ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This case where entropy is a flux function is the natural one to consider when also plasma rotation would be incorporated., This case where entropy is a flux function is the natural one to consider when also plasma rotation would be incorporated.3 The equation for the density for all three cases can easily be derived by inserting the corresponding pressure equation into the equation for the momentum parallel to the poloidal magnetic field lines given in Eq., The equation for the density for all three cases can easily be derived by inserting the corresponding pressure equation into the equation for the momentum parallel to the poloidal magnetic field lines given in Eq.4"(9).. The resulting equation is Here, the flux function po corresponds to the density of a related static equilibrium without gravity."," The resulting equation is Here, the flux function $\rho_{0}$ corresponds to the density of a related static equilibrium without gravity."5" As we will adopt them for the actual stability analysis in our accompanying paper, we briefly discuss the 'straight field line’ coordinates."," As we will adopt them for the actual stability analysis in our accompanying paper, we briefly discuss the `straight field line' coordinates."6 These coordinates are an essential ingredient of an accurate stability analysis., These coordinates are an essential ingredient of an accurate stability analysis.7" For the conversion from the Cartesian (x,y,z) to straight field line coordinates (z!=φ,αξJ,a°z), one needs the metric tensor and the Jacobian associated with the non—orthogonal coordinates in which the equilibrium field lines appear to be straight."," For the conversion from the Cartesian $(x,y,z)$ to straight field line coordinates $(x^{1}\equiv\psi, x^{2}\equiv\vartheta, x^{3}\equiv z)$, one needs the metric tensor and the Jacobian associated with the non--orthogonal coordinates in which the equilibrium field lines appear to be straight."8 Such a transformation is standard practice in MHD stability studies for laboratory tokamak plasmas., Such a transformation is standard practice in MHD stability studies for laboratory tokamak plasmas.9 The metric elements gj; and the Jacobian J are respectively., The metric elements $g_{ij}$ and the Jacobian $J$ are respectively.10" Here, the poloidal angle ὁ is constructed such that the magnetic field lines are straight in the (9,z)— plane."," Here, the poloidal angle $\vartheta$ is constructed such that the magnetic field lines are straight in the $(\vartheta, z)$ --plane."11 The slope of these lines is a flux function where q is the safety factor., The slope of these lines is a flux function where $q$ is the safety factor.12" Comparing this expression with the one for tokamak plasmas (?),, one should realize that for tokamak plasmas the safety factor q is dimensionless, while here the factor q has a length dimension."," Comparing this expression with the one for tokamak plasmas \citep{Wesson_2004}, one should realize that for tokamak plasmas the safety factor $q$ is dimensionless, while here the factor $q$ has a length dimension."13" As for tokamak plasmas (???),, we introduce an expression for the poloidal curvature of the magnetic surfaces where the unit vectors n.=Vw/|Vy| and t=Bo/Bo, and By is the poloidal magnetic field."," As for tokamak plasmas \citep{Goedbloed_1975,vanderHolst_2000B,Blokland_2007B}, we introduce an expression for the poloidal curvature of the magnetic surfaces where the unit vectors $\vf{n} = \grad{\psi} / |\grad{\psi}|$ and $\vf{t} = \vf{B}_{\vartheta} / \Btheta$ , and $\Btheta$ is the poloidal magnetic field."14" The toroidal curvature & that is present in actual tokamak equilibria, is ofcourse zero for a translational symmetric equilibrium."," The toroidal curvature $\kt$ that is present in actual tokamak equilibria, is ofcourse zero for a translational symmetric equilibrium."15" It is important to realize that the straight field coordinates can only be constructed when the solution v(x,y) has been computed from the extended Grad-Shafranov equation given in Eq."," It is important to realize that the straight field coordinates can only be constructed when the solution $\psi(x,y)$ has been computed from the extended Grad-Shafranov equation given in Eq."16"(10).. In the previous section, we derived equations for the prominence equilibrium."," In the previous section, we derived equations for the prominence equilibrium."17" In this section, we quantify the effect of gravity by means of a small gravity expansion."," In this section, we quantify the effect of gravity by means of a small gravity expansion."18" We will demonstrate in our companion paper that gaps will appear in the continuous MHD spectrum because of mode coupling, which is the result of the presence of gravity."," We will demonstrate in our companion paper that gaps will appear in the continuous MHD spectrum because of mode coupling, which is the result of the presence of gravity."19" This kind of expansion is similar to thesmall inverse aspect ratio e=a/Ro expansion for tokamak plasmas, where a and Ro are the minor radius of the plasma and the geometry axis of the tokamak, respectively (?).."," This kind of expansion is similar to thesmall inverse aspect ratio $\epsilon = a/R_{0}$ expansion for tokamak plasmas, where $a$ and $R_{0}$ are the minor radius of the plasma and the geometry axis of the tokamak, respectively \citep{Shafranov_1958}."20" Mathematically, both expansions, small gravity expansion and the small inverse aspect ratio expansion, are Taylor expansions."," Mathematically, both expansions, small gravity expansion and the small inverse aspect ratio expansion, are Taylor expansions."21" In the remaining part of this paper, we assume the following gravitational potential in which the prominence is embedded where zo is the location of the center of the last closed flux surface of the prominence and the gravity is represented by the constant g."," In the remaining part of this paper, we assume the following gravitational potential in which the prominence is embedded where $x_{0}$ is the location of the center of the last closed flux surface of the prominence and the gravity is represented by the constant $g$."22 The solarprominence equilibrium is expanded assuming that the gravity is small and that the outer flux surface is circular., The solarprominence equilibrium is expanded assuming that the gravity is small and that the outer flux surface is circular.23" Using these approximations, the flux surfaces can be represented by slightly displaced circles (?)), which allows for the exploitation of non-orthogonal polar coordinates (r,0,2), where r and 0 are the radius and the polar angle, respectively."," Using these approximations, the flux surfaces can be represented by slightly displaced circles \cite{Shafranov_1958}) ), which allows for the exploitation of non-orthogonal polar coordinates $(r,\theta,z)$, where $r$ and $\theta$ are the radius and the polar angle, respectively."24" Up to first order, we approximate where A(r) is the Shafranov shift (?)), which is expected to be in the downwards direction and caused by the gravity."," Up to first order, we approximate where $\Delta(r)$ is the Shafranov shift \cite{Shafranov_1958}) ), which is expected to be in the downwards direction and caused by the gravity."25" As mentioned before, these polar coordinates are non-orthogonal and the associated metric elements are which means that the Jacobian J=r[1—A’ cos(0)]."," As mentioned before, these polar coordinates are non-orthogonal and the associated metric elements are which means that the Jacobian $J \approx r [ 1 - \Delta' \cos(\theta) ]$ ."26" Using the polar coordinates and expanding the extended Grad-Shafranov equation given in Eqs. (12),, (14),,"," Using the polar coordinates and expanding the extended Grad-Shafranov equation given in Eqs. , ,"27 and up to first order leads to, and up to first order leads to28between regions of overlap in separate frames. and the images were averaged.,"between regions of overlap in separate frames, and the images were averaged."29 At this stage. the separate sets were averaged together to produce the final image.," At this stage, the separate sets were averaged together to produce the final image."30 The secing was measured from stars in the individual exposures to be in the range L.2aaresec EWIIM. (about 4 pixels) and the registration uncertainties did not cause the ENIM of stars in the final coacdcded images to increase by à measurable amount., The seeing was measured from stars in the individual exposures to be in the range arcsec FWHM (about 4 pixels) and the registration uncertainties did not cause the FWHM of stars in the final coadded images to increase by a measurable amount.31 Images of photometric standard stars were. taken hroughout the course of each night., Images of photometric standard stars were taken throughout the course of each night.32 One standard. star was imaged five times in cach filter for each radio galaxy., One standard star was imaged five times in each filter for each radio galaxy.33 Alultiple coadds were used. both to improve the signal-O-noise ratio. and to ensure that each observation had a similar exposure time to the individual radio galaxy observations.," Multiple coadds were used both to improve the signal-to-noise ratio, and to ensure that each observation had a similar exposure time to the individual radio galaxy observations."34 In this wav. the point spread function (PSE) of he standard star would sample the same longer-term seeing variations as the galaxy images.," In this way, the point spread function (PSF) of the standard star would sample the same longer-term seeing variations as the galaxy images."35 Flux calibration solutions were determined: separately for cach night of observation. with the dedispersion for cach night typically being aJ and A and at L' and AL.," Flux calibration solutions were determined separately for each night of observation, with the dispersion for each night typically being at $J$ and $K$ and at $L'$ and $M$."36 Aperture photometry from our images agrees with that of Lilly Longair (1984) and Lilly. Longair Miller (1985a) to within the quoted uncertainties.," Aperture photometry from our images agrees with that of Lilly Longair (1984) and Lilly, Longair Miller (1985a) to within the quoted uncertainties."37 In Table 2 we list the photometry measured in a 3-arcsec aperture. which is more appropriate for detecting red nuclear sources.," In Table \ref{tab:phot} we list the photometry measured in a 3-arcsec aperture, which is more appropriate for detecting red nuclear sources."38 Thermal emission from the telescope is very strong longware of jum. resulting in à vastly increased. background and a large drop in sensitivity.," Thermal emission from the telescope is very strong longward of $\mu$ m, resulting in a vastly increased background and a large drop in sensitivity."39 Lo addition. the strength. of the quasar nucleus relative to the host galaxy Increases. with wavelength. due to its red. colour.," In addition, the strength of the quasar nucleus relative to the host galaxy increases with wavelength due to its red colour."40 We therefore. undertake different’ analyses for the short. C/A) and. long (LA) wavelength data., We therefore undertake different analyses for the short ) and long ) wavelength data.41 In ow J and A images. the host galaxies are well-detected out to. large. radii ancl are likely to. dominate over the nuclei. even in fairly small apertures.," In our $J$ and $K$ images, the host galaxies are well-detected out to large radii and are likely to dominate over the nuclei, even in fairly small apertures."42 Methods which attempt to estimate the [lux of a nuclear source bv using aperture photometry to correct. small aperture measurcments for starlight are prone to overestimate the strength of the source (Simpson LOOLh) and it is necessary (ο model the galaxy in order to obtain a reliable measurement., Methods which attempt to estimate the flux of a nuclear source by using aperture photometry to correct small aperture measurements for starlight are prone to overestimate the strength of the source (Simpson 1994b) and it is necessary to model the galaxy in order to obtain a reliable measurement.43 At longer wavelengths. the host galaxy is not detected with &reat significance due to the bright thermal background. and simpler methods can be emploved.," At longer wavelengths, the host galaxy is not detected with great significance due to the bright thermal background, and simpler methods can be employed."44 To enable the most direct comparison possible of our results with those of T96. we have used an almost identical analysis technique on our data.," To enable the most direct comparison possible of our results with those of T96, we have used an almost identical analysis technique on our data."45 We refer the reader to that paper fora more detailed description of the method. and for a discussion of its advantages over the more common (and simpler) one-dimensional analysis SSimpson et 11995).," We refer the reader to that paper for a more detailed description of the method, and for a discussion of its advantages over the more common (and simpler) one-dimensional analysis Simpson et 1995)."46 The two-cimensional approach involves constructing a model image derived from fitting parameters and comparing this with the actual data. using an error frame to allow a quantitative 47 minimization.," The two-dimensional approach involves constructing a model image derived from fitting parameters and comparing this with the actual data, using an error frame to allow a quantitative $\chi^2$ minimization."47 The assumed model was an elliptical. galaxy obeving a de Vaucouleurs law (de Vaucouleurs 1948) and an unresolved nuclear source., The assumed model was an elliptical galaxy obeying a de Vaucouleurs law (de Vaucouleurs 1948) and an unresolved nuclear source.48 There are live parameters used to Construct the model: The pixel location of the centre of the galaxy. Gros). was determined using iterative centroiding. and construction of the model galaxy proceeded as follows.," There are five parameters used to construct the model: The pixel location of the centre of the galaxy, $x_{\rm c}$ $y_{\rm49c}$ ), was determined using iterative centroiding, and construction of the model galaxy proceeded as follows."50 Each pixel in the image was divided into 400 subpixels. and the flux in each of these subpixels was computed. based on the parameters of the galaxy model.," Each pixel in the image was divided into 400 subpixels, and the flux in each of these subpixels was computed based on the parameters of the galaxy model."51 This amount of subpixellation ensures that the flux in the central pixel is never uncerestimated, This amount of subpixellation ensures that the flux in the central pixel is never underestimated52"The local star formation rate volume density pg in a cell is calculated as where py, is the local mass density of molecular hydrogen.",The local star formation rate volume density $\dot{\rho}_\mathrm{S}$ in a cell is calculated as where $\rho_\mathrm{H_2}$ is the local mass density of molecular hydrogen.53" The star formation time scale is given by where rg=(32Gpa/37)- is the free-fall time, and pa the local gas density (including!/? all hydrogen and helium "," The star formation time scale is given by where $\tau_\mathrm{ff} = (32 G \rho_\mathrm{G} / 3\pi)^{-1/2}$ is the free-fall time, and $\rho_\mathrm{G}$ the local gas density (including all hydrogen and helium species)."54"The maximum timescale Tmax is set to the free-fall species).time of gas with a hydrogen number density of ng=4-nga2ng,50cm?."," The maximum timescale $\tau_\mathrm{max}$ is set to the free-fall time of gas with a hydrogen number density of $n_\mathrm{H} = n_\mathrm{H\,\textsc{i}}+n_\mathrm{H\,\textsc{ii}}+2 n_\mathrm{H_2} = 50 ~\mathrm{cm}^{-3}$."55 The star formation efficiency per local free-fall time is set to eg=0.007., The star formation efficiency per local free-fall time is set to $\epsilon_\mathrm{ff} = 0.007$.56" To ensure that star formation happens only in our numerical analogs of real molecular clouds, we allow star formation only in cells with the molecular mass fraction above fu,=2ng,/ng0.1."," To ensure that star formation happens only in our numerical analogs of real molecular clouds, we allow star formation only in cells with the molecular mass fraction above $f_\mathrm{H_2} = 2 n_\mathrm{H_2}/n_\mathrm{H} = 0.1$."57" These cells have a range of total gas density from 50 to 104 amu cm""? for the main halo at z=3 (Figure 1)).", These cells have a range of total gas density from 50 to $10^4$ amu $^{-3}$ for the main halo at $z \approx 3$ (Figure \ref{fig:disc}) ).58 Stellar particles are created via a Poisson process with a characteristic timescale of 2x107 yr., Stellar particles are created via a Poisson process with a characteristic timescale of $2 \times 10^{7}$ yr.59 This star formation prescription is similar to the recipe SF2 in ?.. , This star formation prescription is similar to the recipe SF2 in \cite{2009ApJ...697...55G}. .60"Figure shows the disc of the most massive galaxy in our simulation1 at z73, which we call the main halo."," Figure \ref{fig:disc} shows the disc of the most massive galaxy in our simulation at $z \approx 3$, which we call the main halo."61 The molecular hydrogen forms only in high density regions and hence the stars are confined to these central regions., The molecular hydrogen forms only in high density regions and hence the stars are confined to these central regions.62" In traditional star formation prescriptions based on the total gas density instead of the molecular hydrogen density, stars would be formed over a much larger volume filled with the lower-density atomic gas."," In traditional star formation prescriptions based on the total gas density instead of the molecular hydrogen density, stars would be formed over a much larger volume filled with the lower-density atomic gas."63" We ran three versions of the simulation, which are summarized in Table 1.."," We ran three versions of the simulation, which are summarized in Table \ref{tab:simulationsummary}."64 Simulation A is a full physics run with radiative transfer and non-equilibrium cooling., Simulation A is a full physics run with radiative transfer and non-equilibrium cooling.65 Simulation Anp is the same as simulation A but without supernova thermal feedback., Simulation $_\mathrm{NF}$ is the same as simulation A but without supernova thermal feedback.66 Metal enrichment due to supernovae is still included., Metal enrichment due to supernovae is still included.67 Simulation B is a non-radiative version without cooling and star formation., Simulation B is a non-radiative version without cooling and star formation.68" In all simulations, the top level |—0 grid is 256? and we allow for up to 9 more refinement levels =9) where each higher level is refined by a factor(Imax 2 with respect to the parent level."," In all simulations, the top level $l=0$ grid is $256^3$ and we allow for up to 9 more refinement levels $l_\mathrm{max}=9$ ) where each higher level is refined by a factor 2 with respect to the parent level."69 This results in a size of the smallest cells Lo=-279pe , This results in a size of the smallest cells $L_9 = L_\mathrm{box}/(256 \cdot 2^9) = 279 ~\mathrm{pc}$ (comoving).70"A cell is refined if itsLyox/ dark(256 matter2°) or gas mass(comoving). exceeded 1.07109Mo or 1.3310?Mo, respectively."," A cell is refined if its dark matter or gas mass exceeded $1.07 \times 10^{6} ~\Mo$ or $1.33 \times 10^{5} ~\Mo$, respectively."71" For the dark matter, this threshold corresponds to the mass of about 6 high resolution particles."," For the dark matter, this threshold corresponds to the mass of about 6 high resolution particles."72" On each refinement level {, the time step is refined as well according to Av;=Avo/2"", where Avy is the global time step on the top level mesh."," On each refinement level $l$, the time step is refined as well according to $\Delta \nu_l = \Delta \nu_0 / 2^l$, where $\Delta \nu_0$ is the global time step on the top level mesh."73 The value of Avg is set at the beginning of each top level step so that the Courant-Friedrichs-Lewy condition is fulfilled on all levels (?)..," The value of $\Delta \nu_0$ is set at the beginning of each top level step so that the Courant-Friedrichs-Lewy condition \citep{1928MatAn.100...32C,1967IBMJ...11..215C} is fulfilled on all levels \citep{2002ApJ...571..563K}."74 In total our simulation (??)A contains 2.89x105 dark matter particles and 3.89x108 gas cells at z=2., In total our simulation A contains $2.89 \times 10^8$ dark matter particles and $3.89 \times 10^8$ gas cells at $z \approx 2$.75" For the analysis presented in this paper, we mainly concentrate on three snapshots at redshifts around 4, 3, and 2 exact redshifts are 3.76, 2.85, and 2.03) in run A. These (theepochs correspond to 1.69 Gyr, 2.32 Gyr, and 3.29 Gyr after the Big Bang in our cosmology."," For the analysis presented in this paper, we mainly concentrate on three snapshots at redshifts around 4, 3, and 2 (the exact redshifts are 3.76, 2.85, and 2.03) in run A. These epochs correspond to 1.69 Gyr, 2.32 Gyr, and 3.29 Gyr after the Big Bang in our cosmology."76 T'he output redshifts for different runs match to within Az—0.005., The output redshifts for different runs match to within $\Delta z = 0.005$.77 Simulation Awp at full resolution was stopped at z=2.77 to save computing time., Simulation $_\mathrm{NF}$ at full resolution was stopped at $z = 2.77$ to save computing time.78 We ran also a lower-resolution version of Anr with the 8 times more massive dark matter particles but otherwise the same gas physics and parameters., We ran also a lower-resolution version of $_\mathrm{NF}$ with the 8 times more massive dark matter particles but otherwise the same gas physics and parameters.79 We use the z&2 snapshot from this version in our analysis., We use the $z \approx 2$ snapshot from this version in our analysis.80" In all snapshots we ran avariant of the Bound Density Maxima halo finder (?) and selected all massive objects with Mago,>10!!Mo in the high resolution region of run A. We then matched simulation A with the other"," In all snapshots we ran avariant of the Bound Density Maxima halo finder \citep{2004ApJ...609..482K} and selected all massive objects with $M_\mathrm{200b} \geq 10^{11}\, \Mo$ in the high resolution region of run A. We then matched simulation A with the other"81freely available software SExtractor (Bertin&Arnouts 1996)..,freely available software SExtractor \citep{1996A&AS..117..393B}.82 Although SEsxtractor was developed for the analysis ofoptical data. several authors (Bondietal.2003:Garnct2008a.b:ναetal.2007). have shown that it is able to generate reliable noise maps and locate objects within racio images.," Although SExtractor was developed for the analysis of optical data, several authors \citep{2003A&A...403..857B,2008MNRAS.383...75G,2008MNRAS.387.1037G,2007AJ....133.1331H} have shown that it is able to generate reliable noise maps and locate objects within radio images."83 It should be noted that SExtractor is highly sensitive to input. parameters and there is no single output. catalogue that will be suitable for all applications., It should be noted that SExtractor is highly sensitive to input parameters and there is no single output catalogue that will be suitable for all applications.84 We make two radio catalogues., We make two radio catalogues.85" Firstly we ereate a more conservative ""gold set based on the catalogue of Biges&Lvi- (2006)..", Firstly we create a more conservative `gold' set based on the catalogue of \citet{2006MNRAS.371..963B}.86" ""Phat work used the 10’.10 VLA pointing alone with an independent reduction. detecting objects at Se in the VLA image alone."," That work used the $10^{\prime}\times10^{\prime}$ VLA pointing alone with an independent reduction, detecting objects at $5\sigma$ in the VLA image alone."87 The catalogue contains 537 sources. SA of which are contained within the co-acedecd images we use here: the others are either outside the field or resolved away by the much higher. MEBRLLIN resolution.," Their catalogue contains 537 sources, 83 of which are contained within the co-added images we use here; the others are either outside the field or resolved away by the much higher MERLIN resolution."88 We used SIxtractor in mode to produce an output catalogue of these sources., We used SExtractor in mode to produce an output catalogue of these sources.89 In order to produce a Larger. fainter catalogue we use Slxtractor in the standard mode to detect islands of (ux above a given threshold.," In order to produce a larger, fainter catalogue we use SExtractor in the standard mode to detect islands of flux above a given threshold."90 This requires a reliable noise map. which is made by estimating the local background noise at each mesh point of grid across the image (Bertin&Arnouts 1996)..," This requires a reliable noise map, which is made by estimating the local background noise at each mesh point of a grid across the image \citep{1996A&AS..117..393B}."91 The mesh asize is an important input parameter: if chosen to be too small the background. estimation is allected: by the presence of real objects: if chosen to be too large the small scale variations in the background cannot be reproduced., The mesh size is an important input parameter; if chosen to be too small the background estimation is affected by the presence of real objects; if chosen to be too large the small scale variations in the background cannot be reproduced.92 We adopt a size of 32 pixels. which corresponds to a2” scale.," We adopt a size of 32 pixels, which corresponds to a scale."93 We find 3.454]y I rms noise in the resulting map. in close agreement with Muxlowetal. (2005)..," We find $\mu$ Jy $^{-1}$ rms noise in the resulting map, in close agreement with \citet{2005MNRAS.358.1159M}."94 Using this noise map. sources with a total flux ereater than I05j-]y. (730) were extracted.," Using this noise map, sources with a total flux greater than $\mu$ Jy $(\sim\!\!3\sigma)$ were extracted."95" This catalogue contains GOL objects and we refer to as the ""silver. set. of objects.", This catalogue contains 691 objects and we refer to as the `silver' set of objects.96 The optical data we use. forms part of the Great Observatories Origins Deep Survey (GOODS) based on multiband LIST imaging of the WDE and €DE., The optical data we use forms part of the Great Observatories Origins Deep Survey (GOODS) based on multiband HST imaging of the HDF and CDF.97 The HLDE-N has been imaged in the ACS E435W. FGOGW. FSI4W and FSSOLP bands (D.V./andz respectively) although for the purposes of this work we make use of only the z-band image and catalogue.," The HDF-N has been imaged in the ACS F435W, F606W, F814W and F850LP bands $B, V, i \mbox{ and } z$ respectively) although for the purposes of this work we make use of only the $z$ -band image and catalogue."98 The 2 band images were observed in 5 epochs separated by 40-50 davs., The $z-$ band images were observed in 5 epochs separated by 40-50 days.99 In the odd numbered epochs each 10;G ⋅∕⋅fick was tileck: with. a grid. of ⋅⋅3ο individua⋠⋠⋠ ACS pointings., In the odd numbered epochs each $10\arcmin\times16\arcmin$ field was tiled with a grid of $3\times5$ individual ACS pointings.100 In the even numbered epochs the field was rotated by 45° ancl tiled with 16 separate. pointings., In the even numbered epochs the field was rotated by $45^{\circ}$ and tiled with 16 separate pointings.101 The band image exposure time was typically 2100s. civicdec into 4 exposures to ensure good cosmic ray rejection., The $z-$ band image exposure time was typically 2100s divided into 4 exposures to ensure good cosmic ray rejection.102 In each exposure the telescope field of view was shifted by à smal amount to allow optimal sampling of the PSE., In each exposure the telescope field of view was shifted by a small amount to allow optimal sampling of the PSF.103 The multiple epochs were then combined into a single mosaic., The multiple epochs were then combined into a single mosaic.104 The observations and image reduction are described in detail in Giavaliseoctal.(2004)..., The observations and image reduction are described in detail in \citet{2004ApJ...600L..93G}.105 We use the publicly. available 5Extractor configuration files (specified. for each band a /archive.stsci.edu/pub/hlsp/goods/catalog. r2/) το make our catalogues: these configuration [iles have been line tuned to minimise the number of false detections., We use the publicly available SExtractor configuration files (specified for each band at $\mbox{catalog}_{-}$ r2/) to make our catalogues; these configuration files have been fine tuned to minimise the number of false detections.106 In this section we describe the methods. used. to make estimators of the shear for all of our radio ancl optical SOULCOS., In this section we describe the methods used to make estimators of the shear for all of our radio and optical sources.107 Lere we summarize the shapelets method which is described more fully in ltefregier(20032)... Relreeier&Bacon(2003) and Massey&Itefregier(2005)...," Here we summarize the shapelets method which is described more fully in \citet{2003MNRAS.338...35R}, , \citet{2003MNRAS.338...48R} and \citet{2005MNRAS.363..197M}. ."108" In this approach. in the Cartesian formalism. the surface brightness f(x) of a galaxy is decomposed into a series of localisecl orthonormal basis functions D,ss called shapelets: where and where ££5,6]) is the Hermite polvnomial of order m. with the characteristic scale of the basis described. by 3."," In this approach, in the Cartesian formalism, the surface brightness $f(\mathbf{x})$ of a galaxy is decomposed into a series of localised orthonormal basis functions $B_{n_{1},n_{2}}$ called shapelets: where and where $H_{m}(\eta)$ is the Hermite polynomial of order $m$, with the characteristic scale of the basis described by $\beta$ ."109 Phe series converges most quickly if the characteristic scale 3 ds chosen to be similar to the size of the galaxy. and the centroid of the object is located: accurately.," The series converges most quickly if the characteristic scale $\beta$ is chosen to be similar to the size of the galaxy, and the centroid of the object is located accurately."110 The sum of ny ancl mo is referred to as the order of the basis functions., The sum of $n_{1}$ and $n_{2}$ is referred to as the order of the basis functions.111 In practice any decomposition has to be truncated at some order my such that the decomposition vields a sullicienthy accurate model of the galaxy. while also being computationally ellicient. as the computation time of each object's. decompositione Is. AXuias1," In practice any decomposition has to be truncated at some order $n_{\rm max}$ such that the decomposition yields a sufficiently accurate model of the galaxy while also being computationally efficient, as the computation time of each object's decomposition is $\propto n_{\rm max}^4$."112 From orthonormality. we can find shapelet coellicients for à galaxy by. calculating We use the publicly available shapelets software described in Massev&Relregier(2005) in order to make shapelet decompositionsfor all our objects.," From orthonormality, we can find shapelet coefficients for a galaxy by calculating We use the publicly available shapelets software described in \citet{2005MNRAS.363..197M} in order to make shapelet decompositionsfor all our objects."113 This code is well tested using optical data (c., This code is well tested using optical data (c.f.114 Llevmansctal.2006 ancl Masseyetal. 2007)). ancl we seek to extend its applicability to radio data here.," \citealp{2006MNRAS.368.1323H} and \citealp{2007MNRAS.376...13M}) ), and we seek to extend its applicability to radio data here."115 The code usually fits convolved shapelet cocllicicnts to a galaxy while also optimizing centroid x. 2 and mas using a non-linear algorithm.," The code usually fits convolved shapelet coefficients to a galaxy while also optimizing centroid $\mathbf{x}_{c}$, $\beta$ and $n_{\rm max}$ using a non-linear algorithm."116 For the radio objects we found that us led to a large number of failures. due to the incorrect stimation of 3 or the centroid wandering olf the edge of 106 postage stamp: in order to stabilise the behaviour. we ix the centroid. position X. to the SExtractor detection 'entroid.," For the radio objects we found that this led to a large number of failures, due to the incorrect estimation of $\beta$ or the centroid wandering off the edge of the postage stamp; in order to stabilise the behaviour, we fix the centroid position $\mathbf{x}_{c}$ to the SExtractor detection centroid."117 We also have the freedom to fix 3 to 0.4 times 1ο SExtractor ENIM. which we findconsistentlyleads to models with reasonablylow max., We also have the freedom to fix $\beta$ to 0.4 times the SExtractor FWHM which we findconsistentlyleads to models with reasonablylow $n_{\max}$ .118 Figure | shows some of 1 radio objects and their resulting shapelet models (still convolved with the beam), Figure \ref{fig:shapeletsexamples} shows some of the radio objects and their resulting shapelet models (still convolved with the beam).119 ‘To deconvolve the beam/PSE from the radio/optical data.," To deconvolve the beam/PSF from the radio/optical data,"120"SuperWASP-N lightcurve, which comprises 3969 data points obtained over a 118 day period.","SuperWASP-N lightcurve, which comprises 3969 data points obtained over a 118 day period."121 In the original SuperWASP-N photometry 17 transits were observed with >50% of a transit observed on 10 ocassions., In the original SuperWASP-N photometry 17 transits were observed with $>$ of a transit observed on 10 ocassions.122" These data led to an ephemeris of 75,—2453139.1748 and P=1.846800 which was used to arrange followup observations.", These data led to an ephemeris of $T_o$ =2453139.1748 and $P$ =1.846800 which was used to arrange followup observations.123 The transit here has a depth of 0.013 mag., The transit here has a depth of 0.013 mag.124 and is 137 minutes in duration., and is 137 minutes in duration.125 WASP-3 was observed with the ccm telescope as part of the Canarian Observatories’ for 2007., WASP-3 was observed with the cm telescope as part of the Canarian Observatories' for 2007.126 The imaging camera on this telescope has an e2v Technology PLC CCD of 2148x pixels giving a scale of 0.33 arcseconds/pixel and a total field of view of 10.6 arcminutes., The imaging camera on this telescope has an e2v Technology PLC CCD of $2148 \times 2148$ pixels giving a scale of 0.33 arcseconds/pixel and a total field of view of 10.6 arcminutes.127" Observations were taken during the transit of 2007 August 4, and consist of 327 images of 30and 20 seconds integration in the V and J bands respectively."," Observations were taken during the transit of 2007 August 4, and consist of 327 images of 30and 20 seconds integration in the $V$ and $I$ bands respectively."128" This night was photometric but suffered from significant Saharan dust extinction, estimated to be ~ 0.4mmag on La Palma from the SuperWASP-N real-time pipeline."," This night was photometric but suffered from significant Saharan dust extinction, estimated to be $\sim 0.4$ mag on La Palma from the SuperWASP-N real-time pipeline."129 The images were bias subtracted with a stacked bias frame and flat-fielded with a stacked twilight flat field image obtained in both filters using individual flats gathered over the course of the run., The images were bias subtracted with a stacked bias frame and flat-fielded with a stacked twilight flat field image obtained in both filters using individual flats gathered over the course of the run.130" After the instrumental signatures were removed, source detection and aperture photometry were performed on all science frames using the CASU catalogue extraction software "," After the instrumental signatures were removed, source detection and aperture photometry were performed on all science frames using the CASU catalogue extraction software \citep{il2001}."131"We chose an aperture size matched to the typical seeing (5 pixels, 1.5"") and selected 5 non-variable comparison stars in the field of WASP-3 to use in deriving the differential photometry."," We chose an aperture size matched to the typical seeing (5 pixels, $^{\prime\prime}$ ) and selected 5 non-variable comparison stars in the field of WASP-3 to use in deriving the differential photometry."132" For each exposure, we summed the fluxes of the 5 comparison stars and divided by the flux of the target star to derive the differential magnitude of the target."," For each exposure, we summed the fluxes of the 5 comparison stars and divided by the flux of the target star to derive the differential magnitude of the target."133 The resulting V and I band lightcurves (Figure[I)) of WASP-3 have a precision of ~ 4millimag., The resulting $V$ and $I$ band lightcurves (Figure \ref{fig:lc}) ) of WASP-3 have a precision of $\sim 4$ millimag.134 Further observations of WASP-3 were made with the Keele University Observatory 60cm Thornton Reflector on 2007 September 10., Further observations of WASP-3 were made with the Keele University Observatory 60cm Thornton Reflector on 2007 September 10.135" This telescope is equipped with a T65 x 510 pixel Santa Barbara InstrumentGroup (SBIG) ST7 CCD at the f/4.5 Newtonian focus, giving a 0.68 arcsecond/pixel resolution and a 8.63x 5.75 arcminute field of view."," This telescope is equipped with a 765 $\times$ 510 pixel Santa Barbara InstrumentGroup (SBIG) ST7 CCD at the f/4.5 Newtonian focus, giving a 0.68 arcsecond/pixel resolution and a $\times$ 5.75 arcminute field of view."136 During most of the period the weather was photometric except post egress where some cloud appeared., During most of the period the weather was photometric except post egress where some cloud appeared.137 Altogether 644x20 sec observations in the R band were obtained., Altogether $\times$ 20 sec observations in the $R$ band were obtained.138" After applying corrections for bias, dark current and flat fielding in the usual way, aperture photometry on two comparisons were performed using the commercial software AIPAWin "," After applying corrections for bias, dark current and flat fielding in the usual way, aperture photometry on two comparisons were performed using the commercial software AIP4Win \citep{berry2005}."139Tracking errors and spurious ∙∙electronic noise mean that systematic noise is introduced into the system at an estimated level of 2 millimag with periodicities of 2 and ~20 minutes., Tracking errors and spurious electronic noise mean that systematic noise is introduced into the system at an estimated level of 2 millimag with periodicities of 2 and $\sim$ 20 minutes.140 No corrections have been applied for this effect., No corrections have been applied for this effect.141" WASP-3 was observed with the Observatoire de Haute-Provence's mm telescope and the SOPHIE spectrograph (Bouchyetal]2006),, over the 8 nights 2007 July 2 5 and August 27 — 30; a total of 7 usable spectra were acquired."," WASP-3 was observed with the Observatoire de Haute-Provence's m telescope and the SOPHIE spectrograph \citep{b1}, over the 8 nights 2007 July 2 -- 5 and August 27 – 30; a total of 7 usable spectra were acquired."142 SOPHIE is an environmentally stabilized spectrograph designed to give long-term stability at the level of a few ss!., SOPHIE is an environmentally stabilized spectrograph designed to give long-term stability at the level of a few $^{-1}$.143" We used the instrument in its high efficiency mode, acquiring simultaneous star and sky spectra through separate fibres with a resolution of R=40000."," We used the instrument in its high efficiency mode, acquiring simultaneous star and sky spectra through separate fibres with a resolution of R=40000."144" Thorium-Argon calibration images were taken at the start and end of each night, and at 2- to 3-hourly intervals throughout the night."," Thorium-Argon calibration images were taken at the start and end of each night, and at 2- to 3-hourly intervals throughout the night."145" The radial-velocity drift never exceeded 2-3 m/s, even on a night-to-night basis."," The radial-velocity drift never exceeded 2-3 m/s, even on a night-to-night basis."146" Conditions during both runs varied from photometric to cloudy, but all nights were affected by strong moonlight."," Conditions during both runs varied from photometric to cloudy, but all nights were affected by strong moonlight."147" As WASP-3 has magnitude V~10.5, integrations of ssec give a peak signal-to-noise per resolution element of around 40-50."," As WASP-3 has magnitude $V\sim10.5$, integrations of sec give a peak signal-to-noise per resolution element of around 40-50."148" The 2MASS colours and reduced proper motion for WASP-3 suggest a spectral type of about F7-8V, hence we cross-correlated the spectra against a G2V template provided by the SOPHIE control and reduction software."," The 2MASS colours and reduced proper motion for WASP-3 suggest a spectral type of about F7-8V, hence we cross-correlated the spectra against a G2V template provided by the SOPHIE control and reduction software."149 In all spectra the cross-correlation functions (CCF) were contaminated by the strong moonlight., In all spectra the cross-correlation functions (CCF) were contaminated by the strong moonlight.150 We corrected them by using the CCF from the background lights spectrum (mostly the Moon) in the sky fibre., We corrected them by using the CCF from the background light's spectrum (mostly the Moon) in the sky fibre.151 We then scaled both CCFs using the difference of efficiency between the two fibres., We then scaled both CCFs using the difference of efficiency between the two fibres.152" Finally we subtracted the corresponding CCF of the background light from the star fibre, and fitted the resulting function by a Gaussian."," Finally we subtracted the corresponding CCF of the background light from the star fibre, and fitted the resulting function by a Gaussian."153" The parameters obtained allow us to compute the photon-noise uncertainty of the corrected radial velocity measurement (cv), using the relation detailed in (20072): Overall our RV measurements have an average photon-noise uncertainty of 14 m/s. As our radial velocity measurements are not photon-noise limited, we quadratically added a radial velocity component to those uncertainties of about 10 m/s (more details in Section 3.2.1)."," The parameters obtained allow us to compute the photon-noise uncertainty of the corrected radial velocity measurement $\sigma_{RV}$ ), using the relation detailed in \citet{c4}: Overall our RV measurements have an average photon-noise uncertainty of 14 m/s. As our radial velocity measurements are not photon-noise limited, we quadratically added a radial velocity component to those uncertainties of about 10 m/s (more details in Section 3.2.1)."154 The log of the observations and barycentric RV is given in Table 1., The log of the observations and barycentric RV is given in Table 1.155" The SOPHIE spectra are individually of modest signal-to-noise, but when summed together they are suitable for a preliminary photospheric analysis of WASP-3."," The SOPHIE spectra are individually of modest signal-to-noise, but when summed together they are suitable for a preliminary photospheric analysis of WASP-3."156" However, from experience we have found that the SOPHIE standard pipeline reduction does not fully remove the scattered light component within the spectrograph."," However, from experience we have found that the SOPHIE standard pipeline reduction does not fully remove the scattered light component within the spectrograph."157" While this does not affect radial velocities significantly, it can nonetheless have subtle effects on absorption line depths, adversely affecting the derived spectral synthesis parameters."," While this does not affect radial velocities significantly, it can nonetheless have subtle effects on absorption line depths, adversely affecting the derived spectral synthesis parameters."158 Therefore we carefully re-reduced the first three raw images taken over 2—5 July 2007 with the echelle data reduction package paying careful attention to the issue of scattered light.," Therefore we carefully re-reduced the first three raw images taken over 2--5 July 2007 with the echelle data reduction package \citep{pv2002}, paying careful attention to the issue of scattered light."159 ⊓These data are least affected by moonlight., These data are least affected by moonlight.160" Following our analysis of WASP-1 (Stempels 2007),, we employed the methodology of (2005).., using the same tools, techniques and model atmosphere grid."," Following our analysis of WASP-1 \citep{s2}, , we employed the methodology of \citet{v2}, , using the same tools, techniques and model atmosphere grid."161 We used the IDL-based software Easy (SME) 1996) to calculate and fit synthetic spectra using a multi-dimensional least squares approach., We used the -based software ) \citep{v1} to calculate and fit synthetic spectra using a multi-dimensional least squares approach.162sriehtest Cluster Galaxies (BCCis) include the most massive ealaxies in the Universe.,Brightest Cluster Galaxies (BCGs) include the most massive galaxies in the Universe.163 Models. of hierarchical structure formation naturally feature the ongoing growth of the most massive galaxies bv mergers (Peebles&Yu1970).. and BCCs are predicted to have undergone more mergers than loss massive galaxies (e.g. DeLucia&Dlaizot2007..," Models of hierarchical structure formation naturally feature the ongoing growth of the most massive galaxies by mergers \citep{peebles70}, and BCGs are predicted to have undergone more mergers than less massive galaxies (e.g. \citealt{delucia07}."164 Thus determining the merging history of BCCs is a particularly sensitive test of current formation models., Thus determining the merging history of BCGs is a particularly sensitive test of current formation models.165 As the analvtic models of Bowerctal.