ones of the dark matter haloes predicted by theoretical studies \citep{Gao-2008} at different $z$ (see Section \ref{sec:section6}) ), the results seem to show that galaxies have a similar concentration to dark matter at $z\sim 1$ but subsequently they become more concentrated with decreasing redshift."
 This may be due to the οσο of non-gravitational or eravitational processes. such as: gas cooling. AGN feedback. dynamical friction. merging and tidal stripping. which have significantly. modified the ealaxy distribution within the dark matter halo over the last ~9Gyr.," This may be due to the effect of non-gravitational or gravitational processes, such as: gas cooling, AGN feedback, dynamical friction, merging and tidal stripping, which have significantly modified the galaxy distribution within the dark matter halo over the last $\sim 9$."
 This growth is dominated by the continuously refined physics of the SAAIs (c.g... ?2)). and given this sensitivity. a elance at the data in Fig.," This growth is dominated by the continuously refined physics of the SAMs (e.g., \citealp{Duffy-2010}) ), and given this sensitivity, a glance at the data in Fig."
 10. suggests the need for a thorough and homogeneous study of e in observed. galaxy clusters and. groups over à wide range in We study the evolution of cluster. galaxies with z using {ντα photometry of a cluster. sample made. of 15 of the highest-z (0.8<z 1.5) X-ray clusters observed. so far., \ref{fig:Figure10} suggests the need for a thorough and homogeneous study of $c_{\rm g}$ in observed galaxy clusters and groups over a wide range in We study the evolution of cluster galaxies with $z$ using -band photometry of a cluster sample made of 15 of the $z$ $0.8<z<1.5$ ) X-ray clusters observed so far.
 In. particular. we investigate the A7 Llubble ciagram out to 213 in comparison with SSP (no evolution in absolute A-band magnitude and passive evolution) and SAM evolutionary models.," In particular, we investigate the ${\it K}^{\ast}$ Hubble diagram out to $z\sim 1.3$ in comparison with SSP (no evolution in absolute -band magnitude and passive evolution) and SAM evolutionary models."
 “Phis allows us to explore the process of galaxy formation., This allows us to explore the process of galaxy formation.
" We also study the HOD of this sample. by investigating £N3. as a function of M and z. and c, with z in comparison with cg."," We also study the HOD of this sample, by investigating $\langle N \rangle$, as a function of $M$ and $z$, and $c_{\rm g}$ with $z$ in comparison with $c_{\rm dm}$."
 All our analysis is carried out in strict comparison with simulations. through the use of mock cluster samples taken from MS at 0cz<L3 and populated with galaxies by means of the SAM. by 7..," All our analysis is carried out in strict comparison with simulations, through the use of mock cluster samples taken from MS at $0<z<1.3$ and populated with galaxies by means of the SAM by \citet{Bower-2006}."
" In addition to being an important test for SAMs. this allows us to investigate in details the evolution of 3. CN and e, with z and to study how the relationship between galaxies and clark matter spatial distributions within haloes changes with cosmic time."," In addition to being an important test for SAMs, this allows us to investigate in details the evolution of $\beta$, $\langle N \rangle$ and $c_{\rm g}$ with $z$ and to study how the relationship between galaxies and dark matter spatial distributions within haloes changes with cosmic time."
 This kind of study is fundamental for understanding the role non-gravitational processes. as part of the physics of galaxy formation. take in influencing the way galaxies populate dark matter haloes.," This kind of study is fundamental for understanding the role non-gravitational processes, as part of the physics of galaxy formation, take in influencing the way galaxies populate dark matter haloes."
 Our main conclusions are: The authors thank the referee. Cedric. Lacey for a report which significantly improved the paper., Our main conclusions are: The authors thank the referee Cedric Lacey for a report which significantly improved the paper.
 We also thank Shaun Cole for the useful. discussion. about the SAM models and Adam. Muzzin for kindly providing his data., We also thank Shaun Cole for the useful discussion about the SAM models and Adam Muzzin for kindly providing his data.
 DC expresses his gratitude to Ivan. Baldry ancl Maurizio Paolillo for the valuable discussions and. support., DC expresses his gratitude to Ivan Baldry and Maurizio Paolillo for the valuable discussions and support.
 DC also thanks Corard. Lemson for the helpful suggestions with regards to the AIS database., DC also thanks Gerard Lemson for the helpful suggestions with regards to the MS database.
 CAC and JPS acknowledge financial support from STEC., CAC and JPS acknowledge financial support from STFC.
 MID acknowledges financial support from the Leverhulme Trust., MH acknowledges financial support from the Leverhulme Trust.
 This work is based in part on data collected. at the Subaru Telescope. which is operated by the National Astronomy Observatory of Japan and the XMM-Newton. an ESA science mission funded. by contributions from ESA member states and from ΗΛ is) distributed by the National Optical Astronomy Observatorics. which are operated by the Association of Universities for Research in Astronomy. Inc.. under Cooperative agrecment with the National Science Foundation.," This work is based in part on data collected at the Subaru Telescope, which is operated by the National Astronomy Observatory of Japan and the XMM-Newton, an ESA science mission funded by contributions from ESA member states and from IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation."
mass distribution aud the orbits of the tracer particles in a completely non- way MMemitt Tremblay 1991).,mass distribution and the orbits of the tracer particles in a completely non-parametric way Merritt Tremblay 1994).
 However. if the mass distribution interred from N-ray observations aud the assumption of hydrostatic οπι in the hot gas is adopted. the orbits ofthe elobular clusters can be constrained.," However, if the mass distribution inferred from X-ray observations and the assumption of hydrostatic equilibrium in the hot gas is adopted, the orbits of the globular clusters can be constrained."
 Conversely. if assimuptious are mace about the cluster orbits tthat they are isotropic). then the mass distribution can be estimated.," Conversely, if assumptions are made about the cluster orbits that they are isotropic), then the mass distribution can be estimated."
 In practice. a sensible approach is to check for cousisteucy ofthe mass distribution determined via the N-rayv observations of the hot eas with dynamical measurements (possibly both from elobulars aud planctary nebulae) eiven sinmplifvius assumptions about the orbits. as cach technique las its own systematic concerns which are mitigated if the independent approaches agrec.," In practice, a sensible approach is to check for consistency of the mass distribution determined via the X-ray observations of the hot gas with dynamical measurements (possibly both from globulars and planetary nebulae) given simplifying assumptions about the orbits, as each technique has its own systematic concerns which are mitigated if the independent approaches agree."
 Iu Figure lL. we preseut the mass profile of NCC 1172. estimated frou he velocity dispersion profile 8elven iu Fieureg 3 and the deusitv profile of ∐↸∖↸⊳↕∏↴∖↴↑↸∖↥⋅↴∖↴∶↴∙⊾↕↖⇁↸∖∐↕∐⊟," 	In Figure 4, we present the mass profile of NGC 4472, estimated from the velocity dispersion profile given in Figure 3 and the density profile of the clusters given in Figure 1."
∶↴⋁↿∐⋅↸∖↕∙∖↖⊽↸∖⋜↧↕↴∖↴∪↴∖↴∐∪↖↖↽↕≯∪↥⋅↸⊳∪∐∏≻⋜∐⋅↕↴∖↴∪∐↑∐↸∖↕⊔⋜↧↴∖∷∖↴↻↥⋅∪∐↕↸∖ ↸∖↴∖↴↑↕⋯⋜↧↑↸∖↴⋝⋜↧↴∖↴↸∖≺↧∪∐⊸∖⊽≓⋯⋅↖⇁∪↴⋝↴∖↴↸∖↥⋅↖⇁⋜, We also show for comparison the mass profile estimate based on X-ray observations of the hot gas around this galaxy.
↧↑↕∪∐↴∖↴∪↕≯↑∐↸∖∐∪↑∶↴∙⊾⋜↧↴∖↴⋜∐⋅∪∏∐≼↧↑↕∐↴∖↴∶↴∙⊾⋜↧↕⋜⋯⋅↖⇁∙⊺↕↸∖ ∶↴∙⊾↸∖∐↸∖↕⋅⋜↧↕⋜↧∶↴∙⊾↥⋅↸∖↸∖⋯↸∖∐↑↕∐∐↸∖↴∖↴↸∖↑↖↖↽∪⋯⋜↧↴∖∷∖↴↸∖↴∖↴↑↕⋯⋜↧↑↸∖↴∖↴↴∖↴∏∶↴∙⊾∶↴∙⊾↸∖↴∖↴↑↴∖↴↴⋝∪↑∐↑↸∖↸⊳∐↕∐≺∣⋯∖↴∖↴⋜∐⋅↸∖ ∐⋅∪↴⋝⋜∏⋝↕⋅↖⇁↕∪↑↴⋝↸∖↴∖↴↸∖↑↴⋝∙↖⇁↑↸∖↥⋅↥⋅∏⋝↕↸∖↴∖↴∙↖↽↴∖↴↑↸∖↕⊔⋜↧↑↕↸⊳↸∖∐⋅∪," The general agreement in these two mass estimates suggests both techniques are probably not beset by terrible systematic errors, and thus provides further evidence for the existence of massive dark halos around elliptical galaxies."
↥⋅↴∖↴∙⋜⋯≼↧↑∐∏↴∖↴↻↥⋅∪↖⇁↕≼∐∖↴∖↴↕≯↿∐⋅↑∐∖↥⋅ ↸∖↖↽↕≼∐∖∐↸⊳↸∖↕⋟∪↥⋅↑↕∐∖↸∖↘↕↴∖↴↑↸∖∐⊳↸∖∪↕⋟↕⊔⋜↧↴∖↴↴∖↴↕↖↽↸∖≼↧⋜↧∏↘↽∐⋜↧↕∪↴∖↴⋜⋯∏∐↕≼↧↸∖∐∏≻↑↕↸⊳⋜↧↕∶↴∙⊾⋜↧↕⋜↧⊼↕↸∖↴∖↴∙⊺↕↸∖ ⋜↧∶↴∙⊾↥⋅↸∖↸∖⋯↸∖∐↑↴⋝↸∖↑↖↖↽↸∖↸∖∐↑∐↸∖↑↖↖↽∪↕∐≼∐↰⋉∖⋯∐∖∐↑∐↓⋜↧↴∖∷∖↴↸∖↴∖↴↑↕⋯⋜↧↑↸∖↴∖↴⋜↧↕↴∖, The agreement between the two independent mass estimates also suggests that the assumption of isotropic orbits used to obtain the mass estimate from the globular cluster velocities is unlikely to be dramatically off.
↴∪↴∖↴∏∶↴∙⊾∶↴∙⊾↸∖↴∖↴↑↴∖↴↑↕⋜↧↑ ∐↸∖⋜↧↴∖↴↴∖↴∏∐∩↑↕∪∐∪↕≯↕↴∖↴∪⊓⋅∪↻↕↸⊳∪↥⋅↴⋝↕↑↴∖↴∏↴∖↴↸∖≺↧↑∪∪↴⋝↑⋜↧↕∐↑∐↸∖∐↓⋜↧↴∖↴↴∖↴↸∖↴∖↴↑↕↕⊔⋜↧↑↸∖↕≯↥⋅∪⋯∐∖ ∶↴∙⊾↕∪↴⋝∏↕⋜∐⋅↸⊳∏↴∖↴↑↸∖↥⋅↖⇁↸∖↕∪↸⊳↕↑↕↸∖↴∖↴↕↴∖↴⋯∐∐↘↽↸∖↕⋅↖⇁↑∪↴⋝↸∖≺⊔⋅⋜∐⊔⋜↧↑↕↸⊳⋜↧∐⋅↖⇁∪↕−↥∎∙≋↕⋯∐⋜∐⋅↥⋅↸∖↴∖↴↿↑↴∖↴ are found for MS? CCotté et 22001. Romanowsky Ixochanek 2001. Cohen Ryzhov 1997).," Similar results are found for M87 Côtté et 2001, Romanowsky Kochanek 2001, Cohen Ryzhov 1997)."
 In detail. anisotropy is required at some level for the NGC L172 elobular cluster svstem because the flattening of svstem can not be supported by the negligible rotation observed.," In detail, anisotropy is required at some level for the NGC 4472 globular cluster system because the flattening of system can not be supported by the negligible rotation observed."
 This is not necessarily true of the ALS7 system., This is not necessarily true of the M87 system.
 One of the potential advantages of the study of individual tracers (either globular clusters or planetary nebulae) is that both shape aud kinematic information covering the full two-dimensional projected distribution ou the skv are obtained (απκο sinele slices from standard long-slit spectroscopy). which may be useful for future larger studies that attempt to constraiu the dimensional shape of galactic halos.," One of the potential advantages of the study of individual tracers (either globular clusters or planetary nebulae) is that both shape and kinematic information covering the full two-dimensional projected distribution on the sky are obtained (unlike single slices from standard long-slit spectroscopy), which may be useful for future larger studies that attempt to constrain the three-dimensional shape of galactic halos."
 The research described here would uot have been carried out successfully without the contributions of many collaborators., 	The research described here would not have been carried out successfully without the contributions of many collaborators.
 The plotometric studies are primarily the thesis work of INatherime Rhode. aud were mace feasible by the CCD Mosaic imagers at NOAO.," The photometric studies are primarily the thesis work of Katherine Rhode, and were made feasible by the CCD Mosaic imagers at NOAO."
 The dynamical study of NGC 1172 is based ou data obtained at the CFOT and WHT aud came to fruition through the hard work of nw many colleagues on that project. inchiding Mike. Beasley.," The dynamical study of NGC 4472 is based on data obtained at the CFHT and WHT and came to fruition through the hard work of my many colleagues on that project, including Mike Beasley,"
systems would thus be the analogs of the A-type companion of SS Lep.,systems would thus be the analogs of the A-type companion of SS Lep.
 The spectrum of HD 101584 is very complex. combining emission lines with P-Cygni profiles indicative of ongoing mass loss and absorption lines.," \nocite{Paczynski-Rudak-80,Iben-Tutukov-1996} The spectrum of HD 101584 is very complex, combining emission lines with P-Cygni profiles indicative of ongoing mass loss and absorption lines."
 The remarkable characteristic of the optical spectrum of HD 101584 is the fact that different spectral regions resemble different spectral types., The remarkable characteristic of the optical spectrum of HD 101584 is the fact that different spectral regions resemble different spectral types.
 There is therefore no agreement about the effective temperature of the central star. with proposed values ranging from 8500 K (?) to 120000 K (?).. or 8500+1000 K for the post-AGB star and about 0000 K for its companion (?)..," There is therefore no agreement about the effective temperature of the central star, with proposed values ranging from 8500 K \citep{Sivarani-1999} to 000 K \citep{Bakker-1996}, or $8500\pm1000$ K for the post-AGB star and about 000 K for its companion \citep{Kipper-2005}."
 There ts thus no clear evidence from recent works for the companion of the post-AGB star HDIO1584 to be an M giant. despite the early suggestion by ?..," There is thus no clear evidence from recent works for the companion of the post-AGB star HD101584 to be an M giant, despite the early suggestion by \citet{Humphreys-1976}."
 In the spectral energy distributions presented by ? for HD 213985 and IRAS 05208-2035. neither is there evidence for the presence of à cool giant companion. as it was the case for SS Lep (?)..," In the spectral energy distributions presented by \citet{DeRuyter-2006} for HD 213985 and IRAS 05208-2035, neither is there evidence for the presence of a cool giant companion, as it was the case for SS Lep \citep{Verhoelst-2007}."
 Nevertheless. if the luminosity ratio between the post-AGB and the giant components is of the order 5 to10*.. one may wonder whether the cool giant could at all be noticed (fitting the complex spectral energy distributions of post-AGB systems is à delicate operation involving many free parameters —like the reddening- with no unique solution; Van Winckel. priv.," Nevertheless, if the luminosity ratio between the post-AGB and the giant components is of the order 5 to, one may wonder whether the cool giant could at all be noticed (fitting the complex spectral energy distributions of post-AGB systems is a delicate operation involving many free parameters –like the reddening– with no unique solution; Van Winckel, priv."
 comm.)., comm.).
 For the SS Lep system. the luminosity ratio is 1.6 1n favour of the A component (?)..," For the SS Lep system, the luminosity ratio is 1.6 in favour of the A component \citep{Verhoelst-2007}."
 HD 172481 is another example of a F2la supergiant traditionally considered to be a post-AGB star. but which is more likely a white dwarf burning hydrogen accreted from its AGB companion (?)..," HD 172481 is another example of a F2Ia supergiant traditionally considered to be a post-AGB star, but which is more likely a white dwarf burning hydrogen accreted from its AGB companion \citep{Whitelock-2001}."
 For that system. the presence of an M giant companion is apparent from the detection of TIO bands. from the SB2 nature of the CORAVEL cross-correlation dip (2).. and from Mira-type pulsations with a period of 312 d. From the SED. the luminosity ratio turns out to be similar to SS Lep: Zg/Ls;=1.8 (although that ratio is somewhat dependent upon the adopted reddening).," For that system, the presence of an M giant companion is apparent from the detection of TiO bands, from the SB2 nature of the CORAVEL cross-correlation dip \citep{Reyniers-2001}, and from Mira-type pulsations with a period of 312 d. From the SED, the luminosity ratio turns out to be similar to SS Lep: $L_{\rm F}/L_{\rm
 M} = 1.8$ (although that ratio is somewhat dependent upon the adopted reddening)."
 No radial-velocity variations hinting at à period of à few hundred days have been detected for HD 172481 (?).., No radial-velocity variations hinting at a period of a few hundred days have been detected for HD 172481 \citep{Reyniers-2001}.
 The papers mentioned above suggest different types of accreting components in SS Lep and HD 172481 but. in the absence of stringent constraints on the mass and luminosity of the accreting star. there Is in fact no easy way to distinguish between WD and main-sequence accretors.," The papers mentioned above suggest different types of accreting components in SS Lep and HD 172481 but, in the absence of stringent constraints on the mass and luminosity of the accreting star, there is in fact no easy way to distinguish between WD and main-sequence accretors."
 In summary. we conclude that some systems currently flagged as hosting a post-AGB star could in fact be better described as systems where an M giant dumps matter on its white-dwarf or main-sequence companion which then acquires supergiant dimensions. thus mimicking a post-AGB star.," In summary, we conclude that some systems currently flagged as hosting a post-AGB star could in fact be better described as systems where an M giant dumps matter on its white-dwarf or main-sequence companion which then acquires supergiant dimensions, thus mimicking a post-AGB star."
 Such systems. currently plotted in panel 3 of Fig.," Such systems, currently plotted in panel 3 of Fig."
 2. (post-AGB systems). do in fact belong to panel 2 (M giants). were it not for the light of the M giant being lost in the glow of its supergiant- companion.," \ref{Fig:elogP_panels} (post-AGB systems), do in fact belong to panel 2 (M giants), were it not for the light of the M giant being lost in the glow of its supergiant-like companion."
 In this scenario. one might however worry whether the accreting component could indeed become more luminous than the moss-losing giant.," In this scenario, one might however worry whether the accreting component could indeed become more luminous than the moss-losing giant."
 Another possible scenario to account for systems like HD 172481 could therefore be as follows. now stating instead that the post-AGB star is genuine. but its giant. companion is fake.," Another possible scenario to account for systems like HD 172481 could therefore be as follows, now stating instead that the post-AGB star is genuine, but its giant companion is fake."
" In a system with components of initial masses (Mj.AM5)=(3.1)M... the star of mass Af,=>Mo evolves faster. fills its Roche lobe on the AGB around the first thermal pulse and becomes a white dwarf (WD) with a mass of 0.55 citepBloecker-95.."," In a system with components of initial masses $(M_1,M_2) = (3,1)$, the star of mass $M_1 > M_2$ evolves faster, fills its Roche lobe on the AGB around the first thermal pulse and becomes a white dwarf (WD) with a mass of 0.55 \\citep{Bloecker-95}."
 It is not exactly clear what happens to the orbit. although ? presented arguments for the orbital period remaining more or less unchanged (see also the discussion in Sect. 2.3)).," It is not exactly clear what happens to the orbit, although \citet{Frankowski-2007a} presented arguments for the orbital period remaining more or less unchanged (see also the discussion in Sect. \ref{Sect:Ba}) )."
 Then the star of mass 1» (which could by now have reached 2-3 aas a result of accretion) evolves in turn along the AGB. but having a lighter companion it can grow bigger and brighter without filling its Roche lobe. say up to acore mass of 0.6.," Then the star of mass $M_2$ (which could by now have reached 2–3 as a result of accretion) evolves in turn along the AGB, but having a lighter companion it can grow bigger and brighter without filling its Roche lobe, say up to a core mass of 0.6."
"... Eventually star 1» fills its Roche lobe and ejects most of its envelope. transferring part of it back to star 1, (afewagaintogiantdimensions: ?).."," Eventually star $M_2$ fills its Roche lobe and ejects most of its envelope, transferring part of it back to star $M_1$ \citep[a few 
0.01~\Msun\ is enough for $M_1$ to reignite its H shell and to swell again to giant dimensions;][]{Frankowski-2003}."
 There are now two cores with comparable envelope masses. both burning hydrogen in shells. the younger (A5. i.e. the true-post AGB) burning it faster (as it has a more massive core).," There are now two cores with comparable envelope masses, both burning hydrogen in shells, the younger $M_2$, i.e. the true-post AGB) burning it faster (as it has a more massive core)."
 The younger core is brighter and evolves (contracts) faster., The younger core is brighter and evolves (contracts) faster.
" The difference in evolutionary speed becomes enormous as star 1» gets to its post-AGB stage (3000tureoflogTy, = while star A, still sits on the AGB."," The difference in evolutionary speed becomes enormous as star $M_2$ gets to its post-AGB stage \citep[3000 years off the AGB, the 0.6~\Msun\ core has already a temperature of $\log 
T_{\mathrm eff} = while star $M_1$ still sits on the AGB."
 Soon we are left with a giant configuration around 14's core and a hot. brighter post-AGB A/».," Soon we are left with a giant configuration around $M_1$ 's core and a hot, brighter post-AGB $M_2$."
 In this particular case the brightness difference is a factor of 3 to 5., In this particular case the brightness difference is a factor of 3 to 5.
 The mass function would be high (0.16 ffor the sample case above. assuming ο=(hf907 which makes it very similar to SS Lep. which has f(A)0.26 AL..)).," The mass function would be high (0.16 for the sample case above, assuming $e = 0, i = 90^\circ$ -- which makes it very similar to SS Lep, which has $f(M) = 0.26$ )."
 In any case. the suggestion that some stars flagged as post-AGB could in fact be components of binary systems caught in the act of mass transfer would have several interesting consequences.," In any case, the suggestion that some stars flagged as post-AGB could in fact be components of binary systems caught in the act of mass transfer would have several interesting consequences."
 It could explain the unexpectedly large number of post-AGB systems (as compared to their short evolution time scale). the similarity between the orbital elements of post-AGB and M binaries (if. post-AGB stars were post-mass-transfer systems rather than systems with mass transfer as we suggest. the orbital elements should have been altered. at least to some extent).," It could explain the unexpectedly large number of post-AGB systems (as compared to their short evolution time scale), the similarity between the orbital elements of post-AGB and M binaries (if post-AGB stars were -mass-transfer systems rather than systems with mass transfer as we suggest, the orbital elements should have been altered, at least to some extent)."
 It would also explain why we could not find any other systems with characteristics similar to SS Lep [namely. early-type star with cool dust ma disc and spectral features typical of (super)giants]. since they would all already have been flagged às post-AGB systems!," It would also explain why we could not find any other systems with characteristics similar to SS Lep [namely, early-type star with cool dust in a disc and spectral features typical of (super)giants], since they would all already have been flagged as post-AGB systems!"
 The star 3 Pup (HD 62623) 1s sometimes presented as the twin of SS Lep (?).. but the exact nature of this star is still much debated.," The star 3 Pup (HD 62623) is sometimes presented as the twin of SS Lep \citep{Jura-2001}, but the exact nature of this star is still much debated."
 At this point. it should be mentioned that the d symbiotic systems could be related as well to post-AGB systems and SS Lep: they host a warm. fast-rotating giant (F to early K) with a hot," At this point, it should be mentioned that the d' symbiotic systems could be related as well to post-AGB systems and SS Lep: they host a warm, fast-rotating giant (F to early K) with a hot"
"from P(C,|o;) based on the same σι set as used for the BR estimator.",from $P(C_{\ell}|\sigma_{\ell})$ based on the same $\sigma_{\ell}$ set as used for the BR estimator.
 This csscutially correspouds to computing the Blackwell-Rao estimator by Monte Carlo. aud the conrputational cost of producing these extra samples is sinall. (," This essentially corresponds to computing the Blackwell-Rao estimator by Monte Carlo, and the computational cost of producing these extra samples is small. ("
"The computational expense of the Ciübbs sampler is driven by sampling from P(s|C;.d). uot by P((GC,[s).)","The computational expense of the Gibbs sampler is driven by sampling from $P(\mathbf{s}|C_{\ell},\mathbf{d})$ , not by $P(C_{\ell}|\mathbf{s})$ .)"
 Note that this approach naturally supports arbitrary C biuuime schemes (Eriksen&Weltus2008).. aud. also interfaces naturally with the hwbrid AICAIC scheme described by Jewelletal.(2001).," Note that this approach naturally supports arbitrary $C_{\ell}$ binning schemes \citep{wehus:2008}, and also interfaces naturally with the hybrid MCMC scheme described by \citet{jewell:2004}."
. Civen these spline approximations to P(C;;d) for cach ἐν we compute the correspouding cumulative distributions by nmuucrical iuteeration. This ids subsequently ideutified with a stanclard Gaussian distribution with zero mean aud unity variance.," Given these spline approximations to $P(C_{\ell}|\mathbf{d})$ for each $\ell$, we compute the corresponding cumulative distributions by numerical integration, This is subsequently identified with a standard Gaussian distribution with zero mean and unity variance."
 Explicitly. we fiud πι) over a eid in C; such that where crf is the error function.," Explicitly, we find $x_\ell(C_\ell)$ over a grid in $C_\ell$ such that where $\textrm{erf}$ is the error function."
 This equation is straightforward to solve using standard uunucrical findiug routines., This equation is straightforward to solve using standard numerical root-finding routines.
 The result is a couvenieut set of look-up tables a(Cy). again stored in the form of cubic splines. that allows for very efficient transformation from standard to Caussian variables for arbitrary values of Ci.," The result is a convenient set of look-up tables $x_{\ell}(C_{\ell})$, again stored in the form of cubic splines, that allows for very efficient transformation from standard to Gaussian variables for arbitrary values of $C_{\ell}$ ."
 Frou these splines. it is also easy to compute the derivatives required for the Jacobian inEquation 7..," From these splines, it is also easy to compute the derivatives required for the Jacobian inEquation \ref{eq:transformation}."
 ILwius defined a chanec-of-variables for cach ἐν the remaining task is to estimate the joint distribution. P(x|d). iu the new variables.," Having defined a change-of-variables for each $\ell$, the remaining task is to estimate the joint distribution, $P(\mathbf{x}|\mathbf{d})$, in the new variables."
 In this paper. we approximate this distribution by a joint Gaussian. but any parametric function could of course serve this purpose.," In this paper, we approximate this distribution by a joint Gaussian, but any parametric function could of course serve this purpose."
 For example. we nuplemieuted support for the skew-Gaussian distribution (e.9..Azgzalini&Capitanio2003) in our codes. but found that the improvement over a simple Cassiani was very sul.," For example, we implemented support for the skew-Gaussian distribution \citep[e.g.,][]{azzalini:2003} in our codes, but found that the improvement over a simple Gaussian was very small."
 The ouly free parameters in this multivariate Gaussian distribution are the mean. gj. and the covariance. C.," The only free parameters in this multivariate Gaussian distribution are the mean, $\mu$, and the covariance, $\mathbf{C}$."
 These are again estimated from the saurples produced by the Cabbs sampler., These are again estimated from the samples produced by the Gibbs sampler.
" First. we draw NOονOo"") C, samples from P(C;|o;). as described above. but this time including all Cs for cach sample."," First, we draw $N \sim \mathcal{O}(10^6)$ $C_{\ell}$ samples from $P(C_{\ell}|\sigma_{\ell})$, as described above, but this time including all $\ell$ 's for each sample."
 Then we Caussianize these (-by-f. by evaluating (C7)}) for cach siuuple aud multipole moment.," Then we Gaussianize these $\ell$ $\ell$, by evaluating $x_{\ell}(C_{\ell})$ for each sample and multipole moment."
 Finalky. we couipute the correspouding means aud standard deviatious. where the suis run over sample iudex.," Finally, we compute the corresponding means and standard deviations, where the sums run over sample index."
 Before applying the machinery described in the previous section to the 5-vear WALAP data. we verity the method by a analyzing a simulated low-resolutiou data set.," Before applying the machinery described in the previous section to the 5-year WMAP data, we verify the method by a analyzing a simulated low-resolution data set."
 The reason for cousideriug a low-resolution simulation is that only in this case is it possible to evaluate the exact likelihood by brute force im pixel space. without making auv approximations.," The reason for considering a low-resolution simulation is that only in this case is it possible to evaluate the exact likelihood by brute force in pixel space, without making any approximations."
 The simulation is made by drawing ai Caussian realization from the best-fit 5-vear WALAP ACDM power spectrmm (I&oiiatsuctal.2008).. smoothing this with a 107 PWOIAL Gaussian beam. aud projecting it on au Nuae16 exid.," The simulation is made by drawing a Gaussian realization from the best-fit 5-year WMAP $\Lambda$ CDM power spectrum \citep{komatsu:2008}, smoothing this with a $10^{\circ}$ FWHM Gaussian beam, and projecting it on an $N_{\textrm{side}}=16$ grid."
 Finally. 200K RAIS white noise is added to each pixel. aud the (degraded) WALAP KOSS sky cut (Coldetal.2008) is applied to the data.," Finally, $20\mu\textrm{K}$ RMS white noise is added to each pixel, and the (degraded) WMAP KQ85 sky cut \citep{gold:2008} is applied to the data."
 The masini multipole considered iu this analvsis was Gas=L7. and the spectra was binned with a biu size of Af=5 from (=20.," The maximum multipole considered in this analysis was $\ell_{\textrm{max}} = 47$, and the spectrum was binned with a bin size of $\Delta \ell=5$ from $\ell=20$."
 The signal-to-noise is unity at f=19. aud negligible bevoud (6z30.," The signal-to-noise is unity at $\ell=19$, and negligible beyond $\ell \ge 30$."
 We now compute slices for each (6 through the full multivariate likelibood. both with the method described in refsecinethod and by brute-force pixel space evaluation (e.g.Eriksenetal.2007a).. fixing all other (s at the input ACDAL spectrum.," We now compute slices for each $\ell$ through the full multivariate likelihood, both with the method described in \\ref{sec:method} and by brute-force pixel space evaluation \citep[e.g.,][]{eriksen:2007a}, fixing all other $\ell$ 's at the input $\Lambda$ CDM spectrum."
 For comparison. we also compute the the mareial distributions for cach f.," For comparison, we also compute the the marginal distributions for each $\ell$."
 The results from this exercise ave shown in Figure 1.., The results from this exercise are shown in Figure \ref{fig:verification}.
 Black lines indicate the brute-force likeliboods. aud red lues show the Caussianized Blackwell-Rao likelihoods.," Black lines indicate the brute-force likelihoods, and red lines show the Gaussianized Blackwell-Rao likelihoods."
 The ereen diues show the marginal cistributious. visualizing the effect of mode coupling due to the skv cut.," The green lines show the marginal distributions, visualizing the effect of mode coupling due to the sky cut."
 Fist. wesee that all distributions agree very closely at ( <8.," First, wesee that all distributions agree very closely at $\ell\le8$ ."
 In this very laree-scale regiae. alb harmonic modes are sufficiently well sampled with the KQs5 sky cut that mode coupling is ucelicible.," In this very large-scale regime, all harmonic modes are sufficiently well sampled with the KQ85 sky cut that mode coupling is negligible."
 Iowoever. from (>10the mareial distributions are noticeably different from the likelihood. slices. with a typical shift," However, from $\ell\ge10$the marginal distributions are noticeably different from the likelihood slices, with a typical shift"
 , 
The starting poiut is the general expression of the differential rate (DeRujulaetal. 19913) IuEq.(53). fle.) is the transverse velocity distribution and difdji(s.jf) is the halo lens ME: iu the reasonable hypothesis of homogeneity. this latter may be factorizedas beiug p. the local mass density of the model aud didi the local ME.,"The starting point is the general expression of the differential rate \cite{DeR91}) ) In \ref{eq: dgamma}) ), $f(v_{\perp})$ is the transverse velocity distribution and $dn/d\mu(s,\mu)$ is the halo lens MF; in the reasonable hypothesis of homogeneity, this latter may be factorized: being $\rho_{\odot}$ the local mass density of the model and $dn_0/d\mu$ the local MF."
" Changing variable from ce, to fg and inteerating we ect being (t.µη) the lower aud upper limit for the mass of MACTIOs."," Changing variable from $v_{\perp}$ to $t_E$ and integrating we get being $(\mu_l, \mu_u)$ the lower and upper limit for the mass of MACHOs."
 From Eq.(7)) one inuiediatelvy see that to eo ou further we need to assign the transverse velocity distribution. the local AIF aud the mass ceusity of the halo moclel.," From \ref{eq: dgammadtgen}) ) one immediately see that to go on further we need to assign the transverse velocity distribution, the local MF and the mass density of the halo model."
 Since we do not consider anisotropy in the velocity Space. We mayo assume the following maxwellian distribution of the trausverse velocities where eg is the velocity dispersion which we fix as 210 laus. With regard to the local ME. it is usual to assiuue that all the NLACTIOs have the same mass which means that diy fdpisad DDirac centred on the common mass.," Since we do not consider anisotropy in the velocity space, we may assume the following maxwellian distribution of the transverse velocities where $v_{H}$ is the velocity dispersion which we fix as 210 km/s. With regard to the local MF, it is usual to assume that all the MACHOs have the same mass which means that $dn_0/d\mu$ is a $\delta$ Dirac centred on the common mass."
 This js just a first approximation: it is worthwhile to explore different possibilities., This is just a first approximation: it is worthwhile to explore different possibilities.
" As a generalization we consider the case of a homogenous Haw ME for the ΣΤΑΠο», Lc. we assume being C(a) a normalization constant fixed such that this gives: Coucerning the mass deusity of the dark halo we will restrict our analysis to a class of spheroidal nou singular isothermal models whose density distribution is eiven by where ο=VlL———54 with- 4 the halo flattening.. p;E+) is. the local mass for the splierical case. Ry is tle ealactocentiic distance of the Sun aud £7. is the core radius."," As a generalization we consider the case of a homogenous law MF for the MACHOs, i.e. we assume being $C(\alpha)$ a normalization constant fixed such that this gives: Concerning the mass density of the dark halo we will restrict our analysis to a class of spheroidal non singular isothermal models whose density distribution is given by where $e = \sqrt{1-q}$ with $q$ the halo flattening, $\rho_{\odot}^{(s)}$ is the local mass for the spherical case, $R_0$ is the galactocentric distance of the Sun and $R_c$ is the core radius."
 luserting now Eqs.(8)). (9)) aud (12)) iuto Eq.(7)) and expressing (2.2) im terms of (5.7.5) (with (.5) ealactic aueular coordinates of the target). we finally ect beige aud we lave defined for sake of shortucss with Given pCR.i) it is quite straightforward to ect all the observable quantities we need in the following.," Inserting now \ref{eq: fvperp}) ), \ref{eq: mfpowlaw}) ) and \ref{eq: rho}) ) into \ref{eq: dgammadtgen}) ) and expressing $(R,z)$ in terms of $(s, l, b)$ (with $(l,b)$ galactic angular coordinates of the target), we finally get being and we have defined for sake of shortness with Given $\rho(R, z)$ it is quite straightforward to get all the observable quantities we need in the following."
 The first one is the number of observable eveuts. which is simply eiven by Tutroducing the expression given by (133) iuto Eq.(15)) one ects having posed Also. from Eq.(13)) aud. definition (3)). woe get the following expression for the observable optical depth: being now Now it is uot dificult to eet the predicted mean duration: in order to take into account the detection efficiency. we define this quantity as definition is nothiug else but a straightforward generalization of the usual one (Jetzer 1998)) to which it reduces in the case of perfect detection efficiency. ic.," The first one is the number of observable events, which is simply given by Introducing the expression given by \ref{eq: dgammadtfin}) ) into \ref{eq: nevobledef}) ) one gets having posed Also, from \ref{eq: dgammadtfin}) ) and definition \ref{eq: tauker}) ), we get the following expression for the observable optical depth: being now Now it is not difficult to get the predicted mean duration; in order to take into account the detection efficiency, we define this quantity as This definition is nothing else but a straightforward generalization of the usual one \cite{J98}) ) to which it reduces in the case of perfect detection efficiency, i.e."
"and can be expressed as The ratio of the electric field of the electrosphere of quark stars and of the critical electric field E,=mZ/e is represented. as a function of the distance from the quark star surface and for different. values of the temperature. in Fie.","and can be expressed as The ratio of the electric field of the electrosphere of quark stars and of the critical electric field $E_{cr}=m_e^2/e$ is represented, as a function of the distance from the quark star surface and for different values of the temperature, in Fig."
 1., 1.
" Let us consider a quantized Dirac field coupled to a classical external electromagnetic field described by the potential l,,."," Let us consider a quantized Dirac field coupled to a classical external electromagnetic field described by the potential $A_{\mu
}$."
" The probability P? to remain in the ground state. ie.. the probability of emitting no pairs. is given by P?=|(0]9]0)|. where S is the 5 matrix defined as S=Texp[i{L,d.i] .T is the time ordering operator and L,; is the interaction Lagrangian (Solfeletal. 1982).."," The probability $P$ to remain in the ground state, i.e., the probability of emitting no pairs, is given by $P=\left|
\left\langle 0\left| S\right| 0\right\rangle
\right| ^{2}$ , where $S$ is the $S$ matrix defined as $S=\hat{T}\exp \left[ i\int L_{I}d^{4}x%
\right] , $\hat{T}$ is the time ordering operator and $L_{I}$ is the interaction Lagrangian \citep{So82}. ."
 The probability P? can also be written as 7?=exp[-{ieCr)d-r]. where wr)ο where Lgp(x) is the one-loop ellective Lagrangian density. which includes allorders in the external field. but neglects sel[-interactions of the matter fields.," The probability $P$ can also be written as $P=\exp %
\left[ -\int w(x)d^{4}x\right], where $w\left( x\right) =2{\rm Im}%
L_{eff}\left( x\right), where $L_{eff}\left( x\right) $ is the one-loop effective Lagrangian density, which includes allorders in the external field, but neglects self-interactions of the matter fields."
 The quantity Cr) can be interpreted as (he pair production rate per unit Gime ancl unit volume at the space-time point ©=Cry.r4.2.03) (Greineretal.L985: 1989).," The quantity $%
w(x ) can be interpreted as the pair production rate per unit time and unit volume at the space-time point $x=\left(
x_{0},x_{1},x_{2},x_{3}\right) $ \citep{Gr85,Ma89}."
. An alternative deseription of the pair creation process can be obtained by assuming that (he vacuum clecavs if there exists an ingoimeg anliparticle mode which is at (he same {ime an oulgoing particle mode., An alternative description of the pair creation process can be obtained by assuming that the vacuum decays if there exists an ingoing antiparticle mode which is at the same time an outgoing particle mode.
" An in-vacuum is defined. via the ingoing (anti)-particle basis. [invac)=a,jin.0. whereas the out-vacuum is defined by the outgoing states afoul.vac)=aylout. 0. where «e are the particle creation and annihilation operators. respectively (Solfeletal.1982)."," An in-vacuum is defined via the ingoing (anti)-particle basis, $_{-}a_{l}\left| {\rm in},{\rm
vac}\right\rangle =_{+}a_{k}\left| {\rm in},{\rm vac}\right\rangle
=0$, whereas the out-vacuum is defined by the outgoing states $^{-}a_{l}\left| {\rm out},{\rm vac}\right\rangle =^{+}a_{k}\left|
{\rm out},{\rm vac}\right\rangle =0$ , where $a$ are the particle creation and annihilation operators, respectively \citep{So82}."
". The number of the outgoing particles in the mocle created in the in-vacium is Nyy=(vac.in|a, ayvac.in)=j|o0:—M). where the coefficients 3;,; are the elements of the single-particle 5 matrix."," The number of the outgoing particles in the mode $k$ created in the in-vacuum is $N_{kk^{\prime }}\equiv \left\langle {\rm
vac},{\rm in}\right| ^{+}a_{k}^{+}$ $^{+}a_{k^{\prime }}\left|
{\rm vac},{\rm in}\right\rangle =\sum_{l}\left| \beta _{kl}\right|
^{2}\delta \left( k-k^{\prime }\right) $, where the coefficients $\beta _{kl}$ are the elements of the single-particle $S$ matrix."
" Due to the validity. οἱ ihe energv and momentum conservation laws. one can generally choose oj=2,05; aud thus the number of created particles in the mode / is simply given by INτοιBo(k—M)."," Due to the validity of the energy and momentum conservation laws, one can generally choose $\beta _{kl}=\beta _{k}\delta _{kl}$ and thus the number of created particles in the mode $k$ is simply given by $N_{kk^{\prime }}=\left| \beta _{k}\right| ^{2}\delta
\left( k-k^{\prime }\right) $."
" The della function can be re-expressed as a delta function overthe frequencies ofthe associated modes.Jj=7,9(wj— ay)."," The delta function can be re-expressed as a delta function overthe frequencies ofthe associated modes,$\beta _{kl}=\mathcal T_{k}\delta \left( \omega
_{l}-\omega _{k}\right) $ ."
 Then the rule {0(wy—c)p(1/2x)0(wu;ey)fdl maybe used (o caleulate a continuous rate of creation of particle-antiparticle pairs 2002)..," Then the rule $\left\{ \delta \left(
\omega _{l}-\omega _{k}\right) \right\} ^{2}\rightarrow \left(
1/2\pi \right) \delta \left( \omega _{l}-\omega _{k}\right) \int
dt$ maybe used to calculate a continuous rate of creation of particle-antiparticle pairs \citep{So82,Kim02}, ,"
produce other emissiou line shifts.,produce other emission line shifts.
 Let us finally note that it is not quite clear to what extent the small absolute redshift of the ‘| line centre relative to the systemic aud cool giaut velocities is real., Let us finally note that it is not quite clear to what extent the small absolute redshift of the ] line centre relative to the systemic and cool giant velocities is real.
 In anv case the very incomplete phasing of the TST/STIS spectra makes it hard to draw more conclusions., In any case the very incomplete phasing of the HST/STIS spectra makes it hard to draw more conclusions.
 A aunuuber of new results have been obtained. fom a more detailed analysis of relative emission line shifts. which conclude the study of suitable ultraviolet spectra. which are available.," A number of new results have been obtained, from a more detailed analysis of relative emission line shifts, which conclude the study of suitable ultraviolet spectra, which are available."
 The relative shift ]vetween the radial velocities of tle resonance nes aud the intercombiuation lines of niultiplv ionised atoms is confirmed for nost svstems and appears to be not due to various artifacts, The relative shift between the radial velocities of the resonance lines and the intercombination lines of multiply ionised atoms is confirmed for most systems and appears to be not due to various artifacts.
 Jt is rather probably due to the absorption componeut of P Cveni profiles of the cool componcut’s windl. which must iu many Cases be able to absorb cinissiou from the enüssiou part of line profiles and uot onlv radiation frou the continuous spectrim.," It is rather probably due to the absorption component of P Cygni profiles of the cool component's wind, which must in many cases be able to absorb emission from the emission part of line profiles and not only radiation from the continuous spectrum."
 That places stroug coustraiuts on the ecometry. which we might try to iuterpret as for mstauce involving absorption of line radiation frou near the outer οσο of an accretion diss.," That places strong constraints on the geometry, which we might try to interpret as for instance involving absorption of line radiation from near the outer edge of an accretion disk."
 The variation of the shifts with orbital phase. especialy forAud.. ca1 be understood as due to a greater optical thickness of regions connected with the cool compoucut’s wind on its far side with respect to the colmpact component.," The variation of the shifts with orbital phase, especialy for, can be understood as due to a greater optical thickness of regions connected with the cool component's wind on its far side with respect to the compact component."
 However he wide vedshifted profile of of wear phase zero during outburst may still be due to a radiative trausfer effect., However the wide redshifted profile of of near phase zero during outburst may still be due to a radiative transfer effect.
 Touisation potential dependent stratification of radial velocity is present for the intercombination lines. beime much more redshifted than iutercoiibiuation lines of less ionised atoinis.," Ionisation potential dependent stratification of radial velocity is present for the intercombination lines, being much more redshifted than intercombination lines of less ionised atoms."
 This could be connected with occultation by au accretion disk. which is optically thick in the coutimm.," This could be connected with occultation by an accretion disk, which is optically thick in the continuum."
. However let us note tha our data clo rot enable us to be certain aboi any ciffereuce or and in outburst. if à comparison is nacle with quiescence We might expec hat as a change in the oxoperties of an accretion disk might be expected.," However let us note that our data do not enable us to be certain about any difference for and in outburst, if a comparison is made with quiescence We might expect that as a change in the properties of an accretion disk might be expected."
 Differences can be due to different ecometrics and netal abunucdauces., Differences can be due to different geometries and metal abundances.
 in particular has a strong netal underabundance., in particular has a strong metal underabundance.
 Streams and cool componcut winds affected by the presence of the hot compoucut. navy play a major role.," Streams and cool component winds affected by the presence of the hot component, may play a major role."
 Towever the saluple οἳ syiubiotic svstenis with high spectral resolution ultraviolet observations at many different orbital plascs ds very πα. τις it difheult to look for correlations with he properties of these systems.," However the sample of symbiotic systems with high spectral resolution ultraviolet observations at many different orbital phases is very small, making it difficult to look for correlations with the properties of these systems."
 It is therefore probably rot convenient to make more detailed speculations at the oresent tic., It is therefore probably not convenient to make more detailed speculations at the present time.
ocal counterparts: 8056 of carly-types im this redshift interval are stualler than galaxies of the sane mass iu he local Universe.,local counterparts: $\sim$ of early-types in this redshift interval are smaller than galaxies of the same mass in the local Universe.
 Taterestinely. Tarsett et al. (," Interestingly, Targett et al. ("
2011) ound that submillimeter galaxies at 5~2 have similar sizes to those that we measure for ETCs at the same epoch. sugeesting a possible evolutionary counectiou )tween the two classes of galaxies.,"2011) found that submillimeter galaxies at $z\sim2$ have similar sizes to those that we measure for ETGs at the same epoch, suggesting a possible evolutionary connection between the two classes of galaxies."
 On the other mand the evolution at :<Lois much milder., On the other hand the evolution at $z<1$ is much milder.
 In this phase. the compact galaxies continuously iuerease in size. eventually disappearing. most Likely undergoing a series of dav and wet iudinor iuergers or by slowine accreting a σα] amount of mass in their outskirts (6.8. Vau Dokki ct al.," In this phase, the compact galaxies continuously increase in size, eventually disappearing, most likely undergoing a series of dry and wet minor mergers or by slowing accreting a small amount of mass in their outskirts (e.g. Van Dokkum et al."
 2010: IIopkius et al., 2010; Hopkins et al.
 2009)., 2009).
 At the sale time. new ETCs are formed. driving the ΙΟ density increase of a factor 1.5 that we observe frou οονἆ το:--," At the same time, new ETGs are formed, driving the number density increase of a factor 1.5 that we observe from $z\sim1$ to $z\sim0$."
 These new ETCs have small masses and laree sizes. indicating that the mechanism through which they are formed is different from the one that at 2>lo eenerated the compact ETCs.," These new ETGs have small masses and large sizes, indicating that the mechanism through which they are formed is different from the one that at $z>1$ generated the compact ETGs."
greater than 6Beg.,greater than $6\Beq$ .
" ? argue that if Bo>(Hp/a)!/?Beg, Bo being the field strength in the shear layer and Hp the local pressure scale height, a buoyant flux-tube of radius a may rise without experiencing the convective drag force."," \cite{fan+etal_03} argue that if $B_0 > (H_{\rm P}/a)^{1/2} \Beq$, $B_0$ being the field strength in the shear layer and $H_{\rm P}$ the local pressure scale height, a buoyant flux-tube of radius $a$ may rise without experiencing the convective drag force."
" Here, although the shape of the magnetic field is not a tube, we compute the same condition using a= d,."," Here, although the shape of the magnetic field is not a tube, we compute the same condition using $a=d_z$ ."
" We obtain values of Bo going from 3.4.B,, in Run D04 to 2.2Beq in Run T04 (2.3Beq in higher resolution runs).", We obtain values of $B_0$ going from $3.4 \Beq$ in Run D04 to $2.2\Beq$ in Run T04 $2.3\Beq$ in higher resolution runs).
 This indicates that the dynamo generated magnetic field is insufficient to reach the surface without being modified by the convection., This indicates that the dynamo generated magnetic field is insufficient to reach the surface without being modified by the convection.
" There are, however, a few cases in Runs D04, TO4 and AROI, where strongest magnetic fields are able to reach the surface."," There are, however, a few cases in Runs D04, T04 and AR01, where strongest magnetic fields are able to reach the surface."
 When this occurs the magnetic field reacts back on the flow and modifies the convective pattern., When this occurs the magnetic field reacts back on the flow and modifies the convective pattern.
 Broad convection cells elongated in the y direction are formed., Broad convection cells elongated in the $y$ direction are formed.
 In Fig., In Fig.
 7 we present one of these events for Run AROI., \ref{fig:3d} we present one of these events for Run AR01.
" In the upper layers, the field lines show a turbulent pattern except in the center and the right edge of the box where the field lines at the surface cross the entire domain in the y direction."," In the upper layers, the field lines show a turbulent pattern except in the center and the right edge of the box where the field lines at the surface cross the entire domain in the $y$ direction."
" In the higher resolution cases, we do not observe events where the field lines, in the uppermost layers, remain horizontal accross the whole toroidal direction."," In the higher resolution cases, we do not observe events where the field lines, in the uppermost layers, remain horizontal accross the whole toroidal direction."
" Nevertheless, the expanding magnetic field may reach the surface forming broad convection cells (at least two times larger than the regular cells)."," Nevertheless, the expanding magnetic field may reach the surface forming broad convection cells (at least two times larger than the regular cells)."
" One of these cases, corresponding to Run T04c is shown in the bottom panels of Fig. 7.."," One of these cases, corresponding to Run T04c is shown in the bottom panels of Fig. \ref{fig:3d}."
" In this event two stripes of magnetic field of opposite polarity are reaching the surface simultaneously, the magnetic field lines of these ropes reconnect forming a large scale loop oriented in the z-direction."," In this event two stripes of magnetic field of opposite polarity are reaching the surface simultaneously, the magnetic field lines of these ropes reconnect forming a large scale loop oriented in the $x$ -direction."
" In order to compute the rise speed of the magnetic field in these cases we have used the horizontal averages of B, and constructed the time-depth ""butterfly"" diagram shown in Fig. 8..", In order to compute the rise speed of the magnetic field in these cases we have used the horizontal averages of $B_y$ and constructed the time-depth “butterfly” diagram shown in Fig. \ref{fig:but}.
" The toroidal field is amplified in the shear layer, below —0 (see dotted line)."," The toroidal field is amplified in the shear layer, below $z=0$ (see dotted line)."
 When it becomes buoyant it travels through the convection zone., When it becomes buoyant it travels through the convection zone.
" The tilt observed in the contours of B, may give a rough estimate of the vertical velocity.", The tilt observed in the contours of $B_y$ may give a rough estimate of the vertical velocity.
 In the same figure we have drawn white dashed lines to guide the eye., In the same figure we have drawn white dashed lines to guide the eye.
" For the emergence events in Run D04 (ARO1), the estimated rise speed isuy~0.034(dg)!/? (zz 0.030(dg)!/?)."," For the emergence events in Run D04 (AR01), the estimated rise speed is$u_b\approx0.034 (dg)^{1/2}$ $\approx
0.030(dg)^{1/2}$ )."
 These values are small in comparison to the Uyms of the models, These values are small in comparison to the $\urms$ of the models
"field f.,;,, used in equation (23).",field ${\bf f}_{stir}$ used in equation \ref{eq:mom}) ).
 A more detailed description of the forcing module applied here is provided in ?.., A more detailed description of the forcing module applied here is provided in \citet{FederrathDuvalKlessenSchmidtMacLow2009}.
 The time-dependent Fourier modes for constructing. the forcing patterns Εν were calculated and written to a file before the actual numerical experiments., The time-dependent Fourier modes for constructing the forcing patterns ${\bf f}_{stir}$ were calculated and written to a file before the actual numerical experiments.
 Both the SPH and the grid code read exactly the same forcing sequence from this file., Both the SPH and the grid code read exactly the same forcing sequence from this file.
 Thus. it was guaranteed that both codes were using exactly the same forcing at all times during the comparison experiments.," Thus, it was guaranteed that both codes were using exactly the same forcing at all times during the comparison experiments."
 (22) is an adaptive-mesh retinement code (2). that uses the yecewise parabolic method (PPM.?) to solve the equations of ivdrodynamies.," \citep{FryxellEtAl2000,DubeyEtAl2008} is an adaptive-mesh refinement code \citep{BergerColella1989} that uses the piecewise parabolic method \citep[PPM,][]{ColellaWoodward1984} to solve the equations of hydrodynamics."
 The PPM provides a shock capturing scheme to keep shocks and contact discontinuities sharp (typically spreading over 2-3 zones). while maintaining third order accuracy in smooth Hows through a parabolic reconstruction scheme.," The PPM provides a shock capturing scheme to keep shocks and contact discontinuities sharp (typically spreading over 2-3 zones), while maintaining third order accuracy in smooth flows through a parabolic reconstruction scheme."
 In this study. v3 was used. which provides a uniform grid mode.," In this study, v3 was used, which provides a uniform grid mode."
 Thus. the overhead in storing and iterating the adaptive mesh hierarchy was completely removed. which yields a speed-up of factors of a few.," Thus, the overhead in storing and iterating the adaptive mesh hierarchy was completely removed, which yields a speed-up of factors of a few."
 is parallelised using the message passing interface (MPI)., is parallelised using the message passing interface (MPI).
 For the resolutions studied here (1287. 256° and 512° grid cells). 1. 8 and 64 MPI processes respectively were used in à mode of sarallel computation. each calculation taking roughly 12. 250 and 5000 CPU-hours respectively.," For the resolutions studied here $128^3$, $256^3$ and $512^3$ grid cells), 1, 8 and 64 MPI processes respectively were used in a mode of parallel computation, each calculation taking roughly 12, 250 and 5000 CPU-hours respectively."
 has been extensively tested against laboratory experiments (2). and other codes (222).," has been extensively tested against laboratory experiments \citep{CalderEtAl2002} and other codes \citep{DimonteEtAl2004,HeitmannEtAl2005,kitsionasetal09}."
 provides an option for Lagrangian tracer particles. which can be evolved alongside the hydrodynamics.," provides an option for Lagrangian tracer particles, which can be evolved alongside the hydrodynamics."
 Similar to SPH particles. tracer particles provide information in the Lagrangian frame. but unlike SPH particles. the tracer particles have no feedback on the hydrodynamics. ie. the variables on the grid are independent of the tracers.," Similar to SPH particles, tracer particles provide information in the Lagrangian frame, but unlike SPH particles, the tracer particles have no feedback on the hydrodynamics, i.e. the variables on the grid are independent of the tracers."
 The tracer particles’ a. y and 2 positions can be any real number within the computational domain. not bound to the grid.," The tracer particles' $x$, $y$ and $z$ positions can be any real number within the computational domain, not bound to the grid."
 However. they are moved with the velocity computed on the grid.," However, they are moved with the velocity computed on the grid."
 The velocity is interpolated at the exact position of each tracer particle for each timestep using a first order cloud-in-cell interpolation scheme., The velocity is interpolated at the exact position of each tracer particle for each timestep using a first order cloud-in-cell interpolation scheme.
 Higher-order interpolation schemes like the triangular-shaped-cloud scheme can also be used instead., Higher-order interpolation schemes like the triangular-shaped-cloud scheme can also be used instead.
 However. we used the first-order scheme here. because various tests Suggested no strong dependence of our results on the interpolation scheme.," However, we used the first-order scheme here, because various tests suggested no strong dependence of our results on the interpolation scheme."
 The tracer particles were moved on the hydrodynamic timestep with the grid-interpolated velocity using a first-order scheme., The tracer particles were moved on the hydrodynamic timestep with the grid-interpolated velocity using a first-order scheme.
 We initialised 1287. 256 and 5127 tracer particles at /=0 on a uniform grid at exactly the same positions as the SPH particles were initialised in the calculations (see refsee:sphinit)). matching the grid and SPH resolutions (128°. 256° and 5127. respectively).," We initialised $128^3$, $256^3$ and $512^3$ tracer particles at $t=0$ on a uniform grid at exactly the same positions as the SPH particles were initialised in the calculations (see \\ref{sec:sphinit}) ), matching the grid and SPH resolutions $128^3$, $256^3$ and $512^3$, respectively)."
 Adding the tracer particles does not add any significant computational overhead to the caleulations. apart from the additional memory requirements.," Adding the tracer particles does not add any significant computational overhead to the calculations, apart from the additional memory requirements."
 In order to extract the maximum possible information from the tracer particles. we have computed — in post-processing — a density field based solely on the tracer particle positions.," In order to extract the maximum possible information from the tracer particles, we have computed — in post-processing — a density field based solely on the tracer particle positions."
 This is achieved by assuming they are particles of tixed mass (dividing the total mass in the simulation by the number of tracer particles) and using the SPH density calculation routine from where the density and smoothing length are iterated self-consistently (based on Eqs., This is achieved by assuming they are particles of fixed mass (dividing the total mass in the simulation by the number of tracer particles) and using the SPH density calculation routine from where the density and smoothing length are iterated self-consistently (based on Eqs.
 6 and 7))., \ref{eq:rhosum} and \ref{eq:hrho}) ).
 Column-integrated and cross-section slice plots of the density field were then produced as for the results using (2)., Column-integrated and cross-section slice plots of the density field were then produced as for the results using \citep{splashpaper}.
 is a low-memory. highly efficient SPH code written especially for studying non-self-gravitating problems.," is a low-memory, highly efficient SPH code written especially for studying non-self-gravitating problems."
 The code is made very efficient by using a simple neighbour finding scheme based on a fixed grid and linked lists of particles., The code is made very efficient by using a simple neighbour finding scheme based on a fixed grid and linked lists of particles.
 The calculations shown in this paper have used only the shared memory parallelisation inPHANTOM... using +. 8 and 32 processors and requiring 267 5050 and 120.000 CPU-hours for the 1287. 256° and 512° calculations. respectively.," The calculations shown in this paper have used only the shared memory parallelisation in, using 4, 8 and 32 processors and requiring 265, 5050 and 120,000 CPU-hours for the $128^{3}$, $256^{3}$ and $512^{3}$ calculations, respectively."
 Thus the 256° calculation was roughly comparable in computational cost to the 512 calculation. and similarly for the 1287 vs. 256° (though some caution is required here due to the different machines and architectures used to run each code).," Thus the $256^{3}$ calculation was roughly comparable in computational cost to the $512^{3}$ calculation, and similarly for the $128^{3}$ vs. $256^{3}$ (though some caution is required here due to the different machines and architectures used to run each code)."
" One may also consider that was found to be roughly an order of magnitude faster than ""standard! SPH codes in the ? turbulence comparison.", One may also consider that was found to be roughly an order of magnitude faster than `standard' SPH codes in the \citet{kitsionasetal09} turbulence comparison.
" For hydrodynamics implements the full variable smoothing length SPH formulation developed by ? and ?.. whereby the smoothing length. /i. and density. p. are mutually dependent via the density sum (for particle e) which is an exact solution to CL). and the relation where n is the particle mass and M,=MtroVala) is the SPH smoothing kernel (see e.g. ??? for reviews of SPH)."," For hydrodynamics implements the full variable smoothing length SPH formulation developed by \citet{pm04b} and \citet{pm07}, whereby the smoothing length, $h$, and density, $\rho$ , are mutually dependent via the density sum (for particle $a$ ) which is an exact solution to \ref{eq:cty}) ), and the relation where $m$ is the particle mass and $W_{ab} \equiv W(\vert {\bf r}_{a} - {\bf r}_{b}\vert, h_{a})$ is the SPH smoothing kernel (see e.g. \citealt{monaghan92,price04,monaghan05} for reviews of SPH)."
 Equations (6)) and (7)) are iterated self-consistently using a Newton-Raphson method as described in ?.. where in this paper we have used 7j=1.2. giving approximately 58 neighbours per particle in a smooth distribution.," Equations \ref{eq:rhosum}) ) and \ref{eq:hrho}) ) are iterated self-consistently using a Newton-Raphson method as described in \citet{pm07}, where in this paper we have used $\eta=1.2$, giving approximately 58 neighbours per particle in a smooth distribution."
 The fact that the smoothing length has a functional dependence on (ultimately) the particle position means that the derivatives of / can be accounted for in the equations of motion. resulting in eXact conservation of momentum. angular momentum. energy and entropy in the SPH equations.," The fact that the smoothing length has a functional dependence on (ultimately) the particle position means that the derivatives of $h$ can be accounted for in the equations of motion, resulting in exact conservation of momentum, angular momentum, energy and entropy in the SPH equations."
 In the equations of motion (29) take the form where /? is the pressure. Q is a dimensionless quantity related to the smoothing length gradients (see ? Το details) and q represents the artificial viscosity term (discussed below).," In the equations of motion \ref{eq:mom}) ) take the form where $P$ is the pressure, $\Omega$ is a dimensionless quantity related to the smoothing length gradients (see \citealt{pm07} for details) and $q$ represents the artificial viscosity term (discussed below)."
 In the absence of shock dissipation (¢= 0) there is zero numerical dissipation contained in the above equations and energy is conserved to the accuracy of the timestepping scheme— here a Kick-Drift-Kick leapfrog integrator equivalent to the velocity Verlet method. implemented with individual particle timesteps.," In the absence of shock dissipation $q=0$ ) there is zero numerical dissipation contained in the above equations and energy is conserved to the accuracy of the timestepping scheme— here a Kick-Drift-Kick leapfrog integrator equivalent to the velocity Verlet method, implemented with individual particle timesteps."
forms on PAH surfaces.,forms on PAH surfaces.
" The presence of PAHs in NGC 6720 cannot be fully excluded, but seems very unlikely."," The presence of PAHs in NGC 6720 cannot be fully excluded, but seems very unlikely."
 Accordingly our observations are the first indication for Hy formation on oxygen-rich dust grains in an astrophysical environment to our knowledge., Accordingly our observations are the first indication for $_2$ formation on oxygen-rich dust grains in an astrophysical environment to our knowledge.
" We can divide the Hz image into 3 regions: the inner ring, with a semimajor axis of ~45"",, an inner set of arcs with a radius of ~70"" ((the inner halo), and an outer set of arcs with a radius of ((the outer halo)."," We can divide the $_2$ image into 3 regions: the inner ring, with a semimajor axis of $\sim45$, an inner set of arcs with a radius of $\sim70$ (the inner halo), and an outer set of arcs with a radius of $\sim110$ (the outer halo)."
" There is also fainter emission outside of these outer arcs, but this is not very easy to see on the printed map."," There is also fainter emission outside of these outer arcs, but this is not very easy to see on the printed map."
 Comparing the H» and the sub-mm maps it is clear that the size and shape of the inner ring is reproduced on all images., Comparing the $_2$ and the sub-mm maps it is clear that the size and shape of the inner ring is reproduced on all images.
" The same can be said for the inner halo, which can be seen clearly on all maps."," The same can be said for the inner halo, which can be seen clearly on all maps."
" In the NW part of the inner halo, the Hy emission region is broader than in the SE—this too is the case on the SPIRE images, and less clearly so on the PACS images."," In the NW part of the inner halo, the $_2$ emission region is broader than in the SE—this too is the case on the SPIRE images, and less clearly so on the PACS images."
" Finally, the outer halo on the Hz image is also visible on the sub-mm images—as extended emission on the SPIRE images and as a faint circular ring shape on the PACS images (on the 70 um image most clearly)."," Finally, the outer halo on the $_2$ image is also visible on the sub-mm images—as extended emission on the SPIRE images and as a faint circular ring shape on the PACS images (on the $70$ $\mu$ m image most clearly)."
" On the zoomed PACS 70 um with overlaid H» contours (Fig. 1,,"," On the zoomed PACS $70$ $\mu$ m with overlaid $_2$ contours (Fig. \ref{composite},"
 lower right panel) the clear correspondence between the optical and sub-mm emission in the ring and the inner halo is highlighted., lower right panel) the clear correspondence between the optical and sub-mm emission in the ring and the inner halo is highlighted.
 From the ground-based H5 images it is clear that most of the H» resides in high density knots in the inner ring (?).., From the ground-based $_2$ images it is clear that most of the $_2$ resides in high density knots in the inner ring \citep{Sp03}.
 In this section we will investigate the origin of this Hy., In this section we will investigate the origin of this $_2$.
" The halo also shows Hy emission, which has a very different morphology though."," The halo also shows $_2$ emission, which has a very different morphology though."
 The latter will not be discussed here., The latter will not be discussed here.
 It is clear that H5 was formed in the denseAGB wind., It is clear that $_2$ was formed in the denseAGB wind.
" In the post-AGB phase three different scenarios will be investigated: 1) this Hy survived in the ionized region, 2) this Hz survived in the knots, which formed before the gas was ionized and 3) this Hz was destroyed and then was formed again later inside the knots when they formed."," In the post-AGB phase three different scenarios will be investigated: 1) this $_2$ survived in the ionized region, 2) this $_2$ survived in the knots, which formed before the gas was ionized and 3) this $_2$ was destroyed and then was formed again later inside the knots when they formed."
 These scenarios were already investigated for the Helix nebula by ?.., These scenarios were already investigated for the Helix nebula by \citet{Ma09}. .
 In order to determine the physical, In order to determine the physical
of maguetic resonance.,of magnetic resonance.
" This wavevector corresponds to the axial wavelength A,=2z/|k|—(2xz)Msfmn)", This wavevector corresponds to the axial wavelength $\lambda_z =2 \pi / |k_z| \sim (2 \pi \varepsilon)(s/m)$.
" A sanall 5, the axial waveleneth of the most rapidly erowine perturbations should be very small"," At small $\varepsilon$, the axial wavelength of the most rapidly growing perturbations should be very small."
 Therefore. if the longitudinal magnetic field is weaker than the azimutha one. we expect that the instability ecucrates structures in jets with a ναν short leugth scale in the +-direction.," Therefore, if the longitudinal magnetic field is weaker than the azimuthal one, we expect that the instability generates structures in jets with a very short length scale in the $z$ -direction."
 Note that this behaviour cau cause problems in uuuerica modeling of the instability because a very high resolutiou in the axial direcion 1s required., Note that this behaviour can cause problems in numerical modelling of the instability because a very high resolution in the axial direction is required.
 When the ratio of the axial and azinutha fields becomes comparable ο or greater than 1. the behaviour of the instability as a function of a ds qualitatively simular. although he erowth rate is significantly smaller.," When the ratio of the axial and azimuthal fields becomes comparable to or greater than 1, the behaviour of the instability as a function of $m$ is qualitatively similar, although the growth rate is significantly smaller."
 Tn this case perturbations with relatively siall 0 are substantially suppressed. but we still find a uuncerical evidence for a saturation trend as we increase a. although it is reached for πιο. higher values of a than iu the os] case.," In this case perturbations with relatively small $m$ are substantially suppressed, but we still find a numerical evidence for a saturation trend as we increase $m$, although it is reached for much higher values of $m$ than in the $\varepsilon< 1$ case."
 It is nuaportau y stress that even a~LOO in the azimuthal direction is still à macroscopic scale. aud dissipative effects are negligible iu this case.," It is important to stress that even $m 
\sim 100$ in the azimuthal direction is still a macroscopic scale, and dissipative effects are negligible in this case."
 The coulusion that the instability can arise even if 2 witha characteristic azimuthal wavemmubher iZ9 Lis at variance with the widely accepted opinion that magnetic configurations should be stabilised at D.~B.," The conlusion that the instability can arise even if $\varepsilon 
\geq 1$ with a characteristic azimuthal wavenumber $m\gg 1$ is at variance with the widely accepted opinion that magnetic configurations should be stabilised at $B_z \sim B_{\varphi}$."
 Note that the simular conclusion has been obtained by Goedbloed Ilagebruk 1972) for the maeuetic configuration with the constant pitch. Bo/sD.=const.," Note that the similar conclusion has been obtained by Goedbloed Hagebruk 1972) for the magnetic configuration with the constant pitch, $B_{\varphi} / s B_z=const$."
 Our study. also does not allow us fo answer the question what type of the magnetic configuration 1s formed because of the development of instability., Our study also does not allow us to answer the question what type of the magnetic configuration is formed because of the development of instability.
 To answer this question. one needs 3D munerical simulations.," To answer this question, one needs 3D numerical simulations."
 However. it is possible that the much better understanding of the nature of the magnetic field iu jets is required to answer this question.," However, it is possible that the much better understanding of the nature of the magnetic field in jets is required to answer this question."
 For exinuple. the resulting large scale maeuetic field cau be formed by balancing the rate of field decay caused by instability and the rate of generation owing fo sole πιοαιστι (e.g. dynamo).," For example, the resulting large scale magnetic field can be formed by balancing the rate of field decay caused by instability and the rate of generation owing to some mechanism (e.g., dynamo)."
 It would be iuportaut to Investigate he cousequences of our findings for jets by performing more realistic uuierical simulations. aud we hope to address this question in the near future.," It would be important to investigate the consequences of our findings for jets by performing more realistic numerical simulations, and we hope to address this question in the near future."
 VU thanks the INAF-Osscrvatorio Astrofisico di Catania for hospitality aud financial support., VU thanks the INAF-Osservatorio Astrofisico di Catania for hospitality and financial support.
where the q; salisfv the integrator equations(2).,where the $q_i$ satisfy the integrator equations.
". Taking one exterior derivative of S elves ihe terms involving dqa.....day,4 ave identically zero because the trajectory. satisfies equations(2a).. and(2c)."," Taking one exterior derivative of $\mathcal{S}$ gives the terms involving $dq_2, \ldots, dq_{M-1}$ are identically zero because the trajectory satisfies equations, and."
. Two exterior derivatives of S give zero. vielding Instead of considering evolution on phase space (q.p). consider the corresponding evolution on the discrete state space (qi.qo).," Two exterior derivatives of $\mathcal{S}$ give zero, yielding Instead of considering evolution on phase space $(q,p)$, consider the corresponding evolution on the discrete state space $\left( q_1,
q_2 \right)$."
" Evolution maps the initial state-space for Lf. I"". to an isomorphic space. (qaj1-day)€IE""xI"". where m is the dimensionality of configuration space."," Evolution maps the initial state-space for $H$, $\left(q_1,q_2 \right) \in \mathbb{R}^m \times \mathbb{R}^m$ , to an isomorphic space, $\left( q_{M-1}, q_{M} \right) \in \mathbb{R}^m
\times \mathbb{R}^m$, where $m$ is the dimensionality of configuration space."
 Equation can be written using the pushlorward map under evolution. £*.," Equation can be written using the pushforward map under evolution, $F^*$."
" All forms in equation live on the colangent buuelle of the state space IE""xIE"".", All forms in equation live on the cotangent bundle of the state space $\mathbb{R}^m \times \mathbb{R}^m$.
 We see (hat the integrator conserves (he discrete svinplectic form on (he state space of IT. This is the direct analog of (he svanplecticity of continuous time-evolution in a Tamiltonian svslenm.," We see that the integrator conserves the discrete symplectic form on the state space of $H$, This is the direct analog of the symplecticity of continuous time-evolution in a Hamiltonian system."
 Using equation(2a).. we see that ≀↧↴∐≼⇂⊔∐↲↕⋅≼↲↓⋟∪↕⋅≼↲≺∢∪∐⋟∖⊽≼↲↕⋅∖↽≀↧↴∐∪∐∪↓⋟⊔∐↲≼∐⋟∖⊽≺∢↕⋅≼↲↥≼↲⋟∖⊽⋡∖⇁∐↓↕↽≻↥≼↲≺∢∐≺∢↓⋟∪↕⋅∐↓↕∐≼↲≺⇂∏≀↕↴∐∪∐⋖⋡⋖↽∖⋟⋮⋝↕∐↓↕↽≻∐≼↲⋟∖⊽≺∢∪∐⋟∖⊽≼↲↕⋅∖↽≀↧↴∐∪∐ of the Poincaré integral invariant on phase space:," Using equation, we see that and therefore conservation of the discrete symplectic form in equation implies conservation of the Poincaré integral invariant on phase space:"
epochs will be required over a span of weeks to years to detect the rise aud decline of the radio light. curve oliowius a CAV detection (Equation 6)). for a total of about ~300 hr of EVLA time (6. to search the best-bet rate of ~10 CAV triggers per vear will require essentially 1005€ of the EVLA time).,"epochs will be required over a span of weeks to years to detect the rise and decline of the radio light curve following a GW detection (Equation \ref{eqn:tdec}) ), for a total of about $\sim 300$ hr of EVLA time (i.e., to search the best-bet rate of $\sim 40$ GW triggers per year will require essentially $100\%$ of the EVLA time)."
 Thus. a reasonable exposure time por pointing is =10 amin. which at 1 GIIz corresponds to a 5o of about (0.25 παν.," Thus, a reasonable exposure time per pointing is $\lesssim 10$ min, which at 1 GHz corresponds to a $5\sigma$ of about 0.25 mJy."
" Since a convincing detection will require the briehtuess to rise to about twice the hreshold. the uium detectable peak flux is F5,%1.5 Jv."," Since a convincing detection will require the brightness to rise to about twice the threshold, the minimum detectable peak flux is $F_{\rm\nu,p}\approx 0.5$ mJy."
" We note that the threshold may be even higher in the compact EVLA configurations (C and D) due o substantial source confusiou imposed bv the large svuthesizedbeam size (1 11"").", We note that the threshold may be even higher in the compact EVLA configurations (C and D) due to substantial source confusion imposed by the large synthesized beam size $12-44''$ ).
 Observations at a higher frequency of 5 GIIz can in xinciple providebetter scusitivity (and reduce source confusion problems). but in reality will actually require even iore observing time.," Observations at a higher frequency of 5 GHz can in principle provide better sensitivity (and reduce source confusion problems), but in reality will actually require even more observing time."
 This is mainly |)ocamse the Bold of view at 5 GIIz is sufficiently small(0.02 deg?) that a ore prAitable strategy is to target the LOO ealaxics with ouly£0.L within a typical CW error region.," This is mainly because the field of view at 5 GHz is sufficiently small (0.02 $^2$ ) that a more profitable strategy is to target the $\sim 400$ galaxies with $L\gtrsim 0.1\,L^*$ within a typical GW error region."
 Even with 5 min per pointing this will require about LO hr per epoch. with a resulting 5o limit of 0.1 uJy.," Even with only 5 min per pointing this will require about 40 hr per epoch, with a resulting $5\sigma$ limit of 0.1 mJy."
" A couvincing detection will therefore require Fy,20.2 uty. which given a typical spectrum of Fj,xf is equivalent to a limit of 0.7 wv at 1 GIIz. worse than the 1 CIIz observing strategv.z with even more time required per epoch."," A convincing detection will therefore require $F_{\rm\nu,p}\gtrsim 0.2$ mJy, which given a typical spectrum of $F_{\rm\nu,p}\propto \nu^{-0.75}$ is equivalent to a limit of $\gtrsim 0.7$ mJy at 1 GHz, worse than the 1 GHz observing strategy, with even more time required per epoch."
 ~Jbservations with ture wide-field raclio interferometers (ee. ASKADP) will cover atypical CAV error region with —a few poiutings. requiring only a few hows per epoch.," Observations with future wide-field radio interferometers (e.g., ASKAP) will cover a typical GW error region with a few pointings, requiring only a few hours per epoch."
 However. these instruments suffer from poorer augular resolution compared to what is possible with the EV LA(e.e.. ASKAP with ~10” resolution).," However, these instruments suffer from poorer angular resolution compared to what is possible with the EVLA (e.g., ASKAP with $\sim 10''$ resolution)."
 This will lead to significant source confusion at the required low flux density levels., This will lead to significant source confusion at the required low flux density levels.
 More critically. radio cussion frou the host galaxy itself will preseut a challenge: at 200 AIpe a star formation rate of only AL. + correspouds to a d Cz flux. density of about 0.6 uy (Yun&Carili2002).," More critically, radio emission from the host galaxy itself will present a challenge; at 200 Mpc a star formation rate of only 1 $_\odot$ $^{-1}$ corresponds to a 1 GHz flux density of about 0.6 mJy \citep{yc02}."
".. At a resolution of 10"" (10 kpc at 200 Mpc) galaxies will ecuerally appear as nuresolyed point sources. and will prevent the detection of significantly faimter coincident radio counterparts."," At a resolution of $10''$ (10 kpc at 200 Mpc) galaxies will generally appear as unresolved point sources, and will prevent the detection of significantly fainter coincident radio counterparts."
 Thus. an iustineut like ASIAP will cover a GW error region faster than the EVLA. but to a simil effective depth limited by source confusion.," Thus, an instrument like ASKAP will cover a GW error region faster than the EVLA, but to a similar effective depth limited by source confusion."
 A final complication with radio detectious is the lone time delay between a CAV trigger and the peak of the putative radio signal. which could negate a robus association.," A final complication with radio detections is the long time delay between a GW trigger and the peak of the putative radio signal, which could negate a robust association."
 For a sub-rvelativistic counterpart (3~ 0.2) with au optimistic deusity of à~1 ocu7. a detection requies E1075 cre (Equation τὸ). and as a resul fas©6 vr vequirine> observations for over a decade.," For a sub-relativistic counterpart $\beta\sim 0.2$ ) with an optimistic density of $n\sim 1$ $^{-3}$ , a detection requires $E\gtrsim 10^{51}$ erg (Equation \ref{eqn:fomr}) ), and as a result $t_{\rm dec}\approx 6$ yr, requiring observations for over a decade."
 For the relativisticcase CJ2 1) with bà~ C. the peal time corresponding to a detectable signal is face70.1 ," For the relativistic case $\beta\approx 1$ ) with $n\sim 1$ $^{-3}$, the peak time corresponding to a detectable signal is $t_{\rm dec}\approx 0.1$ yr."
The lattercase will require a ~weels cadence to -- siuuple the helt curve. corresponding to abou 1520% of the EVLA time (with ~30 hr per epoch).," The latter case will require a $\sim\,{\rm week}$ cadence to robustly sample the light curve, corresponding to about $15-20\%$ of the EVLA time (with $\sim 30$ hr per epoch)."
 The absence of a credible detection will require a vear cadence to search for a non-relativistic counterpart.," The absence of a credible detection will require a $\sim\,{\rm year}$ cadence to search for a non-relativistic counterpart."
 Of course. With a iulti-vcar timescale the probability of uis-identification with an unrelated radio transicut becomes larecr.," Of course, with a multi-year timescale the probability of mis-identification with an unrelated radio transient becomes larger."
 Despite the vious difficulties outlined above. a clear advantage of radio searches is the lower umber of contaminating sources compared to the optical baud.," Despite the various difficulties outlined above, a clear advantage of radio searches is the lower number of contaminating sources compared to the optical band."
 As discussed in NPLI1. contusion with ACN radio variability can be reduced by requiring an offset from the center aurao.edu/tfacilines/evla/calibratiost. the host galaxy. although this may boe difficult with an angular resolution of zLO” (EVLA in its compact configurations and ASIKAP).," As discussed in NP11, confusion with AGN radio variability can be reduced by requiring an offset from the center of the host galaxy, although this may be difficult with an angular resolution of $\gtrsim 10''$ (EVLA in its compact configurations and ASKAP)."
 Similarly. while sole normal Type Ib/c superuovae have simular radio it curves to those expected for NS-NS mergers (since they produce ejecta with §~0.3). they are generally less energetic. with oulv ~10/7—10/5 ere coupled to the fast Mejecta (Bereeretal.2002.2003).," Similarly, while some normal Type Ib/c supernovae have similar radio light curves to those expected for NS-NS mergers (since they produce ejecta with $\beta\sim 0.3$ ), they are generally less energetic, with only $\sim 10^{47}-10^{48}$ erg coupled to the fast ejecta \citep{bkc02,bkf+03}."
. These eveuts will also acconipauied by optical supernova eniüssiou on a simular timescale. providing an additional source of discrinunation.," These events will also be accompanied by optical supernova emission on a similar timescale, providing an additional source of discrimination."
 Finally. relativistic Type Ib/c supernovae (with or without an associated CRB) lave ~οLar’ ere coupled toAL their fast ejecta (ντιetal.1998:Soderberge 2010).. 1mt these are also accompanied by a bright optical supernovae.," Finally, relativistic Type Ib/c supernovae (with or without an associated GRB) have $\sim
10^{49}-10^{50}$ erg coupled to their fast ejecta \citep{kfw+98,scp+10}, but these are also accompanied by a bright optical supernovae."
 To couclide. the utility of radio onuüssiou as an EM counterpart is particularly scusitive to the typical enuergv and circuburst density.," To conclude, the utility of radio emission as an EM counterpart is particularly sensitive to the typical energy and circumburst density."
 Ii the case of off-axis afterelows. detections require a high cuerev aud deusity that exceed those of known SGRB afterelows (Figure 6)).," In the case of off-axis afterglows, detections require a high energy and density that exceed those of known SGRB afterglows (Figure \ref{fig:fom}) )."
 Iu the nou-relativistic case. even higher energy and/or density are DIM such that for an expected upper bouud of The<ol ocn7 the required eucrey is EO> or," In the non-relativistic case, even higher energy and/or density are required, such that for an expected upper bound of $n\lesssim 1$ $^{-3}$ the required energy is $E\gtrsim
10^{51}$ erg."
e required telescope time for an effective search ds hundreds of hows (EVLA). with perhaps ouly tens of hours using future wide-field) iustruineuts (e.g. ASIKADP).," The required telescope time for an effective search is hundreds of hours (EVLA), with perhaps only tens of hours using future wide-field instruments (e.g., ASKAP)."
 The time delavs range from mouths to vears. Which may complicate a robust association.," The time delays range from months to years, which may complicate a robust association."
 The kev advantages are the spherical geometry at f.=tice aud the simaller number of contaminating sources compared. to the optical baud., The key advantages are the spherical geometry at $t\gtrsim t_{\rm dec}$ and the smaller number of contaminating sources compared to the optical band.
 The detectability of SCRBs aud their afterelows is sensitive to uncertainties in the degree of relativistic beaming aud. in the case of afterglows. the propertics of the circiunuburst euviromnnent.," The detectability of SGRBs and their afterglows is sensitive to uncertainties in the degree of relativistic beaming and, in the case of afterglows, the properties of the circumburst environment."
 Of course. it is also possible that not all NS-NS iuergers produce SGRBs.," Of course, it is also possible that not all NS-NS mergers produce SGRBs."
" ILowever. independent of this association. the mergers are expected to be acconipanied by isotropic thermal Cluission. powered by the radioactive decay of heavy eleiieuts in the mergerejecta (Li&Paczvüski1998: jiereafter LP98: Ikulkar""2005:RosswogMot- 2011))."," However, independent of this association, the mergers are expected to be accompanied by isotropic thermal emission, powered by the radioactive decay of heavy elements in the merger ejecta \citealt{Li&Paczynski98}; hereafter LP98; \citealt{Kulkarni05,Rosswog05,Metzger+10,Roberts+11,Goriely+11}) )."
" Uulike Type Ia supernovae. which are powered w the decay of Ni aud Co. the ejecta (electronfrou NS- inerecrs is primarily neutron-rich fraction Jj,« (0.5) and thus produce little nickel."," Unlike Type Ia supernovae, which are powered by the decay of $^{56}$ Ni and $^{56}$ Co, the ejecta from NS-NS mergers is primarily neutron-rich (electron fraction $Y_{e}\ll 0.5$ ) and thus produce little nickel."
 Tusteac. javier radioactive elements (mass nuniber 42 130) are expected to formi as neutrons capture onto nuclei (r-processuucleosvutliesis) after the ejecta decompresses roni nuclear densities (6.8... Lattimer&Schrauun197I:Eichleretal.1989:Freiburehaus 1999).," Instead, heavier radioactive elements (mass number $A\gtrsim 130$ ) are expected to form as neutrons capture onto nuclei $r$ -processnucleosynthesis) after the ejecta decompresses from nuclear densities (e.g., \citealt{Lattimer&Schramm74,Eichler+89,Freiburghaus+99}) )."
 Although he r process itself lasts at most a few seconds. these rewhy-svuthesized clemeuts uudergo unclear fission aud veta decays on much longer timescales.," Although the $r-$ process itself lasts at most a few seconds, these newly-synthesized elements undergo nuclear fission and beta decays on much longer timescales."
 The resulting, The resulting
test whether particular outcomes are physically realizable.,test whether particular outcomes are physically realizable.
 These models also provide direct fests will observables. such as (he current. mass in Ας and the complete ABO size distribution.," These models also provide direct tests with observables, such as the current mass in KBOs and the complete KBO size distribution."
 Because these models do not allow arbitrary ο and 7. they are less flexible than the constant e moclels.," Because these models do not allow arbitrary $e$ and $i$, they are less flexible than the constant $e$ models."
 To provide some Ποαν in models with gravitational stirring. we calculated models with and without stirring bv Neptune at 30 AU.," To provide some flexibility in models with gravitational stirring, we calculated models with and without stirring by Neptune at 30 AU."
 In models without Neptune. large KBOs with radii of 1000.3000 kin stir up smaller ΕΟΝ (o the disruption velocity.," In models without Neptune, large KBOs with radii of 1000–3000 km stir up smaller KBOs to the disruption velocity."
" The NBO size distribution. including the break radius. then depends on the radius of the largest. IKRBO ""ipo lormed during the caleulation."," The KBO size distribution, including the break radius, then depends on the radius of the largest KBO $r_{L,KBO}$ formed during the calculation."
" Because rj,po depends on Q, and Q, INenvon.| 2002).. 7, also depends on (Q, and Q,."," Because $r_{L,KBO}$ depends on $Q_b$ and $Q_g$ \citep[e.g.,][]{kl99a, ken02}, $r_b$ also depends on $Q_b$ and $Q_g$."
 In models with Neptune. long-rauge stirring by Neptune can dominate stirring by local large IKDOs.," In models with Neptune, long-range stirring by Neptune can dominate stirring by local large KBOs."
 The break radius (hen depends on the long-range stirring Formula (WeidenschillingOhtsuki.Stewart.&Ida2002) and the timescale lor Neptune formation.," The break radius then depends on the long-range stirring formula \citep{wei89,oht02} and the timescale for Neptune formation."
 ILere. we assume a LOO Myr formation time lor Neptune. whose semimajor axis is fixed at 30 AU throughout the calculation.," Here, we assume a 100 Myr formation time for Neptune, whose semimajor axis is fixed at 30 AU throughout the calculation."
 The mass of Neptune erows with time as where C's; is a constant and {μι /4. and {ο are reference limes.," The mass of Neptune grows with time as where $C_{Nep}$ is a constant and $t_0$, $t_1$ , and $t_2$ are reference times."
 For most calculations. we sel /y = 50 Myr. /4 = 3 Myr. and fo = 100 Myr.," For most calculations, we set $t_0$ = 50 Myr, $t_1$ = 3 Myr, and $t_2$ = 100 Myr."
 These choices allow our model Neptune to reach | AZ) in 50 Myr. when the largest INDOs have formed at 4050 AU. and reach its current mass in LOO Myr.," These choices allow our model Neptune to reach 1 $M_{\oplus}$ in 50 Myr, when the largest KBOs have formed at 40–50 AU, and reach its current mass in 100 Myr."
 This prescription is not intended as a model for Neptune formation. but it provides sullicient extra stirring to test (he prediction that the break radius depends on the amount of local stirring.," This prescription is not intended as a model for Neptune formation, but it provides sufficient extra stirring to test the prediction that the break radius depends on the amount of local stirring."
 Calculations with constant eccentricity allow a direct. test of the analvtic model., Calculations with constant eccentricity allow a direct test of the analytic model.
" We performed asuite of  200 4.5 Gyr calculations for a range in Iragmentation parameters. with log Q, = 18. 3, = 0.52.0. and log Cy 4- 5 3, = 0.0120."," We performed asuite of $\sim$ 200 4.5 Gyr calculations for a range in fragmentation parameters, with log $Q_b$ = 1–8, $\beta_g$ = 0.5–2.0, and log $C_g$ + 5 $\beta_g$ = 0.01–20."
 The initial size distribution of icv planetesimals has sizes of d m to 100 km in mass bins with 0=m;4/70; = 1.5 and equal mass per mass bin., The initial size distribution of icy planetesimals has sizes of 1 m to 100 km in mass bins with $\delta = m_{i+1}/m_i$ = 1.7 and equal mass per mass bin.
 The planetesimals lie in 32 annuli extending from 40 AU to 75 AU., The planetesimals lie in 32 annuli extending from 40 AU to 75 AU.
 The central star hasa mass of 1. M..., The central star hasa mass of 1 $_{\odot}$ .
 The initial surface density. Xy=10 g ? to 10! ," The initial surface density, $\Sigma_0 = 10^{-3}$ g $^{-2}$ to $10^{-1}$ "
find that for e=0. Rysx1.τα. which corresponds to ~13.5 AU. still larger. but much closer to the wall radius estimated in DOS.,"find that for $e=0$ , $R_{cb}\approx 1.7a$, which corresponds to $\sim 13.5$ AU, still larger, but much closer to the wall radius estimated in D05."
" In this section. we show that the value lor Ha, given in Artvmowics&Lubow(1994). results in a model of Colxu Tau/4. that fits the observed SED. as shown in Figure 30.."," In this section, we show that the value for $R_{cb}$ given in \citet{Artymowicz1} results in a model of CoKu Tau/4, that fits the observed SED, as shown in Figure \ref{fig-Draine-4Myr}."
 In Figure 20 one can see that for e>0 the wall is too cold. because the 10j/mi band does not match the observations.," In Figure \ref{fig-Draine-4Myr-exc} one can see that for $e>0$ the wall is too cold, because the $10\mu$ m band does not match the observations."
 Even in some cases there is no band at. 10j05., Even in some cases there is no band at $10\mu m$.
 Thus. a nearly circular binary orbit seems (o be more consistent with the observed SED.," Thus, a nearly circular binary orbit seems to be more consistent with the observed SED."
 We present a moclel.for a 4Myrs system (model Ml in table 5)) in Figure 30. for Colxu Tau/4 (labeled Series Colxu Tau/4). where only the parameters of (he wall are presented.," We present a model,for a $4 \ Myrs$ system (model M1 in table \ref{table-models}) ) in Figure \ref{fig-Draine-4Myr} for CoKu Tau/4 (labeled Series CoKu Tau/4), where only the parameters of the wall are presented."
 Indeed. (his corresponds to the fiducial model (model El) but here it is repeated for clarity.," Indeed, this corresponds to the fiducial model (model E1) but here it is repeated for clarity."
 The spectral tvpes and masses of (he stars consistent with the observed. spectrum ab high frequencies are. AMI and 0.5... and AZO and 0.6... respectively.," The spectral types and masses of the stars consistent with the observed spectrum at high frequencies are $M1$ and $0.5M_\odot$ and $M0$ and $0.6M_\odot$, respectively."
 The spectrum corrected using (he Draines law is better fitted by pyroxene dust erains., The spectrum corrected using the Draine's law is better fitted by pyroxene dust grains.
 The higher wall temperature when olivines are used produces a Πας larger (han observed., The higher wall temperature when olivines are used produces a flux larger than observed.
 Figure 18. presents the observations deredclened with Draine (2003).. Mathis(1990)... MeClure(2009) and Alonetietal.(2001). laws.," Figure \ref{fig-stars-spectrum} presents the observations dereddened with \citet{Draine1}, , \citet{Mathis2}, \citet{McClure} and \citet{Moneti} laws."
 The flux lor the observations deredcdened with the al.(2001) law is larger than that using the Draine(2003) law. the latter being taken here.," The flux for the observations dereddened with the \citet{Moneti} law is larger than that using the \citet{Draine1} law, the latter being taken here."
 Thus. olivine is a good option Lor modeling Colxu. Tau/4. when using the Moneti law.," Thus, olivine is a good option for modeling CoKu Tau/4, when using the Moneti law."
 A change in / can also increase the flux. but the depth of the θα feature changes (see Figure 22)).," A change in $h$ can also increase the flux, but the depth of the $10\mu$ m feature changes (see Figure \ref{fig-Draine-4Myr-i-h}) )."
 The spectrum dereddened with the MeClure(2009). law using ον=2.5 is indistinguishable [rom the data dereddened with Draine s law and Ay=3., The spectrum dereddened with the \citet{McClure} law using $A_{V}=2.5$ is indistinguishable from the data dereddened with \citeauthor{Draine1}' 's law and $A_{V}=3$.
 Thus. the moclel presented here can be used lor both cases.," Thus, the model presented here can be used for both cases."
 We use 5h=0.28 (fh=0.15224) as a Iree parameter adjusted to fit the observed SEDs. but in the future it would be good to have an estimated range of  consistent with hvdrodvnamical arguments.," We use $h=0.28a$ $h=0.15R_{cb}$ ) as a free parameter adjusted to fit the observed SEDs, but in the future it would be good to have an estimated range of $h$ consistent with hydrodynamical arguments."
 Also. the wall cannot have a larger abundance of water ice (Qj>5.6x 10°): otherwise. it would change the shape of the 10 yam observed band. as described in 4.1. and shown in Figure 25..," Also, the wall cannot have a larger abundance of water ice $\zeta_{ice}>5.6\times 10^{5}$ ); otherwise, it would change the shape of the 10 $\mu$ m observed band, as described in \ref{sec-var-param-wall} and shown in Figure \ref{fig-4Myr-pyr-graf-hielo}."
 From Figure one can conclude that amorphous carbon instead of graphite does not help to improve the fit. because the resulting 10jan band does not match the observed SED.," From Figure \ref{fig-4Myr-pyr-graf-carb} one can conclude that amorphous carbon instead of graphite does not help to improve the fit, because the resulting $10\mu$ m band does not match the observed SED."
 In the case of Colxu. Tau/4. there is no evidence for circumstellar disks: thus. only a very small amount of mass should be able to cross the inner boundary of the CB disk.," In the case of CoKu Tau/4, there is no evidence for circumstellar disks; thus, only a very small amount of mass should be able to cross the inner boundary of the CB disk."
 Bul even so. il could be enough material to produce a contribution to the mic-IR SED.," But even so, it could be enough material to produce a contribution to the mid-IR SED."
 Our wall enussion model forColxu. Tau/4 shown in Figure 30. seems to produce a reasonable fit to the observed SED., Our wall emission model forCoKu Tau/4 shown in Figure \ref{fig-Draine-4Myr} seems to produce a reasonable fit to the observed SED.
 This fit can be improved if optically thin material in (the hole should be included., This fit can be improved if optically thin material in the hole should be included.
 The fiducial model requires moreflux at the right side of the LOjam band., The fiducial model requires moreflux at the right side of the $10\mu$ m band.
" Thus. looking at (he inner hole emission models in 4.2.. we choose the one with p= 1. A,,;,=1.4« and pyroxenes dust erains (see Figure 27))."," Thus, looking at the inner hole emission models in \ref{sec-gap-models}, , we choose the one with $p=1$ $R_{min}=1.4a$ and pyroxenes dust grains (see Figure \ref{fig-4Myr-thin-p}) )."
" A model with alower 4,5, or with graphite has", A model with alower $R_{min}$ or with graphite has
"At least two other methods for determining Ry, have iypeared in the literature.",At least two other methods for determining $R_\mathrm{in}$ have appeared in the literature.
" In one. a CO temperature (and density) profile is assumed. and A, is fit as a single free variable in a disk model (c.g..Blake&Doosgert2001:xSalvkctal.2009:Bastet 2011)."," In one, a CO temperature (and density) profile is assumed, and $R_\mathrm{in}$ is fit as a single free variable in a disk model \citep[e.g.,][]{Blake04, Salyk09, Bast11}."
. Iu our model. in contrast. the temperature. density. level populations. iid cluitting area are all wrapped up iuto Lew(PR).," In our model, in contrast, the temperature, density, level populations, and emitting area are all wrapped up into $L_\mathrm{CO}(R)$."
 To compare the two models. we fit model liue. profiles. constructed using the procedure described in Salvketal. (2009)... with the simple model described here. setting p=oq.," To compare the two models, we fit model line profiles, constructed using the procedure described in \citet{Salyk09}, with the simple model described here, setting $p=q$."
" We find that disk temperature profiles of the form TxBR"" with p—0.6 are equivalent to models with Leg(R)x Ὁ, and ToxRY? ds equivalent to .LoouR)ARlO"," We find that disk temperature profiles of the form $T\propto R^{\rho}$ with $\rho=-0.6$ are equivalent to models with $L_\mathrm{CO}(R)\propto R^{-3}$, and $T\propto R^{-0.2}$ is equivalent to $\sim L_\mathrm{CO}(R) \propto R^{-1.5}$."
 Compared to the values derived by Salvketal.(2009).. we find similar radi for many sources. with the notable exception of ΠΟ 111569 A. LxIIo. 330. and SR 21. for which Salvketal.(2009) Sud radii larger by factors of a fow to ~ 10.," Compared to the values derived by \citet{Salyk09}, we find similar radii for many sources, with the notable exception of HD 141569 A, $\alpha$ 330, and SR 21, for which \citet{Salyk09} find radii larger by factors of a few to $\sim$ 10."
" All three of these sources. however. are ones iu which 4? is not sensitive to Ry, at radii lareer than the best-hit value."," All three of these sources, however, are ones in which $\chi^2$ is not sensitive to $R_\mathrm{in}$ at radii larger than the best-fit value."
 We also find radii cousisteut with Bastctal.(2011) for AS 205 A and TW Ilva. who estimate inner radii of O.OL and 0.1. AU. respectively (although they caution that the parameter space for these models was uot well explored: J. BBast. private communication).," We also find radii consistent with \citet{Bast11} for AS 205 A and TW Hya, who estimate inner radii of 0.04 and 0.1 AU, respectively (although they caution that the parameter space for these models was not well explored; J. Bast, private communication)."
 Qur respective results areinconsistent for VV Ser. for which Bast et dderive an inner radius of 0.05 AU and we derive an inner radius of 0.72 AU: however. a closer look at their model reveals that they are in a reguue siuilar to our p=0 case. in which 4? is simply not very sensitive to the choice of iuner radius.," Our respective results are for VV Ser, for which Bast et derive an inner radius of 0.08 AU and we derive an inner radius of 0.72 AU; however, a closer look at their model reveals that they are in a regime similar to our $p=0$ case, in which $\chi^2$ is simply not very sensitive to the choice of inner radius."
" Another common approach to estimating Ry, is to siuplv choose some velocity. (typically either ὃν the half-width at half maxima (ΤΠΝΠΝΟ or the haltwidth at zero intensity). aud set AH to the radius with that Keplerian velocity."," Another common approach to estimating $R_\mathrm{in}$ is to simply choose some velocity (typically either $\times$ the half-width at half maximum (HWHM), or the half-width at zero intensity), and set $R_\mathrm{in}$ to the radius with that Keplerian velocity."
 The difficulty of this approach is that it is not obvious which velocity to choose., The difficulty of this approach is that it is not obvious which velocity to choose.
" In Figure 5.. we compare Ry, to iuner radii derived from fitting the profiles with siugle or double (emission plus absorption) Caussimus (2,4."," In Figure \ref{fig:radcomp}, we compare $R_\mathrm{in}$ to inner radii derived from fitting the profiles with single or double (emission plus absorption) Gaussians $R_\mathrm{gauss}$ )."
" Iu particular. we show solutions in which A, is derived from the velocity at < TIWOAL which comes closest to reproducing our results."," In particular, we show solutions in which $R_\mathrm{in}$ is derived from the velocity at $\times$ HWHM, which comes closest to reproducing our results."
 Deviations from L:l are of order a factor of a few. and so this simple approach is remarkably cousisteut with our more conplex model.," Deviations from 1:1 are of order a factor of a few, and so this simple approach is remarkably consistent with our more complex model."
" Thus. we suggest that using the velocitv at τν IINVIIM is a reasonable choice for calculating Aj, using simple Caussian fits."," Thus, we suggest that using the velocity at $\times$ HWHM is a reasonable choice for calculating $R_\mathrm{in}$ using simple Gaussian fits."
 We use this result to incorporate LkCa 15 into our analysis. utilizing the EFWIINE measured by Najitaetal.(2003)...," We use this result to incorporate LkCa 15 into our analysis, utilizing the FWHM measured by \citet{Najita03}."
 This result also gives us confidence that the mocel-derived Ry is reflecting the bulk line shape aud EWIIM. and is not mstead some spurious result heavily biased by the Iine/coutiuuua ratio. the noise level. or auy other aspects of the data.," This result also gives us confidence that the model-derived $R_\mathrm{in}$ is reflecting the bulk line shape and FWHM, and is not instead some spurious result heavily biased by the line/continuum ratio, the noise level, or any other aspects of the data."
" Four sources in our sample (IID 1353114 D. SR 21. TW να, and VV Ser) have inner radii derived from a combined line shape aud spectro-astrometric (SA) profile analvsis (Poutoppidanetal.2008.2011)."," Four sources in our sample (HD 135344 B, SR 21, TW Hya, and VV Ser) have inner radii derived from a combined line shape and spectro-astrometric (SA) profile analysis \citep{Pontoppidan08,Pontoppidan11}."
". Although the overlapping sample is small. aud two of these are sources for which we do not have a stroug upper init on Z4, (sce Section £.2.0)). our results appear broadly cousisteut with these results."," Although the overlapping sample is small, and two of these are sources for which we do not have a strong upper limit on $R_\mathrm{in}$ (see Section \ref{sec:benchmark}) ), our results appear broadly consistent with these results."
 Pontoppidanetal.(2008) ineasured CO inner radi for ΠΟ 135311 D. SR 21 aud TW να assuming a power-law disk temperature profile. aud derived values within a factor of 3.5 of our A.," \citet{Pontoppidan08} measured CO inner radii for HD 135344 B, SR 21 and TW Hya assuming a power-law disk temperature profile, and derived values within a factor of 3.5 of our $R_\mathrm{in}$."
 Note that the SA signal is most sensitive to the of the CO cluission. and also provides a hard upper lait ou Γι.," Note that the SA signal is most sensitive to the of the CO emission, and also provides a hard upper limit on $R_\mathrm{in}$."
" However. the SA profile is not very scusitive to Ry. aud so modeling that incorporates SA is subject to the same uncertainties iu the gas temperature profile. and does not necessarily determine A, more accurately,"," However, the SA profile is not very sensitive to $R_\mathrm{in}$, and so modeling that incorporates SA is subject to the same uncertainties in the gas temperature profile, and does not necessarily determine $R_\mathrm{in}$ more accurately."
 Poutoppidauetal.(2011) report SA radii. which they define as the radius at the peak of the SA profile. for ITD 135311 D. SR 21. TW IIa aud VV Ser.," \citet{Pontoppidan11} report SA radii, which they define as the radius at the peak of the SA profile, for HD 135344 B, SR 21, TW Hya and VV Ser."
 The SA signal is the fluxcweighted mean position of the emission at cach velocity aud is therefore sensitive to the distribution of clnission rather than simply the inner boundary., The SA signal is the flux-weighted mean position of the emission at each velocity and is therefore sensitive to the distribution of emission rather than simply the inner boundary.
" The SA radi will therefore alwavs be larecr than 7, uuless the cluitting region is iufinitesinallv thin.", The SA radii will therefore always be larger than $R_\mathrm{in}$ unless the emitting region is infinitesimally thin.
 In the coutext of our two-power-law model. the SA radii would be affected wp. qand fug. stace these all affect the amount of fiux i laree radi.," In the context of our two-power-law model, the SA radii would be affected by $p$ , $q$ and $R_\mathrm{mid}$, since these all affect the amount of flux at large radii."
 Thus. the SA profiles are complementary o the results from line shape analysis. aud the two cau votentially be used in concert to derive the shape of Lew(R).," Thus, the SA profiles are complementary to the results from line shape analysis, and the two can potentially be used in concert to derive the shape of $L_\mathrm{CO}(R)$."
 The SA radii (Roa) derived by (Poutoppidauetal.2011) are factors of 25 larecr than our 722., The SA radii $R_\mathrm{SA}$ ) derived by \citep{Pontoppidan11} are factors of 2–5 larger than our $R_\mathrm{in}$.
" We ave tested our two-power-law models with a simple code ο caleulate Roy and find that we can sinimltaucouslv reproduce the observed Ry, aud μα by adjusting other nodel parameters.", We have tested our two-power-law models with a simple code to calculate $R_\mathrm{SA}$ and find that we can simultaneously reproduce the observed $R_\mathrm{in}$ and $R_\mathrm{SA}$ by adjusting other model parameters.
" Therefore. our Ry, are consistent with and complementary to the SA results."," Therefore, our $R_\mathrm{in}$ are consistent with and complementary to the SA results."
" Rotation diagrams cau be used to derive characteristic colunun deusitics, cutting areas and teniperatures for the CO eiitting laver."," Rotation diagrams can be used to derive characteristic column densities, emitting areas and temperatures for the CO emitting layer."
 Rotational levels are assuined to be populated according to LTE., Rotational levels are assumed to be populated according to LTE.
 Although these paralcters are not fully realistic. since the ciissiou actually comes frou a range of radi aud heights iu the disk atimosphere. they provide a couvenient wav to roughly characterize and compare the enuission withina," Although these parameters are not fully realistic, since the emission actually comes from a range of radii and heights in the disk atmosphere, they provide a convenient way to roughly characterize and compare the emission withina"
is uniformly tilled. this should not be excessively optimistic.,"is uniformly filled, this should not be excessively optimistic."
 It could be enforced in practice by discarding high-A data so that equivalent (and completely filled) areas of the plane are retained in each frequency band., It could be enforced in practice by discarding $k$ data so that equivalent (and completely filled) areas of the plane are retained in each frequency band.
 The noise is dealt with slightly differently., The noise is dealt with slightly differently.
 We consider pixels in the plane where the sampling function is non-zero to be encompassed by our coverage. and we generate uncorrelated Gaussian noise at each such pixel.," We consider pixels in the plane where the sampling function is non-zero to be encompassed by our coverage, and we generate uncorrelated Gaussian noise at each such pixel."
 Pixels outside our coverage are set to zero., Pixels outside our coverage are set to zero.
" We (inverse) Fourier transform to return to the image plane. then normalize this ""noise image’ such that it has the correctris."," We (inverse) Fourier transform to return to the image plane, then normalize this `noise image' such that it has the correct."
 This procedure yields noise that is almost uncorrelated between independent resolution elements (though the noise on adjacent pixels is correlated)., This procedure yields noise that is almost uncorrelated between independent resolution elements (though the noise on adjacent pixels is correlated).
 We tit out the foregrounds in the dirty cubes in the same way as before., We fit out the foregrounds in the dirty cubes in the same way as before.
 The skewness of the residual images exhibits the same problem seen in Fig. 4..," The skewness of the residual images exhibits the same problem seen in Fig. \ref{fig:rskew3},"
 being dominated by the noise., being dominated by the noise.
 In this case. the smoothing procedure used above would not be expected to help. since the noise is correlated on the scale of our smoothing kernel.," In this case, the smoothing procedure used above would not be expected to help, since the noise is correlated on the scale of our smoothing kernel."
 In addition. since our resolution is comparable to the scale of features in the original signal. using a broader kernel simply washes out the signal as well as the noise.," In addition, since our resolution is comparable to the scale of features in the original signal, using a broader kernel simply washes out the signal as well as the noise."
 We therefore require a more sophisticated denoising seheme., We therefore require a more sophisticated denoising scheme.
 With the results of Section ??. in mind. we use the differing correlation properties of the signal and noise in our extraction.," With the results of Section \ref{subsec:extracskew} in mind, we use the differing correlation properties of the signal and noise in our extraction."
 To be explicit. suppose that we write the residuals as a vector d. where (d; is the residual at the ‘th pixel of a map at a given frequency.," To be explicit, suppose that we write the residuals as a vector $\boldsymbol{d}$, where $d_i$ is the residual at the $i$ th pixel of a map at a given frequency."
 We relate d to the image from the uncorrupted simulation. s. by The matrix R encodes the convolution of the signal with the PSF. while € represents the noise.," We relate $\boldsymbol{d}$ to the image from the uncorrupted simulation, $\boldsymbol{s}$, by The matrix $\mathbfss{R}$ encodes the convolution of the signal with the PSF, while $\boldsymbol{\epsilon}$ represents the noise."
 We neglect any contribution to € coming from errors in the fitting procedure. so we can assume that the correlation matrix of the noise. N=tee). is known there. εἰ is the conjugate transpose of €).," We neglect any contribution to $\boldsymbol{\epsilon}$ coming from errors in the fitting procedure, so we can assume that the correlation matrix of the noise, $\mathbfss{N}=\langle\boldsymbol{\epsilon\epsilon}^\dag\rangle$, is known (here, $\boldsymbol{\epsilon}^\dag$ is the conjugate transpose of $\boldsymbol{\epsilon}$ )."
 We consider a very optimistic situation for extracting the skewness. which occurs if the correlation matrix of the signal. ss‘). is also known.," We consider a very optimistic situation for extracting the skewness, which occurs if the correlation matrix of the signal, $\mathbfss{S}=\langle\boldsymbol{ss}^\dag\rangle$ , is also known."
 We can then perform a Wiener deconvolution on each residual image to recover an estimate of the CS., We can then perform a Wiener deconvolution on each residual image to recover an estimate of the CS.
 That is. we compute s=Fd where the Wiener filter F is given by (see.e.g..2)..," That is, we compute $\hat{\boldsymbol{s}}=\mathbfss{F}\boldsymbol{d}$ where the Wiener filter $\mathbfss{F}$ is given by \citep[see, e.g.,][]{ZAR95}."
 In the absence of noise. this procedure reduces to an ideal inverse filter that estimates the orignal image before corruption by the PSF.," In the absence of noise, this procedure reduces to an ideal inverse filter that estimates the orignal image before corruption by the PSF."
 In the presence of noise. the Wiener filter suppresses power in the image at those values of & for which the signal-to-noise ratio (SNR) is low. while retaining power for modes where the SNR is high (see. e.g.. 23).," In the presence of noise, the Wiener filter suppresses power in the image at those values of $\boldsymbol{k}$ for which the signal-to-noise ratio (SNR) is low, while retaining power for modes where the SNR is high (see, e.g., \citealt{NR86}) )."
 The algorithm is optimal in the least-squares sense., The algorithm is optimal in the least-squares sense.
 The skewness of these deconvolved images as a function of redshift is shown in Fig. 7.., The skewness of these deconvolved images as a function of redshift is shown in Fig. \ref{fig:skewdb}.
 Comparing to Figs., Comparing to Figs.
 2. and 3.. one can see that this procedure gives excellent results. recovering the general trends in skewness seen in the original simulations.," \ref{fig:skewo} and \ref{fig:skewandmean}, one can see that this procedure gives excellent results, recovering the general trends in skewness seen in the original simulations."
 Indeed. using an optimal filter with precise knowledge of the signal and noise properties means that we recover larger values for the skewness than were seen after applying the simple smoothing to the uncorrelated noise case of Section ?? (Fig. 6).," Indeed, using an optimal filter with precise knowledge of the signal and noise properties means that we recover larger values for the skewness than were seen after applying the simple smoothing to the uncorrelated noise case of Section \ref{subsec:extracskew}
 (Fig. \ref{fig:rskew3s}) )."
 We can realistically expect a situation intermediate between the results of Figs., We can realistically expect a situation intermediate between the results of Figs.
 4 and 7..," \ref{fig:rskew3}
 and \ref{fig:skewdb}."
 The lines representing f250C and the T-QSO simulation do not extend all the way to.=6 in Fig. 7.., The lines representing f250C and the T-QSO simulation do not extend all the way to $z=6$ in Fig. \ref{fig:skewdb}.
 At these redshifts. the variance in the CS is so small compared to that of the noise that the deconvolution becomes unstable.," At these redshifts, the variance in the CS is so small compared to that of the noise that the deconvolution becomes unstable."
 For the same reason. we cannot estimate the errors in the same way as for Fig.," For the same reason, we cannot estimate the errors in the same way as for Fig."
 6. (that is. by generating realizations with no CS at all).," \ref{fig:rskew3s}
 (that is, by generating realizations with no CS at all)."
 None the less. the errors can be inferred to be small since we do not see the same effect as in Fig. 6..," None the less, the errors can be inferred to be small since we do not see the same effect as in Fig. \ref{fig:rskew3s},"
 in which the extracted signal from the datacube generated with the f250C and T-QSO simulations is very similar at high and low redshift. being dominated by noise.," in which the extracted signal from the datacube generated with the f250C and T-QSO simulations is very similar at high and low redshift, being dominated by noise."
 An obvious objection to the method presented here is that if the correlation matrix of the CS is known. this means that we have already detected a signal from the EoR. so higher-order statistics are not required to extract it.," An obvious objection to the method presented here is that if the correlation matrix of the CS is known, this means that we have already detected a signal from the EoR, so higher-order statistics are not required to extract it."
" The force of this objection depends on how good an estimate of the correlation matrix of the signal is required for the deconvolution to give an acceptable result,", The force of this objection depends on how good an estimate of the correlation matrix of the signal is required for the deconvolution to give an acceptable result.
 We resent a test of this in Fig. 8.., We present a test of this in Fig. \ref{fig:diffcorr}.
 The three lines in the figure show the skewness extracted rom the f250C residuals using three different assumption for he correlation matrix. S. used in the Wiener deconvolution. The solid. blue line shows. for reference. the skewness extracted when we use the correct correlation matrix Syosyc(2). calculated from he original simulation. in performing the deconvolution.," The three lines in the figure show the skewness extracted from the f250C residuals using three different assumption for the correlation matrix, $\mathbfss{S}$, used in the Wiener deconvolution, The solid, blue line shows, for reference, the skewness extracted when we use the correct correlation matrix $\mathbfss{S}_\mathrm{f250C}(z)$, calculated from the original simulation, in performing the deconvolution."
 The dashed. magenta line shows the extracted skewness when we use iSo(2) instead.," The dashed, magenta line shows the extracted skewness when we use $\frac{1}{2}\mathbfss{S}_\mathrm{f250C}(z)$ instead."
 Underestimating the correlation matrix by a uctor of two clearly has only a minimal effect on the extraction of the skewness., Underestimating the correlation matrix by a factor of two clearly has only a minimal effect on the extraction of the skewness.
 Finally the dot-dashed. evan line shows the result when we use the correlation matrix of the T-star simulation.," Finally the dot-dashed, cyan line shows the result when we use the correlation matrix of the T-star simulation."
 Even though the redshift evolution of the two simulations is very different. the dip and peak in the skewness at are recovered. though it is not clear that they can be easily distinguished from the spurious variations at high redshift.," Even though the redshift evolution of the two simulations is very different, the dip and peak in the skewness at are recovered, though it is not clear that they can be easily distinguished from the spurious variations at high redshift."
 This preliminary result is encouraging. but it would be preferable to use a correlation matrix estimated from the data themselves.," This preliminary result is encouraging, but it would be preferable to use a correlation matrix estimated from the data themselves."
 For, For
"12 the spectra of concatenated structures (3a) to (3f), which include many more hydroxyls, attached to a greater variety of substructures.","12 the spectra of concatenated structures (3a) to (3f), which include many more hydroxyls, attached to a greater variety of substructures."
" As a result, the wagging frequencies now cover a much broader band, which probably corresponds to the 33.1-ym listed by Smith et al. (2007),"," As a result, the wagging frequencies now cover a much broader band, which probably corresponds to the $\mu$ m listed by Smith et al. \cite{smi07},"
", and to the broad FIR bands documented by Kwok and coll. (", and to the broad FIR bands documented by Kwok and coll. (
"see Hrivnaket al. (2009),","see Hrivnaket al. \cite{hri09},"
", and bibliography therein).", and bibliography therein).
 Table 1 lists the atomic composition of the various families of structures included in the model dust which deliver the spectra of Fig., Table 1 lists the atomic composition of the various families of structures included in the model dust which deliver the spectra of Fig.
 12 and 13., 12 and 13.
" The last column gives the corresponding abundance fractions, f."," The last column gives the corresponding abundance fractions, $f$."
 The last row lists the total numbers of atoms in the case of Fig., The last row lists the total numbers of atoms in the case of Fig.
" 13, where the concatenated structures type 3 are included."," 13, where the concatenated structures type 3 are included."
" The relative number abundances are: H/C—1.15,O/C—6.410-?,N/C=2.610-3,S/C 1.31072."," The relative number abundances are: $H/C=1.15,\,\,O/C=6.4\,10^{-2},\,\,N/C=2.6\,10^{-3},\,\,S/C=1.3\,10^{-2}$ ."
 dedays/epoch).,– days/epoch).
 Wo examine the median. measurement uncertainties as a proxy for cata quality. we see for example that 220782. which has the lowest measurement uncertainties at I. has tvpically higher. period detectabilities. despite. maniss.having lower observation density han 1179049.," If examine the median measurement uncertainties as a proxy for data quality, we see for example that 20782, which has the lowest measurement uncertainties at $^{-1}$, has typically higher period detectabilities, despite having lower observation density than 179949."
" ""Phis suggests that once again a complicated: combination of observation density and. data quality are important in selection functions for Doppler λαοί search data.", This suggests that once again a complicated combination of observation density and data quality are important in selection functions for Doppler planet search data.
" We also consider the detectability at. cach P. the measured period. denoted 25,iu(D,). and compare it with he DXllb(P5). discussed. above."," We also consider the detectability at each $P_m$, the measured period, denoted $D^\prime_{\mathrm{int}}(P_m)$, and compare it with the $D^\prime_{\mathrm{int}}(P_i)$ discussed above."
 We caleulate Di)Alb by counting the number of correct detections in equally spaced ης of logον. normalised by the number of simulations in each of bin.," We calculate $D^\prime_{\mathrm{int}}(P_m)$ by counting the number of correct detections in equally spaced bins of $\log P_m$, normalised by the number of simulations in each of bin."
 At periods up to 1000«dd (logP= 3.0). the ierence in detectabilities are less than for all stars.," At periods up to d $\log P=3.0$ ), the difference in detectabilities are less than for all stars."
" Phere is a small olfset for the two longest periods of up to δα. which is caused by poorly constrained long periods (log2= 3.6) ""leaking"" into the next shorter. period bin "," There is a small offset for the two longest periods of up to $\pm$, which is caused by poorly constrained long periods $\log P=3.6$ ) “leaking” into the next shorter period bin $\log
P=3.3$ )."
The integrated. detectability as a function. of planet mass. £D'6M;) is. more complicated.. than the integrated. etectability as a function of period or eccentricity. because planet mass is à function of both of these parameters (as well as semi-amplituck) through Equation 2..," The integrated detectability as a function of planet mass, $D^\prime_{\mathrm{int}}(M_i)$ is more complicated than the integrated detectability as a function of period or eccentricity, because planet mass is a function of both of these parameters (as well as semi-amplitude) through Equation \ref{eq:semiamp}."
" Figure 19 garows Di,(AE) as a function of planet mass for the three 1179049 subsets.", Figure \ref{fig:Mselfunc1} shows $D^\prime_{\mathrm{int}}(M_i)$ as a function of planet mass for the three 179949 subsets.
 As one might naively expect. we see that more data results in higher detectabilities for a given mass of planet. (," As one might naively expect, we see that more data results in higher detectabilities for a given mass of planet. ("
Recall also that at low masses false positives begin to have a significant impact on [alse positives. [or spareslv sampled: data hey represent up to as a fraction of the total detections at M&0.2Mau... leading to an apparently higher detectabilitv than data sets with more observations.),"Recall also that at low masses false positives begin to have a significant impact on false positives for sparesly sampled data – they represent up to as a fraction of the total detections at $<$, leading to an apparently higher detectability than data sets with more observations.)"
" Once again. if we examine the LX,CM;) curves. lor simulations of each star we find variations (see Figure 20))."," Once again, if we examine the $D^\prime_{\mathrm{int}}(M_i)$ curves for simulations of each star we find variations (see Figure \ref{fig:Mselfunc2}) )."
 The 220782 observations. which have the highest quality with a median measurement uncertainty of allow the detection of the lowest. planet masses. (after false positives are removed). as shown in Figure 20.," The 20782 observations, which have the highest quality with a median measurement uncertainty of $^{-1}$ , allow the detection of the lowest planet masses (after false positives are removed), as shown in Figure \ref{fig:Mselfunc2}."
. Even though there are more observations of. 1179949. the mecian uncertainty of 220782 is less than half that stars value.," Even though there are more observations of 179949, the median uncertainty of 20782 is less than half that star's value."
 In the case of 338382. the median uncertainty of the observations. the number of epochs appear to be," In the case of 38382, the median uncertainty of the observations the number of epochs appear to be"
of optimal matched filtering by a factor of about. ν00~7. and an improvement by a factor ol ν1000 2230 over second order methods for signals around. 1 κ».,"of optimal matched filtering by a factor of about $\sqrt{50}\sim 7$, and an improvement by a factor of $\sqrt{1000}\simeq$ 30 over second order methods for signals around 1 kHz."
 In Section 2. we discuss the astronomical origin of long GRBs from possible both CC-SNe and mergers.," In Section 2, we discuss the astronomical origin of long GRBs from possible both CC-SNe and mergers."
 In Section 3. we introduce a model ancl template lor long GWDs from rapidly rotating Ixerr black holes.," In Section 3, we introduce a model and template for long GWBs from rapidly rotating Kerr black holes."
 In Section 4. we describe the proposed time sliced matched filtering search algorithm and the evaluation of the sensitivitv. distance for a reasonably. accurate ex(raction of trajectories in the lime frequency domain.," In Section 4, we describe the proposed time sliced matched filtering search algorithm and the evaluation of the sensitivity distance for a reasonably accurate extraction of trajectories in the time frequency domain."
 Our findings are summarized in Seclion 5., Our findings are summarized in Section 5.
 As a universal inner engine. rapidly rotating err black holes can explain long GRBs from both CC-SNe and some of the mergers.," As a universal inner engine, rapidly rotating Kerr black holes can explain long GRBs from both CC-SNe and some of the mergers."
 They. enable lone GRBs with supernovae exclusively in star forming regions with stellar wind host environments ancl without supernovae such as GIDOGOG614. both in and away [rom star forming regions including the halo such as GRD 070125.," They enable long GRBs with supernovae exclusively in star forming regions with stellar wind host environments and without supernovae such as GRB060614, both in and away from star forming regions including the halo such as GRB 070125."
 Some recent and Fermi-LAT detections of long GRBs show events with and without. X-ray. afterglows such as GRDBO050911. ISM-like constant or wind-like ¢7 density profiles in the local host environments. ancl a diversity in distances from a local host galaxy. as sununarizecd in Table I. This phenomenology is not accounted for by CC-SNe alone. and suggests that some of the long GRBs are associated with mergers. otherwise sharing a common long-lived inner engine.," Some recent and LAT detections of long GRBs show events with and without X-ray afterglows such as GRB050911, ISM-like constant or wind-like $r^{-2}$ density profiles in the local host environments, and a diversity in distances from a local host galaxy, as summarized in Table I. This phenomenology is not accounted for by CC-SNe alone, and suggests that some of the long GRBs are associated with mergers, otherwise sharing a common long-lived inner engine."
 Raclialive processes around herr black holes are driven by lrame-drageine. expressed in terms of a non-zero angular velocity w of zero-angular momentum observers.," Radiative processes around Kerr black holes are driven by frame-dragging, expressed in terms of a non-zero angular velocity $\omega$ of zero-angular momentum observers."
" It gives rise to high energy entissions along the spin axis by the induced potential energy E=£2, [or particles with angular momentum 4, (vanPutten&Gupta2009) and. contemporaneously. to a spin connection to surrounding matter by equivalence in topology to pulsar magnetospheres (vanPutten1999)."," It gives rise to high energy emissions along the spin axis by the induced potential energy $E=\Omega J_p$ for particles with angular momentum $J_p$ \citep{van09} and, contemporaneously, to a spin connection to surrounding matter by equivalence in topology to pulsar magnetospheres \citep{van99}."
. Thus. observations on high-energy. emissions (in gamma-rays. allerglow enissions. possibly ultra-high energy cosmic ravs) from leptonic jets as well as on low-energy enissions (in gravitational waves. MeV-neutrinos and magnetic winds. powering a supernova or a racio-burst) emanating Irom matter is required for full calorimetry.," Thus, observations on high-energy emissions (in gamma-rays, afterglow emissions, possibly ultra-high energy cosmic rays) from leptonic jets as well as on low-energy emissions (in gravitational waves, MeV-neutrinos and magnetic winds, powering a supernova or a radio-burst) emanating from matter is required for full calorimetry."
 Accordinge to the Ixerr metrice. rotatinge black holes are energeticallye very. similar to spinning tops in the sense of having a ratio," According to the Kerr metric, rotating black holes are energetically very similar to spinning tops in the sense of having a ratio"
"128 cells until the number density of hydrogen atoms exceeds ny=10?cm-?, at which point we extract the central lpc of the simulations and deactivate further refinement.","$128$ cells until the number density of hydrogen atoms exceeds $n_{\rm H}=10^9\,{\rm cm}^{-3}$, at which point we extract the central $1\,{\rm pc}$ of the simulations and deactivate further refinement."
" We reinitialize the simulations in this smaller box with reflective boundary conditions (seeSpringel 20102), which ensures that the gas remains confined by external pressure."," We reinitialize the simulations in this smaller box with reflective boundary conditions \citep[see][]{springel10a}, which ensures that the gas remains confined by external pressure."
" We also discard all DM particles, since the gravitational potential at these densities is dominated by the gas: the radius at which the gas mass exceeds the DM mass by an order of magnitude is 0.76, 0.67, 0.58, 0.71 and 1.1pc, respectively, which is comparable to the spatial extent of the resimulations."," We also discard all DM particles, since the gravitational potential at these densities is dominated by the gas: the radius at which the gas mass exceeds the DM mass by an order of magnitude is $0.76$, $0.67$, $0.58$, $0.71$ and $1.1\,{\rm pc}$, respectively, which is comparable to the spatial extent of the resimulations."
" Due to the deactivation of the refinement, the particle mass within the central ~1000AU remains roughly constant at 107M."," Due to the deactivation of the refinement, the particle mass within the central $\simeq 1000\,{\rm AU}$ remains roughly constant at $10^{-4}\,{\rm M}_\odot$."
" We note that shocks from inflows into the innermost region are still well resolved under these conditions, thanks to the ability ofAREPO to capture shocks on ~1—2 cells."," We note that shocks from inflows into the innermost region are still well resolved under these conditions, thanks to the ability of to capture shocks on $\sim 1-2$ cells."
" Assuming a temperature of 1000K, the Truelove criterion is thus expected to be violated at a density of ~10! cm-?,which is"," Assuming a temperature of $1000\,{\rm K}$ the Truelove criterion is thus expected to be violated at a density of $\simeq 10^{17}\,{\rm cm}^{-3}$ ,which is"
"where ry, is expressed in meters.",where $r_p$ is expressed in meters.
 Equations (13)) and (19)) together give with r in km., Equations \ref{tauc}) ) and \ref{N}) ) together give with $r$ in km.
 Lines of constant collision (nme Irom Equation (20)) are plotted in Figure (9))., Lines of constant collision time from Equation \ref{tauc2}) ) are plotted in Figure \ref{tauc_plot}) ).
 Inpacted asteroid (596) Scheila is marked on Figure (9)) with an error bar indicating different estimates of the projectile radius from Jewitt et al. (, Impacted asteroid (596) Scheila is marked on Figure \ref{tauc_plot}) ) with an error bar indicating different estimates of the projectile radius from Jewitt et al. (
2011: α 17 m) and Ishiguro et al. (,2011; $a \sim$ 17 m) and Ishiguro et al. (
2011: a~ 40 m). respectively.,"2011; $a \sim$ 40 m), respectively."
" The corresponding collision times are 3x 10* €7,«3x 107 vr.", The corresponding collision times are $\times$ $^{3}$ $\le \tau_c \le$ $\times$ $^{4}$ yr.
 Given that there are ~250 known asteroids as large as or larger than (596) Scheila. ihe mean interval between similar events is (10 - 100) vr. statistically consistent with the detection of Scheila within the first decade of effieient. nearly real-time skv monitoring.," Given that there are $\sim$ 250 known asteroids as large as or larger than (596) Scheila, the mean interval between similar events is $\sim$ (10 - 100) yr, statistically consistent with the detection of Scheila within the first decade of efficient, nearly real-time sky monitoring."
 Disruptecl asteroid P/2010 A? (interpreted as a ο m radius object impacted by a projectile of characteristic size 2 to 4 meters: Jewitt et al., Disrupted asteroid P/2010 A2 (interpreted as a $\sim$ 60 m radius object impacted by a projectile of characteristic size 2 to 4 meters; Jewitt et al.
" 2010) is also marked in Figure (9)). indicating a collision time 7.e 7 to 50x10"" vr."," 2010) is also marked in Figure \ref{tauc_plot}) ), indicating a collision time $\tau_c \sim$ 7 to $\times$ $^6$ yr."
 With V(>60)~ 4x LOS (Equation 19)). the expected rate of similar events is ~8 to 60 |.," With $N (\ge 60) \sim$ $\times$ $^8$ (Equation \ref{N}) ), the expected rate of similar events is $\sim$ 8 to 60 $^{-1}$."
 Jewitt οἱ al. (, Jewitt et al. (
2011) estimated the detection probability of P/2010 A2 clones as <6%.. so that of & to GO similar events per vear we would currently detect only ~0.5 (o 4.,"2011) estimated the detection probability of P/2010 A2 clones as $\lesssim$, so that of 8 to 60 similar events per year we would currently detect only $\sim$ 0.5 to 4."
 This is sill higher Chan the actual rate of detection. counted as one object in perhaps a decade of ellicient. nearly real-time sky monitoring by LINEAR. and other survey telescopes.," This is still higher than the actual rate of detection, counted as one object in perhaps a decade of efficient, nearly real-time sky monitoring by LINEAR and other survey telescopes."
 The high rate could simply indicate ihe extreme uncertainwv in using Equation (19)) to estimate the number of meter-sized projectiles., The high rate could simply indicate the extreme uncertainty in using Equation \ref{N}) ) to estimate the number of meter-sized projectiles.
" For example. the equation gives ΑΣ5) = 3x 10H, while published estimates of (his number range [rom ~10°°? to ~LOY (Davis et al."," For example, the equation gives $N_p (\ge 5)$ = $\times$ $^{11}$, while published estimates of this number range from $\sim$ $^{9.5}$ to $\sim$ $^{12}$ (Davis et al."
 2002). indicating a large uncertainty in 7. ad small projectile sizes.," 2002), indicating a large uncertainty in $\tau_c$ at small projectile sizes."
 Or it could indicate that activity in P/2010 A2 is eaused by another process. possibly YORDP spin-up. as remarked in Section (4.3)).," Or it could indicate that activity in P/2010 A2 is caused by another process, possibly YORP spin-up, as remarked in Section \ref{p2010a2}) )."
 Further progress in understanding the impact rate in the asteroid bell hinges strongly upon better measurements of the sub-kilometer size distribution., Further progress in understanding the impact rate in the asteroid belt hinges strongly upon better measurements of the sub-kilometer size distribution.
 Future wide-area sky survevs may help elucidate the mechanisms operating (to cause asteroidal mass loss., Future wide-area sky surveys may help elucidate the mechanisms operating to cause asteroidal mass loss.
 For example. we expect the spatial distribution of collisionally produced or (riggerecl objects to be correlated with the regions of the asteroid belt in which the collision probability per unit time is highest.," For example, we expect the spatial distribution of collisionally produced or triggered objects to be correlated with the regions of the asteroid belt in which the collision probability per unit time is highest."
 Unfortunately. the published survevs for active asteroids so [ar are either biased (IIsieh. 2009) or. if unbiased. detected no objects and so provide insufficient information (Gilbert aud. Wiegert 2009. 2010. Sonnett οἱ al.," Unfortunately, the published surveys for active asteroids so far are either biased (Hsieh 2009) or, if unbiased, detected no objects and so provide insufficient information (Gilbert and Wiegert 2009, 2010, Sonnett et al."
 2011)., 2011).
 All but one of the known active asteroids were discovered serendipitously by a variety of survevs and methods. most too poorly quantified in terms of reported areal coverage ancl limiting," All but one of the known active asteroids were discovered serendipitously by a variety of surveys and methods, most too poorly quantified in terms of reported areal coverage and limiting"
he PA swings seen simultaneously at. cülferent. [requencies.,the PA swings seen simultaneously at different frequencies.
 In Figure 7 νο plot the PA at longitudes where the inear polarized. emission is strong cnough to exceed a signal-to-noise ratio threshold of 4., In Figure \ref{fig:pa1} we plot the PA at longitudes where the linear polarized emission is strong enough to exceed a signal-to-noise ratio threshold of 4.
 Phe agreement between he different frequencies is extremely good. demonstrating he general broad-bancl character of the PA swing. while simultaneously validating our calibration procedures.," The agreement between the different frequencies is extremely good, demonstrating the general broad-band character of the PA swing, while simultaneously validating our calibration procedures."
 Note hat the agreement is found for both the ALP and HP. with he only exception being the LP data measured at 1.4 Cillz during session S.," Note that the agreement is found for both the MP and IP, with the only exception being the IP data measured at 1.4 GHz during session 8."
 Having calibrated the absolute position angles for both 4.9 Gllz and 8.4 CGllz. we use a measured offset of ALL=10€2 to infer a rotation measure of RAl=|TL144 rad ," Having calibrated the absolute position angles for both 4.9 GHz and 8.4 GHz, we use a measured offset of $\Delta PA = -10^\circ\pm2^\circ$ to infer a rotation measure of $=+71\pm14$ rad $^{-2}$."
As was evident from a comparison of the PA swings in Figure 3.. the PA changed between the observing sessions.," As was evident from a comparison of the PA swings in Figure \ref{fig:align}, the PA changed between the observing sessions."
 In Figure S.. we show the evolution of the PA as a function of time in more detail for both the MP and LIP as measured for 4.9 GlLlz and 8.4 Cllz.," In Figure \ref{fig:pa2}, we show the evolution of the PA as a function of time in more detail for both the MP and IP as measured for 4.9 GHz and 8.4 GHz."
 For reasons of clarity. we have ollset the PA swings to each other by a fixed amount which is the same each for both the ALP and LP.," For reasons of clarity, we have offset the PA swings to each other by a fixed amount which is the same each for both the MP and IP."
 A clear trend is visible where the previously discussed dip becomes less prominent from. session l1 to session 2 before it has disappeared. at session 5., A clear trend is visible where the previously discussed dip becomes less prominent from session 1 to session 2 before it has disappeared at session 5.
 Interestingly. the longitude range where the dip was present is later replaced. by DX. values which show a significant scatter. (vpically much larger than at other pulse longitudes.," Interestingly, the longitude range where the dip was present is later replaced by PA values which show a significant scatter, typically much larger than at other pulse longitudes."
 A slight change in the overall slope is also visible., A slight change in the overall slope is also visible.
 The figure also demonstrates again how the leading MP component disappears with time. while the most trailing component of the ALP remains essentially detectable at all times. at least at S4 Gz.," The figure also demonstrates again how the leading MP component disappears with time, while the most trailing component of the MP remains essentially detectable at all times, at least at 8.4 GHz."
 Surprisingly. observations at both frequencies with both Elfelsberg and Westerbork show an interesting wigele or oscillation in parts of the PA swing which follows the longitudes of the “dip seen in session 1.," Surprisingly, observations at both frequencies with both Effelsberg and Westerbork show an interesting 'wiggle' or oscillation in parts of the PA swing which follows the longitudes of the 'dip' seen in session 1."
 When studying the evolution ofthe PA swing measured in the LP. it is obvious that it changes significantly with time.," When studying the evolution of the PA swing measured in the IP, it is obvious that it changes significantly with time."
"mainly stays at the bubble surface, resulting in a CR distribution that increases toward the bubble edges, which is a key requirement to produce the observed flat gamma-ray surface brightness distribution.","mainly stays at the bubble surface, resulting in a CR distribution that increases toward the bubble edges, which is a key requirement to produce the observed flat gamma-ray surface brightness distribution."
" Such an edge-favored CR distribution is hard to achieve by other physical mechanisms, suggesting that viscosity may indeed play significant role in jet evolution."," Such an edge-favored CR distribution is hard to achieve by other physical mechanisms, suggesting that viscosity may indeed play a significant role in jet evolution."
" 'The observeda bubbles have very sharp gamma-ray edges, indicating that CR diffusion across bubble edges is suppressed significantly below the CR diffusion rate estimated in the solar vicinity."," The observed bubbles have very sharp gamma-ray edges, indicating that CR diffusion across bubble edges is suppressed significantly below the CR diffusion rate estimated in the solar vicinity."
" However, if CR diffusion is also suppressed in the bubble interior, viscous runs produce limb-brightened gamma-ray bubbles in the projected Galactic coordinate system, which are also inconsistent with observations."," However, if CR diffusion is also suppressed in the bubble interior, viscous runs produce limb-brightened gamma-ray bubbles in the projected Galactic coordinate system, which are also inconsistent with observations."
" Interestingly, if CR. diffusivity in the bubble interior is close to that estimated in the solar vicinity, CR diffusion transports CRs from the bubble edges to the interior, resulting in a roughly flat projected CR distribution."," Interestingly, if CR diffusivity in the bubble interior is close to that estimated in the solar vicinity, CR diffusion transports CRs from the bubble edges to the interior, resulting in a roughly flat projected CR distribution."
" Thus, by including CR diffusion within, but not across, the bubble edges, our viscous runs produce CR-filled bubbles very similar to those observed."," Thus, by including CR diffusion within, but not across, the bubble edges, our viscous runs produce CR-filled bubbles very similar to those observed."
" Given that we already invoke magnetic draping-which is inevitable and has been observed in numerous systems ranging from comets to the Sun's coronal mass ejections—to suppress CR diffusion, it might seem superfluous to invoke viscosity as stabilizing mechanism, since magnetic tension in the drapea may also stabilize the KH instability (Lyutikov2006;Ruszkowskietal.2007;Dursi&Pfrommer 2008)."," Given that we already invoke magnetic draping--which is inevitable and has been observed in numerous systems ranging from comets to the Sun's coronal mass ejections—to suppress CR diffusion, it might seem superfluous to invoke viscosity as a stabilizing mechanism, since magnetic tension in the drape may also stabilize the KH instability \citep{lyutikov06, ruszkowski07, dursi08}."
". Assuming that the results of subsonic draping described in Dursi&Pfrom-mer apply here, the field strength in the drape is independent(2008) of the ambient galactic field strength and will build up to be in rough equipartition with ram pressure (for the parameters we have chosen, it is ~10 LG); this means that the Alfven speed is of order the shear velocity, which is the requirement for the KH instability to be quenched (Dursi2007)."," Assuming that the results of subsonic draping described in \citet{dursi08} apply here, the field strength in the drape is independent of the ambient galactic field strength and will build up to be in rough equipartition with ram pressure (for the parameters we have chosen, it is $\sim 10$ $\mu$ G); this means that the Alfven speed is of order the shear velocity, which is the requirement for the KH instability to be quenched \citep{dursi07}."
". We have four comments on this: (1) a further requirement for stabilization by magnetic tension is that the swept up ambient field has a coherence length Ag which is larger than or of order the bubble size R; otherwise, the bubble will still be shredded apart, as demonstrated in MHD simulations (Ruszkowskietal.2007;D"," We have four comments on this: (1) a further requirement for stabilization by magnetic tension is that the swept up ambient field has a coherence length $\lambda_{\rm B}$ which is larger than or of order the bubble size $R$; otherwise, the bubble will still be shredded apart, as demonstrated in MHD simulations \citep{ruszkowski07,dursi08}."
"ursi&Pfrommer 2008).. While Ag~£ is plausible for bubbles in galaxy clusters, it is as yet unclear whether the halo of our Galaxy has a field coherent on ~10 kpc scales, without significant small scale irregularities."," While $\lambda_{\rm B}\sim R$ is plausible for bubbles in galaxy clusters, it is as yet unclear whether the halo of our Galaxy has a field coherent on $\sim 10$ kpc scales, without significant small scale irregularities."
" If other constraints on magnetic coherence can be placed, such as polarized emission from the drape (Pfrommer&JonathanDursi this would indirectly probe the halo magnetic field 2010),(while there has been no detection of polarization of the haze/bubbles by WMAP, this may be due to the significant noise in the data; Dobler 2012)). "," If other constraints on magnetic coherence can be placed, such as polarized emission from the drape \citep{pfrommer10}, this would indirectly probe the halo magnetic field (while there has been no detection of polarization of the haze/bubbles by WMAP, this may be due to the significant noise in the data; \citealt{dobler12}) ). ("
"Viscosity is also required to stabilize internal flows (2)within the bubble, which also induce KH instabilities—indeed, our studies suggest that this source of shear is the dominant component.","2) Viscosity is also required to stabilize internal flows within the bubble, which also induce KH instabilities—indeed, our studies suggest that this source of shear is the dominant component."
 The influence of the swept up magnetic sheath is less clear in this case. , The influence of the swept up magnetic sheath is less clear in this case. (
"As discussed earlier in this section, viscosity effectively (3)suppresses the backward motions of the jet backflow and the circulating motions in the bubble interior, naturally leading to an edge-favored CR distribution, which is a key ingredient to produce the observed flat gamma ray intensity distribution. (","3) As discussed earlier in this section, viscosity effectively suppresses the backward motions of the jet backflow and the circulating motions in the bubble interior, naturally leading to an edge-favored CR distribution, which is a key ingredient to produce the observed flat gamma ray intensity distribution. ("
4) The dynamics of draping in a supersonic flow where a strong shock forms - as simulated here - could be substantially different from the subsonic case simulated by previous authors.,4) The dynamics of draping in a supersonic flow where a strong shock forms - as simulated here - could be substantially different from the subsonic case simulated by previous authors.
excluding them uniformly from everywhere Is not possible due to the spread in the intrinsic colors of stars which mimics dust extinetion.,excluding them uniformly from everywhere is not possible due to the spread in the intrinsic colors of stars which mimics dust extinction.
 In the following. we introduce the practical implementation of the technique used in this paper.," In the following, we introduce the practical implementation of the technique used in this paper."
 For the description of the basics of the method itself. we refer to Lombardi&Alves(2001) (seealsoLombardi2005.whotechnique)..," For the description of the basics of the method itself, we refer to \citet{lom01} \citep[see also][who presents an analysis of the effect of foreground stars for the technique]{lom05}."
 We retrieved from the UKIDSS archive the /HKs data for the chosen complexes., We retrieved from the UKIDSS archive the $JHK_S$ data for the chosen complexes.
 For the NIR reddening-law. we adopted the coefficients from Cardelletal.(1989): The extinction mapping procedure itself consisted of three steps which were required especially to deal with the large umber of foreground sources.," For the NIR reddening-law, we adopted the coefficients from \citet{car89}: The extinction mapping procedure itself consisted of three steps which were required especially to deal with the large number of foreground sources."
 This procedure is illustrated as a flow-chart in Fig. |.., This procedure is illustrated as a flow-chart in Fig. \ref{fig:flow}.
" In the first step. a ""dirty"" extinction map was calculated in order to find a low-extinetion region to be used as a control field for the next step of the mapping."," In the first step, a ""dirty"" extinction map was calculated in order to find a low-extinction region to be used as a control field for the next step of the mapping."
 The map was also used to determine high extinction regions from which the surface number density of foreground stars. needed 1 the next step of the map derivation. could be determined.," The map was also used to determine high extinction regions from which the surface number density of foreground stars, needed in the next step of the map derivation, could be determined."
 In the second step. the contribution of foreground stars was statistically subtracted from the mean colors of the control field in order to calculate the mean color of stars to the IRDC complex.," In the second step, the contribution of foreground stars was statistically subtracted from the mean colors of the control field in order to calculate the mean color of stars to the IRDC complex."
 In the statistical subtraction. the density of the foreground stars was first subtracted from the density of all control field stars to yield a foreground corrected source density in each color-color bin.," In the statistical subtraction, the density of the foreground stars was first subtracted from the density of all control field stars to yield a foreground corrected source density in each color-color bin."
 Then. the source number in each color-color bin of the control field was reduced to correspond to this corrected value.," Then, the source number in each color-color bin of the control field was reduced to correspond to this corrected value."
 The foreground corrected mean colors were then computed using this reduced set of control field stars., The foreground corrected mean colors were then computed using this reduced set of control field stars.
 The subtraction is important. because the control field is not a truly non-extincted field. but suffers from extinction due to the diffuse. extended dust component along the line of sight in the Galactic plane.," The subtraction is important, because the control field is not a truly non-extincted field, but suffers from extinction due to the diffuse, extended dust component along the line of sight in the Galactic plane."
 This diffuse extinction at the plane varies between Ay=|—4 mag kpe! (e.g..Marshalletal.2006).," This diffuse extinction at the plane varies between $A_\mathrm{V} \approx1-4$ mag $^{-1}$ \citep[e.g.,][]{mar06}."
.. As a result. the stars away than an IRDC complex are expected to be clearly redder than those than 1t.," As a result, the stars away than an IRDC complex are expected to be clearly redder than those than it."
 In order to estimate the reddening caused by the IRDC complex itself. it is then necessary to estimate the color of the background population by eliminating the contribution of the foreground sources from the mean colors of the control field.," In order to estimate the reddening caused by the IRDC complex itself, it is then necessary to estimate the color of the background population by eliminating the contribution of the foreground sources from the mean colors of the control field."
 The reddening of the sources in the control field is illustrated in Fig. 2..," The reddening of the sources in the control field is illustrated in Fig. \ref{fig:reffield},"
 left panel. which shows the NIR color-color diagram of the sources in the control field chosen for 38.94-00.46.," left panel, which shows the NIR color-color diagram of the sources in the control field chosen for 38.94-00.46."
 For better visibility. only sources with the photometric errors 7x0.3 mag are plotted.," For better visibility, only sources with the photometric errors $\sigma \lesssim 0.3$ mag are plotted."
 The figure clearly shows how a large fraction of sources is heavily reddened along the reddening line., The figure clearly shows how a large fraction of sources is heavily reddened along the reddening line.
 The effect of removing the contribution of the foreground stars from the control field is demonstrated in Fig., The effect of removing the contribution of the foreground stars from the control field is demonstrated in Fig.
 2 center panel., \ref{fig:reffield} center panel.
 The figure shows the color-color diagram of all sources in the control field of the 38.94-00.46. complex with a greyscale., The figure shows the color-color diagram of all sources in the control field of the 38.94-00.46 complex with a greyscale.
 The greyscale represents the number density of stars in each color-color bin., The greyscale represents the number density of stars in each color-color bin.
 The mean colors calculated for this distribution is shown with a green plus sign., The mean colors calculated for this distribution is shown with a green plus sign.
 The red contours in the figure show the number density of the foreground stars identified from the 38.94-00.46 cloud region (identification procedure is explained in more detail later)., The red contours in the figure show the number density of the foreground stars identified from the 38.94-00.46 cloud region (identification procedure is explained in more detail later).
 The colors of foreground stars are clearly less reddened. as expected for stars that on average are closer to the observer and thus suffer less from diffuse extinction.," The colors of foreground stars are clearly less reddened, as expected for stars that on average are closer to the observer and thus suffer less from diffuse extinction."
 Using the surface number density of these foreground stars. we subtracted their statistical contribution to the mean colors.," Using the surface number density of these foreground stars, we subtracted their statistical contribution to the mean colors."
 This resulted in estimates of the mean colors ofcomplex.. indicated 1n the figure with a green cross.," This resulted in estimates of the mean colors of, indicated in the figure with a green cross."
 This change in mean color was significant for all mapped clouds. and clearly required for à reasonable definition of the point in the extinction mapping technique.," This change in mean color was significant for all mapped clouds, and clearly required for a reasonable definition of the zero-point in the extinction mapping technique."
 The variability of the diffuse extinction component (and the uncertainty in determining the foreground population in the control field) induces uncertainty to the zero-point of the extinction determination., The variability of the diffuse extinction component (and the uncertainty in determining the foreground population in the control field) induces uncertainty to the zero-point of the extinction determination.
" We assessed the level of this uncertainty by performing for one cloud the zero-point ""Setermination using 10 different control fields.", We assessed the level of this uncertainty by performing for one cloud the zero-point determination using 10 different control fields.
 The standard deviation of the derived zero-points was about Ay=| mag., The standard deviation of the derived zero-points was about $A_\mathrm{V} = 1$ mag.
 We note that such assessment was not possible for all clouds (or for numerous control fields for one cloud). since finding on-extineted control fields close to the complexes ts a problem in general.," We note that such assessment was not possible for all clouds (or for numerous control fields for one cloud), since finding non-extincted control fields close to the complexes is a problem in general."
 We consider the result of this experiment to be indicative of the zero-point uncertainty in our method., We consider the result of this experiment to be indicative of the zero-point uncertainty in our method.
 In the third and final step the extinction map was correctec for the contribution of foreground sources in the field., In the third and final step the extinction map was corrected for the contribution of foreground sources in the field.
 The identification (and removal) of foreground sources Is trivial i regions where the extinction is high compared to the scatter i the intrinsic colors of stars., The identification (and removal) of foreground sources is trivial in regions where the extinction is high compared to the scatter in the intrinsic colors of stars.
 The uncertainty of the extinctior determination for an individual source is approximately (Ay)x3 mag. so the sources that are located in a regio of intermediate local mean of extinction (9magxAy20mag mag) can be trivially removed.," The uncertainty of the extinction determination for an individual source is approximately $\sigma (A_\mathrm{V}^*) \approx 3$ mag, so the sources that are located in a region of intermediate local mean of extinction $ 9 \mathrm{\ mag}\lesssim A_\mathrm{V} \lesssim 20 \mathrm{\ mag}$ mag) can be trivially removed."
 The effect of foreground stars can be eliminated also at lower extinctions by estimating the surface number density of foreground objects from high Ay regions and subtracting the estimated contribution of the foreground population to the local mean colors., The effect of foreground stars can be eliminated also at lower extinctions by estimating the surface number density of foreground objects from high $A_\mathrm{V}$ regions and subtracting the estimated contribution of the foreground population to the local mean colors.
 This procedure is explained in the following., This procedure is explained in the following.
 We estimated the surface number density of the foreground population by examining the sources in regions where the local mean extinction is higher than Ay=6 mag (about 2-c error of an individual extinction measurement)., We estimated the surface number density of the foreground population by examining the sources in regions where the local mean extinction is higher than $A_\mathrm{V} \gtrsim 6$ mag (about $\sigma$ error of an individual extinction measurement).
 Fig., Fig.
 2 right panel illustrates this procedure by showing the frequency distributior of individual extinction measurements. Αν. towards such regions of the 38.94-00.46 complex where the local meat extinction is above Ay>6 mag.," \ref{fig:reffield} right panel illustrates this procedure by showing the frequency distribution of individual extinction measurements, $A_\mathrm{V}^*$, towards such regions of the 38.94-00.46 complex where the local mean extinction is above $A_\mathrm{V} > 6$ mag."
" Clearly. the foregrounc stars form a separate ""bump' in the distribution slightly below Ay=0 mag."," Clearly, the foreground stars form a separate 'bump' in the distribution slightly below $A_\mathrm{V} = 0$ mag."
 The surface number density of the foreground sources was estimated by fitting a Gaussian to this bump anc integrating the number of stars within it., The surface number density of the foreground sources was estimated by fitting a Gaussian to this bump and integrating the number of stars within it.
 In principle. it would be possible to use the determinec foreground source density to statistically subtract the foreground stars from the observed field down to Ay=0 mag.," In principle, it would be possible to use the determined foreground source density to statistically subtract the foreground stars from the observed field down to $A_\mathrm{V} = 0$ mag."
 In practice. however. doing this would impose an assumptior that all extinetion features are caused by a dust component at," In practice, however, doing this would impose an assumption that all extinction features are caused by a dust component at"
star bursts. these arguments duplv that the IMFE becomes top-heavy in star-bursts (cf. 7)).,"star bursts, these arguments imply that the IMF becomes top-heavy in star-bursts (cf. \citealt{weidner2010a}) )."
 This fincing stands in contrast to the prevaleut notion that the IME is invariant (7777) and thereby has iuportaut iuplicatious.," This finding stands in contrast to the prevalent notion that the IMF is invariant \citep{kroupa2001a,kroupa2002a,bastian2010a,kroupa2012a} and thereby has important implications."
 For mstance. estimates of the SFR of à galaxv based on observations that are sensitive ouly to hieliauass stars aud the assumption of an invariaut IME (like Equation 31)) are too high if the IME actually is op-heavy.," For instance, estimates of the SFR of a galaxy based on observations that are sensitive only to high-mass stars and the assumption of an invariant IMF (like Equation \ref{eq:SFR}) ) are too high if the IMF actually is top-heavy."
 Consequently. estimates for the time scale ou which the population of low-mass star in hat galaxy is built up until the eas of the galaxy is depleted become too short.," Consequently, estimates for the time scale on which the population of low-mass star in that galaxy is built up until the gas of the galaxy is depleted become too short."
 Also the chemical evolution of galaxies is different if the IAIF in hei can become top-heavy. since the nuclear reactions that occur in a star mainly depend on its mass.," Also the chemical evolution of galaxies is different if the IMF in them can become top-heavy, since the nuclear reactions that occur in a star mainly depend on its mass."
 This has maplicatious ou their coutent of netals and plauctary svstcms (2).., This has implications on their content of metals and planetary systems \citep{ghezzi2010a}.
 Furthermore. as niore dark renuinants are formed if the IMPE is op-heavy. more dark-reninant mergers and thus eravitationalwave cluitters should be detected iu his case.," Furthermore, as more dark remnants are formed if the IMF is top-heavy, more dark-remnant mergers and thus gravitational-wave emitters should be detected in this case."
 Finally. the dynamical evolution of star clusters critically depends ou the shape of the IME (?j..," Finally, the dynamical evolution of star clusters critically depends on the shape of the IMF \citep{dabringhausen2010a}."
 J.D acknowledges support through DFC-erant KR1635/13 and thanks ESO for financial support via a eraut from the Director Ceneral Discretionary Fund in 2009., J.D acknowledges support through DFG-grant KR1635/13 and thanks ESO for financial support via a grant from the Director General Discretionary Fund in 2009.
 The authors wish to thank To Maccarone for some uxcful comments., The authors wish to thank Tom Maccarone for some useful comments.
Be-Fe relation in stars with similar metallicities. ancl this may be the case for LP 815-43 as well.,"Be-Fe relation in stars with similar metallicities, and this may be the case for LP 815-43 as well."
 Israelianοἱal.(2004) analvzed nitrogen abundances in 31 metal-poor stars and found that both LP 815-48 and G 64-12 are more N rich Chan average., \citet{Israelian04} analyzed nitrogen abundances in 31 metal-poor stars and found that both LP 815-43 and G 64-12 are more N rich than average.
 The abundances of the relevant elements in these (wo stars are listed in Table 1.., The abundances of the relevant elements in these two stars are listed in Table \ref{tbl-obs}.
 We adopt the values obtained by 1-D LTE analyses to ensure consistency., We adopt the values obtained by 1-D LTE analyses to ensure consistency.
 Mevnetοἱal.(2006) simulated the evolution of metal-poor —6.6. —3.6) massive (60 M.) stus will rapid rotation (800 kin/s) and found Chat C is enhanced in the outer lavers bv rotation-nduced mixing. promoting intense stellar winds and significant loss of {heir envelopes in spite of their initial low metallicities.," \citet{Meynet06} simulated the evolution of metal-poor $-6.6$, $-3.6$ ) massive $60 \Msun$ ) stars with rapid rotation (800 km/s) and found that C is enhanced in the outer layers by rotation-induced mixing, promoting intense stellar winds and significant loss of their envelopes in spite of their initial low metallicities."
 At the same time. the mixing results in enrichment of N in the Ie lavers.," At the same time, the mixing results in enrichment of N in the He layers."
 [fa fraction of the He laver is still remaining when the SN explodes. it is expected that the N within is accelerated at the shock breakout. aud a significant amount of Be will be produced through the reaction N+He—°Be. thanks to its low threshold and high cross section al peak.," If a fraction of the He layer is still remaining when the SN explodes, it is expected that the N within is accelerated at the shock breakout, and a significant amount of Be will be produced through the reaction ${\rm N + He} \rightarrow {\rm ^9Be}$, thanks to its low threshold and high cross section at peak."
 Thus. we consicer stars (hat have lost all of their HE laver and most of their He/N laver before the explosion.," Thus, we consider stars that have lost all of their H layer and most of their He/N layer before the explosion."
 Ilere we use an explosion model of a 15M. core. originating [rom a main-sequence star will mass Mj~40AL. (Nakamuraοἱal.2001)..," Here we use an explosion model of a $\sim 15 \Msun$ core, originating from a main-sequence star with mass $M_{\rm ms} \sim 40 \Msun$ \citep{Nakamura01}."
 The explosion energy is assumed (o be 3x107? eres. corresponding lo an energetic explosion similar to SN 1998bw.," The explosion energy is assumed to be $3 \times 10^{52}$ ergs, corresponding to an energetic explosion similar to SN 1998bw."
 The mass of the ejecta becomes 13.M... containing LOM. of oxvgen.," The mass of the ejecta becomes $13 \Msun$, containing $10 \Msun$ of oxygen."
 The accelerated ejecta consisting of He and CNO will collide with the circumstellar Heand N stripped from the progenitor star and produce LiBeb through the reactions He.CNO+N— 116.," The accelerated ejecta consisting of He and CNO will collide with the circumstellar Heand N stripped from the progenitor star and produce LiBeB through the reactions ${\rm He,CNO} + {\rm He, N} \rightarrow {\rm LiBeB}$ ."
 The energy distribution of the C/O ejecta belore interaction is that caleulated in Nakannmra&Shigevama(2004).. shown in Figure together with the cross sections for selected reactions (Reacl&Viola1934:Mercer 2001).," The energy distribution of the C/O ejecta before interaction is that calculated in \citet{Nakamura04}, shown in Figure \ref{fig-Ecs} together with the cross sections for selected reactions \citep{Read84, Mercer01}."
. Rather than recaleulating the explosion Lywdrodvnamics with (the added IHe/N laver. we approximate by changing the composition of (he accelerated outermost ejecta from C/O to He/N. This will not lead to considerable errors as long as the replaced mass is small.," Rather than recalculating the explosion hydrodynamics with the added He/N layer, we approximate by changing the composition of the accelerated outermost ejecta from C/O to He/N. This will not lead to considerable errors as long as the replaced mass is small."
" The ""thick target"" approximation is used. that is. the cireumstellar He is so thick that light element production occurs entirely within the CSM while (he ejecta particles lose energy mainlv by Coulomb collisions with Iree electrons."," The “thick target"" approximation is used, that is, the circumstellar He is so thick that light element production occurs entirely within the CSM while the ejecta particles lose energy mainly by Coulomb collisions with free electrons."
 This assumption is valid when the mass logs rate M is ereater (han 10°AL. | for the tvpical wind velocity of ey. 01.000. kin las can be seen by comparing the windblown material's mass columndensitv o with the," This assumption is valid when the mass loss rate $\dot{M}$ is greater than $10^{-6}\,M_\odot$ $^{-1}$ for the typical wind velocity of $v_{\rm w} \sim$ 1,000 km $^{-1}$ , as can be seen by comparing the windblown material's mass columndensity $\sigma$ with the"
was determined using D aud V magnitudes frou Tycho-2 as standards with the approximation The color slope term. s=0.15. was derived from linear fits to sample CCD data with many refercuce stars and solving for both the slope and coustant term.,"was determined using B and V magnitudes from Tycho-2 as standards with the approximation The color slope term, $s = 0.45$, was derived from linear fits to sample CCD data with many reference stars and solving for both the slope and constant term."
 The average resulting slope term was adopted aud used to solve only for the photometric zero-point coustaut in all R-baud CCD frames., The average resulting slope term was adopted and used to solve only for the photometric zero-point constant in all R-band CCD frames.
 Fie., Fig.
 8 shows the distribution of the standard error of this photometric constant., 8 shows the distribution of the standard error of this photometric constant.
" For most Bones this error is 20 to. £0 πάπας,", For most frames this error is 20 to 40 millimag.
 The absolute photometric error of stars in the BSCC has to be ]lurger than this photometric coustaut error. while the internal. photometric precision is better for well exposed stars.," The absolute photometric error of stars in the BSCC has to be larger than this photometric constant error, while the internal, photometric precision is better for well exposed stars."
 The BSCC coutaiius 13.771.775 stars north of |19.67 declination aud is sorted by declination.," The BSCC contains 13,771,775 stars north of $+49.6^{\circ}$ declination and is sorted by declination."
 Of these. 13.157.292 do have aanatch with a 2\TASS star within 2 arcsec. aud J. IT. IK; photometry with errors were copied from the 2MÁSS iuto DSC'C.," Of these, 13,157,292 do have a match with a 2MASS star within 2 arcsec, and J, H, $_{s}$ photometry with errors were copied from the 2MASS into BSCC."
 Stars based on a single CCD observation aud not matched with 2ATASS did uot euter the released catalog., Stars based on a single CCD observation and not matched with 2MASS did not enter the released catalog.
 Fig., Fig.
 9 shows the distribution of stars in the BSCC by B and V inaeuitucle., 9 shows the distribution of stars in the BSCC by R and V magnitude.
 Coupleteness is expected up to about R = 17.5 with a limiting magnitude of about R = 19., Completeness is expected up to about R = 17.5 with a limiting magnitude of about R = 19.
 There are 583.013 stars in the catalog without BR maeuitude. and 1.311.081 do not have a V magnitude.," There are 583,043 stars in the catalog without R magnitude, and 4,311,081 do not have a V magnitude."
 The BSCC data file is 1.7 GB. formatted. ASCIL," The BSCC data file is 1.7 GB, formatted, ASCII."
 Some sample lines are Listed in Table l. with the data format explained in Table 2.," Some sample lines are listed in Table 1, with the data format explained in Table 2."
 This is an observational catalog of mean positions at a mean epoch. which is sliehtlv differcut for cach star.," This is an observational catalog of mean positions at a mean epoch, which is slightly different for each star."
" The positions are ou the Iuternational Celestial Reference. System, (CRS) by mcaus of the Tycho-2 reference star catalog.", The positions are on the International Celestial Reference System (ICRS) by means of the Tycho-2 reference star catalog.
 There are no proper motions provided., There are no proper motions provided.
 Stars are identified by the IAU registered. acrouvin BSCC. followed by a fxed-leugth. S-dieit running record ΙΟ without a space.," Stars are identified by the IAU registered acronym ""BSCC"", followed by a fixed-length, 8-digit running record number without a space."
 Fie., Fig.
 10 shows the mean astrometric errors (per coordinate] of the BSCC as a fiction of Ro inaguitude., 10 shows the mean astrometric errors (per coordinate) of the BSCC as a function of R magnitude.
 The filled circles show the errors as derived from the aocdel Gucluding ον fit precision and expected coutribution from the “plate” adjustinent solution). wlile the open squares show the error from the observed scatter of individual positions.," The filled circles show the errors as derived from the model (including $x,y$ fit precision and expected contribution from the “plate"" adjustment solution), while the open squares show the error from the observed scatter of individual positions."
 These are small umber statistics for individual stars (with typically 2 to timages) but become meaningful when averaged over mnanv stars (for the R = 9 range)., These are small number statistics for individual stars (with typically 2 to 4 images) but become meaningful when averaged over many stars (for the R $\ge$ 9 range).
 Many stars in the 10 to 15 mae range have internal errors of about 20 mas in Dec and about 25 mas in RÀ., Many stars in the 10 to 15 mag range have internal errors of about 20 mas in Dec and about 25 mas in RA.
 A near saturation effect secius to be preseut for stars brighter than R = 11 mae showing a slightly lareer. observed. scatter error than at R = 11 ag.," A near saturation effect seems to be present for stars brighter than R = 11 mag showing a slightly larger, observed, scatter error than at R = 11 mag."
 Fie., Fig.
 11 shows the formal. photometric errors iu the BSCC R aud V imaenitudes derived frou the scatter of individual magnitudes.," 11 shows the formal, photometric errors in the BSCC R and V magnitudes derived from the scatter of individual magnitudes."
 Data shown for stars brighter than about 9th mag are affected by simil umber statistics., Data shown for stars brighter than about 9th mag are affected by small number statistics.
 Systematic errors are not included here., Systematic errors are not included here.
 The precision of the photometry is ou the 3 to 5 level for the 10 to 15 mae raugc. then increasingC» accordingC» to the lower sieual-to-noise ratio to about 0.15 mag at R = I8.," The precision of the photometry is on the 3 to 5 level for the 10 to 15 mag range, then increasing according to the lower signal-to-noise ratio to about 0.15 mag at R = 18."
 Uinweighted position differcuces of BSCC minus Tyceho-2. averaged over 100 stars per dot are shown in Fie.," Unweighted position differences of BSCC minus Tycho-2, averaged over 100 stars per dot are shown in Fig."
 12 as a function of magnitude., 12 as a function of magnitude.
 Tvcho-2 proper niofions lave been applied to bring the positions to the epoch of individual BSCC stars., Tycho-2 proper motions have been applied to bring the positions to the epoch of individual BSCC stars.
 The small overall offset ii declination is caused by the weighted adjustineut in the CCD reductions of individual frames combined with the magnitude dependent pattern shown in Fie., The small overall offset in declination is caused by the weighted adjustment in the CCD reductions of individual frames combined with the magnitude dependent pattern shown in Fig.
 6., 6.
 The differences in RA average to about zero. as expected.," The differences in RA average to about zero, as expected."
 Position differences of BSCC with respect to 2ATASS are shown in Fig., Position differences of BSCC with respect to 2MASS are shown in Fig.
 13., 13.
 No proper motions have heen applied because neither the 2MLASS nor the DSCC€ do have proper motions., No proper motions have been applied because neither the 2MASS nor the BSCC do have proper motions.
 The epoch difference between individual DSCC and. 221ASS observations of a star is within + 3 vears., The epoch difference between individual BSCC and 2MASS observations of a star is within $\pm$ 3 years.
 Over 1l anillion stars were matched., Over 11 million stars were matched.
 There is a siall systematic difference along RA increasing toward faint stars reaching about 30 mas at R=Ls. while for Dec there is a remarkable cousisteucv between the DSCC aud 2ATASS data with oulv about 1 mas differenees at the very faint cud at R=18 aud systematic differences less than about 5 mas for," There is a small systematic difference along RA increasing toward faint stars reaching about 30 mas at R=18, while for Dec there is a remarkable consistency between the BSCC and 2MASS data with only about 10 mas differences at the very faint end at R=18 and systematic differences less than about 5 mas for"
listed in the (Vhompson et al.,listed in the (Thompson et al.
 1978) provided a good guide [ον selecting targets wilh satisfactory brightness levels., 1978) provided a good guide for selecting targets with satisfactory brightness levels.
" To increase (he chance that the C I features arose from truly intervening material rather than cireumstellar disks or shells around the target stars. the survey did not include candidates Chat had spectral (vpes will an emission-line ""e designation (Llolfleit Jaschek 1982: Slettebak 1932) or an excess IRAS flux at μην relative to the normal expectation."," To increase the chance that the C I features arose from truly intervening material rather than circumstellar disks or shells around the target stars, the survey did not include candidates that had spectral types with an emission-line “e” designation (Hoffleit Jaschek 1982; Slettebak 1982) or an excess IRAS flux at $12\mu$ m relative to the normal expectation."
 Short-period binaries were also rejected. since they. could have interacting gas streams.," Short-period binaries were also rejected, since they could have interacting gas streams."
 As a final precaution against skewing the results with cases dominated by gaseous material verv near the stars. there was an exclusion of targets that had excess diffuse infrared enussion nearby in (he sky (Gaustad Van Buren 1993). signilving the possible presence of dust grains being heated by the star.," As a final precaution against skewing the results with cases dominated by gaseous material very near the stars, there was an exclusion of targets that had excess diffuse infrared emission nearby in the sky (Gaustad Van Buren 1993), signifying the possible presence of dust grains being heated by the star."
 Four stars that were ultimately. chosen for the survey are listed in Table 1.., Four stars that were ultimately chosen for the survey are listed in Table \ref{target_stars}.
 Their locations with respect to the Local Bubble boundaries mapped by Sfeir οἱ al. (, Their locations with respect to the Local Bubble boundaries mapped by Sfeir et al. (
1999) are shownin Figure 1..,1999) are shownin Figure \ref{sfeirplt}. .
each olo w four QSO fields.,each of our four QSO fields.
 Star IDs are the june as those in PAM and. ALP. for the corresponcdit [ielcS.," Star IDs are the same as those in PAM and ALP, for the corresponding fields."
 Tle PM tucertainties correspoud to the error in the determination of the slope of the liue., The PM uncertainties correspond to the error in the determination of the slope of the best-fit line.
 |ispectior ol these tables shows that the PM uncertainty of most of the refereuce stars 1 COLLparable to. or ‘eer than. their derived PAL value. implying that these PM do uot represei internal motions i ie LNC.," Inspection of these tables shows that the PM uncertainty of most of the reference stars is comparable to, or larger than, their derived PM value, implying that these PM do not represent internal motions in the LMC."
 In Fieure ] we pesent the PM maps fo‘the reerence stars listed in Tables 3-6., In Figure 1 we present the PM maps for the reference stars listed in Tables 3-6.
 The dispersio1 around the mez uidur edou to be 40.3I. 0.79. 0.5L. and 40.0) mas | in RwA.. and ).52. 0.71. 0.58. 0.63 las in Deel.," The dispersion around the mean turned out to be $\pm$ 0.34, $\pm$ 0.79, $\pm$ 0.54, and $\pm$ 0.41 mas $^{-1}$ in R.A., and $\pm$ 0.52, $\pm$ 0.71, $\pm$ 0.58, $\pm$ 0.62 mas $^{-1}$ in Decl.,"
 fo: Q0159-6127. Q0557-6713. Q0558-6707 aud Q0615-6612. -'espectively.," for Q0459-6427, Q0557-6713, Q0558-6707 and Q0615-6615, respectively."
" Bzwed o1 the above argument. the scatter seen in the plots probably stems eitirely ‘om the randoLL erro ""ln he measturemeus. aud does not rep'esent the actal velocity dispersion ---1 the LMC."," Based on the above argument, the scatter seen in the plots probably stems entirely from the random errors in the measurements, and does not represent the actual velocity dispersion in the LMC."
 In Figure 32 we p‘esell| position es. e»och diagrams for the QSO fields i1 R.A. (AXacosd) an Decl., In Figure 2 we present position $vs.$ epoch diagrams for the QSO fields in R.A. $\Delta\alpha$ $\delta$ ) and Decl.
 (.N8). were Aac ‘osd aud Ad represent tlie positious of the QSOs on «|ferent CCD fralies. 'elative to the baryceuer of the SRE.," $\Delta\delta$ ), were $\Delta\alpha$ $\delta$ and $\Delta\delta$ represent the positions of the QSOs on different CCD frames, relative to the barycenter of the SRF."
 These cdiagraiis were constructed usi© individual posilior cata or the QSO in e:wh CCD image as a function of epoch., These diagrams were constructed using individual position data for the QSO in each CCD image as a function of epoch.
 Iu Table 7 we give. for each epoch. the neal. barycentric positious of the QSOs aloug with heir mean errors. the 1lnyer of points sec o caleulate the meat for each coordinate. αμα the €‘CD detectors used.," In Table 7 we give, for each epoch, the mean barycentric positions of the QSOs along with their mean errors, the number of points used to calculate the mean for each coordinate, and the CCD detectors used."
 ΟΥο| sizes in Figure 2 are proportional to tl enuuber of times the measureuents vielded the same coo‘inate value for a »articular epoch., Symbol sizes in Figure 2 are proportional to the number of times the measurements yielded the same coordinate value for a particular epoch.
 The bes-[it straight lines resulting from sitiple linear regression analysis oL the data points are also sLOWL., The best-fit straight lines resulting from simple linear regression analysis on the data points are also shown.
 The negative values of te line sk)pes correspoud to tle measwed PM oL the barycenter of tve LAS. in each QSO field. relative to the SRE.," The negative values of the line slopes correspond to the measured PM of the barycenter of the LRS, in each QSO field, relative to the SRF."
 Tabe 8 πιαίσος ow results for the measure PAL of te LMC., Table 8 summarizes our results for the measured PM of the LMC.
 Column (1) gives tle (quasar ilentification. colum lo aud (3) the R.A. aid Decl.," Column (1) gives the quasar identification, columns (2) and (3) the R.A. and Decl."
 comj»ouenuts of the LNC's PAM (togetlier with their standard «eviaious) respectively. aid. fiially. columns (1). (5) and (6) the uunber of frames. the number o .epochs. and the observation period. respectively.," components of the LMC's PM (together with their standard deviations) respectively, and, finally, columns (4), (5) and (6) the number of frames, the number of epochs, and the observation period, respectively."
 It should be noted that the rather siiall quoted errors for the PM. come ott directly. [ro1 what the least-square fit. vields as the uuce‘tainty in the determination of the slope of the best it liue., It should be noted that the rather small quoted errors for the PM come out directly from what the least-square fit yields as the uncertainty in the determination of the slope of the best fit line.
 Tk1dle 9 lists the 'esults of all available measurements of the LNC's PA haviug uncertainties s1ualler that l mas 1 in both components. as well as the reference system used iu each case.," Table 9 lists the results of all available measurements of the LMC's PM having uncertainties smaller than 1 mas $^{-1}$ in both components, as well as the reference system used in each case."
" With tle exception of hose cases noted as ""Field"" in the first columu. all the PM listed in Table 9 are relaive o the LNC""s center."," With the exception of those cases noted as ""Field"" in the first column, all the PM listed in Table 9 are relative to the LMC's center."
 To facilitate comparisons. we present our current results in both ways.," To facilitate comparisons, we present our current results in both ways."
 As exjxlained in he next section. our PM. values relative to the ΓΕΛΙΟs center were obtained correctiu[n]) l1e field PA for the rotation of the plaue of the LMC.," As explained in the next section, our PM values relative to the LMC's center were obtained correcting the field PM for the rotation of the plane of the LMC."
 Ou ‘results are in reasonable agreement with most of the available data., Our results are in reasonable agreement with most of the available data.
 They agree particularly well with those of Ire)ipa et al. (, They agree particularly well with those of Kroupa et al. (
199D). who used the Positions aud Proper Motious Star Catalog,"1994), who used the Positions and Proper Motions Star Catalog"
‘The integral diameter clistribution of rregions in spiral galaxies usually follows an exponential law: with ΑοςD) the total number of rregions with clameters larger than D (van den ουσ 1981: Lloclge 1987: Ye 1992).,The integral diameter distribution of regions in spiral galaxies usually follows an exponential law: with $N(>D)$ the total number of regions with diameters larger than $D$ (van den Bergh 1981; Hodge 1987; Ye 1992).
 Ehe slope of the diameter distribution is correlated with the luminosity of the galaxy (Mlodge LOST: see also Rozas et al., The slope of the diameter distribution is correlated with the luminosity of the galaxy (Hodge 1987; see also Rozas et al.
 1996b). and the slopes tend to be steeper for rregions located. between the spiral arms than for those within them in the few cases where this has been explicitly stuclicd (Hodge 1987: IXnapen et al.," 1996b), and the slopes tend to be steeper for regions located between the spiral arms than for those within them in the few cases where this has been explicitly studied (Hodge 1987; Knapen et al."
 1993a)., 1993a).
 The integral diameter distribution of the rregions in the disc of MIOO is shown in Fig., The integral diameter distribution of the regions in the disc of M100 is shown in Fig.
 7. (full dots)., \ref{diams} (full dots).
 Apart from the first point. and the last three points in the Figure. the data are fitted very well with an exponential of the type described above.," Apart from the first point, and the last three points in the Figure, the data are fitted very well with an exponential of the type described above."
 As usual. the fit to the data points is indicated. in the Figure.," As usual, the fit to the data points is indicated in the Figure."
 | also show integral diameter distributions for the rregions in the CNR. (opencircles in Fig. 7)).," I also show integral diameter distributions for the regions in the CNR (opencircles in Fig. \ref{diams}) ),"
 and in the arm and interarm areas of the disc separately (Eig. S))., and in the arm and interarm areas of the disc separately (Fig. \ref{aiadiams}) ).
 In all cases the data points can be well fitted with an exponential of the type described above., In all cases the data points can be well fitted with an exponential of the type described above.
 The fitted. values to the slopes are Dy= T42pc and No=(4210.31)1Y for the whole disc. 48+ 2pc ancl (0.66+0.08)10* for the CNR. rregions only. and τὸ+ 2pe and (2.52£0.19). 10%: and," The fitted values to the slopes are $D_0=74\pm2$ pc and $N_0=(4.27\pm0.37)\times10^3$ for the whole disc, $48\pm2$ pc and $(0.66\pm0.08)\times10^3$ for the CNR regions only, and $78\pm2$ pc and $(2.52\pm0.19)\times10^3$ ; and"
If there are clumps of higher densities within the haloes. however. this estimate of the density will likely be too low.,"If there are clumps of higher densities within the haloes, however, this estimate of the density will likely be too low."
 Then. because the gas can cool faster at. higher densities. due to the more rapid formation of HH» and HD molecules. the cooling times shown in Fig.," Then, because the gas can cool faster at higher densities, due to the more rapid formation of $_2$ and HD molecules, the cooling times shown in Fig."
 5 may be overestimates for high density clumps within haloes., 5 may be overestimates for high density clumps within haloes.
 The initial post-shock fractional ionization of the various chemical species composing the gas were taken from Shapiro & Ixang (1987) and Wane & Shapiro (1992). for the cases of shock velocities of 20. 30. 50. and 100 km sf.," The initial post-shock fractional ionization of the various chemical species composing the gas were taken from Shapiro $\&$ Kang (1987) and Kang $\&$ Shapiro (1992), for the cases of shock velocities of 20, 30, 50, and 100 km $^{-1}$."
 As deuterium was not treated in this earlier work. we take it that the fractional abundances of D. and LD are reduced. from those of LI. and Ho. respectively. by a factor of the cosmic abundance of deuterium. taken to be ~ 4. 10°.," As deuterium was not treated in this earlier work, we take it that the fractional abundances of D, $^+$, and HD are reduced from those of H, $^+$, and $_2$, respectively, by a factor of the cosmic abundance of deuterium, taken to be $\sim$ 4 $\times$ $^{-5}$."
 As was demonstrated by Shapiro & Wang (1987). even at shock velocities Ἑ 100 km which characterize the collapse of DAL haloes at redshifts 2 2 10. enough out-of-equilibrium. formation of molecular hydrogen takes place that the gas cancool to S LOO Ix within the age of the Universe. at high enough. redshift (see also Murray & Lin 1990).," As was demonstrated by Shapiro $\&$ Kang (1987), even at shock velocities $\la$ 100 km $^{-1}$, which characterize the collapse of DM haloes at redshifts $z$ $\ga$ 10, enough out-of-equilibrium formation of molecular hydrogen takes place that the gas cancool to $\la$ 100 K within the age of the Universe, at high enough redshift (see also Murray $\&$ Lin 1990)."
 Phat I» elliciently cools the eas behind these shocks is also shown in Fig., That $_2$ efficiently cools the gas behind these shocks is also shown in Fig.
 5. where the temperature of the primordial gas does indeed fall to  100 Ix within a Llubble time.," 5, where the temperature of the primordial gas does indeed fall to $\sim$ 100 K within a Hubble time."
 The abundance of HD at low temperatures (z; 100 Ix) [or the case of shocks due to DM halo collapse is found to be of the same order as that found for the SN case. that is Nup < 10 again well above the minimum necessary [or cllicient LID cooling.," The abundance of HD at low temperatures $\la$ 100 K) for the case of shocks due to DM halo collapse is found to be of the same order as that found for the SN case, that is $X_{\rm HD}$ $\ga$ $^{-6}$, again well above the minimum necessary for efficient HD cooling."
 Minihaloes. with masses of the order of LOPAL.. merge at velocities too low to strongly shock or ionize the primordial eas they contain. as can be seen from Fig.," Minihaloes, with masses of the order of $10^6 {\rmn M}_{\odot}$, merge at velocities too low to strongly shock or ionize the primordial gas they contain, as can be seen from Fig."
 4., 4.
 Haloes of such low mass collide at. velocities of only a [ον kilometers per second. which are not high enough to ionize the hydrogen inside the haloes. and so are not high enough to allow significant [ree electron-catalvzed formation of molecules to take place.," Haloes of such low mass collide at velocities of only a few kilometers per second, which are not high enough to ionize the hydrogen inside the haloes, and so are not high enough to allow significant free electron-catalyzed formation of molecules to take place."
 Thus. the gas in minihaloes is expected to remain largely. un-ionizecl and with only the primordial fractions of 1I» ancl LED until the formation of the first stars within them.," Thus, the gas in minihaloes is expected to remain largely un-ionized and with only the primordial fractions of $_2$ and HD until the formation of the first stars within them."
 Without the large fractions of HD formed in shocked. ionized primordial gas. the gas from which the first stars formed in minihaloes at redshifts of 2&20 could not cool below ~200 Ix. and thus the first stars were likely very massive (Bromm et al.," Without the large fractions of HD formed in shocked, ionized primordial gas, the gas from which the first stars formed in minihaloes at redshifts of $z\ga 20$ could not cool below $\sim 200$ K, and thus the first stars were likely very massive (Bromm et al."
 1999. 2002).," 1999, 2002)."
 Fie., Fig.
" 6 shows the thermal evolution of unshocked gas of primordial composition with an initial ionization fraction of te = n 7owhich. collapses uncer its. own gravity.. its. density. evolving according to dnd!=η νε where n is the number density of the eas and fy, is the free-fall time. given by"," 6 shows the thermal evolution of unshocked gas of primordial composition with an initial ionization fraction of $x_{\rmn e}$ = $^{-4}$ which collapses under its own gravity, its density evolving according to $dn/dt = n/t_{\rmn ff}$ , where $n$ is the number density of the gas and $t_{\rmn ff}$ is the free-fall time, given by"
The H-band light curve has not been fitted. because of insufficient sampling.,"The $H$ -band light curve has not been fitted, because of insufficient sampling."
 The H-band upper limit would suggest a much steeper decay than observed in the other bands., The $H$ -band upper limit would suggest a much steeper decay than observed in the other bands.
 Although we have no reason to believe that the upper limit ts not reliable. owing to the scarcity of measurements in this band we do not speculate about this faster decay.," Although we have no reason to believe that the upper limit is not reliable, owing to the scarcity of measurements in this band we do not speculate about this faster decay."
 To study the broadband spectral variability of the afterglow. we subtracted the host galaxy spectrum from the observed fluxes in optical and NIR bands at five epochs after the GRB. at which the sampling has the widest spectral coverage.," To study the broadband spectral variability of the afterglow, we subtracted the host galaxy spectrum from the observed fluxes in optical and NIR bands at five epochs after the GRB, at which the sampling has the widest spectral coverage."
 In the cases ia which the data in different bands were not simultaneous. the flux density was interpolated to the reference epoch by using the best-fit power-law decay « = 1.48.," In the cases in which the data in different bands were not simultaneous, the flux density was interpolated to the reference epoch by using the best-fit power-law decay $\alpha$ = 1.48."
 Magnitudes \vere corrected for Galactic reddening and converted into flux censities following the procedure already described., Magnitudes were corrected for Galactic reddening and converted into flux densities following the procedure already described.
 The simultaneous afterglow SFDs thus obtained. not further corrected for the intrinsic extinction. within the host galaxy. are reported in Fig.," The simultaneous afterglow SFDs thus obtained, not further corrected for the intrinsic extinction within the host galaxy, are reported in Fig."
 6., 6.
 Despite the uncertainties (due to the rather large errors on the host galaxy flux densities). a spectral steepening with time is suggested.," Despite the uncertainties (due to the rather large errors on the host galaxy flux densities), a spectral steepening with time is suggested."
 Assuming a spectrum F(v)«v? for all epochs. the V—R color at 1.4 days after the GRB implies a spectral slope f = —0.7734.," Assuming a spectrum $F(\nu) \propto \nu^{-\beta}$ for all epochs, the $V-R$ color at 1.4 days after the GRB implies a spectral slope $\beta$ = $-$ $^{+3.4}_{-3.2}$."
 A fit to the broad-band optical/NIR SFDs at the following 4 epochs yields p = 0.8x1.3 (5.03 days after GRB000911). 8 = 1.10.3 (10.94 days).B = 1.041.2 (16.90 days) and6 = 1.940.7 (25.00 days).," A fit to the broad-band optical/NIR SFDs at the following 4 epochs yields $\beta$ = $\pm$ 1.3 (5.03 days after GRB000911), $\beta$ = $\pm$ 0.3 (10.94 days), $\beta$ = $\pm$ 1.2 (16.90 days) and $\beta$ = $\pm$ 0.7 (25.00 days)."
 The results obtained for the epochs between ~5 and «17 days after the GRB trigger are broadly consistent with those derivec by Lazzati et al. (, The results obtained for the epochs between $\sim$ 5 and $\sim$ 17 days after the GRB trigger are broadly consistent with those derived by Lazzati et al. (
2001).,2001).
 We remark that the huge errors on the value of B referring to the first epoch (September 12.74) are due to two effects: the moderately large uncertainties (0.1 mag) oi the magnitudes and the very narrow (~0.1 dex) SFD baseline., We remark that the huge errors on the value of $\beta$ referring to the first epoch (September 12.74) are due to two effects: the moderately large uncertainties $\sim$ 0.1 mag) on the magnitudes and the very narrow $\sim$ 0.1 dex) SFD baseline.
 If we correct the afterglow data for the absorption. às derived from the best fits of the host galaxy SFD. we obtain for the OT the spectral slopes 8 = —1.323.3. 0.21.3. 0.60.3. 1.2 and 1.30.7 at the 5 considered epochs.," If we correct the afterglow data for the absorption as derived from the best fits of the host galaxy SFD, we obtain for the OT the spectral slopes $\beta$ = $-$ $\pm$ 3.3, $\pm$ 1.3, $\pm$ 0.3, $\pm$ 1.2 and $\pm$ 0.7 at the 5 considered epochs."
 No substantial difference is found among the considered reddening laws (Stb. SMC and LMC: see also Kann 2004).," No substantial difference is found among the considered reddening laws (Stb, SMC and LMC; see also Kann 2004)."
 Our late-time observational campaign on GRBOOO911] has allowed us. for the first time. to directly observe and thus extract important information on its host galaxy: this in. turn has helped us to better model the shape and evolution of the light curves and SFDs of the GRBOOO911 afterglow in the optical/NIR domain.," Our late-time observational campaign on GRB000911 has allowed us, for the first time, to directly observe and thus extract important information on its host galaxy; this in turn has helped us to better model the shape and evolution of the light curves and SFDs of the GRB000911 afterglow in the optical/NIR domain."
 In the following we discuss the results obtained on each of these three issues., In the following we discuss the results obtained on each of these three issues.
 The temporal decay index of the afterglow of this GRB is consistent with the decline being wavelength-independent., The temporal decay index of the afterglow of this GRB is consistent with the decline being wavelength-independent.
 In the first week. the spectral slope B~| (assuming no intrinsic absorption local to the host). combined with the average temporal index a~1.5. is consistent with a spherical fireball expansion into a constant-density circumburst medium under the hypothesis that the cooling break frequency of the synchrotron radiation. νο. is above the optical range (Sari et al.," In the first week, the spectral slope $\beta \sim 1$ (assuming no intrinsic absorption local to the host), combined with the average temporal index $\alpha \sim 1.5$, is consistent with a spherical fireball expansion into a constant-density circumburst medium under the hypothesis that the cooling break frequency of the synchrotron radiation, $\nu_{\rm c}$, is above the optical range (Sari et al."
 1998)., 1998).
 This implies an electron energy distribution index p~ 3. to be compared with the range 2—2.5 found for the p values of GRBs studied by Frontera et al. (," This implies an electron energy distribution index $p\sim$ 3, to be compared with the range 2–2.5 found for the $p$ values of GRBs studied by Frontera et al. ("
2000).,2000).
 It should however be remarked that Masetti et al. (, It should however be remarked that Masetti et al. (
2000) suggested that p> 2.6 for the afterglow of GRB990705.,2000) suggested that $p >$ 2.6 for the afterglow of GRB990705.
 Unfortunately. the lack of information concerning the high-energy afterglow of GRBOO00911 does not allow us to explore in detail more complex models for the fireball expansion.," Unfortunately, the lack of information concerning the high-energy afterglow of GRB000911 does not allow us to explore in detail more complex models for the fireball expansion."
 Price et al. (, Price et al. (
2002). assuming that a light curve break due to collimated emission (as described in Sari et al.,"2002), assuming that a light curve break due to collimated emission (as described in Sari et al."
 1999) occurred ~1 day after the GRBO0091I onset. derived p = 1.5.," 1999) occurred $\sim$ 1 day after the GRB000911 onset, derived $p$ = 1.5."
 The spectral index at 25 days after the GRB. -1.9. is again not supportive of a jet geometry of the afterglow emission in the classical collimated fireball scenario (Sari et al.," The spectral index at 25 days after the GRB, $\beta \sim 1.9$, is again not supportive of a jet geometry of the afterglow emission in the classical collimated fireball scenario (Sari et al."
 1999). unless the light curve changes slope at late epochs. possibly implying a more significant supernova contribution.," 1999), unless the light curve changes slope at late epochs, possibly implying a more significant supernova contribution."
 The data are not sufficient to test a change of temporal slope of the afterglow., The data are not sufficient to test a change of temporal slope of the afterglow.
 A collimated fireball before the jet break (Sari et al., A collimated fireball before the jet break (Sari et al.
 1999; Rhoads 1999) and an isotropic fireball (Sart et al., 1999; Rhoads 1999) and an isotropic fireball (Sari et al.
 1998) are, 1998) are
"The bulk of the neutral gas in the Universe is contain in clouds of highest. column density. Ng;721o?"" 7. the dampec (DLA) absorbers.","The bulk of the neutral gas in the Universe is contained in clouds of highest column density, ${\mathrm N_{HI}}>2\times 10^{20}$ $^{-2}$, the damped (DLA) absorbers."
 Phe incidence of these objects with dillerent Ng; in the spectra. of background. quasars allows one to determine the comoving densitv of neutral gas as a function. of recshilt or time., The incidence of these objects with different ${\mathrm N_{HI}}$ in the spectra of background quasars allows one to determine the comoving density of neutral gas as a function of redshift or time.
 Atos8m 23 this density was roughly equal to the presen comoving density. of luminous stars., At $z\approx$ 2–3 this density was roughly equal to the present comoving density of luminous stars.
 This observation has lec to the standard. interpretation of the DLA absorbers as the gas reservoirs from which stars form. Le. as the interstellar components of galaxies and protogalaxics (Wolfe et al.," This observation has led to the standard interpretation of the DLA absorbers as the gas reservoirs from which stars form, i.e., as the interstellar components of galaxies and protogalaxies (Wolfe et al."
 1986)., 1986).
 This interpretation is supported: by global studies of chemical evolution. which relate the evolution of the comoving densities of stars. gas. heavy elements. and dust in galaxies (Pei. Fall. Llauser. 1999).," This interpretation is supported by global studies of chemical evolution, which relate the evolution of the comoving densities of stars, gas, heavy elements, and dust in galaxies (Pei, Fall, Hauser 1999)."
 This. &lobal approach. however. tells us nothing about the properties of individual DLA galaxies. such as their luminosities. sizes. and morphologies.," This global approach, however, tells us nothing about the properties of individual DLA galaxies, such as their luminosities, sizes, and morphologies."
 Deep imaging is needed to detect anc characterize the stellar components of individual DLA galaxies., Deep imaging is needed to detect and characterize the stellar components of individual DLA galaxies.
 This would also. provide impact parameters for absorption. which. from the measured incidence πας. would allow the caleulation of the space density (Aloller Warren 1998).," This would also provide impact parameters for absorption, which, from the measured incidence $dn/dz$, would allow the calculation of the space density ller Warren 1998)."
 The combination of information on both the stellar, The combination of information on both the stellar
he probability to reach a linear density thresholdὃν (associated with the formation of virialized halos of ionliuear deusitv contrast 04).,the probability to reach a linear density threshold$\deltaLs$ (associated with the formation of virialized halos of nonlinear density contrast $\deltas$ ).
" As ij 7.. we uprove his iuocl by takine iuto account the motion of ialos. associated with the chanee from Laeraugian to Eulerian space νο, frou the linear density feld to the actual uoiliσαjcar density field)."," As in \citet{Valageas2009d}, we improve this model by taking into account the motion of halos, associated with the change from Lagrangian to Eulerian space (i.e., from the linear density field to the actual nonlinear density field)."
 Ilowever. we sinality the oyescriptiou used in ? as wel aid aa collapse 1iodel to estimae these displacements but use the iuitial momenta of both alos (.¢.. the linear displacement field).," However, we simplify the prescription used in \citet{Valageas2009d} as we no longer use a spherical collapse model to estimate these displacements but use the initial momenta of both halos (i.e., the linear displacement field)."
 Du adition. we add a further inerecicut to tje study of ?.. as we explicitly οvforce the normalization to unitv of the liaο jas (when inteerated over all halo ποο.," In addition, we add a further ingredient to the study of \citet{Valageas2009d}, as we explicitly enforce the normalization to unity of the halo bias (when integrated over all halo masses)."
 We describe below this simple model., We describe below this simple model.
 We first consider he two-poiut correlation function of idos in Lagrangian space. that js within the linear deusitv field. dp(q). where we identify future halos of Euleriau radius r and nonlinear density contrast à (with vpically à 200) with spherical regions of Laeraneian radius q and linear density contrast μοι Ilpugs:," We first consider the two-point correlation function of halos in Lagrangian space, that is within the linear density field $\delta_L(\vq)$, where we identify future halos of Eulerian radius $r$ and nonlinear density contrast $\deltas$ (with typically $\deltas\sim 200$ ) with spherical regions of Lagrangian radius $q$ and linear density contrast $\deltaLs$."
