ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 These objects (see Fig. A4)).," These objects (see Fig. \ref{oxspec}) ),"3 appear to be part of the population of red QSOs discussed e.g. by and?.. which on average are absorbed by columns below Nj=109 em..," appear to be part of the population of red QSOs discussed e.g. by and, which on average are absorbed by columns below $N_H=10^{23}$ ."4 On the contrary. VIO selected their objects from the sample of?.. in which strict eriteria on the line width have been adopted. producing an ensamble of pure type-2 objects.," On the contrary, V10 selected their objects from the sample of, in which strict criteria on the line width have been adopted, producing an ensamble of pure type-2 objects."5 As a simple check. when considering only those [Ne V]-selected objects which look like pure type-2 spectra(e.g.," As a simple check, when considering only those [Ne V]-selected objects which look like pure type-2 spectra(e.g."6 Mell FWHM x2000 km s7!) the fraction of CT candidates increases to 50% (2/4)., MgII FWHM $\lesssim2000$ km $^{-1}$ ) the fraction of CT candidates increases to $\approx$ (2/4).7 Despite the very low statistics. this fraction is consistent with what has been found by VIO. suggesting that. when the search is restricted to pure type-2 objects. [Ne V] selection may be an efficient way to pick up CT AGN at =~I.," Despite the very low statistics, this fraction is consistent with what has been found by V10, suggesting that, when the search is restricted to pure type-2 objects, [Ne V] selection may be an efficient way to pick up CT AGN at $z\sim 1$."8 Synthesis models predict that from to about of the XRB at 30 keV is not accounted for by the integrated emission of Compton-Thin AGN., Synthesis models predict that from to about of the XRB at 30 keV is not accounted for by the integrated emission of Compton-Thin AGN.9 This “missing” background is expected to be produced by Compton-Thick AGN. and most of it is expected to be produced by CT AGN with Seyfert-like intrinsic luminosities at a redshift of z~1.," This “missing” background is expected to be produced by Compton-Thick AGN, and most of it is expected to be produced by CT AGN with Seyfert-like intrinsic luminosities at a redshift of $z\sim1$."10 The [Ne V]-selected CT QSOs in the SDSS represent the high-luminosity. low space density tail of the distribution of CT AGN at z I. and are expected to provide only a minor contribution to the missing XRB.," The [Ne V]-selected CT QSOs in the SDSS represent the high-luminosity, low space density tail of the distribution of CT AGN at $z\sim1$ , and are expected to provide only a minor contribution to the missing XRB."11 Selection of lower-luminosity CT AGN at zo1 is therefore needed. which can in principle be done by applying the X/NeV diagnosties to objects in sky areas with deep spectroscopic surveys and deep X-ray coverage.," Selection of lower-luminosity CT AGN at $z\sim 1$ is therefore needed, which can in principle be done by applying the X/NeV diagnostics to objects in sky areas with deep spectroscopic surveys and deep X-ray coverage."12 As an example. the combination between the zCOSMOS-bright spectroscopic survey and the Chandra--COSMOS X-ray survey in the COSMOS field would be able to identify CT AGN at z~1 down to intrinsic Ly~I0Pere s7!.. i.e. the population which is thought to produce a large fraction of the," As an example, the combination between the zCOSMOS-bright spectroscopic survey and the -COSMOS X-ray survey in the COSMOS field would be able to identify CT AGN at $z\sim 1$ down to intrinsic $L_X\sim10^{43}$ , i.e. the population which is thought to produce a large fraction of the"13component.,.14".. To estimate the region of the star probed by the observed g-modes, we first examined a propagation diagram of the asteroseismological model of0"," To estimate the region of the star probed by the observed $g$ -modes, we first examined a propagation diagram of the asteroseismological model of."15122+200., In Fig.16". In Fig. 1 we plot the logarithm of the squared Brunt-Vaiisalla and the Lamb frequencies, along with the location of the nodes corresponding to g-modes (the zeros of the radial eigenfunctions) marked with (blue) plus symbols."," \ref{propa} we plot the logarithm of the squared Brunt-Väiisällä and the Lamb frequencies, along with the location of the nodes corresponding to $g$ -modes (the zeros of the radial eigenfunctions) marked with (blue) plus symbols."17 The nodes associated to the eigenmodes exhibited by aare emphasized with black dots., The nodes associated to the eigenmodes exhibited by are emphasized with black dots.18" Note that these modes have nodes in the region 0.1<r/R.x1, implying that they have an oscillatory character in almost the whole star."," Note that these modes have nodes in the region $0.1 \lesssim r/R_* \lesssim 1$, implying that they have an oscillatory character in almost the whole star."19 We also examined the rotational kernels computed from our asteroseismological model for, We also examined the rotational kernels computed from our asteroseismological model for.2001224-20, In Fig.21"0.. In Fig. 2 we show the normalized K,,(r) for k=12 and k=24, corresponding to the shortest and the longest pulsation periods observed in0122--200."," \ref{kernel} we show the normalized $K_{k\ell}(r)$ for $k= 12$ and $k= 24$, corresponding to the shortest and the longest pulsation periods observed in."22". As can be seen, the rotation kernels have the largest amplitudes at the outer regions of the model, but have also appreciable amplitudes (up to = 0.3) throughout thefull model of0122+200,, implying that the observed g-modes are sensitive to the entire rotation profile."," As can be seen, the rotation kernels have the largest amplitudes at the outer regions of the model, but have also appreciable amplitudes (up to $\approx 0.3$ ) throughout the model of, implying that the observed $g$ -modes are sensitive to the entire rotation profile."23" T'his is in contrast to the case of DBV or DAV stars, in which rotational kernels sample only the outer regions of the star — see Kawaler et al. ("," This is in contrast to the case of DBV or DAV stars, in which rotational kernels sample only the outer regions of the star — see Kawaler et al. ("241999) — because of the larger degeneracy of the core.,1999) — because of the larger degeneracy of the core.25" First, we assumed that rrotates as a rigid body, that is, the rotation rate €) is constant throughout the star."," First, we assumed that rotates as a rigid body, that is, the rotation rate $\Omega$ is constant throughout the star."26" We variated the value of 2 from 1.15x10"" Hz (P~100 days) to 2.77x10 Hz (P~1 minutes) and for each value of 2 we computed* the theoretical frequency splittings (dvge,) by means of Eq. (2)),"," We variated the value of $\Omega$ from $1.15 \times 10^{-7}$ Hz $P \sim 100$ days) to $2.77 \times 10^{-4}$ Hz $P \sim 1$ minutes) and for each value of $\Omega$ we computed the theoretical frequency splittings $\delta \nu_{k \ell m}^{\rm T}$ ) by means of Eq. \ref{rota-rigid}) ),"27" where the coefficients Cy, were assessed for each mode through Eq. (3))", where the coefficients $C_{k \ell}$ were assessed for each mode through Eq. \ref{coefi-c1}) )28" and not by means of the asymptotic relation, Cr,©1/£(£4-1)."," and not by means of the asymptotic relation, $C_{k \ell} \approx 1 / \ell(\ell+1)$."29" The results of this optimization procedure are shown in Fig. 3,,"," The results of this optimization procedure are shown in Fig. \ref{rigid},"30 that shows the x? function versus the rotation rate., that shows the $\chi^2$ function versus the rotation rate.31 The best-fit solution corresponds to a rotation rate of Q=6.915 µΗΖ., The best-fit solution corresponds to a rotation rate of $\Omega= 6.915$ $\mu$ Hz.32" It corresponds to a rotation period of P—40.17 hours, in good agreement with the approximate value of P—37.2 hours quoted by Fu et al. ("," It corresponds to a rotation period of $P= 40.17$ hours, in good agreement with the approximate value of $P= 37.2$ hours quoted by Fu et al. ("332007).,2007).34" Note that the rotation period (of the order of 10° s) is much longer than the longest pulsation period exhibited by (~600 s), thus justifying the use of the perturbative theory to a first order in the calculation of óv,,."," Note that the rotation period (of the order of $10^5$ s) is much longer than the longest pulsation period exhibited by $\sim 600$ s), thus justifying the use of the perturbative theory to a first order in the calculation of $\delta\nu_{k \ell35m}^{\rm T}$."36" Here, we lift the assumption of solid-body rotation."," Here, we lift the assumption of solid-body rotation."37" Because the exploratory nature of this study, we try very simplified functional forms for Q(r)."," Because the exploratory nature of this study, we try very simplified functional forms for $\Omega(r)$."38" Specifically, we adopt a family of differential rotation profiles defined as: where € and Ως are the rotation rates at the stellar surface and center,respectively’."," Specifically, we adopt a family of differential rotation profiles defined as: where $\Omega_{\rm s}$ and $\Omega_{\rm c}$ are the rotation rates at the stellar surface and center,."39. This family of linear profiles includes rotation rates that decrease and increase linearly with r and also “flat” rotation profiles (when Ὡς= Ὡς) that represent the case of rigid rotation already examined in Sect. 3.1.., This family of linear profiles includes rotation rates that decrease and increase linearly with $r$ and also “flat” rotation profiles (when $\Omega_{\rm s}= \Omega_{\rm c}$ ) that represent the case of rigid rotation already examined in Sect. \ref{rig}.40" We performed our optimization procedures varying the parameters Ως and €, in the range 0—20 wHz.", We performed our optimization procedures varying the parameters $\Omega_{\rm s}$ and $\Omega_{\rm c}$ in the range $0-20$ $\mu$ Hz.41" We computed the theoretical frequency splittings by means of Eq. (4)),"," We computed the theoretical frequency splittings by means of Eq. \ref{rota-diff}) ),"42 where the rotation kernels are computed by using Eq. (5))., where the rotation kernels are computed by using Eq. \ref{rot-kernel}) ).43" The results are shown in Fig. 4,,"," The results are shown in Fig. \ref{linear-pg0122},"44" where we prefer to plot 1/x? instead of x? to emphasize the location of the values (Ως, Ως) providing good agreement between observed and theoretical frequency splittings."," where we prefer to plot $1/\chi^2$ instead of $\chi^2$ to emphasize the location of the values $\Omega_{\rm45 c},\Omega_{\rm s}$ ) providing good agreement between observed and theoretical frequency splittings."46" The region of good solutions (that is, the smallest values of x?) has an elongated shape."," The region of good solutions (that is, the smallest values of $\chi^2$ ) has an elongated shape."47" As can be seen, there exists a unique, well-localized best-fit solution at (Q-,Qs)=(10.62,4.41) wHz, marked with a black dot in the plot."," As can be seen, there exists a unique, well-localized best-fit solution at $(\Omega_{\rm c},\Omega_{\rm s})= (10.62, 4.41)\, \mu$ Hz, marked with a black dot in the plot."48" This solution is substantially different from rigid-rotation, which should fall at some point along the green dashed line."," This solution is substantially different from rigid-rotation, which should fall at some point along the green dashed line."49 The existence of the best fit solution suggests that the central regions of ccould be rotating more than twice faster than the surface., The existence of the best fit solution suggests that the central regions of could be rotating more than twice faster than the surface.50 We studied the sensitivity of our result to each of, We studied the sensitivity of our result to each of51detailed analysis by Burkert&Odell(1993).. and ODelletal.(2000).,"detailed analysis by \cite{burkert98}, and \cite{odell00}."52. The emereine optical picture of the cometary knots reveals (hat thev are neutral gas condensations Chat appear as comet like structures with rims bright in Ha. and tails that appear as shadows in [OI] and that point away [rom the central star., The emerging optical picture of the cometary knots reveals that they are neutral gas condensations that appear as comet like structures with rims bright in $\alpha$ and tails that appear as shadows in [OIII] and that point away from the central star.53 The rim of low-excitation ionize gas has a steep temperature eradient indicating that the knots are photo-evaporating and that ionization fronts are advancing into the knots (O'Delletal.2000)., The rim of low-excitation ionize gas has a steep temperature gradient indicating that the knots are photo-evaporating and that ionization fronts are advancing into the knots \citep{odell00}.54. A recent anlavsis of knots over the whole Helix nebula by ODelletal.(2004) revealed a new 3-D picture for (he main ring of the ]lelix: it is composed of a disk structure and an outer ring tilted almost perpendicularly with respect to Che disk., A recent anlaysis of knots over the whole Helix nebula by \cite{odell04} revealed a new 3-D picture for the main ring of the Helix: it is composed of a disk structure and an outer ring tilted almost perpendicularly with respect to the disk.55 Within each of these components. they observed a similar. progressive evolution in the structure of the knots.," Within each of these components, they observed a similar, progressive evolution in the structure of the knots."56 The knots closest to the central star and clearly inside ol the ionization front were elegantly carved with the brightest rims., The knots closest to the central star and clearly inside of the ionization front were elegantly carved with the brightest rims.57 The knots furthest from the central star appeared slightly more amorphous in their structure wilh less well defined rims., The knots furthest from the central star appeared slightly more amorphous in their structure with less well defined rims.58 The culmination of these optical observations appear to support the theory that these knots were iniiallv formed earlier by instabilities at (he ionization Iront or perhaps bv the interaction of the last stellar wind ancl (hen have been sculpted by interaction with the harsh radiation field of the central star (Capriotti1973)., The culmination of these optical observations appear to support the theory that these knots were initially formed earlier by instabilities at the ionization front or perhaps by the interaction of the fast stellar wind and then have been sculpted by interaction with the harsh radiation field of the central star \citep{capriotti73}.59". In contrast to the high angular resolution (—0.01"")) optical studies of the ionized eas lines in the cometary knots. the molecular gas observations have had lower angular resolution 11"")) and sensitivity making it difficult to determine the detailed structure and excitation of the main gas component of the cometary knots."," In contrast to the high angular resolution $\sim$ ) optical studies of the ionized gas lines in the cometary knots, the molecular gas observations have had lower angular resolution ) and sensitivity making it difficult to determine the detailed structure and excitation of the main gas component of the cometary knots."60 These low resolution studies have revealed that the IIelix has retained a significant amount of molecular gas (Youngetal.Healy1986:Specketal.2002) ancl that the molecular gas appears to be very clumpy. and is probably confined {ο cometary knot structures (Speckllugeinsetal. 