(2006):Crotonet(2006) show. massive galaxies are over-produced in. N-body. dark matter cosmological simulations. and [feedback mechanisms are required to bring the luminosity function into agreement with observations.," As the semi-analytic models of \cite{bower06,croton06} show, massive galaxies are over-produced in N-body dark matter cosmological simulations, and feedback mechanisms are required to bring the luminosity function into agreement with observations."166 Tracing the recent assembly history of BC's is vital to future development of galaxy formation models., Tracing the recent assembly history of BCGs is vital to future development of galaxy formation models.167 Observationally the evidence for X€ erowth is contraclictorv: Studies of the luminosities and stellar masses of BCCGs show little evolution in mass since z~115 (e.g. Broughetal.2002:Collins 2009)) and their steep metallicity gracicnts are consistent with passive evolution since 2— (Broughetal.2007).," Observationally the evidence for BCG growth is contradictory: Studies of the luminosities and stellar masses of BCGs show little evolution in mass since $z\sim1-1.5$ (e.g. \citealt{brough02, collins09}) ) and their steep metallicity gradients are consistent with passive evolution since $z\sim2$ \citep{brough07}."168. However. the large radii ancl low surface brightnesses of BCCs compared to normal elliptical galaxies are consistent with products. of major. dissipationless mergers (c.g. Ocgerle&Hoessel1991:Broughetal.2005:vonderLindenct2007:Lauer 2007)).," However, the large radii and low surface brightnesses of BCGs compared to normal elliptical galaxies are consistent with products of major, dissipationless mergers (e.g. \citealt{oegerle91,brough05, vDL07, lauer07}) )."169" Their sizes ancl velocity. dispersions may have also evolved faster than less-massive early-type galaxies since z0.3 (Bernardi2009 although. οἱ, Stottetal. 2011))."," Their sizes and velocity dispersions may have also evolved faster than less-massive early-type galaxies since $z\sim0.3$ \citealt{bernardi09} although, c.f. \citealt{stott11}) )."170 While BCGs are frequently observed to have multiple nuclei and close companions (c.g. Schneideretal. 1983)). there are only," While BCGs are frequently observed to have multiple nuclei and close companions (e.g. \citealt{schneider83}) ), there are only"171the accretion disk emission when the svnchrotron emission decreased (Abdoetal.2009b).,the accretion disk emission when the synchrotron emission decreased \citep{abd09b}.172. It is likely also the case in X-ray waveband (e.g.Foschinietal.2009a).. (hough it is elaimed that in most radio loud quasars the contribution from a hot disk corona to the observed N-ravs is jeglieible (in the hard. X-ray band >2 keV). except for the steep-spectrum soft. X-ray excess below 1 keV (e.g.. Brinkmann et al.," It is likely also the case in X-ray waveband \cite[e.g.][]{fos09a}, though it is claimed that in most radio loud quasars the contribution from a hot disk corona to the observed X-rays is negligible (in the hard X-ray band $>$ 2 keV), except for the steep-spectrum soft X-ray excess below 1 keV (e.g., Brinkmann et al."173 1997; Yuan el al., 1997; Yuan et al.174 2000)., 2000).175 Indeed. the integrated model including svnchrotron jet emission. disk-corona emission and inverse Compton emission [rom jet has been used to model SED of NLSIs. trom which the nature of radio loud NLS1s can be well studied (Abdoetal.2009a.b.c:Fosehini2009b).," Indeed, the integrated model including synchrotron jet emission, disk-corona emission and inverse Compton emission from jet has been used to model SED of NLS1s, from which the nature of radio loud NLS1s can be well studied \citep{abd09a,abd09b,abd09c,fos09b}."176. While it strongly confirms the presence of a relativistic jet in radio-loud NLSIs. the —rav detection is also important to study the jet properties bx modeling the SEDs. e.g. the jet power. from which the characteristic of radio-loud NLS1s can be explored.," While it strongly confirms the presence of a relativistic jet in radio-loud NLS1s, the $\gamma-$ ray detection is also important to study the jet properties by modeling the SEDs, e.g. the jet power, from which the characteristic of radio-loud NLS1s can be explored."177 Through the model fit including svuchrotron sell-Compton (5C). external Compton (EC). and accretion disk-corona in four gamuna-ray detected NLSIs. their jet powers are found in (he average range of blazars with (wo sources in (he region of quasars. and another (wo in the range of ivpical of BL Lac objects (Abdoοἱal.2009€).," Through the model fit including synchrotron self-Compton (SSC), external Compton (EC), and accretion disk-corona in four gamma-ray detected NLS1s, their jet powers are found in the average range of blazars with two sources in the region of quasars, and another two in the range of typical of BL Lac objects \citep{abd09c}."178. ILowever. the main differences with respect to blazars are in the black hole masses and accretion rates. as argued in Abdoetal.(2009€). with the former about. 1-2 orders of magnitude lower than the (vpical blazar masses. aud the later obviously higher than (hose of blazars.," However, the main differences with respect to blazars are in the black hole masses and accretion rates, as argued in \cite{abd09c}, with the former about 1-2 orders of magnitude lower than the typical blazar masses, and the later obviously higher than those of blazars."179 Moreover. blazars are usually hosted by elliplical galaxies. while it is likely to be spiral ones in raclio-loud NLSIs (e.g.Zhouetal. 2006).," Moreover, blazars are usually hosted by elliptical galaxies, while it is likely to be spiral ones in radio-loud NLS1s \cite[e.g.][]{zho06}."180. From these observational eviclences. Abdoetal.(20090). claimed. that racio-Ioud NLS1s may represent a third subset of 5—rav AGNs. besides blazars and radio galaxies.," From these observational evidences, \cite{abd09c} claimed that radio-loud NLS1s may represent a third subset of $\gamma-$ ray AGNs, besides blazars and radio galaxies."181 If this is (hie case. il remains unclear whether radio-oud NLS1s should follow the blazar sequence (e.g. RAS J1629024-4007 in Chis work).," If this is the case, it remains unclear whether radio-loud NLS1s should follow the blazar sequence (e.g. RXS J16290+4007 in this work)."182 This certainly needs Iurther investigations., This certainly needs further investigations.183 On the other hand. it is still not clear why racio-loud NLS1s host a relativistic jet. aud Low ib is formed.," On the other hand, it is still not clear why radio-loud NLS1s host a relativistic jet, and how it is formed."184 It can be even more complicated in terms of the fact that the host galaxies ol NLSIs is generally of spiral (wpe. which breaks the paradigm: associating relativistic jets with giant elliptical (e.g.Marscher2009).," It can be even more complicated in terms of the fact that the host galaxies of NLS1s is generally of spiral type, which breaks the paradigm associating relativistic jets with giant elliptical \cite[e.g.][]{mars09}."185. Although the accretion disk and jet are found to be closely related (e.g. 2009a).. the details of disk-jet coupling is not known vet. besides that jet formation and radio loud/cquiet clichotonw of AGNs are not well understood 2009).," Although the accretion disk and jet are found to be closely related \cite[e.g.][]{cao01,gu09a}, the details of disk-jet coupling is not known yet, besides that jet formation and radio loud/quiet dichotomy of AGNs are not well understood \cite[e.g.][]{tch09}."186. As one possibility. jel activity can be intermittent. due to. lor example. the accretion disk instability (e.g.Czernyetal.2009).. which is recently adopted to explain CSS/GPS sources (Wu2009a).," As one possibility, jet activity can be intermittent, due to, for example, the accretion disk instability \cite[e.g.][]{cze09}, which is recently adopted to explain CSS/GPS sources \citep{wu09a}."187. The existence of double double radio sources seems {ο support the intermittent scenario (e.g.Marecki&Szablewski2009)., The existence of double double radio sources seems to support the intermittent scenario \cite[e.g.][]{mar09}.188. Optically. NLSIs are thought to be voung AGNs with small black hole mass accreting at high accretion rate. implving the central accretion process are al the early stage of accretion history.," Optically, NLS1s are thought to be young AGNs with small black hole mass accreting at high accretion rate, implying the central accretion process are at the early stage of accretion history."189 In. radio band. the compact nature of radio structure of CSS sources are believed to be due to the [act," In radio band, the compact nature of radio structure of CSS sources are believed to be due to the fact"190"is approximately linear, the slope is shallower than expected.","is approximately linear, the slope is shallower than expected."191" An accurate calibration of o is important, because in turn it is used as an input for the evaluation and fitting of the warp diffusion coefficient a2."," An accurate calibration of $\alpha$ is important, because in turn it is used as an input for the evaluation and fitting of the warp diffusion coefficient $\alpha_2$."192" The disagreement found in ? prompted us to examine the method used to calibrate o in greater detail, resulting in our implementation of the fitting procedure described in Section 4.2 — essentially a quantitative version of the procedure performed in ?.."," The disagreement found in \citetalias{LP07} prompted us to examine the method used to calibrate $\alpha$ in greater detail, resulting in our implementation of the fitting procedure described in Section \ref{sec:fit} — essentially a quantitative version of the procedure performed in \citetalias{LP07}."193" In considering this issue, we have also explored the effect of the inner boundary condition of the 1D disc evolution on the measurement of a."," In considering this issue, we have also explored the effect of the inner boundary condition of the 1D disc evolution on the measurement of $\alpha$."194" Indeed, the main feature which is used for the"," Indeed, the main feature which is used for the"195"emission), are variable at different wavelengths.","emission), are variable at different wavelengths."196 Only and of the sources above the black-body line and below the power-law line. respectively. show variability.," Only and of the sources above the black-body line and below the power-law line, respectively, show variability."197 One aim of this paper is to study the possible evolutionary stages of the AGN in the CJF sample., One aim of this paper is to study the possible evolutionary stages of the AGN in the CJF sample.198 Different subsamples of the CJF. and the individual sources within them. can probe these different evolutionary stages.," Different subsamples of the CJF, and the individual sources within them, can probe these different evolutionary stages."199 Mergers. starburst activity. and BBH systems are integral parts of this study.," Mergers, starburst activity, and BBH systems are integral parts of this study."200 One of the most prominent examples supporting the link between starburst and BBH systems 1s NGC 6240. one of few sources directly observed to have a binary core (?)).," One of the most prominent examples supporting the link between starburst and BBH systems is NGC 6240, one of few sources directly observed to have a binary core \citealt{Komossa2003}) )."201 This system ts an ULIRG. hosts two AGN. and also clearly exhibits ongoing starburst activity. making it an archetype of the evolutionary scenario discussed here.," This system is an ULIRG, hosts two AGN, and also clearly exhibits ongoing starburst activity, making it an archetype of the evolutionary scenario discussed here."202 By selecting sources with a companion. one can investigate the earliest stages of the merging process.," By selecting sources with a companion, one can investigate the earliest stages of the merging process."203 Accordingly. by selecting the sources with disturbed morphologies and large infrared fluxes. we probe an intermediate phase (e.g.. Mrk 231).," Accordingly, by selecting the sources with disturbed morphologies and large infrared fluxes, we probe an intermediate phase (e.g., Mrk 231)."204 Finally. sources with relaxed morphologies but almost periodic variability at multiple wavelengths are likely to represent systems in. which an assumed BBH has sunk to the center of the system.," Finally, sources with relaxed morphologies but almost periodic variability at multiple wavelengths are likely to represent systems in which an assumed BBH has sunk to the center of the system."205 ? conducted simulations of equal-mass gas-rich mergers. classifying the sources into six distinct merging phases: pre-merger. first pass. maximal separation. merger. post-merger. and remnant.," \citet{Lotz2008} conducted simulations of equal-mass gas-rich mergers, classifying the sources into six distinct merging phases: pre-merger, first pass, maximal separation, merger, post-merger, and remnant."206 Using this classification scheme for our sources. we classify objects into pre and post-merger stages.," Using this classification scheme for our sources, we classify objects into pre and post-merger stages."207 The incompleteness of the information. available. about our sample does not allow us to make unambiguous claims for the classification of some sources (especially when differentiating between for example either. pre-merger and maximal separation. or post-merger and remnant classes).," The incompleteness of the information available about our sample does not allow us to make unambiguous claims for the classification of some sources (especially when differentiating between for example either pre-merger and maximal separation, or post-merger and remnant classes)."208 Among the distorted sources. those with companions can be classified as either a pre-merger or maximal separation phase. while those with no companions can be categorized as being in either the first pass. the post-merger. or remnant phase.," Among the distorted sources, those with companions can be classified as either a pre-merger or maximal separation phase, while those with no companions can be categorized as being in either the first pass, the post-merger, or remnant phase."209 For the last group. this translates. roughly. to an age of 2- Gyr after the initial approach of the progenitor systems.," For the last group, this translates, roughly, to an age of 2-4 Gyr after the initial approach of the progenitor systems."210 Exceptions to the above constitute four sources (3C. 84. Mrk 231. 3C 371. and Mrk 501) that exhibit both distorted morphologies and considerable starburst activity (e.g. 2:; 2)).," Exceptions to the above constitute four sources (3C 84, Mrk 231, 3C 371, and Mrk 501) that exhibit both distorted morphologies and considerable starburst activity (e.g., \citealt{Richards2005}; \citealt{Condon2002}) )."211 These characteristics put them in the merger phase and would constrain their age to be «2 Gyr after the initial approach., These characteristics put them in the merger phase and would constrain their age to be $<2$ Gyr after the initial approach.212 In Table 10 we indicate the 27 most suitable representatives of different evolutionary phases (following ?))., In Table \ref{tab:evolution_candidates} we indicate the 27 most suitable representatives of different evolutionary phases (following \citealt{Lotz2008}) ).213 Sources with companions but no sign of disturbed morphologies. are selected as pre-merger systems.," Sources with companions but no sign of disturbed morphologies, are selected as pre-merger systems."214 Sources with disturbed morphologies but no companions and no apparent starburst activity. are assigned to the first pass phase when the two systems are at a minimum separation for the first time.," Sources with disturbed morphologies but no companions and no apparent starburst activity, are assigned to the first pass phase when the two systems are at a minimum separation for the first time."215 The next phase corresponds to that of the maximal separation between the merging systems., The next phase corresponds to that of the maximal separation between the merging systems.216 For this phase. sources with disturbed morphologies and detected companions are selected.," For this phase, sources with disturbed morphologies and detected companions are selected."217 Sources identified as undergoing the first pass may also be merger remnants., Sources identified as undergoing the first pass may also be merger remnants.218 More information is required to make this distinction., More information is required to make this distinction.219MCG-6-30-15 (Miniutti et al.,MCG–6-30-15 (Miniutti et al.220 2007)., 2007).221" For this reason, it is not possible to constrain simultaneously all the line parameters (see Table 1)): these include the disc inner radius (rin) and inclination with respect to the line of sight and the emissivity index q (under the assumption of a radial emissivity profile e(r)οςr~%)."," For this reason, it is not possible to constrain simultaneously all the line parameters (see Table \ref{t1}) ): these include the disc inner radius $r_\rmn{in}$ ) and inclination with respect to the line of sight and the emissivity index $q$ (under the assumption of a radial emissivity profile $\epsilon (r) \propto r^{-q}$ )."222" None the less, we note that the best-fitting inner radius of ~13 rg does not necessarily require the extreme gravity regime typical of rapidly rotating black holes."," None the less, we note that the best-fitting inner radius of $\sim$ 13 $r_\rmn{g}$ does not necessarily require the extreme gravity regime typical of rapidly rotating black holes."223" It is important to stress that alternative explanations invoking a spectral upturn due to complex absorption effects, such as those proposed for the same MCG-6-30-15, are definitely not viable in the case of Ark 120."," It is important to stress that alternative explanations invoking a spectral upturn due to complex absorption effects, such as those proposed for the same MCG–6-30-15, are definitely not viable in the case of Ark 120."224" 4) In the latter stage, the properties of the two narrow lines are exactly the same as found in the original model."," 4) In the latter stage, the properties of the two narrow lines are exactly the same as found in the original model."225" Thus, it is worth investigating another possibility by retaining the basic template and allowing the width of the two lines to vary."," Thus, it is worth investigating another possibility by retaining the basic template and allowing the width of the two lines to vary."226" The consequent fit refinement is not as significant as when a disc line is involved, being now x2/d.o.f.=0.735/282: the difference of Ax?~—15.2 obtained with the loss of two degrees of freedom is not likely to be simply a chance improvement and supports the relativistic line detection."," The consequent fit refinement is not as significant as when a disc line is involved, being now $\chi^2_\nu/\rmn{d.o.f.}=0.735/282$: the difference of $\Delta \chi^2 \simeq -15.2$ obtained with the loss of two degrees of freedom is not likely to be simply a chance improvement and supports the relativistic line detection."227" Moreover, although the double-peaked energy of the blended feature is still consistent within the errors with neutral and H-like iron emission (Table 1)), the resulting width of c=113(+21) eV poses the question about the physical location wherein these lines arise."," Moreover, although the double-peaked energy of the blended feature is still consistent within the errors with neutral and H-like iron emission (Table \ref{t1}) ), the resulting width of $\sigma = 113 (\pm 21)$ eV poses the question about the physical location wherein these lines arise."228" Such a value, in fact, corresponds to a full width at half-maximum (FWHM) broadening of ~12x10? km s!, which is a factor of —2 larger than that observed in the optical permitted lines (FWHM Hf c5800 km s7!; Wandel, Peterson Malkan 1999)."," Such a value, in fact, corresponds to a full width at half-maximum (FWHM) broadening of $\sim 12 \times 10^3$ km $^{-1}$, which is a factor of $\sim$ 2 larger than that observed in the optical permitted lines (FWHM $\beta$ $\simeq 5800$ km $^{-1}$; Wandel, Peterson Malkan 1999)."229 This could hint at a sort of X-ray broad-line region (BLR) internal to the optical one., This could hint at a sort of X-ray broad-line region (BLR) internal to the optical one.230" Any further discussion on the possible origin of these lines (either broad or narrow) is deferred to the next section, in which we address this issue within the context of X-ray reflection models."," Any further discussion on the possible origin of these lines (either broad or narrow) is deferred to the next section, in which we address this issue within the context of X-ray reflection models."231" We are confident that relativistic effects are in place and have to be taken into account also when considering the entire spectral range, since all the interpretations of the iron emission profile in Ark 120 making no resort to a disc line turn out to be less successful and convincing."," We are confident that relativistic effects are in place and have to be taken into account also when considering the entire spectral range, since all the interpretations of the iron emission profile in Ark 120 making no resort to a disc line turn out to be less successful and convincing."232" We now extend our analysis to the whole 0.640 keV energy range, in order to understand the origin of the spectral Excess emission beyond ~20-30 keV is usually interpreted as due to the reprocessing of the primary X-ray radiation: the combination of photoelectric absorption and Compton scattering in the illuminated material gives rise to a broad reflection hump (e.g. George Fabian 1991, and references therein)."," We now extend our analysis to the whole 0.5–40 keV energy range, in order to understand the origin of the spectral Excess emission beyond $\sim$ 20–30 keV is usually interpreted as due to the reprocessing of the primary X-ray radiation: the combination of photoelectric absorption and Compton scattering in the illuminated material gives rise to a broad reflection hump (e.g. George Fabian 1991, and references therein)."233" Besides this additional continuum component and iron fluorescence, below ~2 keV the reflected spectrum is expected to be dominated by a wealth of emission lines from oxygen and other abundant elements, like C, N, Ne, Mg, Si, S (Ross Fabian 1993)."," Besides this additional continuum component and iron fluorescence, below $\sim$ 2 keV the reflected spectrum is expected to be dominated by a wealth of emission lines from oxygen and other abundant elements, like C, N, Ne, Mg, Si, S (Ross Fabian 1993)."234" Since it is fairly conceivable that in many cases the accretion flow itself acts as the most efficientmirror, depending on the ionization stage of the disc outer layers and on the relativistic motions of the inner regions, the stack of individual features can be blurred into the smooth shape of the soft excess."," Since it is fairly conceivable that in many cases the accretion flow itself acts as the most efficient, depending on the ionization stage of the disc outer layers and on the relativistic motions of the inner regions, the stack of individual features can be blurred into the smooth shape of the soft excess."235" As stated above, the slight spectral curvature observed at ~6 keV in Ark 120 cannot be explained as the product of (multiple) covering effects, suggesting instead the presence of a broad skewed profile within the iron emission feature and indicating a strong gravity regime."," As stated above, the slight spectral curvature observed at $\sim$ 6 keV in Ark 120 cannot be explained as the product of (multiple) covering effects, suggesting instead the presence of a broad skewed profile within the iron emission feature and indicating a strong gravity regime."236" It is therefore reasonable to include in our general model two reflection components, for which we have used the self-consistent table models of Ross Fabian (2005): the first one is expected to arise from almost neutral material at great distance from the X-ray emitting region, likely situated on the dusty torus scale."," It is therefore reasonable to include in our general model two reflection components, for which we have used the self-consistent table models of Ross Fabian (2005): the first one is expected to arise from almost neutral material at great distance from the X-ray emitting region, likely situated on the dusty torus scale."237" The second one can be ascribed to the partially ionized surface of the disc, and has been convolved with the kernel in to account for relativistic effects."," The second one can be ascribed to the partially ionized surface of the disc, and has been convolved with the kernel in to account for relativistic effects."238" The model obviously comprises the primary power law, absorbed by the Galactic column density, and also the two unresolved gaussian lines identified above, corresponding to neutral and H-like iron emission."," The model obviously comprises the primary power law, absorbed by the Galactic column density, and also the two unresolved gaussian lines identified above, corresponding to neutral and H-like iron emission."239" Galactic absorption is found to be consistent with Nu=0.98x107?! cm?, and has been frozen accordingly."," Galactic absorption is found to be consistent with $N_\rmn{H}=0.98 \times 10^{-21}$ $^{-2}$, and has been frozen accordingly."240" The reflection templates include among their free parameters iron abundance (which has been assumed to be single-valued across the source), ionization state (described by the quantity £=47F/ny, where ng is the hydrogen number density of the gas exposed to an X-ray flux F) and photon index of the illuminating power law (which has been taken to be one and the same with the direct power law)."," The reflection templates include among their free parameters iron abundance (which has been assumed to be single-valued across the source), ionization state (described by the quantity $\xi = 4 \pi F/n_\rmn{H}$, where $n_\rmn{H}$ is the hydrogen number density of the gas exposed to an X-ray flux $F$ ) and photon index of the illuminating power law (which has been taken to be one and the same with the direct power law)."241particle’ for each cluster that initially moves with the average velocity of the gas.,particle' for each cluster that initially moves with the average velocity of the gas.242" On scales =100 pc this effect plays only a small role presumably, as the typical distance that stars travel within 20 Myr is of the order of ~100 pc (assuming an rms velocity of ~5 km s~')."," On scales $\gtrsim{}100$ pc this effect plays only a small role presumably, as the typical distance that stars travel within 20 Myr is of the order of $\sim{}100$ pc (assuming an rms velocity of $\sim{}5$ km $^{-1}$ )."243 Some scatter on large scales may arise from high-velocity run-away stars (Blaauw1961;Stone ," Some scatter on large scales may arise from high-velocity run-away stars \citep{1961BAN....15..265B, 1991AJ....102..333S}."244The decline of the scatter 1991)..with increasing averaging scale is obviously related to the spatial averaging over a larger number of resolution elements Nyes., The decline of the scatter with increasing averaging scale is obviously related to the spatial averaging over a larger number of resolution elements $N_{\rm res}$.245" Naively, we would expect a scaling proportional to 1/9Νιος, where Nus«d? if the Ha is filling the volume relatively uniformly, or ος1? if the H» is confined to a disk."," Naively, we would expect a scaling proportional to $1/\sqrt{N_{\rm res}}$, where $N_{\rm res}\propto{}l^3$ if the $\H2$ is filling the volume relatively uniformly, or $\propto{}l^2$ if the $\H2$ is confined to a disk."246" However, the scale dependence shown in Fig."," However, the scale dependence shown in Fig."247 4 seems to be much shallower., \ref{fig:scaleScatter} seems to be much shallower.248" In order to understand this better, we now include a log-normal (intrinsic) scatter of the in equation with ranging from 0.1 to 1 dex on the 65 pe (1)),scale."," In order to understand this better, we now include a log-normal (intrinsic) scatter of the in equation \ref{eq:SFR}) ), with $\sigma/\ln{}10$ ranging from 0.1 to 1 dex on the 65 pc scale."249 Fig., Fig.250 5 c/1n10shows that this scatter decreases with increasing averaging scale roughly as a power law l? with exponent α=0.5., \ref{fig:scaleScatter2} shows that this scatter decreases with increasing averaging scale roughly as a power law $\sigma_l\propto{}l^{-\alpha}$ with exponent $\alpha\approx{}0.5$.251" As we discuss in more detail in Appendix B the rather gradual decline is caused by both the finite width c, of the Hy density distribution and the geometrical arrangement of the molecular hydrogen.", As we discuss in more detail in Appendix \ref{sect:dep} the rather gradual decline is caused by both the finite width $\sigma_\rho$ of the $\H2$ density distribution and the geometrical arrangement of the molecular hydrogen.252" In particular, we find that a sensible value σρ©1.5 (McKee&Ostriker2007) and a two-dimensional (2D, disk) arrangement of the molecular hydrogen naturally leads to ae0.5."," In particular, we find that a sensible value $\sigma_\rho\approx{}1.5$ \citep{2007ARA&A..45..565M} and a two-dimensional (2D, disk) arrangement of the molecular hydrogen naturally leads to $\alpha\approx{}0.5$."253" On the other hand, a purely one-dimensional (1D) arrangement of the Hg is only consistent with az0.5 if the width in the density distribution is very small («&1), while a three-dimensional (3D) configuration would require σρ72.5."," On the other hand, a purely one-dimensional (1D) arrangement of the $\H2$ is only consistent with $\alpha\approx{}0.5$ if the width in the density distribution is very small $\ll{}1$ ), while a three-dimensional (3D) configuration would require $\sigma_\rho\approx{}2.5$."254" We have also tested that the exponent decreases if the inserted intrinsic scatter becomes large, ie. o>1."," We have also tested that the exponent decreases if the inserted intrinsic scatter becomes large, i.e., $\sigma\gg{}1$."255" In fact, the top curves (c=2.3) in Fig."," In fact, the top curves $\sigma=2.3$ ) in Fig."256 5 clearly show this flattening., \ref{fig:scaleScatter2} clearly show this flattening.257" Since the Πο density distribution depends on the metallicity and radiation field (see Fig. 2)),"," Since the $\H2$ density distribution depends on the metallicity and radiation field (see Fig. \ref{fig:regfit}) ),"258" α should depend on it, too."," $\alpha$ should depend on it, too."259" With the data points shown in Fig. 5,,"," With the data points shown in Fig. \ref{fig:scaleScatter2},"260" we obtain a=0.52+0.04 for Z=0.1, Umw=100, and a=0.43€0.04 for Z=1, Umw=0.1."," we obtain $\alpha=0.52\pm{}0.04$ for $Z=0.1$, $\UMW=100$, and $\alpha=0.43\pm{}0.04$ for $Z=1$, $\UMW=0.1$ ."261 Let us now consider the case in which a scatter σι is inserted on scale | (we assume a set of discrete scales that change by a factor 2)., Let us now consider the case in which a scatter $\tilde{\sigma}_l$ is inserted on scale $l$ (we assume a set of discrete scales that change by a factor 2).262" If the different scatter contributions add in quadrature, the total scatter σι on a given scale { is simply given by With knowledge of a, this equation allows the computation of the amount of scatter σι that is introduced on scale { from the measurement of the scatter on scales { and 1/2."," If the different scatter contributions add in quadrature, the total scatter $\sigma_l$ on a given scale $l$ is simply given by With knowledge of $\alpha$, this equation allows the computation of the amount of scatter $\tilde{\sigma}_l$ that is introduced on scale $l$ from the measurement of the scatter on scales $l$ and $l/2$."263" Presumably, different physical mechanisms may introduce different amounts of scatter on different scales."," Presumably, different physical mechanisms may introduce different amounts of scatter on different scales."264 Studying the scale dependence of the scatter may therefore be helpful to uncover the responsible physical mechanism(s)., Studying the scale dependence of the scatter may therefore be helpful to uncover the responsible physical mechanism(s).265" The scatter in the relation on the scale of ~100 pc has been attributed to the evolution of molecular clouds over their life time (see, e.g., Onoderaetal.2010;Schruba 2010))."," The scatter in the relation on the scale of $\sim{}100$ pc has been attributed to the evolution of molecular clouds over their life time (see, e.g., \citealt{2010arXiv1009.1971O, 2010arXiv1009.1651S}) )."266" In this picture, young molecular clouds have not yet formed stars, but contain large amounts of Πο and hence fall “below” the average relation."," In this picture, young molecular clouds have not yet formed stars, but contain large amounts of $\H2$ and hence fall “below” the average relation."267" On the other hand, clouds that are near the end of their lives are heavily star forming and/or have lost some fraction of their molecular hydrogen, hence they lie “above” the relation."," On the other hand, clouds that are near the end of their lives are heavily star forming and/or have lost some fraction of their molecular hydrogen, hence they lie “above” the relation."268 This picture cannot be reconciled with an Ho-based star formation law of the form of equation as long as the gas consumption time scale TsrR/esrn is (1))treated as a constant., This picture cannot be reconciled with an $\H2$ -based star formation law of the form of equation \ref{eq:SFR}) ) as long as the gas consumption time scale $\tau_{\rm SFR}/\epsilon_{\rm SFR}$ is treated as a constant.269" Hence, this explanation of the scatter in the relation implies that has to be a time-dependent quantity."," Hence, this explanation of the scatter in the relation implies that $\epsilon_{\rm SFR}/\tau_{\rm SFR}$ has to be a time-dependent quantity."270" If Tspg is espn/Tsrmapproximately constant, then the star formation efficiency will need to change over the life time of a molecular cloud (e.g., Murray2011,, but see Feldmann&Gnedi"," If $\tau_{\rm SFR}$ is approximately constant, then the star formation efficiency will need to change over the life time of a molecular cloud (e.g., \citealt{2010arXiv1007.3270M}, but see \citealt{FeldmannM}) )."271n Our interpretation is 2011)).different., Our interpretation is different.272" We show that a large amount of scatter in the relation can be explained by the fact that observations do not measure the instantaneous rate of star formation, butrather the number of stars that formed within a finite time interval in the past."," We show that a large amount of scatter in the relation can be explained by the fact that observations do not measure the instantaneous rate of star formation, butrather the number of stars that formed within a finite time interval in the past."273 Our numerical models predict that the scatter seen on scales of ~100 pc should be small, Our numerical models predict that the scatter seen on scales of $\sim{}100$ pc should be small274"Integrating dT from the shock towards the upstream, the value of Γ/Τ,, (for values larger than 1/T,) has a universal profile (independent of T,,) as a function of n,ozz'(14-2]n|T2])/T2.","Integrating $d\G$ from the shock towards the upstream, the value of $\G/\Gu$ (for values larger than $1/\Gu$ ) has a universal profile (independent of $\G_u$ ) as a function of $n_u \sigma_T275z'(1+2\ln[\Gu^2])/\Gu^2$."276 'This profile is presented in figure 3.., This profile is presented in figure \ref{fig3}.277" This profile implies that the shock width in unit of pair unloaded Thomson optical depth in the shock frame isroughly!!,, οςI?."," This profile implies that the shock width in unit of pair unloaded Thomson optical depth in the shock frame is, $\propto \G_u^2$."278" The value of the proportionality coefficient is somewhat arbitrary and it depends on the value of D/T, that defines the “shock width""."," The value of the proportionality coefficient is somewhat arbitrary and it depends on the value of $\G/\Gu$ that defines the “shock width""."279" We chose I'/T,,=0.9 obtaining n,orz’£z0.011? (the value of thelogarithmic factor is 5—10 for Γι=2— 10).", We chose $\G/\Gu=0.9$ obtaining $n_u \sigma_T z' \approx 0.01 \G_u^2$ (the value of thelogarithmic factor is $5-10$ for $\G_u =2-10$ ).280" Choosing a different value of ['/T,,, to define the shock width, changes the coefficient, which in turn has a very weak effect on equation δ.."," Choosing a different value of $\G/\Gu$, to define the shock width, changes the coefficient, which in turn has a very weak effect on equation \ref{eq gmaxi}."281" Now, since the length scale in the upstream frame, z, is shorter by a factor Γι than in the shock frame (i.e., 2’= Tz), and defining τι= n,oyz, we approximate the shock width"," Now, since the length scale in the upstream frame, z, is shorter by a factor $\G_u$ than in the shock frame (i.e., $z'=\Gu z$ ), and defining $\tau_u = n_u \sigma_T z$ , we approximate the shock width"282core binary fraction from the primordial value.,core binary fraction from the primordial value.283 Thus we do not agree with Ivanova et al. (, Thus we do not agree with Ivanova et al. (2842005) that the binary fraction in the core will be depleted in time.,2005) that the binary fraction in the core will be depleted in time.285 We also do not agree that models of elobular cluster evolution need necessarily include large populations of primordial binaries., We also do not agree that models of globular cluster evolution need necessarily include large populations of primordial binaries.286 Our simulations have shown that the binary population in the core of a cluster is continually being replenished by stars from outside the core. many of which were previously in (he core.," Our simulations have shown that the binary population in the core of a cluster is continually being replenished by stars from outside the core, many of which were previously in the core."287 This is a process we have termedconvection., This is a process we have termed.288 We also find that the binary content of an evolved star cluster is dominated by exchange binaries provided that the stellar density is relatively high., We also find that the binary content of an evolved star cluster is dominated by exchange binaries provided that the stellar density is relatively high.289 This is (rue of our moderate-size globular cluster models aud we expect it (o be true in more massive clusters., This is true of our moderate-size globular cluster models and we expect it to be true in more massive clusters.290 We also show that increasing the primordial binary fraction does not necessarily lead (ο an increase in the final binary fraction in [acl 1 gives more scope for binary depletion., We also show that increasing the primordial binary fraction does not necessarily lead to an increase in the final binary fraction – in fact it gives more scope for binary depletion.291 A kev ancl paracloxical result is that a final binary fraction Chat can be achieved by choosing a higher primordial binary fraction may also be replicated by choosing an initially lower binary fraction., A key and paradoxical result is that a final binary fraction that can be achieved by choosing a higher primordial binary fraction may also be replicated by choosing an initially lower binary fraction.292 We find that the overall binary fraction of a cluster does not vary appreciably from the prinordial value as a cluster evolves., We find that the overall binary fraction of a cluster does not vary appreciably from the primordial value as a cluster evolves.293 This is a result of binary destruction being balanced bv a greater rate of escape of single stars compared (o. binaries., This is a result of binary destruction being balanced by a greater rate of escape of single stars compared to binaries.294 We also find that the prinordial binary frequency of a cluster is well preserved. outside of the cluster hall-mass radius., We also find that the primordial binary frequency of a cluster is well preserved outside of the cluster half-mass radius.295 Therefore. observations of the current binary [fraction in these regions is a good indieator of the primordial binary fraction while determination of the core binary. lraction provides an upper limit.," Therefore, observations of the current binary fraction in these regions is a good indicator of the primordial binary fraction while determination of the core binary fraction provides an upper limit."296 We acknowledge the generous support of the Cordelia Corporation and that of Edw Norton which has enabled AMNII to purchase GRAPE-G boards and supporting hardware., We acknowledge the generous support of the Cordelia Corporation and that of Edward Norton which has enabled AMNH to purchase GRAPE-6 boards and supporting hardware.297 We (hank the anonymous referee for extremely helpful comments and especially for alerting us (o (he scaling considerations., We thank the anonymous referee for extremely helpful comments and especially for alerting us to the scaling considerations.298"flux related to the SDSS automatic procedures, we visually inspected the 94 SDSS spectra above and found 11 objects in which the listed detection of [Ne V] emission is seriously affected by instrumental features and sky residuals.","flux related to the SDSS automatic procedures, we visually inspected the 94 SDSS spectra above and found 11 objects in which the listed detection of [Ne V] emission is seriously affected by instrumental features and sky residuals."299 These objects were then removed from the sample., These objects were then removed from the sample.300 We also noticed that the line parameters listed in the SDSS spectroscopic tables are not accurate for weak emission lines over a steep continuum., We also noticed that the line parameters listed in the SDSS spectroscopic tables are not accurate for weak emission lines over a steep continuum.301" For instance, in about one quarter of SDSS QSOs, the [O ΠΙ3727 emission line (see the Discussion) appears as an absorption line due to an overestimate of the continuum."," For instance, in about one quarter of SDSS QSOs, the [O II]3727 emission line (see the Discussion) appears as an absorption line due to an overestimate of the continuum."302" We then retrieved the SDSS spectra and performed a Gaussian fit to the emission lines we were interested in, deriving fluxes, luminosities, and rest frame equivalent widths."," We then retrieved the SDSS spectra and performed a Gaussian fit to the emission lines we were interested in, deriving fluxes, luminosities, and rest frame equivalent widths."303 All the emission line parameters used in this work for SDSS objects are derived from our direct fits., All the emission line parameters used in this work for SDSS objects are derived from our direct fits.304" Whenever we compared our line measurements with those performed by other Authors on the same SDSS spectra (e.g. for a subsample of type-2 QSOs in 2)), we found an excellent agreement."," Whenever we compared our line measurements with those performed by other Authors on the same SDSS spectra (e.g. for a subsample of type-2 QSOs in ), we found an excellent agreement."305 The X/NeV vs Ny relation for the 83 SDSS QSOs selected above is shown in Fig. 2.., The X/NeV vs $N_H$ relation for the 83 SDSS QSOs selected above is shown in Fig. \ref{xnevsdss}.306 Most objects are unobscured and populate the same region of local Seyfert 1 galaxies., Most objects are unobscured and populate the same region of local Seyfert 1 galaxies.307" The median X/NeV ratio for SDSS QSOs is 370, almost identical to the value of 400 found for local Seyfert 1s."," The median X/NeV ratio for SDSS QSOs is 370, almost identical to the value of 400 found for local Seyfert 1s."308" The few objects showing significant intrinsic X-ray absorption appear in the optical as intermediate type Seyferts (i.e. 1.8-1.9) rather than pure type-1 To check for possible outliers, e.g. blue SDSS QSOs with very low X/NeV ratios («15, as observed for local CT Seyferts), we also considered those objects in the Υ09 catalog showing significant [Ne V] emission and which were either"," The few objects showing significant intrinsic X-ray absorption appear in the optical as intermediate type Seyferts (i.e. 1.8-1.9) rather than pure type-1 To check for possible outliers, e.g. blue SDSS QSOs with very low X/NeV ratios $<15$, as observed for local CT Seyferts), we also considered those objects in the Y09 catalog showing significant [Ne V] emission and which were either"309uodeliudepeudenut approach which does not assmue any articular shape for the profile.,model-independent approach which does not assume any particular shape for the profile.310 While the uncertainties are larec. the flewre indicates a clear tendency of an Increasing 2 with radius.," While the uncertainties are large, the figure indicates a clear tendency of an increasing $\beta$ with radius."311" The o, profile. as obtained from he Jeaus equation (eq. 2))."," The $\sigma_r$ profile, as obtained from the Jeans equation (eq. \ref{Jeans equation}) ),"312 is shown in figure 7.., is shown in figure \ref{sigma_r profile}.313 The analytical expression we used for ον eq. (7)).," The analytical expression we used for $\beta$, eq. \ref{beta analytic314expression}) ),"315 constrains to equal unity at large radii. corresponding o purely radial orbits.," constrains $\beta$ to equal unity at large radii, corresponding to purely radial orbits."316 D99 analyzed N-body simulatious and derived values somewhat simaller than 1 at their Huitine radius. Grogy.," D99 analyzed N-body simulations and derived values somewhat smaller than 1 at their limiting radius, $6r_{200}$."317 To allow for deviation frou unitv we also fit⋅ the expression⋅ (€.4|OoPEC. where a ds a free parameter which governs the asviuptotic vchavior of 9.," To allow for deviation from unity we also fit the expression $(C+a)\frac{(r/r_c)^2}{(r/r_c)^2+1}-C$, where $a$ is a free parameter which governs the asymptotic behavior of $\beta$."318 The value of &=1 eave the best fit. also consistent with the value obtained by the independent mcthod at the largest radial point.," The value of $a=1$ gave the best fit, also consistent with the value obtained by the model-independent method at the largest radial point."319 In l| we used the mass profile as derived from N-rav and lensing data together with the new data ou the projected velocity dispersion and the galaxy surface munber deusitv to derive the 3D profiles of the velocity anisotropy aud ealaxy nuuniber density., In \ref{The galaxy dynamical properties} we used the mass profile as derived from X-ray and lensing data together with the new data on the projected velocity dispersion and the galaxy surface number density to derive the 3D profiles of the velocity anisotropy and galaxy number density.320 Alternatively. there are at least two different wavs to derive the total mass profile of the cluster directly from the data sets on ealaxy dynamics.," Alternatively, there are at least two different ways to derive the total mass profile of the cluster directly from the data sets on galaxy dynamics."321 Perhaps the simplest approach is to use oulv the velocity caustics derived above. the auiplitude of which is related to the escape velocity. which is a tracer of the cluster mass profile.," Perhaps the simplest approach is to use only the velocity caustics derived above, the amplitude of which is related to the escape velocity, which is a tracer of the cluster mass profile."322 The second approach is to use both data sets (of the projected velocity dispersion and ealaxy surface number deusitv) together with the Jeaus equation to fit an NEW inass profile., The second approach is to use both data sets (of the projected velocity dispersion and galaxy surface number density) together with the Jeans equation to fit an NFW mass profile.323 Thus. we have two indepeucent methods for estimating the cluster lass profile.," Thus, we have two independent methods for estimating the cluster mass profile."324 As meutioned already. D99 has shown that the 3D mass profile can be fairly well estimated directly frou," As mentioned already, D99 has shown that the 3D mass profile can be fairly well estimated directly from"325"model with cosmological constant O4=0.7. Oy,=0.3. and a baryon density O1,=0.04. the Hubble constant is Z4,=100 hb km ! |. with h=0.7. and oy=0.8.","model with cosmological constant $\Omega_\Lambda= 0.7$ , $\Omega_\textrm{m} = 0.3$, and a baryon density $\Omega_\textrm{b} = 0.04$, the Hubble constant is $H_0=100$ h km $^{-1}$ $^{-1}$ , with $\textrm{h} = 0.7$, and $\sigma_8 = 0.8$."326 The gravitational softening was set as ep;—7.5 ! kpe.," The Plummer-equivalent gravitational softening was set as $\epsilon_{Pl}=3277.5$ $^{-1}$ kpc."328 The code used to perform the simulation is the TREESPII code GADGET-2 Springeletal.(2001):(2005).," The code used to perform the simulation is the TREESPH code GADGET-2 \cite{Springel01, Springel05}."329. The siniulation follows the evolution of 480* dark matter (DM) particles and as many barvonic eas particles [from redshift 2=49 (o -0., The simulation follows the evolution of $480^3$ dark matter (DM) particles and as many baryonic gas particles from redshift $z = 49$ to $z=0$.330" The box for the simulation is a cube of side 192 ! Mpe. the DM and gas particles have initial masses ni;=4.62xLO’ IM. and ni,=6.03xLOS tM. respectively."," The box for the simulation is a cube of side 192 $^{-1}$ Mpc, the DM and gas particles have initial masses $\textrm{m}_{\textrm{\tiny DM}} = 4.62 331\times 10^9$ $^{-1}$ $_\odot$ and $\textrm{m}_{\textrm{\tiny gas}} = 3326.93 \times 10^8$ $^{-1}$ $_\odot$ respectively."333 The physical processes involved in the simulation are eravitv. non-radiative hvdrodynamies. star formation. feedback from SNe with the effect of weak galactic outflows. radiative gas cooling and heating bv a uniform. ünme-dependent. »xhotoionizinge ultraviolet backeround.," The physical processes involved in the simulation are gravity, non-radiative hydrodynamics, star formation, feedback from SNe with the effect of weak galactic outflows, radiative gas cooling and heating by a uniform, time-dependent, photoionizing ultraviolet background."334e The treatment of radiative cooling assumes an optically thin gas in CIE and uses only the primordial abunelances (hydrogen mass fraction N=0.76. helium Y=0.24).," The treatment of radiative cooling assumes an optically thin gas in CIE and uses only the primordial abundances (hydrogen mass fraction $=0.76$ , helium $=0.24$ )."335 Metals generated bv the simulation itself are not considered for radiative cooling., Metals generated by the simulation itself are not considered for radiative cooling.3365 A uniform. time-dependent UV background Laarcdt&Macau(1996) reionizes the Universe al z~6.," A uniform, time-dependent UV background \cite{Haardt96} reionizes the Universe at $z\sim6$."337 Star formation is introduced following a hybrid multiphase model for the interstellar medium Springel&llernquist(2003)., Star formation is introduced following a hybrid multiphase model for the interstellar medium \cite{Springel03}.338. The interstellar medium. where star formation Lakes place. is represented as cold clouds (cold gas) embedded in a hot gas.," The interstellar medium, where star formation takes place, is represented as cold clouds (cold gas) embedded in a hot gas."339 Clouds are not accounted for individually in a given star-lormine particle. but rather μον are (treated. all together as a fraction of the total mass of the given star-forming particle.," Clouds are not accounted for individually in a given star-forming particle, but rather they are treated all together as a fraction of the total mass of the given star-forming particle."340 Every gas particle is considered as composed of (wo parts. the hot gas. with its own mass and density. and the cold cloud fraction. temperature and density. determine (he relative abundances of the two components.," Every gas particle is considered as composed of two parts, the hot gas, with its own mass and density, and the cold cloud fraction, temperature and density determine the relative abundances of the two components."341 Whenever star lormation takes place. a new star particle is spawnecl (with just a fraction of the starting gas particle). Uus increasing the number of star particles.," Whenever star formation takes place, a new star particle is spawned (with just a fraction of the starting gas particle), thus increasing the number of star particles."342 Stars are created. following a Salpeter initial mass function Salpeter(1955).. and instantly produce metals and release energv as supernovae.," Stars are created, following a Salpeter initial mass function \cite{Salpeter55}, and instantly produce metals and release energy as supernovae."343 Metals aid energy. are carried to the intracluster and intergalactic medium by galactic winds., Metals and energy are carried to the intracluster and intergalactic medium by galactic winds.344 Winds are introduced in the simulation as mass outflows wilh rate equal to (vice the star formation rate and wilh a wind velocity of 360 kms !., Winds are introduced in the simulation as mass outflows with rate equal to twice the star formation rate and with a wind velocity of $360$ km $^{-1}$.345 The output of the simulation consists of 102 boxes. equally spaced in the logarithm of ihe expansion [actor between z=9 and z=0.," The output of the simulation consists of 102 boxes, equally spaced in the logarithm of the expansion factor between $z=9$ and $z=0$."346 As shown in previous work(e.g.. (2006)))," As shown in previous work(e.g., \cite{Ursino06}) )"347 the X-ray emission above redshift 2 is negligible., the X-ray emission above redshift 2 is negligible.348 For our work we therefore onlv used (he simulationup to redshilt 2., For our work we therefore only used the simulationup to redshift 2.349 Desides (he improvement in spatial resolution compared to ourprevious work. (his simulation suites well our needs due to ils large scale that. allows us enough statistics for distant regions.," Besides the improvement in spatial resolution compared to ourprevious work, this simulation suites well our needs due to its large scale that allows us enough statistics for distant regions."350More recent cosmological simulations have box sizes of al mostLOO | Mpe,More recent cosmological simulations have box sizes of at most100 $^{-1}$ Mpc351The black-hole spin in AIB3 7 has been very accurately measured to he in climensiouless spin paraiuceter (Liuetal.2008).,The black-hole spin in M33 $-$ 7 has been very accurately measured to be in dimensionless spin parameter \citep{Liu08}.352. The authors of this paper show that holes” (Shatecet aud MeCliutocketal. (2006)))., The authors of this paper show that \citet{Sha06} and \citet{McC06}) ).353 However. etal(2003) noted that their spin derivation is model aud subject to possible svstematic errors.," However, \citet{Liu08} noted that their spin derivation is model-dependent and subject to possible systematic errors."354 Leeetal.(2002) predicted the spin parameters of Nova Sco (X-ray Nova Scorpii 1991) aud Il Lupi (1U I7) to be ~OLS. with small effects after they were born in the explosion frou mass accretion: 1.6.. predicted them as natal.," \citet{Lee02} predicted the spin parameters of Nova Sco (X-ray Nova Scorpii 1994) and Il Lupi (4U $-$ 47) to be $\sim0.8$, with small effects after they were born in the explosion from mass accretion; i.e., predicted them as natal."355 However Brownctal.(2007) showed that the rotational energv im such binaries scaled inversely with the donor mass at the time of conunonu-envelope evolution preceding the explosion in which the black hole was born., However \citet{BLMM07} showed that the rotational energy in such binaries scaled inversely with the donor mass at the time of common-envelope evolution preceding the explosion in which the black hole was born.356 The donor masses of Nova Sco aud Ib Lupi are ~27M. whereasthat of M33 7 was ~SOM... so Brownctal.(2007). sugeested that the 3.15 day period of N33. 7 resulted. from a dark explosion: the high spin parameter would have resulted from mass accretion.," The donor masses of Nova Sco and Il Lupi are $\sim2\msun$ whereasthat of M33 $-$ 7 was $\sim80\msun$, so \citet{BLMM07} suggested that the $3.45$ day period of M33 $-$ 7 resulted from a dark explosion; the high spin parameter would have resulted from mass accretion."357 This mass accretion would have had to take placeat wperciitical rate as we discuss in this letter., This mass accretion would have had to take placeat hypercritical rate as we discuss in this letter.358 We breflv comunent on the lywpercritical accretion ov M/Mrg;g;~lO or groater (Brown&Weineart-rer1991)., We briefly comment on the hypercritical accretion for $\dot{M}/\dot{M}_{Edd}\sim10^3$ or greater \citep{Bro94}.359 The scenario begius with Boudi accretion hrough the sonic poiut. which is often ereatlv larger han accretion at the Eddiugton lait.," The scenario begins with Bondi accretion through the sonic point, which is often greatly larger than accretion at the Eddington limit."360 Because it had recone worked out for a value of 0.31«10!ALEay by Brown&Weineartuer(1991). aud because this value is in the widdle of those we shall use in stellar evolution. we use this value. although it could be much. ercater.," Because it had been worked out for a value of $0.31\times10^4\dot{M}_{Edd}$ by \citet{Bro94} and because this value is in the middle of those we shall use in stellar evolution, we use this value, although it could be much greater."361 The Brown&Weinegartuer(1991) work had been carried out earlier in all detail bv IIouck&Chevalier(1991). and checked by Chevalier(1995)., The \citet{Bro94} work had been carried out earlier in all detail by \citet{Hou91} and checked by \citet{Che95}.362.. We uote that there is still considerable controversy in the astroplivsical community about whether hypererifical accretion cau take place or iof., We note that there is still considerable controversy in the astrophysical community about whether hypercritical accretion can take place or not.363" Tlowever. the general point we address is that if AL exceeds τμ, then some of the accretion energv uust be removed by meaus other than photons."," However, the general point we address is that if $\dot{M}$ exceeds $\dot{M}_{Edd}$, then some of the accretion energy must be removed by means other than photons."364 In the case of lvpercritical accretion. this excess cucrey cau ve carried off bv neutrino pairs (Brown&Weingartucr199 D.," In the case of hypercritical accretion, this excess energy can be carried off by neutrino pairs \citep{Bro94}."365. In the case of a neutron star. neutrino losses allow he matter flow to join smoothly onto the neutron star surface.," In the case of a neutron star, neutrino losses allow the matter flow to join smoothly onto the neutron star surface."366 In the case of a black hole. the neutring losses et the matter flow smoothlv over the event horizon aud disappear iuto the black hole.," In the case of a black hole, the neutrino losses let the matter flow smoothly over the event horizon and disappear into the black hole."367" Iu the work of Podsiadlowskietal. (2003).. we uote wo possible stages where hypercritieal (M/Mag2, 107)or supercritical acerction may take place."," In the work of \citet{Pod03}, , we note two possible stages where hypercritical $\dot M/\dot M_{Edd} \gsim 10^3$ )or supercritical accretion may take place."368 Podsiadlowski evolve a binary with Ap;= 19211... Wsecondary=20M.. auc orbital period of 6.8 davs.," \citet{Pod03} evolve a binary with $M_{BH}=12\msun$ , $m_{secondary}=25\msun$ and orbital period of 6.8 days."369photometry is accurate to 0.02 mags. and the velocity dispersions to about SU (see Bernardi et al.,"photometry is accurate to 0.02 mags, and the velocity dispersions to about $8$ (see Bernardi et al."370 2003a)., 2003a).371 We work with de Vaucouleurs (1918) magnitudes and sizes. and SDSS colors throughout: these are colors measured within au aperture which scales with the de Vaucouleurs μαΠο radius iu the k-baud.," We work with de Vaucouleurs (1948) magnitudes and sizes, and SDSS colors throughout: these are colors measured within an aperture which scales with the de Vaucouleurs half-light radius in the $r$ -band."372 The most important reason for analyzing a new sample (other than size) is that the old photometric reductions output bv the SDSS pipeline were incorrect (see documentation on DR2. the Second Data Release).," The most important reason for analyzing a new sample (other than size) is that the old photometric reductions output by the SDSS pipeline were incorrect (see documentation on DR2, the Second Data Release)."373 A comparison of the properties of objects for which old aud new photometric reductions are available shows that the new corrected photometry has made most magnitudes slightly fainter (~0.13 mags). and most halt-light radii smaller (~ )).," A comparison of the properties of objects for which old and new photometric reductions are available shows that the new corrected photometry has made most magnitudes slightly fainter $\sim 0.13$ mags), and most half-light radii smaller $\sim$ )."374 It is customary to report velocity dispersions at sole fraction (woe use 1/8) of the halflieht radius., It is customary to report velocity dispersions at some fraction (we use 1/8) of the half-light radius.375 The half-lieht radii of the galaxies which cuter our sample are typically about 2 arcsecs. approximately iudepenudoeut of redshift. whereas the SDSS fiber used to measure the spectruni from which the velocity dispersion is estimated has a diameter of 3 arcsec.," The half-light radii of the galaxies which enter our sample are typically about 2 arcsecs, approximately independent of redshift, whereas the SDSS fiber used to measure the spectrum from which the velocity dispersion is estimated has a diameter of 3 arcsec."376 Since the velocity dispersious of carly-type galaxies are kuown to merease towards the center (following Joregcusen et al., Since the velocity dispersions of early-type galaxies are known to increase towards the center (following rgensen et al.377 1995 we assume the sealing is X(rr)991 where ris the hal£ligbt radius). all ucasured velocity dispersions are aperture corrected’. aud it is these which are usually reported (the mean correction is )).," 1995 we assume the scaling is $\propto (r/r_e)^{0.04}$, where $r_e$ is the half-light radius), all measured velocity dispersions are `aperture corrected', and it is these which are usually reported (the mean correction is )."378 Although the measured velocity dispersions have rot changed. the new photometry has chaneed the haltight radius.," Although the measured velocity dispersions have not changed, the new photometry has changed the half-light radius."379 Hence. aperture corrected velocity dispersious differ from those associated with the old plotometiy (1.6.. hose reported iu Bernardi et al.," Hence, aperture corrected velocity dispersions differ from those associated with the old photometry (i.e., those reported in Bernardi et al."380 2003a) by less than one vercent (the new values ave laveer by a factor of 1.184)., 2003a) by less than one percent (the new values are larger by a factor of $1.1^{0.04}$ ).381 Bernardi et al. (, Bernardi et al. (3822003b) showed that the huninosities in their sample (~9000 ealaxies with :< 0.3) evolve: Aff.)=ALO)O52. where AL(2) denotes the mean absolute magnitude at redshift +.,"2003b) showed that the luminosities in their sample $\sim 9000$ galaxies with $z\le 0.3$ ) evolve: $M_*(z) = M_*(0) - 0.85z$, where $M_*(z)$ denotes the mean absolute magnitude at redshift $z$."383" We fud similar evolution in the new sample: the main differcuce is that the new photometric reductions makeA, fainterby about 0.125 mags.", We find similar evolution in the new sample: the main difference is that the new photometric reductions make $M_*$ fainter by about 0.125 mags.384 The evolution is consistent with that of a passively aging »pulatiou., The evolution is consistent with that of a passively aging population.385 Thus. in the analysis which follows. we will © careful to separate trends with redshift that are due o the magnitude lait of the sample. from trends that απο due to evolution.," Thus, in the analysis which follows, we will be careful to separate trends with redshift that are due to the magnitude limit of the sample, from trends that are due to evolution."386 Maux of the following figures preseut ueasureineuts made dm a series of narrow redshift bins: L02xi«cQT. OOFxoiozQ(LQ09. 0009.—loxO2. A12x:<O15. and 0.15xs<0.2.," Many of the following figures present measurements made in a series of narrow redshift bins: $0.02\le z<0.07$, $0.07\le z<0.09$, $0.09\le z < 0.12$, $0.12\le z< 0.15$, and $0.15\le z<0.2$."387" In all of these Ποπος, sviubols show the median value of the variable ou hne v-axis as a function of the observable ou the x-axis. error bars show the rius error of the median. and hashed regious indicate where the central of the sample in cach redshift bin lies."," In all of these figures, symbols show the median value of the variable on the y-axis as a function of the observable on the x-axis, error bars show the rms error of the median, and hashed regions indicate where the central of the sample in each redshift bin lies."388" Figure ld displavs correlations between Πορτν, size [ει aud velocity dispersion σ in this sample. ("," Figure \ref{lvrm} displays correlations between luminosity, size $R_r$, and velocity dispersion $\sigma$ in this sample. ("389"The light radius in kpc. &,. is defined similarly to the quantity called Π by Bernardi et al.","The half-light radius in kpc, $R_r$, is defined similarly to the quantity called $R_o$ by Bernardi et al."390 2003a. for the r-baud.)," 2003a, for the $r$ -band.)"391 The dashed lines show fits to these correlations. stmunarizec in Table 1..," The dashed lines show fits to these correlations, summarized in Table \ref{MLcov}."392 Tn all cases. luminosities have been corrected or evolution by 0.852.," In all cases, luminosities have been corrected for evolution by $z$."393 In the Table. AZ. aud σα are the uean and rms values of a Gaussian fit to the evolution-corrected ας huuinosity function. Q quantifies the rate of Iuniuositv evolution. aud R. aud V are the values of ogyy(size/h type) aud logyy(velocity dispersion/liu 1) or an L. galaxy.," In the Table, $M_*$ and $\sigma_M$ are the mean and rms values of a Gaussian fit to the evolution-corrected $r$ -band luminosity function, $Q$ quantifies the rate of luminosity evolution, and $R_*$ and $V_*$ are the values of $\log_{10}$ $h^{-1}$ kpc) and $\log_{10}$ (velocity dispersion/km $^{-1}$ ) for an $L_*$ galaxy."394 Iu general. these values are all qualitatively simular to those reported in Bernardi et al. (," In general, these values are all qualitatively similar to those reported in Bernardi et al. ("39520035). but here are quantitative differences. most noticably iu the uean size Πο. which is simaller by about ten percent.,"2003b), but there are quantitative differences, most noticably in the mean size $R_*$, which is smaller by about ten percent."396 Table 1 also reports values of a ΠΙΟ of pairwise correlations in the following format., Table \ref{MLcov} also reports values of a number of pairwise correlations in the following format.397 Caven a pair of observables X aud Y. (YVAINfoyy=&£xyv(X.Noy.," Given a pair of observables $X$ and $Y$, $\langle Y-Y_*|X\rangle/\sigma_{YY} = \xi_{XY}(X-X_*)/\sigma_{XX}$."398 The results of a similar analysis of the correlations between color. magnitude aud velocity dispersion is given in Table 2..," The results of a similar analysis of the correlations between color, magnitude and velocity dispersion is given in Table \ref{MLcmag}."399 Figure 2 shows the coloranagnitude relation im our sample., Figure \ref{cmag} shows the color-magnitude relation in our sample.400 The top of seriespancls shows the raw mcasureient. and bottom panels show the result of accounting for evolution by adding 0.852 mags to the maguitudes. aud adding 0.3: mages to the colors (see Table 2)).," The top series of panels shows the raw measurement, and bottom panels show the result of accounting for evolution by adding $0.85z$ mags to the magnitudes, and adding $0.3z$ mags to the colors (see Table \ref{MLcmag}) )."401 Ou both tiers. the left-ost paucl shows the color-magnitude relation in the full sample. aud the other two panels show the relation in siunall bius in velocity dispersion.," On both tiers, the left-most panel shows the color-magnitude relation in the full sample, and the other two panels show the relation in small bins in velocity dispersion."402 The füsgure makes two miportaut poiuts: (1) at fixed velocity dispersion. there is no relation between color aud magnitude. aud (i) the slope of the relation in the loftinost panel is approximately the same im all redshift bius.," The figure makes two important points: (i) at fixed velocity dispersion, there is no relation between color and magnitude, and (ii) the slope of the relation in the leftmost panel is approximately the same in all redshift bins."403 We also find no evidence that the scatter around the mean relations changes with redshift. but placing a precise limit of the evolution is difficult. because the expected sienal is small so the auswer is scusitive to uncertainties in the SDSS photometry (0.02 1iags) aud the &-correction.," We also find no evidence that the scatter around the mean relations changes with redshift, but placing a precise limit of the evolution is difficult, because the expected signal is small, so the answer is sensitive to uncertainties in the SDSS photometry (0.02 mags) and the $k$ -correction."404Compton scatterime (IC) with thermal photons im the Wlein-Nishina regiue. with a cooling time-scale τι~3.108(eui/80TCV)l(es/2keV) d. which is shorter than the piondecay time Tey22.6«105s5.=5.5«10s(eti/30 TeV).,"Compton scattering (IC) with thermal photons in the Klein-Nishina regime, with a cooling time-scale $\tau_{\rm IC} \sim 3 \times 10^{-4}~{\rm s}~405(\epsilon_{\pi^{+}}/30{\rm TeV})^{-1} (\epsilon_\gamma/2{\rm keV})^{-4}$ , which is shorter than the piondecay time $\tau_{decay} \simeq4062.6 \times 10^{-8}~{\rm s}~\gamma_{\pi^{+}}=5.5\times 10^{-3}~{\rm s}~407(\epsilon_{\pi^{+}}/30~{\rm TeV})$ ."408 Thus the pious undereo some IC cooling before they decay. aud the typical neutrino enerey is down by a factor f.=(0.3/5.5)?~0.23 relative to the ἐν," Thus the pions undergo some IC cooling before they decay, and the typical neutrino energy is down by a factor $f_{c}=(0.3/5.5)^{1/2}\sim 0.23$ relative to the $\epsilon_{\nu,th}$."409 Therefore for discrete sources. the typical neutrine euergv is The final πιο huninositv is = Logf. y? plu )..," Therefore for discrete sources, the typical neutrino energy is The final neutrino luminosity is = f_c )^2 )^4."410"3) Since the spiudown buninositv is Le,=LA«LO?tore:SDRPSs) νο the neutro eiission efficiency is then 0.01 RAED) Lb We"," Since the spindown luminosity is $L_{sd}=1.5\times 10^{34}411{\rm erg/s}B_{p,15}^2 R_6^6 (P/5{\rm s})^{-4}$ , the neutrino emission efficiency is then = 0.04 )^2 ) R_6^4 )^4."412" (Gs)asstune that this Iuninuositv is beamed iuto a sweep-averaged solid angle AQ,~0.1. which is typical for a polar cap angle 0.01 and a moderate inclination angele of the rotator."," We assume that this luminosity is beamed into a sweep-averaged solid angle $\Delta \Omega_\nu \sim 0.1$, which is typical for a polar cap angle $\sim 0.01$ and a moderate inclination angle of the rotator."413" A smaller/lareer AO, increasesdecreases the on-heam neutrino flux. but decreases/iucreascs the probability of on-heam detection."," A smaller/larger $\Delta \Omega_{\nu}$ increases/decreases the on-beam neutrino flux, but decreases/increases the probability of on-beam detection."414 For au ou-beam observer. the neutrino nuniber fix at earth is MGT)? Bas «(Enteste temennam where D is the distance to the (psource.," For an on-beam observer, the neutrino number flux at earth is = )^2 ) ^3 )^4, where $D$ is the distance to the source."415" The probability of detecting a neutrinoduduced upward muon with planned netitrino telescopes is Z2,wy&1.3«10(e,'TeV) (Halzeu Ilooper 2002). eiviug au on-beam upward muon event rate dAdtidiserotey~L.7(i028)144) REE)"," The probability of detecting a neutrino-induced upward muon with planned neutrino telescopes is $P_{\nu\to\mu}\simeq 1.3\times 10^{-6} (\epsilon_{\nu}/{\rm TeV})$ (Halzen Hooper 2002), giving an on-beam upward muon event rate ) 1.7 ) ^3 )^4."416 The chances for the observer to be in the neutrino beau are not large., The chances for the observer to be in the neutrino beam are not large.417 Nonetheless. there is a small but finite probability for directly detecting some neutrinos frou these objects.," Nonetheless, there is a small but finite probability for directly detecting some neutrinos from these objects."418 In Table 1. we give the predicted muon event rates for the four magnuetar candidates which may be neutrino loud under favorable conditions. assumnius an ou-bea observation.," In Table 1, we give the predicted muon event rates for the four magnetar candidates which may be neutrino loud under favorable conditions, assuming an on-beam observation."419" Since other mnaguetars all lic below the most favorable f,=1/2 death valley. they are definetely below the photomesou threshold. aud we do uot consider them as neutrino cussion candidates."," Since other magnetars all lie below the most favorable $f_g=1/2$ death valley, they are definetely below the photomeson threshold, and we do not consider them as neutrino emission candidates."420 Frou Table 1. we see that SCR 1900111 and TE 10185-5937 may be detected by: kan? telescopes with several years of operation. if they are above the photomesonu threshold aud if their neutrino beams sweep the Earth.," From Table 1, we see that SGR 1900+14 and 1E 1048-5937 may be detected by $^3$ telescopes with several years of operation, if they are above the photomeson threshold and if their neutrino beams sweep the Earth."421" Accoupauving the neutrinos there should also be clectromaguctic signals frou z""-decay aud z! cooling aud cascading.", Accompanying the neutrinos there should also be electromagnetic signals from $\pi^{0}$ -decay and $\pi^{+}$ cooling and cascading.422 Thehieh 5D aud 55 pair-formation aud photon splitting opacity in the strong maeguetic fields may deerade the typical photon energy to < 140 MeV. below the EGRET baud (c.c. Ibuxiug. Baring Couthier 1997: Baring Tarding 2001). but it mav fall into the INTEGRAL baud.," Thehigh $\gamma B$ and $\gamma\gamma$ pair-formation and photon splitting opacity in the strong magnetic fields may degrade the typical photon energy to $\lesssim$ 40 MeV, below the EGRET band (e.g. Harding, Baring Gonthier 1997; Baring Harding 2001), but it may fall into the INTEGRAL band."423 A direct inference from the above proposal is that the eutire population of vouug magnetars in the universe will contribute to a diffuse neutrino backeround. before crossing the neutrino death valley.," A direct inference from the above proposal is that the entire population of young magnetars in the universe will contribute to a diffuse neutrino background, before crossing the neutrino death valley."424 The number flux of this backeround cau be generally estimated as where Dy~1075 cin is the Hubble distance. aud εν is the typical energy of the ueutrino background.," The number flux of this background can be generally estimated as where $D_H \sim 10^{28}$ cm is the Hubble distance, and $\bar425\epsilon_\nu$ is the typical energy of the neutrino background."426 The inner mteeral is the average total neutriuo energv fiueuce oer luaeuctar enütted towards earth duriug its neutrino-oud Tite fine Taga75«105 sy. which is based on he known magnetars being marginal neutrino enütters.," The inner integral is the average total neutrino energy fluence per magnetar emitted towards earth during its neutrino-loud life time $\tau_{mag,\nu} \sim 5\times 10^3$ yr, which is based on the known magnetars being marginal neutrino emitters."427 Since 9imaenetars have heen discovered in the Galaxy with ypical ages of 101 vr. the local (redslift 2=0) maguctar arth rate cau be conservatively estimated Ίο).~10?xvrtealaxyTR4792«107?vr!MpeOR s fora nunber density of ealaxies n4=0.02Mpc* (Allen 1973).," Since 9 magnetars have been discovered in the Galaxy with typical ages of $10^4$ yr, the local (redshift $z=0$ ) magnetar birth rate can be conservatively estimated ${\cal R}(0) \simeq 10^{-3}~{\rm yr^{-1} galaxy^{-1}} {\cal R}_{-3} 428\simeq 2\times 10^{-5}~{\rm yr^{-1} Mpc^{-3}} {\cal R}_{-3}$ , for a number density of galaxies $n_g=0.02~{\rm Mpc}^{-3}$ (Allen 1973)."429 Asuniug that the magnetar birth rate follows the star ornüug rate. R(:)=RIOD foro: «2 (Lilly et al.," Assuming that the magnetar birth rate follows the star forming rate, ${\cal R}(z) \simeq {\cal R}(0) (1+z)^3$ for $z<2$ (Lilly et al."430 1996)., 1996).431 The time-dependent beaming paraicter faf) Qvhich is the fraction of maguctars whose neutrino beams are directed towards us. so the sweep-averaged solid angle of the neutrino beam is AO(f)= πμ) cancels out.," The time-dependent beaming parameter $f_b(t)$ (which is the fraction of magnetars whose neutrino beams are directed towards us, so the sweep-averaged solid angle of the neutrino beam is $\Delta432\Omega(t)=4\pi f_b(t)$ ) cancels out."433 The outer integral is over the Wubble volume., The outer integral is over the Hubble volume.434 For remote maegnetars. the neutrino flux of au individual source drops as D7 while the total munber of maguctars increases as D? foy ;<1.," For remote magnetars, the neutrino flux of an individual source drops as $D^{-2}$ while the total number of magnetars increases as $D^3$ for $z\ll1$."435 Therefore most of the diffuse neutiiuo Cluission cones from the farthest magnuetars whose birth rate is the highest., Therefore most of the diffuse neutrino emission comes from the farthest magnetars whose birth rate is the highest.436" For wouug iaeuetars. the time-dependent neutrine ""numositv may be estimated as in 833."," For young magnetars, the time-dependent neutrino luminosity may be estimated as in 3."437 There are some joficeable differences. however.," There are some noticeable differences, however."438" For cxaimple. due to radiation reaction aud possible pair screcning effect. 