" to he conservation of nass. the Lagrangian and Eulerian xoperties of halos of mass AL are related by ΔΕ ἐπSpe, δν ο], where p is the mean matter density."," Thanks to the conservation of mass, the Lagrangian and Eulerian properties of halos of mass $M$ are related by M= q^3, q^3 = ) r^3 ), where $\rhob$ is the mean matter density."
" As pointed out im 7.. the function F describesthe spherical collapse dynamics. so that ina ACDM cosmology with 0,,=0.27. Q4=0.73. we have 6;c1.59 at 2=0 for 6.=200. lusteack of the usual vaue à,2«1.675 associated with full colapse to a point. that is with à—x."," As pointed out in \citet{Valageas2009d}, the function $\cF$ describesthe spherical collapse dynamics, so that in a $\Lambda$ CDM cosmology with $\Om=0.27$, $\OL=0.73$, we have $\deltaLs \simeq 1.59$ at $z=0$ for $\deltas=200$, instead of the usual value $\delta_c\simeq 1.675$ associated with full collapse to a point, that is with $\deltas=\infty$."
" Deiune haos by the linear threshold 8p,=F+6). rat101) han bv the fiIL collapse value. à. is closer to observalonal aid nunnuercal procedures. since (in the bes Cases)(ne defje “halos” in ealaxy or cluster survevs. and in miuerical simations. bv the radius aud mass of overdeusities within a eiveu nonlinear density threshok às."," Defining halos by the linear threshold $\deltaLs=\cF^{-1}(\deltas)$, rather than by the full collapse value $\delta_c$, is closer to observational and numerical procedures, since (in the best cases)one defines “halos” in galaxy or cluster surveys, and in numerical simulations, by the radius and mass of overdensities within a given nonlinear density threshold $\deltas$."
 Moreover. us gives the freedom to chose different thresholds. such as à=200 or 100 (02)...," Moreover, this gives the freedom to chose different thresholds, such as $\deltas=200$ or $100$ \citep{Valageas2009d}."
" As discusse iu Sect.3 in ?.. or massive (A~10575. £A£.) aud rare halos. the choice à,=200 also roughly correspoids to the separation between outer shells. dominated by radia accretion. and iuner shells. with a significant transverse velocity dispersion. that have experienced shell crossing."," As discussed in Sect.3 in \citet{Valageas2009d}, for massive $M\sim 10^{15} h^{-1}M_{\odot}$ ) and rare halos, the choice $\deltas=200$ also roughly corresponds to the separation between outer shells, dominated by radial accretion, and inner shells, with a significant transverse velocity dispersion, that have experienced shell crossing."
 The case of typical halos (i6. below the knee of the halo nass funclon) Is more intricate as they do uot show such a clear separation., The case of typical halos (i.e. below the knee of the halo mass function) is more intricate as they do not show such a clear separation.
 This cau also be secu in nunierical snmlations. such as Fie.) du 7.," This can also be seen in numerical simulations, such as Fig.3 in \citet{Cuesta2008}."
 At hieh redshift. where nonlinear objects have a snaller mass.this Uvinalization radius shifts to higher density coutrasts for ACDM cosmologics. because of the change of slope of the linear matter power spectrum with scale (ee. ὃς~500 for M~10th1ALL as seen du Fig.5 in ?)).," At high redshift, where nonlinear objects have a smaller mass,this “virialization” radius shifts to higher density contrasts for $\Lambda$ CDM cosmologies, because of the change of slope of the linear matter power spectrum with scale (e.g., $\deltas \sim 500$ for $M\sim 10^{11} h^{-1}M_{\odot}$, as seen in Fig.5 in \citet{Valageas2009d}) )."
" Then. defining the halo correlation as the fractional excess of halo pairs (27)... we write in Lagrangian space ο”... Lihiger use splicrical, dede, ds, "," Then, defining the halo correlation as the fractional excess of halo pairs \citep{Kaiser1984,Peebles1980}, we write in Lagrangian space _2) M_1 M_2 _1 _2 = _L(M_1) _L(M_2) [ 1 + _L(M_1,M_2;s) ] M_1 M_2 _1 _2."
Tere aud iu the following we use the letter 5 for the position of halos in Lagraugiau space to avoid confusiou with their Lagraugian radius 4. aud we introduced the Lagraigian distauce. s=|s2sy]. between both objects.," Here and in the following we use the letter $\vs$ for the position of halos in Lagrangian space to avoid confusion with their Lagrangian radius $q$, and we introduced the Lagrangian distance, $s=|\vs_2-\vs_1|$, between both objects."
We also note with a subscript £ the quantities associated with the linear fields or the Lagrangian space.,We also note with a subscript $L$ the quantities associated with the linear fields or the Lagrangian space.
 Then. following ? and ?.. we obtain the fractional excess of halo pais from the bivariate density distribution είδειδυο) over the two spheres of radii qq and qo. where we considered a single population. that is halos defined by the sane density thresholds ὅρ aud dFlop Ἡ," Then, following \citet{Kaiser1984} and \citet{Valageas2009d}, we obtain the fractional excess of halo pairs from the bivariate density distribution $\cP_L(\delta_{L1},\delta_{L2})$ over the two spheres of radii $q_1$ and $q_2$, 1 + _L(M_1,M_2;s) = = ), where we considered a single population, that is halos defined by the same density thresholds $\deltaLs$ and $\deltas=\cF(\deltaLs)$ ."
 Tere we asstumed Cassia initial conditions aud we 111roduced the cross-correlation of the sumoothed linear density contrast at scales q4 and qo. at positions sj and So. dk I? PyVU haWE (ga) where W(eq) is the Fourier transform of the top-hat window of radius q. Jyi syrinlhy) . and Pp(hk) is the lear matter power spectrum. defined by ," Here we assumed Gaussian initial conditions and we introduced the cross-correlation of the smoothed linear density contrast at scales $q_1$ and $q_2$, at positions $\vs_1$ and $\vs_2$, (s) = _1) ) = k k^2 P_L(k) (kq_1) (kq_2) , where $\tW(kq)$ is the Fourier transform of the top-hat window of radius $q$ , (kq) = _V = 3 , and $P_L(k)$ is the linear matter power spectrum, defined by ) = ) , _2) = _2) P_L(k_1) ."
"Iu particular, oy=o,4,00) is the usual rius linear density contrast at scale 4."," In particular, $\sigma_q=\sigma_{q,q}(0)$ is the usual rms linear density contrast at scale $q$ ."
 In Eq.(5)) we also used the, In \ref{xiL-s}) ) we also used the
10 can give more indications.,10 can give more indications.
" In particular, it seems that assuming primary N from massive stars overproduces N with respect to O in the gasdex."," In particular, it seems that assuming primary N from massive stars overproduces N with respect to O in the gas."
" Here we add that at [Fe/H]=-1.15 the model has an age of 100 Myr, therefore we confirm that must be young."," Here we add that at [Fe/H]=-1.15 the model has an age of 100 Myr, therefore we confirm that must be young."
 Fig., Fig.
 10 and Fig., \ref{mgfe} and Fig.
 11 show the predicted [Mg/Fe] and [Si/Fe] vs. [Fe/H] compared to observational data for the LBG (Pettini et al., \ref{sife} show the predicted [Mg/Fe] and [Si/Fe]  vs. [Fe/H] compared to observational data for the LBG  (Pettini et al.
 2002)., 2002).
 Our predicted [Mg/Fe] and [Si/Fe] ratios are still lower than observed in1512-cB58., Our predicted [Mg/Fe] and [Si/Fe] ratios are still lower than observed in.
" On the other hand, the predicted values arehigher by ~ 0.2 dex than predicted by Matteucci Pipino (2002), Note that in the so-called “horseshoe” LBG (Quider et al.,"," On the other hand,  the predicted values arehigher by $\sim$ 0.2 dex than predicted by Matteucci Pipino (2002), Note that in the so-called “horseshoe” LBG (Quider et al.,"
" 2009), the Si/Fe ratio is very close to the one observed in cB58, thus confirming the discrepancy between theory and observations."," 2009),  the Si/Fe ratio is very close to the one observed in cB58, thus confirming the discrepancy between theory and observations."
" We do not believe that the discrepancy could indicate a problem related to too low Mg and Si yields in the adopted nucleosynthesis, since a [Mg/Fe] 2 0.6 dex in the gas for a large fraction of the galaxy evolution would imply [<Mg/Fe>ως] >0.3-0.4 dex, which exceeds the observed value observed in present day low mass ellipticals."," We do not believe that the discrepancy could indicate a problem related to too low Mg and Si yields in the adopted nucleosynthesis, since a [Mg/Fe] $\ge$ 0.6 dex in the gas for a large fraction of the galaxy evolution would imply $<$ $>_{stars}$ ] $>$ 0.3-0.4 dex, which exceeds the observed value observed in present day low mass ellipticals."
 there is the possibility that this, there is the possibility that this
"energy, therefore no significant restructuring occurs.","energy, therefore no significant restructuring occurs."
 The aggregates stick at the first contact and we refer to this as the hit&sstick (S1) collision type., The aggregates stick at the first contact and we refer to this as the stick (S1) collision type.
 We adopt the hit&sstick porosity model of Okuzumial.(2009) in this paper., We adopt the stick porosity model of \cite{Okuzumi2009a} in this paper.
 In Paper II we used the porosity model of Ormeletal.(2007) which only treats PCA and CCA collisions and constructs semi-analytical recipes if the size (or mass) ratio of the two colliding aggregates are intermediate., In Paper II we used the porosity model of \cite{Ormel:2007p93} which only treats PCA and CCA collisions and constructs semi-analytical recipes if the size (or mass) ratio of the two colliding aggregates are intermediate.
" However, Okuzumietal.(2009) improved on this by modeling these intermediate regions, so called quasi-CCA collisions (QCCA), where two clusters with a given mass ratio can collide."," However, \cite{Okuzumi2009a} improved on this by modeling these intermediate regions, so called quasi-CCA collisions (QCCA), where two clusters with a given mass ratio can collide."
 The porosity model of Ormel et al., The porosity model of Ormel et al.
 produces aggregates with a fractal dimension of 2.5., produces aggregates with a fractal dimension of 2.5.
 The Okuzumi et al., The Okuzumi et al.
" model results in fluffy, fractal dimension 2 aggregates."," model results in fluffy, fractal dimension 2 aggregates."
" As the Ormel model analytically interpolates between PCA and CCA collisions, whereas the Okuzumi et al."," As the Ormel model analytically interpolates between PCA and CCA collisions, whereas the Okuzumi et al."
" model directly simulates these collisions, we prefer the Okuzumi model as the fiducial hit&sstick porosity model."," model directly simulates these collisions, we prefer the Okuzumi model as the fiducial stick porosity model."
" As the particles grow, their collisional energy is increasing and we cannot neglect restructuring."," As the particles grow, their collisional energy is increasing and we cannot neglect restructuring."
 This phase starts when the collisional energy is a few times larger than the rolling energy between the monomers., This phase starts when the collisional energy is a few times larger than the rolling energy between the monomers.
" As compaction occurs, the fractal dimension of the aggregates increases."," As compaction occurs, the fractal dimension of the aggregates increases."
" At the same time, the average number of connections a monomer has (coordination number) increases as well."," At the same time, the average number of connections a monomer has (coordination number) increases as well."
 The further evolution of the dust aggregates is as of yet unclear and a matter of ongoing debate., The further evolution of the dust aggregates is as of yet unclear and a matter of ongoing debate.
 Currently there are two competing collision models., Currently there are two competing collision models.
 The Braunschweig collision model (Paper I) is mostly based on laboratory experiments performed by using fractal dimension 3 ageregates (so called dust cakes and their pieces)., The Braunschweig collision model (Paper I) is mostly based on laboratory experiments performed by using fractal dimension 3 aggregates (so called dust cakes and their pieces).
" As such, it postulates that the aggregates at one point during their evolution in the protoplanetary disk reach a rather compact state with a fractal dimension of 3."," As such, it postulates that the aggregates at one point during their evolution in the protoplanetary disk reach a rather compact state with a fractal dimension of 3."
 The validity, The validity
Moreover. if cosmic ravs of a few times 1015 eV are protons of Galactic origin. he isotropic distribution observed at these energies is indicative of the diffusive effect of the Galactic maguctic ficlds on iron at ~1030 eV. This proposal should © constrained once the primary composition is clearly determined (see in Table 1).,"Moreover, if cosmic rays of a few times $10^{18}$ eV are protons of Galactic origin, the isotropic distribution observed at these energies is indicative of the diffusive effect of the Galactic magnetic fields on iron at $\sim 10^{20}$ eV. This proposal should be constrained once the primary composition is clearly determined (see in Table 1)."
 It has also been suggested that voung extragalactic highly magnetized jeutron stars (1iagnetars) may be sources of UITE protous which are accelerated Ww reconnection events!! These would be prone to a GZK cut spectiun aud would need a very hard injection spectimm to become viable explanations., It has also been suggested that young extragalactic highly magnetized neutron stars (magnetars) may be sources of UHE protons which are accelerated by reconnection \cite{GL00} These would be prone to a GZK cut spectrum and would need a very hard injection spectrum to become viable explanations.
 Trausicut high energy. phenomena such as bursts (GRBs) may also be a source of ultra-high enereies protous.t? Tn addition to both phenomena having unknown origins. GRBs and UITECTRs have other simularitics that may argue for a common source.," Transient high energy phenomena such as gamma-ray bursts (GRBs) may also be a source of ultra-high energies \cite{WV95} In addition to both phenomena having unknown origins, GRBs and UHECRs have other similarities that may argue for a common source."
 Like UIIECTs. CRBs are distributed isotropically in the sky. aud the average rate of y-ray energy enütted by GRBs is comparable to the energy. ecucration rate of UITECTi« of cnuerey >1017 eV in a redshift independent cosmological distribution of sources. both have z10ttereApe’VI Iowever. recent CRB counterpart identifications argue for a strong cosmological evolution for GRBs.," Like UHECRs, GRBs are distributed isotropically in the sky, and the average rate of $\gamma$ -ray energy emitted by GRBs is comparable to the energy generation rate of UHECRs of energy $>10^{19}$ eV in a redshift independent cosmological distribution of sources, both have $ 
\approx 10^{44}{\rm erg\ /Mpc}^{3}/{\rm yr}.$ However, recent GRB counterpart identifications argue for a strong cosmological evolution for GRBs."
 The redshitt dependence of CRB distribution is such that the flux of CITECR associated with nearby CRBs would be too small to fit the UIIECR observatious!? Tn addition. the distribution of UIIECR arrival directions and arrival times argues against the GRBUITECR common origin.," The redshift dependence of GRB distribution is such that the flux of UHECR associated with nearby GRBs would be too small to fit the UHECR \cite{Ste99} In addition, the distribution of UHECR arrival directions and arrival times argues against the GRB–UHECR common origin."
 Eveuts past the GZIN cutoff require that ouly CRBs from S50 Mpc contribute., Events past the GZK cutoff require that only GRBs from $\la 50$ Mpc contribute.
 Since less than aboutone burst is expected to have occurred within this reeion over a period of 100 vr. the unique source would appear as a conceutration of VITECR eveuts iun a small part of the sky (a in Table 1).," Since less than about burst is expected to have occurred within this region over a period of 100 yr, the unique source would appear as a concentration of UHECR events in a small part of the sky (a in Table 1)."
 In addition. the signal would be very narrow in energv AE/E~1.," In addition, the signal would be very narrow in energy $\Delta E/E\sim1$."
 Again. a strong intergalactic maenetic field can ease some of these difficultics ceiving a very laree dispersion in the arrival time and direction of protons produced in a siugle burst(lerye [δολ m Table 15 Finally. if the observed small scale clusteriug of arrival directions is confirmed by future exporiueuts with clusters having some lower οποιον events clearly precede higher energy oues. bursts would be invalidated?'o7 The UITECR. puzzle has inspired a number of different models that involve phivsies bevond the standard model of particle phivsies.," Again, a strong intergalactic magnetic field can ease some of these difficulties giving a very large dispersion in the arrival time and direction of protons produced in a single burst $B_{IGM}$ in Table \cite{WV95} Finally, if the observed small scale clustering of arrival directions is confirmed by future experiments with clusters having some lower energy events clearly precede higher energy ones, bursts would be \cite{SLO97}
 The UHECR puzzle has inspired a number of different models that involve physics beyond the standard model of particle physics."
" New Plhivsies proposals can be top-down nodels or a hwbrid of astroplivsical Zevatrons with new particles,", New Physics proposals can be top-down models or a hybrid of astrophysical Zevatrons with new particles.
 Top-down models involve the decay of very high mass relics that, Top-down models involve the decay of very high mass relics that
Fasssberg|1.Chemicalmainlyinmodelstheform Gottingen. predict that. gas-phase oxygen should be of Os and CO in the cold interstellar medium (seeforinstance??)..,"sberg\tikzmark{mainBodyEnd0} \tikzmark{mainBodyStart1}11,\tikzmark{mainBodyEnd1} \tikzmark{mainBodyStart2}D-37077\tikzmark{mainBodyEnd2} G\tikzmark{mainInlineStart3}$\rm \ddot{o}$\tikzmark{mainInlineEnd3}\tikzmark{mainBodyStart4}ttingen,\tikzmark{mainBodyEnd4} \tikzmark{mainBodyStart5}Germany\tikzmark{mainBodyEnd5}
 % \email{c.ptolemyhipparch.uheaven.space}
% \thanks{The university of heaven temporarily does not
 % accept e-mails}
 \tikzmark{mainBodyStart6}}\tikzmark{mainBodyEnd6}
 \date{Received xxx ; accepted xxx}


% \abstract{}{}{}{}{}
% 5 {} token are mandatory

 \abstract
 % context heading (optional)
 % {} leave it empty if necessary
 {Dark cloud chemical models usually predic\tikzmark{mainBodyStart7}ct\tikzmark{mainBodyEnd7} \tikzmark{mainBodyStart8}large\tikzmark{mainBodyEnd8} \tikzmark{mainBodyStart9}amounts\tikzmark{mainBodyEnd9} \tikzmark{mainBodyStart10}of\tikzmark{mainBodyEnd10} O\tikzmark{mainInlineStart11}$_2$\tikzmark{mainInlineEnd11}\tikzmark{mainBodyStart12},\tikzmark{mainBodyEnd12} \tikzmark{mainBodyStart13}often\tikzmark{mainBodyEnd13} \tikzmark{mainBodyStart14}above\tikzmark{mainBodyEnd14} \tikzmark{mainBodyStart15}observational\tikzmark{mainBodyEnd15} \tikzmark{mainBodyStart16}limits.\tikzmark{mainBodyEnd16} \tikzmark{mainBodyStart17}}\tikzmark{mainBodyEnd17}
 % aims heading (mandatory)
 {We investigate the reason for this discrepancy from a theoretical point of view, inspired by the studies of Jenkins and Whittet on oxygen depletion.}\tikzmark{mainBodyStart18}}\tikzmark{mainBodyEnd18}
 % methods heading (mandatory)
 {We use the gas-grain code Nautilus with an up-to-date gas-phase network to study the sensitivity of the molecular oxygen abundance to the oxygen elemental abundance. We use the rate coefficient for the reaction O + OH at 10~K recommended by the KIDA (KInetic Database for Astrochemistry) experts. }\tikzmark{mainBodyStart19}}\tikzmark{mainBodyEnd19}
 % results heading (mandatory)
 {The updates of rate coefficients and branching ratios of the reactions of our gas-phase chemical network, especially N + CN and H$_3^+$ + O, have changed the model sensitivity to the oxygen elemental abundance. In addition, the gas-phase abundances calculated with our gas-grain model are less sensitive to the elemental C/O ratio than those computed with a pure gas-phase model. The grain surface chemistry plays the role of a buffer absorbing most of the extra carbon. Finally, to reproduce the low abundance of molecular oxygen observed in dark clouds at all times, we need an oxygen elemental abundance smaller than $1.6\times 10^{-4}$.}\tikzmark{mainBodyStart20}}\tikzmark{mainBodyEnd20}
%The abundance of molecular oxygen, and so the chemical model, are particularly sensitive to the updates of some reactions such as N + CN and H$_3^+$ + O.
 % conclusions heading (optional), leave it empty if necessary
 {The chemistry of molecular oxygen in dense clouds is quite sensitive to model parameters that are not necessarily well constrained. That O$_2$ abundance may be sensitive to nitrogen chemistry is an indication of the complexity of interstellar chemistry. }\tikzmark{mainBodyStart21}} $\rm \ddot{o}$ Chemical models predict that gas-phase oxygen should be mainly in the form of $_2$ and CO in the cold interstellar medium \citep[see for instance][]{2006A&A...451..551W,Quan2008}."
 Since the 1980s. there have been searches for O» in the interstellar medium using ground-based and space telescopes (see?.andreferencesthereim)..," Since the 1980's, there have been searches for $_2$ in the interstellar medium using ground-based and space telescopes \citep[see][and references therein]{2003A&A...402L..77P}."
 First. analyses of data from the satellite gave an upper limit of about 107? in dense clouds (?)..," First, analyses of data from the satellite gave an upper limit of about $10^{-6}$ in dense clouds \citep{2000ApJ...539L.123G}."
 The ODIN satellite also initially gave negative results (2). with improved upper limits of =(1—2)x107° for nine sources., The ODIN satellite also initially gave negative results \citep{2003A&A...402L..77P} with improved upper limits of $\approx (1-2)\times 10^{-7}$ for nine sources.
 However. a reanalysis by ?.. using more precise knowledge of the telescope behavior. resulted in a detection of O» in p Ophiuchi cloud. with a abundance of 5x107? relative to H+.," However, a reanalysis by \cite{2007A&A...466..999L}, , using more precise knowledge of the telescope behavior, resulted in a detection of $_2$ in $\rho$ Ophiuchi cloud, with a beam-averaged abundance of $5\times 10^{-8}$ relative to $_2$."
 Using observations of 'O'*O and C'*O lines. ?. argue that the emitting region may be much smaller than the beam of ODIN thus the O» abundance could be larger by one or two orders of magnitude.," Using ground-based observations of $^{16}$ $^{18}$ O and $^{18}$ O lines, \citet{2010A&A...510A..98L} argue that the emitting region may be much smaller than the beam of ODIN thus the $_2$ abundance could be larger by one or two orders of magnitude."
 Regardless of the exact numbers. the sparsity of O2 detections in the various target molecular clouds is an indication that this molecule may not be a reservoir of oxygen.," Regardless of the exact numbers, the sparsity of $_2$ detections in the various target molecular clouds is an indication that this molecule may not be a reservoir of oxygen."
 Many explanations have been proposed to reconcile observations and models., Many explanations have been proposed to reconcile observations and models.
 From a chemical modeling point of View. pure gas-phase chemical models can explain the observec upper limits for clouds younger than 10° yr (?).. ?," From a chemical modeling point of view, pure gas-phase chemical models can explain the observed upper limits for clouds younger than $10^{5}$ yr \citep{2006A&A...451..551W}. ."
 explored the possibility that chemical models can display bistabilities (?).., \citet{2001A&A...370..557V} explored the possibility that chemical models can display bistabilities \citep{1993ApJ...416L..87L}.
 In the parameter space where bistability exists. one of the solutions 1s characterized by a very low abundance of Os.," In the parameter space where bistability exists, one of the solutions is characterized by a very low abundance of $_2$."
 Ii this solution however. all molecular specie abundances are very small. including the CO abundance (2).. which is not what is observed.," In this solution however, all molecular specie abundances are very small, including the CO abundance \citep{2006A&A...459..813W}, which is not what is observed."
 As another possibility. the effect of uncertainties 11 the rate coefficient of the main reaction of production of O» (O + OH -— O» + H) was explored by ?..," As another possibility, the effect of uncertainties in the rate coefficient of the main reaction of production of $_2$ (O + OH $\longrightarrow$ $_2$ + H) was explored by \citet{Quan2008}."
 One needs however to decrease this rate coefficient by à considerable amount to modify the predicted abundance of O2., One needs however to decrease this rate coefficient by a considerable amount to modify the predicted abundance of $_2$.
 In the presence of dust. molecular oxygen in the gas phase can be adsorbed onto grain surfaces.," In the presence of dust, molecular oxygen in the gas phase can be adsorbed onto grain surfaces."
 Adsorption of O» onto dust grains is insufficient in itself to lower the O» abundance after 10° yr. because of the balance with thermal evaporation andcosmic-ray-induced desorption.," Adsorption of $_2$ onto dust grains is insufficient in itself to lower the $_2$ abundance after $10^{6}$ yr, because of the balance with thermal evaporation andcosmic-ray-induced desorption."
 However. the adsorbed O molecule can be successively hydrogenated to form HO» and H:O».," However, the adsorbed $_2$ molecule can be successively hydrogenated to form $_2$ and $_2$ $_2$."
 Then H:O» reacts with H to form water (seealso?).. which 1s more difficult to release from the grains.," Then $_2$ $_2$ reacts with H to form water \citep[see also][]{2002A&A...395..233R}, which is more difficult to release from the grains."
 This surface chemistry allows one to decrease the abundance of O» after 10° years. but a peak in the abundance larger than observational limits remains between 10? and 10° years.," This surface chemistry allows one to decrease the abundance of $_2$ after $10^{6}$ years, but a peak in the abundance larger than observational limits remains between $10^{5}$ and $10^{6}$ years."
 Unfortunately. this time range encompasses the oof cold cores determined by the comparison between large network chemical models anc observations of more than 30 species in TMC-1 (CP) anc LI34N (N) (see222).," Unfortunately, this time range encompasses the of cold cores determined by the comparison between large network chemical models and observations of more than 30 species in TMC-1 (CP) and L134N (N) \citep[see][]{2006A&A...451..551W,2007A&A...467.1103G,2004MNRAS.350..323S}."
" ?. found a small abundance of O» in the gas at all times. i agreement with observations. using a simplified version of grain surface chemistry assuming conversion of O to H:O and C to CH,. and choosing the branching ratio of the reaction H3O7 + e. —> H + H:O that equals 0.33 to reproduce the H:O abundance."," \citet{2000ApJ...539L.129B} found a small abundance of $_2$ in the gas at all times, in agreement with observations, using a simplified version of grain surface chemistry assuming conversion of O to $_2$ O and C to $_4$, and choosing the branching ratio of the reaction $_3$ $^+$ + $^-$ $\longrightarrow$ H + $_2$ O that equals 0.33 to reproduce the $_2$ O abundance."
 Experimental measurements from ? showed that this branching ratio ts 0.25., Experimental measurements from \citet{2000ApJ...543..764J} showed that this branching ratio is 0.25.
 Finally. ? studied the chemistry of O» as a function of the depth in molecular clouds using a one-dimensional steady-state PDR model.," Finally, \citet{2009ApJ...690.1497H} studied the chemistry of $_2$ as a function of the depth in molecular clouds using a one-dimensional steady-state PDR model."
 The authors studied the influence of many parameters and found that the O» abundance peaks at Av between 4 and 6 and that molecules would be strongly depleted at larger Av., The authors studied the influence of many parameters and found that the $_2$ abundance peaks at Av between 4 and 6 and that molecules would be strongly depleted at larger Av.
 In this paper. we revisit the question of the O» abundancein dark elouds using thegas-grain model Nautilus with the most recent gas-phase network fromthe KIDA database and new insight into the oxygen elemental abundances provided by ?.. ," In this paper, we revisit the question of the $_2$ abundancein dark clouds using thegas-grain model Nautilus with the most recent gas-phase network fromthe KIDA database and new insight into the oxygen elemental abundances provided by \citet{2009ApJ...700.1299J}. ."
In the next two sections. we introduce the problem of the choice of oxygen elemental abundance for dense cloud chemical modeling and describe our chemical model.," In the next two sections, we introduce the problem of the choice of oxygen elemental abundance for dense cloud chemical modeling and describe our chemical model."
 The results of our simulations and comparisons with observations in the two dark, The results of our simulations and comparisons with observations in the two dark
and with sullicient spatial resolution to remove the X-rav emission. from AGN within the groups.,and with sufficient spatial resolution to remove the X-ray emission from AGN within the groups.
 Important additional diagnostics will be provided. by deep NALALNewton surveys. which will measure the evolution of the eroup Ly-T relation anc metallicities of groups at. high redshifts.," Important additional diagnostics will be provided by deep XMM-Newton surveys, which will measure the evolution of the group $_X$ -T relation and metallicities of groups at high redshifts."
 Major observational advances in the evolution of eroups of galaxies are expected., Major observational advances in the evolution of groups of galaxies are expected.
 We have identified groups anc poor clusters of galaxies. via their X-ray emission. at high redshifts z0.3-0.6.," We have identified groups and poor clusters of galaxies, via their X-ray emission, at high redshifts $\sim$ 0.3-0.6."
 These bound svstenis. confiemed as such by their X-ray. emission. represent some of the lowest X-ray luminosity (and probably lowest mass) overdensities vet found. at. moderate to high redshifts.," These bound systems, confirmed as such by their X-ray emission, represent some of the lowest X-ray luminosity (and probably lowest mass) overdensities yet found at moderate to high redshifts."
 These observations support. and extend to groups of galaxies. the growing consensus from several deep cluster surveys that there is little or no evolution of the cluster X-ray luminosity. function to high redshifts (z—0.8) at moclerate X-ray. luminosities.," These observations support, and extend to groups of galaxies, the growing consensus from several deep cluster surveys that there is little or no evolution of the cluster X-ray luminosity function to high redshifts $\sim$ 0.8) at moderate X-ray luminosities."
 The X-ray luminosity evolution of low mass galaxy eroups is particularly sensitive to. the thermal history of the X-ray. gas. including non-gravitational processes.," The X-ray luminosity evolution of low mass galaxy groups is particularly sensitive to the thermal history of the X-ray gas, including non-gravitational processes."
 Alassive. luminous clusters are better suited. to deriving cosmological parameters.," Massive, luminous clusters are better suited to deriving cosmological parameters."
 Our results are consistent. either with no evolution. or slight positive evolution. of the X-rav luminosity function at the luminosities of eroups and »oo0r clusters. to z=0.5.," Our results are consistent either with no evolution, or slight positive evolution, of the X-ray luminosity function at the luminosities of groups and poor clusters, to z=0.5."
 Phe evolution of the eroup rav luminosity [function can constrain the epoch of non-eravitational enerey injection into the intra-group medium (clue to supernova-driven winds or AGN)., The evolution of the group X-ray luminosity function can constrain the epoch of non-gravitational energy injection into the intra-group medium (due to supernova-driven winds or AGN).
 The current results suggest that any such energy injection occured mostly at recshilts 20.5., The current results suggest that any such energy injection occured mostly at redshifts $>$ 0.5.
 Examples of energv injection ustories Consistent with our results are those which follow he star formation rate. at least in semi-analytical models of galaxy formation which include feedback. and preheating models in which the energy injection occured at 27:2.," Examples of energy injection histories consistent with our results are those which follow the star formation rate, at least in semi-analytical models of galaxy formation which include feedback, and preheating models in which the energy injection occured at $\gtrsim$ 2."
 The identification. of groups. and poor clusters of galaxies at high redshifts also opens the wav for studies of galaxy evolution in a common. but poorly studied. environment.," The identification of groups and poor clusters of galaxies at high redshifts also opens the way for studies of galaxy evolution in a common, but poorly studied, environment."
 Galaxy evolution. in groups 1s predicted. to differ from evolution in rich clusters or in the field. because the low velocity dispersion. ancl relatively high galaxy density favour merging. tidally-trigecred star formation and other galaxv-galaxy We are grateful to Harald. Ebeling for providing WEP flux corrections ancl to Nicola Alenci and Richard Bower for providing model predictions.," Galaxy evolution in groups is predicted to differ from evolution in rich clusters or in the field because the low velocity dispersion and relatively high galaxy density favour merging, tidally-triggered star formation and other galaxy-galaxy We are grateful to Harald Ebeling for providing VTP flux corrections and to Nicola Menci and Richard Bower for providing model predictions."
 “Phe WEP source searching was initially clone for the WARDS cluster survey. (Scharl L997)., The VTP source searching was initially done for the WARPS cluster survey (Scharf 1997).
 This research has made use of data obtained from the Leicester Database and. Archive Service at. the Department of Physics and Astronomy. Leicester University.," This research has made use of data obtained from the Leicester Database and Archive Service at the Department of Physics and Astronomy, Leicester University."
 Analvsis was performed. on Starlink computing facilities., Analysis was performed on Starlink computing facilities.
 L1tJ acknowledges PPARC support., LRJ acknowledges PPARC support.
" Allineton-Smith JOR. Ellis IS... Zirbel EL... Ocomler A.. 1993. ApJ. 404. Avni Y. Bachall J.N.. 1980. ApJ. 235. Baheall NX... 1981. ApJ. 247. Balogh ALL. Babul A.. Patton D.lt.. 1999. NINILAS. 307. Bower ζω. Bohringer LL. Briel U.C... Ellis. Rus.. Castander E.J.. Couch. NJ. 1994. MNILAS. 268. Bower ια... Lasinger G.. Castancer E.J... Xragon-Salamanca A. Ellis I5... Gioia LAL. Henry J.P. Burg I. Hluchra «)1. Bohringer HL. Briel U.G.. AleLbean D... 1996. AINRAS 281. Bower It... 1997. MNILAS. 288. Bower lt... Benson A.J. Baugh οδα. Cole ον Lrenk οι. Lacey €.€.. 2000. AINRAS submitted. Drvan G.L.. 2000. ApJ. 544. L1 Durg lt. CGiacconi lt. dHluchra J... Maclxentw— ο. AMeLean B.. Geller AL. Hasinger €... Marzke. I... Schmidt AL. Trumper J.. 1992. AA 250. Burke D.J.. Collins CX... Sharples RM... Romer A... Loleden 12.1. Nichol RC. 1997. ApJ. 488. Suurns J.O.. Ledlow MJ... Loken C.. IxIvpin X... Voges W.. Bryan. G.L.. Norman ALL... White HX... 1996. ApJ. 467. Canizares CLR. Fabbiano C.. Trinchieri G.. 1987. ApJ Cavaliere A. Menei N.. Tozz P.. 1997. ApJ. 484. Cavaliere A.. Menei N.. Tozzi P... 1999. MNILAS. 308. Cole οι, Lacey. αν, Baugh C.M... Frenk οοι. 2000. AINRAS. 319. Collins CLA. Mann It. 1998. MNILAS. 297. De Grandi S.. Guzzo L.. Bohringer H.. Alolendi S.. Chincarini €. Collins €... Cruddace It. Neumann D.. Schindler S.. Schuecker P.. Voges W.. 1999. ApJ. 513."," Allington-Smith J.R., Ellis R.S., Zirbel E.L., Oemler A., 1993, ApJ, 404, Avni Y., Bachall J.N., 1980, ApJ, 235, Bahcall N.A., 1981, ApJ, 247, Balogh M.L., Babul A., Patton D.R., 1999, MNRAS, 307, Bower R.G., Bohringer H., Briel U.G., Ellis R.S., Castander F.J., Couch W.J., 1994, MNRAS, 268, Bower R.G., Hasinger G., Castander F.J., Aragon-Salamanca A., Ellis R.S., Gioia I.M., Henry J.P., Burg R., Huchra J.P., Bohringer H., Briel U.G., McLean B., 1996, MNRAS 281, Bower R.G., 1997, MNRAS, 288, Bower R.G., Benson A.J., Baugh C.M., Cole S., Frenk C.S., Lacey C.G., 2000, MNRAS submitted, Bryan G.L., 2000, ApJ, 544, L1 Burg R., Giacconi R., Huchra J., MacKenty J., McLean B., Geller M., Hasinger G., Marzke R., Schmidt M., Trumper J., 1992, A 259, Burke D.J., Collins C.A., Sharples R.M., Romer A.K., Holden B.P., Nichol R.C., 1997, ApJ, 488, Burns J.O., Ledlow M.J., Loken C., Klypin A., Voges W., Bryan G.L., Norman M.L., White R.A., 1996, ApJ, 467, Canizares C.R., Fabbiano G., Trinchieri G., 1987, ApJ 312, Cavaliere A., Menci N., Tozzi P., 1997, ApJ, 484, Cavaliere A., Menci N., Tozzi P., 1999, MNRAS, 308, Cole S., Lacey, C.G., Baugh C.M., Frenk C.S., 2000, MNRAS, 319, Collins C.A. Mann R.G. 1998, MNRAS, 297, De Grandi S., Guzzo L., Bohringer H., Molendi S., Chincarini G., Collins C., Cruddace R., Neumann D., Schindler S., Schuecker P., Voges W., 1999, ApJ, 513,"
Iun such a ft one can anticipate (based ou the closed isovelocity contours) that the rotation curve would be falling aud (based ou the kinks iu the isovelocity curves ou the eastern and western edges of the disk) that either the rotation curve would ueed to rise again towards the edge of the disk. or the edges of the disk would ueed to be warped.,"In such a fit one can anticipate (based on the closed isovelocity contours) that the rotation curve would be falling and (based on the kinks in the isovelocity curves on the eastern and western edges of the disk) that either the rotation curve would need to rise again towards the edge of the disk, or the edges of the disk would need to be warped."
 We discuss rotation aud other models for producing the observed velocity field iu more detail in the next section., We discuss rotation and other models for producing the observed velocity field in more detail in the next section.
 As described in the last two sections. the morphology aud οποιαιός of GRS are somewhat peculiar.," 	As described in the last two sections, the morphology and kinematics of GR8 are somewhat peculiar."
 If he III eas aud the stars in GR& are both in disks. then the stellar disk. would have to be both more inclined aud have a ciffercut oositiou angle than the eas disk.," If the HI gas and the stars in GR8 are both in disks, then the stellar disk would have to be both more inclined and have a different position angle than the gas disk."
 It is more likely that he star formation iu GRS has occurred. prefercutially iu ἃ non axisviunnetric svuuuetric region iu the ceuter of the ealaxy., It is more likely that the star formation in GR8 has occurred preferentially in a non axisymmetric symmetric region in the center of the galaxy.
 In the extreme case. the stars would have a more xw like distribution than the eas.," In the extreme case, the stars would have a more bar like distribution than the gas."
 A central stellar bar could affect the eas dynamics. however since the stellar nass is probably not ανασα dominant (from the observed D-V color of 0.38 for GB8 aud the low metallicity nodels of Dell & de Jong (2001). the the stellar Lass Is ~ 5«109 NL... ic. a factor of 2 less than the IIT mass) this (ffect lav no be iurportant.," A central stellar bar could affect the gas dynamics, however since the stellar mass is probably not dynamically dominant (from the observed B-V color of 0.38 for GR8 and the low metallicity models of Bell $\&$ de Jong (2001), the the stellar mass is $\sim$ $\times 10^6$ $_\odot$, i.e. a factor of 2 less than the HI mass) this effect may not be important."
 Apart from having a peculiar morpholoey. the kinematics of GR& is also ΠΠπα," Apart from having a peculiar morphology, the kinematics of GR8 is also unusual."
 The ποιαισα] iid HI major axis of this ealaxy are perpendicular to each other. the kinematical center is offset. from the morphological eeuter aud the observed velocity field is systelatically asvuuuctric.," The kinematical and HI major axis of this galaxy are perpendicular to each other, the kinematical center is offset from the morphological center and the observed velocity field is systematically asymmetric."
 CRS is uot the ouly chwart ealaxv which shows nüsalieumnieut between kincmatical and morphological axes. such nüsalieumients lave also been seen in. for c.g. Sextaus A (Skillman et al.," GR8 is not the only dwarf galaxy which shows misalignment between kinematical and morphological axes, such misalignments have also been seen in, for e.g. Sextans A (Skillman et al."
 LOssa). NGC 625 (Cotté et al.," 1988a), NGC 625 (Côtté et al."
 2000) and DDO 26 (IIuuter Wileots 2002)., 2000) and DDO 26 (Hunter Wilcots 2002).
 However. the nüsalieument and off-centered kinematics does imply that CRS caunot be modeled as a pure axisviunietric rotating disk (for which all axis aud ceuters would be aligned).," However, the misalignment and off-centered kinematics does imply that GR8 cannot be modeled as a pure axisymmetric rotating disk (for which all axis and centers would be aligned)."
 Although. Carignanetal.(1990) had noted some of these problems. they had nouetheless. modeled +the kinematics of (ιδ as an aNisvuuuetric rotating disk.," Although, \cite{carignan90} had noted some of these problems, they had nonetheless, modeled the kinematics of GR8 as an axisymmetric rotating disk."
" Their derived rotation cirve had a maximo amplitude of ~8ον, and fell sharply with increasing ealacto-ceutric clistance."," Their derived rotation curve had a maximum amplitude of $\sim 8$, and fell sharply with increasing galacto-centric distance."
 Our attempts to derive a rotation curve from our velocity field were not successful., 	Our attempts to derive a rotation curve from our velocity field were not successful.
 The errors iu ιο estimated piarineters were laree. as Were the residuals between the model aud the observed velocity Geld.," The errors in the estimated parameters were large, as were the residuals between the model and the observed velocity field."
 Our failwe to fd a good fit (as opposed to Carignanetal.(1990)... who were able to ft a rotation curve) is probably related to our better sampling of ιο velocity field. which. as noted above. makes the wisaliguinents aud asvuuuetrics in the velocity field more PAviking.," Our failure to find a good fit (as opposed to \cite{carignan90}, who were able to fit a rotation curve) is probably related to our better sampling of the velocity field, which, as noted above, makes the misalignments and asymmetries in the velocity field more striking."
 To provide a feel for the velocity field tha would © produced by circular rotation. we show in Fig. 5||," To provide a feel for the velocity field that would be produced by circular rotation, we show in Fig. \ref{fig:model}[ ["
"B] 16 model velocity field that corresponds to the rotation ""urve of Carignanctal.(1990}.",B] the model velocity field that corresponds to the rotation curve of \cite{carignan90}.
. The disk has been taken o be intrinsically elliptical (with an axis ratio of 2:1). so iat despite having an inclination of 60° (the inclination anele derived from the velocity field) by Carignan ct al.," The disk has been taken to be intrinsically elliptical (with an axis ratio of 2:1), so that despite having an inclination of $60^o$ (the inclination angle derived from the velocity field by Carignan et al."
 1990) the projected model UT disk matches the fairly circular appearance of the observed. TT disk., 1990) the projected model HI disk matches the fairly circular appearance of the observed HI disk.
 Essentially. the foreshorteniug aloug the kinematical minor axis is offset by the iuberent cllipticity of the disk.," Essentially, the foreshortening along the kinematical minor axis is offset by the inherent ellipticity of the disk."
 As expected. although the model produces closed isovelocity contours along the apparent morphological III iuinor axis. the asvuuuetrics seen iu the closed coutours between northern and southern halfof the galaxy. the kiuks iu the isovelocity contours towards the edees of the disk. as well as the offset between the kinematical and morphological ceuter are not reproduced.," As expected, although the model produces closed isovelocity contours along the apparent morphological HI minor axis, the asymmetries seen in the closed contours between northern and southern half of the galaxy, the kinks in the isovelocity contours towards the edges of the disk, as well as the offset between the kinematical and morphological center are not reproduced."
 As discussed iu Sect. 3.2..," As discussed in Sect. \ref{ssec:HI_Kin},"
 kinks in the outer isovelocity coutours can be produced by requiring the rotation curve to rise again. or by requiring the outer parts of the disk to be extremely warped.," kinks in the outer isovelocity contours can be produced by requiring the rotation curve to rise again, or by requiring the outer parts of the disk to be extremely warped."
 Quautitatively. to reproduce the observed kinks. the inclination angle is required to chauge by an amount sufficient to cause the observed velocity at the edges to ierease by a factor of ~ 2 compared to the muavarped 10del.," Quantitatively, to reproduce the observed kinks, the inclination angle is required to change by an amount sufficient to cause the observed velocity at the edges to increase by a factor of $\sim$ 2 compared to the unwarped model."
 Such extreme warps can. in principle. lead to multiply peaked line profiles.," Such extreme warps can, in principle, lead to multiply peaked line profiles."
 However. because of the low signal to noise ratio towards the edges. we cannot reliably distinguish. between single peaked aud multiply peaked line profiles in these regions.," However, because of the low signal to noise ratio towards the edges, we cannot reliably distinguish between single peaked and multiply peaked line profiles in these regions."
 A inore serious concern iu imodelius the velocity field of GR& as a rotating disk is the observed παπαΜοιο! between the kinematical aud TT major axes., A more serious concern in modeling the velocity field of GR8 as a rotating disk is the observed misalignment between the kinematical and HI major axes.
 As noted, As noted
quadrupole is equal for the two masses.,quadrupole is equal for the two masses.
 And. because of the symmetry. only £o. Ley.day. aud di. are in⋅ principle⋅⋅ nonzero.," And, because of the symmetry, only $I_{xx}$ , $I_{xy}$,$I_{yy}$, and $I_{zz}$ are in principle nonzero."
" In particular.⋅ 4,p=—ὴ9neryἹ aud 4...=—ETESEin(a?MM+Ἱag."," In particular, $I_{xy}=-\sum 
m xy$ and $I_{zz}=-\sum\frac{1}{3}m (x^2+y^2)$."
5 Note that the deflection augle is of Ομ)000)., Note that the deflection angle is of $O(m/bv_0)$.
 Consistent with our approximation. we keep onlv the lowest powers of C/G) iu computing multipoles.," Consistent with our approximation, we keep only the lowest powers of $(m/b)$ in computing multipoles."
 Our approach is encapsulated. iu the following rules: This approach is similar to those of Oohara&Nakamura(1989). ancl Blanchetetal.(1990)., Our approach is encapsulated in the following rules: This approach is similar to those of \cite{1989PThPh..82..535O} and \cite{1990MNRAS.242..289B}.
. We. demonstrate the approach by evaluating. {η(3) Using⋅ our prescription., We demonstrate the approach by evaluating $I^{(3)}_{xy}$ using our prescription.
"⋅⋅ We- treat only oue hole (the one with v,2 409): As another example. we explicitly⋅⋅ evaluate (3)£2: Introducing the notationw= 57. the triply differentiated mass quadrupole for one black hole is:"," We treat only one hole (the one with $v_x \approx +v_0$ ): As another example, we explicitly evaluate $I^{(3)}_{zz}$: Introducing the notation$w=\frac{v_0t}{b}$ the triply differentiated mass quadrupole for one black hole is:"
 , 
morphologies strongly suggests the 1.1 Giz cussion traces starburst rather than ACN cmission.,morphologies strongly suggests the 1.4 GHz emission traces starburst rather than AGN emission.
 Deep VLT/FORSL spectroscopy (De Breuck ln preparation) also revealed a faint featureless continuum. but no ciission lines.," Deep VLT/FORS1 spectroscopy (De Breuck in preparation) also revealed a faint featureless continuum, but no emission lines."
 Am unconstrained Gaussian fit to the MAMBO S/N imap vields a size of «18/00. but the S/N of our detection is onlv 3.7 in a smoothed map. so the detection of spatially exteuded enission is tentative at best. (," An unconstrained Gaussian fit to the MAMBO S/N map yields a size of $\times$ 0, but the S/N of our detection is only 3.7 in a smoothed map, so the detection of spatially extended emission is tentative at best. ("
Fig. 39):,Fig. \ref{RMAMBOSNVLAIDs}) ):
 We obtained SCUBA photometry at the oositiou of a very faint radio aud optical identification. confiuüuug the reality of this faint NLAMDO source.," We obtained SCUBA photometry at the position of a very faint radio and optical identification, confirming the reality of this faint MAMBO source."
 Note hat the apparent spatial extent of the MANDO cinission cannot be trusted because this source is ouly detected at he 3.10 level. (, Note that the apparent spatial extent of the MAMBO emission cannot be trusted because this source is only detected at the $\sigma$ level. (
Fie. 3):,Fig. \ref{RMAMBOSNVLAIDs}) ):
 Although his is one of the brightest ALAMDBO sources. there is no obvious radio or optical identification.," Although this is one of the brightest MAMBO sources, there is no obvious radio or optical identification."
" We have obtained SCUBA photometry of the radiofoptical souree at RÀ-—1338"" 30.227, 1113337006. but obtained ouly a 1.56 signal of Sysym=3-7£2.5 nid. while at the nominal NAMDO position. we obtain a slightly higher signal (see Table 2))."," We have obtained SCUBA photometry of the radio/optical source at $^h$ $^m$ $^s$, $-$ 06, but obtained only a $\sigma$ signal of $S_{\rm 850\mu m}$ $\pm$ 2.5 mJy, while at the nominal MAMBO position, we obtain a slightly higher signal (see Table \ref{MAMBOphotometry}) )."
 We do not have a good candidate optical or radio counterpart for this MAMDO source. (, We do not have a good candidate optical or radio counterpart for this MAMBO source. (
Fie. 3)):,Fig. \ref{RMAMBOSNVLAIDs}) ):
 This faint NLAMDO source lies 6777 from an extremely red object (ERO) with A —19.2x0.1 aud Ro W=6.140.15., This faint MAMBO source lies 7 from an extremely red object (ERO) with $K$ $\pm$ 0.1 and $R-K$ $\pm$ 0.15.
 We have obtained deep FORS2/MXU spectroscopy of this ERO (Overzieral... in preparation). detecting a faint red continuum aud an enüssion liue atSI20A.. which we tentatively identify as aat z—1.18.," We have obtained deep FORS2/MXU spectroscopy of this ERO (Overzier, in preparation), detecting a faint red continuum and an emission line at, which we tentatively identify as at $z$ =1.18."
 Note that from blauk-field ERO survevs. the density of objects with Ro W>6 and W<19.2 is 0.10 ? (Daddietab.2000).. so the chance of finding such au object within τι is P=O.," Note that from blank-field ERO surveys, the density of objects with $R-K$$>$ 6 and $K$$<$ 19.2 is 0.10 $^{-2}$ \citep{dad00}, so the chance of finding such an object within 7 is $P$."
1%.. It is therefore yoxsible that MOS is a απκ ERO (ey.Cimattietal. 2005)...," It is therefore possible that M08 is a dusty ERO \citep[\eg][]{cim98,dey99,sma02b,tak03}."
 However. because the ERO is not the closest xossible identification. it is statistically uotthe most likely identification.," However, because the ERO is not the closest possible identification, it is statistically notthe most likely identification."
 Note that the appareut spatial extent of 1 MAMDO cinission cannot be trusted because this source is onlv detecte at the 1o level., Note that the apparent spatial extent of the MAMBO emission cannot be trusted because this source is only detected at the $\sigma$ level.
 This may also oeidicate that this source has made it iuto our sample due o the coutsion of two sources too close to be detected oexdividuallv., This may also indicate that this source has made it into our sample due to the confusion of two sources too close to be detected individually.
 Deeper nuu/subnmui observatious would be jceded to verity this. aud to determine if the dust emission is related to the ERO or not. (," Deeper mm/submm observations would be needed to verify this, and to determine if the dust emission is related to the ERO or not. ("
Fie. 2):,Fig. \ref{KMAMBOSNVLA}) ):
 Wo find no radio source within ouc MAMDO beasize. aud 1ο clear IR identifications. (," We find no radio source within one MAMBO beamsize, and no clear $-$ IR identifications. ("
Fie. 5)):,Fig. \ref{RMAMBOSNVLAnoIDs}) ):
 This NAMDO source falls just outside the VLT HR baud nuage., This MAMBO source falls just outside the VLT $R-$ band image.
 It coincides with a strong 0.2 την radio source. (, It coincides with a strong 0.2 mJy radio source. (
Fig. 1)):,Fig. \ref{RMAMBOSN}) ):
 This is a ποσαΤον bright radio source with a ER II (Fauaroff&Rilev.197) morphology., This is a moderately bright radio source with a FR II \citep{fan74} morphology.
 We detect no 1.2 nuu emission from this source., We detect no 1.2 mm emission from this source.
 At least oue (MO2) of the three sources detected with S/N»5. and possibly the weaker source M5 appear to have significantly exteuded 1.2 wan emission.," At least one (M02) of the three sources detected with $>$ 5, and possibly the weaker source M05 appear to have significantly extended 1.2 mm emission."
 MO2 appears to consist of two barely resolved compoucuts. though none of them have a clear candidate optical or radio identification.," M02 appears to consist of two barely resolved components, though none of them have a clear candidate optical or radio identification."
 Spatially exteuded μπι. enüssion has been reported before m several HzBRCs aud at least two conipauion sources (Ivisonetal..2000:Stevens2003. prep.).," Spatially extended submm emission has been reported before in several HzRGs and at least two companion sources \citep[][Ivison \etal, in prep.]{ivi00,ste03}. ."
. This suggests that star formation in these objects occurs over scales of several tens of kpe., This suggests that star formation in these objects occurs over scales of several tens of kpc.
"We detine the luminosity at a certain wavelength band by £=£L, G is the corresponding frequency).",We define the luminosity at a certain wavelength band by $L\equiv\nu L_\nu$ $\nu$ is the corresponding frequency).
" Then the luminosity function is defined as a number density of galaxies whose luminosity lies between a logarithmic interval logL.logL|clogL]: where we denote log.r=log,,.r and ln.=Log,c."," Then the luminosity function is defined as a number density of galaxies whose luminosity lies between a logarithmic interval $[\log L, \log L + \pd\log L]$: where we denote $\log x \equiv \log_{10} x$ and $\ln x \equiv \log_e x$."
 For mathematical simplicity. we define the LF asnormalized. i.e.. Hence. this corresponds to a probability density function (PDF). a commonly used terminology in the field of mathematical statistics.," For mathematical simplicity, we define the LF as, i.e., Hence, this corresponds to a probability density function (PDF), a commonly used terminology in the field of mathematical statistics."
 We also detine the cumulative LF as where Livin is the minimum luminosity of galaxies considered., We also define the cumulative LF as where $L_{\rm min}$ is the minimum luminosity of galaxies considered.
 This corresponds to the DF., This corresponds to the DF.
" If we denote univariate LFs as ON(La) and OY(La). then the bivariate PDF 6'7'(L,.£2) is described by a differential copula Cinq.us) as For the FGM copula. the BLF leads from Equation (20)) The parameter & is proportional to the correlation coefficient p between logL, and logLe."," If we denote univariate LFs as $\phi^{(1)}_1(L_1)$ and $\phi^{(1)}_2(L_2)$, then the bivariate PDF $\phi^{(2)}(L_1,L_2)$ is described by a differential copula $c(u_1, u_2)$ as For the FGM copula, the BLF leads from Equation \ref{eq:fgm_copula_density}) ) The parameter $\kappa$ is proportional to the correlation coefficient $\rho$ between $\log L_1$ and $\log L_2$."
 For the Gaussian copula. the BLF is obtained as where and X is again defined by Equation (255).," For the Gaussian copula, the BLF is obtained as where and $\vmatrix$ is again defined by Equation \ref{eq:vmatrix}) )."
 Here. to make our model BLF astrophysically realistic. we construct the FUV-FIR BLF by the copula method.," Here, to make our model BLF astrophysically realistic, we construct the FUV–FIR BLF by the copula method."
 For the IR. we use the analytic form for the LF proposed by Saundersetal.(1990) which is detined as We adopt the parameters estimated by Takeuchietal.(2003b) which are obtained from the PSC galaxies (Saundersetal.2000).," For the IR, we use the analytic form for the LF proposed by \citet{saunders90} which is defined as We adopt the parameters estimated by \citet{takeuchi03b} which are obtained from the $z$ galaxies \citep{saunders00}."
. For the UV. we adopt the Schechter function (Schechter1976).," For the UV, we adopt the Schechter function \citep{schechter76}."
 We use the parameters presented by Wyderetal.(2005). forGALEX ΕΟΝ (Aww=1530 Ad: L..1.35«107h?Mpe ?).," We use the parameters presented by \citet{wyder05} for FUV $\lambda_{\rm eff} = 1530\;$ ): $(\alpha_2, L_{*2}, \phi_{*2}) = (1.21, 1.81\times 10^9h^{-2}\;L_\odot, 
1.35 \times 10^{-2}h^3\;\mbox{Mpc}^{-3})$ ."
 For simplicity. we neglect the A’-correction.," For simplicity, we neglect the $K$ -correction."
 We show the constructed BLFs from the FGM and Gaussian copulas in Figures 2. and 3.. respectively.," We show the constructed BLFs from the FGM and Gaussian copulas in Figures \ref{fig:fgm_lf} and \ref{fig:gauss_lf}, respectively."
 The FGM-based BLF cannot have a linear correlation coefficient larger than 2-0.3 as explained above. while the Gaussian-based BLF may have a much higher linear correlation.," The FGM-based BLF cannot have a linear correlation coefficient larger than $\simeq 0.3$ as explained above, while the Gaussian-based BLF may have a much higher linear correlation."
 We note that both copulas allow negative correlations. which are not discussed in this article.," We note that both copulas allow negative correlations, which are not discussed in this article."
 First. even if the linear correlation coefficients are the same. the detailed structures of the BLFs with the FGM and Gaussian copulas are different (see the case of p= 0.0-0.3).," First, even if the linear correlation coefficients are the same, the detailed structures of the BLFs with the FGM and Gaussian copulas are different (see the case of $\rho = 0.0 \mbox{--} 0.3$ )."
 For the Gaussian-based BLFs. we see a decline at the faint end. while we do not have such structure," For the Gaussian-based BLFs, we see a decline at the faint end, while we do not have such structure"
of the background map will not deteriorate the galaxy Hux we first subtract the galaxy with the help of a mioclel constructed. withBMODEL.,of the background map will not deteriorate the galaxy flux we first subtract the galaxy with the help of a model constructed with.
. After we have removed. the model we create a fully resolved. background map which we subtract from the initial image., After we have removed the model we create a fully resolved background map which we subtract from the initial image.
 The sky background. values derived. from the method. described above can be found in Table 2 and are used [ater as an input toGALFIT3., The sky background values derived from the method described above can be found in Table \ref{table:info} and are used later as an input to.
. All background. values have. been independently. checked: using and agree within the quality errors., All background values have been independently checked using and agree within the quality errors.
 Nevertheless we do note in particular the extensive structure in the background of the NGCAESG possibly. cue to the Νο reduction pipeline., Nevertheless we do note in particular the extensive structure in the background of the NGC4486 possibly due to the UKIDSS reduction pipeline.
 The NGC44S6 case will be discussed. further in Section 4.4., The NGC4486 case will be discussed further in Section \ref{sec:index}.
 Two PSEs are created for cach galaxy. based on stars taken from the same cata frame and using the packageD," Two PSFs are created for each galaxy, based on stars taken from the same data frame and using the package."
AOPHOT.. ο PSE model is described bx a penny? function., The PSF model is described by a penny2 function.
 Penny2 has a Gaussian core and Lorentzian wings which are [ree to be tilted in different directions., Penny2 has a Gaussian core and Lorentzian wings which are free to be tilted in different directions.
 We construct the PSE from a sample of 10-15 stars selected. (rom. each ealaxyimage in interactive mode., We construct the PSF from a sample of 10-15 stars selected from each galaxy/image in interactive mode.
 A cillerent set of. stars is used. for cach PSE., A different set of stars is used for each PSF.
 Saturated stars. or stars very close to the galaxy with unclear background levels. are excluded from the sample.," Saturated stars, or stars very close to the galaxy with unclear background levels, are excluded from the sample."
 After the creation of the PSE we use it to subtract all stars from the original image., After the creation of the PSF we use it to subtract all stars from the original image.
 The left panel anc the middle panel of Figure 2. show an example ealaxy image before and after removing the stars., The left panel and the middle panel of Figure \ref{fig:clean} show an example galaxy image before and after removing the stars.
 In some images the main ogalaxy is surrounded. by satellite ealaxies (e.g. ὃνUGCOTIO). bad pixels and saturated stars (e.g. NGC44590).," In some images the main galaxy is surrounded by satellite galaxies (e.g. UGC9799), bad pixels and saturated stars (e.g. NGC4459)."
 T1e Ddight. distribution [from the neighbouring ealaxies and 10 area that the bad. pixels cover cannot be cleaned: with the same technique we used for the stars., The light distribution from the neighbouring galaxies and the area that the bad pixels cover cannot be cleaned with the same technique we used for the stars.
 In these cases we use an image mask that indicates to which areas of the image should not be used., In these cases we use an image mask that indicates to which areas of the image should not be used.
 We create these maps using segmentation maps., We create these maps using segmentation maps.
 Lhe right panel of Figure 2 shows the segmentation maps with pixels having a non zero value in the map being excluded [rom the fitting process., The right panel of Figure \ref{fig:clean} shows the segmentation maps with pixels having a non zero value in the map being excluded from the fitting process.
dianeters at higher redshifts.,diameters at higher redshifts.
 Finally. while broadly consistent with the scenario of a highly turbuleut intergalactic iuediuni ow observations do lot place significant coustraints ou its properties.," Finally, while broadly consistent with the scenario of a highly turbulent intergalactic medium, our observations do not place significant constraints on its properties."
 We thank the referee for suggestions that nuproved the presentation of these results., We thank the referee for suggestions that improved the presentation of these results.
" The National Radio Astrououw Observatory is a facility of the National Scicuce Foundation operated uuder cooperative agreement by Associated Universities. luc. This research has made use of the United States Naval Observatory (USNO) Badio Reference Frame huage Database (RREID): NASAs Astroplivsics Data System bibliographic services: the SIAIBAD database. operated atCDS.. Strasbourg. France: and the NASA/TIPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. Califormia Tustitute of Techuoloey. under contract with the National Aeronautics and Space Ανναο,"," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research has made use of the United States Naval Observatory (USNO) Radio Reference Frame Image Database (RRFID); NASA's Astrophysics Data System bibliographic services; the SIMBAD database, operated at, Strasbourg, France; and 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."
 Basic research in radio astronomy at the NRL is supported by the NRL Base fuudiug., Basic research in radio astronomy at the NRL is supported by the NRL Base funding.
Iu this work we use the self-cousisteut radiated accretion disk models frou D'Alessio et al. (,In this work we use the self-consistent irradiated accretion disk models from D'Alessio et al. (
1998. 1999 aud 2001) to fit the SEDs of ΠΟ 31282 aud ΠΟ 111569.,"1998, 1999 and 2001) to fit the SEDs of HD 34282 and HD 141569."
 The methods used here were applied succesfully to f the SEDs of vouug T Tami stars with au approximate age of d My., The methods used here were applied succesfully to fit the SEDs of young T Tauri stars with an approximate age of 1 Myr.
 This approach is valid for these two stars since they are vouug (see Section 5)) aud at least one of them seenis to be still actively accreting., This approach is valid for these two stars since they are young (see Section \ref{THEPARAMS}) ) and at least one of them seems to be still actively accreting.
 Since the calculations vield the vertical structure ancl emission properties of the disk selbconsistently with the stellar parameters. and we have characterized the stellar phoospheres with precision. a good fit to the SED would provide a plivsically based picture of the svstem without the use ofhoc pariunetrizatious for the disk temperature or surface deusity profiles.," Since the calculations yield the vertical structure and emission properties of the disk self-consistently with the stellar parameters, and we have characterized the stellar photospheres with precision, a good fit to the SED would provide a physically based picture of the system without the use of parametrizations for the disk temperature or surface density profiles."
 The iodels involve the following assmuptious: the disk is du a steady. state (M=dMÁE is coustaut). it is econmetrically thin CT/FR<<1. where IT is the scale height of the disk and AH is the radia distauce). the accretion viscosity is computed with v=afe. following the a-prescription from Shakura Suuvaev (1973). in which ος is the sound speed.," The models involve the following assumptions: the disk is in a steady state $ \dot{M}\!={\rm d}M\!/\!{\rm d}t$ is constant), it is geometrically thin $H/R\!<<\!1$, where $H$ is the scale height of the disk and $R$ is the radial distance), the accretion viscosity is computed with $\nu\!=\!\alpha\,H\,c_{\rm s}$, following the $\alpha$ -prescription from Shakura Sunyaev (1973), in which $c_{\rm
 s}$ is the sound speed."
 The dust and eas are well mixed in the whole disk with the usual dust to eas mass ratio of 1/100., The dust and gas are well mixed in the whole disk with the usual dust to gas mass ratio of 1/100.
 For the dust we use a grain size distribution ma)=nyaP! xith p values of 2.5 or 3.5 and a minium erain size of 0.005 sau. Possible values for the maximal erain size are l yan to 10 cm.," For the dust we use a grain size distribution $n(a)\,=\,n_0\,a^{-p}$ with $p$ values of 2.5 or 3.5 and a minimum grain size of 0.005 $\mu$ m. Possible values for the maximum grain size are 1 $\mu$ m to 10 cm."
 The abundances are those eiven bv Pollack- et al. (, The abundances are those given by Pollack et al. (
1991).,1994).
 The radiation. field is considered in two separate regimes (one characteristic of the disk local teniperature aud one characteristic of the stellar effective eniperature) as in C'alvet et al {, The radiation field is considered in two separate regimes (one characteristic of the disk local temperature and one characteristic of the stellar effective temperature) as in Calvet et al. (
1991. 1992) aud finally the radiative trauster is done by solving the first two moments of the radiative transfer equatiou with the Eddinetou approximation (sco D'Alessio ot al.,"1991, 1992) and finally the radiative transfer is done by solving the first two moments of the radiative transfer equation with the Eddington approximation (see D'Alessio et al."
" 19985. 1999 and 2001 for ""urtherfur details)."," 1998, 1999 and 2001 for further details)."
 The disk is the solution of the detailed vertical structure equations for each aunulus. and the svuthetic SEDs are obtained bv solving the radiative transport equation in ravs parallel to the line of sight aud integrating (in solid angle) the disks emissio-," The disk is the solution of the detailed vertical structure equations for each annulus, and the synthetic SEDs are obtained by solving the radiative transport equation in rays parallel to the line of sight and integrating (in solid angle) the disk's emission."
 Note that. although the models we have applied are amonest the nos sophisticated available. they have lamitations inherent iu the complexity of the physics and the computational techuiques.," Note that, although the models we have applied are amongst the most sophisticated available, they have limitations inherent in the complexity of the physics and the computational techniques."
 For example. they asstuuce a dust size distribution with a maximal eral size μιας and the same viscosity paracter a throughout. which iu some real cases precludes fitting the observed SED with a compoucut.," For example, they assume a dust size distribution with a maximum grain size $a_{\rm max}$ and the same viscosity parameter $\alpha$ throughout, which in some real cases precludes fitting the observed SED with a component."
 For ΠΟ 31282 a conmibiuation of two disk models is needed: one for the long wavelength part of the SED. with high viscosity and a ΠΑΝΙ grain size of 1 ci (subsection 6.2.2)) and a second one for the mid-infrared region of the SED. with lower viscosity auc a παπα grain size of 1 jan (subsection 6.2.3)): the first one will be referred to as thedisk aud the latter as thedisk according to their vertical scale heights. of which the frst has a lower value.," For HD 34282 a combination of two disk models is needed: one for the long wavelength part of the SED, with high viscosity and a maximum grain size of 1 cm (subsection \ref{LONGWAVE}) ) and a second one for the mid-infrared region of the SED, with lower viscosity and a maximum grain size of 1 $\mu$ m (subsection \ref{MIDIR}) ); the first one will be referred to as the and the latter as the according to their vertical scale heights, of which the first has a lower value."
 We found that these two models were the ouly combination able to reproduce the whole SED of this star. luuplving that some vertical grain scerceation niav be present in the disk around IID 31252.," We found that these two models were the only combination able to reproduce the whole SED of this star, implying that some vertical grain segregation may be present in the disk around HD 34282."
 Tn addition. to explain the bump at 3 san we propose the preseuce of a styucture at the inner edee of the disk (subsection 6.2.1)).," In addition, to explain the bump at 3 $\mu$ m we propose the presence of a structure at the inner edge of the disk (subsection \ref{NEARIR}) )."
 For ΠΟ 111569 a sinele disk model accounts for the whole SED (subsection 6.3))., For HD 141569 a single disk model accounts for the whole SED (subsection \ref{MODELHD141569}) ).
 The disk around IID 31282 shows sigus of activity: optical and uear-IR variability. Πα variable cussion aud high fractional IR excess.," The disk around HD 34282 shows signs of activity: optical and near-IR variability, $\alpha$ variable emission and high fractional IR excess."
 Hence. to fit the SED of ΠΟ 31252. we assume that the disk is heated by irracliatiou fromm the central star and viscous dissipation from the nass accretion onto the star.," Hence, to fit the SED of HD 34282, we assume that the disk is heated by irradiation from the central star and viscous dissipation from the mass accretion onto the star."
 For the ceutral star the following stellar parameters are assumed (Table D) Tig=8625 Ik. OR.=1.66 R.. AL—1.59 M... £.=13.61 L. and d=3ls pe. where the stellar radius was calculated from the stellar mass aud the surface gravity.," For the central star the following stellar parameters are assumed (Table \ref{STARS}) ): $T_{\rm eff}\!=\!8625$ K, $R_*\!=\!1.66$ $_\odot$ , $M_*\!=\!1.59$ $_\odot$, $L_*\!=\!13.64$ $_\odot$ and $d\!=\!348$ pc, where the stellar radius was calculated from the stellar mass and the surface gravity."
" For the disk we take au inchnation angle of 56"" (Picttu et al.", For the disk we take an inclination angle of $i\!=\!56^\circ$ (Piéttu et al.
 2003) and an outer radius of 705 AU. which is the disk radius eiveu by these authors scaled roni their distance of LOO pe to our value of 318 pc.," 2003) and an outer radius of 705 AU, which is the disk radius given by these authors scaled from their distance of 400 pc to our value of 348 pc."
 The inner disk radius is calculated seltconsisteutlv using the xoxition of the near-IR bump. the result being 0.31. AU (sce subsection 6.2. 11).," The inner disk radius is calculated self-consistently using the position of the near-IR bump, the result being 0.31 AU (see subsection \ref{NEARIR}) )."
 To find the remainingC» input disk parameters we need o know the mass accretion rate towards the star (which will be derived from ultraviolet Walraveu photometry). he disk viscosity à @vhich wil be fitted to raise the appropriate flux at millimetre wavelengths once we kuow he mass accretion rate) and the dust properties (related o the slope in the millinetre ranee and the IR excess shape at shorter wavelengths).," To find the remaining input disk parameters we need to know the mass accretion rate towards the star (which will be derived from ultraviolet Walraven photometry), the disk viscosity $\alpha$ (which will be fitted to raise the appropriate flux at millimetre wavelengths once we know the mass accretion rate) and the dust properties (related to the slope in the millimetre range and the IR excess shape at shorter wavelengths)."
 The fractional IR excess. FigFL. of TID 31282. namely 63 + 0.19 (Table tj). is a little bit lavecr than the values measured in the SEDs of the TAcBe stars studied w Natta ct al. (," The fractional IR excess, $F_{\rm IR}/F_*$, of HD 34282, namely 0.63 $\pm$ 0.19 (Table \ref{STARS}) ), is a little bit larger than the values measured in the SEDs of the HAeBe stars studied by Natta et al. ("
2001). all of thei beiug simaller than 15.,"2001), all of them being smaller than 0.45."
 These authors reproduce the SEDs assuming that no accretion is preseut. the reprocessa.ie of radiation being the uechanisui invoked to explain the IR excess.," These authors reproduce the SEDs assuming that no accretion is present, the reprocessing of radiation being the mechanism invoked to explain the IR excess."
 We propose hat. eiven the more prominent IR excess of this star compared to those of the TAcBe stars in Natta et al. (," We propose that, given the more prominent IR excess of this star compared to those of the HAeBe stars in Natta et al. ("
2001) aud the higher fractiona TR excess (slightly larecr han 0.5). accretion may be present in this object.,"2001) and the higher fractional IR excess (slightly larger than 0.5), accretion may be present in this object."
 For lis reason. we first try toestimate the mass accretion rate towards ΠΟ 31282.," For this reason, we first try toestimate the mass accretion rate towards HD 34282."
 This paramcter has beenstudied using Walraven ultraviolet photometry of IID 31282 (de Geus et al., This parameter has beenstudied using Walraven ultraviolet photometry of HD 34282 (de Geus et al.
 1990), 1990)
OB runaway stars are massive. early-type stars which have high peculiar velocities relative to the local standard of rest.,"OB runaway stars are massive, early-type stars which have high peculiar velocities relative to the local standard of rest."
 These may reach values as large as 200kms..'. though most are below IQ0Kkms.|.," These may reach values as large as $200 \, {\rm kms}^{-1}$, though most are below $100 \, {\rm kms}^{-1}$."
 The lower velocity limit for a star to be considered a runaway varies between studies but is generally between 20 40kms|.," The lower velocity limit for a star to be considered a runaway varies between studies but is generally between $20$ -- $40 \,{\rm kms}^{-1}$."
 There are also a number of early-type stars at high Galactic latitudes which require high velocities if they were formed in the plane in order to reach their current locations within their lifetimes (Conlon et al., There are also a number of early-type stars at high Galactic latitudes which require high velocities if they were formed in the plane in order to reach their current locations within their lifetimes (Conlon et al.
 1992. Allen Kinman 2004).," 1992, Allen Kinman 2004)."
 In this paper we take the threshold velocity for a star to be deemed runaway to be 30kms'.," In this paper we take the threshold velocity for a star to be deemed runaway to be $30 \, {\rm kms}^{-1}$."
 Despite their high masses. 10 — 30 of O stars and 5 — 10 of B stars have runaway status (Gies 1987).," Despite their high masses, 10 – 30 of O stars and 5 – 10 of B stars have runaway status (Gies 1987)."
 There are two likely ways in which such relatively massive stars can acquire high velocities., There are two likely ways in which such relatively massive stars can acquire high velocities.
 First. they may have been members of close binary systems which were disrupted by the supernova explosion of the companion (the Binary Supernova Scenario (BSS). Blaauw 1961).," First, they may have been members of close binary systems which were disrupted by the supernova explosion of the companion (the Binary Supernova Scenario (BSS), Blaauw 1961)."
 In this case the runaway velocity must be similar to the star's orbital velocity before the supernova., In this case the runaway velocity must be similar to the star's orbital velocity before the supernova.
 Second. runaway velocities can arise because the star interacted dynamically with members of its natal star cluster (the Dynamica Ejection Scenario (DES). Poveda. Ruiz Allen 1967).," Second, runaway velocities can arise because the star interacted dynamically with members of its natal star cluster (the Dynamical Ejection Scenario (DES), Poveda, Ruiz Allen 1967)."
 As early—type runaway stars are fairly massive. this suggests that the interaction was with a binary system of two massive stars. anc the most likely process is binary—binary scattering. in which the eventual runaway was a member of a binary which was disrupted by a more massive one.," As early--type runaway stars are fairly massive, this suggests that the interaction was with a binary system of two massive stars, and the most likely process is binary–binary scattering, in which the eventual runaway was a member of a binary which was disrupted by a more massive one."
 Clear examples of both types of of runaway (supernova disruption and dynamical interaction) are known (Hoogerwert. de Bruijne de Zeeuw 2000).," Clear examples of both types of of runaway (supernova disruption and dynamical interaction) are known (Hoogerwerf, de Bruijne de Zeeuw 2000)."
" The fraction of runaways originating from either route is less clear: significant numbers of runaways do show signs of interaction with a close companion, suggesting that supernovae must be implicated for a substantial fraction."," The fraction of runaways originating from either route is less clear; significant numbers of runaways do show signs of interaction with a close companion, suggesting that supernovae must be implicated for a substantial fraction."
 However. high-latitude early-type stars have normal rotational velocities for their stellar type (Lynn et al.," However, high-latitude early-type stars have normal rotational velocities for their stellar type (Lynn et al."
 2004) as opposed to the fast rotation which might be expected for the secondary from an interacting binary., 2004) as opposed to the fast rotation which might be expected for the secondary from an interacting binary.
 Hoogerwerf. de Bruijne de Zeeuw (2001) trace the paths of runaway stars back to their parent clusters. and find. perhaps two thirds are the result of supernova ejection.," Hoogerwerf, de Bruijne de Zeeuw (2001) trace the paths of runaway stars back to their parent clusters, and find perhaps two thirds are the result of supernova ejection."
 Blaauw (1993) finds that over of massive runaways have enhanced surface He abundances and high rotational velocities. suggesting that their parent systems experienced mass transfer and therefore are good candidates for supernova separation.," Blaauw (1993) finds that over of massive runaways have enhanced surface He abundances and high rotational velocities, suggesting that their parent systems experienced mass transfer and therefore are good candidates for supernova separation."
 It should be noted that rapid rotation. and enhanced abundances are not in themselves unambiguous signs of accretion having taken place. since if a star is formed with rapid rotation then this will affect the surface abundances over its lifetime (e.g. Fliegner. Langer Venn 1996): however the high proportion of runaways displaying hese properties suggests that they are related in these cases o the circumstances which make a runaway.," It should be noted that rapid rotation and enhanced abundances are not in themselves unambiguous signs of accretion having taken place, since if a star is formed with rapid rotation then this will affect the surface abundances over its lifetime (e.g. Fliegner, Langer Venn 1996); however the high proportion of runaways displaying these properties suggests that they are related in these cases to the circumstances which make a runaway."
 This favours the BSS. which is expected to make such stars.," This favours the BSS, which is expected to make such stars."
 Whilst theoretically dynamical ejection could occur in an interacting system after it ws undergone mass transfer. producing a DES runaway with BSS-expected abundances. it it is more likely to have occurred on he main sequence before mass transfer: furthermore. as tighter systems. those with early interaction present a smaller cross-section o collision and are harder to unbind.," Whilst theoretically dynamical ejection could occur in an interacting system after it has undergone mass transfer, producing a DES runaway with BSS-expected abundances, it it is more likely to have occurred on the main sequence before mass transfer; furthermore, as tighter systems, those with early interaction present a smaller cross-section to collision and are harder to unbind."
 On the other hand. population synthesis suggests that only a relatively small fraction of O star runaways ean have come about via the BSS (e.g. Portegies Zwart 2000).," On the other hand, population synthesis suggests that only a relatively small fraction of O star runaways can have come about via the BSS (e.g. Portegies Zwart 2000)."
 The two pictures sketched above predict in principle what Kinds of stars become runaways., The two pictures sketched above predict in principle what kinds of stars become runaways.
 However the O and/or B phases, However the O and/or B phases
Westerbork Synthesis Raclio Telescope data at 150 MlIz and aremin scales.,Westerbork Synthesis Radio Telescope data at 150 MHz and arcmin scales.
 They found that the rms value for polarised foreground is 77.2 l& on 4 are minute scales., They found that the rms value for polarised foreground is $\approx 7.2$ K on 4 arc minute scales.
 Using a polarisation fraction of 0.7. the fluctuations in our polarised foreground at the same frequency with a 5 are minute full width half maximum beam are of the same order. of maenituce (0.7.25Ix— 1519).," Using a polarisation fraction of 0.7, the fluctuations in our polarised foreground at the same frequency with a 5 arc minute full width half maximum beam are of the same order of magnitude $0.7 \times 25~{\rm K} = 18 ~{\rm K}$ )."
 The rotation. of the plane of polarisation of radiation (specified by \) propagating through a magneto-ionic medium results. from the birefringence of the plasma., The rotation of the plane of polarisation of radiation (specified by $\chi$ ) propagating through a magneto-ionic medium results from the birefringence of the plasma.
 This elfect. known as Faraday rotation. has a nonlinear dependence on frequeney such that where © is the Faraday depth anc xo is the non-rotated polarisation angle.," This effect, known as Faraday rotation, has a nonlinear dependence on frequency such that where $\phi$ is the Faraday depth and $\chi_0$ is the non-rotated polarisation angle."
 Faraday. depth is defined by where n. ds the electron. density in cm 7. B is the magnetic field in Gauss. L is the distance. between the point of emission and the observer in. parsec and. dr is an infinitesimal path vector in parsec from the point of emission).," Faraday depth is defined by where $n_e$ is the electron density in $^{-3}$ , $\textit{\textbf{B}}$ is the magnetic field in Gauss, $L$ is the distance between the point of emission and the observer in parsec and $\ud\textit{\textbf{r}}$ is an infinitesimal path vector in parsec from the point of emission)."
 A positive Faracay depth indicates an integrated magnetic field. pointing toward the observer. however. the Faraday depth may. be negative due to the. integrated orientation of the magnetic field. pointing away from the observer along the line of sight.," A positive Faraday depth indicates an integrated magnetic field pointing toward the observer, however, the Faraday depth may be negative due to the integrated orientation of the magnetic field pointing away from the observer along the line of sight."
 Along any particular line of sight. there may be any number of Faraday screens at dillerent. Faraday. depths by which polariscd radiation may be Faraday rotated having been emitted with a unique initial polarisation angle.," Along any particular line of sight, there may be any number of Faraday screens at different Faraday depths by which polarised radiation may be Faraday rotated having been emitted with a unique initial polarisation angle."
 We include only one screen. per line of sight in our simulations in order to show the principle behind. the instrumental polarisation leakage cleaning process., We include only one screen per line of sight in our simulations in order to show the principle behind the instrumental polarisation leakage cleaning process.
 There are two planned target Lolt fields for the MW. centred on (a.d)=μμ.307) and. (T4099.107). which correspond to the Galactic coordinates (fb)e(249) and (2097.|15°) respectively.," There are two planned target EoR fields for the MWA, centred on $(\alpha,\delta) = (4^{\rm h},\,-30^{\circ})$ and $^{\rm h}40^{\rm m},10^{\circ})$, which correspond to the Galactic coordinates $(l,b) \approx (228^{\circ},-49^{\circ})$ and $(209^{\circ},+15^{\circ})$ respectively."
 Ehe interpolated RAL values (and thus Faraday depth) of both of these fields including extragalactic sources are 20zo<50 mum (?)..," The interpolated RM values (and thus Faraday depth) of both of these fields including extragalactic sources are $20 \lsim \,\, \phi \lsim \,\, 50$ $^{-2}$ \citep{johnston-hollitt2004}."
 Ht is reasonable to assume that the magnitude of Faraday depth is either less than or not much larger than extragalacticRAL values in the same direction., It is reasonable to assume that the magnitude of Faraday depth is either less than or not much larger than extragalacticRM values in the same direction.
 RAL ranges in other directions iwe been given by 7. 17zὦὁ10 7j and ? (|ó|z10 radmum 7).," RM ranges in other directions have been given by \cite{haverkorn2003} $-17 \lsim \,\, \phi \lsim \,\, 10$ $^{-2}$ ) and \cite{bernardi2010} $|\phi|\,\lsim\,\,10$ $^{-2}$ )."
 In our svnthetie data cube. we iive chosen to include a single Galactic Faraday. screen with 1<6<5 7 in every line of sight.," In our synthetic data cube, we have chosen to include a single Galactic Faraday screen with $1 \lsim \,\, \phi \lsim \,\, 5$ $^{-2}$ in every line of sight."
 This range of gosshallow Faraday depth has been chosen despite the arger observed values since we have found contamination by »olarised. signal passing through sereens at small Faraday depth more troublesome to clean., This range of shallow Faraday depth has been chosen despite the larger observed values since we have found contamination by polarised signal passing through screens at small Faraday depth more troublesome to clean.
 Fherefore. our results represent a worst case scenario.," Therefore, our results represent a worst case scenario."
 We model the angular distribution of Faraday depth. of the Galactic screen. by a small-eradient-plane over the sky-plane (such that. for generality. Vor.y)xa| 9).," We model the angular distribution of Faraday depth of the Galactic screen by a small-gradient-plane over the sky-plane (such that, for generality, $\nabla \phi(x,y) \propto \hat{\xvec} + \hat{\yvec}$ )."
 This is done to approximate the small. slowly varying Faraday depth over the proposed Loh. fields of the MIWA.," This is done to approximate the small, slowly varying Faraday depth over the proposed EoR fields of the MWA."
 In dealing with the RAL synthesis of a distribution of svnchrotron-emitting ancl Faraday rotating regions along a line of sight. we Follow thework of ? and direct. readers to their paper for à more thorough explanation. as well as ? for an application of the technique.," In dealing with the RM synthesis of a distribution of synchrotron-emitting and Faraday rotating regions along a line of sight, we follow thework of \cite{brentjens2005} and direct readers to their paper for a more thorough explanation, as well as \cite{schnitzeler2009} for an application of the technique."
 The Faraday dispersion. function. (6). can be defined through where the frequency dependence of P? has been given in terms of A7 since. A7 and ὁ form a Fourier-variable pair.," The Faraday dispersion function, $F(\phi)$, can be defined through where the frequency dependence of $P$ has been given in terms of $\lambda^2$ since $\lambda^2$ and $\phi$ form a Fourier-variable pair."
 In. practice. the sampling of A? will be limited by the finite frequency. bandpass of the correlator.," In practice, the sampling of $\lambda^2$ will be limited by the finite frequency bandpass of the correlator."
 Therefore. we introduce a weighting or sampling function. VV(A7). such that where. for example. Other forms of the sampling function may include non-uniform weighting to account lor non-ideal response for certain channels (at the shoulders. of the banclpass. for example).," Therefore, we introduce a weighting or sampling function, $W(\lambda^2)$, such that where, for example, Other forms of the sampling function may include non-uniform weighting to account for non-ideal response for certain channels (at the shoulders of the bandpass, for example)."
 Equation (11)) can be Fourier inverted. to find £(6) and convolved with the inverse Fourier transform of the sampling function., Equation \ref{eq:Pobs}) ) can be Fourier inverted to find $F(\phi)$ and convolved with the inverse Fourier transform of the sampling function.
 This gives the Faraday. clispersion function that would be obtained given the limited sampling of P. where the rotation measure spread function. 2). is defined by and the appropriate normalisation factor is The rotation measure spread function is a complex-valued. function whose magnitude is peaked and svnimetric about ó=O," This gives the Faraday dispersion function that would be obtained given the limited sampling of $P$, where the rotation measure spread function, $R(\phi)$, is defined by and the appropriate normalisation factor is The rotation measure spread function is a complex-valued function whose magnitude is peaked and symmetric about $\phi = 0$."
 The lower panel of Figure 3. shows the magnitude. real part ancl imaginary part of (o) for a 32 Mllz bandpass of uniform response centred on 117.5 MllIz.," The lower panel of Figure \ref{fig:RMSF} shows the magnitude, real part and imaginary part of $R(\phi)$ for a 32 MHz bandpass of uniform response centred on 177.5 MHz."
 Ht can be seen that both the real and imaginary partsoscillate rapidly throughout the central response peak., It can be seen that both the real and imaginary partsoscillate rapidly throughout the central response peak.
 This makes it difficult to determine x. which given the form of Equations (13)) ancl (14)) is the polarisation angle derotated back to A7.= 0.," This makes it difficult to determine $\chi$ , which given the form of Equations \ref{eq:Fobs}) ) and \ref{eq:RMSF}) ) is the polarisation angle derotated back to $\lambda^2 = 0$ ."
 It is possible. instead. to shift," It is possible, instead, to shift"
nreenlar intervals of typically 2090 mun. depending on skv stability and presence of the Moon.,"irregular intervals of typically 20–90 min, depending on sky stability and presence of the Moon."
 The sky counts were then interpolated lincarly aud subtracted., The sky counts were then interpolated linearly and subtracted.
 Di a few cases we used a cubic spline for the sky interpolation. when it was clear that this procedure was giving better results than the linear fit.," In a few cases we used a cubic spline for the sky interpolation, when it was clear that this procedure was giving better results than the linear fit."
 All the PAIT data were then corrected for extinction., All the PMT data were then corrected for extinction.
 Afterwards. they were used to exanune possible transparency variations.," Afterwards, they were used to examine possible transparency variations."
 Iu a few cases of high sky instability. the count ratio between channel 1 and channel 2 was used iustead of channel 1 counts ouly.," In a few cases of high sky instability, the count ratio between channel 1 and channel 2 was used instead of channel 1 counts only."
 Some sinoothing of the chaunel 2 data was applied when possible., Some smoothing of the channel 2 data was applied when possible.
 Systematic long time scale treads (7 2 hours). probably due to tube drifts and/or to residual extinction. were finally compensated by means of linear or cubic spline interpolation.," Systematic long time scale trends $>$ 2 hours), probably due to tube drifts and/or to residual extinction, were finally compensated by means of linear or cubic spline interpolation."
 For the Calw Alto CCD data. LO comparison stars were selected. after having becu tested for photometric constancy.," For the Calar Alto CCD data, 10 comparison stars were selected, after having been tested for photometric constancy."
 Their average maeuitucde was subtracted from the 225321 measurements on a point by point basis., Their average magnitude was subtracted from the 2324 measurements on a point by point basis.
 Differential extinction was corrected by ποστς of a cubic spline., Differential extinction was corrected by means of a cubic spline.
 Finally all the single data sets (PNE. | CCD) were set to adean value of zero., Finally all the single data sets (PMT + CCD) were set to a mean value of zero.
 The times of all data were then converted to Barvceutric Julian Date using the algorithin of Stuupff (1980)., The times of all data were then converted to Barycentric Julian Date using the algorithm of Stumpff (1980).
 The accuracy of the original times was of the order of τε 0.35 (Beijing). d ss (Loiano). + 0.2s8 (MeDonald) and + Iss (Calay Alto).," The accuracy of the original times was of the order of $\pm$ s (Beijing), $\pm$ s (Loiano), $\pm$ s (McDonald) and $\pm$ s (Calar Alto)."
 For Calar Alto Iss is also the time accuracy of each measurement., For Calar Alto s is also the time accuracy of each measurement.
 Moreover. to have a iore homiogeueous data set. we have binned the PAIT data to an effective iuteeration time of 90s. The value of 90ss has been choseu because it corresponds to the mean distance between consecutive CCD observations.," Moreover, to have a more homogeneous data set, we have binned the PMT data to an effective integration time of s. The value of s has been chosen because it corresponds to the mean distance between consecutive CCD observations."
 When more than one site was active at the same time. in the overlap regions. we applied a weighted average of the data obtained at the different sites.," When more than one site was active at the same time, in the overlap regions, we applied a weighted average of the data obtained at the different sites."
 In this wav even lower quality data cau be used to inuprove the S/N ratio (see Moskalik 1993)., In this way even lower quality data can be used to improve the S/N ratio (see Moskalik 1993).
 Iu. its final form. the data set is coustituted by the time of each integration. the fractional departure of the count rate from the mean Guodulation iuteusitv). aud the error.," In its final form, the data set is constituted by the time of each integration, the fractional departure of the count rate from the mean (modulation intensity), and the error."
 We computed a simele sine function with unit amplitude at the same sample times of the cutire data set. (window function)., We computed a single sine function with unit amplitude at the same sample times of the entire data set (window function).
 The discrete Fourier transform of the window function eives the spectral window. which is shown in Figure 2.," The discrete Fourier transform of the window function gives the spectral window, which is shown in Figure 2."
 For more completeness. both the amplitude aud the power (amplitude squared) spectra of the window," For more completeness, both the amplitude and the power (amplitude squared) spectra of the window"
until the universe in enriched by metals. the quick start allows the holes in the most massive halos to reach the high SMDII masses suggested bv the SDSS quasars.,"until the universe in enriched by metals, the quick start allows the holes in the most massive halos to reach the high SMBH masses suggested by the SDSS quasars."
 [Cis worth noting that super-critical accretion in the fashion described here occurs at very high redshift. and. that stops well belorez6.," It is worth noting that super-critical accretion in the fashion described here occurs at very high redshift, and that stops well before$z\simeq 6$."
 We do not expect. therefore. that SDSS quasars are accreting above the Eddington value. consistently with observations (Barth et al.," We do not expect, therefore, that SDSS quasars are accreting above the Eddington value, consistently with observations (Barth et al."
 2003. Willott. MeLure Jarvis 2003).," 2003, Willott, McLure Jarvis 2003)."
 A signature of super-eritical accretion is the occurrence of outflows. that we envisage would quench activity.," A signature of super-critical accretion is the occurrence of outflows, that we envisage would quench activity."
 Outllows from these sources could leave their imprint by spreading metals into the IGM early-on., Outflows from these sources could leave their imprint by spreading metals into the IGM early-on.
 One might be concerned (hat this model overproduces large SMDIIS at. low redshift This is not the case. since only a tiny [fraction of halos have Ti210K. when the Universe is still metal free.," One might be concerned that this model overproduces large SMBHs at low redshift This is not the case, since only a tiny fraction of halos have $T_\vir\gta 10^4\,$ K, when the Universe is still metal free."
 Assuming that metal pollution starts allecting the dise cooling and [fragmentation al 2ZiLO. only a fraction zz2xLO* of halos at this time is likely to be the outcome of a merger hierarchy which involves a seed MBIT at 2:220.," Assuming that metal pollution starts affecting the disc cooling and fragmentation at $z\lta10$, only a fraction $\approx 2\times 10^{-3}$ of halos at this time is likely to be the outcome of a merger hierarchy which involves a seed MBH at $z\gta20$."
" So. even if all these halos with mass Af,~10!""AL. hosted a MDII with mass 105M... the density Ovipy=(0.002O1;Alpi)ο* would still be much lower than the local one."," So, even if all these halos with mass $M_h\sim10^{10}\msun$ hosted a MBH with mass $\sim 10^6\msun$, the density $\Omega_{\rm MBH}=(0.002\,\Omega_M\,\langle M_{\rm BH}\rangle)/{M_h}=10^{-8}$ would still be much lower than the local one."
" We will discuss this issue in detail. along with the possibility that black holes can be displaced from ealaxy centers and ejected into the IGM by the ""gravitational rocket effect in a subsequent paper."," We will discuss this issue in detail, along with the possibility that black holes can be displaced from galaxy centers and ejected into the IGM by the `gravitational rocket' effect in a subsequent paper."
 As a side result. this model allows a very economic’ re-jonization in terms of DII seeds density.," As a side result, this model allows a very 'economic' re-ionization in terms of BH seeds density."
" Macau (2004) found that preealactic quasars powered by MDIIs forming in 3.50 peaks will reionize the IGM if thev accrete at the Ecddington rate a mass of order 10"" the mass of the host halo in every major merger.", Madau (2004) found that pregalactic quasars powered by MBHs forming in $\sigma$ peaks will reionize the IGM if they accrete at the Eddington rate a mass of order $10^{-3}$ the mass of the host halo in every major merger.
 Alternatively. seed holes must be more numerous (e.g. o density [Iuetuations) at the start in order to sustain the early production of ionizing radiation.," Alternatively, seed holes must be more numerous (e.g. $\sigma$ density fluctuations) at the start in order to sustain the early production of ionizing radiation."
" This latter assumption would imply (that all galaxies in the local Universe with total mass My>5xLO?NL, are expected to host a central MDII.", This latter assumption would imply that all galaxies in the local Universe with total mass $M_h>5\times10^{9}\msun$ are expected to host a central MBH.
 Allowing for a super-crilical accretion phase. the number of ionizing photons per hydrogen atom produced by pregalactic quasars approaches unity al 2Z15. even assuming a very low initial densitw in seeds (e.g. 4-7. peaks). thus relieving the need for a very large number of seeds - diffieult to reconcile with low redshift constraints.," Allowing for a super-critical accretion phase, the number of ionizing photons per hydrogen atom produced by pregalactic quasars approaches unity at $z\gtrsim 15$, even assuming a very low initial density in seeds (e.g. $\sigma$ peaks), thus relieving the need for a very large number of seeds - difficult to reconcile with low redshift constraints."
 The growth of SMBIIs that can power SDSS quasars can be explained within a ACDM universe also assumüng a more optimistic view in terms of accretion ancl mereine., The growth of SMBHs that can power SDSS quasars can be explained within a $\Lambda$ CDM universe also assuming a more optimistic view in terms of accretion and merging.
 Yoo Miralda-Escudé (2004) showed z6 quasars can be explained assuming contünued Eddington-limited. accretion onto MBlIIs forming in halos with Zi;> 2000lN al z<40., Yoo Miralda-Escudé (2004) showed $z\simeq 6$ quasars can be explained assuming continued Eddington-limited accretion onto MBHs forming in halos with $T_{\rm vir} >2000$ K at $z\leq 40$.
 Their model assumes. also. à much higher influence of DII mergers in increasing the MDII mass: a contribution by itself of order 10? M.," Their model assumes, also, a much higher influence of BH mergers in increasing the MBH mass: a contribution by itself of order $10^9\msun$ ."
 Their investigation takes into account the negalive feedback that dynamical processes al DII mergers Ceravitational rocket. see also," Their investigation takes into account the negative feedback that dynamical processes at BH mergers (`gravitational rocket', see also"
"This perturbation theory is visualised through a Lic triangle: In the part ""TAy we put the averaged quadratic. Hamiltonian. explained. in. the previous. section.",This perturbation theory is visualised through a Lie triangle: In the part ${\mathcal H}^0_0$ we put the averaged quadratic Hamiltonian explained in the previous section.
. In agHY we put what remains.. i.c. the perturbation containing the higher order terms in C. V. M. Z. and the short-period In the principal diagonalὃν we will find the averagedo Hamiltonian: H=SOawit)Hi.," In ${\mathcal H}^0_1$ we put what remains, i.e. the perturbation containing the higher order terms in $U$ , $V$, $W$, $Z$, and the short-period In the principal diagonal we will find the averaged Hamiltonian: $\bar {\mathcal H}=\sum_{i=0}^{\text{order}} {\mathcal H}^i_0/i!$."
} Lo oget this averagedὃν Hamiltonian we use the following homological equation: with the intermediate AY computed as follows: where HW; is the generator of the th Dlloor of the Lie triangle. €:) designates the Poisson bracket and |.| is the binomial coellicient.," To get this averaged Hamiltonian we use the following homological equation: with the intermediate ${\mathcal H}^n_j$ computed as follows: where $W_i$ is the generator of the $i$ th floor of the Lie triangle, $(\; ; \; )$ designates the Poisson bracket and $\left(\begin{array}{c}\!\!j\!\!\\\!\!i\!\!\end{array}\right)$ is the binomial coefficient."
 Note that the order (or the number of Hloors of the Lie triangle) is chosen in such a wav that the transformation converges numerically. in other words we stop when we do not get more significant information by &oing one order further.," Note that the order (or the number of floors of the Lie triangle) is chosen in such a way that the transformation converges numerically, in other words we stop when we do not get more significant information by going one order further."
 These generators will help us to compute the evolution of any variable., These generators will help us to compute the evolution of any variable.
 Let us show how to get the &enerator of the first lloor., Let us show how to get the generator of the first floor.
 . . ⋅ ∖∖⋖⋅≼∙∪⊔≱∖⊔⇂⋖⋅↓⋅↥⇂↥∢⊾∐↓⋅⊳∖∣↓↕∪⊔↓∪↓∪⋃⊔↛⋜↧↓⋖⊾⊏⇂⋯↿↓∪⊔∶⋥−↙∣⊏∶⋥−↙∣↾↖↿∖∣⊏↾∶⊓⊥∃⊳↓⊔↿↓⊔⊳∖⋖⋅⊏⋯⊔↓∪, We consider the first homological equation: ${\mathcal H}_0^1={\mathcal H}_1^0+({\mathcal H}_0^0;W_1)$.
⊔⋥−↙∣↾↓⊳∖↓∡⊔∪∖∖⋎⊔⋜⋯∠⇂∖∖⊽∢⋅≼∙⇂↥∪∪≱∖⋖⋅⋥−↙∣⊏⊥↿∪∣⋊⋅5. 1. PHIDPE1PP⇁ . 1. PETEN1 ∕) the average of 241., In this equation ${\mathcal H}_1^0$ is known and we choose ${\mathcal H}_0^1$ to be the average of ${\mathcal H}_1^0$.
 In other words. Ha will contain only terms without short. periods ancl of order larger or equal to 3.," In other words, ${\mathcal H}_0^1$ will contain only terms without short periods and of order larger or equal to 3."
 So. expanding the Poisson bracket. ancl using equation (39)). we have the following equation to solve: Since Hi only consists of all the terms of 240 without short. periods. the right-hand side term of the previous equation only contains short periodic terms.," So, expanding the Poisson bracket, and using equation \ref{h00}) ), we have the following equation to solve: Since ${\mathcal H}_0^1$ only consists of all the terms of ${\mathcal H}_1^0$ without short periods, the right-hand side term of the previous equation only contains short periodic terms."
" Lt is then easy to compute M, and see that this is also only composed of short periodi terms.", It is then easy to compute $W_1$ and see that this is also only composed of short periodic terms.
 The computation of the other orders is done in a similar With the generators. we can now compute the evolution of any function of the variables.," The computation of the other orders is done in a similar With the generators, we can now compute the evolution of any function of the variables."
 First. we go back to cartesian coordinates to avoid the singularities when any of the moment is 0 (the angle is then undefined) and the formula is where the Poisson bracket is evaluated at the equilibria wy.re.£1.£5.Ji.HoΗνtp. After the use of this Lic algorithm. we have our transformed. Hamiltonian in the diagonal. without short. periods: HeaLi0Hg," First, we go back to cartesian coordinates to avoid the singularities when any of the moment is 0 (the angle is then undefined) and the formula is where the Poisson bracket is evaluated at the equilibria $\bar x_1,\bar x_2,\bar \xi_1,\bar \xi_2,\bar y_1,\bar y_2,\bar \eta_1,\bar \eta_2$ After the use of this Lie algorithm, we have our transformed Hamiltonian in the diagonal, without short periods: $\bar{\mathcal H}=\sum_{i=0}^{\text{order}} {\mathcal H}^i_0/i!$."
 Until here. except for the fact that we have 2 additional degrees of freedom. our process is very similar to the one described in our previous study (Duleyetal.2009).," Until here, except for the fact that we have 2 additional degrees of freedom, our process is very similar to the one described in our previous study \citep{dnrl09}."
.. Phe main dilference is the change of fundamental In this Hamiltonian. the linear terms in C. V. MW and Z changed with the transformation process. vielding correctionsto the free frequencies.," The main difference is the change of fundamental In this Hamiltonian, the linear terms in $U$, $V$, $W$ and $Z$ changed with the transformation process, yielding correctionsto the free frequencies."
 These corrections also appeared in our 2-degree of freedom work. but so imperceptibly that we did not mention," These corrections also appeared in our 2-degree of freedom work, but so imperceptibly that we did not mention"
temperature and density structure.,temperature and density structure.
" For details on the used iron model atom, see Wassermann (2010)."," For details on the used iron model atom, see Wassermann (2010)."
 We employ new versions of iron datasets (Kurucz2009)!., We employ new versions of iron datasets (Kurucz.
". They include many more levels and lines, in particular the four lines discussed in this paper."," They include many more levels and lines, in particular the four lines discussed in this paper."
 Properties of the newly detected lines are listed in Table 1.., Properties of the newly detected lines are listed in Table \ref{tab:levels}.
 They all arise from the same lower level., They all arise from the same lower level.
" We specify the Kurucz wavelengths, as well as those measured by Landi Young (2010)."," We specify the Kurucz wavelengths, as well as those measured by Landi Young (2010)."
 The differences are all smaller thanAA., The differences are all smaller than.
. The largest deviation AA)) is shown by the lline., The largest deviation ) is shown by the line.
 The Kurucz wavelengths should be more accurate than the measured wavelengths since the energy levels involved were determined from more than one line., The Kurucz wavelengths should be more accurate than the measured wavelengths since the energy levels involved were determined from more than one line.
 We also list the f-values from the Kurucz data., We also list the f-values from the Kurucz data.
" A simplified Grotrian diagram indicating the observed line transitions is shown in reffig,,odelatom..", A simplified Grotrian diagram indicating the observed line transitions is shown in \\ref{fig_modelatom}.
" We computed a small model grid in order to study the dependence of the lines onΤεῃ,,g,, and Fe abundance."," We computed a small model grid in order to study the dependence of the lines on, and Fe abundance."
" The result for 2 iis displayed in reffig,ariation, , andtheotherlinesbehave similarly."," The result for $\lambda$ is displayed in \\ref{fig_variation}, and the other lines behave similarly."
 Itturnsoutthatefectiv aarethemostfavourable f orthedetectionof, It turns out that effective temperature and gravity of are the most favourable for the detection of.
 Vit1.[talsoex plainswhyFe, It also explains why lines are not seen in objects that are much cooler or hotter.
appropriate the relationship between 7? and ov derived by Melxee Zweibel. we are then positing an isothermal equation of state: llere «yp. the effective isothermal sound speed. is taken to be a fixed constant al a given instant of time.,"appropriate the relationship between $P$ and $\delta v$ derived by McKee Zweibel, we are then positing an isothermal equation of state: Here $a_T$, the effective isothermal sound speed, is taken to be a fixed constant at a given instant of time."
 This same equantity varies temporally; indeed. (his latter variation essentially drives the cloud's evolution.," This same quantity varies temporally; indeed, this latter variation essentially drives the cloud's evolution."
 We emphasize that ay does not. as in ordinary gas dinamies. give the magnitude of random. microsopic velocities.," We emphasize that $a_T$ does not, as in ordinary gas dynamics, give the magnitude of random, microsopic velocities."
" Instead. (his quantity represents. however crudely. the bulk motion of turbulent. eddies: (hese eddies create (he pressure J? via MIID Waves,"," Instead, this quantity represents, however crudely, the bulk motion of turbulent eddies; these eddies create the pressure $P$ via MHD waves."
 since we are modeling the cloud as an isothermal sphere. we [ace the familiar difficulty (hat ils mass is infinite unless the configuration is bounded externally.," Since we are modeling the cloud as an isothermal sphere, we face the familiar difficulty that its mass is infinite unless the configuration is bounded externally."
" We therelore picture (he cloud as being surrounded by a low-density. high-temperature mecdium will an associated pressure J?,."," We therefore picture the cloud as being surrounded by a low-density, high-temperature medium with an associated pressure $P_\circ$."
 This latter quantity is also the pressure at the boundary of our spherical cloud., This latter quantity is also the pressure at the boundary of our spherical cloud.
 The cloud density at the boundary. p.. isfound from equation (3). given knowledge of «5.," The cloud density at the boundary, $\rho_\circ$, isfound from equation (3), given knowledge of $a_T^2$."
 The mathematical description of a sell-eravilating.isothermal cloud in hwvdrostatic balance is well known (seeStahler&Palla2004.Chap.9).," The mathematical description of a self-gravitating,isothermal cloud in hydrostatic balance is well known \citep[see][Chap.~9]{sp04}."
. All structural properties follow from the isothermal Lane-Eimelen equation: ∖∖↽↕⊔↥∣↽≻∪∏∐≼⇂≀∐⋅⋡∖↽≺∢∪∐≼, All structural properties follow from the isothermal Lane-Emden equation: with boundary conditions.
∐∐∪∐⋝∖⊽∣⋎⋜⋝∪↕⋝∶∣⋎∣⋜⋝∪↕⋟∶∪⋅⋅∐≼↲↕⋅≼↲⋅∣⋎↕⋝∖⊽⊔∐↲≺∐∐∐↲∐⊳∖⊽↕∪↕∐≼↲⊳∖⋱∖⊽↓⋟∪↕⋅∐↓∪↓⋟⊔∐↲ ≸↽↔↴↕⋅≀↧↴∖⇁∐≀↧↴∐∪↕⋯↥↕↽≻∪∩↲∐∐≀↧↴↥∩∙↙∕∶ The nondimensional radius € is obtained from the dimensional r using G. a5. and the central clensity p:,"Here, $\psi$ is the dimensionless form of the gravitational potential $\phi_g$ : The nondimensional radius $\xi$ is obtained from the dimensional $r$ using $G$ , $a_T^2$ , and the central density$\rho_c$ :"
Crouud-based loug-slit spectra of N32 suitable fo| Lick/IDS index analysis were obtained at the MDMNL Observatory 2.1 m telescope cduriug three ruis: 1993 September. 1991 October. aud 1997 June.,"Ground-based long-slit spectra of M32 suitable for Lick/IDS index analysis were obtained at the MDM Observatory 2.4 m telescope during three runs: 1993 September, 1994 October, and 1997 June."
" The Mark 3 spectrograph was used witli blue-seusitive chips (""Charlotte in 1993 aud 1901 and “Templeton” in 1997). with wavelength: coverage [from about 3800 to 6100 aal 2.3 | dispersion."," The Mark 3 spectrograph was used with blue-sensitive chips (“Charlotte” in 1993 and 1994 and “Templeton” in 1997), with wavelength coverage from about 3800 to 6100 at 2.3 $^{-1}$ dispersion."
 The resolution was a function of waveleneth and run but was always less than Lick/IDS and therefore easily transformable to the Lick/LDS system given the nightly set of staucdad stars observed., The resolution was a function of wavelength and run but was always less than Lick/IDS and therefore easily transformable to the Lick/IDS system given the nightly set of standard stars observed.
 Both chips had the same pixel size. so the spatial scale was coustaut at τς xel|.," Both chips had the same pixel size, so the spatial scale was constant at $0\farcs
78$ $^{-1}$."
 The M32 spectra were obtained witl the slit oriented north-south., The M32 spectra were obtained with the slit oriented north-south.
 This is 107 away from tle major axis of the galaxy [PA = 170°: deVaucouleursetal. (1991)]] mie amoults toa foreshertening of only15€... which is less than the uncertainty iu the spatial scale.," This is $\arcdeg$ away from the major axis of the galaxy [PA = $\arcdeg$; \citet{RC3}] ] but amounts to a foreshortening of only, which is less than the uncertainty in the spatial scale."
 Tiree exposures iu 1993. three in 199f. and our iu 1997. with exposure tines rane& from 600 to 1200 s. were bias-subtracted aud flat-fielclecl using IRAE tasks.," Three exposures in 1993, three in 1994, and four in 1997, with exposure times ranging from 600 to 1200 s, were bias-subtracted and flat-fielded using IRAF tasks."
 Ouly tle 1901 ex2051165 wele sUliciently Lomogeneous to be co-added., Only the 1994 exposures were sufficiently homogeneous to be co-added.
 This was done. aud we analyzed he 1jedian image iu conjunction with the others.," This was done, and we analyzed the median image in conjunction with the others."
 The sky was sampled more than 100” away aid was dominated yy ter'estrial sky rather than galaxy Digit., The sky was sampled more than $\arcsec$ away and was dominated by terrestrial sky rather than galaxy light.
 The galaxy [ades by [actors of 15— I0 roni the last extraced spectra at -Ó to where the sky was sampled., The galaxy fades by factors of $-$ 40 from the last extracted spectra at $\arcsec$ to where the sky was sampled.
 Ludices are affected by such seκ |n secoud order., Indices are affected by such self-subtraction in second order.
 For example. if the LH 1jeasureiment of Hj is 2.0 yout the sky region of M32 has He=1.5A. the 55” iueasurement will be decreased by. at most. (3.0—1.5)/15=0.03A.," For example, if the $\arcsec$ measurement of $\beta$ is 2.0 but the sky region of M32 has $\beta = 1.5$, the $\arcsec$ measurement will be decreased by, at most, $(2.0 - 1.5)/15 = 0.03$."
 I£1je sky has tle saine index value as the target region. uo chauge will 'esult.," If the sky has the same index value as the target region, no change will result."
 Other defects were present in some images., Other defects were present in some images.
 Two images πας saturated pixels rear the nucleus. hree sullered a sky oversubtraction probeim duriug processiig that had to be corrected by hand. auc all images had a [air nuiiber of cosmic ray tracks excep for the oue meciau-combined image rou 199[.," Two images had saturated pixels near the nucleus, three suffered a sky oversubtraction problem during processing that had to be corrected by hand, and all images had a fair number of cosmic ray tracks except for the one median-combined image from 1994."
 Seventy 1 pixel wide spectra were exracted from each side of the nucleis. plus 1 central pixel.," Seventy 1 pixel wide spectra were extracted from each side of the nucleus, plus 1 central pixel."
 These were cross-correated with svuthetic stellar temslates to put them on a zero-velocity waveleugth scale., These were cross-correlated with synthetic stellar templates to put them on a zero-velocity wavelength scale.
 Lick/I1D5 indices were measured from each s»ectruu., Lick/IDS indices were measured from each spectrum.
 Eac iiudex had 11 incepeuclent 1οο... al eacl1 slit location. so with symunetri¢ north-south pairs aialvzed together. all radii except the central pixel had 22 measurements.," Each index had 11 independent measurements at each slit location, so with symmetric north-south pairs analyzed together, all radii except the central pixel had 22 measurements."
 The expectaion was that most iudices would cluster arouud the true index value. but some would be afected by a cosmic ray aud would be very wild.," The expectation was that most indices would cluster around the true index value, but some would be affected by a cosmic ray and would be very wild."
 The mediau was therefore adopted as the statistic of choice., The median was therefore adopted as the statistic of choice.
 The error was computed by oolstrap resampling., The error was computed by bootstrap resampling.
 The couiplete table of inedian index vaues and errors shown in Fig 3. is avalable [rom the author., The complete table of median index values and errors shown in Fig \ref{fig3ab} is available from the author.
 Note that the iudex TiO» is uot included because it falls past the red eud of the NDNI spectra., Note that the index $_2$ is not included because it falls past the red end of the MDM spectra.
 Fieure 3. shows the main gracieit results. compared with uuclear values from tle original Lick/IDS data set aud also C93 for overlapping indices.," Figure \ref{fig3ab} shows the main gradient results, compared with nuclear values from the original Lick/IDS data set and also G93 for overlapping indices."
 & polvnomial-sinoothec version of the, A polynomial-smoothed version of the
"Withinlo, two classes of solutions are found, either on the PMS (30—40 MMa) or on the MS (for ages >800 MMa with no spots, or >100 MMa when including spots).","Within$1\sigma$, two classes of solutions are found, either on the PMS $30-40$ Ma) or on the MS (for ages $>800$ Ma with no spots, or $>100$ Ma when including spots)."
" The range of stellar radii (which are directly proportional to the planetary radii that are inferred) extend from 0.88 to 0.93Ro at lo, but the smallest values are obtained for either the youngest or oldest solutions."," The range of stellar radii (which are directly proportional to the planetary radii that are inferred) extend from $0.88$ to $0.93\,\rm R_\odot$ at $1\sigma$, but the smallest values are obtained for either the youngest or oldest solutions."
 The other panels in Fig., The other panels in Fig.
" 5 highlight the consequences of the different hypotheses on the solutions, when considering only solar composition models."," \ref{fig:rstar_age} highlight the consequences of the different hypotheses on the solutions, when considering only solar composition models."
" Varying the mixing length parameter has consequences for the 1c solutions: a lower α value leads to a wider range of solutions at intermediate ages, while a higher o increases the separation between the very young and the very old solutions."," Varying the mixing length parameter has consequences for the $1\sigma$ solutions: a lower $\alpha$ value leads to a wider range of solutions at intermediate ages, while a higher $\alpha$ increases the separation between the very young and the very old solutions."
" However, when considering the global 3c envelope and accounting for spots, the solutions are very similar."," However, when considering the global $3\sigma$ envelope and accounting for spots, the solutions are very similar."
" The solutions obtained by using the p, value of ? are quite similar to the nominal ones, but are regarded as slightly constrained due to the assumption of a circular orbit."," The solutions obtained by using the $\rho_\star$ value of \citet{Alonso+08} are quite similar to the nominal ones, but are regarded as slightly over-constrained due to the assumption of a circular orbit."
 The last four panels in Fig., The last four panels in Fig.
 5 provide another test of the robustness of the solutions by a comparison with YY and BCAH98 evolution models., \ref{fig:rstar_age} provide another test of the robustness of the solutions by a comparison with YY and BCAH98 evolution models.
 All models appear to be in excellent agreement at least to the 2c level., All models appear to be in excellent agreement at least to the $2\sigma$ level.
" A minor difference is the absence of lo PMS solutions in the no-spot case for BCAH98, contrary to the CESAM and YY results."," A minor difference is the absence of $1\sigma$ PMS solutions in the no-spot case for BCAH98, contrary to the CESAM and YY results."
 Additional constraints on the stellar age may be derived from CoRoT-2 being a rapid rotator., Additional constraints on the stellar age may be derived from CoRoT-2 being a rapid rotator.
" According to ?,, the 4.5 day rotation period with B—V=0.854 (?) implies an age typical of that of the Pleiades, i.e., 130 Ma."," According to \citet{MH08}, the 4.5 day rotation period with $\rm B-V=0.854$ \citep{Lanza+09} implies an age typical of that of the Pleiades, i.e., $\sim 130\,$ Ma."
" Given the absence of stars with similar B-V and periods shorter than 8 days in the Hyades (~625 Ma), we estimate that CoRoT-2 is less than MMa old, which thus restricts the ensemble of solutions from Fig."," Given the absence of stars with similar B-V and periods shorter than 8 days in the Hyades $\sim 625\,$ Ma), we estimate that CoRoT-2 is less than Ma old, which thus restricts the ensemble of solutions from Fig."
 5 quite significantly., \ref{fig:rstar_age} quite significantly.
" We now focus on the young (« 500MMa) solutions and compare CESAM with BCAH98 in the (R,, M,, age) parameter space. ("," We now focus on the young $<500$ Ma) solutions and compare CESAM with BCAH98 in the $R_\star$, $M_\star$, age) parameter space. ("
"We do not show the comparisons with YY, since it closely ressembles CESAM).Figure 6 shows that in the no-spot case, the lo solutions are limited to the PMS phase for CESAM, and there are no solutions when using the BCAH98 models.","We do not show the comparisons with YY, since it closely ressembles CESAM).Figure \ref{fig:ms} shows that in the no-spot case, the $1\sigma$ solutions are limited to the PMS phase for CESAM, and there are no solutions when using the BCAH98 models."
" At 2 and 3c, the solutions spanthe entire age range and both models yield very similar results."," At $2$ and $3\sigma$, the solutions spanthe entire age range and both models yield very similar results."
" We note that MS solutions imply stellar masses slightly above that of the Sun, whereas PMS solutions are distributed between ~0.9 and 1.0Ms."," We note that MS solutions imply stellar masses slightly above that of the Sun, whereas PMS solutions are distributed between $\sim 0.9$ and $1.0\rm\,M_\odot$."
" Figure 7 compares the solutions in the (R,, M.) space."," Figure \ref{fig:msrs} compares the solutions in the $R_\star$, $M_\star$ ) space."
 There is a clear positive correlation between the two quantities., There is a clear positive correlation between the two quantities.
" For ages older than 50MMa, the solutions are confined to high mass values and there is a very good agreement between CESAM and BCAH98."," For ages older than Ma, the solutions are confined to high mass values and there is a very good agreement between CESAM and BCAH98."
" At young ages however, as seen in previous diagrams, the CESAM and BCAH98 solutions differ."," At young ages however, as seen in previous diagrams, the CESAM and BCAH98 solutions differ."
 The influence of the presence of spots is relatively small., The influence of the presence of spots is relatively small.
 The results in terms of the stellar mass and radius are summarized in Table 2 for the different age classes., The results in terms of the stellar mass and radius are summarized in Table \ref{tab:star} for the different age classes.
When no solutions were found within 16. the 2c solutions are indicated.,"When no solutions were found within $1\sigma$ , the $2\sigma$ solutions are indicated."
" Physical parameters for the planet are derived from the solution for the star using the period Po», the radii ratio k= Rp/R,, and the semi-amplitude star velocity K (see Table 1)) using the following equations (e.g.??) "," Physical parameters for the planet are derived from the solution for the star using the period $P_{\rm orb}$ , the radii ratio $k=R_{\rm p}/R_\star$ , and the semi-amplitude star velocity $K$ (see Table \ref{tab:obs}) ) using the following equations \citep[e.g.][]{Sozzetti2007, Beatty2007}
 "
The historical development of closed model equations for the stress tensor in a turbulent Duid is described in the review article of Speziale (1991).,The historical development of closed model equations for the stress tensor in a turbulent fluid is described in the review article of Speziale (1991).
 Early studies were based on the concepts of eddy viscosity and mixing length introduced by Joussinesq and. Prandtl., Early studies were based on the concepts of eddy viscosity and mixing length introduced by Boussinesq and Prandtl.
 A systematic investigation of the equation for the mean Itevnolds stress was initiated in the 1950s., A systematic investigation of the equation for the mean Reynolds stress was initiated in the 1950s.
 Out of this arose (among others) the A. c model. which is widely. used in engineering applications despite its numerous deficiencies.," Out of this arose (among others) the $K$ $\epsilon$ model, which is widely used in engineering applications despite its numerous deficiencies."
 More recent. approaches have aimed at a greater fidelity to experimental ancl numerical results. tvpically by elaborating algebraic models of the pressurestrain correlation and trving to fix the coellicients therein.," More recent approaches have aimed at a greater fidelity to experimental and numerical results, typically by elaborating algebraic models of the pressure--strain correlation and trying to fix the coefficients therein."
 The present work is related. to these Itevnolds-stress closure models in. that. E have worked with the exact equations for the mean Reynolds and Maxwell. tensors. retaining the form of the linear terms and pro»osing closures for the non-linear terms.," The present work is related to these Reynolds-stress closure models in that I have worked with the exact equations for the mean Reynolds and Maxwell tensors, retaining the form of the linear terms and proposing closures for the non-linear terms."
 However. L have 1ried to take a fundamentally different approach to the non-linear effects bv recognizing the essential role of the length-scale L in the saturation of the turbulence and. by. icentifving cach non-linear term with a known physical process.," However, I have tried to take a fundamentally different approach to the non-linear effects by recognizing the essential role of the length-scale $L$ in the saturation of the turbulence and by identifying each non-linear term with a known physical process."
 In the absence of a magnetic stress. the equations adopted. here for the Ievnolds tensor are considerably sim.er than those advocated by. e.g... Speziale (1991). vet. trev do ensure realizability. allow for the return to isotropy. and may well give a more accurate representation of the linear and. linear stability properties of rotating shear {OWS.," In the absence of a magnetic stress, the equations adopted here for the Reynolds tensor are considerably simpler than those advocated by, e.g., Speziale (1991), yet they do ensure realizability, allow for the return to isotropy, and may well give a more accurate representation of the linear and non-linear stability properties of rotating shear flows."
 The application. of Revnolels-stress closure models. to accretion discs has been proposed in a series of papers by Ixato (1994). Wato Inagaki (1994) and Wato Yoshizawa (1998. 1995. 1997).," The application of Reynolds-stress closure models to accretion discs has been proposed in a series of papers by Kato (1994), Kato Inagaki (1994) and Kato Yoshizawa (1993, 1995, 1997)."
 In some of these papers the Maxwell stress is also modelled., In some of these papers the Maxwell stress is also modelled.
 While these studies have a fair amount in common with the present approach. some important cdilferences must » emphasized.," While these studies have a fair amount in common with the present approach, some important differences must be emphasized."
 In the absence of a magnetic stress. Ixato Yoshizawa (1997) have argued that steady hvdrodynamic urbulence may be sustained in a Weplerian accretion disc.," In the absence of a magnetic stress, Kato Yoshizawa (1997) have argued that steady hydrodynamic turbulence may be sustained in a Keplerian accretion disc."
 In fact. their closure model is based. on one by Launecler. teece odi (1975). which predicts stability for a Ixeplerian shear Dow (see Speziale 1991): only. by modifying one of the erms were Kato Yoshizawa able to find a steady turbulent state.," In fact, their closure model is based on one by Launder, Reece Rodi (1975), which predicts stability for a Keplerian shear flow (see Speziale 1991); only by modifying one of the terms were Kato Yoshizawa able to find a steady turbulent state."
 More importantly. the work of Ixato ancl co-workers does not address the issue of the non-lincar saturation of welrodyvnamic or ALLD turbulence.," More importantly, the work of Kato and co-workers does not address the issue of the non-linear saturation of hydrodynamic or MHD turbulence."
 Although it. predicts he relative magnitudes of the various components of the tevnolds (and. Maxwell) tensors. it does not predict. the magnitude of the turbulent energy in the saturated state.," Although it predicts the relative magnitudes of the various components of the Reynolds (and Maxwell) tensors, it does not predict the magnitude of the turbulent energy in the saturated state."
 Some further connections with the astrophysical Herature can be made., Some further connections with the astrophysical literature can be made.
 Schramkowski et al. (, Schramkowski et al. (
1996) devised a kinematic mean-field theory for the evolution of the Maxwell ensor in a turbulent accretion disc. as an alternative to studying the mean magnetic field itself.,"1996) devised a kinematic mean-field theory for the evolution of the Maxwell tensor in a turbulent accretion disc, as an alternative to studying the mean magnetic field itself."
 Their theory. is covariant and includes the interaction of the Maxwell tensor with the mean velocity. field., Their theory is covariant and includes the interaction of the Maxwell tensor with the mean velocity field.
 In. addition to the ‘alpha’ and ‘beta’ ellects of standard. mean-Lielcl electrodynamics. they emphasized the role of the ‘gamma’ ellect by which a turbulent Dow amplifics small-scale magnetic energy.," In addition to the `alpha' and `beta' effects of standard mean-field electrodynamics, they emphasized the role of the `gamma' effect by which a turbulent flow amplifies small-scale magnetic energy."
" This can be related to the C', term of the present mocdel.", This can be related to the $C_4$ term of the present model.
 Soon after Balbus Llawley (1991) first wrote on the magnetorotational instability in accretion discs. Tout Prinele (1992) presented. a simple model of a magnetic dvnanmo evele that uses the dillerential rotation to &enerate azimuthal field from. racial field. the Parker instability to convert azimuthal field into vertical field. and the," Soon after Balbus Hawley (1991) first wrote on the magnetorotational instability in accretion discs, Tout Pringle (1992) presented a simple model of a magnetic dynamo cycle that uses the differential rotation to generate azimuthal field from radial field, the Parker instability to convert azimuthal field into vertical field, and the"
lines identified with LH-like emission from N. O. Ne. Ale and $i. lines compatible with blends of He-like complexes of the same ionic species are detected.,"lines identified with H-like emission from N, O, Ne, Mg and Si, lines compatible with blends of He-like complexes of the same ionic species are detected."
 However. the EPIC pn moderate energv resolution does not allow to resolve any of them. while only thevi. and systems are actually separated. into their. forbidden and. resonant components in the RCS spectra.," However, the EPIC pn moderate energy resolution does not allow to resolve any of them, while only the, and systems are actually separated into their forbidden and resonant components in the RGS spectra."
 In. these cases. (taking tentatively also into account the EPIC pn centroid energies of the blends). the results suggest an important role of the Forbidden line. which is usually interpreted as the signature of emission. predominantly. from. photoionised. rather than collisional plasmas (e.g.2)..," In these cases (taking tentatively also into account the EPIC pn centroid energies of the blends), the results suggest an important role of the forbidden line, which is usually interpreted as the signature of emission predominantly from photoionised rather than collisional plasmas \citep[e.g. ][]{pd00}."
 Moreover. the very presence of the andOvi Hadiative Recombination Continua (RRC) argues against a collisional plasma. since in that case his feature would be much broader anc very dillicult. to detect (22)..," Moreover, the very presence of the and Radiative Recombination Continua (RRC) argues against a collisional plasma, since in that case this feature would be much broader and very difficult to detect \citep{lied99,lp96}."
 In the MITECGO data. some olf the Heike complexes are resolved. showing possibly a larger contribution from the resonant line (except for Vil) that was interpreted. in terms of photoexcitation of resonant ransitions. expected to occur in photoionised plasmas (?)..," In the HETG data, some of the He--like complexes are resolved, showing possibly a larger contribution from the resonant line (except for ) that was interpreted in terms of photoexcitation of resonant transitions, expected to occur in photoionised plasmas \citep{sako00b}."
 ‘These authors argued against the presence of an additional collisionally ionized. plasma component (that could explain he anomalous strong resonance lines) because strong [e L-shell emission is lacking. a result. which appears to be confirmed by the NATALNewton spectrum.," These authors argued against the presence of an additional collisionally ionized plasma component (that could explain the anomalous strong resonance lines) because strong Fe L-shell emission is lacking, a result which appears to be confirmed by the XMM–Newton spectrum."
 Therefore. plasma diagnostics with both arc seems. to. confirm that emission. from a photoionised material dominates the soft Nray spectrum. of Mrk 3.," Therefore, plasma diagnostics with both and seems to confirm that emission from a photoionised material dominates the soft X–ray spectrum of Mrk 3."
 The (tentative) dillerence. between the role of forbidden and resonance lines in the two spectra may be due to the spatial resolution of the two instruments. which coulc also play a relevant role. given that the observation showed. extended: emission. which is not spatially resolvec byNMM-NOcieton.," The (tentative) difference between the role of forbidden and resonance lines in the two spectra may be due to the spatial resolution of the two instruments, which could also play a relevant role, given that the observation showed extended emission which is not spatially resolved by."
. The cata might. simply indicate the importance of photoionisation not onlv in the innermost nuclear region (as shown by. data) bu also at larger radii. corresponding to the extended emission revealed byChandra.," The data might simply indicate the importance of photoionisation not only in the innermost nuclear region (as shown by data) but also at larger radii, corresponding to the extended emission revealed by."
 In the nucleus. low column densities may be the origin of stronger resonant lines. while larger column densities in the extended region could be responsible for predominant. Forbidden lines (seec.g.functionofthecolumn density)..," In the nucleus, low column densities may be the origin of stronger resonant lines, while larger column densities in the extended region could be responsible for predominant forbidden lines \citep[see e.g.][for a full discussion on the relative role of the He-like transitions as a function of the column density]{bianchi05}."
 A Ίνα line is recquired in the EPIC pn spectrum. with a centroid energv of 6.71Ne keV (see Table 4)).," A $\alpha$ line is required in the EPIC pn spectrum, with a centroid energy of $6.71^{+0.03}_{-0.02}$ keV (see Table \ref{hotlines}) )."
 This line is actually composed of four transitions. the resonance line(102: 6.700 keV). two intercombination lines andyi: mean οποιον 6.675 keV) and the forbidden line(2:: 6.637 keV).," This line is actually composed of four transitions, the resonance line: 6.700 keV), two intercombination lines and: mean energy 6.675 keV) and the forbidden line: 6.637 keV)."
 The best fit energy in our data suggests that the dominant transition is the resonancei., The best fit energy in our data suggests that the dominant transition is the resonance.
 This is generally taken as a sign that the gas is mainly in collisional equilibrium (scoe.g.7)., This is generally taken as a sign that the gas is mainly in collisional equilibrium \citep[see e.g.][]{pd00}.
 However. the line can be significantly enhanced by resonant scattering. which is expected to occur in photoionised plasma.," However, the line can be significantly enhanced by resonant scattering, which is expected to occur in photoionised plasma."
 This process is very ellective at low column densities and the resulting resonance line becomes the strongest in the Le-like iron spectrum (seee.g.27.andreferences therein)...," This process is very effective at low column densities and the resulting resonance line becomes the strongest in the He-like iron spectrum \citep[see e.g.][and references therein]{mbf96,bianchi05}."
 In NGC LOGS. theXXV. and lines were actually resolved and the large ratio between the former to the latter allowed ? to estimate a column density of a few 1075 72," In NGC 1068, the and lines were actually resolved and the large ratio between the former to the latter allowed \citet{bianchi05} to estimate a column density of a few $10^{21}$ $^{-2}$."
 A similar estimate can be done for Mrk 3. if the centroid energy of the blend of the Lle-like iron lines is indeed. interpreted as the result of a dominant line.," A similar estimate can be done for Mrk 3, if the centroid energy of the blend of the He-like iron lines is indeed interpreted as the result of a dominant line."
 A line from highly ionisecl Ni is also detected. possibly associated with the same reflector. while we only found an upper limit for a line (sce Table 3)).," A line from highly ionised Ni is also detected, possibly associated with the same reflector, while we only found an upper limit for a line (see Table \ref{lines}) )."
" A much stronger lle-like iron line suggests that the ionisation parameter of the gas is likely lower than log,~—0.5 (see7.for details)..", A much stronger He-like iron line suggests that the ionisation parameter of the gas is likely lower than $\log U_x\simeq-0.5$ \citep[see][ for details]{bianchi05}.
 On the other hand. the ionisation parameter appropriate for the observed is much higher than the one consistent. with the production of the other lines found in the soft. X-ray spectrum. requiring at least two clillerent ionised rellecting materials in the circumnuclear region. of Alrk 3. similarly to what found. for example. for NGC LOGS (7.andreferencestherein)..," On the other hand, the ionisation parameter appropriate for the observed is much higher than the one consistent with the production of the other lines found in the soft X-ray spectrum, requiring at least two different ionised reflecting materials in the circumnuclear region of Mrk 3, similarly to what found, for example, for NGC 1068 \citep[][and references therein]{matt04}."
 As shown in lieure 5.. a bright source is apparent στ arcmün southeast of the nucleus.," As shown in figure \ref{ixo30image}, , a bright source is apparent $\simeq1.6$ arcmin southeast of the nucleus."
" The much better astrometry of allows us to locate it at 2000.=GIS 157. ds=|131702/05"".. fully consistent with source INO 30 (?).."," The much better astrometry of allows us to locate it at $\alpha_{2000}=06^h15^m15^s$ , $\delta_{2000}=+71\degr 02\arcmin 05\arcsec$, fully consistent with source IXO 30 \citep{cp02}."
 ‘This source was first detected by and discussed w ? and ?.., This source was first detected by and discussed by \citet{tum93} and \citet{morse95}.
 We present here the first. X-ray. spectrum for INO 30., We present here the first X-ray spectrum for IXO 30.
 X combined. pn-MOS fit with a simple absorbed »owerlaw. leads to an acceptable fit C=S6/7T5 d.o.f.).," A combined pn-MOS fit with a simple absorbed powerlaw leads to an acceptable fit $\chi^2=86/75$ d.o.f.),"
 out. the addition of an unresolved (σ<GOO eV) gaussian . reUS Da ↓⊔∢⊾⋜∐↻⋅⋅↱≻↕⋮∙↳⋖⋅∖↓⊳∖↓⋅∢⊾⊏↥⋯↓⋅⋖⋅∠⇂⋜∐↿↓↥⋖⋅≤⋗⋀⊲∕⋰∣≼⇍∪⊔↓⊓⇂⋖⋅⊔≼∼∢⊾↓⋖⋅∖⇁∢⋅⇂⋡. ⋅ ⋯∙≼∙∪↓⋅," but the addition of an unresolved $\sigma<600$ eV) gaussian line at $6.5^{+0.3}_{-0.2}$ keV is required at the confidence level, according to F-test."
∠⇂⊀↓⊔⋏∙≟↿∪↓⊲↸−↿∢⊾⊳∖⇂⊳↾↓∖↓↕⋖⊾∐⊔⇀∖∪⇂⋅↿∐⊲↓⊳∖⇂⋅⋖⋅⋜⋯⊔⋅⋖⋅⊳∐↓∡∢⊾↓∙∖⇁↕∠⇂⋖⊾↓↥⇂↕↓↕⋖⋅∠⇂ as an iron line. even if the [arge errors prevent us [rom stating whether it is tonisecl or not. is (8+6)10' ph 2os corresponding to a very. laree ΝΔ of 1.0d0.8 keV. Phe final fit is good (C=76/72 cdo).," The flux of this feature, likely identified as an iron line, even if the large errors prevent us from stating whether it is ionised or not, is $(8\pm6)\times10^{-7}$ ph $^{-2}$ $^{-1}$ corresponding to a very large EW of $1.0\pm0.8$ keV. The final fit is good $\chi^2=76/72$ d.o.f.),"
 with Ny=(1.7E04)«107  and μμ figure 6))., with $N_{H}=(1.7\pm0.4)\times10^{21}$ $^{-2}$ and $\Gamma=1.77^{+0.13}_{-0.10}$ (see figure \ref{ixo30fit}) ).
 X fit of comparable quality (C=77/73 do), A fit of comparable quality $\chi^2=77/73$ d.o.f.)
 is achieved by a bremsstrahlung component at a temperature of 7.5vl keV.absorbed only by the Galactic column density. plus an iron line with the same propertics as for theprevious model," is achieved by a bremsstrahlung component at a temperature of $7.5^{+2.1}_{-1.6}$ keV,absorbed only by the Galactic column density, plus an iron line with the same properties as for theprevious model."
 Finally. we have also tried. a single," Finally, we have also tried a single"
2009).,.
. However. very rich galaxy clusters. such as ÀT54 (Godlowski1998).. Al4 (Baier.Gocllowski&MacGillivray2003) or A1656 (Djorgovski1983:Wu1997.1998). have shown non-random clistvibution of galaxies.," However, very rich galaxy clusters, such as A754 \citep{Godlowski98}, A14 \citep{Baier03} or A1656 \citep{Djorgovski83,Wu97,Wu98} have shown non-random distribution of galaxies."
 Godlowskietal.(2005) suggestion that alignment should increase with richness of the cluster was already confirmed by Arval(2007) (based on the series of paper 2006))).," \citet{Godlowski05} suggestion that alignment should increase with richness of the cluster was already confirmed by \citet{Aryal07} (based on the series of paper \citep{Aryal04,Aryal05a,Aryal06}) )."
 Thev analvzed totally 32 clusters of dillerent richness and DM (xvpes. founding that alignment is changing with the richness as well as DM (vpe of the clusters.," They analyzed totally 32 clusters of different richness and BM types, founding that alignment is changing with the richness as well as BM type of the clusters."
 IIowever. both Goclowskietal.(2005) and Arval(2007) analvsis was qualitative only.," However, both \citet{Godlowski05} and \citet{Aryal07} analysis was qualitative only."
 Our aim is to test (this hypothesis both qualitatively and quantitatively., Our aim is to test this hypothesis both qualitatively and quantitatively.
 Therelore we decided lo examine if alignment of galaxies in clusters depends ou (he number of their constitutive menibers and (he DM (ypes using statistical tests., Therefore we decided to examine if alignment of galaxies in clusters depends on the number of their constitutive members and the BM types using statistical tests.
 Plionisetal.(2003). suggested that galaxy. alignment in cluster depends on the velocity dispersion of member galaxies., \citet{Plionis03} suggested that galaxy alignment in cluster depends on the velocity dispersion of member galaxies.
 In order (o verily this finding we also analvzed correlation between alignmente and. velocity dispersion., In order to verify this finding we also analyzed correlation between alignment and velocity dispersion.
 The present paper is organized in standard manner., The present paper is organized in standard manner.
 Section 2 describes our optical data. section 3 presents the statistical method used in our analvsis.," Section 2 describes our optical data, section 3 presents the statistical method used in our analysis."
 Section 4 is devoted to our results and their discussion. while section 5 contains conclusions which ends the paper.," Section 4 is devoted to our results and their discussion, while section 5 contains conclusions which ends the paper."
 Our paper is based on the analvsis of structures taken [rom PF catalogue 2006)., Our paper is based on the analysis of structures taken from PF catalogue \citep{Panko06}.
. The structures were extracted from the Muenster Recl Skv Survey (AIRSS hereafter) (AIRSS2003)., The structures were extracted from the Muenster Red Sky Survey (MRSS hereafter) \citep{MRSS03}.
. ALRSS is optical large scale survey covering an area of 5000 square degrees in the southern hemisphere., MRSS is optical large scale survey covering an area of 5000 square degrees in the southern hemisphere.
 After scanning 217 ESO plates. it gives the information about 5.5 million galaxies.," After scanning 217 ESO plates, it gives the information about 5,5 million galaxies."
 PF catalogue. like MIRSS. is statistically complete till magnitude value," PF catalogue, like MRSS, is statistically complete till magnitude value"
sspectral features.,spectral features.
 We have argued that the bursts [rom anre very similar to those of197., We have argued that the bursts from are very similar to those of.
. Interestingly. the two sources show other similarities.," Interestingly, the two sources show other similarities."
 They both have sinusoidal profiles while all other ANPs exhibit rich harmonie content in (heir pulse profiles (seeGaviiil&Ixaspi2002:Gotthelfetal.2002).," They both have sinusoidal profiles while all other AXPs exhibit rich harmonic content in their pulse profiles \citep[see][]{gk02,
ggk+02}."
. Thev have shown lone-lived (> months) pulsed [αν variations which are not due to cooling of the crust alter the impulsive injection of heat [rom bursts., They have shown long-lived $>$ months) pulsed flux variations which are not due to cooling of the crust after the impulsive injection of heat from bursts.
 Furthermore. their (ning properties are ihe most reminiscent of (he SGRs.," Furthermore, their timing properties are the most reminiscent of the SGRs."
 The pulsed Iraction decrease we have observed lends further evidence that the pulsed flux variations observed by Gavriil&Ixaspi(2004) represent a new phenomenon seen exclusively in (he AXPs., The pulsed fraction decrease we have observed lends further evidence that the pulsed flux variations observed by \citet{gk04} represent a new phenomenon seen exclusively in the AXPs.
 The fact that the pulsed fraction decreased as the pulsed flux increased without anv pulse morphology changes implies that there was a greater fractional increase in the unpulsed flux than in the pulsed flux. in agreement will what was found by (2004).," The fact that the pulsed fraction decreased as the pulsed flux increased without any pulse morphology changes implies that there was a greater fractional increase in the unpulsed flux than in the pulsed flux, in agreement with what was found by \citet{mts+04}."
. Such a flix enhancement cannot be attributed to à particular active region., Such a flux enhancement cannot be attributed to a particular active region.
 Thus we can rule out the flux enhancements were due to the injection of heat [rom bursts that were beamed away from us. because in Chat scenario one would expect a larger fractional change in pulsed flux than in total flux.," Thus we can rule out the flux enhancements were due to the injection of heat from bursts that were beamed away from us, because in that scenario one would expect a larger fractional change in pulsed flux than in total flux."
 Indeed. during (he burst afterglow pulsed flux enhancement in SG. 1900-14. Lentersetal.(2003). found a pulsed flux and pulse fraction increase.," Indeed, during the burst afterglow pulsed flux enhancement in SGR $+$ 14, \citet{lwg+03} found a pulsed flux and pulse fraction increase."
 We reported on the discovery of the latest burst from the direction of ANP5937., We reported on the discovery of the latest burst from the direction of AXP.
. This burst was discovered as pert of our long-term monitoring campaign of ANPs wilhTE., This burst was discovered as part of our long-term monitoring campaign of AXPs with.
. Contemporaneously with the burst we discovered. a pulsed-flux enhancement which unambiguously identified aas the burst’s origin., Contemporaneously with the burst we discovered a pulsed-flux enhancement which unambiguously identified as the burst's origin.
 The clear identification of aas the burster in this case argues that it was indeed the emitter of the two bursts discovered from the direction of this source in 2001. as already inferred by Gavriiletal.(2002).," The clear identification of as the burster in this case argues that it was indeed the emitter of the two bursts discovered from the direction of this source in 2001, as already inferred by \citet{gkw02}."
. All three bursts trom ccan only be explained within the context of the magnetar model. however many of (heir properties differentiate (hem from canonical SGI bursts.," All three bursts from can only be explained within the context of the magnetar model, however many of their properties differentiate them from canonical SGR bursts."
 This aud the first burst discovered from (his source had very long-tails. >699 s and ~51 5 respectively. as opposed to the 0.15 duration SGR. bursts.," This and the first burst discovered from this source had very long-tails, $>699$ s and $\sim$ 51 s respectively, as opposed to the $\sim$ 0.1 s duration SGR bursts."
 Two ks-long SGI bursts have been reported but we argued that they were a verv different phenomenon (Ibrahimetal.2001:Lenters2003).," Two ks-long SGR bursts have been reported but we argued that they were a very different phenomenon \citep{isw+01, lwg+03}."
. Specifically the extended-tail SGR bursts had. very. energetic initial spikes and (he long tails were argued, Specifically the extended-tail SGR bursts had very energetic initial spikes and the long tails were argued
of galaxies in the projected radius-redshift diagram.,of galaxies in the projected radius-redshift diagram.
 For a spherically svuuuetric system. taking an azimuthal average amplifies the signal of the caustics im redshift space and smooths over small-scale substructures.," For a spherically symmetric system, taking an azimuthal average amplifies the signal of the caustics in redshift space and smooths over small-scale substructures."
" We isolate the clusters initially bw studving only ealaxics within &, x10INMpe and £5000kn s! of the nominal cluster centers from the X-ray catalogs.", We isolate the clusters initially by studying only galaxies within $R_p\leq$ $\Mpc$ and $\pm$ $\kms$ of the nominal cluster centers from the X-ray catalogs.
 We perform a luerarchical structure analysis to locate the centroid of the laveest svstem in each volume (see Appeudix A of D99)., We perform a hierarchical structure analysis to locate the centroid of the largest system in each volume (see Appendix A of D99).
 This analysis cousists of creating a binary tree based on estimated binding enersies. identibvius the largest cluster in the field. and determing its ceuter from the two-dimensional distribution of celestial coordinates determined with adaptive kernel z200thiug.," This analysis consists of creating a binary tree based on estimated binding energies, identifying the largest cluster in the field, and determining its center from the two-dimensional distribution of celestial coordinates determined with adaptive kernel smoothing."
 This analysis soluctimes finds the ceuter of another svstem in the field., This analysis sometimes finds the center of another system in the field.
 Iu these cases. limiting the galaxies to a smaller radial and/or redshift range enables the aleorithia to ceuter on the desired cluster.," In these cases, limiting the galaxies to a smaller radial and/or redshift range enables the algorithm to center on the desired cluster."
 Table 10. lists these restrictions., Table \ref{centerproblems} lists these restrictions.
 We adaptively s1100th. the azimuthally averaged plase space diagram (the ensemble of redshift. radius data points) aud the algorithm chooses a threshold im phase space density as the edge of the caustic envelope.," We adaptively smooth the azimuthally averaged phase space diagram (the ensemble of redshift, radius data points) and the algorithm chooses a threshold in phase space density as the edge of the caustic envelope."
 The upper and lower caustics at a given radius are the redshifts at which this threshold deusitv is exceeded when approaching the ceutral redshift from the “top” and “bottom respectively of the redshift-racdins diagram., The upper and lower caustics at a given radius are the redshifts at which this threshold density is exceeded when approaching the central redshift from the “top” and “bottom” respectively of the redshift-radius diagram.
 Because the caustics of a spherical svstem are sviunetric. we adopt the smaller of the upper aud lower caustics as the caustic amplitude να). at that radius.," Because the caustics of a spherical system are symmetric, we adopt the smaller of the upper and lower caustics as the caustic amplitude $\mathcal{A}\mathnormal{(r)}$ at that radius."
 This xocedure reduces the systematic uncertaiuties introduced x iuterlopers. which generally lead to au overestimate of the caustic amplitude.," This procedure reduces the systematic uncertainties introduced by interlopers, which generally lead to an overestimate of the caustic amplitude."
" The threshold is defined by the aleovithin to minimize the quantity |£e,4 . where Rois a viriallike radius (see D99 for details)."," The threshold is defined by the algorithm to minimize the quantity $|<$$v_{esc}^2$$>_R - 4 <$$v^2$$>_R|$ , where R is a virial-like radius (see D99 for details)."
 ? explore the effects of altering some of these assuniptious and find that the differences are generally smaller than the estimated mucertaitics., \citet{rines02} explore the effects of altering some of these assumptions and find that the differences are generally smaller than the estimated uncertainties.
 D99 described this method in detail and showed that. when applied to simulated clusters containing galaxies modelled with semi-analvtie techniques. it recovers the actual mass profiles to radii of 5!Mpe from the cluster centers.," D99 described this method in detail and showed that, when applied to simulated clusters containing galaxies modelled with semi-analytic techniques, it recovers the actual mass profiles to radii of $~\Mpc$ from the cluster centers."
 D99 cives a prescription for cstimating the uncertainties i the caustic iass profiles., D99 gives a prescription for estimating the uncertainties in the caustic mass profiles.
 The uncertainties estimated using this prescription reproduce the actual differences between the caustic mass profiles and the true amass profiles of the simulated clusters iucluding systematic effects such as departures from spherical sviunietryv., The uncertainties estimated using this prescription reproduce the actual differences between the caustic mass profiles and the true mass profiles of the simulated clusters including systematic effects such as departures from spherical symmetry.
 The uncertainties in the caustic lass profiles of observed clusters may be smaller than the uncertainties in the simulations (2).., The uncertainties in the caustic mass profiles of observed clusters may be smaller than the uncertainties in the simulations \citep{cairnsi}.
 This differeuce is due in part to the large number of redshifts in the CIRS redshift catalogs relative to the simulated catalogs., This difference is due in part to the large number of redshifts in the CIRS redshift catalogs relative to the simulated catalogs.
 Futhenuuore. the caustics are generally iore cleaulv defined in the data than im the simulations.," Furthermore, the caustics are generally more cleanly defined in the data than in the simulations."
 Clearly. more simulations which better reproduce the appearance of observed caustics and/or inchide faünter galaxies would be useful iu determining the limits of the systematic unucertainties iu the caustic technique.," Clearly, more simulations which better reproduce the appearance of observed caustics and/or include fainter galaxies would be useful in determining the limits of the systematic uncertainties in the caustic technique."
 We are currently conducting au analysis for the lvcdvodvuamical simulations of ? with these eoals (A. Diaferio et al., We are currently conducting an analysis for the hydrodynamical simulations of \citet{borgani04} with these goals (A. Diaferio et al.
 2006. iu preparation).," 2006, in preparation)."
 We calculate the shapes of the caustics with the technique described in D99 using a smoothing parameter of q—25., We calculate the shapes of the caustics with the technique described in D99 using a smoothing parameter of $q$ =25.
 The smoothing paramcter g is the scaling between the velocity smoothing aud the radial smoothing in the adaptive kernel estimate of the underlviug phase space distribution (e.g... a particle which has a siioothiug window in the radial direction of 0.0172.1 Mpe will have a sinoothling window in the velocity direction of 100 1s for q—25 aud LO kms| fox q—10).," The smoothing parameter $q$ is the scaling between the velocity smoothing and the radial smoothing in the adaptive kernel estimate of the underlying phase space distribution (e.g., a particle which has a smoothing window in the radial direction of $h^{-1}$ Mpc will have a smoothing window in the velocity direction of 100 $\kms$ for $q$ =25 and 40 $\kms$ for $q$ =10)."
 Previous investigations show that the mass profiles are inscusitive to chauges of a factor of 2 in the smoothing parameter (??7)..," Previous investigations show that the mass profiles are insensitive to changes of a factor of 2 in the smoothing parameter \citep{gdk99,rines2000,rines02}."
 Table 8. lists the hierarchical centers., Table \ref{centers} lists the hierarchical centers.
 These ceuters eoncrally agree with the N-vav positions (Table 8)) with a median differcuce of fh!pe and with the redshift centers frou the N-rav catalogs with a median differeuce of-17 kms+., These centers generally agree with the X-ray positions (Table \ref{centers}) ) with a median difference of $~\kpc$ and with the redshift centers from the X-ray catalogs with a median difference of -17 $\kms$.
 The hierarchical ceuters disagree by iore than 5005.!kpe in four clusters aud by more than 1000 kins© for seven clusters., The hierarchical centers disagree by more than $\kpc$ in four clusters and by more than 1000 $\kms$ for seven clusters.
 The hierarchical redslüft ceuters are more reliable than those in the N-rav cluster catalogs because the former are based on mach larger redshift saluples., The hierarchical redshift centers are more reliable than those in the X-ray cluster catalogs because the former are based on much larger redshift samples.
 We diseuss some of the individual cases in 81.., We discuss some of the individual cases in $\S$ \ref{individual}.
 Figures ?7—77 show the caustics aud Figures 77-77 show the associated mass profiles., Figures \ref{allcirs1}- \ref{allcirs6} show the caustics and Figures \ref{allcirsm1}- \ref{allcirsm6} show the associated mass profiles.
 Note that the caustics extend to different radi for different clusters., Note that the caustics extend to different radii for different clusters.
 D99 show that the appearance of the caustics depends strongly ou the line of sight: projection effects can therefore account for most of the differences in profile shape in Figures ??- -27 without invoking non-homologv among clusters., D99 show that the appearance of the caustics depends strongly on the line of sight; projection effects can therefore account for most of the differences in profile shape in Figures \ref{allcirs1}- \ref{allcirs6} without invoking non-homology among clusters.
 The uucertainties in the caustic mass profiles are estimated with the prescription of D99 for Coma-size clusters., The uncertainties in the caustic mass profiles are estimated with the prescription of D99 for Coma-size clusters.
 Under this prescription. more densely sanrpled clusters and those with ligher coutrast between the caustics aud the backeround have simaller uüucertaiuties than sparsely salupled clusters or those with poorer coutrast.," Under this prescription, more densely sampled clusters and those with higher contrast between the caustics and the background have smaller uncertainties than sparsely sampled clusters or those with poorer contrast."
 Thus. the uncertainties in the caustic mass profiles for some CIRS clusters (those with smaller masses or unusually clupty backerouuds) computed with this prescription iav underestimate the total svstematic nnucertainuties.," Thus, the uncertainties in the caustic mass profiles for some CIRS clusters (those with smaller masses or unusually empty backgrounds) computed with this prescription may underestimate the total systematic uncertainties."
 We use the caustics to determine cluster membership., We use the caustics to determine cluster membership.
" Uere. the term ""cluster πιονο refers to galaxies both in the virial region aud in the iufall region."," Here, the term “cluster member” refers to galaxies both in the virial region and in the infall region."
 Figures ??—?? show that the caustics effectively separate cluster 1ienibers from background aud foreground galaxies. although some iuterlopers iuav lie within the caustics.," Figures \ref{allcirs1}- \ref{allcirs6} show that the caustics effectively separate cluster members from background and foreground galaxies, although some interlopers may lie within the caustics."
 This clean separation affirms our adoption of velocity cispersious calculated from chister members as defined by the caustics (853.2)., This clean separation affirms our adoption of velocity dispersions calculated from cluster members as defined by the caustics $\S$ 3.2).
 We find a measureable signal for the caustic profile for all 72 N-vav clusters in the CIRS sample (that is. all show an identifiable cluster of galaxies with a surrounding intall pattern).," We find a measureable signal for the caustic profile for all 72 X-ray clusters in the CIRS sample (that is, all show an identifiable cluster of galaxies with a surrounding infall pattern)."
 This amazing success rate demonstrates the power and ubiquity ofthe caustic teclinique in idenutifving the galaxies associated with clusters and the infall roeglous., This amazing success rate demonstrates the power and ubiquity of the caustic technique in identifying the galaxies associated with clusters and their infall regions.
 Iu the simulations of D99. the degree of definition of the caustics depends on the underlving cosmology: caustics are better defined ina low-ceusity universe than a flat. niatter-doiminated universe.," In the simulations of D99, the degree of definition of the caustics depends on the underlying cosmology; caustics are better defined in a low-density universe than a flat, matter-dominated universe."
 Surprisingly. the coutrast of the phase space deusitv between regions inside and outside the caustics is mich stronger in the data than iu both the zCDM and ACDM simulated clusters in D99.," Surprisingly, the contrast of the phase space density between regions inside and outside the caustics is much stronger in the data than in both the $\tau$ CDM and $\Lambda$ CDM simulated clusters in D99."
 The difference iav arise from the cosimological model used or the semiu-analytic tecliniques for defining ealaxy, The difference may arise from the cosmological model used or the semi-analytic techniques for defining galaxy
of galaxies bluer than an hregular galaxy is compatible with the ummber found im our sample.,of galaxies bluer than an Irregular galaxy is compatible with the number found in our sample.
 The flattening of the curve for carly type sources may be duc to a decrease in deusity at higher redshift of elliptical galaxies. but it is also expected by thea>Ἰ slope of the LF of carly tvpc ealaxies (e.g. Miuzke ot al.," The flattening of the curve for early type sources may be due to a decrease in density at higher redshift of elliptical galaxies, but it is also expected by the $\alpha>-1$ slope of the LF of early type galaxies (e.g. Marzke et al."
 1998)., 1998).
 Number counts models nevertheless show that an a1l LF does not accouu for such a steep ecrease (Figure 12))., Number counts models nevertheless show that an $\alpha>-1$ LF does not account for such a steep decrease (Figure \ref{morph_c}) ).
 Brinchinann et al. (, Brinchmann et al. (
1998). Tha et al. (,"1998), Im et al. ("
1999) aud Driver ( al. (,1999) and Driver et al. (
L998) studied the redshift cistvibution for ditfereu morphological types m deep surveys.,1998) studied the redshift distribution for different morphological types in deep surveys.
 Brinclinauu et al. (, Brinchmann et al. (
1998) analyzed 311 galaxies at 5<1 from the Canada-France Redshift Survey (CFRS. Lilly et al.,"1998) analyzed 341 galaxies at $z<1$ from the Canada-France Redshift Survey (CFRS, Lilly et al."
 1995. lute at Wy p=22.5). aud Autofil/Low-Dispersion Survey spectrograph (LDSS. Ellis et al.," 1995, limited at $_{AB}$ =22.5), and Autofib/Low-Dispersion Survey Spectrograph (LDSS, Ellis et al."
 1996. linüted at 5;= 21).," 1996, limited at $b_j=24$ )."
 They find the distribution of elliptical o6alaxies peaked at 220.5. while spiral galaxies have a shallow distribution and the excess of peculiar sources bogus at izm0.1.," They find the distribution of elliptical galaxies peaked at $z\approx0.5$, while spiral galaxies have a shallow distribution and the excess of peculiar sources begins at $z\approx0.4$."
 According to their couclisions. the number of reeular ealaxies is compatible with a passive evolution model. while the excess of poculi ones suggests al active DIuninuositv evolution aud-or uuuber evolution.," According to their conclusions, the number of regular galaxies is compatible with a passive evolution model, while the excess of peculiar ones suggests an active luminosity evolution and-or number evolution."
 hu et al. (, Im et al. (
1999) for a sample of 161 galaxies lanited at I=21.5 do aeree with Brinchinannu et al. (,1999) for a sample of 464 galaxies limited at $=21.5$ do agree with Brinchmann et al. (
1998).,1998).
 Driver ot al. (, Driver et al. (
1998) analyzed IIDE-N sources. with photometric redshifts. aud underline the excess both iu spiral galaxies at 2=1.5 and mregulars at 2>1. sugeesting uuniber evolution aud passive evolution for dwart LSDG at :«1 eivine the density of nreeular galaxies at low redshift.,"1998) analyzed HDF-N sources, with photometric redshifts, and underline the excess both in spiral galaxies at $z=1.5$ and irregulars at $z>1$, suggesting number evolution and passive evolution for dwarf LSBG at $z<1$ giving the density of irregular galaxies at low redshift."
"CGauss-LHlermite polvnomials. 4 (Gerhard (1993)... van der AMarel Franx (1993))) : Ig. a binary fraction a=0.6 raises the kurtosis of a 0;—6 km/s Gaussian to 5.09 (4z 0.1) and that of aa, = km/s Gaussian to 3.47 (fh.z 0.025).","Gauss-Hermite polynomials, $h_4$ (Gerhard \cite{ger}, van der Marel Franx \cite{vdm}) ): E.g. a binary fraction $\alpha=0.6$ raises the kurtosis of a $\sigma_{\rm i}=6$ km/s Gaussian to 5.09 $h_4 \approx 0.1$ ) and that of a $\sigma_{\rm i}=9$ km/s Gaussian to 3.47 $h_4 \approx 0.025$ )."
 For stellar svstenis with lower intrinsic velocity. dispersions. the LOSVDs will be even more cistinethy non-Gaussian.," For stellar systems with lower intrinsic velocity dispersions, the LOSVDs will be even more distinctly non-Gaussian."
" The maximum additional velocity dispersion due to binary stars is estimated at σι,223 km/s. in good agreement with other authors."," The maximum additional velocity dispersion due to binary stars is estimated at $\sigma_{\rm b} \approx 3$ km/s, in good agreement with other authors."
 Only stellar svstems with intrinsic velocity dispersions comparable to this value will have observed velocity. dispersions that are noticeably allected by the presence of binaries. ic. dwarf Spheroidals such as those found in the Local Group (Dekel Silk (1986))). globular clusters. low-surface-brightness cisk galaxies (Dottema (1993))) and the central regions of nucleated chvarl ellipticals.," Only stellar systems with intrinsic velocity dispersions comparable to this value will have observed velocity dispersions that are noticeably affected by the presence of binaries, i.e. dwarf Spheroidals such as those found in the Local Group (Dekel Silk \cite{ds}) ), globular clusters, low-surface-brightness disk galaxies (Bottema \cite{bot}) ) and the central regions of nucleated dwarf ellipticals."
 Not only the velocity dispersion. but also. the shape of the galaxvs LOSVD is altered., Not only the velocity dispersion but also the shape of the galaxy's LOSVD is altered.
 “Phe presence of binaries has a measurable elfect on the kurtosis of the observed LOSVD for stellar systems with a velocity distribution as high as 10 km/s. For stellar svstems with lower velocity. dispersions. the LOSVDs will be even more distinctly non-Ciaussian. being strongly peakecl with broac wings.," The presence of binaries has a measurable effect on the kurtosis of the observed LOSVD for stellar systems with a velocity distribution as high as 10 km/s. For stellar systems with lower velocity dispersions, the LOSVDs will be even more distinctly non-Gaussian, being strongly peaked with broad wings."
 This feature can mimic radial anisotropy which combined with the enhanced. velocity dispersion could. Lea to an over-estimation of the dark matter content ofdSphs and. eglobulars., This feature can mimic radial anisotropy which combined with the enhanced velocity dispersion could lead to an over-estimation of the dark matter content of dSphs and globulars.
 Ifthe kinematies ofa galaxy are derived from the raclia velocities of discrete stars as is the case for the dwarl spheroidals in the Local Group — repeated observations can eliminate the binaries from the star sample., If the kinematics of a galaxy are derived from the radial velocities of discrete stars – as is the case for the dwarf spheroidals in the Local Group – repeated observations can eliminate the binaries from the star sample.
 Methods tha rely on integrated light spectra — e.g. the crowded regions of elobular clusters or ciwarf galaxies outside the Local Croup will be plagued by the above mentioned οσοι»., Methods that rely on integrated light spectra – e.g. the crowded regions of globular clusters or dwarf galaxies outside the Local Group – will be plagued by the above mentioned effects.
of sight at relativistic velocity.,of sight at relativistic velocity.
" To evaluate the plausibility of this model, we consider knot S4."," To evaluate the plausibility of this model, we consider knot S4."
" If we assume that all of the radio emission from this region originates in the beamed component and it occupies the entire volume of S4, a bulk Lorentz factor, I, of ~2 or greater is required, and the direction of motion must be close to the line of sight (8~1/T)."," If we assume that all of the radio emission from this region originates in the beamed component and it occupies the entire volume of S4, a bulk Lorentz factor, $\Gamma$, of $\sim$ 2 or greater is required, and the direction of motion must be close to the line of sight $\theta\sim 1/\Gamma$ )."
 Assuming a smaller volume would only push I' higher., Assuming a smaller volume would only push $\Gamma$ higher.
" There is some evidence for mildly relativistic flows behind FR II hot spots, although nothing of this magnitude."," There is some evidence for mildly relativistic flows behind FR II hot spots, although nothing of this magnitude."
 We conclude that it is unlikely that the X-ray emission from these regions can be accounted for by relativistic motions of sub-components., We conclude that it is unlikely that the X-ray emission from these regions can be accounted for by relativistic motions of sub-components.
" It is also extremely unlikely that the X-ray emission from these regions is due to hot gas that has been swept up, since the host galaxy of 3C 33 resides in a poor environment."," It is also extremely unlikely that the X-ray emission from these regions is due to hot gas that has been swept up, since the host galaxy of 3C 33 resides in a poor environment."
" Assuming that the X-ray emission of the SHS is from a thermal plasma with fy;7=1.5 keV and Z20.5 times Solar, the density of the gas would be ~10 ? em assuming a uniform filling factor."," Assuming that the X-ray emission of the SHS is from a thermal plasma with $k_BT$ =1.5 keV and $Z$ =0.5 times Solar, the density of the gas would be $\sim$ $^{-2}$ $^{-3}$ assuming a uniform filling factor."
" The pressure and mass of this gas would be ~6.2x | dyn ? and —10"" M., respectively."," The pressure and mass of this gas would be $\sim$ $\times$ $^{-11}$ dyn $^{-2}$ and $\sim$ $^9$ $M_\odot$, respectively."
 The gas pressure of this putative shell would exceed the equipartition pressure of the diffuse regions behind the hot spot (S1) by a factor of ~6 (Rudnick1988)., The gas pressure of this putative shell would exceed the equipartition pressure of the diffuse regions behind the hot spot (S1) by a factor of $\sim$ 6 \citep{rud88}.
. This is not implausibly large as the equipartition pressure of lobes and jets of FR I radio galaxies is often less than the pressure in the ambient medium (c.g.Krattetαἰ. 2003).. although it would be unusual for an FR Η.," This is not implausibly large as the equipartition pressure of lobes and jets of FR I radio galaxies is often less than the pressure in the ambient medium \citep[e.g. the inner radio lobes of Cen A, see][]{kra03}, although it would be unusual for an FR II."
" If the extended diffuse X-ray emission described in subsection 3.3 is from an extended corona, the mass of gas in the NHS and SHS would each be ~5% of the total gas mass, which is implausibly large."," If the extended diffuse X-ray emission described in subsection 3.3 is from an extended corona, the mass of gas in the NHS and SHS would each be $\sim$ of the total gas mass, which is implausibly large."
" The only other possibility 1s that the X-ray emission is synchrotron radiation from a population of ultra-relativistic electrons, although the observed flux density distributions cannot be simply described with single or continuous injection models."," The only other possibility is that the X-ray emission is synchrotron radiation from a population of ultra-relativistic electrons, although the observed flux density distributions cannot be simply described with single or continuous injection models."
" There are, in fact, several arguments that support the multi-zone synchrotron hypothesis for regions S2, S3, S4, NI. and N2."," There are, in fact, several arguments that support the multi-zone synchrotron hypothesis for regions S2, S3, S4, N1, and N2."
" First, the radiative lifetime of the ultra-relativistic particles is a few tens of years in the equipartition magnetic fields of the regions."," First, the radiative lifetime of the ultra-relativistic particles is a few tens of years in the equipartition magnetic fields of the regions."
" All of the knots are resolved in the X-rays, so the particles must be along the length of the regions."," All of the knots are resolved in the X-rays, so the particles must be re-energized along the length of the regions."
" Thus, in each knot there must be many sites of particle acceleration."," Thus, in each knot there must be many sites of particle acceleration."
 There is therefore no reason to expect that a single injection model will accurately describe the broad band flux density distribution from such a scenario., There is therefore no reason to expect that a single injection model will accurately describe the broad band flux density distribution from such a scenario.
" Second, it is clear from Chandra observations of nearby FR I jets, whose radio through X-ray emission is believed to be synchrotron, that the morphological relationships between the radio, IR, optical, and X-ray synchrotron emitting electrons are complicated (Kraftetal.rall 2001)."," Second, it is clear from Chandra observations of nearby FR I jets, whose radio through X-ray emission is believed to be synchrotron, that the morphological relationships between the radio, IR, optical, and X-ray synchrotron emitting electrons are complicated \citep{kra01,mjh01}."
" It is clear, however, that the simple model described in Hardeastleοἱaf,(2004)., in which a single continuous-injection spectrum describes the radio through X-ray spectrum of these regions, does not apply to 3C 33."," It is clear, however, that the simple model described in \citet{mjh04}, in which a single continuous-injection spectrum describes the radio through X-ray spectrum of these regions, does not apply to 3C 33."
" The resolved nature of the X-ray emission, coming from throughout the bright 10-kpe SHS, in fact makes it clear that a model in which the X-rays are generated by"," The resolved nature of the X-ray emission, coming from throughout the bright 10-kpc SHS, in fact makes it clear that a model in which the X-rays are generated by"
 , 
pulsar wind wave. such as is expected if the sheets are formed by the migration of particles within the wave. as described qualitatively by Michel(1971).,"pulsar wind wave, such as is expected if the sheets are formed by the migration of particles within the wave, as described qualitatively by \citet{michel71}."
. For the particle distribution. we adopt an isotropic electron/positron distribution given by NCBperl)=WOE? where A(r.1) is related to the number density of emitting particles.," For the particle distribution, we adopt an isotropic electron/positron distribution given by $N(E,\vec{p},\vec{r},t) = K(\vec{r},t) \,
E^{-p}$ where $K(\vec{r},t)$ is related to the number density of emitting particles."
 The radial motion of the wind imposes an overall 1/7? dependence on this quantitx. which is further modulated because the energization occurs primarily in (he current sheet.," The radial motion of the wind imposes an overall $1/r^2$ dependence on this quantity, which is further modulated because the energization occurs primarily in the current sheet."
 The precise value in each sheet is chosen to fit the observed intensity of each sub-pulse., The precise value in each sheet is chosen to fit the observed intensity of each sub-pulse.
 In acdition. a small de component is added. eiving the off-pulse intensity.," In addition, a small dc component is added, giving the off-pulse intensity."
 For the emissivity. we use (he standard expressions for incoherent svnchrotron radiation of ultrarelativistic particles in the Airy function approximation (Ginzburg&Svrovatskii1969:Melrose1971).," For the emissivity, we use the standard expressions for incoherent synchrotron radiation of ultrarelativistic particles in the Airy function approximation \citep{ginzburgsyrovatskii69,melrose71}."
. Following lxirketal.(2002).. we assume (he emission commences when the wind crosses the surface raryDan ," Following \citet{kirkskjaeraasengallant02}, we assume the emission commences when the wind crosses the surface $r=r_0\gg r_{\rm L}$."
The calculation of the Stokes parameters as measured in the observer [rame involves simply integrating (he emissivity over the wind., The calculation of the Stokes parameters as measured in the observer frame involves simply integrating the emissivity over the wind.
 However. this requires special care. because the Lorentz boost from the rest frame of the emitting plasma involves not only beaming aud Doppler shilt. but also a change in the polarization angle due to the ellects of aberration.," However, this requires special care, because the Lorentz boost from the rest frame of the emitting plasma involves not only beaming and Doppler shift, but also a change in the polarization angle due to the effects of aberration."
 Lyutikovetal.(2003). performed this caleulation in the context ofa gamma-ray burst model. assuming a relativistic shell of emitting plasma containing only a toroidal magnetic fiel.," \citet{lyutikovparievblandford03} performed this calculation in the context of a gamma-ray burst model, assuming a relativistic shell of emitting plasma containing only a toroidal magnetic field."
 llowever. (he relatively simple form of (he emissivity function in (hat case means that (wo of the four Stokes parameters integrate to zero: C=V.0. corresponding to linear polarization with constant position angle.," However, the relatively simple form of the emissivity function in that case means that two of the four Stokes parameters integrate to zero: $U=V=0$, corresponding to linear polarization with constant position angle."
 Ποιο we extend (his method by adding a By component and allowing for a more general. space and time dependent emissivily.," Here we extend this method by adding a $B_\theta$ component and allowing for a more general, space and time dependent emissivity."
 After straightforward but lengthy manipulations involving Lorentz transformations. we lind the Stokes parameters as nieasured by an observer al tme {ως ave eiven by the following integrals: where the retarded time is given by fee=ωςP:r/c and 7 is a unit vector along the line of sieht from the pulsar to the observer.," After straightforward but lengthy manipulations involving Lorentz transformations, we find the Stokes parameters as measured by an observer at time $t_{\rm obs}$ are given by the following integrals: where the retarded time is given by $t_{\rm ret} = t_{\rm obs} +
\vec{n}\cdot\vec{r}/c$ and $\vec{n}$ is a unit vector along the line of sight from the pulsar to the observer."
 In this approximation the circular polarization vanishes: V—0., In this approximation the circular polarization vanishes: $V=0$.
" The function s, is defined bv: where w is (he (angular) frequency of the emitted radiation. ancl & is a constant. [actor"," The function $s_0$ is defined by: where $\omega$ is the (angular) frequency of the emitted radiation, and $\kappa$ is a constant factor"
on July 16. 2010 (Waagen2010).,"on July 16, 2010 \citep{Waagen2010}."
. Eleven dilferent observers attempted observations of this Larget during (he following six month period. and total of 214 positive observations of were made between JD 2455365.9 and JD 2455565.6 (2010 June 18 to 2011 January 4).," Eleven different observers attempted observations of this target during the following six month period, and total of 214 positive observations of M31-V1 were made between JD 2455365.9 and JD 2455565.6 (2010 June 18 to 2011 January 4)."
 The resulting light curve of all AAVSO data is shown in Figure 1l.., The resulting light curve of all AAVSO data is shown in Figure \ref{allaavsodat}.
 An approximate ephemeris was calculated using these data. and{191 successfully imaged this region of M31 over several weeks. obtaining their desired data set (Soderblom2011).," An approximate ephemeris was calculated using these data, and successfully imaged this region of M31 over several weeks, obtaining their desired data set \citep{Soderblom2011}."
. The eleven observers who contributed data to the HST campaign are given in Table 1.., The eleven observers who contributed data to the HST campaign are given in Table \ref{observertable}.
 The majority of the observations (152 of 214 (total) were obtained using Cousins Ro (He) filters. and our analvsis is based upon these Ae-band observations.," The majority of the observations (152 of 214 total) were obtained using Cousins R $R_{C}$ ) filters, and our analysis is based upon these $R_{C}$ -band observations."
 Each observer has a unique telescope and camera svstem: in general (he observers were able (o reach a signal io noise of at least 3. but a [ew observers were able to obtain verv good signal to noise. with photometric accuracy much better than 0.1 magnitudes per observation.," Each observer has a unique telescope and camera system; in general the observers were able to reach a signal to noise of at least 3, but a few observers were able to obtain very good signal to noise, with photometric accuracy much better than 0.1 magnitudes per observation."
 All of the observations used in this paper are publicly available in theDatabase. and may be downloaded from the AAVSO's website (http://www.aavso.org/data-download) using the name V1.," All of the observations used in this paper are publicly available in the, and may be downloaded from the AAVSO's website (http://www.aavso.org/data-download) using the name ”."
 The observations are not on a common standard system. but for the purpose of time series analysis. (his is nol necessary.," The observations are not on a common standard system, but for the purpose of time series analysis, this is not necessary."
 Observers are using common conparison stars ancl similar (if not identical) fillers. which is sufficient.," Observers are using common comparison stars and similar (if not identical) filters, which is sufficient."
 For our analysis we simply require that the amplitude each observer observes is the same: all zero-point dillerences were removed prior {ο Uime-series analysis via an iterative procedure described below., For our analysis we simply require that the amplitude each observer observes is the same; all zero-point differences were removed prior to time-series analysis via an iterative procedure described below.
 To find the relative zero points of each observer. we first phased the data using a rough period of 31.41 days. obtained by Fourier transforming the raw data [rom a single observer (GED. 65 He observations).," To find the relative zero points of each observer, we first phased the data using a rough period of 31.41 days, obtained by Fourier transforming the raw data from a single observer (GFB, 65 $R_{C}$ observations)."
 The entire data set are (hen folded on that period. vielding a phased light curve of all observers.," The entire data set are then folded on that period, yielding a phased light curve of all observers."
" We then divided the light. curves into equal bins of 1/20 of a period. and performed an iterative adjustment of each observers magnitude offset to minimize the sum of the variances of the 20 bins: where .V, is the number of bins. .N, the number of observations per bin. mj, the magnitude of the j-th observation by observer & in each bin. and 0; (he magnitude offset of the f-th observer."," We then divided the light curves into equal bins of 1/20 of a period, and performed an iterative adjustment of each observer's magnitude offset to minimize the sum of the variances of the 20 bins: where $N_{b}$ is the number of bins, $N_{o}$ the number of observations per bin, $m_{j,k}$ the magnitude of the $j$ -th observation by observer $k$ in each bin, and $\delta_{k}$ the magnitude offset of the $k$ -th observer."
" Each observers offset 6, was ileratively adjusted up or down bv a maxinmmumn of 0.01 magnitudes per step. aud (he process was repeated until the sum of the variances of the bins reached a minimum."," Each observer's offset $\delta_{k}$ was iteratively adjusted up or down by a maximum of 0.01 magnitudes per step, and the process was repeated until the sum of the variances of the bins reached a minimum."
 These offsets were then applied to each observer's data. with observer HQ. used as the reference magnitude: the olfsets are given in Table 2..," These offsets were then applied to each observer's data, with observer HQA used as the reference magnitude; the offsets are given in Table \ref{offsettable}, ,"
energies of >107.,energies of $\gamma \gtrsim 10^4$.
 Racliative cooling is the dominant process affecting the electron spectra after the end of the flaring injection episode at /=2/444.," Radiative cooling is the dominant process affecting the electron spectra after the end of the flaring injection episode at $t = 2 \, t_{\rm dyn}$."
 The time-dependent photon spectra as well as the light curves demonstrate that we do not expect significant peak time delays within the svnchrotron component al [requencies v=10! Hz. but that the high-energv (SSC) component is delaved by ~1 dynamical time scale due (to the gradual accumulation of seed photons for Compton scattering.," The time-dependent photon spectra as well as the light curves demonstrate that we do not expect significant peak time delays within the synchrotron component at frequencies $\nu \gtrsim 
10^{14}$ Hz, but that the high-energy (SSC) component is delayed by $\sim 1$ dynamical time scale due to the gradual accumulation of seed photons for Compton scattering."
 The figure also indicates the verv moderate flux variability al energies just above (the svnchrotron eut-off. which is located at ~1 keV in our example.," The figure also indicates the very moderate flux variability at energies just above the synchrotron cut-off, which is located at $\sim 1$ keV in our example."
 Fig., Fig.
 4 illusirates the spectral hvsteresis phenomenon (keeping in mind that additional contributions from previous injection episodes should close the tracks in (he sense that thev are expected to start out near the end points of the tracks shown in (he figure)., \ref{sim2_hic} illustrates the spectral hysteresis phenomenon (keeping in mind that additional contributions from previous injection episodes should close the tracks in the sense that they are expected to start out near the end points of the tracks shown in the figure).
 In agreement with Li&Ilxusunose(2000) we find that al least in this generic case — the spectral hyvsteresis (racks can change their orientation from clockwise to counterclockwise as one goes from photon energies below the svnchrotron cutoff to energies above the cutoll. where the spectrum is dominated by Compton scattering (55C).," In agreement with \cite{lk00} we find that — at least in this generic case — the spectral hysteresis tracks can change their orientation from clockwise to counterclockwise as one goes from photon energies below the synchrotron cutoff to energies above the cutoff, where the spectrum is dominated by Compton scattering (SSC)."
 In the following. we are focusing on the time-averaged photon spectra. the light curves. and the X-ray spectral hysteresis. aud investigate how those aspects are alfected by variations of individual parameters.," In the following, we are focusing on the time-averaged photon spectra, the light curves, and the X-ray spectral hysteresis, and investigate how those aspects are affected by variations of individual parameters."
 The effect of an increasing injection power corresponding to a higher density of injected. relativistic particles in the emitting region is illustrated in Figs.," The effect of an increasing injection power — corresponding to a higher density of injected, relativistic particles in the emitting region — is illustrated in Figs."
 5 1.., \ref{L_inj_intspectra} – \ref{L_inj_hic}.
" In addition {ο a corresponding increase in the overall bolometric bhuninositv. (his leads also lo a stronger relative energv output in the S5C-dominated Compton emission al X- and -crav energies, as expressed. e.g.. in Eq. ("," In addition to a corresponding increase in the overall bolometric luminosity, this leads also to a stronger relative energy output in the SSC-dominated Compton emission at X- and $\gamma$ -ray energies, as expressed, e.g., in Eq. ("
19) of Chiang&Dótteher(2002).,19) of \cite{cb02}.
". The photon spectral index of the time-averaged enmüssion al optical — soft. X-ray [requencies remains robust ala,y1.25 due to optically thin svnchrotron emission from (he cooled electron spectrum with injection spectral index 4=2.5.", The photon spectral index of the time-averaged emission at optical – soft X-ray frequencies remains robust at $\alpha_{o - X} \sim 1.25$ due to optically thin synchrotron emission from the cooled electron spectrum with injection spectral index $q = 2.5$.
" As the bolometric bhuminositv (and the electron cooling) becomes dominated by the SSC mechanism. one would expect that this changes to the canonical value of a,y=1.5. which is a result of the decaving electron cooling rate in an SSC-clominated cooling scenario (Chiang&Bottcher2002)."," As the bolometric luminosity (and the electron cooling) becomes dominated by the SSC mechanism, one would expect that this changes to the canonical value of $\alpha_{o - X} = 1.5$, which is a result of the decaying electron cooling rate in an SSC-dominated cooling scenario \citep{cb02}."
. ILowever. in (he situation simulated here. the first-order SSC peak is rapidly. (within ~3 lay.) decaying into the keV οποίον range ancl dominating over the instantaneous svnchrotron emission at UV X-ray energies.," However, in the situation simulated here, the first-order SSC peak is rapidly (within $\sim 3 \, 
t_{\rm dyn}$ ) decaying into the keV energy range and dominating over the instantaneous synchrotron emission at UV – X-ray energies."
" This leads (o a significant hardening of the lime-averagecl optical X-ray spectrum. which even becomes inverted in pP, space in our most extreme lest case (simulation no."," This leads to a significant hardening of the time-averaged optical – X-ray spectrum, which even becomes inverted in $\nu F_{\nu}$ space in our most extreme test case (simulation no."
 3)., 8).
absorption is minimum at long wavelengths (Figure 7).,absorption is minimum at long wavelengths (Figure 7).
" Therefore, the best strategy for discovering Cepheids is to observe at visible wavelengths; to minimize the effect of dust luminosities are best measured in the infrared."," Therefore, the best strategy for discovering Cepheids is to observe at visible wavelengths; to minimize the effect of dust luminosities are best measured in the infrared."
" HST brought a number of strengths to the Cepheid distance scale: linear detectors, multiwavelength observations, and a planned cadence of observations."," HST brought a number of strengths to the Cepheid distance scale: linear detectors, multiwavelength observations, and a planned cadence of observations."
 Figure 8 shows for M33 (Freedman et al 1991) how an absolute distance modulus is obtained with knowledge of the reddening law., Figure 8 shows for M33 (Freedman et al 1991) how an absolute distance modulus is obtained with knowledge of the reddening law.
" Figure 9 shows how a power law observing cadence is superior for luminosity measurement to equally spaced observations (Madore Freedman 2002, 2005)."," Figure 9 shows how a power law observing cadence is superior for luminosity measurement to equally spaced observations (Madore Freedman 2002, 2005)."
 The results are shown in Figure 10., The results are shown in Figure 10.
 The light curves for these periods are unmistakably Cepheids., The light curves for these periods are unmistakably Cepheids.
 Our observations populated the range 10-100 days in galaxies with distances of order 10 Mpc., Our observations populated the range 10–100 days in galaxies with distances of order 10 Mpc.
" Figure 11 shows a typical field placement for the Key Project in the large face-on spiral galaxy in the Virgo cluster, M100."," Figure 11 shows a typical field placement for the Key Project in the large face-on spiral galaxy in the Virgo cluster, M100."
 Twelve V observations were obtained during the sequence and four I observations., Twelve V observations were obtained during the sequence and four I observations.
 Cosmic ray splits were used and a fixed roll angle was adopted., Cosmic ray splits were used and a fixed roll angle was adopted.
 Photometry was carried out on the frames using DoPhot and a custom version of DAOPHOT called ALLFRAME (Stetson 1994)., Photometry was carried out on the frames using DoPhot and a custom version of DAOPHOT called ALLFRAME (Stetson 1994).
 A composite I-band period-luminosity relation for 800 Cepheids in 24 galaxies is shown in Figure 12 (corrected for distance) (Ferrarese et al 2000)., A composite I-band period-luminosity relation for 800 Cepheids in 24 galaxies is shown in Figure 12 (corrected for distance) (Ferrarese et al 2000).
" Ferrarese (2000) also carried out a comprehensive comparison of Key Project distances with other prominent distance indicators, such as the tip of the red giant branch (e.g. Sakai 1997) and surface brightness fluctuations (Tonry 2001) (Figure 13) and the planetary nebula luminosity function (Ciardullo Jacoby 1992) and the globular cluster luminosity function (Secker Harris 1993) (Figure 14)."," Ferrarese (2000) also carried out a comprehensive comparison of Key Project distances with other prominent distance indicators, such as the tip of the red giant branch (e.g. Sakai 1997) and surface brightness fluctuations (Tonry 2001) (Figure 13) and the planetary nebula luminosity function (Ciardullo Jacoby 1992) and the globular cluster luminosity function (Secker Harris 1993) (Figure 14)."
expansion speed is 0.018c.,expansion speed is $\sim$ 0.018c.
 VPhis would imply an age of the outer structure of 96 and. 134. Myr for the northern and southern lobes respectively. significantly. smaller than the fon estimate of 215 Myr given by. 2000.," This would imply an age of the outer structure of $\sim$ 96 and 134 Myr for the northern and southern lobes respectively, significantly smaller than the $t_{\rm out}$ estimate of 215 Myr given by K2000."
 ]t is worth noting that our derived. age estimate. Lor the inner double structure is similar to i of IX2000., It is worth noting that our derived age estimate for the inner double structure is similar to that of K2000.
 Indeed. the fit with the Cl model (cf," Indeed, the fit with the CI model (cf."
 Pig., Fig.
" Sb) gives ei;=(cr and vi,=856In Gllz (he cle error is enormous due to the practically straight. spectrum)", 8b) gives $\alpha_{\rm inj}=0.566^{+0.052}_{-0.064}$ and $\nu_{\rm br}=856^{+1{\rm E}11}_{-848}$ GHz (the $\pm 1\sigma$ error is enormous due to the practically straight spectrum).
 Our calculation of the magnetic field in the inner lobes gives Bo—0.5630.11 nE which implies its spectral age to be 2 Myr and an apparent advance velocity of ~O.Le for the lobe heads., Our calculation of the magnetic field in the inner lobes gives $B_{\rm eq}=0.56\pm0.11$ nT which implies its spectral age to be $\sim$ 2 Myr and an apparent advance velocity of $\sim$ 0.1c for the lobe heads.
 However these values have large uncertainties because the spectrum is practically straight., However these values have large uncertainties because the spectrum is practically straight.
 Nevertheless. while interpreting these numbers caveats related. to the evolution of the local magnetic field in the lobes need to be borne in mind (e.g. Itudnick. Ixatz-Stone Anderson 1904: Jones. wu Engel 1999: Blunelell Rawlings 2000).," Nevertheless, while interpreting these numbers caveats related to the evolution of the local magnetic field in the lobes need to be borne in mind (e.g. Rudnick, Katz-Stone Anderson 1994; Jones, Ryu Engel 1999; Blundell Rawlings 2000)."
 While IN2000 have suggested that spectral and dynamical ages are comparable if. bulk backtlow and both radiative and adiabatic losses are taken into account in a self-consistent. manner. Blundell Rawlines (2000) suggest that this may be so only in the voung sources with ages much less than 10. Myr.," While K2000 have suggested that spectral and dynamical ages are comparable if bulk backflow and both radiative and adiabatic losses are taken into account in a self-consistent manner, Blundell Rawlings (2000) suggest that this may be so only in the young sources with ages much less than 10 Myr."
 In the study. of the ETUL tvpe giant radio galaxy. J1343|3758. Jamrozy. et al. (," In the study of the FRII type giant radio galaxy, J1343+3758, Jamrozy et al. ("
2005) find the dynamical age to be approximately 4 times the maximum svnchrotron age of the emitting particles.,2005) find the dynamical age to be approximately 4 times the maximum synchrotron age of the emitting particles.
 We present the results of multifrequeney racio observations of the clouble-double radio galaxy (DDR). 1453|3308. using both the GAIRT and the VLA.," We present the results of multifrequency radio observations of the double-double radio galaxy (DDRG), J1453+3308, using both the GMRT and the VLA."
How atomic gas turns molecular and forms stars 1s one of the questions that is paramount to understanding the process of star formation in galaxies.,How atomic gas turns molecular and forms stars is one of the questions that is paramount to understanding the process of star formation in galaxies.
 This process plays a fundamental role in the transformation of baryonie matter and is the main driver of galaxy formation and evolution., This process plays a fundamental role in the transformation of baryonic matter and is the main driver of galaxy formation and evolution.
 It is well known that star—formation depends on the local physical conditions of the gas such às the pressure., It is well known that star--formation depends on the local physical conditions of the gas such as the pressure.
 It depends on the molecular gas column density by way of the Schmidt-Kennicutt law (222??)..," It depends on the molecular gas column density by way of the Schmidt–Kennicutt law \citep{schmidt1959a,kennicutt1998b,kennicutt2007a,leroy2008a,bigiel2008a}."
 On the large scale it is. however. still not well understood how star formation depends on feedback. spiral density waves or shear. and more generally on the global environment such as in the case of mergers (22??)..," On the large scale it is, however, still not well understood how star formation depends on feedback, spiral density waves or shear, and more generally on the global environment such as in the case of mergers \citep{barnes2004a,chien2010a,teyssier2010a,bournaud2011a}."
 One way to test for the effect of the environment is to use star-forming regions located i collisional debris which are the offsprings of galaxy interactions., One way to test for the effect of the environment is to use star–forming regions located in collisional debris which are the offsprings of galaxy interactions.
 Indeed. depending or the parameters of the collision (relative velocity. impact factor. prograde versus retrograde. ete.).," Indeed, depending on the parameters of the collision (relative velocity, impact factor, prograde versus retrograde, etc.),"
 a varying amount of gas and stars can be stripped from the parent galaxies and injectec into the intergalactic medium., a varying amount of gas and stars can be stripped from the parent galaxies and injected into the intergalactic medium.
 In addition to atomic gas pullec from the parent galaxies. these collisional debris actually contain surprisingly large amounts of molecular gas formed in-situ (222222)...," In addition to atomic gas pulled from the parent galaxies, these collisional debris actually contain surprisingly large amounts of molecular gas formed in–situ \citep{braine2000a,braine2001a,lisenfeld2002a,lisenfeld2004a,petitpas2005a,duc2007a}."
" As the gas subsequently collapses. starforming regions are created with masses ranging from a few hundred solar masses. creating OB associations. the “emissio1 line dots"" (22222222?) to objects as massive as dwarf galaxies named Tidal Dwarf Galaxies (TDGs.222222)..."," As the gas subsequently collapses, star--forming regions are created with masses ranging from a few hundred solar masses, creating OB associations, the “emission line dots” \citep{gerhard2002a,yoshida2002a,sakai2002a,weilbacher2003a,ryan2004a,mendes2004a,cortese2006a,werk2008a,werk2010a} to objects as massive as dwarf galaxies named Tidal Dwarf Galaxies \citep[TDGs,][]{duc1995a,duc1998a,duc2000a,duc2007a,hancock2007a,hancock2009a}."
 These objects. even though formec from material once pertaining to their parent. galaxies. have a radically different and. simpler environment.," These objects, even though formed from material once pertaining to their parent galaxies, have a radically different and simpler environment."
 Recently. ?? showed that star-formation tracers such as ultraviolet. mid-infrared. and Πα. are as reliable in intergalactic star-forming regions as they are in spiral galaxies.," Recently, \cite{boquien2007a,boquien2009a} showed that star–formation tracers such as ultraviolet, mid–infrared, and $\alpha$, are as reliable in intergalactic star–forming regions as they are in spiral galaxies."
 ? showed that the depletion timescale of the molecular gas is similar to that of spiral galaxies even though the collision debris they studied have the lummosity. mass and colour of dwarf galaxies.," \cite{braine2001a} showed that the depletion timescale of the molecular gas is similar to that of spiral galaxies even though the collision debris they studied have the luminosity, mass and colour of dwarf galaxies."
 As collision debris probably have a conversion factor close to that of spiral galaxies with a solar neighbourhood metallicity. this eliminates a major source of uncertainty.," As collision debris probably have a conversion factor close to that of spiral galaxies with a solar neighbourhood metallicity, this eliminates a major source of uncertainty."
 There are still many open questions regarding starformation in collision debris and how the process compares to star formation in spiral disks or in other environments., There are still many open questions regarding star--formation in collision debris and how the process compares to star formation in spiral disks or in other environments.
 It has been observed that star formation is particularly efficient in ultraluminous infrared galaxies (ULIRGs) deduced from a high L¢TIRYL(CO) (?).. as Well as in galaxies that have a subsolar metallicity (????)..," It has been observed that star formation is particularly efficient in ultraluminous infrared galaxies (ULIRGs) deduced from a high L(TIR)/L(CO) \citep{solomon2005a}, as well as in galaxies that have a subsolar metallicity \citep{leroy2006a,gardan2007a,gratier2010a,braine2010b}."
 Conversely. other systems like intergalactic collisional gas bridges contain molecular gas but form stars inefficiently. such as the UGC ο13/6 pair (?)..," Conversely, other systems like intergalactic collisional gas bridges contain molecular gas but form stars inefficiently, such as the UGC 813/6 pair \citep{braine2004b}."
 Recent results by ? and ? showed that starbursts and mergers follow different modes of star formation compared to more quiescent spiral galaxies., Recent results by \cite{daddi2010a} and \cite{genzel2010a} showed that starbursts and mergers follow different modes of star formation compared to more quiescent spiral galaxies.
 Starbursts appear to be forming stars at a higher rate than spiral galaxies for the same gas column density., Starbursts appear to be forming stars at a higher rate than spiral galaxies for the same gas column density.
 However. the discrepancy between the 2 regimes Is increased by the use of a different Xco conversion factor between starforming galaxies and starbursting ones.," However, the discrepancy between the 2 regimes is increased by the use of a different $_\mathrm{CO}$ conversion factor between star--forming galaxies and starbursting ones."
 Can we observe such a difference within a single interacting system. hence retrieving this result in a resolved fashion?," Can we observe such a difference within a single interacting system, hence retrieving this result in a resolved fashion?"
 Are there deviations in the Schmidt-Kennicutt law between intergalactic star formation regions and what is seen in galactic disks (2)??, Are there deviations in the Schmidt–Kennicutt law between intergalactic star formation regions and what is seen in galactic disks \citep{bigiel2008a}?
 To address these questions we compare star formation in different parts of a single interacting system. Arp 158. and its tidal debris.," To address these questions we compare star formation in different parts of a single interacting system, Arp 158, and its tidal debris."
 This system is particularly suited for this study as it presents evidence of extended star formation., This system is particularly suited for this study as it presents evidence of extended star formation.
 Using an homogeneous dataset on a single system means there are no internal calibration or methodological differences for the study of star formation in the interacting galaxies and their tidal debris., Using an homogeneous dataset on a single system means there are no internal calibration or methodological differences for the study of star formation in the interacting galaxies and their tidal debris.
 Arp 158 is an intermediate-stage merger in the, Arp 158 is an intermediate–stage merger in the
like Europa offer potential “incubators” for life. they might - through forward contamination (e.g. Gladimanetal. (2006))) - offer relatively safe haven for microbial life set adrift due to calaclysnuc events on inner. lerrres(tial-(vpe. worlds.,"like Europa offer potential “incubators” for life, they might - through forward contamination (e.g. \citet{gladman06}) ) - offer relatively safe haven for microbial life set adrift due to cataclysmic events on inner, terrrestrial-type, worlds."