2002).," These low resolution studies have revealed that the Helix has retained a significant amount of molecular gas \citep{young99,huggins86,speck02} and that the molecular gas appears to be very clumpy and is probably confined to cometary knot structures \citep{speck02, huggins02}."61. The only detailed study of an isolated cometary knot. whieh is close to the central star. shows no evidence for large velocities in the molecular gas. ruling out a stellar wind shaping the knot. ancl reveals a stratified structure for the ionized aud molecular eas emissions (hat is expected in a photodissociation region (PDR) (IIugeinsetal.2002).," The only detailed study of an isolated cometary knot, which is close to the central star, shows no evidence for large velocities in the molecular gas, ruling out a stellar wind shaping the knot, and reveals a stratified structure for the ionized and molecular gas emissions that is expected in a photodissociation region (PDR) \citep{huggins02}."62. Ilowever. since recent optical studies show an evolution of the knot structure with radial distance from (he central star (ODelletal.2004)... it is not clear Chat this single knot study is representative of all (he knots in the nebula.," However, since recent optical studies show an evolution of the knot structure with radial distance from the central star \citep{odell04}, it is not clear that this single knot study is representative of all the knots in the nebula."63" Ii order to determine the structure and excitation of the Is emission in the cometary knots at comparable resolution to optical images across (he Helix. we pursued high angular resolution (70.2 ) NICMOS/NIC3 F212N II, images at several locations in the nebula. in parallel with the HST/ACS program recently published by O'Delletal.(2004)."," In order to determine the structure and excitation of the $_2$ emission in the cometary knots at comparable resolution to optical images across the Helix, we pursued high angular resolution $\sim$ 0.2 ) NICMOS/NIC3 F212N $_2$ images at several locations in the nebula, in parallel with the HST/ACS program recently published by \cite{odell04}."64. The remainder of this paper is organized as follows., The remainder of this paper is organized as follows.65 In section 2. we report the observation and data processing procedures.," In section 2, we report the observation and data processing procedures."66 In section 3. we discuss the major observational results ancl how these relate to the optical ionized gas line emissions imaged by ODelletal. (2004)..," In section 3, we discuss the major observational results and how these relate to the optical ionized gas line emissions imaged by \cite{odell04}. ."67tails themselves appear clearly brighter in the residual maps produced by subtraction of these models from the origina images.,tails themselves appear clearly brighter in the residual maps produced by subtraction of these models from the original images.68 TPhis shows that without masking. some of the lieh from the tails is included in the model. mocdifving the fi parameters.," This shows that without masking, some of the light from the tails is included in the model, modifying the fit parameters."69" 7? constructed a ""merger sequence! from. a sample of galaxies that are good. candidates for ongoing mergers anc remnants of mergers between two approximately equal mass disc galaxies.", \scite{keelwu95} constructed a `merger sequence' from a sample of galaxies that are good candidates for ongoing mergers and remnants of mergers between two approximately equal mass disc galaxies.70" Phey assigned a ""merger stage’ to each galaxy sed: upon dynamical crossing times. with zero age define o be the point of nuclear coalescence."," They assigned a `merger stage' to each galaxy based upon dynamical crossing times, with zero age defined to be the point of nuclear coalescence."71 They noted that the raction of galaxy starlight contained within the tails roughly anti-correlates with this merger stage., They noted that the fraction of galaxy starlight contained within the tails roughly anti-correlates with this merger stage.72 This allows us make a very rough estimate of the time-scale since the merger event hat created the tails within NGC 1700., This allows us make a very rough estimate of the time-scale since the merger event that created the tails within NGC 1700.73 This analvsis was performed. on the long exposure residual images., This analysis was performed on the long exposure residual images.74 As we wanted to include as much of the ail light in the residual images as possible. we used. the residual images produced. by excluding the tails from the elliptical fit of the galaxy.," As we wanted to include as much of the tail light in the residual images as possible, we used the residual images produced by excluding the tails from the elliptical fit of the galaxy."75 As mentioned. above. if the tails are not masked out during the fit. some of their light= is included. in the model. mocifving the fit. parameters and resulting in the subtraction of a significant amount of tail light from the galaxy image.," As mentioned above, if the tails are not masked out during the fit, some of their light is included in the model, modifying the fit parameters and resulting in the subtraction of a significant amount of tail light from the galaxy image."76 The total Dux contained within 300 small circular apertures positioned on the tails was measured using the utilityIMENAMINE., The total flux contained within $\sim300$ small circular apertures positioned on the tails was measured using the utility.77. This was used to derive a mean surface brightness for the tails. which was then multiplied by their total area (i6. including the area missed due to contaminating bright sources).," This was used to derive a mean surface brightness for the tails, which was then multiplied by their total area (i.e. including the area missed due to contaminating bright sources)."78 The resulting surface brightnesses were 26.6. 25.9 and 24.4 mag [or the B. V. and. { bands respectively.," The resulting surface brightnesses were 26.6, 25.9 and 24.4 mag for the $B$, $V$ and $I$ bands respectively."79 The total light. in the tails was divided by the total galaxy light to give the ‘tail fraction’., The total light in the tails was divided by the total galaxy light to give the `tail fraction'.80 We also roughly estimated the total tail light using polvgon-shaped apertures., We also roughly estimated the total tail light using polygon-shaped apertures.81 This method gave a similar result to the mean surface brightness method but included he light from contaminating point sources and was thus less reliable., This method gave a similar result to the mean surface brightness method but included the light from contaminating point sources and was thus less reliable.82 The tail fractions inthe D. V and { bands were found to o L84. 1.0 and 1.72 percent respectively.," The tail fractions in the $B$, $V$ and $I$ bands were found to be $1.84$ , $1.64$ and $1.72$ per cent respectively."83 Phe tail fractions in ? were derived in the V. band. with a few exceptions.," The tail fractions in \scite{keelwu95} were derived in the $V$ band, with a few exceptions."84 We hus use our V band tail fraction (which is similar to the D and 4 values) for NGC 1700 in the following analvsis., We thus use our $V$ band tail fraction (which is similar to the $B$ and $I$ values) for NGC 1700 in the following analysis.85 We fitted a linear least-square to the points obtained from he ? data., We fitted a linear least-square to the points obtained from the \scite{keelwu95} data.86 This fit is shown as a dashed line in Fig. 7.., This fit is shown as a dashed line in Fig. \ref{fig:TF}.87 The solid horizontal line represents the measured. V. band all fraction for NGC 1700., The solid horizontal line represents the measured $V$ band tail fraction for NGC 1700.88 ΠΕ we extrapolate the fit we ind that the V. band tail fraction measured for NGC 1700 corresponds to a merger stage of 8.13.8., If we extrapolate the fit we find that the $V$ band tail fraction measured for NGC 1700 corresponds to a merger stage of $8.1\pm3.8$.89 Ehe large error on his stage estimate is due to the scatter of the data points of ?.., The large error on this stage estimate is due to the scatter of the data points of \scite{keelwu95}.90 We also performed a quadratic fit on the heel Wu data., We also performed a quadratic fit on the Keel Wu data.91 Extrapolating this fit vielded a stage comparable with he result. using a linear least-square fit., Extrapolating this fit yielded a stage comparable with the result using a linear least-square fit.92 ὃν comparing the spectroscopic (1.0. central starburst) ages of several galaxies in the 7. sample with their assigned merger stage. we determined the time since nuclear coalescence.," By comparing the spectroscopic (i.e. central starburst) ages of several galaxies in the \scite{keelwu95} sample with their assigned merger stage, we determined the time since nuclear coalescence."93 For the stage of NGC 1700. the time since the central starburst and hence tail formation is approximately 3.2+1.5 Gvr.," For the stage of NGC 1700, the time since the central starburst and hence tail formation is approximately $3.2\pm1.5$ Gyr."94 A lower limit for the age of the ticaltails can be, A lower limit for the age of the tidaltails can be95conditions cnvisagecl here. there are two grain destruction mechanisms that must be considered.,"conditions envisaged here, there are two grain destruction mechanisms that must be considered."96 First. if the grains hemselves become too hot. they will rapidly sublime.," First, if the grains themselves become too hot, they will rapidly sublime."97 The eran temperature will be set by the thermal equilibrium oetween the AGN radiation incident on a given grain and the hermal raciation emitted by that grain (e.g. see Barvainis 1987)., The grain temperature will be set by the thermal equilibrium between the AGN radiation incident on a given grain and the thermal radiation emitted by that grain (e.g. see Barvainis 1987).98 For 6-30-15. the (1.0. the radius from the ACN within which dust. grains become so ιοί that they sublime) is ~101Tem.," For $-$ 6-30-15, the (i.e. the radius from the AGN within which dust grains become so hot that they sublime) is $\sim 10^{17}\cm$."99 Thus. any dust. &rains within the inner warm absorber would be rapidly sublimed ow the intense radiation field.," Thus, any dust grains within the inner warm absorber would be rapidly sublimed by the intense radiation field."100 Dust in the outer warn absorber would not be subject to significant sublimation., Dust in the outer warm absorber would not be subject to significant sublimation.101 The second. dust. destruction. mechanism that we must) consider is thermal sputtering., The second dust destruction mechanism that we must consider is thermal sputtering.102 Lf we make the standard: assumption that the (outer) warm. absorber is photoionized. then photoionization models suggest that the eas temperature is only Z—510Ix and thermal sputtering is negligible.," If we make the standard assumption that the (outer) warm absorber is photoionized, then photoionization models suggest that the gas temperature is only $T\sim 5\times 10^4\K$ and thermal sputtering is negligible."103" HL. instead. we suppose that the outer warm absorber is purely collisionallv-ionized. gas temperatures of Z10""Ix are required. in order to achieve 16 observed ionization states (Shull van Steenberg 1982)."," If, instead, we suppose that the outer warm absorber is purely collisionally-ionized, gas temperatures of $T\sim 10^6\K$ are required in order to achieve the observed ionization states (Shull van Steenberg 1982)."104 —_from. the expressions of Burke Silk (1974). the thermal sputtering timescale for this temperature is where n ids the electron. number censity in the gas.," From the expressions of Burke Silk (1974), the thermal sputtering timescale for this temperature is where $n$ is the electron number density in the gas."105 Suppose that r is the distance of the outer warm absorber from the central engine. and L is the (ionizing)luminosity of the central engine.," Suppose that $r$ is the distance of the outer warm absorber from the central engine, and $L$ is the (ionizing)luminosity of the central engine."106 Furthermore. define δριμάν822Ocrgems to be the ionization parameter of a photoionized plasma in which oxveen is ionized to the same degree às seen in the outer warm absorber of 6-30-15.," Furthermore, define $\xi_{\rm equiv}\approx 20\erg\cm\ps$ to be the ionization parameter of a photoionized plasma in which oxygen is ionized to the same degree as seen in the outer warm absorber of $-$ 6-30-15."107 Given our (temporary) hypothesis that the plasma is collisionallv-ionized. the density must. satisfy or else photoionization would dominate the ionization state.," Given our (temporary) hypothesis that the plasma is collisionally-ionized, the density must satisfy or else photoionization would dominate the ionization state."108 Evaluating the sputtering timescale for the parameters of 6-30-15 gives For comparison. the How timescale of the outer warn absorber is where we have acoptec a typical value of eg=1000kins for the velocity of the outer warm absorber. as indicated by UV. absorption line studies of other ACN (Alathur. Elvis Wilkes 1995).," Evaluating the sputtering timescale for the parameters of $-$ 6-30-15 gives For comparison, the flow timescale of the outer warm absorber is where we have adopted a typical value of $v_{\rm flow}=1000\kmps$ for the velocity of the outer warm absorber, as indicated by UV absorption line studies of other AGN (Mathur, Elvis Wilkes 1995)."109 It can be seen that. the low timescale of the warm absorber always exceeds the sputtering timescale unless rxLOOpe., It can be seen that the flow timescale of the warm absorber always exceeds the sputtering timescale unless $r\approxgt 100\pc$.110 LE the outer warm absorber was situated at such a laree distance. then either we would have to be viewing the AGN along a very special line of sight. or else the mass. A. and kinetic energy. Lic. associated with the outflow would both be huge.," If the outer warm absorber was situated at such a large distance, then either we would have to be viewing the AGN along a very special line of sight, or else the mass, $M$, and kinetic energy, $L_{\rm K}$, associated with the outflow would both be huge."111 From the expressions of Revnolds Fabian (1995). and. assuming a global covering fraction of f.