5, 1."," For example, due to radiation reaction and possible pair screening effect, $\eta_p \ll 1$ ."439 On the other haud. the pair screening altitude could be uuch higher than the altitude where pious are generated. so that pions could undergo substautial reacceleration fore decaviug.," On the other hand, the pair screening altitude could be much higher than the altitude where pions are generated, so that pions could undergo substantial reacceleration before decaying."440 As a result f. could be c1., As a result $f_c$ could be $\gg 1$.441 Notice hat these uncertainties oulv influence the typical energy of the neutrino background. ἐν. but do not iufluence he number counts of the neutro backeround (17)). which can be estimated as follows.," Notice that these uncertainties only influence the typical energy of the neutrino background, $\bar \epsilon_\nu$ , but do not influence the number counts of the neutrino background \ref{barphinu}) ), which can be estimated as follows."442" The time-depeudoeut )cutrino luminosity is L,(f)=aA, (f)enzi(f)ez. where Aydt)1=ποΠο is the time-dependent polar. cap"," The time-dependent neutrino luminosity is $L_\nu (t) = A_{pc}(t) c n_{\pi^{+}}(t)\bar \epsilon_\nu$ , where $A_{pc}(t)=\pi \Omega(t)R^3/c$ is the time-dependent polar cap"443Data reduction was performed with the MIRIAD package (Sault. Teuben Wright 1995).,"Data reduction was performed with the MIRIAD package (Sault, Teuben Wright 1995)."444 In most cases naturally weighted. cleaned maps. Were used for image analysis.," In most cases naturally weighted, cleaned maps, were used for image analysis."445 We were able to produce a combined map from all the data using visibilities calibrated individually at each epoch., We were able to produce a combined map from all the data using visibilities calibrated individually at each epoch.446 Fig 2 presents a 4.8 GHz map of the field of XTE J1701-462 in which all sixteen datasets were combined. resulting in slightly more than 24 hr on-source.," Fig 2 presents a 4.8 GHz map of the field of XTE J1701-462 in which all sixteen datasets were combined, resulting in slightly more than 24 hr on-source."447 The radio counterpart of XTE 11701-462 is clearly detected at RA 17:00:58.43 Dee -46:11:08.44. with an uncertainty of about 0.3 aresec in each coordinate.," The radio counterpart of XTE J1701-462 is clearly detected at RA 17:00:58.43 Dec -46:11:08.44, with an uncertainty of about 0.3 arcsec in each coordinate."448 In order to compare the radio and X-ray properties of XTE we have made an estimate of which part of the Z the source was on at or close to the time of each radio observation., In order to compare the radio and X-ray properties of XTE we have made an estimate of which part of the 'Z' the source was on at or close to the time of each radio observation.449 XTE 1701—162. was observed 97 times with RXTE between 2006 Jan 22 - March 20. and once on 2006 April 23. providing simultaneous X-ray coverage for three of our radio observations and X-ray covergage within a few hours for the others.," XTE J1701–462 was observed 97 times with RXTE between 2006 Jan 22 - March 20, and once on 2006 April 23, providing simultaneous X-ray coverage for three of our radio observations and X-ray covergage within a few hours for the others."450 The RXTE observations before March 20 were all classified according to their iming properties and position in X-ray colour-colour diagrams by Homan et (007) and a separate analysis of the 2006 April 23 RXTE observation was done for this paper., The RXTE observations before March 20 were all classified according to their timing properties and position in X-ray colour-colour diagrams by Homan et (2007) and a separate analysis of the 2006 April 23 RXTE observation was done for this paper.451 The location along he Z tracks was estimated for the RXTE observations that were closest in time to our radio observations. by determining their xosition (upper/middle/lower) along the branches of full Z tracks hat were traced out in various time intervals (see Fig.," The location along the Z tracks was estimated for the RXTE observations that were closest in time to our radio observations, by determining their position (upper/middle/lower) along the branches of full Z tracks that were traced out in various time intervals (see Fig."452 3 in Homan et 22007)., 3 in Homan et 2007).453 These estimates are indicated in Table |., These estimates are indicated in Table 1.454 The radio detections and upper limits are also indicated as a function of branch of the Z in Fig 2., The radio detections and upper limits are also indicated as a function of branch of the Z in Fig 2.455 Our observations appear to indicate that XTE J1701-462 is most likely to be detected as a radio source when on the horizonta or normal branches (HB. NB) of the Z. There are no detections on the flaring branch. including the most stringent upper limi (observation P3.," Our observations appear to indicate that XTE J1701-462 is most likely to be detected as a radio source when on the horizontal or normal branches (HB, NB) of the Z. There are no detections on the flaring branch, including the most stringent upper limit (observation P)."456 This is consistent with the behaviour noted firs noted for GX 17-2 by Penninx et al. (, This is consistent with the behaviour noted first noted for GX 17+2 by Penninx et al. (4571988) and possibly universa or all Z sources (Penninx 1989).,1988) and possibly universal for all Z sources (Penninx 1989).458 These periods of relatively strong radio emission almost certainly correspond to the formation ofjet- ike outflows and/or their interaction with the surrounding medium (as directly observed in the Z/Z-like sources Sco X-I1 and Cir Fomalont et al., These periods of relatively strong radio emission almost certainly correspond to the formation of jet-like outflows and/or their interaction with the surrounding medium (as directly observed in the Z/Z-like sources Sco X-1 and Cir X-1; Fomalont et al.459 2001: Fender et al., 2001; Fender et al.460 2004)., 2004).461 In particular. based orimarily on results for Sco X-1. Migliari Fender (2006) suggest hat the HB / NB vertex may correspond to the point at which the most powerful eject events occur. and that the jet is suppressed on he FB.," In particular, based primarily on results for Sco X-1, Migliari Fender (2006) suggest that the HB / NB vertex may correspond to the point at which the most powerful eject events occur, and that the jet is suppressed on the FB."462 The Z sources are likely to be accreting persistently (in most cases) at close to the Eddington limit., The Z sources are likely to be accreting persistently (in most cases) at close to the Eddington limit.463 It may be useful to compare hem to black hole X-ray binaries accreting at comparably high Eddington ratios. such as GRS 19154105.," It may be useful to compare them to black hole X-ray binaries accreting at comparably high Eddington ratios, such as GRS 1915+105."464 Both classes of object make dramatic and rapid state transition and are associated with episodic production of powerful relativistic jets., Both classes of object make dramatic and rapid state transition and are associated with episodic production of powerful relativistic jets.465 Such objects may. in turn. be our best ‘local’ equivalents of quasars accreting at very high rates at redshifts of ς=1.," Such objects may, in turn, be our best `local' equivalents of quasars accreting at very high rates at redshifts of $z \geq 1$."466 Therefore careful comparison of objects such as XTE J1701-462 with black holes acereting at high rates may provide our best test of the effects of e.g. event horizons. static limits on accretion and jet formation.," Therefore careful comparison of objects such as XTE J1701-462 with black holes accreting at high rates may provide our best test of the effects of e.g. event horizons, static limits on accretion and jet formation."467 The two-point radio spectra of these detections are plotted in Fig 3., The two-point radio spectra of these detections are plotted in Fig 3.468" It is interesting to note that for the majority of the radio detections of XTE H701-462 the source radio spectrum is flat / inverted (spectral index à.=OQ. where S,x ov)."," It is interesting to note that for the majority of the radio detections of XTE J1701-462 the source radio spectrum is flat / inverted (spectral index $\alpha \geq 0$, where $_{\nu} \propto469\nu^{\alpha}$ )."470 This seems to be in contrast to most emission associated. with transient outbursts from X-ray binaries which generally has an optically thin spectrum (aX 1.6).," This seems to be in contrast to most emission associated with transient outbursts from X-ray binaries which generally has an optically thin spectrum $\alpha \leq471-0.6$ )."472 Optically thin emission is also observed in Cir X-| (Fender et al., Optically thin emission is also observed in Cir X-1 (Fender et al.473 1998: 2004) and Sco X-I (Fomalont et. al., 1998; 2004) and Sco X-1 (Fomalont et al.474 20013. although in both sources episodes of flat-spectrum core emission has been seen.," 2001), although in both sources episodes of flat-spectrum core emission has been seen."475 The flat/inverted radio spectrum is in fact more reminiscent of the steady. flat-spectrum radio emission observed from black holes in hard X-ray states (Fender 2001). although Migliari Fender (2006) do suggest that it should also be observed in hard state neutron stars.," The flat/inverted radio spectrum is in fact more reminiscent of the steady, flat-spectrum radio emission observed from black holes in hard X-ray states (Fender 2001), although Migliari Fender (2006) do suggest that it should also be observed in hard state neutron stars."476 Such flat-spectrum emission is believed to arise in a partially self-absorbed jet (Blandford Kónnigl 1979: Kaiser 2006)., Such flat-spectrum emission is believed to arise in a partially self-absorbed jet (Blandford Könnigl 1979; Kaiser 2006).477 Given the rather poor coverage and, Given the rather poor coverage and478do not proceed rapidly.,do not proceed rapidly.479 Doiual anion destruction mechanisms are by reaction with H and and by photodetachiment., Dominant anion destruction mechanisms are by reaction with H and $^+$ and by photodetachment.480 Photodetachinen rates were calculated according to Equation (2) of Milareal.(2007)., Photodetachment rates were calculated according to Equation (2) of \citet{mil07}.481. As a result. of its large electron detachinent energv. t1ie photodetachinent rate thus calculated is ~100 times less than the value in the RATEOG database.," As a result of its large electron detachment energy, the $^-$ photodetachment rate thus calculated is $\sim100$ times less than the value in the RATE06 database."482" Carbon chain anions ul η=2— 7). aud C,H (η=2. 1.6) have yee. shown to react witi atomic nitrogen and result in t formation of products that include the nitrile anions C,,N 0 (i0=1.3.5) (Eichelbergerοἱal. 2007)."," Carbon chain anions $_n^-$ $n=2-7$ ), and $_n$ $^-$ $n=2, 4, 6$ ) have been shown to react with atomic nitrogen and result in the formation of products that include the nitrile anions $_n$ $^-$ $n=1, 3, 5$ ) \citep{eic07}."483. We have included these reactions in he model as part of our investigation iuto the yossible mechanistus for the formaion of auc the receuly ¢iscovered CaN (ThadcleIsetal. 2008)., We have included these reactions in the model as part of our investigation into the possible mechanisms for the formation of $^-$ and the recently discovered $_3$ $^-$ \citep{tha08}.484. Branching ratios were calculated TOL EichelP)ergeretal.(2007) 5 ο‘ginal experimeuta data by Veronica Biebaum (private comumunication)., Branching ratios were calculated from \citet{eic07}' 's original experimental data by Veronica Bierbaum (private communication).485" The braiching ratio or the associative electron detachrent (AED) »roduct. channel could not. be derive [rom he experimental data. so we have assuiued. arbitrarily, a ratio of 0.5."," The branching ratio for the associative electron detachment (AED) product channel could not be derived from the experimental data, so we have assumed, arbitrarily, a ratio of 0.5."486 This assumption coustitutes potentially the most signilicaut source of error in these reaction rates., This assumption constitutes potentially the most significant source of error in these reaction rates.487 Mutual neutralisation reactions between anions and catious were shown by Lepp&Dalearuo(1988) to have important ellects ou interstellar chemistry., Mutual neutralisation reactions between anions and cations were shown by \citet{lep88} to have important effects on interstellar chemistry.488" Thus. reactions of the kinel ~3N4+Y(1)X* have been included for the twenty most abundant catious ). and for all auious ).in the model. with a rate coefficient of 75x10CD/300)"" cm? ! (seeHarada&Herbst2008.(or exzinple).."," Thus, reactions of the kind ^+ + }^- + have been included for the twenty most abundant cations $^+$ ), and for all anions $^-$ ), in the model, with a rate coefficient of $\times10^{-8}(T/300)^{-0.5}$ $^3$ $^{-1}$ \citep[see][for example]{har08}. ."489 The final chemical network contains 126 e@as-plase species coupled by 5539 reactious., The final chemical network contains 426 gas-phase species coupled by 5539 reactions.490 Initially the rate equations are solved as a funetion of radius (inthesamewayasMil-laretal.2¢)00).. starting [firon Lol? Cn and 1roving out (o ry=—20x1013 cin where photodissociation destroys all the molecules (apar [rom H»).," Initially the rate equations are solved as a function of radius \citep[in the same way as][]{mil00}, starting from $r_i=10^{15}$ cm and moving out to $r_f=3\times10^{18}$ cm where photodissociation destroys all the molecules (apart from $_2$ )."491 Then in a separate routine the ¢relmical abuudauces iusile the cdesilv-enhatced shells are caleulated as a fuicllou of racius., Then in a separate routine the chemical abundances inside the density-enhanced shells are calculated as a function of radius.492 The chemical rate equatio15 of a cleisltπι packet lying halfway betweeLa shells iner and outer radius fal a radius ry with «ensily (9+1)n(ry) are solved. starting [rou r; aud moving out to 2xLO” cnlw lere the density is sullicieutly low that 4he she uo longer makes aly sigIcanl c‘Outrilion to the total amount of matter il1 le 11odel.," The chemical rate equations of a density-enhanced packet lying halfway between a shell's inner and outer radius (at a radius $r_p$ with density $(\beta+1) n(r_p)$ ), are solved, starting from $r_i$ and moving out to $2\times10^{17}$ cm where the density is sufficiently low that the shell no longer makes any significant contribution to the total amount of matter in the model."493 The motion of the ceusity-enhanced stells iu the outflow are Followed so lia they move oward over tiiJe. SVLironised with je outward radial motion ve deuse packet.," The motion of the density-enhanced shells in the outflow are followed so that they move outward over time, synchronised with the outward radial motion of the dense packet."494 The adiation [field is culatec for the deuse pac‘ket at each tii1e- taking iuO account tle new positious | the stells.," The radiation field is recalculated for the dense packet at each time-step, taking into account the new positions of all the shells."495 The clensity factor (9). he inter-sliel W.paciug and thes rell thickness are iclenical for every shell so that the chemical yttclances Caculated for the cleuse pacsel al a give1 radius represent the abunclauces in a densitv-euliauced. shell centered at that raclius.," The density factor $\beta$ ), the inter-shell spacing and the shell thickness are identical for every shell so that the chemical abundances calculated for the dense packet at a given radius represent the abundances in a density-enhanced shell centered at that radius."496 The effects on the model results of variations in the mass-loss rate. radiation field strength. eas-lo-dust ratio. shell thickuess. inter-s1ell spaciiο ΠΠ factor aud stellar distauce have been analysed.," The effects on the model results of variations in the mass-loss rate, radiation field strength, gas-to-dust ratio, shell thickness, inter-shell spacing, density-enhancement factor and stellar distance have been analysed."497 The resits presetted in this study. are forthe inodel tiat Ies the parameters that we believe best natch the observational COnlslrallls., The results presented in this study are forthe model that uses the parameters that we believe best match the observational constraints.498 Moclification of these parameters. particularly thliose hat affect the radiation field strength.," Modification of these parameters, particularly those that affect the radiation field strength,"499 , 500surveys obtained through STScEs DSS Web interface.,surveys obtained through STScI's DSS Web interface.501 All of the data analysis presented in this paper was carried out using the Interactive Data Language (IDL)., All of the data analysis presented in this paper was carried out using the Interactive Data Language (IDL).502 We are greatly indebted to all who contributed to the various IDL User's Libraries: the routines of the IDL Astronomy Users Library (maintained by Wayne Landsman) have been used particularly extensively., We are greatly indebted to all who contributed to the various IDL User's Libraries; the routines of the IDL Astronomy User's Library (maintained by Wayne Landsman) have been used particularly extensively.503 HE thanks the Time Allocation Committee of the Institute for Astronomy for their support of the spectroscopic follow-up observations of eBCS clusters., HE thanks the Time Allocation Committee of the Institute for Astronomy for their support of the spectroscopic follow-up observations of eBCS clusters.504 HE also gratefully acknowledges partial financial support from a European Union EARA Fellowship. SAO contract SV4-64008. and NASA LTSA grant NAG 45-8253.," HE also gratefully acknowledges partial financial support from a European Union EARA Fellowship, SAO contract SV4-64008, and NASA LTSA grant NAG 5-8253."505 ACE. ACF and CSC thank the Royal Society for support.," ACE, ACF and CSC thank the Royal Society for support."506 This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service. provided by the NASA-Goddard Space Flight Center. and the NASA/IPAC Extragalactic Database (NED).," This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA-Goddard Space Flight Center, and the NASA/IPAC Extragalactic Database (NED)."507medium-resolution optical wavelength spectra. spanning a wavelength range from 3474 to 7418A.,"medium-resolution optical wavelength spectra, spanning a wavelength range from 3474 to 7418."508". All data were taken using the 3"" slit and a mmm! grating. producing a resolution of À/AA~ 1.000 at6.000A.."," All data were taken using the 3"" slit and a $^{-1}$ grating, producing a resolution of $\lambda / \Delta\lambda\sim$ 1,000 at."509 Exposure times varied widely based on the magnitude of the star. but ranged from ~3 to 300 s. The two-dimesional spectra were bias-subtracted and flat-fielded by the observatory standard data reduction procedure.," Exposure times varied widely based on the magnitude of the star, but ranged from $\sim$ 3 to 300 s. The two-dimesional spectra were bias-subtracted and flat-fielded by the observatory standard data reduction procedure."510 After extraction. and the one-dimensional spectra were wavelength calibrated.," After extraction, and the one-dimensional spectra were wavelength calibrated."511 We used standard star spectra taken each night of the observations to produce sensitivity curves and flux calibrated spectra., We used standard star spectra taken each night of the observations to produce sensitivity curves and flux calibrated spectra.512 An extinetion correction file from Kitt Peak National Observatory was also applied to correct for major atmospheric effects., An extinction correction file from Kitt Peak National Observatory was also applied to correct for major atmospheric effects.513 The standard calibration. stars used to create the sensitivity curve are BD+26 2606. BD+33 2642. BD+17 4708. Feige 34. and HD 19445.," The standard calibration stars used to create the sensitivity curve are BD+26 2606, BD+33 2642, BD+17 4708, Feige 34, and HD 19445."514 Flux calibration and extinetion corrections were performed using the package and the task in IRAF., Flux calibration and extinction corrections were performed using the package and the task in IRAF.515 We used a combination of observatory logs and night-to-night comparison of the sensitivity function to determine whether the calibrated target spectra were reliable enough to use in color analysis., We used a combination of observatory logs and night-to-night comparison of the sensitivity function to determine whether the calibrated target spectra were reliable enough to use in color analysis.516 We rejected some of the initial data sample based on concerns about non-photometric conditions and atmospheric distortion., We rejected some of the initial data sample based on concerns about non-photometric conditions and atmospheric distortion.517 Other nights are included in the final data for analysis because while the data may not be entirely photometric. it remains reliable enough for color analysis because of the non-wavelength dependent nature of most remaining distortions.," Other nights are included in the final data for analysis because while the data may not be entirely photometric, it remains reliable enough for color analysis because of the non-wavelength dependent nature of most remaining distortions."518 We discuss the errors in our derived SDSS colors further in refsec:colors, We discuss the errors in our derived SDSS colors further in \\ref{sec:colors1}.519 Many of ]..the targets are luminous enough in red wavelengths that longer exposure times cause parts of the spectrum to saturate., Many of the targets are luminous enough in red wavelengths that longer exposure times cause parts of the spectrum to saturate.520 The wavelengths from onward are of particular concern., The wavelengths from onward are of particular concern.521 However. shorter exposure times limited the amount of information we could derive from wavelengths below because of low signal-to-noise ratios.," However, shorter exposure times limited the amount of information we could derive from wavelengths below because of low signal-to-noise ratios."522 To create an S star spectral atlas. when possible we interpolated between two different exposure times: a shorter exposure time that produced accurate. unsaturated spectra at the longer wavelengths. and a longer exposure that resulted in higher signal-to-noise at shorter wavelengths.," To create an S star spectral atlas, when possible we interpolated between two different exposure times: a shorter exposure time that produced accurate, unsaturated spectra at the longer wavelengths, and a longer exposure that resulted in higher signal-to-noise at shorter wavelengths."523 Generally. we determined by hand which spectra were reliable in a particular wavelength region by comparing multiple exposure times and examining long exposures for nonlinear behavior in areas from onward.," Generally, we determined by hand which spectra were reliable in a particular wavelength region by comparing multiple exposure times and examining long exposures for nonlinear behavior in areas from onward."524 For stars with only one available exposure time. we rejected a star as saturated if the counts exceeded 60.000.," For stars with only one available exposure time, we rejected a star as saturated if the counts exceeded 60,000."525 After interpolating between spectra to eliminate saturated regions and rejecting some data. we were left with 46 S star spectra.," After interpolating between spectra to eliminate saturated regions and rejecting some data, we were left with 46 S star spectra."526 We use S star line identifications (Wyckoff&Clegg1978) to identify major spectral features and select objects with unique characteristics to include in the final spectral atlas. which includes 14 objects marked in reftab:stars..," We use S star line identifications \citep{1978MNRAS.184..127W} to identify major spectral features and select objects with unique characteristics to include in the final spectral atlas, which includes 14 objects marked in \\ref{tab:stars}."527 The objects were chosen to be a representative sample of the larger FAST sample. which includes many fundamentally similar objects.," The objects were chosen to be a representative sample of the larger FAST sample, which includes many fundamentally similar objects."528 Two sample spectra with associated molecular line identifications are plotted in reffig:speclines.., Two sample spectra with associated molecular line identifications are plotted in \\ref{fig:speclines}.529 While the spectra display the same molecular bands. most notably those associated with ZrO. they have different overall colors. which may be due to differences in abundances and/or effective temperatures.," While the spectra display the same molecular bands, most notably those associated with ZrO, they have different overall colors, which may be due to differences in abundances and/or effective temperatures."530 We also note that these spectra show some TiO bands. indicating that they are not pure S stars. but instead probably belong to the MS classification.," We also note that these spectra show some TiO bands, indicating that they are not pure S stars, but instead probably belong to the MS classification."531 The appearance of TiO bands indicates the possibility of a C/O ratio slightly less than 0.95., The appearance of TiO bands indicates the possibility of a C/O ratio slightly less than 0.95.532 The creation of a spectral atlas allows for greater investigation into the similarities and differences within the S star class., The creation of a spectral atlas allows for greater investigation into the similarities and differences within the S star class.533" For instance. some members of the spectral atlas exhibit. in addition to prominent ZrO features. Ho. H7, and H7 emission lines."," For instance, some members of the spectral atlas exhibit, in addition to prominent ZrO features, $\alpha$, $\beta 534$, and $\gamma$ emission lines."535 The presence of these emission lines indicates that these objects are almost certainly AGB stars. e.g.. Miras.," The presence of these emission lines indicates that these objects are almost certainly AGB stars, e.g., Miras."536 The spectral atlas is made available digitally as 14 individual FITS files via this journal., The spectral atlas is made available digitally as 14 individual FITS files via this journal.537 We can immediately use the first digital spectral atlas of S stars to derive some medium-resolution spectral indices. potentially useful to classify stars as M. S. or C even where they may have very similar broadband colors.," We can immediately use the first digital spectral atlas of S stars to derive some medium-resolution spectral indices, potentially useful to classify stars as M, S, or C even where they may have very similar broadband colors."538 Apart from our own FAST spectra of 48 S stars. we use M giants from the Indo-US spectral atlas (ValdesΕ..etal.2004).," Apart from our own FAST spectra of 48 S stars, we use M giants from the Indo-US spectral atlas \citep{Valdes04}."539. We use eight carbon star spectra also obtained with the FAST for a separate project (Green et al., We use eight carbon star spectra also obtained with the FAST for a separate project (Green et al.540 2011. in preparation).," 2011, in preparation)."541 These latter spectra span a wide range of spectral band strengths. but are selected from the SDSS color wedge defined by Margon.B..et(2002).," These latter spectra span a wide range of spectral band strengths, but are selected from the SDSS color wedge defined by \citet{Margon02}."542 We defined three indices. one each for TiO. ZrO. and Cs.," We defined three indices, one each for TiO, ZrO, and $_2$."543 We follow the basic premise of using ratios of mean flux per Ángstrómm across key molecular bands. so that spectra of differing resolution should yield similar results.," We follow the basic premise of using ratios of mean flux per ngströmm across key molecular bands, so that spectra of differing resolution should yield similar results."544 We use a neighboring comparison region for each band. so that sensitivity to broadband flux calibration is minimized.," We use a neighboring comparison region for each band, so that sensitivity to broadband flux calibration is minimized."545 For the ZrO index. we divide the mean flux across 6400 — (ZrO off-band) by that between 6475 — (ZrO band).," For the ZrO index, we divide the mean flux across 6400 – (ZrO off-band) by that between 6475 – (ZrO band)."546 For the TiO index. we use mean Av! flux from 7065 — (TiO band) divided by 6965 — (TIO off-band).," For the TiO index, we use mean $^{-1}$ flux from 7065 – (TiO band) divided by 6965 – (TiO off-band)."547 The C index is derived from 5025 — (Cs band) and 5238 — (off-band)., The C index is derived from 5025 – $_2$ band) and 5238 – (off-band).548 Thus. lower flux in the denominator caused by strong molecular bands yields a larger spectral index value.," Thus, lower flux in the denominator caused by strong molecular bands yields a larger spectral index value."549" We note that the C index near can also be substantially contaminated by TiO. so we label it ""CT517 hereafter."," We note that the C index near can also be substantially contaminated by TiO, so we label it “CT51” hereafter."550 At least within this representative sample of stars. a combination of these indices yields à preliminary S star classification. as shown in Figure 2..," At least within this representative sample of stars, a combination of these indices yields a preliminary S star classification, as shown in Figure \ref{fig:specind}."551 The objects most reliably classified as S stars would have ZrO index >1.2 and C» index <L.4., The objects most reliably classified as S stars would have ZrO index $>1.2$ and $_2$ index $<1.4$.552 To use the SDSS database to find likely candidates for both S giants anddwarfs. we need reliable colors for our objects in as many SDSS bandpasses as possible.," To use the SDSS database to find likely candidates for both S giants anddwarfs, we need reliable colors for our objects in as many SDSS bandpasses as possible."553 The spectra from FAST cover the bandpasses for the g and r filters completely. and we are thus able to convolve our spectra with these bandpasses and generate SDSS colors.," The spectra from FAST cover the bandpasses for the $g$ and $r$ filters completely, and we are thus able to convolve our spectra with these bandpasses and generate SDSS colors."554 Each of the FAST spectra contains 2681 data points. with approximate wavelength separation of 1.47 A.," Each of the FAST spectra contains 2681 data points, with approximate wavelength separation of 1.47 ."555. To convolve the spectra with the filter transmission curves. we use linear interpolation," To convolve the spectra with the filter transmission curves, we use linear interpolation"556((Nova Per 1901: Campbell 1903). belongs to a subgroup of cataclysmic variables (CVs) called Intermediate: Polars (IPs).,"(Nova Per 1901; Campbell 1903), belongs to a subgroup of cataclysmic variables (CVs) called Intermediate Polars (IPs)."557 In. these systems. an asvnchronously-rotating. magnetic white dwarl accretes material [rom a less-massive. ate-type companion filling its Roche lobe.," In these systems an asynchronously-rotating, magnetic white dwarf accretes material from a less-massive, late-type companion filling its Roche lobe."558 Cas leaving the Companion star attempts to form an accretion disc around he primary star but its magnetic field either prevents the ormation of the cise or truncates it near the white chart., Gas leaving the companion star attempts to form an accretion disc around the primary star but its magnetic field either prevents the formation of the disc or truncates it near the white dwarf.559 wawas identified with the X-ray source 0327|43 by line. ticketts Warwick (1979) and confirmed as an LP? by the detection of a 351ss X-ray spin pulse by Watson. Kine Osborne (1985: hereafter WIxXO) and Norton. Watson lxing (1988).," was identified with the X-ray source A0327+43 by King, Ricketts Warwick (1979) and confirmed as an IP by the detection of a s X-ray spin pulse by Watson, King Osborne (1985; hereafter WKO) and Norton, Watson King (1988)."560 The same period was subsequently found. in optical photometry by. Patterson (1991)., The same period was subsequently found in optical photometry by Patterson (1991).561" hhas the longest orbital period from the sample of known CVs. Po, = 2dd. (Crampton. Cowley Fisher 1986: hereafter CCE)."," has the longest orbital period from the sample of known CVs, $_{\mbox{orb}}$ = d, (Crampton, Cowley Fisher 1986; hereafter CCF)."562 Phe wide binary separation combined with a relatively weak magnetic field (~ 1 MG) means that a truncated aceretion disc must be present if current theories of disc formation are correct (Llameury. ling Lasota 1986).," The wide binary separation combined with a relatively weak magnetic field $\sim$ 1 MG) means that a truncated accretion disc must be present if current theories of disc formation are correct (Hameury, King Lasota 1986)."563 The presence of a disc has vet to be confirmed by direct. observation. although the system. does. undergo dwarf nova outbursts every 3vyvears. where its optical brightness increases from 13th to LOth magnitude (Sabbacdin Bianehini 1983).," The presence of a disc has yet to be confirmed by direct observation, although the system does undergo dwarf nova outbursts every years where its optical brightness increases from 13th to 10th magnitude (Sabbadin Bianchini 1983)."564 The most-likely mechanism for cwart nova outbursts is a thermal instability within an accretion disc (Osaki 1974)., The most-likely mechanism for dwarf nova outbursts is a thermal instability within an accretion disc (Osaki 1974).565 ooutbursts have been modelled: as such by Cannizzo Ixenvon (1986) and Kim. Wheeler Mineshige (1992).," outbursts have been modelled as such by Cannizzo Kenyon (1986) and Kim, Wheeler Mineshige (1992)."566 This paper is à continuation of paper (Alorales-Rueda. sull Roche 1996). in which we presented spectrophotometric observations of ttaken on the rise to its 1996 outburst (Mattei 1996).," This paper is a continuation of paper (Morales-Rueda, Still Roche 1996), in which we presented spectrophotometric observations of taken on the rise to its 1996 outburst (Mattei 1996)."567 We reported the detection of quasi-periodic oscillations (QPOs) within the Doppler-broadened emission lines of LL and Le11., We reported the detection of quasi-periodic oscillations (QPOs) within the Doppler-broadened emission lines of H and He.568 Phis provides an opportunity to map the velocity structure of the oscillations., This provides an opportunity to map the velocity structure of the oscillations.569 QPOs are defined as. Iow-coherence brightness oscillations thought to be associated with material within the inner accretion [lows of CVs., QPOs are defined as low-coherence brightness oscillations thought to be associated with material within the inner accretion flows of CVs.570 Theoretical models developed to explain QPOs consider the presence of dense blobs of material orbiting in the inner regions of the accretion disc (Bath 1973). or non-racial pulsations over the surface of the white dwarf (Papaloizou," Theoretical models developed to explain QPOs consider the presence of dense blobs of material orbiting in the inner regions of the accretion disc (Bath 1973), or non-radial pulsations over the surface of the white dwarf (Papaloizou"571spectra. one of them was summed (ice). so that the correct spectrum obtained from OBS! shows an excess with respect to the thermal component with the average gas temperature measured by (8.112:0.07. 9095: David 1993) at a somewhat lower confidence level of ~3.40 (see Table 1).,"spectra, one of them was summed twice), so that the correct spectrum obtained from OBS1 shows an excess with respect to the thermal component with the average gas temperature measured by $\pm$ 0.07,; David 1993) at a somewhat lower confidence level of $\sim 3.4\sigma$ (see Table 1)."572 The fit with a single temperature gives ~9.91.3(71 keV. above je average gas temperature nieasured by (will a fiekl of view comparable to that of 1e PDS). implving the presence of a second spectral component.," The fit with a single temperature gives $\sim 9.9^{+1.3}_{-1.1}$ keV, above the average gas temperature measured by (with a field of view comparable to that of the PDS), implying the presence of a second spectral component."573 The fit with two thermal 'oónponents (one fixed at 8.1 keV) requires an unrealistic second temperature (> 50 keV) wal stronglv supports a mechanism for the additional component. present in je spectrum of the Coma cluster., The fit with two thermal components (one fixed at 8.1 keV) requires an unrealistic second temperature $>$ 50 keV) that strongly supports a mechanism for the additional component present in the spectrum of the Coma cluster.574 1 we consider a power-law lor the second component. 1e PDS data are not able to fix the photon index. but the flux is rather stable against index variations.," If we consider a power-law for the second component, the PDS data are not able to fix the photon index, but the flux is rather stable against index variations."575 We assume a photon index Dy. = 2.0 (o derive the fux iab results to be (2.341.0)x10|ergem7s+ in the 2080 keV οποιον range., We assume a photon index $\Gamma_X$ = 2.0 to derive the flux that results to be $(2.3\pm 1.0)\times 10^{-11}\erg$ in the 20–80 keV energy range.576 The observed count rate of ODS2 is 0.7240.02 c(s/s in the 15100 keV energv range. at the confidence level of ~366.," The observed count rate of OBS2 is $\pm$ 0.02 cts/s in the 15–100 keV energy range, at the confidence level of $\sim57736\sigma$."578 Al energies above 20 keV the spectrum shows an excess with respect to the thermal emission (KT = 8.1 keV) at a confidence level of ~3.40. (see Table 1)., At energies above 20 keV the spectrum shows an excess with respect to the thermal emission (kT = 8.1 keV) at a confidence level of $\sim 3.4\sigma$ (see Table 1).579 The fit with a single temperature gives ~9.5(5 keV. Also ODS2 indicates the presence of an additional spectral feature and also in this case the fit with a second thermal component requires unrealistic values for the temperature., The fit with a single temperature gives $\sim 9.5^{+0.8}_{-0.6}$ keV. Also OBS2 indicates the presence of an additional spectral feature and also in this case the fit with a second thermal component requires unrealistic values for the temperature.580 The flux (Dy —2.0) is (13(5)x10.Hergem7?«!1 in the band 2080 keV. consistent with the flux reported in ODSI1.," The flux $\Gamma_X$ =2.0) is $(1.3^{+0.5}_{-0.6})\times 10^{-11}\erg$ in the band 20–80 keV, consistent with the flux reported in OBS1."581 The fIuxes are (marginally) consistent also at a conlidence level: (2.30.7)x10I!ergem7s1 in the first observation and “ereem7s! in the second one., The fluxes are (marginally) consistent also at a confidence level: $(2.3\pm 0.7)\times 10^{-11}\erg$ in the first observation and $(1.3^{+0.3}_{-0.4})\times 10^{-11}\erg$ in the second one.582 The combined spectrum is obtained by sunming (he spectra of the (wo observations (see Fie., The combined spectrum is obtained by summing the spectra of the two observations (see Fig.583 1)., 1).584 The total count rate is 0.74040.017 cts/s in the 15100 keV energy range. αἱ the confidence level of ~44o.," The total count rate is $0.740\pm5850.017$ cts/s in the 15–100 keV energy range, at the confidence level of $\sim 44\sigma$."586 Al energies 220 keV the ΗΝ excess is at the confidence level of ~4.80 (see Table 1)., At energies $>$ 20 keV the HXR excess is at the confidence level of $\sim 4.8\sigma$ (see Table 1).587 Even the inclusion of a svstematic to the data. necessary for sources with high S/N/ ratio but not [or [nint sources like Coma (Frontera 1991b). does not change the significance of our IINR excess.," Even the inclusion of a systematic to the data, necessary for sources with high S/N ratio but not for faint sources like Coma (Frontera 1997b), does not change the significance of our HXR excess."588 The fit with a single thermal component gives 9.70.6 keV. well above the average gas temperature measured byGinga. wilh a statistically unacceptable 4? value (—2.1 for 8 d.o.f.).," The fit with a single thermal component gives $\pm0.6$ keV, well above the average gas temperature measured by, with a statistically unacceptable $\chi^2$ value (=2.1 for 8 d.o.f.)."589 The presence of a second component is more evident from the 4? value that has a signilicant decrement when a second component. a power law. is added to the thermal component with KT—8.1 keV. The improvement passing from the first model (42 = 4.10 for 9 d.o.L)," The presence of a second component is more evident from the $\chi^2$ value that has a significant decrement when a second component, a power law, is added to the thermal component with kT=8.1 keV. The improvement passing from the first model $\chi^2_\nu$ = 4.10 for 9 d.o.f.)"590 to the second one (47 = 1.2 for 7 d.o.L.), to the second one $\chi^2_\nu$ = 1.2 for 7 d.o.f.)591 is significant at more than confidence level. according to the F-test.," is significant at more than confidence level, according to the F-test."592 Also. the combined spectrum cannot be fitted with a second thermal component unless an unrealistic value for the temperature is assunied. (hus supporting the origin for," Also, the combined spectrum cannot be fitted with a second thermal component unless an unrealistic value for the temperature is assumed, thus supporting the origin for"593(or even more elficient) in exchanging enerev with the equilibrium flow.,(or even more efficient) in exchanging energy with the equilibrium flow.594 We know from previous studies that in the absence of the gravitv-induced stratification among the MITD waves. the fast magnetosonic waves are (he most efficient ones in exchanging enerev with (he equilibrium flow (Poedts.Rogava&Mahajanivan 2000).," We know from previous studies that in the absence of the gravity-induced stratification among the shear-modified MHD waves, the fast magnetosonic waves are the most efficient ones in exchanging energy with the equilibrium flow \citep{prm99,rpm00}."595. It is of great. interest to check whether the fast Gravito-magnetosonic waves vive (he same quality. and (o determine what their contribution in the angular momentum redistribution could be., It is of great interest to check whether the fast Gravito-magnetosonic waves have the same quality and to determine what their contribution in the angular momentum redistribution could be.596 The study of the linear. dynamics of all Gravito-MIID. waves is currently initiated and the results will be published in a subsequent paper., The study of the linear dynamics of all Gravito-MHD waves is currently initiated and the results will be published in a subsequent paper.597 Finally. one has to remember (hat the non-modal approach that has been applied in the present paper. provides no information about the spatial aspects of the shear-induced processes. because (he study of (he Spatial Fourier LLarmonics is confined to the phase space of the wave number vectors k(/).," Finally, one has to remember that the non-modal approach that has been applied in the present paper, provides no information about the spatial aspects of the shear-induced processes, because the study of the Spatial Fourier Harmonics is confined to the phase space of the wave number vectors ${\bf k}(t)$."598 In order to have a clear idea about the spatial appearance of (hese processes. one has to study (hem numerically (similarly to the uniform. non-stratilied flow study made by Bodoetal... (2001))) and to check how the non-mocdal phenomena couple with the traditional rotational instabilities.," In order to have a clear idea about the spatial appearance of these processes, one has to study them numerically (similarly to the uniform, non-stratified flow study made by \citet{b01}) ) and to check how the non-modal phenomena couple with the traditional rotational instabilities."599 These results were obtained in the framework of the projects GOA 2004/01 (IX.U.Leuven). G.0304.07 (FWO-Vlaanderen) aud C90203 (ESA Prodex 8).," These results were obtained in the framework of the projects GOA 2004/01 (K.U.Leuven), G.0304.07 (FWO-Vlaanderen) and C90203 (ESA Prodex 8)."600 Andria Rogava wishes to thank the (Leuven. Belgium) and the Physics(CIrieste. Italv) for supporting him. in part. through a Senior Postdoctoral Fellowship and Senior Associate Membership Award. respectively.," Andria Rogava wishes to thank the (Leuven, Belgium) and the (Trieste, Italy) for supporting him, in part, through a Senior Postdoctoral Fellowship and Senior Associate Membership Award, respectively."601 The research ol Andria Rogava and Grigol Gogoberidze was supported in part by the Georgian National science Foundation grant GNSE/ST06/4-096., The research of Andria Rogava and Grigol Gogoberidze was supported in part by the Georgian National Science Foundation grant GNSF/ST06/4-096.602 The research of Grigol Gogoberidze was supported in part bv the INTAS erant. 