 It is not unreasonable to speculate Chat moon and ring svstems will eventually be detected using more sensitive instrumentation and current and future observational techniques., It is not unreasonable to speculate that moon and ring systems will eventually be detected using more sensitive instrumentation and current and future observational techniques.
 Indeed. such detections appear plausible even with current transit methods (Sartoretii5chneider 1999).. especially when applied to future missions such as orCOROT which may even be able to detect the signature of equivalent svstens (o. Jupiter-Europa using eclipse timing (e.g. Dovle&Deee (2003))).," Indeed, such detections appear plausible even with current transit methods \citep{sartoretti99}, especially when applied to future missions such as or which may even be able to detect the signature of equivalent systems to Jupiter-Europa using eclipse timing (e.g. \citet{doyle03}) )."
 With the eventual construction of 20-30 meter class telescopes the detection during transit of massive moons and their associated abmospheres will also become significantly more feasible (Ehrenreichetal.2006)., With the eventual construction of 20-30 meter class telescopes the detection during transit of massive moons and their associated atmospheres will also become significantly more feasible \citep{ehrenreich06}.
. In this paper we present an initial evaluation of the potential lor a subset of currently known extrasolar giant planets to harbor satellite and moon systems., In this paper we present an initial evaluation of the potential for a subset of currently known extrasolar giant planets to harbor satellite and moon systems.
 We also investigate the Likely impact of stellar insolation on icy moons around these exoplanets by considering the orbital inevrsions within various zones of stellar insolation. the time-averaged stellar insolation. and the sublimation rates of water-ice [rom a moon surface.," We also investigate the likely impact of stellar insolation on icy moons around these exoplanets by considering the orbital incursions within various zones of stellar insolation, the time-averaged stellar insolation, and the sublimation rates of water-ice from a moon surface."
 We further consider the potential combination of stellar insolation aud tidal heating of moous in creating habitable environments. such as temperate moons. and examine (he related. constraints on system parameters.," We further consider the potential combination of stellar insolation and tidal heating of moons in creating habitable environments, such as temperate moons, and examine the related constraints on system parameters."
 Previous works have investigated the longevity of satellite svstems due (o tides and migrations. and in particular Earth-nass moons around giant planets on close orbits to the parent star (Ward&Reid1972:BarnesO'Brien2002).," Previous works have investigated the longevity of satellite systems due to tides and migrations, and in particular Earth-mass moons around giant planets on close orbits to the parent star \citep{ward73,barnes02}."
". Barnes O'Brien (2002) note that for parent stars with M,>0.15... Earth sized moons of Jovian planets can remain in stable orbits for some 5 Gyr: they also point out that bevond approximately ~0.6 AU there are essentially no meaningful dynamical constraints on moon masses and survival times."," Barnes O'Brien (2002) note that for parent stars with $M_*>0.15 M_{\odot}$, Earth sized moons of Jovian planets can remain in stable orbits for some 5 Gyr; they also point out that beyond approximately $\sim 0.6$ AU there are essentially no meaningful dynamical constraints on moon masses and survival times."
 Moons around such planets could therefore be both massive and long-livecl., Moons around such planets could therefore be both massive and long-lived.
" In (his present work we therefore restrict our investigation to the potential orbital ranges of stable satellite svstems around known planets whose semimajor axes are a,>0.6 AU.", In this present work we therefore restrict our investigation to the potential orbital ranges of stable satellite systems around known planets whose semimajor axes are $a_p>0.6$ AU.
" A simple consideration of the Hill Sphere radius: yy=a,(AL,/3AL)! (Burns1986) from the restricted 3-body problem. leads to a broad constraint ou (heouler physical extent ol anv svstem in terms of the satellite semi-major axis ay."," A simple consideration of the Hill Sphere radius; $R_H=a_p(M_p/3M_*)^{1/3}$ \citep{burns86} from the restricted 3-body problem, leads to a broad constraint on the physical extent of any system in terms of the satellite semi-major axis $a_s$."
 The critical semimajor axis the location of the outermost satellite orbit that remains bound to the planet has been, The critical semimajor axis - the location of the outermost satellite orbit that remains bound to the planet has been
responsible for the spectral turnover. the magnetic fields must be either. much stronger than previously thought. or well below equipartition values. with the energv in relativistic electrons. greatly exceeding that in magnetic fields.,"responsible for the spectral turnover, the magnetic fields must be either much stronger than previously thought, or well below equipartition values, with the energy in relativistic electrons greatly exceeding that in magnetic fields."
 Orienti ct al. (, Orienti et al. (
2008) find that. equipartition does hold for high frequeney peaking sources. requiring stronger magnetic fields than previously estimated. by Slee et. al. (,"2008) find that equipartition does hold for high frequency peaking sources, requiring stronger magnetic fields than previously estimated by Slee et al. ("
2004).,2004).
 For sources larger than 1 mmas SSA is no longer viable., For sources larger than $\sim1$ mas SSA is no longer viable.
 Higherresolution observations of our GPS sample are needed to determine the angular size and. structure of the central emission region., Higher–resolution observations of our GPS sample are needed to determine the angular size and structure of the central emission region.
 GPS galaxies are the least variable class of compact racio sources (Rucloick and Jones. 1982).," GPS galaxies are the least variable class of compact radio sources (Rudnick and Jones, 1982)."
 GPS radio sources in general show a low incidence of variability (~1054. O'Dea 1998 and references therein). and many of the hieh frequeney peaking (LIED). sources. are QSOs that show peaked spectrum only during outburst/llare events.," GPS radio sources in general show a low incidence of variability $\sim 10\%$, O'Dea 1998 and references therein), and many of the high frequency peaking (HFP) sources are QSOs that show peaked spectrum only during outburst/flare events."
 “This is supported. by TForniainen et al. (, This is supported by Torniainen et al. (
2005) who [ind that nearly all quasar type GPS sources are variable both in spectral shape and. radio power with only a small fraction being ‘genuine’ GPS sources.,2005) who find that nearly all quasar type GPS sources are variable both in spectral shape and radio power with only a small fraction being 'genuine' GPS sources.
 As our sample of sources contains only galaxies we might therefore expect very little variability to be present. but. longer-term: monitoring is needed to test. this.," As our sample of sources contains only galaxies we might therefore expect very little variability to be present, but longer-term monitoring is needed to test this."
 At least two objects in the sample. JO51103 255450 and 471000. alreacky show some evidence of variability. as noted in 844.," At least two objects in the sample, $-$ 255450 and $-$ 471000, already show some evidence of variability, as noted in 4."
 At least two of the sources in our sample. J074618 570258 and 550815. show extended lowfrequeney racio emission on scales of κκρο or Larger.," At least two of the sources in our sample, $-$ 570258 and $-$ 550815, show extended low–frequency radio emission on scales of kpc or larger."
 These may be “restarted” radio galaxies in which the current. phase of nuclear activity has been caught at an carly stage., These may be “restarted” radio galaxies in which the current phase of nuclear activity has been caught at an early stage.
 lt is particularly remarkable that our GPS sample. selected at CLIz. includes the giant radio galaxy JOT4618 570258 which was first identified by Saripalli et al. (," It is particularly remarkable that our GPS sample, selected at GHz, includes the giant radio galaxy $-$ 570258 which was first identified by Saripalli et al. ("
2005) on the basis of its extended. low surface-brightness radio emission at MMITz.,2005) on the basis of its extended low surface-brightness radio emission at MHz.
 When the redshift coverage of the AP20G GPS sample is completed. it should allow a more detailed study of the duty evele of activity in nearby racio galaxies.," When the redshift coverage of the AT20G GPS sample is completed, it should allow a more detailed study of the duty cycle of activity in nearby radio galaxies."
 We have presented Gem e-VLBL observations of 10. low redshift. low radio power GPS galaxies selected from. the AT20€. survey.," We have presented 6cm e-VLBI observations of 10 low redshift, low radio power GPS galaxies selected from the AT20G survey."
 The angular resolution of the cVLBI observations was sullicient to confirm the compact nature of the targets. but not high enough to differentiate between edge-brightened. ancl jet dominated. GPS sources.," The angular resolution of the eVLBI observations was sufficient to confirm the compact nature of the targets, but not high enough to differentiate between edge-brightened and jet dominated GPS sources."
 Such a cdilferentiation is required. to investigate the possibility of a [uminositv-morphology. relationship in radio galaxy progenitors. similar to the PR-L/FR-L relationship.," Such a differentiation is required to investigate the possibility of a luminosity-morphology relationship in radio galaxy progenitors, similar to the FR-I/FR-II relationship."
 The eVLDBI observations do allow us to devise follow-up VLBI observations using the full LBA at a higher. observing [requeney. to obtain higher angular resolution.," The eVLBI observations do allow us to devise follow-up VLBI observations using the full LBA at a higher observing frequency, to obtain higher angular resolution."
 The value of eVLBI observations in this context is that fast feedback can be obtained regarding the detectability of the targets. allowing the rapid selection of a sample for more detailed follow-up observations.," The value of eVLBI observations in this context is that fast feedback can be obtained regarding the detectability of the targets, allowing the rapid selection of a sample for more detailed follow-up observations."
 The Australia Telescope Long Baseline Array is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO., The Australia Telescope Long Baseline Array is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.
 This research has made use of the NASA/LPAC Extragalactic Database (NIED) 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."
 Blank D. L. et al., Blank D. L. et al.
 2005. MNILAS. 356. 734 Brosch N. et al..," 2005, MNRAS, 356, 734 Brosch N. et al.,"
 2000. NINILAS. 313. 641 Condon J. J. et al.," 2000, MNRAS, 313, 641 Condon J. J. et al.,"
 1998. AJ. 115. 1693 Deller A. T. et ab.," 1998, AJ, 115, 1693 Deller A. T. et al.,"
 2007. PASP. 119. 318 de Vaucouleurs. C... de Vaucouleurs. A. Corwin Ihc... Buta Rod. Paturel. €. Fouque PL. Fhird. Reference Catalogue of Bright Galaxies.," 2007, PASP, 119, 318 de Vaucouleurs, G., de Vaucouleurs A., Corwin H.G., Buta R.J., Paturel, G., Fouque P., Third Reference Catalogue of Bright Galaxies."
 Dovle MT. et al., Doyle M.T. et al.
" 2005. MNICAS. 361. 34 Fabiano αν, Miller L.. Frinchieri G.. Longair M.. Elvis AL. 1984. ApJ. 277."," 2005, MNRAS, 361, 34 Fabiano G., Miller L., Trinchieri G., Longair M., Elvis M., 1984, ApJ, 277,"
Properties of equilibrium states differing frou theoretical predictions iu the interval of negative specific heat were found (see above).,Properties of equilibrium states differing from theoretical predictions in the interval of negative specific heat were found (see above).
 Let ux. now study the nonlinear structure erowth in this interval for an increased dissipation streueth. ic. outside of equilibrimu. when TaiSSΤΗ.," Let us, now study the nonlinear structure growth in this interval for an increased dissipation strength, i.e., outside of equilibrium, when $\tau_{\rm dis}\la\tau_{\rm ff}$."
 As previously. a relaxed. unperturbed. cofined V- body sphere with s=1 serves as initia e for the sinulations.," As previously, a relaxed, unperturbed, confined $N$ -body sphere with $\varepsilon=1$ serves as initial state for the simulations."
 Tn order to dissipate the cucrey cifferent cIssipation schemes are applied., In order to dissipate the energy different dissipation schemes are applied.
 Before we discuss the appearance of long-range correlations iu uustable dissipative svstenis let us brieflv discuss the effect of the different «Issipation schemes on the global svstem structure., Before we discuss the appearance of long-range correlations in unstable dissipative systems let us briefly discuss the effect of the different dissipation schemes on the global system structure.
 The differcut applied «issipation schemes (see Sect. , The different applied dissipation schemes (see Sect. \ref{dissip}) )
lead to collapsed ghases with cüffereut eloba structures., lead to collapsed phases with different global structures.
 That is. they ive different nass fractious contained in the core aud the halo.," That is, they have different mass fractions contained in the core and the halo."
" A typical ordering is. DanaPasaDy Where. Dat Da aud Picea are the density coutrasts resulting frou simulations with il dissipation scheme. dvuamical friction aud a loca dissipation scheme. respectively,"," A typical ordering is, ${\cal D}_{\rm global}>{\cal D}_{\rm
 dyn}>{\cal D}_{\rm local}$, where, ${\cal D}_{\rm global}$, ${\cal
 D}_{\rm dyn}$ and ${\cal D}_{\rm local}$ are the density contrasts resulting from simulations with a global dissipation scheme, dynamical friction and a local dissipation scheme, respectively."
 The deusity contrast is. D-log(Poupul. where po and py are the ceuter of lass density aud the peripheric density. respectively.," The density contrast is, ${\cal D}\equiv\log(\rho_{\rm cm}/\rho_0)$, where $\rho_{\rm cm}$ and $\rho_0$ are the center of mass density and the peripheric density, respectively."
" This nieans that for a global dissipation scheme alinost all the nass ds concentrated in a dense core. whereas a loca dissipation scheme cau form a persistent ""massive halo."," This means that for a global dissipation scheme almost all the mass is concentrated in a dense core, whereas a local dissipation scheme can form a persistent “massive” halo."
 The evolution of the mass distribution resulting frou siunulatious with the different dissipation sclienies is show- in Fie. 6.., The evolution of the mass distribution resulting from simulations with the different dissipation schemes is shown in Fig. \ref{cooling}.
 The collapse of the iuner shells takes in all systenis about the same time., The collapse of the inner shells takes in all systems about the same time.
 Yet. the uucollapsed matter distributed iu the halo is for the elobal dissipation scheme less than 2%. whereas it is LO% for the local dissipation scheme.," Yet, the uncollapsed matter distributed in the halo is for the global dissipation scheme less than $2 \%$, whereas it is $10 \%$ for the local dissipation scheme."
 Next. temporary long-range correlations that develo in unforced eyavitating Ssvstenus are presented idu dependence of the differcut svsteni parameters.," Next, temporary long-range correlations that develop in unforced gravitating systems are presented in dependence of the different system parameters."
 A sufficicutly strong global dissipation. i.c.. Tin TH: of a eravitating svstem leads duiug the uoulinear plase of the collapsing transition to fragicutation and lone-range phase-space correlations. so that the iudex. ó(r). of the velocity-cdispersion size relation. σX/S7 Decomes positivo.," A sufficiently strong global dissipation, i.e., $\tau_{\rm
 dis}\la\tau_{\rm ff}$ , of a gravitating system leads during the nonlinear phase of the collapsing transition to fragmentation and long-range phase-space correlations, so that the index, $\delta(r)$, of the velocity-dispersion size relation, $\sigma\propto r^{\delta(r)}$, becomes positive."
 Fie., Fig.
 7 shows the evolution of the velocity-dispersiou-size relation. 1.6.. of à for different dissipation streneths.," \ref{kk3_1} shows the evolution of the velocity-dispersion-size relation, i.e., of $\delta$ for different dissipation strengths."
 The relatious result from 23 different simulations with elobal dissipation schemes ane different dissipation streneths., The relations result from 3 different simulations with global dissipation schemes and different dissipation strengths.
 The dissipation streneth is given through the paranieter à., The dissipation strength is given through the parameter $\alpha$.
 Here a=1.0.5.0.9.0.," Here $\alpha=1.0,\;5.0,\;9.0$."
 This corresponds to Tdis=2.0.0.1.0.2TH.," This corresponds to $\tau_{\rm dis}=2.0,\;0.4\;,0.2\;\tau_{\rm ff}$."
 Whereas the velocities remain uncorrelated in the siuulation with à=1.0. ó becomes temporary positive over the whole dvuamical range in the simulations with he stronger dissipation.," Whereas the velocities remain uncorrelated in the simulation with $\alpha=1.0$, $\delta$ becomes temporary positive over the whole dynamical range in the simulations with the stronger dissipation."
 The velocity correlations start to develop at largest scales after the svseiu has become seLeravitating., The velocity correlations start to develop at largest scales after the system has become self-gravitating.
 After he system has euered the interval of negative specific reat the correlation growth is accelerated., After the system has entered the interval of negative specific heat the correlation growth is accelerated.
 It attains a Παππια aud finally disappears when the collapse cuds., It attains a maximum and finally disappears when the collapse ends.
 The dvnaimical range over which à>0 during maxiumuui correlation is z2 dex., The dynamical range over which $\delta>0$ during maximum correlation is $\approx 2$ dex.
 Correlations at simall scales straight above the softening leneth are strouger for α stronger enorev dissipation., Correlations at small scales straight above the softening length are stronger for a stronger energy dissipation.
 The maxima correlation established im the negative specific heat interval persists for O(0.1)τ aud is characteristic for the applied dissipation strength and softening., The maximum correlation established in the negative specific heat interval persists for ${\cal O}(0.1)\;\tau_{\rm ff}$ and is characteristic for the applied dissipation strength and softening.
 For iustauce. the simulation with the strongest Issipation cevelops during 0.37 a roughly constant à over a range of 1.5 dex that resembles Larson's relation.," For instance, the simulation with the strongest dissipation develops during $0.3\;
\tau_{\rm ff}$ a roughly constant $\delta$ over a range of 1.5 dex that resembles Larson's relation."
 Yot. correlations at small scales decay rapidly aud the oeidex à becomes even negative at iuterinediate scales.," Yet, correlations at small scales decay rapidly and the index $\delta$ becomes even negative at intermediate scales."
 The end of the collapse aud with it the disappearance of the correlated velocity. structure is marked bv a ENivoreiug ucgative specific heat e>x , The end of the collapse and with it the disappearance of the correlated velocity structure is marked by a diverging negative specific heat $c_V\rightarrow -\infty$.
This is shown 1 Fig. δ., This is shown in Fig. \ref{kk3kappa}.
", Systems with cdvnamical friction aud local dissipation evelop also velocity correlatious.", Systems with dynamical friction and local dissipation develop also velocity correlations.
 Fig., Fig.
 9 shows the correlations resulting from siulatious with a local dissipatii scheme., \ref{kb_1} shows the correlations resulting from simulations with a local dissipation scheme.
 Coutrary to the elobal dissipation scheme. a stroug local dissipation does not exteud the collapse of the whole system.," Contrary to the global dissipation scheme, a strong local dissipation does not extend the collapse of the whole system."
 Tli4 local Yiction forces. that are strong euough to develop correlations lead also to a fast collapse and correlatious persist accordinglv a short time courpared to simulations with global dissipation.," Thus, local friction forces, that are strong enough to develop correlations lead also to a fast collapse and correlations persist accordingly a short time compared to simulations with global dissipation."
 The correspouding evolution of the Lagrangian radii and the interval of negative specific heat are shown iu Fie. 10.., The corresponding evolution of the Lagrangian radii and the interval of negative specific heat are shown in Fig. \ref{kbkappa}.
 Iu the dynamical friction scheme. energy dissipation depends. as iu the global dissipation scheme. on the absolute particle velocity.," In the dynamical friction scheme, energy dissipation depends, as in the global dissipation scheme, on the absolute particle velocity."
 Thus aisroug ανασα] friction extends the eravitational collapse aud the “lifetime” of the correlations., Thus a strong dynamical friction extends the gravitational collapse and the “lifetime” of the correlations.
 Yet. the observed plase-space correlations are weaker. compared to those appearing in ΠΙΟ with global aud local dissipation. respectively. came that the reduced. dissipation streneth for fast particles. accordinely o the cyvnamiical friction scheme. destrovs the correlations.," Yet, the observed phase-space correlations are weaker, compared to those appearing in simulations with global and local dissipation, respectively, meaning that the reduced dissipation strength for fast particles, accordingly to the dynamical friction scheme, destroys the correlations."
 So far the velocity correlations im dependence of the different dissipative factors were studied., So far the velocity correlations in dependence of the different dissipative factors were studied.
 Next the effect of different short distance reguluizations of the Newtonian potential. removing its sineularity. are checked.," Next the effect of different short distance regularizations of the Newtonian potential, removing its singularity, are checked."
 That is. stations withand without short distance repulsive," That is, simulations withand without short distance repulsive"
NGC 4203 has been observed with$779 twice using the GT50M erating and once using (he G430L grating.,NGC 4203 has been observed with twice using the G750M grating and once using the G430L grating.
 Table 1 stmimarizes the observations and (he archival spectra are presented in Fig 1., Table 1 summarizes the observations and the archival spectra are presented in Fig 1.
 ASTIS specirum showing the broad Ilo emission line has been presented previously by Shieldsοἱal.(2000.2007) based on observations obtained under PID 7361. Shieldsetal. (2000).. Dassin&Bonatto(2003).," A spectrum showing the broad ${\alpha}$ emission line has been presented previously by \cite{Shi00, Shi07} based on observations obtained under PID 7361. \cite{Shi00}, , \cite{Bas03},"
.. GonzalesDelgadoet and Sarzielal.(2005) have all presented the G430L spectrum obtained under PID 7361., \cite{GD04} and \cite{Sar05} have all presented the G430L spectrum obtained under PID 7361.
 llowever. the GT750M spectrum obtained under PID 11571 is shown for the first me in Fig.," However, the G750M spectrum obtained under PID 11571 is shown for the first time in Fig."
 l., 1.
 Alultiple exposures obtained using the same erating and al (he same position have been combined using the taskocrreject., Multiple exposures obtained using the same grating and at the same position have been combined using the task.
 Dithered exposures were shifted using the (ask prior to combining., Dithered exposures were shifted using the task prior to combining.
 Subsequently. the task was used (o perform a 7 pixel wide extraction along the slit direction aud centered on the nucleus.," Subsequently, the task was used to perform a 7 pixel wide extraction along the slit direction and centered on the nucleus."
 Each extraction samples > of the encircled energy [or an unresolved point source 2010)., Each extraction samples ${\ge}$ of the encircled energy for an unresolved point source \citep{Pro10}.
. The GT50M spectra reveal a broad La line with a EWILIM ~ 3000 kim/s that briehtened bv more than a factor of two in the almost 11 vear interval since the first spectirum. was obtained., The G750M spectra reveal a broad ${\alpha}$ line with a FWHM ${\sim}$ 3000 km/s that brightened by more than a factor of two in the almost 11 year interval since the first spectrum was obtained.
 Two narrow but resolved [8 LH] lines appear on the red side of the broad [la line at  and (wo narrow but resolved |O I| lines appear on the blue side at 6350., Two narrow but resolved [S II] lines appear on the red side of the broad ${\alpha}$ line at ${\sim}$ and two narrow but resolved [O I] lines appear on the blue side at ${\sim}$.
 These narrow lines are virtually identical in the two datasets., These narrow lines are virtually identical in the two datasets.
 Thus. the brightening appears to be limited to just the broad IIo. + [N II] emission line complex which is remarkable because the more recent observations were obtained with a smaller.," Thus, the brightening appears to be limited to just the broad ${\alpha}$ + [N II] emission line complex which is remarkable because the more recent observations were obtained with a smaller."
. The G430L spectrumreveals a wide swath of emission lines., The G430L spectrumreveals a wide swath of emission lines.
" Collectively, the G750M ancl G420L spectra resolve ihe Ho. and H lines."," Collectively, the G750M and G430L spectra resolve the ${\alpha}$, ${\beta}$ and ${\gamma}$ lines."
 A more detailed description of the spectra follows. beginning with the ILvdrogen (11) Balmer lines.," A more detailed description of the spectra follows, beginning with the Hydrogen (H) Balmer lines."
 The Ila emission line profile exhibits broad shoulders (hat are accentuated in the 2010 spectrum compared to the one obtained in 1999., The ${\alpha}$ emission line profile exhibits broad shoulders that are accentuated in the 2010 spectrum compared to the one obtained in 1999.
 Both of the [N II] vacuum wavelength 6549.85 and 6535.28 emission lines ancl (he narrow componentof the vacuum wavelength, Both of the [N II] vacuum wavelength 6549.85 and 6585.28 emission lines and the narrow componentof the vacuum wavelength
2007).. to be used in the analyses.,", to be used in the analyses."
 With differing noise levels for each of these sets. we calculated the revised orbital parameters for the » And planetary system with four planetary companions (Table 8)).," With differing noise levels for each of these sets, we calculated the revised orbital parameters for the $\upsilon$ And planetary system with four planetary companions (Table \ref{upsAnd_parameters}) )."
 Because our four-planet solution of the RV's of v And differs significantly from the proposed solution of Curieletal.(2011) with respect to the orbital period of the outer planet. numerical integrations of the orbits are needed to assess the stability of our solution.," Because our four-planet solution of the RV's of $\upsilon$ And differs significantly from the proposed solution of \citet{curiel2011} with respect to the orbital period of the outer planet, numerical integrations of the orbits are needed to assess the stability of our solution."
 The lower estimate for the orbital period of v And e does not support the conclusion that the d and e planets could be in à 3:1 mean motion resonance (MMR)., The lower estimate for the orbital period of $\upsilon$ And e does not support the conclusion that the d and e planets could be in a 3:1 mean motion resonance (MMR).
 However. our solution coincides roughly with à 2:1 MMR. which could enable the stability of the system over long time-scales.," However, our solution coincides roughly with a 2:1 MMR, which could enable the stability of the system over long time-scales."
 Investigating the stability of our solution 1s necessary to be able to determine whether it corresponds to a physically viable system and is not simply an artefact caused by noise. data sampling. and possible biases in the measurements.," Investigating the stability of our solution is necessary to be able to determine whether it corresponds to a physically viable system and is not simply an artefact caused by noise, data sampling, and possible biases in the measurements."
 For successful detections. it is crucial that the noise — Le. all the other variations except the Keplerian signals — in the valuable measurements is modelled as realistically as possible and not simply minimised as is commonly the case when using simple y minimisations and related methods.," For successful detections, it is crucial that the noise – i.e. all the other variations except the Keplerian signals – in the valuable measurements is modelled as realistically as possible and not simply minimised as is commonly the case when using simple $\chi^{2}$ minimisations and related methods."
 Our method can be used readily to detect whether the statistical model indeed describes the data adequately with respect to the selected noise model as well., Our method can be used readily to detect whether the statistical model indeed describes the data adequately with respect to the selected noise model as well.
 The application of our criterion. to measurements of any complex systems is obvious., The application of our criterion to measurements of any complex systems is obvious.
 Systems whose behaviour. time-evolution. and dependence on different physical and other factors cannot be derived from fundamental physical principles. are difficult to model because the models are necessarily empirical descriptions. whose validity can only be assessed using measurements.," Systems whose behaviour, time-evolution, and dependence on different physical and other factors cannot be derived from fundamental physical principles, are difficult to model because the models are necessarily empirical descriptions, whose validity can only be assessed using measurements."
 In such systems. there can be numerous small-scale effects and/or biases. whose existence is not known and whose magnitude cannot be measured.," In such systems, there can be numerous small-scale effects and/or biases, whose existence is not known and whose magnitude cannot be measured."
 These effects cannot therefore be taken into account in the nodel constructed to describe some desired features of the system., These effects cannot therefore be taken into account in the model constructed to describe some desired features of the system.
 As briefly noted in Kaasalainen(2011).. the ability to show that a model is an insufficient. description of the neasurements is therefore needed to be able to determine whether the model needs to be improved further to extract all the valuable information from the noisy data.," As briefly noted in \citet{kaasalainen2011}, the ability to show that a model is an insufficient description of the measurements is therefore needed to be able to determine whether the model needs to be improved further to extract all the valuable information from the noisy data."
 According to the demonstrations in this article. our method can be said to satisfy these needs to significant extent.," According to the demonstrations in this article, our method can be said to satisfy these needs to significant extent."
 Also. as we dic not make any assumptions regarding the exact nature of the model. the criterion can be applied to any problem for which it is possible to calculate the likelihoods of the measurements using the model.," Also, as we did not make any assumptions regarding the exact nature of the model, the criterion can be applied to any problem for which it is possible to calculate the likelihoods of the measurements using the model."
 Finally. we note that if the model has been constructed prior to the measurements. the model inadequacy means that the earlier data sets used to construct the model. i.e. to select the model formulae and calculate the posterior densities of the model parameters. conflict with the new ones with respect to the model.," Finally, we note that if the model has been constructed prior to the measurements, the model inadequacy means that the earlier data sets used to construct the model, i.e. to select the model formulae and calculate the posterior densities of the model parameters, conflict with the new ones with respect to the model."
 It could also be that the model is being developed using a single data set in hand., It could also be that the model is being developed using a single data set in hand.
 Then. despite being the best model in the sense of having the greatest posterior probability. the model could still be inadequate in describing some part of the data set with respect to another part (Kaasalainen.2011).," Then, despite being the best model in the sense of having the greatest posterior probability, the model could still be inadequate in describing some part of the data set with respect to another part \citep{kaasalainen2011}."
. Either way. the measurements cannot be described adequately using the selected model and we say that the model is inadequate.," Either way, the measurements cannot be described adequately using the selected model and we say that the model is inadequate."
 Our eriterion can be used in these cases as well., Our criterion can be used in these cases as well.
"realizations of the celestial reference system should correct source coordinates for this effect, possibly by providing source positions, together with a corrective formula.","realizations of the celestial reference system should correct source coordinates for this effect, possibly by providing source positions, together with a corrective formula."
 The European optical astrometry mission Gaia (Perryman et al., The European optical astrometry mission Gaia (Perryman et al.
" 2001), scheduled for 2012, should be able to determine the components of the acceleration vector with a relative precision of (Mignard 2002)."," 2001), scheduled for 2012, should be able to determine the components of the acceleration vector with a relative precision of (Mignard 2002)."
" To improve the VLBI determination of the Galactocentric acceleration and to confirm the significance of the quadrupole systematics, more proper motions of extragalactic radio sources need to be measured over the next decade."," To improve the VLBI determination of the Galactocentric acceleration and to confirm the significance of the quadrupole systematics, more proper motions of extragalactic radio sources need to be measured over the next decade."
 Concentrating on sources showing a high positional stability and having a low structure index would reduce unwanted effects of intrinsic motion caused by the relativistic jets and other modification of the source structure., Concentrating on sources showing a high positional stability and having a low structure index would reduce unwanted effects of intrinsic motion caused by the relativistic jets and other modification of the source structure.
" In addition, it is necessary to run a dedicated program to measure the redshift of the reference radio sources using large optical facilities, especially in the southern hemisphere (Maslennikov et al."," In addition, it is necessary to run a dedicated program to measure the redshift of the reference radio sources using large optical facilities, especially in the southern hemisphere (Maslennikov et al."
 2010)., 2010).
Note (hat (he restuling expression on the rieglt-haud-sicle differs by a factor of A (which we consider to be large) from (he corresponding expression in the standard incompressible Sweet.Parker theorv.,Note that the resulting expression on the right-hand-side differs by a factor of $A$ (which we consider to be large) from the corresponding expression in the standard incompressible Sweet–Parker theory.
 As we shall see shortly. this fact will turn out to be significant when we determine (he outflow velocity at the next step.," As we shall see shortly, this fact will turn out to be significant when we determine the outflow velocity at the next step."
 Now. consider the (wo components of the equation of motion.," Now, consider the two components of the equation of motion."
 Since we expect the reconnection inflow velocity into the laver. ry... to be much smaller than the Alfvénn speed. the y component of the equation of motion simply becomes the pressure balance condition.," Since we expect the reconnection inflow velocity into the layer, $v_{\rm rec}$, to be much smaller than the Alfvénn speed, the $y$ component of the equation of motion simply becomes the pressure balance condition."
 Neglecting for simplicity the upstream plasma pressure compared with the magnetic pressure (which is justified by for magnetically-dominant coronal environments). we can (hen write P=Po.0)=," Neglecting for simplicity the upstream plasma pressure compared with the magnetic pressure (which is justified by for magnetically-dominant coronal environments), we can then write P P(0,0) =."
 Next. we consider (he equation of motion along the laver (at the lavers midplane. y=0): PCO p= OP jo By ," Next, we consider the equation of motion along the layer (at the layer's midplane, $y=0$ ): v_x _x v_x = _x P - j_z B_y /c."
In the original incompressible Sweet.Parker model. the magnetic tension Lorce (the second term on the right-hand side) (uris out to be comparable to the pressure-gracdient foree.," In the original incompressible Sweet–Parker model, the magnetic tension force (the second term on the right-hand side) turns out to be comparable to the pressure-gradient force."
 Then. since one is only interested in getting a rough. order-of-magnitude estimate. one can drop the magnetic tension term and integratetheresulting equation Irom «=0 to rocL. vielding the standard result =p (0.0) -- PIL.0)~ P=.," Then, since one is only interested in getting a rough, order-of-magnitude estimate, one can drop the magnetic tension term and integratetheresulting equation from $x=0$ to $x=L$, yielding the standard result u^2 P(0,0) - P(L,0) P = ."
Iu essence these results confined one of the basic features of the RPAL. namely the nearly quadratic dependence of the nodal precession frequency ou the o-frequeucy.,"In essence these results confirmed one of the basic features of the RPM, namely the nearly quadratic dependence of the nodal precession frequency on the $\phi$ -frequency."
" If the NS spin frequency is measured. then for anv value of 4, the model vields a predicted nodal precession frequency which is uucertain oulv by a factor of a few. μααν due to the allowed range of {τν1 (Stella Vietii 19982)."," If the NS spin frequency is measured, then for any value of $\nu_\phi$ the model yields a predicted nodal precession frequency which is uncertain only by a factor of a few, mainly due to the allowed range of $I_{45}m^{-1}$ (Stella Vietri 1998a)."
 Ouly in the Atoll source IUT728-31 burst oscillations aud simultaneous kIIz QPOs aud WBOs have so far been detected tnambiguously (Strolunaver ct al., Only in the Atoll source 4U1728-34 burst oscillations and simultaneous kHz QPOs and HBOs have so far been detected unambiguously (Strohmayer et al.
 1996: Ford van dev Klis 1998: Mendez van der EKlis 1999)., 1996; Ford van der Klis 1998; Mendez van der Klis 1999).
 Therefore its QPO frequencies can be used to test both the vy50 and Av versus 15 rclationships predicted by the RPM. when the NS spin derived from burst oscillations is used (Veypst2361 IIz).," Therefore its QPO frequencies can be used to test both the $\nu_{HBO}$ and $\Delta\nu$ versus $\nu_2$ relationships predicted by the RPM, when the NS spin derived from burst oscillations is used $\nu_{burst} \simeq 364$ Hz)."
 In order to take fully iuto account of all the effects that contribute determine ecocdetic motion iu the vicinity of the NS. we adopted a umuuerical approach aud. computed the spacetime motrice of the star using Stergioulas (1995) code. au equivalent of that of Cook et al.(1992): see also Stergioulas and Friediuau (1995).," In order to take fully into account of all the effects that contribute determining geodetic motion in the vicinity of the NS, we adopted a numerical approach and computed the spacetime metric of the star using Stergioulas' (1995) code, an equivalent of that of Cook et al.(1992); see also Stergioulas and Friedman (1995)."
" From this. (7. and on,,4; Were derived as a function of 14, for παπατοςαν small tilt augles aud eccentiicities (Morsink Stella 1999: Stella. Vietri Morsiuk 1999)."," From this, $\nu_{r}$ and $\nu_{nod}$ were derived as a function of $\nu_\phi$ for infinitesimally small tilt angles and eccentricities (Morsink Stella 1999; Stella, Vietri Morsink 1999)."
 Fie., Fig.
 1€ shows the measured values of Av iud vype versus ro in IUI728-31., 1C shows the measured values of $\Delta\nu$ and $\nu_{HBO}$ versus $\nu_2$ in 4U1728-34.
 Relatively high NS masses (sce also Sect., Relatively high NS masses (see also Sect.
 2) and stiff EOSs such as AU aud UU (Wirinea et al., 2) and stiff EOSs such as AU and UU (Wiringa et al.
 1988) are required iu this application of the RPM., 1988) are required in this application of the RPM.
 The solid lines in Fie., The solid lines in Fig.
 1€ are for à 1.93 AD. NS with EOS AU and νι=361 Iz., 1C are for a $1.93$ $_\odot$ NS with EOS AU and $\nu_s=364$ Hz.
 A good agreement is obtained if the WBO frequency. the lower of the two brauches seeu in U1728-3L. is identified with the 2ud harmonics of ο ρω see also Morsink Stella 1999: Stella Vietri 1999a).," A good agreement is obtained if the HBO frequency, the lower of the two branches seen in 4U1728-34, is identified with the 2nd harmonics of $\nu_{nod}$ $2\nu_{nod}$ ; see also Morsink Stella 1999; Stella Vietri 1999a)."
 Correspondinely the upper ΠΟ brauch is well fit by lear, Correspondingly the upper HBO branch is well fit by $4\nu_{nod}$.
 The ecometry of tilted orbits in the iucrmost disk reeious might be such that a stronger signal is produced at the even harmonics of the nodal precession frequeucyv (e.c. Psaltis et al., The geometry of tilted orbits in the innermost disk regions might be such that a stronger signal is produced at the even harmonics of the nodal precession frequency (e.g. Psaltis et al.
 1999)., 1999).
" The frequency range and treud of the epievclic frequency vy, in this model are also iu reasonable agreciment with the Av measurements: a nore conrplex model is clearly required in order to fit these data more accuratelv.", The frequency range and trend of the epicyclic frequency $\nu_r$ in this model are also in reasonable agreement with the $\Delta\nu$ measurements; a more complex model is clearly required in order to fit these data more accurately.
 Iu summary. the model preseuted here is capable of reproducing the salicut eatures of both the Av versus 15 and vypo. versus i relationships. with just two ree puiriuneters (AL and the EOS). the allowed range of which is fairly limited (anoreover the EOS cannot even be varied coutinuously !).," In summary, the model presented here is capable of reproducing the salient features of both the $\Delta\nu$ versus $\nu_2$ and $\nu_{HBO}$ versus $\nu_2$ relationships, with just two free parameters $M$ and the EOS), the allowed range of which is fairly limited (moreover the EOS cannot even be varied continuously !)."
 Concerning Z-sources and all other Atoll sources for which burst oscillations have not been detected vet. he NS spin can still be regarded as a free parameter.," Concerning Z-sources and all other Atoll sources for which burst oscillations have not been detected yet, the NS spin can still be regarded as a free parameter."
 The application of the RPM o the IIBOs of these sources can therefore be used to constrain the spin of their NSs., The application of the RPM to the HBOs of these sources can therefore be used to constrain the spin of their NSs.
" Couversely. in those Atoll source in which 1,4; Is measured. but IIDOs have rot been detected vet. the RPM. can be used to predict 7jpo."," Conversely, in those Atoll source in which $\nu_{burst}$ is measured, but HBOs have not been detected yet, the RPM can be used to predict $\nu_{HBO}$."
 These issues are xieflv addressed in the next Section., These issues are briefly addressed in the next Section.
 Psaltis. Belloui van der WNlis (1999) recently ideutified two QPOs and peaked noise components the frequency of which follows a tight correlation over nearly three decades.," Psaltis, Belloni van der Klis (1999) recently identified two QPOs and peaked noise components the frequency of which follows a tight correlation over nearly three decades."
 This correlation (hereafter PBY correlation) involves both NS aud BOC LAINRBs spanning ciffereut classesand a wide range of Iuuinosities (sce the poiuts, This correlation (hereafter PBV correlation) involves both NS and BHC LMXRBs spanning different classesand a wide range of luminosities (see the points
V να is a cool evolved N type carbon star with several unusual properties. inchidineg: (1) two variability periods. of about 530 and 6000. days (Mavall 19653): (2) possible shock-excited forbidden-lue enmission similar to that seen from Uerbie-Taro objects (Llovd Evans 1991)): (3) contiuuuna enission at radio wavelengths far in excess of the expected plotospheric fiux (Lattermoser Brown 1992)): C1) a cirectunstelar euvelope which has a fattened or disk-like shape (Tsuji ct al. LO88:: ,"V Hya is a cool evolved N type carbon star with several unusual properties, including: (1) two variability periods, of about 530 and 6000 days (Mayall \cite{mayall}) ); (2) possible shock-excited forbidden-line emission similar to that seen from Herbig-Haro objects (Lloyd Evans \cite{lloyd}) ); (3) continuum emission at radio wavelengths far in excess of the expected photospheric flux (Luttermoser Brown \cite{lb}) ); (4) a circumstellar envelope which has a flattened or disk-like shape (Tsuji et al. \cite{tsuji}; ;"
Wahane et al. LOSS: Isa, Kahane et al. \cite{kahane88};
haue et al. 1996)):, Kahane et al. \cite{kahane96}) );
 and (5) a 200 kinsl possibly bipolar. wind secu in CO(v = 01) absorption (Sahai Wonuier 1988)). in KI absorption aud cussion (Plez Lambert 1991)). iu optical forbiddeu-liue euission (Llovd Evans 1991)) aud in CO nilimeterwaveleusth spectral lue cussion (παρ ot al. 1997..," and (5) a 200 $\rm km~s^{-1}$, possibly bipolar, wind seen in CO(v = 0–1) absorption (Sahai Wannier \cite{sahai88}) ), in KI absorption and emission (Plez Lambert \cite{plez}) ), in optical forbidden-line emission (Lloyd Evans \cite{lloyd}) ) and in CO millimeter-wavelength spectral line emission (Knapp et al. \cite{knapp},"
 hereafter Paper I)., hereafter Paper I).
 Because V Iva is oue of only two known evolved stars with a fast molecular wind which still has the infrared colors of an ACB star (the other being Π Cau). it wey be in the very carlicst stages of evolution away from the AGB.," Because V Hya is one of only two known evolved stars with a fast molecular wind which still has the infrared colors of an AGB star (the other being $\rm \Pi^1$ Gru), it may be in the very earliest stages of evolution away from the AGB."
 The preseut paper discusses several new observations of V Tha aud its cuvelope. which we integrate with previous observational results to learn about the evolutionary status of V να and the behavior of stars as they evolve away from the ACB.," The present paper discusses several new observations of V Hya and its envelope, which we integrate with previous observational results to learn about the evolutionary status of V Hya and the behavior of stars as they evolve away from the AGB."
 The main wart of the paper (Sect., The main part of the paper (Sect.
 2) is an analysis of archival observations of the stars dicht curve inade between October 1961 aud July 1996., 2) is an analysis of archival observations of the star's light curve made between October 1961 and July 1996.
 Appendix Α suumuniarizes iw observations of the stars radio frequency enissiou and of the molecular circumstellar envelope., Appendix A summarizes new observations of the star's radio frequency emission and of the molecular circumstellar envelope.
" Section 3 discusses the implications of these and previous data or the evolutionary status of VW να, and cives the conclusions."," Section 3 discusses the implications of these and previous data for the evolutionary status of V Hya, and gives the conclusions."
 Basic data for V Uva. inchiding properties derived in this paper. are sununuarized in Table 1.," Basic data for V Hya, including properties derived in this paper, are summarized in Table 1."
 Recently. Ilipparcos (Perrvinan et al. 1997))," Recently, Hipparcos (Perryman et al. \cite{perryman}) )"
 has provided accurate astrometric data for V Ia., has provided accurate astrometric data for V Hya.
 The parallax of the star is too small to measure (7=0.16+1.29 milliaresecouds} eiviug a 2o lower lait to the distauce of LOO pc.," The parallax of the star is too small to measure $\rm \pi ~ = ~ 0.16
~ \pm ~ 1.29$ milliarcseconds) giving a $\sigma$ lower limit to the distance of 400 pc."
 Berecat et al. (1998)), Bergeat et al. \cite{bergeat}) )
 discuss the period-luninosity relatiouship of carbon variables using IHipparcos data. aud sugeest au absolute IX magnitude of —9.05 for V να based on its variability period of 530 davs. giving a distance of 550 pe.," discuss the period-luminosity relationship of carbon variables using Hipparcos data, and suggest an absolute K magnitude of $\rm -9.05^m$ for V Hya based on its variability period of 530 days, giving a distance of 550 pc."
 We assine a round-uuuuberdistance of 500 pc iu this paper., We assume a round-numberdistance of 500 pc in this paper.
suggests (hat the periodic [ας density variations in Sev A* are also related to an instability of the accretion disk.,suggests that the periodic flux density variations in Sgr A* are also related to an instability of the accretion disk.
 However. the X-ray luminosity (~2x105 L.) of GRS 19154-105 is 20 limes greater than the Edclington limit for à 3 M. black hole (Mirabel Rodriguez 1999) and (he radio jets are produced by the overwhelming radiation pressure.," However, the X-ray luminosity $\sim2\times10^6$ $_\odot$ ) of GRS 1915+105 is 20 times greater than the Eddington limit for a 3 $_\odot$ black hole (Mirabel Rodriguez 1999) and the radio jets are produced by the overwhelming radiation pressure."
 On the other hand. the low N-rav luminosity (< 100 L.. ~10 orders in magnitude below the Eddington limit [or a 2.5x10* M. object) of Ser A* indicates that the gravity [ar exceeds the radiation pressure.," On the other hand, the low X-ray luminosity $<$ 100 $_\odot$, $\sim$ 10 orders in magnitude below the Eddington limit for a $\times10^6$ $_\odot$ object) of Sgr A* indicates that the gravity far exceeds the radiation pressure."
 Because of the strong gravity. and weak radiation pressure. the consequence of the eas dynamics in Ser À* on the AU scales would be different [rom GRS 19152-105.," Because of the strong gravity and weak radiation pressure, the consequence of the gas dynamics in Sgr A* on the AU scales would be different from GRS 1915+105."
" In Lact. (he tme variability and the limit on the intrinsic source size («0.5 mas or 100 R, or 5 AU) ol Ser A* trom the 7 mm observations (Lo 1998 and Bower and Backer 1998) suggest that anv variability in the jet occurs in a region where the gravitational field of the black hole dominates."," In fact, the time variability and the limit on the intrinsic source size $<$ 0.5 mas or 100 $_g$ or 5 AU) of Sgr A* from the 7 mm observations (Lo 1998 and Bower and Backer 1998) suggest that any variability in the jet occurs in a region where the gravitational field of the black hole dominates."
 Any collimations of jets or outflows related to the observed radio variability appear to be disrupted within Ser A* on a scale of ~5 AU., Any collimations of jets or outflows related to the observed radio variability appear to be disrupted within Sgr A* on a scale of $\sim$ 5 AU.
 A model consisting of a jet nozzle Faleke 1996) seems useful to study i a sell-consistent dynamic theory for the disk instability can be constructed., A model consisting of a jet nozzle Falcke 1996) seems useful to study if a self-consistent dynamic theory for the disk instability can be constructed.
 A convection process is now considered in the advection dominated. accretion flow (ADAF) that could well provide a reasonable dvnamie model for the accretion disk and possible outflows (Naravan 2000: Quataert Gruzinoy 2000: Igeumenshehey Abramowiez. 1999: Stoneal... 1999).," A convection process is now considered in the advection dominated accretion flow (ADAF) that could well provide a reasonable dynamic model for the accretion disk and possible outflows (Narayan 2000; Quataert Gruzinov 2000; Igumenshchev Abramowicz, 1999; Stone, 1999)."
 In this theory. hot dense bubbles are produced in the inner part of a low-viscosity disk through convection caused by thermal instabilitv.," In this theory, hot dense bubbles are produced in the inner part of a low-viscosity disk through convection caused by thermal instability."
 The most attractive result. [rom the convective-ADAF theory is that quasiperiodie production of convective bubbles has been observed in numerical simulations. although the observed period aud (he small cvcle Irequency. width. have not been predicted in detail from the theory. (levmenshchey Abramowicz. 1999).," The most attractive result from the convective-ADAF theory is that quasiperiodic production of convective bubbles has been observed in numerical simulations, although the observed period and the small cycle frequency width have not been predicted in detail from the theory (Igumenshchev Abramowicz, 1999)."
 The current. results appear to [avor the convective-ADAF model, The current results appear to favor the convective-ADAF model
Llowever. all of the periods are robust to within 5 per cent of our favoured: values. ancl as we noted earlier this is the criterion by which we consider a svstem to be solved. since or the practical purpose of comparing the population of sdBD stars to theoretical models knowing the periods to within 5 yer cent is normally sullicient.,"However, all of the periods are robust to within 5 per cent of our favoured values, and as we noted earlier this is the criterion by which we consider a system to be solved, since for the practical purpose of comparing the population of sdB stars to theoretical models knowing the periods to within 5 per cent is normally sufficient."
 In. a number of cases. the xobabilitv of the orbital period being further than 1 and 5 »er cent from our favoured value is the same., In a number of cases the probability of the orbital period being further than 1 and 5 per cent from our favoured value is the same.
 This is because all the significant probability [ies within a very small range around the best. period. with all the significant competition (i.c. next best alias) placed. outside the 5 per cent. region around the best alias.," This is because all the significant probability lies within a very small range around the best period, with all the significant competition (i.e. next best alias) placed outside the 5 per cent region around the best alias."
 We also compute the uncertainty that when. added in quacdrature to our raw error estimates gives a reduced voLo , We also compute the uncertainty that when added in quadrature to our raw error estimates gives a reduced $\chi^2 = 1$.
This systematic uncertainty accounts Lor sources of errors such as true variability of the star or slit-filling errors., This systematic uncertainty accounts for sources of errors such as true variability of the star or slit-filling errors.
 These errors are most. probably not correlated. with the orbit or the statistical errors determined. ancl thus are πιο in quadrature., These errors are most probably not correlated with the orbit or the statistical errors determined and thus are added in quadrature.
" In all cases we use a minimum value of 2kms+ corresponding to 1/10""! ofa pixel which we believe to be a fair estimate of the true limits of our data."," In all cases we use a minimum value of $2\,{\rm km}\,{\rm s}^{-1}$ corresponding to $^{\rm th}$ of a pixel which we believe to be a fair estimate of the true limits of our data."
 These determinations are also given in Table 3.., These determinations are also given in Table \ref{tab:probs}.
 In most cases. the systematic uncertainty does not exceed the minimum value.," In most cases, the systematic uncertainty does not exceed the minimum value."
 We measured. the elective temperature. Tar; the surface eravity. logg. and the helium abundance. οσο). for 13 of the 28 sclBs Listed in Table 2.. and list these measurements in Table 4..," We measured the effective temperature, $_{\rm eff}$, the surface gravity, $\log g$, and the helium abundance, $\log ({\rm He}/{\rm H})$, for 13 of the 28 sdBs listed in Table \ref{tab:results}, and list these measurements in Table \ref{tab:tefflogg}."
 Due to the various instrument setups we used we are not able to do this for all the svstems. because data in which the spectral range only encompasses a small number of lines is insullicient to constrain these parameters with any srecision.," Due to the various instrument setups we used we are not able to do this for all the systems, because data in which the spectral range only encompasses a small number of lines is insufficient to constrain these parameters with any precision."
 We used the procedure of ? to fit the profiles of the Balmer. the and the lines present in the spectra by a grid of svnthetie spectra.," We used the procedure of \citet{Saffer94} to fit the profiles of the Balmer, the and the lines present in the spectra by a grid of synthetic spectra."
 The svnthetie spectra obtained rom the metal line-blanketed LEE: model atmospheres of ? were matched to the data simultaneously., The synthetic spectra obtained from the metal line-blanketed LTE model atmospheres of \citet{Heber00} were matched to the data simultaneously.
 For the two jiotlest stars the model grid. with enhanced. metal line Xanketing was used. which substantially improved the fits (Lor details see. 2)).," For the two hottest stars the model grid with enhanced metal line blanketing was used, which substantially improved the fits (for details see \citealt{OToole06}) )."
 Before the fitting was carried out. we convolved the synthetic spectra with a Gaussian function o account for the instrumental profile.," Before the fitting was carried out, we convolved the synthetic spectra with a Gaussian function to account for the instrumental profile."
 IKDD2215|5037 was weviously analvsed with the same set of models in. 2.. the results of which are in exact agreement with our finding here.," KPD2215+5037 was previously analysed with the same set of models in \citet{Heber02}, the results of which are in exact agreement with our finding here."
 We plot these results in the T logg plane and ind that all but. two of the objects lic in the band defined » the zero-age extreme horizontal branch. the terminal- extreme horizontal branch and the He main sequence," We plot these results in the $_{\rm eff}$ / $\log g$ plane and find that all but two of the objects lie in the band defined by the zero-age extreme horizontal branch, the terminal-age extreme horizontal branch and the He main sequence"
the correlation coefficient. decreases slowly with increasing depth Ul close to the base of the convection zone.,the correlation coefficient decreases slowly with increasing depth till close to the base of the convection zone.
 Near the base of the convection zone there is a sharp dip and C'(r.1) becomes negative lor flows obtained with GONG data.," Near the base of the convection zone there is a sharp dip and $C(r,T)$ becomes negative for flows obtained with GONG data."
 The position of this dip may be interpreted as a lower limit on the depth to which the zonal-How pattern penetrates into the solar interior., The position of this dip may be interpreted as a lower limit on the depth to which the zonal-flow pattern penetrates into the solar interior.
 This gives another indication that the zonal flows penetrate to depths near the base of the convection zone as has been claimed by Vorontsov et al. (, This gives another indication that the zonal flows penetrate to depths near the base of the convection zone as has been claimed by Vorontsov et al. (
2002). Basu Antia (2003). Antia οἱ al. (,"2002), Basu Antia (2003), Antia et al. ("
2008) and others.,2008) and others.
 For MDI data also the results ave similar. though the dip near the base of the convection zone is less marked.," For MDI data also the results are similar, though the dip near the base of the convection zone is less marked."
 The correlation coefficients obtained when we restrict the summation in Eq. (2)), The correlation coefficients obtained when we restrict the summation in Eq. \ref{eq:cor}) )
 to the low-latitude regions is shown in Figure 4.., to the low-latitude regions is shown in Figure \ref{fig:corlow}.
 It can be seen that [or the GONG data these results are not very different. from those shown in Figure 10 that were obtained [or the full latitucle range., It can be seen that for the GONG data these results are not very different from those shown in Figure \ref{fig:cor} that were obtained for the full latitude range.
 The only difference is that the correlation coefficient for the low-Iatitude regions is generally higher and the drop near the base of (he convection zone is sharper., The only difference is that the correlation coefficient for the low-latitude regions is generally higher and the drop near the base of the convection zone is sharper.
 The value of T lor which the correlation coefficient is highest does not change much with depth., The value of $T$ for which the correlation coefficient is highest does not change much with depth.
 The peak occurs al 7=11.7 vears., The peak occurs at $T=11.7$ years.
 Since the low-Jatitude pattern of zonal flows is more well defined than the hieh-latitude pattern. it is perhaps more meaningful to restrict (he analysis to the low-latitude regions.," Since the low-latitude pattern of zonal flows is more well defined than the high-latitude pattern, it is perhaps more meaningful to restrict the analysis to the low-latitude regions."
 For the low-latitude region MDI data result in smoother curves that are very similar to those lor GONG., For the low-latitude region MDI data result in smoother curves that are very similar to those for GONG.
 The peak in MIDI data also occurs al the same value of T while considering only low latitude region., The peak in MDI data also occurs at the same value of $T$ while considering only low latitude region.
 Ou the other hand. if (he summation is restricted to high latitudes. then the variation of the correlation coefficient. with 1 is similar (ο that obtained using both low- and high-latitude regions.," On the other hand, if the summation is restricted to high latitudes, then the variation of the correlation coefficient with $T$ is similar to that obtained using both low- and high-latitude regions."
 This is probably because zonal flow. velocities are generally higher in the high-latitucle regions. thereby giving larger contribution to the summation.," This is probably because zonal flow velocities are generally higher in the high-latitude regions, thereby giving larger contribution to the summation."
 Thus most of the difference between GONG and MDI data appears to be for high latitudes., Thus most of the difference between GONG and MDI data appears to be for high latitudes.
 Since the zonal-flow pattern is better defined in the low latitude reeions near (he surface we use (he estimate of period in this region to represent the length of solar evele 23 defined by solar cdvnamics., Since the zonal-flow pattern is better defined in the low latitude regions near the surface we use the estimate of period in this region to represent the length of solar cycle 23 defined by solar dynamics.
 This value is around 11.7 vears., This value is around 11.7 years.
 Although it is difficult to define the period of minimum activity using zonal-Iow pattern. once (he length of solar evele 23 is estimated we can use the known epoch of the minimum (1996.4) to caleulate the epoch of recent minimum.," Although it is difficult to define the period of minimum activity using zonal-flow pattern, once the length of solar cycle 23 is estimated we can use the known epoch of the minimum (1996.4) to calculate the epoch of recent minimum."
 This turns out to be 2008.1. which is consistent with time at which the high latitude band of faster (han average rotation ends.," This turns out to be 2008.1, which is consistent with time at which the high latitude band of faster than average rotation ends."
 This is when the minimum in sunspot numbers is used (o define the minimum of solar evcle 23., This is when the minimum in sunspot numbers is used to define the minimum of solar cycle 23.
 If instead (he 10.7 cm solar radio (hax is used to define the minimum. the estimate for current minimun will shift to 2008.5.," If instead the 10.7 cm solar radio flux is used to define the minimum, the estimate for current minimum will shift to 2008.5."
 The minimum in sunspot nunber or 10.7 em radio {lis for solar evele 24 occurred a few months later., The minimum in sunspot number or 10.7 cm radio flux for solar cycle 24 occurred a few months later.
 Thus the solar dvnamies seems (0 suggest a slightly smaller period [or solar cycle 23 compared to some other activity indices., Thus the solar dynamics seems to suggest a slightly smaller period for solar cycle 23 compared to some other activity indices.
 Nevertheless. the difference is within the variations between different activitv indices.," Nevertheless, the difference is within the variations between different activity indices."
 Our estimate of length ol the last solar evele is consistent with that obtained bv Lowe et al. (, Our estimate of length of the last solar cycle is consistent with that obtained by Howe et al. (
2009) also from the,2009) also from the
 Table 5 summarises our measured angular separations and position angles. and published results for previously known components.," Table 5 summarises our measured angular separations and position angles, and published results for previously known components."
 This star. also known as GJ 3060A or NLTT 2805. is a flare star (2). with a known stellar companion. NLTT 2804.," This star, also known as GJ 3060A or NLTT 2805, is a flare star \citep{Norton2007} with a known stellar companion, NLTT 2804."
" The Catalog of Components of Double Multiple Stars (CCDM.?) provides the astrometric measurements p=LO"" and 6=315° for epoch 1960."," The Catalog of Components of Double Multiple Stars \citep[CCDM,][]{Dommanget2002} provides the astrometric measurements $\rho=1.0\arcsec$ and $\theta=315\degr$ for epoch 1960."
" observations provide positions of the two components ofp=2.080"" and 4=316° (epoch1991.25.2).."," observations provide positions of the two components of $\rho=2.080\arcsec$ and $\theta=316\degr$ \citep[epoch 1991.25, ][]{Perryman1997}."
 ? present photometric and astrometric observations of visual double stars and for this binary estimate the angular separation to be p=1.648” and the position angle ¢=317.12° (epoch 2002.64)., \citet{StrigachevLampens2004} present photometric and astrometric observations of visual double stars and for this binary estimate the angular separation to be $\rho = 1.648\arcsec$ and the position angle $\theta=317.12\degr$ (epoch 2002.64).
 Our measured separation iso=1.305” and position angle 6= 318.97. indicating orbital motion.," Our measured separation is $\rho=1.305\arcsec$ and position angle $\theta=318.9\degr$ , indicating orbital motion."
 This 1s a high proper motion star with 4454 =-235.5 mas/yr and jpic2-351.6 mas/yr., This is a high proper motion star with $\mu_{\rm RA}$ =-235.5 mas/yr and $\mu_{\rm DEC}$ =-351.6 mas/yr.
" Also known as HIP 5443. it is a double star (2). with separation p=2.7"" and position angle 6=77° (epoch 1991.25)."," Also known as HIP 5443, it is a double star \citep{Perryman1997} with separation $\rho=2.7\arcsec$ and position angle $\theta=77\degr$ (epoch 1991.25)."
" We measure the separation p.=2.554"" and position angle @=74.5”. hence both components form à common proper motion pair."," We measure the separation $\rho=2.554\arcsec$ and position angle $\theta=74.5\degr$, hence both components form a common proper motion pair."
 The small change in separation and position angle in the more than 15 years that have passed between the and our measurements can be attributed to orbital motion., The small change in separation and position angle in the more than 15 years that have passed between the and our measurements can be attributed to orbital motion.
 The primary star is a high proper motion star for which ?. estimated an age between 25 and 300 Myr., The primary star is a high proper motion star for which \citet{Shkolnik2009} estimated an age between 25 and 300 Myr.
 Because of its faint magnitude. the secondary star could not beseen at the time of observation but only after additional analysis.," Because of its faint magnitude, the secondary star could not beseen at the time of observation but only after additional analysis."
where ua(a) is analytic about a=1.,where $u_3(a)$ is analytic about $a=\frac{1}{2}$.
 By Proposition 3.2. the behavior of the sign of ®(r) in a neighborhood of +=Q is relevant.," $\Box$ By Proposition 3.2, the behavior of the sign of $\Phi(x)$ in a neighborhood of $x=0$ is relevant."
 If (c) is of one sign in some neighborhood. then g4(z2) has an analvtic extension into Re z>42 with no singularities. implving the absence of z; here.," If $\Phi(x)$ is of one sign in some neighborhood, then $g_1(z)$ has an analytic extension into Re $z>\frac{1}{2}$ with no singularities, implying the absence of $z_k$ here."
 However. (his requires inlormation on the point wise behavior of dr). which goes bevond the relatively weaker integrabilitv property (21)).," However, this requires information on the point wise behavior of $\Phi(x)$, which goes beyond the relatively weaker integrability property \ref{EQN_A2}) )."
 To make astep in (his direction. we next apply a linear transform to (0)) to derive the asvimplotic behavior of Cr) in terms of the distribution 2;.," To make astep in this direction, we next apply a linear transform to \ref{EQN_B2}) ) to derive the asymptotic behavior of $\Phi(x)$ in terms of the distribution $z_k$."
 We next clefine and its Fourier transform As a consequence of (e.g. Dorwein et al., We next define and its Fourier transform As a consequence of (e.g. Borwein et al.
 2006) IIere includes contributions [rom the logarithmic derivative of the factor to Q(z) in (34)). whose singularities are restricted to the trivial zeros of Q(z ," 2006) where $B$ is a constant, so that Here includes contributions from the logarithmic derivative of the factor to $\zeta(z)$ in \ref{EQN_zet1}) ), whose singularities are restricted to the trivial zeros of $\zeta(z)$ ."
). , $\Box$ 
"As to the wind component, we use the following expressions corresponding to the so-called ""split monopole” solution (Michel 1973; Bogovalov 1999) Here ὕΨιοι=27f-(Q/c)|m| is the total magnetic flux through the polar cap, and f,~1 and fy~1 are the dimensionless constants.","As to the wind component, we use the following expressions corresponding to the so-called ”split monopole” solution (Michel 1973; Bogovalov 1999) Here $\Psi_{\rm tot} = 2\pi f_{r} (\Omega/c) |\bf{m}|$ is the total magnetic flux through the polar cap, and $f_{r} \sim 1$ and $f_{\varphi} \sim 1$ are the dimensionless constants."
 We see that the former termdescribes the quasi-monopole radial magnetic field., We see that the former term the quasi-monopole radial magnetic field.
 Such a structure was obtained not only for the axisymmetric force-free (Contopoulos et al., Such a structure was obtained not only for the axisymmetric force-free (Contopoulos et al.
 1999; Timokhin 2006) and MHD (Komissarov 2006) numerical simulations but it describes well enough the magnetic field of the inclined rotator as well (Spitkovsky 2006)., 1999; Timokhin 2006) and MHD (Komissarov 2006) numerical simulations but it describes well enough the magnetic field of the inclined rotator as well (Spitkovsky 2006).
" As we are actually in the disturbance of the dipole magnetic field inside the light cylinder only, we do not include here into consideration the switching of the radial field in the current sheet in the equatorial region."," As we are actually in the disturbance of the dipole magnetic field inside the light cylinder only, we do not include here into consideration the switching of the radial field in the current sheet in the equatorial region."
" As the total magnetic flux through the polar cap depends only weakly on the inclination angle « (BGI; Spitkovsky 2006), we put here for simplicity f,=1 (for zero longitudinal current f, changes from 1.592 to 1.93)."," As the total magnetic flux through the polar cap depends only weakly on the inclination angle $\alpha$ (BGI; Spitkovsky 2006), we put here for simplicity $f_{r} = 1$ (for zero longitudinal current $f_{r}$ changes from 1.592 to 1.93)."
" Besides, the latter term B, (46)) corresponds to the toroidal magnetic field connected with the longitudinal electric current flowing in the magnetosphere."," Besides, the latter term ${B}_{\varphi}$ \ref{Bb2}) ) corresponds to the toroidal magnetic field connected with the longitudinal electric current flowing in the magnetosphere."
" It is well-known that to support the MHD (in particular, force-free) outflow up to infinity the the total longitudinal current I is to be close to the Michel (1973) current Im=QWtot/47 (Contopoulos et al."," It is well-known that to support the MHD (in particular, force-free) outflow up to infinity the the total longitudinal current $I$ is to be close to the Michel (1973) current $I_{\rm M} = \Omega \Psi_{\rm tot}/4\pi$ (Contopoulos et al."
 1999)., 1999).
 It corresponds to f;z&1., It corresponds to $f_{\varphi} \approx 1$.
" On the other hand, this current for inclined rotator with dipole magnetic field, it is necessary to suppose that the current density is much larger than the local Goldreich-Julian current ja;jj©QBcosa/2n (Beskin 2010)."," On the other hand, this current for inclined rotator with dipole magnetic field, it is necessary to suppose that the current density $j_{\parallel}$ is much larger than the local Goldreich-Julian current $j_{\rm GJ} \approx \Omega B \cos \alpha/2\pi$ (Beskin 2010)."
" As it is not clear whether the Michel current Iq>[σι can be realized in the pulsar magnetosphere, in what follows the parameter f can be considered as a free one."," As it is not clear whether the Michel current $I_{\rm M} > I_{\rm GJ}$ can be realized in the pulsar magnetosphere, in what follows the parameter $f_{\varphi}$ can be considered as a free one."
 In Table 1 we present the notation of the models which will be used in what follows., In Table \ref{table00} we present the notation of the models which will be used in what follows.
 Magnetic field structure for model C (and for orthogonal rotator) is shown in Fig 5.., Magnetic field structure for model C (and for orthogonal rotator) is shown in Fig \ref{figmagnfield}.
 It the numerical model obtained by Spitkovsky (2006)., It the numerical model obtained by Spitkovsky (2006).
 Recall the well-known property of the one-photon particle production in a strong magnetic field: the secondary particles are produced only if the photon moves at large enough angle to the magnetic field line (Sturrock 1971; Ruderman Sutherlend 1975; Arons Scharlemann 1979)., Recall the well-known property of the one-photon particle production in a strong magnetic field: the secondary particles are produced only if the photon moves at large enough angle to the magnetic field line (Sturrock 1971; Ruderman Sutherlend 1975; Arons Scharlemann 1979).
" Since the relativistic particles near the neutron star surface can move only along the field lines with a Lorentz factor y=(1-vi/c?)1? (vj is the particle velocity along the magnetic field), the hard gamma-quanta emitted through curvature mechanism also begin to move along the field lines."," Since the relativistic particles near the neutron star surface can move only along the field lines with a Lorentz factor $\gamma=(1-v_{\parallel}^2/c^2)^{-1/2}$ $v_{\parallel}$ is the particle velocity along the magnetic field), the hard gamma-quanta emitted through curvature mechanism also begin to move along the field lines."
" As a result, the production of secondary particles will be supressed near the magnetic poles, where the magnetic field is nearly rectilinear."," As a result, the production of secondary particles will be supressed near the magnetic poles, where the magnetic field is nearly rectilinear."
" Therefore, one would expect the secondary plasma density to be suppressed in the central region of the open field lines (see Fig. 6))."," Therefore, one would expect the secondary plasma density to be suppressed in the central region of the open field lines (see Fig. \ref{fig0}) )."
 It is this property that lies in the ground of the hollow cone model., It is this property that lies in the ground of the hollow cone model.
 Bellow we assume that the plasma number density on a polar cap is known., Bellow we assume that the plasma number density on a polar cap is known.
" It is convenient to rewrite it in the form Here πο)=ΩΒ/2ποε is the amplitude of the Goldreich-Julian number density, i.e., it does not depend on the inclination angle a."," It is convenient to rewrite it in the form Here $n_{\rm GJ}^{(0)} = \Omega B/2\pi c e$ is the amplitude of the Goldreich-Julian number density, i.e., it does not depend on the inclination angle $\alpha$."
" Further, the multiplicity parameter determining the efficiency of the pair creation is (Daughertyπο, Harding 1982; Gurevich Istomin 1985; Istomin Sobyanin 2009; Medin Lai 2010) Finally, the dimensionless factor g(05,5)~1 describes the real number density of the secondary plasma in the vicinity of the neutron star surface as a function of magnetic pole angles 0,, and Ym."," Further, the multiplicity parameter determining the efficiency of the pair creation is (Daugherty Harding 1982; Gurevich Istomin 1985; Istomin Sobyanin 2009; Medin Lai 2010) Finally, the dimensionless factor $g(\theta_{m}, \varphi_{m}) \sim 1$ describes the real number density of the secondary plasma in the vicinity of the neutron star surface as a function of magnetic pole angles $\theta_{m}$ and $\varphi_{m}$."
 The procedure described below allows us to determine the properties of the outgoing radiation for arbitrary number density ne within the polar cap., The procedure described below allows us to determine the properties of the outgoing radiation for arbitrary number density $n_{\rm e}$ within the polar cap.
" For illustration we consider an axially symmetric distribution where f=r2/Πὸ is the dimensionless distance to the magnetic axis, Ro=(QR/c)!/?R is the polar cap radius,"," For illustration we consider an axially symmetric distribution where $f = r_{\perp}^2/R_0^2$ is the dimensionless distance to the magnetic axis, $R_0 = (\Omega R/c)^{1/2} R$ is the polar cap radius,"
The dillerence in the number of interlopers between the top two panels (halos vs. galaxies) for the most massive SAIBLIs arises because the observed. SAIBIL samples. vield an internally inconsistent set of Ad σ.o0 and AlL relations. as mentioned above.,"The difference in the number of interlopers between the top two panels (halos vs. galaxies) for the most massive SMBHs arises because the observed SMBH samples yield an internally inconsistent set of $M-\sigma$ , $L-\sigma$ and $M-L$ relations, as mentioned above."
" While the interpretation of his inconsistency is beyond the scope of our paper. we note hat ""undoetal.(2007). cüscussed this issue. and concluded hat the intrinsic scatter in the relations produces a selection jas: using the observed. DII samples vields a biased Lo0 relation (too low { for given 0)."," While the interpretation of this inconsistency is beyond the scope of our paper, we note that \cite{Tundo+07} discussed this issue, and concluded that the intrinsic scatter in the relations produces a selection bias: using the observed BH samples yields a biased $L-\sigma$ relation (too low $L$ for given $\sigma$ )."
 This suggests that the ALL galaxy relation we adopted may also be biased and it under-oediets L: correcting this bias would decrease the number of galaxy interlopers., This suggests that the $M-L$ galaxy relation we adopted may also be biased and it under-predicts $L$; correcting this bias would decrease the number of galaxy interlopers.
" Ifthe GAY signal can be used to constrain M and D, of he source via statistical inference. as suggested by CCL1O.. hen the numbers of interloping halos. luminous galaxies and AGN are given by respectively."," If the GW signal can be used to constrain $\mathcal{M}$ and $D_{L}$ of the source via statistical inference, as suggested by \citetalias{CorCor10}, then the numbers of interloping halos, luminous galaxies and AGN are given by respectively."
" Above. the redshifts :4=z2(D;+AD,) bound the radial extent of the error box."," Above, the redshifts $z_{\pm}= z(D_{L}\pm\Delta D_{L})$ bound the radial extent of the error box."
" We adopt. and AD,/Dp=20%.", We adopt and $\Delta D_{L}/D_{L}=20\%$.
 We ignore errors due to weal: ensing. which are expected to be on the order of severa sereent for sources with 2%1.5 (Ixoesisetal.2006:Lirata.Holz&Cutler2010:ShaneLaiman 2011).," We ignore errors due to weak lensing, which are expected to be on the order of several percent for sources with $z\ltsim 1.5$ \citep{Kocsis+06, Hirata+10, ShangHaiman11}."
. We do no dace an upper limit on the host halo mass (or on the hos galaxy luminosity)., We do not place an upper limit on the host halo mass (or on the host galaxy luminosity).
 In. principle. such an upper limit coul » computed. eiven. P'PA’s observational error on the chirp mass and the spread in the ratio between the chirp mass anc he gravitational mass of the binary (i.0.. [rom the mocel-dependent mass ratio distribution of resolved. sources).," In principle, such an upper limit could be computed, given PTA's observational error on the chirp mass and the spread in the ratio between the chirp mass and the gravitational mass of the binary (i.e., from the model-dependent mass ratio distribution of resolved sources)."
 For example. CC10. provide a chirp mass error estimate of AM~5%.," For example, \citetalias{CorCor10} provide a chirp mass error estimate of $\Delta\Mch\sim 5\%$."
 Converting the chirp mass to the gravitationa mass. however. can introduce a large uncertainty. e.g. a [actor of ~2 depending on whether the mass ratio is 0.1or 1.," Converting the chirp mass to the gravitational mass, however, can introduce a large uncertainty, e.g. a factor of $\sim 2$ depending on whether the mass ratio is $0.1$or $1$."
 Since the number density of interlopers decrease rapidly with increasing halo mass (or luminosity). this simplification should not allect our estimates.," Since the number density of interlopers decrease rapidly with increasing halo mass (or luminosity), this simplification should not affect our estimates."
 In Figure 2.. we plot the number of interloping host candidates against the source redshift z.," In Figure \ref{fig:CCcount}, we plot the number of interloping host candidates against the source redshift $z$."
 Not surprisingly. he prospects for IM identification improve dramatically in he CCLO scenario.," Not surprisingly, the prospects for EM identification improve dramatically in the \citetalias{CorCor10} scenario."
" For massive (M10"" AZ.) resolved *TA sources. we anticipate that the error box will contain a single host candidate at zz;0.2. and several hundred aonXO07."," For massive $M\gta 10^{9}\Msol$ ) resolved PTA sources, we anticipate that the error box will contain a single host candidate at $z\ltsim 0.2$, and several hundred at $z\ltsim 0.7$."
 We expect only a single eroup-sized halo (AL=Low10734. ) in the error box atany redshift in the CCLO scenario.," We expect only a single group-sized halo $M\ga {\rm
 few}\times 10^{13}\Msol$ ) in the error box atany redshift in the \citetalias{CorCor10} scenario."
 Note that the number Αν of interlopers is not necessarily a monotonically increasing function of 2. as he decline in the number densities of the interloping objects," Note that the number $N_g$ of interlopers is not necessarily a monotonically increasing function of $z$ , as the decline in the number densities of the interloping objects"
Defining we take the rotation matrix to be corresponding to a first rotation about (ποτ axis by an angle X. a second rotation about the y axis by an angle η. and a third rotation about the + axis again by an angle A.,"Defining we take the rotation matrix to be corresponding to a first rotation about the $z$ axis by an angle $\chi$, a second rotation about the $y$ axis by an angle $\eta$, and a third rotation about the $z$ axis again by an angle $\lambda$ ."
" In other words. A=F(z.Αμ.Πέιν\). where Πως,0) is a standard matrix describing a rotation by an angle ( about the ο; axis."," In other words, $\tilde{A} \equiv R(z,~\lambda) R(y,~\eta) R(z,~\chi)$, where $R(x_{i},~\theta)$ is a standard matrix describing a rotation by an angle $\theta$ about the $x_{i}$ axis."
 The angles X. 7). and A can take arbitrary values (positive or negative). with the sense of rotation determined by the right hand rule.," The angles $\chi$, $\eta$, and $\lambda$ can take arbitrary values (positive or negative), with the sense of rotation determined by the right hand rule."
 For example. the orbital angular momentum for a coplanar collision is L(t)>=Loa. implying We consider first the case of non-coplanar encounters in which the perturber moves along a straight-line. generalizing the results of $3.1.," For example, the orbital angular momentum for a coplanar collision is $\overrightarrow{L}_{cop}(t) = L_{orb} \hat{z}$, implying We consider first the case of non-coplanar encounters in which the perturber moves along a straight-line, generalizing the results of 3.1."
 The coplanar trajectory is given by eq. (11)).," The coplanar trajectory is given by eq. \ref{pathsl}) ),"
 the phase angle of the stars along their orbits in the victim Is. as earlier. defined by eq. (12).," the phase angle of the stars along their orbits in the victim is, as earlier, defined by eq. \ref{phaset}) ),"
 and we employ the parameter à. as defined by eq. (14)).," and we employ the parameter $\alpha$, as defined by eq. \ref{alphapar}) )."
 Note. however. that now the sign of O does not determine if the encounter is prograde orretrograde. but merely fixes the direction of the spin angular momentum of the victim. either along the |+ axis (positive O) or c axis (negative O).," Note, however, that now the sign of $\Omega$ does not determine if the encounter is prograde orretrograde, but merely fixes the direction of the spin angular momentum of the victim, either along the $+z$ axis (positive $\Omega$ ) or $-z$ axis (negative $\Omega$ )."
 For non-coplanar collisions. the condition of whether the encounter is mainly prograde versus retrograde is set by ?=F(t).>S(ft)/(LS). where L>(f) and 5>(f) are the orbital angular momentum of the encounter and the spin angular momentum of the victim disk. respectively.," For non-coplanar collisions, the condition of whether the encounter is mainly prograde versus retrograde is set by $\beta = \overrightarrow{L}(t) \cdot \overrightarrow{S}(t)/
(L S)$, where $\overrightarrow{L}(t)$ and $\overrightarrow{S}(t)$ are the orbital angular momentum of the encounter and the spin angular momentum of the victim disk, respectively."
 The quantity ./ lies between |1 (purely prograde) and 1 (purely retrograde) and takes the value ./=0 for a polar orbit., The quantity $\beta$ lies between $+1$ (purely prograde) and $-1$ (purely retrograde) and takes the value $\beta = 0$ for a polar orbit.
 Starting from the expressions for the velocity perturbations in eq. (9)), Starting from the expressions for the velocity perturbations in eq. \ref{impulse}) )
 we find. after algebra: Here. the factors are the relevant components of the rotation matrix sl. and the upper signs in the = and + terms refer to the case with ©=>0 «;;while the lower signs are for the case with O)—0.," we find, after algebra: Here, the factors $a_{ij}$ are the relevant components of the rotation matrix $\tilde{A}$, and the upper signs in the $\mp$ and $\pm$ terms refer to the case with $\Omega > 0$ while the lower signs are for the case with $\Omega < 0$."
 It is straightforward to show that these expressions reduce to the appropriate ones for coplanar encounters given in $3.1 if the rotation angles are set to zero., It is straightforward to show that these expressions reduce to the appropriate ones for coplanar encounters given in 3.1 if the rotation angles are set to zero.
 As a simple illustration. consider a straight-line path where the original orbit is in the.»4 plane and is given by 0). and employ the Euler angle convention summarized above.," As a simple illustration, consider a straight-line path where the original orbit is inthe $x-y$ plane and is given by $\overrightarrow{R}_{cop}(t) = (b, V_{sl} \, t, 0)$ , and employ the Euler angle convention summarized above."
" Rotate this path by an angle +) around the y-axis. so /?,,,(7)that In this case."," Rotate this path by an angle $\eta$ around the $y$ -axis, so that In this case,"
temperature deviation values in the regions of shock waves are =S0% of those of the gas temperature.,temperature deviation values in the regions of shock waves are $\simeq$ of those of the gas temperature.
 The increase of the standard temperature deviation in the “are-like” regions compared with other regions shows the presence of temperature inhomogeneities along the line-of-sight in these regions., The increase of the standard temperature deviation in the “arc-like” regions compared with other regions shows the presence of temperature inhomogeneities along the line-of-sight in these regions.
"problems, it is important to find nearby examples of this kind of interaction where a detailed study can be carried out.","problems, it is important to find nearby examples of this kind of interaction where a detailed study can be carried out."
 NGC 1068 is an ideal object in this case., NGC 1068 is an ideal object in this case.
 It is one of the nearest and probably the most intensely studied Seyfert 2 galaxy., It is one of the nearest and probably the most intensely studied Seyfert 2 galaxy.
 Observations in all wavelength bands from radio to hard X-rays have formed a uniquely detailed picture of this source., Observations in all wavelength bands from radio to hard X-rays have formed a uniquely detailed picture of this source.
 NGC 1068 hosts a prominent narrow-line region (NLR) that is approximately co-spatial with a linear radio source with two lobes (Wilson Ulvestad 1983)., NGC 1068 hosts a prominent narrow-line region (NLR) that is approximately co-spatial with a linear radio source with two lobes (Wilson Ulvestad 1983).
" Star formation activity coexistent with the active galactic nucleus (AGN) was detected on both larger (e.g., Telesco Decher 1988) and smaller scales (Macchetto et al."," Star formation activity coexistent with the active galactic nucleus (AGN) was detected on both larger (e.g., Telesco Decher 1988) and smaller scales (Macchetto et al."
 1994; Thatte et al., 1994; Thatte et al.
 1997)., 1997).
" However, the link between all the processes is still under debate."," However, the link between all the processes is still under debate."
" The Near Infrared Region (NIR) is particularly interesting to help unveiling this link because it is accessible to ground-based telescopes and, at the same time, able to probe highly obscured sources."," The Near Infrared Region (NIR) is particularly interesting to help unveiling this link because it is accessible to ground-based telescopes and, at the same time, able to probe highly obscured sources."
" However, tracking the star formation in the NIR is not simple (Origlia Oliva 2000) although recent studies exploring this region have already shown its strong potential at detecting intermediate-age stellar population not easily tracked in the optical without ambiguity (e.g. Riffel et al."," However, tracking the star formation in the NIR is not simple (Origlia Oliva 2000) although recent studies exploring this region have already shown its strong potential at detecting intermediate-age stellar population not easily tracked in the optical without ambiguity (e.g. Riffel et al."
" 2009, Davies et al."," 2009, Davies et al."
 2007)., 2007).
" At near-IR wavelengths stellar photospheres usually remain the dominant sources of light, and galaxy spectra are shaped by red supergiants (RSG) shortly after starbursts, and then by giants of the first and of the asymptotic giant branches (AGB)."," At near-IR wavelengths stellar photospheres usually remain the dominant sources of light, and galaxy spectra are shaped by red supergiants (RSG) shortly after starbursts, and then by giants of the first and of the asymptotic giant branches (AGB)."
 AGB stars are rare members of stellar populations., AGB stars are rare members of stellar populations.
" However, they are among the most luminous cool stars and can therefore be detected sometimes even individually in galaxies."," However, they are among the most luminous cool stars and can therefore be detected sometimes even individually in galaxies."
" The TP-AGB stars leave a unique fingerprint on the integrated spectra, like the 1.1 um CN band (Maraston 2005, Riffel et al."," The TP-AGB stars leave a unique fingerprint on the integrated spectra, like the 1.1 $\micron$ CN band (Maraston 2005, Riffel et al."
" 2007, 2009)."," 2007, 2009)."
" Hence when detected, they can help to determine the age of the stellar population through the integrated light."," Hence when detected, they can help to determine the age of the stellar population through the integrated light."
 The contribution of this stellar phase in stellar population models has been recently included in both the energetics and the spectral features (Maraston 2005)., The contribution of this stellar phase in stellar population models has been recently included in both the energetics and the spectral features (Maraston 2005).
" In particular these models employ empirical spectra of oxygen-rich and carbon stars (Langoon Wood 2000), which are able to foresee characteristic NIR absorption features."," In particular these models employ empirical spectra of oxygen-rich and carbon stars (Lançoon Wood 2000), which are able to foresee characteristic NIR absorption features."
" With this in mind, we present here for the first time in the literature a detailed fitting of the continuum emission components in the 0.8—2.4 um interval of NGC 1068 across the central 15"" (~ 1100 pc) of this source."," With this in mind, we present here for the first time in the literature a detailed fitting of the continuum emission components in the $-$ 2.4 $\micron$ interval of NGC 1068 across the central 15"" $\sim$ 1100 pc) of this source."
 The main purpose is to determine the fraction with which the different components contributes to the observed integrated light and how they are related to each other., The main purpose is to determine the fraction with which the different components contributes to the observed integrated light and how they are related to each other.
 The paper is structured as follows: in 82 we describe the observations., The paper is structured as follows: in 2 we describe the observations.
 In 83 we describe the fitting method and in 84 the results are presented and discussed., In 3 we describe the fitting method and in 4 the results are presented and discussed.
 Final remarks are given in 86., Final remarks are given in 6.
" The spectra were obtained at the NASA 3m Infrared Telescope Facility (IRTF) in October 30, 2007."," The spectra were obtained at the NASA 3m Infrared Telescope Facility (IRTF) in October 30, 2007."
" The SpeX spectrograph (Rayner et al.,"," The SpeX spectrograph (Rayner et al.,"
" 2003) was used in the short cross-dispersed mode (SXD, 0.8- 2.4 jm)."," 2003) was used in the short cross-dispersed mode (SXD, 0.8- 2.4 $\mu$ m)."
" The employed detector consisted of a 1024x1024 ALADDIN InSb array with a spatial scale of 0.15""/ pixel"," The employed detector consisted of a 1024x1024 ALADDIN 3 InSb array with a spatial scale of 0.15""/ pixel."
" A 0.8""x3 15"" slit oriented in the north-south direction was used, providing a spectral resolution of 360 km/s. For more details about the instrumental configuration see Martins et al. ("," A 0.8""x 15"" slit oriented in the north-south direction was used, providing a spectral resolution of 360 km/s. For more details about the instrumental configuration see Martins et al. ("
"2010, hereafter Paper I).","2010, hereafter Paper I)."
 Figure 1 shows the position of the slit superimposed on the galaxy contours obtained from Galliano et al. (, Figure 1 shows the position of the slit superimposed on the galaxy contours obtained from Galliano et al. (
2003).,2003).
 The gray contours show the 6 cm emission (Gallimore et al., The gray contours show the 6 cm emission (Gallimore et al.
 1996) and the red dotted contours show the 20 um image (Alloin et al., 1996) and the red dotted contours show the 20 $\micron$ image (Alloin et al.
 2000)., 2000).
" For NGC1068, 17 extractions were made along the spatial direction: one centred at the peak of light distribution (nuc) and eight more at each side of it (apertures 01 to 08 in the south direction and 09 to 16 in the north direction)."," For NGC1068, 17 extractions were made along the spatial direction: one centred at the peak of light distribution (nuc) and eight more at each side of it (apertures 01 to 08 in the south direction and 09 to 16 in the north direction)."
 Figures 5 to 7 of Paper I show the individual extractions along the spatial direction as well as the most important emission and absoprtion features relevant to this work., Figures 5 to 7 of Paper I show the individual extractions along the spatial direction as well as the most important emission and absoprtion features relevant to this work.
" Our main goal is to study the NIR spectral energy distribution components of NGC 1068 and their variations across the central 15""."," Our main goal is to study the NIR spectral energy distribution components of NGC 1068 and their variations across the central 15""."
 For this purpose we fit the underlying continuum between 0.8 and 2.4 um applying the same method described in Riffel et al. (, For this purpose we fit the underlying continuum between 0.8 and 2.4 $\micron$ applying the same method described in Riffel et al. (
2009).,2009).
 The spectral synthesis is done using the code STARLIGHT (Cid Fernandes et al., The spectral synthesis is done using the code STARLIGHT (Cid Fernandes et al.
" 2004, 2005a, Mateus et al."," 2004, 2005a, Mateus et al."
" 2006, Asari et al."," 2006, Asari et al."
" 2007, Cid Fernandes et al."," 2007, Cid Fernandes et al."
 2009)., 2009).
 STARLIGHT mixes computational techniques originally developed for semi empirical population synthesis with ingredients from evolutionary synthesis models., STARLIGHT mixes computational techniques originally developed for semi empirical population synthesis with ingredients from evolutionary synthesis models.
" Basically the code fits an observed spectrum Ολ with a combination, in different proportions, of a number of simple stellar"," Basically the code fits an observed spectrum $_\lambda$ with a combination, in different proportions, of a number of simple stellar"
Hux density. and bandpass calibration and. the secondary calibrator was used to solve for antenna gains. phases and polarisation leakage terms.,"flux density and bandpass calibration and the secondary calibrator was used to solve for antenna gains, phases and polarisation leakage terms."
 After calibration. the data consist of 13 independent. frequency channels cach s MIIz wide for each of the 16 phase bins.," After calibration, the data consist of 13 independent frequency channels each 8 MHz wide for each of the 16 phase bins."
 Subsequent analysis of the data was carried out as described in Connors et al. (2002)., Subsequent analysis of the data was carried out as described in Connors et al. \nocite{cjmm02}.
. ligure 1 shows the complete timing resicluals from63., Figure \ref{timing} shows the complete timing residuals from.
. Phere are more than 1200 independent timing points. with a data span from 1991 January to 2004 September including five periastron passages.," There are more than 1200 independent timing points, with a data span from 1991 January to 2004 September including five periastron passages."
 As described in earlier. papers. the DAL of the pulsar changes near periastron and this extra DAL needs to be accounted for in the timing solution.," As described in earlier papers, the DM of the pulsar changes near periastron and this extra DM needs to be accounted for in the timing solution."
 For this periastron. observations were mace at frequencies between 0.64 and 8.4 CGllz and the DAL was calculated by measuring the time olfset. between the TOAS at thedilferent frequencies (see eg. Wex et al. 1998).," For this periastron, observations were made at frequencies between 0.64 and 8.4 GHz and the DM was calculated by measuring the time offset between the TOAs at the different frequencies (see e.g. Wex et al. \nocite{wjm+98}."
. In Wang et al. (, In Wang et al. (
2004) we determined that the best fit solution involved. adding jumps in the value of esin; at periastron and that a small eliteh occured at ND 50691.,2004) we determined that the best fit solution involved adding jumps in the value of $a\sin i$ at periastron and that a small glitch occured at MJD 50691.
 We have now extended that model to cover the 2004 periastron passage. obtaining successive jumps in @sin? of 60.7. 26.3. 2.85. 4.2 and τὸ ms.," We have now extended that model to cover the 2004 periastron passage, obtaining successive jumps in $a\sin i$ of 60.7, $-$ 26.3, 2.8, 4.2 and $-$ 7.8 ms."
 The fitted. jumps for the first 4 periastrons are within a few percent of those obtained. by Wangin] et al. (, The fitted jumps for the first 4 periastrons are within a few percent of those obtained by Wang et al. (
2004).,2004).
 Column 3 of Table 1. lists the DM variations ancl these are displayed in Figure 2.., Column 3 of Table \ref{dmrm} lists the DM variations and these are displayed in Figure \ref{ddm}.
 Phe typical error in the DAL values are 0.2 pe., The typical error in the DM values are 0.2 $^{-3}$ pc.
 Although the pulsar was undetected at 1.4. 3.1 and S.4CGllz on 18.8. the last detection before periastron occurred on 17.8 when the DM change was 19.5 em.“pe.," Although the pulsar was undetected at 1.4, 3.1 and 8.4 GHz on $-$ 18.8, the last detection before periastron occurred on $-$ 17.8 when the DM change was 19.5 $^{-3}$ pc."
 Subsequent observations on 15.8 failed. to detect. the pulsar., Subsequent observations on $-$ 15.8 failed to detect the pulsar.
 The eclipse lastecl until |16.1 although on this date the pulsar was not detected at Εαν., The eclipse lasted until +16.1 although on this date the pulsar was not detected at 1.4 GHz.
 Two davs later. there is a marginal detection of the pulsar at 3.1 Cillz but not at higher or lower frequencies.," Two days later, there is a marginal detection of the pulsar at 3.1 GHz but not at higher or lower frequencies."
 After the exit from the eclipse the DAL change was only 3.2 and decaved: over an interval of —20 davs., After the exit from the eclipse the DM change was only 3.2 and decayed over an interval of $\sim$ 20 days.
 This is broadly in line with changes seen during previous periastron passages (see Figure 2 in Wang et al., This is broadly in line with changes seen during previous periastron passages (see Figure 2 in Wang et al.
 2004)., 2004).
 Column 4 of Table. 1. shows the RAL as a function. of epoch., Column 4 of Table \ref{dmrm} shows the RM as a function of epoch.
 The tvpical error bars are of order 10 per cent., The typical error bars are of order 10 per cent.
 The RAL changes significantly both in magnitude and in sign between the observations but there is little evidence of a change in RAL within the curation of a single observation., The RM changes significantly both in magnitude and in sign between the observations but there is little evidence of a change in RM within the duration of a single observation.
 On Feb 2 34) we were unable to measure an RAL even at S4 Cllz. on 30 the polarisation quality. of the data is poor and on 2s the pulsar is very weak and no RAL information could be extracted.," On Feb 2 $-$ 34) we were unable to measure an RM even at 8.4 GHz, on $-$ 30 the polarisation quality of the data is poor and on $-$ 28 the pulsar is very weak and no RM information could be extracted."
 Following the very large RAL value on 26. the pulsar appeared. completely depolarised at all frequencies.," Following the very large RM value on $-$ 26, the pulsar appeared completely depolarised at all frequencies."
 After the pulsar re-emerged from the eclipse. no RAs could. initially be measured.," After the pulsar re-emerged from the eclipse, no RMs could initially be measured."
 A high. positive RAL was measured on |24. subsequent values were negative thereafter.," A high, positive RM was measured on +24, subsequent values were negative thereafter."
 Lt is noticeable that the RAL varies by more than a factor of 10 in the post-periastron observrations and vet the DAT varies only by a factor of 2., It is noticeable that the RM varies by more than a factor of 10 in the post-periastron observrations and yet the DM varies only by a factor of 2.
 There are three potential explanations for the depolarisation of the signal., There are three potential explanations for the depolarisation of the signal.
 Lt is possible that the RAL is so high that even across a single frequency channel the position angle varies significantly. thus depolarising the signal.," It is possible that the RM is so high that even across a single frequency channel the position angle varies significantly, thus depolarising the signal."
 Vhis would imply an RAL greater than 10° rad > for the 8.4 GLlz observations., This would imply an RM greater than $10^5$ rad $^{-2}$ for the 8.4 GHz observations.
 Secondly. the RAL could be highly. variable on," Secondly, the RM could be highly variable on"
"Concerning the background galaxy population, object B3 is probably the most striking case as the object is well resolved in our images, in spite of its relatively large redshift, and therefore was included in our photometry (see Table Al and A2)).","Concerning the background galaxy population, object B3 is probably the most striking case as the object is well resolved in our images, in spite of its relatively large redshift, and therefore was included in our photometry (see Table \ref{a2}
 and \ref{a3}) )."
" Its Sérrsic index (n= 0.22) corresponds to a profile steeper than a de Vaucouleurs law, while the spectrum revealed an active elliptical with strong H6 and [Οήροοτ line emission."," Its Sérrsic index $n=0.22$ ) corresponds to a profile steeper than a de Vaucouleurs law, while the spectrum revealed an active elliptical with strong $\beta$ and $_{5007}$ line emission."
" In addition to the redshift information, the good spectroscopic material allowed us to tackle in finer detail the study of spectral properties of member and background galaxies in our sample."," In addition to the redshift information, the good spectroscopic material allowed us to tackle in finer detail the study of spectral properties of member and background galaxies in our sample."
" In particular, spectral resolution of both theEso and observations closely matched the canonical prescription 8 FFWHM)to consistently reproduce the Lick system (Wortheyetal. 1994),, thus allowing a wide set of narrow-band indices to be easily computed from the original data."," In particular, spectral resolution of both the and observations closely matched the canonical prescription $\sim 8$ FWHM)to consistently reproduce the Lick system \citep{worthey94}, , thus allowing a wide set of narrow-band indices to be easily computed from the original data."
" As for the observations, our calculations have been carried out after slightly degrading the spectra to the Lick resolution by convolution with a Gaussian kernel."," As for the observations, our calculations have been carried out after slightly degrading the spectra to the Lick resolution by convolution with a Gaussian kernel."
 'This transformation cannot be carried out with equivalent accuracy for the data., This transformation cannot be carried out with equivalent accuracy for the data.
" Given their slightly poorer resolution (10 FWHM), in fact, these spectra tend to display shallower spectral features, and therefore lower index strengths."," Given their slightly poorer resolution (10 FWHM), in fact, these spectra tend to display shallower spectral features, and therefore lower index strengths."
 The effect can be assessed by means of Fig., The effect can be assessed by means of Fig.
 14 for the three galaxies in common between and spectra.," \ref{f14}
 for the three galaxies in common between and spectra."
 The least-squares fit to the data indicates that the corresponding indices (in ppseudo-equivalent width) relate with p=0.60 and o=0.22., The least-squares fit to the data indicates that the corresponding indices (in pseudo-equivalent width) relate with $\rho = 0.60$ and $\sigma = 0.22$.
" Although the lack of Lick primary calibrators in our sample prevented us to fully standardize our index scale, nevertheless a direct comparison can be done of our output for NGC 5044 itself with two reference sources in the literature, namely the work of Trageretal.(1998) and Annibalietal.(2006)."," Although the lack of Lick primary calibrators in our sample prevented us to fully standardize our index scale, nevertheless a direct comparison can be done of our output for NGC 5044 itself with two reference sources in the literature, namely the work of \citet{trager98} and \citet{annibali06}."
". As shown in Fig. 15,,"," As shown in Fig. \ref{f15}, ,"
" in both cases the index correlation is quite good ([p,o]=[0.96,0.13] with Trager’s data in the log-log index domain and [p,a]= with the Annibali’s ones) assuring that the Lick standard system is correctly reproduced, on average, by our observations."," in both cases the index correlation is quite good $[\rho, \sigma] = [0.96, 0.13]$ with Trager's data in the $\log$ $\log$ index domain and $[\rho, \sigma] = [0.91, 0.15]$ with the Annibali's ones) assuring that the Lick standard system is correctly reproduced, on average, by our observations."
 Table 8 gives a general summary of our results., Table \ref{t8} gives a general summary of our results.
 An instructive view can be gained for the NGC 5044 group (and its surrounding background galaxies) in the Lick-index domain., An instructive view can be gained for the NGC 5044 group (and its surrounding background galaxies) in the Lick-index domain.
" The Magnesium Mego index, together with the Balmer Hf strength are certainly among the most popular reference tracers for this kind of analysis for their better dependence on metallicity (Mg2) and age (Ηβ), as extensively studied in the literature (see,e.g.Gorgas,Efs-discussion)."," The Magnesium $_2$ index, together with the Balmer $\beta$ strength are certainly among the most popular reference tracers for this kind of analysis for their better dependence on metallicity $_2$ ) and age $\beta$ ), as extensively studied in the literature \citep[see, e.g.][for a discussion]{gorgas90, buzzoni95, thomas03, tantalo04}."
" The distribution of our sample is displayed in Fig. 16,,"," The distribution of our sample is displayed in Fig. \ref{f16},"
" comparing with the theoretical expectations for simple stellar population models (Buzzoni,Gariboldi, along an age range between 5 and 15 Gyr, and with metallicity spanning the interval —1.3<[Fe/H]+0.25."," comparing with the theoretical expectations for simple stellar population models \citep{buzzoni92,buzzoni94} along an age range between 5 and 15 Gyr, and with metallicity spanning the interval $-1.3 \le [Fe/H] \le +0.25$."
" The sample of 50 old M31 and Galactic globular clusters, and 370 standard ellipticals from the work of Trageret is also superposed to the plot, together with a supplementary sample of 108 ellipticals with mild emission lines from Rampazzoetal.(2005) and Annibalietal.(2006) for a differential comparison with the distribution of high-mass systems likely experiencing some moderate star-formation activity."," The sample of 50 old M31 and Galactic globular clusters, and 370 standard ellipticals from the work of \citet{trager98} is also superposed to the plot, together with a supplementary sample of 108 ellipticals with mild emission lines from \citet{rampazzo05} and \citet{annibali06}
 for a differential comparison with the distribution of high-mass systems likely experiencing some moderate star-formation activity."
" As a guideline for the distribution of young (metal-poor) stellar systems, we also added to the plot the sample of 14 globular clusters belonging to the Magellanic Cloud systems, according to deFreitasPacheco,Barbuy,&Idiart (1998)."," As a guideline for the distribution of young (metal-poor) stellar systems, we also added to the plot the sample of 14 globular clusters belonging to the Magellanic Cloud systems, according to \citet{freitas98}."
". As expected, the Mgo-H@ diagnostic is very poor for late-type galaxies, for which the Hf index is strongly affected by gas emission; the location of the Im galaxy N49 in the plotis illustrative in this sense, once considering its strong spectral emission, as in Fig. 13.."," As expected, the $_2$ $\beta$ diagnostic is very poor for late-type galaxies, for which the $\beta$ index is strongly affected by gas emission; the location of the Im galaxy N49 in the plotis illustrative in this sense, once considering its strong spectral emission, as in Fig. \ref{f13}. ."
" As far as theearly- galaxy component is concerned, however, one has to remark a pretty clean distribution of our dE--dS0 sample,"," As far as theearly-type galaxy component is concerned, however, one has to remark a pretty clean distribution of our dE+dS0 sample,"
We have shown that the velocitv-space substructure revealed by citepDehn98. and the citepNordOd.LLNAXO is also present among the nearby pe) stars in the aand SDSS//Segue2 samples.,"We have shown that the velocity-space substructure revealed by \\citep{Dehn98} and the \\citep{Nord04,HNA9} is also present among the nearby $d<200\;$ pc) stars in the and /Segue2 samples."
 We find that. the. velocity space substructure closely resembles that. found. for the independent sample of sstars even though the present sample is barely half the size and velocity uncertainties are several times larger: most of he significant star “streams” of the ihave counterparts in the new sample. although the precise velocities of the streams do not match perfectby.," We find that the velocity space substructure closely resembles that found for the independent sample of stars even though the present sample is barely half the size and velocity uncertainties are several times larger; most of the significant star “streams” of the have counterparts in the new sample, although the precise velocities of the streams do not match perfectly."
 Analysis of the action variables constructed. from our vest estimates of the full phase space coordinates of cach star in the sample reveals an excess of stars along a resonance scattering trajectory in action-space at a similar frequency o that found in Paper E (ονους2010). for the ssample., Analysis of the action variables constructed from our best estimates of the full phase space coordinates of each star in the sample reveals an excess of stars along a resonance scattering trajectory in action-space at a similar frequency to that found in Paper I \citep{Sell10} for the sample.
 While still statistically highly significant. the eature in Fie.," While still statistically highly significant, the feature in Fig."
 6 stands out less clearly than in Paper | »ecause the sample is smaller ancl uncertainties are larecr., 6 stands out less clearly than in Paper I because the sample is smaller and uncertainties are larger.
 The evidence for resonant trapping in Fig S. ids also weaker han that found for the ssanmiple. but again reveals peaks at the same phases.," The evidence for resonant trapping in Fig \ref{restest} is also weaker than that found for the sample, but again reveals peaks at the same phases."
 We herefore consider this sample of stars to support the evidence for a Lindblad resonance found in Paper L although rere again the data do not constrain the multiplicity of the xdtern.," We therefore consider this sample of stars to support the evidence for a Lindblad resonance found in Paper I, although here again the data do not constrain the multiplicity of the pattern."
 While it is unfortunate that these data do not rule out rapping at an aas the cause of the EEvades stream. it is worth noting that Dehnen(2000) examined the elfect on the local phase space clue to the oof the bar and did not find any Livacles stream-like features.," While it is unfortunate that these data do not rule out trapping at an as the cause of the Hyades stream, it is worth noting that \citet{Dehn00} examined the effect on the local phase space due to the of the bar and did not find any Hyades stream-like features."
 Since the Llvades stream stars form the tongue in space that stands out Fig., Since the Hyades stream stars form the tongue in action-space that stands out Fig.
 3 of Paper E and our Fig. 6..," 3 of Paper I and our Fig. \ref{actplt},"
 it seems to us Far more likely that the stream was created by an ILR., it seems to us far more likely that the stream was created by an .
. Selbwood(1994.2000). reported that features that extend: upward: towards smaller J.(=L.) for increasing Je (or fang) ave created by LLRs in his simulations.," \citet{Sell94,Sell00} reported that features that extend upward towards smaller $J_\phi \;(\equiv L_z)$ for increasing $J_R$ (or $E_{\rm rand})$ are created by s in his simulations."
 Since scattering at an ninioves stars in action space in a direction that is roughly perpendicular to the resonance locus. as discussed. in 833 above. stars do not move far before leaving the resonance.," Since scattering at an moves stars in action space in a direction that is roughly perpendicular to the resonance locus, as discussed in 3 above, stars do not move far before leaving the resonance."
 Only in the case of an dedo stars stay close to resonance as they get pushed by the disturbance. thereby. allowing stars to be moved from the dense Low-5 region up to higher Jj where the overdensity stands out.," Only in the case of an do stars stay close to resonance as they get pushed by the disturbance, thereby allowing stars to be moved from the dense $J_R$ region up to higher $J_R$ where the overdensity stands out."
 Note that if the cause is a spiral (other tvpes of disturbance could be responsible). the oof a bisvmmoetric spiral seems unlikely. since it would place corotation unreasonably far out in the disk. but an m=4. or perhaps even an m= 3. spiral would seem more likely. as noted in Paper L This speculation could be tested by data from Gaia (DPerrvmanefa£2001).. which will obtain phase space information over a much more extensive region of the Galaxy.," Note that if the cause is a spiral (other types of disturbance could be responsible), the of a bisymmetric spiral seems unlikely, since it would place corotation unreasonably far out in the disk, but an $m=4$, or perhaps even an $m=3$ , spiral would seem more likely, as noted in Paper I. This speculation could be tested by data from Gaia \citep{Perr01}, which will obtain phase space information over a much more extensive region of the Galaxy."
 Correspondence with Paul McMillan has been most helpful., Correspondence with Paul McMillan has been most helpful.
 Wealso thank Ralph Schónnrich and an anonvmous referee for constructivecomments on an earlier draft of this paper., Wealso thank Ralph Schönnrich and an anonymous referee for constructivecomments on an earlier draft of this paper.
be the NW lobe of the SE-NW outflow.,be the NW lobe of the SE-NW outflow.
 But it is also possible that (his feature is due to another low-mass (proto)star whose mass is below our detection limit., But it is also possible that this feature is due to another low-mass (proto)star whose mass is below our detection limit.
 The vo outflows are both well collimated with overall collimation [actors ~3 for the NE outflow and ~+ lor the SE-NW outflow., The two outflows are both well collimated with overall collimation factors $\sim3$ for the NE outflow and $\sim4$ for the SE-NW outflow.
 The estimated collimation factors should be the lower limits considering ihe unknown inclination angles ancl the spatial resolution limit., The estimated collimation factors should be the lower limits considering the unknown inclination angles and the spatial resolution limit.
 In Fie., In Fig.
 3bb. the redshifted SiO enmission is shown in (wo velocity ranges. ie. the high-velocity component (IC) with velocities Ae=3—21 |. and the verv-high-velocitv component (VIIC) with velocities Av=22-60 |.," \ref{sioint1}b b, the redshifted SiO emission is shown in two velocity ranges, i.e. the high-velocity component (HC) with velocities ${\Delta}v = 3 - 21$ $^{-1}$, and the very-high-velocity component (VHC) with velocities ${\Delta}v = 22 - 60$ $^{-1}$."
 The definition of the velocity ranges here is based on the morphological changes in the SiO emission in (he velocity channel maps and (he characteristics in the posilion-velocily and mass-velocitv. diagrams (hat will be discussed below., The definition of the velocity ranges here is based on the morphological changes in the SiO emission in the velocity channel maps and the characteristics in the position-velocity and mass-velocity diagrams that will be discussed below.
 The redshilted SE outflow in the VIIC is shilted toward north aud its remote peak is closer to the criving source than that in the HC., The redshifted SE outflow in the VHC is shifted toward north and its remote peak is closer to the driving source than that in the HC.
 We will discuss this jet-like outflow in detail in Sect. 4.3.., We will discuss this jet-like outflow in detail in Sect. \ref{kin}.
 Thanks to the continuous velocity structures in (his dominant outflow. we derive the dvnamical time following where Zpj. is the length of the jet-like SE outflow and Όρων is Che maxiniunm velocity of the SE outflow.," Thanks to the continuous velocity structures in this dominant outflow, we derive the dynamical time following where $L_{flow}$ is the length of the jet-like SE outflow and ${\Delta}v_{max}$ is the maximum velocity of the SE outflow."
" Assuming the optically thin thermal SiO (2-1) emission in local thermodynamic equilibrium (LTE). weestimate (he gas mass in the outflow according to where jig is (he permanent dipole moment. AQ is the FWIIM of the svnthesized beam. [lg=1.36 is the mean atomic weight of the gas. my, is the mass of a hydrogen molecule. d is the distance of the source. S, is the [αν density. and other svimbols have common meanings."," Assuming the optically thin thermal SiO (2-1) emission in local thermodynamic equilibrium (LTE), weestimate the gas mass in the outflow according to where $\mu_d$ is the permanent dipole moment, $\Delta\Omega$ is the FWHM of the synthesized beam, $\mu_g=1.36$ is the mean atomic weight of the gas, $m_{H_2}$ is the mass of a hydrogen molecule, $d$ is the distance of the source, $S_{\nu}$ is the flux density, and other symbols have common meanings."
" The mean excitation temperature J; is estimated to be 24 Ix from the NIL,(1.1). (2.2) emission."," The mean excitation temperature $T_{ex}$ is estimated to be 24 K from the $_3$ (1,1), (2,2) emission."
 It should be noted that [5]SiOHE has large uncertainty since the SiO abundance can be greatly enhanced by shocks as a result of grain destruction leading to Si injection into the gas phase (Seab&Shull1983)., It should be noted that $[\frac{H_{2}}{SiO}]$ has large uncertainty since the SiO abundance can be greatly enhanced by shocks as a result of grain destruction leading to Si injection into the gas phase \citep{Seab83}.
. In contrast to the typical SiO abundance 10.P to 10.ΤΕ in dark clouds (Ziurvsοἱal. 1989)... Mikamietal.(1992) and. Zhangοἱal.(1995) detect the SiO enhancement of four to five orders of magnitude toward the L1157 outflow.," In contrast to the typical SiO abundance $10^{-12}$ to $10^{-11}$ in dark clouds \citep{Ziurys89}, , \citet{Mikami92} and \citet{Zhang95} detect the SiO enhancement of four to five orders of magnitude toward the L1157 outflow."
 Iliranoetal.(2001). estimate the SiO abundance to be 10.1 to LO* toward the multiple outflows in IRAS 16293-2422., \citet{Hirano01} estimate the SiO abundance to be $10^{-10}$ to $10^{-8}$ toward the multiple outflows in IRAS 16293-2422.
 We adopt an SiO abundance of 10.7. which corresponds to an enhancement of three to four orders ofmagnitude with respect to that in dark clouds.," We adopt an SiO abundance of $10^{-8}$ , which corresponds to an enhancement of three to four orders ofmagnitude with respect to that in dark clouds."
 Then, Then
"Compact. Ulat-spectrum. raclio-loucd extragalactic sources. sometimes also known as ""blazars! (Angel Stockman 1980. Antonucci 1993). exhibit many common characteristics.","Compact, flat-spectrum, radio-loud extragalactic sources, sometimes also known as `blazars' (Angel Stockman 1980, Antonucci 1993), exhibit many common characteristics."
 1n particular. they show core-jet morphology. in VLBI images with a succession of synchrotron self-absorbe knot-like structures combining to give the overall Uatness of the radio spectrum. and frequently. exhibit. apparen superluminal motion along with larec-amplituce variability at all wavelengths. from radio to ganima-ravs.," In particular, they show core-jet morphology in VLBI images with a succession of synchrotron self-absorbed knot-like structures combining to give the overall flatness of the radio spectrum, and frequently exhibit apparent superluminal motion along with large-amplitude variability at all wavelengths from radio to gamma-rays."
 Signilican and variable linear polarisation is also seen at al wavelengths where measurements have been attempted., Significant and variable linear polarisation is also seen at all wavelengths where measurements have been attempted.
 A millimetre/submillimetre. wavelengths. the emission arises hrough the synchrotron. mechanism in the core regions of the jets. Le. close to their origin (see e.g. Gear. LOSS). which are completely unresolved on even. the highest-requencey VLBI maps.," At millimetre/submillimetre wavelengths the emission arises through the synchrotron mechanism in the core regions of the jets, i.e. close to their origin (see e.g. Gear 1988), which are completely unresolved on even the highest-frequency VLBI maps."
 Photometric monitoring in this band las greativ improved our understanding of the physical oocesses in the sub-parsec scale. jets and has led to he development of the canonical paradigm (Marscher Gear 1985 and Hughes. Aller Aller 1985. 1989a. 1989h).," Photometric monitoring in this band has greatly improved our understanding of the physical processes in the sub-parsec scale jets and has led to the development of the canonical paradigm (Marscher Gear 1985 and Hughes, Aller Aller 1985, 1989a, 1989b)."
 Xn essential ingredient of jet models that has so [ar been missing is the geometry of the magnetic field on these verv small scales and how it may vary on dillerent physical scales., An essential ingredient of jet models that has so far been missing is the geometry of the magnetic field on these very small scales and how it may vary on different physical scales.
 Phe niullimetre/submillimetre emission. is expected. to be linearly polarised if the magnetic field. is ordered. and. with very rare exception (e.g. Robson 1983). it is always optically thin.," The millimetre/submillimetre emission is expected to be linearly polarised if the magnetic field is ordered and, with very rare exception (e.g. Robson 1983), it is always optically thin."
 This means that internal svnchrotron self-asorption and external Faraday rotation of he polarisation vector can be ignored., This means that internal synchrotron self-asorption and external Faraday rotation of the polarisation vector can be ignored.
 Therefore. we can reliably assume that the magnetic field. direction must. lie »pendiceular to the observed: polarisation position angle (sce c.g. Pacholezvk 1970).," Therefore, we can reliably assume that the magnetic field direction must lie perpendicular to the observed polarisation position angle (see e.g. Pacholczyk 1970)."
 The advent of polarisation-sensitive VLBI imaging ws been a powerful tool in investigating magnetic field xaviour (e.g. Cawthorne 1993. Gabuzda 1994).," The advent of polarisation-sensitive VLBI imaging has been a powerful tool in investigating magnetic field behaviour (e.g. Cawthorne 1993, Gabuzda 1994)."
 Llowever. no information has been available on the degree of order and the orientation. of the magnetic field: close o the point of creation of the jet.," However, no information has been available on the degree of order and the orientation of the magnetic field close to the point of creation of the jet."
 In the early 19908. we ean a 1.1 and 0.8 mnm polarisation survey of a significant sample of ILlat-specteum radio sources. most of which have subsequently been measured over several epochs at 1.1 nun.," In the early 1990s we began a 1.1 and 0.8 mm polarisation survey of a significant sample of flat-spectrum radio sources, most of which have subsequently been measured over several epochs at 1.1 mm."
As is usual with IPs (Warner 2004) we found no evidence for dwarf nova oscillations in the Ps of V397 Pup.,As is usual with IPs (Warner 2004) we found no evidence for dwarf nova oscillations in the FTs of V397 Pup.
 The drop in luminosity from 2008 to 2009 revealed. an LP in the orbital period gap (Warner 1995). with a rotation period of 8.7 min.," The drop in luminosity from 2008 to 2009 revealed an IP in the orbital period gap (Warner 1995), with a rotation period of 8.7 min."
 The reduction in amplitudes. of the spin modulations over the vear is probably the result of diminishing AZ as the primary cools and lessens its irracliation of the secondary., The reduction in amplitudes of the spin modulations over the year is probably the result of diminishing $\dot{M}$ as the primary cools and lessens its irradiation of the secondary.
 lt is not possible. with the Llickering ancl variations from orbit to orbit. to give precise values for eclipse ingress and egress timings. but we can show the effect in the light curve of the various components.," It is not possible, with the flickering and variations from orbit to orbit, to give precise values for eclipse ingress and egress timings, but we can show the effect in the light curve of the various components."
 First. a simple calculation shows that the measured widths of the eclipses imply an unusually large disc radius.," First, a simple calculation shows that the measured widths of the eclipses imply an unusually large disc radius."
 Prom the expected. high. mass or à very fast nova. and the mass ane radii relationships or CV secondaries (Warner 1995). we adopt. AZ(1) = 1.3 δις AM(2) = 022 M.. R(2) = 19«107 em.," From the expected high mass for a very fast nova, and the mass and radii relationships for CV secondaries (Warner 1995), we adopt $M(1)$ = 1.3 $_{\odot}$ , $M(2)$ = 0.22 $_{\odot}$, $R(2)$ = $1.9 \times 10^{10}$ cm."
" These Lead ο à separallon @=7.8210"" em. a radius ROL) of the toche lobe of the primary of 4.2«107 em. and. expected radius of a high Al disc of Ry=O.7TR(L)22.910! em."," These lead to a separation $a = 7.82 \times 10^{10}$ cm, a radius $R(L)$ of the Roche lobe of the primary of $4.2 \times 10^{10}$ cm, and expected radius of a high $\dot{M}$ disc of $R_d = 0.7 R(L) = 2.9 \times 10^{10}$ cm."
 The first ancl last contact phases co of eclipses. relative to yhase 0 assuming an inclination near 90 is found [rom sino=er where Ads selected from. above.," The first and last contact phases $\pm \phi$ of eclipses, relative to phase 0, assuming an inclination near $^{\circ}$, is found from $\sin \phi = \frac{[R(2) + R]}{a}$ , where $R$ is selected from above."
 For the usual 4?=Ry we find ó = 0.10. but for R=RGLE) we have Ó = 0.14. which is close to the observed ὁ~0.15.," For the usual $R = R_d$ we find $\phi$ = 0.10, but for $R = R(L)$ we have $\phi$ = 0.14, which is close to the observed $\phi \sim 0.15$."
 ‘Phe disc in V597 Pup fills the primary’s Roche lobe to its maximal possible extent., The disc in V597 Pup fills the primary's Roche lobe to its maximal possible extent.
 The radius of the disc is considerably larger than that of the secondary star. which results in the [lat bottomed secondary. eclipse.," The radius of the disc is considerably larger than that of the secondary star, which results in the flat bottomed secondary eclipse."
 The phases of first and last contacts in the secondary eclipse. as the secondary star (mace visible by irradiation rom the hot primary) is eclipsed. by. the disc. relative to ohase 0.5. are also zo. and the phases between second and hired contact are z(ó—0). where sin6=-. which are £0.09. in reasonable agreement with what is observed or the emergence of the secondary. but. immergence takes onger than predicted. possibly because at that. phase the illuminated gas stream is also being eclipsed by the disc.," The phases of first and last contacts in the secondary eclipse, as the secondary star (made visible by irradiation from the hot primary) is eclipsed by the disc, relative to phase 0.5, are also $\pm \phi$, and the phases between second and third contact are $\pm (\phi - \theta)$, where $\sin \theta = \frac{[R(L) - R(2)]}{a}$, which are $\pm$ 0.09, in reasonable agreement with what is observed for the emergence of the secondary, but immergence takes longer than predicted, possibly because at that phase the illuminated gas stream is also being eclipsed by the disc."
 The general agreement between observed and expected ime scales of the secondary. eclipses. adds weight to. our interpretation of this unusual light curve., The general agreement between observed and expected time scales of the secondary eclipses adds weight to our interpretation of this unusual light curve.
" With the short orbital period. and mass ratio MS/AM,= adopted here. we might have expected an elliptical disc and superhumps to be present (see. Chapter 3 of Warner 1995). but there is no evidence for them in the light curves and EPs."," With the short orbital period, and mass ratio $M_2/M_1 = 0.22$ adopted here, we might have expected an elliptical disc and superhumps to be present (see Chapter 3 of Warner 1995), but there is no evidence for them in the light curves and FTs."
 Phe reason may be that with an accretion disce of such large radius. greatly exceeding the 3:1 resonance radius that excites ellipticitv. the resonance is inelfectual: Osaki Alever (2003) have shown how in a disc of large racius the 2:1 Lindblad resonance can suppress the 3:1 resonance.," The reason may be that with an accretion disc of such large radius, greatly exceeding the 3:1 resonance radius that excites ellipticity, the resonance is ineffectual: Osaki Meyer (2003) have shown how in a disc of large radius the 2:1 Lindblad resonance can suppress the 3:1 resonance."
 Our estimate of ó~0.15 in fact puts the outer eclee of the accretion disc very close to the 2:1 resonance raclius., Our estimate of $\phi \sim 0.15$ in fact puts the outer edge of the accretion disc very close to the 2:1 resonance radius.
 Alukai (2008) lists over 30 bona fide LPs. among which there are none with relatively rapid. rotations that possess deep eclipses suitable to provide detailed information about the structure of an IP.," Mukai (2008) lists over 30 bona fide IPs, among which there are none with relatively rapid rotations that possess deep eclipses suitable to provide detailed information about the structure of an IP."
 Eclipses are seen in NY Ari but it is an X-dHtay source. hidden behind a cust cloud: DO Ier is far more favourable for observation but is not ideal as it has an inclination so high that much of the central region of the disc is hidden from view: DD Cen (Woudt Warner 2003) is too faint to study fully.," Eclipses are seen in XY Ari but it is an X-Ray source, hidden behind a dust cloud; DQ Her is far more favourable for observation but is not ideal as it has an inclination so high that much of the central region of the disc is hidden from view; DD Cen (Woudt Warner 2003) is too faint to study fully."
 Phus V597 Pup is the first relatively standard LP? found to have eclipses — which can be expected to grow a little deeper over the next few. wears as the residual emission from the ejecta decavs., Thus V597 Pup is the first relatively standard IP found to have eclipses – which can be expected to grow a little deeper over the next few years as the residual emission from the ejecta decays.
 We analyse our observations further in order to develop a model for the svsteor., We analyse our observations further in order to develop a model for the system.
 The standard interpretation of multiple sidebands in. LPs (Warner 1986) ascribes the (often. very strong) w9 component to reprocessing of w from the secondary. star or the disc thickening near the bright spot or the inner Lagrangian point (where in such a large disc the vertical eravitv is verylow)*.. all of which may vary in Cross section ab frequencies Q anc 20. and can thus generate aw 2O. w and w| signals. as well as w©.," The standard interpretation of multiple sidebands in IPs (Warner 1986) ascribes the (often very strong) $\omega - \Omega$ component to reprocessing of $\omega$ from the secondary star or the disc thickening near the bright spot or the inner Lagrangian point (where in such a large disc the vertical gravity is very, all of which may vary in cross section at frequencies $\Omega$ and $\Omega$, and can thus generate $\omega - 2\Omega$, $\omega$ and $\omega + \Omega$ signals, as well as $\omega - \Omega$."
 This gives only four components. a quadruüplet. whereas in W597 Pup we uniquely see a quintuplet.," This gives only four components, a quadruplet, whereas in V597 Pup we uniquely see a quintuplet."
 We suggest. that the clue tounderstanding this comes from the unusual presence of a secondary eclipse: the w© componentis therefore modulated. not. only at © (vith maximum. at superior conjunction and minimum at inferior conjunction of the, We suggest that the clue tounderstanding this comes from the unusual presence of a secondary eclipse: the $\omega - \Omega$ componentis therefore modulated not only at $\Omega$ (with maximum at superior conjunction and minimum at inferior conjunction of the
"find that most K+A galaxies in this sample exhibit significant excess above the predicted stellar component at A>5 jum from WISE data, suggesting that dust heated by some unknown source is present in these objects.","find that most K+A galaxies in this sample exhibit significant excess above the predicted stellar component at $\lambda>5$ $\mu$ m from WISE data, suggesting that dust heated by some unknown source is present in these objects."
" Buyleetal.(2006) pointed out that K+A galaxies contain significant amounts of gas and therefore the current quiescent star formation may only be temporary, while Poggianti&Wu(2000) proposed a model where star formation continues in K+A but is hidden dust."," \cite{buyle06} pointed out that K+A galaxies contain significant amounts of gas and therefore the current quiescent star formation may only be temporary, while \cite{poggianti00} proposed a model where star formation continues in K+A galaxies but is hidden by dust."
" However, Dressler(2009) galaxiesdetected no 24 uum emissionby for K+A galaxies in Abell 851."," However, \cite{dressler09} detected no 24 $\mu$ m emission for K+A galaxies in Abell 851."
 Another possible contribution to the radio flux is that K+A galaxies may host an AGN., Another possible contribution to the radio flux is that K+A galaxies may host an AGN.
" Most K+A galaxies have significant bulges (Yangetal.2008) and therefore should contain a supermassive central black hole (e.g., Ferrarese&Merritt 2000))."," Most K+A galaxies have significant bulges \citep{yang08} and therefore should contain a supermassive central black hole (e.g., \citealt{ferrarese00}) )."
" In the general field, K+A galaxies are often involved in mergers and interactions (Blakeetal.2004;Goto2005;Yangetal.2008) and show inverted color gradients indicative of central star formation (Yangetal.2008),, which is expected if mergers drive gas to the center (Hernquist 1989)."," In the general field, K+A galaxies are often involved in mergers and interactions \citep{blake04,goto05,yang08} and show inverted color gradients indicative of central star formation \citep{yang08}, which is expected if mergers drive gas to the center \citep{hernquist92}."
. Liuetal.(2007) find evidence of a weak AGN in a nearby K+A galaxy., \cite{liu07} find evidence of a weak AGN in a nearby K+A galaxy.
" However, Shinetal.(2011) find only a few AGNs in a subset of our sample and they argue that these"," However, \cite{shin11} find only a few AGNs in a subset of our sample and they argue that these"
the centrifugal force ancl pushes the particles toward (he core if the vortex is an antievelone. whereas both forces are conspiring to eject the particles for a evclone.,"the centrifugal force and pushes the particles toward the core if the vortex is an anticyclone, whereas both forces are conspiring to eject the particles for a cyclone."
 This capture-in-vortex mechanism is a verv efficient one ancl results in strong density enhancements inside the vortex. by al least (wo order of magnitude in ~200 rotation periods.," This capture-in-vortex mechanism is a very efficient one and results in strong density enhancements inside the vortex, by at least two order of magnitude in $\sim 200$ rotation periods."
 The capture rate is estimated under (he assumption that the particles are continuously renewed near the vortex orbit due (o the inward. drift under the svstematic headwind drag (Weidenschilling 19771. D595).," The capture rate is estimated under the assumption that the particles are continuously renewed near the vortex orbit due to the inward drift under the systematic headwind drag (Weidenschilling 1977, BS95)."
 One obvious and important consequence of this density enhancement is (hat. inside a vortex. particle growth is made easier and will couple with confinement and segregation.," One obvious and important consequence of this density enhancement is that, inside a vortex, particle growth is made easier and will couple with confinement and segregation."
 On the other hand. dust is depleted from the region insicle the vortex orbit as the particles either are feeding tlie vortex or are falling to the star under the systematic cdit.," On the other hand, dust is depleted from the region inside the vortex orbit as the particles either are feeding the vortex or are falling to the star under the systematic drift."
 Inside the vortex. the trapped. particles are also submitted to a background. small scale turbulence which makes them cliffuse and tends to reduce their global concentration.," Inside the vortex, the trapped particles are also submitted to a background small scale turbulence which makes them diffuse and tends to reduce their global concentration."
 Chavanis(2000) investigated this question in terms of a diffusion equation in an idealized circular vortex. ancl derived a time dependant solution for the surface density inside the vortex: the initial state being a delta function centered at ro: fy is the diffusion scale length and hk=esxp(—l/Teapr) in which Tap is the characteristic time Lor a particle to reach the center of the vortex., \citet{Cha00} investigated this question in terms of a diffusion equation in an idealized circular vortex and derived a time dependant solution for the surface density inside the vortex: the initial state being a delta function centered at $r_0$; $l_{\rm d}$ is the diffusion scale length and $k = \exp(-t/T_{\rm capt})$ in which $T_{\rm capt}$ is the characteristic time for a particle to reach the center of the vortex.
 In the case of light particles and. very. elongated vortices Tí&29/(307.) and /;~\/ay/qrsHy where F& is the vortex radius and q its aspect ratio: ἂν is the non- parameter measuring the small scale turbulence efficiency inside (he vortex., In the case of light particles and very elongated vortices $T_{\rm capt} \simeq 2q/(3\Omega\taus)$ and $l_d\sim \sqrt{\alpha_{\rm v}/q\taus}~R_{\rm v}$ where $R_{\rm v}$ is the vortex radius and $q$ its aspect ratio; $\alpha_{\rm v}$ is the non-dimensioned parameter measuring the small scale turbulence efficiency inside the vortex.
" In order to estimate the size of the trapped particles. we will choose a standard mocel ol nebula. the minimum mass solar nebula. in which the surface densities (both for gas and ↽⋅⊾ ↕≻≀↧↴↕⋅⊔≺∢↥≼↲⊳∖∁⋝≀↧↴∐≼⇂⊔∐↲∩↲↕∐↕≻≼↲↕⋅≀↧↴⊓∐⋅≼↲≀⋯↲⊔∐↲≼⇂≼↲≺∢↕⋅≼↲≀↧↪∖⊽↕∐↖↳↴↕≻∪∖∖↽≼↲↕⋅↥≀↧↴∖∖↽⋝∖⊽∣⋮↽ −↽↽ ∶⋉≱⋡⊇ and i1/2. respectively:↽− at | AU the densities are set to 1700 σα7 [or the gas and 20 eem7 for the particles. whereas ihe temperature is assumed to be XIX. At 0.2 AU from the star and with our numerical values. the optimal size for particle capture is 545,731/7(r/LAUJ""?oLE eem. ie. pebble size."," In order to estimate the size of the trapped particles, we will choose a standard model of nebula, the minimum mass solar nebula, in which the surface densities (both for gas and particles) and the temperature are the decreasing power laws $r^{-3/2}$ and $r^{-1/2}$, respectively; at 1 AU the densities are set to 1700 ${\rm g\,cm}^{-2}$ for the gas and 20 ${\rm g\,cm}^{-2}$ for the particles, whereas the temperature is assumed to be K. At 0.2 AU from the star and with our numerical values, the optimal size for particle capture is $s_{\rm opt} \simeq 31\sqrt{\taus}(r/1{\rm AU})^{5/8}\simeq 11$ cm, i.e. pebble size."
 Lighter non optimal particles with πι«1 can be also captured by (he vortex but remain trapped at the periphery of the vortex., Lighter non optimal particles with $\taus<1$ can be also captured by the vortex but remain trapped at the periphery of the vortex.
" These particles remain in the Stokes regime. al 0.2 AU [rom the star. as far as their size is larger than the critical size s,=9A/420.3 mum."," These particles remain in the Stokes regime, at 0.2 AU from the star, as far as their size is larger than the critical size $s_{\rm c} = 9\lambda /4\simeq 0.3$ mm."
 We assume the disk is seen nearly edge on. under an inclination 7 less than the flaring angle of the gas disk.," We assume the disk is seen nearly edge on, under an inclination $i$ less than the flaring angle of the gas disk."
 / must be small enough for the line of sight to cross the vortex in, $i$ must be small enough for the line of sight to cross the vortex in
to that for the Lax-Woudroff scheme.,to that for the Lax-Wendroff scheme.
 For A<1 the dispersion relation w(h} for the first-order upwiud scheme is different from the exact solution where ος= ck., For $\lambda<1$ the dispersion relation $\omega(k)$ for the first-order upwind scheme is different from the exact solution where $\omega_\circ=vk$ .
 This scheme is both diffusive aud dispersive., This scheme is both diffusive and dispersive.
 Since it is ouly first-order accurate. the amount of diffusion is large.," Since it is only first-order accurate, the amount of diffusion is large."
 In Figure (3)) we compare the dispersion relation of the upwind scheme to that of the Lax-Wendroff scheme., In Figure \ref{fig:uwdispersion}) ) we compare the dispersion relation of the upwind scheme to that of the Lax-Wendroff scheme.
 The Fourier modes iu the wpwind scheme also have phase errors but they will be damped away., The Fourier modes in the upwind scheme also have phase errors but they will be damped away.
 The low frequency modes which coutribute to the oscillations in the Lax-Woencdrotf solution are more damped in the upwind solution., The low frequency modes which contribute to the oscillations in the Lax-Wendroff solution are more damped in the upwind solution.
" Ποσο, oue does not expect to see oscillations resulting from phase crrors."," Hence, one does not expect to see oscillations resulting from phase errors."
 Tn Figure (1)) we show how the first-order upwiud scheme does at advecting the Ricmamun shock wave., In Figure \ref{fig:uw}) ) we show how the first-order upwind scheme does at advecting the Riemann shock wave.
 This scheme is well-behaved aud produces uo spurious oscillations. but since it is ouly first-order. it is üghlv diffusive.," This scheme is well-behaved and produces no spurious oscillations, but since it is only first-order, it is highly diffusive."
 The first-order upwind scheme has he property of having monotonicity preservation., The first-order upwind scheme has the property of having monotonicity preservation.
 When applied to the linear advection equation. it docs rot allow the creation of new extrema in the form of spurious oscillations.," When applied to the linear advection equation, it does not allow the creation of new extrema in the form of spurious oscillations."
 The Lax-Woeudroff scheme does not have the property of having monotonicity oeservation., The Lax-Wendroff scheme does not have the property of having monotonicity preservation.
 The flux assieuimenut schemes that we have discussed so far are all linear schemes., The flux assignment schemes that we have discussed so far are all linear schemes.
 Codunov(1959). showed that all linear schemes are either ciffusive or dispersive or a combination of both., \citet{god59} showed that all linear schemes are either diffusive or dispersive or a combination of both.
 The Lax-Woendrotf scheme is hiehlv dispersive while the first-order upwind scheme is liehly diffusive., The Lax-Wendroff scheme is highly dispersive while the first-order upwind scheme is highly diffusive.
 Godunovs theorem also states that linear monotonicitv preserving sclicmes are ouly first-order accurate., Godunov's theorem also states that linear monotonicity preserving schemes are only first-order accurate.
 In order to obtain higher order accuracy and prevent spurious oscillations. nonlinear schemes are needed to solve couscrvation laws.," In order to obtain higher order accuracy and prevent spurious oscillations, nonlinear schemes are needed to solve conservation laws."
 Tarten(1983). proposedthediminishing (TVD) coudition. which guarantees that a scheme have monotonicity preservation., \citet{har83} proposed the (TVD) condition which guarantees that a scheme have monotonicity preservation.
 Applying Godunovs theorem. we know that all linear TWD schemes are ouly first-order accurate.," Applying Godunov's theorem, we know that all linear TVD schemes are only first-order accurate."
 Iu fact. the oulv linear TWD schemes are the class of first-order upwind sclicines.," In fact, the only linear TVD schemes are the class of first-order upwind schemes."
 Therefore. higher order accurate TWD schemes inst be nonlinear.," Therefore, higher order accurate TVD schemes must be nonlinear."
 The TVD condition is a noulinear stability condition., The TVD condition is a nonlinear stability condition.
 The total variation of a discrete solution. defined as," The total variation of a discrete solution, defined as"
"is rich in neutral Uvdrogen content (AA/Ato,=824) and hosts a patchy circinunnclear structure (??)..","is rich in neutral Hydrogen content $M_\mathrm{HI}/M_\mathrm{Tot} = 82\%$ ) and hosts a patchy circumnuclear structure \citep{GiovanelliHaynes1983, Bokeretal2002}."
 The irofation curve displavs almost a solid body rotation im the inner LO kpe., The rotation curve displays almost a solid body rotation in the inner 10 kpc.
" Our analvsis shows that Q,=ontt iis well outlined in Fig.", Our analysis shows that $\Omega_p= 25_{-5}^{+1}$ is well outlined in Fig.
 1. with the location of the (CR) at 6.5 kpc., \ref{fig:allmaps} with the location of the $r(CR)$ at 6.5 kpc.
" displavs the largest iuisaliennmnienut (36 degrees) 55961.between the aandoj... Which could o,be caused by the projection effect siuce this galaxy is near face-on."," 5964 displays the largest misalignment $36$ degrees) between the and, which could be caused by the projection effect since this galaxy is near face-on."
 Such uusplacement can also be seen as an indication of strong streamine along the spiral axius and prominent bar., Such misplacement can also be seen as an indication of strong streaming along the spiral arms and prominent bar.
In Fig.,In Fig.
 mdl. we show that the r(CR) agrees with the radius where patchy spiral structure starts. indicating that the bar ancl spiral arms rotate at the same rate (seo?)..," \ref{fig:allmaps} we show that the $r(CR)$ agrees with the radius where the patchy spiral structure starts, indicating that the bar and spiral arms rotate at the same rate \citep[see ][]{Taggeretal1987}."
 Theoretical work such as that by? lave shown that floceulent spirals can form via swine amplification of star formation patches. aud thus should have uo pattern speed.," Theoretical work such as that by \citet{ElmegreenThomasson1993} have shown that flocculent spirals can form via swing amplification of star formation patches, and thus should have no pattern speed."
 Although their proposed mechanisia explains the patchiness of these galaxies. it does not exclude the presence of density waves in the galaxies where swing auplification builds patchy spiral structure.," Although their proposed mechanism explains the patchiness of these galaxies, it does not exclude the presence of density waves in the galaxies where swing amplification builds patchy spiral structure."
" Support for such a scenario comes from simulations bv (72). as well as observational studies bv οον, "," Support for such a scenario comes from simulations by \citep{WadaNorman2001} as well as observational studies by \citet{ThornleyMundy1997, GrosbolPatsis1998, ElmegreenElmegreenLeitner2003}."
Notably. ia 55055. 7? could outline the spiral aiiis by a spline fit to the A-baud miage aud show that the non-circular notions in their residual yvelocity field follow1 these arms.," Notably, in 5055, \citet{ThornleyMundy1997} could outline the spiral arms by a spline fit to the $K$ -band image and show that the non-circular motions in their residual velocity field follow these arms."
 These authors combined the photometry with kinematics to derive the pattern speed for the underlying deusitv wave at 35-10 and conclude that iu some focculenut ealaxies the underline deusitv wave ids difficult to observe due to their overall lower eas surface density (oe. that in 55055 a factor of 6 lower than he eas density iu 551).," These authors combined the photometry with kinematics to derive the pattern speed for the underlying density wave at 35-40, and conclude that in some flocculent galaxies the underlying density wave is difficult to observe due to their overall lower gas surface density (e.g., that in 5055 is a factor of 6 lower than the gas density in 51)."
" To sumnnuarise. our results or 55961 imply au underlving density wave with Q,=25E-th."," To summarise, our results for 5964 imply an underlying density wave with $\Omega_p= 25_{-5}^{+1}$."
" is a erand-design barred spiral galaxy with τους main gravitational distortions: a laree oval with radius Re La RomD »prinuarv stellar bar with ellipticitv 0.15. and a 28"" inmcelear bar with Q.4. which ds Mal rpeudieulu to the Uiptieitymainbar."," is a grand-design barred spiral galaxy with three main gravitational distortions: a large oval with radius $R\approx4.5$, a $R\approx 1$ primary stellar bar with ellipticity 0.15, and a $R\approx 8$ nuclear bar with ellipticity 0.4, which is almost perpendicular to the main bar."
" We have preseutedthis: detailed analysis of the resonance structure iu ealaxv iu ον, and confirm that the maps preseuted iu his paper are fully consistent with our previous work."," We have presented a detailed analysis of the resonance structure in this galaxy in \citet{Fathietal2007TW}, and confirm that the maps presented in this paper are fully consistent with our previous work."
 is an exteusivoelv. studied. starburst galaxy (em.TT?) with a massive. 2.2«1010 stella bar with axis ratio of 1 iurcoetion.0.25-0.Mulllt(27)..," is an extensively studied starburst galaxy \citep[e.g., ][]{Hawardenetal1986, Aguerrietal2000, Laine2001} with a massive, $2.2\times10^{10}$ stellar bar with axis ratio of 0.25-0.4 \citep{Burbidgeetal1960, Martin1995}."
. Although here is no evidence of recent have found uanv kineniatic and morphological features consistent with a πλου merger event for this ealaxy. proposing the wpothesis that this galaxy is on its wav to evolve toward an earlier Dabble type.," Although there is no evidence of recent interaction, \citet{LaineHeller1999} have found many kinematic and morphological features consistent with a minor merger event for this galaxy, proposing the hypothesis that this galaxy is on its way to evolve toward an earlier Hubble type."
 Several studies lave found the i(CR) tobe hetween TTT)í aud tto be between3-27 and ↽LOO (2?)..," Several studies have found the $r(CR)$ to be between \citep[][]{ElmegreenElmegreen1985, Quillenetal1995, BeckmanCepa1990} and to be between 27 and 100 \citep{Laineetal1998, delRioCepa1998}."
 The mean star formation efficiency in the bar. although asvuuuetric. is 0.4 aud increasescremmumeloan to 0.63soosAL. in the ‘e. indicating inflow along the bar.," The mean star formation efficiency in the bar, although asymmetric, is 0.4 and increases to 0.63 in the circumnuclear regions \citep{MartinFriedli1997}, indicating inflow along the bar."
 Qur rrotation curve is consistent with that derived bv 7? with a prominent aud rapidly rotating componcut in the central30”., Our rotation curve is consistent with that derived by \citet{Garridoetal2005} with a prominent and rapidly rotating component in the central.
.. This curve. as well as the aueular frequeucy curve. cannot be determined iu the central kpe region due to the weak ecinission. aud hence we cannot coufiri the preseuce of the ILR reported by ?..," This curve, as well as the angular frequency curve, cannot be determined in the central kpc region due to the weak emission, and hence we cannot confirm the presence of the ILR reported by \citet{Laineetal1998}."
" We find Q,=Is!bo and r(CGRzm13 kpe."," We find $\Omega_p = 18_{-3}^{+3}$, and $r(CR) \approx 13$ kpc."
" Our r(CR) is almost twice the 55"" found by ?.. the r((CR) sugeested » nunerncal simulations of ?.. aud thecarried 58""found from xotential-deusitv phasc-slitt analysis out bv ?.."," Our $r(CR)$ is almost twice the $55\arcsec$ found by \citet{PuerariDottori1997}, the $r(CR)$ suggested by numerical simulations of \citet{Laineetal1998}, and the $58\arcsec$ found from potential-density phase-shift analysis carried out by \citet{ButaZhang2009}."
" Using the r(CR) found by these authors. our angular requency curve implies 0,z25SEU slightly above the value preseuted here."," Using the $r(CR)$ found by these authors, our angular frequency curve implies $\Omega_p \approx 23$, i.e., slightly above the value presented here."
 This would also uake the bar with rtCR)/r(bur)gzz0.9. to within the errors. coniparable with the value we preseut in Table 5..," This would also make the bar with $r(CR)/r(bar)_F \approx 0.9$, to within the errors, comparable with the value we present in Table \ref{tab:CRoverLength}."
" has a prominent bar with axis ratio 0.36. two short aud flocculent spiral avis iucludiug a siguificaut αλλο! of diffuse ionised eas and many iregious (e.g.77δν, "," has a prominent bar with axis ratio 0.36, two short and flocculent spiral arms including a significant amount of diffuse ionised gas and many regions \citep[e.g., ][]{Duvaletal1991, Blocketal2004, Laurikainenetal2004}."
This bulee-less galaxy has a mica star formation efficiency of 01 (2)... with very weak ccoutent iu the bar (7)..," This bulge-less galaxy has a mean star formation efficiency of 0.1 \citep{MartinFriedli1997}, with very weak content in the bar \citep{Braineetal1993}."
 ?. found strong ionised eas flows in the bar region and a ratio of between the bar mass and that of the immer disk inside the bar radius., \citet{Duvaletal1991} found strong ionised gas flows in the bar region and a ratio of between the bar mass and that of the inner disk inside the bar radius.
 Our rotation curve agrees with the low-resolution curve of? and ?., Our rotation curve agrees with the low-resolution curve of \citet{Duvaletal1985} and \citet{Garridoetal2002}.
".The inethod results in 0,=Tremaine-Weinherg(CRI19!7 Tor he main bar with r(ma=0,5 kpe. c£. OX"," The method results in $\Omega_p = 19_{-6}^{+8}$ for the main bar with $r(CR) \approx 6.5$ kpc, c.f.,"
nen from ον., 31 from \citet{Duvaletal1985}.
 We find the location of an outer ILR at z1.3 kpe. inside which the rotation curve suggests 1 presence of dynamically cold rapidly rotating component.," We find the location of an outer ILR at $\approx 1.3$ kpc, inside which the rotation curve suggests the presence of a dynamically cold rapidly rotating component."
 We find also an inner ILR at z300 pc. and 10 hint of a higher pattern speed inside the outer or 1ο inner ILR.," We find also an inner ILR at $\approx 300$ pc, and no hint of a higher pattern speed inside the outer or the inner ILR."
 In 77711. like in 77179. the ILR radii given here are based on the asswuption that epicvelic approximation can be applied. aud it should o0 noted that in strong bars. such as iu 77711. where epievelic approximation breaks down. the actual resonances nav be in cliffereut locations (e.g...2).," In 7741, like in 7479, the ILR radii given here are based on the assumption that epicyclic approximation can be applied, and it should be noted that in strong bars, such as in 7741, where epicyclic approximation breaks down, the actual resonances may be in different locations \citep[e.g., ][]{ReganTeuben2004}."
 Tere. we have shown that an iuteusity-velocity map 1u oof the type obtained using a Fabry-Perot interferometer. can be successfully used to derive the eas kinematics of disk galaxies with coverage and precision sufücient to derive the ffor those where star formation is well spread across the ealaxv.," Here, we have shown that an intensity-velocity map in of the type obtained using a Fabry-Perot interferometer, can be successfully used to derive the gas kinematics of disk galaxies with coverage and precision sufficient to derive the for those where star formation is well spread across the galaxy."
 Although this technique is not new (777).. its precision aud the ummber of galaxies analysed here eive our results considerable value.," Although this technique is not new \citep{Hernandezetal2005TW, Emsellemetal2006, Fathietal2007TW}, , its precision and the number of galaxies analysed here give our results considerable value."
 It is clear that the cecluitting eas does uot act as a linear probe for the ealaxyvs surface deusitv., It is clear that the emitting gas does not act as a linear probe for the galaxy's surface density.
 However. oulv a fraction of the pixels iu our maps are attributed to the compact iregious.," However, only a fraction of the pixels in our maps are attributed to the compact regions."
 The, The
Ευ f(Nyy) Ένα (e.g..Péórouxetal.2003: FCNyp) FUN),"$\fn$ $\fn$ $\alpha$ \citep[e.g.,][]{Peroux03, Pro04c, Peroux05, Pro05, Pro08c, Noterdaeme09}."
" A 22.22h*AIpe. 2«617 (0,,,04.ος)=(1.0.0.0.0.05). ΓΔ) ;— vy and Jy=10 teem js |."," $\fn$ $\fn$ $\Lam$ \citet{Katz96b}, $\himpc$ $2\times 64^3$ $(\Omega_m, \Omega_{\Lam}, \Omega_b) = (1.0, 0.0, 0.05)$ $\fn$ $J(\nu) = J_0 (\nu_0/\nu)$ $z=3$ $\nu_0$ and $J_0= 10^{-22}$ $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$."
 The UVB is usually treated with au optically thin lait regardless of gas clensity in cosmological ντοςπαλιο simulations owing to the computational lint., The UVB is usually treated with an optically thin limit regardless of gas density in cosmological hydrodynamic simulations owing to the computational limit.
 This simplified approxination Ίαν artificially increase the ionization fraction of gas. and givesrise to the discrepancy in FUN).," This simplified approximation may artificially increase the ionization fraction of gas, and givesrise to the discrepancy in $\fn$."
" Naganuueetal.(2002007) updated the work of Ikatzetal.(1996b) using cosmological[. SPIT iuulatious with a comoving box size of 105.1Mpe. 2«321? particles. aud (Q,,.04.05)=(0.5.0.7.0.001)."," \citet{Nag04g, Nag07a} updated the work of \citet{Katz96b} using cosmological SPH simulations with a comoving box size of $\himpc$, $2\times 324^3$ particles, and $(\Omega_m, \Omega_{\Lam}, \Omega_b)=(0.3, 0.7, 0.044)$."
 Tuterestingly. they also found a similar wnderprediction of ΕΝ) compared to the observations. despite significantly higher resolution than that of watzetal.(1996b).," Interestingly, they also found a similar underprediction of $\fn$ compared to the observations, despite significantly higher resolution than that of \citet{Katz96b}."
. Their simulations included. a mutorm UVB of Taardt&Madau(1996) spectrin. modified by Davéetal.(1999). to match the Ίσα forest observations.," Their simulations included a uniform UVB of \citet{Haardt96} spectrum, modified by \citet{Dave99} to match the $\alpha$ forest observations."
 We have attempted to resolve this discrepancy by mocditving the models of star formation (SE) and supernova feedback: e... changing the SE threshold density. SE time-scale. feedback strengths. or adding metalline cooling (Choi&Nagamine2009b.a).," We have attempted to resolve this discrepancy by modifying the models of star formation (SF) and supernova feedback; e.g., changing the SF threshold density, SF time-scale, feedback strengths, or adding metal-line cooling \citep{Choi09a, Choi09b}."
. However. none of these changes iu the plivsical| mocels resolved the discrepancy in ΓΔ) fundamentally.," However, none of these changes in the physical models resolved the discrepancy in $\fn$ fundamentally."
 Tn this Letter. we show that the effect of UWB is the kev in determining the shape of flNyy) at logNin= 21.6.," In this Letter, we show that the effect of UVB is the key in determining the shape of $\fn$ at $\log \NHI \lesssim 21.6$ ."
 Tn addition. we consider the effect of local stellar radiation on ΑΠ) by. performing a radiative transfer (RT) caleulation.," In addition, we consider the effect of local stellar radiation on $\fn$ by performing a radiative transfer (RT) calculation."
 Our paper is organized as follows., Our paper is organized as follows.
 TnSection 2..webriefly describe the setup of our siuulations. and present the resultsiu Section 3..," InSection\ref{sec:sim}, ,webriefly describe the setup of our simulations, and present the resultsin Section \ref{sec:result}. ."
 We then discuss the comparison with other receut works. aud conclude in Section L..," We then discuss the comparison with other recent works, and conclude in Section \ref{sec:discussion}. ."
 We use the updated version of the tree-particleauesh, We use the updated version of the tree-particle-mesh
The study ofprocesses is an important. issue in. modern astrophysics.,The study of is an important issue in modern astrophysics.
 In particular. this issue plavs an important role in the formation and evolution of galaxies. at high and low redshilt (see for references “Taniguchi Shiova 2000: Lipari et al.," In particular, this issue plays an important role in the formation and evolution of galaxies, at high and low redshift (see for references Taniguchi Shioya 2000; Lipari et al."
 2004a.b.c).," 2004a,b,c)."
 Motivated by this. we began a project of study of nearby star forming | CAV galaxies and. distant Ενα emitters (for. references see. Lipari ct al.," Motivated by this, we began a project of study of nearby star forming + GW galaxies and distant $\alpha$ emitters (for references see Lipari et al."
 20042.b.c).," 2004a,b,c)."
 The first step for this project is to understand the extreme star formation process in nearby galaxies because we can obtain more detailed. anc unambiguous information., The first step for this project is to understand the extreme star formation process in nearby galaxies because we can obtain more detailed and unambiguous information.
 Thus. our group started a study of nearby HU mergers/OSOs. with ealactic winds.," Thus, our group started a study of nearby IR mergers/QSOs, with galactic winds."
 Luminous infrared (11i) galaxies (Lisipn2101: L.. LIRGs) are dusty strong LR emitters -Lip fle~ 5300- where frequently a strong enhancement of star formation is taking place. and a very high per cent of LIRGs 954) are mergers.," Luminous infrared (IR) galaxies $_{IR[8-1000 \mu m]} \geq 10^{11}
L_{\odot}$ , LIRGs) are dusty strong IR emitters $_{IR}$ $_{B} \sim$ 5–300- where frequently a strong enhancement of star formation is taking place, and a very high per cent of LIRGs $\%$ ) are mergers."
 Pherefore. at low z. Iuminous Ik mergers (z x 0.1) and IR QSOs (z < 0.5) are excellent laboratories for the study of extreme star formation processes.," Therefore, at low z, luminous IR mergers (z $\leq$ 0.1) and IR QSOs (z $\leq$ 0.5) are excellent laboratories for the study of extreme star formation processes."
 In. these systems. very high star formation and supernova (SN) rates are expected., In these systems very high star formation and supernova (SN) rates are expected.
 Llubble Space Telescope (HST) observations confirmed. that star cluster. forming frequeney is highest during violent burst of star formation. in Ilt mergers (for references see the reviews of Schweizer 2002: and Whitmore 2001).," Hubble Space Telescope ) observations confirmed that star cluster forming frequency is highest during violent burst of star formation, in IR mergers (for references see the reviews of Schweizer 2002; and Whitmore 2001)."
 Recently. Lipari et al. (," Recently, Lipari et al. ("
2003) reported several galactic shells and ares. in nearby LR mergers and LR QSOs with galactic winds.,"2003) reported several galactic shells and arcs, in nearby IR mergers and IR QSOs with galactic winds."
 SNe. shells/ares ancl voung star clusters are thus good tracers of extreme starburst events.," SNe, shells/arcs and young star clusters are thus good tracers of extreme starburst events."
ks of the XRT light-curve with respect to the optical-NIR one is consistent with the existence of an undetected X-ray cursor at the mitial time of the second component.,ks of the XRT light-curve with respect to the optical-NIR one is consistent with the existence of an undetected X-ray post-cursor at the initial time of the second component.
International N.rav Optical Survey (RINOS. Mason 2000). Mittaz (1999) concluded that at faint fluxes. < )]) ⋅ ⊐∪⇂≱∖∩⇂⊔⋅≼↛⋖⋅⊳∖↓↥⋜↧∖⇁∢⋅⊳∖↓≻⋖⋅≼⇍↿↓⋅⋜↧↓⋯↓⋅∠⇂∢⊾↓⋅⇂↓⋯⊔⇂↓⋯↿∪⇂↿↓∐⋅ background. compared with only Jalbrighter fluvres.,"International X–ray Optical Survey (RIXOS, Mason 2000), Mittaz (1999) concluded that at faint fluxes < ) of sources have spectra harder than that of the background, compared with only at brighter fluxes."
 Lhisisprobablythebrighttailofthehardsourec ΜπΑΜ iyaha hells bsp ΡΕ SM beregeoundateven fain , This is probably the bright tail of the hard source population that must make a substantial contribution to the background at even fainter fluxes.
ddelectedhardsourcesshouldi here foreprovideuswil haprevicwo fh MDE odiePO palion, These detected hard sources should therefore provide us with a preview of the XRB producing population.
HU PANT PH WE theyaretiked ylober ," As relatively bright examples, they are likely to be much easier to study at all wavelengths than their more numerous, but fainter, cousins."
This paper describes the survey of PPSPC pointed. observations for examples of this faint. hard spectrum population anc presents the catalogue of hard spectrum sources.," This paper describes the survey of PSPC pointed observations for examples of this faint, hard spectrum population and presents the catalogue of hard spectrum sources."
 Optical identification. spectroscopy and imaging of these sources are the subjects of companion papers.," Optical identification, spectroscopy and imaging of these sources are the subjects of companion papers."
 We cleseribe the construction of the source catalogue and the ddata reduction method in Section 2.., We describe the construction of the source catalogue and the data reduction method in Section \ref{sec:method}.
 The Monte Carlo simulations which were used to calculate the elfective area of the survey and quantify the spectral selection ellects are described in Section 4.., The Monte Carlo simulations which were used to calculate the effective area of the survey and quantify the spectral selection effects are described in Section \ref{sec:monte}.
 The results of the simulations are taken into account in Section 5 to derive the characteristic Xray spectral properties of the hard sources. their source counts. and their contribution to the 1 - 2 keV. ARB.," The results of the simulations are taken into account in Section \ref{sec:results} to derive the characteristic X–ray spectral properties of the hard sources, their source counts, and their contribution to the 1 - 2 keV XRB."
 The source catalogue is also presented in this section., The source catalogue is also presented in this section.
 The implications of our findings are discussed in Section 6.. and our conclusions are presented in Section 7..," The implications of our findings are discussed in Section \ref{sec:discussion}, and our conclusions are presented in Section \ref{sec:conclusions}."
 The primary goal of the survey is {ο investigate the properties of extragalactic sources which have Xrav spectra harder than the extragalactic background emission. because such sources must exist in abundance at faint [luxes to resolve the spectral paradox.," The primary goal of the survey is to investigate the properties of extragalactic sources which have X--ray spectra harder than the extragalactic background emission, because such sources must exist in abundance at faint fluxes to resolve the spectral paradox."
 We chose to construct our source catalogue using archival PPSPC data., We chose to construct our source catalogue using archival PSPC data.
 This was well suited to our purposes: the PPSPC has sullicient. οποιον resolution {ο cllectively discriminate hard. from soft. sources. while the excellent spatial resolution means we can expect to make unambiguous optical identifications for many of the hare SOULCES.," This was well suited to our purposes: the PSPC has sufficient energy resolution to effectively discriminate hard from soft sources, while the excellent spatial resolution means we can expect to make unambiguous optical identifications for many of the hard sources."
 The PPSPC fields were chosen according to the following preferences: high Galactic Iatitude. low Galactic f .longerposurcltime.obsereationtargebswhichdidnolillalarge sodbrddayce rid ypesvham Mopical followup.," The PSPC fields were chosen according to the following preferences: high Galactic latitude, low Galactic, long exposure time, observation targets which did not fill a large fraction of the field of view, and sky positions suitable for optical follow up."
Onlyl ," Only PSPC observations with the `open' filter were used, and observations targeted on the Magellanic clouds were excluded."
, Some 188 PSPC datasets were searched for hard sources; a complete list of these observations is given in table \ref{tab:fields}.
For maximum reliability ancl reproducibility only REV2 processed data have been used., For maximum reliability and reproducibility only REV2 processed data have been used.
 For consistency every PSPC dataset was reduced using the same sequence of operations which will now be described., For consistency every PSPC dataset was reduced using the same sequence of operations which will now be described.
 Each PSPC dataset was first passed through the PPCPICOR. task to correct. lor PSPC spatial/temporal eain. variations., Each PSPC dataset was first passed through the PCPICOR task to correct for PSPC spatial/temporal gain variations.
"""A MThe dataset was then converted to SEARLINIS ASTIERIX format and reduced. using the STARLINI ASTERIX package.", The dataset was then converted to STARLINK ASTERIX format and reduced using the STARLINK ASTERIX package.
 Phe data were screened to remove times of poor attitude solution. high particle background. and high overall background countrate.," The data were screened to remove times of poor attitude solution, high particle background, and high overall background countrate."
 fraduvingd search psocfadild, An image for source searching was then produced.
 chose to use the central 20 areminute radius region where the point spread. function and sensitivity are. best. and," We chose to use the central 20 arcminute radius region where the point spread function and sensitivity are best, and"
condition wy2he/(28.2) is satisfied.,condition $\omega_A>\omega_\eta\omega_\nu k/(2k_z\Omega)$ is satisfied.
 Notice however. that even if theuuo magnetic diffusivity is high. a weal magnetic field is capable of generating the MBI.," Notice however, that even if the magnetic diffusivity is high, a weak magnetic field is capable of generating the MRI."
 Next. let us consider the hvdrodyviiuauical V40) with arbitrary Couctte flow profiles. (¢z0).," Next, let us consider the hydrodynamical $V_A=0$ ) with arbitrary Couette flow profiles, $a\neq0$ )."
 In this case. AxO0 in general and we have to go back to eq. (103) ," In this case, $\kappa\neq0$ in general and we have to go back to eq. \ref{dis}) )"
for deriving solutions., for deriving solutions.
 Two trivial solutions are >= yh. corresponding to the electromagnetic brauch. aud the secoud is given by which is the hivdrodvuaiical brauch.," Two trivial solutions are $\gamma=-\eta k^2$ , corresponding to the electromagnetic branch and the second is given by which is the hydrodynamical branch."
a The effect offinite & and high v is shown in Fig. 2..," The effect of finite $\kappa$ and high $\nu$ is shown in Fig. \ref{fig2},"
 where the rotation speed of the evluders. viscosity. aud magnetic diffusivity of Fig.," where the rotation speed of the cylinders, viscosity, and magnetic diffusivity of Fig."
 2aa correspouds to the point € of Jiet (2001)... audthe waveumuber is fined at (A206)=(1.1) for Fig.," \ref{fig2}a a corresponds to the point C of \citet{ji01}, and the wavenumber is fixed at $(k_z, r_r)=(1,1)$ for Fig."
 2aa. 2cc and (1.1) for Fig.," \ref{fig2}a a, \ref{fig2}c c and $(4,1)$ for Fig."
 2bb. 2dd. respectively.," \ref{fig2}b b, \ref{fig2}d d, respectively."
 The erowth rates of the four roots of eq. (10)), The growth rates of the four roots of eq. \ref{dis}) )
 are shown as a function of the axial niaguetie field streneth B.., are shown as a function of the axial magnetic field strength $B_z$.
 The epicvelie frequency & is finite in Figs., The epicyclic frequency $\kappa$ is finite in Figs.
 2aa and 2cc. whereas w= Qin Figs.," \ref{fig2}a a and\ref{fig2}c c, whereas $\kappa=0$ in Figs."
 2bb aud 2dd. The kinematic viscosity 7 is taken as the actual value of Callim |Fig., \ref{fig2}b b and \ref{fig2}d d. The kinematic viscosity $\nu$ is taken as the actual value of Gallium [Fig.
 ~ 2aa| aud Sodium [Fig 2bb]. whereas we make it artificially high (7> 5) in Figs.," \ref{fig2}a a] and Sodium [Fig \ref{fig2}b b], whereas we make it artificially high $\nu>\eta$ ) in Figs."
 2cc aud 244 to see the effect of anomalous increase of i due to possible turbuleuce., \ref{fig2}c c and \ref{fig2}d d to see the effect of anomalous increase of $\nu$ due to possible turbulence.
 Iu the bydrodvuamiical παο.= 0) in Fig., In the hydrodynamical $B_z=0$ ) in Fig.
 2aa. the solutions of the lycvodvuamical brauch. (5~ 0) are couples [eq. (17))].," \ref{fig2}a a, the solutions of the hydrodynamical branch, $\gamma\sim0$ ) are complex [eq.\ref{sol4}) )]."
" Near B,=2000 gauss. these solutions are separated and both become real."," Near $B_z=2000$ gauss, these solutions are separated and both become real."
 Ouly one solution becomes unstable., Only one solution becomes unstable.
 Thus. if the flow is uot a maxima shear flow profile (&# 0). the MRI is stabilized for weals maenetic fields.," Thus, if the flow is not a maximum shear flow profile $\kappa\neq0$ ), the MRI is stabilized for weak magnetic fields."
 Figures (2cc) and (2dd) show that the turbulence suppresses the unstable NBI mode., Figures \ref{fig2}c c) and \ref{fig2}d d) show that the turbulence suppresses the unstable MRI mode.
 Since the Έλαια laver may inake the fluid weakly turbulent. it is nuportaut to estimate the scale of this turbulence. which will be discussed in Sec. 5..," Since the Ekman layer may make the fluid weakly turbulent, it is important to estimate the scale of this turbulence, which will be discussed in Sec. \ref{sec5}."
 Tu the next section. stability diagrams are presented aud compared for both experiments.," In the next section, stability diagrams are presented and compared for both experiments."
 The comparison| between the NAID aud Princeton experiuents is done by comparing their typical parameters in Table 1., The comparison between the NMD and Princeton experiments is done by comparing their typical parameters in Table 1.
 In order to evaluate the plivsical differences )etween the experiments. we compare the dimensionless xuwanieters. prescuted iu the secoud column of Table 1.," In order to evaluate the physical differences between the experiments, we compare the dimensionless parameters, presented in the second column of Table 1."
" We use Ry aud las units of length and time to obtain he dimenusiouless OQ,quautities.", We use $R_2$ and $\Omega_2^{-1}$ as units of length and time to obtain the dimensionless quantities.
 We choose O4=sla Uz aud O5=10.31 IIz as he typical values for the eallinm experiment. which corresponds to point C of Jietal.(2001).," We choose $\Omega_1=84.8$ Hz and $\Omega_2= 10.34$ Hz as the typical values for the gallium experiment, which corresponds to point C of \citet{ji01}."
". The global uaenetie Revnolds προ becomes The BR, is hieher in the sodium] experiment. which is designed to observe the aw dyiiuno (Colgate.etal.2001:Paviev 2001)."," The global magnetic Reynolds number becomes The $R_m$ is higher in the sodium experiment, which is designed to observe the $\alpha\omega$ dynamo \citep{col01b, par01}."
. All the erowth rates ire evaluated at the radius 7 =r. which satisfies O(r)= O40».," All the growth rates are evaluated at the radius $r=\bar{r}$ , which satisfies $\Omega(\bar{r})=\sqrt{\Omega_1\Omega_2}$ ."
" We also define the elobal Πα, Revuolds umuuber as Using these paramcters. the erowth rate is obtained by solving eq. (10))"," We also define the global fluid Reynolds number as Using these parameters, the growth rate is obtained by solving eq. \ref{dis}) )"
 uuuericallv. aud the uustable regious are plotted in τοπο. as a function of axial magnetic field streneth aud wave number ιν," numerically, and the unstable regions are plotted in \\ref{fig3} as a function of axial magnetic field strength and wave number $k_z$."
 The unit of &; is g/(RoRy). hy is w/b in reffies.. [. 5. 6.8.9 and 10.," The unit of $k_z$ is $\pi/(R_2-R_1)$, $k_r$ is $\pi/L$ in \\ref{fig3}, \ref{fig4}, \ref{fig5}, \ref{fig51}, \ref{fig10}, \ref{fig7} and \ref{fig6}."
" The minima possible values for the dimensionless &, aud A. are unity.", The minimum possible values for the dimensionless $k_r$ and $k_z$ are unity.
" We fixed ky, as unity in roefües..", We fixed $k_r$ as unity in \\ref{fig3}.
 Notice that iu both experiucuts. a strong field suppresses hieh & modes because of the magnetic diffusivity and magnetic tension.," Notice that in both experiments, a strong field suppresses high $k$ modes because of the magnetic diffusivity and magnetic tension."
 In the sodimm case roefüe3aa). higher #&. aoces are destabilized. aud the erowth rate is higher compared to the eallimm case roefüe3bb).," In the sodium case \\ref{fig3}a a), higher $k_z$ modes are destabilized, and the growth rate is higher compared to the gallium case \\ref{fig3}b b)."
 In the galliuuni case. the suppressiou of the uustable modes with low magnetic field occurs due to finite Ho (see 33 for details).," In the gallium case, the suppression of the unstable modes with low magnetic field occurs due to finite $\kappa$ (see 3 for details)."
 Figures Lo and 5. clemonstrate the dependence of the erowth rate on the wave nunbers in the sodiunu aud σαι experiueuts., Figures \ref{fig4} and \ref{fig5} demonstrate the dependence of the growth rate on the wave numbers in the sodium and gallium experiments.
 In Fie. L.," In Fig. \ref{fig4},"
 an axial magnetic field B. is fixed at 3&10? eauss. aud iu Fig. 5.," an axial magnetic field $B_z$ is fixed at $3\times10^3$ gauss, and in Fig. \ref{fig5},"
 at LOO eauss., at $400$ gauss.
" When B,—3«10° gauss. a umber of ke ποσα.«8) are destabilized iu the sodium τοπο laa}. while in the eallimm χοπο Lbb) only the A.=1 ode is destabilized."," When $B_z=3\times10^3$ gauss, a number of $k_z$ $k_z<8$ ) are destabilized in the sodium \\ref{fig4}a a), while in the gallium \\ref{fig4}b b) only the $k_z=1$ mode is destabilized."
 A inore significant differcuce between the sodium aud ealliun experiments is shown in rofüeb.., A more significant difference between the sodium and gallium experiments is shown in \\ref{fig5}.
 For weak magnetic fields no mode is unstable im thegallium whereas higher 4. iiodes (fh.750) are excited in the sodiuu reffisbaa).," For weak magnetic fields no mode is unstable in thegallium \\ref{fig5}b b), whereas higher $k_z$ modes $k_z>50$ ) are excited in the sodium \\ref{fig5}a a)."
 As we noted before. the fiuite & suppresses the uustable MBRI modes with weak magnetic field.," As we noted before, the finite $\kappa$ suppresses the unstable MRI modes with weak magnetic field."
 Tn order to show the iniportauce of the maxima shear. we plot the growth rate for the σαπα experiment with Ho= Oin Fig. 6..," In order to show the importance of the maximum shear, we plot the growth rate for the gallium experiment with $\kappa=0$ in Fig. \ref{fig51}."
 We reproduce Figs., We reproduce Figs.
 3bb. [bb aud 5bb in Fies.," \ref{fig3}b b, \ref{fig4}b b and \ref{fig5}b b in Figs."
 6aa. 6bb and Gec respectively. except we take QO.—O4/9 for the nixa shear [see Eqs. (3))," \ref{fig51}a a, \ref{fig51}b b and \ref{fig51}c c respectively, except we take $\Omega_2=\Omega_1/9$ for the maximum shear [see Eqs. \ref{ab}) )"
 aud (7) η., and \ref{c}) )].
 Iu rofüeblaa. high A. modes are unstable with low magnetic field. which are stable with finite &(Fie. rreffie3b).," In \\ref{fig51}a a, high $k_z$ modes are unstable with low magnetic field, which are stable with finite $\kappa$ b)."
" Maxima velocity shear also destabilizes high lk, modes rofüeblbb aud Geo). so many modes will be excited iun the calli experiment at maximum shear."," Maximum velocity shear also destabilizes high $k_r$ modes \\ref{fig51}b b and \ref{fig51}c c), so many modes will be excited in the gallium experiment at maximum shear."
 In all cases. the (k..kh.)=(1.1) mode is dominant. but moce coupling nay occur in the nonlinear regine to excite turbulence in he ealliuui experiuent.," In all cases, the $(k_z, k_r)=(1,1)$ mode is dominant, but mode coupling may occur in the nonlinear regime to excite turbulence in the gallium experiment."
 While the masxinuun shear flow profile leads to easv excitation of AMIRI. it falls on the border line for pure ivdrodyvuauical iustabilitv.," While the maximum shear flow profile leads to easy excitation of MRI, it falls on the border line for pure hydrodynamical instability."
 We show the contour plot of he unstable region for the modes (μι)=(1.2) and (3.5) of the sodium experiment in refüe9..," We show the contour plot of the unstable region for the modes $(k_r, k_z)=(1, 2)$ and $(3,5)$ of the sodium experiment in \\ref{fig9}. ."
 In the τοσο O5/04<< 0.25. sodiun is warodvuamically unstable.," In the regime $\Omega_2/\Omega_1<0.25$ , sodium is hydrodynamically unstable."
The miaxiumuu shear flow1s indicated as a solid line.,The maximum shear flowis indicated as a solid line.
 [πο waveunuber nodes are unstable only near the maxima shear flow sud weak naenetic field in the hywdrodsausuicallv stable region (Fig., High wavenumber modes are unstable only near the maximum shear flow and weak magnetic field in the hydrodynamically stable region (Fig.
 ΤΟ]., \ref{fig9}b b).
 Growth rates for the fuite & shear case are shown iu Fig 5.., Growth rates for the finite $\kappa$ shear case are shown in Fig \ref{fig10}. .
 High wave απνο modes are stabilized. compared, High wave number modes are stabilized compared
plotted iu Fig. 2..,plotted in Fig. \ref{fig_2}.
 The typical uncertainty of the individual points is at least 40.3 mae aud the spread of the leh curve goes up to 0.5 mae ata eiven epoch. although the observers used mainly the same sequence of comparison stars.," The typical uncertainty of the individual points is at least $\pm$ 0.3 mag and the spread of the light curve goes up to 0.5 mag at a given epoch, although the observers used mainly the same sequence of comparison stars."
 As a first appronimation. we estimated the momen of visual iiaxinuu light beime JD 21.50933.," As a first approximation, we estimated the moment of visual maximum light being JD 24,50933."
 Usine this epoch we determined the approximate phase of our spectra as d week before maxiuun. 9 davs after maxima are 28 davs after maxiuuu. respectively (sce also Table 1).," Using this epoch we determined the approximate phase of our spectra as 1 week before maximum, 9 days after maximum and 28 days after maximum, respectively (see also Table 1)."
 Although the spectra presented in Fig., Although the spectra presented in Fig.
 1 clearly have inadequate wavelength coverage for a detailed comparison with other SNe spectra. some basic properties of SNe Type Ta can be recognized iu these data.," 1 clearly have inadequate wavelength coverage for a detailed comparison with other SNe spectra, some basic properties of SNe Type Ia can be recognized in these data."
 The most prominent feature in the two earlier spectra is the Si II AG355 absorption liue as noted by other observers., The most prominent feature in the two earlier spectra is the Si II $\lambda$ 6355 absorption line as noted by other observers.
 This is the characteristic feature of SNe Ta (e.g. Filippeuko. 19973).," This is the characteristic feature of SNe Ia (e.g. Filippenko, \cite{filip}) )."
 Ou the xeanaxiuunu spectrum. the line profile is asvuuuetric aud has a ποτ P. Cyve-tvpe “bump” toward longer waveleneths. similarly to SN 1991D (Patat ct al. 1996)).," On the pre-maximum spectrum, the line profile is asymmetric and has a slight P Cyg-type “bump” toward longer wavelengths, similarly to SN 1994D (Patat et al., \cite{patat}) )."
" Later. this absorption line deepens ancl broadens senificautlv at about 1 mouth post-masximaiu. which is also simular to the spectral behaviour of SN 199LD in this wavelength regime. although Berlind Calkins reported ""unusuallv shallow Type Ila features (see Cuunavich ct al. 1995)."," Later, this absorption line deepens and broadens significantly at about 1 month post-maximum, which is also similar to the spectral behaviour of SN 1994D in this wavelength regime, although Berlind Calkins reported “unusually shallow Type Ia features” (see Garnavich et al., \cite{garnav}) )."
 The other $i II absorption trough at 5700 becomes stronger as the SN gets older. but it also becomes bleuded from its blue side.," The other Si II absorption trough at 5700 becomes stronger as the SN gets older, but it also becomes blended from its blue side."
 Moreover. woad enisson bump at A6500 at 2010. days post-aunaxinmun. which is probably due to Fe ID aud [Fe TH] (Filippeuko. 1997)) is also reproduced well on the third spectrum.," Moreover, the broad emission bump at $\lambda$ 6500 at $20-40$ days post-maximum, which is probably due to Fe II and $[$ Fe $]$ (Filippenko, \cite{filip}) ) is also reproduced well on the third spectrum."
 These observed features indicate that SN 1998a«q closely reseiibles to a “prototvpe” SN Iain the 55006700 spectral interval., These observed features indicate that SN 1998aq closely resembles to a “prototype” SN Ia in the $5500-6700$ spectral interval.
 We have derived velocities of the expaucding gas 1ieasuriig the Doppler-shift of the line core of the A6355 Si II line (Table 1)., We have derived velocities of the expanding gas measuring the Doppler-shift of the line core of the $\lambda 6355$ Si II line (Table 1).
 Such line-core velocities have been prescutecd for a nuuber of other SNe Ia by Patat et al. (1996..," Such “line-core” velocities have been presented for a number of other SNe Ia by Patat et al. \cite{patat},"
 see their Fie.lO)., see their Fig.10).
 According to that diagram. the velocities of SN 1998aq agree well with those of SN 1991D and SN I1989D. ILowever. as it was also noted by Patat et al. (19963).," According to that diagram, the velocities of SN 1998aq agree well with those of SN 1994D and SN 1989B. However, as it was also noted by Patat et al. \cite{patat}) ),"
 the velocities derived from strong lines. such as Si II AG355. are ambiguous. especially at later phases. because these lines are formed over a considerably large velocity range.," the velocities derived from strong lines, such as Si II $\lambda 6355$, are ambiguous, especially at later phases, because these lines are formed over a considerably large velocity range."
 It would be interesting to derive bisector velocities of both observed and svuthesized SN spectra to reveal the effect of velocity gradients. as it was recently," It would be interesting to derive bisector velocities of both observed and synthesized SN spectra to reveal the effect of velocity gradients, as it was recently"
Faraday depths ranging between —32 rad m? and -16 rad m? and using 50 (220 üuJy) as detection limit.,Faraday depths ranging between –32 rad $^{-2}$ and –16 rad $^{-2}$ and using $\sigma$ (220 $\mu$ Jy) as detection limit.
 The image is presented in Fig. 17.., The image is presented in Fig. \ref{A2255RMBEAVERCOMPOSITE}.
 The clear gradient between head and tail can give strong constraints on the possible location of these two structures withinA2255., The clear gradient between head and tail can give strong constraints on the possible location of these two structures within.
. It is worth noting that the head and the initial part of the tail show RM values that are similar to those of the Galactic foreground at the location of (see Sect. 3.1))., It is worth noting that the head and the initial part of the tail show RM values that are similar to those of the Galactic foreground at the location of (see Sect. \ref{the30sources}) ).
" This suggests that the head of the Beaver is located on the outskirts of the cluster and, in particular, in the foreground ofA2255,, where only a small portion of ICM is crossed by the radio signal before reaching the observer."," This suggests that the head of the Beaver is located on the outskirts of the cluster and, in particular, in the foreground of, where only a small portion of ICM is crossed by the radio signal before reaching the observer."
 That the tail appears at negative Faraday depths instead implies that it should be located deeper in the ICM., That the tail appears at negative Faraday depths instead implies that it should be located deeper in the ICM.
" Therefore, the Beaver could not lie in the plane of the sky, but with the tail pointing towards the central radio halo, possibly connecting with it."," Therefore, the Beaver could not lie in the plane of the sky, but with the tail pointing towards the central radio halo, possibly connecting with it."
 This interpretation is supported by the common spectral index values found for the end of the tail and the southern region of the halo (?).., This interpretation is supported by the common spectral index values found for the end of the tail and the southern region of the halo \citep{pizzospectrum}.
 The sketch in Fig., The sketch in Fig.
 18 illustrates this situation., \ref{beaversketch} illustrates this situation.
 Our polarimetric data confirm the strong polarization of the filaments and add important information that can help to explain their nature., Our polarimetric data confirm the strong polarization of the filaments and add important information that can help to explain their nature.
" The filaments show similar polarimetric properties to those found for the external radio galaxies ofA2255,, i.e. the Embryo, the Beaver, and the Bean."," The filaments show similar polarimetric properties to those found for the external radio galaxies of, i.e. the Embryo, the Beaver, and the Bean."
" Their RM distributions are characterized by low values of ory and «RM», with Faraday spectra showing only one peak."," Their RM distributions are characterized by low values of $\sigma_{RM}$ and $<$ $>$, with Faraday spectra showing only one peak."
" Following the interpretation given for the radio galaxies (see Sect. 4.9)),"," Following the interpretation given for the radio galaxies (see Sect. \ref{theradiogalaxies}) ),"
" these results suggest that the filaments are not located deep in the ICM, but at the periphery of the cluster."," these results suggest that the filaments are not located deep in the ICM, but at the periphery of the cluster."
" Moreover, given their high polarization levels and their small spatial variance in RM (see Fig. 16)),"," Moreover, given their high polarization levels and their small spatial variance in RM (see Fig. \ref{rmimagescomposite}) ),"
 we conclude that they should be located in the foreground of the cluster and not in the background., we conclude that they should be located in the foreground of the cluster and not in the background.
 This is compatible with the polarization of the Galactic foreground as detected in regions Al and A2 in the high-frequency RM cube (Fig. ??))., This is compatible with the polarization of the Galactic foreground as detected in regions A1 and A2 in the high-frequency RM cube (Fig. \ref{RM252118_frame103}) ).
 The RM distribution and the complexity of the spectra for regions A1 and A2 are similar to those of the Bean (the most external radio galaxy belonging to A2255)) and of the filaments., The RM distribution and the complexity of the spectra for regions A1 and A2 are similar to those of the Bean (the most external radio galaxy belonging to ) and of the filaments.
 This indicates that most of the contribution to the Faraday depth of these structures comes from our Galaxy and suggests that the filaments should lie at large distance from the cluster center., This indicates that most of the contribution to the Faraday depth of these structures comes from our Galaxy and suggests that the filaments should lie at large distance from the cluster center.
" The observed central location of the filaments, therefore, should be considered as due to a projection effect."," The observed central location of the filaments, therefore, should be considered as due to a projection effect."
 At 85 cm and at 2 m we do not detect any polarized emission associated with the radio filaments., At 85 cm and at 2 m we do not detect any polarized emission associated with the radio filaments.
 At the Faraday depths at, At the Faraday depths at
 , 
will dominate the total spectrum.,will dominate the total spectrum.
 To test at what mass fractions the old population is actually seen. several young and old SSPs were generated and co-added with different mass fractions.," To test at what mass fractions the old population is actually seen, several young and old SSPs were generated and co-added with different mass fractions."
 To find an observability criterium for the older population. the colourin IRAC Chl was calculated.," To find an observability criterium for the older population, the colour in $-$ IRAC Ch1 was calculated."
 This was compared to the typical Lo error bar in the photometry in these two bands., This was compared to the typical $1\sigma$ error bar in the photometry in these two bands.
 We calculated the colour significance according to: where rf is the mass fraction., We calculated the colour significance according to: where $mf$ is the mass fraction.
 The number in the denominator is the typical error on the colour based on the data at hand., The number in the denominator is the typical error on the colour based on the data at hand.
 If this colour significance is more than 16. the old population is considered to be observed.," If this colour significance is more than $1\sigma$, the old population is considered to be observed."
 A plot of these limits can be found in Fig. 2.., A plot of these limits can be found in Fig. \ref{fig:massfrac}.
 Based on this figure. all objects with more than 90% of its data-points above the fitted lines are considered to be single young populations.," Based on this figure, all objects with more than $90$ of its data-points above the fitted lines are considered to be single young populations."
" First we stacked the candidates in three different. light-weighted stacks for the fitting: the total sample of ""LAE best"" and GALEX-detected non-AGN LAEs. as well as the total sample divided into a ""red""−⋅ and a ""blue"" sample (with /“| colours greater or less than zero respectively)."," First we stacked the candidates in three different, light-weighted stacks for the fitting; the total sample of “LAE best” and GALEX-detected non-AGN LAEs, as well as the total sample divided into a “red” and a “blue” sample (with $-i^+$ colours greater or less than zero respectively)."
 These stacks are similar to those in Nilsson et al. (, These stacks are similar to those in Nilsson et al. (
"2009a). but updated with spectroscopic results and new photometry from the UKIRT J and CFHT K, images.","2009a), but updated with spectroscopic results and new photometry from the UKIRT J and CFHT $_s$ images."
 The magnitudes for the three samples can be found in Table 5.., The magnitudes for the three samples can be found in Table \ref{tab:sedmags}.
" Secondly. we also fit all individual objects with at least one detection in the Spitzer bands and/or in the K, band."," Secondly, we also fit all individual objects with at least one detection in the Spitzer bands and/or in the $_s$ band."
" This sample consists of a total of 58 objects (8 with only Spitzer detections. 19 with only a K, detection and 31 with detections in both Spitzer and K,)."," This sample consists of a total of 58 objects (8 with only Spitzer detections, 19 with only a $_s$ detection and 31 with detections in both Spitzer and $_s$ )."
 Redshifts are set to 2.25 for all galaxies since varying the redshift within the range of the narrow-band filter does not change the fitting results significantly., Redshifts are set to 2.25 for all galaxies since varying the redshift within the range of the narrow-band filter does not change the fitting results significantly.
 For the main results presented here. the Monte Carlo Markov Chain SED fitting code was run with 20 000 iterations. and fitted the data with two single stellar populations.," For the main results presented here, the Monte Carlo Markov Chain SED fitting code was run with $20$ $000$ iterations, and fitted the data with two single stellar populations."
 To find the probabilities in the parameter space. the first 2000 runs were omitted to allow the X? to level out.," To find the probabilities in the parameter space, the first $2000$ runs were omitted to allow the $\chi^2$ to level out."
 The best fit parameters are calculated as the first and second moments of the distribution in each dimensio. weighted by the 42.," The best fit parameters are calculated as the first and second moments of the distribution in each dimension, weighted by the $\chi^2_r$ ."
 The full set of results of this run are found in Table 6.., The full set of results of this run are found in Table \ref{tab:fullresults}.
 When interpreting the dust parameter. Ay-. it is important to keep in mind that this is a galaxy averaged dust absorption.," When interpreting the dust parameter, $_V$, it is important to keep in mind that this is a galaxy averaged dust absorption."
 Different parts of the galaxy will be observable at different wavelengths., Different parts of the galaxy will be observable at different wavelengths.
 The results for the dust parameter will be dominated by the absorption of the restframe UV part of the spectrum. see also section ??..," The results for the dust parameter will be dominated by the absorption of the restframe UV part of the spectrum, see also section \ref{sec:ulirgs}."
 When doing SED fitting. many of the fitted parameters can be degenerate with other parameters.," When doing SED fitting, many of the fitted parameters can be degenerate with other parameters."
 In Fig., In Fig.
 3 we show. as an example. the contours of probability for the parameters of old population age. mass fraction in the young population. dust Aj. stellar mass. and young population age for two example objects (LAE-CCOSMOS_337 and 154). one that has a single young population and one that has a detectable older population (see also section ??)).," \ref{fig:contour} we show, as an example, the contours of probability for the parameters of old population age, mass fraction in the young population, dust $_V$, stellar mass, and young population age for two example objects 37 and 154), one that has a single young population and one that has a detectable older population (see also section \ref{sec:indresults}) )."
 Of the parameters fitted for. the stellar mass 1s the best constrained.," Of the parameters fitted for, the stellar mass is the best constrained."
 Secondly. the dust Ay- is also well fit.," Secondly, the dust $_V$ is also well fit."
 Age of the old population. mass fractions and metallicities are theleast constrained parameters.," Age of the old population, mass fractions and metallicities are theleast constrained parameters."
 As can be seen in Fig. 3..," As can be seen in Fig. \ref{fig:contour}, ,"
massive (han Jupiter. Msin5>Mj. with orbital periods less than one vear. P?<1vr. the velocity semi-amplitude Aq>30m$5.|. large enough to be detectable in most survevs.,"massive than Jupiter, $M\sin\gamma>M_\mathrm{J}$, with orbital periods less than one year, $P<1\mbox{ yr}$, the velocity semi-amplitude $K_\mathrm{RV}>30\,\mbox{m
 s}^{-1}$, large enough to be detectable in most surveys."
 In (his mass and period range our sample contains 46 planet-hostng stars and estimate Chat the fraction of stars with planets is 0.019zc0.007. which implies pnl=2400+ 900.," In this mass and period range our sample contains 46 planet-hosting stars and \cite{cum08} estimate that the fraction of stars with planets is $0.019\pm0.007$, which implies $n_\mathrm{tot}^\mathrm{RV}=2400\pm
900$ ."
 Altering the period range to P?«100d gives nl=2500d:1200 (based on 21 host stars): altering the mass cutoff to Msin>0.5M; gives nPY=19002:500 (based on 63 host stars)., Altering the period range to $P<100\mbox{ d}$ gives $n_\mathrm{tot}^\mathrm{RV}=2500\pm 1200$ (based on 21 host stars); altering the mass cutoff to $M\sin\gamma>0.5M_\mathrm{J}$ gives $n_\mathrm{tot}^\mathrm{RV}=1900\pm 500$ (based on 63 host stars).
 This last estimate of nl is probably low because the surveys we have used are not all complete al (his level. d, This last estimate of $n_\mathrm{tot}^\mathrm{RV}$ is probably low because the surveys we have used are not all complete at this level. (
i) We may estimate η using the tranet frequency derived. from the Kepler mission.,ii) We may estimate $n_\mathrm{tot}^\mathrm{RV}$ using the tranet frequency derived from the Kepler mission.
 Once again. we restrict the Kepler sample to host stars thal are F. G. and IX clwarls KIN<Zar< KINaud logg> 4).," Once again, we restrict the Kepler sample to host stars that are F, G, and K dwarfs $<T_\mathrm{eff} < $ Kand $\log g > 4$ )."
" We then carry out the following steps for a eiven orbital period P and velocitv semi-unplitude Aq: (i) compute the corresponding nass MOP.Way)=My(yyy/20ms(bvr/P)? assuming a circular orbit and. a ass host star: (ii) find the number nf(P.Nyy) of RV planets with period less than  and nass greater (han M(GP.Aq): (11) find all IXepler tranets wilh mass greater (han MP.Iq) and period less (han P. using an empirical mass-radius relation found by fitting mass ancl radius measurements from transiting planets in the range 1037; (see Figure 10)) to a log-equacdratic relation (iv) compute the total number of Kepler planets in this range nP""(P.Aq) by counting each iranet as €! planets. to correct [or geometric selection effects releq:goneone)):V (v). estimate. the total number of. RV- host stars as nyTU—nnlΊνα(Poi)./nPCPandy),"," We then carry out the following steps for a given orbital period $P$ and velocity semi-amplitude $K_\mathrm{RV}$: (i) compute the corresponding mass $M(P,K_\mathrm{RV})=M_{J}(K_\mathrm{RV}/30\mbox{\,m
 s}^{-1})(1\mbox{\,yr}/P)^{1/3}$ assuming a circular orbit and a solar-mass host star; (ii) find the number $n^\mathrm{RV}(P,K_\mathrm{RV})$ of RV planets with period less than $P$ and mass greater than $M(P,K_\mathrm{RV})$; (iii) find all Kepler tranets with mass greater than $M(P,K_\mathrm{RV})$ and period less than $P$, using an empirical mass-radius relation found by fitting mass and radius measurements from transiting planets in the range $10M_J$ (see Figure \ref{fig:mr}) ) to a log-quadratic relation (iv) compute the total number of Kepler planets in this range $n^\mathrm{Kep}(P,K_\mathrm{RV})$ by counting each tranet as $\epsilon^{-1}$ planets, to correct for geometric selection effects \\ref{eq:goneone}) ); (v) estimate the total number of RV host stars as $n_\mathrm{tot}^\mathrm{RV}=n_\mathrm{tot}^\mathrm{Kep}n^\mathrm{RV}(P,K)/n^\mathrm{Kep}(P,K)$."
" The results are shown in Figure 9 [orΑν=10.15.20.25ms1,"," The results are shown in Figure \ref{fig:n0} for$K_\mathrm{RV}=10, 15, 20,
25\,\mbox{m s}^{-1}$."
 As the majority of RV survevs have reached. precisions of ~L5nis| or better over the last decade. it is reassuring but not surprising that the estimates of ην for Ayy=15.20.25ms.! are consistent.," As the majority of RV surveys have reached precisions of $\sim 15\mbox{\,m s}^{-1}$ or better over the last decade, it is reassuring but not surprising that the estimates of $n_\mathrm{tot}^\mathrm{RV}$ for $K_\mathrm{RV}=15,20,25\mbox{\,m s}^{-1}$ are consistent."
 The vise in nf! ad small periods is likely due to the known discrepancy in hot Jupiter frequency between (transit and RV survevs (the frequency of hot Jupiters estimated from (ransil surveys is [actor of ~2 smaller (han Chat derived. from RV survevs. perhaps because the average metallicities are different: see Gouldetal.2006:ILoward 2011)).," The rise in $n^\mathrm{RV}_\mathrm{tot}$ at small periods is likely due to the known discrepancy in hot Jupiter frequency between transit and RV surveys (the frequency of hot Jupiters estimated from transit surveys is factor of $\sim 2$ smaller than that derived from RV surveys, perhaps because the average metallicities are different; see \citealt{gould, howard}) )."
 These independent approaches vield nf’2250041000 and nBY-3000+41000. respectivelv. which are consistent within the errors.," These independent approaches yield $n^\mathrm{RV}_\mathrm{tot}\simeq2500\pm1000$ and $n^\mathrm{RV}_\mathrm{tot}\simeq3000\pm1000$, respectively, which are consistent within the errors."
 The corresponding inclination ranges from Figure 8 are 0<(sin?/)?«0.08 and 0.02<(in)?«0.09 which correspond to an rms or mean inclination range of5° (as shown in relsec:fisher.. for a Ravleigh distribution the rms inclination is only larger than the mean inclination by 12%... which is much less than the uncertainty).," The corresponding inclination ranges from Figure \ref{fig:rv_test} are $0<\langle\sin^2i\rangle^{1/2}<0.08$ and $0.02<\langle\sin^2i\rangle^{1/2}<0.09$ which correspond to an rms or mean inclination range of$5^\circ$ (as shown in \\ref{sec:fisher}, , for a Rayleigh distribution the rms inclination is only larger than the mean inclination by , which is much less than the uncertainty)."
 The success of the separability assumption in modeling survev selection effects, The success of the separability assumption in modeling survey selection effects
"in the kinematic regime (ie., the regime in which the magnetic energy is much smaller than the kinetic ","in the kinematic regime (i.e., the regime in which the magnetic energy is much smaller than the kinetic energy)."
"Indications of the Kazantsev spectrum are also energy).found in simulations of the intra-galaxy cluster medium by Xuetal.(2009,2010)."," Indications of the Kazantsev spectrum are also found in simulations of the intra-galaxy cluster medium by \citet{XuEtAl2009,XuEtAl2010}."
" However, in both their simulations and in ours, the scaling range for measuring the slope is too narrow to draw final conclusions."," However, in both their simulations and in ours, the scaling range for measuring the slope is too narrow to draw final conclusions."
 It is not clear whether the k?/?-power law would persist at higher resolution., It is not clear whether the $k^{3/2}$ -power law would persist at higher resolution.
" In turbulence-in-a-box simulations with external forcing by Haugenetal.(2004) with up to 512? grid cells, there is strong indication that the magnetic energy spectra indeed converge to the Kazantsev slope with increasing resolution."," In turbulence-in-a-box simulations with external forcing by \citet{HaugenBrandenburgDobler2004} with up to $512^3$ grid cells, there is strong indication that the magnetic energy spectra indeed converge to the Kazantsev slope with increasing resolution."