=0.1. we get AZ~LO?M. and Ly~32107eresL.," From the expressions of Reynolds Fabian (1995), and assuming a global covering fraction of $f_{\rm c}=0.1$, we get $M\sim 10^6\Msun$ and $L_{\rm K}\sim 3\times 10^{42}\ergps$."112C The initial acceleration of this material would. be extremely problematic to. understand., The initial acceleration of this material would be extremely problematic to understand.113 We consider this possibility to be unphysical., We consider this possibility to be unphysical.114 Thus. in the absence of a viable. collisionally-ionizecl model. Whilst dust can survive in warn photoionizecl gas. it is extremely dillieult to form dust in such an environment: the grains could. never assemble at. such tempcratures.," Thus, in the absence of a viable, collisionally-ionized model, Whilst dust can survive in warm photoionized gas, it is extremely difficult to form dust in such an environment: the grains could never assemble at such temperatures."115 Furthermore. a comparison of the column density of the warm absorber with the cold column expected. to. be associated. with the reddening reveals that the warni-eas/dust ratio in the warm absorber must be very. similar to the cold-gas/dust. ratio in our Galaxy.," Furthermore, a comparison of the column density of the warm absorber with the cold column expected to be associated with the reddening reveals that the warm-gas/dust ratio in the warm absorber must be very similar to the cold-gas/dust ratio in our Galaxy."116 These two facts taken together suggest that the warm material. originates from cdusty. cold material. possibility via radiative heating. and that a substantial fraction. of the dust. survives the heating process.," These two facts taken together suggest that the warm material originates from dusty cold material, possibility via radiative heating, and that a substantial fraction of the dust survives the heating process."117 The putative cust’ molecular torus. of Sevlert unification schemes might be a possible progenitor of such a raciativelv-driven. warm. dusty outflow.," The putative dusty molecular torus of Seyfert unification schemes might be a possible progenitor of such a radiatively-driven, warm, dusty outflow."118 We have constructed photoionization models of dusty warm absorbers using the photoionization codeCLOUDY., We have constructed photoionization models of dusty warm absorbers using the photoionization code.119 Cirids of such models were constructed for various values of the column cdensitv Nw. ionization. parameter £ ancl X-ray whoton indices E.," Grids of such models were constructed for various values of the column density $N_{\rm W}$, ionization parameter $\xi$ and X-ray photon indices $\Gamma$."120 Since we are interested in the behaviour of the outer warm absorber. the distance of the absorber rom the primary source was fixed at ppc.," Since we are interested in the behaviour of the outer warm absorber, the distance of the absorber from the primary source was fixed at pc."121 Otherwise. these models are identical to those of Fabian et al. (," Otherwise, these models are identical to those of Fabian et al. ("1221994) and tevnolds et al. (,1994) and Reynolds et al. (1231995) except for the inclusion of dust grains.,1995) except for the inclusion of dust grains.124 The grain models used are described in (the manual o CLOUDY) pp., The grain models used are described in (the manual to ) pp.125 284., 284.126 Prompted by the observations of the »wevious paragraph. we have fixed the gas/clust ratio to Galactic value.," Prompted by the observations of the previous paragraph, we have fixed the gas/dust ratio to Galactic value."127 Two such grids were computed: one contains a standard (ic. local) mixture of silicate and graphite grains whereas the other contains only graphite grains., Two such grids were computed: one contains a standard (i.e. local) mixture of silicate and graphite grains whereas the other contains only graphite grains.128 These models were fitted to the data., These models were fitted to the data.129 Since we are interested in modeling fine details of the soft. spectrum. only cata from the best calibrated: solid-state imaging spectrometer (SISO) were used in the spectral fitting," Since we are interested in modeling fine details of the soft spectrum, only data from the best calibrated solid-state imaging spectrometer (SIS0) were used in the spectral fitting"130(seee.g.[T996)..,\citep[see e.g.][]{1996JOSAA..13.2266M}.131" Although this is in principle not impossible, for irregularly shaped constituents the computational demand of such an approach is very high, and at the moment not feasible."," Although this is in principle not impossible, for irregularly shaped constituents the computational demand of such an approach is very high, and at the moment not feasible."132" If the constituents themselves are very small while most of the interactions take place over relatively large distances, like in a large aggregate of many very small constituents, the dominant interaction is dipole-dipole interaction."," If the constituents themselves are very small while most of the interactions take place over relatively large distances, like in a large aggregate of many very small constituents, the dominant interaction is dipole-dipole interaction."133 The optical properties of such an aggregate of coupled dipoles can be computed using the Coupled Dipole Approximation (CDA)., The optical properties of such an aggregate of coupled dipoles can be computed using the Coupled Dipole Approximation (CDA).134 In this approximation each aggregate constituent is considered to interact as a single dipole with a given polarizability., In this approximation each aggregate constituent is considered to interact as a single dipole with a given polarizability.135" The difference with the well-known Discrete Dipole Approximation (DDA,seee.g.[[988) is that in DDA the volume of the constituents themselves have to be discretized using multiple dipoles."," The difference with the well-known Discrete Dipole Approximation \citep[DDA, see e.g.][]{1973ApJ...186..705P, 1988ApJ...333..848D} is that in DDA the volume of the constituents themselves have to be discretized using multiple dipoles."136 This has to be done in order to account for the shape of the aggregate constituents., This has to be done in order to account for the shape of the aggregate constituents.137 In the CDA we account for the shape of the constituents by using for each constituent a polarizability representative of an irregularly shaped grain., In the CDA we account for the shape of the constituents by using for each constituent a polarizability representative of an irregularly shaped grain.138 The mathematical formulation of both the CDA and the DDA is exactly the same; it describes the interaction of dipoles., The mathematical formulation of both the CDA and the DDA is exactly the same; it describes the interaction of dipoles.139" However, the numerical implementation might be slightly different."," However, the numerical implementation might be slightly different."140 In the DDA one can choose the dipoles to be located on a rectangular grid., In the DDA one can choose the dipoles to be located on a rectangular grid.141 This allows for the use of Fast Fourier Transform (FFT) methods to increase the numerical performance significantly [1991] [I998)..," This allows for the use of Fast Fourier Transform (FFT) methods to increase the numerical performance significantly \citep{Goodman1991, Hoekstra}."142" Since the constituents of an aggregate are usually not located on a rectangular grid, this is in general not possible when using the CDA."," Since the constituents of an aggregate are usually not located on a rectangular grid, this is in general not possible when using the CDA."143" In addition, the speedup in DDA using the FFT method requires one to fill a rectangular box circumscribing the aggregate with dipoles."," In addition, the speedup in DDA using the FFT method requires one to fill a rectangular box circumscribing the aggregate with dipoles."144" Since we wish to consider very fluffy grains with a low volume filling factor, this is very inefficient and would require many additional dipoles."," Since we wish to consider very fluffy grains with a low volume filling factor, this is very inefficient and would require many additional dipoles."145 A method providing a similar speedup as the FFT method is being developedMethod for the CDA computations using the Fast Multipole (Κος&Chew2001;[AminiProfi2003).," A method providing a similar speedup as the FFT method is being developed for the CDA computations using the Fast Multipole Method \citep{Koc2001, Amini2003}."146 As we mentioned above the approach of only considering the dipole-dipole interactions is valid if the constituents are small and the long range interactions between them dominate., As we mentioned above the approach of only considering the dipole-dipole interactions is valid if the constituents are small and the long range interactions between them dominate.147 This is the situation we are currently interested in., This is the situation we are currently interested in.148" Future computations, using a method taking into account the multipole interactions, like the superposition T-matrix method or large scale DDA simulations using multiple dipoles per constituent, can be employed to check the accuracy of the approximation we employ here."," Future computations, using a method taking into account the multipole interactions, like the superposition T-matrix method or large scale DDA simulations using multiple dipoles per constituent, can be employed to check the accuracy of the approximation we employ here."149" When we consider for each particle of the aggregate only dipole interactions we have [1988) where P; is the local dipole moment at the position of particle j, a; is the polarizability of particle j, Ej; is the incoming field at the location of particle j, and N is the total number of constituents in the aggregate."," When we consider for each particle of the aggregate only dipole interactions we have \citep{1988ApJ...333..848D}150 where $\vec{P}_j$ is the local dipole moment at the position of particle $j$, $\alpha_j$ is the polarizability of particle $j$, $\vec{E}_{\mathrm{inc},j}$ is the incoming field at the location of particle $j$, and $N$ is the total number of constituents in the aggregate."151 The matrix Ajx determines the electric field at the position of particle j due to the dipole field emitted by particle k (fordetails[[988).., The matrix $\matrix{A}_{jk}$ determines the electric field at the position of particle $j$ due to the dipole field emitted by particle $k$ \citep[for details see e.g.][]{1988ApJ...333..848D}.152 When Eq. (3)), When Eq. \ref{eq:DDA}) )153" is solved for the P; the mass absorption coefficient can be computed by where V is the total material volume of the aggregate, o is the average material density, and the asterisks denote the complex conjugates."," is solved for the $\vec{P}_j$ the mass absorption coefficient can be computed by where $V$ is the total material volume of the aggregate, $\rho$ is the average material density, and the asterisks denote the complex conjugates."154 The dipole polarizability of a homogeneous spherical particle is given by where m is the complex refractive index of the particle material., The dipole polarizability of a homogeneous spherical particle is given by where $m$ is the complex refractive index of the particle material.155 The polarizability of irregularly shaped particles depends on the particle shape., The polarizability of irregularly shaped particles depends on the particle shape.156" However, a reasonable approximation for the average polarizability of an ensemble of highly irregular particles is given by the Continuous Distribution of Ellipsoids (CDE;see[BohrenHuffman| [2006b).."," However, a reasonable approximation for the average polarizability of an ensemble of highly irregular particles is given by the Continuous Distribution of Ellipsoids \citep[CDE; see][]{BohrenHuffman, 2006JQSRT..97..161M}."157 The CDE polarizability is& given by More realistic polarizabilities can be computed using the method of (2006b).., The CDE polarizability is given by More realistic polarizabilities can be computed using the method of \citet{2006JQSRT..97..161M}.158" However, here we wish to study only the effects of using irregularly shaped particles as monomers so we employ the frequently used CDE polarizability for the aggregate constituents."," However, here we wish to study only the effects of using irregularly shaped particles as monomers so we employ the frequently used CDE polarizability for the aggregate constituents."159 In the following subsections we will first define two quantities we use for the analysis of the emission spectra of the aggregates., In the following subsections we will first define two quantities we use for the analysis of the emission spectra of the aggregates.160 Then we will discuss how the aggregates are constructed and what composition we will assume., Then we will discuss how the aggregates are constructed and what composition we will assume.161 The mass absorption coefficient as given by Eq. (4), The mass absorption coefficient as given by Eq. \ref{eq:total kappa}) )162 is basically the sum over the absorption contributions of each component of the aggregate., is basically the sum over the absorption contributions of each component of the aggregate.163 We can thus easily compute the effective mass absorption coefficient of a part of the aggregate by summing over only that part of the components., We can thus easily compute the effective mass absorption coefficient of a part of the aggregate by summing over only that part of the components.164 In this way we can create an for each, In this way we can create an for each165where Q(I) is given bv (27). F; and /; are the place and time of injection. repectivelv.,"where $Q(E_0)$ is given by , $\vec{r_i}$ and $t_i$ are the place and time of injection, repectively."166 We note. that the energv. 2 of a particle al time / is linked (ο ils οποιον Ey al injection by ).," We note, that the energy $E$ of a particle at time $t$ is linked to its energy $E_0$ at injection by )."167 The anisotropy in the CR flux can be calculated in the context of diffusion as where V.N denotes the gradient of ./N.," The anisotropy in the CR flux can be calculated in the context of diffusion as \citep{1964ocr..book.....G}168 where $\nabla N$ denotes the gradient of $N$."169 The expected anisotropy in the positron LIS was calculated. assuming the contribution of a nearby source. as given by(35).. on top of an isotropic background.," The expected anisotropy in the positron LIS was calculated assuming the contribution of a nearby source, as given by, on top of an isotropic background."170 For the background we assumed a power law [it given by (1998).., For the background we assumed a power law fit given by \citet{1998ApJ...498..779B}.171 The calculated anisotropies are given in the right panels of Figs., The calculated anisotropies are given in the right panels of Figs.172 1 and 2 (thin lines)., \ref{fig:geminga} and \ref{fig:bo656} (thin lines).173 To get an estimate of the maximum expected anisotropy. we also calculate the anisotropy assumine (hat the whole CR positron {lux originates [rom a point source (thick lines in the rightpanels of Figs.," To get an estimate of the maximum expected anisotropy, we also calculate the anisotropy assuming that the whole CR positron flux originates from a point source (thick lines in the rightpanels of Figs."174 1 aud 2)).For energy-independent diffusion. Mao&Shen(1972) derived (he simple relation," \ref{fig:geminga} and \ref{fig:bo656}) ).For energy-independent diffusion, \citet{1972ChJPh..10...16M} derived the simple relation"175can be traced back to pioneeding works by Giovanelli (1946) and Dungey (1953).,can be traced back to pioneeding works by Giovanelli (1946) and Dungey (1953).176 The uncertainties with understanding of fast reconnection were one of the impediments for applying the process to energetic particle acceleration (see Lazarian Opher 2009)., The uncertainties with understanding of fast reconnection were one of the impediments for applying the process to energetic particle acceleration (see Lazarian Opher 2009).177" We appeal to the model of reconnection of weakly stochastic field in Lazarian Vishniac (1999), which was identified as a cause of First Order Fermi acceleration (see de Gouveia dal Pino Lazarian 2005, Lazarian 2005)."," We appeal to the model of reconnection of weakly stochastic field in Lazarian Vishniac (1999), which was identified as a cause of First Order Fermi acceleration (see de Gouveia dal Pino Lazarian 2005, Lazarian 2005)."178" In what follows