06-10000177-9258., The research of Grigol Gogoberidze was supported in part by the INTAS grant 06-1000017-9258.603High-mass stars (OB spectral type. M>8M. and L10° Ls). although few in number. play a major role in the energy budget of galaxies. through their radiation. wind and the supernovae.,"High-mass stars (OB spectral type, $M>8\,M_{\odot}$ and $L>10^3\,L_{\odot}$ ), although few in number, play a major role in the energy budget of galaxies, through their radiation, wind and the supernovae."604 They are believed to form by accretion in dense cores within molecular cloud complexes2002::2003: 2005) and/or coalescence (e.g. 2001))., They are believed to form by accretion in dense cores within molecular cloud complexes; ) and/or coalescence (e.g. ).605 The intense radiation field emitted by a newly-formed central star heats and ioizes its parental molecular cloud. leading to the formation of a hot core (HC. e.g. 1997)) and afterwards an HII region.," The intense radiation field emitted by a newly-formed central star heats and ionizes its parental molecular cloud, leading to the formation of a hot core (HC, e.g. ) and afterwards an HII region."606 Our current understanding of their formation remains poor. especially concerning the earliest phases of the process.," Our current understanding of their formation remains poor, especially concerning the earliest phases of the process."607 The main observational difficulty is that high-mass stars are fewer in number thar low-mass stars and the molecular clouds that are able to form high-mass stars are statistically more distant than those forming low-mass stars., The main observational difficulty is that high-mass stars are fewer in number than low-mass stars and the molecular clouds that are able to form high-mass stars are statistically more distant than those forming low-mass stars.608 Therefore. current observational studies of high-mass star formatiot suffer both from the lack of spatial resolution and. consequently. from a lack of theoretical understanding.," Therefore, current observational studies of high-mass star formation suffer both from the lack of spatial resolution and, consequently, from a lack of theoretical understanding."609 The high-mass star-forming region G19.61-0.243 is an interesting target for the study of star cluster formation given its richness in terms of young stellar objects (YSOs). as indicated by studies at centimeter (e.g.1998:: 2000)). millimeter (e.g. 2005)) and (MIR: 2003)) wavelengths.," The high-mass star-forming region G19.61-0.23 is an interesting target for the study of star cluster formation given its richness in terms of young stellar objects (YSOs), as indicated by studies at centimeter (e.g.; ), millimeter (e.g. ) and mid-infrared (MIR; ) wavelengths."610 is located at a distance of 12.6 kpe (see 2003)). based on the 21 em HI absorption spectrum toward the source.," G19.61-0.23 is located at a distance of 12.6 kpc (see ), based on the 21 cm HI absorption spectrum toward the source."611 The total bolometric luminosity 1997)) is about 2x10°L...," The total bolometric luminosity ) is about $2\times10^6\,L_{\odot}$."612" The region contains OH1983:; 1989)), water 1996)) and methanol1995:;2000:: 2000)) masers. and a grouping of UC HII regions and extended radio continuum. indicating that it is an active region of massive star formation."," The region contains OH; ), water ) and methanol; ) masers, and a grouping of UC HII regions and extended radio continuum, indicating that it is an active region of massive star formation."613 The radio continuum emission from this region comes from five main sources. all of which are discussed in detail in (1998).," The radio continuum emission from this region comes from five main sources, all of which are discussed in detail in ."614. The region has been mapped in CS. NH; and CO1999::1992:: 1998)).," The region has been mapped in CS, $_3$ and CO; )."615 Extended mid- emission associated with the region is also detected by the MSX satellite 2003))., Extended mid-infrared emission associated with the region is also detected by the MSX satellite ).616 Single-dish observations of molecular lines with high critical densities show the presence of dense molecular gas over a broad range in velocity 1992))., Single-dish observations of molecular lines with high critical densities show the presence of dense molecular gas over a broad range in velocity ).617 In this paper we present a spectroscopic study of the region surrounding G19.61-0.23 in several transitions of CO isotopologues at an angular resolution of ~46” (about 2.8 pc at the distance of 12.6 kpc). on a large region of about 23x23’ (roughly 85 pe) centered on G19.61-0.23.," In this paper we present a spectroscopic study of the region surrounding G19.61-0.23 in several transitions of CO isotopologues at an angular resolution of $\sim46^{\prime\prime}$ (about 2.8 pc at the distance of 12.6 kpc), on a large region of about $23^{\prime}\times23^{\prime}$ (roughly 85 pc) centered on G19.61-0.23."618 Millimeter observations of carbon monoxide provide useful information on the physical properties of dense interstellar clouds as well as on their dynamical state., Millimeter observations of carbon monoxide provide useful information on the physical properties of dense interstellar clouds as well as on their dynamical state.619 Moreover. supplementary measurements of continuum emission in the sub-millimeter range with APEX. based on ATLASGAL data. and in the mid-infrared with Spitzer. based on GLIMPSE and MIPSGAL data. are presented.," Moreover, supplementary measurements of continuum emission in the sub-millimeter range with APEX, based on ATLASGAL data, and in the mid-infrared with Spitzer, based on GLIMPSE and MIPSGAL data, are presented."620 The aim is to study the global scale physical properties and their relation with the small-scale characteristics., The aim is to study the global large-scale physical properties and their relation with the small-scale characteristics.621 We analyzed the physical conditions and the velocity structure of the molecular components across the region., We analyzed the physical conditions and the velocity structure of the molecular components across the region.622 We finally consider the possible implications for, We finally consider the possible implications for623"In summary. (he ordering of Gime scales (hat will affect the physics of supernovae is roughly: where Tyl ms is the dynamical time scale. 7,,, is the (sub-Ixeplerian) rotation (niescale. 744,por ο rotation times. is (he timescale for dynamical bar formation. ms is the time lor the shock to form and stall. 74554~30 ms is the time for the MRI to erow the magnetic field to saturation. Tyεν~50—100 ms is the time for non-axisvmmetrie an = 1) modes (to grow. Τρ»0.1— Ls is the time to spin down due to magnetosonic huninosity. Τωρα0.1— Ls is the time lor a secular bar mode to grow. 7;4,,~1—10s is the de-leptonization time of the PNS to contract to [orm a neutron stab. 77,4655,~LO 8 is (he time lor the successful shock to propagate oul of the infalling iron core ancl into the surrounding star. e. g.. the helium core. and τος, 15 the time to dissipate angular momentum and rotational energv of the core by gravitational radiation reaction forces.","In summary, the ordering of time scales that will affect the physics of supernovae is roughly: where $\tau_{dyn} \sim 1 $ ms is the dynamical time scale, $\tau_{rot}$ is the (sub-Keplerian) rotation timescale, $\tau_{dyn-bar}$, a few rotation times, is the timescale for dynamical bar formation, $\tau_{shock} \sim 10$ ms is the time for the shock to form and stall, $\tau_{MRI} \sim 30 $ ms is the time for the MRI to grow the magnetic field to saturation, $\tau_{NAXI} \sim 50 -100$ ms is the time for non-axisymmetric (m = 1) modes to grow, $\tau_{mhd} \sim 0.1 - 1$ s is the time to spin down due to magnetosonic luminosity, $\tau_{secular} \sim 0.1 - 1$ s is the time for a secular bar mode to grow, $\tau_{delep} \sim 1 - 10 s$ is the de-leptonization time of the PNS to contract to form a neutron star, $\tau_{explosion} \sim 10$ s is the time for the successful shock to propagate out of the infalling iron core and into the surrounding star, e. g., the helium core, and $\tau_{grr}$ is the time to dissipate angular momentum and rotational energy of the core by gravitational radiation reaction forces."624 In the current context. Trrpfosion 15 meant to be the Gime bevond which physical processes in the PNS will no longer affect the ultimate outcome. perhaps because the density has decreased sufficiently that even if magnetoacoustic Πας is liberated. it cannot propagate outward aud hence affect the explosion.," In the current context, $\tau_{explosion}$ is meant to be the time beyond which physical processes in the PNS will no longer affect the ultimate outcome, perhaps because the density has decreased sufficiently that even if magnetoacoustic flux is liberated, it cannot propagate outward and hence affect the explosion."625 In the absence of a detailed model of this process. we have taken (he time for a successful shock to propagate into the helium core as a representative measure of this scale.," In the absence of a detailed model of this process, we have taken the time for a successful shock to propagate into the helium core as a representative measure of this scale."626 We note that the epoch of the onset of convection within the PNS is of order of tens of ms and that of convection in the post-shock region is of order 100 ms., We note that the epoch of the onset of convection within the PNS is of order of tens of ms and that of convection in the post-shock region is of order 100 ms.627 This emphasizes that (imescales of order 0.1 to 1 s. not epochs of tradiüonal concentration. will involve a varletv. of interacting physical processes (hat. will need to be more deeply understood.," This emphasizes that timescales of order 0.1 to 1 s, not epochs of traditional concentration, will involve a variety of interacting physical processes that will need to be more deeply understood."628" We also note that the timescale τος, is long. so all the physics associated with the other time scales represented here must be solved to know the conditions that might be relevant to the production of gravity waves once (if ever) those become (he dominant sink."," We also note that the timescale $\tau_{grr}$ is long, so all the physics associated with the other time scales represented here must be solved to know the conditions that might be relevant to the production of gravity waves once (if ever) those become the dominant sink."629 The contraction phase (Burrows&Lattimer1956:NeilJanka1995;Villainetal.2004) will lead to spin up and perhaps to crossing the threshold for NANI or enhancing the growth rate of these instabilities. (he amplitude of which max depend on T/Wl.," The contraction phase \citep{bur86,kei95,pon99,vil04} will lead to spin up and perhaps to crossing the threshold for NAXI or enhancing the growth rate of these instabilities, the amplitude of which may depend on $\tw$."630 These instabilities will cause some loss of rotation energy and angular momentum as (he core contracts. perhaps altering the specific nonaxisvuunetric modes (hat come into play.," These instabilities will cause some loss of rotation energy and angular momentum as the core contracts, perhaps altering the specific non–axisymmetric modes that come into play."631 The core will dissipate its differential rotation and angular momentum until the loss rales become comparable to. or longer than. the contraction (time scale.," The core will dissipate its differential rotation and angular momentum until the loss rates become comparable to, or longer than, the contraction time scale."632 The celeptonization, The de–leptonization633a sinele average before performing aperture plotomietry ou UY Vol aud a comparison star (both shown in Fie. 1)).,a single average before performing aperture photometry on UY Vol and a comparison star (both shown in Fig. \ref{ImageFig}) ).634 All photometry was done differentially relative to the comparison star using standard tecbuiques. and this star was then calibrated separately relative to standard stars A.C. aud D in the field of T Phe observed ou inultiple photometric nights (Landolt1992)..," All photometry was done differentially relative to the comparison star using standard techniques, and this star was then calibrated separately relative to standard stars A, C, and D in the field of T Phe observed on multiple photometric nights \citep{Landolt:1992a}."635. Our estimate of the calibrated magnitude of the comparison is R=11.66-20.03., Our estimate of the calibrated magnitude of the comparison is $R=14.66\pm0.03$.636 The uncertainty quoted is the might-to-might standard deviation., The uncertainty quoted is the night-to-night standard deviation.637 Systematic errors may be larger as color corrections were not possible since only &R baud observatious were performecl., Systematic errors may be larger as color corrections were not possible since only $R$ band observations were performed.638 Om deduced average magnitude for UY Vol is R=22.39c 0.01., Our deduced average magnitude for UY Vol is $R=22.39\pm0.04$ .639 This is the formal error on the mean and systematic uncertaiutfies in the calibration may be larger., This is the formal error on the mean and systematic uncertainties in the calibration may be larger.640 We show the long-term Lehtcurve iu Fie. 2.., We show the long-term lightcurve in Fig. \ref{LongLCFig}.641 Considerable nieht-to-uight variability is preseut but there is no obvious lone-terim trend., Considerable night-to-night variability is present but there is no obvious long-term trend.642 We will quantity this statement after removing some of the intrinsic variability in Section [.., We will quantify this statement after removing some of the intrinsic variability in Section \ref{LightcurveSection}.643 To verify the significance of the variability seen we also show a lightcurve for another nearby star at R=22.124001., To verify the significance of the variability seen we also show a lightcurve for another nearby star at $R=22.42\pm0.04$.644" The standard deviation of the individual UY Vol data is πας, while that for the nuon-variable star is uma."," The standard deviation of the individual UY Vol data is mag, while that for the non-variable star is mag."645 IR data were obtained iu a T-poiut dither pattern., IR data were obtained in a 7-point dither pattern.646 ον 50ss images were taken at 6 of the 7 positious. and 2 at the other.," $3\times50$ s images were taken at 6 of the 7 positions, and 2 at the other."647 For cach might. à sky image derived from the median of the dithered inages was subtracted. and flat-fields were applied.," For each night, a sky image derived from the median of the dithered images was subtracted, and flat-fields were applied."648 We excluded: images with the highest sky values and those with a sky value sieuificautlv deviating from the nightly mean to minimize residuals in the background subtraction., We excluded images with the highest sky values and those with a sky value significantly deviating from the nightly mean to minimize residuals in the background subtraction.649 We then filtered the remaining nuages based ou visibility of the faintest stars in the field., We then filtered the remaining images based on visibility of the faintest stars in the field.650 Our final combination of these best nuages used 122 individual frames. all of which had beeu oeidividuallv checked.," Our final combination of these best images used 422 individual frames, all of which had been individually checked."651 The target is mareinally detected oei this combined IR image at a position consistent with hat measured frou optical inages., The target is marginally detected in this combined IR image at a position consistent with that measured from optical images.652 Photometry relative ο several 2ATASS stars iu the field vields 7=21.84 L2., Photometry relative to several 2MASS stars in the field yields $J=21.3\pm0.2$ .653 At this level. we caution that svstematic errors in vackeround subtraction are likely to be larger than the cornu statistical error quoted.," At this level, we caution that systematic errors in background subtraction are likely to be larger than the formal statistical error quoted."654 It was innucdiately apparent that the data appeared consistent with modulation ou the published orbital veriod of ανν = 0.1593«dd (Wolffetal.2002) with a snele-huniped modulation., It was immediately apparent that the data appeared consistent with modulation on the published orbital period of hrs = d \citep{Wolff:2002a} with a single-humped modulation.655 To verity this we fitted the full dataset with a sinusoidal modulation of variable period. allowing the plasing. amplituce aud uean brightuess to vary freely.," To verify this we fitted the full dataset with a sinusoidal modulation of variable period, allowing the phasing, amplitude and mean brightness to vary freely."656 We find several strong uinina iu the dd period ranee (Fie. 39)., We find several strong minima in the d period range (Fig. \ref{SineFitFig}) ).657 One of these is consistent with the orbital period. aud the others are consistent with one-day aliases of the orbital xriod. as expected given our ouce-per-day sampling.," One of these is consistent with the orbital period, and the others are consistent with one-day aliases of the orbital period, as expected given our once-per-day sampling."658 No sienificant minimuia are seen other than these aliases., No significant minima are seen other than these aliases.659" Choosing the alias corresponding to the X-ray period. we derive an optical period of P=60.159351+000012 dd. The 1...@ uncertainty quoted corresponds o the range of periods with which 4?x:4Z,,|1."," Choosing the alias corresponding to the X-ray period, we derive an optical period of $P=0.159331\pm0.000012$ d. The $1-\sigma$ uncertainty quoted corresponds to the range of periods with which $\chi^2 \leq \chi^2_{min}+1$."660 This 2ο1οςἱ is conusisteut with the secure A-rav orbital period of dd to within errors., This period is consistent with the secure X-ray orbital period of d to within errors.661 The uucertaiutv is ~0.01 xeriod is mdeed orbital not sisuificautlv longer as would ο expected from a superluup modulation., The uncertainty is $\sim0.01$ period is indeed orbital not significantly longer as would be expected from a superhump modulation.662"lis fainter than the normal stars with the same effective temperature in the far-UV on wavelengths lower than 2400A, whereas it is brighter than normal stars in the near-UV and visible regions.","is fainter than the normal stars with the same effective temperature in the far-UV on wavelengths lower than $2400\,$, whereas it is brighter than normal stars in the near-UV and visible regions."663" Although the comparison of the narrow-band variations revealed the regions where the disagreement between the observed and predicted flux variations occurs, the narrow-band variations are inadequate to figure out the origin of these"," Although the comparison of the narrow-band variations revealed the regions where the disagreement between the observed and predicted flux variations occurs, the narrow-band variations are inadequate to figure out the origin of these"664in this fit.,in this fit.665 The recoil velocities as given in Eq. (1)), The recoil velocities as given in Eq. \ref{eqn:Fit3}) )666 are plotted in Fig., are plotted in Fig.667 b. as a functiou of mass ratio ancl spiLI parameter., \ref{Fig-v-recoil} as a function of mass ratio and spin parameter.668 Iu order to compute the probability that au. IMDII ronuünus in its elobular cluster. our caleulation shall proceed as follows.," In order to compute the probability that an IMBH remains in its globular cluster, our calculation shall proceed as follows."669 First we begim bv assunimg that an IMDITI has formed within a elobular cluster wit1 a particularinitial mass. A_yppiy. which we shall vary.," First we begin by assuming that an IMBH has formed within a globular cluster with a particularinitial mass, $M_{\mathrm{IMBH}}$, which we shall vary."670 Second. we further assunie a certain mass distribution for the DIIs in the vicinity of the ΤΑΠΟΠ. which we shall also vary.," Second, we further assume a certain mass distribution for the BHs in the vicinity of the IMBH, which we shall also vary."671 Third. we subject this IMIBIT to a number of mergers expected within a proto globular cluster environnent that we shall describe below.," Third, we subject this IMBH to a number of mergers expected within a proto globular cluster environment that we shall describe below."672 Finally. we deteriuue the probability that the kick velocity for the IMDII has remained below the canonical globular cluster escape velocity (50kms 7) during the entire chain of nergers.," Finally, we determine the probability that the kick velocity for the IMBH has remained below the canonical globular cluster escape velocity $50 \KMS$ ) during the entire chain of mergers."673 Even in the absence of an INDIT. DITs eject themselves yon globular clusters via standard few-hody interactions on a timescale of ~1Cyr after the onset of dass segregation (22?2)..," Even in the absence of an IMBH, BHs eject themselves from globular clusters via standard few-body interactions on a timescale of $\sim 1~{\rm Gyr}$ after the onset of mass segregation \citep{Kulkarni:93bhgc,Sigurdsson:93bhgc,Portegies:00bhmerge,Oleary:2005bm}."674 Therefore. due to such Newtoniau ew-body interactions. the supply of DIIS is eveutually depleted.," Therefore, due to such Newtonian few-body interactions, the supply of BHs is eventually depleted."675 With an IMDBIL however. this process speeds up lupressively. as ejections by interactions with an IMDII ecole the doninaut source of stellar-imass DII ejections (?)..," With an IMBH, however, this process speeds up impressively, as ejections by interactions with an IMBH become the dominant source of stellar-mass BH ejections \citep{Gultekin:2006tb}."676 As iu most few-body interactions. the ejection of one object tighteus the orbit of a remaining bound pair. in this case an IMDBIL-DII binary and after several subsequent ejections. the INIBU-BU binary mcrecs.," As in most few-body interactions, the ejection of one object tightens the orbit of a remaining bound pair, in this case an IMBH-BH binary – and after several subsequent ejections, the IMBH-BH binary merges."677 Soon iter all the DII« have been evacuated. the short epoch of IAIBU-BIT inerecrs euds.," Soon after all the BHs have been evacuated, the short epoch of IMBH-BH mergers ends."678 Within this theoretical framework. it is possible to construct a fiducial nuniber of mergers for a proto elobular cluster.," Within this theoretical framework, it is possible to construct a fiducial number of mergers for a proto globular cluster."679 This πανο can be written as Gultekin et al., This number can be written as Gultekin et al.680 2006 predict Mae~25 per IMDIT. and we adopt this for the fiducial number of mergers that the IMIBIT eucouuters.," 2006 predict $N_{\mathrm{merge}} \sim 25$ per IMBH, and we adopt this for the fiducial number of mergers that the IMBH encounters."681 Although we do vary this parameter in figure 2.. the dependence of the retention probability on the wmmber of niergers is relatively iinor. since the IMIBIT erows in mass over cach merger aud the kick velocity increases with increasing mass ratio.," Although we do vary this parameter in figure \ref{Fig-ret-prob}, the dependence of the retention probability on the number of mergers is relatively minor, since the IMBH grows in mass over each merger and the kick velocity increases with increasing mass ratio."682 Tn order to assign a kick velocity to each of tle merecrs. we choose the orieutation. spin. nass. and eccentricity.," In order to assign a kick velocity to each of the mergers, we choose the orientation, spin, mass, and eccentricity."683 We outline the assumptions made for cach distribution below., We outline the assumptions made for each distribution below.684 Let us first discuss the issue of the initial spin orientation., Let us first discuss the issue of the initial spin orientation.685 Uvdrodvuamic interactions between a gas disk aud a black hole binary are believed to align the spin directions to the angular momentum axis of the binary orbital plane im many active galaxies (?).., Hydrodynamic interactions between a gas disk and a black hole binary are believed to align the spin directions to the angular momentum axis of the binary orbital plane in many active galaxies \citep{tamara:07spin}.686 Towever. the euvironnieut of a globular cluster is not particularly eas-rich. so there is nomitio roason to expect the black role spins to be aligued.," However, the environment of a globular cluster is not particularly gas-rich, so there is no reason to expect the black hole spins to be aligned."687 We therefore assuue au isotropic distribution of orientation angeles for cach encouuter., We therefore assume an isotropic distribution of orientation angles for each encounter.688 Let us now discuss the choice of spin magnitude., Let us now discuss the choice of spin magnitude.689 Most heories predict a non-zero spin for a black hole produced via stellar runaway (7) or frou a supernovae renuit (2).., Most theories predict a non-zero spin for a black hole produced via stellar runaway \citep{Rees:07mbh} or from a supernovae remnant \citep{Fryer:01spin}.690 If au IMDBIT started with zero spin. a imerecr is likely o spin up the remnant through transfer of orbital to spin augular iiomenutuim (?)..," If an IMBH started with zero spin, a merger is likely to spin up the remnant through transfer of orbital to spin angular momentum \citep{Gammie:2003qi}."691 Towever. a I&err black hole can spindowo when magnetic field lines thread through he ergosphere to magueticalle brake the svstein (?).. oovided there is a gaseous disk around the reumaut.," However, a Kerr black hole can $spin692 down$ when magnetic field lines thread through the ergosphere to magnetically brake the system \citep{Blandford:77spin}, provided there is a gaseous disk around the remnant."693 Taking all these consideration iuto account. we shall explore three cases: (1) the spin maguitude is selected roni a uniformi initial spin distribution (fiducial case): (2) the initial spin maeuitude of the IMDIT κους is set ο U.998MRrays and (3) the spin is initially set to zero.," Taking all these consideration into account, we shall explore three cases: (1) the spin magnitude is selected from a uniform initial spin distribution (fiducial case); (2) the initial spin magnitude of the IMBH seed is set to $0.998 M_{\mathrm{IMBH}}^2$; and (3) the spin is initially set to zero."694 We asstune the spin of the secondary. DII to be randomly selected from a distribution of [0.0998]AL? where M. is the mass of the secoudary BID.," We assume the spin of the secondary BH to be randomly selected from a distribution of $[0,0.998]~M_{\mathrm{sec}}^2$ , where $M_{\mathrm{sec}}$ is the mass of the secondary BH."695 Since these stelbu- DIIS originate as a supernova renimant. though. the," Since these stellar-mass BHs originate as a supernova remnant, though, the"696Efforts in understanding the physics at work in active ealactic nuclei (AGN) started four decades ago.,Efforts in understanding the physics at work in active galactic nuclei (AGN) started four decades ago.697 The origin ol the infrared (Hi) continuum of AGN was initially a matter of controversy. as it could be non-thermal but. could equally be due to thermal emission from dust. grains.," The origin of the infrared (IR) continuum of AGN was initially a matter of controversy, as it could be non-thermal but could equally be due to thermal emission from dust grains."698 Η was long ago sugeested(Reesetal.1969). that Ht emission radiation from Sevlort galaxies in the 2.2. 22 wavelength range was produced by dust grains heated by ultraviolet (UV) and optical emission [from the nucleus.," It was long ago suggested\citep{rees69}699 that IR emission radiation from Seyfert galaxies in the 2.2 – 22 wavelength range was produced by dust grains heated by ultraviolet (UV) and optical emission from the nucleus."700 Work carried out. later on sugeests the LIU emission to be the reprocessed emission of the UV/optical radiation from the accretion disk by the particles composing the torus. namely silicate and graphite erains (e.g. Pier&Ixrolik.1992: Granato&Danese 1904: Efstathiou&Rowan-Robinson 1995: Nenkovaetal. 2002)).," Work carried out later on suggests the IR emission to be the reprocessed emission of the UV/optical radiation from the accretion disk by the particles composing the torus, namely silicate and graphite grains (e.g. \citealt{pier92}; \citealt{granato94}; \citealt{efstathiou95}; \citealt{nenkova02}) )."701 Various configurations of the dust distribution gcometry and compositions havebeen since suggested (e.g. Pier&Ixrolik 1992: vanBenumel&Dullemond 2003:: Dullemond&van 2005::Fritzetal. 2006:: Elitzur&Shlosman 2006))., Various configurations of the dust distribution geometry and compositions havebeen since suggested (e.g. \citealt {pier92}; ; \citealt{vanbemmel03}; ; \citealt{dullemond05}; \citealt{fritz06}; ; \citealt{elitzur06}) ).702 Recentobservations (Jalleetal.2004). indicate that, Recentobservations \citep{jaffe04} indicate that703ollects of arbitrarily strong electromagnetic fields using a QED one-loop ellective Lagrangian approach.,effects of arbitrarily strong electromagnetic fields using a QED one-loop effective Lagrangian approach.704 These effects are discussed. in section 2.2.., These effects are discussed in section \ref{sec:tensors}.705 Plasma elfects. are included bv assuming free electrons moving under the Lorentz force without any selt-interactions., Plasma effects are included by assuming free electrons moving under the Lorentz force without any self-interactions.706 The model is that. of a cold magnetohyelrodyvnamic plasma ancl is. discussed. in section 2.3..., The model is that of a cold magnetohydrodynamic plasma and is discussed in section \ref{sec:plasma}.707 We have also assumed. that the medium is homogeneous in agreement with the travelling-wave ansatz., We have also assumed that the medium is homogeneous in agreement with the travelling-wave ansatz.708 OL course the actual situation is more complicated: with a thermally excited. plasma (e.g.7) and. inhomogeneities the latter can result in a whole slew of interesting interactions between the wave modes (2???) that are especially crucial to our understanding. of the thermal radiation from their surfaces. but these are bevond the scope of this paper.," Of course the actual situation is more complicated with a thermally excited plasma \citep[e.g.][]{Gill09BW}709 and inhomogeneities — the latter can result in a whole slew of interesting interactions between the wave modes \citep{Heyl99polar,Heyl01qed,Heyl01polar,2003PhRvL..91g1101L} that are especially crucial to our understanding of the thermal radiation from their surfaces, but these are beyond the scope of this paper."710 The formation of electromagnetic shocks is expected to be an important phenomenon for electromagnetic waves in the magnetized vacuum since. electromagnetic: waves can evolve discontinuities under the inlluence of nonlinear interactions. (272)..," The formation of electromagnetic shocks is expected to be an important phenomenon for electromagnetic waves in the magnetized vacuum since electromagnetic waves can evolve discontinuities under the influence of nonlinear interactions \citep{PhysRev.113.1649,711 zheleznyakov1982shock, heyl1998electromagnetic}."712 Such. shocks can form even in the presence of a plasma (?7).., Such shocks can form even in the presence of a plasma \citep{PhysRevD.59.045005}.713 1n this study. through our explicit focus on travelling waves. we examine an alternate class of solutions to the wave equations which do not suller this fate.," In this study, through our explicit focus on travelling waves, we examine an alternate class of solutions to the wave equations which do not suffer this fate."714" αφίσας, they are stabilized against the formation of discontinuities by nonlinear features."," Instead, they are stabilized against the formation of discontinuities by nonlinear features."715 “Phese waves travel as periodic wave trains without anv change to their form. such as wave steepening or shock formation.," These waves travel as periodic wave trains without any change to their form, such as wave steepening or shock formation."716 Waves such as these may contribute to the formation of pulsar microstructures (??)," Waves such as these may contribute to the formation of pulsar microstructures \citep{1987STIN...8816622C,2001ApJ...558..302J}."717 The vacuum of QED in the presence of large. magnetic fields can be described as a non-linear optical medium (?).., The vacuum of QED in the presence of large magnetic fields can be described as a non-linear optical medium \citep{1997JPhA...30.6485H}.718 We also choose to treat the ellect of the plasma on the waves through source terms py and Ji: therefore. we begin bv considering. Alaxwell’s equations in the presence. of a medium and plasma sources.," We also choose to treat the effect of the plasma on the waves through source terms $\rho_p$ and $\Jp$; therefore, we begin by considering Maxwell's equations in the presence of a medium and plasma sources."719 In. Lleavisicle-Lorentz units with e=1. Maxwell's equations can be used to derive the wave equations For clarity. we will avoid making cancellations or dropping vanishing terms.," In Heaviside-Lorentz units with $c=1$, Maxwell's equations can be used to derive the wave equations For clarity, we will avoid making cancellations or dropping vanishing terms."720 We cleline the vacuum cliclectric and inverse magnetic permeability tensors as follows (?) In the next few sections we build a mocdel describing travelling waves in a magnetar's atmosphere from. these equatIons.," We define the vacuum dielectric and inverse magnetic permeability tensors as follows \citep{Jack75}721 In the next few sections we build a model describing travelling waves in a magnetar's atmosphere from these equations."722 In this section. we describe our model of the QED vacuum in strong background. fields in terms of vacuum cielectric and inverse magnetic permeability tensors.," In this section, we describe our model of the QED vacuum in strong background fields in terms of vacuum dielectric and inverse magnetic permeability tensors."723 These are most conveniently described in terms of two Lorentz invariant combinations of the fields., These are most conveniently described in terms of two Lorentz invariant combinations of the fields.724 In order to examine the nonlinear ellects of the vacuum. nonperturbatively. we wish to use vacuum ciclectric aud inverse magnetic permeability tensors which are valid to all orders in the fields.," In order to examine the nonlinear effects of the vacuum nonperturbatively, we wish to use vacuum dielectric and inverse magnetic permeability tensors which are valid to all orders in the fields."725 Analytic expressionsfor these tensors were derived by? for the case of wrenchless fields (A.=(4E.BY?= 0) from the LUcisenbere-Euler-Weisskopl- (??7) one-loop ellective Lagrangian in ? and expressed in terms of a set of analytic functions.," Analytic expressionsfor these tensors were derived by \citet{1997JPhA...30.6485H} for the case of wrenchless fields $K=-(4\efi \cdot \bfi)^2=0$ ) from the Heisenberg-Euler-Weisskopf-Schwinger \citep{heisenberg-1936-98,726 weisskopf1936kongelige, Schwinger:1951} one-loop effective Lagrangian in \citet{1997PhRvD..55.2449H} and expressed in terms of a set of analytic functions."727 where and The tensors we need are derived in 7.. except that we have kept terms up to linear order in the expansion about ἐν=0 instead of dealing with the strictly wrenchless case.," where and The tensors we need are derived in \citet{1997JPhA...30.6485H}, except that we have kept terms up to linear order in the expansion about $K=0$ instead of dealing with the strictly wrenchless case."728 Our analysis therefore requires that A« Bi}., Our analysis therefore requires that $K \ll B_k^4$ .729, where730Several scintillation phenomena in the interstellar medium have posed challenges to any physical model to explain them?)..,Several scintillation phenomena in the interstellar medium have posed challenges to any physical model to explain \citep{2007ASPC..365..207R}.731 These include: (1) extreme scatering events (ESE) (?).., These include: (1) extreme scattering events (ESE) \citep{1987Natur.326..675F}.732 Compact racio sources are occassionally observed. to. σο through a period. of demagnilicaion at low frequencies by roughly a [actor of (2) pulsar parabolic ares (2): (3) galactic center scattering., Compact radio sources are occassionally observed to go through a period of demagnification at low frequencies by roughly a factor of (2) pulsar parabolic arcs \citep{2001ApJ...549L..97S}; (3) galactic center scattering.733 In each of these cases. a simple application of Snell's law with the assumption of spherical symmetry of the lens requires [ree electron. densities up to ~1013 5," In each of these cases, a simple application of Snell's law with the assumption of spherical symmetry of the lens requires free electron densities up to $\sim 10^4$ $^{-3}$."734 bree electrons are at temperatures of at least  LOT. and the inferred. pressures are dillieult. to reconcile with pressure balance in the interstellar medium.," Free electrons are at temperatures of at least $\sim 10^4$ K, and the inferred pressures are difficult to reconcile with pressure balance in the interstellar medium."735 A solution to case (3)λ has been proposed by ?.. who pointed out that scattering for sheet-like structures is dominated by the ones most aligned. with the line of sight.," A solution to case (3) has been proposed by \cite{2006ApJ...640L.159G}, who pointed out that scattering for sheet-like structures is dominated by the ones most aligned with the line of sight."736 The alignment lowers the required three dimensional electron density., The alignment lowers the required three dimensional electron density.737 In this paper. we compute the quantitative consequences of plasma lenses. and show —that triaxial structures are consistent with all observational data without requiring any unusual physical conditions.," In this paper, we compute the quantitative consequences of plasma lenses, and show that triaxial structures are consistent with all observational data without requiring any unusual physical conditions."738 Large axis ratios are generic consequences of reconnection., Large axis ratios are generic consequences of reconnection.739 In ideal resistive ΑΗ with ohmie conversion of magnetic fields. current sheets would be overdense in pressure equilibrium.," In ideal resistive MHD with ohmic conversion of magnetic fields, current sheets would be overdense in pressure equilibrium."740 Since the resistivity. is almost certainly not ohmic. the actual density is not. known.," Since the resistivity is almost certainly not ohmic, the actual density is not known."741 Phe phenomelogy suggests underdense current sheets. which is a probe of the physics of reconnection.," The phenomelogy suggests underdense current sheets, which is a probe of the physics of reconnection."742 Geometric factors cause the scattering to be dominated. by ravealigned events., Geometric factors cause the scattering to be dominated by rarealigned events.743 We follow the notation of ?.. reproducing their. lensing eeometry in reffig:lens..," We follow the notation of \cite{1992grle.book.....S}, reproducing their lensing geometry in \\ref{fig:lens}."744 The diameter distances from the observer. to he lens plane and to the source. plane are Dy and. D. respectively. and the distance of the source plane from the ens plane is Di.," The diameter distances from the observer to the lens plane and to the source plane are ${\rm D}_{\rm d}$ and ${\rm D}_{\rm s}$ respectively, and the distance of the source plane from the lens plane is ${\rm D}_{\rm745 ds}$."746" Physical coordinates in the source and ens planes are i and £ respectively, defined with respect to he optic axis connecting the observer with the centre of the ens."," Physical coordinates in the source and lens planes are $\vec\eta$ and $\vec\xi$ respectively, defined with respect to the optic axis connecting the observer with the centre of the lens."747 The deflection ofa light rav at the lens plane is denoted w à., The deflection of a light ray at the lens plane is denoted by $\vec{\hat\alpha}$.748 The angular position of a source at iis 3. and @ is he apparent angular position from which the dellected. ray ravels.," The angular position of a source at $\vec\eta$ is $\vec\beta$, and $\vec\theta$ is the apparent angular position from which the deflected ray travels."749" “Phev are related through the lens equation: = D.,——=—-—— theta)) =", They are related through the lens equation: = ) =750varlalions (hal can be interpreted as the horizontal velocities (wanWerkwijkThompsonetal. 