" As in previous turbulence-in-box calculations with external forcing (e.g.,Choetal. we find that the magnetic energy grows exponentially 2009),,on all scales, which is a typical feature of the small-scale dynamo (Brandenburg&Subramanian but has (to the best of our knowledge) not been 2005),shown before in a gravity-driven turbulent gas core."," As in previous turbulence-in-box calculations with external forcing \citep[e.g.,][]{ChoEtAl2009}, we find that the magnetic energy grows exponentially on all scales, which is a typical feature of the small-scale dynamo \citep{BrandenburgSubramanian2005}, but has (to the best of our knowledge) not been shown before in a gravity-driven turbulent gas core."
 We also measure the exponential growth rates of the magnetic field as a function of Jeans resolution in section 4 below., We also measure the exponential growth rates of the magnetic field as a function of Jeans resolution in section \ref{sec:newjeansresol} below.
" The magnetic energy spectra in Figure 4 suggest that the spectra fall off more steeply than the k9/? Kazantsev law toward large scales, outside the Jeans volume (seealsothespectrainXuetal. 2010).."," The magnetic energy spectra in Figure \ref{fig:spect_jeans} suggest that the spectra fall off more steeply than the $k^{3/2}$ Kazantsev law toward large scales, outside the Jeans volume \citep[see also the spectra in][]{XuEtAl2010}."
" In order to clarify this and to investigate the field structure outside the Jeans volume, we introduce and apply a new method to infer the spectrum over more than four orders of magnitude in length scales."," In order to clarify this and to investigate the field structure outside the Jeans volume, we introduce and apply a new method to infer the spectrum over more than four orders of magnitude in length scales."
" Since we aim to investigate the field structure in the fixed frame of reference at the largest available scales in the simulation, but at the same time would like to include spectral information on the very smallest scales, we apply a two-step approach."," Since we aim to investigate the field structure in the fixed frame of reference at the largest available scales in the simulation, but at the same time would like to include spectral information on the very smallest scales, we apply a two-step approach."
" First, we re-normalize the high-resolution spectra obtained inside the Jeans volume (Fig. 4)),"," First, we re-normalize the high-resolution spectra obtained inside the Jeans volume (Fig. \ref{fig:spect_jeans}) ),"
 by shifting them to the correct position with respect to the fixed frame of reference., by shifting them to the correct position with respect to the fixed frame of reference.
" However, the spectra at late times during the collapse, obtained with this method, do not contain any information on scales far outside the Jeans volume."," However, the spectra at late times during the collapse, obtained with this method, do not contain any information on scales far outside the Jeans volume."
" Thus, in the second step, we add spectral information on large scales, by gradually extracting larger boxes, centered on the core at a fixed grid resolution."," Thus, in the second step, we add spectral information on large scales, by gradually extracting larger boxes, centered on the core at a fixed grid resolution."
" Using this method, we can test the spectral energy scale-by-scale."," Using this method, we can test the spectral energy scale-by-scale."
 We call this method 'scale-by-scale extraction'., We call this method `scale-by-scale extraction'.
" The result of this two-step approach is shown in Figure 5, where we plot the spectra of magneticenergy in the fixed frame of reference, i.e., as a function of the initial (at 7r= 0) Jeans wavenumber, kjo, of the collapsing system."," The result of this two-step approach is shown in Figure \ref{fig:spect_fixed}, where we plot the spectra of magneticenergy in the fixed frame of reference, i.e., as a function of the initial (at $\tau=0$ ) Jeans wavenumber, $\kJzero$, of the collapsing system."
" The first thing to note is that the spectra on large scales, obtained with the scale-by-scale extraction method connect reasonably well with the spectra computed inside the Jeans volume and re-normalized to match the fixed frame of reference."," The first thing to note is that the spectra on large scales, obtained with the scale-by-scale extraction method connect reasonably well with the spectra computed inside the Jeans volume and re-normalized to match the fixed frame of reference."
" Some deviation is seen only at k/kjg~300 for the spectrum at 7—12, which can be taken as a measure of the uncertainty in the spectra obtained with our scale-by-scale extraction method."," Some deviation is seen only at $k/\kJzero\approx300$ for the spectrum at $\tau=12$, which can be taken as a measure of the uncertainty in the spectra obtained with our scale-by-scale extraction method."
" Given the total range of scales that we aim to probe here, the difference in the spectra obtained with our two-step approach is acceptable."," Given the total range of scales that we aim to probe here, the difference in the spectra obtained with our two-step approach is acceptable."
 We also tested whether extending the scale-by-scale extraction to smaller scales (inside the Jeans volume) matches the high-resolution spectra of step one., We also tested whether extending the scale-by-scale extraction to smaller scales (inside the Jeans volume) matches the high-resolution spectra of step one.
" We found that they do within an uncertainty of about2596, i.e., the slopes and peak positions are reproduced reasonably well with the scale-by-scale extraction method."," We found that they do within an uncertainty of about, i.e., the slopes and peak positions are reproduced reasonably well with the scale-by-scale extraction method."
" However, the high-resolution spectra inside the Jeans volume are more accurate, and we thus prefer the two-step approach described above."," However, the high-resolution spectra inside the Jeans volume are more accurate, and we thus prefer the two-step approach described above."
 'Three main results can be extracted from Figure 5.., Three main results can be extracted from Figure \ref{fig:spect_fixed}. .
" First, the magnetic field always grows fastest on the smallest available scales in the simulation, with the peak"," First, the magnetic field always grows fastest on the smallest available scales in the simulation, with the peak"
while we refer to BGW for further details on the its implementation in cluster simulations.,while we refer to BGW for further details on the its implementation in cluster simulations.
 The hierarchical merging of DAL halos is followed by means of the extended. PressSeheehter formalism (c.g. Lacey Cole 1993). while model parameters. describing the gas physics. such as cooling. star formation and stellar [cedback. are chosen so as to reproduce observed. properties of the local galaxv population. such as the “PullyFisher relation. or optical luminosity functions and clisksizes (e.g. Poli et al.," The hierarchical merging of DM halos is followed by means of the extended Press–Schechter formalism (e.g. Lacey Cole 1993), while model parameters describing the gas physics, such as cooling, star formation and stellar feedback, are chosen so as to reproduce observed properties of the local galaxy population, such as the Tully–Fisher relation, or optical luminosity functions and disk–sizes (e.g. Poli et al."
 2001)., 2001).
 The mocel prediction we are interested in here is the integrated star formation history. maiz.Mu) οἱ all the condensations which are incorporated into a structure of total mass Aly by the present time.," The model prediction we are interested in here is the integrated star formation history, $\dot m_*(z,M_0)$ ,of all the condensations which are incorporated into a structure of total mass $M_0$ by the present time."
 For a halo of size similar to our Virgolike cluster. the SER. peaks at 24 in this semi-analytie mocel. while itis z22.5 3 for the groupsized halos (see BGW. for a plot of the Mo. dependence of the cluster SER).," For a halo of size similar to our Virgo–like cluster, the SFR peaks at $z\simeq 4$ in this semi-analytic model, while it is $z\simeq2.5$ –3 for the group--sized halos (see BGW, for a plot of the $M_0$ –dependence of the cluster SFR)."
 The rate of total energy. feedback released by type-Lh SN is then computed asissil where go is the number of SN per solar mass of formed stars.," The rate of total energy feedback released by type-II SN is then computed as, where $\eta_0$ is the number of SN per solar mass of formed stars."
 This value depends on the assumed. initial mass function (LAE). and is obtained by integrating over the EME for stellar masses >SAM. .," This value depends on the assumed initial mass function (IMF), and is obtained by integrating over the IMF for stellar masses $>8M_\odot$ ."
" In the following. we will use the values yo=3:2«10.72A,5. which follows from a Scalo IME (Scalo 1986). jj=T10PAL.Ἐν from the Salpeter IME (Salpeter 1955) and go=1.5107Ag+ as an extreme Case,"," In the following, we will use the values $\eta_0=3.2\times
10^{-3}M_\odot^{-1}$, which follows from a Scalo IMF (Scalo 1986), $\eta_0=7\times 10^{-3}M_\odot^{-1}$, from the Salpeter IMF (Salpeter 1955) and $\eta_0=1.5\times 10^{-2}M_\odot^{-1}$, as an extreme case."
 Since our simulations include cooling. radiative losses of SN energy do not need to be assumed. a priori. rather they are selfconsistently computed by the code.," Since our simulations include cooling, radiative losses of SN energy do not need to be assumed a priori, rather they are self–consistently computed by the code."
 However. we need to specily the gas overdensity. 04. at which the SN heating energy is assigned to the gas.," However, we need to specify the gas overdensity, $\delta_g$, at which the SN heating energy is assigned to the gas."
" In the following we take 0,=50 or 500. and assume that Lox is shared. in equal parts among all the gas particles at overdensity larger than 6,."," In the following we take $\delta_{g}=50$ or 500, and assume that $E_{\rm
SN}$ is shared in equal parts among all the gas particles at overdensity larger than $\delta_g$."
" The choice 0,=50 corresponds to assuming that he virial region of the whole halo is heated and. therefore. hat physical processes like galactic winds. for example. are rather efficiently transferring energy to the IGM."," The choice $\delta_g=50$ corresponds to assuming that the virial region of the whole halo is heated and, therefore, that physical processes like galactic winds, for example, are rather efficiently transferring energy to the IGM."
" Increasing dy, implies two competitive elfects: on one hand. it decreases he number of heated: eas particles. therefore it. increases he amount of extra energy assigned to each of them: on the other hand. the energy is assigned to denser particles. which wave shorter cooling time and. therefore. larger radiative OSSCS."," Increasing $\delta_g$ implies two competitive effects: on one hand, it decreases the number of heated gas particles, therefore it increases the amount of extra energy assigned to each of them; on the other hand, the energy is assigned to denser particles, which have shorter cooling time and, therefore, larger radiative losses."
 As we have already. discussed. introducing cooling causes a too large fraction of gas to be converted into stars.," As we have already discussed, introducing cooling causes a too large fraction of gas to be converted into stars."
 This is a well known feature of hvdrodvnamical simulations. which has been widely discussed in the literature (e.g.. Suginohara Ostriker 1998. BOA).," This is a well known feature of hydrodynamical simulations, which has been widely discussed in the literature (e.g., Suginohara Ostriker 1998, BGW)."
 Even worse. the runaway nature of the cooling process causes its cllicieney to be. highly sensitive to numerical resolution (see Fig.3.. see also Balogh et al.," Even worse, the runaway nature of the cooling process causes its efficiency to be highly sensitive to numerical resolution (see \ref{fi:fc_star}, see also Balogh et al."
 2001)., 2001).
" Therefore. one should be very cautious in the interpretation of results from simulations that do not resolve halos with luminosity well below L,."," Therefore, one should be very cautious in the interpretation of results from simulations that do not resolve halos with luminosity well below $L_\ast$."
 In Figure 5.. we show the effect of the dillerent heating schemes on the resulting cold. fraction. within the virial radius of our simulated structures.," In Figure \ref{fi:fst}, we show the effect of the different heating schemes on the resulting cold fraction within the virial radius of our simulated structures."
 As expected. we find a ecrease of foci when nongravitational heating is included.," As expected, we find a decrease of $f_{\rm
cold}$ when non–gravitational heating is included."
 Llowever. the ellicieney of this suppression of star.formation oes not exclusively depend on the amount of. dumped energy.," However, the efficiency of this suppression of star–formation does not exclusively depend on the amount of dumped energy."
" For instance. imposing an entropy. Loor of 50 keV cm- at cy,=9 (left panel of Fie.5)) is far more ellicient than at 2,=3."," For instance, imposing an entropy floor of 50 keV $^2$ at $z_h=9$ (left panel of \ref{fi:fst}) ) is far more efficient than at $z_h=3$."
 The reason for this is illustrated by the ilferent. patterns of SER. history. that we show in Figure 4..," The reason for this is illustrated by the different patterns of SFR history, that we show in Figure \ref{fi:sfr}."
 The impulsive heating5 at ον=3 causes à suppression of the SER at later epochs. but a fair amount of stars are already inplace at zz (central panel of Fig. 4)).," The impulsive heating at $z_h=3$ causes a suppression of the SFR at later epochs, but a fair amount of stars are already inplace at $z_h$ (central panel of Fig. \ref{fi:sfr}) )."
 Quite interestingly. the results for the two runs with heating at ο=3 produce quite," Quite interestingly, the results for the two runs with heating at $z_h=3$ produce quite"
parents of most presolar grains (Zinner2005)..,parents of most presolar grains \citep{zin1}.
 Extra-mixing in these objects was considered as necessary by various authors (loppeetal.1997:Zinnerοἱ2006:Leck2007:Nittleretal. 2008).," Extra-mixing in these objects was considered as necessary by various authors \citep{hoppe,zinner,heck,nit2}."
. ILowever. a recent. paper (Ixarakasetal.2010.hereafterACS1O) sheds doubts on this requirement. suggesting that slow mass circulation on the RGB might be sufficient.," However, a recent paper \citep[][hereafter KCS10]{kar} sheds doubts on this requirement, suggesting that slow mass circulation on the RGB might be sufficient."
 In order to solve the above dilemma. we have to look al the observational data. asking whether there is anv clear requirement for extra-mixing on the AGB.," In order to solve the above dilemma, we have to look at the observational data, asking whether there is any clear requirement for extra-mixing on the AGB."
 Our answer will be that (his requirement exists and comes primarily from oxide presolar grains (NittlerChoietal.1993:Clavton&Nittler2004: 2008).," Our answer will be that this requirement exists and comes primarily from oxide presolar grains \citep{nit1,choi,clay,nit2}."
. Then one must look for a similarly clear constraint from stars. and we find it in the carbon isotope ratios of C(N) giants.," Then one must look for a similarly clear constraint from stars, and we find it in the carbon isotope ratios of C(N) giants."
 Other pieces of evidence (rom Da stars. C-enhanced metal poor stars. etc.).," Other pieces of evidence (from Ba stars, C-enhanced metal poor stars, etc.),"
 alihough relevant. will not be addressed here for reasons of space.," although relevant, will not be addressed here for reasons of space."
 In order to demonstrate all (his we generalize the calculations bv NBWO3. extending them to cover also RGB stages and including (wo more values of the mmitial mass.," In order to demonstrate all this we generalize the calculations by NBW03, extending them to cover also RGB stages and including two more values of the initial mass."
 In Section 2 we compare our results for RGB phases with constraints coming [rom presolar oxide grains of group 2., In Section 2 we compare our results for RGB phases with constraints coming from presolar oxide grains of group 2.
 In Section 3 we integrate this bv considering extra-mixing also in AGB stages: critical tests come again [rom presolar oxide grains (of group 2. but also of group 1).," In Section 3 we integrate this by considering extra-mixing also in AGB stages; critical tests come again from presolar oxide grains (of group 2, but also of group 1)."
 The evidence from O-rich AGB stars is also discussed., The evidence from O-rich AGB stars is also discussed.
 Finally. in Section 4 we comment on the information coming from C(N) stus and we derive preliminary conclusions. also addressing the physical mechanisms necessary (o drive (he transport.," Finally, in Section 4 we comment on the information coming from C(N) stars and we derive preliminary conclusions, also addressing the physical mechanisms necessary to drive the transport."
 For the sake of comparison will previous works we perform parametric calculations. using the [ree parameters AJ and Tp. as in NBWO3.," For the sake of comparison with previous works we perform parametric calculations, using the free parameters $\dot M$ and $T_P$, as in NBW03."
 We adopt the same NACRE compilation for reaction rates and we compute our extra-nixing results as post-process calculations. starting [rom detailed stellar models by Stranieroetal. (2003)..," We adopt the same NACRE compilation for reaction rates and we compute our extra-mixing results as post-process calculations, starting from detailed stellar models by \citet{stran}. ."
 Masses in the range 1.2, Masses in the range 1.2
abruptly in the ceutral few arcsecouds.,abruptly in the central few arcseconds.
 The nuclear velocity «Ispersjous of wo dE.Ns. VCC 1073 and VCC 1876. are lower than the surrouidiue galaxy. whereas the nuclear velocity dispersion of VCC 1251 is üeher.," The nuclear velocity dispersions of two dE,Ns, VCC 1073 and VCC 1876, are lower than the surrounding galaxy, whereas the nuclear velocity dispersion of VCC 1254 is higher."
 The origin of clei in dEs is largely unknown. but their presence has heeli COLOated to ybal galaxy parameters such as shape aud specific elobilar οuser frequency vden Terudrup 1991: Miller 1998).," The origin of nuclei in dEs is largely unknown, but their presence has been correlated to global galaxy parameters such as shape and specific globular cluster frequency (Ryden Terndrup 1994; Miller 1998)."
 A favored hypotLOSIS IS hat the clei are dense star clusters. possibly renmants of lareer stripxd or 1larassed. jects (Moore 1998).," A favored hypothesis is that the nuclei are dense star clusters, possibly remnants of larger stripped or harassed objects (Moore 1998)."
 Alore work is needed to deernuiue wheher the icniatie profiles preseuted rere are consistent with thesο SCC111105., More work is needed to determine whether the kinematic profiles presented here are consistent with these scenarios.
 Dynamical mass modclinsoκ of classical ellipticals has plzced strone constraints i their origin and evolutioji., Dynamical mass modeling of classical ellipticals has placed strong constraints on their origin and evolution.
 We are m the process of TOCclue frese dE ποιατο data using technicues simular to those described in van der A\larel 1991)., We are in the process of modeling these dE kinematic data using techniques similar to those described in van der Marel (1994).
 We will investigate fhe variation of M/L ratio across our sguuple of ealaxies and as a function of galactic radius within each galaxy., We will investigate the variation of $M/L$ ratio across our sample of galaxies and as a function of galactic radius within each galaxy.
 In addition. we plan to study the positio1i of these dEs in the Fuudiineutal Plaine.," In addition, we plan to study the position of these dEs in the Fundamental Plane."
 These results will be presented in a1 forthcoming paper., These results will be presented in an forthcoming paper.
core and outer convection zone. the so-called «Q dynamo.,"core and outer convection zone, the so-called $\alpha\,\Omega$ dynamo."
" Its efficiency is characterized by the inverse square of the Rossby number P/r,). defined as the ratio between rotational period and convective turnover time. whereas magnetic activity saturates for fast rotators at an activity level of logLx/Lis —3."," Its efficiency is characterized by the inverse square of the Rossby number $P/\tau_{c}$ ), defined as the ratio between rotational period and convective turnover time, whereas magnetic activity saturates for fast rotators at an activity level of $\log L_{\rm X}/L_{\rm bol} \approx -3$ ."
 However. towards hotter. more massive stars the outer convection zone becomes increasingly thinner and therefore the dynamo efficiency declines strongly even for fast rotating stars.," However, towards hotter, more massive stars the outer convection zone becomes increasingly thinner and therefore the dynamo efficiency declines strongly even for fast rotating stars."
 In this scenario Altair’s very low activity level points to the presence of a very inefficient dynamo due to a large Rossby number. i.e. a thin convection zone/small turnover time.," In this scenario Altair's very low activity level points to the presence of a very inefficient dynamo due to a large Rossby number, i.e. a thin convection zone/small turnover time."
 In the regime of mid A-type stars at effective temperatures above Tay=8200 KK the outer convective layer vanishes. às expected theoretically and as indicated by FUSE observations of chromospheric emission lines (?)..," In the regime of mid A-type stars at effective temperatures above $T_{\rm eff}\approx 8200$ K the outer convective layer vanishes, as expected theoretically and as indicated by FUSE observations of chromospheric emission lines \citep{sim02}."
 Consequently. magnetic activity is absent or extremely weak in these stars.," Consequently, magnetic activity is absent or extremely weak in these stars."
 X-ray emission was also detected from several stars of earlier spectral type., X-ray emission was also detected from several stars of earlier spectral type.
 In a comparison study of several hundred ROSAT X-ray sources and positions from the Bright Star Catalog. the detection fraction is fairly constant at a level around 0.1 over the spectral range AAG (?)..," In a comparison study of several hundred ROSAT X-ray sources and positions from the Bright Star Catalog, the detection fraction is fairly constant at a level around 0.1 over the spectral range A6 \citep{schroeder07}."
 It increases strongly towards early B-stars. the realm of wind driven. rays from hot stars. as well as towards early F-stars. the realm of magnetic activity of cool stars.," It increases strongly towards early B-stars, the realm of wind driven X-rays from hot stars, as well as towards early F-stars, the realm of magnetic activity of cool stars."
 However. when compared to late A-type stars. the X-ray detected stars in the spectral range from mid-B to mid-A exhibit harder X-ray spectra and/or significantly higher X-ray luminosities.," However, when compared to late A-type stars, the X-ray detected stars in the spectral range from mid-B to mid-A exhibit harder X-ray spectra and/or significantly higher X-ray luminosities."
 Many of these are pre-main sequence Herbig Ae/Be stars or peculiar Ap/Bp stars. where different intrinsic X-ray generation mechanisms may operate. e.g. a magnetic shear dynamo in young Ae/Be stars (?) or magnetically confined wind-shocks as proposed for the AOp star IQ Aur (?)..," Many of these are pre-main sequence Herbig Ae/Be stars or peculiar Ap/Bp stars, where different intrinsic X-ray generation mechanisms may operate, e.g. a magnetic shear dynamo in young Ae/Be stars \citep{tou95}
 or magnetically confined wind-shocks as proposed for the A0p star IQ Aur \citep{bab97}."
 Otherwise unresolved binary components are suspected to be responsible for the observed X-ray emission., Otherwise unresolved binary components are suspected to be responsible for the observed X-ray emission.
 Altogether. à common origin of their X-ray emission with those of Altair appears rather unlikely.," Altogether, a common origin of their X-ray emission with those of Altair appears rather unlikely."
 In this paper we present a deep observation of Altair., In this paper we present a deep observation of Altair.
 Beside light curves and medium resolution spectra it provides the first well exposed high resolution X-ray spectrum of a late A-type star so far., Beside light curves and medium resolution spectra it provides the first well exposed high resolution X-ray spectrum of a late A-type star so far.
 This unique data set allows us to study X-ray variability. plasma properties like temperatures. emission measures and abundances and to address the topics of coronal structures. Ne/O ratio or dynamo efficiency in a star with a very shallow convection zone.," This unique data set allows us to study X-ray variability, plasma properties like temperatures, emission measures and abundances and to address the topics of coronal structures, Ne/O ratio or dynamo efficiency in a star with a very shallow convection zone."
 Our paper is structured as follows: in refana we describe the data used and analysis methods. in refress we present our results. discuss our findings in refdis and in refcon we give our conclusions.," Our paper is structured as follows; in \\ref{ana} we describe the data used and analysis methods, in \\ref{ress} we present our results, discuss our findings in \\ref{dis} and in \\ref{con} we give our conclusions."
 Altair was observed by during two observing blocks separated by two weeks in October 2007 for a total of roughly kks., Altair was observed by during two observing blocks separated by two weeks in October 2007 for a total of roughly ks.
 obtained useful data in all X-ray instruments. i.e. the EPIC (European Photon Imaging Camera. 112.0 keV) as well as the RGS (Reflection Grating Spectrometer. 338 .)).," obtained useful data in all X-ray instruments, i.e. the EPIC (European Photon Imaging Camera, 12.0 keV) as well as the RGS (Reflection Grating Spectrometer, 38 )."
 The EPIC consists of three detectors. two MOS and one PN. whereas the PN provides a larger effective area and the MOS a higher spectral resolution.," The EPIC consists of three detectors, two MOS and one PN, whereas the PN provides a larger effective area and the MOS a higher spectral resolution."
" For our Altair observation roughly All EPIC instruments were operated in ""Full Frame? mode with the thick filter to block optical/UV loading. the OM (Optical Monitor) had to be closed due to Altair's optical brightness."," For our Altair observation roughly All EPIC instruments were operated in `Full Frame' mode with the thick filter to block optical/UV loading, the OM (Optical Monitor) had to be closed due to Altair's optical brightness."
 Both observations again consist of two exposures each and include a data gap of a few hours due to telemetry problems: see also refle.. which shows the respective X-ray light curves.," Both observations again consist of two exposures each and include a data gap of a few hours due to telemetry problems; see also \\ref{lc}, which shows the respective X-ray light curves."
 The observing times of Altair are summarized in reflog.., The observing times of Altair are summarized in \\ref{log}.
 data analysis was carried out with the Science Analysis System (SAS) version 7.1 (2?) and current calibration files., data analysis was carried out with the Science Analysis System (SAS) version 7.1 \citep{sas} and current calibration files.
 Standard selection criteria were applied to the data and periods of enhanced background due to proton flares were discarded from spectral analysis., Standard selection criteria were applied to the data and periods of enhanced background due to proton flares were discarded from spectral analysis.
 EPIC spectra were derived for each instrument and each observations by combining the respective exposures., EPIC spectra were derived for each instrument and each observations by combining the respective exposures.
" To increase the SNR for the analysis of the RGS data. we extracted high resolutior spectra only from the PSF core merged all exposures using the tool ""rescombine."," To increase the SNR for the analysis of the RGS data, we extracted high resolution spectra only from the PSF core merged all exposures using the tool '."
 For line fitting purposes we used the CORA program (?).. using ai identical line. width and assuming a Lorentzian line shape.," For line fitting purposes we used the CORA program \citep{cora}, using an identical line width and assuming a Lorentzian line shape."
 This analysis utilizes total spectra. Le. we determine one background (+continuum) level in the respective region around each line or group of lines.," This analysis utilizes total spectra, i.e. we determine one background (+continuum) level in the respective region around each line or group of lines."
 Theoretical line emissivities were calculated with the CHIANTI ((4.2) code (??)..," Theoretical line emissivities were calculated with the CHIANTI (4.2) code \citep{chi,anti}."
 Global spectral analysis was performed with XSPEC V11.3 (?) using multi-temperature models with variable abundances as calculated with the APEC code (?).., Global spectral analysis was performed with XSPEC V11.3 \citep{xspec} using multi-temperature models with variable abundances as calculated with the APEC code \citep{apec}.
 Data of the individual detectors were analyzed simultaneously. but spectra were not co-added.," Data of the individual detectors were analyzed simultaneously, but spectra were not co-added."
 We find that three temperature components best deseribe the data and that no additional absorption column is required., We find that three temperature components best describe the data and that no additional absorption column is required.
 In our models temperatures. emission measures (EM= [ncnydV) and abundances of elements with significant features in the measured X-ray spectra are free parameters. other elemental abundances were set to solar values.," In our models temperatures, emission measures $EM=\int n_{e}n_{H}dV$ ) and abundances of elements with significant features in the measured X-ray spectra are free parameters, other elemental abundances were set to solar values."
 All elemental abundances are given relative to solar photospheric values from ?.., All elemental abundances are given relative to solar photospheric values from \citet{grsa}.
 Some of the fit parameters are interdependent. especially the absolute values of emission measure and abundances of elements with emission lines in the respective temperature range.," Some of the fit parameters are interdependent, especially the absolute values of emission measure and abundances of elements with emission lines in the respective temperature range."
 Consequently. models with different absolute values of these parameters. but only marginal," Consequently, models with different absolute values of these parameters, but only marginal"
In the ISM resistive and diffusive damping become important near resistive scales.,In the ISM resistive and diffusive damping become important near resistive scales.
 llowever. it is well known that collisionless damping effects are also present (Lvsak&etal.2005).. ancl quite possibly dominate over collisional damping in larger scales near (he ion Larmor radius.," However, it is well known that collisionless damping effects are also present \citep{lysak96,bale05}, and quite possibly dominate over collisional damping in larger scales near the ion Larmor radius."
 The collisional damping in the present work is understood as a heuristic approach that facilitates analvsis of the effects of dillerent damping regimes on the statistics of electron densitv fluctuations., The collisional damping in the present work is understood as a heuristic approach that facilitates analysis of the effects of different damping regimes on the statistics of electron density fluctuations.
 By varving the ratio of resistive and diffusive damping we can. as suggested above. control the (wpe of structure present in the turbulence.," By varying the ratio of resistive and diffusive damping we can, as suggested above, control the type of structure present in the turbulence."
 This allows us to isolate and study the statistics associated will each (wpe of structure., This allows us to isolate and study the statistics associated with each type of structure.
 It also allows us to assess and examine (he tvpe of environment conducive to formation of the structure., It also allows us to assess and examine the type of environment conducive to formation of the structure.
 We consider regimes with large and small camping parameters. enabling us to explore damping effects on structure formation across a range from inertial to cdissipative.," We consider regimes with large and small damping parameters, enabling us to explore damping effects on structure formation across a range from inertial to dissipative."
 Future work will address collisionless damping in greater detail., Future work will address collisionless damping in greater detail.
 The coherent structures observed in numerical solutions of decaving IAW. turbulence. whether elongated sheets or localized filaments. are similar to structures observed in decaving MID turbulence. as in Ixinnev&MeWilliams(1995).," The coherent structures observed in numerical solutions of decaying KAW turbulence, whether elongated sheets or localized filaments, are similar to structures observed in decaying MHD turbulence, as in \citet{kinney95}."
.. In that work. the flow field initially eives rise to sheet-like structures.," In that work, the flow field initially gives rise to sheet-like structures."
 After selective decay of the velocity field energy. the system evolves into a state with sheets and filaments.," After selective decay of the velocity field energy, the system evolves into a state with sheets and filaments."
 During the merger of like-signecl filaments. large-amplibicde sheets arise. limited (o the region between (he merging filaments.," During the merger of like-signed filaments, large-amplitude sheets arise, limited to the region between the merging filaments."
 These short-lived sheets exist in addition to the long-lived sheets not associated with the merger of filaments., These short-lived sheets exist in addition to the long-lived sheets not associated with the merger of filaments.
 In the two-field NAW svstem. however. there is no flow: the sheet and filament eeneralion is due to a dillerent mechanism. of which the filament generation has previously been discussed (Terry&Smith2007).," In the two-field KAW system, however, there is no flow; the sheet and filament generation is due to a different mechanism, of which the filament generation has previously been discussed \citep{terry-smith07}."
. Other work (Biskamp&Welter1989:Politanoetal.1989). observed the spontaneous eeneralion of current sheets and filaments in numerical solutions. with both Orszag-Toug vortex and randomized initial conditions.," Other work \citep{biskamp89,politano89} observed the spontaneous generation of current sheets and filaments in numerical solutions, with both Orszag-Tang vortex and randomized initial conditions."
 These 2D reduced MILD numerical solutions modeled the evolution of magnetic flux ancl vorlicity with collisional dissipation coefficients η. the resislivily. and v. the kinematic viscosity.," These 2D reduced MHD numerical solutions modeled the evolution of magnetic flux and vorticity with collisional dissipation coefficients $\eta$, the resistivity, and $\nu$, the kinematic viscosity."
 The magnetic Prandil number. 7/7. was set to unitv.," The magnetic Prandtl number, $\nu / \eta$, was set to unity."
 These systems are incompressible and not suitable for modeling the KAW svstem we consider here thev do however illustrate the ubiquity of current sheets ancl filaments. and serve as points of comparison.," These systems are incompressible and not suitable for modeling the KAW system we consider here – they do however illustrate the ubiquity of current sheets and filaments, and serve as points of comparison."
 For Orszag-Tane-like initial conditions with large-scale flux tubes smooth in profile. current sheets are preferred at the interfaces between tubes.," For Orszag-Tang-like initial conditions with large-scale flux tubes smooth in profile, current sheets are preferred at the interfaces between tubes."
 Tearing instabiliies can give rise (o filamentary current structures that persist for long times. bul the large-scalee ancl smoothness of flux tubes do not exgive rise (o stronge current. filaments," Tearing instabilities can give rise to filamentary current structures that persist for long times, but the large-scale and smoothness of flux tubes do not give rise to strong current filaments"
where Farther from the Sun. Agi22zly. and ας deviates from the Spitzer value.,"where Farther from the Sun, $\lambda_{\rm mfp}\gtrsim l_T$, and $q_{\rm e}$ deviates from the Spitzer value."
 We follow in taking the collisionless heat flux in this region to be approximately where αμ Is a constant that we treat as a free parameter.," We follow \cite{hollweg74a,hollweg76}
 in taking the collisionless heat flux in this region to be approximately where $\alpha_{\rm H}$ is a constant that we treat as a free parameter."
 ? argued that the transition between the collistonal and collisionless regimes occurs at the radius at which Ayr)~ 0.5r., \cite{hollweg76} argued that the transition between the collisional and collisionless regimes occurs at the radius at which $\lambda_{\rm mfp} \simeq 0.5 r$ .
 To interpolate smoothly between the two regimes. we set the electron heat flux equal to where and rj is a constant that we choose to coincide with the radius at which Ag=0.5. For the numerical solutions presented in Sections 4+ and 5.7.. we set rjj=5R.. and confirm post facto that À20.5r at r=rj (see Figure 6))," To interpolate smoothly between the two regimes, we set the electron heat flux equal to where and $r_{\rm H}$ is a constant that we choose to coincide with the radius at which $\lambda_{\rm mfp} = 0.5 r$ For the numerical solutions presented in Sections \ref{sec:solution}
 and \ref{sec:swani_cyclotron}, we set $r_{\rm H} = 5 R_{\sun}$, and confirm post facto that $\lambda
\simeq 0.5 r$ at $r=r_{\rm H}$ (see Figure \ref{fig:swq}) )."
 If the proton temperature-anisotropy ratio becomes either too large or too small. the plasma becomes unstable.," If the proton temperature-anisotropy ratio becomes either too large or too small, the plasma becomes unstable."
 Spacecraft measurements show that the values of R found in the solar wind are bounded from below by the instability threshold of the oblique firehose mode and from above by the instability threshold of the mirrormode (22? )..," Spacecraft measurements show that the values of $R$ found in the solar wind are bounded from below by the instability threshold of the oblique firehose mode and from above by the instability threshold of the mirrormode \citep{kasper02,hellinger06,bale09}. ."
" In particular. most of the measured values of & correspond to plasma parameters for which yy,< where Yn is the maximum growth rate of the oblique 1070.firehose or mirror instability and £2, 1s the proton cyclotron frequency."," In particular, most of the measured values of $R$ correspond to plasma parameters for which $\gamma_{\rm max} < 10^{-3}\Omega_{\rm p}$, where $\gamma_{\rm
 max}$ is the maximum growth rate of the oblique firehose or mirror instability and $\Omega_{\rm p}$ is the proton cyclotron frequency."
" The value ofR for which ys;=1070, Is approximately for the mirror instability. and ‘pews for the oblique firehose instability (?).."," The value of $R$ for which $\gamma_{\rm max} = 10^{-3} \Omega_{\rm p}$ is approximately for the mirror instability, and approximately for the oblique firehose instability \citep{hellinger06}."
 Presumably. when the plasma becomes unstable. small-scale electromagnetic fluctuations grow and enhance the proton pitch-angle scattering rate. preventing the temperature anisotropy from increasing further.," Presumably, when the plasma becomes unstable, small-scale electromagnetic fluctuations grow and enhance the proton pitch-angle scattering rate, preventing the temperature anisotropy from increasing further."
 We incorporate this effect into our model through the term vVjjg. 1n Equation (22)). with =Rj. and Re=max(Ry.1079).," We incorporate this effect into our model through the term $\nu_{\rm inst}$ in Equation \ref{eq:nupp}) ), with $\nu_0 = 0.02\sqrt{G M_{\sun}/R_{\sun}^3}$, and $\overline{ R}_{\rm f} =
\max ( R_{\rm f}, 10^{-6})$."
" A. similar approach was 0.02,/GM.employed by ? in numerical simulations of accretion flows around black holes.", A similar approach was employed by \cite{sharma06a} in numerical simulations of accretion flows around black holes.
 The Sun launches different types of waves that propagate outward into the solar atmosphere., The Sun launches different types of waves that propagate outward into the solar atmosphere.
 In our model. we retain only the non-compressive Alfvénn wave (AW). in part for simplicity and in part because the AW is the most promising wave type for transporting energy over large distances into the corona and solar wind (22222)..," In our model, we retain only the non-compressive Alfvénn wave (AW), in part for simplicity and in part because the AW is the most promising wave type for transporting energy over large distances into the corona and solar wind \citep{barnes66,velli89,matthaeus99b,suzuki05,cranmer05}."
 For AW fluctuations. the fluctuating velocity vector óv and magnetic field vector 6B lie in the plane perpendicular to By.," For AW fluctuations, the fluctuating velocity vector $\delta \bm{v}$ and magnetic field vector $\delta \bm{B}$ lie in the plane perpendicular to $\bm{B}_0$ ."
 We define the Elsassérr variables and. as mentioned previously. take By to point away from the Sun.," We define the Elsassërr variables and, as mentioned previously, take $\bm{B}_0$ to point away from the Sun."
 In the small-amplitude limit. z fluctuations are AWs that propagate with an outward radial velocity of U|v4. while the z fluctuations are AWs that propagate with a radial velocity Uva.," In the small-amplitude limit, $\bm{z}^+$ fluctuations are AWs that propagate with an outward radial velocity of $U + v_{\rm A}$, while the $\bm{z}^-$ fluctuations are AWs that propagate with a radial velocity $U-v_{\rm A}$."
 Near the Sun. U—v4 and z fluctuations propagate towards smaller 7.," Near the Sun, $U<v_{\rm A}$ and $z^-$ fluctuations propagate towards smaller $r$."
 To a good approximation. AWs in the solar corona and solar wind can be described within the framework of reduced MHD (????)..," To a good approximation, AWs in the solar corona and solar wind can be described within the framework of reduced MHD \citep{kadomtsev74,strauss76,zank92,schekochihin09}."
 In reduced MHD. the outward-propagating z waves generated by the Sun do not interact with one another.," In reduced MHD, the outward-propagating $z^+$ waves generated by the Sun do not interact with one another."
 However. we assume that most of the AW energy is at periods of tens of minutes to hours. which makes the wavelengths in the radial direction. sufficiently long that the AWs undergo significant non-WKB reflection. converting some of the 2 waves into z waves (?2).," However, we assume that most of the AW energy is at periods of tens of minutes to hours, which makes the wavelengths in the radial direction sufficiently long that the AWs undergo significant non-WKB reflection, converting some of the $z^+$ waves into $z^-$ waves \citep{heinemann80, velli93}."
 Interactions between fromz* and zscales fluctuations then cause wave energy to cascade large tto small scales (2222?)..," Interactions between $z^+$ and $z^-$ fluctuations then cause wave energy to cascade from large scales to small scales \citep{iroshnikov63,kraichnan65,velli89,
 matthaeus99b,vanballegooijen11}."
 At sufficiently small scales. the z fluctuations dissipate.," At sufficiently small scales, the $z^\pm$ fluctuations dissipate."
" Although some reflection occurs. we assume that and neglect the contribution of z to the wave energy density ""A.which is then given by where z.is the rms amplitude of <> fluctuations."," Although some reflection occurs, we assume that and neglect the contribution of $z^-$ to the wave energy density ${\cal E}_{\rm w}$,which is then given by where $z^+_{\rm rms}$ is the rms amplitude of $z^+$ fluctuations."
 To describe the cascade of wave energy in the presence of wave reflections. we adopt the phenomenological model of ?.. which was later extended by ?— to account for the solar-wind outflow velocity.," To describe the cascade of wave energy in the presence of wave reflections, we adopt the phenomenological model of \cite{dmitruk02}, , which was later extended by \cite{chandran09c} to account for the solar-wind outflow velocity."
 The essence of these models is to balance the rate at which z waves are produced by wave reflections against the rate at which the z waves cascade and dissipate via interactions with z waves., The essence of these models is to balance the rate at which $z^-$ waves are produced by wave reflections against the rate at which the $z^-$ waves cascade and dissipate via interactions with $z^+$ waves.
" This balance leads to the following estimate for the rms amplitude of <7 (2): where L, is the correlation length (outer scale) of the Alfvénnie fluctuations in the plane perpendicular to By.", This balance leads to the following estimate for the rms amplitude of $z^-$ \citep{chandran09c}: where $L_{\perp}$ is the correlation length (outer scale) of the Alfvénnic fluctuations in the plane perpendicular to $\bm{B}_0$ .
 Therate at which energy cascades and dissipates per unit volume is then wherecy is a dimensionless number., Therate at which energy cascades and dissipates per unit volume is then where$c_{\rm d}$ is a dimensionless number.
" Since our estimate of IS proportional to LZ). the value of Qin equation (43)) is zi,independent of Lj.Because of Equation (40)). we have omittedH a term ezi-+(z,,)-—? that isH some timesH includedH inH the turbulent heating rate (?).."," Since our estimate of $z^-_{\rm rms}$ is proportional to $L_{\perp}$ the value of $Q$in equation \ref{eq:Q}) ) is independent of $L_\perp$ .Because of Equation \ref{eq:zpzm}) ), we have omitted a term $\propto z_{\rm
 rms}^+ \,(z_{\rm rms}^-)^2$ that is some times included in the turbulent heating rate \citep{hossain95}. ."
investigation of the braking index for a set of realistic EOS should be performed.,investigation of the braking index for a set of realistic EOS should be performed.
 A higher spin-down rate than in isolated pulsars might be possible for rotating neutron stars with mass accretion., A higher spin-down rate than in isolated pulsars might be possible for rotating neutron stars with mass accretion.
 Tn that case. at high rotation frequency the angular momentum transfer frou accreting matter and the influence of maenetic fields cau then be neglected (Shapiro Teukolsky 1983) so that the evolution of the angular velocity is determined by the dependence of the moment of inertia on the total mass. 1.6. barvou unuuber. where J={οcoust has heen assuuced.," In that case, at high rotation frequency the angular momentum transfer from accreting matter and the influence of magnetic fields can then be neglected (Shapiro Teukolsky 1983) so that the evolution of the angular velocity is determined by the dependence of the moment of inertia on the total mass, i.e. baryon number, where $J=I~\Omega={\rm const}$ has been assumed."
 Tn Fig., In Fig.
 9 we consider the change ofthe pulsar timine due to lass accretion with a constaut accretion rate Np for fixed otal augular momentum as a functiou of the total barvon uuuboer., \ref{fig9} we consider the change of the pulsar timing due to mass accretion with a constant accretion rate $\dot N_B/N_B$ for fixed total angular momentum as a function of the total baryon number.
 Tere the change four spiu-down to spin-up behaviour durius the ιν evolution sjeuals the decomfinemenut rausition., Here the change from spin-down to spin-up behaviour during the pulsar evolution signals the deconfinement transition.
" When the oulsar has developed. a quark matter core then the chanec of the monent of inertia due to further lass accretion is uceligible aud is no lonegcr imfüuence ou the pulsar Πιο,", When the pulsar has developed a quark matter core then the change of the moment of inertia due to further mass accretion is negligible and has no longer influence on the pulsar timing.
 However. i real systems the transfer of angular moment from the accreting matter cau lead to a spiu-up already.," However, in real systems the transfer of angular momentum from the accreting matter can lead to a spin-up already."
 Then the transition to the quark matter core reeime should be observable as an iucrease im the spin-wp rate., Then the transition to the quark matter core regime should be observable as an increase in the spin-up rate.
 It will be interesting to investigate in the future whether e.g. low-mass A-rayv binarics (LAINBs) with mass accretion might be discussed as possible candidates for rapidly rotating neutron stars for which consequences of the trausition to the quark core regime due to mass accretion. nüeght be detected., It will be interesting to investigate in the future whether e.g. low-mass X-ray binaries (LMXBs) with mass accretion might be discussed as possible candidates for rapidly rotating neutron stars for which consequences of the transition to the quark core regime due to mass accretion might be detected.
 Recently. quasi-periodic brightuess oscillations (ΟΡΟs). with frequeuces up. to ~1200 Uz have been observed (Lamb et al.," Recently, quasi-periodic brightness oscillations (QPO's) with frequences up to $\sim 1200$ Hz have been observed (Lamb et al."
 1998) which eutail new mass aud radius coustraimts for compact objects., 1998) which entail new mass and radius constraints for compact objects.
 Note iu this context that the assumption of a decoufined. matter iuterior of the compact star din sole LAINBs as e.g. SAX JIsü8.1-3658 (Li et al., Note in this context that the assumption of a deconfined matter interior of the compact star in some LMXBs as e.g. SAX J1808.4-3658 (Li et al.
 1999) seems to be more consistent than that of an ordinary hidronic inatter mterior., 1999) seems to be more consistent than that of an ordinary hadronic matter interior.
 It has been demonstrated. through the example of the decoufineiuent transition from laconic to (quar- latter. that the rotational characteristics of neutron starpA (braking iudex. spin-down rate) are sensitive to chiaugey. of their inner structure aud can thus be investigated i- order to detect structural phase trausitions.," It has been demonstrated, through the example of the deconfinement transition from hadronic to quark matter, that the rotational characteristics of neutron stars (braking index, spin-down rate) are sensitive to changes of their inner structure and can thus be investigated in order to detect structural phase transitions."
 The theoretical basis for the present work was a perturbation method for the solution of the Liustei- equations for axial sviunietry which allows us to calculate the «itxibutiou of differeut rotational effects to. the change of the moment of inertia., The theoretical basis for the present work was a perturbation method for the solution of the Einstein equations for axial symmetry which allows us to calculate the contribution of different rotational effects to the change of the moment of inertia.
 This quantity cau be used as a tool for the investigation of the changes in the rotation timing for different scenarios of the neutrou star evolutiou., This quantity can be used as a tool for the investigation of the changes in the rotation timing for different scenarios of the neutron star evolution.
 The eviation of the braking iudex from the value ο=3 GQuaenetic dipole radiation) as a function of he angular velocity has beeu suggested as a possible signal for the deconfinement transition aud the occurrence of a quark matter core m pulsars., The deviation of the braking index from the value $n=3$ (magnetic dipole radiation) as a function of the angular velocity has been suggested as a possible signal for the deconfinement transition and the occurrence of a quark matter core in pulsars.
 We have reivestigated this signal within our approach and could show that the magnitude of this deviation is correlated with the size of the quark. core. since the influence of the Ae phase crust on such Xocesses Is negligible.," We have reinvestigated this signal within our approach and could show that the magnitude of this deviation is correlated with the size of the quark core, since the influence of the $Ae$ phase crust on such processes is negligible."
 For neutron stars with amass accretion. we have sugecsted that under the assumption of total angular nolenti conservation a flip from spin-down to spiu-up behaviour signals the appearance of a quark matter core.," For neutron stars with mass accretion, we have suggested that under the assumption of total angular momentum conservation a flip from spin-down to spin-up behaviour signals the appearance of a quark matter core."
" A more detailed investigation is necessary to identify »ossible candidates of rotating compact objects with mass accretion (see e.g, Lambetal. (1998))) for which the sugeested deconfinenieut «eua could be relevant.", A more detailed investigation is necessary to identify possible candidates of rotating compact objects with mass accretion (see e.g. \cite{rxte}) ) for which the suggested deconfinement signal could be relevant.
 Although the quautitative details of the reported decoufinenient signals are quite model-dependeut and nuelt chanee when oue uses more realistic equations of, Although the quantitative details of the reported deconfinement signals are quite model-dependent and might change when one uses more realistic equations of
of planet to the | bar pressure level in the atmosphere. 7 is heating efficiency. and p is ihe mean densitv of planet.,"of planet to the 1 bar pressure level in the atmosphere, $\eta$ is heating efficiency, and $\rho$ is the mean density of planet."
 Here A(£)—1—z-2621<] is a non-liner potential energy reduction factor due to the stellar tidal lorce (Erkaev οἱ al., Here $K(\xi)=1-\frac{3}{2\xi}+\frac{1}{2\xi^{2}} < 1$ is a non-liner potential energy reduction factor due to the stellar tidal force (Erkaev et al.
" 2007). and ς=df; Roche lobe boundary distance. where A, is (he mass of star and d is the orbital clistance."," 2007), and $\xi=d(\frac{4\pi\rho}{9M_{*}})^{1/3}$ is Roche lobe boundary distance, where $M_{*}$ is the mass of star and $d$ is the orbital distance."
 Dased on the hydrodvnamic model of Watason et al. (, Based on the hydrodynamic model of Watason et al. (
1981). Lammer et al. (,"1981), Lammer et al. ("
"2003) estimated o=3. but it could be unit according to recent hydrodynamic models which showed that the expansion radius could be 1 - 1.5 A, (Yelle 2004: Miwray-Clay οἱ al.","2003) estimated $\beta=3$, but it could be unit according to recent hydrodynamic models which showed that the expansion radius could be 1 - 1.5 $R_{p}$ (Yelle 2004; Murray-Clay et al."
 2009)., 2009).
 Lammers et al. (, Lammers et al. (
2009) also thought the mass loss rate was overestimated with 3= by Barralfe οἱ al. (,2009) also thought the mass loss rate was overestimated with $\beta=3$ by Barraffe et al. (
2004).,2004).
 With the full energy-Iimited condition. the heating efficiency y=100560.," With the full energy-limited condition, the heating efficiency $\eta=100\%$."
 In fact. the heating elliciency is about25%.," In fact, the heating efficiency is about."
. In this paper. we set 2=L1 and heating effideney 7)=0.1—0.25 (Murrav-Clay οἱ al.," In this paper, we set $\beta=1.1$ and heating efficiency $\eta=0.1-0.25$ (Murray-Clay et al."
 2009 and refer therein)., 2009 and refer therein).
 Thus. Equation (23) describes a mocified enerev-limiil approach.," Thus, Equation (23) describes a modified energy-limit approach."
 For comparison with the energv-Iimited mass loss rate. we calculated the mass loss rate of WD 189733b as a function of UV. Πας and the results is shown in Figure 6 (left panel).," For comparison with the energy-limited mass loss rate, we calculated the mass loss rate of HD 189733b as a function of UV flux and the results is shown in Figure 6 (left panel)."
 The mass loss rates given in our models are a [actor of 3-10 lower than those calculated bv Equation (23) at the assumption of A(£)=1 and η=0.1—0.25., The mass loss rates given in our models are a factor of 3-10 lower than those calculated by Equation (23) at the assumption of $k(\xi)=1$ and $\eta=0.1-0.25$.
 For completeness we also caleulated the single-f£luid model (Miuray-Clay. et al., For completeness we also calculated the single-fluid model (Murray-Clay et al.
 2009) ancl [ound a systemic difference in comparing with the mass loss rates predicted by the model of this paper., 2009) and found a systemic difference in comparing with the mass loss rates predicted by the model of this paper.
 For sinele-fhud model. it can predict a comparable value for M when the heating elliciency in the enerey-limit method is decreased to 4=0.1 (the left panel of Fig.6).," For single-fluid model, it can predict a comparable value for $\dot{M}$ when the heating efficiency in the energy-limit method is decreased to $\eta=0.1$ (the left panel of Fig.6)."
 However. this is not consistent with our results.," However, this is not consistent with our results."
 The mass loss rates calculated by single-fluid model is still higher than these of our model., The mass loss rates calculated by single-fluid model is still higher than these of our model.
" With the increase of Fri. (he ratios of Masa/Minispay, decrease [rom 5CFj4:2450) to 2.50F).,.= 10°)."," With the increase of $F_{UV}$, the ratios of $\dot{M}_{single}/\dot{M}_{this paper}$ decrease from $F_{UV}$ =450) to $F_{UV}=10^{5}$ )."
 As discussed in Section 3.2. our results fit the observations well.," As discussed in Section 3.2, our results fit the observations well."
 Thus. a lower heating efficiency is required for hieh ionized wind.," Thus, a lower heating efficiency is required for high ionized wind."
 Our caleulation results show that the winds are highlv ionized aud almost composed, Our calculation results show that the winds are highly ionized and almost composed
(he mass-luminosily GUL) relation predicted by canonical evolutionary (racks by Castellani et al. (,the mass-luminosity $ML$ ) relation predicted by canonical evolutionary tracks by Castellani et al. (
1992. hereafter CCS).,"1992, hereafter CCS)."
 This theoretical framework also provides (he boundaries of the instability strip., This theoretical framework also provides the boundaries of the instability strip.
 In subsequent papers. we presented similar results. but for different masses. huninosiües. and helium contents.," In subsequent papers, we presented similar results, but for different masses, luminosities, and helium contents."
 That set of models has been huther implemented with new computations lor the present investigation., That set of models has been further implemented with new computations for the present investigation.
 The assumptions on the input physics and computing procedures have already been presented (see Dono οἱ al., The assumptions on the input physics and computing procedures have already been presented (see Bono et al.
 1999a. Paper E: Dono et al.," 1999a, Paper I; Bono et al."
 2000a. Paper HI: Dono et al.," 2000a, Paper III; Bono et al."
 2000c. Paper VI). and will not be discussed here.," 2000c, Paper VI), and will not be discussed here."
 The complete set of available fundamental models with Z=0.02 is listed in Table1!., The complete set of available fundamental models with Z=0.02 is listed in Table.
. For each given mass. several huminositw levels are explored. (hus covering current uncertainties on canonical |L relations (Castellani et al.," For each given mass, several luminosity levels are explored, thus covering current uncertainties on canonical $ML$ relations (Castellani et al."
 1992: Dono et al., 1992; Bono et al.
 2000b: hereafter DO). as well as accounting for the occurrence of “overluminous” stellar structures as produced by convective core overshooting and/or mass loss.," 2000b: hereafter B0), as well as accounting for the occurrence of “overluminous” stellar structures as produced by convective core overshooting and/or mass loss."
 The Period-Luminosity distribution of all the Z=0.02 [fundamental pulsators is shown in Fie., The Period-Luminosity distribution of all the $Z$ =0.02 fundamental pulsators is shown in Fig.
 1. where solid points display the models computed adopting the BO canonical ALL relation (see Section 3).," 1, where solid points display the models computed adopting the B0 canonical $ML$ relation (see Section 3)."
 Following the procedure discussed in our previous works. the bolometric light curve of ihe pulsating models was (ranslormed into the observational bands DVRLS by means of model aüimospheres by Castelli et al. (," Following the procedure discussed in our previous works, the bolometric light curve of the pulsating models was transformed into the observational bands $BVRIJK$ by means of model atmospheres by Castelli et al. ("
1997a.. 1991b). and these light curves are used to derive for each pulsator the magnitude-averaged (M;) and the intensity-averaged (Mj) magnitudes over the pulsation evele.,"1997a, 1997b), and these light curves are used to derive for each pulsator the magnitude-averaged $M_i)$ and the intensity-averaged $\langle M_i\rangle$ magnitudes over the pulsation cycle."
 Figure shows the ensuing CU) and CU) magnitudes as a function of the period., Figure shows the ensuing $\langle M_V\rangle$ and $\langle M_K\rangle$ magnitudes as a function of the period.
 As expected. the intrinsic scatter of the Period-\agnitude distribution. which for anv given ML relation is due to the finite width of the instability strip. shows a substantial decrease when passing [rom visual to near-intrarecl magnitudes.," As expected, the intrinsic scatter of the Period-Magnitude distribution, which for any given $ML$ relation is due to the finite width of the instability strip, shows a substantial decrease when passing from visual to near-infrared magnitudes."
 Concerning the distribution of the fundamental pulsators in the color-magnitude diagram. we show in Fig.," Concerning the distribution of the fundamental pulsators in the color-magnitude diagram, we show in Fig."
" 3 the (V4, magnitudes versus the (Mj)—CV) colors."," 3 the $\langle M_V\rangle$ magnitudes versus the $\langle
M_B\rangle -\langle M_V\rangle$ colors."
 It is well known that a restatement of the Stelan’s law for pulsating variables vields that the pulsation period is uniquely defined by the mass. the Iuminosity. ancl the effective temperature of (he variable.," It is well known that a restatement of the Stefan's law for pulsating variables yields that the pulsation period is uniquely defined by the mass, the luminosity, and the effective temperature of the variable."
 Once bolometric corrections and color-temperature relations are adopted. (his means that (he pulsator absolute magnitude AM; in a given photonmetric bandpass is à function of the pulsator period. stellar mass. and color index [CT]. i.e. As a matter of fact. a linear interpolation through all the models listed in Table 1 gives.," Once bolometric corrections and color-temperature relations are adopted, this means that the pulsator absolute magnitude $M_i$ in a given photometric bandpass is a function of the pulsator period, stellar mass, and color index $CI$ ], i.e., As a matter of fact, a linear interpolation through all the models listed in Table 1 gives,"
meet (he MSN criteria in order (to be included in (he MSN sample.,meet the MSN criteria in order to be included in the MSN sample.
 There are 68.203 spectra from 18.512 individual stars in the MSN sample.," There are 68,203 spectra from 18,512 individual stars in the MSN sample."
 The spectral (wpe distribution of (1ο MISN spectra is also shown in Figure 3.., The spectral type distribution of the MSN spectra is also shown in Figure \ref{fig:spt_by_s2n}.
 For completeness. we note that [or ~20% of the stars in the original sample. the individual component spectra have low SNR that did not meet the MSN cut.," For completeness, we note that for $\sim$ of the stars in the original sample, the individual component spectra have low SNR that did not meet the MSN cut."
 This LSN sample may well contain flares but. cannot be used in the detailed analvsis presented here., This LSN sample may well contain flares but cannot be used in the detailed analysis presented here.
 The spectral (wpe of each star was determined by Westetal.(2008). [rom the co-acdded DR5 spectra using the Hammer spectral (vping facility (Coveyetal.2007)., The spectral type of each star was determined by \citet{West2008} from the co-added DR5 spectra using the Hammer spectral typing facility \citep{Covey2007}.
. The Ilamuiner uses measurements of molecular bands and line strengtlis to estimate a spectral (wpe and is accurate to within one sublype., The Hammer uses measurements of molecular bands and line strengths to estimate a spectral type and is accurate to within one subtype.
 We adopted the Westοἱal.(2008). tvpes for our analysis of the individual component spectra. which have lower SNR. than (he co-added spectra.," We adopted the \citet{West2008} types for our analysis of the individual component spectra, which have lower SNR than the co-added spectra."
 The Ilamuner is tuned (o identifv and classify M dwarls during quiescence by fitting templates to molecular band depths and overall spectral shape., The Hammer is tuned to identify and classify M dwarfs during quiescence by fitting templates to molecular band depths and overall spectral shape.
 Large flares produce optical continuum emission that veils (he molecular features and makes the spectral shape significantly bluer., Large flares produce optical continuum emission that veils the molecular features and makes the spectral shape significantly bluer.
 Therelore. we verified that the sample does not exclude continuum flares that cause the star to be misidentifiel bv the Hammer.," Therefore, we verified that the sample does not exclude continuum flares that cause the star to be misidentified by the Hammer."
 We spectral tvped the dM4.5e flare star YZ CAH curing equiescencee and curing a giant flare of AU ~ -6 mags (Ixowalskietal.2010)., We spectral typed the dM4.5e flare star YZ CMi during quiescence and during a giant flare of $\Delta$ U $\sim$ -6 $mags$ \citep{Kowalski2010}.
. The quiescent spectral tvpe returned by the ILammer was MA. while during some stages of the flare. (vpes of M2 and. AIS were found. still reasonably close to the quiet value.," The quiescent spectral type returned by the Hammer was M4, while during some stages of the flare, types of M2 and M3 were found, still reasonably close to the quiet value."
 To further establish Chat the spectral (vpe determination was not biased against flares. we also searched [or flares in all spectroscopic objects whose photometric colors (taken al a clilferent time than the spectroscopy) were consistent with M dwarls Q09).. but were not identified as M chwarls by the Hammer.," To further establish that the spectral type determination was not biased against flares, we also searched for flares in all spectroscopic objects whose photometric colors (taken at a different time than the spectroscopy) were consistent with M dwarfs \citep{West2008,Kowalski2009}, but were not identified as M dwarfs by the Hammer."
 There were no large. flares identified among these objects.," There were no large, continuum-enhancement flares identified among these objects."
 These (wo tests confirm that we did not select against continuum flares by relying on automatic spectral typing., These two tests confirm that we did not select against continuum flares by relying on automatic spectral typing.
 The unique SDSS data set provides an opportunity lo observe the spectroscopic time evolution of a large number of (lares., The unique SDSS data set provides an opportunity to observe the spectroscopic time evolution of a large number of flares.
 It does. however. present some challenges.," It does, however, present some challenges."
 First. the total length of consecutive observations is generally short (45 minutes). and if a flare does occur. it may start before or al any time during the individual observations.," First, the total length of consecutive observations is generally short $\sim$ 45 minutes), and if a flare does occur, it may start before or at any time during the individual observations."
 Second. the," Second, the"
Behind the expanding bright frout. we detect localized reeious of secoudary dinnmüus (Figure .[)).,"Behind the expanding bright front, we detect localized regions of secondary dimming (Figure \ref{fig:f4}) )."
 Secoucdary dinniues were originallv reported bv Thompsonetal.(2000)., Secondary dimmings were originally reported by \cite{Thompson00b}.
.. Such dimunines may be uuderstood iu a wave contest (ee.asinWuetal.2001).. since a rarefactioa shock develops trailing a large-amplitude perturbatio (Landau&Lifshitz1987).," Such dimmings may be understood in a wave context \citep[e.g. as in][]{Wu01}, since a rarefaction shock develops trailing a large-amplitude perturbation \citep{Landau87}."
 Tlowever. such οήτο;ne would be short-lived. with a duration oun Alfvén timescales (~ few muuutes) contrary to observation:τν (Cliverctal.2005:Delumée2007).," However, such dimmings would be short-lived, with a duration on Alfvénn timescales $\sim$ few minutes) contrary to observations \citep{Cliver05,Delannee07}."
. Althoug SCCOidary ciines have a uuch lower average intensity level (e.g. ~ DU ¢‘outs/pixel) before the eveut. compared to tlre core cilning ( 10! countspixel). the relative magnitudes of both the core and secondary ολος are substantial (ee. ~ and ~20%.. respectively).," Although secondary dimmings have a much lower average intensity level (e.g. $\sim$ 50 counts/pixel) before the event, compared to the core dimming $\sim$ 100 counts/pixel), the relative magnitudes of both the core and secondary dimmings are substantial (e.g. $\sim$ and $\sim$, respectively)."
 Further. like the core dimuuines. the secondary dinuuiugs remain at a reduced intensity level for an extended period (> 1 hour).," Further, like the core dimmings, the secondary dimmings remain at a reduced intensity level for an extended period $>$ 1 hour)."
 The locatious of these secondary diniminugs also appear to be closely associated with the magnetic fields reconnected through CME expausion., The locations of these secondary dimmings also appear to be closely associated with the magnetic fields reconnected through CME expansion.
 For example. Figure 6 shows a secondary diuuumg to the north of the source region that corresponds to the secondary cavity in the simulation seen at 06:05 UT.," For example, Figure \ref{fig:f6} shows a secondary dimming to the north of the source region that corresponds to the secondary cavity in the simulation seen at 06:05 UT."
 This diunuus extends the CADE cavity northward (sce COR1joini.mov)., This dimming extends the CME cavity northward (see ).
 Further evideuce of this can be found in Fieure 15. (alsoseeMancinietal.2007)., Further evidence of this can be found in Figure \ref{fig:f11} \citep[also see][]{Mandrini07}.
".. These results show that overlying and neighboring maguctic field is ""opeued through magnetic reconnection. extending the CME footprint iu the low corona."," These results show that overlying and neighboring magnetic field is “opened” through magnetic reconnection, extending the CME footprint in the low corona."
 Therefore. we also interpret the secondary dinuuiues in this event as bee due to density depletion. although spectral diagnostics have vet to confirm or refute this interpretation.," Therefore, we also interpret the secondary dimmings in this event as being due to density depletion, although spectral diagnostics have yet to confirm or refute this interpretation."
 Our results show that the bright front observed in difference EUV data aud the CALE are strongly coupled (c.c. Figure 6))., Our results show that the bright front observed in difference EUV data and the CME are strongly coupled (e.g. Figure \ref{fig:f6}) ).
 These higher-inteusity brightcnines are due to the CME compressing the plasma (against both smrounding and overlying maenetic field)., These higher-intensity brightenings are due to the CME compressing the plasma (against both surrounding and overlying magnetic field).
 The brightest concentrations iu the data aud simulations in Figure 3 show correspondence with the regions of reconnection in Figure 6.. both red aud vellow field lines.," The brightest concentrations in the data and simulations in Figure \ref{fig:f3} show correspondence with the regions of reconnection in Figure \ref{fig:f7}, both red and yellow field lines."
 Figure 11 shows a direct comparison., Figure \ref{fig:f10} shows a direct comparison.
 When the CME has expanded to its maxinuun lateral extent. the brightest parts of the coronal wave either disappear or become stationary before facing (81.2.0).," When the CME has expanded to its maximum lateral extent, the brightest parts of the coronal wave either disappear or become stationary before fading \ref{subsec:two_component_bf}) )."
 This is the result of multiple factors: the CME is uo longer directly compressing plasma the overlying field has already stretched. and magnetic recounectious with sumrounudiue favorably-oricutated field have had time to occur.," This is the result of multiple factors: the CME is no longer directly compressing plasma, the overlying field has already stretched, and magnetic reconnections with surrounding favorably-orientated field have had time to occur."
 What remains is a weaker. more uniform componcut that is consistent with an MIID wave interpretation.," What remains is a weaker, more uniform component that is consistent with an MHD wave interpretation."
 The dynamic expansion of the CME is a highly. energetic. nupulsive event. therefore wave(s) are expected to be eenerated.," The dynamic expansion of the CME is a highly energetic, impulsive event, therefore wave(s) are expected to be generated."
 The simulation results show that this weaker conrponeut exists throughout the expansion of the CALE., The simulation results show that this weaker component exists throughout the expansion of the CME.
 The later frames of the simulation show that it coutinues to expand even after the cousiderable CALE lateral expansion has finished., The later frames of the simulation show that it continues to expand even after the considerable CME lateral expansion has finished.
 Iu this later stage. the coronal wave ds freely propagating (e.g.Veromigetal.2008).," In this later stage, the coronal wave is freely propagating \citep[e.g.][]{Veronig08}."
. Iu the difference EUVI-À data rdiff.mov). which highlights the of the disturbauce. the Western expansion cau be followed considerably later iui in the base difference nuages. until at least 06:55 —E (cu," In the difference EUVI-A data ), which highlights the of the disturbance, the Western expansion can be followed considerably later than in the base difference images, until at least 06:55 UT (c.f."
 06:25 UT. the reader is eucouraged to compare je running and base difference movies for EUVLA: uud diff.mov).," 06:25 UT, the reader is encouraged to compare the running and base difference movies for EUVI-A: and )."
 It is more likely iat the weaker component cau be detected iu rine lifference images. which better show subtle changes.," It is more likely that the weaker component can be detected in running difference images, which better show subtle changes."
 With this analysis. we believe we are able to reconcile ie different (wave and non-wave) interpretations of coronal waves.," With this analysis, we believe we are able to reconcile the different (wave and non-wave) interpretations of coronal waves."
 When EIT waves were first discovered. jov were studied using diffevenee data.," When EIT waves were first discovered, they were studied using difference data."
 This uecthod highlishts the (often faint) leading edge of the disturbance. makiug it useful for ideutifving waves: this echuique was probably perpetuated because researchers (e.g.Thompsonetal.1999) originally identified their observations as a strous candidate for the predicted coronal counterpart to the chromospheric Moreton wave (Aloreton1960:Uchida1965).," This method highlights the (often faint) leading edge of the disturbance, making it useful for identifying waves; this technique was probably perpetuated because researchers \citep[e.g.][]{Thompson99} originally identified their observations as a strong candidate for the predicted coronal counterpart to the chromospheric Moreton wave \citep{Moreton60a,Uchida68}."
. Tn the late 1990s. Delaunéce et ab. (," In the late 1990s, Delannéee et al., ("
and later Chenu et al.,"and later Chen et al.,"
 and Αι et aL).," and Attrill et al.),"
 preferentially used difference images because they show real brightcnines and cdimunines (e.g.Chertok&Cacchnuey2005)., preferentially used difference images because they show real brightenings and dimmings \citep[e.g.][]{Chertok05}.
. The motivation for using base difference miages is due to the focus of these authors on coronal dimunines. which are strouglv connected with coronal waves aud CATE events.," The motivation for using base difference images is due to the focus of these authors on coronal dimmings, which are strongly connected with coronal waves and CME events."
 It is uot possible to study coronal cnuuiues with rine differcuce images., It is not possible to study coronal dimmings with running difference images.
 However. base difference images do not show faint features so well.," However, base difference images do not show faint features so well."
 We have shown that the differeuce brightcnines are closely linked to the CALE aud maeguetic field evolution: hence. the development of uou-wave models.," We have shown that the difference brightenings are closely linked to the CME and magnetic field evolution; hence, the development of non-wave models."
 For some time. both of these methods have been applied. with different studies producing disparate conclusions.," For some time, both of these methods have been applied, with different studies producing disparate conclusions."
 Iu most cases; however. researchers have attempted to find a siugle solutioneither wave or non-waveapplicable to all aspects of diffuse coroual wave events.," In most cases, however, researchers have attempted to find a single solution–either wave or non-wave–applicable to all aspects of diffuse coronal wave events."
 Over time. this has led to secminely contradictory evidence. sclectively supportiug wave or non-wave models. depending of the focus of the study.," Over time, this has led to seemingly contradictory evidence, selectively supporting wave or non-wave models, depending of the focus of the study."
 Zhukov&Auchere(2001). first introduced the concept of a coupled coronal wave. consisting of an cruptive mode and a wave mode. based on comparative analysis of EIT ruuniug aud base differcuce data.," \cite{Zhukov04} first introduced the concept of a coupled coronal wave, consisting of an eruptive mode and a wave mode, based on comparative analysis of EIT running and base difference data."
 Our resulta are consistent with such a picture., Our results are consistent with such a picture.
 The combined observational and simulation results preseuted here allow us to firmly establish aud iunderstaud the coutributiou from cach of the various imiechauisnis., The combined observational and simulation results presented here allow us to firmly establish and understand the contribution from each of the various mechanisms.
 Iu retrospect. it is not surprising that wave aud non-wave interpretations have failed to be reconciled when the differeut data sets hiehlieht different thines!," In retrospect, it is not surprising that wave and non-wave interpretations have failed to be reconciled when the different data sets highlight different things!"
 Tn interplanetary space. field lines following the Parker spiral connect the western longitudes of the Sun to spacecraft at 1 AU.," In interplanetary space, field lines following the Parker spiral connect the western longitudes of the Sun to spacecraft at 1 AU."
 When an impulsive electron. eveut occurs in the corona. energetic particles travel along these field lines to 1 AU.," When an impulsive electron event occurs in the corona, energetic particles travel along these field lines to 1 AU."
 However. sometimes impulsive electron events are clearly related to flares that occur ou the eastern half of the solar disk. up to ~ LH. from the Parker spiral footpoiut.," However, sometimes impulsive electron events are clearly related to flares that occur on the eastern half of the solar disk, up to $\sim$ $1R_\odot$ from the Parker spiral footpoint."
 Ixuckeretal.(1999) suggested that ETT waves nieht explain how the flare site and Sun-spacecraft. magnetic field lines are connected., \cite{Krucker99} suggested that EIT waves might explain how the flare site and Sun-spacecraft magnetic field lines are connected.
 They couclided that at the time of electron release. the EIT wave had not expauded far enough to reach the," They concluded that at the time of electron release, the EIT wave had not expanded far enough to reach the"
We caleulate the average peak signal-to-noise ratio. Psy. over 200 input haloes (Figure 2/— markers: black solid line): dashed lines represent deviation error range.,"We calculate the average peak signal-to-noise ratio, $\langle P_{\rm S} \rangle$, over 200 input haloes (Figure \ref{fig:betascale} – markers; black solid line); dashed lines represent the one-standard deviation error range."
 On the basis of this analysis.the we one-stancardchoose Ju=OLS as providing the best fit to the input halo shapes. presenting a reasonable comprimise to a full optimisation process.," On the basis of this analysis, we choose $\beta_{\rm scale} = 0.8$ as providing the best fit to the input halo shapes, presenting a reasonable comprimise to a full optimisation process."
 Vo avoid orientation-dependent effects. haloes are rotated such that their principle axes are aligned with the coordinate axes (sce Appendix B)).," To avoid orientation-dependent effects, haloes are rotated such that their principle axes are aligned with the coordinate axes (see Appendix \ref{app:triax}) )."
 Halo particles are then smoothed to a grid. using the triangle-shaped: cloud smoothing strategy. providing number counts per voxel. which is equivalent to a density. p;jj.," Halo particles are then smoothed to a grid using the triangle-shaped cloud smoothing strategy, providing number counts per voxel, which is equivalent to a density, $\rho_{ijk}$."
 To deal with the large dynamic range in ος. the input shape is actually: Since each halo has a cillerent mass and hence physical extent. the ; value for each halo is ecüllerent— see Table 1..," To deal with the large dynamic range in $\rho_{ijk}$, the input shape is actually: Since each halo has a different mass and hence physical extent, the $\beta$ value for each halo is different – see Table \ref{tbl:shapfits}."
" The other columns in this table are: the cellavidth. Aw. as defined in equation (75)): the maximum voxel value from the input shape. Jans. and the minimum. ancl maximum shapelet-recovered values. Sy,t and ""Sys. respectively."," The other columns in this table are: the cell-width, $\Delta x$, as defined in equation \ref{eqn:deltax}) ); the maximum voxel value from the input shape, $I_{\rm max}$, and the minimum and maximum shapelet-recovered values, $S_{\rm min}$ and $S_{\rm max}$, respectively."
". rpsTo enable quantitative comparisons between the input and reconstructed shapes we compute the quantities nnd Xs=» ""nmand P."," To enable quantitative comparisons between the input and reconstructed shapes we compute the quantitites and $\Sigma_{S} 
= \sum_{i,j,k} \hat{f}_{ijk}$ ,and $P_s$."
 Numerical testing. 2544where reconstructions were optimised by hand. suggested that Xj—Xs and Pz45 (Figure 2)) represented a σου shapelet fit for the grid resolution used.," Numerical testing, where reconstructions were optimised by hand, suggested that $\Sigma_{I} \sim \Sigma_S$ and $P_s \geq 45$ (Figure \ref{fig:betascale}) ) represented a good shapelet fit for the grid resolution used."
" The m-th most dominant shapelet component of the reconstruction has nm=D,,. with amplitude {ο=fv auax."," The $m$ -th most dominant shapelet component of the reconstruction has $\bmath{n} = \bmath{D}_{m}$, with amplitude $f_{3,\bmath{D}_m} = f_{m,{\rm max}}$ ."
 Except. where indicated. Dy=(0.0.0). so we also report the value of D».," Except where indicated, $\bmath{D}_1 = (0,0,0)$, so we also report the value of $\bmath{D}_2$."
" Phe final two columns of Table 1 represent the result of ""by-eye"" classifications of the spatia characteristics of cach halo. C'(/). and the shapelet profiles. CUS). into the three halo classes see Section 5.2. below."," The final two columns of Table \ref{tbl:shapfits} represent the result of `by-eye' classifications of the spatial characteristics of each halo, $C(I)$, and the shapelet profiles, $C(S)$, into the three halo classes – see Section \ref{sct:auto} below."
 lies., Figs.
 3 and 4 show the results of the shapele decomposition., \ref{fig:heavy} and \ref{fig:light} show the results of the shapelet decomposition.
 For each halo. the left-hand panel shows the input shape. and the right-hand. panel is reconstructed. in shapelet space.," For each halo, the left-hand panel shows the input shape, and the right-hand panel is reconstructed in shapelet space."
 Each image pair presents two-dimoensiona xojections of fully three-dimensional. volume rendere structures.," Each image pair presents two-dimensional projections of fully three-dimensional, volume rendered structures."
" Visual comparsion of pairs of images suggests hat. qualitatively, Cartesian shapelets represent an appropriate basis set fordecomposition of dark matter jaloes."," Visual comparsion of pairs of images suggests that, qualitatively, Cartesian shapelets represent an appropriate basis set fordecomposition of dark matter haloes."
 Quantitatively. we find that: and Psο 45. so that even without a halo-specilic," Quantitatively, we find that: and $P_S \geq 45$ so that even without a halo-specific"
The CE model-Sttiug results are shown in Figures 5 and 9..,The CE model-fitting results are shown in Figures \ref{img_noise_synth_J1} and \ref{img_noise_synth_J2}.
 We note that the choice N=23.6 for jet JI aud AVLA. and 7 for jet J2 provides more homogencous and less pealked. residual maps.," We note that the choice $N_\mathrm{s}=3-6$ for jet J1 and $N_\mathrm{s}=4, 5$, and 7 for jet J2 provides more homogeneous and less peaked residual maps."
 Considering the uncertainties. there is a plateau after AV=3 in the Sa eraph in the top panel of Figure 10.," Considering the uncertainties, there is a plateau after $N_\mathrm{s}=3$ in the $S_\mathrm{prod}^{1/6}$ graph in the top panel of Figure \ref{fitness_img_noise_J1}."
. This means that only a lower limit for ANY can be derived from such plots., This means that only a lower limit for $N_\mathrm{s}$ can be derived from such plots.
 The bottom panel of Figure 10 points out that residuals are minimized for 3<NLx6., The bottom panel of Figure \ref{fitness_img_noise_J1} points out that residuals are minimized for $3\le N_\mathrm{s}\le 6$.
 To break the degeueracv in ANY. we analyze the values listed in Table 5..," To break the degeneracy in $N_\mathrm{s}$, we analyze the values listed in Table \ref{tab_J1_modfit_noise}."
 As in the case of the noiseless images. the optimized parameters of the three sources found for NL= also appear when we assed L<ALx6.," As in the case of the noiseless images, the optimized parameters of the three sources found for $N_\mathrm{s}=3$ also appear when we assumed $4\le N_\mathrm{s}\le 6$."
 The extra colpoucuts are dinuiner and sometimes superpose conipletelv with the brightest componeut (coro)., The extra components are dimmer and sometimes superpose completely with the brightest component (core).
 Thus. Ny= 3540s fully favored in relation to the other possibilities.," Thus, $N_\mathrm{s}=3$ is fully favored in relation to the other possibilities."
 Iu the case of jet J2. there is also a plateau-like feature for N.z5 in eraph in the top panel of Figure 1l...," In the case of jet J2, there is also a plateau-like feature for $N_\mathrm{s}\gtrsim 5$ in $S_\mathrm{prod}^{1/6}$ graph in the top panel of Figure \ref{fitness_img_noise_J2}."
 Solutious with DiodNZ—5 aud 7 are slightlv favored over the others in the case of the mean and maxiumui residuals shown in the bottom panel of Figure 11.., Solutions with $N_\mathrm{s}=5$ and 7 are slightly favored over the others in the case of the mean and maximum residuals shown in the bottom panel of Figure \ref{fitness_img_noise_J2}.
 The colmbination of both results sugeests the existence of five Or seven components in jet J2., The combination of both results suggests the existence of five or seven components in jet J2.
 Comparison between the values listed in Table 6 reveals that coiiponenuts 1-5 for No=5 were also found in the CE optimization using AN.=7 (components 1. 2. 3. 6. and 7. respectively).," Comparison between the values listed in Table \ref{tab_J2_modfit_noise} reveals that components 1-5 for $N_\mathrm{s}=5$ were also found in the CE optimization using $N_\mathrm{s}=7$ (components 1, 2, 3, 6, and 7, respectively)."
 As in the case of the noisy jet Jl. the extra two compoucuts are too dim. compatible with null intensity considering the uncertainties.," As in the case of the noisy jet J1, the extra two components are too dim, compatible with null intensity considering the uncertainties."
 Thus. a five-componenuts solution is favored. as expected for this benchmark test.," Thus, a five-components solution is favored, as expected for this benchmark test."
 The equations to caleulate the model-fittiug parameters. as well as their respective uncertainties. were mtroduced im Section 2.3.," The equations to calculate the model-fitting parameters, as well as their respective uncertainties, were introduced in Section 2.3."
" To show that Equations (10) aud (11) provide a reasonable estimation of the model parameters aud their errors. we used the three optimization runs performed for he noisy jet JI for IN,—3."," To show that Equations (10) and (11) provide a reasonable estimation of the model parameters and their errors, we used the three optimization runs performed for the noisy jet J1 for $N_\mathrm{s}=3$."
 The reasou for not choosing a roiscless nuage is to keep this analysis as close as possible ο real situations. which we kuow to lave a structured roise pattern enibedded iuto the source signal.," The reason for not choosing a noiseless image is to keep this analysis as close as possible to real situations, which we know to have a structured noise pattern embedded into the source signal."
 From the 18.000. best-value data generated iu this est (three optimization rms. cach one composed of 6000. iterations). we deterinined the distribution of the ogarithin of Shoda ta the Ge. g)-. (ει @)-. aud (a.Ly )-plaies or each of the three Caussian sources. as is displaved iu Figure 12test...," From the 18,000 best-value data generated in this test (three optimization runs, each one composed of 6000 iterations), we determined the distribution of the logarithm of $S_\mathrm{prod}$ in the $x,y$ )-, $\epsilon,\theta$ )-, and $a,I_0$ )-planes for each of the three Gaussian sources, as is displayed in Figure \ref{mapping_Nelite}."
" Although the Aya. distribution is very irregular. showing several local ninimia in all planes. the CE algorithm was able to &ud the ο ΕΠ of 5,444. returmine the correct parameter values of the ellipses if the error bars were considered."," Although the $S_\mathrm{prod}$ distribution is very irregular, showing several local minima in all planes, the CE algorithm was able to find the global minimum of $S_\mathrm{prod}$, returning the correct parameter values of the ellipses if the error bars were considered."
 For example. the differences between the «andy values listed in Table 1 aud those calculated from our technique are much siualler than one pixel iu both directions.," For example, the differences between the $x-$ and $y-$ values listed in Table \ref{tab_J1} and those calculated from our technique are much smaller than one pixel in both directions."
 The larger discrepancies were found iu the (6.7) planes but. even in these cases. such differences remain within the 360 CLYOLS.," The larger discrepancies were found in the $(\epsilon,\theta)-$ planes but, even in these cases, such differences remain within the $3\sigma$ errors."
 Our results show also that it is possible to calculate statistically the values of the mocdeltitting parameters and their associated uncertainties by applying Equations (10) aud (11) to the tentative solutions eeucrated in the 6otimization process., Our results show also that it is possible to calculate statistically the values of the model-fitting parameters and their associated uncertainties by applying Equations (10) and (11) to the tentative solutions generated in the optimization process.
 However. as the real nature of the noise present in interferometric images is uot sufficiently -town. such error estimates should be considered as a lower limit for the true uncertaiuties of the derived Gaussian parameters.," However, as the real nature of the noise present in interferometric images is not sufficiently known, such error estimates should be considered as a lower limit for the true uncertainties of the derived Gaussian parameters."
 Error estimations based on the properties of the restoring eam or differences in the fits to two or nore observations acquired very close im finie (o.@.. Pineretal.2007:Lister200953) max be used as coniplemeuts or alternatives to Equations (10) and (11) in eeneral situations.," Error estimations based on the properties of the restoring beam or differences in the fits to two or more observations acquired very close in time (e.g., \citealt{pin07,lis09b})) may be used as complements or alternatives to Equations (10) and (11) in general situations."
 The tages in the noiscless validation tests had a formal oeifte S/N. while for the JL and J2 noise nuages S/R was ~100.," The images in the noiseless validation tests had a formal infinite S/N, while for the J1 and J2 noise images S/R was $\sim 100$ ."
 To check the performance of our CE modoel-fitting alegoritlim im terms of S/R. we created svuthetic nuages composed of the same noise backerouud showu in the top panel of Figure 5. aud au elliptical Gaussian source centered at ow=17.2 pixels aud gy=48d yincls.," To check the performance of our CE model-fitting algorithm in terms of S/R, we created synthetic images composed of the same noise background shown in the top panel of Figure \ref{noise_plus_map_J1} and an elliptical Gaussian source centered at $x=17.2$ pixels and $y=48.1$ pixels."
 We placed this source at this particular position oei order tfo superpose if on a region in which there is a strong eracdicut iu the noise intensity iu the southeast o northwest direction. which introduces extra difficulty o the iiodel-fittiug procedure.," We placed this source at this particular position in order to superpose it on a region in which there is a strong gradient in the noise intensity in the southeast to northwest direction, which introduces extra difficulty to the model-fitting procedure."
 The additional parameters were chosen to be ο=L8 pixels. e=0:50. and 0=6773.," The additional parameters were chosen to be $a=4.8$ pixels, $\epsilon=0.85$, and $\theta=67\fdg 3$."
 The peak intensity of this source was varied from 1 to 50 wy beau1. which corresponds to S/R raneing from 2 to 100.," The peak intensity of this source was varied from 1 to 50 mJy $^{-1}$, which corresponds to S/R ranging from 2 to 100."
 An exiuuple of one of these control images is displaved in Figure 13.., An example of one of these control images is displayed in Figure \ref{im_1gauss_SNR30}.
 The efficiency of our algorithm) idu recoveriug the elliptical Gaussian source parameters as a function of the S/R cau be seen in Figure L1.., The efficiency of our algorithm in recovering the elliptical Gaussian source parameters as a function of the S/R can be seen in Figure \ref{onegaussSNR}.
 The values of the Catssiau- coordinates .«« and y were recovered with a relative error below the 10% level for S/BRz 10., The values of the Gaussian-peak coordinates $x$ and $y$ were recovered with a relative error below the $\%$ level for $\gtrsim 10$ .
 The same error level was achieved for the parameters e aud 0 for S/Rz20. Iy for S/Rz30. aud α for S/R50.," The same error level was achieved for the parameters $\epsilon$ and $\theta$ for $\gtrsim 20$, $I_0$ for $\gtrsim 30$, and $a$ for $\gtrsim 50$."
 For SNR = 100 all parameters were found with a relative error below the 5% level., For SNR = 100 all parameters were found with a relative error below the $\%$ level.
 Tn terms of the absolute values aud thei respective uncertainties. our CE model fitting technique was able to recover the parameter Ly within the 37 level for S/Rz20. while for the other parameters the same applied for 10.," In terms of the absolute values and their respective uncertainties, our CE model fitting technique was able to recover the parameter $I_0$ within the $3\sigma$ level for $\gtrsim 20$, while for the other parameters the same applied for $\gtrsim 10$ ."
 The aiu of this subsection is to conrpare our findiugs with those obtained from the traditional aud widely used two-dimensional Caussian fitting task IMEIT iucluded in the Astronomical Guage Processing System Package (AIPS)., The aim of this subsection is to compare our findings with those obtained from the traditional and widely used two-dimensional Gaussian fitting task IMFIT included in the Astronomical Image Processing System Package (AIPS).
 A comparison between CE aud IMFIT modelfitting results in the case of the S/R Init tests is shown in Figure LL. , A comparison between CE and IMFIT model-fitting results in the case of the S/R limit tests is shown in Figure \ref{onegaussSNR}. .
Taking iutoaccount the uncertainties. both techniques have very similar behavior iu terms of recovering the source parameters for thisparticular test.," Taking intoaccount the uncertainties, both techniques have very similar behavior in terms of recovering the source parameters for thisparticular test."
 We applied the task IMEIT to the image of the noisy jet JL displaved in Figure 5.., We applied the task IMFIT to the image of the noisy jet J1 displayed in Figure \ref{noise_plus_map_J1}. .
 A comparison between the, A comparison between the
The orbital parameter error. distribution functions contain information that is useful. however. in that. they allow us to empirically calibrate the relationship between he uncertainties that arise [rom the covariance matrix in a east-squares Keplerian fit (1.6. the source of the traditional uncertainties in orbital parameters. produced. in. analysing Doppler cata sets) and our observed. error distributions.,"The orbital parameter error distribution functions contain information that is useful, however, in that they allow us to empirically calibrate the relationship between the uncertainties that arise from the covariance matrix in a least-squares Keplerian fit (i.e. the source of the traditional uncertainties in orbital parameters produced in analysing Doppler data sets) and our observed error distributions."
 To examine these relationships we compare the uncertainties rom the least-squares Ixeplerian fit and the confidence range from the simulations., To examine these relationships we compare the uncertainties from the least-squares Keplerian fit and the confidence range from the simulations.
" In Figure 6 we show the confidence limit as a ""unction of the median. uncertainty of the fit 075, (top). Od, Cniidelle) and de,,, (bottom) for 220782 at at fixed yates of P; ande; or P; and fy; (as in Section 3.1))."," In Figure \ref{fig:errors} we show the confidence limit as a function of the median uncertainty of the fit $\delta P_m$ (top), $\delta K_m$ (middle) and $\delta e_m$ (bottom) for 20782 at at fixed pairs of $P_i$ and$e_i$ or $P_i$ and $K_i$ (as in Section \ref{sec:distro}) )."
 There is clearly a correlation between these parameters. which we rave characterised in the figure with a power-law for each parameter.," There is clearly a correlation between these parameters, which we have characterised in the figure with a power-law for each parameter."
" The power laws have the form: confidence = 10°XN ὃν where XN=02,,.06¢,, and confidence = a|slogdds, for semi-amplitude."," The power laws have the form: confidence = $^\alpha X^\beta$ where $X=\delta P_m, \delta e_m$ and confidence = $\alpha+\beta\log\delta K_m$ for semi-amplitude."
 The xwameters à and 2 from these fits for 220782 are listed in Table 4 (along with the equivalent parameters for similar its to the equivalent data for 338382 and 1179949)., The parameters $\alpha$ and $\beta$ from these fits for 20782 are listed in Table \ref{tab:errors} (along with the equivalent parameters for similar fits to the equivalent data for 38382 and 179949).
 For the period data. it is clear that the power-law slope is consistent with an index of 1 that is. the confidence imits are linearly related to the 1e [it uncertainties o» factors of 26-47. or equivalently Ciaussian statistics overestimate the limits for a period determination from. hese simulated Doppler data by factors of between 10-18.," For the period data, it is clear that the power-law slope is consistent with an index of 1 – that is, the confidence limits are linearly related to the $\sigma$ fit uncertainties by factors of 26-47, or equivalently Gaussian statistics overestimate the limits for a period determination from these simulated Doppler data by factors of between 10-18."
 For cecentricity the correlation is weaker. and the power-law it inclicated is slightly above 1.," For eccentricity the correlation is weaker, and the power-law fit indicated is slightly above 1."
 More importantly. the confidence limits are about 10-50. times larger than those which would be derived from simply trusting the Gaussian nature of the uncertainties coming from a least-squares Ixeplerian fit.," More importantly, the confidence limits are about 10-50 times larger than those which would be derived from simply trusting the Gaussian nature of the uncertainties coming from a least-squares Keplerian fit."
 This rellects the fact that eccentricity is. in general. very poorly constrained by Doppler data sets. as was seen in our analvsis of the 2DINLS.," This reflects the fact that eccentricity is, in general, very poorly constrained by Doppler data sets, as was seen in our analysis of the 2DKLS."
 The correlation between the observed confidence limits and the Keplerian [i uncertainties for semi-amplitude A is poor. and again the conlidence limits in A are lareer than those one woulc predict from the Ixeplerian fit uncertainties.," The correlation between the observed confidence limits and the Keplerian fit uncertainties for semi-amplitude $K$ is poor, and again the confidence limits in $K$ are larger than those one would predict from the Keplerian fit uncertainties."
 From our analvsis of these three data sets. it. woul not appear that there are any general conclusions tha can be reached. for every star and everv data set. on how to relatereal confidence limits to Ixeplerian fi uncertainties (other than that Weplerian fit. uncertainties significantly under-estimate bv factors of greater than 1O — the real confidence limits).," From our analysis of these three data sets, it would not appear that there are any general conclusions that can be reached, for every star and every data set, on how to relate confidence limits to Keplerian fit uncertainties (other than that Keplerian fit uncertainties significantly under-estimate – by factors of greater than 10 – the real confidence limits)."
 However. it is clear that [or a simulated data set. that meaningful correlations can be derived: and. applied.," However, it is clear that for a simulated data set, that meaningful correlations can be derived and applied."
 We have therefore used. these relationships to convert fit uncertainties into meaningful confidence limits for our subsequent analysis of false positives., We have therefore used these relationships to convert fit uncertainties into meaningful confidence limits for our subsequent analysis of false positives.
 Lt is important that the number of false positives (i.e. the number of incorrect. detections) triggered. by our detection criteria be (a) quantifiable. and (b) as small as possible.," It is important that the number of false positives (i.e. the number of incorrect detections) triggered by our detection criteria be (a) quantifiable, and (b) as small as possible."
" We adopt as our ""incorrectness"" criterion. that. the measured orbital parameter cdilfers from the input orbital parameter » more than the confidence limit. for that orbital xuwameter (as derived in Section 4.3)).", We adopt as our “incorrectness” criterion that the measured orbital parameter differs from the input orbital parameter by more than the confidence limit for that orbital parameter (as derived in Section \ref{sub:errors}) ).
" For cach simulation that results in a detection. we test or ""correctness"" by asking: Η both the period. ancl the semi-amplitude are determined to be incorrect (at the level). we describe this as an incorrect. detection. or false positive."," For each simulation that results in a detection, we test for “correctness” by asking; If both the period and the semi-amplitude are determined to be incorrect (at the level), we describe this as an incorrect detection, or false positive."
 Phe false positive rate is then the ratio of the number of incorrect detections to the total number of detections., The false positive rate is then the ratio of the number of incorrect detections to the total number of detections.
 Averaging over all parameters. we find the false positive rate due to incorrect period anc semi-amplitude to be for 1179949. for 220782. ancl [or 338382.," Averaging over all parameters, we find the false positive rate due to incorrect period and semi-amplitude to be for 179949, for 20782, and for 38382."
 In the sections that follow. we look in more detail at these numbers and at their trends as a function of input orbital parameters.," In the sections that follow, we look in more detail at these numbers and at their trends as a function of input orbital parameters."
 We are now in a position to demonstrate our reasons for include this particular criterion. whieh we do in Figure 7. which shows the false positive fraction. as a function of simulated input. eccentricity. both with this. criterion applied (open squares) and. not applied. (filled: squares).," We are now in a position to demonstrate our reasons for include this particular criterion, which we do in Figure \ref{fig:testfalse}, which shows the false positive fraction as a function of simulated input eccentricity both with this criterion applied (open squares) and not applied (filled squares)."
 {4 imnmeciately becomes apparent that without this particular criterion. being applied. our data set is subject to an unacceptably large fraction of false positives at high eccentricity.," It immediately becomes apparent that without this particular criterion being applied, our data set is subject to an unacceptably large fraction of false positives at high eccentricity."
 Even with this criterion being applied. the number of false positives shows an increase over the. “base” level of seen at low cecentricity. up to at e-0.9. (," Even with this criterion being applied the number of false positives shows an increase over the “base” level of seen at low eccentricity, up to at $e$ =0.9. ("
Similar patterns are seen for the other sets of simulations for the other stars.),Similar patterns are seen for the other sets of simulations for the other stars.)
 We show in the top panel of Figure S the rate of false positives for each object as a function of input eccentricity.at all values of 2? ancl Ad;.," We show in the top panel of Figure \ref{fig:efp} the rate of false positives for each object as a function of input eccentricity,at all values of $P_i$ and $M_i$ ."
 For 1179949 and 220782.," For 179949 and 20782,"
"temperature &,.","temperature $\theta_{\mathrm 
b}$."
" his temperature follows from the condition that the net energy Dux at depth τι, vanishes: This is à result. of our assumption that the internal enerev production rate in the cool disk can be neglected in comparison with the incident proton enerev [lux (eencralizations are casily mace by adding. a term corresponding to the internal disspation in the disk).", This temperature follows from the condition that the net energy flux at depth $\tau_{\mathrm b}$ vanishes: This is a result of our assumption that the internal energy production rate in the cool disk can be neglected in comparison with the incident proton energy flux (generalizations are easily made by adding a term corresponding to the internal disspation in the disk).
 The condition of energv. balance between the assumed heating rate f(r) and the Compton cooling by the soft photons is ," The condition of energy balance between the assumed heating rate $h(\tau)$ and the Compton cooling by the soft photons is =h, where the energy flux $F$ is given by ^3(n_i^+-n_i^-)."
The equations (10)) are cliseretizecl in. optical depth bv centered first. order dillerences., The equations \ref{treq}) ) are discretized in optical depth by centered first order differences.
 Phe resulting set. of nonlinear algebraic equations is solved. by an iterative process., The resulting set of nonlinear algebraic equations is solved by an iterative process.
 Lt turned out that full simultaneous. linearization of the transfer equation. the boundary. conditions and. the energy equation had. very poor convergence properties.," It turned out that full simultaneous linearization of the transfer equation, the boundary conditions and the energy equation had very poor convergence properties."
 Instead. an iteration was done in which only the transfer equation and the upper boundary condition were linearized. while the lower boundary condition and the energy equation were dealt with by à modified succesive-substitution process after cach iteration of the transfer equation.," Instead, an iteration was done in which only the transfer equation and the upper boundary condition were linearized, while the lower boundary condition and the energy equation were dealt with by a modified succesive-substitution process after each iteration of the transfer equation."
 Convergence. however. was still problematic for large optical depths and for cases where the assumed photon energy range extended too far bevond the ο energy.," Convergence, however, was still problematic for large optical depths and for cases where the assumed photon energy range extended too far beyond the cutoff energy."
 For the cases reported here. where the optical depth is not too large. on the order of 30100 iterations were required for an accuracy of 10.7 in luminosity.," For the cases reported here, where the optical depth is not too large, on the order of 30–100 iterations were required for an accuracy of $10^{-3}$ in luminosity."
 The parameters of the problem are the total energy Dux. f° (per unit surface area of the disk). the velocity of the incident protons. and the optical depth zi. of the. thermalizing lower boundary.," The parameters of the problem are the total energy flux $F$ (per unit surface area of the disk), the velocity of the incident protons, and the optical depth $\tau_{\mathrm 
b}$ of the thermalizing lower boundary."
" Assuming the protons to be thermal and virialized. their mean vertical velocity component 3. as a function of the distance r from the compact object is The temperature as a function. of depth is shown in figure 1 lor a [ow values of f£ for rír,=7."," Assuming the protons to be thermal and virialized, their mean vertical velocity component $\beta_z$ as a function of the distance $r$ from the compact object is The temperature as a function of depth is shown in figure \ref{et} for a few values of $F$ for $r/r_{\mathrm g}=7$."
 These fluxes correspond. to elfective temperatures θε=(Bio)μι} of 3107. 107 and 310.7. respectively.," These fluxes correspond to effective temperatures $\theta_{\mathrm eff}=(F/\sigma)^{1/4}/(m_{\mathrm e}c^2)$ of $3\,10^{-4}$, $10^{-3}$ and $3\,10^{-3}$, respectively."
" The emergentὃν spectrum for these energy.Ip Uuxes is shown in figure 4.. for r/r,=7."," The emergent spectrum for these energy fluxes is shown in figure \ref{sr}, for $r/r_{\mathrm g}=7$."
 The dependence of the spectrum on rfr. ata fixed £F is shown in figure 3..," The dependence of the spectrum on $r/r_{\mathrm 
g}$ at a fixed $F$ is shown in figure \ref{sf}."
 The penetration depths are shown in figure 5.., The penetration depths are shown in figure \ref{pen}.
" ALL of these cases were computed for 5,= 1. The jump in temperature at 7—7, is à consequence of the fact that the heating rate jumps at 7.", All of these cases were computed for $\tau_{\mathrm b}=1$ The jump in temperature at $\tau=\tau_{\mathrm s}$ is a consequence of the fact that the heating rate jumps at $\tau_{\mathrm s}$.
 The photon ield is continuous at 7 as shown in figure 2.. as expected recause Of their dilfusion through the scattering laver.," The photon field is continuous at $\tau_{\mathrm 
s}$ as shown in figure \ref{sz}, as expected because of their diffusion through the scattering layer."
 In order to balance the energy. input. the electrons have to oose enough energy by scattering soft photons.," In order to balance the energy input, the electrons have to loose enough energy by scattering soft photons."
 This requires hem to be hot where the energy. input rate is large. and causes the temperature to follow the heating rate.," This requires them to be hot where the energy input rate is large, and causes the temperature to follow the heating rate."
 The jump will be smoothed if a more realistic model for the proton »enetration is used., The jump will be smoothed if a more realistic model for the proton penetration is used.
 LE the protons are not monoenergetic and unidirectional but taken from a thermal distribution. or exaniple. the transition in heating rate will be smoother.," If the protons are not monoenergetic and unidirectional but taken from a thermal distribution, for example, the transition in heating rate will be smoother."
The similarity of the spectra. apart from shifts,"The similarity of the spectra, apart from shifts"
"Next. we plot in Figure 3 the ratio of the damping time to the period, rp/P. as a function of κ.α corresponding to the kink mode for //a=0.2.","Next, we plot in Figure \ref{fig:ratio} the ratio of the damping time to the period, $\tau_{\rm D} / P$, as a function of $k_z a$ corresponding to the kink mode for $l/a = 0.2$."
 In this Figure. we compare the numerical results with those obtained from the TB approximation.," In this Figure, we compare the numerical results with those obtained from the TB approximation."
" At first sight, we see that the slow resonance (dashed line in Fig. 3))"," At first sight, we see that the slow resonance (dashed line in Fig. \ref{fig:ratio}) )"
 is much less efficient than the Alfvénn resonance (symbols) in damping the kink mode., is much less efficient than the Alfvénn resonance (symbols) in damping the kink mode.
 The individual contribution of cach resonance in the TB approximation has been determined by solving equation (7)) and only taking the term on the right-hand side related to the desired resonance into account., The individual contribution of each resonance in the TB approximation has been determined by solving equation \ref{eq:disperalfven}) ) and only taking the term on the right-hand side related to the desired resonance into account.
" For the wavenumbers relevant to prominence oscillations, 1075. the value of tp/P related to the slow resonance is between 4 and 8 orders of magnitude larger than the ratio obtained by the Alfvénn resonance."," For the wavenumbers relevant to prominence oscillations, $10^{-3} < k_z a < 10^{-1}$ , the value of $\tau_{\rm D} / P$ related to the slow resonance is between 4 and 8 orders of magnitude larger than the ratio obtained by the Alfvénn resonance."
 The result of the thin tube limit (eq. [14]]), The result of the thin tube limit (eq. \ref{eq:ratiotaus}] ])
 agrees with this., agrees with this.
" On the other hand, the complete numerical solution (solid line) is close to the result for the Alfvénn resonance."," On the other hand, the complete numerical solution (solid line) is close to the result for the Alfvénn resonance."
 In agreement with Arreguietal.(2008)... we obtain rp/Px3 in the relevant range of &.a.," In agreement with \citet{arregui}, we obtain $\tau_{\rm D} / P \approx 3$ in the relevant range of $k_z a$."
" As was stated by Arreguietal.(2008.Fig.2d). the discrepancy between the numerical result and the TB approximation increases with //a, the difference being around for //a=1."," As was stated by \citet[Fig.~2$d$]{arregui}, the discrepancy between the numerical result and the TB approximation increases with $l/a$, the difference being around for $l/a = 1$."
" However, for small, realistic values of //α this discrepancy is less important and the TB approach is a very good approximation to the numerical result."," However, for small, realistic values of $l/a$ this discrepancy is less important and the TB approach is a very good approximation to the numerical result."
" For short wavelengths (κ.α 10"") the value of rp/P increases and the efficiency of the Alfvénn resonance as a damping mechanism decreases.", For short wavelengths $k_z a \gtrsim 10^0$ ) the value of $\tau_{\rm D} / P$ increases and the efficiency of the Alfvénn resonance as a damping mechanism decreases.
 For Ka~107 both the slow and the Alfvénn resonances produce similar (and inefficient), For $k_z a \approx 10^2$ both the slow and the Alfvénn resonances produce similar (and inefficient)
based on size. we performed our analysis ou the eutire data scHToas well as a subset with FS10 pe. which corresponds to a mass ranec of approximately —104to10?M... typical of CGMICS.,"based on size, we performed our analysis on the entire data set as well as a subset with $r_{\rm e} > 10$ pc, which corresponds to a mass range of approximately $\sim 10^4\: \rm{to}\: 10^5 \:\rm{M}_{\odot}$, typical of GMC's."
 Furthermore. to avoid any pathological cases where an elliptical fit to the cloud shape can bea very )OOT Approxination (M. IT. Hover. 2001. private connnicationjJ. we restricted our sample to those cloucs which span at least 10 spatial pixels in tιο observations (ui even more restrictive threshold of 2) pixels also vields essenutiallv t1C sale final restIt).," Furthermore, to avoid any pathological cases where an elliptical fit to the cloud shape can be a very poor approximation (M. H. Heyer, 2001, private communication), we restricted our sample to those clouds which span at least 10 spatial pixels in the observations (an even more restrictive threshold of 20 pixels also yields essentially the same final result)."
 This criterion reduces the total set to 5685 aud the sbset of GMCUS to 85., This criterion reduces the total set to 5685 and the subset of GMC's to 85.
 Our separate annalvses Call revea whether there is any sienificant share difference i ithe two populations., Our separate analyses can reveal whether there is any significant shape difference in the two populations.
 Figure l shows the results of the \? caleulatious for the triaxial fitting of fjo. CIMC subset., Figure \ref{heyerlarge2d} shows the results of the $\chi^2$ calculations for the triaxial fitting of the GMC subset.
 T1C data set is bes fit bv distributions with axis ratios (£y.συ)=(0.2.0.2) when o=0.1.," The data set is best fit by distributions with axis ratios $(\xi_0,\zeta_0) = (0.2,0.2)$ when $\sigma=0.1$."
 Tn order to determine whetlor values of (£yCy) closer to zero would improve the ft. we repeated the analvsis with a value of oO=0.05. (," In order to determine whether values of $(\xi_0,\zeta_0)$ closer to zero would improve the fit, we repeated the analysis with a value of $\sigma=0.05$. ("
As the mean value of the Cassiai gets closer to the eudpoiuts of he allowed ταιige [0.1]. a larger fraction of the Caussian distrinition falls outside this range. for a eiven a.,"As the mean value of the Gaussian gets closer to the endpoints of the allowed range [0,1], a larger fraction of the Gaussian distribution falls outside this range, for a given $\sigma$."
 There oes no ideal wav to correct for this xoblenm as expaa.red in 22 of this paper and in Ll of Paper T)., There is no ideal way to correct for this problem as explained in 2 of this paper and in 4 of Paper I).
 Ilowever. even with oe=0.05. the vest fi mca axis ratios (£g.Q9) are not closer to ZCLO axd aeree Wih our result for &=0.1 within estimated error.," However, even with $\sigma=0.05$, the best fit mean axis ratios $(\xi_0,\zeta_0)$ are not closer to zero and agree with our result for $\sigma=0.1$ within the estimated error."
 See Ll. for a ciscussion of the errors which we estimate to be a Πακαι of 0.1 iu the mea- value of cach axis ratio.," See 4.1 for a discussion of the errors which we estimate to be a maximum of $\pm \, 0.1$ in the mean value of each axis ratio."
 Figure 2. shows he result of he 47D caleulati-n for the compleTe set of AXÓS ratios based. «n our selection criteria in the Πονα et al. (, Figure \ref{heyertotal2d} shows the result of the $\chi^2$ calculation for the complete set of axis ratios based on our selection criteria in the Heyer et al. (
2001) cataloere.,2001) catalogue.
 The hes fitd based ou the 4D values Is (Cy.Qu)=(0.3.0.3).," The best fit based on the $\chi^2$ values is $(\xi_0,\zeta_0) = (0.3,0.3)$."
 For both the total set aud for the subset based ou laree effecive radius. the vost-fit triaxial distiutions require £j=cy. as shown very clearly in Figure 1 and Figure 2..," For both the total set and for the subset based on large effective radius, the best-fit triaxial distributions require $\xi_0 = \zeta_0$, as shown very clearly in Figure \ref{heyerlarge2d} and Figure \ref{heyertotal2d}."
 This mcans that the distiutions emphasize prolate objects., This means that the distributions emphasize prolate objects.
 However. since £y and Cy are the meaus ofdistributions. most individual objects cannot be considered strictly prolae and are. in fact. triastal.," However, since $\xi_0$ and $\zeta_0$ are the means of, most individual objects cannot be considered strictly prolate and are, in fact, triaxial."
 For the clouds with arge re. the distributions which best fit the observations have thinner objects (smaller& and ¢) than those that best fit the entire set.," For the clouds with large $r_{\rm e}$, the distributions which best fit the observations have thinner objects (smaller $\xi$ and $\zeta$ ) than those that best fit the entire set."
 However. the differcuce is quite sinall and equal tc» our aN estimated error of £0.1.," However, the difference is quite small and equal to our maximum estimated error of $\pm\, 0.1$."
 Fiewre 3 conrpares the best fit distribution of p to ti6 complete biuned datiQset of Πονα et al. (, Figure \ref{heyertotalbest} compares the best fit distribution of $p$ to the complete binned data set of Heyer et al. (
20My.,2001).
 It also reveals. that the histogram of projeced shapes p of molecuar clouds has ποιο nuique features., It also reveals that the histogram of projected shapes $p$ of molecular clouds has some unique features.
 We recall theV our previous analysis (Paper D) of dense cores showed that au observed broad peak im the distribtion at pz0.5 and the presence of a significant uuuber of objects near p=L favored triaxial. but more ucarly oblate intrinsic shapes.," We recall that our previous analysis (Paper I) of dense cores showed that an observed broad peak in the distribution at $p \gtrsim 0.5$ and the presence of a significant number of objects near $p=1$ favored triaxial, but more nearly oblate intrinsic shapes."
 Indeed. flis pattern is reinforced in our subsequent study of other cores. protostellar couleusations (see 3.2 - 3.1).," Indeed, this pattern is reinforced in our subsequent study of other cores, Bok globules, and protostellar condensations (see 3.2 - 3.4)."
 However. the shapes of molecular ds are distinct in that they havea VOYV Darrow seas. and at a low value p0.3.," However, the shapes of molecular clouds are distinct in that they have a very narrow peak, and at a low value $p \approx 0.3$."
 The narrow CAL. favors near-prolate objects. although a pure xolate cloud wihe τςΞ-03 vields a poor fit to the data. as shown iu Figwe 3..," The narrow peak favors near-prolate objects, although a pure prolate cloud with $\xi=\zeta=0.3$ yields a poor fit to the data, as shown in Figure \ref{heyertotalbest}."
 A pure xolate cloud. would have too narrow a peak in observed shape distribution. as well as a eher probability hau observed of a near-circular jection (see discussion and femCs dn 22 of Paper D.," A pure prolate cloud would have too narrow a peak in the observed shape distribution, as well as a higher probability than observed of a near-circular projection (see discussion and figures in 2 of Paper I)."
 Iu fact. Figure 3oPa shows that even a Caussian distribution of trxdal objects iuplies a higher probabiliv of detecting circular objects than observed.," In fact, Figure \ref{heyertotalbest} shows that even a Gaussian distribution of triaxial objects implies a higher probability of detecting near-circular objects than observed."
 The cutoff iu high values of p max be due to an actual cutoff in the distribution of intrinsic axis ratios (£g.Q9) above some vali10. or could be due to some selection effect.," The cutoff in high values of $p$ may be due to an actual cutoff in the distribution of intrinsic axis ratios $(\xi_0,\zeta_0)$ above some value, or could be due to some selection effect."
 One selection effect in the Hever et al. (, One selection effect in the Heyer et al. (
2001) sample is the fact that au object must span at least 5 pixels in the map to be classified as a cloud. (adaitiouallv. we nupose the higher threshold of 10 pixels for our shape analysis).,"2001) sample is the fact that an object must span at least 5 pixels in the map to be classified as a cloud (additionally, we impose the higher threshold of 10 pixels for our shape analysis)."
 Towever. we see no evidence iu the sample for a trend toward gre:der circularity as clouds have smaller projected size.," However, we see no evidence in the sample for a trend toward greater circularity as clouds have smaller projected size."
 Another selection effect is that the edges of the objects in the sample likely correspond to the the CO photodissociaion boundary aud not that of the Il gas (ever ct al., Another selection effect is that the edges of the objects in the sample likely correspond to the the CO photodissociation boundary and not that of the $_2$ gas (Heyer et al.
 2001)., 2001).
 ILowever. it is again not clear that this in amy way biases agalust near- objects.," However, it is again not clear that this in any way biases against near-circular objects."
 Onishi et a. (, Onishi et al. (
1996) aud Tachihara et al. (,1996) and Tachihara et al. (
2000),2000)
apastron.. where ως9.3.9OTGf22. represents. the radius: ofd the companion: O star 2005).,"apastron, where $R_* = 9.3^{+0.7}_{-0.6}\ R_{\odot}$ represents the radius of the companion O star \citep{cas05}."
. For L$5039. spectra and lisht curves of TeV gamma-ray with HESS array of atmospheric Cherenkov telescopes (Aharonianοἱal.2006a).. verv recently. those of GeV eamuma-rayv with Fermi Gamma-ray Space Telescopes (Abdoetal.2009).. ancl those of N-rav with Suzaku (Takahashietal.2009) have already been reported.," For LS5039, spectra and light curves of TeV gamma-ray with HESS array of atmospheric Cherenkov telescopes \citep{aha06a}, very recently, those of GeV gamma-ray with Fermi Gamma-ray Space Telescopes \citep{abd09}, and those of X-ray with Suzaku \citep{tak09} have already been reported."
 These observations show that these fluxes clearly modulate with its binary period. that GeV. σαΠαΤο [Iux anticorrelates with TeV gamma-ray [Iux. and that X-ray [Dux correlates with TeV flux.," These observations show that these fluxes clearly modulate with its binary period, that GeV gamma-ray flux anticorrelates with TeV gamma-ray flux, and that X-ray flux correlates with TeV flux."
 Two kinds of models have been suggested so [ar for explaining 5-rav spectra and light curves emerging from L955039., Two kinds of models have been suggested so far for explaining $\gamma $ -ray spectra and light curves emerging from LS5039.
 The first kind of models is (he microquasar tvpe mocel 2008).," The first kind of models is the microquasar type model \citep[e.g.][]{bos04,par06,bed06,bed07,der06,kha08}."
. Assuming that the compact object in L95039 is a black hole. they computed the propagation of photons Irom the injection site in the jet which is located al a certain cistanee (0 or finite value) from the base of jet.," Assuming that the compact object in LS5039 is a black hole, they computed the propagation of photons from the injection site in the jet which is located at a certain distance (0 or finite value) from the base of jet."
 The other kind of model is the pulsar tvpe model (e.g.Dubus2006b:Sierpowska-Dartosik&Torres2007.2008a.b:elal.2008;Ceruttiet2008. 2009).," The other kind of model is the pulsar type model \citep[e.g.][]{dub06b,sie07,sie08a,sie08b,dub08,cer08,cer09}."
. Assuming that the compact object is a neutron star. they computed the propagation of photons emerging [rom relativistic electrons accelerated well near (he neutron star. namely at the termination shock which is formed by a collision between a pulsar wind and a stellar wind. or near (he pulsar magnetosphere.," Assuming that the compact object is a neutron star, they computed the propagation of photons emerging from relativistic electrons accelerated well near the neutron star, namely at the termination shock which is formed by a collision between a pulsar wind and a stellar wind, or near the pulsar magnetosphere."
 In the papers mentioned above. Bednarek(2006.2007).. Sjierpowska-Dartosik&Torres(2007. 2008a.b).. and Ceruttietal.(2009). took into account electromagnetic cascade process.," In the papers mentioned above, \citet{bed06,bed07}, \citet{sie07,sie08a,sie08b}, and \citet{cer09} took into account electromagnetic cascade process."
 The TeV flux from L95039 was investigated in detail by Khaneulvanetal.(2008)., The TeV flux from LS5039 was investigated in detail by \citet{kha08}.
. Assuming that electrons were injected at a certain point along the jet and the counter-jet. thev calculated spectra aud Leht curves of TeV αν taking into account. anisotropic IC scaltering. 55 absorption. the advection of electrons by the jet flow. and svuchrotron cooling," Assuming that electrons were injected at a certain point along the jet and the counter-jet, they calculated spectra and light curves of TeV flux taking into account anisotropic IC scattering, $\gamma \gamma$ absorption, the advection of electrons by the jet flow, and synchrotron cooling"
"The J — II vs. IL — A, diagram shown in Figure 2. detects warm. massive disks that can be easily distinguished from the host star because (hey. are optically thick at K-band.","The J $-$ H vs. H $-$ $K_s$ diagram shown in Figure \ref{2MASS} detects warm, massive disks that can be easily distinguished from the host star because they are optically thick at K-band."
" The J — II vs. IL — A, diagram does not detect cooler disks that are not optically Chick at K-band and thus have less contrast against the host star.", The J $-$ H vs. H $-$ $K_s$ diagram does not detect cooler disks that are not optically thick at K-band and thus have less contrast against the host star.
" The HL - A, vs. [3.6] - [4.5] diagram also shown in Figure 2. detects massive but slightly. cooler disks that may not be evident in the J — IIl vs. I1 — A, diagram."," The H - $K_s$ vs. [3.6] - [4.5] diagram also shown in Figure \ref{2MASS}
 detects massive but slightly cooler disks that may not be evident in the J $-$ H vs. H $-$ $K_s$ diagram."
 Warm disks may be ascribed to stars obeving all of the following constraints (Gutermuth 2009): for IIS] 0.14. [J—HI] —0.6(3) for [H—N] > 0.14. LJ—H] =0.582.," Warm disks may be ascribed to stars obeying all of the following constraints (Gutermuth 2009): for [H-K] 0.14, [J-H] =0.6 for [H-K] > 0.14, [J-H] =0.58."
. Cold gas and dust at a distance of about 3 to 5 AU from the star emits brightly al (Muzerolle 2004)., Cold gas and dust at a distance of about 3 to 5 AU from the star emits brightly at (Muzerolle 2004).
 Accordingly. excess emission (21.5 mag) in the [5.8] — [24] and [4.5] — [24] colors without associated excesses al shorter wavelengths is generally attributed to the absence of an inner disk and identifies stars with disks that are cold. (1.6. transition disks). although other configurations such as rings are possible as well (Calvet 2008).," Accordingly, excess emission $>$ 1.5 mag) in the [5.8] $-$ [24] and [4.5] $-$ [24] colors without associated excesses at shorter wavelengths is generally attributed to the absence of an inner disk and identifies stars with disks that are cold (i.e. transition disks), although other configurations such as rings are possible as well (Calvet 2008)."
 Source CXNOANC J032929.2--311834 showed excess 24 emission and no corresponding excess in either the 4.5] — [5.8] or [3.6] — 4.5] colors and so is identified as having a transition disk., Source CXOANC J032929.2+311834 showed excess 24 emission and no corresponding excess in either the [4.5] $-$ [5.8] or [3.6] $-$ [4.5] colors and so is identified as having a transition disk.
 Further YSO classifications were obtained from literature searches for six of the ten sources whose Ih photometry did not conclusively place them in an evolutionary class., Further YSO classifications were obtained from literature searches for six of the ten sources whose IR photometry did not conclusively place them in an evolutionary class.
 Several studies were consulted for these data (Flaccomio 2006 lor NGC 2264. obsid 2540. Giardino 22008 for NGC 752. obsid 3752: IXohno 2002 for Mon 15. obsid 1382: Damiani 2004 for NGC 6530 obsid 971: Dahm LHillenbrand 2007 for NGC 2362 and M8 /— obsicls 4469 and 3154 respectively).," Several studies were consulted for these data (Flaccomio 2006 for NGC 2264 – obsid 2540, Giardino 2008 for NGC 752 – obsid 3752; Kohno 2002 for Mon R2 – obsid 1882; Damiani 2004 for NGC 6530 – obsid 977; Dahm Hillenbrand 2007 for NGC 2362 and M8 – obsids 4469 and 3754 respectively)."
upper panel of Fig.,upper panel of Fig.
" 4, where open circles refer to photographic or visual observations, filled circles to CCD or photoelectric ones."," 4, where open circles refer to photographic or visual observations, filled circles to CCD or photoelectric ones."
 As shown in the upper panel of Fig., As shown in the upper panel of Fig.
" 4, the general (O—C), trend can be described by a linear curve with superimposed a periodic fluctuation."," 4, the general $(O-C)_1$ trend can be described by a linear curve with superimposed a periodic fluctuation."
" Therefore, a sinusoidal term was added to a linear ephemeris to get a good fit to the (O—C) curve (solid line in the upper panel of Fig."," Therefore, a sinusoidal term was added to a linear ephemeris to get a good fit to the $(O-C)_1$ curve (solid line in the upper panel of Fig."
 4)., 4).
" obtain a more accurate result, we focus the fit to only primary minima, though follow a similar trend."," obtain a more accurate result, we focus the fit to only primary minima, though follow a similar trend."
" Weight 0.1 and 0.8 were assigned to precision observations (photographic or visual ones) and high-precision observations (CCD or photoelectric ones), respectively."," Weight 0.1 and 0.8 were assigned to lower-precision observations (photographic or visual ones) and high-precision observations (CCD or photoelectric ones), respectively."
" A weighted least-squares solution yields the following equation, The sinusoidal term in Eq. ("," A weighted least-squares solution yields the following equation, The sinusoidal term in Eq. ("
"2) suggests a periodic variation with a period of about 112.2 and an amplitude of about A=07.1977, which is more easily seen from the lower panel of Fig.","2) suggests a periodic variation with a period of about 112.2 and an amplitude of about $\textit{A} = {0^{d}.1977}$, which is more easily seen from the lower panel of Fig."
" 4, where the linear part of Eq. ("," 4, where the linear part of Eq. ("
"2) was subtracted to the (O—C), values.",2) was subtracted to the $(O-C)_1$ values.
 The good fit in Fig., The good fit in Fig.
 4 indicates no long-term steadily period increase or decrease., 4 indicates no long-term steadily period increase or decrease.
" Therefore, we can exclude the presence of mass transfer, which is in accordance with the fact that WW Dra is a detached binary."," Therefore, we can exclude the presence of mass transfer, which is in accordance with the fact that WW Dra is a detached binary."
 The (O—C); values are shown in the fourth and eleventh column of Table 5., The $(O-C)_2$ values are shown in the fourth and eleventh column of Table 5.
 The residuals of the fit with Eq. (, The residuals of the fit with Eq. (
2) are displayed in Fig.,2) are displayed in Fig.
 5 and listed in the fifth and twelfth column of Table 5., 5 and listed in the fifth and twelfth column of Table 5.
 detect possible regular trends in the residuals plotted in Fig., detect possible regular trends in the residuals plotted in Fig.
" 5, more high-precision times of light minimum are needed from future observations."," 5, more high-precision times of light minimum are needed from future observations."
" In Section 4, we displayed the existence of a cyclical period change of WW Dra."," In Section 4, we displayed the existence of a cyclical period change of WW Dra."
" This cyclical variation may be interpreted as due to the magnetic activity of one or both components 1992),, or by the LTTE via the presence of a tertiary companion."," This cyclical variation may be interpreted as due to the magnetic activity of one or both components \cite[]{app92}, or by the LTTE via the presence of a tertiary companion."
" With the following equation given by (2000),,"," With the following equation given by \cite{rov00}, ,"
In our models. gas can occupy one of two phases. cold or hot.,"In our models, gas can occupy one of two phases, cold or hot."
 Halos contain hot gas. which is assumed to be shock-heated to the virial temperature of the halo ancl distributed. like the dark matter in a singular isothermal sphere (SES).," Halos contain hot gas, which is assumed to be shock-heated to the virial temperature of the halo and distributed like the dark matter in a singular isothermal sphere (SIS)."
" After a cooling time /=fos. has elapsed. gas at a sullicientlv high density (corresponding to the gas within the ""cooling radius” ρω) is assumed to cool and condense into a disc."," After a cooling time $t = t_{\rm
cool}$ has elapsed, gas at a sufficiently high density (corresponding to the gas within the “cooling radius” $r_{cool}$ ) is assumed to cool and condense into a disc."
 ‘This cold gas then becomes available for star formation., This cold gas then becomes available for star formation.
 Star formation takes place in both a quiescent and bursting mode., Star formation takes place in both a quiescent and bursting mode.
 Quiescent star formation proceeds in all disces whenever gas is present. according to the expression tear where mon; ds the mass in cold gas and τι is an cllicieney factor that is fixed using nearby galaxy properties (sce below).," Quiescent star formation proceeds in all discs whenever gas is present, according to the expression , where $m_{cold}$ is the mass in cold gas and $\tau_*$ is an efficiency factor that is fixed using nearby galaxy properties (see below)."
 In the bursting mode. which takes place following galaxv-galaxy merecrs. the elliciencv οἱ star formation is sharply increased for a short amount of time (~ 50100 Myr).," In the bursting mode, which takes place following galaxy-galaxy mergers, the efficiency of star formation is sharply increased for a short amount of time $\sim$ 50–100 Myr)."
 The ellicieney and timescale of the starbursts has been calibrated using the results of hyvdrodynamical simulations as ceseribecd in SPE., The efficiency and timescale of the starbursts has been calibrated using the results of hydrodynamical simulations as described in SPF.
 The merger rate is determined by the infall of satellites onto the central galaxy. as described above. and the collision of satellites with one another according to a mocifiecl moean-free path mioclel (see SP and SPE).," The merger rate is determined by the infall of satellites onto the central galaxy, as described above, and the collision of satellites with one another according to a modified mean-free path model (see SP and SPF)."
 In association with star formation. supernovae may reheat and. expell the cold. gas from. the disc and/or the halo.," In association with star formation, supernovae may reheat and expell the cold gas from the disc and/or the halo."
 We model this using the disc-halo model of SP. in which the cllicieney of the feedback. is larger lor galaxies residing in smaller potential wells.," We model this using the disc-halo model of SP, in which the efficiency of the feedback is larger for galaxies residing in smaller potential wells."
 Phese stars also produce metals. which are mixed with the cold. inter-stcllar gas. and may be subsequently ejected. and mixed. with the hot halo gas. or ejected into the dilfuse extra-halo LOAL," These stars also produce metals, which are mixed with the cold inter-stellar gas, and may be subsequently ejected and mixed with the hot halo gas, or ejected into the diffuse extra-halo IGM."
 Our simple constant-vield. instantaneous recvcling model for chemical enrichment: produces. reasonable agreement with observations of metallicities of nearby galaxies (SP). the redshift evolution of the metallicity of cold. gas implied. by observations of DLAS. and the metallicity of the Lyman-a forest (SPE).," Our simple constant-yield, instantaneous recycling model for chemical enrichment produces reasonable agreement with observations of metallicities of nearby galaxies (SP), the redshift evolution of the metallicity of cold gas implied by observations of DLAS, and the metallicity of the $\alpha$ forest (SPF)."
 The main [ree parameters of the model are the star ormation elliciency. τει the supernovac feedback cllicicney I; ⋅ ↙∖↼∖⊽⋜⋯∠⇂↿↓↕⋖⋅⊔⋯⊳∖⊳∖∪⇂⊔↓⋖⋅⋯⇂⊳∖↓≻↓⋅⋯⊔∐⇍∢⊾∠⇂↓≻∢⊾↓⋅⊔⊔↓↿⊔↓⋜↧⊳∖⊳∖∪⇂. stars. or effective vield. jy.," The main free parameters of the model are the star formation efficiency, $\tau_*$, the supernovae feedback efficiency $\epsilon_{SN}^0$ and the mass of metals produced per unit mass of stars, or effective yield, $y$."
" As described in SP. we set these »xuwameters so that a ""reference. galaxy” with a rotation velocity of 220 kms~ at redshift zero has a luminosity. cold gas mass fraction and metallicity in agreement with ocal observations."," As described in SP, we set these parameters so that a “reference galaxy” with a rotation velocity of 220 $\kms$ at redshift zero has a luminosity, cold gas mass fraction and metallicity in agreement with local observations."
 Ciood agreement is then obtained. with optical ancl LIL properties of local galaxies (SP). and optical ooperties of high redshift galaxies (SPE).," Good agreement is then obtained with optical and HI properties of local galaxies (SP), and optical properties of high redshift galaxies (SPF)."
 In this paper our fiducial models are set within a CDM cosmologv with ον0.7.Ot0.3.=0.7. corresponding ↿∪⊔↓⋯⇂∢⊾↓⇀∖≺⊲∐↳∖↓⊳∶⊰⊀↓⊔∺↓↴⊳⋜⋯∠⇂↿↓↕⋖⋅∐∠⊔∐⋰↓⋜↧↓⊔↓⋯⇂∢⊾↓∪⇂⋅∺↓↴↓⊲∖⊳," In this paper our fiducial models are set within a $\Lambda$ CDM cosmology with $\Omega_{\Lambda}=0.7,
\Omega_0=0.3, h=0.7$, corresponding to model $\Lambda$ CDM.3 in SP, and the fiducial model of SPF."
∖∖⊽⋖⋅ have presented similar results for a standard CDM (£3—1) cosmology in (1999)., We have presented similar results for a standard CDM $\Omega_0=1$ ) cosmology in \nocite{mspp:99}{ (1999).
 As recent. observational results seem to favor a cosmological constant ((Perlmutter 1999) and a Yat universe ((Alelebiorri 1999) we feck justified in focusing on only this cosmology., As recent observational results seem to favor a cosmological constant \nocite{perl:99}( 1999) and a flat universe \nocite{boom:99}( 1999) we feel justified in focusing on only this cosmology.
 In section 5 we show that our results are not very sensitive to the assumed cosmology., In section \ref{depend} we show that our results are not very sensitive to the assumed cosmology.
 We focus our analysis on halos at an output redshift of 2=3., We focus our analysis on halos at an output redshift of $z=3$.
 We have also performed an identical analysis on halos at 2= and find no significant dillerences. consistent with the kinematic data ancl column clensity distribution fV). which show little evolution over this range.," We have also performed an identical analysis on halos at $z=2$ and find no significant differences, consistent with the kinematic data and column density distribution $f(N)$, which show little evolution over this range."
 We expect to see evolution both in low redshift (2<1.5) ancl very. high redshift (z24) svstems. however we will defer discussion of this toa future paper.," We expect to see evolution both in low redshift $z < 1.5$ ) and very high redshift $z > 4$ ) systems, however we will defer discussion of this to a future paper."
 The standard SAAIs do not provide us with information on the racial distribution of gas and stars in the model galaxies., The standard SAMs do not provide us with information on the radial distribution of gas and stars in the model galaxies.
 It is reasonable to assume that the surface density of the cold gas is important in determining the star formation rate in the gaseous discs. and in this case the radial distribution of eas should be mocelled. self-consistentlv. within the SAAIs.," It is reasonable to assume that the surface density of the cold gas is important in determining the star formation rate in the gaseous discs, and in this case the radial distribution of gas should be modelled self-consistently within the SAMs."
 This has been done in the models of IX96., This has been done in the models of K96.
 However. there are many uncertainties attached to modelling the structure of the gaseous disc in the initial collapse. and how it may be modified. by mergers. supernovae feedback. ancl secular evolution.," However, there are many uncertainties attached to modelling the structure of the gaseous disc in the initial collapse, and how it may be modified by mergers, supernovae feedback, and secular evolution."
 Therefore here we choose a dilferent. approach., Therefore here we choose a different approach.
 The SAAIs described above produce σους agreement with the observed 2~3 luminosity. function. of Lyman-break ealaxies (SPE)., The SAMs described above produce good agreement with the observed $z\sim 3$ luminosity function of Lyman-break galaxies (SPF).
 The total mass density of cold gas at this redshift is also in agreement with estimates derived. [rom observations from DLAS ((Storrie-Lombardi 1996: 2000).," The total mass density of cold gas at this redshift is also in agreement with estimates derived from observations from DLAS \nocite{stor:96,sw:00}( 1996; 2000)."
 We can therefore ask how this gas must be distributed. relative to these galaxies in order to produce agreement with an independent. set. of observations. the kinematic data.," We can therefore ask how this gas must be distributed relative to these galaxies in order to produce agreement with an independent set of observations, the kinematic data."
 We assume that the vertical profile of the eas is exponential. and consider two functional forms for the radia profiles of the cold. gas: exponential and 1/42. (Alestel).," We assume that the vertical profile of the gas is exponential, and consider two functional forms for the radial profiles of the cold gas: exponential and $1/R$ (Mestel)."
 The exponential racial profile is motivated by observations of local spiral galaxies. which indicate that the ligh distribution. of the disc is well fit. by an. exponentia ( 1970).," The exponential radial profile is motivated by observations of local spiral galaxies, which indicate that the light distribution of the disc is well fit by an exponential \nocite{free:70}( 1970)."
 H£ one assumes that as cold gas is converte into stars its distribution. doesn't change (which many theories of disc sizes implicitly assume). then the profile of cold eas at high recshift should: also be exponential.," If one assumes that as cold gas is converted into stars its distribution doesn't change (which many theories of disc sizes implicitly assume), then the profile of cold gas at high redshift should also be exponential."
" The column density of the gas may then be parameterized by two quantities. the scale length £7, and the central column density VyMsn(2xgRS) (where mas, is the total mass of cold gas in the disc. mg is the mass of the hydrogenatom and fiis the mean molecular weight of the gas. which we take to be 1.3 assuming of the gas is Helium)."," The column density of the gas may then be parameterized by two quantities, the scale length $R_g$ and the central column density $N_0 \equiv m_{\rm gas}/(2\pi
\mu m_H R_g^2)$ (where $m_{\rm gas}$ is the total mass of cold gas in the disc, $m_H$ is the mass of the hydrogenatom and $\mu$ is the mean molecular weight of the gas, which we take to be 1.3 assuming of the gas is Helium)."
 Phe column density as a function, The column density as a function
when age changes from 10 to 11 Gyrs.,when age changes from 10 to 11 Gyrs.
" Therefore. the = 50 Ix uncertainty in the T;,,s of dwarls implies a x 1.3 Gyr uncertainty in the age inlerred from £705 al the metallicity of 47 Tuc."," Therefore, the $\pm$ 50 K uncertainty in the $T_{eff}$ s of dwarfs implies a $\mp$ 1.3 Gyr uncertainty in the age inferred from $H\delta_F$ at the metallicity of 47 Tuc."
 Belore discussing svstematic effects in the input stellar parameters. we assess (he effect ol the mismatch of the theoretical isochrones to the red giant branch of 47 Tuc in Figures 1 and 2..," Before discussing systematic effects in the input stellar parameters, we assess the effect of the mismatch of the theoretical isochrones to the red giant branch of 47 Tuc in Figures \ref{fig1} and \ref{fig2}."
 In Section 2.1. we saw that the Salaris isochrone is bluer by ~ 0.04 mag at the lower eijant branch aud redder by a comparable amount at the upper giant branch., In Section \ref{cmd} we saw that the Salaris isochrone is bluer by $\sim$ 0.04 mag at the lower giant branch and redder by a comparable amount at the upper giant branch.
 In the case of the Padova isochrones. the theoretical prediction is bluer than the observations through all the RGB. by ~ 0.03 mag.," In the case of the Padova isochrones, the theoretical prediction is bluer than the observations through all the RGB, by $\sim$ 0.03 mag."
 Such color differences. if due solely to temperature elfects. translate into T;jj mismatches of z 50 Ix in the case of the Salaris isochrones and + 70 Ix in the case of the Padova isochrones. according to the calibration derived in Paper IL. In the case of the Salaris isochrones. correcting for (hese mismatches amounts to negligible changes in the line index predictions.," Such color differences, if due solely to temperature effects, translate into $T_{eff}$ mismatches of $\pm$ 50 K in the case of the Salaris isochrones and + 70 K in the case of the Padova isochrones, according to the calibration derived in Paper I. In the case of the Salaris isochrones, correcting for these mismatches amounts to negligible changes in the line index predictions."
 In fact. the percentage variations in all indices correspond to less than 0.4 Gvr. so thal we do not need to perform any correction to our model predictions due to the slight mismatch in the red eiant branch.," In fact, the percentage variations in all indices correspond to less than 0.4 Gyr, so that we do not need to perform any correction to our model predictions due to the slight mismatch in the red giant branch."
 This is because there is a compensation between (he opposite 7;;; mismatches in the lower and upper giant branch., This is because there is a compensation between the opposite $T_{eff}$ mismatches in the lower and upper giant branch.
 In the case of the Padova isochrones. as the model RGB is svstematically bluer than the observations. the elfect on speclroscopic age predictions is not negligible. leading to svstematic age overestimates of about 1 Gyr.," In the case of the Padova isochrones, as the model RGB is systematically bluer than the observations, the effect on spectroscopic age predictions is not negligible, leading to systematic age overestimates of about 1 Gyr."
 In section 3.4. we inferred a spectroscopic age of 14 Gvrs trom {1 and slightly above that value Irom 7/5.," In section \ref{padova}
 we inferred a spectroscopic age of 14 Gyrs from $H\beta$ and slightly above that value from $H\gamma$."
 Correcting these predictions for the svstematic temperature error in (he RGB would bring them into better agreement with (he age inferred [rom the position of the turn-olf found in Section 2.1 (12.5 « (€ < 14.1 Gvrs)., Correcting these predictions for the systematic temperature error in the RGB would bring them into better agreement with the age inferred from the position of the turn-off found in Section \ref{cmd} (12.5 $<$ t $<$ 14.1 Gyrs).
 Uncertainties due (o svstematic errors in (he input parameters of dwarf stars are smaller than the variations of the input parameters of giants., Uncertainties due to systematic errors in the input parameters of dwarf stars are smaller than the variations of the input parameters of giants.
 Thus. thev have only a relatively minor impact on model predictions. at the old ages of GCs.," Thus, they have only a relatively minor impact on model predictions, at the old ages of GCs."
" Except lor 70,5. all line indices vary by less (han when varving the 7;;;and scales of clwarls."," Except for $H\delta_F$, all line indices vary by less than when varying the $T_{eff}$and -scales of dwarfs."
 Taking {19 as illustrative. this translates to roughly a 0.5 Gyr uncertainty in age due to the T; py-scale of dwarfs and a 0.25 Gyr uncertainty due to their scale.," Taking $H\beta$ as illustrative, this translates to roughly a 0.5 Gyr uncertainty in age due to the $T_{eff}$ -scale of dwarfs and a 0.25 Gyr uncertainty due to their -scale."
 By comparison. uncertainties of 75 Ix or 0.1 dex in the input 7;jj and /Pe/IHj-scales of giants produce al Gyr uncertainty in the age inferred [rom either 7/5 or δι.," By comparison, uncertainties of 75 K or 0.1 dex in the input $T_{eff}$ and -scales of giants produce a 1 Gyr uncertainty in the age inferred from either $H\beta$ or $H\delta_F$."
 This is particularly important in view ol the current discrepancies in the 7;y j-scales of giant stars among different sets of the most recent theoretical isochrones. which amount (o 200 EK (Salaris et al.," This is particularly important in view of the current discrepancies in the $T_{eff}$ -scales of giant stars among different sets of the most recent theoretical isochrones, which amount to 200 K (Salaris et al."
 2002. Schiavon. Barbuy Druzual 2000).," 2002, Schiavon, Barbuy Bruzual 2000)."
 Such a laree discrepancy is süll lingering. mostly because the position of the theoretical red eiant branch is dependent ou poorly constrained inputs of stellar evolutionary models. such as the mixing length. parameter and the T(7) relation adopted as boundary condition for the interior models.," Such a large discrepancy is still lingering, mostly because the position of the theoretical red giant branch is dependent on poorly constrained inputs of stellar evolutionary models, such as the mixing length parameter and the $\tau$ ) relation adopted as boundary condition for the interior models."
 On the other hand. the present work may be viewed as an important check on the current theoretical Salaris T; pps. as Table 2. shows that," On the other hand, the present work may be viewed as an important on the current theoretical Salaris $T_{eff}$ s, as Table \ref{tbl-4} shows that"
and in the with apparently satisfactoryresults.,and in the with apparently satisfactory.
.. Given the role of the AAS in the community. it could implement such a scheme will relative ease.," Given the role of the AAS in the community, it could implement such a scheme with relative ease."
 The transition from the postdoctoral to junior faculty. level is the least lormalized. especially because there is no single duration of the postdoctoral stage applicable to all researchers.," The transition from the postdoctoral to junior faculty level is the least formalized, especially because there is no single duration of the postdoctoral stage applicable to all researchers."
 Those applicants who did not vet finish their postdoctoral position. but who would like to do so. often engage in a tedious negotiation with the emplover institution about a possible delerral of a junior faculty position.," Those applicants who did not yet finish their postdoctoral position, but who would like to do so, often engage in a tedious negotiation with the employer institution about a possible deferral of a junior faculty position."
 Some institutions have been known to allow several-vear delerrals. while others insist on an immecdiate starting date.," Some institutions have been known to allow several-year deferrals, while others insist on an immediate starting date."
 Every effort should be made to accommodate such deferrals when (μον are requested. with the realization that the junior faculty member will greatly. benelit from the additional (raining (hat (hey can receive Iree of job application pressure.," Every effort should be made to accommodate such deferrals when they are requested, with the realization that the junior faculty member will greatly benefit from the additional training that they can receive free of job application pressure."
 However. in many cases (here will be real financial reasons that would make such deferrals impossible.," However, in many cases there will be real financial reasons that would make such deferrals impossible."
 Therelore. at the very least (he possibility. of deferral and its duration should be part of the job description. (," Therefore, at the very least the possibility of deferral and its duration should be part of the job description. ("
Of course. responsible behavior on the part of the applicant. such as honoring a binding contract. is necessary {ο make delerrals work.),"Of course, responsible behavior on the part of the applicant, such as honoring a binding contract, is necessary to make deferrals work.)"
 The difference between timelines for appointments of junior faculty ancl postdocs presents an additional difficulty For those who apply for both (vpes of positions., The difference between timelines for appointments of junior faculty and postdocs presents an additional difficulty for those who apply for both types of positions.
 Those who accept a postdoctoral offer aud are then offered a junior faculty. position are often in an awkward situation. having to choose between deferring the faculty offer or rejecting (he position thev had. already. accepted.," Those who accept a postdoctoral offer and are then offered a junior faculty position are often in an awkward situation, having to choose between deferring the faculty offer or rejecting the position they had already accepted."
 These issues may even put such applicants al a disadvantage in the considerations for ασ positions., These issues may even put such applicants at a disadvantage in the considerations for faculty positions.
 Finally. one substantial difficulty with the final pairing of applicants with positions are the needs of dual-career couples.," Finally, one substantial difficulty with the final pairing of applicants with positions are the needs of dual-career couples."
 Couples attempting to obtain positions at the same or neighboring institutions must prioritize differently when negotiating and accepting offers., Couples attempting to obtain positions at the same or neighboring institutions must prioritize differently when negotiating and accepting offers.
 It delavs acceptance οἱ an olfer because an applicant must wait until both people have heard [rom all the imstitutions before the couple can jointly make a decision., It delays acceptance of an offer because an applicant must wait until both people have heard from all the institutions before the couple can jointly make a decision.
 Any delay in the application process negatively affects other shortlisted individuals. who often accept other postdocs because (hey cannot wait indefinitely for ear (hal they will not receive a job at all.," Any delay in the application process negatively affects other shortlisted individuals, who often accept other postdocs because they cannot wait indefinitely for fear that they will not receive a job at all."
 Furthermore. some applicants are secretive about. (heir “two-body problem. believing (often correctlv) that they are less likely to receive an olfer if the institution perceives anv conflict of interest.," Furthermore, some applicants are secretive about their “two-body” problem, believing (often correctly) that they are less likely to receive an offer if the institution perceives any conflict of interest."
 We recognize (hat there is no easy. solution here but 10te (hat coordinating the timeline for applications. interviews and offers will make it nicl easier or such couples to make decisions and will streamline the process considerably.," We recognize that there is no easy solution here but note that coordinating the timeline for applications, interviews and offers will make it much easier for such couples to make decisions and will streamline the process considerably."
 We also encourage institutions to develop couple-lviendly hiring practices., We also encourage institutions to develop couple-friendly hiring practices.
 Institutions in cities that. host many other institutions should consider forming joint programs (o coordinate job offers to couples who disclose the need to find geographically compatible jobs., Institutions in cities that host many other institutions should consider forming joint programs to coordinate job offers to couples who disclose the need to find geographically compatible jobs.
 In analogy to family-friendly programs. we expect such hiring practices to present a very. considerable advantage for attracting talented couples.," In analogy to family-friendly programs, we expect such hiring practices to present a very considerable advantage for attracting talented couples."
 The profile of the solid oband toward lis dominated bv a prominent narrow absorption centered at 21101., The profile of the solid band toward is dominated by a prominent narrow absorption centered at 2140.
 Tt shows also absorption on an extended oug waveleneth wine. as well as in a wing to the short wavelength side (Fig. 1)).," It shows also absorption on an extended long wavelength wing, as well as in a wing to the short wavelength side (Fig. \ref{f:obs}) )."
 Broad wing absorption is not detected in the prescut signal-to-noise limited spectrum of he band ofIRS9., Broad wing absorption is not detected in the present signal-to-noise limited spectrum of the band of.
. The origin of the wwines and the decomposition frou the ceutral narrow component is further discussed in , The origin of the wings and the decomposition from the central narrow component is further discussed in 3.2.
ere we will concentrate ol a comparison of the aabsorptiou with the narrow 2110 ccolponcent. which must. eiven their small width. both originate from apolar ices.," Here we will concentrate on a comparison of the absorption with the narrow 2140 component, which must, given their small width, both originate from apolar ices."
 The width of the feature (FWHAI=3.5 1)) is a factor of 2.30.7 (30) arger than the width of the yband., The width of the feature (FWHM=3.5 ) is a factor of $\pm$ 0.7 $\sigma$ ) larger than the width of the band.
 What imechanisnií(s) can make the interstellar να] broader than the ρα, What mechanism(s) can make the interstellar band broader than the band?
 The width of absorption bands of iiolecules embedded in solid matrices is affected by a πο of difficult. to diseutauele iiecliiuisius., The width of absorption bands of molecules embedded in solid matrices is affected by a number of difficult to disentangle mechanisms.
 Iu experiments of CO isolated iu auuealed No matrices. the width of the CO hands was found to depend stronely on the CO/N» ratio (Dubost. Charucau. IEuig 1982).," In experiments of CO isolated in annealed $_2$ matrices, the width of the CO bands was found to depend strongly on the $_2$ ratio (Dubost, Charneau, Harig 1982)."
 This ‘concentration broadening” is the result of shifts in the transition frequency because of static aud dynamic iuteractions between the CO molecules themselves., This `concentration broadening' is the result of shifts in the transition frequency because of static and dynamic interactions between the CO molecules themselves.
 The static interaction is duc to the electric field generated by the permanent dipole moment of one CO inolecule wewhine on other nearby CO molecules or due to the electric field created by crystalline defects;, The static interaction is due to the electric field generated by the permanent dipole moment of one CO molecule working on other nearby CO molecules or due to the electric field created by crystalline defects.
 The dynamic interaction is due to the resonance of oscillating electric fields generated by different. CO molecules., The dynamic interaction is due to the resonance of oscillating electric fields generated by different CO molecules.
 The frequency shifts induced iu both cases result in broadening of the absorption baud because of the distribution of the local field generated by the different configuratious of the ucighboring molecules., The frequency shifts induced in both cases result in broadening of the absorption band because of the distribution of the local field generated by the different configurations of the neighboring molecules.
 The smallness of the permancut dipole moment of CO males the broadening from cyvuamic interaction significautly larecr than broadening induced by static interaction., The smallness of the permanent dipole moment of CO makes the broadening from dynamic interaction significantly larger than broadening induced by static interaction.
 This greatly culauces the width ofthe bbaud with respect to the bbaud. because the couceutration of nunolecules is a factor of 90 higher.," This greatly enhances the width of the band with respect to the band, because the concentration of molecules is a factor of 90 higher."
 There is no dynamic interaction of wwith nunolecules. because their transition frequencies are several tens of waveuuuboers apart.," There is no dynamic interaction of with molecules, because their transition frequencies are several tens of wavenumbers apart."
 Thus. at a mixing ratio of CO:No=1:100. the band of wwas found to be a factor of 5 wider than the bband (Dubostetal.1982).," Thus, at a mixing ratio of $_2$ =1:100, the band of was found to be a factor of 5 wider than the band \citep{dubo82}."
. However. at such a low CO concentration the hands of both isotopes are an order of magnitude too narrow compared to the bands observed towardIRS9.," However, at such a low CO concentration the bands of both isotopes are an order of magnitude too narrow compared to the bands observed toward."
. At higher CO concentrations. the width of both buuds increases. but that of the ybaud erows more slowly because the dynamic aud static xoadenius mechanigus are nof additive. aud in fact the static fields detune the dynamic interactions.," At higher CO concentrations, the width of both bands increases, but that of the band grows more slowly because the dynamic and static broadening mechanisms are not additive, and in fact the static fields detune the dynamic interactions."
 As a result. a pure. annealed CO ice las an EWITIMIT for0Ο. and EWIIMAIA ‘for citepewiu6l.dubos2..," As a result, a pure, annealed CO ice has an FWHM=1.7 for, and FWHM=1.1 for \\citep{ewin61, dubo82}."
 These widths increase by ~0.5 wwhen the CO ice structure is amorphous (Saudfordetal.1988)., These widths increase by $\sim$ 0.5 when the CO ice structure is amorphous \citep{sand88}.
. Thus. a pure CO ice that may be amorphous provides a good fit to the bband (FWIHAL=1.5 13) observed towardIRSO.. but this pure CO ice has a bband that is still à factor of 1.60 too narrow.," Thus, a pure CO ice that may be amorphous provides a good fit to the band (FWHM=1.5 ) observed toward, but this pure CO ice has a band that is still a factor of 1.60 too narrow."
 Au additional mechanisim is therefore needed that cau selectively broaden the Dhaud., An additional mechanism is therefore needed that can selectively broaden the band.
 A viable mechauisii is interaction of light with COrich interstellar icv erains., A viable mechanism is interaction of light with CO–rich interstellar icy grains.
 Electromagnetic radiation can polarize the delipoles. which induces electric fields within the erain that oscillate at the yvibration transition frequency (e.g. Bohren&ITuffiuan1983)).," Electromagnetic radiation can polarize the dipoles, which induces electric fields within the grain that oscillate at the vibration transition frequency (e.g. \citealt{bohr83}) )."
 This creates resonances with the dipole electric field. resulting in frequency shifts aud. band broadening. mit only at sufficicutly high. CO concentrations (30%:: Ticlensetal. 19011).," This creates resonances with the dipole electric field, resulting in frequency shifts and band broadening, but only at sufficiently high CO concentrations $>$; \citealt{tiel91}) )."
 Therefore. the profile aud position of the baud of the diluted uimolecules are not affected by these particle shape effects.," Therefore, the profile and position of the band of the diluted molecules are not affected by these particle shape effects."
 Using the calculations iu the siunall particle luit presented in Elreufreundetal...(1997)... we thus find that acceptable fits to the ρα are obtained for ellipsoidally shaped particles. iu articular with a continous distribution of shapes (CDE: Fie.," Using the calculations in the small particle limit presented in \citet{ehre97}, we thus find that acceptable fits to the band are obtained for ellipsoidally shaped particles, in particular with a continuous distribution of shapes (`CDE'; Fig."
 Όσο)., \ref{f:labfit1}c c).
 Although there is a mismatch on the short wavelength side of the 2110 feature. this can be accounted for by assuming other varticle shapes or by uncertainties in the optical coustauts of CO.," Although there is a mismatch on the short wavelength side of the 2140 feature, this can be accounted for by assuming other particle shapes or by uncertainties in the optical constants of CO."
 A better fit is obtained (Fie., A better fit is obtained (Fig.
 300) if we take the slightly differeut «yptical constants of (1998)., \ref{f:labfit1}e e) if we take the slightly different optical constants of \citet{bara98}.
. Note that the shape of the ybaud indeed remains unchaused for different particle shapes (Fig., Note that the shape of the band indeed remains unchanged for different particle shapes (Fig.
 3bb aud d)., \ref{f:labfit1}b b and d).
 Finally. au alternative wav to preferentially broaden the ybaud is to change the ice composition.," Finally, an alternative way to preferentially broaden the band is to change the ice composition."
 In the database of Ehreufreuudetal.(1997). the ratio of to ybaud width is ~1.3 for most mixtures., In the database of \citet{ehre97} the ratio of to band width is $\sim$ 1.3 for most mixtures.
 At low laboratory eniperatures (Z7=10 Is) the mixture No:CO=1:1 has he largest width ratio (1.5). while at high laboratory eniperatures (Z7= 30 Is) mixtures with OofCO21 have width ratios of up to Ls.," At low laboratory temperatures $T=10$ K) the mixture $_2$ :CO=1:1 has the largest width ratio (1.5), while at high laboratory temperatures $T=$ 30 K) mixtures with $_2$ $\geq$ 1 have width ratios of up to 1.8."
 The No mixture provides the vest fit to the band. aud the heated Ου mixture fits the αλά better (83.1.1: Fie.," The $_2$ mixture provides the best fit to the band, and the heated $_2$ mixture fits the band better 3.1.1; Fig."
 leeh)., \ref{f:labfit2}e e–h).
 We thus consider these nixtures as reasonable. but not as good as pure CO.," We thus consider these mixtures as reasonable, but not as good as pure CO."
 To conclude. the peak position aud width of the band observed in the direction of aare well explained by a pure CO ice that mieht be amorphous.," To conclude, the peak position and width of the band observed in the direction of are well explained by a pure CO ice that might be amorphous."
 To fit the ybaud with the same pure ice a mechanisiu is needed that xeferentially broadeus the, To fit the band with the same pure ice a mechanism is needed that preferentially broadens the
ciameter of 2.1532£0.028 inas?.,diameter of $\pm$ 0.028.
. We then combined our measurement of the stars Opp and the parallax determined by Beneclietetal.(2006) to calculate the sars physical radius: LEO.01 R.., We then combined our measurement of the star's $\theta_{\rm LD}$ and the parallax determined by \citet{2006AJ....132.2206B} to calculate the star's physical radius: $\pm$ 0.01 $R_\odot$.
 Table 3. lists the meastuwements mace bere as well as other stellar paraineers., Table \ref{parameters} lists the measurements made here as well as other stellar parameters.
 The error for tie. LD cliameter Gt was derived. using the 1jethod. descρου. i1 (2010).. who showed that a non-linear least-squares inehod does not sullicleutly accouut for atinospheric effects o itime scales shorter than the wiidow between arget aud calibratoο ious.," The error for the LD diameter fit was derived using the method described in \citet{2010SPIE.7734E.103T}, who showed that a non-linear least-squares method does not sufficiently account for atmospheric effects on time scales shorter than the window between target and calibrator observations."
 They describe a bootstrap lonte Carlo methocl tha treats the obse'vallous as οορ» o‘data poiuts because the NOI colects ¢ala ln scans consistiug [9]“16 chainels simultaneousv., They describe a bootstrap Monte Carlo method that treats the observations as groups of data points because the NOI collects data in scans consisting of 16 channels simultaneously.
 They discovered that when the data poiuts were analyzecl iucdividu:lly. a siugle scans deviation [ron the trend had a large impact o1 the 'esulting clameter aid er‘or caleulation.," They discovered that when the data points were analyzed individually, a single scan's deviation from the trend had a large impact on the resulting diameter and error calculation."
 On the otjer haIc. wheu they preserved the inhereWe srticture of the observatioal data N uslng scaus of 16 ch:inels instead of individual data pejnts. he uncertainty on the aeular clialmeter was larger aud nore realistic.," On the other hand, when they preserved the inherent structure of the observational data by using scans of 16 channels instead of individual data points, the uncertainty on the angular diameter was larger and more realistic."
 This methocl makes nQO assuuptious about uiderN|& errors due to atmospheric effects. which are applicable t« yall stars observed using grouud-base Inst‘uments.," This method makes no assumptions about underlying errors due to atmospheric effects, which are applicable to all stars observed using ground–based instruments."
 Figure 6 SCws {ie. probability density Duucion for e Eris LD cliameter meastuemeM., Figure \ref{error_dist} shows the probability density function for $\epsilon$ Eri's LD diameter measurement.
" Once Opp was determined interferoimetrically. the τςp was calculated usin[n]oO the ‘elation whe'e μοι, is the bolometric fux and σ is the Stefau-Boltzimann constant."," Once $\theta_{\rm LD}$ was determined interferometrically, the $T_{\rm eff}$ was calculated using the relation where $F_{\rm BOL}$ is the bolometric flux and $\sigma$ is the Stefan–Boltzmann constant."
 Apap was compttec in the following wav: the stars V aud Jy maguitudes were ceredceued using the extinctlon curve leseribed in Carclellieal.(1989) alic the interstellar absorption (Ay) value., $F_{\rm BOL}$ was computed in the following way: the star's $V$ and $K$ magnitudes were dereddened using the extinction curve described in \citet{1989ApJ...345..245C} and the interstellar absorption $A_{\rm V}$ ) value.
 The intrinsic b‘oadbatd color (V.— A) was calculated aud the bolometric correction (BC) was deteruiued by terpolating between ile [Fe/H] = 0.0. axl -1.0 tables from Alonsoetal. (1999)..," The intrinsic broadband color $V-K$ ) was calculated and the bolometric correction (BC) was determined by interpolating between the [Fe/H] = 0.0, and -1.0 tables from \citet{1999AandAS..140..261A}."
 They »oiut out that in tie range of 6000 WeeLarLm Il00 Ix. their BC calibration is syuunetrically clistributect wound a EO.LO mag |uidd when coiparec tooher calibratious. so we assigned tle BC a1 error of 0.10.," They point out that in the range of 6000 K $\geq T_{\rm eff} \geq$ 4000 K, their BC calibration is symmetrically distributed around a $\pm$ 0.10 mag band when compared to other calibrations, so we assigned the BC an error of 0.10."
 Fpo was determinec by apply‘ine the BC ancl the Tig was calculated to be 50394126 Ix. The stars luminosity (£L) was :iso caletated islug he absolute V. magnitude aud the BC., $F_{\rm BOL}$ was determined by applying the BC and the $T_{\rm eff}$ was calculated to be $\pm$ 126 K. The star's luminosity $L$ ) was also calculated using the absolute $V$ magnitude and the BC.
 See Table for a list of all these )araiueters., See Table \ref{parameters} for a list of all these parameters.
 Because the BC is au importa| paramete ‘in the Tog determination. we also derived the BC uxing the equatiou reating Tuy aud BC p'eseuted by Flower(1996) and updated by (2010)..," Because the BC is an important parameter in the $T_{\rm eff}$ determination, we also derived the BC using the equation relating $T_{\rm eff}$ ) and BC presented by \citet{1996ApJ...469..355F} and updated by \citet{2010AJ....140.1158T}."
 We used a raige of Tag values that bracketed the Το listed for e Eri in by 150 Ix. The maxinun difference in BC between the Flower ancl Alonso et al.calculations was 0.03. which is we| within our assigned error bar of 0.10. aud ouly chauged the final Teg by a maximum 31 I (0.7% T," We used a range of $T_{\rm eff}$ values that bracketed the $T_{\rm eff}$ listed for $\epsilon$ Eri in \citet{2004AJ....127.1227C} by 450 K. The maximum difference in BC between the Flower and Alonso et al.calculations was 0.03, which is well within our assigned error bar of 0.10, and only changed the final $T_{\rm eff}$ by a maximum 34 K $\%$ )."
Solar photospheric magnetic fields and their associated dynamics have been extensively studied.,Solar photospheric magnetic fields and their associated dynamics have been extensively studied.
 However an understanding of their vertical variation from the photosphere though the chromosphere to the corona needs better comprehension., However an understanding of their vertical variation from the photosphere though the chromosphere to the corona needs better comprehension.
 Direct measurement and diagnosis of magnetic and flow fields in higher layers. especially in the near force-free chromosphere can play an important role im fully understanding their three-dimensional (3D) structures.," Direct measurement and diagnosis of magnetic and flow fields in higher layers, especially in the near force-free chromosphere can play an important role in fully understanding their three-dimensional (3D) structures."
 Nevertheless. such efforts were relatively rare due to the paucity of chromospheric spectral lines with suitable Zeeman-split sensitivity (Dalgarno&Layzer1987) and the complicated dynamics and topology of the magnetized plasma in this particular layer.," Nevertheless, such efforts were relatively rare due to the paucity of chromospheric spectral lines with suitable Zeeman-split sensitivity \citep{Dalgarno+Layzer1987soap.conf.....D} and the complicated dynamics and topology of the magnetized plasma in this particular layer."
 Taking advantage of modern observational techniques and recognizing the critical need to explore chromospheric magnetic fields. Increasing attention has recently been paid to the spectro-polarimetry of the chromosphere (e.g..Socas-Navarroetal.2000:Zhang&etal.2004:Balasubramaniam 2004)... which reveal the height-dependent variation of different types of magnetic features.," Taking advantage of modern observational techniques and recognizing the critical need to explore chromospheric magnetic fields, increasing attention has recently been paid to the spectro-polarimetry of the chromosphere \citep[e.g.,][]{Socas-Navarro+etal2000Sci...288.1396S, Zhang+Zhang2000SoPh..194...19Z, TrujilloBueno+etal2002Natur.415..403T, LopezAriste+Casini2002ApJ...575..529L, Solanki+etal2003Natur.425..692S, leka+metcalf2003, Lagg+etal2004A&A...414.1109L, Balasubramaniam+etal2004ApJ...606.1233B}, which reveal the height-dependent variation of different types of magnetic features."
" Those analyses were made using magnetically sensitive spectral lines formed 1n the chromospheric levels. such as 8849.8 and 854.2 nm. 11083.0 nm and D; line. DD, 589.6 nm. παπά llines."," Those analyses were made using magnetically sensitive spectral lines formed in the chromospheric levels, such as 849.8 and 854.2 nm, 1083.0 nm and $_3$ line, $_1$ 589.6 nm, and lines."
" In particular. the bb: 517.27 nm line is favorable for spectro-polarimetry in the low chromosphere because its core forms in à narrow region near or right above the temperature minimum region (TMR) with a relatively large Landé g,,; factor of 1.75 (e.g..Briand&Solanki 1995).."," In particular, the $_2$ 517.27 nm line is favorable for spectro-polarimetry in the low chromosphere because its core forms in a narrow region near or right above the temperature minimum region (TMR) with a relatively large Landé $_{eff}$ factor of 1.75 \citep[e.g.,][]{Briand+Solanki1995A&A...299..596B}."
 Theoretical calculation (Altrock&Canfield1974:Litesetal.1988;Mauas1988) and observational analysis (Briand&Solanki1998:BriandMartínezPillet2001:Gosain&Choudhary2003) have been carried out on bbs Stokes polarization spectra. which corroborate that it is well suited for probing the magnetic and flow fields in the low chromosphere.," Theoretical calculation \citep{Altrock+Canfield1974, Lites+etal1988, Mauas+etal1988} and observational analysis \citep{Briand+Solanki1998A&A...330.1160B, Briand+MartinezPillet2001ASPC..236..565B, Gosain+Choudhary2003SoPh..217..119G} have been carried out on $_2$ Stokes polarization spectra, which corroborate that it is well suited for probing the magnetic and flow fields in the low chromosphere."
 Doppler shifts of Stokes / and Q.U.V signals can be used to investigate mass flows in and around magnetic elements (Solanki1986:Solanki&Pahlke1988).," Doppler shifts of Stokes $I$ and $Q, U, V$ signals can be used to investigate mass flows in and around magnetic elements \citep{Solanki1986A&A...168..311S,
Solanki+Pahlke1988A&A...201..143S}."
 In contrast to the Stokes / that represents the total intensity of light. the Stokes Q.U (the linearly polarized component) and V (the circularly polarized component) have contribution only from," In contrast to the Stokes $I$ that represents the total intensity of light, the Stokes $Q, U$ (the linearly polarized component) and $V$ (the circularly polarized component) have contribution only from"
the nominal value for the system in the followine.,the nominal value for the system in the following.
 The line paramcters for J123707|621lue and sw correspond to velocityv-inteerated emission line streneths of Teorgy =OL8040.029 and 940.029ku. Ίοline luminosities of L/CO(10) =(5.56-E0.86) aud 180.85) « 1029Ipriune..," The line parameters for J123707+6214ne and sw correspond to velocity-integrated emission line strengths of $I_{\rm
CO(1-0)}$ $\pm$ 0.029 and $\pm$, i.e.,line luminosities of $L'_{\rm CO(1-0)}$ $\pm$ 0.86) and $\pm$ $\times$ $^{10}$."
 We have also detected spatially resolved line cmission at 250 significance toward both components of J123707|6211 refflx))., We have also detected spatially resolved line emission at $\gtrsim$ $\sigma$ significance toward both components of J123707+6214 \\ref{f1x}) ).
" The ne component douinates the iutegrated line enission rofflx.. left), extracted over a velocity range comparable o the nap."," The ne component dominates the integrated line emission \\ref{f1x}, ), extracted over a velocity range comparable to the map."
" The maxiumun signal-to-noise ratio on the sw colmponent is obtained over a narrower velocity rauge vettls.. ο),"," The maximum signal-to-noise ratio on the sw component is obtained over a narrower velocity range \\ref{f1x}, )."
 Tn this map. the sw component is xiehter than the ne component. comparable to what is seen in the unmaps of Tacconi et ((2006.. 2008)).," In this map, the sw component is brighter than the ne component, comparable to what is seen in the maps of Tacconi et \citeyear{tac06}, \citeyear{tac08}) )."
 Only ~60% of the emission from the ne component are seen over lis narrower velocity rauge., Only $\sim$ of the emission from the ne component are seen over this narrower velocity range.
 We do not detect the nuderling coutinmunu enisson at a 36 upper lanit of Lat nam (rest-frame yan)., We do not detect the underlying continuum emission at a $\sigma$ upper limit of $^{-1}$ at mm (rest-frame $\mu$ m).
" From Caussian fitting to the integrated line profile refflx.. right) we obtain S,2Llczü0.snuujJv at de= I85x110—us.. centered at :—2.187520.0006."," From Gaussian fitting to the integrated line profile \\ref{f1x}, , ), we obtain $S_{\nu}$ $\pm$ mJy at $v$ $\pm$, centered at $z$ $\pm$ 0.0006."
. This. corresponds ο Teespy 1240.51aus., This corresponds to $I_{\rm CO(5-4)}$ $\pm$.
" Fitting the ne andJJ sw componcuts individually vields 5,22. [2:0.5 and 2.1250.5 nud. dez 1674121 aud 13241230gus. and Zoo; q;21.174z0.33 aud 140.29sus. respectively."," Fitting the ne and sw components individually yields $S_{\nu}$ $\pm$ 0.5 and $\pm$ mJy, $v$ $\pm$ 124 and $\pm$, and $I_{\rm CO(5-4)}$ $\pm$ 0.33 and $\pm$, respectively."
" We tlius derive Zt,"" ,7(1.392:0.32) and (1.12+0.29) «1029prime.. respectively,"," We thus derive $L'_{\rm
CO(5-4)}$ $\pm$ 0.32) and $\pm$ $\times$ $^{10}$, respectively."
" This implies CO 723 92/1 »0 line brightucss elmperature ratios of 73; =0.3940.09 and 0.27250.10.— (sw). and CO /=h sl/l σα line xiehtuess tempcrature ratios of r5,=0.2640.07 and 20.05."," This implies CO $J$ $\to$ $\to$ 0 line brightness temperature ratios of $r_{31}$ $\pm$ 0.09 and $\pm$ 0.10 (sw), and CO $J$ $\to$ $\to$ 0 line brightness temperature ratios of $r_{51}$ $\pm$ 0.07 and $\pm$ 0.08."
" The aand ecnussion lues are clearly subthermally excited toward th. components (rg, <1 and (04:1).", The and emission lines are clearly subthermally excited toward both components $r_{31}$$<$ 1 and $r_{51}$$<$ 1).
 Iuiterestiugly. both conrponeuts appear to have comparable eas excitation.," Interestingly, both components appear to have comparable gas excitation."
 The ne component is brighter iu all CO transitions., The ne component is brighter in all CO transitions.
 This sugeests that the ne component carries the dominant raction of the molecular gas mass in this svstem., This suggests that the ne component carries the dominant fraction of the molecular gas mass in this system.
" Based ona ULIRG conversion factor κοΞ0.δ 5 to derive Aa, from Loooq (Downes Solomon 1998)). we detcrimime the total uolecular gas masses of J123707|621tne aud sw to be M,ens L3 and «1019 ie. bv more than a factor of 2 higher than previously found based on the ddata (scaled to the same oco). aud corresponding to ~2/3 of the stellar mass in this svstem (Taccoui et 2008))."," Based on a ULIRG conversion factor $\alpha_{\rm
CO}$ $^{-1}$ to derive $M_{\rm gas}$ from $L'_{\rm CO(1-0)}$ (Downes Solomon \citeyear{ds98}) ), we determine the total molecular gas masses of J123707+6214ne and sw to be $M_{\rm
gas}$ =4.3 and $\times$ $^{10}$ i.e., by more than a factor of 2 higher than previously found based on the data (scaled to the same $\alpha_{\rm CO}$ ), and corresponding to $\sim$ 2/3 of the stellar mass in this system (Tacconi et \\citeyear{tac06}, \citeyear{tac08}) )."
 Iu Figure 3.. maps of the eenission are slow in wwidevelocity chanucls.," In Figure \ref{f2}, maps of the emission are shown in widevelocity channels."
" The οσοι τοπατα J123:07]6211ue appears —clvnamuically resolved οι 1.5"" (-12kkpc) seales. which may sugeest that the cussion is more spatially extended than in the Thine (0.57+0.2"". or LItL6kkpe: Tacconi et citeveartac06))."," The emission toward J123707+6214ne appears dynamically resolved on $\sim$ $''$ $\sim$ kpc) scales, which may suggest that the emission is more spatially extended than in the line $''$$\pm$ $''$, or $\pm$ kpc; Tacconi et \\citeyear{tac06}) )."
" 123707|621lsw appears imareinally spatially resolved in position-velocity space at best. consistent with the size measured in celmission within the relative uncertainties (0.97+0.3"". or 7.1425 kkpe: Tacconi ct citeveartacQ06))."," J123707+6214sw appears marginally spatially resolved in position-velocity space at best, consistent with the size measured in emission within the relative uncertainties $''$$\pm$ $''$, or $\pm$ kpc; Tacconi et \\citeyear{tac06}) )."
" Asstunine radii of 6 and kkpc for J123707|621Ine aud sw. this vields dyuiunuical masses of Maa, ssin?/22.9 and «101 (which we estimate to be reliable within a factor of 2)."," Assuming radii of 6 and kpc for J123707+6214ne and sw, this yields dynamical masses of $M_{\rm dyn}$ $^2$$i$ =2.9 and $\times$ $^{11}$ (which we estimate to be reliable within a factor of 2)."
 This is about twice as high as previous estimates based on eenission (Tacconi ct citeveartacüS8)). aud corresponds to gas mass fractious of f4-0.15 aud 0.25 for JL23707|6211ne and sw. respectively.," This is about twice as high as previous estimates based on emission (Tacconi et \\citeyear{tac08}) ), and corresponds to gas mass fractions of $f_{\rm gas}$ =0.15 and 0.23 for J123707+6214ne and sw, respectively."
 Higher resolution observations are required to better constrain how the merecr dvuaiuics mipact the CO line profiles aud the morphology of the eas reservoir. which is necessary to determine more precise dynamical πο," Higher resolution observations are required to better constrain how the merger dynamics impact the CO line profiles and the morphology of the gas reservoir, which is necessary to determine more precise dynamical masses."
 SAIGs are conunonly associated with heavily obscured starbursts., SMGs are commonly associated with heavily obscured starbursts.
 J1237076211 is a particularly inxiehitful exanrple of this population.| as the ne component remains undetected at all wavelengths shortward of fu (vest-frame 1.0422).," J123707+6214 is a particularly insightful example of this population, as the ne component remains undetected at all wavelengths shortward of $\mu$ m (rest-frame $\mu$ m)."
 As shown in Figure. L. the peak of the eenission of the ne component is clearly associated witli peaks in the mid-infrared (8.04211: rest-frame ju) and radio σοιμαι ccun rest-frame 660: see also Taccoui ct citeveartacüs)).," As shown in Figure \ref{f4}, the peak of the emission of the ne component is clearly associated with peaks in the mid-infrared $\mu$ m; rest-frame $\mu$m) and radio continuum cm; rest-frame cm; see also Tacconi et \\citeyear{tac08}) )."
 The ne component also sliebtlv dominates the radio cussion (555€ )). which suggests hat it coutributes the dominant fraction to the sources SFR.," The ne component also slightly dominates the radio emission $\sim$ ), which suggests that it contributes the dominant fraction to the source's SFR."
 As also shown in Fie. L. ," As also shown in Fig. \ref{f4}, ,"
J123707|621sw consists of unultiple components in the optical nuum: rest- l17Innni) that are separated by a few kpc (see also Swinhbank ot 1))., J123707+6214sw consists of multiple components in the optical nm; rest-frame nm) that are separated by a few kpc (see also Swinbank et \\citeyear{swi04}) ).
 This may correspond to multiple star- clamps. enibedded ii a iore complex. extended," This may correspond to multiple star-forming clumps, embedded in a more complex, extended"
"cores, requiring a wall clock time of under 20 minutes for each model.","cores, requiring a wall clock time of under 20 minutes for each model."
" The ty =0.1 and 1 models converged after 3 iterations, while the ty —10 and 100 models converged after 4 iterations."," The $\tau_V=$ 0.1 and 1 models converged after $3$ iterations, while the $\tau_V=$ 10 and 100 models converged after $4$ iterations."
" Figure 2 shows for the most optically thick case (τν 100) the temperature profile for a fixed polar angle 2.5?) as a function of radius r, and the temperature profile for a fixed radius (r=2 AAU) as a function of polar angle 0."," Figure \ref{fig:pasc_temp} shows for the most optically thick case $\tau_V=100$ ) the temperature profile for a fixed polar angle $\theta=2.5^\circ$ ) as a function of radius $r$, and the temperature profile for a fixed radius $r=2$ AU) as a function of polar angle $\theta$."
 The temperatures found by are within the dispersion of the results from the other codes., The temperatures found by are within the dispersion of the results from the other codes.
" Figures 3 shows the SEDs for the code and the reference code in ? (RADICAL) for the four disk masses and three viewing angles, and the fractional difference between the SEDs is shown in each case."," Figures \ref{fig:pasc_seds} shows the SEDs for the code and the reference code in \citeauthor{Pascucci:04:793} (RADICAL) for the four disk masses and three viewing angles, and the fractional difference between the SEDs is shown in each case."
 Also shown in gray are the differences for other codes presented in ?.., Also shown in gray are the differences for other codes presented in \citeauthor{Pascucci:04:793}.
 The SEDs from are within the dispersion of results from the other codes., The SEDs from are within the dispersion of results from the other codes.
" While the ? benchmark includes a case with fairly high visual optical depth through the mid-plane of the disk, the optical depths through realistic protoplanetary disks are much higher (ry>10 in some cases), and are such that computing temperatures in the disk mid-plane becomes computationally challenging and requires approximations to be made (e.g. refsec:propagation and 6 refsec:temperature))."," While the \cite{Pascucci:04:793} benchmark includes a case with fairly high visual optical depth through the mid-plane of the disk, the optical depths through realistic protoplanetary disks are much higher $\tau_V > 10^6$ in some cases), and are such that computing temperatures in the disk mid-plane becomes computationally challenging and requires approximations to be made (e.g. \\ref{sec:propagation} and \\ref{sec:temperature}) )."
 ? developed a complementary benchmark problem consisting of more massive disks with a more extreme radial density profile to test codes in the limit of very optically thick disks., \cite{Pinte:09:967} developed a complementary benchmark problem consisting of more massive disks with a more extreme radial density profile to test codes in the limit of very optically thick disks.
" In addition, the benchmark also tests the ability to compute anisotropic"," In addition, the benchmark also tests the ability to compute anisotropic"
"the “canonical GRB light curve"" as three stages comprising a steep decline followed by a shallower decay and then a final decay phase.",the “canonical GRB light curve” as three stages comprising a steep decline followed by a shallower decay and then a final decay phase.
 O'Brienetal.(2006) showed that not all X-ray light curves for GRBs are of the “cannonical” variety., \cite{obrien2006} showed that not all X-ray light curves for GRBs are of the “cannonical” variety.
 They and Willingaleetal.(2007) suggested that the X-ray light curve comprises two main components. the prompt emission and the afterglow.," They and \cite{willingale2007} suggested that the X-ray light curve comprises two main components, the prompt emission and the afterglow."
 The relative strength of these components determines the observed X-ray light curve., The relative strength of these components determines the observed X-ray light curve.
 A more recent study of all X-ray afterglows by Evans(2009) has reinforced these findings., A more recent study of all X-ray afterglows by \cite{evans2008} has reinforced these findings.
 The initial steep decay ‘ollowing the prompt emission typically has a power law decay with index à.~2.5. where f.xf° (t is the time after the burst in seconds and f is the flux) (OBrienetal.2006).," The initial steep decay following the prompt emission typically has a power law decay with index $\alpha \sim 2-5$, where $f \propto t^{-\alpha}$ (t is the time after the burst in seconds and f is the flux) \citep{obrien2006}."
. Multi-wavelength observations have associated LGRBs with ype Ibe core collapse supernovae at cosmological distances (e.g. 2003).. although not all such supernovae produce long GRBs (Woosley&Bloom2006).," Multi-wavelength observations have associated LGRBs with type Ibc core collapse supernovae at cosmological distances \citep[e.g.][]{hjorth2003, 
stanek2003}, although not all such supernovae produce long GRBs \citep{woosley2006}."
. The wogenitors of SGRBs are less well understood. but the most yopular theory is that they originate from the merger of compact binary systems. for example neutron stars or a neutron star and a black hole (Lattimer&Schramm1976:Eichleretal.1989:arayan.Paezynski.&Piran 1992).," The progenitors of SGRBs are less well understood, but the most popular theory is that they originate from the merger of compact binary systems, for example neutron stars or a neutron star and a black hole \citep{lattimer1976,eichler1989,
narayan1992}."
 It has also been suggested hat both LGRB and SGRB progenitors could produce an unstable nillisecond pulsar., It has also been suggested that both LGRB and SGRB progenitors could produce an unstable millisecond pulsar.
 This is expected to contribute a small fraction of the GRB population (Usov1992:Duncan&ThompsonDai&Lu1998u.b:ZhangMészáros 2001).," This is expected to contribute a small fraction of the GRB population \citep{usov1992, duncan1992, 
dai1998a, dai1998b, zhang2001}."
. Trojaetal.(2007) and Lyonsetal.(2010). found examples of LGRBs that have an observable plateau and steep decay in the X-ray light curve. which have been intepreted as caused by energy injection by an unstable millisecond pulsar which then collapses.," \cite{troja2007} and \cite{lyons2009} found examples of LGRBs that have an observable plateau and steep decay in the X-ray light curve, which have been intepreted as caused by energy injection by an unstable millisecond pulsar which then collapses."
 Magnetar models have also been proposed to explain late central engine activity in SGRBs. for example late time plateaus in the X-ray afterglows (Fan&Xu2006:Yu.Cheng.&Cao2010:Dall'Ossoetal.2010) and X-ray flares (Fan.Zhang.&Proga2005:GaoFan2006).," Magnetar models have also been proposed to explain late central engine activity in SGRBs, for example late time plateaus in the X-ray afterglows \citep{fan2006, yu2010, 
dallosso2010} and X-ray flares \citep{fan2005,gao2006}."
. Here we present an analysis of GRB 090515 which is the best case for an early X-ray plateau in an SGRB., Here we present an analysis of GRB 090515 which is the best case for an early X-ray plateau in an SGRB.
 GRB 090515 was one of the shortest GRBs observed bySwifi. with among the lowest fluence. yet for ~200 s it had the brightest SGRB X-ray afterglow and did not appear to be fading until a sudden steep decline at ~ 240 s. After the first orbit. it was not detected again.," GRB 090515 was one of the shortest GRBs observed by, with among the lowest fluence, yet for $\sim$ 200 s it had the brightest SGRB X-ray afterglow and did not appear to be fading until a sudden steep decline at $\sim$ 240 s. After the first orbit, it was not detected again."
 Explaining this unusual X-ray behaviour is the subject of this paper., Explaining this unusual X-ray behaviour is the subject of this paper.
 We describe the observations of GRB 090515 in section 2. compare it to other GRBs in section 3 and discuss the potential origin of the unusual X-ray emission in section 4.," We describe the observations of GRB 090515 in section 2, compare it to other GRBs in section 3 and discuss the potential origin of the unusual X-ray emission in section 4."
" Throughout the paper we adopt a cosmology with //=71 | DOO,=0.27. O4=0.73."," Throughout the paper we adopt a cosmology with $H_0 = 71$ $^{-1}$ $^{-1}$, $\Omega_m = 0.27$, $\Omega_\Lambda = 0.73$."
 Errors are quoted at confidence for X-ray data and at Lo for optical data., Errors are quoted at confidence for X-ray data and at $\sigma$ for optical data.
 All analysis has been performed by using standard routines inΗΓΑΦΟΓΤ.XSPEC.QDP and the automatic X-ray Telescope (XRT.etal.2005) data products produced by the UK Swift Science Data Centre (Evansetal.2007.2009).," All analysis has been performed by using standard routines in, and the automatic X-ray Telescope \citep[XRT,][]{burrows2005} data products produced by the UK Swift Science Data Centre \citep{evans2007, evans2008}."
" triggered on GRB 090515 at 04:45:09 UT on I5th May 2009 with BAT position RA = 10h 56m 41s and Dec = 614 27! 22"" (Beardmoreetal.2009).", triggered on GRB 090515 at 04:45:09 UT on 15th May 2009 with BAT position RA = 10h 56m 41s and Dec = $^{\circ}$ $^{\prime}$ $^{\prime\prime}$ \citep{beardmore2009}.
". The Ultra-Violet and Optical Telescope (UVOT) enhanced refined XRT position was RA = IO0h 56m 36.1Is and Dec = 14 26 30.3"" with an uncertainty of 2.7"" 2009).", The Ultra-Violet and Optical Telescope (UVOT) enhanced refined XRT position was RA = 10h 56m 36.11s and Dec = $^{\circ}$ $^{\prime}$ $^{\prime\prime}$ with an uncertainty of $^{\prime\prime}$ \citep{osbourne2009}.
. The Yoo duration of GRB 0905153 was 0.036+=0.016 s (Barthelmyetal.2009:)., The $T_{90}$ duration of GRB 090515 was $0.036 \pm 0.016$ s \citep{barthelmy2009}.
. The spectrum of the prompt gamma-ray emission can be fit by a single power law. of photon index IL.= (Barthelmyetal.2009a).," The spectrum of the prompt gamma-ray emission can be fit by a single power law, of photon index $\Gamma_{\gamma} = 1.6 \pm 0.2$ \citep{barthelmy2009}."
. The fluence is 2:00.810.7 erg em. 7 and the peak photon flux is 5.7+0.9 phem 7s. -1., The fluence is $2.0 \pm 0.8 \times 10^{-8}$ erg cm $^{-2}$ and the peak photon flux is $5.7 \pm 0.9$ ph $^{-2}$ $^{-1}$.
 All values are in the 15 — 150 keV energy band., All values are in the 15 – 150 keV energy band.
 The BAT light curve is shown in Figure |. as the grey data points and also shown in the inset with linear time., The BAT light curve is shown in Figure \ref{fig1} as the grey data points and also shown in the inset with linear time.
 The BAT count rates were converted to flux in the energy band 0.3 — 10 keV using the average spectral index for the BAT and the XRT spectra., The BAT count rates were converted to flux in the energy band 0.3 – 10 keV using the average spectral index for the BAT and the XRT spectra.
 There is no evidence of extended emission detected in theBAT energy range (Norris.Gehrels.Seargle 2010)., There is no evidence of extended emission detected in theBAT energy range \citep{norris2010}.
. We completed a spectral lag analysis for GRB 090515 using the cross correlation function method described in Ukwatta (0101. the 8 ms time binned lightcurve and BAT channels |. 2 and 3.," We completed a spectral lag analysis for GRB 090515 using the cross correlation function method described in \cite{ukwatta2010}, the 8 ms time binned lightcurve and BAT channels 1, 2 and 3."
 Channel 4 did not detect enough emission to make a lag measurement., Channel 4 did not detect enough emission to make a lag measurement.
 The lag times are (with. 1o errors): lagtCh2-Chl)—64 ms. Ch3-Ch2)—3cx2 ms and lag¢Ch2-Chlj=10+4 ms.," The lag times are (with $\sigma$ errors): $=6\pm4$ ms, $=3\pm2$ ms and $=10\pm4$ ms."
 Typically SGRBs have negligble lag times (Norris&Bonnell and LGRBs have typical lag times ranging from 20 ms to ~ 1000 ms (Ukwattaetal. 20103... so it is interesting that GRB 090515 appears to have a small lag time.," Typically SGRBs have negligble lag times \citep{norris2006,yi2006} and LGRBs have typical lag times ranging from 20 ms to $\sim$ 1000 ms \citep{ukwatta2010}, , so it is interesting that GRB 090515 appears to have a small lag time."
" The X-ray spectrum in the 0.3 — 10 keV energy band is best fit by an absorbed power law with Py=1.58+0.14 and Vy= 7. in excess of the Galactic Ny=1.9.107"" "," The X-ray spectrum in the 0.3 – 10 keV energy band is best fit by an absorbed power law with $\Gamma_{X} = 1.88 \pm 0.14$ and $N_{\rm H}=6.1^{+3.0}_{-2.8} \times 
10^{20}$ $^{-2}$ , in excess of the Galactic $N_{\rm H}=1.9 \times 10^{20}$ "
 In this appendix we present greyscale plots of the A -band images. the axi-symmetric model fits. and then the residual images after subtraction of the PSF-convolved model.," In this appendix we present greyscale plots of the $K$ -band images, the axi-symmetric model fits, and then the residual images after subtraction of the PSF-convolved model."
 Plots for the radio galaxies are shown in Fig., Plots for the radio galaxies are shown in Fig.
 Al. with the plots for the sub-millimetre galaxies presented in Fig.," A1, with the plots for the sub-millimetre galaxies presented in Fig."
 A2., A2.
 In addition. in Fig.," In addition, in Fig."
 A3. we show comparable greyscale plots of the HST ACS /-band images of the sub-milimeater galaxies N2850.1. N2850.4. N2850.7. and N2850.8. again accompanied by the axi-symmetric model fits. and the model-subtracted residual images.," A3, we show comparable greyscale plots of the HST ACS $I$ -band images of the sub-milimeater galaxies N2850.1, N2850.4, N2850.7, and N2850.8, again accompanied by the axi-symmetric model fits, and the model-subtracted residual images."
 , 
quaternions came before. having been invented. by none other than WR. Hamilton of Llamilton’s equations.),"quaternions came before, having been invented by none other than W.R. Hamilton of Hamilton's equations.)"
 A general quaternion has the form where we will call clo the real part., A general quaternion has the form where we will call $A_0$ the real part.
 A quaternion with no real part is cllectively a vector in three dimensions., A quaternion with no real part is effectively a vector in three dimensions.
 In analogv with complex numbers. we will use the following notation for quaternion conjugates ancl absolute values.," In analogy with complex numbers, we will use the following notation for quaternion conjugates and absolute values."
 lt ds easy to see that reA7]=A] and BA’. and as a result Rotation in quaternion notation is beautifully concise.," It is easy to see that $\tr{\A^*}=\tr{\A}$ and $(\A\B)^*=\B^*\A^*$ , and as a result Rotation in quaternion notation is beautifully concise."
 Sav we want (o rotate a vector P by angle w about a unit vector nm., Say we want to rotate a vector $\r$ by angle $\omega$ about a unit vector $\n$.
 Using quaternion aleebra the rotation is simply where Unlike the equivalent expression using Euler angles. the expression (5)) has no coordinate singularities (or “gimbal lock”) and as a result. is numerically more stable. which explains its popularity in computer graphics.," Using quaternion algebra the rotation is simply where Unlike the equivalent expression using Euler angles, the expression \ref{qrot}) ) has no coordinate singularities (or “gimbal lock”) and as a result is numerically more stable, which explains its popularity in computer graphics."
 For an arbitrary (i.e. non-unit) quaternion. R. the expression (5)) amounts to a rotation combined with scalar multiplication.," For an arbitrary (i.e., non-unit) quaternion $\R$, the expression \ref{qrot}) ) amounts to a rotation combined with scalar multiplication."
 ]t is possible to represent quaternions as matrices (though not necessary. even for numerical work).," It is possible to represent quaternions as matrices (though not necessary, even for numerical work)."
 A familiar representation is in terms of Pauli matrices Or Pauli matrices are most important as operators on «quantum (wo-state. systems (being Llermitian. whereas quaternions are anti-HLermitian).," A familiar representation is in terms of Pauli matrices or Pauli matrices are most important as operators on quantum two-state systems (being Hermitian, whereas quaternions are anti-Hermitian)."
 In recent vears the most exciting two-state quantum svstems have been Obits in «quantum computing., In recent years the most exciting two-state quantum systems have been Qbits in quantum computing.
 It turns out that expressions of the type (5)) appear in the description of quantum-computing gates (see2.whoalsoprovidesaderivationoftheabovethree-cdimensionalrotation formula)..," It turns out that expressions of the type \ref{qrot}) ) appear in the description of quantum-computing gates \citep[see][ who also provides a derivation of essentially the above
three-dimensional rotation formula]{2007qucosc.book}."
 Let denote a point in space., Let denote a point in space.
 The INS transform of q is the quaternion the transformation formula being A solution for Q is as ds easily verified by multiplication. following the quaternion rules.," The KS transform of $\q$ is the quaternion the transformation formula being A solution for $\Q$ is as is easily verified by multiplication, following the quaternion rules."
 But Q4 is not unique. because changing lo leaves Equation (11)) invariant.," But $\Q^{I}$ is not unique, because changing to leaves Equation \ref{Qtoq}) ) invariant."
 Thus c behaves like a σαιισο, Thus $\psi$ behaves like a gauge.
", Everything so far is already in the literature.", Everything so far is already in the literature.
 The new result in this paper is that we can reaclily visualize Q. including its non-uniqueness.," The new result in this paper is that we can readily visualize $\Q$, including its non-uniqueness."
 Comparing (11)) and (5)). it is evident that Q is a rotator that takes the z axis to q.," Comparing \ref{Qtoq}) ) and \ref{qrot}) ), it is evident that $\Q$ is a rotator that takes the $z$ axis to $\q$."
 To visualize Q. let us rewrite q as where r.8.ὦ are the usual polar coordinates.," To visualize $\Q$, let us rewrite $\q$ as where $r,\theta,\phi$ are the usual polar coordinates."
 Rewriting Q! in the solution (12)) ancl simplifying. we have In other words. the zenith distauce of Q4! is hallway along the great. circle from & to q.," Rewriting $\Q^{I}$ in the solution \ref{Qsol}) ) and simplifying, we have In other words, the zenith distance of $\Q^{I}$ is halfway along the great circle from $\k$ to $\q$."
 From (6)) we see the rotation angle aw would be wz., From \ref{qrotang}) ) we see the rotation angle $\omega$ would be $\pi$.
 Now let us apply the gauge transformation (13)) with c—x/2 to Qi., Now let us apply the gauge transformation \ref{gauge}) ) with $\psi=\pi/2$ to $Q^I$.
 ‘This gives Now the implied. rotation is by 0. about an axis perpendicular to both & and q.," This gives Now the implied rotation is by $\theta$, about an axis perpendicular to both $\k$ and $\q$."
 In general. we can write which is to sav. Q could be anvwhere on the great. circle joining Q and Q!!.," In general, we can write which is to say, $\Q$ could be anywhere on the great circle joining $\Q^{I}$ and $\Q^{II}$."
 The telescope-slewing analogy given above Is simply a description ofthe preceding three formulas., The telescope-slewing analogy given above is simply a description of the preceding three formulas.
 An interesting special case is ó=0. which gives gq=r(cos6k|sin62) and οἱ=v/ricos16k|sini).," An interesting special case is $\phi=0$, which gives $\q=r(\cos\theta\,\k+\sin\theta\,\i)$ and $\Q^{I} = \sqrt r
(\cos\half\theta\,\k + \sin\half\theta\,\i)$."
 Then οἱ is ellectively the complex. square root of g (we need to read & as the real axis and 2 as the imaginary axis)., Then $\Q^{I}$ is effectively the complex square root of $\q$ (we need to read $\k$ as the real axis and $\i$ as the imaginary axis).
 In other words. the planar case can be reduced to the Levi-Civita transform by a suitable gauge.," In other words, the planar case can be reduced to the Levi-Civita transform by a suitable gauge."
 Quaternion formulations of the INS transform have been discussed. in several authors: ? mention. quaternions but appear to dislike them. while later authors (for.example77) are more favourable.," Quaternion formulations of the KS transform have been discussed in several authors: \cite{1971QB351.S758.....} mention quaternions but appear to dislike them, while later authors \cite[for
example][]{1994CeMDA..60..291V,2006CeMDA..95..201W} are more favourable."
 Lhe precise definition adopted for the transform. varies. but is equivalent to Eq. (112).," The precise definition adopted for the transform varies, but is equivalent to Eq. \ref{Qtoq}) )."
 That Q represents à rotation ancl shrinking/stretehing of q is also known., That $\Q$ represents a rotation and shrinking/stretching of $\q$ is also known.
 ?7. specifically notes that the rotation axis is unique in two dimensions but not in three., \cite{2003JPhA...36.6963B} specifically notes that the rotation axis is unique in two dimensions but not in three.
 But the explicit description of the implied rotations. as above. appears to be new.," But the explicit description of the implied rotations, as above, appears to be new."
 So far we have just. discussed. geometry. but. of course the real significance of the INS transform is dvnamics. which we now consider.," So far we have just discussed geometry, but of course the real significance of the KS transform is dynamics, which we now consider."
 Let, Let
of carly type galaxies.,of early type galaxies.
" In the following we assume IT,=65 +AAIpe 41.04, 203. 04=0.7."," In the following we assume $H_o = 65$ $^{-1}$ $^{-1}$, $\Omega _M = 0.3$, $\Omega _\Lambda = 0.7$."
 We lave compiled spectra for a sample of 70 hieh redshift quasars (3.5X:2S 5.0) to study the choemica composition of the BELR eas aud its duplications on the star formation history iu quasar host galaxies in the early universe., We have compiled spectra for a sample of 70 high redshift quasars $3.5 \la z \la 5.0$ ) to study the chemical composition of the BELR gas and its implications on the star formation history in quasar host galaxies in the early universe.
 Alost of he quasars at redshift Ὁ| were observed by Constantin et (2002)., Most of the quasars at redshift $z\ga 4$ were observed by Constantin et (2002).
 They recorded hnieh signal-to-noise moderate resolution spectra over multiple observing runs at the Multiple Mirror Telescope Observatory (ADMIT) aud the Wiyeck Observatory., They recorded high signal-to-noise moderate resolution spectra over multiple observing runs at the Multiple Mirror Telescope Observatory (MMT) and the Keck Observatory.