we present the observational evidence for the existence of the cosmic ray excess in the direction of the solar system magnetotail in §2,, discuss existing explanations of this excess in §3.."," In what follows we present the observational evidence for the existence of the cosmic ray excess in the direction of the solar system magnetotail in \ref{sec:obs}, discuss existing explanations of this excess in \ref{sec:interp}."179 The structure of the magnatotail with magnetic field reversals arising from the solar cycle is presented in §4 and the mechanism of acceleration of cosmic rays in the magnetotail is outlined in §5.., The structure of the magnatotail with magnetic field reversals arising from the solar cycle is presented in \ref{sec:magfi} and the mechanism of acceleration of cosmic rays in the magnetotail is outlined in \ref{sec:magrec}.180" The discussion of the results and a short summary are given by 86 and §7,, respectively."," The discussion of the results and a short summary are given by \ref{sec:disc} and \ref{sec:summ}, respectively."181 The observation of the large angular scale anisotropy of sub-TeV cosmic rays (Nagashimaetal.1998;Halletal. revealed the evidence of a superposition of two 1999)different modulations in arrival direction.," The observation of the large angular scale anisotropy of sub-TeV cosmic rays \citep{nagashima,hall} revealed the evidence of a superposition of two different modulations in arrival direction."182 One with a sidereal variation identified with an extended deficit centered around 12 hours that seems to extend mostly across the northern hemisphere (the so-called loss cone)., One with a sidereal variation identified with an extended deficit centered around 12 hours that seems to extend mostly across the northern hemisphere (the so-called loss cone).183" And one with sidereal variation identified with a broad excess centereda around 6 hours, with half opening angle of about 68° that comprises the direction of the heliotail, and extended across part of the northern and the southern hemispheres (the tail-in excess)."," And one with a sidereal variation identified with a broad excess centered around 6 hours, with half opening angle of about $^{\circ}$ that comprises the direction of the heliotail, and extended across part of the northern and the southern hemispheres (the tail-in excess)."184 Figure 1 shows the combined observations of the anisotropy of sub-TeV cosmic rays from telescopes at different latitudes., Figure \ref{fig:nagashima} shows the combined observations of the anisotropy of sub-TeV cosmic rays from telescopes at different latitudes.185" 'The global anisotropy amplitude is found to increase with energy up to about 5-10 TeV, however while the loss-cone structure seems to maintain a similar shape up to the multi-TeV range, the tail-bin excess is still somewhat persistent in the multi-TeV range, but its broad structure appears to dissolve to smaller angular scale spots (Amenomorietal."," The global anisotropy amplitude is found to increase with energy up to about 5-10 TeV, however while the loss-cone structure seems to maintain a similar shape up to the multi-TeV range, the tail-in excess is still somewhat persistent in the multi-TeV range, but its broad structure appears to dissolve to smaller angular scale spots \citep{amenomori}."186"2006).. The apparent seasonal modulation of the tail-in excess, with a minimum amplitude in summer and a maximum (a factor of four in winter, provides a compelling connection to the larger)heliotail."," The apparent seasonal modulation of the tail-in excess, with a minimum amplitude in summer and a maximum (a factor of four larger) in winter, provides a compelling connection to the heliotail."187" Figure 2 shows the multi-TeV cosmic ray arrival direction map, from the MILAGRO collaboration, obtained by eliminating anisotropies with angular structures wider than ~30°."," Figure \ref{fig:milagromap} shows the multi-TeV cosmic ray arrival direction map, from the MILAGRO collaboration, obtained by eliminating anisotropies with angular structures wider than $\sim$ $^{\circ}$."188 The small scale structure is evidenced in this map and it shows two highly significant than 12 localized excess regions in the cosmic rays (morearrival direction., The small scale structure is evidenced in this map and it shows two highly significant (more than 12 $\sigma$ ) localized excess regions in the cosmic rays arrival direction.189"σ) Both regions are inconsistent with gamma, ray emission with high confidence and therefore are claimed to be dominated by cosmic rays.", Both regions are inconsistent with gamma ray emission with high confidence and therefore are claimed to be dominated by cosmic rays.190" They are found to have a constant yearly excess over the seven year period of collected data, however both of them were lowest in summer and highest in winter, with a x? probability relative to a constant fractional excess of only in each region."," They are found to have a constant yearly excess over the seven year period of collected data, however both of them were lowest in summer and highest in winter, with a $\chi^2$ probability relative to a constant fractional excess of only in each region."191" The strongest and more localized of them (called region A, with a fractional excess of ~6x 1072) coincides with the direction of the heliotail (the black dot in Figure 2,, with right ascension aez74? and declination 6z+17° in equatorial coordinates)."," The strongest and more localized of them (called region A, with a fractional excess of $\sim 6\times 10^{-4}$ ) coincides with the direction of the heliotail (the black dot in Figure \ref{fig:milagromap}, with right ascension $\alpha \approx 74^{\circ}$ and declination $\delta \approx +17^{\circ}$ in equatorial coordinates)."192 The corresponding energy spectrum was de-convoluted using the energy-dependent experimental observables., The corresponding energy spectrum was de-convoluted using the energy-dependent experimental observables.193 Figure 3 shows the result of the χ fit to the excess in region A, Figure \ref{fig:regiona} shows the result of the $\chi^2$ fit to the excess in region A194 (Ryuοἱal.2003).. T>10* 7—10°I0* 2005).. forareview)..," \citep{rkhj03}, $T > 10^7$ $T = 10^5 - 10^7$ \citep{co99,krcs05}. \citep[see][for a review]{car02}."195 ~iG 10 (Iximοἱal.1990)., $\sim\mu$ $\sim 10$ \citep{kim90}.196. 100—200radm7 ~5 μα (Clarkeοἱal.2001:Clarke2004).. (Vogt&EnBlin2005).," $\sim100 -200\ {\rm rad\ m^{-2}}$ $\sim 5$ $\mu$ \citep{cla01,cla04}. \citep{vog05},"197. (Guiclettiοἱal.2008) (Bonaledeetal.2010).., \citep{gmgp08} \citep{bfmg10}.198stellaar X-ray and EUV radiation.,ar X-ray and EUV radiation.199"Fiewre ον shows the Afoyya, relation.",Figure \ref{msigma} shows the $M_{200} - \sigma _p$ relation.200 The tieht relation indicates that the caustic asses are well correlated with velocity dispersion estimates., The tight relation indicates that the caustic masses are well correlated with velocity dispersion estimates.201 The eood correlation is perhaps not surprising because both parameters depend on the galaxy velocity distribution., The good correlation is perhaps not surprising because both parameters depend on the galaxy velocity distribution.202 The best-fit slope is Mog)Xο... with the uucertaintv estimated frou jackkuife resampling., The best-fit slope is $M_{200}\propto\sigma_p^{3.18\pm0.19}$ with the uncertainty estimated from jackknife resampling.203 We compare the caustic masses to virial mass estimates iu 512.., We compare the caustic masses to virial mass estimates in $\S$ \ref{virial}.204 The excellent agreement between the caustic masses and the N-ray masses frou previously determined scaling relation between nass and X-ray temperatures confinis the prediction of D99 that the caustic lass estimate is unbiased., The excellent agreement between the caustic masses and the X-ray masses from previously determined scaling relation between mass and X-ray temperatures confirms the prediction of D99 that the caustic mass estimate is unbiased.205 CAIRNS found similar agrecment between caustic masses and κταν and virial mass estimates (2): 7? show eood aerecinent between masses estimated from the caustics and weak Ieusiug., CAIRNS found similar agreement between caustic masses and X-ray and virial mass estimates \citep{cairnsi}; \citet{diaferio05} show good agreement between masses estimated from the caustics and weak lensing.206 We fit the mass profiles of the CAIRNS clusters. to three simple analytic models., We fit the mass profiles of the CAIRNS clusters to three simple analytic models.207 The simplest model of a selferavitating svstem is a sineular isothermal sphere (SIS)., The simplest model of a self-gravitating system is a singular isothermal sphere (SIS).208 The mass of the SIS increases linearly with radius., The mass of the SIS increases linearly with radius.209 7. aud ? propose tsvo-paraieter models based on CDAL simulations of haloes., \citet{nfw97} and \citet{hernquist1990} propose two-parameter models based on CDM simulations of haloes.210 We note that the caustic mass profiles mostly saluple large radi and are therefore not very scusitive to the inner slope of the mass profile., We note that the caustic mass profiles mostly sample large radii and are therefore not very sensitive to the inner slope of the mass profile.211 Thus. we do not consider alternative models which differ only in the iuner slope of the density profile (ee.?)..," Thus, we do not consider alternative models which differ only in the inner slope of the density profile \citep[e.g.,][]{moore99}."212 At lee radii. the best constraiuts on cluster iiass profiles come from galaxy dynamics aud weak lensing.," At large radii, the best constraints on cluster mass profiles come from galaxy dynamics and weak lensing."213 The caustic mass profiles of Coma (2).. À576 (2).. A2199 (7) and the rest of the CAIRNS clusters ο} provided stroug evidence against a sineular isothermal sphere (SIS) profile aud in favor of steeper mass density profiles predicted by 7. (NFA) and ?..," The caustic mass profiles of Coma \citep{gdk99}, A576 \citep{rines2000}, A2199 \citep{rines02} and the rest of the CAIRNS clusters \citep{cairnsi} provided strong evidence against a singular isothermal sphere (SIS) profile and in favor of steeper mass density profiles predicted by \citet{nfw97} (NFW) and \citet{hernquist1990}."214 Oulv recently have weak lensing mass estimates been able to distinguish between SIS and NEW density profiles at large racii (27).," Only recently have weak lensing mass estimates been able to distinguish between SIS and NFW density profiles at large radii \citep{clowe01,kneib03}."215 At large radii. the NEW aass profile increases as In(i) and the mass ofthe Hreruquist model converges.," At large radii, the NFW mass profile increases as $(r)$ and the mass ofthe Hernquist model converges."216 The NEW lass profile is Min) 7 where e6 ds the scale radius and Af(a) is the mass within e., The NFW mass profile is M(<r) = where $a$ is the scale radius and $M(a)$ is the mass within $a$.217" We ft the paramcter AZ(e) rather than the characteristic density à, (M(a)=Ιπὸ,ρ,a?{In(2)1| where p. is the critical deusitv) because Αα} aud « are mich less correlated than 3, and e (?).."," We fit the parameter $M(a)$ rather than the characteristic density $\delta_c$ ${M(a) = 4\pi \delta_c \rho_c a^3 [\mbox{ln}(2) -218\frac{1}{2}]}$ where $\rho_c$ is the critical density) because $M(a)$ and $a$ are much less correlated than $\delta_c$ and $a$ \citep{mahdavi99}."219 The IHeruquist lass profile is Mir) = MiUB where αμ is the scale radius aud A is the total mass., The Hernquist mass profile is M(<r) = M where $a_H$ is the scale radius and $M$ is the total mass.220 Note that ἁαμ)=ALL., Note that $M(a_H) = M/4$.221 The SIS mass profile is M(«ry)X orc.We minimize u and st the best-fit parameters a. Cogo. the couceutration ονε τουα. aud. ουν for the best-ft NEW model and indicate the best-fit profile type in Table 11..," The SIS mass profile is $M(<r)\propto r$ .We minimize $\chi ^2$ and list the best-fit parameters $a$, $r_{200}$, the concentration $c_{NFW}$ $r_{200}/a$, and $M_{200}$ for the best-fit NFW model and indicate the best-fit profile type in Table \ref{mpfitsci}."222 We also list the parameter eyyp=riyt/a: sole authors prefer to use r/4gj as the virial radius., We also list the parameter $c_{101}$ $r_{101}/a$; some authors prefer to use $r_{101}$ as the virial radius.223 We perform the fits on all data points within the maxima radial exteut of the caustics ων listed in Table ϱ aud with caustic amplitude Afr)>100kins," We perform the fits on all data points within the maximum radial extent of the caustics $r_{max}$ listed in Table \ref{radii} and with caustic amplitude $\mathcal{A}224\mathnormal{(r)} > 100~\kms$."225 Because the individual poiuts iu the mass profile are uot independent. the absolutc| values of20 4 are indicative⋅⋅⋅ onlv. mt it is clear that the NEW aud Heruquist profiles provide acceptable fits to he caustic mass profiles: the SIS is excluded. for nearly all clusters.," Because the individual points in the mass profile are not independent, the absolute values of $\chi ^2$ are indicative only, but it is clear that the NFW and Hernquist profiles provide acceptable fits to the caustic mass profiles; the SIS is excluded for nearly all clusters."226 The NEW. profile provides a better fit to the data than the Heruquist profile for 36of the 72 CIRS clusters 35 are better fit bv a IIleruquist profile aud one is bst fit by SIS., The NFW profile provides a better fit to the data than the Hernquist profile for 36of the 72 CIRS clusters; 35 are better fit by a Hernquist profile and one is best fit by SIS.227 A non-ngular isothermal spliere mass profile! vields results simular to the SIS: thus. we report only our results for the SIS.," A non-singular isothermal sphere mass profile yields results similar to the SIS; thus, we report only our results for the SIS."228 Figure ?7 shows the shapes of the caustic mass profiles sealed bv. ου and ALooy along with SIS. NEW. and IIeruquist model profiles.," Figure \ref{scalem} shows the shapes of the caustic mass profiles scaled by $r_{200}$ and $M_{200}$ along with SIS, NFW, and Hernquist model profiles."229 The colored lines show differeut inode mass profiles., The colored lines show different model mass profiles.230 The straight dashed line is the SIS the solid lines are NEW. profles with ¢=3.5. Γ aud 10. aud the curved dashed lines are Heruquist profiles with two cüffereu pacale radii.," The straight dashed line is the SIS, the solid lines are NFW profiles with $c$ =3,5, and 10, and the curved dashed lines are Hernquist profiles with two different scale radii."231 The best-fit average profile is au NEW profile with e2)9=7.2 (this lowers to c29925.2 when the fits are restricted to. irrogo). consistent with Table 11 and with the values expected from simulatious for massive clusters (NEW.?)