2003).,"variations that can be interpreted as the horizontal velocities \citep{vank00,tho03}."751. In neutron stars. we expect that the amplitude of the displacements follows surface thermal variations caused by non-radial oscillations of the neutron star.," In neutron stars, we expect that the amplitude of the displacements follows surface thermal variations caused by non-radial oscillations of the neutron star."752 As with the white dwarl stars. an increase in (he velocities can result in increased thermal emission from the star.," As with the white dwarf stars, an increase in the velocities can result in increased thermal emission from the star."753 In our non-radial oscillation model. each frequency of oscillation has its own periodic velocily (or displacement) amplitude.," In our non-radial oscillation model, each frequency of oscillation has its own periodic velocity (or displacement) amplitude."754 In the pulsars we have studied to date. (he amplitude of the displacements dictates (he average pulse shape (Rosen&Denmorest 2010).. but as the amplitude of the velocities grows. the average pulse shape can change (Clemens&Rosen2008).," In the pulsars we have studied to date, the amplitude of the displacements dictates the average pulse shape \citep{ros08,ros10}, but as the amplitude of the velocities grows, the average pulse shape can change \citep{cle08}."755. In (these pulsars. through fitting a non-radial oscillation model to their cdiifting subpulses. we have also [ound (0 be large compared to that seen in white dwarf stars. consistent with their smaller size.," In these pulsars, through fitting a non-radial oscillation model to their drifting subpulses, we have also found to be large compared to that seen in white dwarf stars, consistent with their smaller size."756 For pulsars DOSQ04-74 and BOOL3+10. values range from 126<( <133 (Rosen&Demorest2010) and 385<< «875 Clemens 2008).. respectivelv.," For pulsars B0809+74 and B0943+10, values range from $126 \leq$ $\leq 133$ \citep{ros10} and $385 \leq$ $\leq 875$ \citep{ros08}, respectively."757 In while dwarl stars. modes with high [ade from view because of geometric cancellation of the stellar surface. leaving only modes of low 4) (Yeatesetal.2005:Thompson2004.2008).," In white dwarf stars, modes with high fade from view because of geometric cancellation of the stellar surface, leaving only modes of low $\leq 4$ ) \citep{yea05,tho04,tho08}."758. By fitting a non-radial oscillation model to the drifting subpulses in P5ls D09434-10 and BOSO9+74. we measured the pulsation period to be on the order of 30—50 ms (Rosen& 2010).," By fitting a non-radial oscillation model to the drifting subpulses in PSRs B0943+10 and B0809+74, we measured the pulsation period to be on the order of $-$ 50 ms \citep{ros08,ros10}."759. These values for the pulsation period are consistent with core (Reisenegeer&Goldreich1992)., These values for the pulsation period are consistent with core \citep{rei92}.760. ILowever. core require large excitation energles. and (therefore surface are a possibility (Strohmaver1993). as they have lower energies ancl larger surface amplitudes than the core modes (McDermott 1983).," However, core require large excitation energies, and therefore surface are a possibility \citep{str93} as they have lower energies and larger surface amplitudes than the core modes \citep{mcd88}."761. The period predictions [or core in neutron stus range from a minimum value of 10 ms (Iteisenegger&Goldreich1992) to 2-88 seconds al.1988). depending on the model for the structure and composition of (he stellar interior., The period predictions for core in neutron stars range from a minimum value of 10 ms \citep{rei92} to $-$ 88 seconds \citep{mcd88} depending on the model for the structure and composition of the stellar interior.762 surface have periods in the 40—400 ms range (McDermottetal.1988)., Surface have periods in the $-$ 400 ms range \citep{mcd88}.763. While the pulsation periods calculated for most models are calculated assuming low(.. the period of the mode decreases for higher spherical degree (McDermottοἱal. 1938).," While the pulsation periods calculated for most models are calculated assuming low, the period of the mode decreases for higher spherical degree \citep{mcd88}. ."764. It is unlikely that the pulsation modes we see in PSRs D09432-10 ancl DO3004-14 are as these modes have periods on the order of tenths of milliseconds (McDermottetal.1988). and have overtones with shorter periods. whereas the overtones of have longer periods.," It is unlikely that the pulsation modes we see in PSRs B0943+10 and B0809+74 are as these modes have periods on the order of tenths of milliseconds \citep{mcd88} and have overtones with shorter periods, whereas the overtones of have longer periods."765 The two oscillation driving mechanisms for white dwarl stars are the &— mechanism and convective driving., The two oscillation driving mechanisms for white dwarf stars are the $\kappa-\gamma$ mechanism and convective driving.766 For pulsating DOVs stars like PG1159—035. characterized bv an abmosphere that lacks hydrogen but shows helium. carbon. and oxvgen absorption lines. the K—5 mechanism drives (he pulsations as (he opacity variessteeply with pressure (Starrlield 2003)..," For pulsating DOVs stars like $-$ 035, characterized by an atmosphere that lacks hydrogen but shows helium, carbon, and oxygen absorption lines, the $\kappa-\gamma$ mechanism drives the pulsations as the opacity variessteeply with pressure \citep{sta83,cor06,cox03}. ."767 In DAV and DDV stars. which have atmospheres," In DAV and DBV stars, which have atmospheres"768presence of background matter from which another nucleus can be captured (for digestion or fusion with the remainder of the old one) this time depends to some extent on the nuclear properties of the surrounding matter.,presence of background matter from which another nucleus can be captured (for digestion or fusion with the remainder of the old one) this time depends to some extent on the nuclear properties of the surrounding matter.769 While the first. postulates are based. on the relations known from atomic and nuclear physics. the latter (ο) postulate follows already. from our experiments.," While the first postulates are based on the relations known from atomic and nuclear physics, the latter (g) postulate follows already from our experiments."770 The discovery ofa nuclear-active radiation propagating with a velocity on the kmescale. Le. ofa population captured into particularly gcocentric orbits. was somewhat unexpected for us.," The discovery of a nuclear-active radiation propagating with a velocity on the km-scale, i.e., of a population captured into particularly geocentric orbits, was somewhat unexpected for us."771 Therefore the next natural step was to increase the observation time of the signals from the bottom scintillator surface from LOO<Af|100pis (Drobyshevski 2000€) to 250xA:|ps with respect to the signal from the top scintillator.," Therefore the next natural step was to increase the observation time of the signals from the bottom scintillator surface from $-100 \le \Delta t \le +100\,\mks$ (Drobyshevski 2000c) to $-250 \le \Delta t \le +250\,\mks$ with respect to the signal from the top scintillator."772 We hoped that bevond the 3100ps interval we would enter the zone of purely random signals with a No(Af)=const distribution.," We hoped that beyond the $\pm773100\,\mks$ interval we would enter the zone of purely random signals with a $N_2(\Delta t) = {\rm const}$ distribution."774 However this conjecture did not gain a support., However this conjecture did not gain a support.775 We start our consideration with Af<0. Le.. with signals belonging to an upward [lux of non-monoenergetic (see Fie.," We start our consideration with $\Delta t < 0$, i.e., with signals belonging to an upward flux of non-monoenergetic (see Fig."776 1) particles., 1) particles.777 Here. except a taking shape maximum at 405κα20pts. which corresponds to the 7 cm interscintillator cistance at the particle normal velocity of —23 km/s one clearly sees another three maxima. with he first one. fairky diffuse. extending from -220 to -160 us. he second. from. -120 to -100. pts. and the third. from. -80 o -60 ps.," Here, except a taking shape maximum at $-40 \le \Delta \le -20\,\mks$, which corresponds to the 7 cm interscintillator distance at the particle normal velocity of $\sim\!2-3$ km/s, one clearly sees another three maxima, with the first one, fairly diffuse, extending from -220 to -160 $\mks$, the second from -120 to -100 $\mks$, and the third, from -80 to -60 $\mks$."778 Bearing in mind our assumptions (see Sec.2). the irst maximum can be due to the bottom scintillator excited ww the Auger electrons. which are emitted in the capture by daemons of air nuclei after getting freed of the Fe and Sn 1eavy nucle: captured in the traversal of the lower part ofthe inned-sheet casing at various angles.," Bearing in mind our assumptions (see Sec.2), the first maximum can be due to the bottom scintillator excited by the Auger electrons, which are emitted in the capture by daemons of air nuclei after getting freed of the Fe and Sn heavy nuclei captured in the traversal of the lower part of the tinned-sheet casing at various angles."779 Phe Auger electrons can be emitted. also in the capture of Sn from the thin tin coating of the iron sheet., The Auger electrons can be emitted also in the capture of Sn from the thin tin coating of the iron sheet.780 After the participation in all these oocesses. part of the daemons reach the top Iuminophor. and it is here that they generate the trigger pulse correlating with the signals of the first dilfuse maximum.," After the participation in all these processes, part of the daemons reach the top luminophor, and it is here that they generate the trigger pulse correlating with the signals of the first diffuse maximum."781" The sharper second and third. maxima are possibly produced. as the daemon captures Ag (Z,= 47) and Zn (Z,= 30) nuclei. respectively. in traversing the bottom Iuminophor."," The sharper second and third maxima are possibly produced as the daemon captures Ag $Z_{\rm n} = 47$ ) and Zn $Z_{\rm n} = 30$ ) nuclei, respectively, in traversing the bottom luminophor."782 Note that the captured S nucleus has a high probability to be shortly. lost when it encounters a Zn nucleus. anc the probability of capturing Ag is not smal despite the low concentration of Ag. because for a velocity of ~2 km/s the daemon free path until meeting an Ag atom is comparable with the ZnSXe) grain size.," Note that the captured S nucleus has a high probability to be shortly lost when it encounters a Zn nucleus, and the probability of capturing Ag is not small despite the low concentration of Ag, because for a velocity of $\sim$ 2 km/s the daemon free path until meeting an Ag atom is comparable with the ZnS(Ag) grain size."783 On traversing a any angle the bottom polystyrene plate into the space before the top Iuminophor. daemons finish digesting the Ae aix Zn nuclei. so that when they capture air atoms. they emi here Auger electrons. which trigger the top Iuminophor.," On traversing at any angle the bottom polystyrene plate into the space before the top luminophor, daemons finish digesting the Ag and Zn nuclei, so that when they capture air atoms, they emit here Auger electrons, which trigger the top luminophor."784 Lf our scenarium is true. the time shift between these maxima relative to Af=0 provides an idea about the time per decay of a dacmon-containing proton.," If our scenarium is true, the time shift between these maxima relative to $\Delta t = 0$ provides an idea about the time per decay of a daemon-containing proton."785 It turns out to be IAN8ToxfyΖανf24. which shows that our estimates of τι based on Solar energeties. (Drobyvsheyski 2000a.b) were clearly unclerestimates.," It turns out to be $\Delta\tau_{\rm ex} \approx \tau_{\rm ex} / n_{\rm p} =786\tau_{\rm ex}/Z_{\rm n} \approx 2\,\mks$, which shows that our estimates of $\tau_{\rm ex}$ based on Solar energetics (Drobyshevski 2000a,b) were clearly underestimates."787 The position of the first maximum (GMz1ο.200 pts) vields ~1.5 km/s for the velocity with which a daemon passes normally the distance of 29 em from the lower box cover to the upper Iuminophor laver.," The position of the first maximum $\Delta t \approx 180-200\,788\mks$ ) yields $\sim$ 1.5 km/s for the velocity with which a daemon passes normally the distance of 29 cm from the lower box cover to the upper luminophor layer."789 Taking into account the random angular clistribution of the trajectories. the average velocity increases to 73 kms. For Al0. the daemons move downward.," Taking into account the random angular distribution of the trajectories, the average velocity increases to $\sim$ 3 km/s. For $\Delta t > 0$, the daemons move downward."790 The first distinct maximum at ~20<Af«dps corresponds apparently to the time needed for a daemon to cross the 7-cm gap separating the scintillator lavers., The first distinct maximum at $\sim\!20 < \Delta t < 40 \mks$ corresponds apparently to the time needed for a daemon to cross the 7-cm gap separating the scintillator layers.791 For an arbitrary trajectory inclination. this time. às we saw before (Drobvshevski 2000€). corresponds to a velocity ~3.5 kms. Le. to objects in geocentric orbits with a perigee inside the Earth.," For an arbitrary trajectory inclination, this time, as we saw before (Drobyshevski 2000c), corresponds to a velocity $\sim\!3-5$ km/s, i.e., to objects in geocentric orbits with a perigee inside the Earth."792 Phe interpretation of this maximum. as well as the 40<A/20tts maximum. should be approached with a certain caution. because the fairly. slow digestion of nuclei by a daemon could give rise to a certain bias toward inclined. trajectories.," The interpretation of this maximum, as well as the $-40<\Delta793t<-20\,\mks$ maximum, should be approached with a certain caution, because the fairly slow digestion of nuclei by a daemon could give rise to a certain bias toward inclined trajectories."794 daemon poisoned by a poorly digested heavy nucleus is less likely to capture a Zn or Ag nucleus from the next scintillator laver and to initiate a scintillation init if it propagates by the fastest (direct) path., A daemon poisoned by a poorly digested heavy nucleus is less likely to capture a Zn or Ag nucleus from the next scintillator layer and to initiate a scintillation in it if it propagates by the fastest (direct) path.795 Another selection arises because of the higher probability of capture of Ag. despite its low content. by a slower-moving daemon (the capture cross section Is proportional to V. 7).," Another selection arises because of the higher probability of capture of Ag, despite its low content, by a slower-moving daemon (the capture cross section is proportional to $V^{-2}$ )."796 Because of the ZnSCXg) coating being not continuous. daemons with nuclei captured both in the upper scintillator have a fairly high probability of turning up also in the space under the bottom scintillator.," Because of the ZnS(Ag) coating being not continuous, daemons with nuclei captured both in the upper scintillator have a fairly high probability of turning up also in the space under the bottom scintillator."797 Pherefore in order to reliably separate and subsequently. identifv the maxima according to their origin (the end of digestion of a Zn or Ag nucleus captured in the top or bottom scintillator ete.), Therefore in order to reliably separate and subsequently identify the maxima according to their origin (the end of digestion of a Zn or Ag nucleus captured in the top or bottom scintillator etc.)798 for, for799the mixed configuration,the mixed configuration800for 6 DOF).,for 6 DOF).801 The fitted value of us about 40 times higher than the average value of the absorption along the line of sight. which indicates that IGR JO9523-6231 1s intrinsically absorbed.," The fitted value of is about 40 times higher than the average value of the absorption along the line of sight, which indicates that IGR $-$ 6231 is intrinsically absorbed."802 The detection of the source in the U-filter and the high X-ray absorption IGR J10147—6354 was first reported by Birdetal.(2007)., The detection of the source in the U-filter and the high X-ray absorption IGR $-$ 6354 was first reported by \citet{bird07}.803 The source was detected in the 40-100 keV energy range at a significance of 4.9c during 1340 ks of observation., The source was detected in the 40–100 keV energy range at a significance of $\sigma$ during 1340 ks of observation.804 The best XRT position is well within the ISGRI error box of There is a single source in the 2MASS point source catalogue within ffrom the XRT position., The best XRT position is well within the ISGRI error box of There is a single source in the 2MASS point source catalogue within from the XRT position.805 2MASS JI0141554-6351500 is at aaway from the centre of the error box., 2MASS J10141554-6351500 is at away from the centre of the error box.806 It is also well detected in the UVOT UVW? filter., It is also well detected in the UVOT UVW2 filter.807 The XRT spectrum has 93 ets for a total exposure of 4538 s. An absorbed power law fits the data well. with a C-statistic value=32.6 for 29 bins.," The XRT spectrum has 93 cts for a total exposure of 4538 s. An absorbed power law fits the data well, with a C-statistic value=32.6 for 29 bins."808 The value of iis a factor about 7.3 times higher than the average value of the absorption along the line of sight which indicates that the absorption is mostly intrinsic to the source., The value of is a factor about 7.3 times higher than the average value of the absorption along the line of sight which indicates that the absorption is mostly intrinsic to the source.809 The detection of a bright UV counterpart. as for the former source. suggests either a very close Galactic or a far and bright extragalactic object.," The detection of a bright UV counterpart, as for the former source, suggests either a very close Galactic or a far and bright extragalactic object."810 Again. the low Galactic latitude would rather tend to point towards a Galactic source rather than an extragalactic one.," Again, the low Galactic latitude would rather tend to point towards a Galactic source rather than an extragalactic one."811Iu atypical imaging observation. a considerable fraction. ifnot most. of tlie detected sources are interlopers.,"In a typical imaging observation, a considerable fraction, if not most, of the detected sources are interlopers."812 Iu a high Galactic latitude field. interlopers are typically background Αλ». plus a small number of foregrouud stars.," In a high Galactic latitude field, interlopers are typically background AGNs, plus a small number of foreground stars."813 The number-Ilux relation of such interlopers lias beeu characterized in various X-ray surveys. including the ACIS-I deep surveys (Moretti et al.," The number-flux relation of such interlopers has been characterized in various X-ray surveys, including the ACIS-I deep surveys (Moretti et al."814 2003 aud references therein)., 2003 and references therein).815 In almost all recent work. this characterization is doue separately in the 0.5-2 keV aud 2-10 keV bands.," In almost all recent work, this characterization is done separately in the 0.5-2 keV and 2-10 keV bands."816 The source populatious detected in these two bauds only. partially overlap: Sources with steep X-ray spectra preferentially appear in the 0.5-2 keV baud. whereas highly-absorbec oues appear in the 2-10 keV baud.," The source populations detected in these two bands only partially overlap: Sources with steep X-ray spectra preferentially appear in the 0.5-2 keV band, whereas highly-absorbed ones appear in the 2-10 keV band."817 In general. is much more seusitive to sources iu the former baud than in the latter baud.," In general, is much more sensitive to sources in the former band than in the latter band."818 Therefore. we focus ou the accumulated nuimnber-flux relation in the 0.5-2 keV band. whieh can be modeled as: where Nj=6150sourcesdeg7. αι= 1.82. ao= 0.60.and Sy=1.18x10.therestem7 ," Therefore, we focus on the accumulated number-flux relation in the 0.5-2 keV band, which can be modeled as: where $N_0 = 6150 {\rm~sources~deg^{-2}}$ $\alpha_1 = 1.82$ , $\alpha_2 = 0.60$ ,and $S_0 = 1.48 \times 10^{-14} {\rm~erg~s^{-1}~cm^{-2}}$ "819Iu the right-hand side o this equation the first term in brackets describes the 1‘clative role of D Inning iu the total energy budget. second teiu represeuts intrinsic stellar luminosity. while tie third term is due to the inflow of the eravitational potential enerev GALAL/R the ratio of this cucrey infow to Ly differs from A only by a coustant factor.,"In the right-hand side of this equation the first term in brackets describes the relative role of $D$ burning in the total energy budget, second term represents intrinsic stellar luminosity, while the third term is due to the inflow of the gravitational potential energy $GM\dot M/R$ – the ratio of this energy inflow to $L_0$ differs from $\Lambda$ only by a constant factor."820 Suppression of L is hugest when A is highest which Is casy fo see by inspecing Figures 1—1.., Suppression of $L$ is largest when $\Lambda$ is highest which is easy to see by inspecting Figures \ref{fig:f1}- \ref{fig:f4}.821 But this automatically meaus that the maxima deviation of the suppression factor X from unitv occus preciselv when the inflow of the gravitational potential energv far exceeds the stella lununosity., But this automatically means that the maximum deviation of the suppression factor $\chi$ from unity occurs precisely when the inflow of the gravitational potential energy far exceeds the stellar luminosity.822 Apparently. uuder these circumstances £L is a subdominant contribution to the stellar energv budect and thus even a significant reduction of L compared to Ly is going to be uceligible conrpared to the eravitational energy influx.," Apparently, under these circumstances $L$ is a subdominant contribution to the stellar energy budget and thus even a significant reduction of $L$ compared to $L_0$ is going to be negligible compared to the gravitational energy influx."823 Moreover. Figure 1 deuoustrates that A reaches its asin when AB> is at its nüunauunu while fp is still very close to unitv.," Moreover, Figure \ref{fig:f1} demonstrates that $\Lambda$ reaches its maximum when $R$ is at its minimum while $f_D$ is still very close to unity."824 At fus point vigorous D burnius columences Inside the sar giving rise to wvorv hieh LpíLg., At this point vigorous D burning commences inside the star giving rise to very high $L_D/L_0$.825 As a result. at tie evolutionary stage when \ is nuninial £ is ποταιant in comparison to not ouly GALAL/R but also Lp.," As a result, at the evolutionary stage when $\chi$ is minimal $L$ is subdominant in comparison to not only $GM\dot M/R$ but also $L_D$."826 Tus additionally downplays the role of the hunuinositv suppression by iradiatiou iu the carly protostellay evolution., This additionally downplays the role of the luminosity suppression by irradiation in the early protostellar evolution.827 This line of reasoning aso explaius why at AM~1 M. we have found AR/R to )o larger for lower AL (see 83)]., This line of reasoning also explains why at $M\sim 1$ $_\odot$ we have found $\Delta R/R$ to be larger for lower $\dot M$ (see \ref{sect:res}) ).828 First. analler M. ποστς lower X so that the ratio of L to the gravitational energy 1vow rate CAZAZR in the low AT case is larecr than iu ιο hieh AL case.," First, smaller $\dot M$ means lower $\Lambda$ so that the ratio of $L$ to the gravitational energy inflow rate $GM\dot M/R$ in the low $\dot M$ case is larger than in the high $\dot M$ case."829 Also. at AL~ AL. one generally finds f;»l (see Figure lee) so that Lp isiaiuly due to the birue of the freshly accreted D (rather tman the D that remained iu the protostar from previous accretion).," Also, at $M\sim$ $_\odot$ one generally finds $f_D\ll 1$ (see Figure \ref{fig:f1}e e) so that $L_D$ is mainly due to the burning of the freshly accreted D (rather than the D that remained in the protostar from previous accretion)."830 Since in the low AL case less fresh D is supplied to the proostar Lp ust also be lower than iu he high AL case., Since in the low $\dot M$ case less fresh $D$ is supplied to the protostar $L_D$ must also be lower than in the high $\dot M$ case.831 As a result. iu the lower AL case L plavs a iore significant role compared to Ly (iu which case ARR should © niore sensitive to changes iu L cause by radiation) thau iu the hieh AT case.," As a result, in the lower $\dot M$ case $L$ plays a more significant role compared to $L_D$ (in which case $\Delta R/R$ should be more sensitive to changes in $L$ caused by irradiation) than in the high $\dot M$ case."832 This conclusion munediately raises the following question: since AR/R ineoases as AL decreases would ouc find AR/R~1 at knv enough Jf?, This conclusion immediately raises the following question: since $\Delta R/R$ increases as $\dot M$ decreases would one find $\Delta R/R\sim 1$ at low enough $\dot M$?833 The answer is no. and it has to do with the fact that 4 appreciadv differs from unity (obviously. a necessary couditiou for ectting AR/R~ 1) oul~ at rather high A.," The answer is no, and it has to do with the fact that $\chi$ appreciably differs from unity (obviously, a necessary condition for getting $\Delta R/R\sim 1$ ) only at rather high $\Lambda$ ."834 This is a eeneric feature of disk irradiation which is illustraed in Fieure 5 where we display Aso the value of X at which \(Asu)=15 as a function of assmued opacity law represented by the parameter ©. see equation (11).," This is a generic feature of disk irradiation which is illustrated in Figure \ref{fig:f5} where we display $\Lambda_{50}$ – the value of $\Lambda$ at which $\chi(\Lambda_{50})=0.5$ – as a function of assumed opacity law represented by the parameter $\xi$, see equation \ref{eq:xi}) )."835 One can see that Asy2 aD↓∩−↕∪↥⋅⋜↧↕≦↓∙⋯↸∖⋜↧⋯∐∶↴⋁ ⋅ that significant hlunimositv suppression requires rather lueh AJ.," One can see that $\Lambda_{50}\gtrsim 10^2$ for all $\xi>4$, meaning that significant luminosity suppression requires rather high $\dot M$."836 This meffücienev of imradialon 1n suppressing Lis caused by the specific eeonetrv of disk inadiatiou in which the radiation flux is a very seusitive fiction (x 0°) of the latitude at t1je stellar surface 0. sec Rafikov (2007).," This inefficiency of irradiation in suppressing $L$ is caused by the specific geometry of disk irradiation in which the irradiation flux is a very sensitive function $\propto \theta^5$ ) of the latitude at the stellar surface $\theta$, see Rafikov (2007)."837 Because of that stellar polar caps can stay cool even at rather high AY allowing unsuppressed flux to be cluitted over a significant portion of the stellar surface., Because of that stellar polar caps can stay cool even at rather high $\dot M$ allowing unsuppressed flux to be emitted over a significant portion of the stellar surface.838 Iu the case of &£=6.5 as appropriate for cool. OW-1uass protostars one finds that Asy=2.2« which according to equation (9)) muuediatelv iuplics hat GALM/IRxL75Ly when 4=0.5.," In the case of $\xi=6.5$ as appropriate for cool, low-mass protostars one finds that $\Lambda_{50}=2.2\times 10^3$ which according to equation \ref{eq:Lambda}) ) immediately implies that $GM\dot M/R\approx 175 L_0$ when $\chi=0.5$."839 Clearly. in his case stellar huuinositv should have μια] effect ou he xotostellu evolution.," Clearly, in this case stellar luminosity should have small effect on the protostellar evolution."840 If AJ ds so that GALAL/R~Ly (aud A~ 1) stellar hunuinositv would ος plaving a siguificaut role in the stellar energv budeet. rowever x would be very close to unity (see Rafikov 20Nn) and the £ suppression by irradiation wold be negligible.," If $\dot M$ is so that $GM\dot M/R\sim L_0$ (and $\Lambda\sim 1$ ) stellar luminosity would be playing a significant role in the stellar energy budget, however $\chi$ would be very close to unity (see Rafikov 2007) and the $L$ suppression by irradiation would be negligible."841 Thus. 1udder no circiustauces should oue expect AR/R argertlan several per celt. camethat quite ecucrally he iradiation. by accretion disk is uulikelv to play a significant role iu the evolution of the protostellar xoperties.," Thus, under no circumstances should one expect $\Delta R/R$ larger than several per cent, meaningthat quite generally the irradiation by accretion disk is unlikely to play a significant role in the evolution of the protostellar properties."842role here because there is no rotational component to the How.,role here because there is no rotational component to the flow.843 Figure 6 summarizes the hydrodynamie state variables at time /=1l., Figure \ref{fig:Sod-200} summarizes the hydrodynamic state variables at time $t=1$.844 To first approximation one ects identical results with the new formalism as compared to the standard approach., To first approximation one gets identical results with the new formalism as compared to the standard approach.845 Linear momentum is not conserved inrpSPtl and we find a linear excess velocity of (105.3.10.7) so per particle an error on the velocity of 0.003 in the a and a completely negligible component along the gy-direction.," Linear momentum is not conserved in and we find a linear excess velocity of $(-105,-3\times 10^{-5})$ so per particle an error on the velocity of $0.003$ in the $x$ -direction and a completely negligible component along the $y$ -direction."846 This is at a time when the r.nis., This is at a time when the r.m.s.847 velocity is O46 so just slightly. above one half of a per cent. error in the dominant w-velocity., velocity is $\sim 0.46$ so just slightly above one half of a per cent error in the dominant $x$ -velocity.848 SPILL has poor behaviour at the contact discontinuities., SPH has poor behaviour at the contact discontinuities.849 For both the one originating [roni he initially smoothec and the the discontinuous interface at the right boundary., For both the one originating from the initially smoothed and the the discontinuous interface at the right boundary.850 Both contacts at ik~3.8 and μον9.3 are better captured byΡΟΗ., Both contacts at $x\sim3.8$ and $x\sim 9.3$ are better captured by.851 The Sod shock tube has few catures and it is reassuring that using as many as 2007 particles can give an excellent answer., The Sod shock tube has few features and it is reassuring that using as many as $200^2$ particles can give an excellent answer.852 There are only slight dilferences in howrpSPH handles one dimensional shock tubes., There are only slight differences in how handles one dimensional shock tubes.853 We will discuss one very »opular application taken from a cosmological context after esting a very strong shock next., We will discuss one very popular application taken from a cosmological context after testing a very strong shock next.854 llere we give another test of a much stronger shock than the one by sod., Here we give another test of a much stronger shock than the one by sod.855 This one has a Mach number close to one hundred., This one has a Mach number close to one hundred.856 We also use the chance to compare this to the cillerence formulation studied by 2.., We also use the chance to compare this to the difference formulation studied by \cite{1996PASA...13...97M}.857 Phe density. and pressure are (1.6.61033 on the left and (1/5.1) on the right.," The density and pressure are $(1,6.6\times85810^4)$ on the left and $(1/5,1)$ on the right."859 ‘This is very similar to the one studied by ? and is well known to work well with standard SPIL, This is very similar to the one studied by \cite{2006MNRAS.367..113P} and is well known to work well with standard SPH.860L Leere we use 35 neighbours. a—4 and 5000 particles.," Here we use $35$ neighbours, $\alpha=4$ and 5000 particles."861 This is à good example where one can makerpSPH and the Morris formulation give unphysical results., This is a good example where one can make and the Morris formulation give unphysical results.862 These methods require the pressure gradient to be resolved., These methods require the pressure gradient to be resolved.863 So if vou start with completely discontinuous left right states one will eet unphysical waves giving unexpected results., So if you start with completely discontinuous left right states one will get unphysical waves giving unexpected results.864 However. this is not a shortcoming of the method but simply are errors that come from not resolving the initial conditions.," However, this is not a shortcoming of the method but simply are errors that come from not resolving the initial conditions."865 We again use the ramp function from above with a width of4 in this very long domain ranging from 0 to 500 in.r and Oto 10 in y., We again use the ramp function from above with a width of 4 in this very long domain ranging from 0 to 500 in $x$ and $0$ to $10$ in $y$.866 We cannot confirm Morris! claim that his formulation gives large post shock oscillations in this method and suspect that he may have set up discontinuous initial conditions., We cannot confirm Morris' claim that his formulation gives large post shock oscillations in this method and suspect that he may have set up discontinuous initial conditions.867 We can see that our new formulation performs somewhat better than the Morris formulation as it does not overshoot the analvtical density jump of 4 raising the density from 0.2 to 0.8 in Figure 7.., We can see that our new formulation performs somewhat better than the Morris formulation as it does not overshoot the analytical density jump of 4 raising the density from $0.2$ to $0.8$ in Figure \ref{fig:StrongShock}.868 Otherwise both approaches work fine and have no problem in modeling strong shocks and evolving it for large distances., Otherwise both approaches work fine and have no problem in modeling strong shocks and evolving it for large distances.869 Another particularly strong shock is formed in the Sedov-‘Tavlor blast wave (2). presenting a cdillieult test. problem for incompressible hvdrodynamies codes., Another particularly strong shock is formed in the Sedov-Taylor blast wave \citep{1959flme.book.....L} presenting a difficult test problem for incompressible hydrodynamics codes.870 One the one hand it is a self similar solution which makes it insensitive to how exactly one sets it up as long as one evolves the svsten for a very long time., One the one hand it is a self similar solution which makes it insensitive to how exactly one sets it up as long as one evolves the system for a very long time.871 On the other hand it is the solution for a point explosion., On the other hand it is the solution for a point explosion.872 For a given finite resolution. however. there is no unique wav of specifving the initial conditions.," For a given finite resolution, however, there is no unique way of specifying the initial conditions."873 llere is where exact momentum anc energy. conservation is very helpful as one can set. up the initial conditions at will and even if one were to make verv large errors in the time evolution the method will still arrive at. the self similar solution., Here is where exact momentum and energy conservation is very helpful as one can set up the initial conditions at will and even if one were to make very large errors in the time evolution the method will still arrive at the self similar solution.874 In conservative grid codes this still can [σας to aspherical solutions if one did. not resolve the spherical central hot region., In conservative grid codes this still can lead to aspherical solutions if one did not resolve the spherical central hot region.875 Since SPLL however uses spherical kernels one can get away sometimes even by just heating one single particle (2)..., Since SPH however uses spherical kernels one can get away sometimes even by just heating one single particle \citep{2002MNRAS.333..649S}.876 This is very useful in applications such as ealaxy formation simulations where one is always far from resolving the relevant length scales of an explosion., This is very useful in applications such as galaxy formation simulations where one is always far from resolving the relevant length scales of an explosion.877 On the other hand any physies that were to occur at a scale. of the shell thickness would. be impossible to resolve in such a single particle energy ejection., On the other hand any physics that were to occur at a scale of the shell thickness would be impossible to resolve in such a single particle energy ejection.878 ForSPL and the Morris formulation we need to resolve the pressure gradients in the initial conditions as we saw above in the strong shock setup., For and the Morris formulation we need to resolve the pressure gradients in the initial conditions as we saw above in the strong shock setup.879 We setup a square lattice of particles with 300 particles on à side in the unit domain., We setup a square lattice of particles with 300 particles on a side in the unit domain.880 For resolved initial conditions we set a spherical region in the center of radius r=0.1 with the same ramp function as above using a width of 0.1. to have a sound speed of one for an aciahatic index of 55/3.," For resolved initial conditions we set a spherical region in the center of radius $r=0.1$ with the same ramp function as above using a width of $0.1$, to have a sound speed of one for an adiabatic index of $\gamma=5/3$."881 For both simulations we used a Courant number of 0.2 (0.1 in Gadget). SO neighbors. artificial viscosity à=2.5 and had the Balsara switch olf.," For both simulations we used a Courant number of 0.2 $0.1$ in Gadget), 80 neighbors, artificial viscosity $\alpha=2.5$ and had the Balsara switch off."882 Figure S shows that there potentially is also an advantage torpSPL simulations when modeling shocks., Figure \ref{fig:Sedov} shows that there potentially is also an advantage to simulations when modeling shocks.883 We have Buled to get standard SPLE to give a stable correct density jump of (5Ες1)=4 for our setup., We have failed to get standard SPH to give a stable correct density jump of $(\gamma+1)/(\gamma-1)=4$ for our setup.884 Also the three dimensional versions shown by ο always sccm to be too low bv as much as a factor of two., Also the three dimensional versions shown by \cite{2002MNRAS.333..649S} always seem to be too low by as much as a factor of two.885 However. stanclare SPIL is much less sensitive to how one sets up the initia conditions and performs much better at low resolutions.," However, standard SPH is much less sensitive to how one sets up the initial conditions and performs much better at low resolutions."886 These strong shock problems can work but clearly are not the biggest strengths ofSPL., These strong shock problems can work but clearly are not the biggest strengths of.887 Llowever. at this poin we simply reused the artificial viscosity. prescription which was designed for standard SPL.," However, at this point we simply reused the artificial viscosity prescription which was designed for standard SPH."888 We believe it is likely tha one can find an alternative formulation for the artificia viscosity that fits better into the discretisation which maw improve its behaviour for highly supersonic conditions., We believe it is likely that one can find an alternative formulation for the artificial viscosity that fits better into the discretisation which may improve its behaviour for highly supersonic conditions.889 Until à better artificial viscosity prescription is designed one may opt to switch between standard SPIEL and based on the local divergence., Until a better artificial viscosity prescription is designed one may opt to switch between standard SPH and based on the local divergence.890 We have successfully applied this strategy by using a switch that evaluates the standard SPL sum if. h;:5;73602; and the sum for less strongly convergent Bow.," We have successfully applied this strategy by using a switch that evaluates the standard SPH sum if $-h_i \div \vec{v}_i > 3891c_{s,i}$ and the sum for less strongly convergent flow."892 Here 5h; and ον denote the smoothing length and the current sound. speed. of the particle.," Here $h_i$ and $c_{s,i}$ denote the smoothing length and the current sound speed of the particle."893 Εις formulation is robust in all our tests., This formulation is robust in all our tests.894 In 1995 a comparison project was initiated. that. aimed to compare all numerical cosmology codes at that time for relevant. realistic initial conditions., In 1995 a comparison project was initiated that aimed to compare all numerical cosmology codes at that time for relevant realistic initial conditions.895 Phe study. focused on three dimensional calculations of the formation of a ealaxy cluster in the standard. CDM. scenario of structure formation., The study focused on three dimensional calculations of the formation of a galaxy cluster in the standard CDM scenario of structure formation.896 The choice was a setup which does not include any other physies than cosmological hyelrodvnanics with an ideal gas equation of state (often referred to as adiabatic simulations despite the entropy. generation in shocks)., The choice was a setup which does not include any other physics than cosmological hydrodynamics with an ideal gas equation of state (often referred to as adiabatic simulations despite the entropy generation in shocks).897 The study. produced a detailed report in (7.E99. herafter).. ," The study produced a detailed report in \cite[][F99, herafter]{1999ApJ...525..554F}. ."898One of the most surprising findings of the study was that while there was very good agreement. between the six dillerent, One of the most surprising findings of the study was that while there was very good agreement between the six different899s!.,.900". Neither the oscillation of the velocity, the continuum nor the core intensity seem to be related to the magnetic flux density (and area) fluctuations, as can be seen in Fig. 3.."," Neither the oscillation of the velocity, the continuum nor the core intensity seem to be related to the magnetic flux density (and area) fluctuations, as can be seen in Fig. \ref{var_resto}."901" Whereas some of the oscillations in area we observe display periods in the range of the p-modes, others have distinctly longer periods, even up to 11 min, and show an abrupt change of the wave period at a given time."," Whereas some of the oscillations in area we observe display periods in the range of the p-modes, others have distinctly longer periods, even up to 11 min, and show an abrupt change of the wave period at a given time."902" Moreover, we find that the area of some magnetic patches located"," Moreover, we find that the area of some magnetic patches located"903The birth of stars. a process so conuuoulv occurring hroughout the whole universe. is as puzzling as it is ascinating.,"The birth of stars, a process so commonly occurring throughout the whole universe, is as puzzling as it is fascinating."904" The current paradienài for star formation. ramed originally by Rant and Laplace in the 1s""! century. sugecsts that stars are born via gravitational collapse of the dense cores of molecular clouds. iu urn coudeused out of the diffuse interstellar medi."," The current paradigm for star formation, framed originally by Kant and Laplace in the $18^{\rm th}$ century, suggests that stars are born via gravitational collapse of the dense cores of molecular clouds, in turn condensed out of the diffuse interstellar medium."905 Unufortunatelv. this compelling visualisation aud its physical uuderpimniug are iu apparent contradiction.," Unfortunately, this compelling visualisation and its physical underpinning are in apparent contradiction."906 The reason for the above statement is that couservatioulit of angular moment curing the collapse results in he progressive inerease of the centrifugal force. which eventually ialts he iufaliug eas aud leads to the development of a central mass (16. a “protostar’) surrounded by a flattened disc of material (an accretion disc’).," The reason for the above statement is that conservation of angular momentum during the collapse results in the progressive increase of the centrifugal force, which eventually halts the infalling gas and leads to the development of a central mass (i.e. a `protostar') surrounded by a flattened disc of material (an `accretion disc')."907 Observational evidence for the presence of such discs around voune stellar objects is compelling., Observational evidence for the presence of such discs around young stellar objects is compelling.908 It conrprises nuaenmg iu the near infrared and optica wavebauds (6.8.seethereviewsbyWatsonetal.2007:AleCaughreanctal.2000) as well as interferometric studies that have resolved. the velocity profile ar structure in the immer regions of cliscs. up to ~ a few tens of AU from the ceutre (e.g.Dutreyetal.2007:Wilner&Lav 2000).," It comprises imaging in the near infrared and optical wavebands \citep[e.g.