 The spectral waveleneth Lange Was chosen. o cover the redshitted Lya to WALGLO cussion lines., The spectral wavelength range was chosen to cover the redshifted $\alpha $ to $\lambda 1640$ emission lines.
 Dietrich et 22002a) observed a small sample of Ll quasars with το| using 11 at the VLT unit telescope in 1998 and 1999., Dietrich et 2002a) observed a small sample of 11 quasars with $z\ga 4$ using 1 at the VLT unit telescope in 1998 and 1999.
 These spectra cover a rest-frame wavelongth rauge of 8502100AA., These spectra cover a rest-frame wavelength range of $\sim 850 - 2100$.
 This wide range allows neasurements of not oulv Lya up to the WA16LO eiission line. but also OVIALOSL. niA1750.. aud du some Cases even nij]A1909.," This wide range allows measurements of not only $\alpha $ up to the $\lambda 1640$ emission line, but also $\lambda 1034$, $\lambda 1750$, and in some cases even $\lambda 1909$."
 The high redshift quasar sanyple Was οςuplemeuted by observations which were kindly provided by Sargent et 11989). Schneider et ((19912a.b). Storric-Lombarci e ((1996). ancl Steidel Sargent (uupublished).," The high redshift quasar sample was complemented by observations which were kindly provided by Sargent et 1989), Schneider et (1991a,b), Storrie-Lombardi et (1996), and Steidel Sargent (unpublished)."
 Tn particular. the quasar spectra obtained by Storric-Lombardi et (1996) cover the wavelength ranec contaiulues OVIALO31. for many of the sources observed bw Coustantin et ((2002).," In particular, the quasar spectra obtained by Storrie-Lombardi et (1996) cover the wavelength range containing $\lambda 1034$ for many of the sources observed by Constantin et (2002)."
 ALultiple spectra of the same object were combiue whenever possible., Multiple spectra of the same object were combined whenever possible.
 Droad-absorption line quasars OQQOSOs) were excluded from this study. although there are indications that their enmiussiou line properties do not differ from non-BAL quasars (Weviiuun ct 11991).," Broad-absorption line quasars QSOs) were excluded from this study, although there are indications that their emission line properties do not differ from non-BAL quasars (Weymann et 1991)."
 In Table 1. we list the quasars used iu this study together with their redshifts. iutriusic continmun Μπορτν L4(1150A) (corrected. for ealactic extinction: Dietrich et 22002bj. the covered resttrame waveleneth range. aud the references for the observations.," In Table 1, we list the quasars used in this study together with their redshifts, intrinsic continuum luminosity $L_\lambda (1450 {\rm \AA})$ (corrected for galactic extinction; Dietrich et 2002b), the covered restframe wavelength range, and the references for the observations."
 Comparing mean spectra of the zz.L quasars with those at :-—2 Constantin ct ((2002) found evideuce for eubhanced NVAL2LO emission strength iu the high-z quasar spectra indicating hnieh imnetalliities., Comparing mean spectra of the $z\ga 4$ quasars with those at $z\simeq 2$ Constantin et (2002) found evidence for enhanced $\lambda 1240$ emission strength in the high-z quasar spectra indicating high metallicities.
 In the following we present quantitative metallicity estimates for cach individual quasar based on several measured cussion line ratios., In the following we present quantitative metallicity estimates for each individual quasar based on several measured emission line ratios.
 The quasar spectra were trausformed to their restframe using the redshifts listed in Table 1., The quasar spectra were transformed to their restframe using the redshifts listed in Table 1.
 To determine the redshift for cach quasar we fit a Gaussian profile to the upper part of the IVAT519 emission line (Z4=50 To measure iutegrated cussion line fiuxes. we corrected each quasar spectriài for Fe emission and the weak contribution of Balmer contiuuua cnussion while simultaneously obtaining à powcr-law ft represcuting the quasar coutimmun.," To determine the redshift for each quasar we fit a Gaussian profile to the upper part of the $\lambda 1549$ emission line $I_\lambda \geq 50$ To measure integrated emission line fluxes, we corrected each quasar spectrum for Fe emission and the weak contribution of Balmer continuum emission while simultaneously obtaining a power-law fit representing the quasar continuum."
" The power-law fit. EF,xv. was calculated using small spectral regions. cach 10 to 20 wwide. which are free of detectable emission lines. at A&1290AA.AA.AA. AA. AA. and . yospectivelv."," The power-law fit, $_{\nu } \propto \nu ^{\alpha}$, was calculated using small spectral regions, each 10 to 20 wide, which are free of detectable emission lines, at $\lambda \simeq 1290$, and , respectively."
 To estimate the coutribution of the Daliier coutimmum and Fe hue emission. we used our results from the analysis of quasar colmposite spectra based on a lareec quasar sample of abou τοῦ quasars (Dietrich et 22900210).," To estimate the contribution of the Balmer continuum and Fe line emission, we used our results from the analysis of quasar composite spectra based on a large quasar sample of about 750 quasars (Dietrich et 2002b)."
 For the Balmer continu enuüssion. we calculated a template spectrmm with T.=15000 KS. το= 1.0. and n.=105 ? following Graudi (1982) aud Storey IInuuuer (1995).," For the Balmer continuum emission, we calculated a template spectrum with $_e = 15\,000$ K, $\tau _{BaC}=1.0$ , and $_e = 10^8$ $^{-3}$ following Grandi (1982) and Storey Hummer (1995)."
 The Fe emission was defued by an enmpiical teniplate spectrum (Vestereaard Wilkes 2001) aud the results of detailed iodol caleulations. (Verner et 11999)., The Fe emission was defined by an empirical template spectrum (Vestergaard Wilkes 2001) and the results of detailed model calculations (Verner et 1999).
 The empirical cussion template accounts for both aan cecluission., The empirical emission template accounts for both and emission.
 The spectra width of the Fe emission features was adjusted to the FWIIM of the IVAT519 emission line profile of each quasar., The spectral width of the Fe emission features was adjusted to the FWHM of the $\lambda 1549$ emission line profile of each quasar.
 We found that the streneth of the Balmer coutiuuua Cluission ancl of the Fe line enuüssion cau be, We found that the strength of the Balmer continuum emission and of the Fe line emission can be
2224 uHz and Νους=8 for the triplet centered at 2493 wHz.,$2224\ \mu$ Hz and $N_{\rm obs}= 8$ for the triplet centered at $2493\ \mu$ Hz.
" In this way, we are discarding the effects of the observed asymmetries in the frequency splittings within both triplets of01224-200."," In this way, we are discarding the effects of the observed asymmetries in the frequency splittings within both triplets of."
". This is consistent with the fact that, in this work, we are using the the perturbative theory to first order in 2 for estimate the frequency splittings, that indeed does not account for possible departures of uniformity of the splittings within a given multiplet (see Sect. 3))."," This is consistent with the fact that, in this work, we are using the the perturbative theory to first order in $\Omega$ for estimate the frequency splittings, that indeed does not account for possible departures of uniformity of the splittings within a given multiplet (see Sect. \ref{forward}) )."
" Next, we estimated an average value of the splittings over the complete set of observations, namely and the fluctuations around this value A,=óv,—(dv) (n=1,---, Νους)."," Next, we estimated an average value of the splittings over the complete set of observations, namely and the fluctuations around this value $\Delta_n=\overline{\delta \nu}_n- \langle \overline{\delta \nu} \rangle$ $n= 1,\cdots, N_{\rm obs}$ )."
" Finally, we computed the mean value of these fluctuations around the average value, We find for the two triplets (A,,)=0.106—0.113 4,Hz and GOA,=0.05—0.06 wHz."," Finally, we computed the mean value of these fluctuations around the average value, and the variance of the fluctuations We find for the two triplets $\langle \Delta_n \rangle= 
0.106-0.113\ \mu$ Hz and $\sigma_{\Delta_n}= 0.05-0.06\ \mu$ Hz."
 We check our results of non-rigid rotation by considering these possible variations of the rotational splittings., We check our results of non-rigid rotation by considering these possible variations of the rotational splittings.
" We have performed new simulations of our optimization procedure, in each of them adding Gaussian noise to the splittings of the seven triplets exhibited by the star, with a standard deviation Onoise."," We have performed new simulations of our optimization procedure, in each of them adding Gaussian noise to the splittings of the seven triplets exhibited by the star, with a standard deviation $\sigma_{\rm noise}$."
" To be consistent, we should adopt Onoise&Ga,~0.055 wHz in order to estimate the uncertainties of the frequency splittings due to the observed time variations, but we prefer to be somewhat conservative and adopt Onoise(An)c0.11 Hz, thus overestimating to a some extent the impact of the frequency drifts on ourresults?."," To be consistent, we should adopt $ \sigma_{\rm noise} \approx
\sigma_{\Delta_n} \sim 0.055\ \mu$ Hz in order to estimate the uncertainties of the frequency splittings due to the observed time variations, but we prefer to be somewhat conservative and adopt $\sigma_{\rm noise}\approx \langle \Delta_n \rangle\sim 0.11\, 
\mu$ Hz, thus overestimating to a some extent the impact of the frequency drifts on our."
". As expected, the results of our simulations are very similar to those shown in the right panel of Fig. 5,,"," As expected, the results of our simulations are very similar to those shown in the right panel of Fig. \ref{errores},"
 indicating that rigid body rotation can be discarded at a level of confidence of more than ~1.50., indicating that rigid body rotation can be discarded at a level of confidence of more than $\sim 1.5 \sigma$.
 We also investigated the internal rotation rate of using the Regularized Least Squares (RLS) fitting technique (Kawaler et al., We also investigated the internal rotation rate of using the Regularized Least Squares (RLS) fitting technique (Kawaler et al.
 1999) that has been extensively applied to the case of the Sun — see Christensen-Dalsgaard et al. (, 1999) that has been extensively applied to the case of the Sun — see Christensen-Dalsgaard et al. (
1990) and references therein.,1990) and references therein.
" In this method, the internal rotation profile Q(r) is obtained by inverting the equation (Jeffrey 1988): where óvP is the ith observed frequency separation"," In this method, the internal rotation profile $\Omega(r)$ is obtained by inverting the equation (Jeffrey 1988): where $\delta \nu_{i}^{\rm O}$ is the $i$ th observed frequency separation"
The acceleration efficiency. and (he normalized escape flux initially increase with time during the Sedov-Tavlor expansion phase.,The acceleration efficiency and the normalized escape flux initially increase with time during the Sedov-Taylor expansion phase.
" This behaviour is related to an analogous trend of the shock modification. as can be clearly seen [rom the time-dependence of f, curve in (he left panel of Figs. 2--4))."," This behaviour is related to an analogous trend of the shock modification, as can be clearly seen from the time-dependence of $R_{tot}$ (dash-dotted curve in the left panel of Figs. \ref{fig:B1n01}- \ref{fig:B1n003}) )."
 In fact. at the beginning of the Sedov phase. the amplified magnetic field is al à maximum. and its dynamical reaction on (he shock is so strong that the acceleration efficiency is reduced.," In fact, at the beginning of the Sedov phase, the amplified magnetic field is at a maximum and its dynamical reaction on the shock is so strong that the acceleration efficiency is reduced."
 As soon as the magnetic field strength starts decreasing. the shock modification increases. and £. and εν wilh it.," As soon as the magnetic field strength starts decreasing, the shock modification increases, and $\xi_c$ and $F_{esc}$ with it."
" Notice. however. (hat (his does not mean that the actual cosmic ray pressure and escape flux increase. because €. and ἔτι are normalized to p,V5) and o,V5()/2 respectively. and both decrease with time rather quickly."," Notice, however, that this does not mean that the actual cosmic ray pressure and escape flux increase, because $\xi_c$ and $F_{esc}$ are normalized to $\rho_0 V_{sh}^2(t)$ and $\rho_0 V_{sh}^3(t)/2$ respectively, and both decrease with time rather quickly."
 Al later times. both £. and £L. start decreasing. with the latter showing a more rapid decline than the former.," At later times, both $\xi_c$ and $F_{esc}$ start decreasing, with the latter showing a more rapid decline than the former."
 This is due to the fact that the shock is slowing down aud progressively becoming unnmocilied: the maximum monmentun is decreasing aud (he spectrum of accelerated, This is due to the fact that the shock is slowing down and progressively becoming unmodified: the maximum momentum is decreasing and the spectrum of accelerated
temperatures of several keV aud therefore sound velocities comparable to the merecr velocity.,temperatures of several keV and therefore sound velocities comparable to the merger velocity.
 As can he seen in Fie., As can be seen in Fig.
 2 the compression caused by the morecr shock wave gives rise to a burst of low frequency enission. but practically no high frequency emission.," \ref{fig:syncA} the compression caused by the merger shock wave gives rise to a burst of low frequency emission, but practically no high frequency emission."
 This is due to the rapid decay of the upper cud of the electrou spectrum durus phase 3. which csseutially wipes out the adiabatic cherey eains of these electrous.," This is due to the rapid decay of the upper end of the electron spectrum during phase 3, which essentially wipes out the adiabatic energy gains of these electrons."
 The source decavs on a time-scale of a few tens of Myr. mostly due to the heavy svuchrotron losses.," The source decays on a time-scale of a few tens of Myr, mostly due to the heavy synchrotron losses."
 If the radio cocoon 1s located in a more peripheral region of the cluster. where the deusitv. the pressure aud therefore the magnetic field strength inside the cocoon is much lower. these losses are also mich milder.," If the radio cocoon is located in a more peripheral region of the cluster, where the density, the pressure and therefore the magnetic field strength inside the cocoon is much lower, these losses are also much milder."
 This leugtheus the time scale over which the radiatively cooling svuchrotron plasma can still ο roevived by the jext passing shock. aud thus reudered radio detectable.," This lengthens the time scale over which the radiatively cooling synchrotron plasma can still be revived by the next passing shock, and thus rendered radio detectable."
 We. therefore. expect the radio relic phenomena to be found ποσααν at larger cluster radi. and less often near the cluster ceuter (although xojection can help some relics to appear near the cluster core).," We, therefore, expect the radio relic phenomena to be found preferentially at larger cluster radii, and less often near the cluster center (although projection can help some relics to appear near the cluster core)."
 The best cuviromment to find cluster radio relies is. herefore. near the edges ofthe clusters.," The best environment to find cluster radio relics is, therefore, near the edges of the clusters."
 The radio cocoon ix assuuued here to be born outside the cluster. in au environment of a deuse galaxy. filament. or a eroup of galaxies. sav. with à=0.3-10c aud kT=0.3 keV.," The radio cocoon is assumed here to be born outside the cluster, in an environment of a dense galaxy filament, or a group of galaxies, say, with $n_{\rm e} =
0.3\cdot 10^{-5} \, {\rm cm^{-3}}$ and $kT = 0.3\, {\rm keV}$ ."
 The freshly injected radio plasuia might be over-pressured by a factor of 100. leading to a short expansion phase.," The freshly injected radio plasma might be over-pressured by a factor of 100, leading to a short expansion phase."
 After this. the electrons within the expauded Mpc sized cocoon suffer mostly the IC-losses. allowing revival of the radio plasma even Af»=ντ later.," After this, the electrons within the expanded Mpc sized cocoon suffer mostly the IC-losses, allowing revival of the radio plasma even $\Delta t_2 = 1 \, {\rm
Gyr}$ later."
 This can happen when the cocoon aloug with the ambicut medi is crossed. by the accretion shock of a cluster of galaxies. which might eutail a pressure juup as laree as 100. in order to leat the iufalliug cool gas to the cluster virial temperature of up to 10keV.," This can happen when the cocoon along with the ambient medium is crossed by the accretion shock of a cluster of galaxies, which might entail a pressure jump as large as $P_3/P_2 = 100$ , in order to heat the infalling cool gas to the cluster virial temperature of up to $10\,{\rm keV}$."
 Scenario D can explain the steep aud boeut radio seetzrumn of the cluster radio relie 0038-096 in Abell 85., Scenario B can explain the steep and bent radio spectrum of the cluster radio relic 0038-096 in Abell 85.
 An eve-fit to the radio spectrum (Fie. 5)), An eye-fit to the radio spectrum (Fig. \ref{fig:A85}) )
 shows that the maximal clectrou momentum iu this case is po=Lot(B/uG)P7.," shows that the maximal electron momentum in this case is $p_* = 10^4\,\,(B/{\mu{\rm G}})^{-1/2}$."
 The maeuctic field streneth of the cluster relic was estimated from the mimi energy aremnent to be Bz Lc aud from the detection of excess N-vav oendsson at the location of the relic. which implies a field strength of 5—0.95d0.10 40€ af this enission refers to the IC) scattered cosmic mucrowave backeround photons. otherwise a higher field strength.," The magnetic field strength of the cluster relic was estimated from the minimum energy argument to be $B \approx 1\,\mu$ G and from the detection of excess X-ray emission at the location of the relic, which implies a field strength of $B = 0.95 \pm 0.10 \,\mu$ G if this emission refers to the IC scattered cosmic microwave background photons, otherwise a higher field strength."
 Using B.— μα and p.=10! aud assuniue a uniforiun environineut without expansion and conipression. an age of 0.2(ανν would result2119.," Using $B= 1\,\mu$ G and $p_* = 10^4$ and assuming a uniform environment without expansion and compression, an age of $0.2\,{\rm
Gyr}$ would result."
 But scenario B demonstrates that the radio plasma can be as old as 2Car.," But scenario B demonstrates that the radio plasma can be as old as $2\,{\rm Gyr}$."
 This resolves the problem of the apparent cooling time of the electrons being too short for any nearby galaxy to have ejected the plasina aud then moved to its present location with a typical velocity of a cluster iieniber., This resolves the problem of the apparent cooling time of the electrons being too short for any nearby galaxy to have ejected the plasma and then moved to its present location with a typical velocity of a cluster member.
 For the long duration of phase 2 the resulting spectrum is fairly steep iu the observable radio vanec., For the long duration of phase 2 the resulting spectrum is fairly steep in the observable radio range.
 But this need not to be the case for a scenario with a shorter fossil phase., But this need not to be the case for a scenario with a shorter fossil phase.
 In order to substantiate the last statement. we choose a πο of paraleters for scenario © which produces a cluster radio relic with relative flat. nearly uubent radio spectrun. like the relic 1253215 at the bouudarv," In order to substantiate the last statement, we choose a set of parameters for scenario C which produces a cluster radio relic with relative flat, nearly unbent radio spectrum, like the relic 1253+275 at the boundary"
this type.,is type.
activity. over 3-5 vear eveles. ,activity over 3-5 year cycles. '
Quasi-cycelic De. star envelope variations’ have been invoked to explain the 4 vear moculation in the amplitude of the periodic radio outbursts in 1617303 (Gregoryetal.1989)... while Lümamel (1998) reported shell-Be-shell transitions in .Cas at 44V4 vears which he attributed to a precessing circumstellar disc.,"Quasi-cyclic Be star envelope variations' have been invoked to explain the 4 year modulation in the amplitude of the periodic radio outbursts in $^\circ$ 303 \cite{gregory1989}, while Hummel \shortcite{hummel1998} reported shell-Be-shell transitions in $\gamma~Cas$ at $4\pm0.4$ years which he attributed to a precessing circumstellar disc."
 Clark et al., Clark et al.
 (2001). also show that NX Per has exhibited clise-loss and dise ‘low states’ separated by intervals of 5 and 6 vears., \shortcite{clark2001} also show that X Per has exhibited disc-loss and disc 'low states' separated by intervals of 5 and 6 years.
 Η disc precession is the root cause of all these evcles. the similarity of evelical period in systems with disparate orbital periods ancl inclinations is intriguing.," If disc precession is the root cause of all these cycles, the similarity of cyclical period in systems with disparate orbital periods and inclinations is intriguing."
 While the disc is probably oustecl from the equatorial plane. by NS interactions. attribution of the to the asvmoetric potential of the oblate OB star is an appealing explanation. as the primaries of DeNIUDs are known to occupy only a small range in w (Porter1906). ancl Al. (Negueruela.1998) and thus should. possess almost. identical eravitationa properties.," While the disc is probably ousted from the equatorial plane by NS interactions, attribution of the to the asymetric potential of the oblate OB star is an appealing explanation, as the primaries of BeXRBs are known to occupy only a small range in $\omega$ \cite{porter1996} and $M_*$ \cite{neg1998} and thus should possess almost identical gravitational properties."
 Behaviour similar to that) observed. in. 0535|26. LS992 and 4U0115|63 is probably restricted. to systems of moderate eccentricity causing the disc to be truncated at a low resonance (i.e. 4:1) so that changes between adjacen resonances cause observable flux changes.," Behaviour similar to that observed in A0535+26, LS992 and 4U0115+63 is probably restricted to systems of moderate eccentricity causing the disc to be truncated at a low resonance (i.e. 4:1) so that changes between adjacent resonances cause observable flux changes."
 The degree of coplanarity of NS orbit ancl Be equator will clearly be an influential parameter profouncdly alfecting the nature of the tidal interactions., The degree of coplanarity of NS orbit and Be equator will clearly be an influential parameter profoundly affecting the nature of the tidal interactions.
 Orientation. on the sky is. also doubtless important for understanding different svstenis: it seems likely that the Be disc of 4U 0115168 intercepts the line-of-sightoD at a specilic evelical phase. causingὃν transient shell lines in that object anc not in. 0535|26.," Orientation on the sky is also doubtless important for understanding different systems; it seems likely that the Be disc of 4U 0115+63 intercepts the line-of-sight at a specific cyclical phase, causing transient shell lines in that object and not in A0535+26."
 Clearly further multiwaveband studies of other BeNRB svstems will demonstrate how general or indeed accurate this mocoel is. particularly as cillerences emerge.," Clearly further multiwaveband studies of other BeXRB systems will demonstrate how general or indeed accurate this model is, particularly as differences emerge."
 The primary findings of this study are the detection of quantisecl disc fluxes strongly supporting the resonant runcation paradigm. association of X-ray outbursts with reductions in truncation resonance. and the rolle of a ~1500 dav Be dise precession period in governing this svstem »haviour.," The primary findings of this study are the detection of quantised disc fluxes strongly supporting the resonant truncation paradigm, association of X-ray outbursts with reductions in truncation resonance, and the rôlle of a $\sim$ 1500 day Be disc precession period in governing this system behaviour."
" Optical observations have revealed. variability at he elfective 2,5. relative to the precessing De disc. and represent Be dise perturbations by the NS."," Optical observations have revealed variability at the 'effective' $P_{orb}$, relative to the precessing Be disc, and represent Be disc perturbations by the NS."
 The standard uminosity. classification. HI. is supported.," The standard luminosity classification, III, is supported."
 This greater. understanding of the 0535|26 svstem appears to be applicable to BeXRBs in general. perhaps allowing deeper insights into De discs ancl quasi-Ixeplerian discs in general.," This greater understanding of the A0535+26 system appears to be applicable to BeXRBs in general, perhaps allowing deeper insights into Be discs and quasi-Keplerian discs in general."
 The Carlos Sánnchez Telescope is operated. at the Teide Observatory (Tenerife) by the Instituto de sica de Canarias., The Carlos Sánnchez Telescope is operated at the Teide Observatory (Tenerife) by the Instituto de sica de Canarias.
 The ING Archive and Service Programmes have provided invaluable data., The ING Archive and Service Programmes have provided invaluable data.
 We acknowledge MNE. data courtesy of Laveock. Crinclay Zhao.," We acknowledge MMT data courtesy of Laycock, Grindlay Zhao."
 Simon Clark is thanked. for. numerous helpful CLISCUSSLOLIS., Simon Clark is thanked for numerous helpful discussions.
"To check for relative sky motions of aandJ19270636+0122577,, we inspected the photographic data available from the Digitized Sky Survey.","To check for relative sky motions of and, we inspected the photographic data available from the Digitized Sky Survey."
" We checked the digitized plates of the Palomar Observatory Sky Surveys from 1951, 1983, and 1991 and the HST Guide Star Catalogue from 1980, but found no indications for a relative transversal motion."," We checked the digitized plates of the Palomar Observatory Sky Surveys from 1951, 1983, and 1991 and the HST Guide Star Catalogue from 1980, but found no indications for a relative transversal motion."
 This finding corroborates the hypothesis that aand aare gravitationally bound and form a wide binary system., This finding corroborates the hypothesis that and are gravitationally bound and form a wide binary system.
 The parameters derived for the companion are summarized in Table 4.., The parameters derived for the companion are summarized in Table \ref{tab:CoRoT2BspecPars}.
" wwas observed by uusing the ACIS-S detector on June 24, 2010 for about 15 ks (Obs.-ID 10989)."," was observed by using the ACIS-S detector on June 24, 2010 for about 15 ks (Obs.-ID 10989)."
" In the reduction and analysis process, we used the standard software package CIAO in version 4.2."," In the reduction and analysis process, we used the standard software package CIAO in version 4.2."
" To obtain the best possible timing, the tool was used to apply a barycentric correction to the photon arrival times."," To obtain the best possible timing, the tool was used to apply a barycentric correction to the photon arrival times."
" In first step, we screened the X-ray image for photons in the 0.3a—4 keV energy band."," In a first step, we screened the X-ray image for photons in the $0.3-4$ keV energy band."
" This step reduces the background contamination and focuses our analysis on the energy band, in which stellar coronal emission is expected to dominate."," This step reduces the background contamination and focuses our analysis on the energy band, in which stellar coronal emission is expected to dominate."
 We show parts of the resulting X-ray image in Fig. 7.., We show parts of the resulting X-ray image in Fig. \ref{fig:CoRoT2ds9}.
" In a second step, we counted all photons within a 2"" radius circular region centered on the nominal position of CoRoT-2A."," In a second step, we counted all photons within a $2\arcsec$ radius circular region centered on the nominal position of ."
". In this region, we found 87 photons with an expected background contribution of z 33 photons, deduced from nearby source-free regions."," In this region, we found $87$ photons with an expected background contribution of $\approx$ 3 photons, deduced from nearby source-free regions."
" Finally, we carried out a spectral analysis of the source photons."," Finally, we carried out a spectral analysis of the source photons."
" Using XSPEC v12.5 ?,, we fitted the ACIS spectrum with an absorbed, thermal APEC (e.g.,?) model."," Using XSPEC v12.5 \citet{Arnaud1996}, we fitted the ACIS spectrum with an absorbed, thermal APEC \citep[e.g.,][]{Smith2001} model."
" Because the abundances are not well constrained by the fit, we fixed them at their solar values for the rest of the analysis, which is in accordance with our optical estimates (cf."," Because the abundances are not well constrained by the fit, we fixed them at their solar values for the rest of the analysis, which is in accordance with our optical estimates (cf."
 Sect 2.3))., Sect \ref{sec:ExcitationIonization}) ).
" For the depth of the absorbing column, the fit provides a value ofcm""?,, which is well compatible with a canonical density of for the interstellar medium and a distance of ~270 pc (see Sect. 2.8)) forCoRoT"," For the depth of the absorbing column, the fit provides a value of, which is well compatible with a canonical density of for the interstellar medium and a distance of $\approx 270$ pc (see Sect. \ref{sec:interstAbsDist}) )"
-2A.., for.
 Figure 8 shows the X-ray spectrum and our best-fit model; the fit results are summarized inTable 5.., Figure \ref{fig:CoRoT2spec} shows the X-ray spectrum and our best-fit model; the fit results are summarized inTable \ref{tab:CoRoT2spec}.
" From our best-fit model, we obtain an X-ray luminosity of Lx=1.9x10? iin the 0.3—4 keV band, corresponding to an activitylevel of logigLx/Lpo1* —4.2, which indicates that iis an active star also by X-ray standards."," From our best-fit model, we obtain an X-ray luminosity of $L_\mathrm{X} = 1.9\times 10^{29}$ in the $0.3-4$ keV band, corresponding to an activitylevel of $\log_{10}{L_\mathrm{X}/L_{\mathrm{bol}}} \approx -4.2$ , which indicates that is an active star also by X-ray standards."
»roportious by 1.530 However. we must note that ihe error estimate given here derives purely rom the EUVS MRES counting statistics.,"proportions by $\pm$ However, we must note that the error estimate given here derives purely from the EUVS MRES counting statistics."
 Our effective area calibration uncertainty 'educe this ratio to z1.2. but i is equally likely to increase the ratio to 2.f: so too. ther ispersion iu the various Hale-B«pp Quiso measurements at peribelion of20%.. which could his ratio to el.Ll. but it is equaly likely to increase the ratio to 2.2. and a quoted uncertal iu ve solar Ar/O ratio (GrevesseaxlSauval1993).," Our effective area calibration uncertainty ) could reduce this ratio to $\approx$ 1.2, but it is equally likely to increase the ratio to 2.4; so too, there is a dispersion in the various Hale-Bopp $Q_{\rm H_2O}$ measurements at perihelion of, which could reduce this ratio to $\approx$ 1.4, but it is equally likely to increase the ratio to 2.2, and a quoted uncertainty in the solar Ar/O ratio \citep {GS98}."
. Addingaff of these errors in quadrati iud Hale-Bopp's coma appears ο vave au Ar/O ratio relative to cosimogonic propoΠοια» 1.5:50.96:1.," Adding of these errors in quadrature, we find Hale-Bopp's coma appears to have an Ar/O ratio relative to cosmogonic proportions that is $\pm$ 0.96:1."
 Because noble gases by thetr nature do not participate in either the cometary ice cheuistry or coma chemistry. noble gases are j»areut species in the coma. aud their abundauce iu the 1eutral coma should reflect their bulk abuncaice within the cometary nucleus.," Because noble gases by their nature do not participate in either the cometary ice chemistry or coma chemistry, noble gases are parent species in the coma, and their abundance in the neutral coma should reflect their bulk abundance within the cometary nucleus."
 We assume this is tle Case in what The lack of depletion of Hale-Boj»p's Ar relative to cosmogonie proportions is interesting iu several respects., We assume this is the case in what The lack of depletion of Hale-Bopp's Ar relative to cosmogonic proportions is interesting in several respects.
 The irst of these concerus the thermal history of Hale-Bopp 1self., The first of these concerns the thermal history of Hale-Bopp itself.
 The fac that Ar is not depleted it Hale-Bopp iudicaes that the deep interior of Hale-Bopps uucleus eani1 have ever reached ecquilibrun temperatures of perhaps 35-10 lx. else the Ar wouk have been lost to sublimation (Bar-NunaudOwen1993).," The fact that Ar is not depleted in Hale-Bopp indicates that the deep interior of Hale-Bopp's nucleus cannot have ever reached equilibrium temperatures of perhaps 35–40 K, else the Ar would have been lost to sublimation \citep{BO98}."
. Neon. which is even more volatile than argon. sublihates vigorously at temper:ures of 16-20 Ix. The EUVE satellite returned spectra of Hale-Bopp i 1996 showing Ne is 225 tinies clepleted relative to cosmogonic proportions (Ixrasnopolskyetal.1997):: this is strong evicderce that Hale-Bopps deep interiorfas been warmed above 20 Ex. Together. the EUVE satellite aud EUVS rocket experimeut results trap Hale-Bopp’s bulk internal temperature as lavug exceeded the Ne sublimation loss rauge of 16-20 lx. but not the Ar sublimatiou rauge of approximaely 35-10 Ex. These temperature coustraluts are consistent with others Hale-Bopp retrieved row H3O ortho-para (Crovisieretal.1997). and D/H ratios 1999).," Neon, which is even more volatile than argon, sublimates vigorously at temperatures of 16–20 K. The EUVE satellite returned spectra of Hale-Bopp in 1996 showing Ne is $>$ 25 times depleted relative to cosmogonic proportions \citep{Kea97}; this is strong evidence that Hale-Bopp's deep interior been warmed above 20 K. Together, the EUVE satellite and EUVS rocket experiment results trap Hale-Bopp's bulk internal temperature as having exceeded the Ne sublimation loss range of 16–20 K, but not the Ar sublimation range of approximately 35–40 K. These temperature constraints are consistent with others Hale-Bopp retrieved from $_2$ O ortho-para \citep{Crea97} and D/H ratios \citep{Bea99}."
. We interpret our rest tas indicatiug that either the solar nebula was far colder aud far richer i LA ‘than models tyicalv predict (Luuineetal.2000).. or that Hale-Bopp was formed iu the cok Lisiper Belt region (i.e.. wel jevyond the 20-30 AU. Uranus-Neptune zone) aud was then subseqieutv ejected to the Oort Cloid (its more recent dynamical home) without ever spending inuch ti me] ithe (warmer) Jupiter-Saurn zone. or both.," We interpret our result as indicating that either the solar nebula was far colder and far richer in Ar than models typically predict \citep{Lea00}, or that Hale-Bopp was formed in the cold, Kuiper Belt region (i.e., well beyond the 20–30 AU Uranus-Neptune zone) and was then subsequently ejected to the Oort Cloud (its more recent dynamical home) without ever spending much time in the (warmer) Jupiter-Saturn zone, or both."
" Although either implication is contrary to “COUVELtional wisdom."" we note that le transport of comets [roi the Ixuiper Belt region (usually alter Neptije-1uduced inward evolution) to the Oort Cloud lias been detected in recent divuzunical simulatLOS of Oort Cloud formation.(Donesetal.2000)."," Although either implication is contrary to “conventional wisdom,” we note that the transport of comets from the Kuiper Belt region (usually after Neptune-induced inward evolution) to the Oort Cloud has been detected in recent dynamical simulations of Oort Cloud \citep{Dea00}."
. This fi‘st’ detection of a uative cometary noble gas. argou. whets our appetite [or more," This first detection of a native cometary noble gas, argon, whets our appetite for more"
iis identified with the Mpg~310AL. super-massive black hole (SAIBII) in the centre of our Galaxy (e.g...22)..,"is identified with the $M_{\rm BH} \sim 3 \times 10^6 \msun$ super-massive black hole (SMBH) in the centre of our Galaxy \citep[e.g., ][]{Schoedel02,Ghez03b}."
 ὃν virtue of its location. Nueler (AGN).," By virtue of its location, Nuclei (AGN)."
 Indeed. this is the only AGN where recent observations detail the origin of the gas in the immediate vicinity of the SML capture radius (c.g.2?777)..," Indeed, this is the only AGN where recent observations detail the origin of the gas in the immediate vicinity of the SMBH capture radius \citep[e.g.,][]{Najarro97, Paumard01, Baganoff03a,
Genzel03a}."
 Phis information. missing for all other AGN because of too great. a distance to them. their large luminosity. or both. is absolutely necessary if the accretion problem is to be mocdelled self-consistentLy.," This information, missing for all other AGN because of too great a distance to them, their large luminosity, or both, is absolutely necessary if the accretion problem is to be modelled self-consistently."
" Areuably the most famous puzzle of lis its low luminosity with respect to estimates of the accretion rate at around. the capture radius. Le. at distances of order 1""~107/450.04 pe. where fs is the Schwarzschilel radius of"," Arguably the most famous puzzle of is its low luminosity with respect to estimates of the accretion rate at around the capture radius, i.e. at distances of order $1'' \sim 10^5 R_{\rm S} \sim 0.04$ pc, where $R_{\rm S}$ is the Schwarzschild radius of."
 Two methods have been deployed. to obtain these estimates., Two methods have been deployed to obtain these estimates.
" From observations of the Galactic centre region. one can measure the gas density and temperature around the inner aresecond and then infer an estimate of the Bondi accretion rate of AP10""M. +(?).."," From observations of the Galactic centre region, one can measure the gas density and temperature around the inner arcsecond and then infer an estimate of the Bondi accretion rate of $\dot M \sim 10^{-6}
\msun$ $^{-1}$ \citep{Baganoff03a}. ."
 However. unlike in the classical textbook. problem (7).. hot gas is continuously. created. in shocked. winds expelled by tens of young massive stars nearA. and there is neither a well defined concept of gas density and temperature at infinity. nor one for the gas capture radius.," However, unlike in the classical textbook problem \citep{Bondi52}, hot gas is continuously created in shocked winds expelled by tens of young massive stars near, and there is neither a well defined concept of gas density and temperature at infinity, nor one for the gas capture radius."
 The other method. addresses this problem: by. direct modelling of the gas cdvnamics of stellar winds. assuming that the properties of the wind sources are known.," The other method addresses this problem by direct modelling of the gas dynamics of stellar winds, assuming that the properties of the wind sources are known."
 Three dimensional simulations of wind accretion around wavere performed by 2)... flatttened svstem.," Three dimensional simulations of wind accretion around were performed by \cite{Coker97}, ttened system."
 7) used a particle-based. code with more detailed information on stellar coordinates and wind properties., \cite{Rockefeller04} used a particle-based code with more detailed information on stellar coordinates and wind properties.
 However. in both cases the stars were at fixed locations. whereas in reality they follow Keplerian orbitsaround the SMDII..," However, in both cases the stars were at fixed locations, whereas in reality they follow Keplerian orbitsaround the SMBH."
Dased on observations obtained withVALA/-New/lon.. an ESA science mission with instruments and contributions clirecthy fanded by LSA Member States and NASA.,"Based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA."
 This research was also based on observations mace at. the William Llerschel Telescope which is 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. and on observations collected at the European Southern Observatory. Chile. ESO No.," This research was also based on observations made at the William Herschel Telescope which is 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, and on observations collected at the European Southern Observatory, Chile, ESO No."
 62.0-0659., 62.O-0659.
 We thank the Roval Socicty [or travel support under their Joint. International Project scheme., We thank the Royal Society for travel support under their Joint International Project scheme.
 SION is) supported. financially by NWO. the Netherlands Organization. for Scientific. Research.," SRON is supported financially by NWO, the Netherlands Organization for Scientific Research."
 LIC acknowledges financial support. from the Spanish Alinisterio cle Ciencia e Innovaciónn (previously Ministerio de Eclueacionn v Ciencia). under cts ESP2006-13608-05-01. AYA2009-08059 ancl AYMAA2010-21490-C'O2-01.," FJC acknowledges financial support from the Spanish Ministerio de Ciencia e Innovaciónn (previously Ministerio de Educaciónn y Ciencia), under projects ESP2006-13608-C02-01, AYA2009-08059 and AYA2010-21490-C02-01."
gas cooling rate. AL.,"gas cooling rate, ${\dot{M}}$."
 Previously. we reported upon OVI observations of two early-(vpe galaxies. NGC 1404 and NGC 4636 (Bregman.Miller.ancIrwin2001).. (wo of the X-ray luminous galaxies widely believed to host cooling flows.," Previously, we reported upon OVI observations of two early-type galaxies, NGC 1404 and NGC 4636 \citep{breg01}, two of the X-ray luminous galaxies widely believed to host cooling flows."
 For NGC 1404. OVI was not detected and the upper limit is several times below the standard cooling flow prediction. based on data.," For NGC 1404, OVI was not detected and the upper limit is several times below the standard cooling flow prediction, based on data."
 However. OVI emission was detected from NGC 4636. and the liminosity of these lines corresponds to a cooling rate of 0.4 M. +.," However, OVI emission was detected from NGC 4636, and the luminosity of these lines corresponds to a cooling rate of 0.4 $_{\odot}$ $^{-1}$."
" This is less than the total rate from the cooling flow model of 2 M, te but the aperture (a 30” square aperture. or an effective radius of about 17"") only takes in a part of the galaxy."," This is less than the total rate from the cooling flow model of 2 $_{\odot}$ $^{-1}$ , but the aperture (a $\arcsec$ square aperture, or an effective radius of about $\arcsec$ ) only takes in a part of the galaxy."
 Correcting for the flux that falls outside the aperture is a model-cepencdent procedure. but if one uses a model with distributed mass drop out (q—1 from SarazinandAshe 1989)). the corrected OVI luminosity approximately equals the cooling flow prediction.," Correcting for the flux that falls outside the aperture is a model-dependent procedure, but if one uses a model with distributed mass drop out =1 from \citealt{sarz89}) ), the corrected OVI luminosity approximately equals the cooling flow prediction."
 Following on this work. we began a OVI emission line survey of an unbiased sample of nearby earlv-tvpe galaxies.," Following on this work, we began a OVI emission line survey of an unbiased sample of nearby early-type galaxies."
 The basic observations define the emission line characteristics of the sample. ancl permit us (to test a few predictions of the model.," The basic observations define the emission line characteristics of the sample, and permit us to test a few predictions of the model."
 One would expect that the N-ray faint galaxies would be very weak OVI emitters. if most of the thermal energy is being carried away in galactic winds.," One would expect that the X-ray faint galaxies would be very weak OVI emitters, if most of the thermal energy is being carried away in galactic winds."
 Secondly. the galaxies with significant hot gas masses should usually possess OVI emission.," Secondly, the galaxies with significant hot gas masses should usually possess OVI emission."
 We defined a sample of optically selected earlv-tvpe galaxies in order to be unbiased with respect lo X-ray properties., We defined a sample of optically selected early-type galaxies in order to be unbiased with respect to X-ray properties.
 In previous work with observations (Brownanclman1998. 2000).. we developed a complete optically selected sample of early-type galaxies. which contains the optically brightest elliptical galaxies (bv total apparent magnitude) in the Faberetal.(1989). sample that do not have AGNs pointing al ts. are not at low Galactic latitude. ancl excluding dwarf galaxies and ¢D systems.," In previous work with observations \citep{brown98,brown00}, we developed a complete optically selected sample of early-type galaxies, which contains the optically brightest elliptical galaxies (by total apparent magnitude) in the \citet{faber89}
 sample that do not have AGNs pointing at us, are not at low Galactic latitude, and excluding dwarf galaxies and cD systems."
 This sample of 33 galaxies have been studied extensively in (he optical region and were observed al X-ray energies wilhROSAT., This sample of 33 galaxies have been studied extensively in the optical region and were observed at X-ray energies with.
 Most of the objects in the sample were observed more recently withChandra., Most of the objects in the sample were observed more recently with.
 This sample was accepted as a program onFUSE. and nearly all were observed. wilh only one exception due to the pointing constraints following the reaction wheel failure.," This sample was accepted as a program on, and nearly all were observed, with only one exception due to the pointing constraints following the reaction wheel failure."
 The redshift range of the sample is -250 kms ! to 1950 kms |. and the apparent magnitude range is 9.3-11.0 (in D): for completeness. we included M87.," The redshift range of the sample is -250 km $^{-1}$ to 1950 km $^{-1}$, and the apparent magnitude range is 9.3-11.0 (in B); for completeness, we included M87."
" The optical properties and exposure limes are given in Table 1. where we list the galaxy name. absolute blue magnitude. R,. one-dimensional stellar velocity dispersion. extinction in D. distance (in km ! and Mpe. total exposuretime. and nieht exposure time (boldflace denotes the cata used)."," The optical properties and exposure times are given in Table 1, where we list the galaxy name, absolute blue magnitude, $_e$, one-dimensional stellar velocity dispersion, extinction in B, distance (in km $^{-1}$ and Mpc, total exposuretime, and night exposure time (boldface denotes the data used)."
Tere we report the results of the full oobservatious kks of PSPC. kks of URI) of the field surrounding NGC 300. concentrating primarily on the point source population within and around the ealaxy.,"Here we report the results of the full observations ks of PSPC, ks of HRI) of the field surrounding NGC 300, concentrating primarily on the point source population within and around the galaxy."
 The plan of the paper is as follows., The plan of the paper is as follows.
" retsec, bscdeseribestheobser vationsandthe preHininar gdata csudiscussestheresultsasrcegavdsth poi ntsoured", \\ref{sec_obse} describes the observations and the preliminary data reduction methods used and \\ref{sec_resu} discusses the results as regards the point sources.
 sccaisciliseusscsthe X ragpropertiesof NGC 300. withregardbothtoitsimenibe shi pDEép cdnspróng ο nerd," \\ref{sec_disc} discusses the X-ray properties of NGC 300, with regard both to its membership of the Sculptor group and to how it compares to spiral galaxies in general."
 scesuimim.., Finally a summary is presented in \\ref{sec_summ}.
 A παν log of the entire PPSPC aud WRI observations of the NGC 300 field is even in Table 1.., A summary log of the entire PSPC and HRI observations of the NGC 300 field is given in Table \ref{table_obse}.
 Because the PSPC is some three times as scusitive as the IIRI. we expect. from the relevant exposure times of the observations. many more couuts from the PSPC data.," Because the PSPC is some three times as sensitive as the HRI, we expect, from the relevant exposure times of the observations, many more counts from the PSPC data."
" We have analysed all the data extensively, aud fiud this to be so."," We have analysed all the data extensively, and find this to be so."
 Nevertheless the IRI data are in themselves of ercat interest. and their analysis and subsequent results are described later.," Nevertheless the HRI data are in themselves of great interest, and their analysis and subsequent results are described later."
 NGC 300 was observed with he ROSAT PSPC twice (seo Table 1))., NGC 300 was observed with the ROSAT PSPC twice (see Table \ref{table_obse}) ).
 Though each PSPC dataset was seen to be very clean. times of both very high and very low accepted event rates and master veto rates were removed.," Though each PSPC dataset was seen to be very clean, times of both very high and very low accepted event rates and master veto rates were removed."
" Source detection ancl position determination were performed over the ful Ποια, of view with the ENSAS local detect. map cletec and masini likelihood algorithiis (Zinunernanun ct al."," Source detection and position determination were performed over the full field of view with the EXSAS local detect, map detect, and maximum likelihood algorithms (Zimmermann et al."
" 1991) using πασος of pixel size15"".", 1994) using images of pixel size.
. The two eventsets were theu shifted with respect to the prominent X-ray aud optical bright star in the field. WD5103. correcting for the proper motion of the star (Perryman 11997) at the epoch of the ROSAT observations.," The two eventsets were then shifted with respect to the prominent X-ray and optical bright star in the field, HD5403, correcting for the proper motion of the star (Perryman 1997) at the epoch of the ROSAT observations."
 The two cleaned and positiou-corrected datasets were then mereed together. aud the source detection procedures were re-ran.," The two cleaned and position-corrected datasets were then merged together, and the source detection procedures were re-ran."
 Sources accepted as PSPC detections were those with a lixelibood L 10., Sources accepted as PSPC detections were those with a likelihood L $\geq$ 10.
 Probabilities P. axe related to maxi likelihood. values L. by the relation P=1.«L," Probabilities P, are related to maximum likelihood values L, by the relation $=1-e^{-\mbox{L}}$."
 Thus a likelihood L of 10 correspouds to a Catssian significance of [0c (CCruddace 11985: Zinuueriann 11991)., Thus a likelihood L of 10 corresponds to a Gaussian significance of $\sigma$ (Cruddace 1988; Zimmermann 1994).
 Iun the ollowing. we concentrate primarily on the sources found within the optical confines of NGC 300. though we discuss a few other interesting sources detected close by in Sect.," In the following, we concentrate primarily on the sources found within the optical confines of NGC 300, though we discuss a few other interesting sources detected close by in Sect."
 3.2. and in Appendix. AppeucdixAs. , \ref{sec_res2} and in Appendix. \ref{sec_appe}. .
1] shows a broad baud (channels 235. corresponding approximately to 2.55 kkeV) contour imaee of the central —29/ «25/ ivegion. overlaved on a Digital Sky Survey (DSS2) red inaee (note the bright optical and X-ray star ITD5103. to the north east. used to register the A-ray coordinates).," 1 shows a broad band (channels $-$ 235, corresponding approximately to $-$ keV) contour image of the central $\sim$ $\times$ region, overlayed on a Digital Sky Survey (DSS2) red image (note the bright optical and X-ray star HD5403, to the north east, used to register the X-ray coordinates)."
 Shown in Fig.22 are equivalent contour images in the soft [1). hardl 90) auc ας 201) PPSPC bands. with the D25 ellipse of the galaxy niarked.," Shown in 2 are equivalent contour images in the soft $-$ 41), hard1 $-$ 90) and hard2 $-$ 201) PSPC bands, with the D25 ellipse of the galaxy marked."
" Within the area covered bv ll. 17 SOlYCCS are μα Ωμ... marked m the figure, 26 s.Satropich lie within (or <1 ffromi) the optical disk of NGC 300 (as indicated by the ΣΣ ΕΟΓ "," Within the area covered by 1, 47 sources are detected, their source numbers marked in the figure, 26 of which lie within (or $<1$ from) the optical disk of NGC 300 (as indicated by the D25 ellipse in 2)."
rele Mas; Table 2 as follows: source umber P1). corrected reht ascension and declination (Cols.32). error on the source position Ll. iucludiug a 3799 svstematic attitude solution error). likelihood of existence 55). net broad band counts aud error 66). aud cout rates and errors after applving deadtime aud vienettiug corrections 77).," These 26 sources are listed in Table \ref{table_Psrc} as follows: source number 1), corrected right ascension and declination 3), error on the source position 4, including a 9 systematic attitude solution error), likelihood of existence 5), net broad band counts and error 6), and count rates and errors after applying deadtime and vignetting corrections 7)."
 Two larducss ratios aro eiven iu Cols.58S 9. IIRI. defined. as | soft) (hard aud soft being the net counts iu the hard(channels 201) and soft (channels 11) bands. respectively). aud IIR2. defined as |hard) (hardl and hird2 being the met counts in the hardl (channels 90) aud hard2 (chanuels 201) bands. respectively).," Two hardness ratios are given in 8 9, HR1, defined as $-$ $+$ soft) (hard and soft being the net counts in the hard(channels $-$ 201) and soft (channels $-$ 41) bands, respectively), and HR2, defined as $-$ $+$ hard1) (hard1 and hard2 being the net counts in the hard1 (channels $-$ 90) and hard2 (channels $-$ 201) bands, respectively)."
 The correspoudiug errors. as per Ciliegi 11997. are also given.," The corresponding errors, as per Ciliegi 1997, are also given."
 While IRI is nost sensitive to variations in the absorbing coluun. IIR2 traces luore the power law iudex or teniperature.," While HR1 is most sensitive to variations in the absorbing column, HR2 traces more the power law index or temperature."
 Tarducss ratios can be used to eive very crude estimates of the spectral parameters that best describe the source photons (compare the tabulated values with plots showing the variation of ITR1 and IIR2 for simple spectral models iu Pietsch 11998)., Hardness ratios can be used to give very crude estimates of the spectral parameters that best describe the source photons (compare the tabulated values with plots showing the variation of HR1 and HR2 for simple spectral models in Pietsch 1998).
 The kkeV flux ancl Nav puainosity. assuniüne a SkkeV thermal broeimisstralilung model aud a source distance of MMpe to NGC 300). are eiven in 140 11.," The $-$ keV flux and X-ray luminosity, assuming a keV thermal bremsstrahlung model and a source distance of Mpc to NGC 300), are given in 10 11."
 Count rates of the PSPC-detectec poiut SOUECCS Ca )o converted iuto fixes. assuniue a varietv of spectral models.," Count rates of the PSPC-detected point sources can be converted into fluxes, assuming a variety of spectral models."
 A LkkeV thermal breimisstralibuug model for instance.Ooeives rise to fluxes C»ereater than those eiven in Table 2..," A keV thermal bremsstrahlung model for instance,gives rise to fluxes greater than those given in Table \ref{table_Psrc}. ."
 Finally note that noue of these 26 sources are observed to be significantly extended., Finally note that none of these 26 sources are observed to be significantly extended.
 A similar table, A similar table
et al.,et al.
 2004) we attempt to illustrate how the {νς- brightness of our two z2+ quasar host galaxies compares both with other estimates of quasar host-galaxy brightness atf comparable redshift. and with the brightness of other well-studied yopulations of high-redshift galaxies.," 2004) we attempt to illustrate how the $K_S$ -band brightness of our two $z \simeq 4$ quasar host galaxies compares both with other estimates of quasar host-galaxy brightness at comparable redshift, and with the brightness of other well-studied populations of high-redshift galaxies."
 Here it can be seen that our quasar hosts lie on the now well-established ντ relation for »owerful radio galaxies (e.g. Lilly Longair 1984: Eales et al., Here it can be seen that our quasar hosts lie on the now well-established $K-z$ relation for powerful radio galaxies (e.g. Lilly Longair 1984; Eales et al.
 1997: van Breugel et al., 1997; van Breugel et al.
 1998: De Breuck et al., 1998; De Breuck et al.
 2002)., 2002).
 As can be seen from Fig., As can be seen from Fig.
 5. and as inferred from a series of deep near- imaging studies of powerful radio galaxies (e.g. Dunlop Peacock 1993: Best et al.," 5, and as inferred from a series of deep near-infrared imaging studies of powerful radio galaxies (e.g. Dunlop Peacock 1993; Best et al."
 1998: Willott et al., 1998; Willott et al.
 2003: Targett et al., 2003; Targett et al.
 2011). the radio-galaxy /vz relation essentially defines the high-mass envelope of the evolving galaxy population.," 2011), the radio-galaxy $K-z$ relation essentially defines the high-mass envelope of the evolving galaxy population."
 Regardless of their precise stellar masses. it is thus clear that. as perhaps expected. the host galaxies of the most luminous SDSS quasars at 2στ4 are amongst the most massive known galaxies at this epoch.," Regardless of their precise stellar masses, it is thus clear that, as perhaps expected, the host galaxies of the most luminous SDSS quasars at $z \simeq 4$ are amongst the most massive known galaxies at this epoch."
 In addition. while we have argued that our data are of higher quality. and our results more robust than those derived from previous studies of quasar hosts at ο24. our host galaxy luminosities are basically consistent with those derived by McLeod Bechtold (2009). Hutchings (2003. 2005) and Peng et al. (," In addition, while we have argued that our data are of higher quality, and our results more robust than those derived from previous studies of quasar hosts at $z \simeq 4$, our host galaxy luminosities are basically consistent with those derived by McLeod Bechtold (2009), Hutchings (2003, 2005) and Peng et al. ("
2006b).,2006b).
 As judged Tom the galaxy evolution models of Rocca-Volmerage et al. (, As judged from the galaxy evolution models of Rocca-Volmerage et al. (
2004) over-plotted on Fig.,2004) over-plotted on Fig.
 5. it would seem that all of the +2 quasar 108t galaxies uncovered to date have stellar masses in the range 110.104AL... which is entirely consistent with our own derived bounds on the possible stellar masses of our two quasar dost galaxies as given in Table 4.," 5, it would seem that all of the $z \simeq 4$ quasar host galaxies uncovered to date have stellar masses in the range $1 - 10 \times 10^{11}\,{\rm M_{\odot}}$, which is entirely consistent with our own derived bounds on the possible stellar masses of our two quasar host galaxies as given in Table 4."
 Our study is. however. the first to yield apparently robust values for the half-light radii of quasar host galaxies at such ugh redshifts.," Our study is, however, the first to yield apparently robust values for the half-light radii of quasar host galaxies at such high redshifts."
 Despite their large stellar masses. the derived half-ight radii of the += quasar hosts Cry:l.S ΚΚκΡο) are clearly much smaller than those of either low-redshift quasar hosts (~10 ΚΚκΡρο: Dunlop et al.," Despite their large stellar masses, the derived half-light radii of the $z \simeq 4$ quasar hosts $r_{1/2} \simeq 1.8$ kpc) are clearly much smaller than those of either low-redshift quasar hosts $\simeq 10$ kpc; Dunlop et al."
 2003) or indeed the vast majority of oresent-day. galaxies of comparable mass (e.g. Hyde Bernardi 2009)., 2003) or indeed the vast majority of present-day galaxies of comparable mass (e.g. Hyde Bernardi 2009).
 However. our small derived values for νο seem broadly as expected given the rapidly growing observational evidence for he increasing compactness of massive galaxies with increasing redshift (Daddi et al.," However, our small derived values for $r_{1/2}$ seem broadly as expected given the rapidly growing observational evidence for the increasing compactness of massive galaxies with increasing redshift (Daddi et al."
 2005: Trujillo et al., 2005; Trujillo et al.
 2006. 2007: Longhetti et al.," 2006, 2007; Longhetti et al."
 2007: Zirm et al., 2007; Zirm et al.
 2007: Cimatti et al., 2007; Cimatti et al.
 2008: Buitrago et al., 2008; Buitrago et al.
 2008: van Dokkum et al., 2008; van Dokkum et al.
 2008: Targett et al., 2008; Targett et al.
 2011) and the expectations from recent simulations of galaxy growth (e.g. Oser et al., 2011) and the expectations from recent simulations of galaxy growth (e.g. Oser et al.
 2012)., 2012).
 Our results are also consistent with the only existing indirect size estimates for several 2—+ quasars based on lensed measurements of the molecular gas content (Riechers et al., Our results are also consistent with the only existing indirect size estimates for several $z\sim4$ quasars based on lensed measurements of the molecular gas content (Riechers et al.
 2008a.b: Riechers et al.," 2008a,b; Riechers et al."
 2009)., 2009).
" We conclude that. just as at low redshift. the properties of quasar host galaxies at 2—4 seem broadly as expected for ""normal"" galaxies of comparable mass at that particular cosmologieal epoch."," We conclude that, just as at low redshift, the properties of quasar host galaxies at $z \simeq 4$ seem broadly as expected for “normal” galaxies of comparable mass at that particular cosmological epoch."
" The derived black-hole masses given in Table 4 are clearly very large. approaching Aj,στLOMAL. for both quasars. and so it is worth pausing to consider whether such values are plausible/expected."," The derived black-hole masses given in Table 4 are clearly very large, approaching $M_{bh} \simeq 10^{10}\,{\rm M_{\odot}}$ for both quasars, and so it is worth pausing to consider whether such values are plausible/expected."
 Our conclusion is that these masses. while high. are certainly not unreasonable given the relative rarity of these ultra-bright quasars. our understanding of quasar demographics. and the results of the latest high-redshift simulations.," Our conclusion is that these masses, while high, are certainly not unreasonable given the relative rarity of these ultra-bright quasars, our understanding of quasar demographics, and the results of the latest high-redshift simulations."
 Specitically. our target objects were selected from a parent sample which contains only | such luminous quasar in the redshift range 4<«5 per 50 deg? on the sky. corresponding to a comoving source density of only c2Cipe7.," Specifically, our target objects were selected from a parent sample which contains only 1 such luminous quasar in the redshift range $4 < z < 5$ per 50 $^2$ on the sky, corresponding to a comoving source density of only $\simeq 2\,{\rm Gpc^{-3}}$."
" These are thus extreme objects. arguably the natural descendents of the most extreme quasars found ats26.5—Y. which already appear to have black-hole masses Aly,c210""M. (Willott. MeLure Jarvis 2003: Mortlock et al."," These are thus extreme objects, arguably the natural descendents of the most extreme quasars found at $ z \simeq 6.5 - 7$, which already appear to have black-hole masses $M_{bh} \simeq 2 \times 10^9\,{\rm M_{\odot}}$ (Willott, McLure Jarvis 2003; Mortlock et al."
 2011)., 2011).
 Only 60 million years of further Eddington-limited growth would be required to boost these black-hole masses by a further factor of 4. to values consistent with those derived here 800 million years later.," Only 60 million years of further Eddington-limited growth would be required to boost these black-hole masses by a further factor of 4, to values consistent with those derived here 800 million years later."
" This viewpoint receives some further theoretica support from recent simulations of black-hole growth in the voung Universe. such as the ""Massive Black"" simulation of Di Matteo e al. ("," This viewpoint receives some further theoretical support from recent simulations of black-hole growth in the young Universe, such as the “Massive Black” simulation of Di Matteo et al. ("
2011).,2011).
 The luminous quasars targeted here are sufficiently rare that. on average. only one would be expected in the ~0.5Cpe? comoving volume followed in this simulation. and Di Matteo e al.," The luminous quasars targeted here are sufficiently rare that, on average, only one would be expected in the $\simeq 0.5\,{\rm Gpc^3}$ comoving volume followed in this simulation, and Di Matteo et al."
" report that the most massive black hole in their simulation has already achieved a mass of Al,25«10M. by zc5."," report that the most massive black hole in their simulation has already achieved a mass of $M_{bh} \simeq 5 \times 10^9\,{\rm M_{\odot}}$ by $z \simeq 5$."
" By this point feedback and shock heating of infalling gas are inferred to limit further growth. but clearly the concept that such rare black holes may achieve masses approaching Aj,cLOMAL. by zc4 is consistent with current observational and theoretical constraints."," By this point feedback and shock heating of infalling gas are inferred to limit further growth, but clearly the concept that such rare black holes may achieve masses approaching $M_{bh} \simeq 10^{10}\,{\rm M_{\odot}}$ by $z \simeq 4$ is consistent with current observational and theoretical constraints."
 Finally. we ean combine our estimates of black-hole mass and galaxy stellar mass to infer the black hole-to-galaxy mass ratio for our τςcd quasars.," Finally, we can combine our estimates of black-hole mass and galaxy stellar mass to infer the black hole-to-galaxy mass ratio for our $z \simeq 4$ quasars."
" The averaged value of Adnan:M, is shown in Fig.", The averaged value of $M_{bh}:M_{gal}$ is shown in Fig.
 6. where we plot two 2&4 data points to indicate the different values which arise from adoption of either the maximum or minimum possible galaxy stellar masses (as derived assuming a formation redshift of σε=LO or z;=5 respectively).," 6, where we plot two $z\simeq4$ data points to indicate the different values which arise from adoption of either the maximum or minimum possible galaxy stellar masses (as derived assuming a formation redshift of $z_f=10$ or $z_f=5$ respectively)."
" The light-grey shaded area illustrates the 3-0.3-dex uncertainty on the local AZ,/Mp1, ratio. centred on ΠΕ.0.002."," The light-grey shaded area illustrates the $\pm0.3$ -dex uncertainty on the local $M_{bh}/M_{bulge}$ ratio, centred on $M_{bh}/M_{bulge} = 0.002$."
 The solid line shows the best fit to the observed evolution in 3CRR galaxies from MeLure et al. (, The solid line shows the best fit to the observed evolution in 3CRR galaxies from McLure et al. (
2006). while the dark-grey shaded area shows the le uncertainty of this fit.,"2006), while the dark-grey shaded area shows the $\sigma$ uncertainty of this fit."
 This evolving MoanfAlouty. ratio result is consistent with results from Peng et al. , This evolving $M_{bh}/M_{bulge}$ ratio result is consistent with results from Peng et al. (
200623. who find a similar evolution out to 2— in a sample of LI quasars.,"2006a), who find a similar evolution out to $z\sim2$ in a sample of 11 quasars."
 Also shown is the +=6.41 quasar observed by Willott. MeLure. Jarvis (2003) who used //-band and A-band spectra covering the MgII broad emission line to derive a black-hole mass of 3...10XI..," Also shown is the $z=6.41$ quasar observed by Willott, McLure, Jarvis (2003) who used $H$ -band and $K$ -band spectra covering the MgII broad emission line to derive a black-hole mass of $3\times10^{9}\,{\rm M_{\odot}}$."
 However. note that in this case the host-galaxy mass refers not to a stellar mass inferred from the sort of host-galaxy imaging attempted here. but is a dynamical mass inferred from Very Large Array measurements of molecular gas in the quasar host galaxy by Walter et al. (," However, note that in this case the host-galaxy mass refers not to a stellar mass inferred from the sort of host-galaxy imaging attempted here, but is a dynamical mass inferred from Very Large Array measurements of molecular gas in the quasar host galaxy by Walter et al. ("
2004).,2004).
" Even given the uncertainties. our results imply a black-hole:host-galaxy mass ratio CUu,:AlgaezmO01. 0.05) which appears to be a factor of c10 higher than typically seen in the low-redshift Universe."," Even given the uncertainties, our results imply a black-hole:host-galaxy mass ratio $M_{bh}:M_{gal} \simeq 0.01 - 0.05$ ) which appears to be a factor of $\simeq 10$ higher than typically seen in the low-redshift Universe."
 Fig., Fig.
 6 demonstrates that this is consistent with the growing body of evidence for a systematic growth in this mass ratio with increasing redshift. at least for objects selected as powerful active galactic nuclei (Decarli et al.," 6 demonstrates that this is consistent with the growing body of evidence for a systematic growth in this mass ratio with increasing redshift, at least for objects selected as powerful active galactic nuclei (Decarli et al."
 2010. and references therein).," 2010, and references therein)."
" Indeed. an order of magnitude increase in. Mo,Myr iS exactly as anticipated given the redshift dependence Ai2:Adgarx(11:) inferred from recent studies of X-ray selectedof AGN (Bennert et al."," Indeed, an order of magnitude increase in $M_{bh}:M_{gal}$ is exactly as anticipated given the redshift dependence of $M_{bh}:M_{gal} \propto (1 + z)^{1.4}$ inferred from recent studies of X-ray selected AGN (Bennert et al."
 2011). and recent numerical simulations of galaxy and black hole growth (e.g. Shankar et al.," 2011), and recent numerical simulations of galaxy and black hole growth (e.g. Shankar et al."
 201I. Power et al.," 2011, Power et al."
 201, 2011).
 The observed evolution in the black-hole:host galaxy mass ratio shown in Fig., The observed evolution in the black-hole:host galaxy mass ratio shown in Fig.
 6. although consistent with numerous results in the literature. could be subject to various selection effects.," 6, although consistent with numerous results in the literature, could be subject to various selection effects."
 The necessity of using black-hole masses derived from the velocity width of broad permitted lines limits candidate objects to luminous rapidly-accreting unobscured Type-! active galactic nuclei. which implies that results will necessarily be biased from the true distribution of a volume-limited sample (e.g. Lauer et al.," The necessity of using black-hole masses derived from the velocity width of broad permitted lines limits candidate objects to luminous rapidly-accreting unobscured Type-1 active galactic nuclei, which implies that results will necessarily be biased from the true distribution of a volume-limited sample (e.g. Lauer et al."
 2007)., 2007).
" For example. the low AZ,,:M, estimated for submillimetre selected galaxies at 2—2.2 (Borys et al."," For example, the low $M_{bh}:M_{gal}$ estimated for submillimetre selected galaxies at $z\sim2.2$ (Borys et al."
 2005) could imply a large scatter in the relationship at high redshift not sampled by quasars., 2005) could imply a large scatter in the relationship at high redshift not sampled by quasars.
 However. the agreement between our results and other studies using both quasars and radio galaxies indicates that. at least for the most," However, the agreement between our results and other studies using both quasars and radio galaxies indicates that, at least for the most"
"typical signature of binarity(i.e.,, a cosine modulation), in agreement with the system main characteristics (separation, position angle, flux ratio; Bonnefoy et al.,","typical signature of binarity, a cosine modulation), in agreement with the system main characteristics (separation, position angle, flux ratio; Bonnefoy et al.,"
 in prep.)., in prep.).
" From the visibilities, one can locate the emission at each velocity and distinguish between various scenarios capable of producing the line."," From the visibilities, one can locate the emission at each velocity and distinguish between various scenarios capable of producing the line."
 The visibility increase within the line implies that the emitting region is more compact than the one responsible for the continuum., The visibility increase within the line implies that the emitting region is more compact than the one responsible for the continuum.
" To derive the characteristic sizes of the region emitting only, for each spectral channel of the HR measurements, one has to substract the underlying continuum to first determine the visibility of the line only (?).."," To derive the characteristic sizes of the region emitting only, for each spectral channel of the HR measurements, one has to substract the underlying continuum to first determine the visibility of the line only \citep{weigelt07}."
" These estimates can only be performed using the data gathered with the ATs, for which reliable absolute values for the visibilities are obtained."," These estimates can only be performed using the data gathered with the ATs, for which reliable absolute values for the visibilities are obtained."
" Using a model of an uniform ring, the emission in the line has a typical extension (ring diameter) of ~1.6 mas at zero velocity, and ~2.5 mas at higher velocities (~100 km/s), i.e.,, from ~1.5 to ~2.6 AU, depending on the distance."," Using a model of an uniform ring, the emission in the line has a typical extension (ring diameter) of $\sim$ 1.6 mas at zero velocity, and $\sim$ 2.5 mas at higher velocities $\sim$ 100 km/s), , from $\sim$ 1.5 to $\sim$ 2.6 AU, depending on the distance."
" As the continuum emission measured with the ATs includes both stars, it is not direct to establish the typical size of the Herbig Be continuum."," As the continuum emission measured with the ATs includes both stars, it is not direct to establish the typical size of the Herbig Be continuum."
" In contrast, the UTs data include only one stellar component."," In contrast, the UTs data include only one stellar component."
" Although no absolute visibility values can be obtained, size ratios between the line and the continuum can be derived."," Although no absolute visibility values can be obtained, size ratios between the line and the continuum can be derived."
" Using the sizes previously estimated for the line from the ATs data, typical sizes of ~3.4 mas (~3.6 AU) for the Herbig Be K-band continuum can be determined, in agreement with the previous estimate (~3.9masin2004; ?).."," Using the sizes previously estimated for the line from the ATs data, typical sizes of $\sim$ 3.4 mas $\sim$ 3.6 AU) for the Herbig Be K-band continuum can be determined, in agreement with the previous estimate \citep[$\sim$3.9~mas
in 2004;][]{monnier05}. ."
" Considering a dust sublimation temperature around 1500-2000 K (?),, and the stellar properties determined by ?,, the inner edge of the dusty disk must be located at ~4-7 AU, in agreement with our findings."," Considering a dust sublimation temperature around 1500-2000 K \citep{pollack94}, and the stellar properties determined by \cite{vandenancker04}, the inner edge of the dusty disk must be located at $\sim$ 4-7 AU, in agreement with our findings."
 An asymmetry in the inclined inner disk could explain the non-zero closure phases measured at a level similar to other Herbig AeBe stars (??)..," An asymmetry in the inclined inner disk could explain the non-zero closure phases measured at a level similar to other Herbig AeBe stars \citep{kraus09, benisty10}."
" The differential phases A® can be expressed in terms of photocenter displacements p (in arcseconds), following ?, given by p= —2zAO/BA, where A and B are the wavelength and the projected baseline length of the observations, respectively."," The differential phases $\Delta\Phi$ can be expressed in terms of photocenter displacements $p$ (in arcseconds), following \citet{lachaume03}, given by $p=-2\pi\Delta\Phi/B\lambda$, where $\lambda$ and $B$ are the wavelength and the projected baseline length of the observations, respectively."
" p is the projection along the baseline direction, of the 2D photocenter vector p in the plane of the sky(i.e.,, of a spectro-astrometric signal)."," $p$ is the projection along the baseline direction, of the 2D photocenter vector $\vec{p}$ in the plane of the sky, of a spectro-astrometric signal)."
" We fitted all the differential phases along the 6 available baselines with a single vector p, independently of each spectral channel."," We fitted all the differential phases along the 6 available baselines with a single vector $\vec{p}$, independently of each spectral channel."
 The results are presented in Fig. 3.., The results are presented in Fig. \ref{fig:disp}.
 The left panels show the differential phases and the best solution for p., The left panels show the differential phases and the best solution for $\vec{p}$.
 The middle plot gives p in a 2D map of the plane of the sky., The middle plot gives $\vec{p}$ in a 2D map of the plane of the sky.
" Clear asymmetric displacements, up to ~150 y-arcseconds, are observed, both at red-shifted and blue-shifted velocities."," Clear asymmetric displacements, up to $\sim$ 150 $\mu$ -arcseconds, are observed, both at red-shifted and blue-shifted velocities."
" In this case, p accounts for the emission of both the line and the continuum."," In this case, $\vec{p}$ accounts for the emission of both the line and the continuum."
" Substracting the continuum contribution to determine the photocenter displacements, pp,,, due to the line only, is difficult, as it has to be done in the complex visibility plane."," Substracting the continuum contribution to determine the photocenter displacements, $\vec{p}_{\rm{Br}_\gamma}$, due to the line only, is difficult, as it has to be done in the complex visibility plane."
" We provide such an attemptin the velocity range where the line is clearly detected ([-350;350] km/s, with line-to- ratio larger than 1.05)."," We provide such an attemptin the velocity range where the line is clearly detected ([-350;350] km/s, with line-to-continuum ratio larger than 1.05)."
" As can beseen in Fig. 3,,"," As can beseen in Fig. \ref{fig:disp}, ,"
"where N is the number of bandpasses (4). Lj, 1s the observed luminosity. Liege; 1s the model luminosity. and στι is the estimated photometric error.","where $N$ is the number of bandpasses (4), $L_{obs}$ is the observed luminosity, $L_{model}$ is the model luminosity, and $\sigma^2_{obs}$ is the estimated photometric error."
 In practice. the age and extinction of each cluster are determined by comparing the shape of the SED to that of the SB99 models. while the mass is the scale factor required to best match the absolute values of the measured fluxes.," In practice, the age and extinction of each cluster are determined by comparing the shape of the SED to that of the SB99 models, while the mass is the scale factor required to best match the absolute values of the measured fluxes."
 Finally. A=/og(M/109M).," Finally, $A = log(M/10^6\,\msun)$."
 As an illustration of the method. we display in Fig.," As an illustration of the method, we display in Fig."
 4. the SED best fits to four YSCs with different y values., \ref{sed4} the SED best fits to four YSCs with different $\chi^2$ values.
 The average (y7) over the whole ensemble of YSCs of the minimized y's is then used to diseriminate among the ditferent combinations of population variables., The average $\langle\chi^2\rangle$ over the whole ensemble of YSCs of the minimized $\chi^2$ 's is then used to discriminate among the different combinations of population variables.
 Such comparison ts also performed separately for inner and outer clusters., Such comparison is also performed separately for inner and outer clusters.
 Table 4 lists the mean and median όν for all the combinations of cluster variables., Table \ref{Tsum} lists the mean and median $\langle\chi^2\rangle$ for all the combinations of cluster variables.
" For the inner clusters we find that (y) has a minimum for Mig,=100.MW31.Fig,2O0. and Ky,,=0. while for outer clusters the minimum is obtained for Ανν=100.LMC2.Fy.= 0. and Kj,=0."," For the inner clusters we find that $\langle\chi^2\rangle$ has a minimum for $M_{max}=100, {\rm MW31}, F_{lkg}=0$, and $K_{dust}=0$, while for outer clusters the minimum is obtained for $M_{max}=100, {\rm LMC2}, F_{lkg}=0$ , and $K_{dust}=0$."
 The distribution of the y for such combinations is shown in Fig. 5.., The distribution of the $\chi^2$ for such combinations is shown in Fig. \ref{chiH}.
 We conclude that the possibility of large-scale variations of the IMF. of radiation leakage. and of dusty HII regions do not appear to be supported by these models that. however. favor a systematic variation in the dust model.," We conclude that the possibility of large-scale variations of the IMF, of radiation leakage, and of dusty HII regions do not appear to be supported by these models that, however, favor a systematic variation in the dust model."
 The best fitting extinction curve for the inner and outer disk in facet differs. varying from Milky Way-type for the inner disk to type for the outer disk.," The best fitting extinction curve for the inner and outer disk in fact differs, varying from Milky Way-type for the inner disk to LMC2-type for the outer disk."
 The best (7) is 14.8 for YSCs in the inner disk and 42.7 for those in the outer disk., The best $\langle\chi^2\rangle$ is 14.8 for YSCs in the inner disk and 42.7 for those in the outer disk.
 These values are rather large. despite the general goodness of the fit. because ofour conservative uncertainty estimate.," These values are rather large, despite the general goodness of the fit, because ofour conservative uncertainty estimate."
 Models with (y) values lower than. 17.1 and 50.2 for the inner and outer disk. respectively. are within the 2c probability level. if we normalize the y values to (y-)=14.8.," Models with $\langle\chi^2\rangle$ values lower than 17.1 and 50.2 for the inner and outer disk, respectively, are within the $\sigma$ probability level, if we normalize the $\chi^2$ values to $\langle\chi^2\rangle=14.8$."
 Thus. they cannot be ruled out.," Thus, they cannot be ruled out."
 This implies that some dust absorption inside the HII region is still a possibility. but a or higher fraction of leakage of radiation ts unlikely.," This implies that some dust absorption inside the HII region is still a possibility, but a or higher fraction of leakage of radiation is unlikely."
" For each YSC. we can then compare the estimates of Ay and Lj, from the available photometry (see eqs. ("," For each YSC, we can then compare the estimates of $A_V$ and $L_{bol}$ from the available photometry (see eqs. ("
1) and (8) to the values obtained with the y minimization method.,1) and (8)) to the values obtained with the $\chi^2$ minimization method.
 This is illustrated in Fig. 6.., This is illustrated in Fig. \ref{chi}.
 While the {ο values are in excellent agreement. the estimated Ays using eq. (," While the $L_{bol}$ values are in excellent agreement, the estimated $A_V$ s using eq. ("
8) are consistently higher than those inferred by the SED fits.,8) are consistently higher than those inferred by the SED fits.
 The relation between the two quantities has a slope of 0.54., The relation between the two quantities has a slope of 0.54.
 Since eq. (, Since eq. (
8) Is purely empirical and does not take into account the evolutionary state of the cluster and the dust model. we consider the fitted value as more reliable.,"8) is purely empirical and does not take into account the evolutionary state of the cluster and the dust model, we consider the fitted value as more reliable."
 The age. mass and extinction distribution of the inner and outer YSCs as derived from the best-fit SED models are shown in Figure 7.. Figure 8 and respectively.," The age, mass and extinction distribution of the inner and outer YSCs as derived from the best-fit SED models are shown in Figure \ref{Hage}, Figure \ref{Hmass} and respectively."
 Among all the models employed in the fitting. we find that the lowest average y corresponds to a solution with the IMF populated up to 100M... with negligible leakage of radiation and dust absorption inside the Strómmgren sphere.," Among all the models employed in the fitting, we find that the lowest average $\chi^2$ corresponds to a solution with the IMF populated up to $100\,\msun$, with negligible leakage of radiation and dust absorption inside the Strömmgren sphere."
 From the (y7) values given in Table 4 we can see that an IMF with a maximum mass lower than 100M.« has a lower probability but it cannot be ruled out.," From the $\langle\chi^2\rangle$ values given in Table \ref{Tsum} we can see that an IMF with a maximum mass lower than $100\,\msun$ has a lower probability but it cannot be ruled out."
 Models with an IMF fully populated only up to 40M.« have been used also to fit the SED of clusters with Loot<2x107 ss7! only. or the sample of clusters beyond 7 kpe (the nominal edge of the star-forming disk).," Models with an IMF fully populated only up to $40\,\msun$ have been used also to fit the SED of clusters with $L_{bol}<2\times 10^{39}$ $^{-1}$ only, or the sample of clusters beyond 7 kpc (the nominal edge of the star-forming disk)."
 However. this choice did not provide an improvement in the average (y7).," However, this choice did not provide an improvement in the average $\langle\chi^2\rangle$."
 Therefore. we consider models with the upper mass cutoff at 100M. as the best representation of the stellar population of YSCs throughout the M33 disk.," Therefore, we consider models with the upper mass cutoff at $100\,\msun$ as the best representation of the stellar population of YSCs throughout the M33 disk."
 There is a clear difference between the mass distribution of clusters which form in the inner disk with respect to those forming at large radi: beyond kkpe clusters more massive than 10Ma are very rare.," There is a clear difference between the mass distribution of clusters which form in the inner disk with respect to those forming at large radii: beyond kpc clusters more massive than $10^4\,\msun$ are very rare."
 Similarly. beyond the Hw edge at 7 kpe. most YSCs have masses smaller than 1000M...," Similarly, beyond the $\alpha$ edge at 7 kpc, most YSCs have masses smaller than $1000\,\msun$."
 If clusters form with total mass below 10M... the number of stars is not high enough for the IMF to be fully populated up to 100Μ...," If clusters form with total mass below $10^4\,\msun$, the number of stars is not high enough for the IMF to be fully populated up to $100\,\msun$."
 It is well known that the most massive stars 1n à cluster tend to have a mass that increases with the cluster mass (?).., It is well known that the most massive stars in a cluster tend to have a mass that increases with the cluster mass \citep{1982MNRAS.200..159L}.
 This correlation leads to the question of whether the upper limit to the stellar mass in a particular cluster depends on the cluster mass because of some physically limiting process. or itis simply the result of random sampling of the IAF.," This correlation leads to the question of whether the upper limit to the stellar mass in a particular cluster depends on the cluster mass because of some physically limiting process, or itis simply the result of random sampling of the IMF."
 In the first case. low-mass clusters cannot produce high-mass stars (??)..," In the first case, low-mass clusters cannot produce high-mass stars \citep{2004MNRAS.348..187W,2006MNRAS.365.1333W}."
 In the second case they could as long as there Is enough gas. and intermediate-mass clusters should occasionally be found with unusually massive stars — “outliers” in the IMF (??)..," In the second case they could as long as there is enough gas, and intermediate-mass clusters should occasionally be found with unusually massive stars – “outliers” in the IMF \citep{2006ApJ...648..572E,2006A&A...451..475C}."
 A consequence of this model. often referred to as stochastic or randomly sampled IMF model. is that the summed IMF from many small mass YSCs should be the same as the IMF of a massive YSC.," A consequence of this model, often referred to as stochastic or randomly sampled IMF model, is that the summed IMF from many small mass YSCs should be the same as the IMF of a massive YSC."
 Considering the case for M33. the higher (7) shown by the IMF model with a mass cutoff lower than 100M... even considering only the low-lumimosity cluster sample or clusters beyond a certain radius. does not favor models which relate the maximum stellar mass to the cluster mass.," Considering the case for M33, the higher $\langle\chi^2\rangle$ shown by the IMF model with a mass cutoff lower than $100\,\msun$, even considering only the low-luminosity cluster sample or clusters beyond a certain radius, does not favor models which relate the maximum stellar mass to the cluster mass."
 We recall that the results on the clusterbirthline of M33 support the stochastic model (2).. which also appears favoured by the analysis of the IMF in more distant galaxies (??)..," We recall that the results on the clusterbirthline of M33 support the stochastic model \citep{2009A&A...495..479C}, , which also appears favoured by the analysis of the IMF in more distant galaxies \citep{2010ApJ...719L.158C,2011arXiv1105.6101F}."
 Hence. in what follows we will compare our data to the predictions of the stochastic IMF.," Hence, in what follows we will compare our data to the predictions of the stochastic IMF."
 We simulate the cluster light and mass. distributions considering a stochastic IMF from 0.1 to 100M. with slope a=-2.3 for stellar masses greater than 0.1M. and a=—].3 for lower masses.," We simulate the cluster light and mass distributions considering a stochastic IMF from 0.1 to $100\,\msun$ with slope $\alpha=-2.3$ for stellar masses greater than $0.1\,\msun$ and $\alpha=-1.3$ for lower masses."
 We simulate 40.000 clusters that are distributed in number according to their mass between 20 and 10!M. as where K is a constant. and 9 is the spectral index of the Initial Cluster Mass Function. which we assume to be 6= --2.," We simulate 40,000 clusters that are distributed in number according to their mass between 20 and $10^4\,\msun$ as where $K$ is a constant, and $\delta$ is the spectral index of the Initial Cluster Mass Function, which we assume to be $\delta=-2$ ."
 This is m close agreement with the mass distribution of our IR selected YSCs (see also next Section) and with previous findings (e.g.?.andreferences therein)... even though the results of the simulations are not very sensitive to the value of ó.," This is in close agreement with the mass distribution of our IR selected YSCs (see also next Section) and with previous findings \citep[e.g.][and references therein]{2007ChJAA...7..155D}, , even though the results of the simulations are not very sensitive to the value of $\delta$ ."
 We populate each cluster with stars randomly selectedfrom, We populate each cluster with stars randomly selectedfrom
have a higher chance of being seen as photometrically variable in the QVS as those nol detected by 2M1ASS versus with GCL >93).,have a higher chance of being seen as photometrically variable in the QVS as those not detected by 2MASS versus with GCL $> 93$ ).
 For reference. the upper-right panel in relFIRSTQSO shows the cumulative distribution for all 933 quasars. repeated [rom relallperc..," For reference, the upper-right panel in \\ref{FIRSTQSO} shows the cumulative distribution for all 933 quasars, repeated from \\ref{allperc}."
 As with the 2500 luminosity density. we calculated the luminosity density at 2yan for every 24ASS match to our data.," As with the 2500 luminosity density, we calculated the luminosity density at $\micron$ for every 2MASS match to our data."
 We used an oplical-infrared composite quasar spectrum from (he SDSS quasars in the SWIRE ELAIS NI field (Latziminaoglouetal.2005) and the J-. H-. and s-band total response curves (Chitrietal. 2001)..," We used an optical-infrared composite quasar spectrum from the SDSS quasars in the SWIRE ELAIS N1 field \citep{Hatz05} and the J-, H-, and $_S$ -band total response curves \citep{Cutri01}. ."
 relprops reports the median. Ist equartile. and 3rd quartile 2/6 luminosity densitv. values for the full population of 205 2MAÀSS-detected quasars. for the variable sample. and for the non-variable sample.," \\ref{props} reports the median, 1st quartile, and 3rd quartile $\micron$ luminosity density values for the full population of 205 2MASS-detected quasars, for the variable sample, and for the non-variable sample."
" As with the 2500 rresult. the median luminosity is noticeably larger for (he non-variable population (han (hat for the variable population (9.51xLO""! versus 1.43x 105). again with overlapping Ist-to- quartile ranges."," As with the 2500 result, the median luminosity is noticeably larger for the non-variable population than that for the variable population $9.51 \times 10^{31}$ versus $1.43 \times 10^{31}$ ), again with overlapping 1st-to-3rd quartile ranges."
 The 2j/mi variable and non-variable samples” luminosity densities were also subjected to a IWS test. showing that the differences between the variable and populations were significant to99.," The $\micron$ variable and non-variable samples' luminosity densities were also subjected to a KS test, showing that the differences between the variable and non-variable populations were significant to."
9%.. As with 2500A.. the μι luminosity density is smaller for optically variable quasars compared to the non-variable quasars.," As with 2500, the $\micron$ luminosity density is smaller for optically variable quasars compared to the non-variable quasars."
 Again. in our likelihooc-selected sample of variable quasars. we see resulls consistent wilh the trend (hat more luminous quasars. even in (he near-LR. are less optically. variable.," Again, in our likelihood-selected sample of variable quasars, we see results consistent with the trend that more luminous quasars, even in the near-IR, are less optically variable."
" The lower-right panel in relFIRSTOSO shows the cumulative percentage of known quasars with GCL >GC'L,. split into RASS detections and non-detections."," The lower-right panel in \\ref{FIRSTQSO} shows the cumulative percentage of known quasars with GCL $> GCL_o$, split into RASS detections and non-detections."
 As was the case with the 2A\LASS cletections. there is a marked difference between (he (wo X-ray. populations.," As was the case with the 2MASS detections, there is a marked difference between the two X-ray populations."
 Quasars which were detected bv the RASS are much more likely to appear photometrically variable., Quasars which were detected by the RASS are much more likely to appear photometrically variable.
 This supports the sugeestion (hat combining optical variability and A-ray [lux measurements is an efficient quasar selection technique (e.g..Sarajedini.Gilliland.&Ixasm2003:Drandt.2004).," This supports the suggestion that combining optical variability and X-ray flux measurements is an efficient quasar selection technique \citep[e.g.,][]{Sarajedini03,Brandt04}."
.. A hard X-ray (0.5— 2.0&6V) flux is caleulated [rom the published RASS counts per second using the PIAIMS v3.5 software application (Mula1993) with T=2.0. a=-I. and the weighted average neutral hydrogen column density. ealeulated. [rom IIBASABRCUs nll application usingthe Dickey&Lockman(1990) III map.," A hard X-ray $0.5 - 2.0 keV$ ) flux is calculated from the published RASS counts per second using the PIMMS v3.5 software application \citep{Mukai93} with $\Gamma = 2.0$, $\alpha = -1$, and the weighted average neutral hydrogen column density calculated from HEASARC's nH application usingthe \citet{Dickey90} HI map."
 From the hard. X-ray thus. the rest-frame 2 keV flix density is determined. which was used to determine the 2 keV," From the hard X-ray flux, the rest-frame 2 keV flux density is determined, which was used to determine the 2 keV"
ffor the MOS CCDs.,for the MOS CCDs.
 Second. the diffuse N-ray emission detected with ffrom the “darkest” regions of the inner oof the Galaxy varies by around a mean value of 2«&10Pere larenün7 (Alimo et al..," Second, the diffuse X-ray emission detected with from the “darkest” regions of the inner of the Galaxy varies by around a mean value of $2\times 10^{-13}$ $^{-2}$ (Muno et al.,"
 in preparatiou)., in preparation).
 We therefore used the fluxes from the faintest sources detected as part of the pipeline processing between and ffrom the aiurpolrut of cach observation as estimates of the upper limit on the count rate from2853., We therefore used the fluxes from the faintest sources detected as part of the pipeline processing between and from the aim-point of each observation as estimates of the upper limit on the count rate from.
". These count rates were 0.009 count + (MOS, 212 keV) for 2001 March 31. 0.003 count + (MOS. 212 keV) for 2001 April 01. aud 0.002 count + (pu. 212 keV) for 2001 September OL"," These count rates were 0.009 count $^{-1}$ (MOS, 2–12 keV) for 2001 March 31, 0.003 count $^{-1}$ (MOS, 2–12 keV) for 2001 April 01, and 0.002 count $^{-1}$ (pn, 2–12 keV) for 2001 September 04."
 We converted hese to euecrev fiuxes usine by asstunine a T=1.9 )ver law and Ny=10&1022 2. and listed them in Table 1..," We converted these to energy fluxes using by assuming a $\Gamma=1.9$ power law and $N_{\rm H} = 10\times10^{22}$ $^{-2}$, and listed them in Table \ref{tab:fluxhistory}."
 The resulting lits are simular to both the ddetectious in. quiescence and the variatious in the backerounud fiux on arcuiuute scales., The resulting limits are similar to both the detections in quiescence and the variations in the background flux on arcminute scales.
 We plot the lone-term history of the persistent DIuniuositv from in Fieure ο (deabsorbed. and assunüus a distance of S kpc).," We plot the long-term history of the persistent luminosity from in Figure \ref{fig:fluxhistory} (deabsorbed, and assuming a distance of 8 kpc)."
 It is clear that this source varies m hwunuinositv bv at least four orders of magnitude ou time scales of mouths., It is clear that this source varies in luminosity by at least four orders of magnitude on time scales of months.
 was fainter than 107 tim Fall 1999. and Fall and Spring 2001.," was fainter than $10^{33}$ in Fall 1999, and Fall and Spring 2001."
 The source has been observed. to reach undinosities above 1079 three times in the last 13 vears: in Spring 1990. Fall 1996. and Fall 2001.," The source has been observed to reach luminosities above $10^{36}$ three times in the last 13 years: in Spring 1990, Fall 1996, and Fall 2001."
 This sugeests that the bright states are ransicut outbursts driven by instabilities in the accretion disk (e.9..Lasota2001).," This suggests that the bright states are transient outbursts driven by instabilities in the accretion disk \citep[e.g.,][]{las01}."
. It is uulikelv that there were any outbursts brighter than 6«1079 lasting more than a mouth between 1996 aud the present. vecause they would have been detectable with the WWFC aud the AASML," It is unlikely that there were any outbursts brighter than $6 \times 10^{36}$ lasting more than a month between 1996 and the present, because they would have been detectable with the WFC and the ASM."
 Thus. aappears to be a genuine low-huninosity transient.," Thus, appears to be a genuine low-luminosity transient."
 Under the disk mstabilitv model. the füutuess of the outbursts can be explained if the amass transfer rate from the colupanion is low. either because it is due to a weak wind. or because the companion is a very low-inass star that fills its Roche-lobe (Ning2000).," Under the disk instability model, the faintness of the outbursts can be explained if the mass transfer rate from the companion is low, either because it is due to a weak wind, or because the companion is a very low-mass star that fills its Roche-lobe \citep{king00}."
. wwas also detected several times at huninosities below 10? ({Fieure 5))., was also detected several times at luminosities below $10^{35}$ (Figure \ref{fig:fluxhistory}) ).
 It was observed with aat a ποπ of 1075 FFall 1991., It was observed with at a luminosity of $10^{34}$ Fall 1994.
 Several other sources have been observed with varving fux at this level including the neutron star LAINBs SAN 2853. (AVijnandsctal.2002).. SAN 3568 AVijnandsetal.2001). 1RNS 102931 Usapteimetal.2000). and SAN 1037 (Cornelisseetal.2002a).," Several other sources have been observed with varying flux at this level, including the neutron star LMXBs SAX $-$ 2853 \citep{wij02b}, SAX $-$ 3568 \citep{wij01}, 1RXS $-$ 402934 \citep{kap00}, and SAX $-$ 1037 \citep{cor02a}."
. Such low-huninosity activity is not addressed by the simplest disk instability models. which generally produce 1001075 outbursts because a large fraction of the accretion disk is expected to be disrupted (e... Dubus. Ibuueury. Lasota 2001).," Such low-luminosity activity is not addressed by the simplest disk instability models, which generally produce $10^{37} - 10^{38}$ outbursts because a large fraction of the accretion disk is expected to be disrupted (e.g., Dubus, Hameury, Lasota 2001)."
 Furthermore. oobservations demonstrate that yyaries in N-ray intensity when its luuinosity is only about 1072 lCTable 3 aud Figure 5)).," Furthermore, observations demonstrate that varies in X-ray intensity when its luminosity is only about $10^{32}$ (Table \ref{tab:counts}
 and Figure \ref{fig:fluxhistory}) )."
 The fact that ls significantly brighter after the Fall 2000. outburst could be attributed to the fiux from the hot (AT~0.3 τον} surface of the neutron star. which may have heen jeated during the outburst (Brownetal.1998).," The fact that is significantly brighter after the Fall 2000 outburst could be attributed to the flux from the hot $kT \sim 0.3$ keV) surface of the neutron star, which may have been heated during the outburst \citep{bbr98}."
. However. he hieh absorption coluun toward the source should uake most of this thermal ciission unobservable (see Figure 2)).," However, the high absorption column toward the source should make most of this thermal emission unobservable (see Figure \ref{fig:spec}) )."
 Ou the other hand. short time-scale variations iive been observed in the fiux from the LAINBs Cou X-1 (Campanaetal.1997:Rutledee2001) auc Aql X-1 (Rutledgeetal.2002) that are inconsistent with a cooling jeutron star.," On the other hand, short time-scale variations have been observed in the flux from the LMXBs Cen X-4 \citep{cam97,rut01} and Aql X-1 \citep{rut02}
 that are inconsistent with a cooling neutron star."
 This cussion has been explained as residual accretion either onto the neutron star surface or onto the uaenetospheric boundary (Campanactal.1998)., This emission has been explained as residual accretion either onto the neutron star surface or onto the magnetospheric boundary \citep{cam98}.
 The cCluission frou wwith huuiuosities between 1077 and 10°! yprobably also represents continued accretion., The emission from with luminosities between $10^{32}$ and $10^{34}$ probably also represents continued accretion.
 These low Tninosities are an important. and relatively unexplored. regine of accretion that challeuge current disk instability nocels for LAINBs.," These low luminosities are an important, and relatively unexplored, regime of accretion that challenge current disk instability models for LMXBs."
 N-rav bursts were observed from wwith the WWEC during the brieht state iu Fall 1996 1999:Sakauoetal. 2002).. aud with dauiug the outburst in Fall 2000 (this work).The WEC observed the Galactic Ceuter for approximately 900 ks each spring and fall from mud-1996 through the cud of 2001. aud detected no further bursts.," X-ray bursts were observed from with the WFC during the bright state in Fall 1996 \citep{coc99,sak02}, and with during the outburst in Fall 2000 (this work).The WFC observed the Galactic Center for approximately 500 ks each spring and fall from mid-1996 through the end of 2001, and detected no further bursts."
 This sugeests that the bursts only occur frequently when the persistent. X- cluission reaches ~1079 Ἐν so that accretion provides 1019 oof fuel to the surface of the neutron star.," This suggests that the bursts only occur frequently when the persistent X-ray emission reaches $\sim 10^{36}$ , so that accretion provides $10^{-10}$ of fuel to the surface of the neutron star."
 It is Likely that some other low-luuinosity bursters are simular. aud," It is likely that some other low-luminosity bursters are similar, and"
approximation (see.e.g..Cutlerοἱal.1993:Finn&Chernoll1993).. the rnedown spectrum for a DDBII with component masses m and m» is given by llere M. is the chirp mass. AMO=mams(nmq+Ms)1/3 Ley SV! and ws=nly1a are constants chosen (o make dE/dy continuous across r4 and ve.,"approximation \citep[see, e.g.,][]{Cutler93,Finn93}, the inspiral-merger-ringdown spectrum for a BBH with component masses $m_1$ and $m_2$ is given by Here $M_c$ is the chirp mass, $M_c^{5/3}=m_1 m_2 (m_1+m_2)^{-1/3}$ , $\omega_1=\nu_{1}^{-1}$ and $\omega_2=\nu_{1}^{-1} \nu_{2}^{-4/3}$ are constants chosen to make $dE/d\nu$ continuous across $\nu_{1}$ and $\nu_{2}$."
 The set of parameters GA.15. 0.14) can be determined by the (wo plivsical parameters (the total mass M. and the sviunelric mass ratio 7) in terms of (ay?+byc)/z M. with coellicients a.b.c given in Table 1 of Ajithetal.(2003).. producing (404. 807. 237. Πω for a 1037.—10A7.. BBII (M.=8.7Mf. ).," The set of parameters $\nu_{1}, \nu_{2}, \sigma,
\nu_{3}$ ) can be determined by the two physical parameters (the total mass $M$ and the symmetric mass ratio $\eta$ ) in terms of $(a
\eta^2 + b \eta + c)/\pi M$ , with coefficients $a, b, c$ given in Table 1 of \citet{IMR}, producing (404, 807, 237, Hz for a $10 M_{\odot}\hspace{-1mm}-\hspace{-1mm}10 M_{\odot}$ BBH $M_c=8.7
M_{\odot}$ )."
" The waveform presented in Ajithetal.(2009).. includes spin effects through a single spin parameter y=(14+0)\,/2+(10)V3/2. with à=(mig—ma)/M and \;=$;/m?."," The waveform presented in \citet{spin_IMR}, includes spin effects through a single spin parameter $\chi = (1+\delta) \chi_{1}/2 +
(1-\delta) \chi_{2}/2$, with $\delta=(m_1-m_2)/M$ and $\chi_{i}=S_{i}/m_{i}^2$ ."
 The parameter 5; represents the spin angular momentum of the /th black hole., The parameter $S_{i}$ represents the spin angular momentum of the $i$ th black hole.
 The corresponding Fourier amplitude includes a minor correction (related to X and 5) for non-spinning BBIIs., The corresponding Fourier amplitude includes a minor correction (related to $\chi$ and $\eta$ ) for non-spinning BBHs.
 We construct energy spectra for BBIIs with non-precessing spins based on their Figure 2 shows ihe GW energy spectra for a 107.—10.M.. DDII assuming: the case; \=0.85; 4=0 and 4=—0.85.," We construct energy spectra for BBHs with non-precessing spins based on their Figure 2 shows the GW energy spectra for a $10
M_{\odot}\hspace{-1mm}-\hspace{-1mm}10 M_{\odot}$ BBH assuming: the non-spinning case; $\chi=0.85$; $\chi=0$ and $\chi=-0.85$."
 The two extreme values for \ are set. by ihe numerical simulations of Ajithetal.(2009).. corresponding to both binary. components having maximal spins aligned or anü-aliened with the orbital angular momentum.," The two extreme values for $\chi$ are set by the numerical simulations of \citet{spin_IMR}, corresponding to both binary components having maximal spins aligned or anti-aligned with the orbital angular momentum."
 The radiation elliciencies for these energy spectra are 6.7%. 9.74%. 5.1576 and 4.28% respectivelv.," The radiation efficiencies for these energy spectra are $6.7\%$, $9.74\%$, $5.15\%$ and $4.28\%$ respectively."
 We note that the radiated GW energy mainly depends on A. and \. and (hat the energy spectra for pS 100 Hz show little variation.," We note that the radiated GW energy mainly depends on $M_c$ and $\chi$, and that the energy spectra for $\nu \lesssim $ 100 Hz show little variation."
 We note that effect of orbital eccentricity is not considered im ourderivation of energv spectrum., We note that effect of orbital eccentricity is not considered in ourderivation of energy spectrum.
 This has little effecton our results as the orbits of coalescingcompact objects are expected to circularise (Peters1964) before (heir GW signals reach the sensitive frequency. banc of eround-based interferometric detectors (Brown&Zimmerman 2010).., This has little effecton our results as the orbits of coalescingcompact objects are expected to circularise \citep{circle} before their GW signals reach the sensitive frequency band of ground-based interferometric detectors \citep{eccen}. .
"where the current radiation component 2,0=4.17367h? («Komatsuetal.2011...",where the current radiation component $\Omega_{r}=4.1736\times 10^{-5}h^{-2}$ \citep{wmap7}.
 Fitting the model to. the combined SN Ia. Bao2. Baoz. WMAP7 and //(2) data. we get the marginalized Lo constraints. yq;=0.07+0.11 and q@=1.43£0.09 with 47.= 542.6.," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $q_1=0.07\pm 0.11$ and $q_2=-1.43\pm 0.09$ with $\chi^2=542.6$ ."
 In terms of -ας=0). we find that qu<0.62 at 30 confidence level. so the evidence of current acceleration is very strong.," In terms of $q_0=q(z=0)$, we find that $q_0<-0.62$ at $3\sigma$ confidence level, so the evidence of current acceleration is very strong."
" Furthermore. we find that the 3c. constraint. on Q,, +is Q,,=0.257..—dkως."," Furthermore, we find that the $3\sigma$ constraint on $\Omega_m$ is $\Omega_m=0.257_{-0.035}^{+0.044}$."
" The contour plot 7for £O, and qu is shown in Fig. ", The contour plot for $\Omega_m$ and $q_0$ is shown in Fig. \ref{u2cont}( (
H4.,d).
" At a low redshift. the radiation is negligible. so Omitz) in this model is By using the best-fitting values of q, andqo. we reconstruct ΟΙ} and the results are plotted in Fig. 24"," At a low redshift, the radiation is negligible, so $Om(z)$ in this model is By using the best-fitting values of $q_1$ and$q_2$, we reconstruct $Om(z)$ and the results are plotted in Fig. \ref{u2omz}( ("
d).,d).
 To further study the evolution of the deceleration parameter q(z). we use the more model-independent piecewise parametrizations.," To further study the evolution of the deceleration parameter $q(z)$, we use the more model-independent piecewise parametrizations."
 We group the data into four bins so that the number of SN Ia in each bin times the width of each bin is around 30. Le. WAZ~30 and No= 4.," We group the data into four bins so that the number of SN Ia in each bin times the width of each bin is around 30, i.e., $N\Delta z\sim 30$ and $N=4$ ."
 The four bins are οι=0.1. το=O40 23=OF. 2QLS and zs extends beyond 1089.," The four bins are $z_1=0.1$, $z_2=0.4$, $z_3=0.7$, $z_4=1.8$ and $z_5$ extends beyond 1089."
 For the redshift in the range 2;qQXo« ihedeceleration parameter q(2) is a constant q;. ασ)=qi.," For the redshift in the range $z_{i-1}\le z<z_i$, thedeceleration parameter $q(z)$ is a constant $q_i$, $q(z)=q_i$."
" Take zu0. then for z;4,x2«z;. we get In this model. we have four parameters p=(qi.qo.qs.qi)."," Take $z_0=0$, then for $z_{i-1}\le z<z_i$, we get In this model, we have four parameters $\mathbf{p}=(q_1,\ q_2,\ q_3,\ q_4)$."
 In general. for the piecewise parametrisation. the parameters such as q; in different bins are correlated and their errors depend upon each other.," In general, for the piecewise parametrisation, the parameters such as $q_i$ in different bins are correlated and their errors depend upon each other."
 We follow Huterer&Cooray(005). to transform the covariance matrix of q;s to decorrelate the errorestimate., We follow \cite{huterer05} to transform the covariance matrix of $q_i$ s to decorrelate the errorestimate.
" Explieitly. the transformation is where the transformationmatrix Z—VEL97V, the orthogonal matrix V. diagonalizes the covariance matrix. C' of q; and Lis the diagonalized matrix of C."," Explicitly, the transformation is where the transformationmatrix $T=V^T\Gamma^{-1/2}V$, the orthogonal matrix $V$ diagonalizes the covariance matrix $C$ of $q_i$ and $\Gamma$ is the diagonalized matrix of $C$."
 For a given 7. 7;; can be thought of as weights for each g; in the transformation from q; to Q;.," For a given $i$, $T_{ij}$ can be thought of as weights for each $q_j$ in the transformation from $q_i$ to ${\mathcal Q}_i$."
 We are free to rescale each Q; without changing the diagonality of the correlation matrix. so we then multiply both sides of the equation above by an amount such that the sum of the weights M1;;is equal to I.," We are free to rescale each ${\mathcal Q}_i$ without changing the diagonality of the correlation matrix, so we then multiply both sides of the equation above by an amount such that the sum of the weights $\sum_j T_{ij}$is equal to 1."
 This allows for easy interpretation of the weights as a Kind of discretized window function., This allows for easy interpretation of the weights as a kind of discretized window function.
" Now the transformation matrix element is 75;»»1i, and the covariance matrix of the uncorrelated parameters is not the identity matrix.", Now the transformation matrix element is $T_{ij}/\sum_k T_{ik}$ and the covariance matrix of the uncorrelated parameters is not the identity matrix.
 The i-th diagonal matrix element becomes Sr1ij)?, The $i$ -th diagonal matrix element becomes $(\sum_j T_{ij})^{-2}$.
 In other words. the error of the uncorrelated parameters Q; is a;1Mlij.," In other words, the error of the uncorrelated parameters ${\mathcal Q}_i$ is $\sigma_i=1/\sum_j T_{ij}$."
 Fitting the model to the combined SN Iu. Bao2. Baoz. WMAP7 and fi(2) data.we get the constraints on the uncorrelated parameters Q; and the result is shown in Fig. 3..," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data,we get the constraints on the uncorrelated parameters $\mathcal{Q}_i$ and the result is shown in Fig. \ref{qzunc}."
 For the cosmological constant. the equation of state parameter the energy density p is a constant.," For the cosmological constant, the equation of state parameter $w=p/\rho=-1$ , and the energy density $\rho_\Lambda$ is a constant."
 For a curved CDM model. the curvature term ©;=0. Friedmann equation is At low redshits. the contribution ofthe radiation term is negligible.," For a curved $\Lambda$ CDM model, the curvature term $\Omega_k\neq 0$, Friedmann equation is At low redshits, the contribution ofthe radiation term is negligible."
" We have two parameters p.=(Q,,,.O,) and one nuisance parameter / in this model."," We have two parameters $\mathbf{p}=(\Omega_m,\ \Omega_k)$ and one nuisance parameter $h$ in this model."
" By fitting the \CDM model to the combined SN Ia. Bao2. Baoz. WMAP7 and //(2) data. we get the marginalized 10 constraints. (,,=0.272(ri and QO,=0.002+0.004 with V?=541.2."," By fitting the $\Lambda$ CDM model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.272^{+0.013}_{-0.011}$ and $\Omega_k=0.002\pm 0.004$ with $\chi^2=541.2$."
" The contours of ©,,, and £3, are plotted in Fig. 4t", The contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( (
).,a).
" By fitting the model to observational data combined with the growth factor data. the marginalized Lo constraints are. Q,,=0.272(ob. O,=0.002+0.004 and ο=0.56c with V=546.3."," By fitting the model to observational data combined with the growth factor data, the marginalized $1\sigma$ constraints are, $\Omega_m=0.272^{+0.013}_{-0.01}$ , $\Omega_k=0.002\pm 0.004$ and $\gamma=0.56^{+0.14}_{-0.09}$ with $\chi^2=546.3$ ."
 In this model. gravity appears four dimensional at short distances while modified at large distances (Dvali.Gabadadze&Porrati2000).," In this model, gravity appears four dimensional at short distances while modified at large distances \citep{dgp}."
.. The model is motivated by brane cosmology in which our Universeisa three-brane embedded in a five dimensional spacetime., The model is motivated by brane cosmology in which our Universeisa three-brane embedded in a five dimensional spacetime.
" The Friedmann equation is modified as where OQ,—(1.©,|O,)/2V1.Ot.", The Friedmann equation is modified as where $\Omega_{d}=(1-\Omega_{m}-\Omega_{k})/2\sqrt{1-\Omega_{k}}$.
" If we take the point of view that Friedmann equation is not moditied and the extra term in equation (243) is dark energy. thenthe equivalent dark energy equation of state parameter (2) for the DGP model is when 2Xl. w(z2)—1/2 and els=0)(1O,L)/(1l|€, £,.9."," If we take the point of view that Friedmann equation is not modified and the extra term in equation \ref{dgpez}) ) is dark energy, thenthe equivalent dark energy equation of state parameter $w(z)$ for the DGP model is when $z\gg 1$, $w(z)\sim -1/2$ and $w(z=0)=-(1-\Omega_{k})/(1+\Omega_{m}-\Omega_{k})$ ."
" Since O, is very small. «(2)=——1 for the DGP model."," Since $\Omega_{k}$ is very small, $w(z)>-1$ for the DGP model."
" By fitting the DGP model to thecombined SN Ta. Bao2. Baoz. WMAP7 and //(2) data. the marginalizedLo constraints are Q,,,= and QO),=0.01940.005 with V?= 561.6."," By fitting the DGP model to thecombined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, the marginalized$1\sigma$ constraints are $\Omega_m=0.288^{+0.015}_{-0.011}$ and $\Omega_k=0.019\pm 0.005$ with $\chi^2=561.6$ ."
" By fitting the DGP model to the combined SN Ia. Bao2.Baoz. WMAP7. H(z) and f(z) data. we get the marginalized le estimations Q,,=0.290 ο. ος=0.019+ 0.005. and =0.46ως with 47= 567.5."," By fitting the DGP model to the combined SN Ia, Bao2,Baoz, WMAP7, $H(z)$ , and $f(z)$ data, we get the marginalized $1\sigma$ estimations $\Omega_m=0.290^{+0.014}_{-0.012}$ , $\Omega_k=0.019\pm 0.005$ , and $\gamma=0.46^{+0.12}_{-0.08}$ with $\chi^2=567.5$ ."
" For the Chevallier-Polarski-Linder (CPL) parametrization (Chevallier&Polarski2001:Linder 2003).. the equation of state parameter 1s sols—0)=ey and είς)wy|0, when zc 1."," For the Chevallier-Polarski-Linder (CPL) parametrization \citep{cpl1,cpl2}, the equation of state parameter is so$w(z=0)=w_0$ and $w(z)\sim w_0+w_a$ when $z\gg 1$ ."
" The corresponding dimensionlessdarkenergy density is where @,=]©,,ο, £2,.", The corresponding dimensionlessdarkenergy density is where $\Omega_x=1-\Omega_{m}-\Omega_r-\Omega_{k}$ .
" In this model. we have four model parameters p=(Q,,,.€.wo. uw)."," In this model, we have four model parameters $\mathbf{p}=(\Omega_{m},\ \Omega_{k}, \ w_0, \ w_a)$ ."
" Fitting the model to the combined SN Iu. Bao2. Baoz. WMAP7 and //(2) data. we get the marginalized""M Lo constraints.: O,,=0.265ορπ0010 ομως 5p. ο""ELAGeOUQS6 ορ. 0,and esEN=0.60.supULLπι with"," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.265^{+0.019}_{-0.009}$ , $\Omega_k=0.008^{+0.005}_{-0.011}$ , $w_0=-1.16^{+0.26}_{-0.06}$ , and $w_a=0.69^{+0.24}_{-1.41}$ with"
" Fitting the model to the combined SN Iu. Bao2. Baoz. WMAP7 and //(2) data. we get the marginalized""M Lo constraints.: O,,=0.265ορπ0010 ομως 5p. ο""ELAGeOUQS6 ορ. 0,and esEN=0.60.supULLπι witha"," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.265^{+0.019}_{-0.009}$ , $\Omega_k=0.008^{+0.005}_{-0.011}$ , $w_0=-1.16^{+0.26}_{-0.06}$ , and $w_a=0.69^{+0.24}_{-1.41}$ with"
" Fitting the model to the combined SN Iu. Bao2. Baoz. WMAP7 and //(2) data. we get the marginalized""M Lo constraints.: O,,=0.265ορπ0010 ομως 5p. ο""ELAGeOUQS6 ορ. 0,and esEN=0.60.supULLπι withaa"," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.265^{+0.019}_{-0.009}$ , $\Omega_k=0.008^{+0.005}_{-0.011}$ , $w_0=-1.16^{+0.26}_{-0.06}$ , and $w_a=0.69^{+0.24}_{-1.41}$ with"
Note that hot Jupiters can also be produced by the dynamical relaxation of a population of planets on inclined orbits. ormed through gravitational instabilities of a cireumstellar envelope or a thick dise (Papaloizou Terquem 2001).,"Note that hot Jupiters can also be produced by the dynamical relaxation of a population of planets on inclined orbits, formed through gravitational instabilities of a circumstellar envelope or a thick disc (Papaloizou Terquem 2001)."
 However. if objects as heavy as 7 Boo may be produced. fragmentation. it is unlikely that lower mass objects would form that way.," However, if objects as heavy as $\tau$ –Boo may be produced fragmentation, it is unlikely that lower mass objects would form that way."
 A planet embedded in a gaseous disc launches density waves at the Lindblad resonances (CGolceich Tremaine 1979. jereafter. το).," A planet embedded in a gaseous disc launches density waves at the Lindblad resonances (Goldreich Tremaine 1979, hereafter GT79)."
 Phe torque exerted by the planet on these waves is responsible for the exchange of angular momentun »etween the dise rotation and the planets orbital motion., The torque exerted by the planet on these waves is responsible for the exchange of angular momentum between the disc rotation and the planet's orbital motion.
 The interaction between the planet ancl the dise inside/outside its orbit leads to a negativespositive torque on the disc. and therefore to a gain/loss of angular momentum for the planet.," The interaction between the planet and the disc inside/outside its orbit leads to a negative/positive torque on the disc, and therefore to a gain/loss of angular momentum for the planet."
 In the inear regime. because in a (even uniform) Ixeplerian disc the outer Lindblad resonances are slightly closer to the planet than he inner Lindblad. resonances. the interaction with the outer parts of the dise leads to a larger Lindblad torque than that with the inner parts (Ward. 1986. 1997).," In the linear regime, because in a (even uniform) Keplerian disc the outer Lindblad resonances are slightly closer to the planet than the inner Lindblad resonances, the interaction with the outer parts of the disc leads to a larger Lindblad torque than that with the inner parts (Ward 1986, 1997)."
 Therefore. the net Lindblad torque exerted by the planet causes it to lose angular momentum and to move inward relative to the gas (tvpe E migration).," Therefore, the net Lindblad torque exerted by the planet causes it to lose angular momentum and to move inward relative to the gas (type I migration)."
 Note that there is also à torque exerted by the planet on the material which corotates with the perturbation., Note that there is also a torque exerted by the planet on the material which corotates with the perturbation.
 Is sign depends on the gradient of vortensity at corotation (το)., Its sign depends on the gradient of vortensity at corotation (GT79).
 However. it is usually found to be Less significant than the net Lindblad: torque.," However, it is usually found to be less significant than the net Lindblad torque."
" Ehe drift timescale for à 110 Mj. planet undergoing type L migration in a standard gaseous disce is tvpically between 103 and. LO"" vears. shorter than the disc lifetime or estimated. planetary formation timescales."," The drift timescale for a 1–10 $_\oplus$ planet undergoing type I migration in a standard gaseous disc is typically between $10^4$ and $10^6$ years, shorter than the disc lifetime or estimated planetary formation timescales."
 When the mass of the planet becomes large enough. the perturbation becomes nonlinear.," When the mass of the planet becomes large enough, the perturbation becomes nonlinear."
 Feedback torques from the disc on the planet. which have to be taken into account in this regime. then opposes the motion of the planet and stops it altogether when the planet is massive enough (Ward 1997).," Feedback torques from the disc on the planet, which have to be taken into account in this regime, then opposes the motion of the planet and stops it altogether when the planet is massive enough (Ward 1997)."
 However. density waves still transport angular momentum outward.," However, density waves still transport angular momentum outward."
 If they ave dissipated locally. the angular momentum they transport is deposited in the disc in the vicinity of the planet and a gap may be cleared: out. (Goldreich Tremaine 1980: Lin Papaloizou 1979. 1993 and references therein).," If they are dissipated locally, the angular momentum they transport is deposited in the disc in the vicinity of the planet and a gap may be cleared out (Goldreich Tremaine 1980; Lin Papaloizou 1979, 1993 and references therein)."
 “Phe planet is then ocked into the angular momentum transport process of the disce. and migrates inward at a rate controlled bv the disc viscous imescale (tvpe LL migration).," The planet is then locked into the angular momentum transport process of the disc, and migrates inward at a rate controlled by the disc viscous timescale (type II migration)."
 Here again. the drift timescale is rather short. being in the range LO? LO” vears for standard »aranmeters.," Here again, the drift timescale is rather short, being in the range $10^3$ $10^5$ years for standard parameters."
 Type HL migration.> which occurs for planets with masses at least comparable to that of Jupiter. can be avoided if after he planet forms there is not enough mass left in the disc to absorb its angular momentum.," Type II migration, which occurs for planets with masses at least comparable to that of Jupiter, can be avoided if after the planet forms there is not enough mass left in the disc to absorb its angular momentum."
 Llowever. type E migration appears inevitable as there has to be enough gas in the dise to push a forming core inward if this core is to acerete a massive envelope o become a giant planet at some point.," However, type I migration appears inevitable as there has to be enough gas in the disc to push a forming core inward if this core is to accrete a massive envelope to become a giant planet at some point."
 Dillerent scenarii for stopping a planet. undergoing inward migration have been considered. (see. ee. Ferquem. Papaloizou «eIson. 2000 and references therein). but none of them can satisfactorily explain the presence of extrasolar planets with semimajor axes from a few 0.01 au all the way up to several au.," Different scenarii for stopping a planet undergoing inward migration have been considered (see, e.g., Terquem, Papaloizou Nelson 2000 and references therein), but none of them can satisfactorily explain the presence of extrasolar planets with semi–major axes from a few 0.01 au all the way up to several au."
 tecently. Papaloizou (2002) has shown that tvpe E migration reverses for reasonable disc models once the eccentricity of the orbit becomes comparable to the disc aspect ratio.," Recently, Papaloizou (2002) has shown that type I migration reverses for reasonable disc models once the eccentricity of the orbit becomes comparable to the disc aspect ratio."
 Εις is because in that case the planet spends more time near apocentre. where it is being speeded up. than near pericentre. where it is being slowed down.," This is because in that case the planet spends more time near apocentre, where it is being speeded up, than near pericentre, where it is being slowed down."
 Although the interaction with the disc tends to cireularize the orbit of the planet (Goldreich Tremaine 1980). significant eccentricity may be maintained by gravitational interactions between different planets forming simultaneously. (Papaloizou Larwood 2000).," Although the interaction with the disc tends to circularize the orbit of the planet (Goldreich Tremaine 1980), significant eccentricity may be maintained by gravitational interactions between different planets forming simultaneously (Papaloizou Larwood 2000)."
 Llere we investigate the cllect of a magnetic field on planet. migration in the linear regime., Here we investigate the effect of a magnetic field on planet migration in the linear regime.
 We consider a planet on a circular orbit and. to keep the problem tractable. restrict ourselves to the case of a purely toroidal field.," We consider a planet on a circular orbit and, to keep the problem tractable, restrict ourselves to the case of a purely toroidal field."
 Vhis tends to be the dominant component in dises as it is produced by the shearing of radial field lines., This tends to be the dominant component in discs as it is produced by the shearing of radial field lines.
 As described above. the torque exerted by a planet on a disc depends mainly on the location of the radii where the perturbation is in resonance with the free oscillations of the disc.," As described above, the torque exerted by a planet on a disc depends mainly on the location of the radii where the perturbation is in resonance with the free oscillations of the disc."
 We therefore expect a magnetic field to modify the tidal torque. as it introduces more degrees of freedom in the disc.," We therefore expect a magnetic field to modify the tidal torque, as it introduces more degrees of freedom in the disc."
 The plan of the paper is as follows., The plan of the paper is as follows.
 In sections 2.. 3. and 4. we give the basic equations. describe the equilibrium disc model and give the expression of the perturbing potential acting on the disc.," In sections \ref{sec:basic}, \ref{sec:equilibrium} and \ref{sec:potential} we give the basic equations, describe the equilibrium disc model and give the expression of the perturbing potential acting on the disc."
 In section 5 we study the dise response to this perturbing potential., In section \ref{sec:response} we study the disc response to this perturbing potential.
 We first linearize the equations and derive the second order dilferential equation describing the disc response 5.1))., We first linearize the equations and derive the second order differential equation describing the disc response \ref{sec:linearization}) ).
 We then carry on a WIXD analysis .5.2)). which shows that magnetosonic waves propagate outside the outermost turning points.," We then carry on a WKB analysis \ref{sec:wkb}) ), which shows that magnetosonic waves propagate outside the outermost turning points."
 In 5.8 westudy the disc response at the locations where it is singular., In \ref{sec:magneticres} we study the disc response at the locations where it is singular.
 We call these raciiresonances., We call these radii.
 There are two such resonances. located on cach side of the planet/s orbit and within the Lindblad. resonances.," There are two such resonances, located on each side of the planet's orbit and within the Lindblad resonances."
 Ing 54 we calculate all the turning points associated. with the disc response., In \ref{sec:turning} we calculate all the turning points associated with the disc response.
 On each side of the planet there are two or wee of them. epending on the value of the azimuthal number m.," On each side of the planet there are two or three of them, depending on the value of the azimuthal number $m$."
 One of these turning points colnneide with the Lindblad resonance., One of these turning points ncide with the Lindblad resonance.
 In contrast to the nonmagnetic case. waves are found to propagate in a restricted region inside the outermost urning points. around the magnetic resonances.," In contrast to the nonmagnetic case, waves are found to propagate in a restricted region inside the outermost turning points, around the magnetic resonances."
 We then proceed to give an expression for the tidal torque in general and in 16 vicinity ofthe magnetic resonances in particular in section 6.., We then proceed to give an expression for the tidal torque in general and in the vicinity of the magnetic resonances in particular in section \ref{sec:torque}.
 Numerical calculations of the torque exerted by the planet n the disc are presented in section 7.., Numerical calculations of the torque exerted by the planet on the disc are presented in section \ref{sec:numerics}.
 We show that the torque exerted in the vicinity of the magnetic resonances tends to ominate the disc response when the magnetic field is large enough., We show that the torque exerted in the vicinity of the magnetic resonances tends to dominate the disc response when the magnetic field is large enough.
 This torque. like the Lindblad torque. is negative inside 10 planet's orbit and positive outside the orbit.," This torque, like the Lindblad torque, is negative inside the planet's orbit and positive outside the orbit."
 Pherefore. Wt—er;fer increases fast enough with radius. the outer magnetic resonance becomes less important. (it disappears altogether when there is no magnetic field outside the planet's orbit) and 16 total torque becomes negative. dominated by the inner magnetic resonance.," Therefore, if $\beta \equiv
c^2/v_A^2$ increases fast enough with radius, the outer magnetic resonance becomes less important (it disappears altogether when there is no magnetic field outside the planet's orbit) and the total torque becomes negative, dominated by the inner magnetic resonance."
 Ες corresponds toa positive torque on the xanet. which leads to outward migration.," This corresponds toa positive torque on the planet, which leads to outward migration."
 Finally. we discuss our results in section S..," Finally, we discuss our results in section \ref{sec:discussion}. ."
lilopirsecs long.,kiloparsecs long.
 Therefore. the RAL structure frou diffuse radiation aud from extragalactic sources eives Information about differeut regions in the Calaxx.," Therefore, the $RM$ structure from diffuse radiation and from extragalactic sources gives information about different regions in the Galaxy."
 The depth depolarization model described iu Sect., The depth depolarization model described in Sect.
 5 ouly describes the properties of the ISAD in a statistical manner. by eiviug a represcutation of an average liue of seht.," \ref{s4:depol}
 only describes the properties of the ISM in a statistical manner, by giving a representation of an average line of sight."
 Therefore. it docs uot pretend to eive a detailed description of the distribution of P. as it is actually observed.," Therefore, it does not pretend to give a detailed description of the distribution of $P$, as it is actually observed."
 Even the global properties of the P distribution. ike the eeucral aligeuiueut with the Calactic plane. is not ut of the model.," Even the global properties of the $P$ distribution, like the general alignment with the Galactic plane, is not part of the model."
 This aligumenut is not only visible iu he Auriga field. but also in other regious observed with he WSRT (ILwerkorn et 220022. Schuitzeler et iiu xep).," This alignment is not only visible in the Auriga field, but also in other regions observed with the WSRT (Haverkorn et 2003a, Schnitzeler et in prep)."
 The large-scale structures in P cannot be caused o» substantial extra emission. because that should be accompanied by corresponding structure in Z. which is not observed.," The large-scale structures in $P$ cannot be caused by substantial extra emission, because that should be accompanied by corresponding structure in $I$, which is not observed."
 Instead. where the polarized intensity is highest. he depolarization is probably the least. so that there the ISAL is relatively transparent to polarized emüsson.," Instead, where the polarized intensity is highest, the depolarization is probably the least, so that there the ISM is relatively transparent to polarized emission."
 Iu eeneral. Ligh depolarization is caused by a large amount of structure iu RAL. along the line of sieht and/or over sky (the latter on the scale of the beam or smaller).," In general, high depolarization is caused by a large amount of structure in $RM$, along the line of sight and/or over the sky (the latter on the scale of the beam or smaller)."
" T explanation of the structure of high P is borne out by the relation between polarized intensity 2 aud0,44... shown iu Fig. 12.."," This explanation of the structure of high $P$ is borne out by the relation between polarized intensity $P$ and, shown in Fig. \ref{f4:srm_pi}."
 This figure shows the width oof a Gaussian fit to the RAL distribution du several intervals of poluized intensity with a width APLOI Jv/benu., This figure shows the width of a Gaussian fit to the $RM$ distribution in several intervals of polarized intensity with a width $\Delta P = 0.01$ Jy/beam.
 Rotation measure clearly varies more at lower polarized intensity. where only well-deterimined RAMsS are used so that the effect caunot be due to noise.," Rotation measure clearly varies more at lower polarized intensity, where only well-determined $RM$ s are used so that the effect cannot be due to noise."
 For he two intervals of highest P (0.08 0.09 Jv/bean aud 1.09 0.10 Jv/beam). not shown in Fie. 12..," For the two intervals of highest $P$ (0.08 – 0.09 Jy/beam and 0.09 – 0.10 Jy/beam), not shown in Fig. \ref{f4:srm_pi},"
 uo Gaussian fit could be macle. as the distributions were binodal.," no Gaussian fit could be made, as the distributions were bimodal."
 The peaks iu these bimodal distributions correspoucd to wo spatially coherent structures. which are shown in the wo pauels of Fie. 13..," The peaks in these bimodal distributions correspond to two spatially coherent structures, which are shown in the two panels of Fig. \ref{f4:angle_highp}."
" In the region around (9.6)(01.67.2naqoon 51.87). ,1.5xz-RAFzO-. while in he region around (9.6)=(92.27.5387). O0XRALxpoe1.9 7."," In the region around $(\alpha,\delta) =
(94.6\dg,51.8\dg)$ , $-1.5\la RM\la 0$, while in the region around $(\alpha,\delta) = (92.2\dg,53.8\dg)$, $0\la RM\la
1.3$ ."
" Clearly, RAL isB indeedB very uniform-- iu+ regions of hieh polarization."," Clearly, $RM$ is indeed very uniform in regions of high polarization."
 The low variation in RAL is also reflected in the uniformity of the polarization angles., The low variation in $RM$ is also reflected in the uniformity of the polarization angles.
 A coustaut RAL over a certain area sets an upper lit on structure iu magnetic field aud thermal electron density., A constant $RM$ over a certain area sets an upper limit on structure in magnetic field and thermal electron density.
 The fac that some of the filamentary structure in P is aligned with Galactic latitude sugecsts a magnetic, The fact that some of the filamentary structure in $P$ is aligned with Galactic latitude suggests a magnetic
This paper presents application of a new weighted. particle scheme for conservation laws to the equations of ideal ivdrodsnamies ancl magnetohvdrodynamies.,This paper presents application of a new weighted particle scheme for conservation laws to the equations of ideal hydrodynamics and magnetohydrodynamics.
 This scheme has no free parameters which control the physics of the interaction., This scheme has no free parameters which control the physics of the inter-particle interaction.
 There only [rec-parameter in our scheme is the average number of neighbours that a particle interacts with. and this depends only on the number of spatial dimensions.," There only free-parameter in our scheme is the average number of neighbours that a particle interacts with, and this depends only on the number of spatial dimensions."
 The interaction between particles is entirely. described » the source terms and. Uuxes., The interaction between particles is entirely described by the source terms and fluxes.
 The latter are given by the solution of the associated. Hüemann problem. which correctly reats dissipative processes and. cliscontinuous solution without explicit. use of artificial viscosity or resistivity.," The latter are given by the solution of the associated Riemann problem, which correctly treats dissipative processes and discontinuous solution without explicit use of artificial viscosity or resistivity."
 Due to use of Uüemann solvers and reconstruction methods. our weighted. particle method is expected to be more dissipative compared to »ure Lagrangian SPILL without any explicit cülfusion terms.," Due to use of Riemann solvers and reconstruction methods, our weighted particle method is expected to be more dissipative compared to pure Lagrangian SPH without any explicit diffusion terms."
 However. further quantitative comparison to SPILL is required to verily this claim in realistic astrophysical problems. where dissipative processes. albeit locally. must. be used.," However, further quantitative comparison to SPH is required to verify this claim in realistic astrophysical problems, where dissipative processes, albeit locally, must be used."
 In our weighted particle scheme. the smoothing length is a property of the particle distribution only. and not the underlving solution.," In our weighted particle scheme, the smoothing length is a property of the particle distribution only, and not the underlying solution."
 As a result. high resolution is obtained in regions with high particle density. which does not need to coincide with high mass density regions.," As a result, high resolution is obtained in regions with high particle density, which does not need to coincide with high mass density regions."
 This therefore permits similar resolution in both low and high density regions. if the scheme is combined with particle refinement. methods.," This therefore permits similar resolution in both low and high density regions, if the scheme is combined with particle refinement methods."
 In our scheme. the physical meaning of the particle as a IHuid element is lost. and the particles should be considered as interpolation points only.," In our scheme, the physical meaning of the particle as a fluid element is lost, and the particles should be considered as interpolation points only."
 Even without the refinement. the mass of the particle can change in the course of simulations. though these changes are small in smooth Lows.," Even without the refinement, the mass of the particle can change in the course of simulations, though these changes are small in smooth flows."
 The advection of a scalar field in our scheme is not as trivial as it is in SPLL, The advection of a scalar field in our scheme is not as trivial as it is in SPH.
 Namely. for every scalar. a transport equations must be solved which further increase. albeit little. both memory and performance footprint of the simulation.," Namely, for every scalar, a transport equations must be solved which further increase, albeit little, both memory and performance footprint of the simulation."
 If one needs to follow multiple Huid composition. the matter is a bit more complicated. since one will be requirecl to use a consistent multi-Huid. advection for chemical species," If one needs to follow multiple fluid composition, the matter is a bit more complicated, since one will be required to use a consistent multi-fluid advection for chemical species"
function in detail in the optical aud Nrav bauds using the PressSchechter formalisin.,function in detail in the optical and X–ray bands using the Press–Schechter formalism.
 Tho litetinie of quasars fo enters iuto our analysis through the dutycycle of quasars. and we find that matching the observed quasar LE to dark inatter halos vields the constraint 109<toSLOS vr: sanaller lifetimes would imply overly massive BIDS. while longer lifetimes would necessitate overly massive halos.," The lifetime of quasars $t_Q$ enters into our analysis through the duty–cycle of quasars, and we find that matching the observed quasar LF to dark matter halos yields the constraint $10^6 \lsim t_Q \lsim 10^8$ yr: smaller lifetimes would imply overly massive BH's, while longer lifetimes would necessitate overly massive halos."
 This rauee reassurinely brackets the Eddington timescale of 1.«10* (e/0.1) νι, This range reassuringly brackets the Eddington timescale of $4\times10^7$ $\epsilon$ /0.1) yr.
 The main conclusion of this paper is that the lifetime (and heuce e. if the Eddiugton time is the relevant timescale for quasar activity) cau be further constrained within this range using the clustering of quasars: for quasars with a fixed Iuuinosity. louger fo Πάρος larger host halo masses. and higher bias.," The main conclusion of this paper is that the lifetime (and hence $\epsilon$, if the Eddington time is the relevant timescale for quasar activity) can be further constrained within this range using the clustering of quasars: for quasars with a fixed luminosity, longer $t_Q$ implies larger host halo masses, and higher bias."
 We find that as a result. the correlation Ieneth ry varies strouglv with the assumed. lifetime.," We find that as a result, the correlation length $r_0$ varies strongly with the assumed lifetime."
 Preliminary data from the 2dF survey already sets mild coustraimts on the lifetime., Preliminary data from the 2dF survey already sets mild constraints on the lifetime.
 Depeucding ou the assumed cosmology. we find foο vy (ACDAL) or to=105795 sy (OCDAL) to within lo statistical uncecitainty.," Depending on the assumed cosmology, we find $t_Q=10^{7.7\pm 0.8}$ yr $\Lambda$ CDM) or $t_Q=10^{8\pm
0.8}$ yr (OCDM) to within $1\sigma$ statistical uncertainty."
 These values are also found to satisfy upper Iuits ou the autocorrelation fiction of the soft Nrav backerouud., These values are also found to satisfy upper limits on the auto–correlation function of the soft X–ray background.
 Forthcoming large quasar samples from SDSS or the colplete 2dF survey are ideally suited for a study of quasar clustering. aud they cau. in principle coustrain he quasar lifetime to high accuracy. with stall statistical errors.," Forthcoming large quasar samples from SDSS or the complete 2dF survey are ideally suited for a study of quasar clustering, and they can, in principle constrain the quasar lifetime to high accuracy, with small statistical errors."
 We expect the moceling of the quasarhalo relation. as well as the possible presence of obscured quasars. to f the dominant sources of svstematic uncertaity.," We expect the modeling of the quasar–halo relation, as well as the possible presence of obscured quasars, to be the dominant sources of systematic uncertainty."
" Not discussed in depth iu this paper is the possibility of using Heher moments (such as skewness). which our moclels also uake definite predictions for. aud will be considered im a ""ture publication."," Not discussed in depth in this paper is the possibility of using higher moments (such as skewness), which our models also make definite predictions for, and will be considered in a future publication."
 Remarkably. our best determination of he lifetime of quasars mieht come from the statistics of Hehredshift quasars. rather than the study of individual objects.," Remarkably, our best determination of the lifetime of quasars might come from the statistics of high–redshift quasars, rather than the study of individual objects."
 Near the completion of this work. we became aware of a similar. indepeudent study by P. Martini D. Weinbere.," Near the completion of this work, we became aware of a similar, independent study by P. Martini D. Weinberg."
 We thank M. Iaehlucelt. I. Menon. E. Quataert. U-L. Pen..," We thank M. Haehnelt, K. Menou, E. Quataert, U-L. Pen.,"
 U. Seljak. R. Sheth and D. Spergel for useful discussious. T. Mivaji for his advice ou the X.rav Iuminosity function. and T. Shauks aud S. Croom for discussious ou the 2dF survey.," U. Seljak, R. Sheth and D. Spergel for useful discussions, T. Miyaji for his advice on the X–ray luminosity function, and T. Shanks and S. Croom for discussions on the 2dF survey."
 Support for this work was provided bv the DOE and the NASA eraut. NAC 5-7092 at Fermilab. bv the NSF evant PITY-9513835. by the Taplin Fellowship to LII and bv NASA through the Hubble Fellowship eraut IIE-01119.01-09À to ZIL. awarded by the Space Telescope Science Institute. which is operated bv the Association of Universities for Research in Ástrououiv. Inc... for NASA under contract NAS 5-26555.," Support for this work was provided by the DOE and the NASA grant NAG 5-7092 at Fermilab, by the NSF grant PHY-9513835, by the Taplin Fellowship to LH and by NASA through the Hubble Fellowship grant HF-01119.01-99A to ZH, awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS 5-26555."
Observations carried out by the Burst and Transient Source Experiment show that GRBs originate from cosmological sources (Alecean et al.,Observations carried out by the Burst and Transient Source Experiment show that GRBs originate from cosmological sources (Meegan et al.
 1992 and Dermer 1992)., 1992 and Dermer 1992).
 Identification ofthe host galaxy for the CRB 971214 (Ixullkarni et al., Identification of the host galaxy for the GRB 971214 (Kulkarni et al.
 1998) and several other bursts causes there is little doubt now hat some. and most likely all GRBs are cosmological.," 1998) and several other bursts causes there is little doubt now that some, and most likely all GRBs are cosmological."
 These »henomena are surely related to ultrarelativistic shocks with he Lorentz factors 2107., These phenomena are surely related to ultrarelativistic shocks with the Lorentz factors $\gamma>10^{2}$.
 Several papers suggested: that ultrarclativistic shocks in GRBs could. be sources of high. energy cosmic rays (cL, Several papers suggested that ultrarelativistic shocks in GRBs could be sources of high energy cosmic rays (cf.
 Waxman 1995. Vietri 1995). and. simulations done by Dednarz Ostrowski (1998) showed that such shocks. are able to accelerate. charged: particles and values of their energy spectral indices converge to 70—2.2 when 5.5x and/or magnetic turbulence amplitudes grow.," Waxman 1995, Vietri 1995), and simulations done by Bednarz Ostrowski (1998) showed that such shocks are able to accelerate charged particles and values of their energy spectral indices converge to $\sigma=2.2$ when $\gamma \rightarrow \infty$ and/or magnetic turbulence amplitudes grow."
 Because the acceleration. mechanism is quite dillerent from that in the non-relativistic and mildly relativistic regime we distinguish a class of ultrarelativistic shocks if their. Lorentz factors 2l., Because the acceleration mechanism is quite different from that in the non-relativistic and mildly relativistic regime we distinguish a class of ultrarelativistic shocks if their Lorentz factors $\gamma\gg 1$.
 Observations scem to confirm this mechanism., Observations seem to confirm this mechanism.
 Waxman (1997) used. a fireball model of GRBs and showed from the functional dependence of the Hux on time and frequency that 6—2.30.1 in the afterglow of CRB 970228., Waxman (1997) used a fireball model of GRBs and showed from the functional dependence of the flux on time and frequency that $\sigma=2.3\pm0.1$ in the afterglow of GRB 970228.
 Calama et al. (, Galama et al. (
1998) mace two independent measurements of the electron spectrum index in the afterglow of GRB 970508 which was very close to 2.2.,1998) made two independent measurements of the electron spectrum index in the afterglow of GRB 970508 which was very close to $2.2$.
 A particle crossing the shock to upstream: medium has a momentum vector nearly parallel to the shock normal., A particle crossing the shock to upstream medium has a momentum vector nearly parallel to the shock normal.
 Then the particle momentum changes its inclination in two wavs bv: 1) scattering in an inhomogeneous magnetic field. and 2) smooth variation in a homogeneous field. component., Then the particle momentum changes its inclination in two ways by: 1) scattering in an inhomogeneous magnetic field and 2) smooth variation in a homogeneous field component.
 llereafter. the mean cellection angle in these two cases will be denoted by AQs and 2g. respectively.," Hereafter, the mean deflection angle in these two cases will be denoted by $\Delta \Omega_{S}$ and $\Delta \Omega_{H}$, respectively."
 The first process is a dilfusive one ancl the second. depends on time linearlv., The first process is a diffusive one and the second depends on time linearly.
 “Phat means that with increasing shock velocity. keeping other parameters constant. AQs decreases slower as a square root of time in comparison with AQy.," That means that with increasing shock velocity, keeping other parameters constant, $\Delta \Omega_{S}$ decreases slower as a square root of time in comparison with $\Delta \Omega_{H}$."
 The Lorentz transformation shows that with >Z»1 even a tiny angular deviation in the upstream plasma rest frame can lead to a large angular deviation in the downstream plasma rest frame., The Lorentz transformation shows that with $\gamma\gg 1$ even a tiny angular deviation in the upstream plasma rest frame can lead to a large angular deviation in the downstream plasma rest frame.
 Let us denote a particle phase by © and. the angle between momentum and a magnetic field. vector by 0 both measured in the downstream: plasma rest frame., Let us denote a particle phase by $\phi$ and the angle between momentum and a magnetic field vector by $\theta$ both measured in the downstream plasma rest frame.
 Values of these parameters at the moment when a particle crosses the shock downstream. determine if it is able to reach the shock again in the case of neglected magnetic field luctuations downstream of the shock., Values of these parameters at the moment when a particle crosses the shock downstream determine if it is able to reach the shock again in the case of neglected magnetic field fluctuations downstream of the shock.
 In fact a motion in he homogeneous magnetic field carries a particle in such a wav that it cannot reach the shock again., In fact a motion in the homogeneous magnetic field carries a particle in such a way that it cannot reach the shock again.
 The magnetic ield Huctuations upstream of the shock perturbing the momenttun cirection lead to broadening the (6.4) range hat allows particles to reach the shock again.," The magnetic field fluctuations upstream of the shock perturbing the momentum direction lead to broadening the $\phi,\theta$ ) range that allows particles to reach the shock again."
 Thus. as we show below for ellicient scattering. when AQ” becomes unimportant in comparison to O5. the spectral index and he acceleration time reach their asymptotic values.," Thus, as we show below for efficient scattering, when $\Delta \Omega_{H}$ becomes unimportant in comparison to $\Delta \Omega_{S}$ , the spectral index and the acceleration time reach their asymptotic values."
 The discussed. relation between AQ” and AQs is reproduced in our simulations and presented in Fig., The discussed relation between $\Delta \Omega_{H}$ and $\Delta \Omega_{S}$ is reproduced in our simulations and presented in Fig.
 1., 1.
 There are shown 11 points [rom > = 100 to 320 and three additional [or  = 640. 1280. 2560.," There are shown 11 points from $\gamma$ = 100 to 320 and three additional for $\gamma$ = 640, 1280, 2560."
 Phe expected linear dependence of these quantitiescan be noticed., The expected linear dependence of these quantitiescan be noticed.
ellipticals.,ellipticals.
 Such inside-out formation scenarios are not new. and have been explored by. e.g.. (2003).Bournaud.Jog. (2007). (2007). and (2008).," Such inside-out formation scenarios are not new, and have been explored by, e.g., (2003), (2007), (2007), and (2008)."
 The tdea is that a compact core is formed through highly dissipative processes at z>3 (see. e.g.. 2006a; 2008). which then grows through increasingly dissipationless mergers at lower redshift.," The idea is that a compact core is formed through highly dissipative processes at $z\gtrsim 3$ (see, e.g., 2006a; 2008), which then grows through increasingly dissipationless mergers at lower redshift."
 Independently. Franx et al.," Independently, Franx et al."
 2008 argues that galaxy growth is mostly inside-out. based both on the regular evolution of the stellar mass-radius relation. and on the fact that star forming galaxies are larger than non-star forming galaxies of the same mass.," 2008 argues that galaxy growth is mostly inside-out, based both on the regular evolution of the stellar mass-radius relation, and on the fact that star forming galaxies are larger than non-star forming galaxies of the same mass."
 As discussed in «Εν various models have been proposed to explain. the apparent growth of massive galaxies since z~2.5.," As discussed in 1, various models have been proposed to explain the apparent growth of massive galaxies since $z\sim 2.5$."
 Here we discuss three possible simple models in the context of the relations shown in reffig:allprop:: equal-mass mergers. minor mergers and expansion at fixed mass.," Here we discuss three possible simple models in the context of the relations shown in \\ref{fig:allprop}: equal-mass mergers, minor mergers and expansion at fixed mass."
 We investigate the effects of these models in reffig:allprop with arrows.," We investigate the effects of these models in \\ref{fig:allprop}
 with arrows."
 The starting point of the arrows is always the mean of the high redshift compact galaxies. and they all imply a growth in effective radius of a factor of 5.," The starting point of the arrows is always the mean of the high redshift compact galaxies, and they all imply a growth in effective radius of a factor of 5."
 We emphasize that we look to constrain the dominant mode of galaxy evolution: while individual galaxies in the sample will likely be affected by all of the processes discussed below. we focus on the overall trends in the larger context of the sample of galaxies.," We emphasize that we look to constrain the dominant mode of galaxy evolution; while individual galaxies in the sample will likely be affected by all of the processes discussed below, we focus on the overall trends in the larger context of the sample of galaxies."
 In this model. the growth is driven by (near-) equal mass mergers.," In this model, the growth is driven by (near-) equal mass mergers."
 These mergers will not only increase the size of the galaxies. but also their mass.," These mergers will not only increase the size of the galaxies, but also their mass."
" Applying straightforward virial arguments implies with Kj,» the kinetic energy of the remnant and ΚΙ. K> the kinetic energy of the progenitors."," Applying straightforward virial arguments implies with $K_{1+2}$ the kinetic energy of the remnant and $K_1$ , $K_2$ the kinetic energy of the progenitors."
" With K21M we have and as Mi,»2MiΕΜ. and Mj=M». we have Ua=στ."," With $K= \frac{1}{2}M\sigma^2$ we have and as $M_{1+2} = M_1+M_2$ and $M_1=M_2$, we have $\sigma_{1+2}^2 = \sigma_1^2$."
 Using 0°~GM/r. we arrive at the familiar result that mergers lead to an increase in size and mass but no change in velocity dispersion (e.g.. 1992).," Using $\sigma^2 \propto GM/r$, we arrive at the familiar result that mergers lead to an increase in size and mass but no change in velocity dispersion (e.g., 1992)."
 We note that these relations are simplifications. which are Inconsistent with the observed slopes of the stellar mass — radius relation and the stellar mass — c relation.," We note that these relations are simplifications, which are inconsistent with the observed slopes of the stellar mass – radius relation and the stellar mass – $\sigma$ relation."
 Simulations which take the initial orbits and effects of energy transfer to the dark matter halos into account generally imply a smaller increase in size for a given change in mass. Boylan-Kolchin.Ma. (," Simulations which take the initial orbits and effects of energy transfer to the dark matter halos into account generally imply a smaller increase in size for a given change in mass. , ("
2006) find that ris/ri~(Myo/Mi). depending on the orbital configuration.,"2006) find that $r_{1+2}/r_1 \sim (M_{1+2}/M_1)^{0.6-1}$, depending on the orbital configuration."
 The blue arrows in reffig:allpropt(a-d) show the effects of equal-mass mergers on the various relations between mass. size. and density.," The blue arrows in \\ref{fig:allprop}( (a-d) show the effects of equal-mass mergers on the various relations between mass, size, and density."
 The density within kkpe. was calculated by assuming that the Sersic indices of the profiles of the compact galaxies do not change., The density within kpc was calculated by assuming that the Sersic indices of the profiles of the compact galaxies do not change.
 The blue arrows imply that the descendants of the compact galaxies are the dominant galaxies in massive groups and clusters. with stellar masses of ~10!7msun.," The blue arrows imply that the descendants of the compact galaxies are the dominant galaxies in massive groups and clusters, with stellar masses of $\sim 10^{12}$."
. As can be seen in paneld. the central densities of these galaxies are nearly identical to those of the compact galaxies.," As can be seen in panel, the central densities of these galaxies are nearly identical to those of the compact galaxies."
 However. as can be seen in panela. the effective radii of these giant. nearby galaxies are a factor of ~10 larger than the compact objects. not a factor of ~5.," However, as can be seen in panel, the effective radii of these giant, nearby galaxies are a factor of $\sim 10$ larger than the compact objects, not a factor of $\sim 5$."
 Therefore. this model is not a very good description of the required evolution in panels -c.," Therefore, this model is not a very good description of the required evolution in panels –."
 In this mode of galaxy growth. the progenitor galaxies accumulate mass via minor mergers with small systems.," In this mode of galaxy growth, the progenitor galaxies accumulate mass via minor mergers with small systems."
 The difference with the equal-mass merger model is that minor mergers are more effective in “puffing up” the size a galaxy for a given change in stellar mass., The difference with the equal-mass merger model is that minor mergers are more effective in “puffing up” the size a galaxy for a given change in stellar mass.
 For minor mergers στ>05 in refeq:virial.. and therefore Again using στxGM/r we have The effective radius grows by the square of the change in mass (rather than linearly. which is the case for equal-mass mergers) and the velocity dispersion decreases by the square root of the change in mass (rather than remaining constant) (see also 2009).," For minor mergers $\sigma_1^2 \gg \sigma_2^2$ in \\ref{eq:virial}, and therefore Again using $\sigma^2 \propto GM/r$ we have The effective radius grows by the square of the change in mass (rather than linearly, which is the case for equal-mass mergers) and the velocity dispersion decreases by the square root of the change in mass (rather than remaining constant) (see also 2009)."
" As an example. eight successive M+:M,=1:10 mergers could lead to a factor of~5 increase in effective radius. while the mass would grow by a factor of ~2 only."," As an example, eight successive $M_2:M_1=1:10$ mergers could lead to a factor of$\sim 5$ increase in effective radius, while the mass would grow by a factor of $\sim 2$ only."
 The effects of this scenario are shown by the green arrows in reffig:allprop.., The effects of this scenario are shown by the green arrows in \\ref{fig:allprop}.
 Again. the density within. Ikkpe was calculated by assuming that the Sersic index of the profiles remains unchanged.," Again, the density within kpc was calculated by assuming that the Sersic index of the profiles remains unchanged."
 The compact galaxies have a median nass of 1.7«10! therefore the minor merger model predicts that their descendants are in galaxies with a median mass of 3—4«10!! ttoday., The compact galaxies have a median mass of $1.7\times10^{11}$ therefore the minor merger model predicts that their descendants are in galaxies with a median mass of $3-4\times 10^{11}$ today.
 The central densities of these galaxies are a very good natch to those of the predicted descendants (panel 4). and the effective radii are a much better match than in the equal-nass merger model (panel a).," The central densities of these galaxies are a very good match to those of the predicted descendants (panel ), and the effective radii are a much better match than in the equal-mass merger model (panel )."
" We note here that what matters is the direction of the arrows. as their length is arbitrarily determined by a growth of a factor of five in »,."," We note here that what matters is the direction of the arrows, as their length is arbitrarily determined by a growth of a factor of five in $r_e$."
 Extending the green arrows slightly would bring them very close to the distribution of nearby elliptical galaxies 1n all panels., Extending the green arrows slightly would bring them very close to the distribution of nearby elliptical galaxies in all panels.
 In the final model that we examine. a galaxy has accumulated most of its mass by z—2 and then gradually expands over time while its mass stays roughly constant.," In the final model that we examine, a galaxy has accumulated most of its mass by $z \sim 2$ and then gradually expands over time while its mass stays roughly constant."
" The motivation for this class of models was provided byFan (2008): they suggest that à QSO may blow out alarge fraction of the mass. leading to a significant ""puffing up"" of the remnant."," The motivation for this class of models was provided by (2008); they suggest that a QSO may blow out alarge fraction of the mass, leading to a significant ""puffing up"" of the remnant."
 We will discuss whether such models are physically plausible in 55.2(see also 2009)., We will discuss whether such models are physically plausible in 5.2(see also 2009).
The validitw/— of equation (1)) ds. (strictly) onlv for observations/ of binary stars made with very narrow bandwidths.,The validity of equation \ref{binary_v2}) ) is (strictly) only for observations of binary stars made with very narrow bandwidths.
 For real detection svstems can reduce theobserved V7. and for the scanning detection system of SUSL the equivalent to equation. (1)) giving V7 for a binary star for the case of a wide spectral bandwidth is (Northetal.20073: where The spectral response is approximated: as a Gaussian of centre wavelength Ag with full-width half-maximum AA.," For real detection systems can reduce theobserved $V^2$ and for the scanning detection system of SUSI, the equivalent to equation \ref{binary_v2}) ) giving $V^2$ for a binary star for the case of a wide spectral bandwidth is \citep{North07}: where The spectral response is approximated as a Gaussian of centre wavelength $\lambda_0$ with full-width half-maximum $\Delta\lambda$."
 The term r(o) corresponds to the autocorrelation of the Gaussian envelope of the interference pattern ancl ρ/λυ is defined for convenience., The term $r(\psi)$ corresponds to the autocorrelation of the Gaussian envelope of the interference pattern and $\psi = 2\pi\bmath{b} \cdot \brho/\lambda_0$ is defined for convenience.
 The measures of V7 are contaminated by the irradiance of the tertiary star (Section 3.1)) such that equation. (4)) is no longer applicable., The measures of $V^2$ are contaminated by the irradiance of the tertiary star (Section \ref{ter_effects}) ) such that equation \ref{wide_v2}) ) is no longer applicable.
 “Phe brightness ratio {ο of the tertiary(primary |. secondary) is approximately 75.= (Section 3.1))., The brightness ratio $I_3$ of the tertiary/(primary + secondary) is approximately $I_3 \simeq 0.128\pm0.023$ (Section \ref{ter_effects}) ).
 Adjusting equation (4)) for the contamination of the tertiary we obtain The term. Z5. reduces the observed V7 and hence the elfect the tertiary component has on the caleulated. V? of he spectroscopic pair is considered. an extra. incoherent source.," Adjusting equation \ref{wide_v2}) ) for the contamination of the tertiary we obtain The term, $I_3$, reduces the observed $V^2$ and hence the effect the tertiary component has on the calculated $V^2$ of the spectroscopic pair is considered an extra incoherent source."
 The addition of this termi will mainly allect the itted. component angular diameters ancl brightness ratio. caving the orbital parameters relatively unallected.," The addition of this term will mainly affect the fitted component angular diameters and brightness ratio, leaving the orbital parameters relatively unaffected."
 As Ad and £5 approach zero. Le. narrow bandwidth observations of a simple binary star. then equation (6)) reduces to equation (1)).," As $\Delta\lambda$ and $I_3$ approach zero, i.e. narrow bandwidth observations of a simple binary star, then equation \ref{eq:sig_Sco_V2}) ) reduces to equation \ref{binary_v2}) )."
 Initial values of the inclination ancl position angle of he ascending node were found by a coarse grid search of parameter space., Initial values of the inclination and position angle of the ascending node were found by a coarse grid search of parameter space.
 The remaining orbital parameters were limited to within three standard. deviations of the values given by Mathiasetal.(1991)., The remaining orbital parameters were limited to within three standard deviations of the values given by \citet{Mathias91}.
.. The inital angular ciameter of the primary star was estimated: from. the distance and spectral type characteristics found in the literature (Cox 2000)., The inital angular diameter of the primary star was estimated from the distance and spectral type characteristics found in the literature \citealt{Cox00}) ).
 By physical arguments ancl inspection of the measured. 17. values. the secondaryς angular diameter and. brightness ratio were limited to the ranges mmas and 0.20.8 respectively.," By physical arguments and inspection of the measured $V^2$ values, the secondary's angular diameter and brightness ratio were limited to the ranges mas and 0.2–0.8 respectively."
 The final estimation of parameters was. completed using v minimization as implemented. by the Levenberg-Marquardt method to fit. equation. (6)) to the observed values of V7., The final estimation of parameters was completed using $\chi^2$ minimization as implemented by the Levenberg-Marquardt method to fit equation \ref{eq:sig_Sco_V2}) ) to the observed values of $V^2$.
 When finding the minimum of the 7 manifold. the inverse of the covariance matrix is calculated. by the non-linear fitting program.," When finding the minimum of the $\chi^2$ manifold, the inverse of the covariance matrix is calculated by the non-linear fitting program."
 The formal uncertainties of the fitted: parameters are derived. from the diagonal elements of this covariance matrix., The formal uncertainties of the fitted parameters are derived from the diagonal elements of this covariance matrix.
 As the visibility measurement errors may not strictly. conform to a normal distribution and equation (6)) is non-linear. the formal uncertainties may be underestimates.," As the visibility measurement errors may not strictly conform to a normal distribution and equation \ref{eq:sig_Sco_V2}) ) is non-linear, the formal uncertainties may be underestimates."
 Following the approach of Northctal. (2007).. three uncertainty estimation methods were adopted to confirm the accuracy of the values derived. from. the covariance matrix.," Following the approach of \citet{North07}, , three uncertainty estimation methods were adopted to confirm the accuracy of the values derived from the covariance matrix."
 These methods: Monte Carlo. bootstrap and Markov chain Monte Carlo (AICAIC) simulations are described bv Northetal.(2007) and references therein.," These methods: Monte Carlo, bootstrap and Markov chain Monte Carlo (MCMC) simulations are described by \citet{North07} and references therein."
"their terms “compact“and Παν,",their terms `compact' and `fluffy'.
 The £7! law only has a horizontal scale term (ro) and a vertical scale term (46. or Ho). the shape. or concentration. is exactly the same for all 71 profiles.," The $r^{1/4}$ law only has a horizontal scale term $r_{\rm e}$ ) and a vertical scale term $\mu_{\rm e}$ or $\mu_0$ ), the shape, or concentration, is exactly the same for all $r^{1/4}$ profiles."
" Ionnendy Cebhardt (2001) discussed variatious in p and r When they referred to ""compact? aud futfv.", Kormendy Gebhardt (2001) discussed variations in $\mu_e$ and $r_e$ when they referred to `compact' and `fluffy'.
" Ueuce, although M32 is regarde as colpact. it’s central conceutration €,—(1/3) is actually rather low."," Hence, although M32 is regarded as compact, it's central concentration $C_{r_{\rm e}}(1/3)$ is actually rather low."
 Dekki et al., Bekki et al.
’s (200!) N-lxlv/SPII simulations of tidal interactions between ΑΟ aud an orbiting early-type spiral ealaxy predict either a coniplete stripping of the disk. ox at least a vertical heaing of the satellites disk to create a thick disk.,"'s (2001) N-body/SPH simulations of tidal interactions between M31 and an orbiting early-type spiral galaxy predict either a complete stripping of the disk, or at least a vertical heating of the satellite's disk to create a thick disk."
 Clearly a faint cisk. with very little eas (Welch Saee 2001). still νιirounds M32.," Clearly a faint disk, with very little gas (Welch Sage 2001), still surrounds M32."
 Much of the gas aud y.ars may indeed Lave! been stripped away. resulting iu the low surface brielituess disk.," Much of the gas and stars may indeed have been stripped away, resulting in the low surface brightness disk."
 Also possible. is the suggestiou by Bekki ct (2001) that tidal iteractions with MI fuuuclled. some of M28 gas to its center. forming a lnassive starburst (see also Noguchi Ishibashi 1986).," Also possible, is the suggestion by Bekki et (2001) that tidal interactions with M31 funnelled some of M32's gas to its center, forming a massive starburst (see also Noguchi Ishibashi 1986)."
 This could account for the excess ceutral flux within the inner ~LO” of ND32 having au age of —1 Cyrs (Vazdekis Arinoto 1999: del Burgo et 22001)., This could account for the excess central flux within the inner $\sim10\arcsec$ of M32 having an age of $\sim$ 4 Gyrs (Vazdekis Arimoto 1999; del Burgo et 2001).
 Compact elliptical ealaxics are a rare class of objects., Compact elliptical galaxies are a rare class of objects.
 A closer inspection of such objects seems warrauted in order to inspect whether the species is indeed real or simply a case of misclassification.," A closer inspection of such objects seems warranted in order to inspect whether the species is indeed real, or simply a case of misclassification."
 I wish to thauk Peter Erwiu for providing me with Isent’s (1987) surface brightuess profile of M32. resampled with equal spacing in radius. and for useful discussions which helped to shape this paper.," I wish to thank Peter Erwin for providing me with Kent's (1987) surface brightness profile of M32, resampled with equal spacing in radius, and for useful discussions which helped to shape this paper."
 I aim also grateful to Carme CGallart for her comments ou this work., I am also grateful to Carme Gallart for her comments on this work.
completely to see growth of the instabilityrpSPH gives the expected behaviour for both perturbation strengths.,completely to see growth of the instability gives the expected behaviour for both perturbation strengths.
 ThatrpSPH is dramatic improvement over Morris’ formulation despite only differing in one index is seen in Figure 5.., That is dramatic improvement over Morris' formulation despite only differing in one index is seen in Figure \ref{fig:mSPH-RT}.
 There we give a Rayleigh Taylor problem at low resolution of 100250 particles and a density ratio of 10 as further discussed in section ??.., There we give a Rayleigh Taylor problem at low resolution of $100x50$ particles and a density ratio of $10$ as further discussed in section \ref{sec:mm}.
 All parameters were the same., All parameters were the same.
" A courant factor of 0.2 is used, a neighbour number of 40, α=1.5, Balsara switch is on, and the initial velocity perturbation amplitude is 0.1."," A courant factor of $0.2$ is used, a neighbour number of 40, $\alpha=1.5$, Balsara switch is on, and the initial velocity perturbation amplitude is $0.1$."
 Clearly our formulation is more stable lending support to our discussion on the different error properties of the two discretisations given above., Clearly our formulation is more stable lending support to our discussion on the different error properties of the two discretisations given above.
 So far we have tested our new formalism only in very weakly compressible situations., So far we have tested our new formalism only in very weakly compressible situations.
 We will use the classic Sod shock tube (?) to comparerpSPH to standard SPH here., We will use the classic Sod shock tube \citep{1978JCoPh..27....1S} to compare to standard SPH here.
" ? recently, gave the results for varying viscosity prescriptions and including artificial conduction terms."," \cite{2009NewAR..53...78R} recently, gave the results for varying viscosity prescriptions and including artificial conduction terms."
 We change the setup only slightly., We change the setup only slightly.
 T'he left state has a density and pressure of unity while the right state has a quarter of the density and a pressure of 0.1795., The left state has a density and pressure of unity while the right state has a quarter of the density and a pressure of $0.1795$ .
 This test is evolved with an adiabatic index of y=1.4 and we set it up as a two dimensional problem with equal mass particles in a box that extendsfrom zero to ten in z and zero to one in the y-direction., This test is evolved with an adiabatic index of $\gamma=1.4$ and we set it up as a two dimensional problem with equal mass particles in a box that extendsfrom zero to ten in $x$ and zero to one in the $y$ -direction.
 We choose 40 rows of particles in the y direction and vary the spacing along x to achieve the given densities using a total of 200? particles which are initially at rest., We choose 40 rows of particles in the $y$ direction and vary the spacing along $x$ to achieve the given densities using a total of $200^2$ particles which are initially at rest.
 Additionally we set the interface to be at x=3 and smooth it with an exponential ramp such that all hydrodynamic variables are given by r+(1exp(2*(x—3)/óz))r) where we take 6x=0.05 and [| and r denote the τίleft and right states.," Additionally we set the interface to be at $x=3$ and smooth it with an exponential ramp such that all hydrodynamic variables are given by $ r + (1+\exp(2*(x-3)/\delta
x))^{-1}(l-r)$ where we take $\delta x = 0.05$ and $l$ and $r$ denote the left and right states."
 We employ periodic boundary conditions which gives us another interface at z=10 which has the reversed left and right states but has an initially discontinuous state., We employ periodic boundary conditions which gives us another interface at $x=10$ which has the reversed left and right states but has an initially discontinuous state.
 This will give us the opportunity to show the difference between smoothed interfaces and artificially sharp to be visible in one figure., This will give us the opportunity to show the difference between smoothed interfaces and artificially sharp to be visible in one figure.
 For the first results we present we have used 80 neighbors and an artificial viscosity parameter of a=3 for both the SPH andthe rpSPH calculation., For the first results we present we have used 80 neighbors and an artificial viscosity parameter of $\alpha=3$ for both the SPH andthe calculation.
 Both employ the Balsara switch to limit the viscosity which will play no, Both employ the Balsara switch to limit the viscosity which will play no
" AT=z,.",T =.
"(19) In the compensated models, the only place where CMB photons are affected by the structure is within ΤΠ."," In the compensated models, the only place where CMB photons are affected by the structure is within $\rII$."
" Hence, the RS effect (and ISW effect in general) does not depend on the location of the hypothetical source surface as long as the compensated structure is enclosed between the observer and the source."," Hence, the RS effect (and ISW effect in general) does not depend on the location of the hypothetical source surface as long as the compensated structure is enclosed between the observer and the source."
" In other words, z$ scales linearly with 1+z, in the uniform background."," In other words, $z_\mathrm{s}^e$ scales linearly with $1+z_\mathrm{s}$ in the uniform background."
" For the uncompensated models, the density evolution just beyond ry is still significantly different from that in the EdS universe, so we place the source far away from the model structure."," For the uncompensated models, the density evolution just beyond $\rII$ is still significantly different from that in the EdS universe, so we place the source far away from the model structure."
 illustrates the RS effect of four LTB model structures., illustrates the RS effect of four LTB model structures.
" The main feature is a temperature decrement of several LK in the inner region and slight temperature increase at the outskirt, regardless whethera the structure is a cluster or a void."," The main feature is a temperature decrement of several $\muK$ in the inner region and a slight temperature increase at the outskirt, regardless whether the structure is a cluster or a void."
" This is distinct from the linear ISW effect in a universe dominated by dark energy, which generally causes a temperature increase for clusters and a decrement for voids."," This is distinct from the linear ISW effect in a universe dominated by dark energy, which generally causes a temperature increase for clusters and a decrement for voids."
" The RS effect of the voids may seem counterintuitive at first, and we find that it is the result of underdensities generally evolving slower than the expansion rate in the EdS universe."," The RS effect of the voids may seem counterintuitive at first, and we find that it is the result of underdensities generally evolving slower than the expansion rate in the EdS universe."
" Because a distant comoving observer or emitter in the uncompensated LTB models would be seen to have a peculiar velocity in the EdS background, the most prominent feature of these models is a CMB temperature dipole."," Because a distant comoving observer or emitter in the uncompensated LTB models would be seen to have a peculiar velocity in the EdS background, the most prominent feature of these models is a CMB temperature dipole."
" Once the dipole is subtracted, the temperature profiles are similar to those of the compensated models."," Once the dipole is subtracted, the temperature profiles are similar to those of the compensated models."
" As mentioned in2, we set a low value for the Hubble constant in the EdS background."," As mentioned in, we set a low value for the Hubble constant in the EdS background."
" If we used instead Hg=T71kms!Mpc the central temperature decrement of the compensated !,cluster (void) in would become 9.94K (4.2uK), nearly tripling the decrement of 3.6uK (1.54K) withMpc!."," If we used instead $H_0=71\,\mbox{km\,s}^{-1}\Mpc^{-1}$, the central temperature decrement of the compensated cluster (void) in would become $9.9 \mu\mathrm{K}$ $4.2 \mu\mathrm{K}$ ), nearly tripling the decrement of $3.6 \mu\mathrm{K}$ $1.5 \mu\mathrm{K}$ ) with."
" shows the dependence of the RS effect on the model parameters rj, ΤΠ, and δι."," shows the dependence of the RS effect on the model parameters $\rI$, $\rII$, and $\dI$."
 We use the difference between the characteristic peak and trough of the temperature profile —T_) in to represent the amplitude of the(T. RS effect and show results for compensated clusters., We use the difference between the characteristic peak and trough of the temperature profile $T_+ - T_-$ ) in to represent the amplitude of the RS effect and show results for compensated clusters.
" Because it takes more time for CMB photons to go through a larger structure, its potential can evolve more to produce stronger RS effects."," Because it takes more time for CMB photons to go through a larger structure, its potential can evolve more to produce stronger RS effects."
 Structures with larger |ó;| evolve faster and also produce larger RS effects., Structures with larger $|\dI|$ evolve faster and also produce larger RS effects.
 These are indeed seen in 2., These are indeed seen in .
". Moreover, the RS effect increases fairly rapidly with rr, rjj, and ój."," Moreover, the RS effect increases fairly rapidly with $\rI$, $\rII$, and $\dI$."
 The several K level RS effect in is significant compared to the detected CMB temperature shift of —+10wK due to super structures and is comparable to the expected maximum linear ISW effect of 4.24K within an aperture of 100-! in the Millennium simulation (Granettetal.2008)., The several $\muK$ level RS effect in is significant compared to the detected CMB temperature shift of $\sim \pm 10\muK$ due to super structures and is comparable to the expected maximum linear ISW effect of $4.2\muK$ within an aperture of $100\Mpch$ in the Millennium simulation \citep{granett08}.
". AlthoughMpc the RS effect could bring the expected total ISW effect of the supervoids more in line with the observed value, it would also widen the discrepancy between the observation and the expected total ISW effect for superclusters."," Although the RS effect could bring the expected total ISW effect of the supervoids more in line with the observed value, it would also widen the discrepancy between the observation and the expected total ISW effect for superclusters."
 illustrates the time delay component (dotted and the redshift component (dashed line) of the RS lines)effect (circles) as given in(4)., illustrates the time delay component (dotted lines) and the redshift component (dashed line) of the RS effect (circles) as given in.
". These two effects are opposite to each other and are of the same order, so that the net result is much smaller than either one."," These two effects are opposite to each other and are of the same order, so that the net result is much smaller than either one."
" In other words, the gravitational time delay in the potential is a more dominant effect than the potential evolution for super structures."," In other words, the gravitational time delay in the potential is a more dominant effect than the potential evolution for super structures."
" Treating recombination as an instantaneous event, which suffices our purpose, one can view the RS effect and the ISW effect in general as a single redshift effect without time delay."," Treating recombination as an instantaneous event, which suffices our purpose, one can view the RS effect and the ISW effect in general as a single redshift effect without time delay."
 This view is fully equivalent to that of Rees&Sciama, This view is fully equivalent to that of \citet{rees68}.
" However, one is no longer comparing photons that (1968)..have started from the same spatial coordinates at different times; rather, the CMB photons received at thesame time were emitted at the"," However, one is no longer comparing photons that have started from the same spatial coordinates at different times; rather, the CMB photons received at thesame time were emitted at the"
"The principal accessible store of energy in a pulsar ds its rotational energy. which is liberated at a rate L,c4PAst/p)nLoe?lO erefs ( sec. for example. a table of oulsars parameters ( Ly.p. P) given in the book of Beskin et al.","The principal accessible store of energy in a pulsar is its rotational energy, which is liberated at a rate $L_p\simeq I\stackrel{.}{p}4\pi
^2/p^3\sim 10^{32}\div 10^{36}$ erg/s ( see, for example, a table of pulsars parameters ( $L_p,p,$ $\stackrel{.}{p}$ ) given in the book of Beskin et al."
1993 ). where 4 & 10g 7 is moment of inertia. p is a period. P is a deceleration of a pulsar.,",1993 ), where $I$ $\simeq 10^{45}$ g $^{-2}$ is moment of inertia, $p$ is a period, $\stackrel{.}{p}$ is a deceleration of a pulsar."
" ""Ehe bulk of the oulsar enerey £L, is transferred to the pulsar wind. which consists of electrons. positrons ancl probably heavy. ions. La=gLy d1. The Lorentz factor of the relativistic xuwilicles. in. the wind. may vary in. range 10""'10 (c.g. Alanchester&’PVTavlor.L977)."," The bulk of the pulsar energy $L_p$ is transferred to the pulsar wind which consists of electrons, positrons and probably heavy ions, $L_w=gL_p$, $g\leq 1.$ The Lorentz factor of the relativistic particles in the wind may vary in range 6$ (e.g. Taylor,1977)."
 The intrinsic gamma ray unminosity of pulsed emission from the short periodic pulsars is of the order of ἐςινz0.01 (see Arons. 1991).," The intrinsic gamma ray luminosity of pulsed emission from the short periodic pulsars is of the order of $L_\gamma /L_p\approx 0.01$ (see Arons, 1991)."
 Below we discuss the dillerent (induced) mechanism of non pulsed gamma radiation generation in binary with a pulsar and an optical star., Below we discuss the different (induced) mechanism of non pulsed gamma radiation generation in binary with a pulsar and an optical star.
 This mechanism could result. in. considerably higher ratio of L-/Li., This mechanism could result in considerably higher ratio of $L_\gamma /L_p$.
 The preliminary results of this work were published in the paper of HlLlarionov. 1997.," The preliminary results of this work were published in the paper of Illarionov, 1997."
 Consider the case. of binary with a pulsar. ejecting relativistic particles and an optical star emitting soft photons in optic anc UV band with the energy awa1.10 eV. These low-cncrey photons are scattered by. the pulsar wind relativistic electrons ancl positrons., Consider the case of binary with a pulsar ejecting relativistic particles and an optical star emitting soft photons in optic and UV band with the energy $\omega \simeq 1-10$ eV. These low-energy photons are scattered by the pulsar wind relativistic electrons and positrons.
 The energy of the photon after the inverse Compton scattering is very high ου.5 in the Thomson limit (cosκmc)2 and Sas780ments dn the opposite case ( m is a mass of an electron. e is a light velocity).," The energy of the photon after the inverse Compton scattering is very high - $\varepsilon
_{\max }\sim \omega \gamma ^2$ in the Thomson limit $(\omega \gamma \ll
mc^2) $ and $\varepsilon _{\max }\sim mc^2\gamma $ in the opposite case ( $m$ is a mass of an electron, $c$ is a light velocity)."
 The scattered photons form a wide spectrum from hard. X-ray. band up to gamma band szc] 1000CieV. The relativistic particle scatters the photon preferably along the direction of the particle velocity.," The scattered photons form a wide spectrum from hard X-ray band up to gamma band $\varepsilon
\simeq 1$ $-1000$ GeV. The relativistic particle scatters the photon preferably along the direction of the particle velocity."
 As a result. while soft. photons are directed. racially from. the optical star. the scattered hard. photons move racially from the pulsar.," As a result while soft photons are directed radially from the optical star, the scattered hard photons move radially from the pulsar."
 Here and bellow we assume that the pulsar wind particles are racially directed. [rom the pulsar inside the elfective scattering volume., Here and bellow we assume that the pulsar wind particles are radially directed from the pulsar inside the effective scattering volume.
 In the case of the presence of an obstacle for the pulsar wind and mainly when the matter Dow from the optical star is rather intensive the radial How of the relativistic wind is destroved., In the case of the presence of an obstacle for the pulsar wind and mainly when the matter flow from the optical star is rather intensive the radial flow of the relativistic wind is destroyed.
 Then the svstem of shock waves resulting from the collision of two winds appears between the pulsar and the optical star and the trajectories of the electrons. and positrons bevond the shock change., Then the system of shock waves resulting from the collision of two winds appears between the pulsar and the optical star and the trajectories of the electrons and positrons beyond the shock change.
 In the work of Tavani ancl Brookshaw (1991) the case of weak (in comparison with the pulsar wind) matter outllow is. discussed., In the work of Tavani and Brookshaw (1991) the case of weak (in comparison with the pulsar wind) matter outflow is discussed.
 The hvdrodvnamices of the collision between the relativistic, The hydrodynamics of the collision between the relativistic
We have generated template SEDs lor a range of stellar initial mass function slopes and stellar mass ranges which reproduce the observed optical and ultraviolet. Iuminosity density al 2~6.,We have generated template SEDs for a range of stellar initial mass function slopes and stellar mass ranges which reproduce the observed optical and ultraviolet luminosity density at $z\sim6$.
 We consider (wo cases. one in which the stellar [AIF extends between 1—200 MAI. and a second in which the mass range is 1—50 MAI.," We consider two cases, one in which the stellar IMF extends between $1-200$ $_{\sun}$ and a second in which the mass range is $1-50$ $_{\sun}$."
 As emphasized earlier. the choice of cutoff at the low mass end is insensitive to the result once a>—2.," As emphasized earlier, the choice of cutoff at the low mass end is insensitive to the result once $\alpha>-2$."
 We assume that the metallicity is ZZ. in either case., We assume that the metallicity is $_{\sun}$ in either case.
 We consider a range of —1>a—2.6 and caleulale the munber of ionizing photons produced for each scenario., We consider a range of $-1>\alpha>-2.6$ and calculate the number of ionizing photons produced for each scenario.
 We then calculate the redshift at which (he number of ionizing photons [from the stellar population exceed the minimuni required to maintain the ionized state of hvdrogen., We then calculate the redshift at which the number of ionizing photons from the stellar population exceed the minimum required to maintain the ionized state of hydrogen.
 It is important to note that (his is not simply a comparison with the solid black lines in Figure 3 and 4 which assume the parüceular reionization historv (and thereby clumping factor) from the simulations of (2007 )., It is important to note that this is not simply a comparison with the solid black lines in Figure 3 and 4 which assume the particular reionization history (and thereby clumping factor) from the simulations of \citet{Trac:07}.
. If reionization were complete al hieher redshifts. (he recombination rate between the end of reionization and z~6 would be higher because of the larger values of ne and my.," If reionization were complete at higher redshifts, the recombination rate between the end of reionization and $z\sim6$ would be higher because of the larger values of $n_{\rm e}$ and $n_{\rm HII}$."
 To estimate this. we simply shift the reionization history ancl clumping [actors of to higher redshifts and assume that the clumping factors remained constant once the IGM was completely ionized.," To estimate this, we simply shift the reionization history and clumping factors of \citet{Trac:07}
 to higher redshifts and assume that the clumping factors remained constant once the IGM was completely ionized."
 The number of ionizing photons per barvon in the scenario Where reionization is complete bv z11 is plotted as the triple dot dashed line in Figure 2., The number of ionizing photons per baryon in the scenario where reionization is complete by $z\sim11$ is plotted as the triple dot dashed line in Figure 2.
 We note that this is a [actor of &4 higher than the “late” reionization history which the models of Trac&Cen(2007). provide.," We note that this is a factor of $\sim$ 4 higher than the “late"" reionization history which the models of \citet{Trac:07} provide."
 Furthermore. even if the clumping factor were {ο increase after the IGM was completely reionized. (his would onlv increase the minimum nunmber of photons per barvon required.," Furthermore, even if the clumping factor were to increase after the IGM was completely reionized, this would only increase the minimum number of photons per baryon required."
 Thus. our estimates are. al worst. a lower limit to the number of photons per barvon required to maintain the ionizecl state of the IGM.," Thus, our estimates are, at worst, a lower limit to the number of photons per baryon required to maintain the ionized state of the IGM."
 We find that as the redshift of reionization increases. the value of a needs to increase (Figure 5).," We find that as the redshift of reionization increases, the value of $\alpha$ needs to increase (Figure 5)."
 This is not surprising since a higher μυ implies a larger number of ionizing photons which are prelerentiallv produced in more massive stars., This is not surprising since a higher $z_{\rm reion}$ implies a larger number of ionizing photons which are preferentially produced in more massive stars.
 We also find that as the hieh mass end of the stellar IME is eut. from 200 AL. to 50 M... the slope a needs to increase such that a larger fraction of massive stars make up the shortfall in ionizine photons.," We also find that as the high mass end of the stellar IMF is cut, from 200 $_{\sun}$ to 50 $_{\sun}$, the slope $\alpha$ needs to increase such that a larger fraction of massive stars make up the shortfall in ionizing photons."
 The relation between aad IME slope is also sensitive to the ratio of the clumping factor to the escape ΠΟΙΟΙ., The relation between and IMF slope is also sensitive to the ratio of the clumping factor to the escape fraction.
 Reduction in the chunping factor decreases the number of ionizing photons recquired since the recombination rate is reduced., Reduction in the clumping factor decreases the number of ionizing photons required since the recombination rate is reduced.
 Similarly. a large escape fraction implies thal a larger nunmber of photons escape star-Iormineg regions.," Similarly, a large escape fraction implies that a larger number of photons escape star-forming regions."
 So. a lewer number of ionizing photons need to be produced to reionize the IGA.," So, a fewer number of ionizing photons need to be produced to reionize the IGM."
 As a result. in Figure 5. we plot the relation between," As a result, in Figure 5, we plot the relation between"
We use the Fisher matrix formalism to compute the errors on the modcl parameters py. given the observational errors on the measured.quantities. LV;.,"We use the Fisher matrix formalism to compute the errors on the model parameters $p_A$, given the observational errors on the measuredquantities $X_i$ ."
 Llere pa includes the optimisation target parameters ϐ as well as other nuisance parameters., Here $p_A$ includes the optimisation target parameters $\theta$ as well as other nuisance parameters.
 Phe Fisher matrix is the curvature at the peak of the likelihood.," The Fisher matrix is the curvature at the peak of the likelihood, = ."
 ]ts inverse is a local approximation to the covariance matrix and provides a lower limit for the errors on the mocel parameters via the WKramer-Rao bound., Its inverse is a local approximation to the covariance matrix and provides a lower limit for the errors on the model parameters via the Kramer-Rao bound.
 We can rewrite the Fisher matrix via the chain rule to depend only on observational quantities. Wpg," We can rewrite the Fisher matrix via the chain rule to depend only on observational quantities, = ."
" The observational Fisher. matrix is taken to be the inverse. of⋅ the data covariance. matrix.. £;;:=1 Cy""."," The observational Fisher matrix is taken to be the inverse of the data covariance matrix, $F_{ij} = C_{ij}^{-1}$ ."
 In our case the model parameter vector is p={QuemLmQuhz.àwous) where the two d. parameters describe the dark energy. equation of state w. the ratio of the pressure to density.," In our case the model parameter vector is $\hat{p}=\{\Omega_m,\omega_m \equiv \Omega_m h^2,w_0,w_a\}$ where the two $w_i$ parameters describe the dark energy equation of state $w$, the ratio of the pressure to density."
 We use the parametrisation w(z) = Wo | Ways., We use the parametrisation w(z) = w_0 + w_a.
" We also assume that the universe is Dlat and. that the inlluence of radiation is negligible so that £259=1,,.", We also assume that the universe is flat and that the influence of radiation is negligible so that $\Omega_{DE} = 1-\Omega_m$.
 From the observations we recover the comoving distance to redshift z. r(2) Crom the transverse modes) ancl its derivative à(2) (from the radial modes).," From the observations we recover the comoving distance to redshift $z$, $r(z)$ (from the transverse modes) and its derivative $r'(z)$ (from the radial modes)."
 More precisely. we recover g(z)—r(z)/s and ες)=r'(z)/s.," More precisely, we recover $y(z)\equiv r(z)/s$ and $y'(z)\equiv r'(z)/s$."
 The quantity 5 is the comoving sound horizon at [astscattering., The quantity $s$ is the comoving sound horizon at lastscattering.
 By using the fitting formula described in a previous paper (Blake aal. 2006) we also recover the fractional errors «=Ay/y and wosAy!fy! Foe a given observational setup.," By using the fitting formula described in a previous paper (Blake al, 2006) we also recover the fractional errors $x=\Delta y/y$ and $x'=\Delta y'/y'$ for a given observational setup."
 We assume that the errors à and a are uncorrelated between each other and between redshift bins., We assume that the errors $x$ and $x'$ are uncorrelated between each other and between redshift bins.
 In this case the covariance niatrix. is diagonal., In this case the covariance matrix is diagonal.
 EExpressed in terms of these quantities the Fisher matrix becomes = | lere. the sums run over the observational bins., Expressed in terms of these quantities the Fisher matrix becomes = _i + _i Here the sums run over the observational bins.
 Separating y into the contributions due to r and s. and writing 1f=log/)/O0pLor the logarithmic derivative ofa function f we can write the above formula as ]t remains: to compute Dyr. Dar' and Djs.," Separating $y$ into the contributions due to $r$ and $s$, and writing $D_A f \equiv \dd \log(f)/\dd p_A$for the logarithmic derivative of a function $f$ we can write the above formula as = _i + _i It remains to compute $D_A r$, $D_A r'$ and $D_A s$."
 The comoving distance is given by rz) =c¢Hin. eu f.à mu ," The comoving distance is given by r'(z) =, r(z) = _0^z r'(x) dx ."
Since we are dealing only with logarithmic derivatives we find that all constants drop out. and we set e=1 from now on.," Since we are dealing only with logarithmic derivatives we find that all constants drop out, and we set $c=1$ from now on."
" For our simplified cosmological model the Hubble parameter is η. (QuLO LO OF ) The function f(z:eo.) deseribes the evolution of the οποιον censity of the dark οποίον and can be integrated directly for our parametrisation of ew(z). (ziwo.tt) = 33 LassT, ο At this point we should rewrite the Llubble parameter in terms of our base parameter set."," For our simplified cosmological model the Hubble parameter is H^2(z) = H_0^2 (1+z)^3 + ) ) The function $f(z;w_0,w_a)$ describes the evolution of the energy density of the dark energy and can be integrated directly for our parametrisation of $w(z)$, f(z;w_0,w_a) = 3 _0^z = At this point we should rewrite the Hubble parameter in terms of our base parameter set."
 Specifically we have to replace He=1/0., Specifically we have to replace $H_0^2 = 10^4 \om/\Om$.
 Here we can again neglect the factor 103 as it will drop out of the Fisher matrix computation., Here we can again neglect the factor $10^4$ as it will drop out of the Fisher matrix computation.
 Eq. (X9)), Eq. \ref{eq:hub}) )
 is now h(z (Gp2)? | )., is now h(z)^2 = ( (1+z)^3 + ) .
 As the redshift integration for r(2) converges. we know that differentiation with respect to py and integration over > commute.," As the redshift integration for $r(z)$ converges, we know that differentiation with respect to $p_A$ and integration over $z$ commute."
 LO is therefore sullicient to calculate dr(2)/Opa-, It is therefore sufficient to calculate $\dd r'(z)/\dd p_A$.
 For r we have that Gyr(s)=Oyh(s)/hF (2)., For $r'$ we have that $\dd_A r'(z) = - \dd_A h(z)/h^2(z)$ .
 Clearly then Dar(s)= Dahtz)., Clearly then $D_A r'(z) = -D_A h(z)$ .
 OFcourse lor Dar(z) we need to compute Dar(z)-— A, Ofcourse for $D_A r(z)$ we need to compute D_A r(z) = .
"E, We will now derive explicitely expressionsfor all Qr.", We will now derive explicitely expressionsfor all $\dd_A r'$ .
 LE Du (up to an irrelevant constant.pre-factor)., r'(z) = - = r'(z) r'(z) = (up to an irrelevant constantpre-factor).
 In this case we canperform formally the z integration andfind, In this case we canperform formally the $z$ integration andfind
Astronomy Observatory (NOAQ).,Astronomy Observatory (NOAO).
 We would like to express our (hanks for the help of John Pilkington and Robin Catchpole (then) of the Roval Greenwich Observatory. anc Sue Tritton of the Roval Observatory Ldinburgh. with the thousands of survey plates we have handled: for the dedicated. help of the night assistants al Cerro Tololo and Witt Peak: and the unfailing support of many TACs. who continued to provide follow-up time through several vears in the face of poor weather and a lack of interim publications.," We would like to express our thanks for the help of John Pilkington and Robin Catchpole (then) of the Royal Greenwich Observatory, and Sue Tritton of the Royal Observatory Edinburgh, with the thousands of survey plates we have handled; for the dedicated help of the night assistants at Cerro Tololo and Kitt Peak; and the unfailing support of many TACs, who continued to provide follow-up time through several years in the face of poor weather and a lack of interim publications."
The bar used has a thickuess of 500 pc. a hal£leungth of l1 kpe aud position angle of 137.,"The bar used has a thickness of 500 pc, a half-length of 4 kpc and position angle of $^\circ$."
 The distribution was assuned to be constant alone the bar but exponential in height above the plane., The distribution was assumed to be constant along the bar but exponential in height above the plane.
 The magnitude huit meaus that the sources would have to have absolute maguitiucdes lrighter than Ag -—-6., The magnitude limit means that the sources would have to have absolute magnitudes brighter than $M_K$ =-6.
 These sources will be principally voung stars and so the scale height will be small., These sources will be principally young stars and so the scale height will be small.
 These sources will be the same as those in the spike seen in II91. which have a scale height of about 50 pc.," These sources will be the same as those in the spike seen in H94, which have a scale height of about 50 pc."
 The luminosity function used was the same as for the disc although the density was then normalized to make the total counts match those at /=27°., The luminosity function used was the same as for the disc although the density was then normalized to make the total counts match those at $l=27^\circ$.
 Whilst the model is simple. it does reproduce the nieasured counts fairly well. apart from the region near the CC. where the extinction model used is alinost. certainly not correct:," Whilst the model is simple, it does reproduce the measured counts fairly well, apart from the region near the GC, where the extinction model used is almost certainly not correct:"
as well as deflagration-detonations. having different initial metallicities.,"as well as deflagration-detonations, having different initial metallicities."
 Dadenes et al. (, Badenes et al. (
2008) computed nucleosvithesis from 4 delaved detonation models. with different metallicities. as well as one deflagration model.,"2008) computed nucleosynthesis from 4 delayed detonation models, with different metallicities, as well as one deflagration model."
 This group finds that Mn. vields decline with decreasing metallicity. despite the differences in (he explosion mechanisms and initial conditions of the modeV.," This group finds that Mn yields decline with decreasing metallicity, despite the differences in the explosion mechanisms and initial conditions of the models."
 In addition to the results for the Galactic thin disk. thick disk and halo noted above. MeWilliam et al. (," In addition to the results for the Galactic thin disk, thick disk and halo noted above, McWilliam et al. ("
2003) added two other populations to the studies of manganese by measuring LTE [Mn/Fe]| abundances for stellar members of the Sagittarius dwarf spheroidal galaxy and stars from the Galactic bulge.,2003) added two other populations to the studies of manganese by measuring LTE [Mn/Fe] abundances for stellar members of the Sagittarius dwarf spheroidal galaxy and stars from the Galactic bulge.
 Both svstems exhibited somewhat different behaviors of (Mn/Fe] with |Fe/IH]. with the Ser dwarf galaxy stars having values of [Mn/Fe] that fall below the general LTE trend found for Milky Way disk or halo stars at a given [Fe/I].," Both systems exhibited somewhat different behaviors of [Mn/Fe] with [Fe/H], with the Sgr dwarf galaxy stars having values of [Mn/Fe] that fall below the general LTE trend found for Milky Way disk or halo stars at a given [Fe/H]."
 Bulge stars exhibit opposite behavior. with their values of [Mn/Fe| falling above the trend defined by the Milkv. Way disk and halo stars.," Bulge stars exhibit opposite behavior, with their values of [Mn/Fe] falling above the trend defined by the Milky Way disk and halo stars."
 The goal of this study is to adel another distinct stellar population to analvses Οἱ manganese and its chemical evolution in different. Galactic environments., The goal of this study is to add another distinct stellar population to analyses of manganese and its chemical evolution in different Galactic environments.
 w Cen exhibits some peculiar characteristics in the nature of its chemical evolution. with perhaps the most striking being the large increase in the abundances of the heavy s-process elements (such as Da or La) as the overall metallieitv of cluster stars. measured by such elements as Fe. Ca. or Ti. increases (e.g. Norris Da Costa 1995).," $\omega$ Cen exhibits some peculiar characteristics in the nature of its chemical evolution, with perhaps the most striking being the large increase in the abundances of the heavy s-process elements (such as Ba or La) as the overall metallicity of cluster stars, measured by such elements as Fe, Ca, or Ti, increases (e.g. Norris Da Costa 1995)."
 ew Centauri. although historically classified as a globular cluster. is now thought possibly to be a surviving remnant of a captured small ealaxy. with multiple populations spanning a large range in metallicity (for a more detailed discussion see (he review bv Smith 2004).," $\omega$ Centauri, although historically classified as a globular cluster, is now thought possibly to be a surviving remnant of a captured small galaxy, with multiple populations spanning a large range in metallicity (for a more detailed discussion see the review by Smith 2004)."
 Recently. Carretta et al. (," Recently, Carretta et al. ("
2010) have pointed oul similarities between the w Cen populations ancl those from the Sagittarius cwarf galaxy.,2010) have pointed out similarities between the $\omega$ Cen populations and those from the Sagittarius dwarf galaxy.
 Five distinct stellar populations each with a different metallicitv have been identified by Pancino et al. (, Five distinct stellar populations each with a different metallicity have been identified by Pancino et al. (
2000) and Sollima et al. (,2000) and Sollima et al. (
2005).,2005).
 These studies label the distinct red giant branches from the w Cen populations as RGB MP. (metal-poor): RGB MlIntl: RGB MIut2: RGB MInt3 (intermediate metallicities): and RGB-a (anomolous. with the highest metallicity).," These studies label the distinct red giant branches from the $\omega$ Cen populations as RGB MP (metal-poor); RGB MInt1; RGB MInt2; RGB MInt3 (intermediate metallicities); and RGB-a (anomolous, with the highest metallicity)."
 Manganese abundances are presented here [for the first (ime in w Cen stars. will the sample consisting of 10 targets: 8 red eiuits ave trom the most metal poor populations (RGB MP and RGB Mlit1) and 2 stars ave [rom thie more metal rich RGB ΔΙΣ and MIBnt3.," Manganese abundances are presented here for the first time in $\omega$ Cen stars, with the sample consisting of 10 targets; 8 red giants are from the most metal poor populations (RGB MP and RGB MInt1) and 2 stars are from the more metal rich RGB MInt2 and MInt3."
 These w Cen stus have been analvzed in previous studies (Suuith et al., These $\omega$ Cen stars have been analyzed in previous studies (Smith et al.
 2000: Cunha οἱ al., 2000; Cunha et al.
 2002). however Mn was not included in the analvsis.," 2002), however Mn was not included in the analysis."
"equated with tidal disruption. of star clusters or dwar galaxies. unlike local disc. ""moving groups” that were once hypothesized to be the result. of disruption of star clusters (Boc1934:EgeenL958) but are now thought to be the result of orbital resonances (Famacyetal.2008)..","equated with tidal disruption of star clusters or dwarf galaxies, unlike local disc “moving groups"" that were once hypothesized to be the result of disruption of star clusters \citep{bok,eggen} but are now thought to be the result of orbital resonances \citep{2008A&A...483..453F}."
 Recenth. searches lor spheroid velocity substructure in SDSS data have concentrated on local (up to 17.5 kpc from the Sun) metal-poor main sequence stars (Ixlemoentetal.2009:SmithSchlaufman 2009).. finding more than a dozen groups of stars with coherent velocities.," Recently, searches for spheroid velocity substructure in SDSS data have concentrated on local (up to 17.5 kpc from the Sun) metal-poor main sequence stars \citep{klement,smith2009,schlaufman}, finding more than a dozen groups of stars with coherent velocities."
 Schlaulmanctal.(2009) estimate that there are 10* cold substructures in the Milkv Ways stellar halo., \citet{schlaufman} estimate that there are $10^3$ cold substructures in the Milky Way's stellar halo.
 Blue horizontal branch (BIIB) stars are particularly important for studies of spheroid substruseture (e.g. Clewevy lxinman 2006) because they can be seen to large distances in the SDSS and because a [large fraction of the SDSS stellar spectra are DIIDs., Blue horizontal branch (BHB) stars are particularly important for studies of spheroid substruscture (e.g. Clewey Kinman 2006) because they can be seen to large distances in the SDSS and because a large fraction of the SDSS stellar spectra are BHBs.