..," The best-fit average profile is an NFW profile with $c_{200}$ =7.2 (this lowers to $c_{200}$ =5.2 when the fits are restricted to $r$$\leq$$r_{200}$ ), consistent with Table \ref{mpfitsci} and with the values expected from simulations for massive clusters \citep[NFW, ][]{bullock01}."232 All three moclel profiles agree. fairly well with the caustic nass profiles iu the range 7209., All three model profiles agree fairly well with the caustic mass profiles in the range $r_{200}$.233 The SIS ouly fails beyoud 71.579599: this is why leusiug has iad trouble distinguishing between SIS aud NEW profiles., The SIS only fails beyond $\sim$ $r_{200}$; this is why lensing has had trouble distinguishing between SIS and NFW profiles.234 As discussed in D99. the causic technique can be subject o large variations for iucdividial clusters due to projection effects.," As discussed in D99, the caustic technique can be subject to large variations for individual clusters due to projection effects."235" The best coustraints οu the shapes of cluster mass xofiles are obtained by averag""uus over many lines of sight. or for real observations. over nany different clusters."," The best constraints on the shapes of cluster mass profiles are obtained by averaging over many lines of sight, or for real observations, over many different clusters."236 The current sample is the largest saluple of nass profiles at arge radii to date aud thus pr'ovides the best possible test of the shapes of cluster mass xofiles., The current sample is the largest sample of mass profiles at large radii to date and thus provides the best possible test of the shapes of cluster mass profiles.237 The concentration parameCIS C299=rogo/0 for the NEW aodels are in the range 260. in good agrecineut with the predictions of numevical simulations (?77)..," The concentration parameters $c_{200}=r_{200}/a$ for the NFW models are in the range 2–60, in good agreement with the predictions of numerical simulations \citep{nfw97,bullock01}."238 The differences iu e should be μπα] (~20% 3) over our mass ranee compared to the scatter iu ο present iu simulated clusters (77)..," The differences in $c$ should be small $\sim$ ) over our mass range compared to the scatter in $c$ present in simulated clusters \citep{nfw97,bullock01}."239" Figure ?? indicates the average values aud Lo scatter of e491=rip,α 1n simniulatious (?)..", Figure \ref{cnfw} indicates the average values and $1\sigma$ scatter of $c_{101}=r_{101}/a$ in simulations \citep{bullock01}.240 The dynamic range of these simulations is uot laree enough to contain many massive clusters. but the CIRS clusters agree well with the extrapolation of the relation fouud in simmilations.," The dynamic range of these simulations is not large enough to contain many massive clusters, but the CIRS clusters agree well with the extrapolation of the relation found in simulations."241 We bin the CIRS clusters iuto six bius of 12 clusters and compute the mean aud median of loge491., We bin the CIRS clusters into six bins of 12 clusters and compute the mean and median of $\mbox{log}c_{101}$.242 There is a weak positive correlation of e with mass (Fieure ??)). but the values of e494 and the scatter (lin errorbars) aeree well with the model of ? (the scatter iu CIRS is huger. indicating that observational uncertainties likely coutribute to the observed scatter).," There is a weak positive correlation of $c$ with mass (Figure \ref{cnfw}) ), but the values of $c_{101}$ and the scatter (thin errorbars) agree well with the model of \citet{bullock01} (the scatter in CIRS is larger, indicating that observational uncertainties likely contribute to the observed scatter)."243" This result addresses one concern from the CAIRNS mass profiles: the concentrations eogy were iu the rauge 5-17 rather than the rauge 1-6 expected frou, nmunerical simulations for massive clusters (27).."," This result addresses one concern from the CAIRNS mass profiles: the concentrations $c_{200}$ were in the range 5-17 rather than the range 4-6 expected from numerical simulations for massive clusters \citep{nfw97,cairnsi}. ."244 Silly. recent mass profiles from weak leusiug similarly find evidence of high concentrations in ÀAl689 (27)..CLOO2 ολων and MS2137 (?)..," Similarly, recent mass profiles from weak lensing similarly find evidence of high concentrations in A1689 \citep{2005ApJ...619L.143B,2005ApJ...621...53B}, ,CL0024 \citep{kneib03}, , and MS2137 \citep{gavazzi05}. ."245 However. Figure ?7 shows that the CIRS clusters have mass profiles consistent with those predicted by simulations. although with large scatter.," However, Figure \ref{cnfw} shows that the CIRS clusters have mass profiles consistent with those predicted by simulations, although with large scatter."246 If this scatter is physical rather than due to projection effects in the caustic mass profiles. then the apparent discrepancies between simulations and observations can be explained by an uulucky. selectiou of clusters.," If this scatter is physical rather than due to projection effects in the caustic mass profiles, then the apparent discrepancies between simulations and observations can be explained by an unlucky selection of clusters."247The best fit parameters somewhat depends on the range of integration.,The best fit parameters somewhat depends on the range of integration.248 For instance. if we use the observed column cleusity profile eq.(2)) out to 42.8 Mpc. regardless of the streueth of weak lensing signals. the core radius in units of rp. aud power-law index. change to 1.25. aud -3.71. respectively.," For instance, if we use the observed column density profile \ref{cpl}) ) out to $\pm$ 2.8 Mpc, regardless of the strength of weak lensing signals, the core radius in units of $r_E$, and power-law index, change to 1.25, and -3.71, respectively."249 Note that the power-law iudex of our choice. -3.11. is closer to that of au NEW profile ol -3. than -3.71.," Note that the power-law index of our choice, -3.41, is closer to that of an NFW profile of -3, than -3.71."250 Since our interest is in the inuer region as we show later. aud since the coutribution of the outer region to the total mass is small. our choice should be justified.," Since our interest is in the inner region as we show later, and since the contribution of the outer region to the total mass is small, our choice should be justified."251 Before proceeding to imodeliue of mass profiles. we first show that at the center of AT689 with volume deusities of order of 1021 (g-cm 3) uourelativistic eV-1uass [ermious can become degenerate.," Before proceeding to modeling of mass profiles, we first show that at the center of A1689 with volume densities of order of $10^{-24}$ $\cdot$ $^{-3}$ ), nonrelativistic eV-mass fermions can become degenerate."252 Since amass of 1 eV corresponds to Lx10.5 e. the iunber density. V/V10H oE and the mean inter-particle spacing is. (V/V)Vs210.! em," Since a mass of 1 eV corresponds to $1.8\times10^{-33}$ g, the number density, $N/V \approx 10^{11}$ $^{-3}$, and the mean inter-particle spacing is, $(N/V)^{-1/3} \approx 2\times 10^{-4}$ cm."253 On the other hand. the de Broglie wavelength for a 1 eV particle with a relative velocity e dis. μυς=hf(poc)(efe)Acompion cur.," On the other hand, the de Broglie wavelength for a 1 eV particle with a relative velocity $v$ is, $h/\mu_0 v = h/(\mu_0c)(c/v)=\lambda_{Compton}\cdot(c/v) = 1.2\times10^{-4}(c/v)$ cm."254 Therefore lor nonrelativistic particles with e«c. the couditiou Lor high degeneracy. (N/V)E«ΑγάςBroglie): ts satisfied.," Therefore for nonrelativistic particles with $v \ll c$, the condition for high degeneracy, $(N/V)^{-1/3} \ll \lambda_{({\rm de \hskip 5pt Broglie})}$, is satisfied."255 We first formulate the modeling procedure oL matter distribution for the case that tle eutire matter cousists purely of fermionic dark matter aud then. modify the formulation for the case that the fractional contribution of fermionic dark matter deusity to the total matter deusity is coustaut.," We first formulate the modeling procedure of matter distribution for the case that the entire matter consists purely of fermionic dark matter and then, modify the formulation for the case that the fractional contribution of fermionic dark matter density to the total matter density is constant."256 First we provide our justification for introduciug au equation of state and assuming lyclrostatic equilibrium for the mixture of degenerate fermious aud non-degenerate Classical collisiouless particles., First we provide our justification for introducing an equation of state and assuming hydrostatic equilibrium for the mixture of degenerate fermions and non-degenerate classical collisionless particles.257 A sell-gravitatiug system composed purely of classical collisiouless particles such as cold dark matter particles may be thermocdyuamically anomalous (Lyudeun-Bell&Wood1968). aud the equation of state may be poorly defined.," A self-gravitating system composed purely of classical collisionless particles such as cold dark matter particles may be thermodynamically anomalous \citep{Lynden-Bell}258 and the equation of state may be poorly defined."259 However. the elfect of fermion degeneracy or introduction of repulsion due to Pauli's exclusion principle is to make the mixture of degenerate [ermious and classical οςlisiouless particles a thermoclyuamically normal system aud an analysis based on lyclrostatic equilibrium valid.," However, the effect of fermion degeneracy or introduction of repulsion due to Pauli's exclusion principle is to make the mixture of degenerate fermions and classical collisionless particles a thermodynamically normal system and an analysis based on hydrostatic equilibrium valid."260 To deal with the general situations in which particle temperature is finite aud degeneracy is partial. we need to know the equation of state (EOS). aud have to determine the temperature prolile along with the density. profile.," To deal with the general situations in which particle temperature is finite and degeneracy is partial, we need to know the equation of state (EOS), and have to determine the temperature profile along with the density profile."261 We adopt two major assumptions that simplify our analysis ol fermioute dark matter distribution., We adopt two major assumptions that simplify our analysis of fermionic dark matter distribution.262 First. we assume that the EOS. or the pressure law. las the following form.," First, we assume that the EOS, or the pressure law, has the following form,"263Accretion onto a central massive black bole (DII) in a galactic nucleus produces energy. in the form. of radiation. relativistic jets. and wider angle (less-collimated) non-relativistic (0~IO!kms+ ) outllows (?)..,"Accretion onto a central massive black hole (BH) in a galactic nucleus produces energy in the form of radiation, relativistic jets, and wider angle (less-collimated) non-relativistic $v \sim 10^4 \kms$ ) outflows \citep{krolik99}."264 The coupling of this energy output to gas in galaxies and in the intergalactie medium is believed to play an important role in. galaxy formation. potentially regulating the growth of massive galaxies and the thermal properties of the intracluster mecdium in galaxy groups and clusters (e.g. 2?)).," The coupling of this energy output to gas in galaxies and in the intergalactic medium is believed to play an important role in galaxy formation, potentially regulating the growth of massive galaxies and the thermal properties of the intracluster medium in galaxy groups and clusters (e.g., \citealt{silk98,croton06}) )."265 The impact of this ‘feedback’ on the gas galaxies is particularly uncertain. both because the interstellar (ISAT) σας is denser. and thus more clillicult to alfect cynamically. anc because much of the ISAT subtends a relatively modest solid angle relative to a central active ealactic nucleus. (AGN).," The impact of this `feedback' on the gas galaxies is particularly uncertain, both because the interstellar (ISM) gas is denser, and thus more difficult to affect dynamically, and because much of the ISM subtends a relatively modest solid angle relative to a central active galactic nucleus (AGN)."266 However. analytic estimates and numerical simulations have demonstrated that if a moclest fraction of the energy. produced by aceretion onto a central DII can couple to the surrounding gas. it can unbine the interstellar eas (e.g... 22).," However, analytic estimates and numerical simulations have demonstrated that if a modest fraction of the energy produced by accretion onto a central BH can couple to the surrounding gas, it can unbind the interstellar gas (e.g., \citealt{silk98,dimatteo05}) )."267 The physical processes most likely to produce such an cllect are winds (22).. radiation pressure (?7).. and/or Compton heating (?) from a central AGN.," The physical processes most likely to produce such an effect are winds \citep{king03, king11}, , radiation pressure \citep{murray05}, and/or Compton heating \citep{sazonov04} from a central AGN."268 Understanding how this works in detail is one of the major challenges in our understanding of the connection between AGN physics and galaxy. formation., Understanding how this works in detail is one of the major challenges in our understanding of the connection between AGN physics and galaxy formation.269 In this paper. we assess the influence of AGN winds on gas in the AGN's host galaxy using threc-dimoensional numerical simulations.," In this paper, we assess the influence of AGN winds on gas in the AGN's host galaxy using three-dimensional numerical simulations."270 Previous analytic work and one and two-dimensional simulations have demonstrated that AGN winds can in principle sweep up and drive gas out of galaxies. potentially explaining the Mgg—0 relation and the dearth of gas and ongoing star formation in massive. earlv-tvpoe. ealaxies (e.g. 27277. and references therein).," Previous analytic work and one and two-dimensional simulations have demonstrated that AGN winds can in principle sweep up and drive gas out of galaxies, potentially explaining the $M_{BH}-\sigma$ relation and the dearth of gas and ongoing star formation in massive, early-type, galaxies (e.g., \citealt{king05,king11,novak10,ostriker10} and references therein)."271 Observationallv. there is strong evidence that ACN indeed drive powerful outllows.," Observationally, there is strong evidence that AGN indeed drive powerful outflows."272 Broac-absorption dine (BAL) quasars. which show blue-shifted absorption lines in the rest-frame ultraviolet with inferred. outflow: velocities ~10.00040.000kins represent over ~40% of quasars in infrared selected samples (2)...," Broad-absorption line (BAL) quasars, which show blue-shifted absorption lines in the rest-frame ultraviolet with inferred outflow velocities $\sim 10,000-40,000 \kms$, represent over $\sim 40\%$ of quasars in infrared selected samples \citep{dai08}."273 similar fraction of racio-quict quasars show evidence for high velocity outllows in X-ray absorption line spectroscopy (τὸν., A similar fraction of radio-quiet quasars show evidence for high velocity outflows in X-ray absorption line spectroscopy \citep{tombesi10}.274 Lt is ikelv thatαἱ quasars possess such outllows but that they ave only observed. when the system is viewed. mocestIvy edegc-on (τι., It is likely that quasars possess such outflows but that they are only observed when the system is viewed modestly edge-on \citep{murray1995}.275 However. determining the mass-loss rate rom spatially unresolved absorption-line observations is notoriously cillicult given uncertainties in the radius of he absorbing gas.," However, determining the mass-loss rate from spatially unresolved absorption-line observations is notoriously difficult given uncertainties in the radius of the absorbing gas."276 In a handful of low-ionization BAL quasars (in particular. FeLoBALS) this degeneracy has been ooken. suggesting mass loss rates significantly larger than he black hole accretion rate (??777)..," In a handful of low-ionization BAL quasars (in particular, FeLoBALs) this degeneracy has been broken, suggesting mass loss rates significantly larger than the black hole accretion rate \citep{moe09, bautista10,dunn10,claude11}."277 These observations race absorbers at large distances from the BLL (~ kpe). in contrast to most of the high ionization UV. and X- absorption seen in BAL quasars. which arises at =1x.," These observations trace absorbers at large distances from the BH $\sim$ kpc), in contrast to most of the high ionization UV and X-ray absorption seen in BAL quasars, which arises at $\lesssim 1$pc."278 In addition to these wellkeharacterizecl outflows. it is," In addition to these well-characterized outflows, it is"279where Muse is the original crror-bar returned. by. the photometry pipeline.,where $\sigma_{\rm mag}$ is the original error-bar returned by the photometry pipeline.280 For all the LMC fields the mean values of the error- parameters were: (57?