~see the reviews by][]{WSWM07, MSC00} as well as interferometric studies that have resolved the velocity profile and structure in the inner regions of discs, up to $\sim$ a few tens of AU from the centre \citep[e.g.][]{DGH07, WL00}."909. This phenomenon is. in fact. not limite to voung sars.," This phenomenon is, in fact, not limited to young stars."910 Many astroplivsical svstenis exlibit the characteristic disc-like structure that naturally results when iuw:ud notion in the plane of rotation is restricted by augular momentum conscrvation. while collapse continues in the perpendicular (polar) directiou.," Many astrophysical systems exhibit the characteristic disc-like structure that naturally results when inward motion in the plane of rotation is restricted by angular momentum conservation, while collapse continues in the perpendicular (polar) direction."911§f Such structures are commonly associated. for example. with the «iscs of material feeding the cores of active ealaxies aux black holes.," Such structures are commonly associated, for example, with the discs of material feeding the cores of active galaxies and black holes."912 The difficulty iu. progressing past this stage ds clear when we recall that these protostellar discs are dynamically stable., The difficulty in progressing past this stage is clear when we recall that these protostellar discs are dynamically stable.913 Ao typica disc is cifferentiallv rotating. with an aneular monenutun (L) profile that," A typical disc is differentially rotating, with an angular momentum $L$ ) profile that"914"A series of exterior MMRs with Neptune shows strong peaks at all grain sizes in the Tmaxv1077 model: 4:3 3:2 7:4 2:1 (2236, 39, 44 and 48 AU).","A series of exterior MMRs with Neptune shows strong peaks at all grain sizes in the $\tau_{\rm{max}} \sim 10^{-7}$ model: 4:3 3:2 7:4 2:1 $\approx$ 36, 39, 44 and 48 AU)."915 Dashed lines show these and a few other MMRs in Figure 4.., Dashed lines show these and a few other MMRs in Figure \ref{fig:semimajoraxis1}.916 Some of these peaks also survive in the total semimajor axis distribution., Some of these peaks also survive in the total semimajor axis distribution.917" They appear in all three source populations, though they are strongest in the cold classical population, probably these objects have small eccentricities and inclinations, making them easier to trap in MMRs."," They appear in all three source populations, though they are strongest in the cold classical population, probably these objects have small eccentricities and inclinations, making them easier to trap in MMRs."918" Though the plutino dust is released from bodies in Neptune's 3:2 MMR, only grains larger than 19.7 wm remain tightly concentrated around that MMR, at z39 AU."," Though the plutino dust is released from bodies in Neptune's 3:2 MMR, only grains larger than $19.7 \ \mu$ m remain tightly concentrated around that MMR, at $\approx 39$ AU."919" Figure 3 shows that at this dust level (Tax~ 1077), the resonant"," Figure \ref{fig:collisions} shows that at this dust level $\tau_{\rm{max}} \sim 10^{-7}$ ), the resonant"920Table 3 shows the resulting fractions for comparison of the distributions of detected parameters and one year of observation.,Table \ref{tab:comptable_1yr} shows the resulting fractions for comparison of the distributions of detected parameters and one year of observation.921 All of the models can be consistently distinguished based on some combination of one or two of their parameter distributions: Naturally. these numbers improve when a longer observation window affords more sources to make the comparison.," All of the models can be consistently distinguished based on some combination of one or two of their parameter distributions: Naturally, these numbers improve when a longer observation window affords more sources to make the comparison."922 Table 4 shows comparison results when sources are chosen from equation 8 according to à 3 year observation window., Table \ref{tab:comptable_3yr} shows comparison results when sources are chosen from equation \ref{psprob} according to a 3 year observation window.923 With the 3 years of sources. the only model parameter distributions that cannot be reliably distinguished are the SE vs. SC distributions and the LE vs. LC distributions. as functions of the masses and 25.," With the 3 years of sources, the only model parameter distributions that cannot be reliably distinguished are the SE vs. SC distributions and the LE vs. LC distributions, as functions of the masses and $D_L$."924" The SE and SC distributions of masses and D,. in particular. are not generally distinguishable."," The SE and SC distributions of masses and $D_L$, in particular, are not generally distinguishable."925" The distributions of InD; and Iuij, for the LE and LC models. on the other hand. are often distinguishable."," The distributions of $\ln{D_L}$ and $\ln{m_1}$ for the LE and LC models, on the other hand, are often distinguishable."926" Since we are interested as much in the limits of LISA's ability to distinguish between the population models as in whether or not LISA will be able to distinguish between these particular sets of models (which will undoubtedly be superseded with improved versions by the time LISA is operational). Figures 20. and 21. show the distributions of InD, and Inn. and of InD; and Ini)»."," Since we are interested as much in the limits of LISA's ability to distinguish between the population models as in whether or not LISA will be able to distinguish between these particular sets of models (which will undoubtedly be superseded with improved versions by the time LISA is operational), Figures \ref{fig:ExampleDLm1distributions} and \ref{fig:ExampleDLm2distributions} show the distributions of $\ln{D_L}$ and $\ln{m_1}$, and of $\ln{D_L}$ and $\ln{m_2}$."927 The plots serve to illustrate distributions which have varying levels of distinguishability., The plots serve to illustrate distributions which have varying levels of distinguishability.928 In order to assess the significance of the effects of parameter estimation error on the distinguishability of the models. we have also performed model comparison tests with no parameter estimation errors.," In order to assess the significance of the effects of parameter estimation error on the distinguishability of the models, we have also performed model comparison tests with no parameter estimation errors."929 The results of these tests. for one year of observations. are shown in Table5..," The results of these tests, for one year of observations, are shown in Table\ref{tab:comptable_noerrs}."930 The differences between these model distinguishability fractions and those found in Table 3 (which incorporate the parameter estimation errors) are shown in Table 6.., The differences between these model distinguishability fractions and those found in Table \ref{tab:comptable_1yr} (which incorporate the parameter estimation errors) are shown in Table \ref{tab:comptable_differences}. .931 These, These932The relation between the skv map we seek and the observed data stream may be cast as a linear algebra system (Wrightetal1996:Teemark1997).,"The relation between the sky map we seek and the observed data stream may be cast as a linear algebra system \cite{WrHi96a,Te97}."933 Let ; and p Judices denote quantities iu the temporal auc spatial domains. and eroup as a data vector. dy. and a noise vector the temporal stream of collected data aud the detector noise stream. both of dimension Ay.," Let $_t$ and $_p$ indices denote quantities in the temporal and spatial domains, and group as a data vector, $d_{t}$, and a noise vector the temporal stream of collected data and the detector noise stream, both of dimension $\mathcal{N}_{tod}$ ."934 We then have |Hg. where obey ds the sigual vector given bw the observation of the uuknown pixelised sky map. or). which lasbeen arranged as a vector of dimecusion Nui," We then have = +, where $A_{tp}x_{p}$ is the signal vector given by the observation of the unknown pixelised sky map, $x_{p}$, which hasbeen arranged as a vector of dimension $\mathcal{N}_{pix}$."935" The Nou- ""observation"" matrix 4 therefore encompasses hne scanunimg strategv aud the beam pattern of the detector."," The $\mathcal{N}_{tod} \times 936\mathcal{N}_{pix}$ “observation” matrix $A$ therefore encompasses the scanning strategy and the beam pattern of the detector."937 Iu the following. we restrict to the case when the beam ρατοι ds svnuuetrical.," In the following, we restrict to the case when the beam pattern is symmetrical."938" We ean therefore take wr, to be a nap of the skv which has already been couvolved. with he beau pattern. and <A oulv deseribes how this sky is reine scanned."," We can therefore take $x_{p}$ to be a map of the sky which has already been convolved with the beam pattern, and $A$ only describes how this sky is being scanned."939 For the total power iieasurement nou-ifferential mieasurenient) we are iterested im here. the joservation matrix A then has a single non-zero clement scr row. Which can be set to one if d and we are expressed oe ithe same units.," For the total power measurement non-differential measurement) we are interested in here, the observation matrix $A$ then has a single non-zero element per row, which can be set to one if $d$ and $x$ are expressed in the same units."940 The model of the measurement is then ute transparent: cach temporal datum is the simu of he pixel value to which the detector is pointing plus the ctector nolse., The model of the measurement is then quite transparent: each temporal datum is the sum of the pixel value to which the detector is pointing plus the detector noise.941 The map-makine step then amounts to best solve for .e eiven d (aud some properties of the noise)., The map-making step then amounts to best solve for $x$ given $d$ (and some properties of the noise).942" We shall seek a estimator of .,,. Wed;e "," We shall seek a estimator of $x_{p}$, = ."943To motivate a particular choice of the NySN matrix VW. a Bavesiau approach is couvenicut.," To motivate a particular choice of the $\mathcal{N}_{pix} \times 944\mathcal{N}_{tod}$ matrix $W$, a Bayesian approach is convenient."945" Iudeed we are secking the optimal solution to this inversion problem which maximises the probability of a deduced set of theory paralucters (here the map .,}) given our data (d;) by inaxinising Pr|d).", Indeed we are seeking the optimal solution to this inversion problem which maximises the probability of a deduced set of theory parameters (here the map $x_p$ ) given our data $d_t$ ) by maximising $\mathcal{P}(x|d)$.946 Baves’ thieoreii simply states that Pat =PidPld)., Bayes' theorem simply states that (x|d) =.947 If weprior. thon 0 follows a uniform distribution as well as 4.," If we, then $x$ follows a uniform distribution as well as $d$."948 Therefore. Pusd) Plait)If we further assume thatCatssian.. we cal write Pitsd) erpl 215} ορ(dAryeNIU where Ny=<?με is the noise covariance matrix.," Therefore, (x|d) (d|x).If we further assume that, we can write (x|d) exp(- /2) exp(-(d-Ax)_t^T where $N_{tt'} = <nn^T>_{tt'}$ is the noise covariance matrix."949" Iu this particular ease. maximising PCr|y) amounts to find the least square solution which was used to analyse the ""CODIZ data (JansenandCulkis1992).. =DATN 3. Tn this paper we will actually deal onlv with this estimator."," In this particular case, maximising $\mathcal{P}(x|y)$ amounts to find the least square solution which was used to analyse the “COBE” data \cite{JaGu92}, , W = A^T. In this paper we will actually deal only with this estimator."950" Nevertheless as a next iteration in the analysis process, we could corporate various theoretical priors by explicitiug P(r)."," Nevertheless as a next iteration in the analysis process, we could incorporate various theoretical priors by expliciting $\mathcal{P}(x)$."951" For example. it is often assumed for the theory. Por)xccptwlpple’2) wherehore €.C,=6pd dsix the signalsienal covariiucecovariiMN matrix."," For example, it is often assumed for the theory, $\mathcal{P}(x) \propto952exp(-x^T_pC^{-1}_{pp'}x_{p'}/2)$ where $C_{pp'}=\langle x_px^T_{p'} \rangle$ is the signal covariance matrix."953atrix Iu that case theαμήν particular solution turus out to be the Wiener filtering solution (Zaroubietal.1995:BouchetaudCüspoer 1998): ={C cq APN TAY)1ATN 1 But this solution παν always be obtained by a further (Wiener) filtering of the CODE solution. aud we do not consider it further.," In that case the particular solution turns out to be the Wiener filtering solution \cite{ZaHo95,BoGi96,TeEf96,BoGi98}: W = + A^T A A^T. But this solution may always be obtained by a further (Wiener) filtering of the COBE solution, and we do not consider it further."954 The prior-less solution demoustrates that as long as the (Caussian) iustrumental noise is not white. a «ΠΙΟ averaging (co-addition) of all the data poiuts corresponding oa given skv pixel is not optimal.," The prior-less solution demonstrates that as long as the (Gaussian) instrumental noise is not white, a simple averaging (co-addition) of all the data points corresponding to a given sky pixel is not optimal."955 If the ποῖκο exhibits some temporal correlations. as induced for instance by a low-frequeucy 1/f behavior of the noise spectrin which prevails iun most CAIB experiueuts. one its to take into account the full time correlation structure of the noise.," If the noise exhibits some temporal correlations, as induced for instance by a low-frequency $1/f$ behavior of the noise spectrum which prevails in most CMB experiments, one has to take into account the full time correlation structure of the noise."956 Additionally. this expression demonstrates hat even if the noise has a simple time structure. he scanning strateev eenerically iuduces a non-trivial correlation matrix [AENL4] ofthe noise map.," Additionally this expression demonstrates that even if the noise has a simple time structure, the scanning strategy generically induces a non-trivial correlation matrix $\left[ A^T N^{-1} A\right]^{-1}$ of the noise map."957 Even if the xoblem is well posed formalhy. a quick looks thyorders of magnitude shows that the actual finding of i solution is non trivia task.," Even if the problem is well posed formally, a quick look at the orders of magnitude shows that the actual finding of a solution is non trivial task."958" Iudeed a brute force method anune at inverting the full matrix [APTN14] loan operation scaliug as ΟΛ). is already. hardly tractable for present long duration balloon flights as MAXIMA. BOOMERanG. ARCIIEOPS or Topllat where A,~ and Ny 10°, "," Indeed a brute force method aiming at inverting the full matrix $\left[ A^T N^{-1} A\right]^{-1} \displaystyle$, an operation scaling as $\mathcal{O}(\mathcal{N}_{pix}^3)$, is already hardly tractable for present long duration balloon flights as MAXIMA, BOOMERanG, ARCHEOPS or TopHat where $\mathcal{N}_{tod}\sim 10^6$ and $\mathcal{N}_{pix} \sim 10^5$ ."959It appears totally impractical for PLANCK since for a single detector (nid LOS) Noo10? and Au~ 10*!, It appears totally impractical for PLANCK since for a single detector (amid $10$ s) $\mathcal{N}_{tod}\sim 10^9$ and $\mathcal{N}_{pix} \sim 10^7$ !960 Onepossibility may be to take advantage of specific scanniue strategies. and actually solvethe inverse of the convolution problem as detailed in," Onepossibility may be to take advantage of specific scanning strategies, and actually solvethe inverse of the convolution problem as detailed in"961This is not trivial. as the rotation velocities and disk. Iuuimositfies are determined completely independently (and by different workers) and ouly the one using the absolute magnitude necds an assumption for the distance scale.,"This is not trivial, as the rotation velocities and disk luminosities are determined completely independently (and by different workers) and only the one using the absolute magnitude needs an assumption for the distance scale."962 e Then using Eq. (, $\bullet $ Then using Eq. (96315). we estimate the vertical velocity dispersion at one photometric scale leneth im the baud.,"15), we estimate the vertical velocity dispersion at one photometric scale length in the -band."964 For this we need a value for the mass-to-light ratio aud we will discuss this first., For this we need a value for the mass-to-light ratio and we will discuss this first.965 We found. that through. Eq. (," We found, that through Eq. ("96613) Bottema’s relation (1) provides a value for Q(AL/£) of about 5.7.,13) Bottema's relation (1) provides a value for $Q (M/L)$ of about 5.7.967 So we make a choice for Q rather than for AL/£., So we make a choice for $Q$ rather than for $M/L$.968 It has become customary to asstume values of Q of order 2. mainly based onu the nuuerical simulations of Sellwood Carlbere (1981). who find thei disks to settle with Q~ 1.7 at all radii.," It has become customary to assume values of $Q$ of order 2, mainly based on the numerical simulations of Sellwood Carlberg (1984), who find their disks to settle with $Q \sim $ 1.7 at all radii."969 In principle we can use the observed properties of the Galaxy to fix Q from Eq. (, In principle we can use the observed properties of the Galaxy to fix $Q$ from Eq. (97017).,17).971" We have (o,fon)?~0.5 Gn the solar uciglbourliood. but assuue for the sake of the argument also at R= 15) aud hh~ (see Sackett 1997 for a receut review). so that indeed Q~L7."," We have $(\sigma _{\rm z}/\sigma972_{\rm R})^{2} \sim 0.5$ (in the solar neighbourhood, but assume for the sake of the argument also at $R = 1h$ ) and $h_{\rm z}/h \sim 0.1$ (see Sackett 1997 for a recent review), so that indeed $Q \sim 1.7$."973 We will make the general assuiiptiou that Q = 2. In agreement with the considerations above: then (AL/L)p — 2m.," We will make the general assumption that $Q$ = 2, in agreement with the considerations above; then $(M/L)_{B}$ = 2.8."974 The rotation velocity version of Dottemias empirical relations (Eq. (, The rotation velocity version of Bottema's empirical relations (Eq. (9751)) cau provide further support for the choice of Q. aloug the lines of the discussion in van der Iruit Freeman (1986).,"1)) can provide further support for the choice of $Q$, along the lines of the discussion in van der Kruit Freeman (1986)."976 In the first place we recall the condition for the prevention of swing amplification in disks (Toomre 1981). as reformulated by Sellwood (1983) where 5s is the number of spiral arius.," In the first place we recall the condition for the prevention of swing amplification in disks (Toomre 1981), as reformulated by Sellwood (1983) where $m$ is the number of spiral arms."977 For a fat rotation curve this can be rewritten as With Eq. (, For a flat rotation curve this can be rewritten as With Eq. (9781) this becomes Q>1.15i5..,1) this becomes $Q \gt 1.15 m$.979 Cousideriueg -iat the coefficient in Eq. (, Considering that the coefficient in Eq. (9801) has au uncertainty of order5%.. this tells us that we wave to assume (Q at least of order 2 to prevent strong barlike (:50—2) disturbances m the disk.,"1) has an uncertainty of order, this tells us that we have to assume $Q$ at least of order 2 to prevent strong barlike =2) disturbances in the disk."981 A similar argument can be made using the egloha stability criterion of Efstathiou et al. (, A similar argument can be made using the global stability criterion of Efstathiou et al. (9821982).,1982).983 This criterion states that for a galaxy with a flat rotation curve and au expoucntial disk. global stability requires a dark halo ac Tere Aquas is the total mass of the disk.," This criterion states that for a galaxy with a flat rotation curve and an exponential disk, global stability requires a dark halo and Here $M_{\rm disk}$ is the total mass of the disk."984 Tlis cau he rewritten as and. when evaluated at R=Lh. vields with Eq. (," This can be rewritten as and, when evaluated at $R = 1h$, yields with Eq. ("9851) 0.69.702LAL. an therefore also implies that Q should be at least about 2.,"1) $0.69 \sqrt{Q} 986\simgt 1.1$, and therefore also implies that $Q$ should be at least about 2."987 Efstathiou et al., Efstathiou et al.988 have also come to this conclusion for our Galaxy; with the use of local parameters for the solar ucighbourhood.," have also come to this conclusion for our Galaxy, with the use of local parameters for the solar neighbourhood."989 Ihwiug adopted a value for Q and throueh this a value for (CM/L)p. we will have to convert it to (ML)j.," Having adopted a value for $Q$ and through this a value for $(M/L)_{B}$, we will have to convert it to $(M/L)_{I}$."990 For this we need a (8B...£) colour for the disks., For this we need a $(B - I)$ colour for the disks.991 From the fits of de Cais (1998) we find that the totaldisk magnitudes show a rather laree variation iu colour: for the sample used here (B.£) has a mean value of 1.9. but the ranis.," From the fits of de Grijs (1998) we find that the total magnitudes show a rather large variation in colour; for the sample used here $(B - I)$ has a mean value of 1.9, but the r.m.s."992 scatter is O.S magnitudes., scatter is 0.8 magnitudes.993 Iu. his discussion.de Cuijs (1998) suspects a systematic effect of the internal dust iu the disks (particularly ou the P-maguitudes. which is another reason for us to use the Vigg-version of the Bottema relation (Eq. (," In his discussion,de Grijs (1998) suspects a systematic effect of the internal dust in the disks (particularly on the -magnitudes, which is another reason for us to use the $V_{\rm rot}$ -version of the Bottema relation (Eq. ("9941)) in our derivation iu the previous section).,1)) in our derivation in the previous section).995 Iustead we turn to the discussion of de Jong (19961). who compares his surface photometry of less inclined spirals to star formation models.," Instead we turn to the discussion of de Jong (1996b), who compares his surface photometry of less inclined spirals to star formation models."996 Frou his Table 3. we infer that for single burst models with solar metallicity and ages of 12 Car CM/L)p=2(U/L).," From his Table 3, we infer that for single burst models with solar metallicity and ages of 12 Gyr $(M/L)_{B} = 2997(M/L)_{I}$."998" So we will use an (AL/£), of 1.1.", So we will use an $(M/L)_{I}$ of 1.4.999 There is a further refinement required., There is a further refinement required.1000 In order to take into account the fact that in late-tvpe galaxies the eas coutributes significautly to the gravitational force. we have to correct for a galaxw’s gas conteut as a function of IIubble type.," In order to take into account the fact that in late-type galaxies the gas contributes significantly to the gravitational force, we have to correct for a galaxy's gas content as a function of Hubble type."1001 Iu the following. we will discuss the observational data regarding the aud the Ty separately.," In the following, we will discuss the observational data regarding the and the $_2$ separately."1002 For 25 ofde Caijs’ sample galaxies observations are available. so hat we can estimate the eas-to-total disk mass.," For 25 of de Grijs' sample galaxies observations are available, so that we can estimate the gas-to-total disk mass."1003 For this we apply a correction of a factor 1/3 to the in order to take account of helimn aud use de Ciijs (1998) Fbaud photometry aud our adopted Ευ ratio of 2.8 (see below) to estimate the total disk mass., For this we apply a correction of a factor 4/3 to the in order to take account of helium and use de Grijs' (1998) -band photometry and our adopted $M/L_B$ ratio of 2.8 (see below) to estimate the total disk mass.1004" As a function of Hubble type we then find We find no dependence on rotation velocity: So. the mass is abot half the stellar mass in disks of Sls aud about similar t that iu σος and σας,"," As a function of Hubble type we then find We find no dependence on rotation velocity: So, the mass is about half the stellar mass in disks of Sb's and about similar to that in Sc's and Sd's."1005 But there is no depenudenuce on rotation velocity., But there is no dependence on rotation velocity.1006" But this is not what we need: we should use surface densities rather than disk. masses,", But this is not what we need; we should use surface densities rather than disk masses.1007 Now. the is usually more exteuded than the," Now, the is usually more extended than the"1008There are nevertheless some sections of spiral arms that appear to cross between two minima.,There are nevertheless some sections of spiral arms that appear to cross between two minima.1009"The stellar spiral arms associated with the N-body simulation are transient, so the minimum will eventually disappear.","The stellar spiral arms associated with the N-body simulation are transient, so the minimum will eventually disappear."1010" However the gaseous spiral arms still retain their spiral structure, even though the minimum dissolves."," However the gaseous spiral arms still retain their spiral structure, even though the minimum dissolves."1011 Eventually the gas reaches another minimum and joins a new spiral arm., Eventually the gas reaches another minimum and joins a new spiral arm.1012 The final panel in Fig., The final panel in Fig.1013 3 shows a different section of spiral arm at a much later time frame., 3 shows a different section of spiral arm at a much later time frame.1014 The selected particles have already passed 3 spiral arms at this point., The selected particles have already passed 3 spiral arms at this point.1015" Gas particles highlighted with y> —2kpcare largely coincident with a potential minimum, and also corresponds to one of the dense arms of gas in Fig."," Gas particles highlighted with $y>-2$ kpc are largely coincident with a potential minimum, and also corresponds to one of the dense arms of gas in Fig."1016 4., 4.1017" On the other hand, gas particles with «>—2 kpc lie between two minima or are forming the new spiral arm seen in the lower part of the figure."," On the other hand, gas particles with $x>-2$ kpc lie between two minima or are forming the new spiral arm seen in the lower part of the figure."1018 In Fig., In Fig.1019" 4, spiral arms lying between the potential minima are most evident when cold gas is present and the densities of the gas are higher."," 4, spiral arms lying between the potential minima are most evident when cold gas is present and the densities of the gas are higher."1020" A further consequence of gas retaining the spiral structure imposed by the potential is that at later times in the simulations (e.g. 3rd time frame, Fig."," A further consequence of gas retaining the spiral structure imposed by the potential is that at later times in the simulations (e.g. 3rd time frame, Fig."1021" 1), most of the gas is in the spiral arms."," 1), most of the gas is in the spiral arms."1022" Regions between the arms are relatively empty, and since little gas is entering the potential, the spiral arms correspond merely to dense regions of gas rather than actual spiral shocks."," Regions between the arms are relatively empty, and since little gas is entering the potential, the spiral arms correspond merely to dense regions of gas rather than actual spiral shocks."1023" In addition to the density, the velocity of the gas which is in the spiral arms largely follows that of the stellar component of the disc, with different pattern speeds emerging for different sections of spiral arm."," In addition to the density, the velocity of the gas which is in the spiral arms largely follows that of the stellar component of the disc, with different pattern speeds emerging for different sections of spiral arm."1024 The rotational velocities of the gas thus indicate that there is no fixed pattern speed or co-rotation radius for the spiral perturbation., The rotational velocities of the gas thus indicate that there is no fixed pattern speed or co-rotation radius for the spiral perturbation.1025"the supergiant ellipticals that lie at the centers of rich clusters of galaxies, which are the very objects that are the main landmarks in the Hubble flow.","the supergiant ellipticals that lie at the centers of rich clusters of galaxies, which are the very objects that are the main landmarks in the Hubble flow."1026 In this paper we present our new measurement of the GCLF turnover for the globular cluster system in NGC 4874. the central cD elliptical in the Coma cluster. and use it to estimate Hy.," In this paper we present our new measurement of the GCLF turnover for the globular cluster system in NGC 4874, the central cD elliptical in the Coma cluster, and use it to estimate $H_0$."1027" The bright end of the GCLF in NGC 4874 has already been studied with ground-based imaging, which indicated that it indeed has a large globular cluster system (Harris 1987:; Thompson&Valdes 1987: Blakeslee&Tonry 1995)."," The bright end of the GCLF in NGC 4874 has already been studied with ground-based imaging, which indicated that it indeed has a large globular cluster system \cite{har87}; ; \cite{tho87}; \cite{bla95}) )."1028" With the much deeper HST photometric limits, we could therefore confidently expect to garner a huge population of clusters to define the GCLE."," With the much deeper HST photometric limits, we could therefore confidently expect to garner a huge population of clusters to define the GCLF."1029 Our raw dataset consists of 18 V (F606W) and 10 7 (F814W) images of various exposure lengths (see Table 1). taken 1997 August 16 and 24 (program GO-5905) with the WFPC2 camera.," Our raw dataset consists of 18 $V$ (F606W) and 10 $I$ (F814W) images of various exposure lengths (see Table \ref{tab:obs}) ), taken 1997 August 16 and 24 (program GO-5905) with the WFPC2 camera."1030The long exposures were sub-pixel-shifted (dithered) in a pentagonal pattern by fractional pixel amounts in order to reconstruct clean composite images free from cosmic-ray contamination and bad-pixel artifacts.,The long exposures were sub-pixel-shifted (dithered) in a pentagonal pattern by fractional pixel amounts in order to reconstruct clean composite images free from cosmic-ray contamination and bad-pixel artifacts.1031" The V exposures, totaling 20940 sec, were taken to probe the GCLF deeply enough to resolve the turnover point. while the 7 exposures, totaling 8720 sec, were used to define the color (metallicity) distribution for the brighter end of the cluster system."," The $V$ exposures, totaling 20940 sec, were taken to probe the GCLF deeply enough to resolve the turnover point, while the $I$ exposures, totaling 8720 sec, were used to define the color (metallicity) distribution for the brighter end of the cluster system."1032" The color distribution, spatial structure of the GCS, and the specific frequency will be discussed in Paper Η (Harrisetal. 1999))."," The color distribution, spatial structure of the GCS, and the specific frequency will be discussed in Paper II \cite{har99a}) )."1033 Here. we analyze the GCLF and use it to estimate the distance to Coma and thus Hi.," Here, we analyze the GCLF and use it to estimate the distance to Coma and thus $H_0$."1034" To maximize the total elobular cluster population falling within the WFPC? field of view, we placed the center of the PCI CCD on the nucleus of NGC 4874."," To maximize the total globular cluster population falling within the WFPC2 field of view, we placed the center of the PC1 CCD on the nucleus of NGC 4874."1035" A few other large elliptical galaxies projected near the center of Coma fall on the outskirts of the WF2.3.4 CCDs: however, these proved not to have significant numbers of globular clusters of their own and thus did not contaminate the NGC 4874 sample."," A few other large elliptical galaxies projected near the center of Coma fall on the outskirts of the WF2,3,4 CCDs; however, these proved not to have significant numbers of globular clusters of their own and thus did not contaminate the NGC 4874 sample."1036" Small areas surrounding them were, in any case, masked out in all subsequent data analysis."," Small areas surrounding them were, in any case, masked out in all subsequent data analysis."1037 We first retrieved the raw data from the HST archive located at theCADC?., We first retrieved the raw data from the HST archive located at the.1038". The CADC pipeline preprocessed the images at this point, with the best calibration images then available."," The CADC pipeline preprocessed the images at this point, with the best calibration images then available."1039 We then combined the exposures in pairs (the pairs of long exposures within each orbit) to define a first set of frames reasonably tree of cosmic-ray contamination., We then combined the exposures in pairs (the pairs of long exposures within each orbit) to define a first set of frames reasonably free of cosmic-ray contamination.1040 The vast majority of detected objects on the frames are the globular clusters in the halo of NGC 4874., The vast majority of detected objects on the frames are the globular clusters in the halo of NGC 4874.1041" At the ~100—Mpc distance of Coma they appear as unresolved point sources even in the PCI frames, so it is readily possible to perform conventional point-spread function (PSP) photometry on the frames."," At the $\sim 100-$ Mpc distance of Coma they appear as unresolved point sources even in the PC1 frames, so it is readily possible to perform conventional point-spread function (PSF) photometry on the frames."1042 We constructed an independent PSF for cach image and each of the four WFPC2 CCDs., We constructed an independent PSF for each image and each of the four WFPC2 CCDs.1043" With DAOPHOT and ALLSTAR (Stetson1994)) we then generated separate lists of candidate starlike (that is, unresolved) objects on cach frame."," With DAOPHOT and ALLSTAR \cite{ste94}) ) we then generated separate lists of candidate starlike (that is, unresolved) objects on each frame."1044 These coordinate lists were used to determine the (small) offsets and rotations to map the images onto a common re-registered coordinate system., These coordinate lists were used to determine the (small) offsets and rotations to map the images onto a common re-registered coordinate system.1045" Next, Stetson’s (1994) MONTAGE? code was used to define a “master” image in each filter as the median (i... 50th percentile) of the individual exposures."," Next, Stetson's (1994) MONTAGE2 code was used to define a “master” image in each filter as the median (i.e., 50th percentile) of the individual exposures."1046" Finally, we summed the master V and / images to generate a single deep. contamination-tree image which maximized the available flux for object detection."," Finally, we summed the master $V$ and $I$ images to generate a single deep, contamination-free image which maximized the available flux for object detection."1047" The photometry must also be designed to avoid false detections and nonstellar objects (noise spikes, small, faint background galaxies, or even compact dwarf galaxies within Coma itself)."," The photometry must also be designed to avoid false detections and nonstellar objects (noise spikes, small, faint background galaxies, or even compact dwarf galaxies within Coma itself)."1048" The real and artificial-star measurements were therefore combined with image shape parameters (the DAOPHOT parameters SHARP and 4, and the radial image moment 7, defined by Kron1980. and Harrisetal. 1991))."," The real and artificial-star measurements were therefore combined with image shape parameters (the DAOPHOT parameters SHARP and $\chi$, and the radial image moment $r_1$ defined by \cite{kro80} and \cite{har91}) )."1049" Several numerical trials were carried out with the artificial-star data to vary the detection threshold (in units of o,. the RMS scatter of the sky background) and the shape selection parameters, and thus to determine the highest values of these thresholds which would not deteriorate the detection efficiency of genuine starlike objects (see Figure 1)."," Several numerical trials were carried out with the artificial-star data to vary the detection threshold (in units of $\sigma_s$, the RMS scatter of the sky background) and the shape selection parameters, and thus to determine the highest values of these thresholds which would not deteriorate the detection efficiency of genuine starlike objects (see Figure \ref{fig:image_moments}) )."1050" We adopted a DAOPHOT/FIND detection threshold of 3.50, above sky (c.f. Stetson 1987)."," We adopted a DAOPHOT/FIND detection threshold of $3.5 \sigma_s$ above sky (c.f. \cite{ste87}) ),"1051 a level which recovered virtually all the brighter input artificial stars while adding almost no false detections from noise., a level which recovered virtually all the brighter input artificial stars while adding almost no false detections from noise.1052" The adopted boundaries for V. SHARP, and r, resulted in the culling of about of the artificial stars, mostly at the faintest levels where the distinction between starlike and nonstellar objects by image shape classification also becomes difficult."," The adopted boundaries for $\chi$, SHARP, and $r_1$ resulted in the culling of about of the artificial stars, mostly at the faintest levels where the distinction between starlike and nonstellar objects by image shape classification also becomes difficult."1053" At the faint end as well. some unwanted nonstellar objects end up being scattered into the “starlike” category, but these must be statistically removed from the final GCLF by subtraction of the background luminosity function (see below)."," At the faint end as well, some unwanted nonstellar objects end up being scattered into the “starlike” category, but these must be statistically removed from the final GCLF by subtraction of the background luminosity function (see below)."1054" With the master list of starlike objects now determined, we used the ALLFRAME code (Stetson 1994)) to measure these objects on the original set of F6060Wand F814W images. employing the individual PSFs for each frame as determined"," With the master list of starlike objects now determined, we used the ALLFRAME code \cite{ste94}) ) to measure these objects on the original set of F606Wand F814W images, employing the individual PSFs for each frame as determined"1055"How galaxies formand the stas within hemd8 one of the major open questions of uoderu costuology,",How galaxies form—and the stars within them—is one of the major open questions of modern cosmology.1056 Early-type galaxies (ETC) iost a large fraction of the stellar mass iu todays universe. ando typically show no evidence for ongoing star∙ formation. so∙↴∖↴↑↸∖↕⋜∐⋅⋜↧∶↴∙⊾↸∖↴∖↴⋜⋯≺⋜∏⋝∏∐≼⋜⋯↸⊳↸∖↴∖↴↕∐⊏⊺≼∶↴∖↴∙⊺∪≼⋜↧∙↖↽ they are natural here arects for the investigation of how and when galaxy asscliubly aud star formation occurred in ho past.," Early-type galaxies (ETGs) host a large fraction of the stellar mass in today's universe, and typically show no evidence for major ongoing star formation, so they are natural targets for the investigation of how and when galaxy assembly and star formation occurred in the past."1057" The task is a difficult one, which has constuned a large amount of observational aud heoretical∙ effort ∙∙in the past several decades."," The task is a difficult one, which has consumed a large amount of observational and theoretical effort in the past several decades."1058 All hat work cannot be fairly sununarized iu a such short |article., All that work cannot be fairly summarized in a such short article.1059 This review is thus narrowly‘ focused ou What has been learned frou stellar ages and based on iuteerated ποτ. studies.. .roni and the new questions. raised. by recent evideuce.," This review is thus narrowly focused on what has been learned from stellar ages and abundances based on integrated light studies, and the new questions raised by recent evidence."1060. Apologies]© ©eo to manytm hard-workingoct© colleaguesUo for auv muportaut onmussions., Apologies go to many hard-working colleagues for any important omissions.1061 Tistorically. the debate on the star forination hnistorv of ETCs was framed in terms of two colupeting scenarios: hierarchical clustering (6.8. White Rees 1978. Searle Zinn 1978). according to which these galaxies were assembled through the mereiue of less massive structures formed at vel redshift: aud monolithic dissipative collapse (c.g.. Egeeu 1962. Larson. 