 In the future we need more complete spectroscopic and proper motion surveys designed. to. discover velocity. substructure in the Milky Way's spheroid., In the future we need more complete spectroscopic and proper motion surveys designed to discover velocity substructure in the Milky Way's spheroid.
 In this paper we present evidence for a tidal moving group of DIID stars. discovered. in the SDSS and Sloan Extension for Galactic Understanding. and Exploration (SEGUE: Yanny et al.," In this paper we present evidence for a tidal moving group of BHB stars, discovered in the SDSS and Sloan Extension for Galactic Understanding and Exploration (SEGUE; Yanny et al."
" 2009). spectroscopic survey,", 2009) spectroscopic survey.
 Additional evidence that the stars are part of a coherent structure comes from the unusually low metallicity of the stars in the moving group., Additional evidence that the stars are part of a coherent structure comes from the unusually low metallicity of the stars in the moving group.
 We are unable to isolate his moving group in density substructure. highlighting the »ower of velocity information to identify low density contrast substructure in the spheroid.," We are unable to isolate this moving group in density substructure, highlighting the power of velocity information to identify low density contrast substructure in the spheroid."
 Listorically many of the spheroic substructures have »een discovered. by eve in incomplete datasets. rather than ον à mechanical analvsis of cata with a well-ünderstood rackerouncl population.," Historically many of the spheroid substructures have been discovered by eye in incomplete datasets, rather than by a mechanical analysis of data with a well-understood background population."
 As the size of the substructures decreases. it becomes more critical to determine whether he observed structure could be a random Iuctuation of the ickeround.," As the size of the substructures decreases, it becomes more critical to determine whether the observed structure could be a random fluctuation of the background."
" In this paper. we present a method. (Appendix A) for estimating the probability that à random fluctuation could. produce an observed. ""Iump."," In this paper, we present a method (Appendix A) for estimating the probability that a random fluctuation could produce an observed “lump."""
 As we work towards the fainter limits of the SDSS data. it becomes more important to understand how stellar parameters derived from spectra are alfected by a low signal-to-noise (S/N) ratio.," As we work towards the fainter limits of the SDSS data, it becomes more important to understand how stellar parameters derived from spectra are affected by a low signal-to-noise (S/N) ratio."
 The stars in the newly detected. halo substructure have S/N ratio between 7 and 10. as measured from the ratio of fluctuations to continuum on the blue side of the spectrum.," The stars in the newly detected halo substructure have S/N ratio between 7 and 10, as measured from the ratio of fluctuations to continuum on the blue side of the spectrum."
 In the past we have successfully used spectra with S/N as low as 5 to measure racial velocities of E turnolf stars in the Virgo Overdensity (Newbergctal. 2007)., In the past we have successfully used spectra with S/N as low as 5 to measure radial velocities of F turnoff stars in the Virgo Overdensity \citep{netal07}.
. In this paper. we show that although higher S/N is preferable. some information about metallicity ancl surface eravity can be gained for DIID stars with S/N ratios loss than 10.," In this paper, we show that although higher S/N is preferable, some information about metallicity and surface gravity can be gained for BHB stars with S/N ratios less than 10."
 Since the strongest evidence that these BIIBs form a coherent. group is that they have unusually low metallicity. even for the spheroid. we also explore the SEGUE metallicity determinations for BIB stars in the outer spheroid.," Since the strongest evidence that these BHBs form a coherent group is that they have unusually low metallicity, even for the spheroid, we also explore the SEGUE metallicity determinations for BHB stars in the outer spheroid."
 A great variety of previous authors have measured a large metallicity dispersion. lor spheroid stars. with average metallicities somewhere in the 1.5<ΟΠΗ]«L7 range (Freeman 1989)..," A great variety of previous authors have measured a large metallicity dispersion for spheroid stars, with average metallicities somewhere in the $-1.5 < \rm [Fe/H] < -1.7$ range \citep{1987ARA&A..25..603F,gwk89}."
 Phese investigations analysed globular clusters (Searle&ZinnLOTS:1985)..lut Lvraes (Saha1985:Suntzelletal.1901). IX giants (Morrisonetal.2003).. and dwarls (Carneyetal.1990)..," These investigations analysed globular clusters \citep{1978ApJ...225..357S,1985ApJ...293..424Z},RR Lyraes \citep{1985ApJ...289..310S,1991ApJ...367..528S}, K giants \citep{2003AJ....125.2502M}, and dwarfs \citep{1990AJ.....99..201C}."
 Norris(1986). found an average Fe/H] of 1.67 for globular clusters in the outer halo. and an average metallicity of 1.89 for field stars in the outer halo. again with a large metallicity dispersion that. does not depend. on. distance.," \citet{1986ApJS...61..667N} found an average [Fe/H] of $-1.67$ for globular clusters in the outer halo, and an average metallicity of $-1.89$ for field stars in the outer halo, again with a large metallicity dispersion that does not depend on distance."
 The Besancoon model of the Alilky Way adopted an average FefM] of L7. with e=0.25. for the stellar halo (Robinet2000)..," The Besançoon model of the Milky Way adopted an average [Fe/H] of $-1.7$, with $\sigma=0.25$, for the stellar halo \citep{2000A&A...359..103R}."
 Recently. Carolloetal.(2007.2010). analysed the full space motions of >10.000 stars within 4 kpc from the Sun. and found. evidence that the ones that are kinematic members of the outer halo have an average metallicity of 2.2.," Recently, \citet{carollo,carollo2} analysed the full space motions of $>10,000$ stars within 4 kpc from the Sun, and found evidence that the ones that are kinematic members of the outer halo have an average metallicity of $-2.2$."
 Our analysis of the SDSS BIIB stars shows that the metallicity of DIID stars in the Galactic spheroid does not change from go=14.5 (6 kpe from the Sun) to go=19.15 (55 kpe from the Sun) at high Galactic latitudes., Our analysis of the SDSS BHB stars shows that the metallicity of BHB stars in the Galactic spheroid does not change from $g_0=14.5$ (6 kpc from the Sun) to $g_0=19.15$ (55 kpc from the Sun) at high Galactic latitudes.
 The mean measured metallicity of these stars is 1.9. butanalyses of globular clusters in the sample show that there could. be a systematic shift in the BIIB measured metallicities of a few tenths of a magnitude. and in fact 2.0 is our best guess for the proper calibrated value.," The mean measured metallicity of these stars is $-1.9$, butanalyses of globular clusters in the sample show that there could be a systematic shift in the BHB measured metallicities of a few tenths of a magnitude, and in fact $-2.0$ is our best guess for the proper calibrated value."
 In order to search the stellar halo for co-moving groups of stars. we selected BIIB stars from the sixth data release (DRG: Actelman-AMeCarthy et al.," In order to search the stellar halo for co-moving groups of stars, we selected BHB stars from the sixth data release (DR6; Adelman-McCarthy et al."
 2008) of the SDSS., 2008) of the SDSS.
 This release contains both Legacy Survey and SEGUE photometric data from 9583. square degrees of sky., This release contains both Legacy Survey and SEGUE photometric data from 9583 square degrees of sky.
.. More technical information for the SDSS survey can be found in Yorketal.(2000):Fukugita(1996):Gunn(1998):al.(2006):Tuckeret (2006)..," More technical information for the SDSS survey can be found in \citet{2000AJ....120.1579Y,1996AJ....111.1748F,1998AJ....116.3040G,2002AJ....123.2121S,
2002AJ....123..485S,2003AJ....126.2081A,2003AJ....125.1559P,
2004AN....325..583I,2006AJ....131.2332G,2006AN....327..821T}."
 We selected S753 spectra with the colors of (X. stars from the SDSS DRG Star database using the color cuts OB<(gMyoOO and OS«(wugu<15. within the magnitude range 15<gy23. where the 0 subscript indicates that the magnitudes have been corrected for redcdening and extinction using the Schlegeletal.(1998) reddening map.," We selected 8753 spectra with the colors of A stars from the SDSS DR6 Star database using the color cuts $-0.3 < (g-r)_0 < 0.0$ and $0.8 < (u-g)_0 < 1.5$, within the magnitude range $15 < g_0 < 23$, where the $0$ subscript indicates that the magnitudes have been corrected for reddening and extinction using the \citet{1998ApJ...500..525S} reddening map."
 Within this color box. the stars that are bluer in Geου tend to be high surface gravity blue strageler (BS) or main sequence stars. ancl those that are redder in (fwq)o tend to be low surface eravity blue horizontal branch (BIIB) stars.," Within this color box, the stars that are bluer in $(u-g)_0$ tend to be high surface gravity blue straggler (BS) or main sequence stars, and those that are redder in $(u-g)_0$ tend to be low surface gravity blue horizontal branch (BHB) stars."
 Using (6.g)u. (gry color selection parameters as described in Figure LO of Yanny.Newbergetal. (2000)... we cliviclecl the sample into 4630 candidate BULB stars ancl 4123 candidate BS stars with spectra.," Using $(u-g)_0$, $(g-r)_0$ color selection parameters as described in Figure 10 of \citet{ynetal00}, we divided the sample into $4630$ candidate BHB stars and $4123$ candidate BS stars with spectra."
 We separated. the stars in surface eravity using a photometric technique. because in 2007 when we were selecting thestars. we were concerned that the S/N of the spectra would degrade more quickly than the S/N of the photometry at. the faint end of our sample.," We separated the stars in surface gravity using a photometric technique, because in 2007 when we were selecting thestars, we were concerned that the S/N of the spectra would degrade more quickly than the S/N of the photometry at the faint end of our sample."
 The S/N of the spectroscopy increases over the whole magnitude range from 15«go< 20.5. while the photometric accuracy degrades only for η 19., The S/N of the spectroscopy increases over the whole magnitude range from $15<g_0<20.5$ while the photometric accuracy degrades only for $u>19$ .
 The photometric degradation allects halo BUB stars lainter than about gy= 18., The photometric degradation affects halo BHB stars fainter than about $g_0=18$ .
 With more recent recluction software (see below). we have found similar sensitivity to surface gravity. in. photometric and spectroscopic indicators for faint SDSS spectra. but. the," With more recent reduction software (see below), we have found similar sensitivity to surface gravity in photometric and spectroscopic indicators for faint SDSS spectra, but the"
precise and accurate ages that we can get.,precise and accurate ages that we can get.
 This is the sample used in this letter., This is the sample used in this letter.
" Let us take only the most secure measurements for the projected spin/orbitangle!,, for planets with stars >1.2Mo."," Let us take only the most secure measurements for the projected spin/orbit, for planets with stars $\geq 1.2\,M_\odot$."
 There are 22 objects in the sample (table 2))., There are 22 objects in the sample (table \ref{tab:Param}) ).
 The sample is divided in two: stars >1.3Μο (8 stars) and stars between 1.2 and 1.3Μο (14 stars).," The sample is divided in two: stars $\geq 1.3\,M_\odot$ (8 stars) and stars between $1.2$ and $1.3\,M_\odot$ (14 stars)."
" The angle and age estimates were obtained from the literature, but for WASP-17, whose error bar on the age was large."," The angle and age estimates were obtained from the literature, but for WASP-17, whose error bar on the age was large."
" It was re-estimated for this letter, using the stellar parameters and density presented in ? and interpolating in the Geneva tracks (Mowlavi et al."," It was re-estimated for this letter, using the stellar parameters and density presented in \citet{Triaud:2010p8039} and interpolating in the Geneva tracks (Mowlavi et al."
 submitted)., submitted).
 The new age estimate is 2.3+0.6 Gyr., The new age estimate is $2.3\pm0.6$ Gyr.
 Its error bar is consistent with age measurements made by other teams., Its error bar is consistent with age measurements made by other teams.
 The new value is presented along with all other values in table 2.., The new value is presented along with all other values in table \ref{tab:Param}.
 Plotting the absolute values of the measured projected spin/orbit angle 6 against stellar age (fig. 2))," Plotting the absolute values of the measured projected spin/orbit angle $\beta$ against stellar age (fig. \ref{fig:betaAge}) ),"
 a pattern is obvious and as sharp as that presented in ?.., a pattern is obvious and as sharp as that presented in \citet{Winn:2010p7311}.
" While observationally, there should be no bias to preferentially detect aligned systems instead of misaligned systems at any age, stars older than ~ GGyr show mostly aligned systems (rms = 22°, median = 5°)."," While observationally, there should be no bias to preferentially detect aligned systems instead of misaligned systems at any age, stars older than $\sim$ Gyr show mostly aligned systems (rms = $22{^\circ}$, median = $5{^\circ}$ )."
" For stars that are younger we have a large range of obliquities (rms = 66°, median = 60°)."," For stars that are younger we have a large range of obliquities (rms = $66^\circ$, median = $60{^\circ}$ )."
 Figure 3 displays the cumulative distributions on either side of the 2.5 Gyr age limit., Figure \ref{fig:betaAgeCumul} displays the cumulative distributions on either side of the 2.5 Gyr age limit.
" To test the robustness of the pattern, a Monte Carlo simulation was performed taking the data with ages <2.5 Gyr as a fiducial zone from which random samples of 8 measurements were drawn, allowing for repetitions."," To test the robustness of the pattern, a Monte Carlo simulation was performed taking the data with ages $< 2.5$ Gyr as a fiducial zone from which random samples of 8 measurements were drawn, allowing for repetitions."
 There is < chance to draw a sample with median <10° and rms <60° which would allow a sample having seven aligned systems and one retrograde system., There is $<$ chance to draw a sample with median $< 10{^\circ}$ and rms $< 60{^\circ}$ which would allow a sample having seven aligned systems and one retrograde system.
" If restricting the rms within 30°, similar to that observed, there is a probability < that the distributions on either side of the 2.5 Gyr age are the same."," If restricting the rms within $30{^\circ}$, similar to that observed, there is a probability $<$ that the distributions on either side of the 2.5 Gyr age are the same."
" Drawing randomly from the overall sample, there is a chance to obtain a cluster containing 7 aligned systems and another at any angle >20°."," Drawing randomly from the overall sample, there is a chance to obtain a cluster containing 7 aligned systems and another at any angle $> 20^\circ$."
" In addition a Kolmogorov-Smirnov test was carried out, also comparing the distribution in B on either side of the 2.5 Gyr limit."," In addition a Kolmogorov-Smirnov test was carried out, also comparing the distribution in $\beta$ on either side of the 2.5 Gyr limit."
 A D=0.661 is obtained corresponding to a probability of that both distributions, A $D = 0.661$ is obtained corresponding to a probability of that both distributions
alter December 6 is not be expected to be large. sell-consistently with the moclels.,"after December 6 is not be expected to be large, self-consistently with the models."
 The data oin December 11 and 14 is not sufficiently sampled to show that further spectral ageing has or has not occurred after December 6., The data on December 11 and 14 is not sufficiently sampled to show that further spectral ageing has or has not occurred after December 6.
 I indeed (here is some spectral ageing. this should not drastically affect the results of the models.," If indeed there is some spectral ageing, this should not drastically affect the results of the models."
 The empirical reason is that the basic extreme inflections in the spectral shape drive the model., The empirical reason is that the basic extreme inflections in the spectral shape drive the model.
 Namely. the approximate values of o are still determined directly by the data.," Namely, the approximate values of $\alpha$ are still determined directly by the data."
 The data clearly indicates a steep energy index for Cl and C2 per the second paragraph of this section., The data clearly indicates a steep energy index for C1 and C2 per the second paragraph of this section.
 Also. the energy spectrum of C3 cannot be steep due to the 234 GlIIz point on December 6 and the 22.5 GlIz point on December 14.," Also, the energy spectrum of C3 cannot be steep due to the 234 GHz point on December 6 and the 22.5 GHz point on December 14."
 It must be remembered that because of the constant spectral index expedience that the solutions presented here ave not unique., It must be remembered that because of the constant spectral index expedience that the solutions presented here are not unique.
 It is however argued that significant departures from the spectral indices used in the analvsis are not supported by the data as discussed above., It is however argued that significant departures from the spectral indices used in the analysis are not supported by the data as discussed above.
 The arguments presented are not a rigorous proof (hat (here is no significant spectral ageing alter December 6. but there is no direct evidence to sav otherwise.," The arguments presented are not a rigorous proof that there is no significant spectral ageing after December 6, but there is no direct evidence to say otherwise."
 In this section. the fit parameters in Table 2 are related to actual physical parameters.," In this section, the fit parameters in Table 2 are related to actual physical parameters."
 There is a finite range of physical parameters that are consistent. with these spectral fits., There is a finite range of physical parameters that are consistent with these spectral fits.
 To make (he connection. one needs (o relate the observed. flux densitv in equation (3) to the local svnchrotron emissivity within the plasma.," To make the connection, one needs to relate the observed flux density in equation (3) to the local synchrotron emissivity within the plasma."
" The svnchrotron emissivily is given in Tucker(1975). as One can transform this to the observed flux density. 5(7,). in the optically thin region of (he spectrum using the relativistictransformation relations from LindandBlaudford(1935).. where D, is the Iuminositv distance and i, is evaluated in (he plasma rest [rame at the observed frequency."," The synchrotron emissivity is given in \citet{tuc75} as One can transform this to the observed flux density, $S(\nu_{o})$, in the optically thin region of the spectrum using the relativistictransformation relations from \citet{lin85}, where $D_{L}$ is the luminosity distance and $j_{\nu}^{'}$ is evaluated in the plasma rest frame at the observed frequency."
 The distance to GRS 19154105 is debatable with estimates in the range of 6 kpe to 12.5 kpe (Miller-Jonesetal2005)., The distance to GRS 1915+105 is debatable with estimates in the range of 6 kpc to 12.5 kpc \citep{mil05}.
. This estimate directly. allects the inferred rates (hat kinematic components are expanding and therefore the determination of 9., This estimate directly affects the inferred rates that kinematic components are expanding and therefore the determination of $\delta$ .
 We, We
Then we calculated the radial variation of .e for the best-fit models in the same mass range of the observed stars: 0.5.<AM.< πω.,Then we calculated the radial variation of $x$ for the best-fit models in the same mass range of the observed stars: $0.5<M/M_{\odot}<m_{TO}$ .
 The radial variations of .c are compared with the observed MFs in Figure 7.., The radial variations of $x$ are compared with the observed MFs in Figure \ref{M55slx}.
 The mass function slopes are shown at the right end of each curve., The mass function slopes are shown at the right end of each curve.
 This plot is similar to those presented in Pryoretal.(1986).. and allows one to obtain the value of the global mass function of the cluster.," This plot is similar to those presented in \cite{Pryor86}, and allows one to obtain the value of the global mass function of the cluster."
 The three observed points follow fairly well the theoretical curves., The three observed points follow fairly well the theoretical curves.
 Also the high-mass MF slope value of Mandushevetal.(1996) (open circle in Figure 7)) is in good agreement with the models and our MPs., Also the high-mass MF slope value of \cite{Mand96} (open circle in Figure \ref{M55slx}) ) is in good agreement with the models and our MFs.
 From these curves. we have that the slope of the high-mass end of the global MF of MSS is.cc—1.0. which is in quite good agreement with the global value of the MF found from the global LF of MSS pprevious section).," From these curves, we have that the slope of the high-mass end of the global MF of M55 is $x\simeq-1.0$, which is in quite good agreement with the global value of the MF found from the global LF of M55 previous section)."
 In Figure 9 we show the model which best fits the observed radial density profile for a global mass function with a slope c=1.0., In Figure \ref{profile} we show the model which best fits the observed radial density profile for a global mass function with a slope $x=-1.0$.
 The relatively flat MF of M55 could be the result of the selective loss of main sequence stars. especially from the outer envelope of the cluster. caused by the strong tidal shocks suffered by M55 during its many passages through the Galactic disk and near the Galactic bulge (Piotto.1993.forageneral problem)..," The relatively flat MF of M55 could be the result of the selective loss of main sequence stars, especially from the outer envelope of the cluster, caused by the strong tidal shocks suffered by M55 during its many passages through the Galactic disk and near the Galactic bulge \cite[for a general discussion of the problem]{Piotto93}."
 A flat MF for M55 agrees well with the results of Capaceiolietal.(1993) who have found that the clusters with a small ος. and/or Ζει show a ME significantly flatter than the cluster in the outer Galactic halo or farther from the Galactic plane., A flat MF for M55 agrees well with the results of \cite{CPS93} who have found that the clusters with a small $R_{GC}$ and/or $Z_{GC}$ show a MF significantly flatter than the cluster in the outer Galactic halo or farther from the Galactic plane.
 Indeed. M55 is near to the Galactic bulge. Rees=LT kpe (RP.=8.0 kpe). and to the Galactic disk Ze;c:=39.0 kpe.," Indeed, M55 is near to the Galactic bulge, $R_{GC}=4.7$ kpc $R_\odot=8.0$ kpc), and to the Galactic disk $Z_{GC}=-2.0$ kpc."
 Figure 8 shows that taking into account observing errors. M55 fairly fits into the relation given by Zoccalietal.(1997)... which is a refined version of the one found by Djorgovskietal.(1993).," Figure \ref{m55xrz} shows that taking into account observing errors, M55 fairly fits into the relation given by \cite{Manu97}, which is a refined version of the one found by \cite{DPC93}."
 A different conclusion has been reached by Mandushevetal.(1996). using their uncorrected (for mass segregation) value for the MF of M55., A different conclusion has been reached by \cite{Mand96} using their uncorrected (for mass segregation) value for the MF of M55.
 As noted by the referee. M55 lies further from the average relation defined by the other clusters: of those with à similar abseissa (0.0+ 0.2). MSS is the one with the lowest value of e.," As noted by the referee, M55 lies further from the average relation defined by the other clusters: of those with a similar abscissa $0.0\pm0.2$ ), M55 is the one with the lowest value of $x$."
 It is not possible to identify the main source of this apparent enhanced mass-loss of M55 compared to the other clusters; a possible cause can be a orbit of the cluster that deeply penetrate into the bulge of the Galaxy., It is not possible to identify the main source of this apparent enhanced mass-loss of M55 compared to the other clusters; a possible cause can be a orbit of the cluster that deeply penetrate into the bulge of the Galaxy.
 This cannot be confirmed until is performed a reliable measure of the proper motion of MSS., This cannot be confirmed until is performed a reliable measure of the proper motion of M55.
 The CMD allows a unique way to obtain a reliable measure of the radial density profiles of GCs., The CMD allows a unique way to obtain a reliable measure of the radial density profiles of GCs.
 In fact. the CMD allows us to sort out the stars belonging to the cluster. limiting the problems generated by the presence of the field stars.," In fact, the CMD allows us to sort out the stars belonging to the cluster, limiting the problems generated by the presence of the field stars."
 This also permits to extract radial profiles for distinct stellar masses., This also permits to extract radial profiles for distinct stellar masses.
 We have first created a profile as in Kingetal.(1968).. in order to compare our results with the existing data in the literature.," We have first created a profile as in \cite{King68}, in order to compare our results with the existing data in the literature."
 The comparison has been done with the radial density profile of M55 published by Pryoretal.(1991) which includes the visual star counts of King et al.. We could not compare our data with Irwin&Trimble(1984) because they have not published their observations in tabular form., The comparison has been done with the radial density profile of M55 published by \cite{Pryor91} which includes the visual star counts of King et al.. We could not compare our data with \cite{Irwin84} because they have not published their observations in tabular form.
 Figure 9. shows the radial density profile for the TO plus SGB stars extracted from the CMD of M55 (from | magnitude below the TO to the brightest limit of our photometry)., Figure \ref{profile} shows the radial density profile for the TO plus SGB stars extracted from the CMD of M55 (from 1 magnitude below the TO to the brightest limit of our photometry).
 We have selected the stars within 2.50 from the fiducial line of, We have selected the stars within $2.5\sigma$ from the fiducial line of
Our sample comes from three observing runs: a threc-nicht run using FORSL at the VLP in November 2004. a three-night run with GAIOS at Gemini-South in. April 2005. and a three-night run using FORS2 at the VLT in September 2007.,"Our sample comes from three observing runs: a three-night run using FORS1 at the VLT in November 2004, a three-night run with GMOS at Gemini-South in April 2005, and a three-night run using FORS2 at the VLT in September 2007."
 Target selection was. in all cases. for isolated. edge-on. late-type galaxies of several arcminutes in diameter. preferentially at a redshift of several thousand kms. which places the Hào line in a relatively (quiet. window of the sky. background.," Target selection was, in all cases, for isolated, edge-on, late-type galaxies of several arcminutes in diameter, preferentially at a redshift of several thousand km/s, which places the $\alpha$ line in a relatively quiet window of the sky background."
 An important. dillerence. among the runs is that the targets for the first. two runs were chosen to be as morphologically undisturbecl and regular as possible. whereas targets for the third run deliberately included: several objects with optical warps. mostly taken from the catalog by Sánchez-Saavedra.ctal.," An important difference among the runs is that the targets for the first two runs were chosen to be as morphologically undisturbed and regular as possible, whereas targets for the third run deliberately included several objects with optical warps, mostly taken from the catalog by \citet{sanchezsaavedra}."
(2003)... At first. it may seem incongruous to include a set of warped galaxies in a lone-slit experiment. because the disk material is eventually going to curve away from the slit at the onset of the warp.," At first, it may seem incongruous to include a set of warped galaxies in a long-slit experiment, because the disk material is eventually going to curve away from the slit at the onset of the warp."
 However. given that nearly all galaxies might oe warped to some extend (Sánchez-Saavedractal.2003).. even if they appear “normal” in the available imaging. it is useful to include a subsample of known warped galaxies o provide the internal control against. which to view our results.," However, given that nearly all galaxies might be warped to some extend \citep{sanchezsaavedra}, even if they appear “normal"" in the available imaging, it is useful to include a subsample of known warped galaxies to provide the internal control against which to view our results."
" Furthermore. warps typically set in around the £o-, racius (Briges1990).. so that several important results [ron he uncisturbed sample within this radial distance may still oe verified. with the warped sample."," Furthermore, warps typically set in around the $R_{25}$ radius \citep{briggs}, so that several important results from the undisturbed sample within this radial distance may still be verified with the warped sample."
 Alb 15 targets are listed in Table. 1.., All 15 targets are listed in Table \ref{tab_sample}.
 The Table lists he Hos radii adopted for this analysis. summarizes which elescope and instrument were used. and identifies whether he galaxy is known to be warped or not.," The Table lists the $_{25}$ radii adopted for this analysis, summarizes which telescope and instrument were used, and identifies whether the galaxy is known to be warped or not."
 Values of Ito; are drawn from (Lauberts&Valentijn1989). for all objects rom the FORSI and GALIOS-S runs and. from the Vhirc teference Catalogue of Bright Galaxies (deVaucouleurseal.1991) for all objects from the FORS2? run., Values of $_{25}$ are drawn from \citep{esolv} for all objects from the FORS1 and GMOS-S runs and from the Third Reference Catalogue of Bright Galaxies \citep{devauc} for all objects from the FORS2 run.
 Phe projectec optical diameter. 2/25. of all galaxies is at most half the sli ength. so that each object is covered completely by the sli in a single observation. along with a substantial sky sample.," The projected optical diameter, $2R_{25}$, of all galaxies is at most half the slit length, so that each object is covered completely by the slit in a single observation, along with a substantial sky sample."
 In our analvsis. we group the galaxies into an unclisturbec and a warped sample.," In our analysis, we group the galaxies into an undisturbed and a warped sample."
" Two of the ""unwarped"" galaxies (ESO 340-C026. MC -01-10-035) were observed during the September 2007 run. which was primarily targeting warpec objects."," Two of the ""unwarped"" galaxies (ESO 340-G026, MCG -01-10-035) were observed during the September 2007 run, which was primarily targeting warped objects."
 We describe the surface brightness profile as a function of projected. radial distance from the galaxy center in. units of the Ios radius so as to permit à comparison between galaxies of different. physical sizes., We describe the surface brightness profile as a function of projected radial distance from the galaxy center in units of the $_{25}$ radius so as to permit a comparison between galaxies of different physical sizes.
 Other characteristic size measures. such as the hall-light radius. As. and the radius containing of the total light. Roy. were also considered.," Other characteristic size measures, such as the half-light radius, $R_{50}$, and the radius containing of the total light, $R_{90}$, were also considered."
 However. all of these are generally strongly correlated (for all galaxies in our sample and in Lauberts&Valentijn(1989).. lio; Roy with a seatter of 15%. and with the exception of a single galaxy. Hoz22. Ray to within 15%).," However, all of these are generally strongly correlated (for all galaxies in our sample and in \citet{esolv}, $_{25}\approx$ $_{90}$ with a scatter of $\%$, and with the exception of a single galaxy, $_{25}\approx
2\times$ $_{50}$ to within $\%$ )."
 We choose to use Res because it is the only such quantity available in the literature for all of our galaxies ancl because it is a robust measure for the “edge” of the disk in this sample where inner-disk size measures can be heavily allected by dust.," We choose to use $_{25}$ because it is the only such quantity available in the literature for all of our galaxies and because it is a robust measure for the ""edge"" of the disk in this sample where inner-disk size measures can be heavily affected by dust."
 All raw spectra are processed using a standard IAE pipeline., All raw spectra are processed using a standard IRAF pipeline.
 Flux calibration is. carried out with spectrophotometric standards taken cach night: calibration [actors for nights in a given run are consistent within1054., Flux calibration is carried out with spectrophotometric standards taken each night; calibration factors for nights in a given run are consistent within.
.. Cosmic ravs are identified by comparing a pixel value to the average of its neighbours within an annulus at distances between 3 ancl 10 pixels and to the standard deviation in this annulus., Cosmic rays are identified by comparing a pixel value to the average of its neighbours within an annulus at distances between 3 and 10 pixels and to the standard deviation in this annulus.
 The locus of pixels to be llagged as cosmic ravs. depending on these quantities. is determined by visual inspection in a plot of the average neighbour pixel value versus the number of standard. deviations.," The locus of pixels to be flagged as cosmic rays, depending on these quantities, is determined by visual inspection in a plot of the average neighbour pixel value versus the number of standard deviations."
 We subtract the sky background. and continuum emission. along the dispersion axis using the appropriate LAL tasks., We subtract the sky background and continuum emission along the dispersion axis using the appropriate IRAF tasks.
 For cach galaxy. we then extract kincmatic data. using our own software.," For each galaxy, we then extract kinematic data, using our own software."
 Line centroiding is carried out and verified interactively for each individual row on the CCL., Line centroiding is carried out and verified interactively for each individual row on the CCD.
 We fit and correct for the local Ho. stellar absorption troughs. which are not removed by the sky subtraction or polynomial stellar continuum subtraction. with Gaussian functions (as now typically done for emission line measurements. see AMoustakas&Kennicutt (2006))). verify. anc. if necessary. adjust the fit manually.," We fit and correct for the local $\alpha$ stellar absorption troughs, which are not removed by the sky subtraction or polynomial stellar continuum subtraction, with Gaussian functions (as now typically done for emission line measurements, see \cite{moustakas}) ), verify, and, if necessary, adjust the fit manually."
 We then transform all spectra onto a common coordinate frame. consisting of the projected separation from the galaxy centroid in units of Ho; and the wavelength ollset from. the interpolated wavelength corresponding to the mean lla rotation velocity. (i.e. we remove the signature of rotation. for an example see Figure & in Christlein&Zaritsky (2008))).," We then transform all spectra onto a common coordinate frame, consisting of the projected separation from the galaxy centroid in units of $_{25}$ and the wavelength offset from the interpolated wavelength corresponding to the mean $\alpha$ rotation velocity (i.e., we remove the signature of rotation, for an example see Figure 8 in \cite{christleinzaritsky}) )."
 Phe transforming process does adversely allect the final signal-to-noise ratio. but has the advantage that all individual spectra can be compared on à Consistent basis despite being taken with three cdillerent instruments and exhibiting clillerentΕΞ rotation curves.," The transforming process does adversely affect the final signal-to-noise ratio, but has the advantage that all individual spectra can be compared on a consistent basis despite being taken with three different instruments and exhibiting different rotation curves."
 From the transformed. spectrum. we measure the La Ilux within a tophat kernel that generously encompasses the entire line. including its deviations from the interpolated rotation curve.," From the transformed spectrum, we measure the $\alpha$ flux within a tophat kernel that generously encompasses the entire line, including its deviations from the interpolated rotation curve."
" Phe [lux is determined by integrating the counts across the entire kernel and renormalizing to units ol⋅ erg s"" 7"" 7. 2o.", The flux is determined by integrating the counts across the entire kernel and renormalizing to units of erg $^{-1}$ $^{-2}$ $^{-2}$.
"We determine. uncertainties ⋠⋠⋠in the extracted [ux by sliding the same tophat kernel along the wavelength axis in a ""background region without strong emission or absorption lines."," We determine uncertainties in the extracted flux by sliding the same tophat kernel along the wavelength axis in a “background"" region without strong emission or absorption lines."
 We finally determine the standard deviation of this residual Lux over all background positions and adopt that. value as the uncertainty in the background., We finally determine the standard deviation of this residual flux over all background positions and adopt that value as the uncertainty in the background.
 We do not specifically include a term to account [or Poisson uncertainties in the emission line Hux. because our analysis focuses on a low-surface brightness regine where background errors are dominant.," We do not specifically include a term to account for Poisson uncertainties in the emission line flux, because our analysis focuses on a low-surface brightness regime where background errors are dominant."
 We calculate the stellar continuum. brightness. using the same spectra without the stellar continuum subtraction. from the mean of background regions that lic adjacent to the Ho line ancl which are free of any strong emission or absorption features.," We calculate the stellar continuum brightness, using the same spectra without the stellar continuum subtraction, from the mean of background regions that lie adjacent to the $\alpha$ line and which are free of any strong emission or absorption features."
 The uncertainty in this quantity is calculated as the error of the mean from the scatter of the incliviclual pixel values., The uncertainty in this quantity is calculated as the error of the mean from the scatter of the individual pixel values.
 Before we begin our discussion. we set the stage hy discussing two Κον considerations.," Before we begin our discussion, we set the stage by discussing two key considerations."
 First. we need to define a set of models that we will test against the data.," First, we need to define a set of models that we will test against the data."
 Our aim is, Our aim is
 (Wheeler&Harkness1990;Filippenko1997).," \citep{wheeler90,filippenko97}."
. Cummingetal.(1996) Μο1.5x1079Mzyr! Uy=10km s!. αςXS2x10~°Ms yr“). Wangetal.(2003) M; (Cummingetal.," \citet{cumming96}
 $\dot{M}\sim1.5\times10^{-5}~M_\Sun~\mathrm{yr}^{-1}$ $v_w = 10$ $^{-1}$ $\frac{\dot{M}}{v_{10}} \lesssim 2\times10^{-5}~M_\Sun$ $^{-1}$ \citet{wang03a} \citet{gerardy04} $_\Sun$ \citep{cumming96}."
"1996).. Wangetal.(2003) Gerardyetal.(2004) (Gerardyetal.2004),,"," \citet{wang03a} \citet{gerardy04} \citep{gerardy04},"
to become relevant with the result of moving at higher energies the cut-off sstate); higher accretion rates lead to high bulk inflow Comptonization efficiency that is seen as an extended hard tail in the spectrum above kkeV sstate).,to become relevant with the result of moving at higher energies the cut-off state); higher accretion rates lead to high bulk inflow Comptonization efficiency that is seen as an extended hard tail in the spectrum above keV state).
" In this state TC becomes less efficient since the coronal plasma is cooled down to -3 kkeV and the emergent spectrum is dominated by a strong thermal bump (with cut-off energy around 10 keV) with overlapped a high-energy PL-like tail up to 100 keV: finally. the sstate spectra. with highest AL. are described by a single TC component (the ""bump) with a low-AT;. and high-7 plasma. as expected in a high AL environment."," In this state TC becomes less efficient since the coronal plasma is cooled down to $\sim$ keV and the emergent spectrum is dominated by a strong thermal bump (with cut-off energy around 10 keV) with overlapped a high-energy PL-like tail up to 100 keV; finally, the state spectra, with highest $\dot{M}$, are described by a single TC component (the “bump”) with a $\kte\ $ and $\tau$ plasma, as expected in a high $\dot{M}$ environment."
 The emission above kkeV is no longer present since the high local pressure gradient either prevents matter to reach the NS or strongly decelerates The study of the average spectra of the twelve NS LMXBs above kkeV allowed P06 to present a qualitative scenario for the X-ray spectral evolution of these sources along with the radio - X-ray connection., The emission above keV is no longer present since the high local pressure gradient either prevents matter to reach the NS or strongly decelerates The study of the average spectra of the twelve NS LMXBs above keV allowed P06 to present a qualitative scenario for the X-ray spectral evolution of these sources along with the radio - X–ray connection.
 Nevertheless. the lack of data below kkeV prevented the authors from drawing more stringent conclusions on the accretion geometry of the systems and on the physical parameters.," Nevertheless, the lack of data below keV prevented the authors from drawing more stringent conclusions on the accretion geometry of the systems and on the physical parameters."
 To overcome these limitations and to obtain a quantitative view of the parameter evolution within a single source we present the study of the broad-band kkeV) spectra of Cyg X-2 in terms of a newly updated version of the mmodel. hereafter referred to as citepfarinelli08..," To overcome these limitations and to obtain a quantitative view of the parameter evolution within a single source we present the study of the broad-band keV) spectra of Cyg X–2 in terms of a newly updated version of the model, hereafter referred to as \\citep{farinelli08}."
 A similar analysis ofBeppoSAX.. aand ddata from a number of LMXBs has been already made by respectively )..," A similar analysis of, and data from a number of LMXBs has been already made by \cite[][hereafter F07 and F08, respectively]{farinelli07,farinelli08}."
 We analyzed two (?) observations of Cyg X-2. the first one performed on 1996 July 23 (00:54:21 to 23:53:06 UT) and the second on 1997 October 26 (15:37:11 UT) to October 28 (04:00:12 UT).," We analyzed two \citep{boella97a} observations of Cyg X–2, the first one performed on 1996 July 23 (00:54:21 to 23:53:06 UT) and the second on 1997 October 26 (15:37:11 UT) to October 28 (04:00:12 UT)."
 This data set has already been presented by Di Salvo et al. (, This data set has already been presented by Di Salvo et al. (
2002. hereafter DS02).,"2002, hereafter DS02)."
 In the analysis carried-out by DSO2. colour-colour and hardness intensity diagrams (CD and HID. respectively) of the source with the 10keV: ?)..," In the analysis carried-out by DS02, colour-colour and hardness intensity diagrams (CD and HID, respectively) of the source with the \citep[1.8-10 keV;][]{boella97b}."
 were produced., were produced.
 The soft colour (SC) was defined as the kkeV count rate ratio. while the hard colour by the kkeV count rate ratio.," The soft colour (SC) was defined as the keV count rate ratio, while the hard colour by the keV count rate ratio."
 On the other hand. in the HID the intensity was defined by the 1.4—10.5 keV count rate.," On the other hand, in the HID the intensity was defined by the 1.4–10.5 keV count rate."
 During the 1996 observation. the source was at HB of the CD/HID diagram: this is much more evident using," During the 1996 observation, the source was at HB of the CD/HID diagram; this is much more evident using"
"periapse corresponds to an observable angle AO,=AO,(1—e)/ +e), where AO, is defined in Eq. 3..","periapse corresponds to an observable angle $\Delta \Theta_p = \Delta \Theta_a
\left(1-e\right)/\left(1+e\right)$ , where $\Delta \Theta_a$ is defined in Eq. \ref{eq:wein}."
 Note that the variations in the inclination i and position angle 2 of the ascending node reach values close to 1 degree for the most massive IBHs considered., Note that the variations in the inclination $i$ and position angle $\Omega$ of the ascending node reach values close to 1 degree for the most massive IBHs considered.
 This is of the same order as the current observational accuracy (c0.7 deg).," This is of the same order as the current observational accuracy $\sim 0.7\,\rm deg$ )."
" In 50 years, this value will drop to about 0.4deg, assuming there are no technological improvements."," In 50 years, this value will drop to about $0.4\,\rm deg$, assuming there are no technological improvements."
" While precession induced by the PN terms is restricted to the orbital plane, an IBH induces more general changes in the orbital elements, including changes in the direction of the orbital angular momentum vector."," While precession induced by the PN terms is restricted to the orbital plane, an IBH induces more general changes in the orbital elements, including changes in the direction of the orbital angular momentum vector."
" We measure the latter via the angle Figure 3 plots ¢ for all the runs, after averaging over the 12 different IBH orientations."," We measure the latter via the angle Figure \ref{fig:phi} plots $\phi$ for all the runs, after averaging over the 12 different IBH orientations."
 The changes in the orbital plane of S2 arelarger for more massive IBHs and can reach values of ~1 degree for q=10?.," The changes in the orbital plane of S2 arelarger for more massive IBHs and can reach values of $\sim 1$ degree for $q =
10^{-3}$."
 Out-of-plane motion is also affected by the size of the MBH/IBH binary orbit such that changes are largest for ας10mpc.," Out-of-plane motion is also affected by the size of the MBH/IBH binary orbit such that changes are largest for $a \simless
10\mpc$."
" The three-body system composed of MBH, IBH and $2 is reminiscent of a Kozai triple (Kozai1962).."," The three-body system composed of MBH, IBH and S2 is reminiscent of a Kozai triple \citep{kozai62}."
" However, the changes that we observe in the orbital elements are not generally attributable to the Kozai mechanism."," However, the changes that we observe in the orbital elements are not generally attributable to the Kozai mechanism."
" Kozai oscillations can be induced if (i) the MBH - 92 - IBH system can be regarded as a hierarchical triple, with well-separated orbital periods for the inner and outer orbit; (ii) the period predicted for the Kozai oscillations is shorter than that of any other precessional period, in this case, GR precession; (iii) the outer orbit is largely inclined with respect to the inner orbit."," Kozai oscillations can be induced if (i) the MBH - S2 - IBH system can be regarded as a hierarchical triple, with well-separated orbital periods for the inner and outer orbit; (ii) the period predicted for the Kozai oscillations is shorter than that of any other precessional period, in this case, GR precession; (iii) the outer orbit is largely inclined with respect to the inner orbit."
" The first condition is only satisfied in the runs with a=10,30mpc."," The first condition is only satisfied in the runs with $a = 10, 30\mpc$."
" 'The timescale for Kozai oscillationscan be written as (Kinoshita&Nakai2007) where Pi, and P, are the period of the inner and outer binary, Cout is the eccentricity of the outer orbit and K is a numerical coefficient which depends only on the initial values of the relative inclination angle o, the inner binary eccentricity €inn and the inner binary argument of periapsis σσ."," The timescale for Kozai oscillationscan be written as \citep{KH07}
 where $\Pinn$ and $\Pout$ are the period of the inner and outer binary, $\eout$ is the eccentricity of the outer orbit and $\mathcal{K}$ is a numerical coefficient which depends only on the initial values of the relative inclination angle $\alpha$, the inner binary eccentricity $\einn$ and the inner binary argument of periapsis $\varpi$ ."
" The maximum eccentricity Cmax attained by the inner binary is also a function of the initial values of a, einn and c only."," The maximum eccentricity $e_{\rm max}$ attained by the inner binary is also a function of the initial values of $\alpha$, $\einn$ and $\varpi$ only."
Figure 4 shows Tx as a function of the black hole binary mass ratio for the assumed values of the eccentricity and for two allowed separations.,Figure \ref{fig:kozai} shows $T_K$ as a function of the black hole binary mass ratio for the assumed values of the eccentricity and for two allowed separations.
 We find that Tx is always longer then S2's GR precession timescaleof 2.5x10!yr for a= 30mpc., We find that $T_K$ is always longer then S2's GR precession timescaleof $2.5\times10^4\yr$ for $a=30\mpc$ .
" For the remaining case a= 10mpc, T is short enough only for qz2.5x103 and ez0.7. This restricts the applicability of the Kozai mechanism to a small subset of our"," For the remaining case $a=10\mpc$ , $T_K$ is short enough only for $q\simgreat 2.5\times10^{-4}$ and $e\simgreat 0.7$ This restricts the applicability of the Kozai mechanism to a small subset of our"
 PA B.) 8. The integrand in equation (43)) is negative5 when S«0. but in these cases @«fy. so the integral remains positive.,"F_2 (A, B, C) = The integrand in equation \ref{eq:F_1}) ) is negative when $S < 0$, but in these cases $\theta < \theta_0$, so the integral remains positive."
" If @ reaches zero at 0= Ay. then S changes sien anc F4 splits into two integrals. with limits 6) to 6, and 8, to 6."," If $\dot{\theta}$ reaches zero at $\theta^{\prime} = \theta_1$ , then $S$ changes sign and $F_1$ splits into two integrals, with limits $\theta_0$ to $\theta_1$ and $\theta_1$ to $\theta$ ."
 Performing the integration in equation (44)). Given. ορ(ο). solved2q0/(nve7b). afb. 64. and. a. equation (39)) can be to ellicientlv. find the arrival angle @," Performing the integration in equation \ref{eq:F_2a}) ), Given $2qp/(mv^2b^2)$, $2qQ/(mv^2 b)$, $a/b$ , $\theta_0$, and $\alpha$, equation \ref{eq:F1F2}) ) can be solved to efficiently find the arrival angle $\theta$."
 X less ellicient.. but. more direct. approach is to integrate the equations. of motion. (13)) (15)).," A less efficient, but more direct, approach is to integrate the equations of motion \ref{eq:r_dot_dot}) \ref{eq:phi_dot_dot}) )."
 We have written subroutines implementing both of these methodsand. found perfect agreement for. numerous combinations of input parameters., We have written subroutines implementing both of these methodsand found perfect agreement for numerous combinations of input parameters.
 ‘To compute the distribution of arrival angles 6 for given values of > and 5g. we examine a €number of trajectories with initial Ay. Lon Uv. bía. and o. where Puy—Ohm). parametersspace," To compute the distribution of arrival angles $\theta$ for given values of $\gamma$ and $\eta$, we examine a large number of trajectories with initial parameters $\theta_0$, $u \equiv v/v_{\mathrm{th}}$, $b/a$ , and $\alpha$ , where $v_{\mathrm{th}} \equiv (2 k_{\mathrm{B}} T_{\mathrm{gas}}/m)^{1/2}$."
"dWe first. select values of 6, from 0 to zx. uniformly in cos&,."," We first select $N_{\theta}$ values of $\theta_0$ from 0 to $\pi$, uniformly spaced in $\cos \theta_0$."
 For cach value of 85. we select ο values of s. starting with v=1.08765. the meclian value assuming n Maxwell speed ¢listributiion.," For each value of $\theta_0$, we select $N_v$ values of $u$ , starting with $u = 1.08765$, the median value assuming the Maxwell speed distribution."
" We then select. CN,1)/2 values with wo1.OS765 spaced in equal-probability intervals. ic. such that4{—.VF apu exp"," We then select $(N_v - 1)/2$ values with $u > 1.08765$ spaced in equal-probability intervals, i.e., such that u u^2 (-u^2) = ."
 Likewise for values with w«1.087select., Likewise for values with $u < 1.08765$.
" ""mFor each (65.t/) pair. buc0. then we next values of bfa between 0 ancl boatfa. uniformly. spaced. in b7."," For each $(\theta_0, u)$ pair, if $b_{\mathrm{crit}} > 0$, then we next select $N_b$ values of $b/a$ between 0 and $b_{\mathrm{crit}}/a$, uniformly spaced in $b^2$."
" Finally. [or each ((Oy.un.bfqa) ewe select IN, values of a. uniformly spaced between 0 and2x."," Finally, for each $(\theta_0, u, b/a)$, we select $N_{\alpha}$ values of $\alpha$, uniformly spaced between 0 and $2\pi$."
 For each trajectory. we compute the arrival angle 8.," For each trajectory, we compute the arrival angle $\theta$."
 The are binned. with trajectories weighted in proportion to resultsbzcrit? Lig.," The results are binned, with trajectories weighted in proportion to $b_{\mathrm{crit}}^2$.Fig."
5 clisplavs gtcos8). the fraction of arriving particles that strike with cosine of the polar angle((relative to the dipole moment) <cos0. [ου=0 and several values of 4.," \ref{fig:g_gamma0} displays $g(\cos \theta)$, the fraction of arriving particles that strike with cosine of the polar angle (relative to the dipole moment) $\le \cos \theta$, for $\gamma =0$ and several values of $\eta$."
 To construct this figure. we adopted 40 bins in 6 and NaΑΝ=Ny=N= 31.," To construct this figure, we adopted 40 bins in $\theta$ and $N_{\theta} = N_v = N_b = N_{\alpha} = 31$ ."
 The distrixitions look very similar to those in fie., The distributions look very similar to those in fig.
 83 when [>|<1., \ref{fig:g_gamma0} when $|\gamma| < 1$.
 Distributions for (+.7) are identical to those for (5.5). except that they are referenced to cos#6= rather than -1.," Distributions for $(\gamma, -\eta)$ are identical to those for $(\gamma, \eta)$, except that they are referenced to $\cos \theta = 1$ rather than -1."
 That is. gis.pcos@)=απ.cos8). with g(cos9) the fraction of particles that strike with cosine of polar angle cos@ when n< ," That is, $g(\gamma, -\eta; \cos \theta) = g(\gamma, \eta; - \cos \theta)$, with $g(\cos \theta)$ the fraction of particles that strike with cosine of polar angle $\ge \cos \theta$ when $\eta < 0$."
As [5| increases. the distribution in cos becomes more uniform. as seen in Lig.," As $|\gamma|$ increases, the distribution in $\cos \theta$ becomes more uniform, as seen in Fig."
 4 for the case that 9y=2107., \ref{fig:g_eta2} for the case that $\eta = 10^2$.
" Electrons arriving at he grain surface can penetrate to within the bulk of the grain. with an e-folding length 7,~ (see paragraphfollowing eq."," Electrons arriving at the grain surface can penetrate to within the bulk of the grain, with an e-folding length $l_e \sim 10 \ \mathrm{\AA}$ (see paragraphfollowing eq."
 13 in WDOI)., 13 in WD01).
 We neglect thispenetration sincef. <a: ie. all arriving electrons are assumed to be located at r= a.Weadopta simplified versionof the procedure in WDOL for calculating the rateatwhich photoelectrons are ejected [rom the grain. Jue WDOL express the photoelectric vield (i... the probability that an electron is ejected. following the absorption of a photon) as a product. of three factors:," We neglect thispenetration since$l_e \ll a$ ; i.e., all arriving electrons are assumed to be located at $r=a$ .Weadopta simplified versionof the procedure in WD01 for calculating the rateatwhich photoelectrons are ejected from the grain, $J_{\mathrm{pe}}$ WD01 express the photoelectric yield (i.e., the probability that an electron is ejected following the absorption of a photon) as a product of three factors:"
We can of course check the extent to which this has happened in our simulated galaxy samples.,We can of course check the extent to which this has happened in our simulated galaxy samples.
 Indeed. for the HUDF simulation shown in Figs 7-9. we find that from an input sample of 82 2=7 galaxies. [2 were scattered out of the sample to low redshift due. in most causes. to their redder {4 colours.," Indeed, for the HUDF simulation shown in Figs 7–9, we find that from an input sample of 82 $z = 7$ galaxies, 12 were scattered out of the sample to low redshift due, in most cases, to their redder $J-H$ colours."
 Finally. for completeness. we show in Fig.," Finally, for completeness, we show in Fig."
 10 the effect of restricting our analysis of the 51. 5=—2 simulation to sources with at least one = S- detection with WPC3/IR. in effect replicating our final analysis of the real data as presented in Fig.," 10 the effect of restricting our analysis of the $z = 7$, $\beta = -2$ simulation to sources with at least one $>8$ $\sigma$ detection with WFC3/IR, in effect replicating our final analysis of the real data as presented in Fig."
 6., 6.
 As with the real data. applying this level of quality control leaves us unable to say anything about 2 at Aiac18.5. but interestingly (and reassuringly) it also reduces the level of bias in the Mic19.5 luminosity bin to 9:7—0.2.," As with the real data, applying this level of quality control leaves us unable to say anything about $\beta$ at $M_{UV} \simeq 
-18.5$, but interestingly (and reassuringly) it also reduces the level of bias in the $M_{UV} \simeq -19.5$ luminosity bin to $\delta \beta \simeq 0.2$."
 Clearly the results presented in Fig., Clearly the results presented in Fig.
 6 are completely consistent with 7—2., 6 are completely consistent with $\beta = -2$.
 Our key results can be summarized as follows., Our key results can be summarized as follows.
" First we tind that. at 2=5 and:=6. the average value of UV slope is perfectly consistent with .?=2 and displays no significant luminosity dependence over the UV luminosity range 22Alisuy<15,"," First we find that, at $z = 5$ and $z = 6$, the average value of UV slope is perfectly consistent with $\beta = -2$ and displays no significant luminosity dependence over the UV luminosity range $-22 < M_{1500} < -18$."
 Second. we find that the same result appears to hold at 2—7. over the more restricted luminosity range 2]«Mis<19. but conclude that no robust statement can yet be made about 1:25 at fainter luminosities at ο26.5.," Second, we find that the same result appears to hold at $z \simeq 7$, over the more restricted luminosity range $-21 < M_{1500} < -19$, but conclude that no robust statement can yet be made about $\langle \beta \rangle$ at fainter luminosities at $z > 6.5$."
 Third. we show. both via data consistency arguments from fields of varying depth. and from simple (yet realistic. and end-to-end) simulations that attempting to extend the measurement of average UV slope into the faintest available luminosity bin (as determined by =45- σ detections) yields values of 67) which are biased to the blue. and can yield apparent average values as low as (2)&—3. even fora rue input value Of 7=—2 for every source.," Third, we show, both via data consistency arguments from fields of varying depth, and from simple (yet realistic, and end-to-end) simulations that attempting to extend the measurement of average UV slope into the faintest available luminosity bin (as determined by $\simeq 4- 5$ $\sigma$ detections) yields values of $\langle \beta \rangle$ which are biased to the blue, and can yield apparent average values as low as $\langle \beta \rangle \simeq - 3$, even for a true input value of $\beta = -2$ for every source."
" Thus. while we cannot rule out the recent claims that the ""intest galaxies vet discovered at 2.—7 have extremely blue slopes. 69)2—3. we do show that such extreme values of (7 are found (from the current data) in any luminosity or redshift bin Where good-quality photometry is available (where “good” here means at least one detection in à WFC3/IR band at a significance evel better than 8-0)."," Thus, while we cannot rule out the recent claims that the faintest galaxies yet discovered at $z \simeq 7$ have extremely blue slopes, $\langle \beta \rangle \simeq -3$, we do show that such extreme values of $\langle \beta \rangle$ are found (from the current data) in any luminosity or redshift bin where good-quality photometry is available (where “good” here means at least one detection in a WFC3/IR band at a significance level better than $\sigma$ )."
 We note here that Finkelstein et al. (, We note here that Finkelstein et al. (
2010). while reporting raw results on £25 at zc7 (their Fig.,"2010), while reporting raw results on $\langle \beta \rangle$ at $z \simeq 7$ (their Fig."
 6) very similar to those reported by Bouwens et al. (, 6) very similar to those reported by Bouwens et al. (
QOLIOb). derive larger errors on 0:2. and conclude that there is as vet no evidence for a dependence of £23) on Mi at zc7.,"2010b), derive larger errors on $\langle \beta \rangle$, and conclude that there is as yet no evidence for a dependence of $\langle \beta \rangle$ on $M_{UV}$ at $z \simeq 7$."
 This. then. provides a very strong and clear motivation for still deeper WFC3/IR imaging in the HUDF. given the importance of testing the astrophysically important possibility that the very faintest high-redshift galaxies do display UV slopes signiticantly bluer that £2;=2.5. with all the associated implications for metallicity. age and —ionizing photon escape fraction (Bouwens et al.," This, then, provides a very strong and clear motivation for still deeper WFC3/IR imaging in the HUDF, given the importance of testing the astrophysically important possibility that the very faintest high-redshift galaxies do display UV slopes significantly bluer that $\langle \beta \rangle = -2.5$, with all the associated implications for metallicity, age and ionizing photon escape fraction (Bouwens et al."
 2010b: Robertson et al., 2010b; Robertson et al.
 2010)., 2010).
 A depth improvement of 5-0.5 mag., A depth improvement of $\simeq 0.5$ mag.
 would be sufficient to convert most of the current 7 5-c detections to & S-o detections. thus enabling proper exploration of 1:2? down to Mpyapc lsat.c7.," would be sufficient to convert most of the current $\simeq 5$ $\sigma$ detections to $\simeq 8$ $\sigma$ detections, thus enabling proper exploration of $\langle \beta \rangle$ down to $M_{UV, AB} \simeq 18$ at $z \simeq 7$."
 Because of its novelty. and potentially crucial implications for reionization. we have focussed most of the above discussion. and indeed our simulations. on the measurement of 9 at zc7.," Because of its novelty, and potentially crucial implications for reionization, we have focussed most of the above discussion, and indeed our simulations, on the measurement of $\beta$ at $z \simeq 7$."
 However. it is also of interest to assess how our results at 2—6 and z25 measure up to previous studies of ή at these and also lower redshifts.," However, it is also of interest to assess how our results at $z \simeq 6$ and $z \simeq 5$ measure up to previous studies of $\beta$ at these and also lower redshifts."
 The most obvious point of comparison is the major study of UV continuum slope over the redshift range 2«ο6 carried out by Bouwens et al. (, The most obvious point of comparison is the major study of UV continuum slope over the redshift range $2 < z < 6$ carried out by Bouwens et al. (
2009).,2009).
 This work presented extremely good evidence for a luminosity dependence of 7 at ς—2.5 and 2στ4., This work presented extremely good evidence for a luminosity dependence of $\beta$ at $z \simeq 2.5$ and $z \simeq 4$.
 We wish to stress that our failure to find any such luminosity dependence in -7 at higher redshifts should not be taken as castingdoubt on these results at lower redshift., We wish to stress that our failure to find any such luminosity dependence in $\beta$ at higher redshifts should not be taken as castingdoubt on these results at lower redshift.
 In particular. the evidence presented by Bouwens et al. (," In particular, the evidence presented by Bouwens et al. ("
2009) for a steady decrease in (2) over the luminosity range 22<MeyelY appears compelling. based as it is on very large samples of Lyman-break galaxies in which 7 can be determined purely from theoptical photometry (i.e. fromHST ACS i7Ίκσυ Colour).,"2009) for a steady decrease in $\langle \beta \rangle$ over the luminosity range $-22 < M_{UV} < -17$ appears compelling, based as it is on very large samples of Lyman-break galaxies in which $\beta$ can be determined purely from the photometry (i.e. from ACS $i_{775} - z_{850}$ colour)."
 However. this luminosity dependence takes the average value of UV slope from 475c1.9 at Adpy=2 to ἐνc]9 at ΑνΞ17.2. and is attributed by Bouwens et al. (," However, this luminosity dependence takes the average value of UV slope from $\langle \beta \rangle \simeq -1.3$ at $M_{UV} = -22.2$ to $\langle \beta \rangle \simeq -1.9$ 	 at $M_{UV} = -17.2$, and is attributed by Bouwens et al. ("
2009) as being primarily a result of decreasing dust obscuration with decreasing UV luminosity (see also Stark et al.,2009) as being primarily a result of decreasing dust obscuration with decreasing UV luminosity (see also Stark et al.
 2010)., 2010).
 Crucially. even at the faintest luminosities probed at >— 4. the bluest value of 0:5 reported by Bouwens et al. (," Crucially, even at the faintest luminosities probed at $z \simeq 4$ , the bluest value of $\langle \beta \rangle$ reported by Bouwens et al. ("
2009) is 6.9)=2.03+0.040.15.,2009) is $\langle \beta \rangle = -2.03 \pm 0.04 \pm 0.15$.
 It is by no means obvious that a decrease in dust content+ with increasing redshift should maintain the slope of the ;;.—Mia relation. simply shifting it to more negative values of 7.," It is by no means obvious that a decrease in dust content with increasing redshift should maintain the slope of the $\beta - M_{UV}$ relation, simply shifting it to more negative values of $\beta$."
" As already discussed here and elsewhere. it is relatively straightforward. for ""normal. essentially dust-free stellarpopulations to produce .7= 2. but the production. of significantly. bluer slopes requires different astrophysics in the form of very young. very low metallicity stellar populations. with low levels of nebular emission."," As already discussed here and elsewhere, it is relatively straightforward for `normal', essentially dust-free stellarpopulations to produce $\beta = -2$ , but the production of significantly bluer slopes requires different astrophysics in the form of very young, very low metallicity stellar populations, with low levels of nebular emission."
 The results presented by Bouwens et al. (, The results presented by Bouwens et al. (
"2009) on Jats&5 and 2)2.6 are inevitably much more uncertain than those at lower redshift. in part because they involved the use of NICMOS data in the measurement of ή, ","2009) on $\beta$ at $z~\simeq~5$ and $z~\simeq~6$ are inevitably much more uncertain than those at lower redshift, in part because they involved the use of NICMOS data in the measurement of $\beta$ ."
Nevertheless. at the brighter end of the luminosity range probed. at λεν 20.5. our morerobust," Nevertheless, at the brighter end of the luminosity range probed, at $M_{UV} 
\simeq -20.5$ , our morerobust"
steady. post-shock accretion flows. Blondinetal.(2003) found in their numerical simulations that the perturbations grow up to the nonlinear regime wilh clear dominance of (6=1 at first and £6=2 later. leading to the global deformation of the shock wave.,"steady, post-shock accretion flows, \citet{blondin_03} found in their numerical simulations that the perturbations grow up to the nonlinear regime with clear dominance of $\ell=1$ at first and $\ell=2$ later, leading to the global deformation of the shock wave."
 Here £ stands lor the azimuthial index of the Legendre polynomials., Here $\ell$ stands for the azimuthal index of the Legendre polynomials.
 One lesson to learn is that we should not impose (he symmetry will respect to the equatorial plane in the simulations., One lesson to learn is that we should not impose the symmetry with respect to the equatorial plane in the simulations.
 As mentioned already. since the large deviation from the spherical svmmetry may have an important consequence to the explosion itself. the finding of Blondinetal.(2003). has much interest of otherresearchers.," As mentioned already, since the large deviation from the spherical symmetry may have an important consequence to the explosion itself, the finding of \citet{blondin_03} has much interest of otherresearchers."
 In their first paper (Dlondinetal.2003).. the neutrino heating and cooling are entirely ignored and (he flow is assumed to be isentropic.," In their first paper \citep{blondin_03}, the neutrino heating and cooling are entirely ignored and the flow is assumed to be isentropic."
 In the recent paper (Blondin&Mezzacappa2005).. the authors took into account the cooling term of a simple analvtic form just as in Houck&Chevalier(1992).. but no heating included vet.," In the recent paper \citep{blondin_05}, the authors took into account the cooling term of a simple analytic form just as in \citet{HC}, but no heating included yet."
 On the other hand. Sehecketal.(2004) demonstrated that similar asymmetric motions with no equatorial symmetry occur in their most realistic numerical models.," On the other hand, \citet{scheck_04} demonstrated that similar asymmetric motions with no equatorial symmetry occur in their most realistic numerical models."
 Although their results show that (he neutrino processes will not nullify SASI. the growths and saturations of individual modes under neutrino-irradiation are not clear. since they used highly complicated flows as an underlving model.," Although their results show that the neutrino processes will not nullify SASI, the growths and saturations of individual modes under neutrino-irradiation are not clear, since they used highly complicated flows as an underlying model."
 Our standing point in this paper is somewhere in between (hese works., Our standing point in this paper is somewhere in between these works.
 We study SASI bv 2D axisvmmetric hedrodynamical simulations., We study SASI by 2D axisymmetric hydrodynamical simulations.
 Although we have in mind the application to the supernova core in the shock-stagnation phase. we take an experimental stance as in Blondinetal.(2003).," Although we have in mind the application to the supernova core in the shock-stagnation phase, we take an experimental stance as in \citet{blondin_03}."
. On the one hand. we emplov a realistic equation of state and take into account the heating and cooling of matter via neutrino emissions and absorptions on nucleons.," On the one hand, we employ a realistic equation of state \citep{shen98} and take into account the heating and cooling of matter via neutrino emissions and absorptions on nucleons."
 As an underlving model. on the other hand. we utilize the spherically svimmetric. steady. shocked accretion [lows (Yamasaki&Yamada2005)... which is stable against radial perturbations.," As an underlying model, on the other hand, we utilize the spherically symmetric, steady, shocked accretion flows \citep{yamasaki}, which is stable against radial perturbations."
 Although this is certainly a crude approximation to what we found in the realistic simulations. it will enable us to do clear mode-analvses from (he linear growthlis through the nonlinear couplings among; various modes up to the eventual saburation of SASI.," Although this is certainly a crude approximation to what we found in the realistic simulations, it will enable us to do clear mode-analyses from the linear growths through the nonlinear couplings among various modes up to the eventual saturation of SASI."
 Due to the neutrino-heating. some initial models have a convectively unstable region in the classical sense (see Foelizzoetal. (2005))) and SASI is inevitably mixed with convection.," Due to the neutrino-heating, some initial models have a convectively unstable region in the classical sense (see \citet{foglizzo05}) ) and SASI is inevitably mixed with convection."
 Dv lowering the neutrino Iuminositv. however. we can also construct models wilh no convectivelv unstable region.," By lowering the neutrino luminosity, however, we can also construct models with no convectively unstable region."
 By comparing these models. we can assess the relative strength of these instabilities.," By comparing these models, we can assess the relative strength of these instabilities."
 We also discuss the implications that ΑΓ might have for the shock revival., We also discuss the implications that SASI might have for the shock revival.
 The plan of (his paper is as follows., The plan of this paper is as follows.
 We describe the numerical methods in section 2.., We describe the numerical methods in section \ref{sec2}.
 The main numerical results are shown in section 3.., The main numerical results are shown in section \ref{sec3}. .
 We conclude this paper in section 4.., We conclude this paper in section \ref{sec4}. .
DDeep Field North(CDF-N:: Brandt et al.,Deep Field North; Brandt et al.
 206010. herea(ter Paper V).," 2001b, hereafter Paper V)."
 Iu addition to probing πιlous active galactic nuclei (ΑΝ) throughout the Universe. this survey is also useful for stuclying X-ray emission [from more “normal” gaaxies where the emission originates [rom X-ray ua‘jes. supernova remuauts. aud low-luninosity AGN (LLACGN: e.g. Horuschemeier et al.," In addition to probing luminous active galactic nuclei (AGN) throughout the Universe, this survey is also useful for studying X-ray emission from more “normal” galaxies where the emission originates from X-ray binaries, supernova remnants, and low-luminosity AGN (LLAGN; e.g., Hornschemeier et al."
 2001. Paper II: Braudt et al.," 2001, Paper II; Brandt et al."
 2001a. Paper IV).," 2001a, Paper IV)."
 Stacliug techniques are particularly powerful in this 'ega«d. since they allow detection of X-ray. emiSM.ion from objects Lying below the detection limit Oriidividual sources.," Stacking techniques are particularly powerful in this regard, since they allow detection of X-ray emission from objects lying below the detection limit for individual sources."
 In Paper IV. we used stacsine techuiques to coustrain the X-ray. emission rour Lormal spiral galaxies out O 2cAv 0.5—1. fliing that their N-ray luminosities were not more hau a factor of zz2 larger (per init B-baud ltnmiuosity) than those of spiral galaxies in the local Universe (2uw 0.01).," In Paper IV we used stacking techniques to constrain the X-ray emission from normal spiral galaxies out to $z\approx$ 0.5–1, finding that their X-ray luminosities were not more than a factor of $\approx 2$ larger (per unit $B$ -band luminosity) than those of spiral galaxies in the local Universe $z<0.01$ )."
 Stacking analyses usiug the [50 ks of data available at the time allowed effective exposures of 5-8 Ms to ye achieved., Stacking analyses using the 480 ks of data available at the time allowed effective exposures of 5–8 Ms to be achieved.
 With the aceitloial ddata recently οἱAained and imyrovelments 1l Olw data processing techniques. we are uow able to extend our coistrallis o Lealaxy X-ray luninsities to higher redshift.," With the additional data recently obtained and improvements in our data processing techniques, we are now able to extend our constraints on galaxy X-ray luminosities to higher redshift."
 This is of cosmological iuterest since the X-ray luminosities of norma ealaxies are expected to evolve wih redshift due to the changing cosilC 5ar-lo‘uation rate (e.g.. vani Paradijs 1978: White Ghosh 1998: Chosh White 2001: Ptak et al.," This is of cosmological interest since the X-ray luminosities of normal galaxies are expected to evolve with redshift due to the changing cosmic star-formation rate (e.g., van Paradijs 1978; White Ghosh 1998; Ghosh White 2001; Ptak et al."
 2001)., 2001).
 Here we preset| constraints on the X-ray. emission from tle Lyman break [n]οalaxy poptlaticym [οιud in the HDE-N itself., Here we present constraints on the X-ray emission from the Lyman break galaxy population found in the HDF-N itself.
 The Galactic coltlul ¢eusity along this ine of sight is (1.620.1)x107? 7 (Stark et al., The Galactic column density along this line of sight is $(1.6\pm 0.4)\times 10^{20}$ $^{-2}$ (Stark et al.
 1992)., 1992).
 Hy=65 kin LM d OV=)1/3. aud Qa2/3 are adopted throughout this paper.," $H_0=65$ km $^{-1}$ $^{-1}$, $\Omega_{\rm M}=1/3$, and $\Omega_{\Lambda}=2/3$ are adopted throughout this paper."
 Coordinates throt1510i this paper are J2000., Coordinates throughout this paper are J2000.
 We have used the Advanced CCD Lnaging Spectrometer (ACIS: GP. Garmire οἱ al.," We have used the Advanced CCD Imaging Spectrometer (ACIS; G.P. Garmire et al.,"
 in preparation) data sets aud basic analysis methods described in Paper V. We employ three standard X-ray bands: 0.5-8.0 keV. (full baud). 0.5-2.0 keV (soft band). and 2-8 keV (hard baud).," in preparation) data sets and basic analysis methods described in Paper V. We employ three standard X-ray bands: 0.5–8.0 keV (full band), 0.5–2.0 keV (soft band), and 2–8 keV (hard band)."
 We use data screened witl the restricted ACIS erace set defiued in Table 2 of Paper V. since this screening srovicdes sieiilicantly improved signal-to-noise lor faint sources.," We use data screened with the restricted ACIS grade set defined in Table 2 of Paper V, since this screening provides significantly improved signal-to-noise for faint sources."
 We restrict our focus to the data obtained within tle HDE-N itself: our N-ray coverage is deepest in this area. aud the o»backgrouud aud j»oiut-spread fuuctioun (PSF) are relatively uuifo‘in over the HDE-N. j»positious witlin he HDE-N are good to within 076.," We restrict our focus to the data obtained within the HDF-N itself; our X-ray coverage is deepest in this area, and the background and point-spread function (PSF) are relatively uniform over the HDF-N. positions within the HDF-N are good to within $0\farcs 6$."
 For the staclXing aualvsis. we selected galaxies in the HDF- itself using the spectroscopic 'edshlift catalogs «) “Cohen et al. (," For the stacking analysis, we selected galaxies in the HDF-N itself using the spectroscopic redshift catalogs of Cohen et al. ("
2000). Cohen (2001). Dawson et aL. (,"2000), Cohen (2001), Dawson et al. ("
2001). and references therein.,"2001), and references therein."
 We considered the z= 2-1 galaxies spectroscopically identified ii the HDF-N: there are 28 such objects. aud most were found usiug the Lyiuau break tecluique (tιο Ua filter has allowed Lyman break galaxies to be fouud «Owl {ο zc;2 in the HDE-N:," We considered the $z=$ 2–4 galaxies spectroscopically identified in the HDF-N; there are 28 such objects, and most were found using the Lyman break technique (the $U_{300}$ filter has allowed Lyman break galaxies to be found down to $z\approx 2$ in the HDF-N;"
properties of stars and GCs within incoming satellites (e.g. GCs are typically at larger galactocentric radii).,properties of stars and GCs within incoming satellites (e.g. GCs are typically at larger galactocentric radii).
" As there are not yet any quantitative predictions, we adopt a schematic model where GC peak metallicities (or colors) are markers of their host galaxies’ masses luminosities), using the known correlations between these(or parameters at low z (see below)."," As there are not yet any quantitative predictions, we adopt a schematic model where GC peak metallicities (or colors) are markers of their host galaxies' masses (or luminosities), using the known correlations between these parameters at low $z$ (see below)."
 The peak GC color in the outer bulge/halo then indicates the characteristic luminosity of the accreted systems., The peak GC color in the outer bulge/halo then indicates the characteristic luminosity of the accreted systems.
" The color-mass relations may well evolve with time, so we take a more general approach of considering the GC color between the central and outlying regions as an indicator of the characteristic mass-ratio that assembled the outer galaxy."," The color-mass relations may well evolve with time, so we take a more general approach of considering the GC color between the central and outlying regions as an indicator of the characteristic mass-ratio that assembled the outer galaxy."
" Using the color-mass relations from for the MPGCs and MRGCs separately, we then generate predicted outer GC peak colors for various stellar mass-ratios 1:x in NGC 3115, overplotting these in Fig."," Using the color-mass relations from \citet{2006ApJ...639...95P} for the MPGCs and MRGCs separately, we then generate predicted outer GC peak colors for various stellar mass-ratios $x$ in NGC 3115, overplotting these in Fig."
 3c., 3c.
 For the MPGCs we find «=200 (15«x2900; the color-mass relation is shallow so this constraint is weak) and for the MRGCs we find z=8 (3«x «19)., For the MPGCs we find $x=200$ $15<x<2900$; the color-mass relation is shallow so this constraint is weak) and for the MRGCs we find $x=8$ $<x<$ 19).
" In combination, we estimate zc 15-20."," In combination, we estimate $x\sim$ 15–20."
" Very roughly, the accreted galaxies had luminosities of ~5x10°Lg.6, equivalent to a dwarf elliptical."," Very roughly, the accreted galaxies had luminosities of $\sim 5\times 10^8 L_{B,\odot}$, equivalent to a dwarf elliptical."
" Such galaxies today each host ~ 20 MPGCs and ~ 3 MRGCs on average (Pengetal. and could therefore account for a total of ~ 350 2008),MPGCs and ~ 50 MRGCs in the outer regions of NGC 3115."," Such galaxies today each host $\sim$ 20 MPGCs and $\sim$ 3 MRGCs on average \citep{2008ApJ...681..197P}, and could therefore account for a total of $\sim$ 350 MPGCs and $\sim$ 50 MRGCs in the outer regions of NGC 3115."
" These numbers are different from the ~ 260 and ~140 GCs that we estimate NGC 3115 to have outside 2 Πο, but this discrepancy is not significant given the uncertainties in these calculations."," These numbers are different from the $\sim$ 260 and $\sim$ 140 GCs that we estimate NGC 3115 to have outside 2 $R_{\rm e}$, but this discrepancy is not significant given the uncertainties in these calculations."
 A fundamental complication arises from biased galaxy assembly (Brodie&Strader|2006). where the low-mass galaxies that were accreted at high z are thought to have hosted GCs of higher metallicity than their present-day counterparts in lower density environments.," A fundamental complication arises from biased galaxy assembly \citep[][]{2006ARA&A..44..193B}, where the low-mass galaxies that were accreted at high z are thought to have hosted GCs of higher metallicity than their present-day counterparts in lower density environments."
 This means that the galaxies accreted by NGC 3115 may have had somewhat lower masses than in our simplified calculation., This means that the galaxies accreted by NGC 3115 may have had somewhat lower masses than in our simplified calculation.
" As a demonstration of the ongoing accretion process, NGC 3115 does have a dwarf companion of this luminosity at 45 kpc projected distance, NGC 3115B. This galaxy hosts ~ 40 GCs andwe estimate the dynamical friction timescale before it disrupts and adds its stars and GCs to the main galaxy to be ~2 Gyr."," As a demonstration of the ongoing accretion process, NGC 3115 does have a dwarf companion of this luminosity at 45 kpc projected distance, NGC 3115B. This galaxy hosts $\sim$ 40 GCs \citep{2001AJ....122.1251K} andwe estimate the dynamical friction timescale before it disrupts and adds its stars and GCs to the main galaxy to be $\sim~2$ Gyr."
" We have found radially-decreasing profiles of rotation and metallicity in the GC system of NGC 3115, and compared these to theoretical expectations."," We have found radially-decreasing profiles of rotation and metallicity in the GC system of NGC 3115, and compared these to theoretical expectations."
" While the central regions were probably formed in violent, dissipative circumstances such as a gas-rich major merger, this event should have produced high or misaligned outer rotation."," While the central regions were probably formed in violent, dissipative circumstances such as a gas-rich major merger, this event should have produced high or misaligned outer rotation."
" A more likely scenario for explaining the assembly of the outer bulge and halo is via dry minor mergers and accretion events, whose mass-ratios we have tentatively quantified via the GC metallicities."," A more likely scenario for explaining the assembly of the outer bulge and halo is via dry minor mergers and accretion events, whose mass-ratios we have tentatively quantified via the GC metallicities."
" Other assembly processes that may contribute to spheroid formation, such as monolithic collapse or quasar-induced expansion (ο. et_al008), have not been considered here andPan merit future study."," Other assembly processes that may contribute to spheroid formation, such as monolithic collapse or quasar-induced expansion (e.g., \citealt{2008ApJ...689L.101F}) ), have not been considered here and merit future study."
 Cosmological simulations exploring two-phase assembly predict that up to 80 percent of the stellar mass present in today’s early-type galaxies has been accreted fet_al2010)..., Cosmological simulations exploring two-phase assembly predict that up to 80 percent of the stellar mass present in today's early-type galaxies has been accreted \citep{2010ApJ...725.2312O}.
" Consequently, kinematical and chemical transitions such as those observed here should be ubiquitous."," Consequently, kinematical and chemical transitions such as those observed here should be ubiquitous."
" We thank Andi Burkert, Avishai Dekel, Loren Hoffman, Chris Moody, and Joel Primack for useful discussions, the referee Igor Chilingarian for helpful comments and suggestions, and Ewan O'Sullivan for contributing observing time."," We thank Andi Burkert, Avishai Dekel, Loren Hoffman, Chris Moody, and Joel Primack for useful discussions, the referee Igor Chilingarian for helpful comments and suggestions, and Ewan O'Sullivan for contributing observing time."
" Based in part on data collected at Subaru Telescope (operated by the National Astronomical Observatory of Japan), via a Gemini Observatory time exchange "," Based in part on data collected at Subaru Telescope (operated by the National Astronomical Observatory of Japan), via a Gemini Observatory time exchange (GN-2008A-C-12)."
"Some of the data presented herein(GN-2008A-C-12). were obtained at the W. M. Keck Observatory, operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration, and made possible by the generous financial support of the W. M. Keck Foundation."," Some of the data presented herein were obtained at the W. M. Keck Observatory, operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration, and made possible by the generous financial support of the W. M. Keck Foundation."
" This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile."," This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile."
" This material is based upon work supported by the National Science Foundation under Grants AST-0808099 and AST-0909237 and a Graduate Research Fellowship, and also by the UCSC University Affiliated Research Center's Aligned Research Program."," This material is based upon work supported by the National Science Foundation under Grants AST-0808099 and AST-0909237 and a Graduate Research Fellowship, and also by the UCSC University Affiliated Research Center's Aligned Research Program."
 AJR was further supported by the FONDAP Center for Astrophysics CONICYT 15010003., AJR was further supported by the FONDAP Center for Astrophysics CONICYT 15010003.
 AJB acknowledges the support of the Gordon and Betty Moore Foundation., AJB acknowledges the support of the Gordon and Betty Moore Foundation.
" We acknowledge financial support from the Programme,a component of the established under the Australian Government's innovation statement, Ability."," We acknowledge financial support from the a component of the established under the Australian Government's innovation statement, ."
"Following Cen anc Ostriker (1992). we assume that star formation is inevitable if a region is contracting (V«6«0). cooling rapidlv (to,<ea and. uuTuin). and is overdense (p2 pou).","Following Cen and Ostriker (1992), we assume that star formation is inevitable if a region is contracting $\nabla \cdot v < 0$ ), cooling rapidly $\mathrm t_{\mathrm {cool}} < \mathrm t_{\mathrm {dyn}}$ and $T_{\mathrm {gas}} \leq T_{\mathrm {min}}$ ), and is overdense $\rho > \rho_{\mathrm {crit}}$ )."
 Since we check the grid on a cell by cell basis to see i£ these conditions are met. cach timescale is computed. for cach eric cell.," Since we check the grid on a cell by cell basis to see if these conditions are met, each timescale is computed for each grid cell."
 Here £4 is the dynamical collapse timescale. Le. fuga=/οo) where pia is the sum of the gas density. p. οand the/O2AC stellar density.," Here $t_{\mathrm {dyn}}$ is the dynamical collapse timescale, i.e. $t_{\mathrm {dyn}} = \sqrt{3.0 \pi/(32 G
\rho_{\mathrm{tot}})}$ where $\rho_{\mathrm{tot}}$ is the sum of the gas density, $\rho$, and the stellar density."
" fou is the cooling timescale. Le. foo,=kn. where n is the eas particle number density."," $\;t_{\mathrm {cool}}$ is the cooling timescale, i.e. $t_{\mathrm {cool}} = \mathrm{k T / n} \Lambda$, where $n$ is the gas particle number density."
" Tai, is the minimum of our cooling curve. 310 Ix. and pog for the dilferent simulations is specified in table 1.."," ${\mathrm {T}}_{\mathrm {min}}$ is the minimum of our cooling curve, 310 K, and $\rho_{\mathrm {crit}}$ for the different simulations is specified in table \ref{sims}."
" fall our star forming criteria are met within a grid. cell then we convert the following amount of eas. Amun,=¢havaAPooAe? into a star particle”. where ο is a star. formation elliciencev WHOSC value Is given ih tablerefsims. ancl A? is the updating timestep."," If all our star forming criteria are met within a grid cell then we convert the following amount of gas, $\Delta m_{\mathrm {gas}} = \epsilon \frac{\Delta t}{t_{\mathrm{dyn}}} 
 \rho_{\mathrm{gas}} \Delta x^3$ into a “star particle”, where $\epsilon$ is a star formation efficiency whose value is given in table, and $\Delta t$ is the updating timestep."
 We only allow at maximum of the eas in a cell to be converted to stars in one timestep., We only allow at maximum of the gas in a cell to be converted to stars in one timestep.
 In practice however. once supernovae inject hot gas into the medium. the updating timestep is short as it is set by the hot. low density gas.," In practice however, once supernovae inject hot gas into the medium, the updating timestep is short as it is set by the hot, low density gas."
 As a resul AMOday. ancl this threshold. is never reached.," As a result $\Delta t < t_{\mathrm{dyn}}$, and this threshold is never reached."
 We eive the new star particle the same velocity as the gas ou ol which it formed and we follow the stars dynamically., We give the new star particle the same velocity as the gas out of which it formed and we follow the stars dynamically.
" The star particle is labeled with its mass. m,. its formation time. fep. and the dynamical time. faga. of the gas out of which i formect."," The star particle is labeled with its mass, $m_{\star}$, its formation time, $t_{\mathrm{SF}}$, and the dynamical time, $t_{\mathrm{dyn}}$, of the gas out of which it formed."
 For the purposes of the feedback however. rather than assume that the “star particle” formed. instantaneously a lap. we spread the star formation over several civnanmica times by computing the amount of eas mass that would form. stars after time fap to be: where 7= max(/as.10.Myr).," For the purposes of the feedback however, rather than assume that the “star particle” formed instantaneously at $t_{\mathrm{SF}}$, we spread the star formation over several dynamical times by computing the amount of gas mass that would form stars after time $t_{\mathrm{SF}}$ to be: where $\tau = \mathrm{max}(t_{\mathrm{dyn}},10 \;{\mathrm {Myr}})$."
 With. this. time-dependent star formation rate. stars. form at. an exponentially decreasing. rate after a dynamical time.," With this time-dependent star formation rate, stars form at an exponentially decreasing rate after a dynamical time."
 If the dynamical timescale of the eas in a star-forming cell is shorter than the tvpical lifespan of a massive star. i.c. 10 Alvr. then 10 Myr is used in place of fay in equation 1. for the value of z.," If the dynamical timescale of the gas in a star-forming cell is shorter than the typical lifespan of a massive star, i.e. 10 Myr, then 10 Myr is used in place of $t_{\mathrm{dyn}}$ in equation \ref{expsfr} for the value of $\tau$."
 Then. as a crude model of a stellar wind. we return. of Ama. to the eas. and since this returned mass has the velocity of the πρίας particle” we alter the momentum of the gas appropriately.," Then, as a crude model of a stellar wind, we return of $\Delta \mathrm{m}_{\mathrm{stars}}$ to the gas, and since this returned mass has the velocity of the “star particle” we alter the momentum of the gas appropriately."
 Finally assuming only he oecurence of ‘Type LL supernovae. we add of the rest-mass energv of Ania. to the gas’ thermal energy (Ostriker Cowie 1981).," Finally assuming only the occurence of Type II supernovae, we add $^{-5}$ of the rest-mass energy of $\Delta \mathrm{m}_{\mathrm{stars}}$ to the gas' thermal energy (Ostriker Cowie 1981)."
 The supernovae input is. acleled ocallv into one cell., The supernovae input is added locally into one cell.
 We explore. the limitations of our supernovae implementation in future work., We explore the limitations of our supernovae implementation in future work.
 As we do not ave the resolution to follow every individual star ancl to herefore sample a realistic Initial Mass Function (ME) for hem. each star particle is more like a small star cluster with a tvpical mass in the range ~120.220M...," As we do not have the resolution to follow every individual star and to therefore sample a realistic Initial Mass Function (IMF) for them, each star particle is more like a small star cluster with a typical mass in the range $\sim 120 - 220 {\mathrm M_{\odot}}$."
 Table 1 presents the simulations we ran. listing the values of the parameters for star formation ancl feedback.," Table \ref{sims} presents the simulations we ran, listing the values of the parameters for star formation and feedback."
 Although we performed several simulations with a density threshold for star formation. pori. set to 1 em? (runs 135. €5 and CG). for the remainder of the paper we focus only on the runs with poi = 10 atom/cnm?.," Although we performed several simulations with a density threshold for star formation, $\rho_{\mathrm {crit}}$, set to 1 $^{3}$ (runs B5, C5 and C6), for the remainder of the paper we focus only on the runs with $\rho_{\mathrm {crit}}$ = 10 $^{3}$."
 This is because we found that dropping the density threshold by one order of magnitude to 1 atom/em did not change the SER. by a factor ten. but merely by about at the peak of star formation.," This is because we found that dropping the density threshold by one order of magnitude to 1 $^{3}$ did not change the SFR by a factor ten, but merely by about at the peak of star formation."
 As Table 1. indicates. we also experimented with the value o£ c and found that taking a value of c = 0.01 (ten times smaller than our fiducial value) left the conclusions presented in this paper unchanged. ie. the medium became porous and the SER peaked at roughly the same value although with a slight time celay compared to the run with (— 0l.," As Table \ref{sims} indicates, we also experimented with the value of $\epsilon$ and found that taking a value of $\epsilon$ = 0.01 (ten times smaller than our fiducial value) left the conclusions presented in this paper unchanged, i.e. the medium became porous and the SFR peaked at roughly the same value although with a slight time delay compared to the run with $\epsilon$ = 0.1."
" We begin by showing the time evolution of one of our simulations. namely D4. which includes. all the physical processes we considered. namely ""turbulent? initial conditions (as defined. in section. 2)). radiative. cooling. sell-gravitv. star formation and feedback."," We begin by showing the time evolution of one of our simulations, namely B4, which includes all the physical processes we considered, namely “turbulent” initial conditions (as defined in section \ref{method}) ), radiative cooling, self-gravity, star formation and feedback."
 In figure 2 we show the gas density. temperature ancl pressure in a 12.8 pc 1.28 kpc 1.28 kpc slice of this run.," In figure \ref{dTp_128} we show the gas density, temperature and pressure in a 12.8 pc $\times$ 1.28 kpc $\times$ 1.28 kpc slice of this run."
 Due o the compression caused by turbulence and. self-gravity. he σας in certain regions. satisfies our criteria [or star ormation.," Due to the compression caused by turbulence and self-gravity, the gas in certain regions, satisfies our criteria for star formation."
 Following their formation. this first. generation of stars soon explodes as supernovae. releasing hot gas into the interstellar medium.," Following their formation, this first generation of stars soon explodes as supernovae, releasing hot gas into the interstellar medium."
 Lhe morphologies of the 100 bubbles are extremely. non-spherical due to the [aet hat the supernovae are releasing their thermal energy into a spatially inhomogeneous ancl non-stationary meciunm., The morphologies of the hot bubbles are extremely non-spherical due to the fact that the supernovae are releasing their thermal energy into a spatially inhomogeneous and non-stationary medium.
 Because this hot. low density gas has a long cooling time ancl because the star formation rate is sulliciently high. subsequent generations of supernovac bubbles overlap. filling more and. more of the volume.," Because this hot, low density gas has a long cooling time and because the star formation rate is sufficiently high, subsequent generations of supernovae bubbles overlap, filling more and more of the volume."
 Ultimately the density and temperature span more than six orders of magnitude in such a simulation ancl are anti-correlated: high density. regions are cold. and low cdensitv regions are hot.," Ultimately the density and temperature span more than six orders of magnitude in such a simulation and are anti-correlated: high density regions are cold, and low density regions are hot."
 As the third column in figure 2 shows. this anti-correlation results in near oessure equilibrium: between these two phases of the gas.," As the third column in figure \ref{dTp_128} shows, this anti-correlation results in near pressure equilibrium between these two phases of the gas."
 evertheless the dense gas is about one order of magnitude ower in pressure than the low density gas indicating that a thermal instability is active., Nevertheless the dense gas is about one order of magnitude lower in pressure than the low density gas indicating that a thermal instability is active.
 Other regions which are out of pressure equilibrium by 1 2 orders of magnitude are hose which have just experienced thermal energy input from. supernovae., Other regions which are out of pressure equilibrium by 1 – 2 orders of magnitude are those which have just experienced thermal energy input from supernovae.
 Self-eravitating gas would also appear out of »essure equilibrium. something we see in later stages of the simulation.," Self-gravitating gas would also appear out of pressure equilibrium, something we see in later stages of the simulation."
 The dynamical state of the stars and of the gas in different) temperature regimes in the simulation is summarized by a plot of the average velocity dispersions (fie. 3))., The dynamical state of the stars and of the gas in different temperature regimes in the simulation is summarized by a plot of the average velocity dispersions (fig. \ref{sigma}) ).
 Guided by some of the features in the cooling curve (see figure 1)). we divide the temperature into the following four categories: (1) P< 2000 Ix. (11) 2000 Ix. & T < 10 Kk. ΕΠ IN & Pet105 I. CV) μυ compute the average velocity dispersion of the gas in cach of these 4 regimes. and in addition. we caleulate the masseweighted velocity dispersion of the gas. as well as the mass-weightec velocity dispersion of the stars.," Guided by some of the features in the cooling curve (see figure \ref{cool_function}) ), we divide the temperature into the following four categories: (I) T $<$ 2000 K, (II) 2000 K $<$ T $<$ $10^5$ K, $10^5$ K $<$ T $<$ $4 \times 10^6$ K, (IV) $4 \times 10^6$ K $<$ T. We compute the average velocity dispersion of the gas in each of these 4 regimes, and in addition, we calculate the mass-weighted velocity dispersion of the gas, as well as the mass-weighted velocity dispersion of the stars."
 As the stars are assigned the velocity of their progenitor gas at formation. their velocity dispersion closely follows the velocity dispersion of the cold gas.," As the stars are assigned the velocity of their progenitor gas at formation, their velocity dispersion closely follows the velocity dispersion of the cold gas."
 Furthermore. we find that with the exception of the hottest. phase (IV). the velocity. dispersion of the other," Furthermore, we find that with the exception of the hottest phase (IV), the velocity dispersion of the other"
and the error on Qy is uncorrelated with the svstematic οος On pr'(h).,and the error on $Q_T$ is uncorrelated with the systematic error on $P_L^{\rm fct}(k)$.
 With the mean optical depth the storv is. more complicated. because there is πο sullicienthy accurate measurement of it.," With the mean optical depth the story is more complicated, because there is no sufficiently accurate measurement of it."
 The PRS data give Q-pps=1.00OLDOLOST while the ALCD cata give νου=1.150.07.," The PRS data give $Q_{\tau,\rm PRS} = 1.00^{+0.11}_{-0.08}$, while the MCD data give $Q_{\tau,\rm MCD} = 1.18\pm0.07$."
 Combining the two values in quadrature (because the data sets they used. are independent). we find Aud for the most conservative estimate. we can include the whole range of quoted numbers: Measurements of [lux power sample power not at a single wavenumber. but rather over a finite band of wavenumbers.," Combining the two values in quadrature (because the data sets they used are independent), we find And for the most conservative estimate, we can include the whole range of quoted numbers: Measurements of flux power sample power not at a single wavenumber, but rather over a finite band of wavenumbers."
" The band power windows b(&.4) in equation (4)) can be extracted by dilferentiating the Hux power spectrum r(À) with respect to the linear power spectrum £7,(4)."," The band power windows $b(k,k^\prime)^2$ in equation \ref{pfll}) ) can be extracted by differentiating the flux power spectrum $P_F(k)$ with respect to the linear power spectrum $P_L(k)$."
 The shape of the band-powers emerges most clearly if they. are scaled with the fiducial powers. so we celine scaled. band-power windows by," The shape of the band-powers emerges most clearly if they are scaled with the fiducial powers, so we define scaled band-power windows by"
A polarimeter sensitive to linear polarization 1s composed of a HWP. rotating at frequency fp. followed by a stationary pollarrizzer.,"A polarimeter sensitive to linear polarization is composed of a HWP, rotating at frequency $f_0$, followed by a stationary zer."
 Monochromatic linearly polarized light. passing through the waveplate. emerges still linearly polarized. but with its polarization vector revolving at 4/5.," Monochromatic linearly polarized light, passing through the waveplate, emerges still linearly polarized, but with its polarization vector revolving at $f_0$."
 Unpolarized radiation is unaffected by the waveplate., Unpolarized radiation is unaffected by the waveplate.
 If we place a polarizer between the waveplate and the detector. only the polarized component of the incoming radiation is modulated by the rotation of the waveplate.," If we place a polarizer between the waveplate and the detector, only the polarized component of the incoming radiation is modulated by the rotation of the waveplate."
 The amplitude of modulation depends on the polarization of the radiation: it is maximum (null) for radiation totally (not) polarized., The amplitude of modulation depends on the polarization of the radiation: it is maximum (null) for radiation totally (not) polarized.
 The signal of interest 1s encoded at fo. far from the spectral region where |/f noise is important.," The signal of interest is encoded at $f_0$, far from the spectral region where $/f$ noise is important."
 Any spurious signal or systematic effect. at a frequency different from fo. is easily removable.," Any spurious signal or systematic effect, at a frequency different from $f_0$, is easily removable."
 The rotating HWP polarimeter offers a substantial advantage with respect to a PSB: a single detector measures both the Stokes parameters of the linear polarization. so that the result is not affected by drift. of uncertainties in the relative calibration of the different detectors of a PSB.," The rotating HWP polarimeter offers a substantial advantage with respect to a PSB: a single detector measures both the Stokes parameters of the linear polarization, so that the result is not affected by drift of uncertainties in the relative calibration of the different detectors of a PSB."
 In some cases it ts preferable to rotate the HWP in discrete steps., In some cases it is preferable to rotate the HWP in discrete steps.
 Our system follows this strategy., Our system follows this strategy.
" The power detected. for a HWP revolved through 7 discrete steps. is (Collett 1993)): where R isthe instrument responsivity. A@ is the step size. and S, are the Stokes parameters for the incoming radiation."," The power detected, for a HWP revolved through $n$ discrete steps, is (Collett \cite{Collett93}) ): where $R$ isthe instrument responsivity, $\Delta \theta$ is the step size, and $S_k$ are the Stokes parameters for the incoming radiation."
" Eq.(1)) is a truncated. Fourier. series from which we can recover. given the total number of steps N. the components S, (k= 0.2) of the Stokes vector. as: The drawback of the diserete rotation is enhanced sensitivity to / f-noise. since the polarized signal is modulated at a frequency of the order of 7,=1/7 where T is the time required to cover the V steps: given the small value of f,. the noise will be dominated by instrumental and atmospheric drifts."," $\,$ \ref{e1}) ) is a truncated Fourier series from which we can recover, given the total number of steps $N$, the components $S_k$ $k=0,2$ ) of the Stokes vector, as: The drawback of the discrete rotation is enhanced sensitivity to $/f$ -noise, since the polarized signal is modulated at a frequency of the order of $f_p=1/T$ where $T$ is the time required to cover the $N$ steps; given the small value of $f_p$, the noise will be dominated by instrumental and atmospheric drifts."
 From (1)) and (2)) we can set upper limits for the error in the polarization degree. I1.—($i4FEM/Sgs. and for the error in the orientation angle. w=larctan(55/54). due to inaccuracies im the position angles of the waveplate.," From $\,$ \ref{e1}) ) and \ref{e2}) ) we can set upper limits for the error in the polarization degree, $\Pi=({S_1^2+S_2^2})^{1/2} /
{S_0}$, and for the error in the orientation angle, $\psi=\frac{1}{2}\arctan{(S_2/S_1)}$, due to inaccuracies in the position angles of the waveplate."
 We find where oy is the uncertainty in the position angle 8 of the waveplate., We find where $\sigma_{\theta}$ is the uncertainty in the position angle $\theta$ of the waveplate.
 To estimate the position accuracy required in a practical case. we model interstellar dust emission as linearly polarized radiation with a typical polarization degree Il.~5% and a typical specific brightness of about 6-107 W/m/sr/Hz.," To estimate the position accuracy required in a practical case, we model interstellar dust emission as linearly polarized radiation with a typical polarization degree $\Pi\sim5\%$ and a typical specific brightness of about $\cdot10^{-16}$ $^2$ /sr/Hz."
" Assuming c;«l. and using (3)) (re. neglecting other sources of error) with N=8. we find an error in. the polarization degree cj,xO4A% (for any direction of the polarization. vector). and an error in. the orientation. of the polarization vector c,x2°."," Assuming $\sigma_{\theta}<1^{\circ}$, and using $\,$ \ref{e3}) ) (i.e. neglecting other sources of error) with $N=8$, we find an error in the polarization degree $\sigma_\Pi \lesssim 0.4\%$ (for any direction of the polarization vector), and an error in the orientation of the polarization vector $\sigma_\psi \lesssim
2^{\circ}$."
 In Fig.2. we plot the upper limits for the two errors. versus the values of the two Stokes parameters of linear polarization.," In $\,$ \ref{fig:1} we plot the upper limits for the two errors, versus the values of the two Stokes parameters of linear polarization."
 Increasing the error in the HWP position doesn't change the shape of the contour levels. given the linear dependence of the upper limits on this angle (see (3))).," Increasing the error in the HWP position doesn't change the shape of the contour levels, given the linear dependence of the upper limits on this angle (see $\,$ \ref{e3}) ))."
 Detector noise ts an additional contribution to the error in the polarization degree and in the orientation of the polarization vector., Detector noise is an additional contribution to the error in the polarization degree and in the orientation of the polarization vector.
" This is quantified by the Noise Equivalent Power (NEP) and by the integration time for each observed pixel (7): we have σι,=NEP/ VT(s). so that: The specs for the PILOT experiment give a NEP of about 3-107 'W/VHz for the GHz band."," This is quantified by the Noise Equivalent Power (NEP) and by the integration time for each observed pixel $T$ ): we have $\sigma_{det}=$ $/\sqrt{T(s)}$, so that: The specs for the PILOT experiment give a NEP of about $\cdot10^{-16}$ $\sqrt{Hz}$ for the $\,$ GHz band."
 In 3 we plot the upper limits on the polarization degree and on the orientation angle in this case. as a function of the two Stokes parameters of linear polarization. taking into account detector noise and integration time as specified above.," In $\,$ \ref{fig:2} we plot the upper limits on the polarization degree and on the orientation angle in this case, as a function of the two Stokes parameters of linear polarization, taking into account detector noise and integration time as specified above."
 For a given degree of polarization. the measurement errors can be dominated either by detector noise or by positioning errors.," For a given degree of polarization, the measurement errors can be dominated either by detector noise or by positioning errors."
 We define the function: When g«I the errors on the polarization. degree and the orientation angles are domminnatted by detector noise. and can be reduced increasing the integration time.," We define the function: When $g<1$ the errors on the polarization degree and the orientation angles are ted by detector noise, and can be reduced increasing the integration time."
 In the conditions described above for PILOT. this happens for cx0.17. as is evviddent from 3..," In the conditions described above for PILOT, this happens for $\sigma_{\theta}\lesssim0.1^{\circ}$, as is dent from $\,$ \ref{fig:2}."
 If this positioning accuracy is achieved. one can fully exploit the sensitivity of the detectors 4)).," If this positioning accuracy is achieved, one can fully exploit the sensitivity of the detectors $\,$ \ref{fig:3}) )."
 (D) is valid if the HWP acts as an ideal phase-shifter with negligible absorption and emission (ideal waveplate).," $\,$ \ref{e1}) ) is valid if the HWP acts as an ideal phase-shifter with negligible absorption and emission (ideal waveplate)."
 The detected power is in general a sine wave with amplitude A= WoiNP)). and offset O=+xW(nA@).," The detected power is in general a sine wave with amplitude $A=max(W(n \Delta \theta))-min(W(n \Delta \theta))$ , and offset $O=\frac{1}{N}\sum_{n=1}^NW(n \Delta \theta)$."
 Non ideal behavior of the HWP. polarizer. and detector. change the amplitude and the offset of the detected power. and can introduce spurious cos(22A0) and sin(2nA0) components.," Non ideal behavior of the HWP, polarizer, and detector, change the amplitude and the offset of the detected power, and can introduce spurious $\cos(2 n \Delta \theta)$ and $\sin(2 n \Delta \theta)$ components."
 We have studied how these non-idealities depend on the pperratting temperature of the polarimeter's components., We have studied how these non-idealities depend on the ting temperature of the polarimeter's components.
 We define two non-ideality parameters: C4—|-|| and, We define two non-ideality parameters: $C_A=|\frac{A_{real}}{A_{ideal}}-1|$ and
"We observed HD 61005 on February 17, 2010 with the NACO instrument (??) at the VLT.","We observed HD 61005 on February 17, 2010 with the NACO instrument \citep{rousset03,lenzen03} at the VLT."
 The observations were obtained in the framework of the NaCo Large Program Collaboration for Giant Planet Imaging (ESO program 184.C0567)., The observations were obtained in the framework of the NaCo Large Program Collaboration for Giant Planet Imaging (ESO program 184.C0567).
" The images were taken in the H-band (1.65 um) in pupil-tracking mode (?) to allow for angular differential imaging (ADI, ?).."," The images were taken in the $H$ -band (1.65 $\mu$ m) in pupil-tracking mode \citep{kasper09} to allow for angular differential imaging \citep[ADI,][]{marois06}. ."
" The field of view was 14""x and the plate scale mmas/pixel.", The field of view was $14\arcsec\times14\arcsec$ and the plate scale mas/pixel.
" We performed the disk observations without a coronagraph, and used the cube-mode of NACO to take 12 data cubes."," We performed the disk observations without a coronagraph, and used the cube-mode of NACO to take 12 data cubes."
" Each cube consisted of 117 saturated exposures of 1.7927ss, yielding a total integration time of mmin."," Each cube consisted of 117 saturated exposures of s, yielding a total integration time of min."
 The saturation radius was 0115., The saturation radius was $\sim$ 15.
 A total of 112° of field rotation was captured while the pupil remained fixed., A total of $^\circ$ of field rotation was captured while the pupil remained fixed.
 Before and after the saturated observations we took unsaturated images with a neutral density filrer to measure the photometry for the central star., Before and after the saturated observations we took unsaturated images with a neutral density filter to measure the photometry for the central star.
 The adaptive optics system provided a point spread function (PSF) with a full-width at half-maximum (FWHM) of mmas with 0788 natural seeing in H-band Strehl ratio)., The adaptive optics system provided a point spread function (PSF) with a full-width at half-maximum (FWHM) of mas with $\sim$ 8 natural seeing in $H$ -band Strehl ratio).
" The data were flat-fielded, bad-pixel corrected, and centered on the star by manually determining the center for the middle frame and aligning the others through cross-correlation."," The data were flat-fielded, bad-pixel corrected, and centered on the star by manually determining the center for the middle frame and aligning the others through cross-correlation."
 We removed 3 bad-quality frames and averaged the remaining images in groups of three for a total of 467 frames., We removed 3 bad-quality frames and averaged the remaining images in groups of three for a total of 467 frames.
" We then used LOCI (locallyoptimizedcombinationofimages,?) and customized ADI to subtract the stellar PSF to search for point sources and extended non-circular structures."," We then used LOCI \citep[locally optimized combination of images,][]{lafreniere07} and customized ADI to subtract the stellar PSF to search for point sources and extended non-circular structures."
" In ADI, each image is divided into annuli of 2 FWHM width."," In ADI, each image is divided into annuli of 2 FWHM width."
" For each frame and each annulus, a frame where the field object has rotated by 2 FWHM is subtracted to remove the stellar halo."," For each frame and each annulus, a frame where the field object has rotated by 2 FWHM is subtracted to remove the stellar halo."
" Additionally, the resulting image is subtracted by a back-rotated version of itself."," Additionally, the resulting image is subtracted by a back-rotated version of itself."
" Finally, all images are derotated and median combined."," Finally, all images are derotated and median combined."
" In LOCI, each annulus is further divided into segments, and for each segment an optimized PSF is constructed from a linear combination of sufficiently rotated frames."," In LOCI, each annulus is further divided into segments, and for each segment an optimized PSF is constructed from a linear combination of sufficiently rotated frames."
 A minimum rotation of FFWHM is optimal for point source detection and has led to several detections around other targets (???)..," A minimum rotation of FWHM is optimal for point source detection and has led to several detections around other targets \citep{marois08,thalmann09,lafreniere10}."
" To reveal the extended nebulosity around LkCa 15, ? used a much larger minimum separation of 3FFWHM."," To reveal the extended nebulosity around LkCa 15, \citet{thalmann10} used a much larger minimum separation of FWHM."
" For the nearly edge-on and therefore very narrow debris disk around HD 61005, we obtain an optimal result for a minimum separation of FFWHM, but using large optimization areas of 10000 PSF footprints to lessen the self-subtraction of the disk."," For the nearly edge-on and therefore very narrow debris disk around HD 61005, we obtain an optimal result for a minimum separation of FWHM, but using large optimization areas of 10000 PSF footprints to lessen the self-subtraction of the disk."
 We also reduced the data with LOCI with a separation criterion of FFWHM and small optimization segments of 300 PSF footprints to set hard detection limits on companions., We also reduced the data with LOCI with a separation criterion of FWHM and small optimization segments of 300 PSF footprints to set hard detection limits on companions.
" Additionally we attempted a classical PSF subtraction using a reference star, which is detailed in Appendix Appendix AL."," Additionally we attempted a classical PSF subtraction using a reference star, which is detailed in Appendix \ref{sec:psf}. ."
 The NACO H-band images obtained by reduction with LOCI and ADI are shown in Fig. 1.., The NACO $H$ -band images obtained by reduction with LOCI and ADI are shown in Fig. \ref{fig:reduc}.
" The circumstellar material is resolved to an off-centered, nearly edge-on debris ring with a clear inner gap and two narrow streamers originating at the NE and SW edges of the ring."," The circumstellar material is resolved to an off-centered, nearly edge-on debris ring with a clear inner gap and two narrow streamers originating at the NE and SW edges of the ring."
 A strong brightness asymmetry is seen between the NE and SW side and between the lower and upper arc of the ring., A strong brightness asymmetry is seen between the NE and SW side and between the lower and upper arc of the ring.
" The inner gap has not been previously resolved by HST, where only the direction of the polarization vectors hinted at a disk-like component separate from the extended material that interacts with the ISM."," The inner gap has not been previously resolved by HST, where only the direction of the polarization vectors hinted at a disk-like component separate from the extended material that interacts with the ISM."
 LOCI provides the cleanest view of the ring geometry with respect to the background because it effectively removes the stellar PSF while bringing out sharp brightness gradients., LOCI provides the cleanest view of the ring geometry with respect to the background because it effectively removes the stellar PSF while bringing out sharp brightness gradients.
 The negative areas near the ring result from oversubtraction of the rotated disk signal embedded in the subtracted PSF constructed by LOCI., The negative areas near the ring result from oversubtraction of the rotated disk signal embedded in the subtracted PSF constructed by LOCI.
" In particular, the ring’s inner hole is enhanced."," In particular, the ring's inner hole is enhanced."
" However, tests with artificial flat disks showed that while self-subtraction can depress the central regions, the resulting spurious gradients are shallow and different from the steep gradients obtained from the edge of a ring."," However, tests with artificial flat disks showed that while self-subtraction can depress the central regions, the resulting spurious gradients are shallow and different from the steep gradients obtained from the edge of a ring."
" Because of significant variable flux loss, photometry is unreliable in the LOCI image."," Because of significant variable flux loss, photometry is unreliable in the LOCI image."
" In the ADI reduction, the self-subtraction is deterministic and can be accounted for, while the stellar PSF is subtracted adequately enough to allow photometric measurements."," In the ADI reduction, the self-subtraction is deterministic and can be accounted for, while the stellar PSF is subtracted adequately enough to allow photometric measurements."
 In the image produced by reference PSF subtraction (Fig. A1)), In the image produced by reference PSF subtraction (Fig. \ref{fig:psf}) )
 the stellar PSF is not effectively removed., the stellar PSF is not effectively removed.
" The image is unsuitable for a quantitative analysis, but it confirms the streamers andthe strong brightness asymmetry, and alsosuggests the presence of a gap on the SW side."," The image is unsuitable for a quantitative analysis, but it confirms the streamers andthe strong brightness asymmetry, and alsosuggests the presence of a gap on the SW side."
halfway down the steep sides of the light curve profile (Figure 11). which correspouds to the brightest part of the disk being covered amd uncoverect.,"halfway down the steep sides of the light curve profile (Figure \ref{lightcurve}) ), which corresponds to the brightest part of the disk being covered and uncovered."
 Spectra covering an entire orbit were taken in June 2008 with additional data taken in August 2008 aud January 2009., Spectra covering an entire orbit were taken in June 2008 with additional data taken in August 2008 and January 2009.
 These were obtaited uxing the 2.lin. Hiltuer telescope at the MDNI Observatory using the modular spectrograp rand a SITe 2018? CCD. which gave a resolution of 3.5Α.," These were obtained using the 2.4m Hiltner telescope at the MDM Observatory using the modular spectrograph and a SITe $2048^2$ CCD, which gave a resolution of 3.5."
. Our coverage was from 121()-7520 with vignetting toward the ends., Our coverage was from 4210-7520 with vignetting toward the ends.
 Exposures were typically 300s in good seeing., Exposures were typically 300s in good seeing.
 We performe our waveleneth calibration using couparison lamp spectra taken during twilight anc| shits from the 5577 wight sky liue., We performed our wavelength calibration using comparison lamp spectra taken during twilight and shifts from the 5577 night sky line.
 The average spectrum slows emiESI lines as well as weak but cletectable asorption [rom he secoudary M-cwarl (top line. Figue 2).," The average spectrum shows emission lines as well as weak but detectable absorption from the secondary M-dwarf (top line, Figure 2)."
 The ejilssion features apyear sinele-peakect tlroughot he orbit., The emission features appear single-peaked throughout the orbit.
 To reline the spectral type of the secoidary Curther. we subtracted a ο3d of AM-dwarl spectra (Boeshaar1976). [rom ole average specirtun aud iuspected he results by eve.," To refine the spectral type of the secondary further, we subtracted a grid of M-dwarf spectra \citep{Boeshaar76} from our average spectrum and inspected the results by eye."
 A the best il spectal type. we should be left with only coutLLLtun auc emission features. whie the AM-dwarl contributiou sliould ideally clisapyear.," At the best fit spectral type, we should be left with only continuum and emission features, while the M-dwarf contribution should ideally disappear."
" The best cawellation of the A-dwarf features occu""sS al type 11.51.0 (see Figure 2 )", The best cancellation of the M-dwarf features occurs at type $1.5 \pm 1.0$ (see Figure \ref{avgspec} ).
 By 'ompariug the coiribution from the M-dwarl in SDSSI5L1 to tle empate spectra used in tlie decomposition (will τον apparent iagnitude). we can determie an apparent maguitude for the «onor star of iy:19.0£0.3.," By comparing the contribution from the M-dwarf in SDSS1544 to the template spectra used in the decomposition (with known apparent magnitude), we can determine an apparent magnitude for the donor star of $m_V = 19.0 \pm 0.3$."
 Ixnigee(2006) predicts a specral ype of IX6.6 — earlier than our «etermination., \citet{Knigge06} predicts a spectral type of K6.6 – earlier than our determination.
 O ater spectral tyye cleteriminatiou implies that lie secondary is evolved., Our later spectral type determination implies that the secondary is evolved.
 Hoardeal.(2001) [oun La similar result iu he system CM Phe., \citet{Hoard01} found a similar result in the system CM Phe.
 Altho here was some zunbiguity in their period determillaion. they deter:ined a spectral type of M: rou a spectral deconvolution. wlule the predicte spectral type (Sunih&Dhillon1998) is IxI-," Although there was some ambiguity in their period determination, they determined a spectral type of M2-5 from a spectral deconvolution, while the predicted spectral type \citep{SmithDhillon98} is K4-M1."
 The subject of late προςral types in CV donor stars is also discussed iu BaralIe&Ixolb(2, The subject of late spectral types in CV donor stars is also discussed in \citet{BK00}.
"000).. au orbital period close to 6 hours. their moclels predict possible spect‘al types of Ix1-M2 depei primarily ou q. In. addiion. two stars (NY Ari LL Lyr) presentec Lin ίσος (2006)""s Ta have orbital periods close to 6 hours with spectra type determinations of MO+0.5 aud M2.54 respectively."," For an orbital period close to 6 hours, their models predict possible spectral types of K4-M2 depending primarily on q. In addition, two stars (XY Ari LL Lyr) presented in \citet{Knigge06}' 's Table 2 have orbital periods close to 6 hours with spectral type determinations of $0 \pm 0.5$ and $2.5 \pm 1.5$, respectively."
 Enuission line velocities fron1 Ha were deterined using a convolution method (SclueicerShalter 1983).," Emission line velocities from $\alpha$ were determined using a convolution method \citep{SY1980, Shafter83}."
. In short. this meth¢xl] uses au antisvinnetrie fuuction consistiig of j»ositive and negative CGatissiaus ollset by an adjustable separation. a. which is convolved with he observed line profile.," In short, this method uses an antisymmetric function consisting of positive and negative Gaussians offset by an adjustable separation, $\alpha$, which is convolved with the observed line profile."
 The zero of the convolion is taken as the liue center., The zero of the convolution is taken as the line center.
 We acloped a value of a=2080 kins ! for SDSSI51L, We adopted a value of $\alpha = 2080$ km $^{-1}$ for SDSS1544.
 To dete‘nine this value. we used the method deveoped Nw Shafter(1083) to create a ¢liagnostic diagrau.," To determine this value, we used the method developed by \citet{Shafter83} to create a diagnostic diagram."
 This procedure allowed us to determine the uaxinui separation of the Craussiaus for which the sigual-to-noise ratio was sulficieut to probe he line wines., This procedure allowed us to determine the maximum separation of the Gaussians for which the signal-to-noise ratio was sufficient to probe the line wings.
 Velocities [rou the absorption compouent of the spectrum were determined using the, Velocities from the absorption component of the spectrum were determined using the
"For the polytropic EOS, we have the following natural units, i.e., polytropic units, to normalize the length, mass, and time scales: Because geometrized units with G=c1 are adopted, the polytropic units Rpoly normalize all of the length, mass, and time scales.","For the polytropic EOS, we have the following natural units, i.e., polytropic units, to normalize the length, mass, and time scales: Because geometrized units with $G=c=1$ are adopted, the polytropic units $R_{\rm poly}$ normalize all of the length, mass, and time scales."
" The second EOS is a piecewise polytrope introduced by Readetal.(2009a,b)."," The second EOS is a piecewise polytrope introduced by \citet{rea09a,rea09b}."
". In the present paper, we set the number of polytrope segments to two."," In the present paper, we set the number of polytrope segments to two."
" Then, the EOS is written as where the dividing density po is close to the nuclear density of order ~1014gcm-? (see below)."," Then, the EOS is written as where the dividing density $\rho_0$ is close to the nuclear density of order $\sim 10^{14}~{\rm g~cm^{-3}}$ (see below)."
" The adiabatic index of the crust is set to a fixed value as Το=1.35692895, whereas we choose three values for the adiabatic index of the core, [Ty=2.4, 2.7, and 3.0."," The adiabatic index of the crust is set to a fixed value as $\Gamma_0=1.35692895$, whereas we choose three values for the adiabatic index of the core, $\Gamma_1=2.4$, 2.7, and 3.0."
" The polytropic constant of the crust, Ko, is set to Ko/c)?=3.99873692x1079((gcm-3)!-T*) in cgs units."," The polytropic constant of the crust, $\kappa_0$, is set to $\kappa_0/c^2=3.99873692 \times 10^{-8}
~(({\rm g~cm^{-3}})^{1-\Gamma_0})$ in cgs units."
" The polytropic constant of the core, &4, is calculated by requiring the continuity of the pressure at the dividing density po as The dividing density po is calculated by setting the fiducial density, p1, and the pressure at the fiducial density, P,."," The polytropic constant of the core, $\kappa_1$, is calculated by requiring the continuity of the pressure at the dividing density $\rho_0$ as The dividing density $\rho_0$ is calculated by setting the fiducial density, $\rho_1$, and the pressure at the fiducial density, $P_1$."
 We take the fiducial density as logy)p1=14.7 where p is in cgs units., We take the fiducial density as $\log_{10} \rho_1 =14.7$ where $\rho_1$ is in cgs units.
" Because pi is larger than the dividing density po, the EOS has the form of P1=Kip? at the fiducial density."," Because $\rho_1$ is larger than the dividing density $\rho_0$, the EOS has the form of $P_1 =\kappa_1 \rho_1^{\Gamma_1}$ at the fiducial density."
" Using this equation and Equation (55)), the dividing density is obtained as The specific internal energy in the crust and that in the core are, respectively, written as where a; is a constant which is calculated by requiring the continuity of the enthalpy at the dividing density po."," Using this equation and Equation \ref{eq:kappa1}) ), the dividing density is obtained as The specific internal energy in the crust and that in the core are, respectively, written as where $a_1$ is a constant which is calculated by requiring the continuity of the enthalpy at the dividing density $\rho_0$."
" We summarize the adiabatic index of the core I, the logarithm of the pressure at the fiducial density log,)Pi, the dividing density po, and the constant a; in Table 1;; we employ nine parameter sets in the present work."," We summarize the adiabatic index of the core $\Gamma_1$, the logarithm of the pressure at the fiducial density $\log_{10} P_1$, the dividing density $\rho_0$, and the constant $a_1$ in Table \ref{table1}; we employ nine parameter sets in the present work."
 Figure 1 plots the mass-radius relation of spherical stars for the chosen EOSs and indicates that a wide variety of EOSs are modeled.," Figure \ref{fig1}
 plots the mass-radius relation of spherical stars for the chosen EOSs and indicates that a wide variety of EOSs are modeled."
 We use tabulated EOSs for zero-temperature nuclear matter which are derived by using various, We use tabulated EOSs for zero-temperature nuclear matter which are derived by using various
Cousidering the imumeciate Solar Neighibourhood. our distauce estimates place 11 of the 150 stars within 10 parsecs of the Sui.,"Considering the immediate Solar Neighbourhood, our distance estimates place 14 of the 180 stars within 10 parsecs of the Sun."
 Those systems include CI 581. 190. 357. 382. 628. CJ 1065 aud LHS 173]. all of which have trigouomeric parallaxes which exceed 0.1 arcseconds.," Those systems include Gl 84, 190, 357, 382, 628, GJ 1065 and LHS 1731, all of which have trigonometric parallaxes which exceed 0.1 arcseconds."
 Four other stars are listed iu the pCNS3: C12510.2 aud LHS 2520. 1723 and 2836.," Four other stars are listed in the pCNS3: Gl 540.2 and LHS 2520, 1723 and 2836."
 The three uew identifications are LP 993-]16 (My=13.15). LHS 6167 ESI1.63) aud C 161-71 (My=1-76).," The three new identifications are LP 993-116 $_V = 13.45$ ), LHS 6167 $_V = 14.63$ ) and G 161-71 $_V = 14.76$ )."
 All three systems have fornal distance estimates betwee16 and 7 parsecs., All three systems have formal distance estimates between 6 and 7 parsecs.
 As noted above. LP 993-116 is identified iu the NLTT as a comiuou proper motiOL COLipauion. separation Ll aresecouds. of CD -1:836. au Νίο dwaX," As noted above, LP 993-116 is identified in the NLTT as a common proper motion companion, separation 44 arcseconds, of CD -44:836, an M5 dwarf."
 The latter star is in our sauple. auc we derive au estimated distance of 10.5 parsecs.," The latter star is in our sample, and we derive an estimated distance of 10.5 parsecs."
 Civen the incdivicual uncertalulies. the agree:vent is reasonable.," Given the individual uncertainties, the agreement is reasonable."
 Theye are crreutly app'oximately 250 systems known with 10 parseces of the Sun., There are currently approximately 250 systems known with 10 parsecs of the Sun.
 Thus. the 5 uew kentificatious listed i this paper ane Paper I reoreseut. ani increase of ouly ~2CYve in the inferred local stelar space derity.," Thus, the 5 new identifications listed in this paper and Paper I represent an increase of only $\sim2\%$ in the inferred local stellar space density."
 However. tlese aclditiols are drawn [rol1 a relatively well-stucliec subset of ou: NLTT candidaes.," However, these additions are drawn from a relatively well-studied subset of our NLTT candidates."
 Combined with the literature data discissed in Paper L. we have optical photomet'v. aud pliotolmetric parallaxes. for 619 0‘the 1215 stars in NLTT Sample 1. while a further 39 iltracool dwarls rave distance estinmates basec Lon eitlier optical spectroscopy or (J-Ix.4) colours.," Combined with the literature data discussed in Paper I, we have optical photometry, and photometric parallaxes, for 649 of the 1245 stars in NLTT Sample 1, while a further 39 ultracool dwarfs have distance estimates based on either optical spectroscopy or $_S$ ) colours."
 Four huidred aud fity-six of those sars are ideitified as poteutlally within 20 parsecs of the 5ui, Four hundred and fifty-six of those stars are identified as potentially within 20 parsecs of the Sun.
 Su»equent papers in this se‘Tes wlll provide distance estimates for the remaining 596 Slars in NLTT Sample 1. as well as exteudiug coverage to include NLTT «warts which lack 2MLASS couuterparts within 10 aresecouds o “tle nominal position.," Subsequent papers in this series will provide distance estimates for the remaining 596 stars in NLTT Sample 1, as well as extending coverage to include NLTT dwarfs which lack 2MASS counterparts within 10 arcseconds of the nominal position."
 The authors thauk the anony110is referee for a uumber of extremely helpful commen, The authors thank the anonymous referee for a number of extremely helpful comments.
" This NStars research was supported λα‘tially by a grant. awarded. as pa1 of the NASA Spae Interferometry Mission Science Prog""al1. aciministered by the Jet Propulsion Laboratory. Pasacer"," This NStars research was supported partially by a grant awarded as part of the NASA Space Interferometry Mission Science Program, administered by the Jet Propulsion Laboratory, Pasadena."
 ΤΙ1is publication makes use of data |ILO(licts [rom the Two Micron All Sky Survey. which is a joi ILOject of the University of Massachisets and the Infrared Processing aud Ajalysis Center/C'alifo ]ustitute of Technology. funded. by the tional Aerospeace and Space Administration and t Mional Scielce 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 Aerospeace and Space Administration and the National Science Foundation."
 We ackiowledge use of the ASA/IPAC Iifrared: Source Archive (IRSA). whic is operated by the Jet p‘opulsion Laboratory. California Institute of Technology. uxler contrac with the National Ae‘ospeace and Space Administration.," We acknowledge use of the NASA/IPAC Infrared Source Archive (IRSA), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aerospeace and Space Administration."
 We also acknowledge uakine exteusive use of the SIMBAD database. maintained w Strasbourg Observatory. aud of the ADS bibliograghie service.," We also acknowledge making extensive use of the SIMBAD database, maintained by Strasbourg Observatory, and of the ADS bibliographic service."
 We would like to thank the Time Assignment Comunittee of the South Alrican Astrotoimical Observatory for the allocation of obse‘vine time for this project., We would like to thank the Time Assignment Committee of the South African Astronomical Observatory for the allocation of observing time for this project.
Iu this paper we investigate the ore aud the consequences of the of the stellar winds of carly-type stars near spectral type DI.,In this paper we investigate the origin and the consequences of the of the stellar winds of early-type stars near spectral type B1.
 This bi-stability juup is observed as a steep decrease in the terminal velocity of the winds from οςz2.60. for supergiauts of types earlier than Bl to οςzL6 for supergiauts of types later than DI (Lamers et al., This bi-stability jump is observed as a steep decrease in the terminal velocity of the winds from $\vinf \simeq 2.6 \vesc$ for supergiants of types earlier than B1 to $\vinf \simeq 1.3 \vesc$ for supergiants of types later than B1 (Lamers et al.
 1995)., 1995).
" We will show hat this juup iu the wind velocity is accompanied bby a juup iu the mass-loss rate with AT Increasing w about a factor of five for supergiauts with between 27 500 aud 22 500 K. The theory of radiation driven winds predicts that he mass-loss rates and terminal velocities of the winds of earh-tvpe stars depend smoothly on the stellar marameters., with ος29]Je; and AFxLIS (Castor et al."," We will show that this jump in the wind velocity is accompanied by a jump in the mass-loss rate with $\Mdot$ increasing by about a factor of five for supergiants with between 27 500 and 22 500 K. The theory of radiation driven winds predicts that the mass-loss rates and terminal velocities of the winds of early-type stars depend smoothly on the stellar parameters, with $\vinf \simeq 3 \vesc$ and $\Mdot \propto L^{1.6}$ (Castor et al."
 1975. Abbott 1982. Pauldrach et al.," 1975, Abbott 1982, Pauldrach et al."
 1986. I&udzitzki et al.," 1986, Kudritzki et al."
 1989)., 1989).
" This theory has not vet oen applied to predict the observed jump iu the ratio vx""vous for supergiants near spectra type Bl.", This theory has not yet been applied to predict the observed jump in the ratio $\ratio$ for supergiants near spectral type B1.
 The change roni a fast to a slow wind is called the bi-stability junp., The change from a fast to a slow wind is called the $bi$ $stability$ jump.
 If the wind momentum ἁος were about coustant across the bi-stability jump. it would imply that tle mass-loss rate would steeply+ by about a factor of two from stars with spectral types earlier than DI to later than Bl.," If the wind momentum $\Mdot \vinf$ were about constant across the bi-stability jump, it would imply that the mass-loss rate would steeply by about a factor of two from stars with spectral types earlier than B1 to later than B1."
 Unfortunately. there are no reliable mass-loss determiuatious frou observations for stars later than spectral type DI.," Unfortunately, there are no reliable mass-loss determinations from observations for stars later than spectral type B1."
 So far. a physical explanation of the nature of this bistability jump has been lacking.," So far, a physical explanation of the nature of this bi-stability jump has been lacking."
 In this paper. we attenip to provide such an explanation iud we investigate," In this paper, we attempt to provide such an explanation and we investigate"
Alass-loss rates for earlv-tvpe stars are uncertain. and so in addition to using the Geneva models with the standard miass-loss rates (setποof.2) we also tried the higher mass-loss rate. set. 767.,"Mass-loss rates for early-type stars are uncertain, and so in addition to using the Geneva models with the standard mass-loss rates \citep[set ``c''of ][]{1994A&A...287..803M} we also tried the higher mass-loss rate, set “e”."
 Comparison of the resulting isochrones for the masses and ages we are interested in shows cdilferences in colour which ave too small to allect our results., Comparison of the resulting isochrones for the masses and ages we are interested in shows differences in colour which are too small to affect our results.
 Finally. we have tested the effect. of using dilferent AIS moclels.," Finally, we have tested the effect of using different MS models."
 As an alternative to the Geneva models with the ? conversions to colour and magnitude we usec the conversions presented with the tsochrones in 7.., As an alternative to the Geneva models with the \cite{1998A&A...333..231B} conversions to colour and magnitude we used the conversions presented with the isochrones in \cite{2001A&A...366..538L}.
 We obtained ages somewhat older than those from the Ceneva-Besscll models. exacerbating the age cillerence problem.," We obtained ages somewhat older than those from the Geneva-Bessell models, exacerbating the age difference problem."
 More importantly. the values of rtr?) are much worse than those for the Geneva-Bessell models. typically around 0.01. or 0.001. showing that these models can be ruled. out as good descriptions of the data.," More importantly, the values of $\Pr(\tau^2)$ are much worse than those for the Geneva-Bessell models, typically around 0.01 or 0.001, showing that these models can be ruled out as good descriptions of the data."
 To test whether this is the interior mocels or the atmospheres. we fitted the data to the Padova models (2). but with the same mocel atmospheres (7) as we used for the Geneva-Dessell models.," To test whether this is the interior models or the atmospheres, we fitted the data to the Padova models \citep{2002A&A...391..195G} but with the same model atmospheres \citep{1998A&A...333..231B} as we used for the Geneva-Bessell models."
 We find this gives slightly vounger ages (a [actor 1.5 older than the PAIS ages in the range 1-10Mvr). but very similar values of ντ} to the Geneva-Dessell models.," We find this gives slightly younger ages (a factor 1.5 older than the PMS ages in the range 1-10Myr), but very similar values of $\Pr(\tau^2)$ to the Geneva-Bessell models."
 In. summary. therefore. our fitting gives strong support for the ? conversions. and there is only a weak elfect. [rom the interior models. which can explain some. but not all of. the age discrepancy.," In summary, therefore, our fitting gives strong support for the \cite{1998A&A...333..231B} conversions, and there is only a weak effect from the interior models, which can explain some, but not all of, the age discrepancy."
 The PAIS ages are much less robust than the MS ones., The PMS ages are much less robust than the MS ones.
 We rave adopted the PAIS age scale of ?.., We have adopted the PMS age scale of \cite{2008MNRAS.386..261M}.
 However. as ? and ? make clear. the primary aim of this scale is an age ordering.," However, as \cite{2008MNRAS.386..261M} and \cite{2007MNRAS.375.1220M}
 make clear, the primary aim of this scale is an age ordering."
 The age scale itself is rather arbitrary. though was chosen o match as closely as possible the commonly. quoted. ages or the voung groups.," The age scale itself is rather arbitrary, though was chosen to match as closely as possible the commonly quoted ages for the young groups."
 The problem is that there is no single PMS age seale. a point nicely illustrated in. 2..," The problem is that there is no single PMS age scale, a point nicely illustrated in \cite{2009MNRAS.393..538J}."
 Γον show hat the ΝΟ association could have a PAIS age between 5 and 15Myr depending on which PALS models are. used. and which part of the sequence is considered.," They show that the $\gamma$ Vel association could have a PMS age between 5 and 15Myr depending on which PMS models are used, and which part of the sequence is considered."
 They estimate hat the association is about 7Myr old on the 7. scale. so doubling the ages of these voung associations is consistent with some PAIS models.," They estimate that the association is about 7Myr old on the \cite{2008MNRAS.386..261M} scale, so doubling the ages of these young associations is consistent with some PMS models."
 Our conclusion. therefore. is that he MS age scale is probably the correct one.," Our conclusion, therefore, is that the MS age scale is probably the correct one."
 3elore discussing the implications of a longer timescale. we should. be wary of over interpreting Figure SN...," Before discussing the implications of a longer timescale, we should be wary of over interpreting Figure \ref{ages}."
 Whilst. it clearly shows a discrepancy. between mean PAIS ancl MS ages. the error bars for individual data points are large.," Whilst it clearly shows a discrepancy between mean PMS and MS ages, the error bars for individual data points are large."
 All we can sav with any certainty is that there is a dillerence of approximately a factor two at. PALS ages of 3Myr., All we can say with any certainty is that there is a difference of approximately a factor two at PMS ages of 3Myr.
 By JMyr our data are consistent with the age scales matching. though a cdilference of a factor 1.5 is still. in the statistical sense. likely.," By 30Myr our data are consistent with the age scales matching, though a difference of a factor 1.5 is still, in the statistical sense, likely."
 We therefore limit. ourselves to discussing the implications of a lengthening of the timescales in the 1-l0Mvr PAIS age range., We therefore limit ourselves to discussing the implications of a lengthening of the timescales in the 1-10Myr PMS age range.
 Even here. however. we find there are problems it might solve.," Even here, however, we find there are problems it might solve."
 There is a long-standing issue that the observed timescale for the dissipation of proto-stellar disces.| (3Myr:7) may be shorter than the time required. by the models or planet formation (10Msyr:?).., There is a long-standing issue that the observed timescale for the dissipation of proto-stellar discs \citep[3Myr;][]{2001ApJ...553L.153H} may be shorter than the time required by the models for planet formation \citep[10Myr;][]{1996Icar..124...62P}.
 In recent. vears there has n significant elfort to find mechanisms which will shorten 10 planet forming timescales., In recent years there has been significant effort to find mechanisms which will shorten the planet forming timescales.
 Whilst a case can be made wt this problem has been solved (2).. there is à view that gaignificant problems remain (see.forexample.theintroduc-orysectionsof22)...," Whilst a case can be made that this problem has been solved \citep{2008ASPC..398..235M}, there is a view that significant problems remain \citep[see, for example, the introductory sections of][]
{2009MNRAS.393...49A, 2008ApJ...688L..99D}."
 A [air summary is probably that whilst vere are mechanisms which could shorten the timescale. gsuch as dust settling (2). and planetary migration (?).. the uncertainties in the physics remain such that it is not clear rev clo.," A fair summary is probably that whilst there are mechanisms which could shorten the timescale, such as dust settling \citep{2005Icar..179..415H} and planetary migration \citep{2005ApJ...626L..57A}, the uncertainties in the physics remain such that it is not clear they do."
 Our result olfers an interesting alternative solution., Our result offers an interesting alternative solution.
 If the clusters used to measure the disc dissipation timescale are 50-100 percent older than previously thought. there may »' no contradiction with the ? 7 S. S 1. ," If the clusters used to measure the disc dissipation timescale are 50-100 percent older than previously thought, there may be no contradiction with the \cite{1996Icar..124...62P} \cite{2007MNRAS.376..580J} \ref{ages} \ref{ages} \ref{ages_table} "
distributious of spectral indices are wider for the outer conal οςuponelr which are comparable in width to those of PSR D11323|16.,distributions of spectral indices are wider for the outer conal component which are comparable in width to those of PSR B1133+16.
 This may be also related to the observation of weaker correlations observed for outer conmpoueuts of PSR B0329|51 and could be linked to a line-ofsight further away from he magnetic uceridian., This may be also related to the observation of weaker correlations observed for outer components of PSR B0329+54 and could be linked to a line-of-sight further away from the magnetic meridian.
 The flux censitics below the spectral low-frequency turu-over seen to be still related. to he spectrum and fiux deusities at the higher frequencies., The flux densities below the spectral low-frequency turn-over seem to be still related to the spectrum and flux densities at the higher frequencies.
 The spectral index distributions for the single pulses of PSR D1132]16 show siguificaut deviations from. a Gaussian shape., The spectral index distributions for the single pulses of PSR B1133+16 show significant deviations from a Gaussian shape.
 This asvuunuetry is caused by strong pulses which qualify as eiut pulses according to their mean flux density at L850 MIIz., This asymmetry is caused by strong pulses which qualify as giant pulses according to their mean flux density at 4850 MHz.
 We have shown that most of these pulses are broadband aud occur at a relatively narrow range of phases in the trailing edge of the leading component., We have shown that most of these pulses are broadband and occur at a relatively narrow range of phases in the trailing edge of the leading component.
 All these properties sugeestOO that these pulses may be indeed related to the eiaut-pulse phenomenon. whereas their relative spectral index is such that they only become dominant at the higher frequencies.," All these properties suggest that these pulses may be indeed related to the giant-pulse phenomenon, whereas their relative spectral index is such that they only become dominant at the higher frequencies."
 However. a power-law behaviour iu the energy distributions has not been observed vet aud better statistics is required.," However, a power-law behaviour in the energy distributions has not been observed yet and better statistics is required."
" Παιος, the main conchisions of this paper are: We have demonstrated that the study of the radio spectra of single pulses represents a so-far untapped reservoir of information directly related to the radiating particles and their cussion process."," Hence, the main conclusions of this paper are: We have demonstrated that the study of the radio spectra of single pulses represents a so-far untapped reservoir of information directly related to the radiating particles and their emission process."
 Undoerstaudius their properties Ginclouded by anv averaging process] appears to be esseutial in the identification of the mnderlving CLUISSIOLL process., Understanding their properties (unclouded by any averaging process) appears to be essential in the identification of the underlying emission process.
 We are very grateful to Christine Jordan and Axel Jessner for help with the observations and. data reduction and acknowledge fruitful cliscussions with Graham Smith., We are very grateful to Christine Jordan and Axel Jessner for help with the observations and data reduction and acknowledge fruitful discussions with Graham Smith.
 It is a pleasure to thank the referee Alisha Popov for a, It is a pleasure to thank the referee Misha Popov for a
"Our statistical localization and weighting scheme identified one outstanding candidate for high energy photon emission, GRB 090228A. The best estimate for the probability of such an occurence by chance alone was obtained by performing identical searches on random LAT fields with the same criteria.","Our statistical localization and weighting scheme identified one outstanding candidate for high energy photon emission, GRB 090228A. The best estimate for the probability of such an occurence by chance alone was obtained by performing identical searches on random LAT fields with the same criteria."
" Thus, 11 out of 17200 random fields generated matched filter weights exceeding the value for our candidate event."," Thus, 11 out of 17200 random fields generated matched filter weights exceeding the value for our candidate event."
 Multiplying by a trials factor of 22 for the number of GBM localized fields considered yields a false positive probability of1., Multiplying by a trials factor of 22 for the number of GBM localized fields considered yields a false positive probability of.
"496.. To check that these correlations were simply not due to preferentially higher background rates for the GBM exposures, we also performed similar calculations for the LAT data confined to an average of 8 uncorrelated directions per exposure and five independent time intervals from the same GBM data sets."," To check that these correlations were simply not due to preferentially higher background rates for the GBM exposures, we also performed similar calculations for the LAT data confined to an average of 8 uncorrelated directions per exposure and five independent time intervals from the same GBM data sets."
" In this case, 2 fields out of 910 exceed the candidate signal for a false positive rate of4."," In this case, 2 fields out of 910 exceed the candidate signal for a false positive rate of."
8%.. The cumulative distributions are plotted in Figure 2., The cumulative distributions are plotted in Figure 2.
 The statistical similarity of the GBM off-axis and random field data demonstrates that the GBM data set is not correlated with anomalous environmental conditions such as higher cosmic ray background rates., The statistical similarity of the GBM off-axis and random field data demonstrates that the GBM data set is not correlated with anomalous environmental conditions such as higher cosmic ray background rates.
 A list of photons associated with this burst is provided in Table 2., A list of photons associated with this burst is provided in Table 2.
" The GBM data for GRB 090228A is described in GCN 8918 (von Kienlin, et al.,"," The GBM data for GRB 090228A is described in GCN 8918 (von Kienlin, et al.,"
 2009)., 2009).
" According to this note, the burst was localized to a 1—e accuracy of better than 1? with an additional systematic uncertainty of the order of 2.5?."," According to this note, the burst was localized to a $1-\sigma$ accuracy of better than $1^\circ$ with an additional systematic uncertainty of the order of $2.5^\circ$."
 The coordinate values obtained by the GBM group and this analysis are listed in Table 2., The coordinate values obtained by the GBM group and this analysis are listed in Table 2.
 The GBM value generated some concern since our cluster finder position disagreed by 8.7?., The GBM value generated some concern since our cluster finder position disagreed by $^\circ$.
" Fortuitously as this manuscript was being drafted, a paper was posted to astro-ph et al.,"," Fortuitously as this manuscript was being drafted, a paper was posted to astro-ph (Guiriec et al.,"
 providing a burst direction with an (Guiriecestimated accuracy2010) of 0.2? and lying 0.5? from our own estimate., 2010) providing a burst direction with an estimated accuracy of $0.2^\circ$ and lying $0.5^\circ$ from our own estimate.
 We believe that this establishes the validity of our identification to near certainty., We believe that this establishes the validity of our identification to near certainty.
" In addition, the positive GRB correlation of Event Class 2 and 3 photon rates discussed in A10 was observed for the ensemble of GBM fields as well."," In addition, the positive GRB correlation of Event Class 2 and 3 photon rates discussed in A10 was observed for the ensemble of GBM fields as well."
 T'he photon clustering is easily observed in the sky map shown in Figure 3., The photon clustering is easily observed in the sky map shown in Figure 3.
 'The one event identified in this paper establishes the validity of our statistical techniques to a level of near certainty., The one event identified in this paper establishes the validity of our statistical techniques to a level of near certainty.
" By using GBM triggers to guide the discovery of photon clusters in the LAT, the phase space for finding counterparts can be reduced from hundreds of"," By using GBM triggers to guide the discovery of photon clusters in the LAT, the phase space for finding counterparts can be reduced from hundreds of"
IHE deficiency larger than 0.7.,HI deficiency larger than 0.7.
" In Figs 2a and 2c all Virgo cluster galaxies are assumed to have a distance moculus equal to the average distance modulus of Virgo cluster A (p, 31.02).", In Figs 2a and 2c all Virgo cluster galaxies are assumed to have a distance modulus equal to the average distance modulus of Virgo cluster A $\mu_o$ =31.02).
 Templates shifted hy + 1 mag are also given., Templates shifted by $\pm$ 1 mag are also given.
 The deviations of the individual objects from the template relations can be converted. into distances to the individual galaxies., The deviations of the individual objects from the template relations can be converted into distances to the individual galaxies.
 The clistances to 134 galaxies in the Vireo cluster are Listed in Tab., The distances to 134 galaxies in the Virgo cluster are listed in Tab.
 2a and b. ‘Tab., 2a and b. Tab.
 2a lists the TE parameters of 75 late-type galaxies as Columns 1-3: COCG. NGC. VCC designations.," 2a lists the TF parameters of 75 late-type galaxies as Columns 1-3: CGCG, NGC, VCC designations."
 Column 4: morphological type as given in the VOC., Column 4: morphological type as given in the VCC.
 Column 5: membership according to the VCC (revised by Bingeeli. Popescu and Pammann 1993).," Column 5: membership according to the VCC (revised by Binggeli, Popescu and Tammann 1993)."
 Column 6: LIL deficiency parameter as. defined. by llavnes Giovanclli (1984)., Column 6: HI deficiency parameter as defined by Haynes Giovanelli (1984).
 Column 7: total Ll band magnitude corrected for internal extinction (see Section 3.1)., Column 7: total H band magnitude corrected for internal extinction (see Section 3.1).
 οςumn 8: NIRo observing run: CA96 refers to Boselli et al. (, Column 8: NIR observing run: CA96 refers to Boselli et al. (
1997). CAST are the observations taken in LOOT at Calar Alto (see Section. 3.1). T95 ancl LOG are found in CGavazzi οἱ al. (,"1997), CA97 are the observations taken in 1997 at Calar Alto (see Section 3.1), T95 and T96 are found in Gavazzi et al. ("
1996a),1996a).
 Column 9: heliocentric recessional velocity from. the literature., Column 9: heliocentric recessional velocity from the literature.
" Column LO: adopted. logarithm of the maxinium rotational velocity. corrected. for inclination. as derived from LIL observations (average of and of the peak value) or from CO observations or Z4, rotation curves (see ‘Tab."," Column 10: adopted logarithm of the maximum rotational velocity, corrected for inclination, as derived from HI observations (average of and of the peak value) or from CO observations or $H_{\alpha}$ rotation curves (see Tab."
 1)., 1).
 Column 11: a quality mark given to each LIL profile after individual inspection: 1 are two-horn. high S/N profiles. 2 are one-horn. high S/N profiles. 5 is for one profile which was not published. but was considered of good quality given the high S/N ratio.," Column 11: a quality mark given to each HI profile after individual inspection: 1 are two-horn, high S/N profiles, 2 are one-horn, high S/N profiles, 5 is for one profile which was not published, but was considered of good quality given the high S/N ratio."
 Column 12: galaxy inclination in the plane of the sky (determined following Haynes Giovanelli 1984)., Column 12: galaxy inclination in the plane of the sky (determined following Haynes Giovanelli 1984).
 Column 13: reference to the adopted rotational velocity., Column 13: reference to the adopted rotational velocity.
" Column 14: distance modulus as obtained in this work using the TE Column 15: revised region of membership (see Section 5.3 for A comment is given in Column 16 for the deficient ealaxies whose maximum rotational velocity is derived from CO profiles or Z4, rotation curves (see Tab.", Column 14: distance modulus as obtained in this work using the TF Column 15: revised region of membership (see Section 5.3 for A comment is given in Column 16 for the deficient galaxies whose maximum rotational velocity is derived from CO profiles or $H_{\alpha}$ rotation curves (see Tab.
 Tab., Tab.
 2b lists the FP parameters of 59. earlv-tvpe ealaxies as Columns 1 to 5 contain the same information as Tab., 2b lists the FP parameters of 59 early-type galaxies as Columns 1 to 5 contain the same information as Tab.
 Column 6: heliocentric recessional velocity., Column 6: heliocentric recessional velocity.
 Column 7 central velocity. dispersion with error (given for the OUP measurements only) anc reference., Column 7-9: central velocity dispersion with error (given for the OHP measurements only) and reference.
 Alelzlroy. (1995) (M95). did a compilation of all dispersion measurements available at the time., McElroy (1995) (M95) did a compilation of all dispersion measurements available at the time.
 Not only the values are averages of various sources. but they are also corrected. for aperture according to the prescriptions of Jorgensen. Franx Ixjeergaard (1996).," Not only the values are averages of various sources, but they are also corrected for aperture according to the prescriptions of rgensen, Franx rgaard (1996)."
" Our data (PAV.) are taken through a 2°x6"" aperture. corrected similarly. (see Section 3.4)."," Our data (T.W.) are taken through a 2""x6"" aperture, corrected similarly (see Section 3.4)."
 Columns 10 to 15 contain the HE band. parameters (see Section 3.3)., Columns 10 to 15 contain the H band parameters (see Section 3.3).
 Column 10-11: Log of the HE band elfective radius r5. corrected. for seeing according to the prescriptions of Saglia et al. (," Column 10-11: Log of the H band effective radius $r_e$, corrected for seeing according to the prescriptions of Saglia et al. ("
1993). with uncertainty (in arcsec).,"1993), with uncertainty (in arcsec)."
 Column 12-13: corrected H1. band effective surface brightness with uncertaintv (Gin magaresec 7)., Column 12-13: corrected H band effective surface brightness with uncertainty (in $mag~arcsec^{-2}$ ).
 The correction includes the cosmological expansion 213 and ]x-correction. (taken to be proportional to 1]z) terms. and the seeing correction. according to Saglia ct al. (," The correction includes the cosmological expansion $^4$ and K-correction (taken to be proportional to 1+z) terms, and the seeing correction, according to Saglia et al. ("
1993).,1993).
 No ealactic absorption correction was applied since Ag — 0.085 Ap (Pahre et al., No galactic absorption correction was applied since $_H$ = 0.085 $_B$ (Pahre et al.
 1995). with Ap0.1 mag in the direction of Virgo.," 1995), with $_B~\leq~0.1$ mag in the direction of Virgo."
 Column 14: seeing during the LE band Column 15: NUR observing run: POT refers to the 1997 run at TIRGO (this work). 9 objects were serencdipitouslv observed at Calar Alto (CA94-96) in WO band and are found in Boselli et al. (," Column 14: seeing during the H band Column 15: NIR observing run: T97 refers to the 1997 run at TIRGO (this work), 9 objects were serendipitously observed at Calar Alto (CA94-96) in K' band and are found in Boselli et al. ("
1997): one of the “LOT objects was also screndipitously observed at Calar Alto in 1997 in LE Column 16: distance modulus as obtained in this work using the EP Column 17: revised region of membership (see Section 5.3 for,1997); one of the T97 objects was also serendipitously observed at Calar Alto in 1997 in H Column 16: distance modulus as obtained in this work using the FP Column 17: revised region of membership (see Section 5.3 for
a few AU of the central star is exposed. to the strong stellar UV flux.,a few AU of the central star is exposed to the strong stellar UV flux.
 Πο molecular hydrogeu both rotationally aud vibrationally excited. las been observed ii various sources of this type (AMartin-Zatdictal. 2008).," Hot molecular hydrogen both rotationally and vibrationally excited, has been observed in various sources of this type \citep{mar08}."
. To investigate the importance of the chemistry of vibrationally excited Πω in such euviromuenuts we take the parameters derived for the warm IH» cutting gas observed by Martin-Zakdüetal.(2008). toward the BO star HD 176836 (see Table ?7))., To investigate the importance of the chemistry of vibrationally excited $_2$ in such environments we take the parameters derived for the warm $_2$ emitting gas observed by \citet{mar08} toward the B9 star HD 176836 (see Table \ref{table-column-densities}) ).
 As shown in Fie., As shown in Fig.
 7 he fraction of vibrationally excited Ts stays around * © and so the abundance of CIL! is increased bv alinost one order of magnitude when reactions with excited Ils are included. although in the case of IID 176386 the total column deusitv (see Table ??)) remains probably too low for being detected.," \ref{fig-hd176386} the fraction of vibrationally excited $_2$ stays around $^{-7}$$-$ $^{-6}$ and so the abundance of $^+$ is increased by almost one order of magnitude when reactions with excited $_2$ are included, although in the case of HD 176386 the total column density (see Table \ref{table-column-densities}) ) remains probably too low for being detected."
 Some other species experience moderate alinidauce ομαπουτς as a consequence of the activation of the reaction between II; (e> 0) and C!, Some other species experience moderate abundance enhancements as a consequence of the activation of the reaction between $_2$ $v>0$ ) and $^+$.
 Iu this paper we have investigated the iupact of various chemical reactions involving vibrationally excited I which have been studied either experimentally or theoretically (concretely those with €!. We!. O. OIL aud CN) on the chemical composition of various astronomical regions.," In this paper we have investigated the impact of various chemical reactions involving vibrationally excited $_2$ which have been studied either experimentally or theoretically (concretely those with $^+$, $^+$ , O, OH, and CN) on the chemical composition of various astronomical regions."
 Among the reactions considered here that of I> (ο> 0) with C! stands out as the most important one., Among the reactions considered here that of $_2$ $v>0$ ) with $^+$ stands out as the most important one.
 This reaction becomes the main formation route of the reactive cation CIT! aud controls the abundance of sone other related species in moderately wari astronomical enviromueuts with fractions of vibrationally excited I. iu excess of some ©. couditious which are fouud to occur in sole types of PDR-like regions.," This reaction becomes the main formation route of the reactive cation $^+$ and controls the abundance of some other related species in moderately warm astronomical environments with fractions of vibrationally excited $_2$ in excess of some $^{-6}$, conditions which are found to occur in some types of PDR-like regions."
 The importance of the chemistry of vibrationally excited Ty las been investigated through PDR 1inodels in the diffuse clouds ¢ Oph and ΠΟ 31078. the Orion Dar. the carbou-rich protoplanetary nebula NGC 7027. aud the circuustellar disk ΠΟ 176386.," The importance of the chemistry of vibrationally excited $_2$ has been investigated through PDR models in the diffuse clouds $\zeta$ Oph and HD 34078, the Orion Bar, the carbon-rich protoplanetary nebula NGC 7027, and the circumstellar disk HD 176386."
The study of à Oph indicates that the fraction of Hs ith(e‘the>0) present (< ) as insufficicut to form CIE! xw abuudance typically observed in diffuse aud transhicent clouds., The study of $\zeta$ Oph indicates that the fraction of $_2$ $v>0$ ) present $<$ $^{-7}$ ) is insufficient to form $^+$ with the abundance typically observed in diffuse and translucent clouds.
 Ou the other hand. in dense aud liehhy FUV ilhuuinated clouds. such as the hot PDR of WD 31078. the Orion Bar amd NCC 7027. reactions of vibrationally excited become crucial to determine the global chemical composition.," On the other hand, in dense and highly FUV illuminated clouds, such as the hot PDR of HD 34078, the Orion Bar and NGC 7027, reactions of vibrationally excited become crucial to determine the global chemical composition."
" In particular. the reaction Πο (06>0) | C! becomes the dominant svuthetic pathway to CII! aud make the related species CIL! and ‘Il,| to reach similar or sliebtlv lower abundances."," In particular, the reaction $_2$ $v>0$ ) + $^+$ becomes the dominant synthetic pathway to $^+$ and make the related species $_2^+$ and $_3^+$ to reach similar or slightly lower abundances."
 These two cations however have not vet been observed in any astronomical region the spectroscopic data of CIL] is poorly known (see e.g. Polehamptonetal.2007)) while CIT. lacks a permanent dipole moment., These two cations however have not yet been observed in any astronomical region $-$ the spectroscopic data of $_2^+$ is poorly known (see e.g. \citealt{pol07}) ) while $_3^+$ lacks a permanent dipole moment.
 Other reactions of vibrationally excited Πο uot vet studied: either experimentally or theoretically. aud thus rot included rere. could become iportaut in regulatiug he chemical valance of iuterstellar clouds.," Other reactions of vibrationally excited $_2$ not yet studied either experimentally or theoretically, and thus not included here, could become important in regulating the chemical balance of interstellar clouds."
" For iustauce. he reactions Il. | € » CI | IL. Il | S » SII [IL and Ho | S! > SH! | EH ave eudothermic by 190 eV 1500 IK). 0.83 eV. (— 9600 ER). aud 0.56 eV (~ 9860 IK) respectively, aud their rate constants lave an exponential terii of about the value of the chdothermicity."," For instance, the reactions $_2$ + C $\rightarrow$ CH + H, $_2$ + S $\rightarrow$ SH + H, and $_2$ + $^+$ $\rightarrow$ $^+$ + H are endothermic by 0.99 eV $\sim$ 11500 K), 0.83 eV $\sim$ 9600 K), and 0.86 eV $\sim$ 9860 K) respectively, and their rate constants have an exponential term of about the value of the endothermicity."
 This mav indicate that. analogously to reaction (1)). the internal energy of excited IT» would be effectively usec to diminish or overcome the activation xuYrier so that for Πο (ο>1). all these reactions being exothermic. they would proceed at about the collision iuit.," This may indicate that, analogously to reaction \ref{reac-h2+cplus}) ), the internal energy of excited $_2$ would be effectively used to diminish or overcome the activation barrier so that for $_2$ $v>1$ ), all these reactions being exothermic, they would proceed at about the collision limit."
 Experimental or theoretical information on these or other potentially important reactions of vibrationally excited IT» would be of ereat interest., Experimental or theoretical information on these or other potentially important reactions of vibrationally excited $_2$ would be of great interest.
 Iu any case we encourage astrochemusts to imclude the reactions of excited Πω for which kinetic data is available (sce Table ??)) when modelling the chemistry of regions with an important fraction of vibrationally excited Πο., In any case we encourage astrochemists to include the reactions of excited $_2$ for which kinetic data is available (see Table \ref{table-h2-reac}) ) when modelling the chemistry of regions with an important fraction of vibrationally excited $_2$.
 At least the reaction between Πο (ο>0) and C! clearly las an importaut impact on the globalchemical composition of such regions., At least the reaction between $_2$ $v>0$ ) and $^+$ clearly has an important impact on the globalchemical composition of such regions.
 We thank the referee for constructive comments on this article., We thank the referee for constructive comments on this article.
 ALA. is supported by a within the European Conuuunitv 7th Framework Proerauuue under erat aerecinent n 235753., M.A. is supported by a within the European Community 7th Framework Programme under grant agreement $^{\circ}$ 235753.
 SRG. was supported bv a Ramoun v Cajal research contract from the Spanish AMOCINN and co-financed by the European Social Fund., J.R.G. was supported by a Ramónn y Cajal research contract from the Spanish MICINN and co-financed by the European Social Fund.
magnetic field line. 7. we find We κος that he potential drop alone field lines iu he corotating frame can be computed directly from the aboratory frame fields.,"magnetic field line, $l$, we find We see that the potential drop along field lines in the corotating frame can be computed directly from the laboratory frame fields."
" Although in resistive solutions articles will acnally cdiift across naenetic field lines. in addition. to acceleratius along them. we choose to study the field-aligued potential drop Va, as a fiducial ucasure of particle| energev gain."," Although in resistive solutions particles will actually drift across magnetic field lines, in addition to accelerating along them, we choose to study the field-aligned potential drop $V_{\rm drop}$ as a fiducial measure of particle energy gain."
 In fact. the exact article trajectories we choose make ittle difference when estimatiug potential drops because the electrk> field is rotential iu the rane corotating with he pulsal.," In fact, the exact particle trajectories we choose make little difference when estimating potential drops because the electric field is potential in the frame corotating with the pulsar."
 Consider field. lineS starting on tje stellar surface in he jfE plane separated by 157 in latitude fron1 pole to equator., Consider field lines starting on the stellar surface in the $\vec{\mu}-\vec{\Omega}$ plane separated by $15^{\circ}$ in latitude from pole to equator.
 For every stich field line we integrate tlicelectric field to fiud he πιακαι potential dro» along each field ine., For every such field line we integrate the electric field to find the maximum potential drop along each field line.
 We then determine the field line with the| largest overall potential οτιjp for a given naenetic inclination., We then determine the field line with the largest overall potential drop for a given magnetic inclination.
 Iuteeratiug field lines separated bv 157 inerenrents on he stelar surface is sufficicut to eive a 2006 OSnuate of the maniwun potential drop along field lues., Integrating field lines separated by $15^{\circ}$ increments on the stellar surface is sufficient to give a good estimate of the maximum potential drop along field lines.
 Fig., Fig.
 3Pa shows the maximd potential drop as a fiMuction of dipole iwluation anele for differcut conductivities., \ref{potential} shows the maximal potential drop as a function of dipole inclination angle for different conductivities.
 All results have been normalized to the poeutial dr‘op frou the pole to the equator of au aligned vacuma rotator iu the aboratory frame. Vy=πιο.).," All results have been normalized to the potential drop from the pole to the equator of an aligned vacuum rotator in the laboratory frame, $V_0=|\vec{\mu}|/(R_{\rm LC}R_*)$."
 As our models do not presetibe a high coiductivitv to tl1ο closed field line region. the available accelerating ]votential is generally Dited by the poe-to-equator ]votential difference. rather than the simaller polar ca )potential. Vix=TUR I. with a few notable exceXions.," As our models do not prescribe a high conductivity to the closed field line region, the available accelerating potential is generally limited by the pole-to-equator potential difference, rather than the smaller polar cap potential, $V_{\rm pc}=V_0 R_*/R_{LC}$ , with a few notable exceptions."
 Low conductivity solutionis. (o/O)2o OL at ligh iucTination angle. ào>157. have| Vaop scaling intermediate between Yo and μοι ," Low conductivity solutions, $(\sigma/\Omega)^2 \lesssim 0.04$ , at high inclination angle, $\alpha > 45^{\circ}$, have $V_{\rm drop}$ scaling intermediate between $V_0$ and $V_{\rm pc}$."
The orthogonal rotator « ropa (σ/ο)”=0.0L scales roughly with , The orthogonal rotator drop at $(\sigma/\Omega)^2 = 0.04$ scales roughly with $V_{\rm pc}$.
Usiie the vacui Deutsch fieks. one can obtain that V5.the aligned vactuni rotator potential drop scales exactly proportioial to Ty. whereas the orthogonal vac rotator drop scales coser to Vy.," Using the vacuum Deutsch fields, one can obtain that the aligned vacuum rotator potential drop scales exactly proportional to $V_0$, whereas the orthogonal vacuum rotator drop scales closer to $V_{\rm
pc}$."
 From Fig., From Fig.
 2. we see that for (0Q2>0.0L the ]»otentia drop is roughly independent of icliuation angle Or fixe σ. lo. there is a one-to-one map between cocuctivitv and maximal potential drop along a field line oriejnating in the fQ plane for all inclination augles.," \ref{potential} we see that for $(\sigma/\Omega)^2>0.04$ the potential drop is roughly independent of inclination angle for fixed $\sigma$, i.e., there is a one-to-one map between conductivity and maximal potential drop along a field line originating in the $\vec{\mu}-\vec{\Omega}$ plane for all inclination angles."
" The Mania potential drop increases frou, zero for force-free (or oí.» x) to Varop/Vo~0.2 for (σQj)?—0.01.", The maximal potential drop increases from zero for force-free (or $\sigma/\Omega \to \infty$ ) to $V_{\rm drop}/V_0\sim 0.2$ for $(\sigma/\Omega)^2=0.04$.
 The fact that potential drop is iudependeut of inclination angle for (0Q2>401 allows us ο relate huuinosity to potential drop 1 1a very simple manner., The fact that potential drop is independent of inclination angle for $(\sigma/\Omega)^2>0.04$ allows us to relate luminosity to potential drop in a very simple manner.
 We present the rest here aud explain its origin 1n more detail below., We present the result here and explain its origin in more detail below.
 Fig., Fig.
 shows the spin-down luninositv as a fuuction of pxtential drop for inclinatioi angeles e=0.30.60.907.," \ref{spindown_potential} shows the spin-down luminosity as a function of potential drop for inclination angles $\alpha=0,30,60,90^{\circ}$."
 Spiu-down luninosity iucreases with Increasing inclinatio1 auele and with decreasing field line potential drops., Spin-down luminosity increases with increasing inclination angle and with decreasing field line potential drops.
We fit the spiu-down curves in Fie.,We fit the spin-down curves in Fig.
 1 with the limear relation This formula applies ouly to the domain for which we have ¢ata shown with solid lines in Fig. l.," \ref{spindown_potential} with the linear relation This formula applies only to the domain for which we have data shown with solid lines in Fig. \ref{spindown_potential},"
 Lc. 0cVagu/To<0.2.," i.e., $0<V_{\rm
drop}/V_0<0.2$."
 A similar spin-down fornmla was constructed by Contopoulos&Spitkovskyv(2006) for the case of a finite eap at the base of the open fiek lines in a force-free inagnetosphere., A similar spin-down formula was constructed by \cite{ContopSpitkovsky06} for the case of a finite gap at the base of the open field lines in a force-free magnetosphere.
 The spin-cdown was also found to be linear in the potential drop in the σα» but had a differeut slope and anenlar dependence of the forma (1Vasp/Vpe)eos?o-2|203suo.," The spin-down was also found to be linear in the potential drop in the gap but had a different slope and angular dependence of the form $(1-{V_{\rm
drop}/V_{\rm pc}}) \cos^2{\alpha} + \sin^2{\alpha}$."
 Thisqc augular dependence was nof a rigorous derivation. but a prediction used onu aligned force-free aud orthogonal vacuum limits.," This angular dependence was not a rigorous derivation, but a prediction based on aligned force-free and orthogonal vacuum limits."
" We uote that our spiu«own formula reduces to the “OrCC-free spin-down forunla from S06 within error bars when VasYo="").", We note that our spin-down formula reduces to the force-free spin-down formula from S06 within error bars when $V_{\rm drop}/V_0=0$.
 For Varop/Vo>0.2 the dependence of spiu«owl Ol the potential drop οiters a different regie (sce dotted lines in Fie. 9)., For $V_{\rm drop}/V_0>0.2$ the dependence of spin-down on the potential drop enters a different regime (see dotted lines in Fig. \ref{spindown_potential}) ).
 We «o not provide a fit hore. as poteitial drop 10 longer scales with Vy at high inclination anele.," We do not provide a fit here, as potential drop no longer scales with $V_0$ at high inclination angle."
 The potential drop along field) lines iun this reguue is due to the reemergeice of the vacua electric Belds as condctivity is reduced., The potential drop along field lines in this regime is due to the reemergence of the vacuum electric fields as conductivity is reduced.
 There are three coutribuloli to the vacuma electric field which are provicdec by the quadrupolar surface charge on a finite-radius star ancl by ciral and surface monopolar charges., There are three contributions to the vacuum electric field which are provided by the quadrupolar surface charge on a finite-radius star and by central and surface monopolar charges.
 The ceitral ΠΟΤΟ»olar component provides part of the radia electric field reeded. for corotation of the naenetize stellar interior., The central monopolar component provides part of the radial electric field needed for corotation of the magnetized stellar interior.
 If the star initially is uuncharged (as is asstined in our simulatious). a slrface charge of opposite sigu conrpeusates the net charge of the iterior of hne star (see Michel&Li1999 or thorough discussioi).," If the star initially is uncharged (as is assumed in our simulations), a surface charge of opposite sign compensates the net charge of the interior of the star (see \citealp*{MichelLi99} for thorough discussion)."
 This surface charge. together with the induced quadrupolar surface charge frou corotation. cadi cave the star and be redistributed. throughout he magnetosphere when conductivity is turned on. or when the work Tuctionof the surfaceis low.," This surface charge, together with the induced quadrupolar surface charge from corotation, can leave the star and be redistributed throughout the magnetosphere when conductivity is turned on, or when the work functionof the surfaceis low."
 Such redistüution lowers the maxim available potential «Lop., Such redistribution lowers the maximum available potential drop.
 The available monopo arosrface charge varies with inclination as cosa (Michel&Li 1999).. so the poteutial drop associated with it disappears for orthogonal," The available monopolar surface charge varies with inclination as $\cos\alpha$ \citep{MichelLi99}, , so the potential drop associated with it disappears for orthogonal"
For data reduction of the observations we used CIAO 3.1 (2). and applied standard selection criteria.,For data reduction of the observations we used CIAO 4.1 \citep{ciao} and applied standard selection criteria.
 The analysis of the data was performed in the 11 keV energy band since the back-illuminated ACIS-S chip has nonzero effective area at X-ray energies below 300 eV. For the HRC imager no energy cuts were used since its energy resolution is low., The analysis of the data was performed in the 1 keV energy band since the back-illuminated ACIS-S chip has nonzero effective area at X-ray energies below 300 eV. For the HRC imager no energy cuts were used since its energy resolution is low.
 51 Peg 15 clearly detected in both instruments., 51 Peg is clearly detected in both instruments.
 In the ACIS observation we detect eight photons in the source region. a circle with 1.5” radius around 51. Peg's nominal position.," In the ACIS observation we detect eight photons in the source region, a circle with $\arcsec$ radius around 51 Peg's nominal position."
 This radius was chosen to contain of the soft (x1 keV) photons from a point-like source., This radius was chosen to contain of the soft $\leq$ 1 keV) photons from a point-like source.
 From nearby source-free regions in the 1506650 eV energy band we expect only 0.03 background counts for this area. therefore we attribute all of the recorded counts to 51 Peg.," From nearby source-free regions in the 650 eV energy band we expect only 0.03 background counts for this area, therefore we attribute all of the recorded counts to 51 Peg."
 The spectral resolution of ACIS-S is similar to the one of the EPIC detectors (= 100 eV)., The spectral resolution of ACIS-S is similar to the one of the EPIC detectors $\approx$ 100 eV).
 In the HRC-I pointing 21 photons were detected in the source region over a background of 0.6 photons sealed to the same area., In the HRC-I pointing 21 photons were detected in the source region over a background of 0.6 photons scaled to the same area.
 At any rate. also the HRC clearly detects 51 Peg.," At any rate, also the HRC clearly detects 51 Peg."
 5] Peg shows a photon excess in the 0.200.45 keV and the band (0.4500.65 keV) in PN and a very weak excess In the same bands in the merged MOS detectors., 51 Peg shows a photon excess in the 0.45 keV and the band 0.65 keV) in PN and a very weak excess in the same bands in the merged MOS detectors.
 The MOS and PN lightcurves show no obvious variability over the whole 55 ks., The MOS and PN lightcurves show no obvious variability over the whole 55 ks.
 As shown in Figure |.. most of PN's excess source photons have energies around 300 eV: another emission feature Is present around 570 eV. the energy of the triplet.," As shown in Figure \ref{spectra}, most of PN's excess source photons have energies around 300 eV; another emission feature is present around 570 eV, the energy of the triplet."
 Because of XMM's moderate intrinsic energy resolution the nominal energies of the detected source photons cannot be regarded as exact values., Because of 's moderate intrinsic energy resolution the nominal energies of the detected source photons cannot be regarded as exact values.
 From the absence of emission features at energies (=650 eV) we can conclude that 51 Peg's corona has an average plasma temperature well below 3 MK., From the absence of emission features at energies $\approx650$ eV) we can conclude that 51 Peg's corona has an average plasma temperature well below 3 MK.
 All the recorded counts have energies between 150 and 450 eV and are distributed quite evenly over the observation. time. supporting a soft. basically constant X-ray source.," All the recorded counts have energies between 150 and 450 eV and are distributed quite evenly over the observation time, supporting a soft, basically constant X-ray source."
 Let us now inspect the energies of the ACIS-S photons in detail: the CIAO software assigns a nominal energy to each recorded photon (see Figure 1))., Let us now inspect the energies of the ACIS-S photons in detail; the CIAO software assigns a nominal energy to each recorded photon (see Figure \ref{spectra}) ).
 The eight source photons have energies of 170. 206. 2]]. 212. 256. 227. 291 and 428 eV: they are hence very soft and obviously none of these photons can be attributed to or even emission.," The eight source photons have energies of 170, 206, 211, 212, 256, 227, 291 and 428 eV; they are hence very soft and obviously none of these photons can be attributed to or even emission."
 This supports our hypothesis of a very low plasma temperature evoked by theXMM data., This supports our hypothesis of a very low plasma temperature evoked by the data.
 The ACIS-S detector is prone to optical contamination. so we have to check whether the extremely soft events could be induced by optical photons.," The ACIS-S detector is prone to optical contamination, so we have to check whether the extremely soft events could be induced by optical photons."
 The threshold for optical contamination in the ACIS-S detector is at V.7.8 for stars with an effective temperature between 5000 and 6500 K; a star this bright would cause a bias level shift of one Analog-to-Digital-Unit (ADU) of 3.4 eV during the standard 3.2 s time frame for the central pixel of the source., The threshold for optical contamination in the ACIS-S detector is at $V\approx 7.8$ for stars with an effective temperature between 5000 and 6500 K; a star this bright would cause a bias level shift of one Analog-to-Digital-Unit (ADU) of 3.4 eV during the standard 3.2 s time frame for the central pixel of the source.
 51 Peg’s visual magnitude is 5.5. so we expect ca.," 51 Peg's visual magnitude is 5.5, so we expect ca."
 8 ADUs per time frame., 8 ADUs per time frame.
 Since the event threshold lies at 20 ADUs. optical," Since the event threshold lies at 20 ADUs, optical"
and Nick Z. (Mpj) ,and Nick Z. $M_{BH}$ 
 Seager&Deming2010)). (Charbonneau (Tarter (Binetal.2009).. (Wawley1993).. Westetal.2008)). (Lacyetal.1976:Παπ]ον2010).," \citealt{sea10}) \citep{cha05,ago10}, \citep{knu07,knu09}. \citep{tar07,seg10}. \citep{irw09}. \citep{haw93}, \citealt{wes08}) \citep{lac76,haw91,kow09,kow10}."
. Ergin > 10?! —10.000I (Ilxowalskietal.," $_{U,flare}$ $>$ $^{34}$ \citep{haw91,cul94,kow10,ost10}."
2010).. (Haleyetal.2003:Osten2005).," $\sim$ \citep{kow10}. \citep{haw03,ost05},"
. Schinidtetal.(2011)16402). Bre. , \citet{sch11} $\mu$ $\gamma$ 
A more intuitive visualization of the differences between the GB and the LGD residual velocity distributions are the contour density plots of the three different velocity planes (see Figure 4).,A more intuitive visualization of the differences between the GB and the LGD residual velocity distributions are the contour density plots of the three different velocity planes (see Figure 4).
 Their disparate shapes and orientations already show that the velocity ellipsoids clearly reflect the distinct kinematic behavior of both stellar svstems., Their disparate shapes and orientations already show that the velocity ellipsoids clearly reflect the distinct kinematic behavior of both stellar systems.
 We have estimated (he main geometrical parameters of the velocity ellipsoids for the whole sample and for (he GB and the LGD members separately., We have estimated the main geometrical parameters of the velocity ellipsoids for the whole sample and for the GB and the LGD members separately.
 The results are displaved on table 1.., The results are displayed on table \ref{tbl-1}.
 Two main results arise [rom this analvsis: The estimation of the vertex deviation in the solar neighborhood [rom different. star samples has produced different values depending on (he nature of the sample aud on the kinematic variables used in the calculation (see Morenoetal.(1999) [or a compilation of previous results)., Two main results arise from this analysis: The estimation of the vertex deviation in the solar neighborhood from different star samples has produced different values depending on the nature of the sample and on the kinematic variables used in the calculation (see \citet{Mor99} for a compilation of previous results).
 In brief. the general conclusion has been that (he vertex deviation becomes more negalive as (he star sample is vounger.," In brief, the general conclusion has been that the vertex deviation becomes more negative as the star sample is younger."
 In fact. one of the classic estimates based on space velocities for OD stars (Filin1957). vielded a value close to {ντ—50* [ον the Galactic disk.," In fact, one of the classic estimates based on space velocities for OB stars \citep{Fil57} yielded a value close to $l_{v} = -50\degr$ for the Galactic disk."
 For vears. this result. has remained a puzzling issue (hat has been given several and varied explanations.," For years, this result has remained a puzzling issue that has been given several and varied explanations."
 Most of them can be classified into (wo classical tvpes: nature or nurture. we could say.," Most of them can be classified into two classical types: nature or nurture, we could say."
 Some authors claim that these voung stars that formed from a molecular cloud show the same kinematics as (he parent cloud at the time of the star formation., Some authors claim that these young stars that formed from a molecular cloud show the same kinematics as the parent cloud at the time of the star formation.
 This wav. the initial velocity and later expansion define the velocity ellipsoicl of the present stellar system.," This way, the initial velocity and later expansion define the velocity ellipsoid of the present stellar system."
 Other authors. though. defend that the effect of different singular aud punctual events (such as (he passing through a spiral zum) could also be the cause of the peculiar velocity ellipsoid observed in the voung stellar component.," Other authors, though, defend that the effect of different singular and punctual events (such as the passing through a spiral arm) could also be the cause of the peculiar velocity ellipsoid observed in the young stellar component."
 What we conclude from our analysis is (hat the classic problem of the negative vertex deviation for voung stus in the solar neishborhood is a consequence of (he presence of the Gb., What we conclude from our analysis is that the classic problem of the negative vertex deviation for young stars in the solar neighborhood is a consequence of the presence of the GB.
ab. IIf we eliminateliminate the stars that belong to the GB.GLB. the remaining samplele of only LGDLGL stars present a positive vertex deviation (FC?= 187). Morenoetal.(1999)," If we eliminate the stars that belong to the GB, the remaining sample of only LGD stars present a positive vertex deviation $l_{v}^{LGD} =
18\degr$ ). \citet{Mor99},"
".. working wilh a sample of dwar! O-B5.5 stars members of the GB. found that the negative vertex deviation (/,~ —64) was caused by the Pleiacles moving eroup."," working with a sample of dwarf O-B5.5 stars members of the GB, found that the negative vertex deviation $l_{v} \sim
-64\degr$ ) was caused by the Pleiades moving group."
" Once removed (his group. Chev obtained a positive vertex deviation (/,= 22°) for the remaining stars in the GB."," Once removed this group, they obtained a positive vertex deviation $l_{v} =
22\degr$ ) for the remaining stars in the GB."
 We now demonstrate the the OD stars of the LGD also have a, We now demonstrate the the OB stars of the LGD also have a
Lt is well known that the ability to parameterize galaxies from ground-based images is severely compromised. by seeing. which scatters light from the objects producing a loss of resolution in the images. lower mean surface brightnesses than the true values anc larger effective radii.,"It is well known that the ability to parameterize galaxies from ground-based images is severely compromised by seeing, which scatters light from the objects producing a loss of resolution in the images, lower mean surface brightnesses than the true values and larger effective radii."
 Phe elfects of secing have been extensively studied. in the case of elliptical galaxies with rt?! profiles (Franx. Hlingworth lHleckman 1989: Saglia et al.," The effects of seeing have been extensively studied in the case of elliptical galaxies with $r^{1/4}$ profiles (Franx, Illingworth Heckman 1989; Saglia et al."
 1993)., 1993).
 Recently. Frujillo et al. (," Recently, Trujillo et al. ("
"2001. hereafter. TOI) extended: previous work by studying analytically the effects. of seeing on. ellipticallv svmametrie surface brightness. distributions. following the Sérrsc (LOGS) rb"" law and assuming a Caussian point spread function. (PSE).","2001, hereafter T01) extended previous work by studying analytically the effects of seeing on elliptically symmetric surface brightness distributions following the Sérrsic (1968) $r^{1/n}$ law and assuming a Gaussian point spread function (PSF)."
 Sérrsies generalization. of the cle Vaucouleurs (1948. 1959) £7 law has been shown to provide a better representation to the distribution of light in both elliptical galaxies (including the dwarl ellipticals) ancl the bulges of Spiral galaxies (Caon. Cappacioli. D'Onofrio 1993: D'Onofrio. Capaccioli. Caon 1994: Young Currie 1994: Xndredakis. Peletier. Balcells 1995).," Sérrsic's generalization of the de Vaucouleurs (1948, 1959) $r^{1/4}$ law has been shown to provide a better representation to the distribution of light in both elliptical galaxies (including the dwarf ellipticals) and the bulges of Spiral galaxies (Caon, Cappacioli, D'Onofrio 1993; D'Onofrio, Capaccioli, Caon 1994; Young Currie 1994; Andredakis, Peletier, Balcells 1995)."
 The existence of “wings” in stellar profiles reveals that the real PSE deviates from the Gaussian form., The existence of “wings” in stellar profiles reveals that the real PSF deviates from the Gaussian form.
 In this paper we show. from the size of the wings present in real images (e.g. Saglia et al.," In this paper we show, from the size of the wings present in real images (e.g. Saglia et al."
 1993). that such deviations from Gaussian DPSES can result in dillerent values for the profile parameters in the range of304.," 1993), that such deviations from Gaussian PSFs can result in different values for the profile parameters in the range of."
. The new generation of ground-based. telescopes and the study of galaxies at high redshifts make these types of studies crucial in order to obtain reliable (unbiased) information from the structural analysis of these objects., The new generation of ground-based telescopes and the study of galaxies at high redshifts make these types of studies crucial in order to obtain reliable (unbiased) information from the structural analysis of these objects.
 This paper presents a further. more detailed. analysis of the clleets of seeing on Sérrsic profiles when “wings” are present in the PSE.," This paper presents a further, more detailed, analysis of the effects of seeing on Sérrsic profiles when “wings” are present in the PSF."
 For this reason we have modelled. the PSE bv à generalization of the Gaussian form: the Molfat function. (Mollat. 1969). whieh describes well the presence of wings.," For this reason we have modelled the PSF by a generalization of the Gaussian form: the Moffat function (Moffat 1969), which describes well the presence of wings."
 Lt should be noted that these Kinds of studies are not only important for grouncd-based observations., It should be noted that these kinds of studies are not only important for ground-based observations.
" In fact. Timages present their own ""narrow PSESs (see a detailed study in οποία, Zavatti Parmeggiani LOST. ancl Ixrist 993)."," In fact, images present their own “narrow” PSFs (see a detailed study in Bendinelli, Zavatti Parmeggiani 1987, and Krist 1993)."
 The use of these steep PSEs presents. numerical problems which can be avoided by modelling the narrow SES with polynomials instead. of exponential expressions ike Gaussians., The use of these steep PSFs presents numerical problems which can be avoided by modelling the narrow PSFs with polynomials instead of exponential expressions like Gaussians.
 ln Section 2 we summarize some general results from the use of Molfat. PSEs., In Section 2 we summarize some general results from the use of Moffat PSFs.
 Section 3 describes he ellects of seeing on the Sérrsie profile. parameters ought about by the Mollat. PSE., Section 3 describes the effects of seeing on the Sérrsic profile parameters brought about by the Moffat PSF.
 A prescription for secing corrections Is given in Section d., A prescription for seeing corrections is given in Section 4.
The origin of X-ray emission from the radio hot spots of FR II radio galaxies is still a subject of considerable debate.,The origin of X-ray emission from the radio hot spots of FR II radio galaxies is still a subject of considerable debate.
" For many sources, inverse-Compton scattering of radio photons by the relativistic electrons of the hot spot (the synchrotron self-Compton mechanism (SSC)) with the magnetic field at or near the equipartition value provides an adequate description of the broad band (radio to X-ray) spectra(Harris.Carilli.&Perley1994:Hardeastleetal. 2002).."," For many sources, inverse-Compton scattering of radio photons by the relativistic electrons of the hot spot (the synchrotron self-Compton mechanism (SSC)) with the magnetic field at or near the equipartition value provides an adequate description of the broad band (radio to X-ray) spectra\citep{har94,mjh02}. ."
respect to a model for a metal-poorgiant}.,respect to a model for a metal-poor.
" As can be seen in this figure, the stratification is critically dependent on the inclusion of convective overshooting in the 1993 grid by Kurucz."," As can be seen in this figure, the stratification is critically dependent on the inclusion of convective overshooting in the 1993 grid by Kurucz."
" 2004)The most up-to-date versions of 2008) and Gustafssonal} both neglect overshoot, and the models shown haveet similar, but not identical parameters for the mixing length, but nevertheless show differences on the KK level."," The most up-to-date versions of \citep{Castelli04} and \citep{Gustafsson08} both neglect overshoot, and the models shown have similar, but not identical parameters for the mixing length, but nevertheless show differences on the K level."
" The middle and lower panels of reffig:markur illustrate the effect on derived LTE and non-LTE Na abundances for the 819.4nnm line, when using different atmospheric models."," The middle and lower panels of \\ref{fig:markur} illustrate the effect on derived LTE and non-LTE Na abundances for the nm line, when using different atmospheric models."
" In both cases the line strengths appear, as expected, to be connected to the temperatures around log(Tsoo)=0."," In both cases the line strengths appear, as expected, to be connected to the temperatures around $\log(\tau_{500})=0$."
" The higher temperatures of the models, especially the one with overshoot, weakens the line compared to for a given Na abundance (i.e. a given line strength generally corresponds to a higher LTE abundance)."," The higher temperatures of the models, especially the one with overshoot, weakens the line compared to for a given Na abundance (i.e. a given line strength generally corresponds to a higher LTE abundance)."
" However, in non-LTE the difference is lessened because of a higher degree of overpopulation of neutral Na in the temperature ""jump' in the overshooting model."," However, in non-LTE the difference is lessened because of a higher degree of overpopulation of neutral Na in the temperature 'jump' in the overshooting model."
 This in turn is caused by the flatter temperature gradient and consequently the less efficient overionising ultra-violet flux in this region., This in turn is caused by the flatter temperature gradient and consequently the less efficient overionising ultra-violet flux in this region.
 This comparison implies that differences between 1D atmospheric models can produce differences of the order of ~0.1 ddex in Na abundance for such a metal-poor giant., This comparison implies that differences between 1D atmospheric models can produce differences of the order of $\sim0.1$ dex in Na abundance for such a metal-poor giant.
" Using our calculated abundance corrections and/or non-LTE curves-of-growth for 11 important neutral Nall lines, Na abundances that are superiour to those inferred with the LTE assumption can easily be obtained for late-type dwarf and giant stars."," Using our calculated abundance corrections and/or non-LTE curves-of-growth for 11 important neutral I lines, Na abundances that are superiour to those inferred with the LTE assumption can easily be obtained for late-type dwarf and giant stars."
" The results show a low sensitivity to uncertainties in input atomic data for collisional cross-sections, but are sensitive to the detailed structure of the atmosphere."," The results show a low sensitivity to uncertainties in input atomic data for collisional cross-sections, but are sensitive to the detailed structure of the atmosphere."
" To minimize the influence from possible systematic errors in the model, unsaturated lines are definitely to be preferred as abundance indicators."," To minimize the influence from possible systematic errors in the model, unsaturated lines are definitely to be preferred as abundance indicators."
" As always, a good test of the soundness of the modelling procedure is to compare Na abundances from lines of different strengths."," As always, a good test of the soundness of the modelling procedure is to compare Na abundances from lines of different strengths."
" Our results satisfactorily agree with earlier non-LTE studies of Π that treated the strength of hydrogen collisions as a free parameter, even though the new quantum mechanical rates for hydrogen impact excitation are considerably lower than the traditational estimates."," Our results satisfactorily agree with earlier non-LTE studies of I that treated the strength of hydrogen collisions as a free parameter, even though the new quantum mechanical rates for hydrogen impact excitation are considerably lower than the traditational estimates."
 This low sensitivity of non-LTE abundances to hydrogen collisions stems from a cancellation between effects in different line-forming regions., This low sensitivity of non-LTE abundances to hydrogen collisions stems from a cancellation between effects in different line-forming regions.
" In a forthcoming paper we will explore the impact of the model atmosphere on the abundance determination more closely, and extend our work to include 3D, hydrodynamical model atmospheres, superseding the crude mixing length recipes used for convection in static 1D models."," In a forthcoming paper we will explore the impact of the model atmosphere on the abundance determination more closely, and extend our work to include 3D, hydrodynamical model atmospheres, superseding the crude mixing length recipes used for convection in static 1D models."
 The model, The model
which peaks at 4)=0.,which peaks at $k_x = 0$.
 This is uot the only possible defiuition for the energy. associated with a shear-DHow disturbance: see the discussion in Appendix A of (LOST)., This is not the only possible definition for the energy associated with a shear-flow disturbance; see the discussion in Appendix A of \cite{ngg87}.
 One can also define an amplification lactor for an individual shwave. un which indicates that an arbitrary amount of transient amplification in kinetic energy can be obtained as one increases tlie amount of swing for a leaclitD>ο slivave VUE—hy).," One can also define an amplification factor for an individual shwave, = 1 + which indicates that an arbitrary amount of transient amplification in kinetic energy can be obtained as one increases the amount of swing for a leading shwave $k_{x0} \ll -k_y$ )."
 This is essentially he mechanisin invoked by Chagelishvili.Zahu.Tevzadze.&Lomiuadze(2003).. Umurhan&Begev(2001) aud Afshordi.Mukhopadhyay.&Narayan(2001) to argue for the onset of turbulence in uiuaguetized Ixepleriau clisks.," This is essentially the mechanism invoked by \cite{cz03}, \cite{ur04} and \cite{amn04} to argue for the onset of turbulence in unmagnetized Keplerian disks."
 Because only a small subset of all Fourier components achieve large amplification (those witli initial wavevector very uearly alieued with the radius vector). oue must ask what amXiflication is achieved for an astropliysically relevant set of initial conditions containing a superposition of Fourier components.," Because only a small subset of all Fourier components achieve large amplification (those with initial wavevector very nearly aligned with the radius vector), one must ask what amplification is achieved for an astrophysically relevant set of initial conditions containing a superposition of Fourier components."
 It is natural to draw such a set of Fourier comyonents from a distribition that is isotropic. or nearly so. when Aj is large.," It is natural to draw such a set of Fourier components from a distribution that is isotropic, or nearly so, when $k_0$ is large."
" Cousider. then. perturbing a disk with a raucom set of incoupressive perturbatiois (initial velocities perpeudicular to Ag) drawn from au isotropic. Craussiau raudom field aud askin,£& how the expectation value for the kinetic enerey associated with tle pertu'bations evolves with ime."," Consider, then, perturbing a disk with a random set of incompressive perturbations (initial velocities perpendicular to $\bk_0$ ) drawn from an isotropic, Gaussian random field and asking how the expectation value for the kinetic energy associated with the perturbations evolves with time."
 The evolution of the expected energy density is given by the following integral: = L 2pp[dEE) = L 2ppd kao where © indicates an average over an ensemble of initial coucitions. the first equality follows [rom Parseval’s theorem. the secoud equality follows from the incompressive sliwave solution (??))- zT ] . ] ⋅↽≻⋅ ⋅⋅ ⋅ ⋅ ⋅ ⋅ ⋜↜∙↗∙↗⊔⋜↕∐≼⊓∐≺↵↕⋅↩↥∩⋅≺↵⋜↕↥↽≻↥↽≻∐≺↵⊳∖∩∐↥⊽∖⊽↥∩↓⋅∣⋅⋮∣∣∐∕∖∕≥∖∕∖↥⋅⋜↕∐≺⇂∠−↥⊳∖⋜↕∐∩↥⋅∐↕⋜≹∐∠⋯∑≟," The evolution of the expected energy density is given by the following integral: = L^2 d^2k_0 = L^2 d^2k_0 _0 where $\<\>$ indicates an average over an ensemble of initial conditions, the first equality follows from Parseval's theorem, the second equality follows from the incompressive shwave solution \ref{IVX}) \ref{IS}) ) and therefore applies only for $k_0 H \gg 1$, and $L^2$ is a normalizing factor with units of length squared."
↥⋜↕∢∙↕∩↓⋅∖∖↽∐∐⋯∐↕⊳∖∩⊔≺↵∐∑∸↕∐ ⊳∖≺↽↓⋃⋜⋃⋅≺↵≺⇂⋅ ∌⊲∩↓⋅↥∐∐↥⋜↕↥∢∙∩∐∐∏∩∐⊳∖↕∐⋜↕↕⋜⋃⋅↩↕⊳∖∩⋃⋅∩↥↽≻↥∢∙↕∐⇂∙⋅∕∣∣↸⋮↙↘⋅∣⋅⊽⋮∣∣⋅∣∣∶↙↘⋅∣∟↸∫∣⋅⋮∣∣⋅∣⊔⊳∖↕∐∩⋅∖∖↽∐≺↵↓⋅≺↵ (crg)X )ds the expectation value for the initial incompressive perturbation as a [uuction of Ay aud tan0= νο). tlie integral becomes = ↼⊿⊳↘⋅ ⋅⊐↘∕↴," For initial conditions that are isotropic in $\bk_0$ $\delta v_{xi0} =
\delta v_\perp (k_0,\theta) \sin \theta$, where $\<\delta v_\perp^2
(k_0)\>$ is the expectation value for the initial incompressive perturbation as a function of $k_0$ and $\tan\theta=k_y/k_{x0}$ ), the integral becomes = _0 L^2 k_0 dk_0 ^2"
We thus selected a comparison star based. on the following set of criteria: firstly. we required a star with no known variations.,"We thus selected a comparison star based on the following set of criteria: firstly, we required a star with no known variations."
 We also required an object whose magnitude was similar to thal of GD 323 (V.—14.52)., We also required an object whose magnitude was similar to that of GD 323 $V=14.52$ ).
 Furthermore. we demanded (hat our comparison object have few spectral lines and a spectral energy. distribution comparable to that of GD 323.," Furthermore, we demanded that our comparison object have few spectral lines and a spectral energy distribution comparable to that of GD 323."
 Finally. we wanted an object that was as close as possible to our target object in the sky.," Finally, we wanted an object that was as close as possible to our target object in the sky."
 Examination of the Catalog of Spectroscopically Identified) White Dwarls of (1999) revealed that the DA star wwas the most judicious choice., Examination of the Catalog of Spectroscopically Identified White Dwarfs of \citet{mccook99} revealed that the DA star was the most judicious choice.
 Past observations of hhave shown no evidence for variability. i( has a visual magnitude of =14.42. and with an effective temperature of Tuy=55.040 Ix (Liebertetal.2005.herealterLDII).. its spectrum consists of a well-defined continuum with only weak lhivdrogen lines.," Past observations of have shown no evidence for variability, it has a visual magnitude of $V=14.42$, and with an effective temperature of $\Te=55,040$ K \citep[][hereafter LBH]{liebert05}, its spectrum consists of a well-defined continuum with only weak hydrogen lines."
 Finally. aand GD 323 are separated bv approximately 15 degrees on the sky.," Finally, and GD 323 are separated by approximately 15 degrees on the sky."
 since we did not knowpriori over what (ümescales variations might occur. we carried oul spectroscopic observations over five consecutive nights. from 2004 February 10 to 14.," Since we did not know over what timescales variations might occur, we carried out spectroscopic observations over five consecutive nights, from 2004 February 10 to 14."
 Both GD 323 and wwere monitored for over 5 hours on the first night. and for about an hour on the remaining niehts.," Both GD 323 and were monitored for over 5 hours on the first night, and for about an hour on the remaining nights."
 These optical spectra were secured using (he Steward Observatory 2.3 m reflector telescope equipped with the Boller Chivens spectrograph and. a Loral CCD detector., These optical spectra were secured using the Steward Observatory 2.3 m reflector telescope equipped with the Boller Chivens spectrograph and a Loral CCD detector.
 A 4.5 arcsec slit and a 000 line ! erating in first order provided a spectral coverage οἱ 3200-5300 aat a resolution of ~ 6 FEWIIM., A 4.5 arcsec slit and a 600 line $^{-1}$ grating in first order provided a spectral coverage of 3200-5300 at a resolution of $\sim$ 6 FWHM.
 Each 600 5 spectroscopic observation of GD 323 was immediately followed by a 000 s exposure of12344482., Each 600 s spectroscopic observation of GD 323 was immediately followed by a 600 s exposure of.
.. The average signal-to-noise ratio per pixel ancl per exposure is ~85 for GD 323 and ~100 for12344482., The average signal-to-noise ratio per pixel and per exposure is $\sim 85$ for GD 323 and $\sim100$ for.
. In total. 27 spectra of GD 323 and 25 spectra of wwere secured. the vast majority of them under excellent observing conditions.," In total, 27 spectra of GD 323 and 25 spectra of were secured, the vast majority of them under excellent observing conditions."
 The optical spectra were extracted and wavelength-calibrated using the Image Reduction and Analysis Facilitv (IAE) standard. package., The optical spectra were extracted and wavelength-calibrated using the Image Reduction and Analysis Facility (IRAF) standard package.