=1.2039. (ο)=0.0046. v)=0.9956. ici?=0.0035.," For all the LMC fields the mean values of the error-correction parameters were: $\langle\gamma_I\rangle = 1.2039$, $\langle\epsilon_I\rangle = 0.0046$, $\langle\gamma_V\rangle= 0.9956$, $\langle\epsilon_V\rangle = 0.0035$."281 As a side product of the error correction. study we obtained alsoa formula for calculating error-bars. of svnthetic Z-band. magnitudes. used. in. the light. curves’ simulations: where £a ds the simulated magnitude for which the error bar (GNL a) is required. fy. and Ades are the magnitude and the error bar of the reference star at a given epoch.," As a side product of the error correction study we obtained alsoa formula for calculating error-bars of synthetic $I$ -band magnitudes used in the light curves' simulations: where $I_{\rm sim}$ is the simulated magnitude for which the error bar $\Delta282I_{\rm sim}$ ) is required, $I_{\rm ref}$ and $\Delta I_{\rm ref}$ are the magnitude and the error bar of the reference star at a given epoch."283 Such caleulated error bars still need to be corrected with eq. (1)., Such calculated error bars still need to be corrected with eq. \ref{eq:errors}) ).284 Error corrections for £ and V passbancds for the first couple of fields are gathered in Table 2.., Error corrections for $I$ and $V$ passbands for the first couple of fields are gathered in Table \ref{tab:errorcor}. .285 Phe full table is available on-line on the OGLE website., The full table is available on-line on the OGLE .286"each of the three energy loss processes, at the position of all the 23 regions.","each of the three energy loss processes, at the position of all the 23 regions."287" For each region, we plot the values of the normalised energy loss rate for the synchrotron (calculated using Breg), ICS and the bremsstrahlung processes."," For each region, we plot the values of the normalised energy loss rate for the synchrotron (calculated using $B_{\rm reg}$ ), ICS and the bremsstrahlung processes."288" All the values were evaluated on the plane of the disc (z= 0) and we used the frequency peak approximation Fe=\/BregXν/νο GeV, where Breg is measured in µία. Since the results were very similar for v—1.4 and v—4.8 GHz, we show only the results obtained for 1.4 GHz."," All the values were evaluated on the plane of the disc $z=0$ ) and we used the frequency peak approximation $E_e=\sqrt{B_{\rm reg}\times\nu/\nu_0}$ GeV, where $B_{\rm reg}$ is measured in $\mu$ G. Since the results were very similar for $\nu=1.4$ and $\nu=4.8$ GHz, we show only the results obtained for 1.4 GHz."289" While ICS is clearly the dominant process in all regions we are studying, the contribution of bremsstrahlung seems to be the the smallest one."," While ICS is clearly the dominant process in all regions we are studying, the contribution of bremsstrahlung seems to be the the smallest one."290" It is however, surely not negligible in at least 3 regions (10, 11 and 14)."," It is however, surely not negligible in at least 3 regions (10, 11 and 14)."291" These processes therefore, cannot be neglected."," These processes therefore, cannot be neglected."292" If we remember that the regions are numbered according to their galactocentric distance, we immediately notice in Fig."," If we remember that the regions are numbered according to their galactocentric distance, we immediately notice in Fig."293" 5 the apparent lack of correlation between the energy loss rates (and therefore of the magnetic field, the ISRF and the hydrogen distribution) and the galactocentric distance, which is clearly a consequence of the irregular nature of the LMC."," \ref{EnergyLoss} the apparent lack of correlation between the energy loss rates (and therefore of the magnetic field, the ISRF and the hydrogen distribution) and the galactocentric distance, which is clearly a consequence of the irregular nature of the LMC."294" We considered two possible WIMPs annihilation channels: XX—bb, in which electrons and positrons will be produced by decaying muons (u—e Ψενμ) and anti-muons DyVe) produced in pions decays (1>pv7, and yt v) and the leptophilic channel yy4μμ."," We considered two possible WIMPs annihilation channels: $\chi \chi \to b \overline{b}$, in which electrons and positrons will be produced by decaying muons $\mu^- \to e^-\, \overline{\nu}_{e} \nu_{\mu}$ ) and anti-muons $\mu^+ \to e^+\, \overline{\nu}_{\mu} \nu_{e}$ ) produced in pions decays $\pi^- \to \mu^- \overline{\nu}_{\mu}$ and $\pi^+ \to \mu^+ \nu_{\mu}$ ) and the leptophilic channel $\chi \chi \to \mu^+ \mu^-$."295 Leptophilic channels have recently raised interest in view of the experimental results on the electron/positron cosmic ray spectra., Leptophilic channels have recently raised interest in view of the experimental results on the electron/positron cosmic ray spectra.296" While Pamela observed an unexpected rise in the positron fraction (Adrianietal.2009),, Fermi-LAT observes a deviation from a simple power-law spectrum (Abdoetal.2009), thus confirming the previous results obtained by HESS (Aharonianetal.2009)."," While Pamela observed an unexpected rise in the positron fraction \citep{PAMELA}, Fermi--LAT observes a deviation from a simple power-law spectrum \citep{b1}, thus confirming the previous results obtained by HESS \citep{Hess}."297". If these results are to be interpreted as due to DM annihilation in the galactic halo, one needs to consider leptophilic channels and high mass scales."," If these results are to be interpreted as due to DM annihilation in the galactic halo, one needs to consider leptophilic channels and high mass scales."298" 'The synchrotron intensity at a frequency v due to DM annihilation coming from a region inside a solid angle dQ on the LMC's disc is: where i is the disc inclination, s is the distance along the line-of-sight and j,(r,2) is the synchrotron emissivity at a position in the LMC’s halo with galactocentric distance r along the disc and height z above or below the disc."," The synchrotron intensity at a frequency $\nu$ due to DM annihilation coming from a region inside a solid angle $d\Omega$ on the LMC's disc is: where $i$ is the disc inclination, $s$ is the distance along the line-of-sight and $j_{\nu}(r,z)$ is the synchrotron emissivity at a position in the LMC's halo with galactocentric distance $r$ along the disc and height $z$ above or below the disc."299 The term cos accounts for the fact that the line-of-sight is not parallel to z.," The term $\,i$ accounts for the fact that the line-of-sight is not parallel to $z$."300 The expression of the emissivity is derived in detail in Borrielloetal.(2009)., The expression of the emissivity is derived in detail in \citet{PaperMW}.301. We evaluated eq. (7)), We evaluated eq. \ref{SynFlux}) )302 for all 23 regions using v—1.4 and 4.8 GHz., for all 23 regions using $\nu=1.4$ and 4.8 GHz.303 The most constraining results were obtained for 1.4 GHz and can be seen in Fig., The most constraining results were obtained for 1.4 GHz and can be seen in Fig.304 6 for both annihilation channels considered., \ref{Results1} for both annihilation channels considered.305" For comparison, we show also the best constraint obtained in Borrielloetal.(2010) for M33 using an NFW profile and assuming equipartition between magnetic fields and cosmic rays, and the best constraint obtained in Borrielloetal.(2009) for the Milky Way using the yx—bb channel."," For comparison, we show also the best constraint obtained in \citet{PaperM33} for M33 using an NFW profile and assuming equipartition between magnetic fields and cosmic rays, and the best constraint obtained in \citet{PaperMW} for the Milky Way using the $\chi \chi \to b \overline{b}$ channel."306 For the yy—pty” channel we show the best constraint obtained for the Milky Way using the same formalism and observations described in Borrielloetal.(2009) and also the favoured region obtained when one attributes to DM annihilation the experimental results described above (Meadeetal.2010)., For the $\chi \chi \to \mu^+ \mu^-$ channel we show the best constraint obtained for the Milky Way using the same formalism and observations described in \citet{PaperMW} and also the favoured region obtained when one attributes to DM annihilation the experimental results described above \citep{Meade}.307". We have imposed constraints on the m,-(cAv) plane using radio observations at 1.4 GHz and 4.8 GHz of the LMC and analysing two different DM annihilation channels, a hadronic and a leptonic one."," We have imposed constraints on the $m_{\chi}$ $\langle\sigma_Av\rangle$ plane using radio observations at 1.4 GHz and 4.8 GHz of the LMC and analysing two different DM annihilation channels, a hadronic and a leptonic one."308" The existence of high resolution observations of the LMC in several frequency bands has allowed us to obtain most of the information needed to calculate the DM annihilation signal, making the least possible number of hypotheses in all the steps of the calculation."," The existence of high resolution observations of the LMC in several frequency bands has allowed us to obtain most of the information needed to calculate the DM annihilation signal, making the least possible number of hypotheses in all the steps of the calculation."309" Being able to escape from this problem and, when necessary, making"," Being able to escape from this problem and, when necessary, making"310thiu shell spherical capacitors at successive values of the radius r. cach of thickness A~O(Ly aud charge AQ(r) eiven by On a very short time scale Of) the QED vacua diclectric breakdown produces a number— deusity of pairs Hel(r) such that Er)ee€.,"thin shell spherical capacitors at successive values of the radius $r$, each of thickness $\lambda\sim O({\hbar\over mc})$ and charge $\Delta Q(r)$ given by On a very short time scale $O({\hbar\over mc^2})$, the QED vacuum dielectric breakdown produces a number density of pairs $n_{e^+e^-}(r)$ such that $E(r)\approx {\cal E}_{\rm c}$."311 This approximate equality sinply neans that the ο)« pair creation exponoenutiallv decreases when the initial electric field is screened to the critical value., This approximate equality simply means that the $e^+e^-$ pair creation exponentially decreases when the initial electric field is screened to the critical value.312 It is iuportaut to emphasize that the first laver of thickuess A outside the horizon produces a uber of pairs sufficient to reduce the charge of the EMDIT to Qe=&n. its critical value in the seuse of eiseuberg and Euler.," It is important to emphasize that the first layer of thickness $\lambda$ outside the horizon produces a number of pairs sufficient to reduce the charge of the EMBH to $Q_{\rm c}={\cal E}_{\rm c}r_+^2$, its critical value in the sense of Heisenberg and Euler."313 The total muuber of pairs actually created in the dvadosphere is verv uuch larger than the number captured by the black hole. since it is amplified by the factor (rasΓΕ]λ.," The total number of pairs actually created in the dyadosphere is very much larger than the number captured by the black hole, since it is amplified by the factor $(r_{\rm ds}-r_+)/\lambda $."314 The deusity of pairs as a function of the radius is then eiven by Tn Figs., 	The density of pairs as a function of the radius is then given by In Figs.315" 2 aud 3.. we plot the density of pais for 10A£.. and 10°AL,. EMBII or selected values of £."," \ref{fig.2} and \ref{fig.3}, we plot the density of pairs for $10M_{\odot}$ and $10^5M_{\odot}$ EMBH for selected values of $\xi$."316 These two values of the mass were chosen to be representative of objects typical of the galactic population or for the uuclei of galaxies compatible with our upper liuüt of the miaxinmui nass of 6:10AZ..., These two values of the mass were chosen to be representative of objects typical of the galactic population or for the nuclei of galaxies compatible with our upper limit of the maximum mass of $6\cdot 10^5M_{\odot}$.317" We are now im a position to compute the total number of pairs Nya created in the dvadosphere aud from a suoledee of the electrostatic energy deusitv iu each shell. ie enerev deusitv of created pairs as a function of the radial coordinate and the total energy ETT, iu the pairs."," We are now in a position to compute the total number of pairs $N_{\rm pair}$ created in the dyadosphere and from a knowledge of the electrostatic energy density in each shell, the energy density of created pairs as a function of the radial coordinate and the total energy $E^{\rm tot}_{e^+e^-}$ in the pairs."318 Finally we can estimate the total energv extracted by ie pair creation process in EMDITIs of different masses or selected values of© and courpare aud coutrast these values with the maxinnun extractable cnerey given by 1ο nass formula for black holes. (see Eqs. (1)), Finally we can estimate the total energy extracted by the pair creation process in EMBH's of different masses for selected values of $\xi$ and compare and contrast these values with the maximum extractable energy given by the mass formula for black holes (see Eqs. \ref{em}) )319 and (3)))., and \ref{s1}) )).320 This comparison shows that the effcieucy. sharply decreases as oue reaches the maxima value of the EMDII uass permitting vacuun polarization. while the efficicucy approaches LOOM iu the low mass Πα (Preparata et al. L998)}).," This comparison shows that the efficiency sharply decreases as one reaches the maximum value of the EMBH mass permitting vacuum polarization, while the efficiency approaches $100\%$ in the low mass limit (Preparata et al. \cite{prx}) )."321 Duc o the very large pair density given by Eq. (8)), Due to the very large pair density given by Eq. \ref{density}) )322 aud to the sizes of the cross-sections for the process €|<>~| +. the system is expected to thermalize to a plasma configuration for which aud reach an average teniperature where & is Boltzmaun’s coustaut.," and to the sizes of the cross-sections for the process $e^+e^-\leftrightarrow \gamma+\gamma$ , the system is expected to thermalize to a plasma configuration for which and reach an average temperature where $k$ is Boltzmann's constant."323" The average energy per pair p is shown as a fiction of the EXIBIT mass for selected values of the charge parameter © iu Fig. 1,", The average energy per pair ${ E^{\rm tot}_{e^+e^-}\over N_{\rm pair}}$ is shown as a function of the EMBH mass for selected values of the charge parameter $\xi$ in Fig. \ref{fig.4}.324 As shown by Buffiui et al.