1971). whereby uassive ETGs were formed at very high redshift jv measof a rapid eravitational collapse.," Historically, the debate on the star formation history of ETGs was framed in terms of two competing scenarios: hierarchical clustering (e.g., White Rees 1978, Searle Zinn 1978), according to which these galaxies were assembled through the merging of less massive structures formed at high redshift; and monolithic dissipative collapse (e.g., Eggen 1962, Larson 1974), whereby massive ETGs were formed at very high redshift by means of a rapid gravitational collapse."1062 Deciding )etween these two scenarios was one of the uai imnofivatious behiud attempts to iueasmre ua, Deciding between these two scenarios was one of the main motivations behind attempts to measure stellar ages and abundances in ETGs.1063jor is little question that galaxies formed üerarchicalle in a A-CDAL universe. and while hat historical debate has been settled. studies of unresolved stellar populations have acquired renewed portance. as they provide umch needed constraints to iucreasinely sophisticated galaxy ‘ormation models.," Today there is little question that galaxies formed hierarchically in a $\Lambda$ -CDM universe, and while that historical debate has been settled, studies of unresolved stellar populations have acquired renewed importance, as they provide much needed constraints to increasingly sophisticated galaxy formation models."1064 Early attempts at dating. stellar populations. .applications of⋅⋅ stellar⋅ population svuthesis. abundances. uodels to observations. of .inteerated light were based on photometricor low-resolution spectroplotonietric observatious. (6.5e. O'Connell 1980. Comm 1981. Renzini 1986) aud hielh-resolution photographic spectroscopy (e.g... Rose 1985).," Early attempts at dating stellar populations from applications of stellar population synthesis models to observations of integrated light were based on photometric or low-resolution spectrophotometric observations (e.g., O'Connell 1980, Gunn 1981, Renzini Buzzoni 1986) and high-resolution photographic spectroscopy (e.g., Rose 1985)."1065 Thev led to pronüsing. vet not cutively conclusive results. due to limitations of the carly models and/or uncertainties associated with the ageauetallicitv degeneracy (0.g.. Reuzini 1986. Wortley 1991).," They led to promising, yet not entirely conclusive results, due to limitations of the early models and/or uncertainties associated with the age-metallicity degeneracy (e.g., Renzini 1986, Worthey 1994)."1066 The latter is a inandfestatiou of the similar dependence of the temperatures of nian sequence, The latter is a manifestation of the similar dependence of the temperatures of main sequence1067Regarding the Sy and control sample. we found à similar incidence of bars. rings. asymmetries. and close companions. considered both on an individual basis and all together. with the Sy bars somewhat weaker.,"Regarding the Sy and control sample, we found a similar incidence of bars, rings, asymmetries, and close companions, considered both on an individual basis and all together, with the Sy bars somewhat weaker."1068 Thus. our results imply that the fueling of Sy nuclei is not directly related to large-scale mechanisms operating over the bulk of the gas.," Thus, our results imply that the fueling of Sy nuclei is not directly related to large-scale mechanisms operating over the bulk of the gas."1069 There are some hints. however. of a link between them.," There are some hints, however, of a link between them."1070 First. it is generally believed that the required fuel is a tiny fraction of the gas in the inner few ppc. especially of spiral galaxies. and angular momentum reduction is the major challenge (e.g..Jogee2006).," First, it is generally believed that the required fuel is a tiny fraction of the gas in the inner few pc, especially of spiral galaxies, and angular momentum reduction is the major challenge \citep[e.g.,][]{J_06}."1071. For instance. typical molecular gas mass of =10°M was reported for the central regions of most galaxies (e.g..Garefa-Burilloetal.2005).," For instance, typical molecular gas mass of $\approx\,$$10^8\,M_\odot$ was reported for the central regions of most galaxies \citep[e.g.,][]{GCS04_05}."1072 A part of this gas is expected to have resulted from secular evolution., A part of this gas is expected to have resulted from secular evolution.1073 A higher molecular gas concentration was found in the central kiloparsee of barred galaxies than in non-barred ones (Sakamotoetal.1999;Sheth2005.seealsoReganetal. 200601: according to the first authors. more than half of the central gas was driven there by the bar.," A higher molecular gas concentration was found in the central kiloparsec of barred galaxies than in non-barred ones \citep[][see also Regan et~al. 2006]{SOI_99,SVR_05}; according to the first authors, more than half of the central gas was driven there by the bar."1074 The gas in nuclear rings. the most evident tracers of recent gas inflow. can be brought under the influence of the SMBH by viscous torques in the scenario of Garefa-Burilloetal.(2005).," The gas in nuclear rings, the most evident tracers of recent gas inflow, can be brought under the influence of the SMBH by viscous torques in the scenario of \citet[][]{GCS04_05}."1075. Furthermore. higher central gas concentration has been associated with interactions and mergers (e.g..Georgakakisetal.2000:Smith2007).," Furthermore, higher central gas concentration has been associated with interactions and mergers \citep[e.g.,][]{GFN_00,SSH_07}."1076" Second. generally weaker bars in Sy than in inactive galaxies have been associated with larger amounts of cold gas in their host galaxies in the framework of central mass concentrations that could destroy x, bar orbits (Shlosmanetal. 2000)."," Second, generally weaker bars in Sy than in inactive galaxies have been associated with larger amounts of cold gas in their host galaxies in the framework of central mass concentrations that could destroy $x_1$ bar orbits \citep[][]{SPK_00}."1077. It has been shown. however. that bars are less fragile than previously thought. and the mass of the central concentration required to dissolve the bar must be very high (e.g..ΓιαShen&Sellwood2004:Debattistaetal.2006;Marinova&Jogee 2007).," It has been shown, however, that bars are less fragile than previously thought, and the mass of the central concentration required to dissolve the bar must be very high \citep[e.g.,][]{SS_04,DMC_06,MJ_07}."1078. Alternatively. the main destruction mechanism could be the transfer of angular momentum from the gas inflow to the bar (e.g..Bournaudetal.2005).. especially in the presence of radiative cooling (e.g..Debattistaetal.2006).," Alternatively, the main destruction mechanism could be the transfer of angular momentum from the gas inflow to the bar \citep[e.g.,][]{BCS_05}, especially in the presence of radiative cooling \citep[e.g.,][]{DMC_06}."1079. Thus. the weaker Sy bars may be related to the generally larger cold gas amounts reported in their disks (e.g..Huntetal.1999.seealsoHoetal.2008) in the context of angular momentum transfer.," Thus, the weaker Sy bars may be related to the generally larger cold gas amounts reported in their disks \citep[e.g.,][see also Ho et~al. 2008]{HMM2_99} in the context of angular momentum transfer."1080 The relatively low accretion rates of Sy nuclei prompt a variety of small-scale processes able to drive the circumnuclear gas down to the very centre (e.g..Martini2004).," The relatively low accretion rates of Sy nuclei prompt a variety of small-scale processes able to drive the circumnuclear gas down to the very centre \citep[e.g.,][]{M_04}."1081. This could be the main reason for a lack of a universal morphological pattern on these scales (e.g..Garefa-Burilloetal.2004).," This could be the main reason for a lack of a universal morphological pattern on these scales \citep[e.g.,][]{GCS_04}."1082.. Seyfert activity. however. has been associated with the presence of dust (SimóesLopesetal.2007) and more disturbed gaseous kinematics (Dumasetal.2007) in the circumnuclear regions.," Seyfert activity, however, has been associated with the presence of dust \citep[][]{SSF_07} and more disturbed gaseous kinematics \citep[][]{DME_07} in the circumnuclear regions."1083 In this regard. we started a study of the circumnuclear regions of a sample of Sy galaxies using HST archival images.," In this regard, we started a study of the circumnuclear regions of a sample of Sy galaxies using HST archival images."1084 The circumnuclear structures of 3352 and 5590 are the first results of this research., The circumnuclear structures of 352 and 590 are the first results of this research.1085 In the framework of our results we have started a study of the circumnuclear regions of à sample of Sy galaxies using HST archival images., In the framework of our results we have started a study of the circumnuclear regions of a sample of Sy galaxies using HST archival images.1086 As first results of this research. we revealed a nuclear bar and ring in 3352 and nuclear dust lanes in 5590.," As first results of this research, we revealed a nuclear bar and ring in 352 and nuclear dust lanes in 590."1087limb darkening and gravity darkening tend to limit their contribution to the line profiles and affect the reconstruction accuracy of low-latitude magnetic features.,limb darkening and gravity darkening tend to limit their contribution to the line profiles and affect the reconstruction accuracy of low-latitude magnetic features.1088 Synthetic Stokes V profiles are computed for all observed rotation phases and compared to the observations., Synthetic Stokes V profiles are computed for all observed rotation phases and compared to the observations.1089 The model adjustment is iterative and based on a maximum entropy algorithm (Skilling Bryan 1984)., The model adjustment is iterative and based on a maximum entropy algorithm (Skilling Bryan 1984).1090 The version of the code used here makes a projection of the surface magnetic field onto a spherical harmonics frame (Donati et al., The version of the code used here makes a projection of the surface magnetic field onto a spherical harmonics frame (Donati et al.1091" 2006), with the magnetic field geometry resolved into its poloidal and toroidal component (Chandrasekhar 1961)."," 2006), with the magnetic field geometry resolved into its poloidal and toroidal component (Chandrasekhar 1961)."1092" We limit the spherical harmonics expansion to €«10, since no improvement in the fit to the data is achieved by increasing further the maximum allowed value for ¢."," We limit the spherical harmonics expansion to $\ell<10$, since no improvement in the fit to the data is achieved by increasing further the maximum allowed value for $\ell$."1093 The first step to reconstruct a relevant topology of the surface field consists in determining the stellar rotation period., The first step to reconstruct a relevant topology of the surface field consists in determining the stellar rotation period.1094" To do so, we follow the approach of Petit et al. ("," To do so, we follow the approach of Petit et al. ("1095"2002) where a set of magnetic maps is calculated, assuming for each map a different value for the rotation period.","2002) where a set of magnetic maps is calculated, assuming for each map a different value for the rotation period."1096 We impose a constant entropy for all images and calculate a reduced hhereafter) by comparing the set of synthetic Stokes V profiles produced by ZDI to the observed time-series of profiles., We impose a constant entropy for all images and calculate a reduced hereafter) by comparing the set of synthetic Stokes V profiles produced by ZDI to the observed time-series of profiles.1097 The resulting vvariations (plotted in Fig. 3)), The resulting variations (plotted in Fig. \ref{fig:period}) )1098 are recorded over the range of rotation periods to determine the period value producing the best magnetic model (identified by the lowest value of the reduced y? goodness-of-fit parameter)., are recorded over the range of rotation periods to determine the period value producing the best magnetic model (identified by the lowest value of the reduced $\chi^2$ goodness-of-fit parameter).1099" Here, we scan 300 values of the period between 0.4 d and 1 d, a range that"," Here, we scan 300 values of the period between 0.4 d and 1 d, a range that"1100"was used to place upper limits on e for 28 isolated pulsars with f,>25 Lz (TheLIGOB.Abbottetal.2004a).",was used to place upper limits on $\epsilon$ for 28 isolated pulsars with $f_* > 25$ Hz \citep{lig04b}.1101". Our results indicate that these (time- and frequency-domain) search strategies must be revised to include the signal al f. (if the mountain is static) and even to collect signal within a bandwidth A/ centered al [, and 2f, Gf the mountain oscillates).", Our results indicate that these (time- and frequency-domain) search strategies must be revised to include the signal at $f_*$ (if the mountain is static) and even to collect signal within a bandwidth $\Delta f$ centered at $f_*$ and $2f_*$ (if the mountain oscillates).1102 This remains true under several of the evolutionary scenarios outlined above when precession is included. depending on the (unknown) competitive balance between driving and damping.," This remains true under several of the evolutionary scenarios outlined above when precession is included, depending on the (unknown) competitive balance between driving and damping."1103 The analvsis in (his paper clisreeards the [act that LIGO I] will be tunable., The analysis in this paper disregards the fact that LIGO II will be tunable.1104" It is important to redo the SNR caleulations with realistic (unable noise curves. (o investigate whether the likelihood of detection is maximized by observing near f, or 2/,."," It is important to redo the SNR calculations with realistic tunable noise curves, to investigate whether the likelihood of detection is maximized by observing near $f_*$ or $2f_*$."1105 We also do nol consider several physical processes that affect magnetic burial. such as sinking of accreted malerial Ohnmüe dissipation. or Ilall currents: their importance is estimated roughly by Alelatos&Payne (2005)..," We also do not consider several physical processes that affect magnetic burial, such as sinking of accreted material, Ohmic dissipation, or Hall currents; their importance is estimated roughly by \citet{mel05}. ."1106 Finally. Doppler shifts due to the Earth's orbit and. rotation (e.g.Donazzola&Gourgoulhon1996) are neglected. as are slow secular cdrifts in sensitivity during acoherent integration.," Finally, Doppler shifts due to the Earth's orbit and rotation \citep[e.g.][]{bon96} are neglected, as are slow secular drifts in sensitivity during acoherent integration."1107L>0.05L galaxies are hosts to absorbing gas halos characterized by a covering fraction of unity and a spherical geometry which truncates at R(L).,$L> 0.05L^{\ast}$ galaxies are hosts to absorbing gas halos characterized by a covering fraction of unity and a spherical geometry which truncates at $R(L)$.1108" Examination of this now ""standard model"" has been the subject of several theoretical studies (e.g..Charlton&Churchill1996:MoMiralda-Escude1996;Lin&Zou2001 )."," Examination of this now “standard model” has been the subject of several theoretical studies \citep[e.g.,][]{cc96,mo96,lin01}."1109. Guillemin&Bergeron(1997) determined a steeper value of ./20.28 for the B-band luminosity obtained from a best fit to the upper envelope of the distribution of impact parameters of 26 absorbing galaxies., \citet{gb97} determined a steeper value of $\beta = 0.28$ for the B–band luminosity obtained from a best fit to the upper envelope of the distribution of impact parameters of 26 absorbing galaxies.1110 They found Δ.=67 kpe., They found $R_{\ast} = 67$ kpc.1111 Using a reverse approach of establishing foreground galaxy redshifts and then searching for absorption in the spectra of background quasars yields results inconsistent with a covering fraction of unity., Using a reverse approach of establishing foreground galaxy redshifts and then searching for absorption in the spectra of background quasars yields results inconsistent with a covering fraction of unity.1112 For example. Bowenetal.(1995) identified 17 low-redshift galaxies with background quasar probing an impact parameter range between 3—162 kpe.," For example, \citet{bowen95} identified 17 low–redshift galaxies with background quasar probing an impact parameter range between $3-162$ kpc."1113 Galaxies that were probed at impact parameters greater than 13 kpe had no absorption in the halo (W.(2796)50.40—0.9 A). however. four of the six galaxies within 13 kpe of the halo produced absorption.," Galaxies that were probed at impact parameters greater than 13 kpc had no absorption in the halo $W_{r}(2796) \geq11140.40-0.9$ ), however, four of the six galaxies within 13 kpc of the halo produced absorption."1115" For intermediate redshift galaxies. Bechtold&Ellingson(1992) reported a covering fraction f.~0.25 for W,(2796)>0.26 for eight galaxies with D<85 kpe."," For intermediate redshift galaxies, \citet{bechtold92} reported a covering fraction $f_c \simeq11160.25$ for $W_{r}(2796) \geq 0.26$ for eight galaxies with $D1117\leq 85$ kpc."1118 Also. Tripp&Bowen(2005). reported f.0.5 for W(2796)>0.15 for ~20 galaxies with D<50 kpe.," Also, \citet{tripp-china} reported $f_c \sim 0.5$ for $W_{r}(2796) \geq 0.15$ for $\sim 20$ galaxies with $D \leq 50$ kpc."1119" These results are also consistent with the findings of Churchill.Kaeprzak.&Steidel(2005) who reported very weak absorption. W,(2796)<0.3A. well inside the R(L) boundary of bright galaxies: these galaxies would be classified as ""non-absorbers"" in previous surveys."," These results are also consistent with the findings of \citet{cwc-china} who reported very weak absorption, $W_{r}(2796) < 0.3$, well inside the $R(L)$ boundary of bright galaxies; these galaxies would be classified as “non–absorbers” in previous surveys."1120 They also report W.(2796)>| absorption out to ~2R(L)., They also report $W_r(2796) > 1$ absorption out to $\simeq 2 R(L)$.1121 All these results suggest that there are departures from the standard model. that the covering fraction of absorbing gas is less than unity. and that the halo sizes and the distribution of the gas appear to diverge from the R(L) relation with spherical geometry.," All these results suggest that there are departures from the standard model, that the covering fraction of absorbing gas is less than unity, and that the halo sizes and the distribution of the gas appear to diverge from the $R(L)$ relation with spherical geometry."1122 Another approach to understanding halo sizes and gas distributions is to determine the. statistical properties of absorbing gas and then compute the statistical cross section from the redshift path density. dN/dz (seeLanzettaetal. 1995)..," Another approach to understanding halo sizes and gas distributions is to determine the statistical properties of absorbing gas and then compute the statistical cross section from the redshift path density, $dN/dz$ \citep[see][]{lanzetta95}. ."1123 The downfall of this method is that a galaxy lummosity function must be adopted in order to estimate R..., The downfall of this method is that a galaxy luminosity function must be adopted in order to estimate $R_{\ast}$.1124" Nestoretal.(2005) acquired a sample of over 1300 absorption systems. with W,(2796)150.3 from the Sloan Digital Sky Survey (SDSS)."," \citet{nestor05} acquired a sample of over 1300 absorption systems, with $W_{r}(2796) \geq 0.3$ from the Sloan Digital Sky Survey (SDSS)."1125" Using the K-band Holmbere-like luminosity scaling and luminosity function of MUNICS (Droryetal.2003).. Nestor computed A.=60—100 kpe for adopted minimum luminosity cutoffs of L,,5,=0.001— 0.253L""."," Using the $K$ –band Holmberg--like luminosity scaling and luminosity function of MUNICS \citep{drory03}, Nestor computed $R_{\ast} = 60-100$ kpc for adopted minimum luminosity cutoffs of $L_{min}=0.001-0.25L^{\ast}$ ."1126 They found no redshift evolution of R. over the explored range of 0.3«z1.2., They found no redshift evolution of $R_{\ast}$ over the explored range of $0.3\leq z \leq 1.2$.1127 Zibettietal.(2007) studied the statistical photometricproperties of ~2800 absorbers in quasar fields imaged with SDSS., \citet{zibetti06} studied the statistical photometricproperties of $\sim2800$ absorbers in quasar fields imaged with SDSS.1128 Using the method of image stacking. they detected low-level surface brightness (SB) azimuthally about the quasar.," Using the method of image stacking, they detected low–level surface brightness (SB) azimuthally about the quasar."1129 The SB profiles follow a decreasing power law with projected distance away from the quasar out to 100—200 kpe., The SB profiles follow a decreasing power law with projected distance away from the quasar out to $100-200$ kpc.1130 These results imply that absorption selected galaxies may reside out to projected distances of 200 kpe., These results imply that absorption selected galaxies may reside out to projected distances of 200 kpc.1131 However. it is worth noting that the extended light profiles may be an artifact of clustering of galaxies.," However, it is worth noting that the extended light profiles may be an artifact of clustering of galaxies."1132 Cluster companions of the absorbing galaxies could extend the observed light profile over hundreds of stacked images., Cluster companions of the absorbing galaxies could extend the observed light profile over hundreds of stacked images.1133 Thus. one would infer that absorbing galaxies are present at a larger impact parameters than would be found in direct observation of individual galaxies.," Thus, one would infer that absorbing galaxies are present at a larger impact parameters than would be found in direct observation of individual galaxies."1134 Motivated by recent expectations from simulations that halo gas is dynamically complex and sensitive to the physics of galaxy formation. we investigate the standard halo model of absorbers.," Motivated by recent expectations from simulations that halo gas is dynamically complex and sensitive to the physics of galaxy formation, we investigate the standard halo model of absorbers."1135 We also aim to provide updated constraints on f. and ./ for galaxy formation simulations., We also aim to provide updated constraints on $f_c$ and $\beta$ for galaxy formation simulations.1136 In. this paper. we demonstrate that f£.<I and question the validity of the Holmbere-like luminosity scaling (Eq. 1)).," In this paper, we demonstrate that $f_c < 1$ and question the validity of the Holmberg–like luminosity scaling (Eq. \ref{eq:rl}) )."1137" Using high resolution quasar spectra. we explore absorption strengths to an order of magnitude more sensitive than previous surveys which allow us to re-identify non-absorbing galaxies as ""weak"" absorbing galaxies."," Using high resolution quasar spectra, we explore absorption strengths to an order of magnitude more sensitive than previous surveys which allow us to re–identify non–absorbing galaxies as “weak” absorbing galaxies."1138 In 2 we describe our sample and analysis., In \ref{sec:data} we describe our sample and analysis.1139 In 3.. we present new calculations of the statistical absorber radius computed using the statistically measured absorption path density dN/dz and the Schechter luminosity function.," In \ref{sec:results}, we present new calculations of the statistical absorber radius computed using the statistically measured absorption path density $dN/dz$ and the Schechter luminosity function."1140 We then compare these values to the empirical results of S95 and to a sample of known absorption selected galaxies with measured luminosities and impact parameters., We then compare these values to the empirical results of S95 and to a sample of known absorption selected galaxies with measured luminosities and impact parameters.1141 We also examine how individual halos behave with respect to the statistical halo., We also examine how individual halos behave with respect to the statistical halo.1142 In 4.. we discuss the properties and distribution of gas in halos.," In \ref{sec:dis}, we discuss the properties and distribution of gas in halos."1143 Our concluding remarks are in 5.., Our concluding remarks are in \ref{sec:conclusion}.1144 We have constructed a sample of 37 galaxies (0.3«=<1.0). with spectroscopically confirmed redshifts. selected by the presence of absorption in quasar spectra.," We have constructed a sample of 37 galaxies $0.3<z<1.0$ ), with spectroscopically confirmed redshifts, selected by the presence of absorption in quasar spectra."1145 The absorption properties were measured from HIRES/Keck (Vogtetal.1994). and UVES/VLT (Dekkeretal.2000) spectra.," The absorption properties were measured from HIRES/Keck \citep{vogt94} and UVES/VLT \citep{dekker00}1146 spectra."1147" The À2796 profileshave been presented in Churchill.Kaeprzak.&Steidel(2005).. where the detection limit is W,(2796)>0.02 (5 c)."," The $\lambda 2796$ profileshave been presented in \citet{cwc-china}, where the detection limit is $W_r(2796)\geq11480.02$ (5 $\sigma$ )."1149 Galaxy properties were measured from F702W or F814WWFEPC-2/HST images of the quasar fields., Galaxy properties were measured from F702W or F814W images of the quasar fields.1150 Images of the galaxies. along with further details of the sample selection. data. and data analysis. can be found in Kaeprzaketal.(2007a).," Images of the galaxies, along with further details of the sample selection, data, and data analysis, can be found in \citet{kacprzak07}."1151. Galaxy absolute magnitudes. Mj. were determined from the A-corrected observed nose Or Aipsigiy adopted from Kaeprzaketal.(2007a).," Galaxy absolute magnitudes, $M_B$, were determined from the $k$ –corrected observed $m_{F702W}$ or $m_{F814W}$ adopted from \citet{kacprzak07}."1152. The A-corrections were computed using the formalism of Kim.Goobar.&Perlmutter(1996) based upon the spectral energy distribution (SED) templates of Kinneyetal.(1996)., The $k$ –corrections were computed using the formalism of \citet{kim96} based upon the spectral energy distribution (SED) templates of \citet{kinney96}.1153. The adopted SED for each galaxy was based upon its rest-frame B—K color (SDP94)., The adopted SED for each galaxy was based upon its rest–frame $B-K$ color (SDP94).1154 For galaxies with no color information. we adopteda Sb SED which is consistent with average color of absorbing galaxies (SDP94:Zibettietal.2007).," For galaxies with no color information, we adopteda Sb SED which is consistent with average color of absorbing galaxies \citep[SDP94;][]{zibetti06}."1155. Our K-corrections are consistent with those from the literature (Kim.Goobar.&Perlmut-ter1996:Fukugita.Shimasaku.," Our $k$ –corrections are consistent with those from the literature \citep{kim96,fukugita95}."1156"&Ichikawa 1995).. B-band luminosities were computed using the DEEP? optimal Mj, of Faberetal.(2007.Table2) in the redshift bin appropriate for each galaxy.", $B$ –band luminosities were computed using the DEEP2 optimal $M^{\ast}_B$ of \citet[][Table~2]{faber05} in the redshift bin appropriate for each galaxy.1157 Mj ranges from —21.07 (£z;2 0.3) to 21.54 (is) =1.1)., $M^{\ast}_B$ ranges from $-21.07$ $\left< z \right> =0.3$ ) to $-21.54$ $\left< z\right> =1.1$ ).1158 We compute the halo gascross section determined from the redshift path density. whereΑς is the statistical absorber radiusfor an L galaxy. and d is the number density of galaxies.," We compute the halo gascross section determined from the redshift path density, where$R_{\rm x}$ is the statistical absorber radiusfor an $L^{\ast}$ galaxy, and $\Phi^{\ast}$ is the number density of $L^{\ast}$ galaxies."1159 RI= f.R7. where R. is the covering fraction correctedL absorbing halo radius.," $R^2_{\rm x}=f_c R^2_{\ast}$ , where $R_{\ast}$ is the covering fraction corrected absorbing halo radius."1160 Note here that we make a distinction between Αν. which is derived from the redshift path density. and R... which is a physical cross section of the absorbing gas accounting for the," Note here that we make a distinction between $R_{\rm x}$ , which is derived from the redshift path density, and $R_{\ast}$ , which is a physical cross section of the absorbing gas accounting for the"1161any process that uses a sieuificance-based detection threshold.,any process that uses a significance-based detection threshold.1162 Were. we briefly set out a ecισα. recΠρο to use in more complicated cases.," Here, we briefly set out a general recipe to use in more complicated cases."1163 For complex detection algoritlius. sole of the steps may require Moute Carlo methods.," For complex detection algorithms, some of the steps may require Monte Carlo methods."1164 We focus below on Sigual-to-Noise (SNR) based detection at a single location as au example application., We focus below on Signal-to-Noise (SNR) based detection at a single location as an example application.1165 The SNR was the primary statistic used for detecting sources in high-cucrey astroplivsics before the introduction of maxiumuu-liselibood aud. wavelet-based methods., The SNR was the primary statistic used for detecting sources in high-energy astrophysics before the introduction of maximum-likelihood and wavelet-based methods.1166 Typically. E=3 owas used as the detection threshold. correspοiding to à=0.003 in the Gaussian regime.," Typically, $\frac{S}{N}=3$ was used as the detection threshold, corresponding to $\alpha=0.003$ in the Gaussian regime."1167 Hore we ayply the recipe in to derive an upper luit with SNR-based detectio1., Here we apply the recipe in \\ref{s:recipe} to derive an upper limit with SNR-based detection.1168 Our methods cau also be applie to more sophisticated «etection algorithius such as sliding-cell detection methods such as (11:uuden et 1198. Dobrzvcki ct 22000. Calderwood et 22001). and wavelet-based detection metlods such as (Darniani et 11997). (Vikhliuin ot 110997). (Freciuan et 2202). ete.," Our methods can also be applied to more sophisticated detection algorithms such as sliding-cell detection methods such as (Harnden et 1984, Dobrzycki et 2000, Calderwood et 2001), and wavelet-based detection methods such as (Damiani et 1997), (Vikhlinin et 1997), (Freeman et 2002), etc."1169 hupleimoeutatio1 of our technique for these methods will vary in detail. aud we leave these developnents for future work.," Implementation of our technique for these methods will vary in detail, and we leave these developments for future work."1170 We beein with a Caussian probability model for the source and background couuts (Step 1 in lpe]), We begin with a Gaussian probability model for the source and background counts (Step 1 in \\ref{s:recipe}) )1171electron-positron pair creation due to the electric Ποια of the electrosphere could be one of (he main observational signatures of quark stars.,electron-positron pair creation due to the electric field of the electrosphere could be one of the main observational signatures of quark stars.1172 It is the purpose of (he present paper to consider (he Schwinger process of pair creation in the electrosphere of the quark stars. by svstematically taking into account (he main physical characteristics of the environment in which pair production takes place.," It is the purpose of the present paper to consider the Schwinger process of pair creation in the electrosphere of the quark stars, by systematically taking into account the main physical characteristics of the environment in which pair production takes place."1173 The electric field in the electrosphere is not a constant. as assumed in the Schwinger model. but it is a rapidly decreasing function of the distance z from the quark star surface.," The electric field in the electrosphere is not a constant, as assumed in the Schwinger model, but it is a rapidly decreasing function of the distance $z$ from the quark star surface."1174 Therefore. in order to realistically describe the pair production process one must consider electron-positron creation in an inhomogeneous electric field.," Therefore, in order to realistically describe the pair production process one must consider electron-positron creation in an inhomogeneous electric field."1175 To study (he pair production process we adopt the tunnelling approach and the fermion production rate in the electric field of the electrosphere is derived., To study the pair production process we adopt the tunnelling approach and the fermion production rate in the electric field of the electrosphere is derived.1176 The production rate is a local quantity. it depends on the distance to the quark stars surface and il is a rapidly decreasing Function of z.," The production rate is a local quantity, it depends on the distance to the quark star's surface and it is a rapidly decreasing function of $z$."1177 The emissivity ancl enereyv [Iux due (o pair creation at the quark star surface is also considered., The emissivity and energy flux due to pair creation at the quark star surface is also considered.1178 An important factor which can reduce significantly the pair production rate is (the presence of a boundary (the quark star surface)., An important factor which can reduce significantly the pair production rate is the presence of a boundary (the quark star surface).1179 For electric Ποιά» perpendicular to the boundary. there is a significant reduction in (he magnitude of the pair production rate. which is also associated with an important qualitative change in the process. which becomes a periodic function of the distance to the quark star surface.," For electric fields perpendicular to the boundary there is a significant reduction in the magnitude of the pair production rate, which is also associated with an important qualitative change in the process, which becomes a periodic function of the distance to the quark star surface."1180 The present paper is organized as follows., The present paper is organized as follows.1181 In Section 2 we review (he basic properties of the electrosphere of quark stars., In Section 2 we review the basic properties of the electrosphere of quark stars.1182 The electron-positron rate production in (he electric field ol the electrosphere is obtained in Section 3., The electron-positron rate production in the electric field of the electrosphere is obtained in Section 3.1183 The boundary effects are considered in Section 4., The boundary effects are considered in Section 4.1184 In Section 5 we calculate the electron-positron pair flux of the electrosphere ancl compare our results with those obtained by Usov(1998a.b.2001).," In Section 5 we calculate the electron-positron pair flux of the electrosphere and compare our results with those obtained by \citet{Us98a,Us98b,Us01}."1185.. A brief summary of our results is given in Section 6., A brief summary of our results is given in Section 6.1186 In the electrosphere. electrons are held to the strange quark matter (5M) surface by an extremely strong electric field.," In the electrosphere, electrons are held to the strange quark matter (SQM) surface by an extremely strong electric field."1187 The thickness of the electrosphere is much smaller than the stellar radius Re109 em. and a plane-parallel approximation may be used to study its structure (Usovetal.2005).," The thickness of the electrosphere is much smaller than the stellar radius $R\simeq 10^6$ cm, and a plane-parallel approximation may be used to study its structure \citep{Us05}."1188. In Chis approximation all values depend only on the coordinate 2. Where (he axis z is perpendicular to (he SQAI surface (2= 0) and directed outward.," In this approximation all values depend only on the coordinate $z$, where the axis $z$ is perpendicular to the SQM surface $z=0$ ) and directed outward."1189 To lind the distributions of electrons and electric fields in (he vicinity of the SQAI surface. we use a simple Thomas-Fermi model considered by Aleocketal.(1986). and takeinto account (he finite temperature effects as discussed bv Nettierοἱal. (1995).," To find the distributions of electrons and electric fields in the vicinity of the SQM surface, we use a simple Thomas-Fermi model considered by \citet{Al86} and takeinto account the finite temperature effects as discussed by \citet{Ke95}. ."1190We construct a simple tov model of the galaxys star formation history (ΕΙ). iu the bulee CR<5 spc}. tuner disk (5«Rx15 kpc) and outer disk CR>15 kpc) of the galaxy.,"We construct a simple toy model of the galaxy's star formation history (SFH), in the bulge $R<5$ kpc), inner disk $5<R<15$ kpc) and outer disk $R>15$ kpc) of the galaxy."1191 Usine coustraiuts derived frou the galaxvs current star formation rate and stellar iuass surface density. we build a simple model that is consistent with observations in all three locations.," Using constraints derived from the galaxy's current star formation rate and stellar mass surface density, we build a simple model that is consistent with observations in all three locations."1192" Our observations show that the current star-forimation is uniformly distributed across the galaxy. πο we postulate that the overall SEIT cau be modeled by a period of coustaut star formation of some length that is the same evervwliere. superimposed on an older stellar population that dominates at the ceuter aud is virtually abseut at large τας,"," Our observations show that the current star-formation is uniformly distributed across the galaxy, so we postulate that the overall SFH can be modeled by a period of constant star formation of some length that is the same everywhere, superimposed on an older stellar population that dominates at the center and is virtually absent at large radii."1193 Our model incorporates the following constraints: A simple schematic of this model ΕΠ is shown iu Figue 10.., Our model incorporates the following constraints: A simple schematic of this model SFH is shown in Figure \ref{sfh}.1194" We then use Druzual Charlot (2003) models to predict D1000, iu the inner disk aud bulec. obtaining values of 1.3 and 1.5. respectively."," We then use Bruzual Charlot (2003) models to predict $D4000_n$ in the inner disk and bulge, obtaining values of 1.3 and 1.5, respectively."1195 These values are iu good agreement with the measured values of 1.1 and 1.6 in the corresponding radial bius., These values are in good agreement with the measured values of 1.4 and 1.6 in the corresponding radial bins.1196 Thus. through oulv a simple partition of mass into old aud voung conrponenuts. we can reasonably reproduce one of the kev spectral features of GASS35981.," Thus, through only a simple partition of mass into old and young components, we can reasonably reproduce one of the key spectral features of GASS35981."1197 We uote that varviug the formation time of the old component or doubliug its timescale to 2 Gar changes the results very little., We note that varying the formation time of the old component or doubling its timescale to 2 Gyr changes the results very little.1198 Likewise. adjusting the leneth of the more recent star-forming episode within the range 0.72 Car does not sienificautly affect our results.," Likewise, adjusting the length of the more recent star-forming episode within the range 0.7–2 Gyr does not significantly affect our results."1199 Finally. we can estimate the total fraction of the stellar nass added to the galaxy in the most recent star formation episode aud find that it is around20%.," Finally, we can estimate the total fraction of the stellar mass added to the galaxy in the most recent star formation episode and find that it is around."1200. Note. however. that at its current star formation rate. CGASS35981 will not exhaust its ITE reservoir for another NT Cr.," Note, however, that at its current star formation rate, GASS35981 will not exhaust its HI reservoir for another 5–7 Gyr."

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