 A first. eut. at the fhix calibration was obtained with IRAF using the various flux standards secured during the observing nights., A first cut at the flux calibration was obtained with IRAF using the various flux standards secured during the observing nights.
 llowever. in the course of our analvsis. we realized that we could take advantage of our multiple spectroscopic observations of12344482... and use this star instead as a flux standard. at least in a relative sense.," However, in the course of our analysis, we realized that we could take advantage of our multiple spectroscopic observations of, and use this star instead as a flux standard, at least in a relative sense."
 This method is analogous to that used for taking photometric observations of variable stars. where a constant comparison star is used," This method is analogous to that used for taking high-speed photometric observations of variable stars, where a constant comparison star is used"
rate.,rate.
" For the optimal parameters (7)). we have The [actor 1/f, is between 200-1200 in the error box of (1))."," For the optimal parameters \ref{EQN_PAR}) ), we have The factor $1/f_r$ is between 200-1200 in the error box of \ref{EQN_PAR}) )."
" Our estimate of the (rue-to-observed GID-event rate 1//, is stvikinely similar to the GHRDB-beaming factor 1//, of about 500 derived by Frail et al. (", Our estimate of the true-to-observed GRB-event rate $1/f_r$ is strikingly similar to the GRB-beaming factor $1/f_b$ of about 500 derived by Frail et al. (
2001).,2001).
 Our analvsis is independent of the mechanism providing a broad distribution in GRB Iuminosities., Our analysis is independent of the mechanism providing a broad distribution in GRB luminosities.
 Without further input. our resulis may reflect. (a) isotropic sources wilh greatly varving energy output. (b) beamed sources with standard energv output. aud. varving opening angles. or (c) anisotropic but geometrically standard sources (Rossiοἱal.2002 ).," Without further input, our results may reflect (a) isotropic sources with greatly varying energy output, (b) beamed sources with standard energy output and varying opening angles, or (c) anisotropic but geometrically standard sources \citep{ros02,zha02}."
. We find that the GRD peak-Iuminosities aud beaming are correlated., We find that the GRB peak-luminosities and beaming are correlated.
" To see (his. we simply note that the case of no correlation between peak-Iuminosities and beamine give rise lo an unseen-but-true GRD event rate which is L/f,xfiyc2.510° times the observed rate."," To see this, we simply note that the case of no correlation between peak-luminosities and beaming give rise to an unseen-but-true GRB event rate which is $1/f_r\times 1/f_b\simeq 2.5\times10^5$ times the observed rate."
 The true GliD-event rate hereby approaches that of Type 11 supernovae — we discard this possibility., The true GRB-event rate hereby approaches that of Type II supernovae – we discard this possibility.
 A correlation between peak-Iuminosities aud beaming is naturally expected sources (b) aud (c) with standard energy output the picture that bears out of Frail (2001)., A correlation between peak-luminosities and beaming is naturally expected sources (b) and (c) with standard energy output – the picture that bears out of \citet{fra01}.
". This introduces a correlation £x1/f; between peak-luninosity ancl beaming factor in (b) ancl. for a ffux-Imited sample. also in (ο),"," This introduces a correlation $L\propto 1/f_b$ between peak-luminosity and beaming factor in (b) and, for a flux-limited sample, also in (c)."
 For a flux-Himited sample. both (b) and (c) eive rise to an anticorrelation between inferred beaming and distance such that (o 0;z ~const.," For a flux-limited sample, both (b) and (c) give rise to an anticorrelation between inferred beaming and distance such that to leading-order $\theta_jz\sim$ const."
 Fig., Fig.
 4 shows that this anticorrelation holds in the sample of (2001).., 4 shows that this anticorrelation holds in the sample of \citet{fra01}. .
 For a related discussion on estimating the GRB beaming factor from [flux limited surveys. see Levinsonetal.(2002).," For a related discussion on estimating the GRB beaming factor from flux limited surveys, see \citet{lev02}."
. A table of 33 GRBs with individually determined redshifts allows an estimate of the GRB-linminosity function. based on constant of proporlionality between the GRB event rate and (he cosmic star-formation rate.," A table of 33 GRBs with individually determined redshifts allows an estimate of the GRB-luminosity function, based on constant of proportionality between the GRB event rate and the cosmic star-formation rate."
 We have tested our fit bv reproducing the distribution of peak Iuminosities in (he IPN sample of 67 GRBs., We have tested our fit by reproducing the distribution of peak luminosities in the IPN sample of 67 GRBs.
" A [Inx-limited sample introduces a ratio 1/f, of unseen GRBs. whose emissions fall below the detector threshold. to observed GRBs."," A flux-limited sample introduces a ratio $1/f_r$ of unseen GRBs, whose emissions fall below the detector threshold, to observed GRBs."
 Abest fit analysis of the himinosity function gives, Abest fit analysis of the luminosity function gives
WwOL November 17 with the 2.3in telescope of the Australian National Uuiversity (ANT) at Siding Spring Observatory.,2004 November $-$ 17 with the 2.3m telescope of the Australian National University (ANU) at Siding Spring Observatory.
 The Dual Beam Spectrograph: (DBS) was utilized iu conjunction with a coated SITE 17524532 CCD., The Dual Beam Spectrograph (DBS) was utilized in conjunction with a coated SiTE $\times$ 532 CCD.
 The 300B erating was used with all light directed iuto the blue an via the insertion of a reflective mirror lustead of the customary dichroic., The 300B grating was used with all light directed into the blue arm via the insertion of a reflective mirror instead of the customary dichroic.
 With a central wavelength of 5200Α.. the above arranecment vielded a dispersion of 2.18 from [OIT|A3727. through Me ThA5175 for the mean redshift of the TRS.," With a central wavelength of 5200, the above arrangement yielded a dispersion of 2.18 $^{-1}$ from $\lambda$ 3727 through Mg $\lambda$ 5175 for the mean redshift of the HRS."
 Waveleneth calibration was based on Cur lamp exposures carried out after each object exposure., Wavelength calibration was based on CuAr lamp exposures carried out after each object exposure.
 For each observation. the spectrograplo was rotated to place two or more galaxies ou the slit.," For each observation, the spectrograph was rotated to place two or more galaxies on the slit."
 Calaxics were selected based on their spatial proximity and them apparent brightness., Galaxies were selected based on their spatial proximity and their apparent brightness.
 Specifically. all ealaxics within a spatial radius of < απ (=O5Rapap ~l Ape) to the published cluster ceuter were cramlned aud arranged in order of decreasing brightness.," Specifically, all galaxies within a spatial radius of $\leq$ $'$ $= 0.5 R_{\rm{Abell}} \sim$ 1 Mpc) to the published cluster center were examined and arranged in order of decreasing brightness."
 We targeted only those galaxies with a blue. by). magnitude brighter than 18.25. as eiven in the SuperCOSMOS catalog (?)..," We targeted only those galaxies with a blue, $b_{\rm{J}}$, magnitude brighter than 18.25, as given in the SuperCOSMOS catalog \citep{ham01}."
 With a typical exposure time of 30 minutes. all spectra rad signal-to-noise ratios of 1911 or ereater aud vielded accurate redshift determinations.," With a typical exposure time of 30 minutes, all spectra had signal-to-noise ratios of 15:1 or greater and yielded accurate redshift determinations."
 Object exposures were reduced in the standard nanucr via the software package., Object exposures were reduced in the standard manner via the software package.
 Specifically. he following steps were completed: debiasing. Hat fielding. «kv subtraction. cosmic-ray removal. and waveleneth calibration.," Specifically, the following steps were completed: debiasing, flat fielding, sky subtraction, cosmic-ray removal, and wavelength calibration."
 Cosmic rays were removed using the variance weighting option iu he routine for aperture extraction., Cosmic rays were removed using the variance weighting option in the routine for aperture extraction.
 For hose objects with iultiple exposures. the reduced spectra were co-added.," For those objects with multiple exposures, the reduced spectra were co-added."
" Tn all. 76 usable ealaxy spectra were obtained over the four nights of observations. and they are listed in Table 1 with their determuncd redshift and associated unecrtainty,"," In all, 76 usable galaxy spectra were obtained over the four nights of observations, and they are listed in Table \ref{tb1} with their determined redshift and associated uncertainty."
 Because the spectrograph positiou angele was adjusted to allow two galaxies to be centered on the slit. observations did not occur at the parallactic angle. aud the uncertaiutv from atmospheric dispersion could im priuciple be as uch as 101.," Because the spectrograph position angle was adjusted to allow two galaxies to be centered on the slit, observations did not occur at the parallactic angle, and the uncertainty from atmospheric dispersion could in principle be as much as 40."
 Radial velocities were determined for the galaxy spectra by the standard technique of cross-correlating the galaxy. spectra aeaiust those of template stars., Radial velocities were determined for the galaxy spectra by the standard technique of cross-correlating the galaxy spectra against those of template stars.
 Stellar spectra of the GSIIT star WD 50199 aud of the CIV. star ITD 106116 from the Indo-US Coudé Feed Spectral library (7?) and two ce-redshiftted DBS stellar spectra (the GO star UD 33771 and a screndipitous Galactic GC dwarf at 45999.= 03:29:38.LE and ὅουυυ— 92:36:08.5) were utilized as templates for the redshift determination using the routine.," Stellar spectra of the G8III star HD 80499 and of the G4V star HD 106116 from the Indo-US Coudé Feed Spectral library \citep{val04} and two de-redshifted DBS stellar spectra (the G0 star HD 33771 and a serendipitous Galactic G dwarf at $\alpha_{\rm {J2000}} =$ 03:29:38.44 and $\delta_{\rm {J2000}} =
-$ 52:36:08.5) were utilized as templates for the redshift determination using the routine."
 Only cross-correlation fits with A 1 (?) were considered reliable and then averaged., Only cross-correlation fits with $R >$ 4 \citep{ton79} were considered reliable and then averaged.
 For the ten galaxies with enission-donmunated features. procedures were followed in a manner similar to that detailed previously inL.," For the ten galaxies with emission-dominated features, procedures were followed in a manner similar to that detailed previously in."
 As a final step. allyedshifts were corrected to the heliocentric reference frame.," As a final step, all redshifts were corrected to the heliocentric reference frame."
 Tn addition to the new data from the ANU/DBS. 12 galaxy redshifts for various clusters in our sample were obtained from other sources.," In addition to the new data from the ANU/DBS, 42 galaxy redshifts for various clusters in our sample were obtained from other sources."
 Eightcecu cluster galaxies were observed durius our survey with the multi-fiber. field iustruimeut (GdF.7) on the UST iu 2001 November.," Eighteen cluster galaxies were observed during our survey with the multi-fiber, field instrument \citep[6dF,][]{par98} on the UKST in 2004 November."
 Although that survey focused ou the intercluster ealaxics in the TRS. otherwise unused fibers were placed ou galaxies within the clusters themselves.," Although that survey focused on the inter-cluster galaxies in the HRS, otherwise unused fibers were placed on galaxies within the clusters themselves."
" UISST/6dF spectra covered the wavelength range from 7600 aand vielded average nstruneutal resolutious of LOA aand 6.6À.. for the 58SOV and 1951 eratines respectively,"," UKST/6dF spectra covered the wavelength range from $-$ 7600 and yielded average instrumental resolutions of 4.9 and 6.6, for the 580V and 425R gratings respectively."
 The automatic 6dF data reductiou package completed the following:a. debiasing. fiber extraction. cosiic-rav removal. flat-fielding. sky subtraction. waveleugth calibration. splicing. aud co-acddition (?)..," The automatic 6dF data reduction package completed the following: debiasing, fiber extraction, cosmic-ray removal, flat-fielding, sky subtraction, wavelength calibration, splicing, and co-addition \citep{jon04}."
 The optical redshift for cach ealaxy was determined via the scui-automated software (?).. which employed both correlation for absorption features and emüssiou- matching for typical features (c.¢.. [OIT/A3727. A 1959/5007. aud Balmer lines).," The optical redshift for each galaxy was determined via the semi-automated software \citep{col01}, which employed both cross-correlation for absorption features and emission-line matching for typical features (e.g., $\lambda$ 3727, $\lambda$ 4959/5007, and Balmer lines)."
 Furthermore. two previously unpublished datasets obtained with the Aunelo-Australian Telescope (AAT) were relied ou for establishing properties of certain clusters.," Furthermore, two previously unpublished datasets obtained with the Anglo-Australian Telescope (AAT) were relied on for establishing properties of certain clusters."
" Specifically, T. Mathias: used the fibre-optic-coupled aperture plate svsteia (FOCAP.sce7) during 1988 to observe ealaxies within A3123 aud APAICC 121 with a dispersion of ~ 2 | from 5600 Α."," Specifically, T. Mathams used the fibre-optic-coupled aperture plate system \citep[FOCAP, see][]{gra83}
 during $-$ 1988 to observe galaxies within A3123 and APMCC 421 with a dispersion of $\sim$ 2 $^{-1}$ from $-$ 5600 ."
. T. Nlamer used the, I. Klamer used the
as an interaction progresses.,as an interaction progresses.
 leas. ou the other haud. being loosely bound to the ealactic disks. tends to ect thrown out to large radi (e.g. Wibbarcd1995: Wane1998)3. leaving depleted levels of atomic gas iu the ceutral regions.," gas, on the other hand, being loosely bound to the galactic disks, tends to get thrown out to large radii (e.g. \cite{hib95}; ; \cite{wan98}) ), leaving depleted levels of atomic gas in the central regions."
 Therefore it may not be possible to explain the observed increases in ccoutent in the nuclear regions of interacting galaxies as the result of enhanced cconversion. because there may not be sufficient quautities of uuear the nuclei to support that process.," Therefore it may not be possible to explain the observed increases in content in the nuclear regions of interacting galaxies as the result of enhanced conversion, because there may not be sufficient quantities of near the nuclei to support that process."
 All of the preceding results are based on the usual assuniption that CO cmission serves as a tracer of aand that there is a connection between the integrated brightuess oof the COU0) line to the cohunn density NOT2) of molecular hydrogen., All of the preceding results are based on the usual assumption that CO emission serves as a tracer of and that there is a connection between the velocity-integrated brightness of the $^{12}$ CO(1–0) line to the column density 2) of molecular hydrogen.
 This iucludes the assuuption that the cconnection can be expressed as a constant ratio jin wits of molecules εν kis. 1)., This includes the assumption that the connection can be expressed as a constant ratio in units of molecules $^{-2}$ /(K km $^{-1}$ ).
 The fundamental calibration of this couversion ratio has been douc using various observations of Galactic molecular clouds in the solar ueighborlood., The fundamental calibration of this conversion ratio has been done using various observations of Galactic molecular clouds in the solar neighborhood.
 Receutlv. however. evidence has beeu accumulatiug that the ccouversion factor mav not be constant with position iu a galaxy. nor from galaxy to ealaxy.," Recently, however, evidence has been accumulating that the conversion factor may not be constant with position in a galaxy, nor from galaxy to galaxy."
 For example. a radial gradient of more than a factor of 10 has been reported in our Galaxy (Sodroskietal. 1995)). and the conversion factor for the central regions of starburst ealaxiessimular to many of the interacting ealaxies in our smuplemay differ by as uinch as two orders of magnitude from that of the dust clouds in the iuer disks of quiescent spirals (e.g. Crawfordetal. 1985: Staceyetal. 1991: Solomonetal. 1997:: Downes&Solomon 1998)).," For example, a radial gradient of more than a factor of 10 has been reported in our Galaxy \cite{sod95}) ), and the conversion factor for the central regions of starburst galaxies—similar to many of the interacting galaxies in our sample—may differ by as much as two orders of magnitude from that of the dust clouds in the inner disks of quiescent spirals (e.g. \cite{cra85}; \cite{sta91}; \cite{sol97}; \cite{dow98}) )."
 These studies suggest that the CO brightucss iu galaxy disks is largely an excitation effect., These studies suggest that the CO brightness in galaxy disks is largely an excitation effect.
 We see in general only the skins of the molecular clouds in the emission line of σοι0)., We see in general only the skins of the molecular clouds in the emission line of $^{12}$ CO(1–0).
 The observed brightuess will therefore depeud directly on the excitation temperatures and beam fllius factors of the clouds., The observed brightness will therefore depend directly on the excitation temperatures and beam filling factors of the clouds.
 Furthermore. because Log/N(U2)XTpi. where T' is the eas temperature aud p ds the density (Dickman. Snell. Schloerb 1986: Maloney&Black1958: Ehucereen1989] ). an increase in the cloud temperatures will give rise to veher CO buninositices per unit nuuass resulting in overestimates of the ccouteut.," Furthermore, because $\ICO/N(\H2) \propto T / \rho^{\frac{1}{2}}$, where $T$ is the gas temperature and $\rho$ is the density (Dickman, Snell, Schloerb 1986; \cite{mal88}; \cite{elm89}) ), an increase in the cloud temperatures will give rise to higher CO luminosities per unit mass, resulting in overestimates of the content."
 Thus the CodY) line will be bright where the ISM is wir. and not recessarily where the ecol censitics are high.," Thus the $^{12}$ CO(1--0) line will be bright where the ISM is warm, and not necessarily where the column densities are high."
 Observations of nearby quiescent spiral galaxies indicate hat the molecular sas iu these galaxies is likely to o eenerallv cold aud therefore faint in CO. enmissiou (Allenetal.1997: Loinard&Allen 1998))., Observations of nearby quiescent spiral galaxies indicate that the molecular gas in these galaxies is likely to be generally cold and therefore faint in CO emission \cite{all97}; \cite{loi98}) ).
 The skins of the molecular clouds may be sufficiently warmed bv rearby UV sources to he visible iu the COM0) linc. mt this enuüssiou will have a simall spatial filling factor. resulting in low observed iuteusities.," The skins of the molecular clouds may be sufficiently warmed by nearby UV sources to be visible in the $^{12}$ CO(1–0) line, but this emission will have a small spatial filling factor, resulting in low observed intensities."
 Iu galaxies with Neher than normal levels of star formation. like many of the interacting svsfenis in our sample. the intense Hux of UV photous fom OD stars together with cosiuic-ravs from supernovae will tend to dissociate the low- regions of molecular clouds. aud the remaining gueh-deusitv reeious will be heated. so that the CO cluission dines will ennate from wart. hielh-densitv chuups (Allenetal.1995)).," In galaxies with higher than normal levels of star formation, like many of the interacting systems in our sample, the intense flux of UV photons from OB stars together with cosmic-rays from supernovae will tend to dissociate the low-density regions of molecular clouds, and the remaining high-density regions will be heated, so that the CO emission lines will emanate from warm, high-density clumps \cite{all95}) )."
 Studies of -CO/PCO aud PCO? 1/2 COW0) fux ratios in starburst aud mucereine systems do in fact indicate that the CO cussion is coming from suall. deuse. and warm (P — 100300 I) clouds (Aalto ct al.," Studies of $^{12}$ $^{13}$ CO and $^{12}$ $^{12}$ CO(1–0) flux ratios in starburst and merging systems do in fact indicate that the CO emission is coming from small, dense, and warm (T = 100–300 K) clouds (Aalto et al."
 19912.b: Aaltoetal.1995)).," 1991a,b; \cite{aal95}) )."
 The observed abundance ratios are sienificautly higher than those in eiut molecular clouds in the Galaxy. aud also show radial variatious within the galaxies.," The observed abundance ratios are significantly higher than those in giant molecular clouds in the Galaxy, and also show radial variations within the galaxies."
 Finally. recent studies of the molecular ISAI in ultvahuninous infrared galaxies have shown that the rratio may be 35 times lower in the centers of these ealaxies than in Calactic molecular clouds (SolomioDeetal1997: Downes&Solomon1998)).," Finally, recent studies of the molecular ISM in ultraluminous infrared galaxies have shown that the ratio may be 3–5 times lower in the centers of these galaxies than in Galactic molecular clouds \cite{sol97}; \cite{dow98}) )."
 Hence the application of the standard ccouversion factoo cads to significant overestimates of tle amount of i— ese ealaxies., Hence the application of the standard conversion factor leads to significant overestimates of the amount of in these galaxies.
 It is possible. therefore. that at least some portioce of the effects seen in this study are due to changes i ie properties of the molecular gas within the sample ealaxies rather than chauges in the gas content itself.," It is possible, therefore, that at least some portion of the effects seen in this study are due to changes in the properties of the molecular gas within the sample galaxies rather than changes in the gas content itself."
 Tustead of the level of star formation activity being driven w molecular eas conteut. the deduced molecular gas content nav be at least partially driven by the level of star formation activity.," Instead of the level of star formation activity being driven by molecular gas content, the deduced molecular gas content may be at least partially driven by the level of star formation activity."
 Portions of the sample of isolated spirals and the subsaniples of weakly interacting svstenis have systematically low levels of current star formation activity., Portions of the sample of isolated spirals and the subsamples of weakly interacting systems have systematically low levels of current star formation activity.
 Thus the molecular gas in these ealaxics will be cold and the observed level of CO emission low. with potentially large aiiounts of rremaiming unsceen.," Thus the molecular gas in these galaxies will be cold and the observed level of CO emission low, with potentially large amounts of remaining unseen."
 Meanwhile the more strongly interacting svstcms lave overall higher current star formation rates. which may lead to higher observed levels of CO emission due to increased cloud heating provided by the larger population of voung. massive stars.," Meanwhile the more strongly interacting systems have overall higher current star formation rates, which may lead to higher observed levels of CO emission due to increased cloud heating provided by the larger population of young, massive stars."
 The increase in observed CO cussion iu the more active ealaxics may be a simple result of having more sites of active star formation within the ealaxies. thus increasing the filliug factor of warm. CO-cinittine regions.," The increase in observed CO emission in the more active galaxies may be a simple result of having more sites of active star formation within the galaxies, thus increasing the filling factor of warm, CO-emitting regions."
 At the same time. the large UV and cosuic-ray fluxes xovided by massive stars will tend to dissociate the ireeions of the clouds. leading to an abnormally high (1159) ratio and a corresponding overestimate of he mass of οσα»," At the same time, the large UV and cosmic-ray fluxes provided by massive stars will tend to dissociate the regions of the clouds, leading to an abnormally high 2) ratio and a corresponding overestimate of the mass of gas."
", The data in Tables 6 aud 8 do iu fact show that the average dust temperatures increase with both interaction strenethl aud level of star ormation activity.", The data in Tables \ref{tbl_subprop} and \ref{tbl_clsprop} do in fact show that the average dust temperatures increase with both interaction strength and level of star formation activity.
 The temperature increase. however. ix rot very large aud the precise connection between observed dust temperatures and molecular eas cloud excitation cluperatures is not well kuown.," The temperature increase, however, is not very large and the precise connection between observed dust temperatures and molecular gas cloud excitation temperatures is not well known."
 The actively star-forming interacting ealaxics iu the saluple studied here appear to have properties that are intermediate between those of the isolated galaxies aud he ultraluninous infrared galaxies in other studies., The actively star-forming interacting galaxies in the sample studied here appear to have properties that are intermediate between those of the isolated galaxies and the ultraluminous infrared galaxies in other studies.
 Thus we assune that an intermediate ccouversion actor would be appropriate for these svstenis., Thus we assume that an intermediate conversion factor would be appropriate for these systems.
 Conversion actors 3 to 5 times lower than the standard have been sugeested for the ultraluninous infrared svsteuis. therefore a conversion factor ~2 times lower than the standard iav )o appropriate for the active svstenmis in this study.," Conversion factors 3 to 5 times lower than the standard have been suggested for the ultraluminous infrared systems, therefore a conversion factor $\sim$ 2 times lower than the standard may be appropriate for the active systems in this study."
 A reduction of a factor of 2 in the derived nuuasses or the galaxies with high SFRs would easily accountfor he increases in mean, A reduction of a factor of 2 in the derived masses for the galaxies with high SFR's would easily accountfor the increases in mean
(NJE) (NJE) (NJE) (NJE) (NJE) Description: Class 0 sources are often. but not always. Stage Ü sources. (,"(NJE) (NJE) (NJE) (NJE) (NJE) Description: Class 0 sources are often, but not always, Stage 0 sources. ("
NJE) Description: Class I sources are often. but uot abwavs. Stage I sources.,"NJE) Description: Class I sources are often, but not always, Stage I sources."
 Connuents: These definitions. whether by mass or by relative infall rate may have problems in describing nore massive stars. (," Comments: These definitions, whether by mass or by relative infall rate may have problems in describing more massive stars. ("
NJE},NJE)
function of the enclosed number of particles.,function of the enclosed number of particles.
" As noted by ? and ?,, obtaining robust results in regions closer to the centre, where the density is higher, demands increasingly large particle numbers."," As noted by \citet{moore1998} and \citet{power2003}, obtaining robust results in regions closer to the centre, where the density is higher, demands increasingly large particle numbers."
 As in Fig., As in Fig.
 14 of ? we have compared the mean inner density measured at different fractions of the virial radius as a function of the enclosed particle number for all the runs., $14$ of \citet{power2003} we have compared the mean inner density measured at different fractions of the virial radius as a function of the enclosed particle number for all the runs.
 The results are displayed in Fig. 16.., The results are displayed in Fig. \ref{power14}.
 The 64? simulation using fixed softening provides converged results at most down to ~6% of the virial radius., The $64^3$ simulation using fixed softening provides converged results at most down to $\simeq 6\%$ of the virial radius.
 At smaller radii the results start to diverge from those obtained at higher resolution and cannot be trusted anymore., At smaller radii the results start to diverge from those obtained at higher resolution and cannot be trusted anymore.
 The two runs with adaptive softening behave instead very well down to 396 of the virial radius., The two runs with adaptive softening behave instead very well down to $3\%$ of the virial radius.
" Similarly, the 128? simulation is reliable down to ~2% of the virial radius when using fixed softening and down to 196 of the virial radius when adaptive softening is employed."," Similarly, the $128^3$ simulation is reliable down to $\simeq 2\%$ of the virial radius when using fixed softening and down to $1\%$ of the virial radius when adaptive softening is employed."
" ? relate the converged side of the enclosed-p vs. enclosed-N plot to the regions where the average collisional relaxation time t,e; exceeds some fraction of the age of Universe to (between 0.6 and 1).", \citet{power2003} relate the converged side of the $\rho$ vs. enclosed-N plot to the regions where the average collisional relaxation time $t_{rel}$ exceeds some fraction of the age of Universe $t_0$ (between $0.6$ and $1$ ).
" In our case, depending on whether we consider the results at 696 of the virial radius converged or not, we could extend the regions down to the radii where tret&0.4to."," In our case, depending on whether we consider the results at $6\%$ of the virial radius converged or not, we could extend the regions down to the radii where $t_{rel} \approx 0.4 t_0$."
" In any case, it is not clear whether the 256? run can be considered converged according to this criterion."," In any case, it is not clear whether the $256^3$ run can be considered converged according to this criterion."
 It is anyway worth of notice that the 128? adaptive run with correction reproduces perfectly the enclosed density of the 256? at 196 of the virial Similar results hold when investigating the properties of substructures., It is anyway worth of notice that the $128^3$ adaptive run with correction reproduces perfectly the enclosed density of the $256^3$ at $1\%$ of the virial Similar results hold when investigating the properties of substructures.
 Fig., Fig.
 17 shows the number of subhalos with mass greater than a certain value; the curves represent the average over the five biggest halos in the simulations and the masses have all been normalised to the virial mass of the host., \ref{shalos} shows the number of subhalos with mass greater than a certain value; the curves represent the average over the five biggest halos in the simulations and the masses have all been normalised to the virial mass of the host.
 Due to the poverty of substructures we are not showing the results for the lowest resolution simulations and we are in general limited to qualitative considerations., Due to the poverty of substructures we are not showing the results for the lowest resolution simulations and we are in general limited to qualitative considerations.
" As can immediately be seen though, the runs with adaptive softening lie closer to the higher resolution simulation than does the run with fixed softening."," As can immediately be seen though, the runs with adaptive softening lie closer to the higher resolution simulation than does the run with fixed softening."
 All the results shown so far hold at redshift zero., All the results shown so far hold at redshift zero.
" As shown in Fig. 19,,"," As shown in Fig. \ref{soft},"
 even at this redshift only ~1% of the particles have softening smaller than 1/40 of the mean interparticle separation and at higher redshifts this behaviour becomes even more extreme., even at this redshift only $\approx 1 \%$ of the particles have softening smaller than $1/40$ of the mean interparticle separation and at higher redshifts this behaviour becomes even more extreme.
 This has the effect of reducing the amplitude of the correlation function more rapidly than in the standard runs when going back in time., This has the effect of reducing the amplitude of the correlation function more rapidly than in the standard runs when going back in time.
 A more quantitative representation of this effect will be given in the next section (Fig. 20))., A more quantitative representation of this effect will be given in the next section (Fig. \ref{mmII_corr}) ).
" The mass functions are not substantially affected though, at least not for objects more massive than the 32-particles limit (Fig. 21))"," The mass functions are not substantially affected though, at least not for objects more massive than the $32$ -particles limit (Fig. \ref{mmII_mfct})"
". As the particle timesteps depends on the value of the gravitational softening (see Eq. 11)),"," As the particle timesteps depends on the value of the gravitational softening (see Eq. \ref{eq:timecriterion}) ),"
 it is natural to expect, it is natural to expect
 (c.g.Frandsenal.2006:Barbanet2007) (Baglinetal.2002) (DeRidder2009;Carrier," \citep[e.g.][]{Frandsen02, Joris06, Barban07} \citep{Baglin02} \citep{Joris09, Hekker09, Carrier10}."
"etal.2010).. Kjeldsen A\v- —/4,4,) Mosseretal.(2010a) Miglioetal.(2009a) Mighioetal.(2009b) ", \cite{KB95} $\Delta\nu$ $\nu_{\rm max}$ \cite{Mosser10} \cite{MiglioPop09} \cite{MiglioPop209} 
rms temperature data measured in. various laboratory experiments at higher Ravieigh number provides a more adequate point of comparison.,rms temperature data measured in various laboratory experiments at higher Rayleigh number provides a more adequate point of comparison.
 We use the rms temperature data of the highest aspect. ratio experiments of DuPuits. Resagk Thess (2007). for Ra = δ.1107.," We use the rms temperature data of the highest aspect ratio experiments of DuPuits, Resagk Thess (2007), for Ra = $8.14 \times
10^8$."
 This dataset exhibits a significant asymptotic range. with a power law close to the one predicted. by the closure model ία-qoi] 77).," This dataset exhibits a significant asymptotic range, with a power law close to the one predicted by the closure model $q \sim
q_0 \eta^{-2/3}$ )."
 Fitting the data vieleds qu0.95+0.05. which provides a first constraint between C5 and €7 (see Fig. 6)).," Fitting the data yields $q_0 = 0.95 \pm 0.05$, which provides a first constraint between $C_6$ and $C_7$ (see Fig. \ref{fig:C6C7}) )."
 Note that other datasets. (from. Alavstrenko. Resagk ‘Thess. 2007. for example) are generally. consistent with this estimate for qu.," Note that other datasets (from Maystrenko, Resagk Thess, 2007, for example) are generally consistent with this estimate for $q_0$."
 A second constraint between C and C's is obtained bv comparing the model predictions. with experimental measurements of Nu(Ita)., A second constraint between $C_6$ and $C_7$ is obtained by comparing the model predictions with experimental measurements of $\mathrm{Nu}(\mathrm{Ra})$.
 The closure model implies that Νααιαν” where the constant AN. is a function of the model parameters (and the Prandtl number)., The closure model implies that ${\rm Nu} = 1 + K {\rm Ra}^{1/3}$ where the constant $K$ is a function of the model parameters (and the Prandtl number).
 The data from Fünnfschilling et al. (, The data from Fünnfschilling et al. (
2005). Niemela Sreenivisan (2006) and DuPuits. Itesagk Thess (2007) are reasonably well approximated bv taking fy=0.06x0.003.,"2005), Niemela Sreenivisan (2006) and DuPuits, Resagk Thess (2007) are reasonably well approximated by taking $K=0.06 \pm 0.003$."
 Variations of AN. with Prandtlnumber. for the range of experiments discussed. are within the errorbars.," Variations of $K$ with Prandtlnumber, for the range of experiments discussed, are within the errorbars."
" Given that ἐν. C2. C. C'; and €, are now known. for fixed Prandtl number. fitting dv provides a unique relationship between CG and C. as seen in lig. 6.."," Given that $C_1$, $C_2$ , $C_\nu$, $C_\kappa$ and $C_{\nu\kappa}$ are now known, for fixed Prandtl number, fitting $K$ provides a unique relationship between $C_6$ and $C_7$, as seen in Fig. \ref{fig:C6C7}."
 ὃν combining these two constraints. we conclude that a good fit to the data can be obtained with The values for (65) quoted in equations (46)). (47)). and (48)) form from here on our selected set of paranicters.," By combining these two constraints, we conclude that a good fit to the data can be obtained with The values for $\{C_i\}$ quoted in equations \ref{eq:C1C2}) ), \ref{eq:Cd}) ), and \ref{eq:C6C7}) ) form from here on our selected set of parameters."
 ‘These values are to be taken as indicative estimates. rather han precise calibrations.," These values are to be taken as indicative estimates, rather than precise calibrations."
 We note that. the. parameters derived do satisfy realizabilitv (see Appendix AJ., We note that the parameters derived do satisfy realizability (see Appendix A).
 Phe solid ines shown in Figs. 3..," The solid lines shown in Figs. \ref{fig:rzzcal},"
 4. and 5 are the universal boundary aver profiles calculated using these parameters. and are seen ο fit all datasets (except For ri; and r4. as discussed above) satisfactorily.," \ref{fig:fzcal} and \ref{fig:qcal} are the universal boundary layer profiles calculated using these parameters, and are seen to fit all datasets (except for $r_{xx}$ and $r_{yy}$ , as discussed above) satisfactorily."
 Fig., Fig.
7 compares our closure model. prediction. for he Nu(Ra) relationship. using the estimated: parameters.,"\ref{fig:RaNu} compares our closure model prediction for the Nu(Ra) relationship, using the estimated parameters,"
lines and in particular forbidden lines.,lines and in particular forbidden lines.
 These forbidden lines have been useful for deriving or constraining gaseous abundances that are relevant for testing models of massive star evolution (e.g.. Barlow. Roche. Aitken 1988: Willis 1997: Dessart 22000: Morris 22000: Morris. Crowther. Houck 2004: Smith Houck 2005: Ignace 22007).," These forbidden lines have been useful for deriving or constraining gaseous abundances that are relevant for testing models of massive star evolution (e.g., Barlow, Roche, Aitken 1988; Willis 1997; Dessart 2000; Morris 2000; Morris, Crowther, Houck 2004; Smith Houck 2005; Ignace 2007)."
 An interesting property of these forbidden lines is that they orm at large radius in the wind of a WR star., An interesting property of these forbidden lines is that they form at large radius in the wind of a WR star.
 Consequently. the line ormation occurs well beyond the wind acceleration thus sampling he flow at the wind terminal speed c4.," Consequently, the line formation occurs well beyond the wind acceleration thus sampling the flow at the wind terminal speed $v_\infty$."
 Being optically thin these orbidden lines should be flat-topped in shape. and so they are excellent for measuring ¢ values (Barlow 11988).," Being optically thin these forbidden lines should be flat-topped in shape, and so they are excellent for measuring $v_\infty$ values (Barlow 1988)."
 But the flat-topped profile morphology only holds ifthe wind is spherically symmetric., But the flat-topped profile morphology only holds if the wind is spherically symmetric.
 If à WR star is part of a binary. then even if the WR wind is intrinsically spherically symmetric. the CWIR ensures that it will not remain so.," If a WR star is part of a binary, then even if the WR wind is intrinsically spherically symmetric, the CWIR ensures that it will not remain so."
 Equally interesting is the faet that forbidden lines can form over tens of thousands of WR stellar radii (e.g.. Ignace 220013. corresponding to scales of several AU and comparable to binary separations in massive star binaries.," Equally interesting is the fact that forbidden lines can form over tens of thousands of WR stellar radii (e.g., Ignace 2001), corresponding to scales of several AU and comparable to binary separations in massive star binaries."
 As a result. forbidden emission profiles should not be flat-topped in general in these systems. and their deviation from flat-top — like the ease for other CWIR emission line diagnosties — ean be used to constrain the properties of the CWIR geometry.," As a result, forbidden emission profiles should not be flat-topped in general in these systems, and their deviation from flat-top – like the case for other CWIR emission line diagnostics – can be used to constrain the properties of the CWIR geometry."
 In this paper we calculate a range of forbidden line profile shapes as a function of wind and orbit parameters., In this paper we calculate a range of forbidden line profile shapes as a function of wind and orbit parameters.
 Section 2 presents a brief overview of forbidden line formation. a derivation of emission profiles in a spherical wind. and then in a colliding wind system.," Section 2 presents a brief overview of forbidden line formation, a derivation of emission profiles in a spherical wind, and then in a colliding wind system."
" Then Section 3 deseribes applications to two systems: WR 147 and , Vel.", Then Section 3 describes applications to two systems: WR 147 and $\gamma$ Vel.
 Concluding remarks are given in Section 4., Concluding remarks are given in Section 4.
 Our presentation of the theory of forbidden line emission generally follows Osterbrock (1989) regarding the atomic physics. Barlow (1988) for application to winds. and Ignace Brimeyer (2006) for notation.," Our presentation of the theory of forbidden line emission generally follows Osterbrock (1989) regarding the atomic physics, Barlow (1988) for application to winds, and Ignace Brimeyer (2006) for notation."
 The following sections describe (a) the two-level approximation for forbidden lines. (b) the solution for the forbidden line emission in a spherical wind. (ο) the adopted model used to describe a CWIR between a WR star and an OB star. and (d) adjustments to the forbidden line profile calculation arising from the CWIR.," The following sections describe (a) the two-level approximation for forbidden lines, (b) the solution for the forbidden line emission in a spherical wind, (c) the adopted model used to describe a CWIR between a WR star and an OB star, and (d) adjustments to the forbidden line profile calculation arising from the CWIR."
 For simplicity the two-level atom approximation is adopted for a fine structure transition of an ion species., For simplicity the two-level atom approximation is adopted for a fine structure transition of an ion species.
 The lower level will bel and the upper level 27., The lower level will be `1' and the upper level `2'.
 It is common to introduce a critical density n that signifies the transition from the higher density medium where de-exeitations are dominated by collisions versus the lower density zone where spontaneous decay dominates., It is common to introduce a critical density $n_{\rm c}$ that signifies the transition from the higher density medium where de-excitations are dominated by collisions versus the lower density zone where spontaneous decay dominates.
 Since excitation is assumed to derive from collisionsον. the emissivity transitions from a function that is linear in density in the collisional regime to one that is quadratic in density in the decay regime.," Since excitation is assumed to derive from collisions, the emissivity transitions from a function that is linear in density in the collisional regime to one that is quadratic in density in the decay regime."
" The critical density is defined as where ;Ao, +] is the Einstein A-value for the transition. and (qoi . .. ↥⊰↾∣↧∁↲∩∖↖⋯↖⋯⊔⋯∣⋯∏∁∁∩∥↥⊰⋯∣⋯∣↳∣∁−∁⋅∖∁↥↾⋡∙⋯⋯∏⊾∸∣↾∁↾∁⋯⊰↴⋅ "," The critical density is defined as where $A_{21}$ $^{-1}$ ] is the Einstein A-value for the transition, and $q_{21}$ is the downward volume collisional de-excitation rate $^3$ $^{-1}$ ]."
"The volume emissivity j feres em ""sr !]is In the two level atom. the entire density of elemental species ££ in ion stage 7 is given by np;=nmi|n»."," The volume emissivity $j$ [erg $^{-1}$ $^{-3}$ $^{-1}$ ] is In the two level atom, the entire density of elemental species $E$ in ion stage $i$ is given by $n_{\rm E,i} = n_1 + n_2$."
" One can derive the ratio nofn, from equilibrium conditions and use that to solve for the population of the upper level: (Barlow 11988): where with for vo, the frequency of the line transition. 7. the electron temperature. and q.; the statistical weight of the level. with 2J| 1."," One can derive the ratio $n_2/n_1$ from equilibrium conditions and use that to solve for the population of the upper level: (Barlow 1988): where with for $\nu_{21}$ the frequency of the line transition, $T_{\rm e}$ the electron temperature, and $g_J$ the statistical weight of the level, with $g_J=2J+1$ ."
 The downward collisional volume rate is given by where wy. is the collision strength., The downward collisional volume rate is given by where $\omega_{12}$ is the collision strength.
 A summary of line transition data and critical densities is given in Table I.., A summary of line transition data and critical densities is given in Table \ref{tab1}.
 Forbidden emission lines in stellar winds are optically thin., Forbidden emission lines in stellar winds are optically thin.
 The above relations are typically combined with the intent of integrating the emissivity over the wind and solving for the ionic abundance. derivable from observed forbidden emission lines anc used to constrain gas abundances in evolved stars to test massive star evolution models.," The above relations are typically combined with the intent of integrating the emissivity over the wind and solving for the ionic abundance, derivable from observed forbidden emission lines and used to constrain gas abundances in evolved stars to test massive star evolution models."
 The primary goal of our paper is quite different., The primary goal of our paper is quite different.
 We seek to derive line profile to determine to wha extent those shapes may be used to deduce the properties of binary orbits and stellar winds in colliding wind systems., We seek to derive line profile to determine to what extent those shapes may be used to deduce the properties of binary orbits and stellar winds in colliding wind systems.
 To do so. we firs review the solution for a spherical wind.," To do so, we first review the solution for a spherical wind."
 It is useful to review briefly the line emission for a forbidden line from a spherically symmetric wind. both to establish notation and as a reference to use with the non-spherical case.," It is useful to review briefly the line emission for a forbidden line from a spherically symmetric wind, both to establish notation and as a reference to use with the non-spherical case."
" For a spherical wind with mass-loss rate aand radial speed ο) for radius r. the mass density is The electron number density is n,=p.nΠΟΠΗ. for jr. the mean molecular weight per free electron."," For a spherical wind with mass-loss rate and radial speed $v(r)$ for radius $r$, the mass density is The electron number density is $n_{\rm e} = \rho_{\rm
sph} / \mu_{\rm e} m_H$, for $\mu_{\rm e}$ the mean molecular weight per free electron."
" The region of line formation is set roughly by the radius at which n,=n.", The region of line formation is set roughly by the radius at which $n_{\rm e} = n_{\rm c}$.
 For hot stars M~10.1 aand larger. with ex~1000 oor more for OB stars (e.g.. Lamers Cassinelli 1999).," For hot stars $\dot{M} \sim 10^{-10}$ and larger, with $v_\infty \sim 1000$ or more for OB stars (e.g., Lamers Cassinelli 1999)."
 To estimate the radius of line formation. we introduce an electron. number density scale factor that depends on these basie wind parameters:," To estimate the radius of line formation, we introduce an electron number density scale factor that depends on these basic wind parameters:"
Under the unified scheme of Active Galactic Nuclei CAGNs). Sevlert I nuclei with broad line regions (BLRs) would be classified as Sevfer( 2 if the BLRs were obscured by encircling,"Under the unified scheme of Active Galactic Nuclei (AGNs), Seyfert 1 nuclei with broad line regions (BLRs) would be classified as Seyfert 2 if the BLRs were obscured by encircling"
The Capella svstem is one of the strongest N-ray enulling coronal sources. aud has been observed numerous times with the past and current X-rav observatories. including both,"The Capella system is one of the strongest X-ray emitting coronal sources, and has been observed numerous times with the past and current X-ray observatories, including both"
profiles that have more pronounced double-horus at greater velocity shifts from line center.,profiles that have more pronounced double-horns at greater velocity shifts from line center.
 For integer values of i. the inteeral is analytic. aud solutions for a=3 anda =Lare given here by wax of example.," For integer values of $m$, the integral is analytic, and solutions for $m=3$ and $m=4$ are given here by way of example."
 For i=3 the result is EE Note that increasing values of a7 also result in profile shapes of lower amplitude.," For $m=3$ the result is and for $m=4$, Note that increasing values of $m$ also result in profile shapes of lower amplitude."
 Iu fact it is possible to solve for the inteerated lieht from a resonance scattering line in some special cases;, In fact it is possible to solve for the integrated light from a resonance scattering line in some special cases.
 Define a few selectedresults ave Επ)=Ez:mFo. Fror(2)=5bx/3:TyFy. Prop(3)=27/37Fy. aud Fu.," Defining a few selectedresults are $F_{\rm tot}(1)=4\pi\cdot\taul{\cal
F}_0$, $F_{\rm tot}(2) = 5\pi/3\cdot\taul\,{\cal F}_0$, $F_{\rm tot}(3)=2\pi/3\cdot\taul\,{\cal F}_0$, and $F_{\rm tot}(4)=\pi/2\cdot\taul\,{\cal F}_0$ ."
 It would appear that with 7=constent. different values of £i. aud thus lines of differeut brightuesslevels. could result.," It would appear that with $\taul=constant$, different values of $F_{\rm tot}$, and thus lines of different brightnesslevels, could result."
 This secs counterintuitive if lines characterized by different values of i have the same optical depth., This seems counterintuitive if lines characterized by different values of $m$ have the same optical depth.
 ILowever. 7 depends oulv ou the density at the iuncr portion of the disk My. uot the value of m.," However, $\taul$ depends only on the density at the inner portion of the disk $\Sigma_0$, not the value of $m$."
 Thus when the line is optically thin. the appropriate optical depth to use is oue that is angle averaged. simular in spirit to 7 iun Brown MeLean (1977) for optically thin clectron scattering.," Thus when the line is optically thin, the appropriate optical depth to use is one that is angle averaged, similar in spirit to $\bar{\tau}$ in Brown McLean (1977) for optically thin electron scattering."
" Tence use of a now optical depth parameter would cusure that lines of different i0 values withisotropic scattering will have the same total line enission (G.c.. ""area under the curve”) even though they have different profile shapes."," Hence use of a new optical depth parameter $T_l = \tau_0\times \tau_0 {\cal
F}_0/F_{\rm tot}(m)$ would ensure that lines of different $m$ values with scattering will have the same total line emission (i.e., “area under the curve”) even though they have different profile shapes."
 For resonance line scattering with £4z0 but with B=0 everywhere. the vector scattering function / ereatlv simplifies.," For resonance line scattering with $E_1 \neq 0$ but with $B=0$ everywhere, the vector scattering function $\vec{h}$ greatly simplifies."
" Following Paper IL. we have that à=4. αυ—0. C=cos25. D=sin25. aud ce,=0."," Following Paper II, we have that $\delta=\varphi$, $\alpha_2 = 0$, $C=\cos 2\varphi$, $D=\sin 2\varphi$, and $\psis =
0$."
 The components of the phase function become The Stokes tux of scattered light is Note that care must be taken in dealing with terms that are odd and even iu y between angles of 0 aud 7., The components of the phase function become The Stokes flux of scattered light is Note that care must be taken in dealing with terms that are odd and even in $\varphi$ between angles of 0 and $\pi$.
 For example. Ji is odd around the loop. cusuring that Zr= 0.," For example, $h_U$ is odd around the loop, ensuring that ${\cal F}_U=0$ ."
" Accounting for the odd/even terms. aud using the fact that sin?=ty/t w2/t solutions for the scattered flux in Stokes-I aud Stokes-Q are: Note at the extrema of the line wines. ZEb""(in)=Fen’) aud ty=1. and q;23Ey/(lLEy) alwavs."," Accounting for the odd/even terms, and using the fact that $\sin^2
\varphi =t_0/t=\wzz/t$ , solutions for the scattered flux in Stokes-I and Stokes-Q are: Note at the extrema of the line wings, $\fiso(m)=\fiso(m')$ and $t_0=1$, and $\qs = 3E_1/(4-E_1)$ always."
situations for how the deceleration of the GRB blastwave. and hence the afterglow. initiates.,"situations for how the deceleration of the GRB blastwave, and hence the afterglow, initiates."
 As in conventional discussions of afterglows. the deceleration may begin when it has swept up enough outline baryonic material. which may occur if the (probably collimated) fireball in our line of sight happens to strike the denser parts of the cutrained SN cjecta fraginents inside the pleriou.," As in conventional discussions of afterglows, the deceleration may begin when it has swept up enough outlying baryonic material, which may occur if the (probably collimated) fireball in our line of sight happens to strike the denser parts of the entrained SN ejecta fragments inside the plerion."
 Alternatively. the deceleration iav result from the blastwave accumulating enough inertia in relativistic particles aud maeunetic field of the pulsar wind material. as discussed by ICGO2.," Alternatively, the deceleration may result from the blastwave accumulating enough inertia in relativistic particles and magnetic field of the pulsar wind material, as discussed by KG02."
 To deseribe the afterglow in this case. KCO2 showed that standard formulae (c.e. Sari. Pian Naravan 1998) can still be used if one replaces parameters such as the züubient iiedium deusity aud electron aud iiagnuetic energv density fractions bv equivalent quautities related to the plevion properties (sce below).," To describe the afterglow in this case, KG02 showed that standard formulae (e.g. Sari, Piran Narayan 1998) can still be used if one replaces parameters such as the ambient medium density and electron and magnetic energy density fractions by equivalent quantities related to the plerion properties (see below)."
 In cousideriug either case. we will assume for simplicity that the decelerating medii is roughly uniform. at least within the timescales we consider. (," In considering either case, we will assume for simplicity that the decelerating medium is roughly uniform, at least within the timescales we consider. ("
Note that this is uot a bad approximation for most of the MITID plerion models discussed by ICU2.),Note that this is not a bad approximation for most of the MHD plerion models discussed by KG02.)
" The standard expressious for the radius r aud bulk Loreutz factor D of the shocked material iu au adiabatic. spherical blastwave decelerating seltsiuilarlyv in a iniforui medium are r(t)=[12EcftranFr|jpDo34)xτοτσEssfitHr,(1l|ut and Tit)=BE|DΜπο.Adou) v. respectively (e.g. Mésszárros Rees 1997. Piran 1999]."," The standard expressions for the radius $r$ and bulk Lorentz factor $\Gamma$ of the shocked material in an adiabatic, spherical blastwave decelerating self-similarly in a uniform medium are $r(t) = [12E ct / 4\pi n m_p c^2 (1+z)]^{1/4}
 \sim 3.6 \times 10^{17} {\rm cm} (E_{52}/n)^{1/4} [t_d/(1+z)]^{1/4}$ and $\Gamma(t) = [3E (1+z)^3/ 256\pi n m_p c^5 t^3)]^{1/8}
 \sim 5.9 (E_{52}/n)^{1/8} [t_d/(1+z)]^{-3/8}$ , respectively (e.g. Mésszárros Rees 1997, Piran 1999)."
 Ποιο E=πρ is the blastwave energy. Πο? the external inediuu deusitv. f£=μίαν the observer time elapsed after the CRB. + is the CRB redshift. aud we lave adopted the kinematic relation t=r(l|:)/1DI?e.," Here $E=10^{52} E_{52} {\rm erg}$ is the blastwave energy, $n {\rm cm^{-3}}$ the external medium density, $t=t_d {\rm day}$ the observer time elapsed after the GRB, $z$ is the GRB redshift, and we have adopted the kinematic relation $t={r(1+z) /4\Gamma^2 c}$."
" The deceleration starts at radius ο,—(3EIETΓρ),5x2.6«ΠΡη.DoSod at observer tie tyerasdoLMAPSe~2dsldpoUEsS/n)PD uo: where Py=3000y.300 is the initial bulls Loreutz factor."," The deceleration starts at radius $r_{dec} = (3E / 4\pi n m_p c^2 \Gamma_0^2)^{1/3}
 \sim 2.6 \times 10^{16} {\rm cm} (E_{52}/n)^{1/3} \Gamma_{0,300}^{-2/3}$ at observer time $t_{dec} = r_{dec}(1+z) /4\Gamma_0^2 c
 \sim 2.4 {\rm s} (1+z) (E_{52}/n)^{1/3} \Gamma_{0,300}^{-8/3}$ , where $\Gamma_0=300 \Gamma_{0,300}$ is the initial bulk Lorentz factor."
 To describe the time-cependenut. multiwavelength afterglow spectrum from the blastwave. we follow standard discussions of the svuclirotron emission (e.g. Mésszárros Rees 1997. Sari. Piran Naravan 1998. Wijers Calauia 1999). and extend it to include cooling and emission bv the EC process in additiou to the svuchrotron-scl&Compton (SSC) process (Panaitescu ναι 2000: Sari Esin 2001. hereafter SEO: Zhang Mésszirros 2001. hereafter ZMOL)," To describe the time-dependent, multiwavelength afterglow spectrum from the blastwave, we follow standard discussions of the synchrotron emission (e.g. Mésszárros Rees 1997, Sari, Piran Narayan 1998, Wijers Galama 1999), and extend it to include cooling and emission by the EC process in addition to the synchrotron-self-Compton (SSC) process (Panaitescu Kumar 2000; Sari Esin 2001, hereafter SE01; Zhang Mésszárros 2001, hereafter ZM01)."
 It is assuuced that constaut fractions ερ=O0lep» aud e.=Ole.4 of the postshock energv are nuparted to magnetic field aud relativistic electrous. respectively.," It is assumed that constant fractions $\epsilon_B=0.01 \epsilon_{B,-2}$ and $\epsilon_e= 0.1 \epsilon_{e,-1}$ of the postshock energy are imparted to magnetic field and relativistic electrons, respectively."
" The comoving mnaguetie field is Bit)=(32repnim,)*?Den023Gej7ES“ta(1|:)] YS "," The comoving magnetic field is $B(t) = (32\pi \epsilon_B n m_p)^{1/2} \Gamma c
 \sim 0.23 {\rm G} \epsilon_{B,-2}^{1/2} E_{52}^{1/8} n^{3/8} [t_d/(1+z)]^{-3/8}$ ."
"Eleetrouns are accelerated in the shock to a power- distributiondo/d5~~ ""iuthe Loreutz factor rauge usSyXo*sap ", Electrons are accelerated in the shock to a power-law distribution$dn/d\gamma \propto \gamma^{-p}$ in the Lorentz factor range $\gamma_m \le \gamma \le \gamma_M$.
We asstune poc2. our standard choice being p=2.5.," We assume $p>2$, our standard choice being $p=2.5$."
" The niniumi Loreutz factor 5,, is given by (note that [3p—2)f(p1)1 wheu p=2.5).", The minimum Lorentz factor $\gamma_m$ is given by (note that $[3(p-2)/(p-1)]=1$ when $p=2.5$ ).
" The electrons radiatively cool by the combination of thesvuchrotrou. SSC aud EC processes; the timescales of which ave fL,—οπλοστΏτον (us—Vt, aud KS=XH respectively, the total cooling tine being (=O87.)10/6,9]b=IY1X)4."," The electrons radiatively cool by the combination of thesynchrotron, SSC and EC processes, the timescales of which are $t'_{sy} \sim 6\pi m_e c / \sigma_T B^2 \gamma$, $t'_{ssc} \equiv Y t'_{sy}$ and $t'_{ec} \equiv X t'_{sy}$ respectively, the total cooling time being $t'_c=[(1/t'_{sy})+(1/t'_{ssc})+(1/t'_{ec})]^{-1} = t'_{sy}(1+Y+X)^{-1}$."
" The maximaOg, Loreutz factor 53; ix deterimuned by balauciug UÜ with the acceleration time f£.—ποσο. (CZAIOL)."," The maximum Lorentz factor $\gamma_M$ is determined by balancing $t'_c$ with the acceleration time $t'_{acc} \sim 2\pi \gamma m_e c / e B$ , (ZM01)."
" The cooling Loreutz factor 2, is where £7 equals the comoving adiabatic expansion time £5,7ΕΤ~(T. The observed characteristic svuchrotron cliission frequency for an electron of Loreutz factor 3 is vo= AVijers Galuna 1999). sothose for cach of 5,4. say and 5, are respectively and At early times (f< fj) ty)>55 and alb electrous cool within £, (fast cooling regime)."," The cooling Lorentz factor $\gamma_c$ is where $t'_c$ equals the comoving adiabatic expansion time $t'_{ad} \sim r/c\Gamma \sim t\Gamma$, The observed characteristic synchrotron emission frequency for an electron of Lorentz factor $\gamma$ is $\nu = (4/3) \Gamma (3/4\pi) (eB/m_e c) \gamma^2 (1+z)^{-1}$ (Wijers Galama 1999), sothose for each of $\gamma_m$, $\gamma_M$ and $\gamma_c$ are respectively and At early times $t<t_t$ ), $\gamma_m > \gamma_c$, and all electrons cool within $t'_{ad}$ (fast cooling regime)."
" The svuclirotrou flux f,then peaks at É. and mainly consists of three power-luy segments: fp=(v/vJOfaunas, for poc onnfe(efe)Εις for v2cν<vy, aud ( vir)i "," The synchrotron flux $f_\nu$then peaks at $\nu_c$ and mainly consists of three power-law segments: $f_\nu=(\nu/\nu_c)^{1/3} f_{\nu,\max}$ for $\nu<\nu_c$ ,$f_\nu=(\nu/\nu_c)^{-1/2} f_{\nu,\max}$ for $\nu_c<\nu<\nu_m$ and $f_\nu=(\nu_m/\nu_c)^{-1/2} (\nu/\nu_m)^{-p/2} f_{\nu,\max}$ for $\nu_m<\nu<\nu_M$ ."
"At late times (ff fh 5,nOMM.c ce and only electrons ↽∕∏∐∖∐↑∐↸∖↴∖↴↻↸∖↸⊳⊓⋅∏↕⊔↻↸∖⋜∐↘↽↴∖↴⋜↧↑↗∕∣⊔∙⋜⋯≼↧⋜↧∶↴∙⊾⋜∏∐∐⋜↧↴∖↴↑↕∐"," At late times $t>t_t$ ), $\gamma_m < \gamma_c$ , and only electrons of $\gamma > \gamma_c$ cool within$t'_{ad}$ (slow cooling regime)."
"⋅↸∖↸∖ parts: te=(vwVin)""Foanax for w« TE ""m— forB VOM aud ""m= forJ MozBox MAL."," Then the spectrum peaks at $\nu_m$ , and again has three parts: $f_\nu=(\nu/\nu_m)^{1/3} f_{\nu,\max}$ for $\nu<\nu_m$ , $f_\nu=(\nu/\nu_m)^{-(p-1)/2} f_{\nu,\max}$ for $\nu_m<\nu<\nu_c$ and $f_\nu=(\nu_c/\nu_m)^{-(p-1)/2} (\nu/\nu_c)^{-p/2} f_{\nu,\max}$ for $\nu_c<\nu<\nu_M$ ."
 TheY peak svuchrotron fux. fius for either fast or slow cooling is," The peak synchrotron flux $f_{\nu,\max}$ for either fast or slow cooling is"
observations of black hole masses in order to fully use these opportunities.,observations of black hole masses in order to fully pursue these opportunities.
 NTE J1650-500 (hereafter J1650) was discovered w RATE on 2001 September 5 (Ποιήματα 2001) and subsequently reached a peak X-ray intensity of 1.5 Crab., XTE J1650-500 (hereafter J1650) was discovered by RXTE on 2001 September 5 (Remillard 2001) and subsequently reached a peak X-ray intensity of 0.5 Crab.
 Based ou subsequent observations. J1650 was established as a strong black hole caudida5 sed on its N-ray spectrum and variability iu the N-rav helt curve (Alarkwardt. Swauk. Sinith 2001: Revuivtsey Sunvacy 2001: Wijinanuds. Aliller. Lewin 2001).," Based on subsequent observations, J1650 was established as a strong black hole candidate based on its X-ray spectrum and variability in the X-ray light curve (Markwardt, Swank, Smith 2001; Revnivtsev Sunyaev 2001; Wijnands, Miller, Lewin 2001)."
 The radio counterpart was discovered with the Australia Telescope Compact Array (ATCA) by Croot et ((2001)., The radio counterpart was discovered with the Australia Telescope Compact Array (ATCA) by Groot et (2001).
 Further radio observations sampled the behavior of NTE J1650-500 along all its N-rav states (Corbel et iin preparation)., Further radio observations sampled the behavior of XTE J1650-500 along all its X-ray states (Corbel et in preparation).
 We highlight two kev results obtained durius its outburst phase., We highlight two key results obtained during its outburst phase.
 First. RATE observations during the third and fourth weeks of the outburs vielded a strong X-ray QPO with an rns amplitude of 5.0+40.1% at a frequeucy of p»=2350435 Ue Uloman et 220031).," First, RXTE observations during the third and fourth weeks of the outburst yielded a strong X-ray QPO with an rms amplitude of $5.0 \pm 0.4\%$ at a frequency of $\nu=250\pm 5$ Hz (Homan et 2003b)."
 Second. observed a broad. skewed emission line due to Fe Ita CMilley et 22002).," Second, observed a broad, skewed emission line due to Fe $\alpha$ (Miller et 2002)."
 Those authors argue that their results imply the primary is à nearly maximal Rerr black hole that is delivering its spiu-down energy to the accretion flow., Those authors argue that their results imply the primary is a nearly maximal Kerr black hole that is delivering its spin-down energy to the accretion flow.
 The first sienificant observational program in the optical was that of Sanchez-Fernaucdez et ((2002. hereafter: SE2002).," The first significant observational program in the optical was that of Sanchez-Fernandez et (2002, hereafter SF2002)."
" They observed J1650 on the night of 2002 June 10 with the ourth &.21n telescope at the European Southeru Observatory. Paranal. aud reported the following orbital clemenuts: an orbital period of P=4,2120.001 days and a velocity scuuiamplitude of Λο=3094 {χα ο, resulting in an optical mass ""nuctiou of f(AL)=0.6140.03AF..."," They observed J1650 on the night of 2002 June 10 with the fourth 8.2m telescope at the European Southern Observatory, Paranal, and reported the following orbital elements: an orbital period of $P=0.212\pm 0.001$ days and a velocity semiamplitude of $K_2=309\pm 4$ km $^{-1}$, resulting in an optical mass function of $f(M)=0.64\pm 0.03\,M_{\odot}$."
 The results in this paper coutradict these fincines., The results in this paper contradict these findings.
 Iun this paper we report the results of our photometric study of J1650., In this paper we report the results of our photometric study of J1650.
 A time series analysis of our photometry rules out the orbital period reported by SE2002., A time series analysis of our photometry rules out the orbital period reported by SF2002.
 Cousequeutly we also report rerein our reanalysis of the SE2002 data obtained yon the ESO archives., Consequently we also report herein our reanalysis of the SF2002 data obtained from the ESO archives.
 We show that the spectroscopic ooriod we derive from these data is consistent with our photometric period P=0.3205 davs. aud we eo on to determine the orbital eleineuts of the system.," We show that the spectroscopic period we derive from these data is consistent with our photometric period $P=0.3205$ days, and we go on to determine the orbital elements of the system."
 We outliue below our observations aud reductions. and our analvsis techniques.," We outline below our observations and reductions, and our analysis techniques."
 We eud with a bref discussion of the duplications of our results regarding the fast QPO observed for J1650., We end with a brief discussion of the implications of our results regarding the fast QPO observed for J1650.
 We observed J1650 with the 6.51 Clay telescope at Las Campanas Observatory of the Carnegic Tustitution 2003 Alay 231 and June 1 using the Magellan Tustaut Camera (MaglIC) aud au £f baud filter., We observed J1650 with the 6.5m Clay telescope at Las Campanas Observatory of the Carnegie Institution 2003 May 31 and June 1 using the Magellan Instant Camera (MagIC) and an $R$ -band filter.
 A total of 17 A-band images with typical exposure fines between 500 and 600 seconds were obtained over the two nights iu eood conditions: the average seeiug was zc0.6 aresee aud it was photometric about of the time., A total of 47 $R$ -band images with typical exposure times between 500 and 600 seconds were obtained over the two nights in good conditions: the average seeing was $\approx 0.6$ arcsec and it was photometric about of the time.
 M. Wolman aud P. Schechter kindly provided an additional 65 images obtained 2003 Aueust Land 2 using the same instrumentation. and the observing conditions were comparable to those just described.," M. Holman and P. Schechter kindly provided an additional 65 images obtained 2003 August 1 and 2 using the same instrumentation, and the observing conditions were comparable to those just described."
 In order to nünnmuize readout time. the MagIC camera is read out siaultaneouslv using four amplifiers.," In order to minimize readout time, the MagIC camera is read out simultaneously using four amplifiers."
 Thus. bias and flat-ficlding is done separately for cach quadrant of the detector.," Thus, bias and flat-fielding is done separately for each quadrant of the detector."
 These calibratious aid the mereine of the quadrant innages iuto a single Huaee were performed using the publiclv-available Mael@C reduction pipeline., These calibrations and the merging of the quadrant images into a single image were performed using the publicly-available MagIC reduction pipeline.
 Stetson's programs DAOPIIOT Πο. ALLSTAR. and DAOMASTER (Stetson1987.1990:Stetson.Davis.&Crabtree1991:Stetson1992a.b) were used to extract the stellar iutensitics and derive the light curve for J1650 (see Orosz Wade 1990 for a detailed discussion of the overall procedure used).," Stetson's programs DAOPHOT IIe, ALLSTAR, and DAOMASTER \citep{ste87,ste90,ste91,ste92a,ste92b}
 were used to extract the stellar intensities and derive the light curve for J1650 (see Orosz Wade 1999 for a detailed discussion of the overall procedure used)."
 This suite of codes gives robust instrumental magnitudes., This suite of codes gives robust instrumental magnitudes.
 DAOPIIOT fits the point spread function (PSF) for cach image using several relatively isolatcc bright stars. aud ALLSTAR uses the PSF iux fiuds iustrmucutal magnitudes for all of the stars on an iuage simultaucously (local backerone subtraction is included).," DAOPHOT fits the point spread function (PSF) for each image using several relatively isolated bright stars, and ALLSTAR uses the PSF and finds instrumental magnitudes for all of the stars on an image simultaneously (local background subtraction is included)."
 Finally DAOMASTER iteratively solves (for zero-point shifts iu the naenitude scales from inage to iniage by essentially using all of the stable stars as “comparison stars., Finally DAOMASTER iteratively solves for zero-point shifts in the magnitude scales from image to image by essentially using all of the stable stars as “comparison” stars.
" Thus the final results are inscusitive to changes in he seeing and to changes in the sky transparency,", Thus the final results are insensitive to changes in the seeing and to changes in the sky transparency.
 rofüefe shows a finding chart for J1650 made from he MagIC data., \\ref{figfc} shows a finding chart for J1650 made from the MagIC data.
 SF2002 observed J1650 on the night of 2002, SF2002 observed J1650 on the night of 2002
keep C4N+0 constant while moclerating the maxinum Y.,keep $+$ $+$ O constant while moderating the maximum $Y$.
 If this was combined with a long enough ILDD lifetime. implving low AGB mass-loss rates such as those obtained when using the Vassiliadis&/Wood(1993). prescription. then the required abundance patterns may be obtained by the essentially pure HBB environment.," If this was combined with a long enough HBB lifetime, implying low AGB mass-loss rates such as those obtained when using the \citet{vw93} prescription, then the required abundance patterns may be obtained by the essentially pure HBB environment."
 The IIDD liletime is also dependent on the convective model. and as shown bv Ventura&D'Antona(2005a) more ellicient convection. coupled with a Iuminositv-driven mass-loss rate. results in a shorter AGB lifetime.," The HBB lifetime is also dependent on the convective model, and as shown by \citet{ventura05a} more efficient convection, coupled with a luminosity-driven mass-loss rate, results in a shorter AGB lifetime."
 If abundances of the bluest stars are closer to Y~0.3. instead of Y~0.4 then an AGB sell-pollution scenario. with a top-heavy IAIF. might work.," If abundances of the bluest stars are closer to $Y \sim 0.3$, instead of $Y \sim 0.4$ then an AGB self-pollution scenario, with a top-heavy IMF, might work."
 How then to justify the existence ol such an IMF for the first generation of GC stars?, How then to justify the existence of such an IMF for the first generation of GC stars?
 There is some observational evidence lor variations in the IMF (Stolteetal.2005) but there is ample evidence supporting a universal IMF. at least in the field (Ixroupa2001).," There is some observational evidence for variations in the IMF \citep{stolte05}
 but there is ample evidence supporting a universal IMF, at least in the field \citep{kroupa01}."
. Moreover. none of the observational evidence [ου variations in (he IAIF comes from environments similar (o galactic GCs.," Moreover, none of the observational evidence for variations in the IMF comes from environments similar to galactic GCs."
 Dwarf spheroidal ealaxies have a total mass comparable to the largest clusters but supposedly did not have such strange IMF's (seefore.g.Pritzletal.2005)., Dwarf spheroidal galaxies have a total mass comparable to the largest clusters but supposedly did not have such strange IMFs \citep[see for e.g.][]{pritzl05}.
. This may change as our ability (ο observe distaut galaxies with voung GC's mereases. but it will be a great challenge to extract a useful mass function from these svstenms.," This may change as our ability to observe distant galaxies with young GCs increases, but it will be a great challenge to extract a useful mass function from these systems."
 Our investigation into the chemical evolution of helium in GCs highlights the difficulty ihe AGB sell-pollution scenario sullers in trving (o explain the large postulated. helium enrichment required to fit the horizontal branch of clusters like NGC 2808., Our investigation into the chemical evolution of helium in GCs highlights the difficulty the AGB self-pollution scenario suffers in trying to explain the large postulated helium enrichment required to fit the horizontal branch of clusters like NGC 2808.
 With a standaxd Salpeter IME. the largest predicted helium abundance in the cluster gas is Y220.29 but this is accompanied by a large increase in the C+N+O abundance.," With a standard Salpeter IMF, the largest predicted helium abundance in the cluster gas is $Y \approx 0.29$ but this is accompanied by a large increase in the $+$ $+$ O abundance."
 Using an independent set of AGB vields from Venturaetal.(2002) we find a maximum Yx0.26 and only a modest increase of C4-N4-O x0.4 dex. probably within the observational errors.," Using an independent set of AGB yields from \citet{ventura02} we find a maximum $Y \approx 0.26$ and only a modest increase of $+$ $+$ O $\approx 0.4$ dex, probably within the observational errors."
 We conclude (hat with a standard IME it does not seem likely that the AGB self-pollution mechanism alone produced the enormous amounts of helium inferred [rom observations of the bluest IID and main-sequence stars of clusters like NGC 2808 and w Centauri., We conclude that with a standard IMF it does not seem likely that the AGB self-pollution mechanism alone produced the enormous amounts of helium inferred from observations of the bluest HB and main-sequence stars of clusters like NGC 2808 and $\omega$ Centauri.
 esinmlations that employ the IMS-enhanced IME show larger helium enhancements of Yx0.35 but only when accompanied by enormous increases in (he total C+N+0O content of the cluster gas. in violation of observations.," Simulations that employ the IMS-enhanced IMF show larger helium enhancements of $Y \approx 0.35$ but only when accompanied by enormous increases in the total $+$ $+$ O content of the cluster gas, in violation of observations."
 The Ventura et al., The Ventura et al.
 vields predict a maximum Ym0.28 and the total CNO abundance stavs constant to within ~ 0.3cddex. although we again point out that (his maximum Y is made uncertain by extrapolating the vields to hieher masses.," yields predict a maximum $Y \approx 0.28$ and the total CNO abundance stays constant to within $\sim 0.3$ dex, although we again point out that this maximum $Y$ is made uncertain by extrapolating the yields to higher masses."
 Even with such an extreme IME we have a problem fitting the observational constraints., Even with such an extreme IMF we have a problem fitting the observational constraints.
 Indeed. the use of such an IME does not help the difficulties Laced by the," Indeed, the use of such an IMF does not help the difficulties faced by the"
Comparing with the molecular gas 1iass estimate. this vields a gas-to-dust ratio This is comparable with values found in other ITzRCis and ULIRGSs 1991).,"Comparing with the molecular gas mass estimate, this yields a gas-to-dust ratio This is comparable with values found in other HzRGs and ULIRGs ."
". Alternatively, we cau also compare the CO aud 850;uu0 fluxes. vielding a comparisou that is independen of the assmned parameters."," Alternatively, we can also compare the CO and $\mu$ m fluxes, yielding a comparison that is independent of the assumed parameters."
 We fiud AVS(CO)/Souja=02 again simular to the values found in the 2 UzRCGs observed by (2000)... the 3o lianit in SBWO022000).. and high redshift quasars2002b).," We find $\Delta V S({\rm CO})/S_{800\mu{\rm m}} = 92$, again similar to the values found in the 2 HzRGs observed by , the $3\sigma$ limit in 53W002, and high redshift quasars."
. This indicates a staucdard gas/dust ratio in D3 J2330|3927., This indicates a standard gas/dust ratio in B3 J2330+3927.
 Figure b. shows the complex velocity structure of the Hine., Figure \ref{B3Lya2D} shows the complex velocity structure of the line.
 The cussion spatially exteuds well bevond the radio lobes., The emission spatially extends well beyond the radio lobes.
 This has been secu in several other WzRCs2002). and excludes shocks as the ionization mechanis at this xositiou.," This has been seen in several other HzRGs, and excludes shocks as the ionization mechanism at this position."
 Because we do not detect a discoutinuity in the profile at the position of the radio lobes. this implies that ohoto-donization bv the ceutra AGN is the dominating ionization miechauisui of the line.," Because we do not detect a discontinuity in the profile at the position of the radio lobes, this implies that photo-ionization by the central AGN is the dominating ionization mechanism of the line."
 Figure ll zooms in on he line in the Neck/LRIS spectiuu (extraction width 1«&1 |., Figure \ref{b3Lyafit} zooms in on the line in the Keck/LRIS spectrum (extraction width $1\arcsec \times 1\arcsec$ ).
 To check if the velocity profile can be explained * pure velocity structure witlou absorption. we have attempted to fit the profile with two or three Gaussian components. but this does not provide a good fit between the two peaks. or on he blue wing.," To check if the velocity profile can be explained by pure velocity structure without absorption, we have attempted to fit the profile with two or three Gaussian components, but this does not provide a good fit between the two peaks, or on the blue wing."
 An alternative interpretation is that the double-pealked structure is caused by associated aabsorptiou., An alternative interpretation is that the double-peaked structure is caused by associated absorption.
 Such absorbers are often seen in the lines of HzBRCs2002)., Such absorbers are often seen in the lines of HzRGs.
. We therefore modeled the profile with a Catssian cluission profile. supplemented by two Voigt absorption components (a second componcut is needed to ft the πο(απορία. blue wing).," We therefore modeled the profile with a Gaussian emission profile, supplemented by two Voigt absorption components (a second component is needed to fit the non-Gaussian blue wing)."
 Figure ll preseuts our best fit. obüued through a 4 nünnuization.," Figure \ref{b3Lyafit} presents our best fit, obtained through a $\chi^2$ minimization."
 We find that the profile can be closely represented with this model., We find that the profile can be closely represented with this model.
 Although the central wavelength of the Ciuissian emission was a free parameter in our fit. if corresponds very well with the redshift obtained from the line. providing a strong plivsical base for our model.," Although the central wavelength of the Gaussian emission was a free parameter in our fit, it corresponds very well with the redshift obtained from the line, providing a strong physical base for our model."
" We can estimate the mass of the associated aabsorber using where a, is the protou nass. Ray. is the size of the absorption svsteni and Vis the column density derived from the Voiet profile fitting."," We can estimate the mass of the associated absorber using where $m_{\rm p}$ is the proton mass, $R_{\rm abs}$ is the size of the absorption system, and $N$ is the column density derived from the Voigt profile fitting."
" In convenieut astroplivsical unitsLOV7a).. this becomes: where R35 is du units of 35 kpe. aud Nyo is in wuits of 10Men, "," In convenient astrophysical units, this becomes: where $R_{35}$ is in units of 35 kpc, and $N_{19}$ is in units of $10^{-19} {\rm cm}^2$."
Because the red absorber has a —10000 times higher column deusity (N28.7«1015 2) than the blue one. we shall only consider the red absorber in the following.," Because the red absorber has a $\sim$ 10000 times higher column density $N=8.7 \times 10^{18}$$^{-2}$ ) than the blue one, we shall only consider the red absorber in the following."
" From Fieure L. we obtain a lower luit of z2"" for the full spatial extent of the red absorber."," From Figure \ref{B3Lya2D}, we obtain a lower limit of $\simgt 2\arcsec$ for the full spatial extent of the red absorber."
" Assuming couscrvatively a size of BRlih,""n kpc. we derive a total mass estimate of the absorber We can also use the colnission to estimate the mass of ionized bydrogcu AFOLID."," Assuming conservatively a size of $R_{\rm abs} \sim 17 h_{65}^{-1}$ kpc, we derive a total mass estimate of the absorber We can also use the emission to estimate the mass of ionized hydrogen $M(\HII)$."
 Following(1990)... we assume pure case D recombination at a temperature of T.—105 Is. Using he eenission corrected for the associatedabsorption (dashed line in Fieure 11)) we obtain ALOUD) using where f5 is the filling factor iu units of . L1 Is the," Following, we assume pure case B recombination at a temperature of $T=10^4$ K. Using the emission corrected for the associatedabsorption (dashed line in Figure \ref{b3Lyafit}) ), we obtain $M(\HII)$ using where $f_{-5}$ is the filling factor in units of $^{-5}$ , $L_{44}$ is the"
We assume an inviscid and compressible gas. and an ideal equation of state wilh constant acdiabatic index.,"We assume an inviscid and compressible gas, and an ideal equation of state with constant adiabatic index."
 We use a Godunov-tvpe solver which is a relativistic generalization of the method due to Hartenetal.(1983).. and Einfeldt(1988).. in which the full solution to the Riemann problem is approximated by (wo waves separated by a piecewise constant state.," We use a Godunov-type solver which is a relativistic generalization of the method due to \citet{hlv}, and \citet{ein}, in which the full solution to the Riemann problem is approximated by two waves separated by a piecewise constant state."
" We evolve mass density Zi. the three components of the momentum density A/,. M, and M.. and the total energy densitv E relative to the laboratory frame."," We evolve mass density $R$, the three components of the momentum density $M_x$, $M_y$ and $M_z$ and the total energy density $E$ relative to the laboratory frame."
 Defining the vector (in terms of its (ranspose lor compactiness) and the three fIux vectors (he conservative lorm of the relativistic Euler equation is The pressure is given by (he ideal gas equation of state p=(L—1)(e—η]. The solvers are. well known for their capability as robust. conservative flow solvers with excellent shock capturing features.," Defining the vector (in terms of its transpose for compactness) and the three flux vectors the conservative form of the relativistic Euler equation is The pressure is given by the ideal gas equation of state $ p = (\Gamma - 1)
(e - n) . $ The Godunov-type solvers are well known for their capability as robust, conservative flow solvers with excellent shock capturing features."
 In this family of solvers one reduces the problem of updating the components of the vector Ü. averaged over a cell. to the computation of fIuxes al the cell interfaces.," In this family of solvers one reduces the problem of updating the components of the vector $U$, averaged over a cell, to the computation of fluxes at the cell interfaces."
 In one spatial dimension the part of the update due to advection of the vector Ü mav be written as In the scheme originally devised by Godunov(1959).. a fundamental emphasis is placed on the strategv of decomposing (he problem into many local Riemann problems. one [ου each pair of values of C; and U; 4.to vield values which allow the computation of the local," In one spatial dimension the part of the update due to advection of the vector $U$ may be written as In the scheme originally devised by \citet{god}, a fundamental emphasis is placed on the strategy of decomposing the problem into many local Riemann problems, one for each pair of values of $U_{i}$ and $U_{i+1}$ ,to yield values which allow the computation of the local"
of an underlyinglerlyingSFR iindex| of ΤΑNo=1.5 and| diffdifferentiatial excitation in HCN (Krumholz&Thompson2007:Narayananetal. 2008c).,"of an underlying index of $N=1.5$ and differential excitation in HCN \citep{kru07,nar08b}."
". This view has been observationally confirmed by Bussmannetal.(2008).. who showed that local galaxies exhibit ansublinear SFR-HCN (J=3-2) relation. and thus follow the trend of decreasing SFR-HCN"" index with increasing transition number characteristic of these models (e.g.Figure1:: see also Figure 7 of 20086)."," This view has been observationally confirmed by \citet{bus08}, who showed that local galaxies exhibit an SFR-HCN (J=3-2) relation, and thus follow the trend of decreasing $^\alpha$ index with increasing transition number characteristic of these models \citep[e.g. Figure~\ref{figure:sfr_lmol}; see also Figure 7 of ."
 Similarly. this model satisties the multi- constraints of local CO observations.," Similarly, this model satisfies the multi-line constraints of local CO observations."
 The SFR-CO (J=1-0) relation in local galaxies appears to have an index ranging from ~13L5., The SFR-CO (J=1-0) relation in local galaxies appears to have an index ranging from $\sim 1.3-1.5$.
 At higher-lying transitions (e.g. CO J23-2).> the index drops to 0.9. in accordance with theoretical predictions (onoetal. 2009).," At higher-lying transitions (e.g. CO J=3-2), the index drops to $\sim
0.9$, in accordance with theoretical predictions \citep{ion09}."
. We note that at lower bolometric luminosities. even the SFR-CO (J=1-0) relation may be subject to differential excitation and serve as a relatively poor tracer of the underlying Schmidt relation.," We note that at lower bolometric luminosities, even the SFR-CO (J=1-0) relation may be subject to differential excitation and serve as a relatively poor tracer of the underlying Schmidt relation."
 Finally. with an eye toward ALMA. we comment on the role of spatial resolution in observational determinations of the KS relation at high-z.," Finally, with an eye toward ALMA, we comment on the role of spatial resolution in observational determinations of the KS relation at ."
. The exact mapping between the observed iindex. a. and the iindex. Α΄. depends on the level of thermalisation of the gas within the beam.," The exact mapping between the observed index, $\alpha$, and the index, $N$, depends on the level of thermalisation of the gas within the beam."
 It is dependent (to first order) on the mean gas density., It is dependent (to first order) on the mean gas density.
 Higher resolution observations which probe just the nucleus of the galaxy will probe higher mean densities. and allow even higher-Iving CO emission lines to directly trace the underlying Schmidt SFR relation.," Higher resolution observations which probe just the nucleus of the galaxy will probe higher mean densities, and allow even higher-lying CO emission lines to directly trace the underlying Schmidt SFR relation."
 Indeed. some very tentative observational evidence for this trend in local galaxies has been shown by Narayananetal.(2008a).," Indeed, some very tentative observational evidence for this trend in local galaxies has been shown by \citet{nar08d}."
. The trends shown in Figures | and 2. are for the central 6 kpe of the galaxy. comparable to the typical resolution of current interferometric observations of 2 galaxies (e.g.Tacconietal.2010).," The trends shown in Figures \ref{figure:sfr_lmol}
 and \ref{figure:ks_molslope} are for the central 6 kpc of the galaxy, comparable to the typical resolution of current interferometric observations of 2 galaxies \citep[e.g. ][]{tac10}."
. Our models suggest that observations of the central —2 kpe will probe sufficiently dense gus that the observed index. o. will trace the underlying iindex. AN.," Our models suggest that observations of the central $\sim$ 2 kpc will probe sufficiently dense gas that the observed index, $\alpha$, will trace the underlying index, $N$."
 Current facilities demand that observations of the molecular Kennicutt-Schmidt relation at 2 probe highly excited CO lines (e.g. CO J=3-2)., Current facilities demand that observations of the molecular Kennicutt-Schmidt relation at 2 probe highly excited CO lines (e.g. CO J=3-2).
 However it is not clear how exactly to map observed rrelations to underlying rrelations: differential excitation of CO with SFR may make interpretation difficult., However it is not clear how exactly to map observed relations to underlying relations: differential excitation of CO with SFR may make interpretation difficult.
 In order to aid in the interpretation of observed molecular Kennicutt-Schmidt relations. we have calculated the first models of CO excitation for star-forming dise galaxies at 2.," In order to aid in the interpretation of observed molecular Kennicutt-Schmidt relations, we have calculated the first models of CO excitation for star-forming disc galaxies at 2."
 Our main results are: We thank Shane Bussmann. Neal Evans. Reinhard Genzel. Patrik Jonsson. Dusan Keres. Mark Krumholz. Charlie Lada. Kai Noeske. Alice Shapley. Amiel Sternberg and Linda Tacconi for enjoyable conversations as the ideas for this study were developed.," Our main results are: We thank Shane Bussmann, Neal Evans, Reinhard Genzel, Patrik Jonsson, Dusan Keres, Mark Krumholz, Charlie Lada, Kai Noeske, Alice Shapley, Amiel Sternberg and Linda Tacconi for enjoyable conversations as the ideas for this study were developed."
 The simulations in thispaper were run on the Odyssey cluster. supported by theHarvard FAS Research Computing Group.," The simulations in thispaper were run on the Odyssey cluster, supported by theHarvard FAS Research Computing Group."
hole namedA®.,hole named.
. These stars are suspected to have been formed in situ. as evidenced by the lack of stars outside the ~0.5 parsec region. (απατάetal...2006:Navakshin&Sunvaeyv. 2005).," These stars are suspected to have been formed in situ, as evidenced by the lack of stars outside the $\sim 0.5$ parsec region \citep{Paumard06,NS05}."
. Several observational [facts are consistent with the hypothesis that these stars formed in à massive gaseous cise (Paumarectal;2006)., Several observational facts are consistent with the hypothesis that these stars formed in a massive gaseous disc \citep{Paumard06}.
.. Had this star formation event not happened. ccould have been accreting gas from the gaseous disc even now.," Had this star formation event not happened, could have been accreting gas from the gaseous disc even now."
 tthus failed to realise itself as an AGN because of the loss of gas to star formation (Navakshin&Cuadra.2005)., thus failed to realise itself as an AGN because of the loss of gas to star formation \citep{NC05}.
. A number of important. gaps in our understanding of young stars near rremain., A number of important gaps in our understanding of young stars near remain.
 The counter clock-wise cise appears to host. stars on more elliptical orbits. and it is also geometrically thicker.," The counter clock-wise disc appears to host stars on more elliptical orbits, and it is also geometrically thicker."
" The same disc also contains a puzzling “mini star cluster"". IRSISE. that consists of more than a dozen stars and may be bound by an Intermediate Mass. Black Hole (AIBIL) of mass Adi,02M. (Paumarelctal.2005:Schódelοἱal.. 2005)."," The same disc also contains a puzzling “mini star cluster”, IRS13E, that consists of more than a dozen stars and may be bound by an Intermediate Mass Black Hole (IMBH) of mass $\mbh
\simgt 10^3 \msun$ \citep{Paumard05,Schoedel05}."
. Phe ALP of the observed stars must. be top-heavy according to several lines of evidence (Navakshin&Sun-Alexanderctal... 2006).. which is not expected in the most basic model of a fragmenting disc. as the Jeans mass there is significantly. sub-solar (e.g. Levin 2006. Navakshin 2006. but see also Larson 2006).," The IMF of the observed stars must be top-heavy according to several lines of evidence \citep{NS05,Nayakshinetal06,Paumard06,AlexanderBA06}, which is not expected in the most basic model of a fragmenting disc, as the Jeans mass there is significantly sub-solar (e.g., Levin 2006, Nayakshin 2006, but see also Larson 2006)."
 In this paper. we discuss numerical simulations of star formation occurring in a gaseous disc aroundA*.," In this paper, we discuss numerical simulations of star formation occurring in a gaseous disc around."
. Given the numerical challenges in the problem. we foresee that a reliable modelling of all the questions raised by the voung stars near wwill require an extended. ellort of constantly increasing complexity.," Given the numerical challenges in the problem, we foresee that a reliable modelling of all the questions raised by the young stars near will require an extended effort of constantly increasing complexity."
 In this study we present numerical experiments with a locallv constant cooling time., In this study we present numerical experiments with a locally constant cooling time.
 This allows a convenicnt comparison with previous analytical and numerical works that predicted. the conditions when ragmentation should take place., This allows a convenient comparison with previous analytical and numerical works that predicted the conditions when fragmentation should take place.
 It might also form a basis or Comparison with future work., It might also form a basis for comparison with future work.
 Within our formalism with a locally constant cooling ime. we find that (i) circular ane eccentric cises alike can gravitationallv fragment and form stars: (ii) the LAL of formed. stars is a strong function. of cooling tine. coming top-heavy lor marginally star-forming clises: (iii) star formation feedback is indeed. able to slow down cisc ragmentation. as suggested. by several earlier. analytical »ipers. but it is not vet clear if it can alleviate the fueling oblem of the SAIBLIs: (iv) our simulations do form some ightly bound binary stars but more populous systems (a La 11312) do not survive long.," Within our formalism with a locally constant cooling time, we find that (i) circular and eccentric discs alike can gravitationally fragment and form stars; (ii) the IMF of formed stars is a strong function of cooling time, becoming top-heavy for marginally star-forming discs; (iii) star formation feedback is indeed able to slow down disc fragmentation, as suggested by several earlier analytical papers, but it is not yet clear if it can alleviate the fueling problem of the SMBHs; (iv) our simulations do form some tightly bound binary stars but more populous systems (a la IRS13E) do not survive long."
 This paper is structured as follows., This paper is structured as follows.
 In Section 2.. we cliscuss our simulation methodology and the basic conditions for disc fragmentation.," In Section \ref{sec:methods}, we discuss our simulation methodology and the basic conditions for disc fragmentation."
 Section ο explains our sink particle approach to treat star formation in more detail., Section \ref{sec:starformation} explains our sink particle approach to treat star formation in more detail.
 We then analyse the evolution after disc fragmentation and the EME of the formed. stars in Section. ??.., We then analyse the evolution after disc fragmentation and the IMF of the formed stars in Section \ref{sec:nofb}.
 The sensitivity of our results to numerical resolution ancl feedback. from stars: is discussed. in Sections ??and. ??.. respectively.," The sensitivity of our results to numerical resolution and feedback from stars is discussed in Sections \ref{sec:sens} and \ref{sec:imfandfb}, respectively."
 We then examine elliptical orbits of à gaseous stream in Section ??.. and the question of the formation of mini star-clusters in Section ??..," We then examine elliptical orbits of a gaseous stream in Section \ref{sec:ecc}, and the question of the formation of mini star-clusters in Section \ref{sec:irs13}."
 Finally. we summarize and. conclude. in Section 9..," Finally, we summarize and conclude in Section \ref{sec:conclusions}."
" We use the N-body code (Springelctal..2001:Springel.2005) to simulate the dynamics of stars and eas in the (Newtonian) gravitational field of a point mass with Aij=3.510""AL.."," We use the $N$ -body code \citep{Springel01,
Springel05} to simulate the dynamics of stars and gas in the (Newtonian) gravitational field of a point mass with $\mbh = 3.5
\times 10^6 \msun$."
 The code solves for the gas hvdrodynamies via the smoothed particle hydrodyvnamies (SPI) formalism., The code solves for the gas hydrodynamics via the smoothed particle hydrodynamics (SPH) formalism.
 Vhe hvdrodvnamic treatment of the gas inclucles adiabatic processes and artificial bulk viscosity to resolve shocks., The hydrodynamic treatment of the gas includes adiabatic processes and artificial bulk viscosity to resolve shocks.
 The stars are modelled. as sink particles. using the approach developed. by Springelet.al.(2005).. mocified in the ways described below.," The stars are modelled as sink particles, using the approach developed by \cite{SpringelEtal05}, modified in the ways described below."
 ‘Table 1 lists some of the parameters and results of the simulations presented in this paper., Table 1 lists some of the parameters and results of the simulations presented in this paper.
" The tests described in this section. are those [isted as SI85 (the 7S7 stands for ""standard"").", The tests described in this section are those listed as S1–S5 (the “S” stands for “standard”).
" The units of length ancl mass used. in the simulations are Re=125105emz0.04 pe. which is equal to 1"" at the 8.0 kpe distance to the GC. and Ale=35I0""M... the mass of Ser X* (e.g.Schódeletal...2002).. respectively."," The units of length and mass used in the simulations are $R_{\rm U} = 1.2 \times
10^{17} \hbox{cm} \approx 0.04$ pc, which is equal to $1''$ at the 8.0 kpc distance to the GC, and $M_{\rm U}=3.5 \times 10^6 \msun$, the mass of Sgr A* \citep[e.g.,][]{Schoedel02}, respectively."
 Ehe dimensionless time unit is fo=AMORC). or about GO vears (© is clelined just. below Eqn. 1)).," The dimensionless time unit is $t_{\rm U} = 1/\Omega(R_{\rm U})$, or about 60 years $\Omega$ is defined just below Eqn. \ref{q}) )."
 The masses of SPILL particles are typically around 0.01 Solar masses (see Table 1)., The masses of SPH particles are typically around $0.01$ Solar masses (see Table 1).
 'Toomre(1964) showed that a rotating disc is subject to gravitational instabilities when the (Q-parameter becomes smaller than a critical value. which is close to unity.," \cite{Toomre64} showed that a rotating disc is subject to gravitational instabilities when the $Q$ -parameter becomes smaller than a critical value, which is close to unity."
 This form of the equation. assumes hiydrostatic equilibrium to relate the disc sound. speed to its. vertical thickness. Lf.," This form of the equation assumes hydrostatic equilibrium to relate the disc sound speed to its vertical thickness, $H$."
" Q=(CGAL(RO)? is the Keplerian angular frequeney, anc p ds the vertically averaged: disc. density."," $\Omega=(G\mbh/R^3)^{1/2}$ is the Keplerian angular frequency, and $\rho$ is the vertically averaged disc density."
 Ciravitational collapse thus takes place when the gas density exceeds Ideally. numerical simulations should resolve the gravitational collapse down to stellar scales.," Gravitational collapse thus takes place when the gas density exceeds Ideally, numerical simulations should resolve the gravitational collapse down to stellar scales."
" In practice. this is impossible for numerical reasons. and instead collisionless ""sink particles? are commonly introduced (Bateetal.1995) to mocdel collapsing regions of very high density."," In practice, this is impossible for numerical reasons, and instead collisionless “sink particles” are commonly introduced \citep{Bate95} to model collapsing regions of very high density."
 To ensure that collapse is well under way when we introduce a sink particle. we require that the gas density exeeeds where po=5.10LL 6 and log ds: a large number (we tested. values from. a few to afew thousand).," To ensure that collapse is well under way when we introduce a sink particle, we require that the gas density exceeds where $\rho_0 = 5 \times 10^{-11}$ g $^{-3}$, and $A_{\rm col}$ is a large number (we tested values from a few to afew thousand)."
 We in general find that our results are not sensitive to the exact values of po and sho). provided they are large enough (Section ??)).," We in general find that our results are not sensitive to the exact values of $\rho_0$ and $A_{\rm
col}$ , provided they are large enough (Section \ref{sec:acol}) )."
 Further details of our sink particle treatment are given in Section ??.., Further details of our sink particle treatment are given in Section \ref{sec:sink}. .
Eq.,Eq.
 1 to be a good estimate of the total luninosity of IRAS/CS sources within — 205)., \ref{eq:Firas} to be a good estimate of the total luminosity of IRAS/CS sources within – ).
 Since we will average the luminosity function of reeions over laree areas of the galactic disk. it is iniportaut o estimate the minm bhuuimositv avove which the disk is properly sampled.," Since we will average the luminosity function of regions over large areas of the galactic disk, it is important to estimate the minimum luminosity above which the disk is properly sampled."
 The lowest flux Finas du ho sample. Fjgas=610D 5. corresponds to οσ(μμ.)=3.6 at a distance of 15 spe.," The lowest flux $F_{IRAS}$ in the sample, $F_{IRAS}=6\, 10^{-13}$ $^{-2}$, corresponds to $\log(L_\mathrm{min}/L_{\odot})=3.6$ at a distance of 15 kpc."
 Figure 1bb shows a histogram of the total iuuber of sources in our siuuple asa function of Fyygs Gvithout the velocity filter Vialxd0lns 5)," Figure \ref{fig:FIR}b b shows a histogram of the total number of sources in our sample as a function of $F_{IRAS}$ (without the velocity filter $|V_{\rm lsr}|\leq 10\, {\rm km}\, {\rm
s}^{-1}$ )."
 The trjiuuegles show the fraction of sources with only upper limits iu the san band (righ rand scale).," The triangles show the fraction of sources with only upper limits in the $\,\mu$ m band (right hand scale)."
 Could a siguificaut iuuber of sources be assed by IRAS near the iiuiuuuu detected flux?, Could a significant number of sources be missed by IRAS near the minimum detected flux?
 A lower Frpys sensitivity would  hiuted at bv au diucreasec raction of upper limits in the repored IRAS fluxes. which is not the case.," A lower $F_{IRAS}$ sensitivity would be hinted at by an increased fraction of upper limits in the reported IRAS fluxes, which is not the case."
 However. the higher far-IR backeroun owards the ceutral regions of the Galaxy results in a completeness hut of loe(Lainνι.=L5 at 8.5 within 10c7« lO 0.3<b«0.3.," However, the higher far-IR background towards the central regions of the Galaxy results in a completeness limit of $\log(L_\mathrm{min}/L_{\odot})=4.5$ at 8.5 kpc, within $-10<l<10$ , $-0.3<b<0.3$."
 But over a broader ongitude rauge. 1ομμνι)=LO at 8.5 kpce. within G0«P60. 0:3<bc0.3.," But over a broader longitude range, $\log(L_\mathrm{min}/L_{\odot})=4.0$ at 8.5 kpc, within $-60<l<60$, $-0.3<b<0.3$."
 As the luninosity functions of the subceutral sources (which are all within 8.5 ος of the Sun) is iu good. agreement witli hat of the whole inner Galaxy (see below). we take loe(LinfL.)= Las the completeness limit of the IRAS/CSsample.," As the luminosity functions of the subcentral sources (which are all within 8.5 kpc of the Sun) is in good agreement with that of the whole inner Galaxy (see below), we take $\log(L_\mathrm{min}/L_{\odot})=4$ as the completeness limit of the IRAS/CS."
 The LF of the whole sample of IRAS/CS sources. our nain observational result. appears to be significautlv different inside and outside the solar circle: in Fig.," The LF of the whole sample of IRAS/CS sources, our main observational result, appears to be significantly different inside and outside the solar circle; in Fig."
 2 we distinguish between R<R. and R>R.., \ref{fig:LF_gal} we distinguish between $R<R_{\circ}$ and $R>R_{\circ}$.
 The LFs cover a very wide range in lhunünositv. over three orders of magnitude. which allows using ogaritlanic luuinosity bius corresporiding to a factor of.," The LFs cover a very wide range in luminosity, over three orders of magnitude, which allows using logarithmic luminosity bins corresponding to a factor of."
. Within the solar circle the LE obtained using the effective huuinosities is confirmed to )o a Good estimate of the actual LF through its close sinuarity with the LF ο© the sources near the subcentral points. shown in dottedline?.," Within the solar circle the LF obtained using the effective luminosities is confirmed to be a good estimate of the actual LF through its close similarity with the LF of the sources near the subcentral points, shown in dotted."
. For comparison. lacing all the sources at the near or “far kinematic distance chanees the peal of the LF as a unction of ogarithinic huninositv from 1.25 to 5.75. while the LF obtained using the effective Iluniuosities peaks at 5.25.," For comparison, placing all the sources at the `near' or `far' kinematic distance changes the peak of the LF as a function of logarithmic luminosity from 4.25 to 5.75, while the LF obtained using the effective luminosities peaks at 5.25."
 The good match with the subceutral source sample LF euds streneth to a comparison of the Iuninosity fuuctious )otween the outer aud inner Galaxy. based ou the effective i1uninosities.," The good match with the subcentral source sample LF lends strength to a comparison of the luminosity functions between the outer and inner Galaxy, based on the effective luminosities."
" We will refer to the luminosity functions for he whole iuner and outer Galaxy by. LE! anc LF,", We will refer to the luminosity functions for the whole inner and outer Galaxy by $^\mathrm{in}$ and $^\mathrm{out}$.
 The dominant source of πουταιν im the LF is shot noise., The dominant source of uncertainty in the LF is shot noise.
 The errors in the ealactic disk surface FIR lhuuinositv amount to about upwards. dowinvards (Fig.," The errors in the galactic disk surface FIR luminosity amount to about upwards, downwards (Fig."
 3 in DCMAN)., 3 in BCMN).
 The fractional error on the FIR surface bhuuinositv represents the typical fractional error ou the luminosity of oue source., The fractional error on the FIR surface luminosity represents the typical fractional error on the luminosity of one source.
" These errors ste.from the IRAS sau band flux wuicertainty, coupled with"," These errors stemfrom the IRAS $\,\mu$ m band flux uncertainty, coupled with"
of recombination (see c.g. Peebles 1993).,of recombination (see e.g. Peebles 1993).
 Llowever. anisotropies observed in the CALBR also indicate that there are spatial Iluctuations superimposed on this uniform hackeround density.," However, anisotropies observed in the CMBR also indicate that there are spatial fluctuations superimposed on this uniform background density."
 Phe initial condition for cach mode of Uuctuation is set before it enters the horizon., The initial condition for each mode of fluctuation is set before it enters the horizon.
 In the present analysis we assume that the [uctuations are adiabatie which means that the entropy per Iuid. particle is conserved., In the present analysis we assume that the fluctuations are adiabatic which means that the entropy per fluid particle is conserved.
 Recent WALAP observations favour this initial condition (Peiris et al., Recent WMAP observations favour this initial condition (Peiris et al.
 2003)., 2003).
 Ehe electrons interact with cach other and with protons through Coulomb scattering., The electrons interact with each other and with protons through Coulomb scattering.
 The mean free paths [or e-e. ορ and p-p collisions are the same in this thermal plasma (see e.g. Shu 1992) and are much smaller than the astrophysically relevant scales (1Alpe).," The mean free paths for $e\hbox{-}e$ , $e\hbox{-}p$ and $p\hbox{-}p$ collisions are the same in this thermal plasma (see e.g. Shu 1992) and are much smaller than the astrophysically relevant scales $\simeq 1\, \rm Mpc$ )."
 Lenee a continuum description treating them as IEuids can be used., Hence a continuum description treating them as fluids can be used.
 In such a macroscopic description the elfect of scattering between dillerent species is taken into account by including a momentum exchange term in the Euler equation., In such a macroscopic description the effect of scattering between different species is taken into account by including a momentum exchange term in the Euler equation.
" For photons however the dominant interaction is Thomson scattering olf free electrons withmean free path (comoving). /;,.. at zc1000 for a fully tonizecl universe being. /-,.=(ασ)53Mpc."," For photons however the dominant interaction is Thomson scattering off free electrons withmean free path (comoving), $l_{\gamma e}$, at $z \simeq 1000$ for a fully ionized universe being, $l_{\gamma e}=1/(a\sigma_{\rss T}
n_{e}) \simeq 3 \, \rm Mpc$."
 Here. oy is the Thomson cross section for ος scattering. nm. is the electron number density and @ is the scale factor.," Here, $\sigma_{\rss T}$ is the Thomson cross section for $e\hbox{-}\gamma$ scattering, $n_{e}$ is the electron number density and $a$ is the scale factor."
 This is comparable to the length scales in consideration and hence a 3Àoltzmann particle description is essential., This is comparable to the length scales in consideration and hence a Boltzmann particle description is essential.
 The photons are described by the phase space distribution function. 8)) where p is the magnitude of photon momentunm. Vsthepropagationdirectionandig is the conformal time.," The photons are described by the phase space distribution function ) where $p$ is the magnitude of photon momentum, is the propagation direction and $\eta$ is the conformal time."
" Since the distribution is blackbods to zeroth order. we can expand it as f=f""|of where f is the Planck function and of is the perturbation."," Since the distribution is blackbody to zeroth order, we can expand it as $f=f^{0}+\delta f$ where $f^{0}$ is the Planck function and $\delta f$ is the perturbation."
 Ht is convenient to describe the evolution of the perturbed distribution in terms of the brightness (x.η.8) defined as: The space-time metric in comovingὃν coordinates ο and Conformal time 7 for the conformal-Newton ogaugeoO is oogiven as (seeHJ oe. Ma Bertschinecr 1995 and cliscussion therein): Llere. e(g) is the scale factor and V. d are the two potentials characterising scalar perturbations in this gauge.," It is convenient to describe the evolution of the perturbed distribution in terms of the brightness $\Delta({\mathbf{x}},\eta,\hat{n})$ defined as: The space-time metric in comoving coordinates $x^{i}$ and conformal time $\eta$ for the conformal-Newton gauge is given as (see e.g. Ma Bertschinger 1995 and discussion therein): Here, $a(\eta)$ is the scale factor and $\Psi$, $\Phi$ are the two potentials characterising scalar perturbations in this gauge."
 The evolution of photons in this metric is then given by the Boltzmann equation for the brightness: Here. over-dots denote derivative with respect to conformal time 9.," The evolution of photons in this metric is then given by the Boltzmann equation for the brightness: Here, over-dots denote derivative with respect to conformal time $\eta$."
 €f] is the collision term accounting for the scattering of photons with electrons., $C[f]$ is the collision term accounting for the scattering of photons with electrons.
 The linearised collision term for Thomson scattering (neglecting polarisation) is given as (see e.g. Llu White 1997): llere. Ay=f“2Ads denotes the isotropic part of A and LL);i is the 1photon anisotropic1 stress tensor which takes into account the angular dependence of Thomson scattering.," The linearised collision term for Thomson scattering (neglecting polarisation) is given as (see e.g. Hu White 1997): Here, $\Delta_{0}\equiv\int\frac{d\Omega}{4\pi}\Delta$ denotes the isotropic part of $\Delta$ and $\Pi_{ij}$ is the photon anisotropic stress tensor which takes into account the angular dependence of Thomson scattering."
 Lt is given by: 10;=Z(min; $80;)A.," It is given by: $\Pi_{ij}=\int\frac{d\Omega}{4\pi}\left
(n_{i}n_{j}-\frac{1}{3}\delta_{ij}\right)\Delta$."
 The nature of individual crs in Cf] suggest that multipole moment expansion in terms of spherical harmonies can give a uscful description., The nature of individual terms in $C[f]$ suggest that multipole moment expansion in terms of spherical harmonics can give a useful description.
 The details of such an expansion are given in the appendix., The details of such an expansion are given in the appendix.
" We finally arrive at à hierarchy. of equations for moment εδω, ", We finally arrive at a hierarchy of equations for moment $\Delta_{\ell m}$.
"We can see that for a given m. each /-momoent Ay, is coupled to an /|1 and an /.—1 moment in the hierarchy."," We can see that for a given $m$, each $l$ -moment $\Delta_{\ell m}$ is coupled to an $l+1$ and an $l-1$ moment in the hierarchy."
 On the other rane. there is no coupling between cilferent m modes.," On the other hand, there is no coupling between different $m$ modes."
" This implies that if there is no source 5;,, CXppendix A) for a given m and if initial conditions are such that εδω=0 for that m. then. A;,,,= Oat all times even if other mn moments evolve."," This implies that if there is no source $S_{\ell m}$ (Appendix A) for a given $m$ and if initial conditions are such that $\Delta_{\ell m}=0$ for that $m$, then, $\Delta_{\ell m}=0$ at all times even if other $m$ moments evolve."
 In he present analysis. our emphasis will be on studying the elect of scalar perturbations which correspond to m=0.," In the present analysis, our emphasis will be on studying the effect of scalar perturbations which correspond to $m=0$."
 For such »erturbations Ll); can be greatly simplified by using azimuthal symmetry about the axis of electron velocity (see c.g. Dodelson Jubas 1994)., For such perturbations $\Pi_{ij}$ can be greatly simplified by using azimuthal symmetry about the axis of electron velocity (see e.g. Dodelson Jubas 1994).
 Llowever our aim here is to study the generation of magnetic field from the evolution of coupled photon-barvon Xdasma., However our aim here is to study the generation of magnetic field from the evolution of coupled photon-baryon plasma.
 Since the generation of this field can explicitly break this svmmetry. one should consider a more general expression or the anisotropic stress tensor.," Since the generation of this field can explicitly break this symmetry, one should consider a more general expression for the anisotropic stress tensor."
 As discussed earlier. since the mean free paths of electrons and protons are very small compared to astrophysical scales. we can describe their evolution accurately using continuity and Euler equations for an ideal Huid.," As discussed earlier, since the mean free paths of electrons and protons are very small compared to astrophysical scales, we can describe their evolution accurately using continuity and Euler equations for an ideal fluid."
" In linear theory. the density Ποιά p,up) is expandedas posultx.)=posGpG.|δν. τὴν where p is the unperturbed background density and ὁ is the fractional perturbation."," In linear theory, the density field $\rho_{ e,p}({\mathbf{x}},\eta)$ is expandedas $\rho_{ e,p}({\mathbf{x}},\eta)=\bar\rho_{e,p}(\eta)(1+\delta_{e,p}({{\mathbf{x}},\eta}))$ , where $\bar{\rho}$ is the unperturbed background density and $\delta$ is the fractional perturbation."
 In what follows quantities denoted with a bar on top are background unperturbed quantities., In what follows quantities denoted with a bar on top are background unperturbed quantities.
 The continuity equations for each of the above species is given as (c.g. Ma Bertschinger 1995):, The continuity equations for each of the above species is given as (e.g. Ma Bertschinger 1995):
with such a large orbital period.,with such a large orbital period.
 Phe double-peaks could arise from emission in dillerent parts of the svstem: however. we note that the standard sites for such localised emission. such as the hot spot where the accretion stream impacts the disk. still require the presence of a disk in the system.," The double-peaks could arise from emission in different parts of the system; however, we note that the standard sites for such localised emission, such as the hot spot where the accretion stream impacts the disk, still require the presence of a disk in the system."
 Finally. it i$ possible that the central dip in the double-»ealked: profile is formed: by absorption in front. between us and the emitter. especially given. the fact that we see absorption in the lines on a dillerent occasion. (sce 3.3)).," Finally, it is possible that the central dip in the double-peaked profile is formed by absorption in front between us and the emitter, especially given the fact that we see absorption in the lines on a different occasion (see \ref{sec:He-I-lines}) )."
 Such lines are seen in svmbiotic stars. such as Cll Cveni. which shows wo symmetric peaks separated bv a deep central reversal (Andersonetal.1980): in this object. the profile is assumed ο arise in a sell-absorbed wind.," Such lines are seen in symbiotic stars, such as CH Cygni, which shows two symmetric peaks separated by a deep central reversal \cite{aon80}; in this object, the profile is assumed to arise in a self-absorbed wind."
 However. in the case of the oliles seen inX-1.. the conditions for such absorption would be hard to produce.," However, in the case of the profiles seen in, the conditions for such absorption would be hard to produce."
 Since the profile is symmetric. he absorbers would. need to be at a very similar velocity o the emitters: and since the central dip is broad and does not reach the continuum. the absorbers would need a wide velocity dispersion and only a small optical depth.," Since the profile is symmetric, the absorbers would need to be at a very similar velocity to the emitters; and since the central dip is broad and does not reach the continuum, the absorbers would need a wide velocity dispersion and only a small optical depth."
 Phe most probable interpretation of the profile is that it arises from. he Doppler motions in an accretion disk., The most probable interpretation of the profile is that it arises from the Doppler motions in an accretion disk.
 The brightness of the enmüssion lines has decreased dramatically over the past 25 vears. from Wy=580 iin 1976 to 25X iin 2000.," The brightness of the emission lines has decreased dramatically over the past 25 years, from $\ew=580\A$ in 1976 to $25\A$ in 2000."
 Our interpretation is that the contribution of dillerent emission sites to the emission lines has been shifting over the vears., Our interpretation is that the contribution of different emission sites to the emission lines has been shifting over the years.
 The contribution from the accretion disk is likelv to have been essentially. constant. since the temperature of the disk is limited by the accretion rate (assumed to be at Edcinegton) and the size of the disk is limited by the size of the orbit.," The contribution from the accretion disk is likely to have been essentially constant, since the temperature of the disk is limited by the accretion rate (assumed to be at Eddington) and the size of the disk is limited by the size of the orbit."
 Phe contribution to the emission line from other regions he outllow. the companion star can change dramatically depending on the state of the system.," The contribution to the emission line from other regions – the outflow, the companion star – can change dramatically depending on the state of the system."
 It is possible that we have seen the disk [or the first time precisely. because the contributions from other sites in the orbit have lessened. so the Lo. Hine is now dominated by emission from the accretion disk.," It is possible that we have seen the disk for the first time precisely because the contributions from other sites in the orbit have lessened, so the $\alpha$ line is now dominated by emission from the accretion disk."
 We thank the ANU RSAA Time Assignment Committee for their generous allocation of time to this project., We thank the ANU RSAA Time Assignment Committee for their generous allocation of time to this project.
 We thank Roberto Soria for assistance with the observations., We thank Roberto Soria for assistance with the observations.
 We also thank the referee for providing useful suggestions and clarifications. particularly for suggestions about the Hat-toppecl profile.," We also thank the referee for providing useful suggestions and clarifications, particularly for suggestions about the flat-topped profile."
 KW acknowledges the support from the ARC through an ARC Australian Research Fellowship., KW acknowledges the support from the ARC through an ARC Australian Research Fellowship.
 This work is partially supported by an ARC/USvd Sesqui DD Grant., This work is partially supported by an ARC/USyd Sesqui D Grant.
superposed on the relatively smooth decline. preferentially. at higher frequencies.,"superposed on the relatively smooth decline, preferentially at higher frequencies."
 Tus is almost certainly indicative of repeated activity in the core. corresponding to fresh ejection events.," This is almost certainly indicative of repeated activity in the core, corresponding to fresh ejection events."
 The spectral indices support. this interoretation: between 1.42.9 Cllz 16 spectrum is significanIv. [latter than expected: for optically. thin. synchrotron emission: between 4.88.6 GL zit is cisplaving the rapidly varving behaviour associated. with ‘core’ ejection events (Fender e al., The spectral indices support this interpretation; between 1.4–2.9 GHz the spectrum is significantly flatter than expected for optically thin synchrotron emission; between 4.8–8.6 GHz it is displaying the rapidly varying behaviour associated with `core' ejection events (Fender et al.
 2002)., 2002).
 Inspection of the total Hux and spectral index. ligh curves indicates there were at. least four separate ejection events contributing to the light curve at this epoch., Inspection of the total flux and spectral index light curves indicates there were at least four separate ejection events contributing to the light curve at this epoch.
 Fig also indicates that this outburst was more prolonged than that in 2001 March. (see below)., Fig 1 also indicates that this outburst was more prolonged than that in 2001 March (see below).
 The CP fux is clearly rising to lower frequencies. bu the exact fractional spectrum is dillieult to determine as the multiple components contributing to the observed emission are unresolved with ATCA.," The CP flux is clearly rising to lower frequencies, but the exact fractional spectrum is difficult to determine as the multiple components contributing to the observed emission are unresolved with ATCA."
 Table 1 lists the mean total. linearly. polarised and circularly polarised lux densities. and Fig 4 plots these both as total and fractional spectra.," Table 1 lists the mean total, linearly polarised and circularly polarised flux densities, and Fig 4 plots these both as total and fractional spectra."
 We also note that there are measurements when the Stokes V [lux is not significantly non-zero. and even a few points where it appears to have changed sign.," We also note that there are measurements when the Stokes V flux is not significantly non-zero, and even a few points where it appears to have changed sign."
 However. (i) the mean Stokes V fluxes are significant. ancl negative (at both epochs). (ii) the apparent Stokes V sien change has a significance «2e and so we do not consider it convincing.," However, (i) the mean Stokes V fluxes are significant, and negative (at both epochs), (ii) the apparent Stokes V sign change has a significance $<2\sigma$ and so we do not consider it convincing."
 In 2001 March. GRS 1915|105 was again observed to [are in our 15 Cllz monitoring program. reaching 160 m.v at MAD. 51990.43.," In 2001 March, GRS 1915+105 was again observed to flare in our 15 GHz monitoring program, reaching $\sim 160$ mJy at MJD 51990.43."
 Vhis time we triggered both ATCA and AMIERLIN — in fact the first epoch of ALERLIN observations started at almost exactly the same time as the ATCA run concluded (Pigs 3.5).," This time we triggered both ATCA and MERLIN – in fact the first epoch of MERLIN observations started at almost exactly the same time as the ATCA run concluded (Figs 3,5)."
 Asa result. we were able to definitively," As a result, we were able to definitively"
We obtained a 20-hr observation of GI using the VLA in its C configuration (maximum baseline length of 3.5 km) at 8.46 GllIz.,We obtained a 20-hr observation of G1 using the VLA in its C configuration (maximum baseline length of 3.5 km) at 8.46 GHz.
 The observation was split into two LO-hr sessions. one each on 2006 November 24/25 and 2006 November 25/26.," The observation was split into two 10-hr sessions, one each on 2006 November 24/25 and 2006 November 25/26."
 Each dav's observation consisted ol repeated eveles of 1.4 minutes observation on the local phase calibrator J0038-2-4131 and 6 minutes observation on the target source GI., Each day's observation consisted of repeated cycles of 1.4 minutes observation on the local phase calibrator J0038+4137 and 6 minutes observation on the target source G1.
 In addition. each daw contained two short observations of 3C 48 (J0131--3309) that were used to calibrate the [lux density scale to that ol Baarsetal.C1977).," In addition, each day contained two short observations of 3C 48 (J0137+3309) that were used to calibrate the flux density scale to that of \citet{baa77}."
. Thus. the total integration time on Gl was 14.1 hr.," Thus, the total integration time on G1 was 14.1 hr."
 We also obtained a total of 9.5 hr of observing in C configuration at 4.86 GlIIz on 2007 January 13/14 and 2007 January 14/15. using a similar observing strategy. and achieving a total of 7.3 hr of integration on source.," We also obtained a total of 9.5 hr of observing in C configuration at 4.86 GHz on 2007 January 13/14 and 2007 January 14/15, using a similar observing strategy, and achieving a total of 7.3 hr of integration on source."
 All data calibration was carried out in NRÀAO's Astronomical Image Processing System (Greisen2003)., All data calibration was carried out in NRAO's Astronomical Image Processing System \citep{gre03}.
.. Absolute antenna gains were determined by the 3C 48 observations. then transferred to JOO38+4137. which was found (o have respective [Iux densities of 0.52 mJy aud 0.53 mJv al 8.4 and 4.9 GIIz.," Absolute antenna gains were determined by the 3C 48 observations, then transferred to J0038+4137, which was found to have respective flux densities of 0.52 mJy and 0.53 mJy at 8.4 and 4.9 GHz."
 In turn. JO0038--4137 was used to calibrate the interferometer amplitudes and phases for the target source. Gl.," In turn, J0038+4137 was used to calibrate the interferometer amplitudes and phases for the target source, G1."
 Erroneous data were flagged bv usine consistency of (he gain solutions as a guide aud by discarding outlving amplitude points., Erroneous data were flagged by using consistency of the gain solutions as a guide and by discarding outlying amplitude points.
 The VLA presently is being replaced gradually by the Expanded VLA (EVLA). which includes complete replacement of virtually all the electronic svstems on (he telescopes.," The VLA presently is being replaced gradually by the Expanded VLA (EVLA), which includes complete replacement of virtually all the electronic systems on the telescopes."
 Since antennas are refurbished one at a time. the VLA at the time of our observations consisted of 1820 ποια VLA antennas and 6 “new” (actually. refurbished) EVLA antennas. having completely different electronics svstems.," Since antennas are refurbished one at a time, the VLA at the time of our observations consisted of 18–20 “old” VLA antennas and 6 “new” (actually, refurbished) EVLA antennas, having completely different electronics systems."
 Although all antennas were eross-correlated for our observations. we found subtle errors in some of the EVLA data.," Although all antennas were cross-correlated for our observations, we found subtle errors in some of the EVLA data."
 Thus. to be conservative. we discarded the data from all EVLA antennas except for 3J) antennas that were confirmed to work very well on 2006 November 24/25.," Thus, to be conservative, we discarded the data from all EVLA antennas except for 3 antennas that were confirmed to work very well on 2006 November 24/25."
 The radio data were Fourier transformed ancl total-intensitv images were produced in each band. covering areas of 17x aal each These images were CLEANed in order to produce the final images.," The radio data were Fourier transformed and total-intensity images were produced in each band, covering areas of $\times$ at each These images were CLEANed in order to produce the final images."
 At 8.4 GIlz. the rms noise was 6.2 μον beam| for à beam size of x 27004772: al 4.9 CIIz. the noise was 15.0 μον ! [or a beam size of x 5700947443.," At 8.4 GHz, the rms noise was 6.2 $\mu$ Jy $^{-1}$ for a beam size of $\times$ 72; at 4.9 GHz, the noise was 15.0 $\mu$ Jy $^{-1}$ for a beam size of $\times$ 43."
 A few racio sources with strengths of hundreds of microjansky to a few millijansky were, A few radio sources with strengths of hundreds of microjansky to a few millijansky were
The water molecule is a key species throughout the formation of stars and planets.,The water molecule is a key species throughout the formation of stars and planets.
 In the gas phase. it acts as a coolant of collapsing interstellar clouds: in the solid state. it acts as glue for dust grams in protoplanetary disks to make planetesimals: and as a liquid. it acts as transporter bringing molecules together on planetary surfaces. a key step towards biogenic activity.," In the gas phase, it acts as a coolant of collapsing interstellar clouds; in the solid state, it acts as glue for dust grains in protoplanetary disks to make planetesimals; and as a liquid, it acts as transporter bringing molecules together on planetary surfaces, a key step towards biogenic activity."
 The first role is especially important for high-mass star formation which depends on the balance between the collapse of a massive gas cloud and its fragmentation (?).., The first role is especially important for high-mass star formation which depends on the balance between the collapse of a massive gas cloud and its fragmentation \citep{review}.
 Interstellar us well known from ground-based observations of the GGHz maser line., Interstellar is well known from ground-based observations of the GHz maser line.
 Previous space-based submm and far-IR observations have measured aabundances ranging from 107? in cold gas to 1077 in warm gas (ISO: ?:: SWAS: ?:: Odin: ?)) but did not have sufficient angular resolution to determine the spatial distribution ofH»O., Previous space-based submm and far-IR observations have measured abundances ranging from $^{-8}$ in cold gas to $^{-4}$ in warm gas (ISO: \citealt{iso}; ; SWAS: \citealt{swas}; Odin: \citealt{odin}) ) but did not have sufficient angular resolution to determine the spatial distribution of.
. In contrast. space-based mid-IR and ground-based mm-wave observations have high angular resolution but only probe the small fraction of the gas at high temperatures (?:: ?)).," In contrast, space-based mid-IR and ground-based mm-wave observations have high angular resolution but only probe the small fraction of the gas at high temperatures \citealt{iram}; \citealt{spitzer}) )."
 This paper presents observations of an eground state line at 23x higher angular resolution. than previously possible for such lines., This paper presents observations of an ground state line at $>$ $\times$ higher angular resolution than previously possible for such lines.
 Through radiative transfer models. we compare the abundance distribution of wwith that of παπά dust.," Through radiative transfer models, we compare the abundance distribution of with that of and dust."
 The source DR21 (Main) is a high-mass protostellar object (245.000 Isol)) located in the Cygnus X region at d=1.7 kkpe (?).. about 3’ South of the well-known DR21(OH) object (also known as W75S).," The source DR21 (Main) is a high-mass protostellar object $L$ ) located in the Cygnus X region at $d$ kpc \citep{schneider}, about $'$ South of the well-known DR21(OH) object (also known as W75S)."
 Maps of the mmm dust emission show a dense core with a mass of aand a size of 0.19x0.14 ppc. FWHM. surrounded by an extended envelope with mass aand size 0.3 pe (?)..," Maps of the mm dust emission show a dense core with a mass of and a size of $\times$ pc FWHM, surrounded by an extended envelope with mass and size 0.3 pc \citep{motte}. ."
 Gas densities of 10-10 aare derived. from both the mm-wave continuum and HCN and HCO™ line emission (?).., Gas densities of $^5$ $^6$ are derived from both the mm-wave continuum and HCN and $^+$ line emission \citep{kirby}.
" Signs of active high-mass star formation are the bright mid-IR emission JJy at jum). the presence of an GGHz maser (see catalog of ?)) and emission from ionized gas extending over 20-30"" (?).."," Signs of active high-mass star formation are the bright mid-IR emission Jy at $\mu$ m), the presence of an GHz maser (see catalog of \citealt{braz}) ) and emission from ionized gas extending over $''$ \citep{pjotr}."
 Together with the powerful molecular outflow (2) these signs indicate that the source Is relatively evolved within the embedded phase of high-mass star formation. beyond the “ultracompact region’ phase.," Together with the powerful molecular outflow \citep{garden} these signs indicate that the source is relatively evolved within the embedded phase of high-mass star formation, beyond the `ultracompact region' phase."
 The DR21 region was observed with the Heterodyne Instrument for the Far-Infrared (HIFI: De Graauw et al. this volume) onboard ESA’s Space Observatory (Pilbratt et al. this volume) on June 22. 2009.," The DR21 region was observed with the Heterodyne Instrument for the Far-Infrared (HIFI; De Graauw et al, this volume) onboard ESA's Space Observatory (Pilbratt et al, this volume) on June 22, 2009."
" Spectra were taken in double sideband mode using receiver band 4b. with Y,o21107.990 GGHz and vj;z6 GGHz."," Spectra were taken in double sideband mode using receiver band 4b, with $\nu_{\rm LO}$ GHz and $\nu_{\rm IF}$ GHz."
 The data were taken during the performance verification (PV) phase using the double beam switch observing mode with a throw of 2/5 to the SW., The data were taken during the performance verification (PV) phase using the double beam switch observing mode with a throw of $2\farcm5$ to the SW.
 The position observed is Κ.Α. 20:39:02.38. Dec +42:19:33.5 (2000). close to radio peak C from ?..," The position observed is R.A. 20:39:02.38, Dec +42:19:33.5 (J2000), close to radio peak C from \citet{pjotr}."
" A strip map was made in the N-S direction. spanning offsets from +90” to —90"" at a 1075 spacing. half the beam size of 21"" FWHM at our observing frequency. which corresponds to ppe at the distance of DR21."," A strip map was made in the N-S direction, spanning offsets from $''$ to $-$ $''$ at a $10\farcs5$ spacing, half the beam size of $''$ FWHM at our observing frequency, which corresponds to pc at the distance of DR21."
 This beam size was neasured before launch and is larger than the diffraction limit due to spillover effects., This beam size was measured before launch and is larger than the diffraction limit due to spillover effects.
 Data were taken with two backends: the acousto-optical Wide-Band Spectrometer (WBS) which covers MMHz bandwidth at MMHz kms)) resolution. and the correlator-based High-Resolution Spectrometer (HRS). which covers MMHz bandwidth at MMHz kms)) resolution.," Data were taken with two backends: the acousto-optical Wide-Band Spectrometer (WBS) which covers MHz bandwidth at MHz ) resolution, and the correlator-based High-Resolution Spectrometer (HRS), which covers MHz bandwidth at MHz ) resolution."
 Two polarizations are available except for the HRS data ofH:O., Two polarizations are available except for the HRS data of.
. The system temperature of our data is 340-360KK eand the integration time ts sseconds per position (ON+OFF)., The system temperature of our data is K and the integration time is seconds per position (ON+OFF).
" Calibration of the raw data onto Zi scale was performed by the in-orbit system (Roelfsema et al. in prep): conversion to T,» Was done assuming a beam efficiency of 0.67 as estimated by the Ruze formula and validated by raster maps of Saturn (M.Olberg. priv."," Calibration of the raw data onto $T_A^*$ scale was performed by the in-orbit system (Roelfsema et al, in prep); conversion to $T_{mb}$ was done assuming a beam efficiency of 0.67 as estimated by the Ruze formula and validated by raster maps of Saturn (M.Olberg, priv."
 comm.)., comm.).
 Currently. theflux scale is accurate," Currently, theflux scale is accurate"
a lo IUMS upper limit to any emission of 22.7 pw beam ab £8 Gllz. and 19.8 py beam| at SA Cllz.,"a $1
\sigma$ RMS upper limit to any emission of 22.7 $\umu$ Jy $^{-1}$ at 4.8 GHz, and 19.8 $\umu$ Jy $^{-1}$ at 8.4 GHz."
 ‘Lo confirm the previous VLA detection. shown in figure l((a). we observed AC Dra on 2000. March. 18. 25 26 at 1010.1130. 06302140 and. 05102250 UT. respectively with MEBRLIN.," To confirm the previous VLA detection, shown in figure \ref{vla_merlin}( (a), we observed AG Dra on 2000 March 18, 25 26 at 1010–1130, 0630–2140 and 0510–2250 UT respectively with MERLIN."
 Due to the superior resolving power of AIERLIN over the VLA we intended: to resolve the two unresolved. components previously detected. ancl obtain some information about the sources structure.," Due to the superior resolving power of MERLIN over the VLA we intended to resolve the two unresolved components previously detected, and obtain some information about the source's structure."
 The AIERLIN image has a beam size of 48.9 68.5 mas at an angle of 27.97. and a la RMS noise of 103 py bean1 at 4.994 6115.," The MERLIN image has a beam size of 48.9 $\times$ 68.5 mas at an angle of $-27.9
\degr$ , and a $1 \sigma$ RMS noise of 103 $\umu$ Jy $^{-1}$ at 4.994 GHz."
 The core component is clearly detected in the ALERLIN image and is resolved. into two point sources at jsoog = 410007. 349500 = 107113 with a flux of 570 wy (designated: as NI in figure 1((b)). and. eye = 4170046. 5425094 — 107446 and a Dux of 420 wy ((designated as N2).," The core component is clearly detected in the MERLIN image and is resolved into two point sources at $\alpha_{\rm J2000}$ = 007, $\delta_{\rm J2000}$ = 13 with a flux of 570 $\umu$ Jy (designated as N1 in figure \ref{vla_merlin}( (b)), and $\alpha_{\rm J2000}$ = 046, $\delta_{\rm J2000}$ = 46 and a flux of 420 $\umu$ Jy (designated as N2)."
 Fhese fluxes imply a lower limit of ~SO00 Ix. for the brightness temperature. consistent with the interpretation of the emission being optically thick Lree-Lrec emission. however. we do not rule out optically thin emission in this paper.," These fluxes imply a lower limit of $\sim$ 8000 K for the brightness temperature, consistent with the interpretation of the emission being optically thick free-free emission, however, we do not rule out optically thin emission in this paper."
 We note that the extension to the north of the component NI is probably due to noise in the image., We note that the extension to the north of the component N1 is probably due to noise in the image.
 The southwest component in the VLA image is not so clearly defined., The southwest component in the VLA image is not so clearly defined.
 ΗΕ the source has not increased in [lux between the epochs. and is a point source then it will be indistinguishable from the noise in the ALERLIN image (shown in figure L((c)).," If the source has not increased in flux between the epochs, and is a point source then it will be indistinguishable from the noise in the MERLIN image (shown in figure \ref{vla_merlin}( (c))."
 We do observe a number of possible point sources with lluxes around 300350 μον. but these are ambiguous compared to the noise.," We do observe a number of possible point sources with fluxes around 300–350 $\umu$ Jy, but these are ambiguous compared to the noise."
 We have lowered the contours compared to figure 1((b) to show the noise in more detail., We have lowered the contours compared to figure \ref{vla_merlin}( (b) to show the noise in more detail.
 All three VLA fields were imaged with a ciameter of 10.2 arcmin in order to check for emission. from. known sources. and to detect new objects in the fields.," All three VLA fields were imaged with a diameter of 10.2 arcmin in order to check for emission from known sources, and to detect new objects in the fields."
 Llowever. interferometric images all suller from bandwidth smearing or chromatic aberration.," However, interferometric images all suffer from bandwidth smearing or chromatic aberration."
 This is particularly important. when the observed bandwidth is large ancl a wide field is imagect., This is particularly important when the observed bandwidth is large and a wide field is imaged.
 The etfects of these are to smear sources in a radial direction from the phase centre. and to reduce the observed. peak Lux.," The effects of these are to smear sources in a radial direction from the phase centre, and to reduce the observed peak flux."
 The consequence of this elfect is that the signal to noise ratio increases with olf-axis beam angle., The consequence of this effect is that the signal to noise ratio increases with off-axis beam angle.
 For an observation taken with a bandwidth of 50 MlIZ ab 8.3 CGllz. and with a circular beam 2 aresec in diameter. a point source will suller a 10 per cent. reduction in Lux at a distance of 3 arcmin 50 arcsec from the phase centre. and a 50 per cent reduction at a distance of around. 11: arcemin. this situation becomes more severe with a smaller beam (see Aridle Schwab(1989) for details).," For an observation taken with a bandwidth of 50 MHz at 8.3 GHz, and with a circular beam 2 arcsec in diameter, a point source will suffer a 10 per cent reduction in flux at a distance of 3 arcmin 50 arcsec from the phase centre, and a 50 per cent reduction at a distance of around 11 arcmin, this situation becomes more severe with a smaller beam (see Bridle Schwab(1989) for details)."
 We have uploaded to the CDS service for Astronomical, We have uploaded to the CDS service for Astronomical
the black hole (represented by μυ).,the black hole (represented by ${\cal L}_{HD}$ ).
 The ellicieney of the disk is increased by the magnetic coupling: e2eg., The efficiency of the disk is increased by the magnetic coupling: $\epsilon > \epsilon_0$.
 For verv small Mp. an elliciency €Z91 can be achieved.," For very small $\dot{M}_D$ , an efficiency $\epsilon\gg 1$ can be achieved."
 If there is no accretion at all. the total elliciencey of the disk is infinite.," If there is no accretion at all, the total efficiency of the disk is infinite."
 If Zgj«0. which is the case when the black hole rotates slower than the disk. energy is transfered [rom the disk to the black hole.," If ${\cal L}_{HD}<0$, which is the case when the black hole rotates slower than the disk, energy is transfered from the disk to the black hole."
 Then. the efficiency. of the disk is decreased by (he magnetic coupling: e<ej.," Then, the efficiency of the disk is decreased by the magnetic coupling: $\epsilon <
\epsilon_0$."
 Since £ cannot be negative. we must have For a disk magnetically coupled to a rapidly rotating black hole. an extremely interesting feature is that the disk can radiate without accretion.," Since ${\cal L}$ cannot be negative, we must have For a disk magnetically coupled to a rapidly rotating black hole, an extremely interesting feature is that the disk can radiate without accretion."
" This can be seen directly from equation (16)) and equation (18)): when Mp—0. F is non-negative over the disk and £ is posilive if for anv r>ry. and From equation (11)). the sign of H is determined by the sign of Qy,25 since 0."," This can be seen directly from equation \ref{flux1}) ) and equation \ref{int_p}) ): when $\dot{M}_D = 
0$, $F$ is non-negative over the disk and ${\cal L}$ is positive if for any $r>r_{ms}$, and From equation \ref{toqh}) ), the sign of $H$ is determined by the sign of $\Omega_H
-\Omega_D$ since $dZ_H/dr < 0$ ."
" Since ο is constant over the horizon of the black hole aud dQ,/dr«0 for r>rj; over the disk. conditions (24)) and (25)) are equivalent to the requirement (hat Jf>0 over the disk and ff>0 at least over an interval of r>ry."," Since $\Omega_H$ is constant over the horizon of the black hole and $d\Omega_D/dr <0$ for $r>r_{ms}$ over the disk, conditions \ref{cond_x}) ) and \ref{cond_y}) ) are equivalent to the requirement that $H\ge 0$ over the disk and $H>0$ at least over an interval of $r>r_{ms}$."
 For such a non-accretion disk. (he radiation flux aud (he internal viscous torque are respectivelyand where // is given bv equation (11)).," For such a non-accretion disk, the radiation flux and the internal viscous torque are respectivelyand where $H$ is given by equation \ref{toqh}) )."
 The power of the disk comes purely [rom the rotational energv of the black hole, The power of the disk comes purely from the rotational energy of the black hole
"However. this is the first time that the analysis has been applied using a ""first principles” central engine model for the jet properties and the location where dissipation occurs.","However, this is the first time that the analysis has been applied using a `first principles' central engine model for the jet properties and the location where dissipation occurs."
 One way reconnection can occur in the jet is if the rotation and magnetic axes of the NS are misaligned (y. 0). such that the outflow develops an alternating or ‘striped’ magnetic field geometry on the scale of the light cylinder radius AL 1990).," One way reconnection can occur in the jet is if the rotation and magnetic axes of the NS are misaligned $\chi > 0$ ), such that the outflow develops an alternating or `striped' magnetic field geometry on the scale of the light cylinder radius $R_{\rm L}$ \citep{Coroniti90}."
. A similar field geometry may result if the jet is susceptible to magnetic instabilities (e.g. Giannios&Spruit2006:: McKinney&Blandford 2009:: Moll 2009)., A similar field geometry may result if the jet is susceptible to magnetic instabilities (e.g. \citealt{Giannios&Spruit06}; \citealt{McKinney&Blandford09}; \citealt{Moll09}) ).
" If this non-axisymmetrie pattern is preserved when the flow is redirected along the polar jet. the resulting geometry is conducive to magnetic reconnection,"," If this non-axisymmetric pattern is preserved when the flow is redirected along the polar jet, the resulting geometry is conducive to magnetic reconnection."
" We adopt the model developed by Drenkhahn&Spruit(2002)... in which magnetic dissipation occurs gradually from. small radii up to the “saturation” radius 7Bas ~ksPe/be, beyond which reconnection is complete and the flow achieves its terminal Lorentz factor. where e=v,/c and v, is the reconnection speed (see also Lvubarsky2010)."," We adopt the model developed by \citet{Drenkhahn&Spruit02}, in which magnetic dissipation occurs gradually from small radii up to the `saturation' radius $r \sim R_{\rm mag} \simeq \sigma_{0}^{2}Pc/6\epsilon$, beyond which reconnection is complete and the flow achieves its terminal Lorentz factor, where $\epsilon = v_{\rm r}/c$ and $v_{\rm r}$ is the reconnection speed (see also \citealt{Lyubarsky10}) )."
 During this process. approximately half the Poynting flux is directly converted into kinetic energy (producing acceleration) and the other half is deposited into the internal (thermal) energy of the flow.," During this process, approximately half the Poynting flux is directly converted into kinetic energy (producing acceleration) and the other half is deposited into the internal (thermal) energy of the flow."
" We assume a fixed value €=0.01 independent of radius (e.g. Uzdenskyetal.20103). but our results would be qualitatively unchanged if reconnection were ""triggered"" abruptly when. for instance. the outflow transitions to a collisionless regime (e.g. McKinney&Uzdenskv2010))."," We assume a fixed value $\epsilon = 0.01$ independent of radius (e.g. \citealt{Uzdensky+10}) ), but our results would be qualitatively unchanged if reconnection were `triggered' abruptly when, for instance, the outflow transitions to a collisionless regime (e.g. \citealt{McKinney&Uzdensky10}) )."
" One important constraint on a potential. UHECR source is the maximum energy £y, to which cosmic rays ean. be accelerated.", One important constraint on a potential UHECR source is the maximum energy $E_{\rm max}$ to which cosmic rays can be accelerated.
 One mechanism for accelerating particles in regions of magnetic reconnection is first-order Fermi acceleration. which occurs When particles are deflected at the converging upstream in the reconnection flow (Giannios2010:: see e.g. Lyutikov&Ouyed2007 for an alternative possibility).," One mechanism for accelerating particles in regions of magnetic reconnection is first-order Fermi acceleration, which occurs when particles are deflected at the converging upstream in the reconnection flow \citealt{Giannios10}; see e.g. \citealt{Lyutikov&Ouyed07} for an alternative possibility)."
" For suthciently fast reconnection. the acceleration timescale is very short. similar to the Larmor gyration timescale face=ωςπΕΟΡΟ where E'2ΕΤ and B'=(EurΤο!Y? are the particle energy and magnetic held strength (evaluated at r=A,4,). respectively. in the jet rest Tame: E7o5/2 is the bulk Lorentz factor in the acceleration zone: and acc| is a fudge factor that parametrizes our ignorance of e.g. the precise reconnection geometry."," For sufficiently fast reconnection, the acceleration timescale is very short, similar to the Larmor gyration timescale $t_{\rm acc}\simeq \eta_{\rm acc}2\pi E'/ZeB'c$, where $E'=E/\Gamma$ and $B' \simeq (\dot{E}_{\rm iso}r^{-2}\Gamma^{-2}c^{-1})^{1/2}$ are the particle energy and magnetic field strength (evaluated at $r = R_{\rm mag}$ ), respectively, in the jet rest frame; $\Gamma \sim \sigma_{0}/2$ is the bulk Lorentz factor in the acceleration zone; and $\eta_{\rm acc} \sim 1$ is a fudge factor that parametrizes our ignorance of e.g. the precise reconnection geometry."
" One constraint on Ey, IS hat fo. must be < the jet expansion timescale fay7Rae/Tc. such hat cosmic rays can be accelerated within the dynamical timescale of the flow (Hillas1984)."," One constraint on $E_{\rm max}$ is that $t_{\rm acc}$ must be $\lesssim$ the jet expansion timescale $t_{\rm exp} \simeq R_{\rm mag}/\Gamma c$, such that cosmic rays can be accelerated within the dynamical timescale of the flow \citep{Hillas84}."
". If the expansion timescale constraint does indeed determine £,4,. heavy nuclei achieve a value of £[TRES hat is a factor of ~Z larger than protons."," If the expansion timescale constraint does indeed determine $E_{\rm max}$, heavy nuclei achieve a value of $E_{\rm max}$ that is a factor of $\sim Z$ larger than protons."
 Another constraint arises because the acceleration competes with cooling of the nucleus., Another constraint arises because the acceleration competes with cooling of the nucleus.
" The dominant cooling mechanism is synchrotron emission, which occurs on a timescale where €,,,. is the fraction of jet power carried by Poynting flux and is ~| in the case of reconnection-powered outflows."," The dominant cooling mechanism is synchrotron emission, which occurs on a timescale where $\epsilon_{\rm mag}$ is the fraction of jet power carried by Poynting flux and is $\sim 1$ in the case of reconnection-powered outflows."
" The top panel of Figure 3. shows £4, in the reconnection model as a function. of time. based on the two independent constraints face<fap and facexo4! and calculated for the same magnetar wind shown in Figure |.. assuming aco=l."," The top panel of Figure \ref{fig:emax} shows $E_{\rm max}$ in the reconnection model as a function of time, based on the two independent constraints $t_{\rm acc} \lesssim t_{\rm exp}$ and $t_{\rm acc} \lesssim t_{\rm cool}$ and calculated for the same magnetar wind shown in Figure \ref{fig:wind}, assuming $\eta_{\rm acc} = 1$."
 We also assume a pure Fe composition. although our results are similar if the composition is instead dominated by heavier nuclei GA> 90).," We also assume a pure Fe composition, although our results are similar if the composition is instead dominated by heavier nuclei $A \gtrsim 90$ )."
 Note that at the earliest times (/xI5 sin this example) synchrotron losses place the most severe constraint on. μι. but at later times U> 159) the expansion timescale constraint Is more severe.," Note that at the earliest times $t \lesssim 15$ s in this example) synchrotron losses place the most severe constraint on $E_{\rm max}$, but at later times $t \gtrsim 15$ s) the expansion timescale constraint is more severe."
 AS we discuss in $3.3 below. a more severe constraint at early times arises because heavy nuclei can be disintegrated by the GRB photons.," As we discuss in $\S\ref{sec:photo}$ below, a more severe constraint at early times arises because heavy nuclei can be disintegrated by the GRB photons."
" The time interval shown in white (20 s </ 50 s) denotes the epoch during which heavy nuclei both survive photodisintegration and achieve values of Eq,>10°? eV which are sutficient to explain UHECRs.", The time interval shown in white (20 s $\lesssim t \lesssim$ 50 s) denotes the epoch during which heavy nuclei both survive photodisintegration and achieve values of $E_{\rm max} \gtrsim 10^{20}$ eV which are sufficient to explain UHECRs.
 During this epoch ~107! ergs of rotational energy is extracted from the magnetar. a large fraction of which could be placed into UHECRs.," During this epoch $\sim 10^{51}$ ergs of rotational energy is extracted from the magnetar, a large fraction of which could be placed into UHECRs."
This source was serendipitouslv discovered by our eroup (Decarlietal.90100) out of the SDSS database. and share some of the properties of JOO12|0900.,"This source was serendipitously discovered by our group \citep{decarli_4c2225} out of the SDSS database, and share some of the properties of J0942+0900."
 The Bahuer lines appear faint aud extremely lluc-shifted (~8700 13).," The Balmer lines appear faint and extremely blue-shifted $\sim 8\,700$ )."
 Also the line shows a bluc-shitt. but its magnitude is poorly constrained since the line is onlv partially covered by the SDSS spectrmu.," Also the line shows a blue-shift, but its magnitude is poorly constrained since the line is only partially covered by the SDSS spectrum."
 This quasar was labeled as a galaxy by the SDSS pipeline., This quasar was labeled as a galaxy by the SDSS pipeline.
 Shenetal.(2010) reported inconsistent velocity offsetsfor (1500 redoxvards) aud (2700 bluc-wards).," \citet{shen10a} reported inconsistent velocity offsetsfor $4\,500$ -wards) and $2\,700$ blue-wards)."
 or This object shows a complex profile (both for he 1959 aud the 50008 enmüssiou lines)., or This object shows a complex profile (both for the 4959 and the 008 emission lines).
 Two peaks are observed. with a velocity difference of ~1LOOL.," Two peaks are observed, with a velocity difference of $\sim 1\,400$."
C The blue peaks axe fainter., The blue peaks are fainter.
 Other narrow cussion inesJ..IIo. u]y appear normal.," Other narrow emission lines, ) appear normal."
 This source was abeled as “anomalous[S profile” by Borosou&Lauer (2010).., This source was labeled as “anomalous profile” by \citet{boroson10}. .
 A peculiar [OLprofile was also reported by Shenctal.(2010).., A peculiar profile was also reported by \citet{shen10a}.
 Thisri]. quasar was uot included iu xevious studies on double-peaked NL objects (c.g.Wangetal.2009:Liu 2010a.b).," This quasar was not included in previous studies on double-peaked NL objects \citep[e.g.][]{wang09,liu10a,liu10b}."
". The Dahuer Lunes of this tx,=0.3783 quasar slow simular properties to those of J1000|2233: The BLs peak. ~(100 blucawards of the NLs."," The Balmer lines of this $z_{\rm NL}=0.3783$ quasar show similar properties to those of J1000+2233: The BLs peak $\sim 6\,000$ blue-wards of the NLs."
 The red wing of aud the blue wing of are not covered., The red wing of and the blue wing of are not covered.
 or This is the only EDPE already known (Strateva 2003)., or This is the only EDPE already known \citep{strateva03}.
. The blue peaks of aud are 70000 bluc-shifted with respect to NLs., The blue peaks of and are 000 blue-shifted with respect to NLs.
 The shift is missed iu the analysis by Shenetal.(2010).. probably because of the faimtuess of the lines.," The shift is missed in the analysis by \citet{shen10a}, probably because of the faintness of the lines."
 Tlus source was discovered by Shieldsetal.(2009). out of the SDSS database., This source was discovered by \citet{shields09} out of the SDSS database.
 The broad component of Balmer lines is clearly shifted (~3400kin bhie-wards: a simular value was fom2010).," The broad component of Balmer lines is clearly shifted \citep[$\sim 3\,400$ \kms{} blue-wards; a similar value was found."
 No NL is observed at the redshift of the BLs., No NL is observed at the redshift of the BLs.
 This quasar was found in the ealaxy sample., This quasar was found in the galaxy sample.
 The broad line peaks 6000 bluecwaxds of the narrow component.," The broad line peaks $\sim 6\,000$ blue-wards of the narrow component."
 Due to its faintuess. the line profile is poorly coustrained.," Due to its faintness, the line profile is poorly constrained."
 The line is equally faint. but no obvious shift is observed.tt supporting the DPE interpretation for this source.," The line is equally faint, but no obvious shift is observed, supporting the DPE interpretation for this source."
 The broad component of this source appears slightly τομήσα with respect to the NL«s., The broad component of this source appears slightly redshifted with respect to the NLs.
 The properties of are difficult to characterize. due to its intrinsic füntness.," The properties of are difficult to characterize, due to its intrinsic faintness."
 The and lines of this τν=0.169 quasar have oeeutical profiles. with a peak ~3500 bhie-vwards ofthe expected wavelengths aud a rather broad red wing.," The and lines of this $z_{\rm NL}=0.469$ quasar have identical profiles, with a peak $\sim 3\,500$ blue-wards of the expected wavelengths and a rather broad red wing."
 The line profiles reseuible the one of other sources with wvunuetiic lines (eg... JOOL2-1022). but the magnitude of the shift aud the similarity between aud support the DIID hwpothesis.," The line profiles resemble the one of other sources with asymmetric lines (e.g., J0012-1022), but the magnitude of the shift and the similarity between and support the BHB hypothesis."
 The low S/N of the PApectiinu of the SDSS spectrum hinder amy couchision ou the nature of this source., The low S/N of the spectrum of the SDSS spectrum hinder any conclusion on the nature of this source.
 or The broad componcut of the Balmer lines of this quasar is rather svnunetric but shifted ~2500 blue-wards with respect to NLs.," or The broad component of the Balmer lines of this quasar is rather symmetric but shifted $\sim 2\,500$ blue-wards with respect to NLs."
 The flux ratio between and is ~L. roughlv constant with respect to the line-of-sight velocity.," The flux ratio between and is $\sim 4$, roughly constant with respect to the line-of-sight velocity."
 This source was notincluded iu the compilation by Shenetal.(2010).., This source was notincluded in the compilation by \citet{shen10a}.
 The bulk of the Balmer line broad componcuts of this source is shifted ~1700 blucecwurds of the NL system (consistentvaluesarereportedinShenetal. 2010)..," The bulk of the Balmer line broad components of this source is shifted $\sim1\,700$ blue-wards of the NL system \citep[consistent values are reported in][]{shen10a}."
 The flux ratio is 1. coustaut aloug the velocity profile.," The flux ratio is $\sim4$, constant along the velocity profile."
 The line shows a bump at ~6000 in the red wine. possibly revealing the DPE-like nature of this source.," The line shows a bump at $\sim 6\,000$ in the red wing, possibly revealing the DPE-like nature of this source."
 Such a feature is not clearly observed for because of the superposition of the doublet., Such a feature is not clearly observed for because of the superposition of the doublet.
 This quasar shows a peculiaz Daliner line profile., This quasar shows a peculiar Balmer line profile.
 The ls of Cluission arises from a bright bump iu the red wine., The bulk of emission arises from a bright bump in the red wing.
 The blue side of the line may also prescut a faint wine. he actual preseuce of which depeuds ou the continua nodeliug.," The blue side of the line may also present a faint wing, the actual presence of which depends on the continuum modeling."
 At zero order. the line shows analogous xofile.," At zero order, the line shows analogous profile."
 However. the feature in the red wing is 11 times züuter than what observed inΠ," However, the feature in the red wing is $\sim 11$ times fainter than what observed in."
"α, The interpretation of lis object is unclear.", The interpretation of this object is unclear.
 Boroson&Lauer(2010). labeled lis source as a uo broad line’ quasar., \citet{boroson10} labeled this source as a `no broad line' quasar.
 The broad emission of this quasar is clearly bluc- (~2300 LH," The broad emission of this quasar is clearly blue-shifted $\sim
2\,300$ )."
) The line profile shows norelevant asviunetrv., The line profile shows norelevant asymmetry.
 The broad compoucut is barely detected. its flux being ~7 times fainter than IIo..," The broad component is barely detected, its flux being $\sim7$ times fainter than ."
For our uext test of MIID. we run finite-amplitude. circularly polarized. Alfvéónu plane waves using the paralucters from Toth(2000) iu a cubic domain with periodic boundary conditions. with the propagation direction parallel to the x-axis.,"For our next test of MHD, we run finite-amplitude, circularly polarized, Alfvénn plane waves using the parameters from \cite{2000JCoPh.161..605T} in a cubic domain with periodic boundary conditions, with the propagation direction parallel to the x-axis."
 This is equivaleut to a= 0in the formalisin of Toth(2000).., This is equivalent to $\alpha=0$ in the formalism of \citet{2000JCoPh.161..605T}.
" Specifically. the initial conditions are p= 1.0. V,—0.0. B,=L0. V,=0,ισπ)= DB, V;=ülcos(2ze)D,. P—041. and 2=5/3."," Specifically, the initial conditions are $\rho=1.0$ , $V_x=0.0$, $B_x = 1.0$, $V_y=0.1\sin(2\pi x)=B_y$ , $V_z=0.1\cos(2\pi x)=B_z$, $P=0.1$, and $\gamma=5/3$."
 The wave. is propagated five waveloneths. returning to its original position.," The wave is propagated five wavelengths, returning to its original position."
 The solutions shown in Figure 2 show that at low resolution. the waveis strougly damped. while as resolution increases the wave rapidly converges.," The solutions shown in Figure \ref{figcircalfvensols} show that at low resolution, the waveis strongly damped, while as resolution increases the wave rapidly converges."
 Figure 23. shows the L4 norm errors. which converee faster than secoud order.," Figure \ref{figcircalfvenerr} shows the $L_1$ norm errors, which converge faster than second order."
 To test performance ou supersonie and super-Alfveunic problems. we set up several shock tube problems.," To test performance on supersonic and super-Alfvénnic problems, we set up several shock tube problems."
 We used. the parameters given in Table 1 ou long rectangular domains with periodic boundaries., We used the parameters given in Table \ref{tabshocktubes} on long rectangular domains with periodic boundaries.
 À spatially coustaut resolution criterion A allows conrparisou to erid based codes. while an appropriately density depeucent resolution criterion allows comparison to other Lagrangian methods.," A spatially constant resolution criterion $\lambda$ allows comparison to grid based codes, while an appropriately density dependent resolution criterion allows comparison to other Lagrangian methods."
 For the constant A tests we denote the distance alone the long axis of the domain in units of A., For the constant $\lambda$ tests we denote the distance along the long axis of the domain in units of $\lambda$.
 We first run the classic Sod(1978) shock tube. in eas with 5=7/5 on a domain of size GL<1«1 units.," We first run the classic \citet{1978JCoPh..27....1S} shock tube, in gas with $\gamma = 7/5$ on a domain of size $64 \times 1 \times 1$ units."
 A smooth transition between the left and right states with a width of 0.3 units is described with a fifth-order spline., A smooth transition between the left and right states with a width of $0.3$ units is described with a fifth-order spline.
 In the first version of this test we use a refinemen criteria A=0.125057? that vields a constant mass per resolution clement (that is. per region with volume of L/3rA°).," In the first version of this test we use a refinement criteria $\lambda = 0.125\rho^{1/3}$ that yields a constant mass per resolution element (that is, per region with volume of $4/3 \pi \lambda^3$ )."
 This is in effect the resolution criterion used by SPI., This is in effect the resolution criterion used by SPH.
 Iu Fieure £. the solution at time tf=13.8 is shown.," In Figure \ref{figsodrho}
 the solution at time $t=13.8$ is shown."
 For this test the x axis ou the plot is denoted im wits of À in the loft initial state., For this test the x axis on the plot is denoted in units of $\lambda$ in the left initial state.
 Unlike SPIT. Phurbas supports more general refinement criteria.," Unlike SPH, Phurbas supports more general refinement criteria."
 As a simple example. we rau the same Sod test problem with spatially consta resolution A=0.125.," As a simple example, we ran the same Sod test problem with spatially constant resolution $\lambda=0.125$."
 Figure 5. shows the result at time #=15., Figure \ref{figsod} shows the result at time $t=15$.
 The result is generally very simular to the resul with mass-based refinement. with the main chauge being that the shock is thinner. as the local resolution is higher iu the constant-refiucment case.," The result is generally very similar to the result with mass-based refinement, with the main change being that the shock is thinner, as the local resolution is higher in the constant-refinement case."
 In either case. the shock speed is reasonably well reproduced.," In either case, the shock speed is reasonably well reproduced."
 We next perform a suite of MIID shock tube tests. selecting from the large set of standard MITD Ricmaun problems used iu the literature.," We next perform a suite of MHD shock tube tests, selecting from the large set of standard MHD Riemann problems used in the literature."
 To tabulate reference solutions. we have used Athena (Stoneetal.2008). at hnieh resolution in 1D. The first test we show is the classical Brio-Wu 1988 shock tube test. which is a standard problem. though not particularly striiugeut.," To tabulate reference solutions, we have used Athena \citep{2008ApJS..178..137S} at high resolution in 1D. The first test we show is the classical Brio-Wu \citeyear{1988JCoPh..75..400B} shock tube test, which is a standard problem, though not particularly stringent."
 The test shown in Figure 2a of Ryu&Jones(1995.denotedRJ2a) provides a more complete test of the appearance of the various possible MIID discoutiuuities., The test shown in Figure 2a of \citet[][denoted RJ2a]{1995ApJ...442..228R} provides a more complete test of the appearance of the various possible MHD discontinuities.
 Ryu&Jones(1995) iu their Figure [d show a test (denoted RJ1d) of other discontinuities., \citet{1995ApJ...442..228R} in their Figure 4d show a test (denoted RJ4d) of other discontinuities.
 The problem described by Falle(2002) in his Figure 6 (denoted FG) is specifically used to demonstrate shock errors in nou-locallv-couservative methods., The problem described by \citet{2002ApJ...577L.123F} in his Figure 6 (denoted F6) is specifically used to demonstrate shock errors in non-locally-conservative methods.
 Finally. the test shown in Figure 6 of Woodward(199 1).. as well as in Figure la of Ryu&Jones(1995.denotedRJ1la) is commonly used as a striugeut test of VB errors in shocks. aud iu the case of Phurbas demonstrates the effects of local nou-couservatiou errors associated with stroug MIID shocks.," Finally, the test shown in Figure 6 of \citet{1994JCoPh.111..354D}, as well as in Figure 1a of \citet[][denoted RJ1a]{1995ApJ...442..228R} is commonly used as a stringent test of $\divb$ errors in shocks, and in the case of Phurbas demonstrates the effects of local non-conservation errors associated with strong MHD shocks."
 Note that with the exception of the Brio-Wi test. all these MIID shock tube tests use an adiabatic eas with 5=5/3.," Note that with the exception of the Brio-Wu test, all these MHD shock tube tests use an adiabatic gas with $\gamma=5/3$."
 The Brio-Wiu 1988 shock tube (see Table 13) isan MIID analog to the Sod shock tube problem., The Brio-Wu \citeyear{1988JCoPh..75..400B} shock tube (see Table \ref{tabshocktubes}) ) is an MHD analog to the Sod shock tube problem.
 We sot up this test in gas with 5=2. on a fully periodic domain of 128\1<1 units. with coustant resolution A=0.125.," We set up this test in gas with $\gamma = 2$, on a fully periodic domain of $128\times 1\times 1$ units, with constant resolution $\lambda =
0.125$."
 A «Ιου transition between the left aud right states witli a width of 3 units was produced with a cosine fiction., A smooth transition between the left and right states with a width of $3$ units was produced with a cosine function.
 The width of the transition region was chosen to avoid excessive start-up trausieuts., The width of the transition region was chosen to avoid excessive start-up transients.
" As the problem was run iu two imiiror images in a periodic volume. ouly half of the periodic volume used is shown in Figure οι, with the «-axis labeled iu A units. at time f=7.3."," As the problem was run in two mirror images in a periodic volume, only half of the periodic volume used is shown in Figure \ref{figbriowupara}, with the $x$ -axis labeled in $\lambda$ units, at time $t=7.3$."
 The solution capturesthe fuudiaiceutal features of the problem. including. from left to right. the rarefaction fan. the compound wave. the contact discontinuity. the slow shock. aud the fast rarefaction wave.," The solution capturesthe fundamental features of the problem, including, from left to right, the rarefaction fan, the compound wave, the contact discontinuity, the slow shock, and the fast rarefaction wave."
 The final panel of Figure 6 shows a measure of the effect of VB.," The final panel of Figure \ref{figbriowupara}
 shows a measure of the effect of $\divb$."
 Tere the quantity A(V-B)/|BI is the fractional magnetic field error on the scale of A., Here the quantity $\lambda(\divb)/|\sB|$ is the fractional magnetic field error on the scale of $\lambda$.
 Cavey points in this panel show the raw values of this quantity. with maxinmn magnitude 107.," Grey points in this panel show the raw values of this quantity, with maximum magnitude $10^{-3}$."
 However. the scatter Is very svuunetric. indicating that most of it can be attributed to the truncatiou error iu the approximation of V-B itself.," However, the scatter is very symmetric, indicating that most of it can be attributed to the truncation error in the approximation of $\divb$ itself."
" To extract the coherent skew from zero. we plot the data binned in bius with width A as the black step curve. demonstrating that the normalized V.B errors ave less than 103,"," To extract the coherent skew from zero, we plot the data binned in bins with width $\lambda$ as the black step curve, demonstrating that the normalized $\divb$ errors are less than $10^{-4}$."
 The Athena solution that we compareour result to. as well as the usually accepted nuuerical solutious to the Drio-Wu problem. show a compound wave structure. seen atczc25 in Figure 6..," The Athena solution that we compareour result to, as well as the usually accepted numerical solutions to the Brio-Wu problem, show a compound wave structure, seen at $x\approx -25$ in Figure \ref{figbriowupara}. ."
 This structure should not formally exist (Falle&I&oiuissimvov. 2001).. but most multidineusioual uunerical methods. iucludiug Phurbas. show it as part of the solution.," This structure should not formally exist \citep{2001JPlPh..65...29F}, , but most multidimensional numerical methods, including Phurbas, show it as part of the solution."
 The test shown iu Figure 2a of Ryu&Jones (also see Dai&Woodward(1991). Table 3a) is, The test shown in Figure 2a of \cite{1995ApJ...442..228R} (also see \cite{1994JCoPh.111..354D} Table 3a) is
"that a supersonic bow shock precedes the hot gas, while the weak lensing mass profile indicates that this X-ray bright component lags behind the sub-cluster galaxies due to ram pressure (Markevitchetal.2002;Barrena2002)..","that a supersonic bow shock precedes the hot gas, while the weak lensing mass profile indicates that this X-ray bright component lags behind the sub-cluster galaxies due to ram pressure \citep{mar02-27,bar02-816}."
 A recent mid-infrared study by Chungetal.(2009) concluded that ram pressure from the merger event had no significant impact on the star formation rates of nearby galaxies., A recent mid-infrared study by \citet{chu09-963} concluded that ram pressure from the merger event had no significant impact on the star formation rates of nearby galaxies.
 We can re-evaluate these previous studies by using data to constrain directly., We can re-evaluate these previous studies by using data to constrain directly.
" In this letter, we present an exploration of obscured star formation in this cluster environment."," In this letter, we present an exploration of obscured star formation in this cluster environment."
" Five bandHerschel imaging was obtained using two instruments:PACS (100,160 um) covering approximately 8'x8' and SPIRE (250,350,500 um) with a wider —17'x17' field."," Five band imaging was obtained using two instruments:PACS (100,160 $\mu$ m) covering approximately $\times$ and SPIRE (250,350,500 $\mu$ m) with a wider $\sim$ $\times$ field."
" Egamietal.(2010) provides details of all the data, and presents FIR maps."," \citet{ega10} provides details of all the data, and presents FIR maps."
 The deep SPIRE maps have detection limits well below the instrument confusion limits., The deep SPIRE maps have detection limits well below the instrument confusion limits.
" To avoid compiling sourcelists from confused maps, fluxes are measured at all MIPS 24 um source positions."," To avoid compiling sourcelists from confused maps, fluxes are measured at all MIPS 24 $\mu$ m source positions."
" The use of mid-infrared source positions has the added advantage of decreasing the significance of flux boosting, which has not been addressed in this study."," The use of mid-infrared source positions has the added advantage of decreasing the significance of flux boosting, which has not been addressed in this study."
 Photometric analysis followed the same procedure in all 5 bands., Photometric analysis followed the same procedure in all 5 bands.
" An average PSF, measured from the brightest unblended sources in the image, was simultaneously fit to all positions in the 24 um catalogue (without re-centering) usingArLsTmAR."," An average PSF, measured from the brightest unblended sources in the image, was simultaneously fit to all positions in the 24 $\mu$ m catalogue (without re-centering) using."
" At the longer SPIRE wavelengths, there is a higher probability of more than one 24 um source falling within the FIR beam."," At the longer SPIRE wavelengths, there is a higher probability of more than one 24 $\mu$ m source falling within the FIR beam."
" In these instances, the objects are grouped together at the 24 um S/N-weighted mean position, treated as a single source, and flagged (see following sub-section)."," In these instances, the objects are grouped together at the 24 $\mu$ m S/N-weighted mean position, treated as a single source, and flagged (see following sub-section)."
 For more details on the photometry technique see Rexetal.(2010)., For more details on the photometry technique see \citet{rex10}.
". The spectroscopic redshift catalogue combines observations from three campaigns: Magellan IMACS multi-slit (856 targets; Chungetal.2010,, Chung et al."," The spectroscopic redshift catalogue combines observations from three campaigns: Magellan IMACS multi-slit (856 targets; \citealt{chu10s}, Chung et al."
" in prep), CTIO Hydra multi-fiber (202; Fadda et al."," in prep), CTIO Hydra multi-fiber (202; Fadda et al."
" in prep) and VLT FORS multi-slit (14; J Richard, private communication)."," in prep) and VLT FORS multi-slit (14; J Richard, private communication)."
 Egamietal.(2010) provides further details., \citet{ega10} provides further details.
 The merged catalogue comprises 929 sources within the SPIRE field., The merged catalogue comprises 929 sources within the SPIRE field.
 Figure 1 presents the distribution of spectroscopic redshifts for the range 0.27 < z < 0.37., Figure \ref{fig:zhist} presents the distribution of spectroscopic redshifts for the range 0.27 $<$ $z$ $<$ 0.37.
 An important aspect of this study is confidence in the cluster membership of galaxies., An important aspect of this study is confidence in the cluster membership of galaxies.
" The Bullet cluster distribution peaks at z = 0.296, and we limit membership to + 3000 km s! (0.286 « z < 0.306)."," The Bullet cluster distribution peaks at $z$ = 0.296, and we limit membership to $\pm$ 3000 km $^{-1}$ (0.286 $<$ $z$ $<$ 0.306)."
" In addition, this study also analyzes galaxies from a at z = 0.350 in the same field, limiting membership to + 2000 km s! (0.343 « z « 0.357)."," In addition, this study also analyzes galaxies from a at $z$ = 0.350 in the same field, limiting membership to $\pm$ 2000 km $^{-1}$ (0.343 $<$ $z$ $<$ 0.357)."
 The sample for this analysis consists of MIPS 24 um sources with spectroscopically confirmed cluster redshifts., The sample for this analysis consists of MIPS 24 $\mu$ m sources with spectroscopically confirmed cluster redshifts.
" These two catalogues were merged by identifying the closest 24 um source, within the RMS pointing error of MIPS (1.4)), to the spectroscopic position."," These two catalogues were merged by identifying the closest 24 $\mu$ m source, within the RMS pointing error of MIPS ), to the spectroscopic position."
" For sample members grouped during the FIR photometry (previous sub-section), we examined the optical and IRAC colours of each group member, identifying the likely source of the mid- and far-IR flux."," For sample members grouped during the FIR photometry (previous sub-section), we examined the optical and IRAC colours of each group member, identifying the likely source of the mid- and far-IR flux."
" In cases where the sample member was not considered to bethe source, or when the situation was unclear, the object was rejected from the sample."," In cases where the sample member was not considered to bethe source, or when the situation was unclear, the object was rejected from the sample."
" In the final sample, there are 47 confirmed Bullet cluster members, and an additional 28 sources in the z = 0.35 system."," In the final sample, there are 47 confirmed Bullet cluster members, and an additional 28 sources in the $z$ = 0.35 system."
" Of these, 23 and 21 galaxies respectively are detected in the bands, highlighted by the filled distribution in Fig. 1.."," Of these, 23 and 21 galaxies respectively are detected in the bands, highlighted by the filled distribution in Fig. \ref{fig:zhist}."
 The background system has a much higher fraction ofHerschel detections than the Bullet cluster50%)., The background system has a much higher fraction of detections than the Bullet cluster.
" For each source, the FIR spectral energy distribution (SED) is fit to all available data points, taking into account the upper limits for non-detections."," For each source, the FIR spectral energy distribution (SED) is fit to all available data points, taking into account the upper limits for non-detections."
" The dust component is modeled by a modified, single-temperature, blackbody where S, is flux density, 6 is dust emissivity index (fixed at 1.5; average) and B,(T) is the Planck blackbody radiation function for a source at temperature T."," The dust component is modeled by a modified, single-temperature, blackbody where $S_{\nu}$ is flux density, $\beta$ is dust emissivity index (fixed at 1.5; ) and $B_{\nu}(T)$ is the Planck blackbody radiation function for a source at temperature $T$ ."
 The shape of this optically thin (rather than thick) blackbody imitates the inclusion of a secondary (warm) dust component., The shape of this optically thin (rather than thick) blackbody imitates the inclusion of a secondary (warm) dust component.
" As we are concerned onlywith and SFR, the parameterization of the data is the most important aspect,"," As we are concerned onlywith and SFR, the parameterization of the data is the most important aspect,"
six outer rellections is present in the solution at [οσον 1.15 but is weakly focusing and is not powerfully activated.,six outer reflections is present in the solution at frequency $1.15$ but is weakly focusing and is not powerfully activated.
 The dissipation rate in the viscous problem appears to converge to a very low value as vs Oat this frequency., The dissipation rate in the viscous problem appears to converge to a very low value as $\nu\to0$ at this frequency.
 The behaviour at frequency 1.05 (Fig. 8S). ," The behaviour at frequency $1.05$ (Fig. \ref{f:image1.05}) ),"
where the dissipation is strongest. is harder to explain.," where the dissipation is strongest, is harder to explain."
 The rav civnamics in the vicinity of this. frequency dis. very complicated., The ray dynamics in the vicinity of this frequency is very complicated.
 Although extremely long attractors mayexist oone at frequeney. 1.05 involving 584 outer reflections) they are of no practical significance., Although extremely long attractors mayexist one at frequency $1.05$ involving 584 outer reflections) they are of no practical significance.
 Llowever. there is a tencdeney for rays to be concentrated. temporarily into the region between the equator of the inner boundary ane the critical latitude on the outer boundary. where the wave enerey is seen to be prominent.," However, there is a tendency for rays to be concentrated temporarily into the region between the equator of the inner boundary and the critical latitude on the outer boundary, where the wave energy is seen to be prominent."
 The ravs escape from this region and reenter it repeatedlv., The rays escape from this region and reenter it repeatedly.
 Lt is απο to identify features of the ray dynamies that lead. to a preference for the frequency. 1.05., It is difficult to identify features of the ray dynamics that lead to a preference for the frequency $1.05$.
 The prominence of ravs emerging from the critical latitucle on the inner boundary has been noticed before (c.g.‘Tilener1999:Ogilvie&Lin 2004)..," The prominence of rays emerging from the critical latitude on the inner boundary has been noticed before \citep[e.g.][]{1999PhRvE..59.1789T,2004ApJ...610..477O}."
 There is a strong systematic dependence of the dissipation rate on the size of the core., There is a strong systematic dependence of the dissipation rate on the size of the core.
 This cllect is examined. in Fie. 12.. ," This effect is examined in Fig. \ref{f:average}, ,"
where we plot an average dissipation rate versus a.The average is obtained from the data for Figs 1 and 2.. by taking the arithmetic mean of the dissipation rates evaluated: at SOO equally spaced. frequencies in the range 2<w/8«2.," where we plot an average dissipation rate versus $\alpha$ .The average is obtained from the data for Figs \ref{f:fricover1}
 and \ref{f:fricover2}, by taking the arithmetic mean of the dissipation rates evaluated at 800 equally spaced frequencies in the range $-2<\omega/\Omega<2$."
" Phe ""baseline dissipation rate. which occurs for frequencies outside this range. is subtracted [rom the average. in order to isolate the contribution due to waves."," The `baseline' dissipation rate, which occurs for frequencies outside this range, is subtracted from the average, in order to isolate the contribution due to waves."
 There may be à systematic error in this procedure owing to the inadequate sampling of narrow peaks in the curve., There may be a systematic error in this procedure owing to the inadequate sampling of narrow peaks in the curve.
 The resulting values are approximately independent. of 5 and increase approximately as the fifth power of the core radius., The resulting values are approximately independent of $\gamma$ and increase approximately as the fifth power of the core radius.
 Interestingly. this dependence is. predicted. by. the recent analysis of Goodman&Lackner(2008).. who consider the scattering of the equilibrium tide olf the core. although they do not predict the intricate variation with frequency.," Interestingly, this dependence is predicted by the recent analysis of \citet{2008arXiv0812.1028G}, who consider the scattering of the equilibrium tide off the core, although they do not predict the intricate variation with frequency."
 A departure from this behaviour occurs as e approaches 1. owing to the toroidal-moce resonance in a thin shell.," A departure from this behaviour occurs as $\alpha$ approaches $1$, owing to the toroidal-mode resonance in a thin shell."
 The dynamies of inertial waves in a spherical annulus is very rich ancl a great deal remains to be explained., The dynamics of inertial waves in a spherical annulus is very rich and a great deal remains to be explained.
 In earlier work (Ogilvie2005) we considered a simpler type of domain in which all wave energv is focused. towards a single wave attractor and a dissipation rate is obtained that is asvimptotically independent of the viscosity or other small-scale camping mechanism for the waves., In earlier work \citep{2005JFM...543...19O} we considered a simpler type of domain in which all wave energy is focused towards a single wave attractor and a dissipation rate is obtained that is asymptotically independent of the viscosity or other small-scale damping mechanism for the waves.
 In a spherical annulus. the closest. parallel to this behaviour occurs in situations such as that illustrated in Pig. 9..," In a spherical annulus, the closest parallel to this behaviour occurs in situations such as that illustrated in Fig. \ref{f:image1.10},"
 although in fact more than one attractor is activated. there., although in fact more than one attractor is activated there.
 The spherical annulus is more complicated: because. simple. attractors occupy only a limited range of frequencies. and also because of the existence of a critical latitude at which rays. are tangent to the inner boundary.," The spherical annulus is more complicated because simple attractors occupy only a limited range of frequencies, and also because of the existence of a critical latitude at which rays are tangent to the inner boundary."
 In fact these features. are related. to cach other. because the range of frequencies in which an attractor exists is bounded by situations in which its ràvs approach the critical latitude on the inner and outer boundaries (Ποος.Georgeot&Valdettaro2001).," In fact these features are related to each other, because the range of frequencies in which an attractor exists is bounded by situations in which its rays approach the critical latitude on the inner and outer boundaries \citep{2001JFM...435..103R}."
. Both attractors and critical latitudes concentrate wave energy ancl promote enhanced. dissipation., Both attractors and critical latitudes concentrate wave energy and promote enhanced dissipation.
 A smooth beam of waves rellecting [from the inner boundary generates a singularitv in an inviscid Bluid. as illustrated. in Fie. 13..," A smooth beam of waves reflecting from the inner boundary generates a singularity in an inviscid fluid, as illustrated in Fig. \ref{f:critlat}. ."
 This οσοιdepends: smoothly: on frequency. in the range 2«w/O2. When the singular beam emanating [rom the, This effectdepends smoothly on frequency in the range $-2<\omega/\Omega<2$ When the singular beam emanating from the
"the growth factor, and ὅμη is the linear matter density contrast.","the growth factor, and $\delta_{\rm{lin}}$ is the linear matter density contrast."
" Thus we have, very roughly, 5;ος(1+z)*Olin which suggests Bassος(+zYBsss."," Thus we have, very roughly, $\delta_I \propto (1+z)^3\,\delta_{\rm lin}$ which suggests $B_{\delta_I\delta\delta} \propto (1+z)^3\,B_{\delta\delta\delta}$."
 The linear alignment model assumes that the intrinsic alignment is linearly related to the local tidal gravitational field2004)., The linear alignment model assumes that the intrinsic alignment is linearly related to the local tidal gravitational field.
" If this holds true, we also expect B;,55 to have a stronger angular scale dependence than B;s5 since tidal gravitational interaction follows the inverse cube law rather than the inverse square law which gravity itself follows."," If this holds true, we also expect $B_{\delta_I\delta\delta}$ to have a stronger angular scale dependence than $B_{\delta\delta\delta}$ since tidal gravitational interaction follows the inverse cube law rather than the inverse square law which gravity itself follows."
" Fora ACDM model, in the weakly nonlinear regime where perturbation theory holds, the dependence of Bss5 on (1+z) has a negative power shallower than —4, and the dependence on k has a power of around —2."," For a $\Lambda$ CDM model, in the weakly nonlinear regime where perturbation theory holds, the dependence of $B_{\delta\delta\delta}$ on $(1+z)$ has a negative power shallower than $-4$, and the dependence on $k$ has a power of around $-2$."
" In this paper we choose r= 0, s=1 as default."," In this paper we choose $r=0$ , $s=1$ as default."
" We also study the cases of r=—2, r=2, and s=0 whose results will be shown in 4 below."," We also study the cases of $r=-2$, $r=2$, and $s=0$ whose results will be shown in $\,$ below."
" As for the amplitude A of the GGI signal, the only direct study up to now is(2008), which suggests an overall GGI/GGG ratio of 10% for a zm=0.7 survey for elliptical galaxies and few percent for a mixed sample of elliptical and spiral galaxies."," As for the amplitude ${\cal A}$ of the GGI signal, the only direct study up to now is, which suggests an overall GGI/GGG ratio of $\,\%$ for a $z_{\rm m} = 0.7$ survey for elliptical galaxies and few percent for a mixed sample of elliptical and spiral galaxies."
" In this paper we adjust A such that the amplitude of the tomographic GGI bispectrum is limited to be within 10% of the amplitude of the lensing GGG signal, i.e. GGI/GGGs1096 at redshift bin combinations with z;« and Zi«zy where the GGI signal is expected to be most significant."," In this paper we adjust ${\cal A}$ such that the amplitude of the tomographic GGI bispectrum is limited to be within $\,\%$ of the amplitude of the lensing GGG signal, i.e. $\lesssim 10\,\%$ at redshift bin combinations with $z_i \ll z_j$ and $z_i \ll z_k$ where the GGI signal is expected to be most significant."
 This leads to a relatively modest overall GGI/GGG ratio at percent level., This leads to a relatively modest overall GGI/GGG ratio at percent level.
 We will show examples of the generated GGI and GGG signals in Fig.3.," We will show examples of the generated GGI and GGG signals in $\,$."
" As an order-of-magnitude estimate, one can also relate the GGI/GGG ratio to that of GI/GG by expanding three-point signals to couples of two-point signals using perturbation theory, in analogy to the fitting formula."," As an order-of-magnitude estimate, one can also relate the GGI/GGG ratio to that of GI/GG by expanding three-point signals to couples of two-point signals using perturbation theory, in analogy to the fitting formula."
" For the case of z;«σι3 zi, the leading order terms would give that the GGI/GGG ratio approximates that of GI/GG evaluated at redshifts z; and zj."," For the case of $z_i\ll z_j \approx z_k$ , the leading order terms would give that the GGI/GGG ratio approximates that of GI/GG evaluated at redshifts $z_i$ and $z_j$."
" This suggests that our adopted GGI/GGG ratio is also consistent with available observational studies of the GI signal2009), although the results of these studies vary a lot according to different median redshift, color and luminosity of the selected galaxy sample."," This suggests that our adopted GGI/GGG ratio is also consistent with available observational studies of the GI signal, although the results of these studies vary a lot according to different median redshift, color and luminosity of the selected galaxy sample."
" As mentioned in Sect.2.2, we would like to construct a single first-order weight function T?(y) for each (i,j) combination which preserves the maximum of information."," As mentioned in $\,$, we would like to construct a single first-order weight function $T^{(ij)}(\chi)$ for each $(i,j)$ combination which preserves the maximum of information."
 This can be seen as a constrained optimization problem., This can be seen as a constrained optimization problem.
 The constraining condition here is the nulling condition and the quantity to beoptimized is the Fisher information after nulling., The constraining condition here is the nulling condition and the quantity to beoptimized is the Fisher information after nulling.
" In JS08, several practical methodswere developed to solve this"," In JS08, several practical methodswere developed to solve this"
exponent a. the damping time 7; and the flare rate py.,"exponent $\alpha$, the damping time $\tau_d$ and the flare rate $p_f$."
 These are sufficient to produce our simulated EUV emission light curves., These are sufficient to produce our simulated EUV emission light curves.
 Pauluhn Solanki (2007) have shown that lor a large number of independent random flares. the distribution of normalized radiance in quiet sun follows a lognormal.," Pauluhn Solanki (2007) have shown that for a large number of independent random flares, the distribution of normalized radiance in quiet sun follows a lognormal."
 The same is true lor active regions as pointed out bv Safari et al. (, The same is true for active regions as pointed out by Safari et al. (
2007) ancl Dazarghan et al.(2008).,2007) and Bazarghan et al.(2008).
 In the following. we focus on the distributions of three selected regions shown in Figure 1..," In the following, we focus on the distributions of three selected regions shown in Figure \ref{fig1}."
 The intensity distributions and the lognormal fits are shown in Figure 2.., The intensity distributions and the lognormal fits are shown in Figure \ref{fig2}.
 The lognormal funelion is given by where. .r. ge. and σ are the radiance. scale parameter. and shape parameter. respectively.," The lognormal function is given by where, $x$, $\mu$, and $\sigma$ are the radiance, scale parameter, and shape parameter, respectively."
 The good fits eive us confidence in applving a stochastic flare model., The good fits give us confidence in applying a stochastic flare model.
 The kev parameters (power law exponents. damping rates and [lare rates) of small scale events (small eruptions) are not identifiable directly from observations.," The key parameters (power law exponents, damping rates and flare rates) of small scale events (small eruptions) are not identifiable directly from observations."
 Pauluhn Solanki (2007) and Safari et al. (, Pauluhn Solanki (2007) and Safari et al. (
2007). estimated that the damping rates ancl flare rates could be deduced by comparing light curves with simulated time series.,"2007), estimated that the damping rates and flare rates could be deduced by comparing light curves with simulated time series."
 They have used the shape parameters ol lognormal fits and wavelet analvsis., They have used the shape parameters of lognormal fits and wavelet analysis.
complete. this sample is expected to be also complete.,"complete, this sample is expected to be also complete."
 The lower z limit (0.008) was chosen to avoid objects with very large angular size. while the upper z limit (0.013) was set to include the largest possible number of objects ancl at (he same (ime to avoid very small angular sizes. especially for the companions that could be confused will stars (see relident)).," The lower z limit (0.008) was chosen to avoid objects with very large angular size, while the upper z limit (0.018) was set to include the largest possible number of objects and at the same time to avoid very small angular sizes, especially for the companions that could be confused with stars (see \\ref{ident}) )."
" It is important to point out that all the objects selected with the former restrictions lie in the luminosity range LOL.<Ly,10?L.. with MIRGs being the wide majority (zz924 are MIBGs. and are LIRGs)."," It is important to point out that all the objects selected with the former restrictions lie in the luminosity range $10^{10}L_{\odot} \leq L_{fir} \leq 10^{12}L_{\odot}$, with MIRGs being the wide majority $\approx 92\%$ are MIRGs, and are LIRGs)."
 The 60/n luminosity (in ergss1A.1) distribution and the ((in solar units) distribution of the BIRG sample are shown in the left and right panels of Fie., The $60\mu$ m luminosity (in $ergs~s^{-1}~\AA^{-1}$ ) distribution and the (in solar units) distribution of the BIRG sample are shown in the left and right panels of Fig.
 l respectively., \ref{Fig01} respectively.
 The control sample for (his study was randomly extracted [rom a list of more than 10.000 objects of the CLA Catalog (IInchraetal.1983).," The control sample for this study was randomly extracted from a list of more than 10,000 objects of the CfA Catalog \citep{huchra93}."
. This control sample matches: (1) (he isophotal diameter. (2) the redshift. and (3)the Lhibble morphological (wpe distribution of the BIRG sample.," This control sample matches: (1) the isophotal diameter, (2) the redshift, and (3)the Hubble morphological type distribution of the BIRG sample."
 Only objects with galactic latitude η>30 wwere included., Only objects with galactic latitude $|b_{II}| \geq 30^{\circ}$ were included.
 The control sample consists of90 objects., The control sample consists of90 objects.
" A V/V, (lest (Schmidt1963). gives a value of 0.48 + 0.04 (rms).", A $V/V_{max}$ test \citep{schmidt68} gives a value of 0.48 $\pm$ 0.04 (rms).
 The CS objects are low infrared emitters as can be seen in Fig. 1.., The CS objects are low infrared emitters as can be seen in Fig. \ref{Fig01}.
 Their flux at GOye is usually much smaller than 5.4 Jv. and their luminosity at this wavelength is svstematically smaller than (the luninosity of the BIRGs.," Their flux at $60 \mu$ is usually much smaller than 5.4 Jy, and their luminosity at this wavelength is systematically smaller than the luminosity of the BIRGs."
 Objects without a detection are treated as upper limits. using the flux density limits of IRAS.," Objects without a detection are treated as upper limits, using the flux density limits of IRAS."
 The distribution of upper limits is shown bv the filled histograms in Fig. 1.., The distribution of upper limits is shown by the filled histograms in Fig. \ref{Fig01}.
 The absolute D magnitude distribution was not matched., The absolute B magnitude distribution was not matched.
 The D luminosity may be partially correlated with the IR luminosity. since both are enhanced through star formation processes.," The B luminosity may be partially correlated with the IR luminosity, since both are enhanced through star formation processes."
 Therefore. anv attempt to match the D huninositw could bias the control sample towards galaxies with hieh infrared. luminosity. which is what we want to avoid.," Therefore, any attempt to match the B luminosity could bias the control sample towards galaxies with high infrared luminosity, which is what we want to avoid."
 As in previous environmental studies (IXrongold.Dultzin-Hacyan.&Miuziani(2001 ).. Dullvin-Hacvanetal. (1999a))). the search for galaxy companions was performed automatically," As in previous environmental studies \citet{k01}, , \citet{dd99a}) ), the search for galaxy companions was performed automatically"
consistent with the scaling of the acoustic cutoff frequency. (Brownοἱal.1991).,consistent with the scaling of the acoustic cutoff frequency \citep{brown91}.
. These modes generate photometric variability ranging from 5 to 1000 parts per million Γιουetal.2011) and have lifetimes of at least 15 davs (uberetal.2010:2011).," These modes generate photometric variability ranging from 5 to 1000 parts per million \citep{mosser11,huber11} and have lifetimes of at least 15 days \citep{huber10,baudin11}."
. Their excitation and damping (and thereby (heir resulting amplitiucles: Kjeldsen&Beclding (1995))) is related to the presence of vigorous convection within the star (see review by Christensen-Dalseaard (201111)., Their excitation and damping (and thereby their resulting amplitudes; \citet{kjeldsen95}) ) is related to the presence of vigorous convection within the star (see review by \citet{christen11}) ).
 The majority of these oscillations are p-uiodes with nearly evenly spaced frequencies al a relation used with equation (1)) to determine the stellar mass. M. and radius 2 from the measured 74. ellective temperature {ο aud Av (lekkeretal.2011)..," The majority of these oscillations are p-modes with nearly evenly spaced frequencies at a relation used with equation \ref{eq:numax}) ) to determine the stellar mass, $M$ , and radius $R$ from the measured $\nu_{\rm max}$, effective temperature $T_{\rm eff}$ and $\Delta \nu$ \citep{hekker11}. ."
" The implied relation between Mya, and Av has also been confirmed observationally Iluberetal. 2011).."," The implied relation between $\nu_{\rm max}$ and $\Delta
\nu$ has also been confirmed observationally \citep{stello09,hekker09,bedding10, huber10, hekker11, mosser11,huber11}."
 Space-based observations (Deddingetal.2010:Beck also enabled (he detection of the angular deeree 6=1 mixed modes. which have panode characteristics in the red giant envelope. bul &-imnode characteristics in the helium. core (Seuflaire1974:Osaki1975;Aizenmanetal.1977:Dziembowski2001:Cristensen-Dupretetal.2009:Montalban 2010).," Space-based observations \citep{bedding10, beck11,mosser11mixed} also enabled the detection of the angular degree $\ell=1$ mixed modes, which have p-mode characteristics in the red giant envelope, but g-mode characteristics in the helium core \citep{scuflaire74,osaki75,aizenman77,
 dziembowski01, christen04, dupret09, montalban10}."
. Modes nearly evenly spaced in period. al AJ)... around the (=1 p-modes were identified bv Decketal.(2011) as a characteristic of the interior core g-modes allowing Beddingetal.(2011) to distinguish firstascent red eiant branch (RGB) stars (i.e. those with degenerate helium cores) from red clamp stars (Le. those with non-degenerate He burning cores).," Modes nearly evenly spaced in period, at $\Delta P_{\rm obs}$, around the $\ell=1$ p-modes were identified by \citet{beck11} as a characteristic of the interior core g-modes allowing \citet{bedding11} to distinguish firstascent red giant branch (RGB) stars (i.e. those with degenerate helium cores) from red clump stars (i.e. those with non-degenerate He burning cores)."
 This separation in the AJ’).—Av diagram was also seen by CoRot (Mosseretal.2011a).. and is à powerful new tool for stellar population stucies.," This separation in the $\Delta P_{\rm obs}-\Delta \nu$ diagram was also seen by CoRot \citep{mosser11mixed}, and is a powerful new tool for stellar population studies."
 We show here that (his new capability to probe the deep interior of a red giant should allow for the identification of those V.2M. stars undergoing the helium core flash., We show here that this new capability to probe the deep interior of a red giant should allow for the identification of those $M \lesssim 2M_\odot$ stars undergoing the helium core flash.
 Known for more than 40 vears as the defining event that ends the ascent of low mass stus up the RGB (and delines the tip of the RGB: Salarisetal. (2002))). this thermally unstable ancl olf-center helium burning leads to a {ος2 Myr phase of successive He subllashes (Thomas1934:Mocáketal.2008). that remove electron degeneracy ancl convert the He core to a stablv burning non-degenerate object.," Known for more than 40 years as the defining event that ends the ascent of low mass stars up the RGB (and defines the tip of the RGB; \citet{salaris02}) ), this thermally unstable and off-center helium burning leads to a $t_f\approx 2$ Myr phase of successive He subflashes \citep{thomas67,ibenrenzini84,mocak08} that remove electron degeneracy and convert the He core to a stably burning non-degenerate object."
 ILowever. there has been debate (see review bv Iben&Renzini (1984))) as to whether the initiating flash can become dynamical in some wav. or rather remainshycrostatic.," However, there has been debate (see review by \citet{ibenrenzini84}) ) as to whether the initiating flash can become dynamical in some way, or rather remainshydrostatic."
 Using the MESA code (Paxtonetal. 2011).. we start in 82 by describing the changes in the red giant envelope and helium core during the core flash.," Using the $\MESA$ code \citep{paxton11}, , we start in 2 by describing the changes in the red giant envelope and helium core during the core flash."
 Wework in the Wentzel. INramers.," Wework in the Wentzel, Kramers,"
 We first determine the implications of the observed interactions only. without applying corrections for the short duration of the mergers.,"}} We first determine the implications of the observed interactions only, without applying corrections for the short duration of the mergers."
 We define a sample which contains both current and future bulge-dominated galaxies. consisting of the 86 bulge-dominated galaxies (classified as E/SO). minus half of the six E/SOs which are interacting with each other. plus the disk-dominated galaxies (classified as S or SO) which are involved in a major merger.," We define a sample which contains both current and future bulge-dominated galaxies, consisting of the 86 bulge-dominated galaxies (classified as E/S0), minus half of the six E/S0s which are interacting with each other, plus the disk-dominated galaxies (classified as S or S0) which are involved in a major merger."
 Among disk-dominated galaxies the only major merger is the spiral/SO pair 18-485/522. whose constituent galaxies have roughly equal luminosity.," Among disk-dominated galaxies the only major merger is the spiral/S0 pair 18-485/522, whose constituent galaxies have roughly equal luminosity."
 The total sample of current and future bulge-dominated galaxies is therefore 86-341=84., The total sample of current and future bulge-dominated galaxies is therefore $86 - 3 + 1 = 84$.
 Among this sample of 84 galaxies there are eighteen current mergers and 41 remnants. and we infer that bulge-dominated galaxies experienced a merger or accretion event in the recent past.," Among this sample of 84 galaxies there are eighteen current mergers and 41 remnants, and we infer that bulge-dominated galaxies experienced a merger or accretion event in the recent past."
 The red ongoing mergers and the red tidal features associated with many of the E/SO galaxies very likely sample the same physical process at different times., The red ongoing mergers and the red tidal features associated with many of the E/S0 galaxies very likely sample the same physical process at different times.
 On average. galaxies with strong tidal features are probably observed shortly after the merger and galaxies with weak features are observed at later times.," On average, galaxies with strong tidal features are probably observed shortly after the merger and galaxies with weak features are observed at later times."
 Assuming that the ongoing mergers are representative for the progenitors of all remnants we can directly infer the mass ratios of the progenitors of the full sample of 59 current and future bulge-dominated early-type galaxies., Assuming that the ongoing mergers are representative for the progenitors of all remnants we can directly infer the mass ratios of the progenitors of the full sample of 59 current and future bulge-dominated early-type galaxies.
 The median lummosity ratio of the ongoing mergers ts 0.31. and the median color difference is negligible after correcting for the slope of the color-magnituderelation.," The median luminosity ratio of the ongoing mergers is 0.31, and the median color difference is negligible after correcting for the slope of the color-magnituderelation."
" Assuming that W/LxM""? (e.g. Jérrgensen et 11996) a luminosity ratio of 0.31 implies a median mass ratio of 0.23. or a 1:4 merger."," Assuming that $M/L \propto M^{0.2}$ (e.g., rgensen et 1996) a luminosity ratio of 0.31 implies a median mass ratio of 0.23, or a 1:4 merger."
 There is also indirect evidence that the progenitors of the remnants were typically major mergers rather thàn low mass aceretion events., There is also indirect evidence that the progenitors of the remnants were typically major mergers rather than low mass accretion events.
 Simulations byJohnston.Sackett. (2001) show that surface brightness levels 28<ji33 are typical for the debris of small satellites such as the Local Group dwarfs.," Simulations by, (2001) show that surface brightness levels $28<\mu<33$ are typical for the debris of small satellites such as the Local Group dwarfs."
 Similarly. the average surface brightness of the giant stream of M31 ts jrz30 ((Ibata et 22001) and that of the debris from the Sagittarius dwarf fryzm31 (Johnston et 22001).," Similarly, the average surface brightness of the giant stream of M31 is $\mu_V
\approx 30$ (Ibata et 2001) and that of the debris from the Sagittarius dwarf $\mu_V \approx 31$ (Johnston et 2001)."
 All these values are well beyond the detection limit of our survey., All these values are well beyond the detection limit of our survey.