(1998)) the further evolution of this plasina leads to a relativistic expausiou. ¢|( annihilation and au enormous pair-clectromaguctic-pulse “PEL pulse”.," As shown by Ruffini et \cite{rwx}) ) the further evolution of this plasma leads to a relativistic expansion, $e^+ e^-$ annihilation and an enormous pair-electromagnetic-pulse “P.E.M. pulse""."325 By introducing a variety of models based on relativistic bydrodvnamucal equations. it has," By introducing a variety of models based on relativistic hydrodynamical equations, it has"326Ultra-luminous X-ray sources (ULXs) are point-like objects with high. (107 erg 1) X-ray luminosities that are not associated with an active galactic nucleus (AGN) or. indeed. the central regions of a host galaxy. (see. Miller Colbert 2004: Roberts 2007: Gladstone 2011).,"Ultra-luminous X-ray sources (ULXs) are point-like objects with high $>$ $^{39}$ erg $^{-1}$ ) X-ray luminosities that are not associated with an active galactic nucleus (AGN) or, indeed, the central regions of a host galaxy (see Miller Colbert 2004; Roberts 2007; Gladstone 2011)."327 The nature of these objects has been the subject of. much speculation. with CCD resolution N-rav. spectroscopy plaving a major role in advancing our understanding.," The nature of these objects has been the subject of much speculation, with CCD resolution X-ray spectroscopy playing a major role in advancing our understanding."328 Although other missions iwe plaved an important part (e.g. detection. of »ossible state transitions in. ULNs. Ixubota ct al.," Although other missions have played an important part (e.g. detection of possible state transitions in ULXs, Kubota et al."329 2001). hese results have predominantly. come from the mission.," 2001), these results have predominantly come from the mission."330 Us first major advance was the detection of a soft excess in the spectra of many ULNs. with a cempcrature consistent with that expected. for the inner edge of an accretion disc around. an intermeciate-mass Xack hole (AAIBII: c.g. Miller ct al.," Its first major advance was the detection of a soft excess in the spectra of many ULXs, with a temperature consistent with that expected for the inner edge of an accretion disc around an intermediate-mass black hole (IMBH; e.g. Miller et al."331 2003: Miller. Fabian Aliller 2004).," 2003; Miller, Fabian Miller 2004)."332 However. later stuclies showed that the second. larder component in these spectra turns over within the bandpass. and so appears much cooler and optically thicker than the corresponding Comptonisation media in Galactic black holes (Stobbart et al.," However, later studies showed that the second, harder component in these spectra turns over within the bandpass, and so appears much cooler and optically thicker than the corresponding Comptonisation media in Galactic black holes (Stobbart et al."333 2006)., 2006).334 This is inconsistent with the identification of a sub-Ecelington state for an IMDBIILI. and more indicative of super-Eddington accretion onto a stellar-mass black hole (Clacstone. Done Roberts 2009).," This is inconsistent with the identification of a sub-Eddington state for an IMBH, and more indicative of super-Eddington accretion onto a stellar-mass black hole (Gladstone, Done Roberts 2009)."335 The apparent divergence of the spectra of more luminous ULXs into two components (see Fig., The apparent divergence of the spectra of more luminous ULXs into two components (see Fig.336 S of Gladstone et al., 8 of Gladstone et al.337 2009) can be interpreted. in terms of the emergence of a radiativelv-driven wind at super-Ecddington accretion rates. with the outllowing material thermalising he underlving disc emission to produce the soft. spectral component as predicted. by e.g. Wing (2004). Poutanen et al. (," 2009) can be interpreted in terms of the emergence of a radiatively-driven wind at super-Eddington accretion rates, with the outflowing material thermalising the underlying disc emission to produce the soft spectral component as predicted by e.g. King (2004), Poutanen et al. ("3382007).,2007).339 The hard component is then produced: within he photospheric radius. with its characteristic optically-hick Comptonisation signature either the result of a thick shroucl of Comptonising electrons around the hot inner disc. or perhaps a change in the opacity of the outer lavers of the jot inner accretion clise itself (Middleton et al.," The hard component is then produced within the photospheric radius, with its characteristic optically-thick Comptonisation signature either the result of a thick shroud of Comptonising electrons around the hot inner disc, or perhaps a change in the opacity of the outer layers of the hot inner accretion disc itself (Middleton et al."340 POLL)., 2011).341 Such a model can explain the startling lack of variability seen in many of these sources (Lleil et al., Such a model can explain the startling lack of variability seen in many of these sources (Heil et al.342 2009)., 2009).343 In those few cases, In those few cases344"combination of five reasons may provide an D) Higher than average rotation velocities in the progenitor stars of these supergiants on the MS may reconcile the situation for some 1) Evolution models for rotating stars that also account for the interaction of rotation and a magnetic dynamo (MM05) predict enhanced mixing signatures of the amount required (dotted r1)) Some stars may have evolved in a close binary, which can also lead to enhanced mixing associated with mass 1V)) Some objects may have been siblings to τ SSco on the MS, climbing up the N/O-N/C relation even further in their further v)) Supergiants may already have evolved through the red supergiant phase (e.g., on a blue loop) to expose first abundance ratios, which could quantitatively also explain the observations (dashed line).","combination of five reasons may provide an ) Higher than average rotation velocities in the progenitor stars of these supergiants on the MS may reconcile the situation for some ) Evolution models for rotating stars that also account for the interaction of rotation and a magnetic dynamo (MM05) predict enhanced mixing signatures of the amount required (dotted ) Some stars may have evolved in a close binary, which can also lead to enhanced mixing associated with mass ) Some objects may have been siblings to $\tau$ Sco on the MS, climbing up the $N/O$ $N/C$ relation even further in their further ) Supergiants may already have evolved through the red supergiant phase (e.g., on a blue loop) to expose first abundance ratios, which could quantitatively also explain the observations (dashed line)."345" More information may be derived from the helium content, which in the case of BA-type supergiants is determined here for a significant number of stars for the first time in a self-consistent analysis."," More information may be derived from the helium content, which in the case of BA-type supergiants is determined here for a significant number of stars for the first time in a self-consistent analysis."346 Our results are displayed in Fig. 6.., Our results are displayed in Fig. \ref{hemix}.347" On the MS no helium surface enrichment is observed, as predicted in the models for stars with masses below about Mo."," On the MS no helium surface enrichment is observed, as predicted in the models for stars with masses below about $M_\odot$."348" After the MS, the picture is blurred by the possible occurrence of a blue loop."," After the MS, the picture is blurred by the possible occurrence of a blue loop."349 Actually the interpretation of the blue supergiant can become really constraining only when we obtain additional hints to the previous evolution of the star., Actually the interpretation of the blue supergiant can become really constraining only when we obtain additional hints to the previous evolution of the star.350" Has the blue supergiant evolved directly from the MS, or has it evolved in that stage after going through a red supergiant stage?"," Has the blue supergiant evolved directly from the MS, or has it evolved in that stage after going through a red supergiant stage?"351" At the moment, from the models the situation would be the following: for models below Mo, He-enrichments at the level observed in the present supergiants are only compatible with models having undergone a dredge-up in the red supergiant phase."," At the moment, from the models the situation would be the following: for models below $M_\odot$, He-enrichments at the level observed in the present supergiants are only compatible with models having undergone a dredge-up in the red supergiant phase."352" This is true whether rotation is considered or not, or a magnetic field is accounted for or not."," This is true whether rotation is considered or not, or a magnetic field is accounted for or not."353 The present track for the magnetic Μο model was computed only up to the end of the MS phase and thus did not yet go through the dredge-up phase., The present track for the magnetic $M_\odot$ model was computed only up to the end of the MS phase and thus did not yet go through the dredge-up phase.354" Depending on the rotation velocity, the presence of a magnetic field or its absence, models, after the red supergiant phase, will populate diverse parts of the region in the plane Ys versus N/O, as illustrated e.g. by the dashed and dotted lines in Fig. 6.."," Depending on the rotation velocity, the presence of a magnetic field or its absence, models, after the red supergiant phase, will populate diverse parts of the region in the plane $Y_{\rm S}$ versus $N/O$, as illustrated e.g. by the dashed and dotted lines in Fig. \ref{hemix}."355" We note, however, that we cannot exclude at present the possibility that the observed helium abundances in the supergiants may be overestimated."," We note, however, that we cannot exclude at present the possibility that the observed helium abundances in the supergiants may be overestimated."356" A systematic downward shift by a mere (which is within the typical systematic uncertainties in our abundance determinations) would be sufficient, e.g., to bring the observations and the magnetic model in Fig."," A systematic downward shift by a mere (which is within the typical systematic uncertainties in our abundance determinations) would be sufficient, e.g., to bring the observations and the magnetic model in Fig."357 6 into agreement., \ref{hemix} into agreement.358 All observed lines arise from two energetically close levels only ?P)), All observed lines arise from two energetically close levels only ).359".Modelatomshortcoming s( suchasinsuficientab linelimitatthecooltemperatureborder, couldtheref ore"," Model atom shortcomings (such as insufficient collisional data), which may become important only in the weak-line limit at the cool temperature border, could therefore remain unnoticed and could give rise to systematics."360remainunnotice," It would not be the first time that uncertainties in atomic data complicate the statistic equilibrium and radiative transfer calculations needed to interpret the observed lines \citep[e.g.][]{przybilla05,najarro06}."361dan," Further investigations are required before firm conclusions on the evolutionary state of the supergiants are drawn from the helium abundances, and a fully coherent picture can be deduced."362order.,order.363 Finally. we add up the re-adjusted co-aligned versions of the copies of the object spectra and get an improved version of the superspectrum.," Finally, we add up the re-adjusted co-aligned versions of the copies of the object spectra and get an improved version of the superspectrum."364 Each of the original. unmodified object spectra is modeled using the improved superspectrum.," Each of the original, unmodified object spectra is modeled using the improved superspectrum."365 In this initial step. we ignore the presence of the faint planetary signal in the data.," In this initial step, we ignore the presence of the faint planetary signal in the data."366 First the superspectrum (model) is corrected for a general linear trend in flux., First the superspectrum (model) is corrected for a general linear trend in flux.367 Second. the model is shifted according to the barycentric velocity of the Earth. the radial velocity of the star. and the aforementioned shifts and stretches/contractions in the sub-pixel regime. so that the positions of absorption lines of the object spectrum and the model are matched.," Second, the model is shifted according to the barycentric velocity of the Earth, the radial velocity of the star, and the aforementioned shifts and stretches/contractions in the sub-pixel regime, so that the positions of absorption lines of the object spectrum and the model are matched."368 This is achieved using a chunk-Brent-spline-approach similar to that described in the previous paragraph., This is achieved using a chunk-Brent-spline-approach similar to that described in the previous paragraph.369 We note that in all analysis steps. modifications are exclusively applied to the model. but the object spectrum are used in their original version. ie. the data are unchangec.," We note that in all analysis steps, modifications are exclusively applied to the model, but the object spectrum are used in their original version, i.e. the data are unchanged."370 At the third stage. the model is sealed chunkwise with respect to the object spectrum.," At the third stage, the model is scaled chunkwise with respect to the object spectrum."371 As we now compare the scaled model with each object spectrum. we notice that the widths and depths of the absorption lines differ slightly.," As we now compare the scaled model with each object spectrum, we notice that the widths and depths of the absorption lines differ slightly."372 These differences originate most likely in the aforementioned effects of residuals wavelength calibration errors. guiding errors. and variations in the instrumental profile. and can be corrected by adding a scaled version of the second derivative of the object spectrum to the model.," These differences originate most likely in the aforementioned effects of residuals wavelength calibration errors, guiding errors, and variations in the instrumental profile, and can be corrected by adding a scaled version of the second derivative of the object spectrum to the model."373 The scaling factor is determined via y minimisation (fourth stage)., The scaling factor is determined via $\chi^2$ minimisation (fourth stage).374 After this. the model is renormalised.," After this, the model is renormalised."375 The final stage Is to iterate twice over all these four processes to Improve the model describing the stellar spectrum., The final stage is to iterate twice over all these four processes to improve the model describing the stellar spectrum.376 For the model of the planetary signal. we use a copy of the improved model of the stellar spectrum. but scaled down by the factors εί)µ(Φ.i) and shifted by velocity Ας.