 Furthermore. the fraction of tidally disturbed galaxies is much lower among disk-dominated galaxies than among bulge-dominated galaxies.," Furthermore, the fraction of tidally disturbed galaxies is much lower among disk-dominated galaxies than among bulge-dominated galaxies."
 Ignoring the ongoing mergers only features compared to This difference ts consistent with the idea that the events responsible for the tidal features were usually sufficiently strong to disturb any dominant disk component., Ignoring the ongoing mergers only features compared to This difference is consistent with the idea that the events responsible for the tidal features were usually sufficiently strong to disturb any dominant disk component.
 Finally. the fact that the features are typically broad and red suggests that the progenitors were dynamically hot systems with old stellar populations. consistent with the properties of the galaxies in the ongoing mergers.," Finally, the fact that the features are typically broad and red suggests that the progenitors were dynamically hot systems with old stellar populations, consistent with the properties of the galaxies in the ongoing mergers."
 We also note that the fraction of light associated with the features (~5 associated with the tidal debris in the 1:3 merger simulation shown in 11., We also note that the fraction of light associated with the features $\sim 5$ associated with the tidal debris in the 1:3 merger simulation shown in 1.
 We conclude that approximately bulge-dominated red galaxies experienced a major merger with mass ratio >1:4 in the time window probed by our observations., We conclude that approximately bulge-dominated red galaxies experienced a major merger with mass ratio $>1:4$ in the time window probed by our observations.
 This result ts direct observational confirmation of the hierarchical assembly of massive galaxies., This result is direct observational confirmation of the hierarchical assembly of massive galaxies.
 Up to this point the analysis did not require an estimate of the timescale of the mergers., Up to this point the analysis did not require an estimate of the timescale of the mergers.
 Such estimates are obviously uncertain. but they are necessary for turning the merger fraction into à merger rate and a mass accretion rate.," Such estimates are obviously uncertain, but they are necessary for turning the merger fraction into a merger rate and a mass accretion rate."
 These numbers are more easily compared to models and other observational studies. and are needed for extrapolating the results to higher redshifts.," These numbers are more easily compared to models and other observational studies, and are needed for extrapolating the results to higher redshifts."
 The merger rate can be defined in a variety of ways (see. e.g.. Patton et 22002).," The merger rate can be defined in a variety of ways (see, e.g., Patton et 2002)."
 Here it is expressed as the number of remnants that are formed per Gyr within our selection area: with fi; the fraction of the galaxy population involved in a merger — with pairs counted as single objects — and fy a characteristic timescale for the mergers., Here it is expressed as the number of remnants that are formed per Gyr within our selection area: with $f_{\rm m}$ the fraction of the galaxy population involved in a merger – with pairs counted as single objects – and $t_{\rm m}$ a characteristic timescale for the mergers.
 We restrict the analysis to the sample of nineteen ongoing mergers. as simulations of the fading of tidal debris around the remnants of dry mergers have not yet been done in a systematic way.," We restrict the analysis to the sample of nineteen ongoing mergers, as simulations of the fading of tidal debris around the remnants of dry mergers have not yet been done in a systematic way."
" Following Patton et ((2000) we assume that the timescale of the mergers can be approximated by the dynamical friction timescale. given by where ris the physical separation of the pairs. v, 1s the circular. velocity. M. is the mass of the lowest mass galaxy. and InA is the Coulomb logarithm (see Binney Tremaine 1987; Patton et 22000)."," Following Patton et (2000) we assume that the timescale of the mergers can be approximated by the dynamical friction timescale, given by where $r$ is the physical separation of the pairs, $v_c$ is the circular velocity, $M$ is the mass of the lowest mass galaxy, and $\ln\,\Lambda$ is the Coulomb logarithm (see Binney Tremaine 1987; Patton et 2000)."
 The median projected separation of the paired galaxies is 876. or 162:3 kpe at z20.10 £0.02.," The median projected separation of the paired galaxies is $8\farcs 6$, or $16\pm 3$ kpc at $z=0.10 \pm 0.02$ ."
 Assuming random orientations this corresponds to à median physical separation r=203-4 kpe., Assuming random orientations this corresponds to a median physical separation $r=20\pm 4$ kpc.
 To obtain an estimate of, To obtain an estimate of
llaving shown that the X-rav. transient. 050109 is not a SN shock breakout event. one is left with two alternative interpretations about the nature of the transient: (1) Lt is a low-Iuminosity NRE (Berger&Soderberg2008: 2008): (2) Ht is a Hare in the X-ray afterglow of a GRB (Burrowsοἱal.2008).,"Having shown that the X-ray transient 080109 is not a SN shock breakout event, one is left with two alternative interpretations about the nature of the transient: (1) It is a low-luminosity XRF \citep{ber08,xu08}; (2) It is a flare in the X-ray afterglow of a GRB \citep{bur08}."
. The transient object happened to be in the BAT field of view in two previous oobservations (ol DZOQ JOGIS| beginning at 13:04:12.33. and of SN 2007ax beginning4620. at 13:12:24.5— UT on 9 Jan 2008).," The transient object happened to be in the BAT field of view in two previous observations (of BZQ J0618+4620 beginning at 13:04:12.33, and of SN 2007ax beginning at 13:12:24.5 UT on 9 Jan 2008)."
 BAT did not trigger during either of he two observations., BAT did not trigger during either of the two observations.
 An examination of the BAT data rom the direction of NGC 2770 during those observations shows no sign of emission in the BAT energy range 15.150 keV. with a Hluence upper limit of ~1.0«10. erg em? in a period of half an hour before the start of observation of the transient 080109 (Burrowsetal.2008).," An examination of the BAT data from the direction of NGC 2770 during those observations shows no sign of emission in the BAT energy range 15–150 keV, with a fluence upper limit of $\sim 
1.0\times 10^{-7}$ erg $^{-2}$ in a period of half an hour before the start of observation of the transient 080109 \citep{bur08}."
. In addition. he UVO'T lighteurve of the transient. closely resembles an carly stage UV-optical lishteurve of a GRB (eg... GRB 005151. rather than a UV-optical afterglow lighteurve during the late declining stage.," In addition, the UVOT lightcurve of the transient closely resembles an early stage UV-optical lightcurve of a GRB (e.g., GRB 060218), rather than a UV-optical afterglow lightcurve during the late declining stage."
 Hence. the interpretation of the transient event as a [lare in the X-ray afterelow of a GRB is also ruled out.," Hence, the interpretation of the transient event as a flare in the X-ray afterglow of a GRB is also ruled out."
 An additional evidence supporting an ARE interpretation of the transient 050109 is in the shape of the X-ray lighteurve. after the prompt emission. phase., An additional evidence supporting an XRF interpretation of the transient 080109 is in the shape of the X-ray lightcurve after the prompt emission phase.
" At the end of an exponential ἄοσαν, the N-rav lighteurve breaks to a power-law ἄοσαν with an index =1.1 up to f=30000 s from the start of observation. which is a characteristic of typical GRB afterglows (Xuetal.2008)."," At the end of an exponential decay, the X-ray lightcurve breaks to a power-law decay with an index $\approx -1.1$ up to $t\approx 30000$ s from the start of observation, which is a characteristic of typical GRB afterglows \citep{xu08}."
. Jased on the above arguments. L conclude that. the transient event OSOLO9 in NGC 2770 is a soft NRE. and XB OSOLOO/SN 2008D well fits the framework of the GILD-SN connection.," Based on the above arguments, I conclude that the transient event 080109 in NGC 2770 is a soft XRF, and XRF 080109/SN 2008D well fits the framework of the GRB-SN connection."
 AREF 080109 is more undoer-Iuminous than the previous most under-uminous burst. Cli 980425. by about. two orders of magnitude.," XRF 080109 is more under-luminous than the previous most under-luminous burst, GRB 980425, by about two orders of magnitude."
 The spectrum. of ARE 0501089 is also softer than that of. GRB 980425., The spectrum of XRF 080109 is also softer than that of GRB 980425.
 During the NIE observation of NIE 080100 which lasted. over 1000. s. the BAT fluence upper limit is 89«10.7 erg > in 15.150 keV (Burrowsetal.2008).," During the XRT observation of XRF 080109 which lasted over 1000 s, the BAT fluence upper limit is $8.9
\times 10^{-8}$ erg $^{-2}$ in 15–150 keV \citep{bur08}."
. Extrapolation of the power-law spectral fit in Section 2. to 15150 keV leads to a Iuence of 34v3.10x erg cni?7. mareinally consistent with the BAP upper limit.," Extrapolation of the power-law spectral fit in Section \ref{data} to 15–150 keV leads to a fluence of $3.4_{-2.2}^{+6.3}\times 10^{-8}$ erg $^{-2}$, marginally consistent with the BAT upper limit."
 Due to the limit in the number of photon counts (433 in total after the piled-up core region being removed) and he small range of energy covered by NICE (0.3. 10 keV). a reliable constraint on the peak spectral energy. cannot be obtained from the NICE. data alone.," Due to the limit in the number of photon counts (433 in total after the piled-up core region being removed) and the small range of energy covered by XRT $0.3$ –10 keV), a reliable constraint on the peak spectral energy cannot be obtained from the XRT data alone."
 However. the fact that he NRT spectrum of NRE 080109 can be fitted hy a single power-law with aphoton index Dzm2.3 suggests that the »eak spectral energy. £o<0.3 keV. X lower limit on the value of Z4 can be obtained from the UVOT observation during the prompt phase of NRE 080109.," However, the fact that the XRT spectrum of XRF 080109 can be fitted by a single power-law with aphoton index $\Gamma\approx 2.3$ suggests that the peak spectral energy $E_\p<0.3$ keV. A lower limit on the value of $E_\p$ can be obtained from the UVOT observation during the prompt phase of XRF 080109."
 The specific (ux density in the. EV band (at ~3 eV) during the prompt phase is ff.«9.0107 pid (Lmmleretal.2008:Soderbergetal. 2008).," The specific flux density in the band (at $\sim 3$ eV) during the prompt phase is $F_\nu<9.0\times 10^2$ $\mu$ Jy \citep{imm08,sod08}."
. Xecording to the svnchrotron model for GRB emissions (Sari.Piran&Naravan1998)... F5x with1/3.," According to the synchrotron model for GRB emissions \citep{sar98}, $F_\nu\propto \nu^\alpha$ with."
 Then. combination with the power-law fit to the NICE spectrum leads to a constraint on Zio Iosc0.037 keV. llence we have 0.037keV.«£a<0.3keV.," Then, combination with the power-law fit to the XRT spectrum leads to a constraint on $E_\p$: $E_\p > 0.037$ keV. Hence we have $0.037~{\rm keV} < E_\p <0.3~{\rm keV}$."
" The power-law spectral fit leads to a total isotropic-equivalent energy. Ai=1.342107"" erg in 110000 keV in the rest [rame of the burst.", The power-law spectral fit leads to a total isotropic-equivalent energy $E_\iso = 1.3_{-0.7}^{+1.5}\times 10^{46}$ erg in 1–10000 keV in the rest frame of the burst.
"- This value of ων together with the constraint on the peak spectral energy obtained above. makes ARE 050100 agree with the Z5, Ey relation of Amati(2006) (see Fig. 2))."," This value of $E_\iso$, together with the constraint on the peak spectral energy obtained above, makes XRF 080109 agree with the $E_\iso$ $E_\p$ relation of \citet{ama06} (see Fig. \ref{eiso_epeak2}) )."
 Alternatively. from the value of £i for NRE 080109. the Amati relation implies that the peak spectral energy of NRE 080109 should be fu80.12onn keV. in good agreement with the constraint inferred from the NICE and UVO'T data.," Alternatively, from the value of $E_\iso$ for XRF 080109, the Amati relation implies that the peak spectral energy of XRF 080109 should be $E_\p \approx 
0.12_{-0.089}^{+0.23}$ keV, in good agreement with the constraint inferred from the XRT and UVOT data."
 The bolometric lighteurve of SN. 2008D in the early stage was derived. from the UVOT cata anc modeled by Soderbergetal.(2008)., The bolometric lightcurve of SN 2008D in the early stage was derived from the UVOT data and modeled by \citet{sod08}.
".. The peak of the lighteurve occurred. at. about 20 cay alter the explosion. with a peak bolometric magnitude =16.65. (corresponding to a maximum. bolometric. luminosity⋠⋠ zz1.45107ip erg "" 7)."," The peak of the lightcurve occurred at about 20 day after the explosion, with a peak bolometric magnitude $\approx -16.65$ (corresponding to a maximum bolometric luminosity $\approx 
1.4\times 10^{42}$ erg $^{-1}$ )."
 Fitting the lighteurve by an analytic model of SN emission powered by the radioactive decay of .and vielded a numass synthesized in the explosion between 0.05 and O.LAL. (Soderbergetal. 2008).., Fitting the lightcurve by an analytic model of SN emission powered by the radioactive decay of and yielded a mass synthesized in the explosion between $0.05$ and $0.1 M_\odot$ \citep{sod08}. .
 These results. together with the peak spectral energy of NRA 080109 derived from the NICE and UVOT data. indicate that NRE 080109/SN 2008D agree withthe relation between the peak spectral energy of GRBs," These results, together with the peak spectral energy of XRF 080109 derived from the XRT and UVOT data, indicate that XRF 080109/SN 2008D agree withthe relation between the peak spectral energy of GRBs"
redshift ~130 and cools aciabatically thereafter (Z56:3;1X(L| <3?) one finds TreaΤέληl before the first huninous objects reheat the universe.,redshift $\sim 130$ and cools adiabatically thereafter $T_{IGM} \propto (1+z)^2$ ) one finds $T_{IGM}/T_{CMB} \ll 1$ before the first luminous objects reheat the universe.
 Here the signal is in absorption against the CAIB. aud it is expected at the waveleugth of 2lem<(Y|νι]. where τω denotes the redshift at which the spin temperature is first coupled to the kinetic gas temperature.," Here the signal is in absorption against the CMB, and it is expected at the wavelength of $21cm \times
(1+z_{Ly\alpha})$, where $z_{Ly\alpha}$ denotes the redshift at which the spin temperature is first coupled to the kinetic gas temperature."
 Once the IGM is heated to a temperature above that of the CMD. the signal will be in cussion aud roughly independent of the spin temperature.," Once the IGM is heated to a temperature above that of the CMB, the signal will be in emission and roughly independent of the spin temperature."
 The dittereutial autenua temperature (the brightuess temperature Lp=Teapp¢LITs]ο 74) observed at Earth between such a patch of IGM at a spin temperature Py and the CMD is approximately eiveu by (TOO). where /7 denotes the current. Hubble coustaut in mits of 100iis+Mpe and O5 eives the barvon density in units of the critical density.," The differential antenna temperature (the brightness temperature $T_B = T_{CMB} \, e^{-\tau} + T_S\, [1-e^{-\tau}] \,$ ) observed at Earth between such a patch of IGM at a spin temperature $T_S$ and the CMB is approximately given by (T00), where $h$ denotes the current Hubble constant in units of $100\kmpspMpc$, and $\Omega_B$ gives the baryon density in units of the critical density."
 ΙΤ is larger bw a factor Toarpp/ts (S18 for reionization redshifts > 6) for the absorption signal than for emüssion., $|\delta T|$ is larger by a factor $T_{CMB}/T_S$ $\approxlt 18$ for reionization redshifts $>6$ ) for the absorption signal than for emission.
 Uufortunately. a velatively large radiatiou fux iu Lya is required to ensure the coupling of the spin temperature to the kinetic gas temperature.," Unfortunately, a relatively large radiation flux in $\alpha$ is required to ensure the coupling of the spin temperature to the kinetic gas temperature."
 Therefore. the recoil from Lv scatterings most likelv heats the ICAL to or above the CNID temperature before a sufficient Lya backgrouud fiux is established (NMNIB97).," Therefore, the recoil from $\alpha$ scatterings most likely heats the IGM to or above the CMB temperature before a sufficient $\alpha$ background flux is established (MMR97)."
 Cousequeutly. the largest signals predicted by TOO aud. MIAIR97 ave S10 uly (at e.g. 150 AIIz if 2~ 9). as expected from equation (1)) aud. the “Cosmic Web” at these times is most likely to be probed πι cussion at 21 cm.," Consequently, the largest signals predicted by T00 and MMR97 are $\approxlt 10$ mK (at e.g., 150 MHz if $z \sim 9$ ), as expected from equation \ref{delT}) ) and the “Cosmic Web” at these times is most likely to be probed in emission at 21 cm."
 The appropriate resolution for casting fluctuations iu the [GAL is of the order of 1 are- with the frequency. window of 1 MIIz around 150 AIIIz (NEM97: T00)., The appropriate resolution for measuring fluctuations in the IGM is of the order of 1 arc-minute with the frequency window of 1 MHz around 150 MHz (MMR97; T00).
 However. if the absorption feature were observed. it would eive valuable insights to the epoch at which the first stars formed (MMBR97: Του).," However, if the absorption feature were observed, it would give valuable insights to the epoch at which the first stars formed (MMR97; T00)."
 At the epoch of reionization “breakthrough” the 21cm signal frou diffuse gas decreases steeply., At the epoch of reionization “breakthrough” the 21cm signal from diffuse gas decreases steeply.
 Oue should be able to observe this signal integrated over most of the sky even with moderate instruments (Shaver ct al., One should be able to observe this signal integrated over most of the sky even with moderate instruments (Shaver et al.
 1999)., 1999).
 Iu the following sections we exauine the confusion noise oetroduced at 150 MITz by extra-galactie radio sources aud iscuss how this might impose serious Bnitatious for the 21-cu tomography., In the following sections we examine the confusion noise introduced at $150$ MHz by extra-galactic radio sources and discuss how this might impose serious limitations for the 21-cm tomography.
 SIKXA isρα planned to operate in the frequency rauge 01-20. GIIz with an augular resolution of about 1-10 are-seconds and a sensitivitv down to a few tens of Wy., SKA is planned to operate in the frequency range 0.01-20 GHz with an angular resolution of about 1-10 arc-seconds and a sensitivity down to a few tens of nJy.
 Linutations on the sensitivity achievable for the ueasureineut of redshifted 21-014 signal will be set ly he contamination from the galactic and extra-galactic oregrounds., Limitations on the sensitivity achievable for the measurement of redshifted 21-cm signal will be set by the contamination from the galactic and extra-galactic foregrounds.
 The dominant galactic contribution is the svuchrotron backeround which comprises a fraction of about at 150 MIIz., The dominant galactic contribution is the synchrotron background which comprises a fraction of about at 150 MHz.
 On the angular scales that are uost rolevaut for the 2lcm tomography. we nonetheless expect the douinant angular fluctuations to be caused by clustering and disercteness of extra-galactic sources (discussed below).," On the angular scales that are most relevant for the 21cm tomography, we nonetheless expect the dominant angular fluctuations to be caused by clustering and discreteness of extra-galactic sources (discussed below)."
 The ealactic foreground could only make a comparable contribution on subareminute scales df there were. throughout the interstellar iuediunmi aud ealactic halo. fluctuations of order unity in its volume enussivitv.," The galactic foreground could only make a comparable contribution on sub–arc–minute scales if there were, throughout the interstellar medium and galactic halo, fluctuations of order unity in its volume emissivity."
 Such fluctuations would exist. but only iu small regions (c.g. active supernova remnants).," Such fluctuations would exist, but only in small regions (e.g. active supernova remnants)."
 On larger angular scales. where the ealactic foreground fluctuations would be relatively more muportaut. it has boen sufficieutlv woelbstudied (although at uch higher radio frequencies than considered here) because of its imuportance for the observatious of the cosmüc microwave backerouud radiation (sec references in Teemark Efstathiou 1996).," On larger angular scales, where the galactic foreground fluctuations would be relatively more important, it has been sufficiently well-studied (although at much higher radio frequencies than considered here) because of its importance for the observations of the cosmic microwave background radiation (see references in Tegmark Efstathiou 1996)."
 A detailed discussion of the Galactic spectral coutamination to the redshlifted 21-1 is giveu in Shaver et al., A detailed discussion of the Galactic spectral contamination to the redshifted 21-cm is given in Shaver et al.
 1999., 1999.
 Detailed multiwavelength observatious of the ealactic radio emission could be modeled sufficiently accurately for our purpose (at least iu some regious of the sky where observations would then take place)., Detailed multi–wavelength observations of the galactic radio emission could be modeled sufficiently accurately for our purpose (at least in some regions of the sky where observations would then take place).
 Hence. we Init our discussion to the confusion noise introduced by extra-ealactic foreground sources such as radio galaxies. ACN and uormal ealaxies which are likely to dominates the radio counts at the low flux cleusity levels.," Hence, we limit our discussion to the confusion noise introduced by extra-galactic foreground sources such as radio galaxies, AGN and normal galaxies which are likely to dominates the radio counts at the low flux density levels."
 The wavelength region of interest is from 50 MIIz 30) to 200 MIIz (2~6)., The wavelength region of interest is from 50 MHz $z\sim 30$ ) to 200 MHz $z\sim 6$ ).
 To evaluate the impact of extra-ealactic foreground radio sources in this waveleneth rauge it is necessary to model the nuniber density of sources as a function of flux (the differcutial counts NOS) per steracian)., To evaluate the impact of extra-galactic foreground radio sources in this wavelength range it is necessary to model the number density of sources as a function of flux (the differential counts $N(S)$ per steradian).
 At present. the appearance of the radio sky at flux ceusity levels below 1j Jw is uot well known.," At present, the appearance of the radio sky at flux density levels below $ 1 \mu$ Jy is not well known."
 However deep VLA survevs have allowed to extend direct eterminations of radio source counts down to a few μὴν (at v& Ll Giz). implying a coverage of about 7 orders of inmagnitude in flux.," However deep VLA surveys have allowed to extend direct determinations of radio source counts down to a few $\mu $ Jy (at $\nu \approxgt$ 1.4 GHz), implying a coverage of about 7 orders of magnitude in flux."
 At lower frequencies the limiting flux deusities are higher because of the confusion nolse oeitroduced by extended sources., At lower frequencies the limiting flux densities are higher because of the confusion noise introduced by extended sources.
 The source counts from the 6C survey (ales. Baldwin Warner 1988) which was carried out at 191 MIIz are a seful euide.," The source counts from the 6C survey (Hales, Baldwin Warner 1988) which was carried out at 151 MHz are a useful guide."
 The radio source counts at all frequencies are typically well deseribed bv a Euclidean power law region at the highest flux densities followed by a flatter portion at lower flux densities (c.g. Formalout et al., The radio source counts at all frequencies are typically well described by a Euclidean power law region at the highest flux densities followed by a flatter portion at lower flux densities (e.g. Formalont et al.
 1991)., 1991).
 We therefore extrapolate the 151 MITz differcutial source counts by a double power-law fitted to the observed counts., We therefore extrapolate the 151 MHz differential source counts by a double power-law fitted to the observed counts.
 This gives: where.)=1[:5. 59= 2.51.4)=by “with ko=L0 per sr per nmJy aud Sy=880 ιν.," This gives: where $\gamma_1 = 1.75$, $\gamma_2 = 2.51$, $k_1=k_2 S_0^{\gamma_2-\gamma_1}$ with $k_2= 4.0$ per sr per mJy and $S_0 = 880 $ mJy."
" This ft also includes the counts from the 3CR survey and the 3 CRR catalogue at 175 MIIz (Laine. Rilev Lousair 1983) transposed to 151 MITIZz assunüus a mean spectral iudex a=0.75 (5Xr ""). typical for the enüssion from extended lobes at these frequencies (6.8: Laing. Rilev Lougai 1983)."," This fit also includes the counts from the 3CR survey and the 3 CRR catalogue at 178 MHz (Laing, Riley Longair 1983) transposed to 151 MHz assuming a mean spectral index $\alpha = 0.75$ $ S\propto
\nu^{-\alpha}$ ), typical for the emission from extended lobes at these frequencies (e.g.; Laing, Riley Longair 1983)."
 The hlnuitiug fux density for these survey was ~LOO idw and our extrapolation is somewhat uncertain., The limiting flux density for these survey was $\sim 100$ mJy and our extrapolation is somewhat uncertain.
 However. we will show that our main conclusious are insensitive to the particular choice of the," However, we will show that our main conclusions are insensitive to the particular choice of the"
 ↓⋋≱⋟≱↸∖∙↕∖↕∏⊔⊔↸↾∆↕≱∪∪↓ the-. Universe. raugiugUx in⋅⋅⋅⋟ size from :dwarf calaxics⋅ ct∖⋠≻ galaxy clusters. jg sourced by a composite nues Cao ofi dark matter.i barvonici matteri inea: gas potential⋅⋅the collapsed asobjects suchstar as stars ealaxie:in ealaxiesἕ eravitational . in clusters.,"The potential of gravitationally bound structures in the Universe, ranging in size from dwarf galaxies to galaxy clusters, is sourced by a composite mass distribution of dark matter, baryonic matter in gas form, and collapsed objects such as stars in galaxies and galaxies in clusters."
 μι investieation ofthese mass Is very aails: ummberER atof onuestions: what isd cannot: be⋅⋅ of the distributions?, The investigation of these mass distributions entails a number of questions: what is the shape of the distributions?
 Is it universal across n principle of masHRS.d aud atatoi :all redshifts?, Is it universal across ten magnitudes of mass and at all redshifts?
 ↴⋅Docs profile↴↽∙ as- on. cosmeologv or ou the merecr historv of s∖⊀ al.ONG: halos?, Does it depend on cosmology or on the merger history of the individual halos?
 Since the dominant component of | “Theowe dark matter. much focus has beou icoretical efforts ATC ianatter-oulv -alos," Since the dominant component of relaxed structures is dark matter, much focus has been aimed at dark matter-only halos."
 underalos. the.: strongest. theoretical understandiug of the uot enough coustraits indi a darki matter alo.halo., There is little theoretical understanding of the distribution of matter in a dark matter halo.
 Themain collisionlessdevelopiueuts Boltzinanuhave equation been found through πιο Ίσα] 1987) whichgoverns formation of structure in the universe oue can fake cosmological model., The main developments have been found through numerical simulations of the formation of structure in the universe within a given cosmological model.
" .Advances lave been simulations such as improvement. of ummerical codesase asespace iο av ""a increase of raw computingκ power“Le on oneoO haud NO ALCL AM refined understanding of which questions that a MSOTLOPN relation answered onthe ↴other.", Advances have been achieved through the improvement of numerical codes as well as the increase of raw computing power on one hand and a more refined understanding of which questions that need to be answered on the other.
 Perhaps the most⋅ predict. au inner: has come out of the nuuerical a Jon ‘ relaxed halos are (uearly) uuiversal 9 1ο μασ] iu lua res]ects. including the distributiou of matter (Navarroetal.1997:Tavlor&Nawvarro2001) aud the dviazuucal structure (Bullocketal.2001a:Hausen&Moore 2006)..," Perhaps the most fundamental idea that has come out of the numerical approach is that relaxed halos are (nearly) universal in many respects, including the distribution of matter \citep{1997ApJ...490..493N,2001ApJ...563..483T} and the dynamical structure \citep{2001ApJ...555..240B,2006NewA...11..333H}."
" However. the μπιτ]Ες --- ≻∐↴∖∐↙↧↖↸∐∪⊓⋝∩∐∖∖ able to reach agreement about he exact behavior of the profiles in the imucrimost regicDLS, where the lmüted force resolution of simulations se na lower linut⋅⋅ to the radial rauge that can be probed."," However, the simulations have not been able to reach agreement about the exact behavior of the profiles in the innermost regions, where the limited force resolution of simulations sets a lower limit to the radial range that can be probed."
 Various authors clain that the logaritlinic slope of the dchsity profile reaches a valuebetween 1 and 1.5. perhaps dependent on mass or merger Ημουν. and there is aso discussion whether the inner slope is actually universal or uot (Mooreοἳal.al.et2008)...," Various authors claim that the logarithmic slope of the density profile reaches a value between $-1$ and $-1.5$, perhaps dependent on mass or merger history, and there is also discussion whether the inner slope is actually universal or not \citep{1998ApJ...499L...5M,2001ApJ...554..903K,2004MNRAS.349.1039N,2004ApJ...606..625F,2006AJ....132.2685M,2006AJ....132.2701G,2008MNRAS.387..536G}."
 A further complication ariseset whem2006: distribution simulations are compared with observations since the : of⋅ the⋅ barvonic. component. whichorm. ur iand fine⋅⋝ consuming to∖⋅ modeln in theBE simulations. distributionsaud cutailsealaxies neglected in the center.," A further complication arises when the simulations are compared with observations since the gravitational potential of the baryonic component, which is very time consuming to model in the simulations, cannot be neglected in the center."
" This complication cau : : voth: chaneehe the slope of the dadshape tanattol enmaeuitudes well as alter the total mass profile (Bhunenthal ae :PeATSC""Elcauseal.5Cue"," This complication can in principle both change the slope of the dark matter profile as well as alter the total mass profile \citep{1986ApJ...301...27B,2001ApJ...560..636E,2004ApJ...616...16G,2009arXiv0906.0573S}."
diuetrelaxed structures ganupored oxlan fTa that. even aimedis at dark simplifving assmuptions. there theare i at cle to obtain u: naque soluThere ionstoids thedistributionlittle of matter (Binney & Tremaine :iaoa ο... ... Tustead.," Theoretical efforts are hampered by the fact that, even under the strongest simplifying assumptions, there are not enough constraints to obtain unique solutions to the collisionless Boltzmann equation \citep{1987gady.book.....B} which governs a dark matter structure."
 simulations of the phenomenological iuput from nmunerical within a giveu the density profile itself. the pseudo- : ‘ .επιστ uvlor »&Navarro Navarro2001:nMΤDelineachievedthroughMthe: 1ο ΟΙ- Ssiopc-η vmVtLATO. 1HN-wellandtaasiorethe (fromB Hansen &Stade (2006)neednto slope of 0.8). hichand impleieut this iuto als . heap: even a jlsisfundamental foopidea he CALthat approach isthat guess (see a πο enmt OT DA(2008)andreferencestherein).," Instead, one can take phenomenological input from numerical simulations such as the density profile itself, the pseudo-phase space density \citep{2001ApJ...563..483T,2005MNRAS.363.1057D}, or the density slope-velocity anisotropy relation (from which \citet{2006JCAP...05..014H} predict an inner slope of $0.8$ ), and implement this into a Jeans equation analysis to predict the consequences of the `inspired guess' (see also \citet{2008ApJ...682..835Z} and references therein)."
" Alternatively oue can attemptal, to model the formeution historv of the halo iucludiug nuajor. mergers auk steady accretion (6.8... Ryden&al.(2007):Dol↼Popolo(2009).. aud references therein)."," Alternatively one can attempt to model the formation history of the halo including major mergers and steady accretion (e.g., \citet{1987ApJ...318...15R,2004MNRAS.352.1109A,2007ApJ...666..181S,2009ApJ...698.2093D}, and references therein)."
⋅ et While these approaches typically vield results iu rough agreement⋠≼∙⋉⋅≼∖≼∖≼∖ iMith slulations. the modeles can also explore the physica connection between the static aud dynamic properties cof the halo as well as offer coustrained extrapolations whic rare not accessible in simulations.," While these approaches typically yield results in rough agreement with simulations, the modeling can also explore the physical connection between the static and dynamic properties of the halo as well as offer constrained extrapolations which are not accessible in simulations."
 Observationallv. trere is a strone discrepancy between," Observationally, there is a strong discrepancy between"
or C2.,for C2.
 This result indicates again that a proto-cluster as massive as C2 is preferred with respect to the poorer CI cluster., This result indicates again that a proto-cluster as massive as C2 is preferred with respect to the poorer C1 cluster.
 The too intense (with respect to observational estimates) star ormation that takes place in the C2. BCG suggests that AG eedback may have already partially quenched star formation in he Spiderweb galaxy., The too intense (with respect to observational estimates) star formation that takes place in the C2 BCG suggests that AGN feedback may have already partially quenched star formation in the Spiderweb galaxy.
" Indeed. the Spiderweb galaxy has been originally identified as a radio-galaxy with extended and distorted radio lobes (?).. consistent with the presence of a ""radio-mode"" AGN."," Indeed, the Spiderweb galaxy has been originally identified as a radio–galaxy with extended and distorted radio lobes \citep{1998ApJ...504..139P}, consistent with the presence of a “radio–mode” AGN."
 Furthermore. ὁ carried out an integral-tield spectroscopic study of the Spiderweb complex and found evidences for massive outflows of gas which are interpreted as due to the action of AGN feedback.," Furthermore, \cite{2006ApJ...650..693N} carried out an integral-field spectroscopic study of the Spiderweb complex and found evidences for massive outflows of gas which are interpreted as due to the action of AGN feedback."
 Deep follow-up observations in the X-ray band of a handful of clusters at +l are now pushing the study of the thermo— and chemo-dynamieal properties of the ICM to large look-back times., Deep follow-up observations in the X–ray band of a handful of clusters at $z>1$ are now pushing the study of the thermo– and chemo–dynamical properties of the ICM to large look-back times.
" Although we have probably to wait for the next generation of X-ray satellites to push these studies to 2x, 2.dtis interesting to make predictions for the X-ray luminosity."," Although we have probably to wait for the next generation of X–ray satellites to push these studies to $z\magcir 2$, it is interesting to make predictions for the X–ray luminosity,"
"where or is the fine structure. constant. Op is the ""Thomson cross-section. and m, and m, are the mass of the electron and the proton.","where $\alpha_f$ is the fine structure constant, $\sigma_T$ is the Thomson cross-section, and $m_e$ and $m_p$ are the mass of the electron and the proton."
 Equation (5)) is exactly. valid for a steady state How with 12er0., Equation \ref{energy}) ) is exactly valid for a steady state flow with $\dot m= v=0$.
 When ez0. the energy equation has another term corresponding to the advection of energy.," When $v \ne 0$, the energy equation has another term corresponding to the advection of energy."
 In advection-dominated accretion [ows. for instance. this term dominates over the cooling term gq (Naravanctal. 1997).," In advection-dominated accretion flows, for instance, this term dominates over the cooling term $q^-$ \citep{NMQ97}."
. In the present case. however. we consider a situation in which the adveetion term is negligible (which corresponds to low m).," In the present case, however, we consider a situation in which the advection term is negligible (which corresponds to low $\dot m$ )."
 Finally. we assume that the spinning star is immersed in a uniform external medium with a density poa. temperature Tis and pressure pest.," Finally, we assume that the spinning star is immersed in a uniform external medium with a density $\rho_{\rm ext}$, temperature $T_{\rm
ext}$ and pressure $p_{\rm ext}$."
 We seek an accretion flow. solution that extends from the spinning star on the inside to the external medium on the outside., We seek an accretion flow solution that extends from the spinning star on the inside to the external medium on the outside.
 As we show below. the solution consists of two distinct. self-similar regimes. plus a third asymptotic regime inside the external medium.," As we show below, the solution consists of two distinct self-similar regimes, plus a third asymptotic regime inside the external medium."
 We first consider the inner regions of the Low. where the pressure p>pou.," We first consider the inner regions of the flow, where the pressure $p\gg p_{\rm ext}$."
 Fhis is the regime of the ALNOL solution. where the variables have the following racial dependences: (6)'Phe subscript 71 in the coefficients is to indicate that this is the first solution. to distinguish it from the second and third solutions described below.," This is the regime of the MN01 solution, where the variables have the following radial dependences:, The subscript “1” in the coefficients is to indicate that this is the first solution, to distinguish it from the second and third solutions described below."
 By substituting the above solution in equations (2)). (3)) and (5)). we see that it satisfies the basic conservation laws.," By substituting the above solution in equations \ref{mmtm}) ), \ref{jdot}) ) and \ref{energy}) ), we see that it satisfies the basic conservation laws."
 We may also solve for the numerical constants: We note that rnz0 then the How has a small constant racial velocity: arr0 as follows from equation (1)).," We may also solve for the numerical constants: We note that if $\dot m \ne 0$ then the flow has a small constant radial velocity: r^0, as follows from equation \ref{v}) )."
 The angular momentum Εις in the solution is given by (S)By assumption. this [lux is much &reater than the angular momentum Lux due to accretion. which sets an upper limit on the mass accretion rate for the solution to be valid (see ALNOL).," The angular momentum flux in the solution is given by ^2 s^3 By assumption, this flux is much greater than the angular momentum flux due to accretion, which sets an upper limit on the mass accretion rate for the solution to be valid (see MN01)."
" The pressure is given by p f. (where &2,=2&71ny."," The pressure is given by p _1, where $c_{s1}^2=2kT_1/m_p$."
 The above self-similar solution describes the Low at radi or(pipoa)! where the pressure pPox.," The above self-similar solution describes the flow at radii $r\ll
(p_1/p_{\rm ext})^{1/3}$, where the pressure $p \gg p_{\rm ext}$."
 As mentioned in &11. the solution has the remarkable property that all the quantities are uniquely determined by a single parameter à the dimensionless spin of the central object specified on the inner boundary.," As mentioned in 1, the solution has the remarkable property that all the quantities are uniquely determined by a single parameter $s$ — the dimensionless spin of the central object — specified on the inner boundary."
 The fact that the solution does not depend on the outer boundary condition in anv wav means that there is no simple way to match it to the external medium., The fact that the solution does not depend on the outer boundary condition in any way means that there is no simple way to match it to the external medium.
 Clearly. there has to be a second solution to bridge the gap between this solution and the external. medium.," Clearly, there has to be a second solution to bridge the gap between this solution and the external medium."
 We derive the bridging solution in the next subsection., We derive the bridging solution in the next subsection.
 We consider next the eas that lies just outside the region of validitv of the first self-similar solution described: above., We consider next the gas that lies just outside the region of validity of the first self-similar solution described above.
 In this zone. the pressure is expected to be approximately equal to the external. pressure pest: pcs posi constant.(1," In this zone, the pressure is expected to be approximately equal to the external pressure $p_{\rm ext}$: c_s^2 = =."
0) This condition replaces the hyelrostatic equilibrium equation (2)). while equations (3)) and (5)) continue to |be valid.," This condition replaces the hydrostatic equilibrium equation \ref{mmtm}) ), while equations \ref{jdot}) ) and \ref{energy}) ) continue to be valid."
 In this region. we find that there is a second. self-similar solution of the form (Llwhere the label 727. refers to the fact that this is our second solution.," In this region, we find that there is a second self-similar solution of the form, where the label “2” refers to the fact that this is our second solution."
" To match the second and first. solutions. we require that the Dusxes of angular momentum in the two solutions must be equal: this vields the constraint (32)p,0,1]?z(9JpQ2 7, "," To match the second and first solutions, we require that the fluxes of angular momentum in the two solutions must be equal; this yields the constraint $(3/2)\rho_1\Omega_1T_1^{1/2}=(9/4)\rho_2\Omega_2T_2^{1/2}$ ."
Making use of this and the other equations. we solve for the numericalcoefficients in equation (113): The pressure in this solution is constant and equal to the external pressure. pesi. auc the angular momentum Lux is also constant anc is equal o J in equation (S)).," Making use of this and the other equations, we solve for the numericalcoefficients in equation \ref{2nd-sol}) ): The pressure in this solution is constant and equal to the external pressure, $p_{\rm ext}$, and the angular momentum flux is also constant and is equal to $\dot J$ in equation \ref{jdot1}) )."
 Lf the How has a small but nonzero accretion rate. iz0. then its radial velocity varies as see eq. (1))]," If the flow has a small but nonzero accretion rate, $\dot m\not=0$, then its radial velocity varies as [see eq. \ref{v}) )]."
 Whereas the original MN) selt-similar solution has a unique profile for a given choice of s. we see that the second solution derived here has an extra degree of freedom. namely the external pressure pe.," Whereas the original MN01 self-similar solution has a unique profile for a given choice of $s$, we see that the second solution derived here has an extra degree of freedom, namely the external pressure $p_{\rm ext}$."
 This. extra degree of. freedom. solves the problem discussed in 811., This extra degree of freedom solves the problem discussed in 1.
 Thus. the full solution consists of two zones: an inner zone described by the first (AINOL) solution (6)) and an outer zone described by the second solution (113).," Thus, the full solution consists of two zones: an inner zone described by the first (MN01) solution \ref{1st-sol}) ) and an outer zone described by the second solution \ref{2nd-sol}) )."
 The radius ruin at which the two solutionsb match is obtained by equating the pressures: (, The radius $r_{\rm match}$ at which the two solutions match is obtained by equating the pressures: .
"13) Vhe second solutionDua matchesBy the external medium at the radius rox, at which its temperature matches that of the medium."," The second solution matches the external medium at the radius $r_{\rm
ext}$ at which its temperature matches that of the medium."
 This gives, This gives
black hole inner engine (vanPutten2003)..,black hole inner engine \citep{van03b}.
 It max reach one per few vears if their event rate is about one order of magnitude larger (han the rate of successhiu GRD-supernovae., It may reach one per few years if their event rate is about one order of magnitude larger than the rate of successful GRB-supernovae.
 The observable event rate could be larger if a traction of the supernovae of Type Il is similarly powered by long-lived black hole inner engines., The observable event rate could be larger if a fraction of the supernovae of Type II is similarly powered by long-lived black hole inner engines.
 A much larger sensitivity distance is anticipated for (he planned 10 km ET in Europe., A much larger sensitivity distance is anticipated for the planned 10 km ET in Europe.
 Conceivably. all skv radio surveys. e.g.. ihe LOw Frequeney Alrav (LOFAR.2010)... will further provide us with a probe for long cduration radio bursts [rom mergers (vanPutten2009) aud. combined with gravitational wave survevs. provide a direct measurement of the relative event rate long GRBs [rom mergers {ο long GRBs from CC-SNe.," Conceivably, all sky radio surveys, e.g., the LOw Frequency ARray \citep{lof10}, will further provide us with a probe for long duration radio bursts from mergers \citep{van09b} and, combined with gravitational wave surveys, provide a direct measurement of the relative event rate long GRBs from mergers to long GRBs from CC-SNe."
 The diversity in the origin of long GRBs in both CC-SNe and mergers and the comparible sensitivity. distances of their potential emissions in gravitational waves and those from binary coalescence suggests the need Lor extended searches over the complete frequency range of both., The diversity in the origin of long GRBs in both CC-SNe and mergers \citep{van09b} and the comparible sensitivity distances of their potential emissions in gravitational waves and those from binary coalescence suggests the need for extended searches over the complete frequency range of both.
 Apart from scaling by black hole mass and a diversity in initial spin. the proposed long CWDs are universal. and their progenitors are revealed only by the absence or presence of a precursor signal in gravitational waves in case of. respectively. a CC-SNe or merger event.," Apart from scaling by black hole mass and a diversity in initial spin, the proposed long GWBs are universal, and their progenitors are revealed only by the absence or presence of a precursor signal in gravitational waves in case of, respectively, a CC-SNe or merger event."
 The initial work for (his research was partially supported by La hégeion Centre during a visit to Le STUDIUM Institute for. Advanced. Studies/CNIBS-Orléaans., The initial work for this research was partially supported by La Réggion Centre during a visit to Le STUDIUM Institute for Advanced Studies/CNRS-Orl\'eaans.
 The authors gratefully acknowledge the TAAIA collaboration for providing the data., The authors gratefully acknowledge the TAMA collaboration for providing the data.
 MVP thanks Lars Herne(quist ancl Ramesh Naravan for stimulating discussions., MVP thanks Lars Hernquist and Ramesh Narayan for stimulating discussions.
knowledge of the differcut surface types of the unresolved planet.,knowledge of the different surface types of the unresolved planet.
 Our data cousist of 25 broadband spectra of Earth for cach of two viewing ecometrics., Our data consist of 25 broadband spectra of Earth for each of two viewing geometries.
 For the equatorial observations (Cowanetal.2009).. we found substantial variability in all wavebauds (though the ucar-IR wavebauds exhibited the most variability. leading to the dominant red eigeucolor).," For the equatorial observations \citep{Cowan_2009}, we found substantial variability in all wavebands (though the near-IR wavebands exhibited the most variability, leading to the dominant red eigencolor)."
 The polar observations also show variability at all wavebauds (Table 2). but as we arene below. the iutriusic cause of this variability is nof necessarily the same surface types rotating in aud out of view.," The polar observations also show variability at all wavebands (Table 2), but as we argue below, the intrinsic cause of this variability is not necessarily the same surface types rotating in and out of view."
 The multibaud. time-resolved observations of Earth can be thought of as a locus of poiuts occupying ao Teduuensional parameter space (oue for each waveband).," The multiband, time-resolved observations of Earth can be thought of as a locus of points occupying a 7-dimensional parameter space (one for each waveband)."
 Principal component analvsis (PCA) allows us to reduce the dimensionality. of these data by definine orthonormal cigenvectors in color space eeiecnicolors)., Principal component analysis (PCA) allows us to reduce the dimensionality of these data by defining orthonormal eigenvectors in color space eigencolors).
 Quautitativels. the observed spectrum of Earth at some time f can be recewvered using the equation: where CV(fA); ds the --- spectruni of Earth. Aj(A) ave the seven orthonormal eieeucolors. aud C(t) ave the instantancous projections of Earth's colors ou the cigencolors.," Quantitatively, the observed spectrum of Earth at some time $t$ can be recovered using the equation: where $\langle A^{*}(t, \lambda)\rangle$ is the time-averaged spectrum of Earth, $A_{i}(\lambda)$ are the seven orthonormal eigencolors, and $C_{i}(t)$ are the instantaneous projections of Earth's colors on the eigencolors."
 The terms im the sum are rauked by the time-variance in C5. from larecst to siuallest.," The terms in the sum are ranked by the time-variance in $C_{i}$, from largest to smallest."
 Tusofar as the color variations are douunated by the first few terms of the sui. the locus does not occupy the full 7-dimenusional color space. but a more restricted manifold.," Insofar as the color variations are dominated by the first few terms of the sum, the locus does not occupy the full 7-dimensional color space, but a more restricted manifold."
 The dimensionality of the manifold is oue fewer than the wumuber of surface types rotating in and out of view., The dimensionality of the manifold is one fewer than the number of surface types rotating in and out of view.
 Eve. a two-dimensional locus (a planar manifold) requires three surface types: a tfhrec-dinieusional locus requires four surface types. ete.," E.g., a two-dimensional locus (a planar manifold) requires three surface types; a three-dimensional locus requires four surface types, etc."
 The general problem of estimating the pure surface spectra based on the morphology of such a locus of poiuts is bevoud the scope of this paper., The general problem of estimating the pure surface spectra based on the morphology of such a locus of points is beyond the scope of this paper.
" Itis a form of spectral wumisine. aud is au area of active researcli in the remote scusing community (οιο,,luLeMoucélicetal.2009)."," It is a form of spectral unmixing, and is an area of active research in the remote sensing community \citep[e.g.,][]{LeMouelic_2009}."
. practice. there are two different wavs to perform PCA. which may give quantitatively different results.," In practice, there are two different ways to perform PCA, which may give quantitatively different results."
 The analysiscan be run using the covariance of the data. Cov(X.3)=Πα where ELX| is the expected value of IX: EAD.or AEDIcau be run using the correlation of the data. Corr{ifjy)-CoviN.YMg(o voy). where ay is the standard deviation of X.," The analysiscan be run using the covariance of the data, ${\rm Cov}(X,Y)= E[(X-E[X])(Y-E[Y])]$, where $E[X]$ is the expected value of $X$ ; or it can be run using the correlation of the data, ${\rm Corr}(X,Y)= {\rm Cov}(X,Y)/(\sigma_{X}\sigma_{Y})$ , where $\sigma_{X}$ is the standard deviation of $X$."
 The correlation matrix is a staudardized version of the covariance matrix: this is useful when the measured data do not all have the same units. siuce division bv the standard deviation renders them uuitless.," The correlation matrix is a standardized version of the covariance matrix; this is useful when the measured data do not all have the same units, since division by the standard deviation renders them unitless."
 When the data are unitless to begin with. as is the case for our albedo measurements. runing covariance-PCA is preferable (c.g..Borgoguoueetal. 2001)..," When the data are unitless to begin with, as is the case for our albedo measurements, running covariance-PCA is preferable \citep[e.g.,][]{Borgognone_2001}. ."
 In Cowanetal. we used covariance-PCA. aud we coutinue todo so h," In \cite{Cowan_2009} we used covariance-PCA, and we continue todo so ."
 In Cowanetal. we used covariance-PCA. aud we coutinue todo so he," In \cite{Cowan_2009} we used covariance-PCA, and we continue todo so ."
 In Cowanetal. we used covariance-PCA. aud we coutinue todo so her," In \cite{Cowan_2009} we used covariance-PCA, and we continue todo so ."
 In Cowanetal. we used covariance-PCA. aud we coutinue todo so here," In \cite{Cowan_2009} we used covariance-PCA, and we continue todo so ."
" In Cowanetal. we used covariance-PCA. aud we coutinue todo so here,"," In \cite{Cowan_2009} we used covariance-PCA, and we continue todo so ."
"for the zeroth-order shapelet, retain this behaviour, while the power in higher shapelet orders is distributed away from the (n1,0,0) values.","for the zeroth-order shapelet, retain this behaviour, while the power in higher shapelet orders is distributed away from the $(n_1, 0, 0)$ values."
 This is not unexpected from the behaviour of 2-d shapelets under rotations (see Refregier 2003)., This is not unexpected from the behaviour of 2-d shapelets under rotations (see Refregier 2003).
" Rotation of Halo 102 (Fig. 8)),"," Rotation of Halo 102 (Fig. \ref{fig:rot3}) ),"
" with two clear components, results in variation in the highest-amplitude shapelet coeffecients, suggesting the following features for identification of haloes of this type: either fimax occurs for a shaplet order other than the zeroth-order, or there are one or more shapelet orders with amplitudes Z0.5f1,max."," with two clear components, results in variation in the highest-amplitude shapelet coeffecients, suggesting the following features for identification of haloes of this type: either $f_{1,{\rm max}}$ occurs for a shaplet order other than the zeroth-order, or there are one or more shapelet orders with amplitudes $\gtrsim 0.5 f_{1,{\rm max}}$."
 We use this heuristic to now attempt a purely (by-eye) shapelet-based selection of haloes with clear multiple sub-structures (Class 3)., We use this heuristic to now attempt a purely (by-eye) shapelet-based selection of haloes with clear multiple sub-structures (Class 3).
" We apply the shapelet decomposition with the same input parameters as used throughout this initial implementation, to a total of 176 haloes."," We apply the shapelet decomposition with the same input parameters as used throughout this initial implementation, to a total of 176 haloes."
" Particle counts for this new set of haloes are in the range 865<N, 20033, noting that these haloes are at intermediate masses to the 24 investigated previously."," Particle counts for this new set of haloes are in the range $865 \leq N_p \leq 20033$ , noting that these haloes are at intermediate masses to the 24 investigated previously."
" We identify 44 Class 3 haloes on the basis of their shapelet representation, the first 36 of which are shown in Fig. 9,,"," We identify 44 Class 3 haloes on the basis of their shapelet representation, the first 36 of which are shown in Fig. \ref{fig:plot36},"
 and all of which exhibit the expected spatial characteristics., and all of which exhibit the expected spatial characteristics.
 Visual inspection of the remaining 132 haloes suggests a futher 10 haloes that should have been identified from their shapelet representations., Visual inspection of the remaining 132 haloes suggests a futher 10 haloes that should have been identified from their shapelet representations.
" In all cases, reinvestigation of the shapelet distribution revealed that they were very close to meeting the criteria for a Class 3-halo."," In all cases, reinvestigation of the shapelet distribution revealed that they were very close to meeting the criteria for a Class 3-halo."
 While a more robust approach to classification is required for a full implementation (e.g. using an appropriately-sized training set and the construction of, While a more robust approach to classification is required for a full implementation (e.g. using an appropriately-sized training set and the construction of
"local sample, 15 out of 26 (58%)); in the RDCS+WARPS, 4 out of 15 (27%)), and in the 400 SD high-z, 2 out of 20 (10%)).","local sample, 15 out of 26 ); in the RDCS+WARPS, 4 out of 15 ), and in the 400 SD high-z, 2 out of 20 )."
" However, a more meaningful quantity would be the cooling time normalized to the age of the cluster, defined as the time elapsed since the last major merger event."," However, a more meaningful quantity would be the cooling time normalized to the age of the cluster, defined as the time elapsed since the last major merger event."
" Considering the age of the Universe at z,,; is misleading, as this is a loose upper bound on the age of the cluster."," Considering the age of the Universe at $z_{obs}$ is misleading, as this is a loose upper bound on the age of the cluster."
 A K-S test to the distributions of {οι in the local and the RDCS+WARPS samples indicates a probability of that these samples derived from the a common population., A K-S test to the distributions of $t_{cool}$ in the local and the RDCS+WARPS samples indicates a probability of that these samples derived from the a common population.
" When comparing the local and distant samples from the 400 SD, the probability derived with the K-S test decreases to4%."," When comparing the local and distant samples from the 400 SD, the probability derived with the K-S test decreases to."
. Again we quantified the impact of using a core temperature in the cooling time measurements., Again we quantified the impact of using a core temperature in the cooling time measurements.
" A K-S test to the central cooling time distributions obtained with a core temperature and a global temperature indicates that it is likely that both samples originate from the same population, with a probability of67%."," A K-S test to the central cooling time distributions obtained with a core temperature and a global temperature indicates that it is likely that both samples originate from the same population, with a probability of."
. The central cooling time measured with a resolved temperature is on average 0.3 Gyr shorter relative to the measurement with a global temperature., The central cooling time measured with a resolved temperature is on average 0.3 Gyr shorter relative to the measurement with a global temperature.
 This effect is obviously stronger for cool-core clusters., This effect is obviously stronger for cool-core clusters.
" We quantified this effect in clusters with central cooling time shorter than 5 Gyr, and we found that in this case, the ratio tegoi(Tetopat) / teoot(T core) reaches a factor 1.4."," We quantified this effect in clusters with central cooling time shorter than 5 Gyr, and we found that in this case, the ratio $t_{cool}$ $T_{global}$ ) / $t_{cool}$ $T_{core}$ ) reaches a factor 1.4."
 We also find a strong anti-correlation between fo; and csp (see Fig. 13))," We also find a strong anti-correlation between $t_{cool}$ and $c_{SB}$ (see Fig. \ref{tcool2}) ),"
 quantified with a Spearman rank test with coefficient p=-0.84 and a probability of no correlation of«10-?., quantified with a Spearman rank test with coefficient $\rho$ =-0.84 and a probability of no correlation $<$ $^{-13}$.
" This anti-correlation was already shown in Santos et al. (2008)),"," This anti-correlation was already shown in Santos et al. \cite{joana}) ),"
 and more recently Hudson et al. (2010)), and more recently Hudson et al. \cite{hudson}) )
 confirmed it using the nearby HIFLUGCS sample., confirmed it using the nearby HIFLUGCS sample.
" In the current scenario, feedback from AGN in the radio mode plays a prominent role in the physics of cool-cores."," In the current scenario, feedback from AGN in the radio mode plays a prominent role in the physics of cool-cores."
 Increasing evidence from radio and X-ray observations of local clusters show that the formation of bubbles due to radio jets associated to the central AGN may effectively satisfy the energy balance between cooling and heating in cool-core regions (see Blanton 2010))., Increasing evidence from radio and X-ray observations of local clusters show that the formation of bubbles due to radio jets associated to the central AGN may effectively satisfy the energy balance between cooling and heating in cool-core regions (see Blanton \cite{blanton}) ).
" In this respect, the radio luminosity of the central galaxy can provide an important link between the black hole activity and the state of the intracluster medium."," In this respect, the radio luminosity of the central galaxy can provide an important link between the black hole activity and the state of the intracluster medium."
" While there are several works pointing out a correlation between the power associated to the radio activity of the central galaxy to the cool-core properties (see Sun et al. 2009)),"," While there are several works pointing out a correlation between the power associated to the radio activity of the central galaxy to the cool-core properties (see Sun et al. \cite{sun}) ),"
 there are no similar studies at high redshift., there are no similar studies at high redshift.
" Using data from the archive of the NRAO VLA Sky Survey (NVSS) at 1.4 GHz (Condon et al. 1998)),"," Using data from the archive of the NRAO VLA Sky Survey (NVSS) at 1.4 GHz (Condon et al. \cite{condon}) ),"
" which is sensitive down to ~ 2.5 mJy, we investigated the presence of radio sources in the cores of our local and distant clusters."," which is sensitive down to $\sim$ 2.5 mJy, we investigated the presence of radio sources in the cores of our local and distant clusters."
 The two distant samples are entirely covered by the NVSS., The two distant samples are entirely covered by the NVSS.
" To determine whether a radio source is related with the cluster core we adopted a conservative criterion of a maximum separation of about 20""between the X-ray centroid and the center of the radio galaxy.", To determine whether a radio source is related with the cluster core we adopted a conservative criterion of a maximum separation of about between the X-ray centroid and the center of the radio galaxy.
" The 400 SD z has three radio sources (3/20), whereas the RDCS+WARPS sample has only 2 out of 15 clusters with a central radio source."," The 400 SD $z$ has three radio sources (3/20), whereas the RDCS+WARPS sample has only 2 out of 15 clusters with a central radio source."
 This is expected since most of the radio sources associated with high-z clusters should be below the flux limit of the NVSS., This is expected since most of the radio sources associated with high-z clusters should be below the flux limit of the NVSS.
" Interestingly, the two clusters in the RDCS+WARPS with radio sources are also considered to be cool-cores with cs, greater than 0.08."," Interestingly, the two clusters in the RDCS+WARPS with radio sources are also considered to be cool-cores with $c_{SB}$ greater than 0.08."
" The local sample is not fully covered by the NVSS (coverage of73%,, 19/26)."," The local sample is not fully covered by the NVSS (coverage of, 19/26)."
" However, we find a high fraction of clusters with a radio source (10/19) all associated with high cs values (i.e., greater than 0.08) It is worth noting that most local clusters without NVSS coverage are non-cool-cores, according to their csg values."," However, we find a high fraction of clusters with a radio source (10/19) all associated with high $c_{SB}$ values (i.e., greater than 0.08) It is worth noting that most local clusters without NVSS coverage are non-cool-cores, according to their $c_{SB}$ values."
" These results are reported in Tables 1, 2 and 3."," These results are reported in Tables 1, 2 and 3."
" We also obtained the 1.4 GHz luminosity, Lj4cGg;. of the radio sources associated with the cluster cores, using the fluxes provided by the NVSS catalog, and applying a K- with a power law with index 0.7."," We also obtained the 1.4 GHz luminosity, $L_{1.4 GHz}$, of the radio sources associated with the cluster cores, using the fluxes provided by the NVSS catalog, and applying a K-correction with a power law with index 0.7."
 We placed upper limits on the non-detections using the NVSS flux detection, We placed upper limits on the non-detections using the NVSS flux detection
Asteroid transits against a white dwarf will be of short duration and may have distinctive profiles.,Asteroid transits against a white dwarf will be of short duration and may have distinctive profiles.
 The time required for the asteroid’s center of mass to cross the diameter of the white dwarf is Toros=2ιν. where viis approximately equal to the orbital velocity.," The time required for the asteroid's center of mass to cross the diameter of the white dwarf is $\tau_{\rm cross} = 2\, R_{\rm wd}/v,$ where $v$ is approximately equal to the orbital velocity."
"I. Because the orbital speed, v. decreases with increasing e, an asteroid offixed size produces a longer event when it is farther from the white dwarf."," Because the orbital speed, $v,$ decreases with increasing $a$, an asteroid of fixed size produces a longer event when it is farther from the white dwarf."
 The crossing time ts larger for less massive white dwarts because the orbital speed is smaller (for à given @) and because the radius of a low-mass white dwarf is larger., The crossing time is larger for less massive white dwarfs because the orbital speed is smaller (for a given $a$ ) and because the radius of a low-mass white dwarf is larger.
 The ingress and egress may be distinctive because many asteroids will not be massive enough to have been pulled into a spherical shape by self gravity., The ingress and egress may be distinctive because many asteroids will not be massive enough to have been pulled into a spherical shape by self gravity.
 We have carried out a set of calculations to determine how large an asteroid must be in order for its transit against a white dwarf of given brightness to be detectable by We use the informationop. on theKepler web to estimate the number of detected photoelectrons per minute: N=1.3x107(1009755717) per minute.," We have carried out a set of calculations to determine how large an asteroid must be in order for its transit against a white dwarf of given brightness to be detectable by We use the information on the web to estimate the number of detected photoelectrons per minute: $N = 1.3\times 10^7 \, (10^{-0.4 (M_{Kepler}-12)})$ per minute."
" For representative examples, we used theKep/er magnitudes of 3 relatively bright white dwarf candidates in theKepler field: My,=12.2.14.8.15.8. Por cach candidate white dwarf we carried out two sets of calculations."," For representative examples, we used the magnitudes of $3$ relatively bright white dwarf candidates in the field: $M_{Kepler} = 12.2, 14.8, 15.8.$ For each candidate white dwarf we carried out two sets of calculations."
" In the first set, we assumed that the mass of the white dwarf was M420.6M.. and used the corresponding radius."," In the first set, we assumed that the mass of the white dwarf was $M_{\rm wd}=0.6\, M_\odot,$ and used the corresponding radius."
 In the second set we used M4=1.3M... and decreased the value of Ryy accordingly.," In the second set we used $M_{\rm wd}=1.3\, M_\odot,$ and decreased the value of $R_{\rm wd}$ accordingly."
" Then, for each of 60 values of the orbital separation e, we computed the diameter of an asteroid for which we would have a lo. 2σ. and 3e detection of the transit, by integrating over the crossing time."," Then, for each of $60$ values of the orbital separation $a$, we computed the diameter of an asteroid for which we would have a $1 \sigma,$ $2 \sigma,$ and $3 \sigma$ detection of the transit, by integrating over the crossing time."
 The results are shown in Figure |., The results are shown in Figure 1.
" For lower-mass white dwarts, asteroids of smaller diameter can produce detectable transits."," For lower-mass white dwarfs, asteroids of smaller diameter can produce detectable transits."
" For the brightest white dwarf, transits of asteroids in the 100-km class can be detected even when they are relatively close to the white dwarf."," For the brightest white dwarf, transits of asteroids in the $100$ -km class can be detected even when they are relatively close to the white dwarf."
" The dimmer the white dwarf, the farther from it must a 100-km asteroid be in order for its transit to be detected by In the solar system, the Kuiper Belt extends from roughly 30 AU to 50 AU."," The dimmer the white dwarf, the farther from it must a $100$ -km asteroid be in order for its transit to be detected by In the solar system, the Kuiper Belt extends from roughly $30$ AU to $50$ AU."
" Large interlopers from the Oort Cloud, such as 2006 50272. are also found in this region, while the bulk of the Oort cloud lies beyond 1000 AU."," Large interlopers from the Oort Cloud, such as 2006 SQ372, are also found in this region, while the bulk of the Oort cloud lies beyond $1000$ AU."
" Although the white dwarf systems we target forKepler study may be verydifferent, the example of the solar system indicates that it is good to be sensitive to asteroids at laree values of a."," Although the white dwarf systems we target for study may be verydifferent, the example of the solar system indicates that it is good to be sensitive to asteroids at large values of $a$ ."
the variation of helium abundance does not exceed: O.1-1 (Aledview Loeb 2001).,the variation of helium abundance does not exceed 0.1-1 (Medvigy Loeb 2001).
 ‘To verify that the assumption of hyclrostatic equilibrium is a valid approximation. we need to check that the sound crossing time. ἐς. in à cloud is smaller than its dvnanical time. fava=(Cp)L7 while both of them are smaller than the Hubble time.," To verify that the assumption of hydrostatic equilibrium is a valid approximation, we need to check that the sound crossing time, $t_{\rm s}$, in a cloud is smaller than its dynamical time, $t_{\rm dyn}=(G\rho)^{-1/2}$, while both of them are smaller than the Hubble time."
 The second. condition. {νιauae ES always satisfied inside the virialized dark matter halos. since faen/fannme=(Si/Beanto~022. where day~200 is the dark matter density contrast.," The second condition, $t_{\rm dyn}< t_{\rm Hubble}$, is always satisfied inside the virialized dark matter halos, since $t_{\rm dyn}/t_{\rm Hubble}=(8\pi/3\delta_{\rm dm})^{1/2}\sim 0.2$, where $\delta_{\rm dm}\sim 200$ is the dark matter density contrast."
" The ratio ἐςανα. in the aciabatically compressed. gas clouds is where 9,4, is the gas density contrast.", The ratio $t_{\rm s}/t_{\rm dyn}$ in the adiabatically compressed gas clouds is where $\delta_{\rm gas}$ is the gas density contrast.
 Thus inside the stellar mass clouds the hyerostatic eequilibrium is indeed a reasonable approximation., Thus inside the stellar mass clouds the hydrostatic equilibrium is indeed a reasonable approximation.
 Moclified gravity has been suggested as an alternative to the collisionless clark matter (Milgrom 1983: Dekenstein. 2004)., Modified gravity has been suggested as an alternative to the collisionless dark matter (Milgrom 1983; Bekenstein 2004).
 ln MOND theory in the limit of weak gravity. gravitational acceleration is given by g=\/gxgo. where gx=GALa is the standard. Newtonian value.," In MOND theory in the limit of weak gravity, gravitational acceleration is given by $g=\sqrt{g_{\rm N}g_0}$, where $g_{\rm N}=GM/r^2$ is the standard Newtonian value."
 Based on the galactic rotation curves the value of go is expected. to be around 10+!mes2., Based on the galactic rotation curves the value of $g_0$ is expected to be around $10^{-10}\; {\rm m\cdot s^{-2}}$.
 Using this in eqs. (4)), Using this in eqs. \ref{VHe}) )
 and (5)) we derive the newclilfusion time-scale The dvnamical time for modified eravity is (Cipg/qx) . so the ratio ἐςην in this case is showing that the assumption of hyedrostatic equilibrium is again reasonable [ου stellar mass clouds.," and \ref{cont}) ) we derive the newdiffusion time-scale The dynamical time for modified gravity is $t_{\rm dyn}=(G\rho g/g_{\rm N})^{-1/2}$ , so the ratio $t_{\rm s}/t_{\rm dyn}$ in this case is showing that the assumption of hydrostatic equilibrium is again reasonable for stellar mass clouds."
 Unlike the case with newtonian gravity. inMOND της is no longer scale independent.," Unlike the case with newtonian gravity, inMOND $\tau_{\rm He}$ is no longer scale independent."
" The cloud virial temperature in the MOND regime (g« gu) is dvà10INCU/M.y. so prior to reionization. when Zi, falls to a few kelvins. the dilfusion is again most ellicient. in clouds of stellar. mass."," The cloud virial temperature in the MOND regime $g\ll g_0$ ) is $T_{\rm vir}\approx 10\;{\rm K} (M/M_{\odot})^{1/2}$, so prior to reionization, when $T_{\rm bg}$ falls to a few kelvins, the diffusion is again most efficient in clouds of stellar mass."
 However. in MOND all σας may undergo ellicient. cülfusion (Le. THeZ2FE gaade) ancl not just a small fraction that resides within dark matter minihalos with AZ~Apu. lta," However, in MOND all gas may undergo efficient diffusion (i.e., $\tau_{\rm He}\lsim t_{\rm Hubble}$ ) and not just a small fraction that resides within dark matter minihalos with $M\sim M_{\rm Jeans}$."
diation pressure [rom the resonant Lye photons is capable of supporting large gas clouds (Braun Dekel 1989)., Radiation pressure from the resonant $\alpha$ photons is capable of supporting large gas clouds (Braun Dekel 1989).
 Since hwvdrogen resonance photons are far more oindant than helium: resonance photons. the radiation pressure exerts stronger force on hydrogen than helium atoms.," Since hydrogen resonance photons are far more abundant than helium resonance photons, the radiation pressure exerts stronger force on hydrogen than helium atoms."
 The magnetic pressure presents a similar case., The magnetic pressure presents a similar case.
 The magnetic field acts directly onlv on charged: particles (i.e. electrons and ions).," The magnetic field acts directly only on charged particles (i.e., electrons and ions)."
 Those in turn collide with the neutral atoms. transferring to them the acquired momentum.," Those in turn collide with the neutral atoms, transferring to them the acquired momentum."
 Since the collisional cross-section of ions with hydrogen atoms is several times larger than with helium atoms (Osterbrock 1961: Westie Schultz 1999). the magnetic pressure also exerts stronger force on hydrogen atoms.," Since the collisional cross-section of ions with hydrogen atoms is several times larger than with helium atoms (Osterbrock 1961; Krstic Schultz 1999), the magnetic pressure also exerts stronger force on hydrogen atoms."
 The eq. (2)), The eq. \ref{vel1}) )
" can thus be expanded to account for all pressure components where piu. pua and py are. respectively. thermal. radiation and magnetic pressure. eu=bop,mgeàQ0.T. and oj, and ay are typically close to unity."," can thus be expanded to account for all pressure components where $p_{\rm th}$, $p_{\rm rad}$ and $p_{\rm B}$ are, respectively, thermal, radiation and magnetic pressure, $\alpha_{\rm th}=1-\mu m_{\rm p}/m_{\rm He}\approx 0.7$ , and $\alpha_{\rm rad}$ and $\alpha_{\rm B}$ are typically close to unity."
 When the total pressure. p=pin|Pratpp. ds constant. but radiation or magnetic pressure have strong variation on the scale Z2. eq. (15))," When the total pressure, $p=p_{\rm th}+p_{\rm rad}+p_{\rm B}$, is constant, but radiation or magnetic pressure have strong variation on the scale $R$, eq. \ref{V2}) )"
 becomes ‘The time-scale for helium enrichment is then From the above equation it follows that when pressure is fixed. the diffusion is most ellicicnt at the highest temperature possible for the neutral gas (2~104 Ix).," becomes The time-scale for helium enrichment is then From the above equation it follows that when pressure is fixed, the diffusion is most efficient at the highest temperature possible for the neutral gas $T\sim 10^4$ K)."
 In the interstellar medium of the Milky Way. where the metallicity and pressure are high (p/A~2-103Wem 7). it generally takes around a few million vears for a cloud with 7—107 Ix either to cool down ancl collapse into a star. or to be destroved. through shockheating or ionization.," In the interstellar medium of the Milky Way, where the metallicity and pressure are high $p/k\sim 2\cdot 10^4\;{\rm K\cdot cm^{-3}}$ ), it generally takes around a few million years for a cloud with $T\sim 10^4$ K either to cool down and collapse into a star, or to be destroyed through shockheating or ionization."
 Since for a given. pressure. THe is ⋠⋅of order 10⋅⋅ vears. the expected helium. variation due to cilfusion in stars that currently form in the Alilky Was. typically should not exceed. one per cent.," Since for a given pressure, $\tau_{\rm He}$ is of order $10^9$ years, the expected helium variation due to diffusion in stars that currently form in the Milky Way, typically should not exceed one per cent."
" By contrast. in the first halos with Zia,107 Ix. which form out ofthe metal-poor gas. and where the pressure is significantIv lower (p/k1010?Kem. 7). the tvpical life-time of a cloud may be comparable to της. Pherefore. significant variation of initial helium abundances may be possible for the carly generations of stars."," By contrast, in the first halos with $T_{\rm vir}\sim 10^4$ K, which form out of the metal-poor gas, and where the pressure is significantly lower $p/k\sim 10^2-10^3\;{\rm K\cdot cm^{-3}}$ ), the typical life-time of a cloud may be comparable to $\tau_{\rm He}$ Therefore, significant variation of initial helium abundances may be possible for the early generations of stars."
 Small-scale turbulent motion tends to reverse the process of helium segregation by mixing the gas [rom regions with different abuncances., Small-scale turbulent motion tends to reverse the process of helium segregation by mixing the gas from regions with different abundances.
 When helium. abundance. gradient. VY. exceeds (Vg.VON Poon. where Vian and Riou ave the characteristic velocity and the length. scale of the turbulence. turbulent mixing prevails over. helium sedimentation.," When helium abundance gradient, $\nabla Y$ , exceeds $(V_{\rm He}-V_{\rm H})/V_{\rm turb}R_{\rm turb}$ , where $V_{\rm turb}$ and $R_{\rm turb}$ are the characteristic velocity and the length scale of the turbulence, turbulent mixing prevails over helium sedimentation."
In case both operate at the sametime. then,"In case both operate at the sametime, then"
 earlier than 06.5). but also several lower-mass stars (~15 Msolar)) forming a distinct subgroup ~2/6 to the SW of the centre and with an estimated age of order MMyr.," earlier than $6.5$ ), but also several lower-mass stars $\sim 15$ ) forming a distinct subgroup $\sim 2\farcm6$ to the SW of the centre and with an estimated age of order Myr."
 The age difference with respect to the O-type stars led these authors to suggest that sequential star formation might have occurred in the region., The age difference with respect to the O-type stars led these authors to suggest that sequential star formation might have occurred in the region.
 Using near- and mid-infrared as well as CO sub-millimetre observations. Contursi et al. (," Using near- and mid-infrared as well as CO sub-millimetre observations, Contursi et al. ("
2000) and Rubio et al. (,2000) and Rubio et al. (
2000) were able to identify several embedded sources in. the bar making up the body of 3346. corresponding to strong emission peaks whose presence may reveal recent and/or ongoing star formation.,"2000) were able to identify several embedded sources in the bar making up the body of 346, corresponding to strong emission peaks whose presence may reveal recent and/or ongoing star formation."
 However. while the peak corresponding with the central 3346 cluster contains unreddened stars. all other peaks are affected by higher reddening. suggesting that the interstellar material has. not been completely ejected and that they could be in à younger stage of evolution.," However, while the peak corresponding with the central 346 cluster contains unreddened stars, all other peaks are affected by higher reddening, suggesting that the interstellar material has not been completely ejected and that they could be in a younger stage of evolution."
 Since the more reddened peaks appear to be located farther away from the central cluster. these authors have suggested that star formation might have taken place in a sequential way along the bar.," Since the more reddened peaks appear to be located farther away from the central cluster, these authors have suggested that star formation might have taken place in a sequential way along the bar."
 More recent observations with the Hubble and Spitzer Space Telescopes have resolved the mid-infrared emission peaks. revealing that they are compact clusters made up of a multitude of pre-main sequence (PMS) stars (Nota et al.," More recent observations with the Hubble and Spitzer Space Telescopes have resolved the mid-infrared emission peaks, revealing that they are compact clusters made up of a multitude of pre-main sequence (PMS) stars (Nota et al."
 2006: Sabbi et al., 2006; Sabbi et al.
 2007: Hennekemper et al., 2007; Hennekemper et al.
 2008) and young stellar objects (YSO: Bolatto et al., 2008) and young stellar objects (YSO; Bolatto et al.
 2007; Simon et al., 2007; Simon et al.
 2007)., 2007).
exception of NCC 5053.,exception of NGC 5053.
 Elsewhere iu the paper. they also uote that NGC 5166 has cuerey aud angular ολο within 1-σ of those of the Ser galaxy.," Elsewhere in the paper, they also note that NGC 5466 has energy and angular momentum within $\sigma$ of those of the Sgr galaxy."
 NGC 6356. NL 5 aud AI 53 have Ree<10 kpe. hence are not included ii our siuuple.," NGC 6356, M 5 and M 53 have $R_{GC} < 10$ kpc, hence are not included in our sample."
 The possible association of NGC 5166 with the Ser dSph is confirmed by our analvsis., The possible association of NGC 5466 with the Sgr dSph is confirmed by our analysis.
 The possible association of NGC 5053. Pal 5 iud Pal 12 is also coufirmed by. the present work.," The possible association of NGC 5053, Pal 5 and Pal 12 is also confirmed by the present work."
 PALJO2 also suggested a possible association of NGC 11107 with a eroup of clusters whose orbits may be related to those of the Magellanic Clouds. but they state that the result is verv uncertain.," PMJ02 also suggested a possible association of NGC 4147 with a group of clusters whose orbits may be related to those of the Magellanic Clouds, but they state that the result is very uncertain."
 Furthermore we note that on the same basis the possible association of ALD 53 (elsewhere classified as a candidate for association with Ser) with the Simall Magellanic Cloud aud Ursa Minor is also suggested by PALJO2., Furthermore we note that on the same basis the possible association of M 53 (elsewhere classified as a candidate for association with Sgr) with the Small Magellanic Cloud and Ursa Minor is also suggested by PMJ02.
 We conclude that there is uo serious disagreement between the present analysis aud the oue by PALIO2., We conclude that there is no serious disagreement between the present analysis and the one by PMJ02.
 The present contribution. however.Wey. aud we place this result on a souud statistical basis. a result nof accomplished by auv of the previous studies;," The present contribution, however, and we place this result on a sound statistical basis, a result not accomplished by any of the previous studies."
 The success of the preseut analysis is due to the direct comparison of the positional aud kineniatical properties of the OTS clusters with a realistic model of the orbit of the Ser dSph aud its relies. that has Όσοι previously tested against independent observations2001a.," The success of the present analysis is due to the direct comparison of the positional and kinematical properties of the OHS clusters with a realistic model of the orbit of the Sgr dSph and its relics, that has been previously tested against independent observations."
")).. Finally. we shall shortly couuueut on ""non-kineniatic criteria that have been used to assess the association of a given cluster to the Ser ealaxy."," Finally, we shall shortly comment on “non-kinematic” criteria that have been used to assess the association of a given cluster to the Sgr galaxy."
 Many. authors have discussed he likeliness of the membership of their candidates ou he basis of the simularity of their metallicity. Horizoutal Branch (IB) morphology and/or structural parameters with those of the four known Ser clusters.," Many authors have discussed the likeliness of the membership of their candidates on the basis of the similarity of their metallicity, Horizontal Branch (HB) morphology and/or structural parameters with those of the four known Sgr clusters."
 In our opinion his approach may not be very useful., In our opinion this approach may not be very useful.
 It is quite clear hat Ser was a mmuch luger and complex svstem in the vast and its present status (as well as its present GC system) Ίαν be not fully representativo of its original range of properties., It is quite clear that Sgr was a much larger and complex system in the past and its present status (as well as its present GC system) may be not fully representative of its original range of properties.
" If. bv chance. the cluster Ter 7 had jen lost bv the Ser ealaxy in the previous perigalactic massage, this kind of criteria would haveerrancotsly classified it as a bad caudidate for Ser membership. since Ter 7 is much more metal rich (ΣοΠ~— 0.5) than auv of the other clusters that are still preseut iu the main body of Ser dSph (οΠ< 1.5)."," If, by chance, the cluster Ter 7 had been lost by the Sgr galaxy in the previous perigalactic passage, this kind of criteria would have classified it as a bad candidate for Sgr membership, since Ter 7 is much more metal rich $[Fe/H]\simeq -0.5$ ) than any of the other clusters that are still present in the main body of Sgr dSph $[Fe/H]<-1.5$ )."
 Moreover. the existence of population aud/or metallicity/— eracieuts may have driven the preferential loss of metal poor populationsthereiu). making the actual low iunetallicitv. luit of the Ser stellar population quite uncertain.," Moreover, the existence of population and/or metallicity gradients may have driven the preferential loss of metal poor populations, making the actual low metallicity limit of the Sgr stellar population quite uncertain."
 The judecment of the likelihood of membership on the basis of the IB morphology is even less justified since it is well known that clusters of different morplologics do actually co-exist iu real galaxiesForuax)., The judgement of the likelihood of membership on the basis of the HB morphology is even less justified since it is well known that clusters of different morphologies do actually co-exist in real galaxies.
. A much more reliable discriminant max be provided. in the future. bv the detailed abundance patterns of the clusters.," A much more reliable discriminant may be provided, in the future, by the detailed abundance patterns of the clusters."
" Forinstance. the behaviour of à elements as a ""nction of [Pc/I| is determined by the star formation ustory of the parent ealaxy that was (probably) not tle same iu he Ser dSph aud iu the Galactic Halo."," Forinstance, the behaviour of $\alpha$ elements as a function of $[Fe/H]$ is determined by the star formation history of the parent galaxy that was (probably) not the same in the Sgr dSph and in the Galactic Halo."
 Iu this context it is interesting to note that Pal 12. Ru 106 aud Pal 5 rave been found to be less a-cuhanced than Galactic Talo elobulars of similar moetallicity.," In this context it is interesting to note that Pal 12, Ru 106 and Pal 5 have been found to be less $\alpha$ -enhanced than Galactic Halo globulars of similar metallicity."
 For the above reasons. we rely only on phase-space waralucters m our analisvs. recalling that by scarching the ost relics of the Ser system we are trviug the reconstruct its original propertics. not the present dav ones.," For the above reasons, we rely only on phase-space parameters in our analisys, recalling that by searching the lost relics of the Sgr system we are trying the reconstruct its original properties, not the present day ones."
 We have demonstrated that there is a σολο! structure in the phase-space distribution of the outer halo elobular cluster of the Milkv. Way. strouely correlated with the orbital path of the Ser dSph ealaxy.," We have demonstrated that there is a coherent structure in the phase-space distribution of the outer halo globular cluster of the Milky Way, strongly correlated with the orbital path of the Sgr dSph galaxy."
 This correlation cannot have originated by chance. as a random realization of an unstructured halo. if such halo has the same distribution of ealactoceutric distance aud radial velocity as the considered OIIS clusters.," This correlation cannot have originated by chance, as a random realization of an unstructured halo, if such halo has the same distribution of galactocentric distance and radial velocity as the considered OHS clusters."
 Several of the ΟΠΣ elobular clusters lave spatial positions and racial velocities compatible with the hypothesis that they are following the same orbit as the Ser dSph. ie. they probably belong to the Ser Stream.," Several of the OHS globular clusters have spatial positions and radial velocities compatible with the hypothesis that they are following the same orbit as the Sgr dSph, i.e. they probably belong to the Sgr Stream."
 Firthermore the spread in phase space around the Ser orbit of such clusters is simular to that predicted for the Ser Stream population. according to the nunuerical simulations by(2001a).," Furthermore the spread in phase space around the Sgr orbit of such clusters is similar to that predicted for the Sgr Stream population, according to the numerical simulations by."
. We conclude. with confidence. thatdSph.," We conclude, with confidence, that."
 It should be noted however. that the analysis prescuted in this contribution is best suited to ideutify clusters that became unbound relatively receuth.," It should be noted however, that the analysis presented in this contribution is best suited to identify clusters that became unbound relatively recently."
 Iu principle. more OIIS elobulu clusters could be associated with the Ser steal.," In principle, more OHS globular clusters could be associated with the Sgr stream."
" Tn Table 1 we report the list of the selected. elobulars having |AV.|«60 Itun/s and Di.<l18kpe. in order of increasing D,,5."," In Table 1 we report the list of the selected globulars having $|\Delta V_r|<60$ Km/s and $D_{orb}<18\kpc$, in order of increasing $D_{orb}$."
 The proper motions predicted by the IL98 inodel are also reported in Table 1., The proper motions predicted by the IL98 model are also reported in Table 1.
 Since the adopted analysis is statistical iu nature it is clear that some of the clusters listed in Tab., Since the adopted analysis is statistical in nature it is clear that some of the clusters listed in Tab.
 1 iav be just occasional iuterlopers of the Ser orbit (up to 10 over LL in the worst case. according to our estimate).," 1 may be just occasional interlopers of the Sgr orbit (up to 10 over 14 in the worst case, according to our estimate)."
 The comparisou with the available proper motion estimates shown in 822.1 docs not provide auv strong indication in this regard., The comparison with the available proper motion estimates shown in 2.1 does not provide any strong indication in this regard.
" While the actual membership to the Ser Stream of each iucdividual cluster can be firmly established ouly with very. accurate proper motion measures (as will be achieved by dedicated space missions like CATA or SIM). it is reasonable to asstune that the clusters with the smaller D,,, are the oues for which the membership is more likely (see 822.1)."," While the actual membership to the Sgr Stream of each individual cluster can be firmly established only with very accurate proper motion measures (as will be achieved by dedicated space missions like GAIA or SIM), it is reasonable to assume that the clusters with the smaller $D_{orb}$ are the ones for which the membership is more likely (see 2.1)."
 We make the hypothesis that the six clusters more closely associated with the Ser orbital path (ie. those put in evidence iu Figures l aud 3) are former members of the Ser dSph., We make the hypothesis that the six clusters more closely associated with the Sgr orbital path (i.e. those put in evidence in Figures 1 and 3) are former members of the Sgr dSph.
 In this case the nuuber of globular clusters originally in the Ser galaxy is δρ=10., In this case the number of globular clusters originally in the Sgr galaxy is $N_{cl}=10$.
 If we adopt for the Sex dSph the samefrequency μμ μα phthathasaglobularclusters yst 26. we obtain an estimate of the total absolute magnitude," If we adopt for the Sgr dSph the same of the only other Galactic dSph that has a globular cluster system, i.e. Fornax $S_N\simeq 26$ , we obtain an estimate of the total absolute magnitude"
The angular correlation function of galaxies has been used to characterize the large-scale. distribution of galaxies for over 2 decades.,The angular correlation function of galaxies has been used to characterize the large-scale distribution of galaxies for over 2 decades.
 H£ the number density on the sky at angular position c is (er). then «(9) is defined as The 3-dimensional unit vectors (c and 6 are used. to define the angular separation ϐ as TCcos(8). and n is the mean galaxy number density on the sky.," If the number density on the sky at angular position $\hat{\psi}$ is $n(\hat{\psi})$ , then $\wth$ is defined as The 3-dimensional unit vectors $\hat{\psi}$ and $\hat{\phi}$ are used to define the angular separation $\theta$ as $ \hat{\psi} \cdot \hat{\phi} = \cos(\theta)$, and $\bar{n}$ is the mean galaxy number density on the sky."
 The observed galaxy clistribution is well described by a power law 0 . with slope 52OS.," The observed galaxy distribution is well described by a power law $\wth\propto \theta^{-\gamma}$ , with slope $\gamma\simeq 0.8$."
 Sincew(A) is a projection on the sky of the 3-dimensional auto-correlation Function £(r.2). the above power law for w(9) has been associated with à power law for £ with slope 1.5 which is close to the observed. value in the nearby galaxy distribution.," Since$\wth$ is a projection on the sky of the 3-dimensional auto-correlation function $\xi(r, z)$, the above power law for $\wth$ has been associated with a power law for $\xi$ with slope $1.8$ which is close to the observed value in the nearby galaxy distribution."
 Measurements of «(8) are dillieult to interpret as it involves a projection of the galaxy distribution out to redshifts of order 1 (c.g. for à sample with limiting /? magnitude of about 24.5)., Measurements of $\wth$ are difficult to interpret as it involves a projection of the galaxy distribution out to redshifts of order 1 (e.g. for a sample with limiting $R$ magnitude of about 24.5).
 Thus the elfects of evolution of large scale structure due to gravitational clustering as well as galaxy evolution need to be understood to interpret w(A)., Thus the effects of evolution of large scale structure due to gravitational clustering as well as galaxy evolution need to be understood to interpret $\wth$.
 Recently Villumsen (1996) has considered the effect on w(8) of gravitational lensing by large-scale structure along the line of sight (Cunn 1967)., Recently Villumsen (1996) has considered the effect on $\wth$ of gravitational lensing by large-scale structure along the line of sight (Gunn 1967).
 Lensing increases the area of a given patch on the sky. thus ciluting the number density.," Lensing increases the area of a given patch on the sky, thus diluting the number density."
 On the other hand. galaxies too faint to be included. in a sample of given limiting magnitude are brightened due to lensing ancl may therefore be included. in the sample.," On the other hand, galaxies too faint to be included in a sample of given limiting magnitude are brightened due to lensing and may therefore be included in the sample."
 The net effect. known as magnification bias. can go either wav: dt can lead to an enhancement or suppression of the observed number density of galaxies. depending on the slope of the number-magnitude relation.," The net effect, known as magnification bias, can go either way: it can lead to an enhancement or suppression of the observed number density of galaxies, depending on the slope of the number-magnitude relation."
 Variations in the number density which are correlated. over some angular separation alter (6)., Variations in the number density which are correlated over some angular separation alter $\wth$.
 Villumsen (1996) showed how the linear evolution of density Uuctuations along the line of sieht can be used to compute the change in «(8) due to magnification bias., Villumsen (1996) showed how the linear evolution of density fluctuations along the line of sight can be used to compute the change in $\wth$ due to magnification bias.
 The dellections of neighbouring photon trajectories due to lensing by large scale structure are very. small. hence the calculation can be done in the limit of weak lensine.," The deflections of neighbouring photon trajectories due to lensing by large scale structure are very small, hence the calculation can be done in the limit of weak lensing."
 In this paper we compute w(@) for different cosmological models taking into account the elects οἱ nonlinear eravitational evolution and gravitational lensing., In this paper we compute $\wth$ for different cosmological models taking into account the effects of nonlinear gravitational evolution and gravitational lensing.
 Since w(8) is à 2-point statistic. even in the fully nonlinear regime it is determined. completely by the 3-dimensional power spectrum.," Since $\wth$ is a 2-point statistic, even in the fully nonlinear regime it is determined completely by the 3-dimensional power spectrum."
 We use extensions of the proposal of Hamilton et al. (, We use extensions of the proposal of Hamilton et al. (
1991) to include the nonlinear evolution of the power spectrum into the calculation of w(9).,1991) to include the nonlinear evolution of the power spectrum into the calculation of $\wth$.
" We also include the dependenceon the cosmological parameters £2,, and ον.", We also include the dependenceon the cosmological parameters $\Omega_m$ and $\Omega_{\Lambda}$ .
 In Section 2 the formalism for computing (8) is presented., In Section 2 the formalism for computing $\wth$ is presented.
 Section 2.1 discusses the elfects of the, Section 2.1 discusses the effects of the
have any racio emission from the ejecta shell down to a 30 upper limit of 7.5(?).,have any radio emission from the ejecta shell down to a $3\sigma$ upper limit of 7.5.
. 3€ 58. also a voung PWN. also has no detectable radio emission [rom the shell to a 3o surface. brightness limit of 55(?2).," 3C 58, also a young PWN, also has no detectable radio emission from the shell to a $3\sigma$ surface brightness limit of $\lesssim \,
5$."
 In other words. the present limits on the radio surface brightness of shell. although low. are not unusual. when compared to those for other bright PWNe.," In other words, the present limits on the radio surface brightness of shell, although low, are not unusual when compared to those for other bright PWNe."
 What is unusual about0.9... however. is that unlike either the Crab or 3C58.. N-rav emission [rom which can reasonably. be attributed to the forward. shock been detected(?2).," What is unusual about, however, is that unlike either the Crab or 3C, X-ray emission from which can reasonably be attributed to the forward shock been detected."
. fit the X-ray spectrum of the limb alter subtracting the halo emission. in. other words the non-thermal part of the X-ray. emission thought to be due to the forward shock. with broad-band models. consisting of a power-law with an exponential high-encrev cutoll]tevnolds1998.," fit the X-ray spectrum of the limb after subtracting the halo emission, in other words the non-thermal part of the X-ray emission thought to be due to the forward shock, with broad-band models consisting of a power-law with an exponential high-energy cutoff."
 Using an assumed. radio spectral index of a=0.5. their. best fit. model would imply Xicg : 1 which is well below our measured 30. Limit of n The absence of radio emission from 0.9'ss forward shock is therefore consistent with the observed thermal X-ray emission.," Using an assumed radio spectral index of $\alpha = -0.5$, their best fit model would imply $\Sigma_{\rm 1 \, GHz} = $ 2.3 , which is well below our measured $3\sigma$ limit of 7 The absence of radio emission from s forward shock is therefore consistent with the observed non-thermal X-ray emission."
 Although we detect no radio emission [from the shell. we do clearly detect 0.9ss northern knot in our deep 1.4-Cllz image.," Although we detect no radio emission from the shell, we do clearly detect s northern knot in our deep 1.4-GHz image."
 A marginal detection at 4.8 Cillz results in a nominal. spectral index..yeas. of 70. albeit. with. large . tp . ⋯∐∼∢⋅↓⋅," A marginal detection at 4.8 GHz results in a nominal spectral index, of $\sim$ 0, albeit with large uncertainties."
⇂⋜⊔↓∐⊓⋅⊳∖⊳∐⊔⊳∖⊔∪⊔∐⊔⋜↧↓∖⇁⋜↧↓⋯⋅∪⇂⋂⊥⊽⊥≺⊽∐⋤ ⋅ ⊀↓⊀↓⊳∖⊳∖⊲↓⊔↓⊲↓↓⋜⊔⋅⋯↿↓⋯↿⇂∎∪↓⋅↥∐⋖⋅∣⋡⇜⇂∖⇁∪⇂∎≺∶⇉↓⊳⋅↱≻∪⋡≤⋗↣⋡∖⊔⋏∙≟⋏∙≟⋖⋅⊳∖↿⊀↓⊔⋏∙≟ ↿↓⋯⇂↿↓↕∢⊾↳⊔∪∣⊳∐∡∢⋅↥∐⋖⋅∣⋡⇜⇂∖⇁∪⇂∎≺∶⇉," This nominal value of is similar to that for the body of, suggesting that the knot, like the body of, consists of electrons energised by the pulsar."
↓⊳⋅↱≻∪⋡≤⋗↣≼∙∪⊔≱∖⋠↓≱∖↥≱∖∪⇂∎ ⋖⋅⇂∢⋅≼∙↥↓⋅∪⊔⊳∖∢⋅⊔⋖⋅↓⋅⋏∙≟⋠↓≱∖∢⋅∠⇂∣⋡∙∖⇁∣↓↕⋖⊾↓≻⊔↓⊳∖⋜⊔⋅⊳∐∪∖∖⋎∢⊾∖⇁∢⋅↓⋅⊳↿⇂⊔⊾⋜↧↓∩⊾↓⋅⊔⋜⋯⋅ hypothesis of the knot consisting of electrons accelerated in the forward⋅ shock and having: 0.5 is not excluded by the data. so no firm conclusions as to its nature can be drawn. We have identified a new shell-like radio source in our racio images. which we have called0.," However, the alternate hypothesis of the knot consisting of electrons accelerated in the forward shock and having $\sim -0.5$ is not excluded by the data, so no firm conclusions as to its nature can be drawn.. We have identified a new shell-like radio source in our radio images, which we have called."
84... In the high-resolution L4-Gllz image (Fig., In the high-resolution 1.4-GHz image (Fig.
 d. top). only the western part of the shell is visible. but most of the shell can be seen in the 327 MlIZ image (Fig. J 3)).," \ref{fwide} top), only the western part of the shell is visible, but most of the shell can be seen in the 327 MHz image (Fig. \ref{fstreamerp}) )."
 Hs radio spectral index of —(Q6 refsstreamerobs)) is consistent with those seen for shell-tvpe SNRs?)., Its radio spectral index of $\sim -0.6$ \\ref{sstreamerobs}) ) is consistent with those seen for shell-type SNRs.
. We examined the δ jm infra-red images [rom the Spitzer CGlimpse survey(7).. and. find no infra-red emission. for0.84... which implies that iis unlikely to be either an rregion or a wind blown bubble. which latter often have a shell-like structure but are almost inevitably accompanied by infra-red emission2).," We examined the $8 \, \mu$ m infra-red images from the Spitzer Glimpse survey, and find no infra-red emission for, which implies that is unlikely to be either an region or a wind blown bubble, which latter often have a shell-like structure but are almost inevitably accompanied by infra-red emission."
. It seems most probable that iis an as-vet uncatalogued supernova remnant., It seems most probable that is an as-yet uncatalogued supernova remnant.
 We noted in 3.2 above that no X-ray emission is seen [rom tto levels of —0.1'4 of the peak brightness of0., We noted in \ref{sstreamerobs} above that no X-ray emission is seen from to levels of $\sim$ of the peak brightness of.
.. ‘The lack of X-ray detection. however. does not argue against the supernova remnant hypothesis: has a comprehensive list of Galactic SNRs and finds that only ~40% of them are detected in X-ray. with high absorption in the X-ray being seen for many.," The lack of X-ray detection, however, does not argue against the supernova remnant hypothesis: has a comprehensive list of Galactic SNRs and finds that only $\sim$ of them are detected in X-ray, with high absorption in the X-ray being seen for many."
 Could rrepresent the radio emission associated. with the forward shock in0.9... the searched for which motivated the observations?," Could represent the radio emission associated with the forward shock in, the searched for which motivated the observations?"
 We think this possibility very unlikely. as he centre olf the new shell is clearly displaced from. the PPANUN.," We think this possibility very unlikely, as the centre off the new shell is clearly displaced from the ."
 LE ibad. been at the center of the newlv-identified radio shell STO vr ago. then its average speed since then must have ~15.000Lo which is far higher than the speeds seen or pulsars.," If had been at the center of the newly-identified radio shell 870 yr ago, then its average speed since then must have $\sim$ 15,000, which is far higher than the speeds seen for pulsars."
 Moreover. N-rav. emission. from 0.97ss orward shock has in [fact been identified. and is not coincident witha.," Moreover, X-ray emission from s forward shock has in fact been identified, and is not coincident with."
 We therefore identity aas a previously unidentified. shell-twpe SNR. which is unrelated to 0.," We therefore identify as a previously unidentified shell-type SNR, which is unrelated to."
9.. SNR shells typically have steeper brightness gradients at their outside edges than the inside ones. thus naturally. explaining the asvmmetry in the profile (Fig. 4)).," SNR shells typically have steeper brightness gradients at their outside edges than the inside ones, thus naturally explaining the asymmetry in the profile (Fig. \ref{fslice}) )."
 Although he partial couble-shell morphology is not common Lor supernova remnants. other remnants with similar structure jwe been observed.," Although the partial double-shell morphology is not common for supernova remnants, other remnants with similar structure have been observed."
" We found that thas an average surface brightness of Syou,o1.4 4."," We found that has an average surface brightness of $\Sigma_{\rm
1\, GHz} \simeq 1.4$ ."
" Vhis SNR is therefore near the peak of he observed. distribution of Sycu, values in the catalogue of7.. but. below his estimated. completeness. limit of. —1 5"," This SNR is therefore near the peak of the observed distribution of $\Sigma_{\rm 1 \, GHz}$ values in the catalogue of, but below his estimated completeness limit of $\simeq 1$ ."
 We note that the catalogued number of supernova remnants in the Galaxy is lower than the ~1000 generally. expected from supernova rates2006).. suggesting that there likely are many more supernova remnants to be discovered: at. these sensitivity levels.," We note that the catalogued number of supernova remnants in the Galaxy is lower than the $\sim$ 1000 generally expected from supernova rates, suggesting that there likely are many more supernova remnants to be discovered at these sensitivity levels."
 A relationship has been observed between the surface-brightness and the diameter (D) for SNRs., A relationship has been observed between the surface-brightness and the diameter $D$ ) for SNRs.
 Although this NoD relation has in the past often been used to determine SNA. distances it has been shown to be only of limited value for this purpose.2?2).," Although this $\Sigma - D$ relation has in the past often been used to determine SNR distances it has been shown to be only of limited value for this purpose,."
. If we take L4 for aand5 compare it to the sample of 47SNRs 21.64.of known distance shown in?.. we can conclude only that the ss diameter is likely between LO and. 100. pe. and itsdistance therefore in the not very restrictiverange of 3~~30 kpc.," If we take $\Sigma_{\rm 1 \, GHz} = 1.4$ for and compare it to the sample of 47 SNRs of known distance shown in, we can conclude only that the s diameter is likely between 10 and 100 pc, and itsdistance therefore in the not very restrictiverange of $3 \sim 30$ kpc."
 The lack of apparent X-ray emission. sugeests high absorption and therefore perhaps argues against theshorter end of this range., The lack of apparent X-ray emission suggests high absorption and therefore perhaps argues against theshorter end of this range.
 , 
In a recent study 7.hereafterGSWO5/— showed that the clustering of dark. matter halos can depend: strongly on their formation redshift.,In a recent study \citet[][hereafter GSW05]{Gao2005} showed that the clustering of dark matter halos can depend strongly on their formation redshift.
 Many current galaxy clustering models adopt simplified: prescriptions for populating halos with ealaxics based on an implicit’ assumption which is inconsistent with this result. namely that the assembly history of a halo of given mass (and thus its galaxy content) is statistically independent. of its larger scale environment ju ," Many current galaxy clustering models adopt simplified prescriptions for populating halos with galaxies based on an implicit assumption which is inconsistent with this result, namely that the assembly history of a halo of given mass (and thus its galaxy content) is statistically independent of its larger scale environment \citep[e.g.][]{Kauffmann1997,Jing1998,Peacock2000, Benson2000,
Berlind2003, Yang2003}."
those halos with Aa<LOHAL. that assembled. at hig1 redshift are substantially more clustered than halos of similar mass hat assembled more recently.," GSW05 found that those halos with $M_{\rm
vir}\!<\!10^{12}{\rm M}_\odot$ that assembled at high redshift are substantially more clustered than halos of similar mass that assembled more recently."
 Earlier stuclies iwl müssed the strength. of this dependence (c.g.2?).. apparently. because they were based. on simulations of insullicient size and. resolution to reliably. reach the relevant regime.," Earlier studies had missed the strength of this dependence \citep[e.g.][]{Lemson1999,Sheth2004}, apparently because they were based on simulations of insufficient size and resolution to reliably reach the relevant regime."
 Following GSWO5. other authors have demonstrated. significant dependences of clustering on halo properties such as concentration and subhalo occupation number. which are strongly correlated with formation redshift (e.g.2?)..," Following GSW05, other authors have demonstrated significant dependences of clustering on halo properties such as concentration and subhalo occupation number, which are strongly correlated with formation redshift \citep[e.g.][]{Wechsler2006, Zhu2006}."
 Ifthe assembly history of dark matter halos is correlated with their large-scale environment. we may expect the same to be true for their content.," If the assembly history of dark matter halos is correlated with their large-scale environment, we may expect the same to be true for their content."
 Fhis will then alfect the larec-scale clustering of galaxies in a way which depends on how galaxy properties are established during halo assembly. i.c. on the physies of galaxy formation.," This will then affect the large-scale clustering of galaxies in a way which depends on how galaxy properties are established during halo assembly, i.e. on the physics of galaxy formation."
 A number of recent studies have addressed: this question. approaching it [rom both observational and. theoretical points of view 22722).," A number of recent studies have addressed this question, approaching it from both observational and theoretical points of view \citep[e.g.][]{Yoo2006,Harker2006, Yang2006, Abbas2006,
Reed2006}."
 ? nd that. at fixed mass. the clustering of galaxy groups correlates quite strongly with the star formation rate of the central galaxy.," \cite{Yang2006} find that, at fixed mass, the clustering of galaxy groups correlates quite strongly with the star formation rate of the central galaxy."
 On the other hand. ? and ?. found the clustering in their analysis of SDSS data to be consistent with mocels with no dependence of halo galaxy populations on halo environment.," On the other hand, \cite{Skibba2006} and \cite{Abbas2006} found the clustering in their analysis of SDSS data to be consistent with models with no dependence of halo galaxy populations on halo environment."
 7. randomly shullle galaxies between halos of similar mass in a small volume simulation (box side length 50hIM pe) and find 510% ellects that are at the level of the statistical uncertainty of their calculation.," \cite{Yoo2006} randomly shuffle galaxies between halos of similar mass in a small volume simulation (box side length $50\,h^{-1}\rm{Mpc}$ ) and find $5-10\%$ effects that are at the level of the statistical uncertainty of their calculation."
 Much of this work was a response to the presentation of carly results from the present project. curing summer2005!., Much of this work was a response to the presentation of early results from the present project during summer.
. The Halo Occupation Distribution (or HOD) method for predicting galaxy clustering has become popular because it bypasses the need to model the physies of galaxy, The Halo Occupation Distribution (or HOD) method for predicting galaxy clustering has become popular because it bypasses the need to model the physics of galaxy
We have analyzed the contribution to the microlensing optical depth towards the LMC of the halo population of white dwarfs with both hydrogen-rich and hydrogen-deficient atmospheres.,We have analyzed the contribution to the microlensing optical depth towards the LMC of the halo population of white dwarfs with both hydrogen-rich and hydrogen-deficient atmospheres.
 We have used three models to describe the atmospheric evolution of white dwarfs., We have used three models to describe the atmospheric evolution of white dwarfs.
 In the first of these models we have assumed a canonical ratio of hydrogen-rich white dwarfs. to independent of the effective temperature.," In the first of these models we have assumed a canonical ratio of hydrogen-rich white dwarfs, to independent of the effective temperature."
 In our second model. which we consider to be the most realistic one. we have adopted a fraction of white dwarfs with helium-rich atmospheres which depend on the effective temperature.," In our second model, which we consider to be the most realistic one, we have adopted a fraction of white dwarfs with helium-rich atmospheres which depend on the effective temperature."
 [Ii these two models the cooling sequences of Salaris et al. (, In these two models the cooling sequences of Salaris et al. (
2000) for DA white dwarfs and those of Benvenuto Althaus (1997) for non-DA white dwarfs were used.,2000) for DA white dwarfs and those of Benvenuto Althaus (1997) for non-DA white dwarfs were used.
 In the thirc set of calculations the fraction of non-DA white dwarfs was assumed to depend on the effective temperature. but the cooling tracks of Bergeron et al. (," In the third set of calculations the fraction of non-DA white dwarfs was assumed to depend on the effective temperature, but the cooling tracks of Bergeron et al. ("
1995) for non-DA white dwarfs were adopted.,1995) for non-DA white dwarfs were adopted.
 We have found that when the contribution of hydrogen-deficient white dwarfs is considered. the theoretical optical depth towards the LMC for both the MACHO and EROS experiments is substantially increased by nearly 34%. with respect to previous calculations.," We have found that when the contribution of hydrogen-deficient white dwarfs is considered, the theoretical optical depth towards the LMC for both the MACHO and EROS experiments is substantially increased by nearly $34\%$, with respect to previous calculations."
 Nevertheless. we have also found that no more than one third of the microlensing optical depth found by the MACHO team can be explained by the halo population of white dwarfs at the lo confidence level. and that no more than three microlensing events could be expected at the same confidence level in reasonable agreement with the results of the EROS experiment.," Nevertheless, we have also found that no more than one third of the microlensing optical depth found by the MACHO team can be explained by the halo population of white dwarfs at the $1\sigma$ confidence level, and that no more than three microlensing events could be expected at the same confidence level in reasonable agreement with the results of the EROS experiment."
 We have also studied the role played by the thick disk populations of white dwarfs and red dwarfs. thus extending our previous calculations.," We have also studied the role played by the thick disk populations of white dwarfs and red dwarfs, thus extending our previous calculations."
 For this purpose we have used two thick disk models., For this purpose we have used two thick disk models.
 The first one is a canonical thick disk model. while the second one corresponds to the most recent model of Carollo et al. (," The first one is a canonical thick disk model, while the second one corresponds to the most recent model of Carollo et al. ("
2009). which is based in the data of the Sloan Digital Sky Survey Data Release 7.,"2009), which is based in the data of the Sloan Digital Sky Survey Data Release 7."
 We have obtained that for both thick disk models. the contribution of these populations to the microlensing optical depth is comparable to that of the halo populations. which is somewhat larger for the canonical thick disk model. which provides an upper limit to this contribution.," We have obtained that for both thick disk models, the contribution of these populations to the microlensing optical depth is comparable to that of the halo populations, which is somewhat larger for the canonical thick disk model, which provides an upper limit to this contribution."
 In particular we have found that the thick disk contribution is dominated by the white dwarf population in both cases. as the contribution of thick disk red dwarfs is only half of that of halo red dwarfs.," In particular we have found that the thick disk contribution is dominated by the white dwarf population in both cases, as the contribution of thick disk red dwarfs is only half of that of halo red dwarfs."
 Besides. we have also found that the average distance of the simulated lenses is very similar for the thick and halo populations. ~3 kpe.," Besides, we have also found that the average distance of the simulated lenses is very similar for the thick and halo populations, $\sim 3$ kpc."
 This unexpected result can be easily explained in terms of the selection criteria used to decide when a star can be considered responsible of a microlensing event., This unexpected result can be easily explained in terms of the selection criteria used to decide when a star can be considered responsible of a microlensing event.
 Since we only consider as reliable microlensing events those in which the lens is dimmer than a certain nagnitude cut. intrinsically bright lenses must be located at larger distances.," Since we only consider as reliable microlensing events those in which the lens is dimmer than a certain magnitude cut, intrinsically bright lenses must be located at larger distances."
 Consequently. since the thick population is intrinsically brighter than the halo population. we only select those thick disk lenses which are far enough away. at distances very similar to those of the halo population. which are naturally located at large distances.," Consequently, since the thick population is intrinsically brighter than the halo population, we only select those thick disk lenses which are far enough away, at distances very similar to those of the halo population, which are naturally located at large distances."
 We have found as well that although both populations have similar average distances and thick disk objects have smaller average velocities. their event timescales are nearly three times more extended than those of the halo population.," We have found as well that although both populations have similar average distances and thick disk objects have smaller average velocities, their event timescales are nearly three times more extended than those of the halo population."
 We have also assessed the compatibility of our simulated populations with the scarce observational data., We have also assessed the compatibility of our simulated populations with the scarce observational data.
 We have found that the thick disk population agrees better with the MACHO observational distribution of event timescales than the halo population., We have found that the thick disk population agrees better with the MACHO observational distribution of event timescales than the halo population.
 Finally. we found that when both the halo and the thick disk populations are considered. nearly half of the measured value of the microlensing optical depth towards the LMC can be explained at the confidence level by our simulated halo and thick disk populations.," Finally, we found that when both the halo and the thick disk populations are considered, nearly half of the measured value of the microlensing optical depth towards the LMC can be explained at the confidence level by our simulated halo and thick disk populations."
 According to our simulations. the fraction of halo dark matter that can be expected from MACHOs increases moderately (to f= 0.06) with respect to our previous simulations when hydrogen-deficient white dwarfs are taken into account.," According to our simulations, the fraction of halo dark matter that can be expected from MACHOs increases moderately (to $f=0.06$ ) with respect to our previous simulations when hydrogen-deficient white dwarfs are taken into account."
From the r-component of the equation of motion (9)) with ó=Oy. we have that We substitute the axisvmmetric terms in the potential of equation (22)) and the velocity in the 8-direction. no=1(Q3) to find ∖∖⋎↓↕⋖⋅↓⋅∢⊾∣⋮⊲↓⊳∖⇂↓↥∢⊾↿∖⊔⊔⊳∖≼⇍⋜↧↓∢⊾∠⊔∠⇂⊲↓⊳∖↿⋜⋯≼⇍∢⊾⇂⋅↓⋅∪⊔↓↿↓↕⋖⋅↓≻↓⋜⋯∢⊾↿⊳↾∐↕∢⊾↓⋅∢⊾⋜⊔⋅,"From the $r$ -component of the equation of motion \ref{eqmot}) ) with $\phi=\phi_{\rm H}$, we have that We substitute the axisymmetric terms in the potential of equation \ref{phiH}) ) and the velocity in the $\theta$ -direction, $u_\theta=r(\Omega - \Omega_{\rm p})$, to find where $r$ is the (unscaled) distance from the planet."
⋖⊾≼∼⋖⋟↓⋅↓⋅⋖⋅≼⇍↿↕∢≱↓↕≻⋯⇂↓↕⊲↓⊳∖↓⋅⋖⋅⊳∖⊔↓↿∠⇂⋯⋅⋯⊔∪⊔∐⊔∢⋅⋜⊔⋅⋖⋅∐∎⋯∙↥≱∖∪⇂∎ nonaxisvmmetrie terms., There are corrections to this result due to nonlinear effects of nonaxisymmetric terms.
 The angular velocity about the planet. 0. is less than Ixeplerian because of the ellects of the star.," The angular velocity about the planet, $\Omega$, is less than Keplerian because of the effects of the star."
 We numerically solved equations (16)) and (17)) to find the trajectories of particles in this potential., We numerically solved equations \ref{xeq}) ) and \ref{yeq}) ) to find the trajectories of particles in this potential.
 We found closed periodic particle orbits in the frame of the planet. along the lines of Paezvnski(1977).. but in the Hill approximation.," We found closed periodic particle orbits in the frame of the planet, along the lines of \cite{paczynski77}, but in the Hill approximation."
 We chose the initial position for the particle to be on the w-axis., We chose the initial position for the particle to be on the $x$ -axis.
 The initial y-velocity is determined so that the particle has zero velocity in the ae direction when it again crosses the w-axis on the other side of the central planet., The initial $y$ -velocity is determined so that the particle has zero velocity in the $x$ direction when it again crosses the $x$ -axis on the other side of the central planet.
 We find that the neighboring particle orbits first intersect for the initial position on the .r-axis ofc=0.410rg (or XN= 0.294). as shown in the left panel of Fig. 1..," We find that the neighboring particle orbits first intersect for the initial position on the $x$ -axis of $x=0.410 r_{\rm H}$ (or $X=0.294$ ), as shown in the left panel of Fig. \ref{orbitcross}."
 This maximum radius of nonintersecting orbits. misc0.410rg. is considered to represent a maximum cise radius for a cold disc. as discussed by Paczvnski(1977).," This maximum radius of nonintersecting orbits, $r_{\rm max} \simeq
0.410 r_{\rm H}$, is considered to represent a maximum disc radius for a cold disc, as discussed by \cite{paczynski77}."
. The orbits in in the left panelFig., The orbits in in the left panelFig.
 1 are asymmetric (lopsided) with respect to the v-axis in that the intersections occur lore«0., \ref{orbitcross} are asymmetric (lopsided) with respect to the y-axis in that the intersections occur for $x<0$.
 On the other hand. the m=2 Hill potential is svnimetric about the v-axis.," On the other hand, the $m=2$ Hill potential is symmetric about the y-axis."
 A more detailed analysis shows at there is another set of orbits for which the intersections occur for ο0., A more detailed analysis shows that there is another set of orbits for which the intersections occur for $x>0$.
 In addition. there is a third set of orbits that remain svmumetric about the v-axis and nonintersecting for rorax:," In addition, there is a third set of orbits that remain symmetric about the y-axis and nonintersecting for $r > r_{\rm max}$."
 However. this set of orbits is dynamically unstable for FOFaaxs," However, this set of orbits is dynamically unstable for $r > r_{\rm max}$."
 bhat ds. there is a bifurcation that occurs at r=ras. as seen in the right panel of Fig. 1..," That is, there is a bifurcation that occurs at $r = r_{\rm max}$, as seen in the right panel of Fig. \ref{orbitcross}."
 Devond this radius. iere continue to exist. v-svmametric nonintersecting orbits. but they are unstable.," Beyond this radius, there continue to exist y-symmetric nonintersecting orbits, but they are unstable."
 There are stable orbits bevond this radius. out they intersect with neighboring orbits.," There are stable orbits beyond this radius, but they intersect with neighboring orbits."
 In any case. this critical radius of ras=0.410rg is the limiting radius for orbits jt represent a cold. steady-state disc.," In any case, this critical radius of $r_{\rm
 max}=0.410\, r_{\rm H}$ is the limiting radius for orbits that represent a cold, steady-state disc."
 To test the validity the Hill approximation. we also solved the equations of motion for the full gravitational potential in 1 frame of the planet.," To test the validity the Hill approximation, we also solved the equations of motion for the full gravitational potential in the frame of the planet."
 We determined the particle orbits in the same way as described above., We determined the particle orbits in the same way as described above.
 We found that the orbits first intersect at à radius of 0.4312ry with a mass ratio so= 0.01.," We found that the orbits first intersect at a radius of $0.412\, r_{\rm H}$ with a mass ratio $\mu=0.01$ ."
 The Hill approximation is then reasonably accurate for these purposes. even for relatively large mass planets.," The Hill approximation is then reasonably accurate for these purposes, even for relatively large mass planets."
The details of the PEGASE evolutionary models are presented in Fioc&BRocca-Volmerange(1997):Mov.Roceca-Volmerange.&Fioe (2001).,"The details of the PEGASE evolutionary models are presented in \citet{FR1997, Moy2001}."
. Drieflv. the model evolves stars with a range ol stellar metallicities From (he main sequence. to the Ile flash. the horizontal branch. the asviptotic giant branch. and finally to demise as supernova or white cwarls.," Briefly, the model evolves stars with a range of stellar metallicities from the main sequence, to the He flash, the horizontal branch, the asymptotic giant branch, and finally to demise as supernova or white dwarfs."
 The star formation scenarios used here are similar to those adopted by Kennicutt(1933): an exponential star formation law with an “extended” Miller-5calo initial mass function. and stellar masses ranging from 0.1 - LOO M..," The star formation scenarios used here are similar to those adopted by \citet{Kennicutt1983}; an exponential star formation law with an “extended” Miller-Scalo initial mass function, and stellar masses ranging from 0.1 - 100 $_{\odot}$."
 PEGASE calculates broad band. colors as well as nebular emission., PEGASE calculates broad band colors as well as nebular emission.
 Additionally. radiative transfer computations provide an internally consistent estimate of dust extinction in the model galaxy.," Additionally, radiative transfer computations provide an internally consistent estimate of dust extinction in the model galaxy."
 The blue color and high equivalent width combination at the upper left of Figure 8 denotes a galaxy that has been converting gas into stars al essentially a constant rate since birth., The blue color and high equivalent width combination at the upper left of Figure 8 denotes a galaxy that has been converting gas into stars at essentially a constant rate since birth.
 The redcdest colors and smallest equivalent widths at the lower right of the diagram denotes a star formation history in which most of the primordial gas was rapidly converted into stars some 3. xLOM years after galaxy formation., The reddest colors and smallest equivalent widths at the lower right of the diagram denotes a star formation history in which most of the primordial gas was rapidly converted into stars some 3 $\times~ 10^{10}$ years after galaxy formation.
 Most earlv-tvpe spirals lie between the (wo extremes described above., Most early-type spirals lie between the two extremes described above.
 Thus. the PEGASE results indicate that the star formation history of earlv-tvpe spirals is diverse: a further testament to their heterogeneous nature already apparent [rom the images.," Thus, the PEGASE results indicate that the star formation history of early-type spirals is diverse; a further testament to their heterogeneous nature already apparent from the images."
 His quite remarkable indeed (hat a history of continuous star formation. or a continuously decreasing star formation rate. together with the effects of reddening. can explain the wide range of colors and equivalent widths observed lor the majority of earlv-(ype spirals plotted in Figure 8.," It is quite remarkable indeed that a history of continuous star formation, or a continuously decreasing star formation rate, together with the effects of reddening, can explain the wide range of colors and equivalent widths observed for the majority of early-type spirals plotted in Figure 8."
 Interestingly. the correlation between the equivalent widths and (D-V). colors breaks down for the objects with the highest equivalent widths (i.e. > 14À)). a result that is substantiated by a Spearman rank correlation test.," Interestingly, the correlation between the equivalent widths and $_e$ colors breaks down for the objects with the highest equivalent widths (i.e. $>$ ), a result that is substantiated by a Spearman rank correlation test."
" Part of the reason may be attributed io the presence of active galactic nuclei (AGNs),", Part of the reason may be attributed to the presence of active galactic nuclei (AGNs).
 NGC 4151. for example. is a well-known sevlert 1 galaxy. and NGC 2273 and NGC 0510 are Sevlert 2s (Ilo.Filippenko.&SargentVeron-C'ettv&Veron 1986).," NGC 4151, for example, is a well-known Seyfert 1 galaxy, and NGC 2273 and NGC 6810 are Seyfert 2's \citep{HFS1997, VV1986}."
. However. not all AGNs exhibit usual colors in Figure 8.," However, not all AGNs exhibit unusual colors in Figure 8."
 Conversely. not all of the errant points in Figure ὃ can be attributed to AGNs.," Conversely, not all of the errant points in Figure 8 can be attributed to AGNs."
 NGC 1432 and NGC 972. [or example. have no documented evidence for an AGN and vet they are among the most deviant of all the outliers in Figure 8.," NGC 1482 and NGC 972, for example, have no documented evidence for an AGN and yet they are among the most deviant of all the outliers in Figure 8."
 The images show evidence lor a nuclear starburst in NGC 1432. and extended nuclear star formation activity in NGC 972.," The images show evidence for a nuclear starburst in NGC 1482, and extended nuclear star formation activity in NGC 972."
 The unusually high equivalent widths. eiven (he red colors of NGC: 1482 and NGC 972. are in fact. exactly what one would expect for a recent starburst superimposed on an older population.," The unusually high equivalent widths, given the red colors of NGC 1482 and NGC 972, are in fact, exactly what one would expect for a recent starburst superimposed on an older population."
 The high equivalent widths indicate that the starburst increased (he star formation activity by at least one order of magnitude over (he pre-existing rate., The high equivalent widths indicate that the starburst increased the star formation activity by at least one order of magnitude over the pre-existing rate.
 Interestinglv. recent IHE observations of NGC 972 reveal a tidal (ail in neutral hydrogen indicative of a past interaction (Illameed&Young2003).," Interestingly, recent HI observations of NGC 972 reveal a tidal tail in neutral hydrogen indicative of a past interaction \citep{HY2003}."
 Note. however. (hat alf interacting earlv-tvpe spirals have unusual colors.," Note, however, that interacting early-type spirals have unusual colors."
 For example. M81(Yun.Ilo.&Lo 1994).. NGC 3471," For example, M81\citep{Yun1994}, , NGC 3471"
After the epoch of reionization. free electrons in the intergalactic medium (IGM) interact with photons in the cosmic microwave background radiation (CMB) via Thompson scattering.,"After the epoch of reionization, free electrons in the intergalactic medium (IGM) interact with photons in the cosmic microwave background radiation (CMB) via Thompson scattering."
 Known as the Sunyaev-Zeldovich (SZ) effect citealpsunyaevzeldovich70.sunyaevzeldovich72:: see also ?. for a review). the result is a characteristic spectral distortion of the CMB.," Known as the Sunyaev-Zel'dovich (SZ) effect \\citealp{sunyaevzeldovich70,sunyaevzeldovich72}; see also \citealp{carlstrometal02} for a review), the result is a characteristic spectral distortion of the CMB."
 The effect can be split into two contributions: that due to the thermal motion of free electrons which causes an overall increase in the apparent temperature of CMB photons (called the thermal SZ or tSZ effect). and that due bulk kinetic motion (the KSZ effect: see ?)).," The effect can be split into two contributions: that due to the thermal motion of free electrons which causes an overall increase in the apparent temperature of CMB photons (called the thermal SZ or tSZ effect), and that due bulk kinetic motion (the kSZ effect; see \citealp{carlstrometal02}) )."
 The tSZ effect. in particular. shows promise as a means of observing the hot plasma surrounding galaxy clusters and other peaks in the matter power spectrum. and recent years have seen a steady growth in both theoretical predictions citealpmoodleyetal09:: 2:: 2)) and actual measurements for massive galaxy clusters citealphalversonetal09.basuetal IO.nordetalQ09)).," The tSZ effect, in particular, shows promise as a means of observing the hot plasma surrounding galaxy clusters and other peaks in the matter power spectrum, and recent years have seen a steady growth in both theoretical predictions \\citealp{moodleyetal09}; \citealp*{scannapiecoetal08}; \citealp{roncarellietal07}) ) and actual measurements for massive galaxy clusters \\citealp{halversonetal09,basuetal10,nordetal09}) )."
 It is interesting to consider what other astrophysical objects may be observable in the near future with the tSZ effect citealpyamadaetal LO)., It is interesting to consider what other astrophysical objects may be observable in the near future with the tSZ effect \\citealp{yamadaetal10}) ).
" In recent years an increasing number of high redshift ""hyper-starbursts' (which we define as objects with an estimated. star formation rate of A,10 M.yr +) have been reported in the literature. often but not always identified with submillimetre galaxies (SMGs). and are believed to represent a significant fraction of the total star formation at these epochs"," In recent years an increasing number of high redshift `hyper-starbursts' (which we define as objects with an estimated star formation rate of $\dot{M}_{*} \gtrsim 10^3$ $_{\odot}$ $^{-1}$ ) have been reported in the literature, often but not always identified with submillimetre galaxies (SMGs), and are believed to represent a significant fraction of the total star formation at these epochs \\citealp{blainetal02,solomonvandenbout05,wangetal08,caseyetal09,martinezetal09,riechersetal09,waggetal09}) )."
" Other recent results suggest that the galaxy wind outflows frequently observed in star-forming galaxy spectra (see. ear. 2. for a review) are ubiquitous wherever there is star formation activity to drive them (2222)... with wind masses and velocities increasing with A4,."," Other recent results suggest that the galaxy wind outflows frequently observed in star-forming galaxy spectra (see, e.g., \citealp*{veilleuxetal05} for a review) are ubiquitous wherever there is star formation activity to drive them \citep{grimesetal09,rubinetal10,weineretal09,krugetal10}, with wind masses and velocities increasing with $\dot{M}_{*}$."
 The winds associated with hyper-starbursts at. high redshift will be extremely energetic. leading to violent interaction with the plasma of the surrounding intergalactic medium (IGM).," The winds associated with hyper-starbursts at high redshift will be extremely energetic, leading to violent interaction with the plasma of the surrounding intergalactic medium (IGM)."
 The following question naturally arises: can we detect the tSZ due to the wind-IGM interaction for these events?, The following question naturally arises: can we detect the tSZ due to the wind-IGM interaction for these events?
 A similar question has been posed for active galaxies citealp?vamadaetal99:: 222223) and for the combined signal due to star-forming winds citealp*mayumdaretalO| babichloebO7)). but individual hyper-starburst objects now also raise interesting possibilities.," A similar question has been posed for active galaxies \\citealp*{yamadaetal99}; \citealp{plataniaetal02,chatterjeekosowsky07,scannapiecoetal08,chatterjeeetal08,yamadaetal10}) ) and for the combined signal due to star-forming winds \\citealp*{majumdaretal01,babichloeb07}) ), but individual hyper-starburst objects now also raise interesting possibilities."
 The temperature increase of CMB photons due to the tSZ effect is redshift independent citealpearlstrometal02)). which potentially opens a new observational window on extreme star— formation at high redshift.," The temperature increase of CMB photons due to the tSZ effect is redshift independent \\citealp{carlstrometal02}) ), which potentially opens a new observational window on extreme star formation at high redshift."
 We examine this question by constructing a simplified adiabatic model of the wind-IGM interaction (Section 191). and then calculate the tSZ effect according to such a model for a variety of possible hyper-starburst targets in the literature (Sections 22. ??» along with observational prospects for the upcoming Atacama Large Millimeter Array (ALMA: see ?)) facility.," We examine this question by constructing a simplified adiabatic model of the wind-IGM interaction (Section \ref{sect:bubble}) ), and then calculate the tSZ effect according to such a model for a variety of possible hyper-starburst targets in the literature (Sections \ref{sect:sz} \ref{sect:targets}) ) along with observational prospects for the upcoming Atacama Large Millimeter Array (ALMA: see \citealp*{brownetal04}) ) facility."
 In Sections ?? we test the adiabatic expansion assumption by caleulating radiative cooling timescales for the hot plasma. and end in Section ??. with a discussion and conclusions.," In Sections \ref{sect:cooling} we test the adiabatic expansion assumption by calculating radiative cooling timescales for the hot plasma, and end in Section \ref{sect:conc} with a discussion and conclusions."
"Galactic globular clusters (GC's) are very old (age ~ 19 Gyr) stellar svstenis populated by LO"" 10° stars.",Galactic globular clusters (GCs) are very old (age $ \sim 10$ –13 Gyr) stellar systems populated by $10^5$ $ 10^6$ stars.
 Initially GCs were thought to be prime examples of simple stellar populations. i.c... populations of coeval stars born with the same initial chemical composition.," Initially GCs were thought to be prime examples of simple stellar populations, i.e., populations of coeval stars born with the same initial chemical composition."
 That situation. began to change in the late τοὺς with the first. spectroscopic surveys that disclosed: star-to-star οremical variations of fight clement abundances within individual clusters. (e.g... Cohen 1978).," That situation began to change in the late 70's with the first spectroscopic surveys that disclosed star-to-star chemical variations of light element abundances within individual clusters (e.g., Cohen 1978)."
 These variations are now known to be present in a large fraction. of GCs anc appear in the form of well defined anticorrelations between he abundances of C-N. Na-O and Ale-Al pairs. that cannot be explained in terms of evolutionary/mixine collects SCO. CLE. CGratton et al.," These variations are now known to be present in a large fraction of GCs and appear in the form of well defined anticorrelations between the abundances of C-N, Na-O and Mg-Al pairs, that cannot be explained in terms of evolutionary/mixing effects (see, e.g., Gratton et al."
 2000. Carretta et al.," 2000, Carretta et al."
 2008. 2009).," 2008, 2009)."
 1n addition there is erowing observational evidence for helium. (He) abundance variations within a few clusters which we discuss below., In addition there is growing observational evidence for helium (He) abundance variations within a few clusters which we discuss below.
 The presence of specific chemical patterns supports a scenario invoking multiple star formation events in some. perhaps most. GCs.," The presence of specific chemical patterns supports a scenario invoking multiple star formation events in some, perhaps most, GCs."
 These took place at the very beginning of the cluster evolution on relatively short time-scales. of the order of 100 Myr.," These took place at the very beginning of the cluster evolution on relatively short time-scales, of the order of $100\,$ Myr."
 The vounger generations could have been born out of eas enriched by the winds of intermediate mass Asvmptotic Ciant Branch stars (AGBs: e.g... Ventura et al.," The younger generations could have been born out of gas enriched by the winds of intermediate mass Asymptotic Giant Branch stars (AGBs; e.g., Ventura et al."
 2009) or massive fast rotating stars (Decressin et al., 2009) or massive fast rotating stars (Decressin et al.
 2007) formecl during the first star formation episode., 2007) formed during the first star formation episode.
 Dynamical simulations. e.g.. bv D'Ercole et al. (," Dynamical simulations, e.g., by D'Ercole et al. ("
2008) and. Decressin et al. (,2008) and Decressin et al. (
2008). have investigated how hese winds could have been retained by the clusters an incorporated. into future eenerations of stars.,"2008), have investigated how these winds could have been retained by the clusters an incorporated into future generations of stars."
 One of t1e challenges facing scll-enrichment scenarios in a [ew clusters is that they must be able to account or appreciable dilferences in the helium mass fraction (Y) tween dilferent. generations. with Y reaching values up to wice the primordial abundance while at the same time not appreciably altering the abundances of most other elements ike iron.," One of the challenges facing self-enrichment scenarios in a few clusters is that they must be able to account for appreciable differences in the helium mass fraction $Y$ ) between different generations, with $Y$ reaching values up to twice the primordial abundance while at the same time not appreciably altering the abundances of most other elements like iron."
 A notable exception is a Centauri (NGC 5139). where the Main Sequence (MS) splitting detected by Becdin et al.," A notable exception is $\omega$ Centauri (NGC 5139), where the Main Sequence (MS) splitting detected by Bedin et al."
 2004 has been interpreted as due to He variation (with he richest population having Yo~0.38: Piotto et al., 2004 has been interpreted as due to He variation (with the richest population having $Y\sim0.38$; Piotto et al.
 2005) and where at least. five distinct. populations with cillerent, 2005) and where at least five distinct populations with different
by a combination of radial expansion and variations in the velocity of zonal flows on the neutron star surface.,by a combination of radial expansion and variations in the velocity of zonal flows on the neutron star surface.
 Another possibility mentioned by CB ts that the burst oscillation is due to a non-radial oscillation in the neutron star surface layers., Another possibility mentioned by CB is that the burst oscillation is due to a non-radial oscillation in the neutron star surface layers.
 Such possibilities remain to be investigated in detail., Such possibilities remain to be investigated in detail.
 We thank Jeremy Heyl and Scott Hughes for many useful discussions. and Yurt Levin for a careful reading of the manuscript.," We thank Jeremy Heyl and Scott Hughes for many useful discussions, and Yuri Levin for a careful reading of the manuscript."
 We are grateful to Chris Matzner for insights into the issues discussed in the Appendix., We are grateful to Chris Matzner for insights into the issues discussed in the Appendix.
 This work began at the program on Spin and Magnetism in. Young Neutron Stars. ITP. Santa Barbara.," This work began at the program on Spin and Magnetism in Young Neutron Stars, ITP, Santa Barbara."
 A. C. and S. M. thank the Canadian Institute for Theoretical Astrophysics for hospitality during its completion., A. C. and S. M. thank the Canadian Institute for Theoretical Astrophysics for hospitality during its completion.
 This research was supported by the National Science. Foundation under grants PHY99-07949 and AY97-31632. by NASA via grant NAG 5-8658. and by the Natural Sciences and Engineering Research Council of Canada.," This research was supported by the National Science Foundation under grants PHY99-07949 and AY97-31632, by NASA via grant NAG 5-8658, and by the Natural Sciences and Engineering Research Council of Canada."
 L. B. is a Cottrell Scholar of the Research Corporation., L. B. is a Cottrell Scholar of the Research Corporation.
For each burst with a given observed Iuminositv we calculate (he expected jet breakout lime from a15M. star with a radius of 10! em. assuming an opening angle of 10°.,"For each burst with a given observed luminosity we calculate the expected jet breakout time from a$15M_\odot$ star with a radius of $10^{11}$ cm, assuming an opening angle of $10^\circ$."
 For the [our associated with SNe we use (he mass estimates [rom the associated SN (see table 1) ancl an opening angle of 30°., For the four associated with SNe we use the mass estimates from the associated SN (see table 1) and an opening angle of $30^\circ$.
 Finely. (o estimate (he jet power we use a radiative efficiency coellicient jj=1/2.," Finely, to estimate the jet power we use a radiative efficiency coefficient $\eta=1/2$."
 Changing the progenitor radius between 5-LOM—1011 cm and the radiative efficiency. between0.1—1 doesn't significantly change our results., Changing the progenitor radius between $5\cdot10^{10} - 5\cdot10^{11}$ cm and the radiative efficiency between$0.1-1$ doesn't significantly change our results.
 Fig., Fig.
 1 depicts the distributions of 755//5ofΠΙΟ. SGRDs and LGRD.," \ref{fig.T90_T_tot} depicts the distributions of $T_{90}/t_B$of, SGRBs and LGRB."
 About 20% of LGRBs have Tj€!y. in agreement with the expected small probability of having νο%{η in à jet that successfully breaks ont.," About $20\%$ of LGRBs have $T_{90}<t_B$, in agreement with the expected small probability of having $t_{eng}\simeq t_B$ in a jet that successfully breaks out."
 All SGRBs are concentrated at low values of 755/15 with To)«0.2/5., All SGRBs are concentrated at low values of $T_{90}/t_B$ with $T_{90} < 0.2 t_B$.
 This is à manilestation of the well accepted concept that SGRDs cannot arise [rom a jet breakout ancl cannot result from Collapsars., This is a manifestation of the well accepted concept that SGRBs cannot arise from a jet breakout and cannot result from Collapsars.
 Although there are two with Toy>fy the overall distribution of ciffers significantly [rom that of LGRBs ancl it closer to the distribution of SGRBs., Although there are two with $T_{90} > t_B$ the overall distribution of differs significantly from that of LGRBs and it closer to the distribution of SGRBs.
 In particular. 3 out of 5 have Toy<0.25!gp. while less than of LGRDs are in this range.," In particular, 3 out of 5 have $T_{90}<0.25t_B$, while less than of LGRBs are in this range."
 Using the IX-S test we can estimate the chance that the observed duration distribution of is taken from the LGRBs duration distribution., Using the K-S test we can estimate the chance that the observed duration distribution of is taken from the LGRBs duration distribution.
 With such a few data points the standard V distribution doesn't give a good estimate for the probability to get a given IX-S distance., With such a few data points the standard $\chi^2$ distribution doesn't give a good estimate for the probability to get a given K-S distance.
 To remedy (his we use a Monte Carlo ο to estimate this probability., To remedy this we use a Monte Carlo K-S to estimate this probability.
 We randomly drew 5 events from the LGRBs distribution and obtain the Ix-S distance between the simulated sample and the LGRDs distribution., We randomly drew 5 events from the LGRBs distribution and obtain the K-S distance between the simulated sample and the LGRBs distribution.
 We repeated this process 10? times and find that less than 5% of the randomly chosen events have larger IN-S distance than the sample., We repeated this process $10^5$ times and find that less than $5\%$ of the randomly chosen events have larger K-S distance than the sample.
 This suggests that the origin of is most likely different than that of LGRBs., This suggests that the origin of is most likely different than that of LGRBs.
 In particular the laree fraction of events with Zon<fy in the sample cislavors the suecessIul jet break scenario., In particular the large fraction of events with $T_{90}\ll t_B$ in the sample disfavors the successful jet break scenario.
 Unlike the LGRD sample that contains only bursts. the sample includes bursts from three different detectors:οι. INTEGRAL and BATSE..," Unlike the LGRB sample that contains only bursts, the sample includes bursts from three different detectors:, INTEGRAL and BATSE,."
 This introduces selection effectis that are bard (0 quantify., This introduces selection effects that are hard to quantify.
 Nevertheless. (here is no clear effect against detection of short duration (Toy</ 5). solt GRBs. by or by the two other detectors.," Nevertheless, there is no clear effect against detection of short duration $T_{90}\ll t_B$ ), soft GRBs, by or by the two other detectors."
 since (he discrepancy between and LGIDs populations is dominated by such events. we do not expect the heterogenic composition of sample to affect our conclusion.," Since the discrepancy between and LGRBs populations is dominated by such events, we do not expect the heterogenic composition of sample to affect our conclusion."
 The Collapsar model introduces two independent time scales. {η and / 5.," The Collapsar model introduces two independent time scales, $t_{eng}$ and $t_B$ ."
 This provides a simple wav to quantify the expected 755 distribution lor bursts with Zoo«{μ Ib).., This provides a simple way to quantify the expected $T_{90}$ distribution for bursts with $T_{90}\ll t_B$ \citep{B11b}. .
" Let p.454) be the probability density Dor /,,,.", Let $p_{eng}(t_{eng})$ be the probability density for $t_{eng}$ .
 Let {η be atypical jetbreakout time., Let $t_B$ be a typical jetbreakout time.
 The munber of bursts per unit of duration time. Zoo. is :," The number of bursts per unit of duration time,$T_{90}$ , is :"
High resolution imaging at optical. near-Infrared. audiillimeter-wave waveleugths have couclusively demonstrated that eireumstellar clisks are ubiquitous arouud youug solar-mass stars (ODell&Wong1996:Padgettetal.1999:Dutrey 1996).,"High resolution imaging at optical, near-infrared, and millimeter-wave wavelengths have conclusively demonstrated that circumstellar disks are ubiquitous around young solar-mass stars \citep{Odell96,Padgett99,Dutrey96}."
. The long-ield notion that planets may frequently form in these disks bas been dramatically confirmed with tie Increasing number of planets detected around nearby imaiu-sequence stars (Marcy.Cochran.&Nlavor2000)., The long-held notion that planets may frequently form in these disks has been dramatically confirmed with the increasing number of planets detected around nearby main-sequence stars \citep{Marcy00}.
. While a consensus lias uot vet. been reached on how planets form in circumstellar «isks. current theories propose that planets form either as gravitational instabilities in an accretion disk (Boss 2001).. or from," While a consensus has not yet been reached on how planets form in circumstellar disks, current theories propose that gas-giant planets form either as gravitational instabilities in an accretion disk \citep{Boss01}, , or from"
works by ?? use a SNR formalism in the analysis of PNe data along with a discussion of these selection effects.,"works by \citet{2007SerAJ.174...73U,2009A&A...495..537U} use a SNR formalism in the analysis of PNe data along with a discussion of these selection effects."
 Although they note that all PN samples suffer from selection effects caused by limitations in survey sensitivity and resolution. the nearby SSV sample. having a X- Dslope of B=—2.6140.21. 15 least influenced by these effects.," Although they note that all PN samples suffer from selection effects caused by limitations in survey sensitivity and resolution, the nearby SSV sample, having a $\Sigma-D$ slope of $\beta=-2.61\pm0.21$, is least influenced by these effects."
 Samples for Monte Carlo simulations are made using sources from Table 1 in ?. that have a known optical diameter (LMC sources only), Samples for Monte Carlo simulations are made using sources from Table 1 in \citet{filipovic_etal09} that have a known optical diameter (LMC sources only)
Fieure 3. shows examples of truncated: Ostriker model fits to regions 1 (left panel) and 2 (right panel).,Figure \ref{fig:OstFit} shows examples of truncated Ostriker model fits to regions 1 (left panel) and 2 (right panel).
 The radial profile of region 1 is smoother and less noisy than (that of region 2. which results in better constrained fits.," The radial profile of region 1 is smoother and less noisy than that of region 2, which results in better constrained fits."
 The gravscale indicates the quality of the solutions: black designates solutions with 4?<1.167. medium gray designates solutions with L.167<4?1333. and light grav is for solutions with 1.333<4?1.5.," The grayscale indicates the quality of the solutions: black designates solutions with $\chi^2 \le 1.167$, medium gray designates solutions with $1.167<\chi^2 \le 1.333$, and light gray is for solutions with $1.333< \chi^2 \le 1.5$."
 We discuss the distribution of these solutions within the parameter space of the Ostriker model below., We discuss the distribution of these solutions within the parameter space of the Ostriker model below.
 Figure5 4 shows (he set of truncated Ostriker solutions in the observationally constrained part of the parameter space (p.a.FCF) for region 1.," Figure \ref{fig:Ost_F1_obs} shows the set of truncated Ostriker solutions in the observationally constrained part of the parameter space $(\rhoc, \sigma, FCF)$ for region 1."
" We found solutions with central nunber densities in the range 0.98x10!em£Xn,<2.4 and velocity dispersion constrained to the range 0.86⋅kms1©Sa<L2kmsbo:©.", We found solutions with central number densities in the range $0.98\times 10^4~{\rm cm}^{-3} \appleq n_c \appleq 2.4\times 10^4~{\rm cm}^{-3}$ and velocity dispersion constrained to the range $0.86~{\rm km~s}^{-1} \appleq \sigma \appleq 1.2~{\rm km~s}^{-1}$.
 The flux conversion factor is constrained to values near the lower limit of the allowed range given by equation 4: 0.27B@em?Jv!beam<FCF<0.535gem beam., The flux conversion factor is constrained to values near the lower limit of the allowed range given by equation \ref{eq:FCFConstraints}: $0.27~{\rm g~cm}^{-2}~{\rm Jy}^{-1}~{\rm beam} \appleq FCF \appleq 0.53~{\rm g~cm}^{-2}~{\rm Jy}^{-1}~{\rm beam}$ .
" Our analysis found a central number density that is somewhat lower than the value given for the southern region by Paper 1. which gave i,=(3.440.6)x10em* for region 1."," Our analysis found a central number density that is somewhat lower than the value given for the southern region by Paper I, which gave $n_c=(3.4\pm 0.6)\times 10^4~{\rm cm}^{-3}$ for region 1."
 The gravscale indicates (he quality of thesolutions. following the same convention outlined in the caption of Figure 3..," The grayscale indicates the quality of thesolutions, following the same convention outlined in the caption of Figure \ref{fig:OstFit}."
 There are no apparent gaps in the solution set. aud the best solutions are surrounded by a sheath of poorer solutions. as expected.," There are no apparent gaps in the solution set, and the best solutions are surrounded by a sheath of poorer solutions, as expected."
 We obtained similar results for region 2. but the solutions are much less well-constrained than in region 1.," We obtained similar results for region 2, but the solutions are much less well-constrained than in region 1."
 The central number density of region 2 is constrainecl {ο the range 3.5x ?. , The central number density of region 2 is constrained to the range $3.5 \times 10^3~{\rm cm}^{-3} \appleq n_c \appleq 2.0\times 10^4~{\rm cm}^{-3}$ .
The velocity dispersion spanned the entire range of allowed values from. 0.8kms19SaS$L2kiuvsi©., The velocity dispersion spanned the entire range of allowed values from $0.8~{\rm km~s}^{-1} \appleq \sigma \appleq 1.2~{\rm km~s}^{-1}$.
 Allowed values of. the flux conversion. factor. ranged from 0.31gem?Jv!bean<FCF1.6beam. which covers a significant fraction of the allowed range.," Allowed values of the flux conversion factor ranged from $0.31~{\rm g~cm}^{-2}~{\rm Jy}^{-1}~{\rm beam} \appleq FCF \appleq 1.6~{\rm g~cm}^{-2}~{\rm Jy}^{-1}~{\rm beam}$, which covers a significant fraction of the allowed range."
 The central number densitv is consistent with the value of (1.12:0.3)x10!em.* obtained in Paper L. but the range of densities that we found indicates that (he uncertainty in (heir estimate was probably underestimatec.," The central number density is consistent with the value of $(1.1\pm 0.3)\times 10^4~{\rm cm}^{-3}$ obtained in Paper I, but the range of densities that we found indicates that the uncertainty in their estimate was probably underestimated."
 As we discussed in relsecmocdels.. our modeling technique combines the temperature (T) and 850 san emissivity (E50) into a single [Iux conversion factor (FCF).," As we discussed in \\ref{sec:models}, our modeling technique combines the temperature (T) and 850 $\micron$ emissivity $\kappa_{850}$ ) into a single flux conversion factor (FCF)."
 Each value of the FCF corresponds to a one parameter sel of CI. &as4) values. according to equation 4..," Each value of the FCF corresponds to a one parameter set of (T, $\kappa_{850}$ ) values, according to equation \ref{eq:FCF}. ."
 Figure 5. plots a random sample, Figure \ref{fig:OstTK} plots a random sample
"relpca,, we outline the pipeline for lensing measurements to show where different sources of error enter.",", we outline the pipeline for lensing measurements to show where different sources of error enter."
 We quanuly the residual systematic errors due to the PSF pattern alter performing the PCA interpolation and show how they scale with survey area., We quantify the residual systematic errors due to the PSF pattern after performing the PCA interpolation and show how they scale with survey area.
" We find that some components of the error scale as Area.!,"," We find that some components of the error scale as ${\rm
Area}^{-1}$."
" However, other components of the error remain roughly constant even with this interpolation scheme."," However, other components of the error remain roughly constant even with this interpolation scheme."
 We discuss how these components are ones that do not recur across different exposures., We discuss how these components are ones that do not recur across different exposures.
" Ins relmuluimage,, we show how to completely eliminate these non-recurring systematic errors by correlating only galaxy shapes measured on distinct exposures."," In \\ref{multiimage}, we show how to completely eliminate these non-recurring systematic errors by correlating only galaxy shapes measured on distinct exposures."
" Since the two- and three-point correlation functions encompass most of the lensing information that will be desired [rom current and future surveys, the combination of these two techniques will lead to the near elimination of systematic errors stemming [rom PSF interpolation."," Since the two- and three-point correlation functions encompass most of the lensing information that will be desired from current and future surveys, the combination of these two techniques will lead to the near elimination of systematic errors stemming from PSF interpolation."
 Ins refdiscussion we discuss the key requirements for a survey to keep residual systematics sulficiently small., In \\ref{discussion} we discuss the key requirements for a survey to keep residual systematics sufficiently small.
 We list the ingredients that determine these residuals and describe how to estimate them [or planned surveys as well as from actual survey data., We list the ingredients that determine these residuals and describe how to estimate them for planned surveys as well as from actual survey data.
 Future work needed to test and refine this approach is discussed., Future work needed to test and refine this approach is discussed.
 We begin by outlining the pipeline used to esümate lensing staustics [rom images of the sky., We begin by outlining the pipeline used to estimate lensing statistics from images of the sky.
 This will help us identify the steps at which different errors enter and how new techniques can reduce certain errors., This will help us identify the steps at which different errors enter and how new techniques can reduce certain errors.
 We will introduce the PCA technique below in step 3 on PSF interpolation and use it in subsequent sections to quantify residuals., We will introduce the PCA technique below in step \ref{interpstep} on PSF interpolation and use it in subsequent sections to quantify residuals.
 The lensing pipeline can be summarized in 5 main steps:, The lensing pipeline can be summarized in \ref{npipesteps} main steps:
Because of the rapid chauge iu intensity during the masts. we calculated upper lanits separately for intervals οπής which the source inteusitv was arecr than 1 peak iutensitv. aud the rest of he data.,"Because of the rapid change in intensity during the bursts, we calculated upper limits separately for intervals during which the source intensity was larger than the peak intensity, and the rest of the data."
 For the ‘alutest burst (no., For the faintest burst (no.
 1) the observed count rate was a factor of ~T lower than for the brightest burst (no., 1) the observed count rate was a factor of $\sim 7$ lower than for the brightest burst (no.
 3). aud ierefore the upper limits wary considerablv from burst o burst.," 3), and therefore the upper limits vary considerably from burst to burst."
 The or oscillations (for the method. see Vaughan et al.," The for oscillations (for the method, see Vaughan et al."
 1991) oeji bursts l and Ll durius the bright aud weak parts are pper limits in the bright aud weak parts are Iu the 11 sources that currently are known to exhibit burst oscillatious. the oscillations may reach hieh amplitudes (>50% nus) during short intervals (typically 0.1 x) if they occur divine the rising phase and low amplitudes (<15% }) divine the decaving phase (for a recent review. see Strolumaver Bildsten 2003).," 1994) in bursts 1 and 4 during the bright and weak parts are upper limits in the bright and weak parts are In the 11 sources that currently are known to exhibit burst oscillations, the oscillations may reach high amplitudes $>$ rms) during short intervals (typically 0.1 s) if they occur during the rising phase and low amplitudes $<$ ) during the decaying phase (for a recent review, see Strohmayer Bildsten 2003)."
 Therefore. our upper Iuits are not very constraining.," Therefore, our upper limits are not very constraining."
 Twelve eclipse iueresses and twelve egresses were observed. in tweuty-one eclipses distributed over seven outbursts.," Twelve eclipse ingresses and twelve egresses were observed, in twenty-one eclipses distributed over seven outbursts."
 Two eclipses were observed completely: for another oue the ineress aud egress was covered with a data θα) during the eclipse: for the rest only the iugress or ceress was covered., Two eclipses were observed completely; for another one the ingress and egress was covered with a data gap during the eclipse; for the rest only the ingress or egress was covered.
 Timune of the trausitious provides the means to improve the accuracy of the orbital ephemeris significantly., Timing of the transitions provides the means to improve the accuracy of the orbital ephemeris significantly.
 The orbital period thus far had oulv a 31 sec accuracy (Iu t£ Zand et al., The orbital period thus far had only a 31 sec accuracy (In 't Zand et al.
 2000)., 2000).
 More accuracy enables studies of chauges in the orbital period., More accuracy enables studies of changes in the orbital period.
 To increase the iuie baseline. we iuclude the timing of the egress observed with the BeppoSAN Narrow Field Tnstrmments on 1998 September 6 (Iu. t Zaud et al.," To increase the time baseline, we include the timing of the egress observed with the BeppoSAX Narrow Field Instruments on 1998 September 6 (In 't Zand et al."
 2000)., 2000).
 Thus. the time yvascline ds 3.9 vr.," Thus, the time baseline is 3.9 yr."
 lugress and egress last between 30 aud £0 sec., Ingress and egress last between 30 and 40 sec.
 We took he mid points between minmuimn and maxiuun flux as a reference for the πιο of the eclipse transitions., We took the mid points between minimum and maximum flux as a reference for the timing of the eclipse transitions.
 The ransition profiles appear too variable to rust methods hat involve profile fitting., The transition profiles appear too variable to trust methods that involve profile fitting.
 Therefore. we resorted o the ollowing procedure.," Therefore, we resorted to the following procedure."
 As a hascline. we used standard 1 data which provides 0.125 s resolution.," As a baseline, we used standard 1 data which provides 0.125 s resolution."
 The times were corrected to the solar systembarvecuter?., The times were corrected to the solar system.
. We ideutified he eclipses in a light curve of the whole data set at a resolution of l s and selected data stretches of 200 x centered on the initial mudpoimt ceteruinations (bv eve) of meress or ceress., We identified the eclipses in a light curve of the whole data set at a resolution of 1 s and selected data stretches of 200 s centered on the initial midpoint determinations (by eye) of ingress or egress.
 The helt curves of the center 120 8 parts of these data stretches are displaved in Fig. 5.., The light curves of the center 120 s parts of these data stretches are displayed in Fig. \ref{figlce}.
 One ineress had to be excluded from the aualvsis (at ATID 52060) because the data stream stopped before total eclipse was reached: one ceress was excluded because the, One ingress had to be excluded from the analysis (at MJD 52060) because the data stream stopped before total eclipse was reached; one egress was excluded because the
reftab:spec-par.. which lists: molecuar line. rest frequency. half power beam width (IIPDW) at the corresponding frequency. min beam brielitucss temperature. Local Standard of Rest (LSR) velocity. f] width to half power (FWIIP) line width. integrated line intensity. estimated optical depth averaged over the liie profile. aud offset position relative to 1220231.,", which lists: molecular line, rest frequency, half power beam width (HPBW) at the corresponding frequency, main beam brightness temperature, Local Standard of Rest (LSR) velocity, full width to half power (FWHP) line width, integrated line intensity, estimated optical depth averaged over the line profile, and offset position relative to 20231."
 The AcSar Values presented imn column 6 are intrinsic liue widths trat were decouvolved by the spectral resolution., The $\Delta$$v_{\rm int}$ values presented in column 6 are intrinsic line widths that were deconvolved by the spectral resolution.
" The 7 value given in column ὃ is estimated from the ratio of inteerated intensities of the siue transiion in two differcut isotoIOS, assidue Isotope ratios of [ο C]21:69.7. [SO]: ""O[:!*0|25.5:1:2856 (Wilson Rood 1991)). aud. |!S:[ ?S|231.3. (Chin et al. 1996))"," The $\bar{\tau}$ value given in column 8 is estimated from the ratio of integrated intensities of the same transition in two different isotopes, assuming isotope ratios of $^{13}$ $^{12}$ C]=1:69.7, $^{18}$ $^{17}$ $^{16}$ O]=5.5:1:2856 (Wilson Rood \cite{Wilson94}) ), and $^{34}$ $^{32}$ S]=31.3 (Chin et al. \cite{Chin96}) )"
 for a egalactocentiie distance of &.2kkpc., for a galactocentric distance of kpc.
" Iu the case ofNIL;,.. the peak optical depth of the main eroup of hvperfBue componcuts is eiveu."," In the case of, the peak optical depth of the main group of hyperfine components is given."
 We assume local thermodvuamic equilibrium (LTE) at an excitation teni]erature and identical beam filliug factors (uuitv) throughout the following aualvsis., We assume local thermodynamic equilibrium (LTE) at an excitation temperature and identical beam filling factors (unity) throughout the following analysis.
 For the line emissiou from linear. rigid rotor molecules such as CO. CS. aai their isotopes. the beam averaged column density iu lis giveu by {Scoville et al. 19863).," For the line emission from linear, rigid rotor molecules such as CO, CS, and their isotopes, the beam averaged column density in is given by (Scoville et al. \cite{Scoville86}) ),"
 where fTypde is the iutegrated intensity in lof the J|1J tausitious with frequency v (Iz) and optical depth τ., where $\int{{T_{\rm MB}}dv}$ is the integrated intensity in of the $J$ $\rightarrow$$J$ transitions with frequency $\nu$ (Hz) and optical depth $\bar{\tau}$.
" k tyand hi (ergss) denote the Boltzmann constaut aud the Plauck coustant. respectively, aud fo ecim) is the permancut dipole moment."," $k$ $^{-1}$ )and $h$ s) denote the Boltzmann constant and the Planck constant, respectively, and $\mu$ cm) is the permanent dipole moment."
 For οσοι densities. see refanu..," For column densities, see \\ref{amm}."
 Fig.2 illustrates the distribution of integrated intensity of he (L1) iain οroup of lines.," \ref{20231-nh3} illustrates the distribution of integrated intensity of the (1,1) main group of lines."
 The whole region can be (livided into three subreeions.g with two cores located close o the two srO;un peaks aud a ridge in between.," The whole region can be divided into three subregions, with two cores located close to the two $\mu$ m peaks and a ridge in between."
 Such a norphologv ecuerally resembles the twin core svsteni (lefined by Jijina et al. (1999)), Such a morphology generally resembles the twin core system defined by Jijina et al. \cite{Jijina99}) )
 iu their extensive study of warby, in their extensive study of nearby
There has been much debate in the literature centering on the X-ray. cluster £x versus Z correlation.,There has been much debate in the literature centering on the X-ray cluster $L_X$ versus $T$ correlation.
 “Phe emission. weighted. mean temperature in. keV. ds. plotted against the bolometric luminosity within the virial radius for all our clusters in figure 2., The emission weighted mean temperature in keV is plotted against the bolometric luminosity within the virial radius for all our clusters in figure 2.
 The filled svmbols represent the relaxed. clusters and the open symbols denote those clusters that show significant substructure., The filled symbols represent the relaxed clusters and the open symbols denote those clusters that show significant substructure.
 Clearly the simulation without cooling produces brighter clusters at the same temperature., Clearly the simulation without cooling produces brighter clusters at the same temperature.
 ALL 3 sets of objects display an LyVF relation although there are insullicient numbers to tie the trend down very tightly., All 3 sets of objects display an $L_X-T$ relation although there are insufficient numbers to tie the trend down very tightly.
 Also plotted in figure 2 are the observational data 1].., Also plotted in figure 2 are the observational data \cite{D95}.
 Our clusters are smaller and cooler because they are not very massive (due to our relatively small computational volume) but span a reasonable range of luminosities and temperatures., Our clusters are smaller and cooler because they are not very massive (due to our relatively small computational volume) but span a reasonable range of luminosities and temperatures.
 Implementing cooling clearly has a cramatic effect on the X-ray properties of galaxy clusters., Implementing cooling clearly has a dramatic effect on the X-ray properties of galaxy clusters.
 Without cooling our clusters closely resemble those found by previous authors (2]. and references therein)., Without cooling our clusters closely resemble those found by previous authors \cite{E98} and references therein).
 Phese clusters appear to have remarkably similar radial densities and bolometric X-ray luminosity profiles. especially when those with significant substructure are removed.," These clusters appear to have remarkably similar radial densities and bolometric X-ray luminosity profiles, especially when those with significant substructure are removed."
 With cooling implemented the cluster bolometric N-ray. luminosity profiles span a broader range., With cooling implemented the cluster bolometric X-ray luminosity profiles span a broader range.
 The formation of a central galaxy within each halo acts to steepen the dark matter profile. supporting the conclusion of the lensing studies. 6]. that the underlving potential that forms the lens only has a small core.," The formation of a central galaxy within each halo acts to steepen the dark matter profile, supporting the conclusion of the lensing studies \cite{K96} that the underlying potential that forms the lens only has a small core."
 For the largest cluster. a significant amount of barvonic material has cooled. anc built up a large central galaxy.," For the largest cluster, a significant amount of baryonic material has cooled and built up a large central galaxy."
 This localised mass deepens the potential well ancl contains hot gas with a steeply rising density (pxrLet in the inner regions).," This localised mass deepens the potential well and contains hot gas with a steeply rising density $\rho \propto
r^{-2.75}$ in the inner regions)."
 For this cluster around SO percent of the bolometric X-ray. emission comes from the galactic region ancl this must therefore be viewed as a lower limit as the central emission is unresolved., For this cluster around 80 percent of the bolometric X-ray emission comes from the galactic region and this must therefore be viewed as a lower limit as the central emission is unresolved.
 Such a large central spike to the X-ray emission is already only. weakly consistent with the latest observational data 3].., Such a large central spike to the X-ray emission is already only weakly consistent with the latest observational data \cite{EF99}.
 For the remaining 19 clusters the central galaxy is not so dominant and a shallower central potential well is formed., For the remaining 19 clusters the central galaxy is not so dominant and a shallower central potential well is formed.
 In these cases the slope of the central hot gas is pxre.7 and the total X-ray emission is well resolved., In these cases the slope of the central hot gas is $\rho \propto r^{-0.5}$ and the total X-ray emission is well resolved.
 In principle. the presence of a large galaxy could resolve the problem of the slope of the X-ray luminosity - temperature relation.," In principle, the presence of a large galaxy could resolve the problem of the slope of the X-ray luminosity - temperature relation."
 In. large clusters. large central galaxies are more likely to be present and this galaxy. deepens the local potential well. boosting the emission above the theoretically expected Lyx7. regression line.," In large clusters, large central galaxies are more likely to be present and this galaxy deepens the local potential well, boosting the emission above the theoretically expected $L_X \propto T^2$ regression line."
 Getting a reasonable amount of material to cool into the central galaxy is seen to be of vital importance., Getting a reasonable amount of material to cool into the central galaxy is seen to be of vital importance.
 We have performed two N-body plus hydrodynamies simulations of structure formation within a volume of side LOOAlpe. including the effects of radiative cooling but neglecting star formation and feedback.," We have performed two N-body plus hydrodynamics simulations of structure formation within a volume of side $100\Mpc$, including the effects of radiative cooling but neglecting star formation and feedback."
 By repeating one of the simulations without radiative cooling of the gas we can both compare to previous work and study the changes caused by the cooling in detail., By repeating one of the simulations without radiative cooling of the gas we can both compare to previous work and study the changes caused by the cooling in detail.
 A summary of our conclusions follows. (, A summary of our conclusions follows. (
a) The bolometric luminosity for the clusters with radiative cooling is around five,a) The bolometric luminosity for the clusters with radiative cooling is around five
However. also the observation by VidalMacdjar et al. (,"However, also the observation by Vidal–Madjar et al. ("
2003. 2001) preseuts a lower luit for the mass loss.,"2003, 2004) presents a lower limit for the mass loss."
 If we use the luninosity distribution described above. it is possible to calculate the mass lost from a plauet for a eiveu density aud orbital distance for a certain starting lass and a given age of star.," If we use the luminosity distribution described above, it is possible to calculate the mass lost from a planet for a given density and orbital distance for a certain starting mass and a given age of star."
 Because of lack of information. we assunie that the density of the planet remains constant in time.," Because of lack of information, we assume that the density of the planet remains constant in time."
 Some implications of this assuuption are discussed in Section [., Some implications of this assumption are discussed in Section 4.
 Thus. we are able to determine the distribution of planetary lnass resulting from a given initial mass because of exposure to different Nταν fluxes.," Thus, we are able to determine the distribution of planetary mass resulting from a given initial mass because of exposure to different X–ray fluxes."
 It should be meutioned. that we are ouly considering hvdrogenrich planets. meaniug that we have no information about a icv/rocky core. which can remain after evaporating all the hydrogen.," It should be mentioned, that we are only considering hydrogen–rich planets, meaning that we have no information about a icy/rocky core, which can remain after evaporating all the hydrogen."
 In Fig. 3..," In Fig. \ref{single_jup},"
 the mass distribution for au initial mass of 1 yup and densities of 0.1 (correspouding to a low censity planet like IID209158b) and 1.1 g/em? (correspouding to a high density planet like TrES-2) aud orbital distances of 0.02. and 0.05 AU after | Cvr are shown.," the mass distribution for an initial mass of 1 $_{jup}$ and densities of 0.4 (corresponding to a low density planet like HD209458b) and 1.4 $^{3}$ (corresponding to a high density planet like TrES-2) and orbital distances of 0.02, and 0.05 AU after 4 Gyr are shown."
" For the closest orbit aud low deusitv. about 95% of the plaucts can survive. and 50% have remaining masses of more than 0.8 Mj,,."," For the closest orbit and low density, about 95 of the planets can survive, and 50 have remaining masses of more than 0.8 $_{jup}$."
" For a high deusity aud an orbital distance of 0.02 AU. more than 95 have a remaining mass of more than 0.8 Mj, while this muuber increases to nearly 100 for a larger orbital distance of 0.05 AU."," For a high density and an orbital distance of 0.02 AU, more than 95 have a remaining mass of more than 0.8 $_{jup}$, while this number increases to nearly 100 for a larger orbital distance of 0.05 AU."
 For orbital distance z0.05 AU. ouly a small fraction is affected by radiation comune frou stars located in the higheuergy tail of the luminosity distribution.," For orbital distance $\geq 0.05$ AU, only a small fraction is affected by radiation coming from stars located in the high–energy tail of the luminosity distribution."
 This is in agreeinent with predictions by Hubbard et al. (, This is in agreement with predictions by Hubbard et al. (
2006. 2007) based on a differcut approach that most of the Tot Jupiters are not stronely influenced by mass loss Fig.,"2006, 2007) based on a different approach that most of the Hot Jupiters are not strongly influenced by mass loss Fig."
 b shows the cumulative distribution fiction for au initial mass of 1 AL.) for the same orbital distances but for deusities of 0.5. 2 (corresponding to the density of the transiting Tot Neptune observed by. Cillon et al. (," \ref{single_nep} shows the cumulative distribution function for an initial mass of 1 $_{nep}$ for the same orbital distances but for densities of 0.8, 2 (corresponding to the density of the transiting Hot Neptune observed by Gillon et al. ("
2007)). and 3 w after | Cyr.,"2007)), and 3 $^{3}$ after 4 Gyr."
 At a closein orbit about 10 of Neptunesized planets with a density of 0.5 e/cm cau survive. while this value increases to more than SO for a deusity of 2 &/cumb. aud to more than 90 for 3 gcn.," At a close–in orbit about 40 of Neptune–sized planets with a density of 0.8 $^{3}$ can survive, while this value increases to more than 80 for a density of 2 $^{3}$, and to more than 90 for 3 $^{3}$."
 At an orbital distance of 0.05 AU. less than 2 of the cxoplancts would uot survive the iupact of their host star radiation for | Cr.," At an orbital distance of 0.05 AU, less than 2 of the low--density exoplanets would not survive the impact of their host star radiation for 4 Gyr."
 Nearly 85 of the Neptunemass planets orbiting at 0.02 AU with a low density could be eroded to SuperEarths (about 10 jJ. aud still more than 20% of the highdensity plancts at the sanie orbits.," Nearly 85 of the Neptune–mass planets orbiting at 0.02 AU with a low density could be eroded to Super–Earths (about 10 $_\oplus$ ), and still more than 20 of the high–density planets at the same orbits."
 Hydrogen euvelopes of 0.2 NL. can be casily lost at the closein orbits., Hydrogen envelopes of 0.2 $_{nep}$ can be easily lost at the close–in orbits.
 At 0.05 AU. 30 of the lowdensity planets cau lose such iu envelope. while the number decreases to about 5% for higheusitv planets;," At 0.05 AU, 30 of the low–density planets can lose such an envelope, while the number decreases to about 5 for high–density planets."
 At 0.1 AU. also for Neptunesized plauets the effects are very siuall.," At 0.1 AU, also for Neptune–sized planets the effects are very small."
pronounced in selections E aud F. This flaring eventually starts to become weaker (see also the ligh-cncrey light curve in Figure 2bb). but it remains present through selection IX. While selections J aud Is cau be classified as atol-like refseciconiparison]). it ds nmuportaunt to note that the flariue that has long been regarded απ bene characteristic of the Sco-like Z sources is still present in these lower count rate intervals.,"pronounced in selections E and F. This flaring eventually starts to become weaker (see also the high-energy light curve in Figure \ref{fig:lc}b b), but it remains present through selection K. While selections J and K can be classified as atoll-like \\ref{sec:comparison}) ), it is important to note that the flaring that has long been regarded as being characteristic of the Sco-like Z sources is still present in these lower count rate intervals."
 In the framework of atoll sources. the brauches traced out as a result of this flaring would be referred to as the atoll wpper-banana branch. but as Figures 2.. 3. aud Ll show. there is uo sharp transition between Z and atoll behavior.," In the framework of atoll sources, the branches traced out as a result of this flaring would be referred to as the atoll upper-banana branch, but as Figures \ref{fig:lc}, \ref{fig:cd}, and \ref{fig:hid} show, there is no sharp transition between Z and atoll behavior."
 To better describe the rapid evolution during the last plase of the outburst and emphasize the relation between the Z source flaring aud the atoll upper-banana brauch. we show the combined CD. ITID. and light curve of selections J. Ik. and L in Figure 5.. resulting in a ‘complete’ atoll track.," To better describe the rapid evolution during the last phase of the outburst and emphasize the relation between the Z source flaring and the atoll upper-banana branch, we show the combined CD, HID, and light curve of selections J, K, and L in Figure \ref{fig:flaring}, resulting in a `complete' atoll track."
 Points on the wpper-banana brauch of the atoll iu the CD were colored red: from the TID and light curve it can be seen that these upper-banana brauch data poiuts correspond to the last few flares that were observed iu ο also with refüe:lebb and 1))., Points on the upper-banana branch of the atoll in the CD were colored red; from the HID and light curve it can be seen that these upper-banana branch data points correspond to the last few flares that were observed in (compare also with \\ref{fig:lc}b b and \ref{fig:hid}) ).
 This is the first time that the Z source flaring branch has been observed to evolve iuto the atoll source upper banana brauch aud it confirms carlicr suspicions (asinger&vanderElis1989) that the two branches wueght be one aud the same phenomenon., This is the first time that the Z source flaring branch has been observed to evolve into the atoll source upper banana branch and it confirms earlier suspicions \citep{hava1989} that the two branches might be one and the same phenomenon.
 The lower banana brauch starts to form around the time of the last flares in selections J aud Ix. As the total count rate drops by a factor of ~3 from solectiou Is. to selection L. the source moves away from the diagonal line followed by (the secular motion of) the uormal/farine brauch vertex in selections A to I (dashed lines in refüe:cd)).," The lower banana branch starts to form around the time of the last flares in selections J and K. As the total count rate drops by a factor of $\sim$ 3 from selection K to selection L, the source moves away from the diagonal line followed by (the secular motion of) the normal/flaring branch vertex in selections A to I (dashed lines in \\ref{fig:cd}) )."
 However. in the TID the lower banana brauch continues along the path traced out by the secular motion ofthis vertex (dashed lines in refüe:hid)). as already pointed out by LRIIO9.," However, in the HID the lower banana branch continues along the path traced out by the secular motion of this vertex (dashed lines in \\ref{fig:hid}) ), as already pointed out by LRH09."
 The transition to the atoll islaud state occurs in selection L during a rapid decrease iu count rate. and is marked by a sudden merease m hard color.," The transition to the atoll island state occurs in selection L during a rapid decrease in count rate, and is marked by a sudden increase in hard color."
 It is followed by the extreme-island state. i which the hard color becomes more or less constant (although poorly coustraimed because of the low count rates).," It is followed by the extreme-island state, in which the hard color becomes more or less constant (although poorly constrained because of the low count rates)."
 Figures and L show that lis the first 3.NS-LAINB in which we can study the eutire evolution from Z source to atoll source behavior in a suele source., Figures \ref{fig:cd} and \ref{fig:hid} show that is the first NS-LMXB in which we can study the entire evolution from Z source to atoll source behavior in a single source.
 Cve-like Z source behavior. characterize x larec intensity swines on the horizontal aud norma xaenches. the presence of a dipping flaring brauch. arc an upturn from the horizontal brauch. is observed at he highest count rates.," Cyg-like Z source behavior, characterized by large intensity swings on the horizontal and normal branches, the presence of a dipping flaring branch, and an upturn from the horizontal branch, is observed at the highest count rates."
 The transition to Sco-like Z source behavior is rapid (75 davs) with maxinuun tota count rates dropping by a factor of ~1.5: this transition uostlv involves changes im the orientation of the branches iu the CD and ΠΟ. as well as the disappearance of he horizontal branch upturn.," The transition to Sco-like Z source behavior is rapid $\sim$ 5 days) with maximum total count rates dropping by a factor of $\sim$ 1.5; this transition mostly involves changes in the orientation of the branches in the CD and HID, as well as the disappearance of the horizontal branch upturn."
" The transition frou, Sco-ike Z behavior to atoll source behavior is mmuch slower (anouths).", The transition from Sco-like Z behavior to atoll source behavior is much slower $\sim$ months).
 Figure Ὁ shows that the last instances of the Z source flaring brauch. at low overall couut rates. can also be classified as the atoll source upper xuuana brauch. providing au iuportaut link between he two subclasses.," Figure \ref{fig:flaring} shows that the last instances of the Z source flaring branch, at low overall count rates, can also be classified as the atoll source upper banana branch, providing an important link between the two subclasses."
 The Sco-like Z to atoll trausition is uarked by the disappearance of the horizoutal brauch. rormal branch. aud fariuz/upper-bauaua branch. as the uaxiuun total count rates dropped by a factor of ~3.," The Sco-like Z to atoll transition is marked by the disappearance of the horizontal branch, normal branch, and flaring/upper-banana branch, as the maximum total count rates dropped by a factor of $\sim$ 3."
 Tn terms of the selections A-L this is a systematic aud nonotonic process: of course. during its initial rise aud. in subsequent decay the source moves back aud forth vetween some of these selections.," In terms of the selections A-L this is a systematic and monotonic process; of course, during its initial rise and in subsequent decay the source moves back and forth between some of these selections."
 The time between he last detection of the flaring brauch/upper banana xanch to the transition from the lower-bauaua braucht o the island state (and later the extreme island state) is Y davs with the count rate dropping bv another actor of ~3.," The time between the last detection of the flaring branch/upper banana branch to the transition from the lower-banana branch to the island state (and later the extreme island state) is $\sim$ 7 days, with the count rate dropping by another factor of $\sim$ 3."
 The evolution curing the atoll phase oreseuts an important departure from the evolution secu in the Z phase of the outburst., The evolution during the atoll phase presents an important departure from the evolution seen in the Z phase of the outburst.
 While in the Sco-like Z source plase the change iu low-cucrey count rate results in eradual changes in the CD/TID tracks (except for occasional visits to the horizontal brauch). in the atoll phase (after the flaring subsides) the low-cucrev cout rate changes result iu motion«long the CD/IIID track.," While in the Sco-like Z source phase the change in low-energy count rate results in gradual changes in the CD/HID tracks (except for occasional visits to the horizontal branch), in the atoll phase (after the flaring subsides) the low-energy count rate changes result in motion the CD/HID track."
 Iu the IIID. motion along the lowerbanana brauch even appears to be a continuation of the eradual motion of the Z source normal/flaring branch vertex (this is nof the case in the CD. however).," In the HID, motion along the lower-banana branch even appears to be a continuation of the gradual motion of the Z source normal/flaring branch vertex (this is not the case in the CD, however)."
 A low-frequency variability study. Gin the 6.960 keV ρα) of the Cyre-like tracks and some of the Sco-LBike tracks was already presented in IIO7., A low-frequency variability study (in the 6.9–60 keV band) of the Cyg-like tracks and some of the Sco-like tracks was already presented in H07.
 Two types of low-frequency QPOs were observed in those tracks. he horizontal brauch oscillations (10 60 Tz) and the ποια]. branch oscillations (~7 9 Iz).," Two types of low-frequency QPOs were observed in those tracks, the horizontal branch oscillations $\sim$ 10–60 Hz) and the normal branch oscillations $\sim$ 7–9 Hz)."
 These QPOs ypeared on the appropriate branches. coufirmine our vauch identification and ow interpretation of the uehest count rate tracks as Z-like tracks.," These QPOs appeared on the appropriate branches, confirming our branch identification and our interpretation of the highest count rate tracks as Z-like tracks."
 We did not yerforun a sinularly detailed analysis for the remainder of the outburst. but a visual inspection of the power spectra indicates that both types of low-frequency QPOs disappear as the overall count rate decreases.," We did not perform a similarly detailed analysis for the remainder of the outburst, but a visual inspection of the power spectra indicates that both types of low-frequency QPOs disappear as the overall count rate decreases."
 The normal xench. oscillations disappear within selection E. where hey are seen in the high count rate IIID tracks. but rot the lower count rate ones.," The normal branch oscillations disappear within selection E, where they are seen in the high count rate HID tracks, but not the lower count rate ones."
 Indications of horizontal xanch oscillatious are still seen in selections Ε aud Ci. mt not in the lower count rate sclections II.L. Iu Figure 6 we show examples of 260 keV lower-alana (a) and upper-banana branch (b) power spectra roni the combined bright-atoll-like selections I aud J. The shapes are consistent with the power spectra of other atolls iu these spectral states (wander[lis 2006).," Indications of horizontal branch oscillations are still seen in selections F and G, but not in the lower count rate selections H–L. In Figure \ref{fig:low-freq} we show examples of 2–60 keV lower-banana (a) and upper-banana branch (b) power spectra from the combined bright-atoll-like selections I and J. The shapes are consistent with the power spectra of other atolls in these spectral states \citep{va2006}."
. The lower-banana power spectra shows a broad (Q=0.740.1) peak at 13.940.7 Tz. ou top of a power- shaped (€xν ΗΤΟ1 noise continu.," The lower-banana power spectrum shows a broad $\pm$ 0.1) peak at $\pm$ 0.7 Hz, on top of a power-law shaped $\propto \nu^{-1.41\pm0.04}$ ) noise continuum."
 The overall variability is weak. with an iutegrated power ruis (1/16100 ITz) of ~3% (2G0 keV).," The overall variability is weak, with an integrated power rms (1/16--100 Hz) of $\sim$ (2–60 keV)."
 The upper-banaua power spectra could be fitted with a single power law pο and the 1/16100 ITz zius was ~2., The upper-banana power spectra could be fitted with a single power law $\propto \nu^{-1.48\pm0.03}$ ) and the 1/16–100 Hz rms was $\sim$.
 A similar study for the atoll-ike selections I& aud L suffers frou low count rates. aud high quality broadbaud power spectra are difficult to produce.," A similar study for the atoll-like selections K and L suffers from low count rates, and high quality broadband power spectra are difficult to produce."
 The shape of the power spectrum of the lower-banana brauch of selection L (from observations with total count rate above 65 counts/s/PCU) is consistent. with that of the, The shape of the power spectrum of the lower-banana branch of selection L (from observations with total count rate above 65 counts/s/PCU) is consistent with that of the
The secondary svuchrotrou enuüssiou is calculated iu the presence of the maeuetic field. which is determined by its value at the base of the je By.,"The secondary synchrotron emission is calculated in the presence of the magnetic field, which is determined by its value at the base of the jet $B_0$."
 We compute the cluission for By=10° G (Mode A) and By=10! C (Model B)., We compute the emission for $B_0=10^5$ G (Model A) and $B_0=10^4$ G (Model B).
 We assume the same epton luaxiuuun cherey. since for simplicity £577 is fxe to 100 TeV for both values of the magnetic field.," We assume the same lepton maximum energy, since for simplicity $E_p^{\rm max}$ is fixed to 100 TeV for both values of the magnetic field."
 For he specific enissiou aud absorption cocticicuts. we used the expressions given by Pacholczvls (1970).," For the specific emission and absorption coefficients, we used the expressions given by Pacholczyk (1970)."
 We then computed the spectral energy distributions anc transformed them iuto the observer fune., We then computed the spectral energy distributions and transformed them into the observer frame.
 As a first-order approach. we assuned that the IC takes place for any lepton cnuerev in the Thomson reeime and under au isotropic photon field.," As a first-order approach, we assumed that the IC takes place for any lepton energy in the Thomson regime and under an isotropic photon field."
 Actually. the Thomson approxiuatioun is not valid for particles with euergies above 210 100 GeV. ic. at the highest euergies of the secondary leptons produced in this scenario.," Actually, the Thomson approximation is not valid for particles with energies above $\ga 10$ $100$ GeV, i.e. at the highest energies of the secondary leptons produced in this scenario."
 Above these energies. the IC interactions occur in the EKleiu Nishina (ISN) regne.," Above these energies, the IC interactions occur in the Klein Nishina (KN) regime."
" This fact doos not affect the radiated svuchrotrom spectrum siguificautly, siuce it is mainly produced in the inner regions of the jet. close to the compact object. where the svuchrotrom process is the main cooling mechanism: ie. the particle spectrum is not noticeably affected by INN cooling there."," This fact does not affect the radiated synchrotron spectrum significantly, since it is mainly produced in the inner regions of the jet, close to the compact object, where the synchrotron process is the main cooling mechanism; i.e. the particle spectrum is not noticeably affected by KN cooling there."
 The KN effec would otherwise affect the highest energies of the IC spectrum. but this enerev range of the spectrum is dominated by neutral piou decay. 5-1ay pliotous (see next section).," The KN effect would otherwise affect the highest energies of the IC spectrum, but this energy range of the spectrum is dominated by neutral pion decay $\gamma$ -ray photons (see next section)."
 Iu Figure 3.. we show the svuchrotron aud IC spectra.," In Figure \ref{pol}, we show the synchrotron and IC spectra."
 These calculations allow us to estimate the power σοι to this radiative channel iu order to compare it with other components like IC cussion from electromagnetic cascades or svuchrotron cluission from the secoudaries inside the jet., These calculations allow us to estimate the power going to this radiative channel in order to compare it with other components like IC emission from electromagnetic cascades or synchrotron emission from the secondaries inside the jet.
 The set of explored parameters illustrate the impact of the IC'svuchrotron energy. loss balance iu the secondary broadband spectra., The set of explored parameters illustrate the impact of the IC/synchrotron energy loss balance in the secondary broadband spectrum.
 It is seen that the svuchrotrou luminosity is at most 1077 cress +. and well below the IC euission for the both values of the adopted maenctic field.," It is seen that the synchrotron luminosity is at most $\sim 10^{32}$ erg $^{-1}$, and well below the IC emission for the both values of the adopted magnetic field."
 The radiation field of carly-type stars provides a suitable areet for the absorption of e@amuua-rayv photons., The radiation field of early-type stars provides a suitable target for the absorption of gamma-ray photons.
 Iu 1l, In Fig.
 we show the optical depth as a function of he gamma-ray euerev for the injection at height := «£2., \ref{tau} we show the optical depth as a function of the gamma-ray energy for the injection at height $z=a/2$ .
 Iereafter we consider that as a representative point or the injected primary cunission., Hereafter we consider that as a representative point for the injected primary emission.
 The plotted optical depths were calculated as in Dubus (2006)., The plotted optical depths were calculated as in Dubus (2006).
 The absorption oxobabilitv is modulated. on the orbital period of the πλαν as a result ofthe phase dependence of the geometric sath (see the sketch iu Szostek Zdzarski 2006)., The absorption probability is modulated on the orbital period of the binary as a result of the phase dependence of the geometric path (see the sketch in Szostek Zdziarski 2006).
 Encrectic electrou-positron pairs are materialized bv xXiotou-phlioton interactions., Energetic electron-positron pairs are materialized by photon-photon interactions.
 These leptous. in turi. boost he stella photons to ligh-cnereics via IC scattering.," These leptons, in turn, boost the stellar photons to high-energies via IC scattering."
 The 5-rav absorption and production mechanisms can proceed very fast. resulting in the development of an electromagnetic cascade (Beduarek 1997. 2000. 2006: Aharonian ct al.," The $\gamma$ -ray absorption and production mechanisms can proceed very fast, resulting in the development of an electromagnetic cascade (Bednarek 1997, 2000, 2006; Aharonian et al."
 2006)., 2006).
 As a result. the enerev of the original photous is distributed between a certain nunboer of secondary particles aud plotous with lower energy.," As a result, the energy of the original photons is distributed between a certain number of secondary particles and photons with lower energy."
 We computed the 5-rav spectra formed in cascades traversing the anisotropic stellar radiation field., We computed the $\gamma$ -ray spectra formed in cascades traversing the anisotropic stellar radiation field.
 Other radiative fields (like the accretion disk field) are less iuportaut in the present context., Other radiative fields (like the accretion disk field) are less important in the present context.
 We implemented a Alonte Carlo simulation code based ou the scheme outlined bv Protheroe (1986) aud Protheroe et al. (, We implemented a Monte Carlo simulation code based on the scheme outlined by Protheroe (1986) and Protheroe et al. (
1992).,1992).
 A description of the treatiuent is given in Orellana ct al. (, A description of the treatment is given in Orellana et al. (
2006).,2006).
"either ungrown or ejected, or where the galaxy never hosted a SMBH in the first place.","either ungrown or ejected, or where the galaxy never hosted a SMBH in the first place."
 We note that the effect of gravitational recoil (ejections) is strongest at intermediate galaxy masses., We note that the effect of gravitational recoil (ejections) is strongest at intermediate galaxy masses.
 This is because low-mass galaxies have few mergers while high-mass galaxies have large escape velocities., This is because low-mass galaxies have few mergers while high-mass galaxies have large escape velocities.
" Since low-mass galaxies have a small number of major mergers, or they have no SMBH, even if the ejection probability — based on the comparison between the escape and recoil velocities — is close to100%,, if a galaxy has no major merger at all, then the ejection probability convolved with the merger probability is zero."," Since low-mass galaxies have a small number of major mergers, or they have no SMBH, even if the ejection probability – based on the comparison between the escape and recoil velocities – is close to, if a galaxy has no major merger at all, then the ejection probability convolved with the merger probability is zero."
 This analytical model therefore predicts the halo mass where the transition from healthy growth by major mergers) to unhealthy SMBHs (in the sense (triggeredthat their masses are not set by merger-driven accretion) occurs., This analytical model therefore predicts the halo mass where the transition from healthy growth (triggered by major mergers) to unhealthy SMBHs (in the sense that their masses are not set by merger-driven accretion) occurs.
" One can integrate Equation 5 at different redshifts to find where this transition occurs at early times, if desired."," One can integrate Equation 5 at different redshifts to find where this transition occurs at early times, if desired."
 The transition corresponds to the halo mass (or circular velocity) where the average number of major mergers drops below unity., The transition corresponds to the halo mass (or circular velocity) where the average number of major mergers drops below unity.
" In Figure 4 we present the Mgg—V. relation for 560 random galaxies in our Monte Carlo sample drawn out of the complete sample of 560,000) and (uniformlycompare it to the Mgg—V. of the 25 galaxies described in Section 2 (from Table 1 in KBC, augmented by the upper limit for M33)."," In Figure \ref{MCgrowth2} we present the $M_{\rm BH}-V_c$ relation for 560 random galaxies in our Monte Carlo sample (uniformly drawn out of the complete sample of 560,000) and compare it to the $M_{\rm BH}-V_c$ of the 25 galaxies described in Section 2 (from Table 1 in KBC, augmented by the upper limit for M33)."
 Here we assume that at every major merger a SMBH increases its mass by 10°M.(V./350kmx109? where A is normally distributed about 0 s-1)*with standard deviation 1 (see section 2 for details)., Here we assume that at every major merger a SMBH increases its mass by $10^8\ \msun (V_{\rm c}/350 \kms)^4\times 10^{0.5\Delta}$ where $\Delta$ is normally distributed about 0 with standard deviation 1 (see section 2 for details).
" These are *healthy"" SMBHs."," These are “healthy"" SMBHs."
" The mass of “ungrown” SMBHs is set to 300M,x1028-1, where R. is randomly distributed between 0 and 1. “"," The mass of “ungrown” SMBHs is set to $300\msun\times10^{2R-1}$, where R is randomly distributed between 0 and 1. “"
Bjected” SMBHs are arbitrarily set to Mpy=10Μα to demarcate the affected galaxies.,"Ejected"" SMBHs are arbitrarily set to $M_{\rm BH}=10\ \msun$ to demarcate the affected galaxies."
 The Monte Carlo sample clearly occupies the same area occupied by the real galaxies., The Monte Carlo sample clearly occupies the same area occupied by the real galaxies.
" Therefore, the deviations from the scaling relation at low masses today reflects the growth history of black holes that is driven principally by the dark matter halo mass."," Therefore, the deviations from the scaling relation at low masses today reflects the growth history of black holes that is driven principally by the dark matter halo mass."
" Analyzing the entire sample of galaxies where black hole mass, velocity dispersion σ and asymptotic circular velocity V. have all been measured, we obtain the best-fit power law relation between aand and find that the scatter and slope are very similar for both relations."," Analyzing the entire sample of galaxies where black hole mass, velocity dispersion $\sigma$ and asymptotic circular velocity $V_c$ have all been measured, we obtain the best-fit power law relation between and and find that the scatter and slope are very similar for both relations."
 This model-independent fit suggests that the correlation is just as strong (or just as weak) as the correlation between ggiven current sample sizes., This model-independent fit suggests that the correlation is just as strong (or just as weak) as the correlation between given current sample sizes.
" As noted by KB, the correlations worsen (or disappears) for σ and V. outside a 180-260 range."," As noted by KB, the correlations worsen (or disappears) for $\sigma$ and $V_c$ outside a 180-260 range."
first one. with pitch angles rotated by 90°.,"first one, with pitch angles rotated by $90^{\circ}$."
 For ιο0.6 this change in the direction of the polarisation vector (P?= 0) happens before the break-time measured. by an on-axis observer. while for smaller angles it happens slightly. after.," For $\theta_o/\theta_{jet} \gsim 0.6$ this change in the direction of the polarisation vector $P=0$ ) happens before the break-time measured by an on-axis observer, while for smaller angles it happens slightly after."
" The polarisation curve of orphan alterglows (8,/06;.,= 1) has two peaks. with the same position angle. that eventually merece in a single maximum."," The polarisation curve of orphan afterglows $\theta_o/\theta_{jet}\ge 1$ ) has two peaks, with the same position angle, that eventually merge in a single maximum."
" For a NSE jet the polarisation at the peak grows with 8,. tending towards Z4 (E "," For a NSE jet the polarisation at the peak grows with $\theta_{o}$, tending towards $P_{0}$ (Fig. \ref{fig:nse_po}) ),"
"while with sideways expansion the peak value reaches a maximun around 6TA; and then it slowly. decreases: in both cases the polarisation peak for an orphan afterglow can be a factor ~2.52.6 larger than what it is expected al A,=Bj."," while with sideways expansion the peak value reaches a maximum around $\theta_{o}\sim 7
\theta_{jet}$ and then it slowly decreases; in both cases the polarisation peak for an orphan afterglow can be a factor $\sim
2.5-2.6$ larger than what it is expected at $\theta_{o}=\theta_{jet}$."
" The polarisation curves for a NSE jet with 8,<6). have been previously published by €GL99. which did not consider EATS."," The polarisation curves for a NSE jet with $\theta_o<\theta_{jet}$ have been previously published by GL99, which did not consider EATS."
 Their curves have our very same temporal behaviour. but their polarisation peaks are lower than ours by a factor from 2 to 4. depending on the viewing angle.," Their curves have our very same temporal behaviour, but their polarisation peaks are lower than ours by a factor from 2 to 4, depending on the viewing angle."
 This is the result of adding EATS to the computation., This is the result of adding EATS to the computation.
 In this case the received intensity. at any given time. peaks at an angular distance L/L from the line of sight. just where the linear polarisation is maximised (see Eq. ," In this case the received intensity, at any given time, peaks at an angular distance $1/\Gamma$ from the line of sight, just where the linear polarisation is maximised (see Eq. \ref{eq:pteta},"
22.., Eq.
 Ίσα. 26 and Iq. 25))., \ref{eq:U} and Eq. \ref{eq:Q}) ).
 As à result. the total expected. polarisation is higher than for a homogeneously emitting surface.," As a result, the total expected polarisation is higher than for a homogeneously emitting surface."
 SOO and. Ciranot. Ixónnigl (2003) have instead explored the polarisation for à spreading jet., S99 and Granot Könnigl (2003) have instead explored the polarisation for a spreading jet.
 The first author uses a simplified model in which the opening angle does not change until i<6; and then 8; increases as L/P: às a consequence he expects a ird polarisation peak to appear at later times for large oll-axis angles. while for small viewing angles only one peak should. be visible.," The first author uses a simplified model in which the opening angle does not change until $\frac{1}{\Gamma}<\theta_{jet}$ and then $\theta_{jet}$ increases as $1/\Gamma$; as a consequence he expects a third polarisation peak to appear at later times for large off-axis angles, while for small viewing angles only one peak should be visible."
 With our complete calculation of the evolution of the opening angle of the jet we do not obtain either of these ellects (see Fig. 9))., With our complete calculation of the evolution of the opening angle of the jet we do not obtain either of these effects (see Fig. \ref{fig:se_po}) ).
 The reason is that the visible area (1/1) erosses both the nearest ancl the farthest edge of the jet for any oll-axis angle and then L/E remains alwavs greater than θε., The reason is that the visible area $1/\Gamma$ ) crosses both the nearest and the farthest edge of the jet for any off-axis angle and then $1/\Gamma$ remains always greater than $\theta_{jet}$.
 Vherefore for a LJ. afterglow polarisation curvesangles.. for all the sideways expansion models considered in this paper.," Therefore for a HJ, afterglow polarisation curves, for all the sideways expansion models considered in this paper."
 Ciranot ct al. (, Granot et al. (
2002) have extended the computation also to orphan alfterglows.,2002) have extended the computation also to orphan afterglows.
 They obtain These effects. are due to an error in their. program. pointed. out recently by the authors themselves: (see Granot Wonniel 2003).," They obtain These effects are due to an error in their program, pointed out recently by the authors themselves (see Granot Könnigl 2003)."
 The results of their corrected code are in general agreement with ours (Ciranot. private communication), The results of their corrected code are in general agreement with ours (Granot private communication).
 Polarisation due to synchrotron emission. 1s in. principle present at any wavelength., Polarisation due to synchrotron emission is in principle present at any wavelength.
 In Fig., In Fig.
" LO we show the light and polarisation curves for the same GIUD afterglow observed at afrequeney v, in three different spectral branches: 4.«ts< Vine VinXOo, anel p, . ∕∕⊓⊳⇂∩↓⋅⋜⋯∪∣⋡⋡∖⋖⋅↓⋅∖⇁⋖⋅↓⋅⋜⊔ fh—⋅0.6."," \ref{fig:xr} we show the light and polarisation curves for the same GRB afterglow observed at a frequency $\nu_o$ in three different spectral branches: $\nu_a<\nu_o<\nu_m$ , $\nu_m<\nu_o<\nu_c$ and $\nu_c<\nu_o$, for an observer at $\frac{\theta_o}{\theta_{jet}}=0.6$."
" In the following we refer to them as the ""radio"" branch.nm the ""optical branch and the N-ray branch respectively. since each waveband usually stavs on that particular branch for most of the afterglow evolution (depending on fireball aud shock parameters)."," In the following we refer to them as the “radio” branch, the “optical” branch and the $X$ -ray branch respectively, since each waveband usually stays on that particular branch for most of the afterglow evolution (depending on fireball and shock parameters)."
 Fie., Fig.
 10. shows that while the polarisation curves in the R anc X-ray bands are very similar. the radio curve has a significantly lower degree of polarisation.," \ref{fig:xr} shows that while the polarisation curves in the $R$ and X-ray bands are very similar, the radio curve has a significantly lower degree of polarisation."
 Disticnt [rom, Disticnt from
extraced source spectra usine circular regious centred ou the source position with radii of and ffor tre pn aud MOS cameras.respectively.,"extracted source spectra using circular regions centred on the source position with radii of and for the pn and MOS cameras,."
 Backeround spectra were extracted from nearby source-free regions of the feld with arods 1.5 tines 16 sonrce extrac‘tion region areas;, Background spectra were extracted from nearby source-free regions of the field with areas 1.5 times the source extraction region areas.