Φ) with respect to the stellar spectrum.," For the model of the planetary signal, we use a copy of the improved model of the stellar spectrum, but scaled down by the factors $\epsilon(\lambda)~\mu(\phi, i)$ and shifted by velocity $V_{\rm{p}}(K_{\rm{p}},\phi)$ with respect to the stellar spectrum."377 Hence. the two free parameters are the planet-to-star flux ratio for the fully-illuminated planet εί). and the orbital inclination 7. which corresponds. to the RV semi-amplitude of the planet 148.9sinikm s!.," Hence, the two free parameters are the planet-to-star flux ratio for the fully-illuminated planet $\epsilon(\lambda)$, and the orbital inclination $i$, which corresponds to the RV semi-amplitude of the planet $K_{\rm{p}}=K_{\rm{p,max}} \sin i=148.9378 \sin i~~{\rm km~s^{-1}}$ ."379 We are now ready to add this planetary signal to the improved model 7 of the stellar spectrum and consequently construct the model M describing the spectrum of the star the reflected one from the planet., We are now ready to add this planetary signal to the improved model $T$ of the stellar spectrum and consequently construct the model $M$ describing the spectrum of the star the reflected one from the planet.380 For each pixel κ. M is given by where c denotes the speed of light.," For each pixel $k$, $M$ is given by where $c$ denotes the speed of light."381 Varying Ay and εἰ). we finally search for the best-fit model M to all the object spectra by y minimisation.," Varying $K_{\rm p}$ and $\epsilon(\lambda)$ , we finally search for the best-fit model $M$ to all the object spectra by $\chi^2$ minimisation."382 The search range for the RV semi-amplitude comprised Ky=40 to 180kms! (corresponding to orbital inclinations ;=15° to 90°. plus twice the error of Kpanax: See Table 1) with a step width of 3kms—.," The search range for the RV semi-amplitude comprised $K_{\rm p} = 40$ to $180~{\rm km~s^{-1}}$ (corresponding to orbital inclinations $i=15^\circ$ to $90^\circ$, plus twice the error of $K_{\rm p,max}$; see Table 1) with a step width of $3~{\rm km~s^{-1}}$."383 This was a good compromise between computing time and sampling the average absorption line profile with the FWHM of =I5kms!.," This was a good compromise between computing time and sampling the average absorption line profile with the FWHM of $\approx384 15~{\rm km~s^{-1}}$."385 Using simulations. we found that for small inclinations of the planetary orbit. where the planets appear only slightly illuminated. the method is unable to detect Jupiter-size objects with veryy high albedos.," Using simulations, we found that for small inclinations of the planetary orbit, where the planets appear only slightly illuminated, the method is unable to detect Jupiter-size objects with very high albedos."386" Once the best model M[A,.eC0] has been evaluated. we determine the confidence level of the y minimum by applying the bootstrap randomisation method (e.g. Kürrster et al."," Once the best model $M[K_{\rm p},\epsilon(\lambda)]$ has been evaluated, we determine the confidence level of the $\chi^2$ minimum by applying the bootstrap randomisation method (e.g. Kürrster et al."387 1997)., 1997).388 Retainmg the orbital phases. we randomly redistribute the observed spectra amongst the phases. thereby creating N different data sets.," Retaining the orbital phases, we randomly redistribute the observed spectra amongst the phases, thereby creating $N$ different data sets."389 Any signal present in the original data is now scrambled i1 these artificial datasets., Any signal present in the original data is now scrambled in these artificial datasets.390 For all these randomised data sets. we again evaluate the model for the two free parameters. and locate the best fit with its specific γ΄ minimum.," For all these randomised data sets, we again evaluate the model for the two free parameters, and locate the best fit with its specific $\chi^2$ minimum."391 We set 77 to be the number of best-fit models to the N randomised data sets that have a minimum y? less or equal than the minimum y- fourd for the original data set., We set $m$ to be the number of best-fit models to the $N$ randomised data sets that have a minimum $\chi^2$ less or equal than the minimum $\chi^2$ found for the original data set.392 The confidence level can then be estimated by =|ΗΝ., The confidence level can then be estimated by $\approx 1-m/N$.393 Applying the data synthesis method to the HD 75289A data. we adopted the following approximations to the atmospheric models by Sudarsky et al. (," Applying the data synthesis method to the HD 75289A data, we adopted the following approximations to the atmospheric models by Sudarsky et al. ("3942000). (,2000). (3951) We adopted a grey-albedo model to resemble the Class Vmodel. which describes the atmospheres of hot Jupiters with temperatures >1500 K.,"i) We adopted a grey-albedo model to resemble the Class Vmodel, which describes the atmospheres of hot Jupiters with temperatures $>1500~{\rm396 K}$ ."397 As can be seen in Figure l.. this was," As can be seen in Figure \ref{fig:albedo}, , this was"398"plots above, except that our error bars are generally larger due to scatter from our estimates of L,.","plots above, except that our error bars are generally larger due to scatter from our estimates of $L_x$."399" Since X- luminosities are generally easier than virial masses to compute from observations, observations of many more radio halos may reduce the statistical uncertainties to such a level as to potentially distinguish the allowed scalings and dependencies."," Since X-ray luminosities are generally easier than virial masses to compute from observations, observations of many more radio halos may reduce the statistical uncertainties to such a level as to potentially distinguish the allowed scalings and dependencies."400" The redshift evolution of the Pi4—L4 relation in particular may provide a way of determining the dominant components of radio power and the average magnetic strength of clusters, as we have discussed above for the P,.4—M, relation.. In general, if the observational uncertainties in and are reduced by approximately a factor of two, Aymany degeneraciesby in the model parameters will be eliminated."," The redshift evolution of the $P_{1.4}-L_x$ relation in particular may provide a way of determining the dominant components of radio power and the average magnetic strength of clusters, as we have discussed above for the $P_{1.4}-M_v$ relation.. In general, if the observational uncertainties in $A_f$ and $b_f$ are reduced by approximately a factor of two, many degeneracies in the model parameters will be eliminated."401 We note that we are basing this analysis on our sample of only 131 clusters., We note that we are basing this analysis on our sample of only $131$ clusters.402" While this is significantly more than the current known number of radio halos, it is still far fewer than we expect to see with instruments such as"," While this is significantly more than the current known number of radio halos, it is still far fewer than we expect to see with instruments such as"403explaain this observational fact.,ain this observational fact.404"x10"".. comparable to the 2003 epoch. and approximately a factor of 2 better than in the 2002 epoch.","$\times$, comparable to the 2003 epoch, and approximately a factor of 2 better than in the 2002 epoch."405" A Gaussian fit to the 2004 detection vields a position of (J2000) right ascension Έτ 45™ 5:009 (20:17). declination —30° +2""). which is consistent with the 2003 and 2002 positions and is approximately 2.5x and 5x more accurate. respectively."," A Gaussian fit to the 2004 detection yields a position of (J2000) right ascension $17^{\mathrm{h}}$ $45^{\mathrm{m}}$ 09 $\pm4060\fs17$ ), declination $-30\arcdeg$ $\pm 2\arcsec$ ), which is consistent with the 2003 and 2002 positions and is approximately $\times$ and $\times$ more accurate, respectively."407 The source position and uncertainty cited above include a correction for ionospheric refraction which is prevalent in low [frequency observations ancl discussed in IHvmanetal.(2006) and Nordetal.(2004)., The source position and uncertainty cited above include a correction for ionospheric refraction which is prevalent in low frequency observations and discussed in \cite{hlrrkn06} and \cite{nlkhlbd04}.408".. separale images were mace for the upper (333 MIIZ) and lower (817 MIIz) sicdebauds ol the observations ancl vield fIux densities of 42.147.2 wiJv and 72.5z9.5 5Hr mJy. respectively,"," Separate images were made for the upper (333 MHz) and lower (317 MHz) sidebands of the observations and yield flux densities of $\pm$ 7.2 mJy and $\pm$ 9.5 mJy, respectively."409 No significant differences are found in the shapes of the separate light curves generated [or each sideband., No significant differences are found in the shapes of the separate light curves generated for each sideband.410 Figure 4. shows the spectrum of oobtained by imaging pairs of adjacent frequency channels across the two sidebands., Figure \ref{fig:spectrum04} shows the spectrum of obtained by imaging pairs of adjacent frequency channels across the two sidebands.411" A power-law fit vields a very steep spectrum of SxvP?—*"" forJ1745—3009..", A power-law fit yields a very steep spectrum of $S \propto \nu^{-13.5 \pm 3.0}$ for.412 An identical analvsis of the data for the nearby strong source G358.638— 1.160 vields a spectral index of —1.5d0.5. consistent with the determination of Nordetal.(2004). who found a spectral index of —1.2 between 330 and 1400 MITz.," An identical analysis of the data for the nearby strong source $-$ 1.160 yields a spectral index of $-1.5 \pm 0.5$, consistent with the determination of \cite{nlkhlbd04} who found a spectral index of $-1.2$ between 330 and 1400 MHz."413 A Monte-Carlo simulation was conducted to assess the confidence level of the steep spectrum obtained for the 2004. detection ofJ1745—3009., A Monte-Carlo simulation was conducted to assess the confidence level of the steep spectrum obtained for the 2004 detection of.414. First. a spectrum was eeneraled based on the fitted spectral index of —13.5 ancl normalized to the observed Πας density al a particular channel.," First, a spectrum was generated based on the fitted spectral index of $-13.5$ and normalized to the observed flux density at a particular channel."415 One thousand spectra were simulated by randomly adding Gaussian noise to the flux densities of the normalized spectrum. based on (hie observed noise level obtained for the individual channel images.," One thousand spectra were simulated by randomly adding Gaussian noise to the flux densities of the normalized spectrum, based on the observed noise level obtained for the individual channel images."416 A flat spectrum fit to the ddata is ruled out with a confidence level of99., A flat spectrum fit to the data is ruled out with a confidence level of.4177%... Unfortunately. however. due to limitations in the analvsis of the 2002 and 2003 observations. we were not able to detect reliable evidence of a steep spectrum for those bursts.," Unfortunately, however, due to limitations in the analysis of the 2002 and 2003 observations, we were not able to detect reliable evidence of a steep spectrum for those bursts."418 No emission is detected [rom wwhen imaging the 2004 observation al times when the burst is not occurring., No emission is detected from when imaging the 2004 observation at times when the burst is not occurring.419" From {hese 2004 observations. we are able to improve the (50) upper limit for quiescent 330 MITz emission between bursts to 6 mJy. as compared to earlier limits of 75 mJy and 25 mJy from the 2002 and 2003 observations. respectively,"," From these 2004 observations, we are able to improve the $\sigma$ ) upper limit for quiescent 330 MHz emission between bursts to 6 mJy, as compared to earlier limits of 75 mJy and 25 mJy from the 2002 and 2003 observations, respectively."420 The upper limit on quiescent emission during periods ol no burst activity is 15 mJv at 330 MIIz (νταetal.2005)., The upper limit on quiescent emission during periods of no burst activity is 15 mJy at 330 MHz \citep{hlkrmy-z05}.421.. In addition. we find an upper limit of circular polarization for the 2004 burst. while an upper limit of was previously determined for both the 2002 and 2003 bursts.," In addition, we find an upper limit of circular polarization for the 2004 burst, while an upper limit of was previously determined for both the 2002 and 2003 bursts."422our conclusions.,our conclusions.423 Although the remaining surveys do not lucet our criteria for selection. we do our best to estimae to what degree these additional data affect the upper limits ou he planet frequency.," Although the remaining surveys do not meet our criteria for selection, we do our best to estimate to what degree these additional data affect the upper limits on the planet frequency."424 Iu iiost of these surveys tje autlors uade no attempt to put upper μμ ou the frequency of plaucts in the fields they observed. often selected rausits by eve. and rarely estimated the nunber of cluster οας observed.," In most of these surveys the authors made no attempt to put upper limits on the frequency of planets in the fields they observed, often selected transits by eye, and rarely estimated the number of cluster members observed."425 We estimate from the couteuts of cach paper the παο of stars with suficicutly precise xiotomietry for planetary transits to be visible. aud he umber of cluster members likely to be within this subset of stars.," We estimate from the contents of each paper the number of stars with sufficiently precise photometry for planetary transits to be visible, and the number of cluster members likely to be within this subset of stars."426 A list of the additional survevs aud estimates of the umber of stars they coutribute to the otal sample of cluster stars is presented in Table 5.., A list of the additional surveys and estimates of the number of stars they contribute to the total sample of cluster stars is presented in Table \ref{tbl:other_surveys}.427 Iu total. the 10 additional surveys add ~5000 stars to our sample.," In total, the 10 additional surveys add $\sim5000$ stars to our sample."428 Assuming an average detecion efficiency of and a maxima cficicucy of this implics hat ..frog.7aun(00010.<6% qm the best case and Foun.d~7TSWURUSES—30eg1 on average.," Assuming an average detection efficiency of, and a maximum efficiency of, this implies that $f_{p_{other}} \approx \frac{3.0}{(5000)(0.01)} \le 6\%$ in the best case and $f_{p_{other}} \approx \frac{3.0}{(5000)(0.005)} \le 12\%$ on average."429"VOT)OO Thehe coustraiutsοfay]; ou the population of 1.0 Ry ILJ planets from the main 6 surveys are the weakest of amy considered here with f,€0.055.", The constraints on the population of 1.0 $R_J$ HJ planets from the main 6 surveys are the weakest of any considered here with $f_p \le 0.055$.430" Using our standard method of combining upper Πές. the addition of the 5000 stars from the other surveys vields a new Tut of f,x0.029. which isa ~DUX tighter coustraint."," Using our standard method of combining upper limits, the addition of the 5000 stars from the other surveys yields a new limit of $f_p \le 0.029$, which is a $\sim50\%$ tighter constraint."431" Iu the case iu which Το0.005. the combined wpper Tit is f,€0.037."," In the case in which $\mathcal{P}_{\epsilon} = 0.005$, the combined upper limit is $f_p \le 0.037$."432" Iu the ΥΠ range. the upper Inuits ou for 1.0 Π plaucts decreases by 18 and 1054 for detectionf£, efficiencies. of 1.054 and 0.554 vesectivelv."," In the VHJ range, the upper limits on $f_p$ for 1.0 $R_J$ planets decreases by $18\%$ and $10\%$ for detection efficiencies of $1.0\%$ and $0.5\%$ respectively."433" At larecr planetary radii tle o‘hauges in f, for | Ry plaucts due to the addition of —rese J5OOU stars 1s ¢ Forder ~ο205€.", At larger planetary radii the changes in $f_p$ for 1.5 $R_J$ planets due to the addition of these 5000 stars is of order $\sim5-20\%$.434 The conclusions do rot qualitatively change with the inclusion of metallicity information., The conclusions do not qualitatively change with the inclusion of metallicity information.435 The mean weighted metallicity of the stars oe1 the unused 10 smvevs is ΡοΠΠ)~--|0.1 (according ο 1ο WEDDA database). comparable to ([Fe/II|;~--LO.y) ound for the 6 surveys utilized in this paper.," The mean weighted metallicity of the stars in the unused 10 surveys is $\langle\textrm{[Fe/H]}\rangle\approx +0.1$ (according to the WEBDA database), comparable to $\langle\textrm{[Fe/H]}\rangle\approx +0.09$ found for the 6 surveys utilized in this paper."436 We expect that by neglecting the observations present oei these other surveys our derived upper limits may be p to a factor of two too high., We expect that by neglecting the observations present in these other surveys our derived upper limits may be up to a factor of two too high.437 However. it is highly ulikely that all of these survevs have achieved the optimistic 1.0% detection efficiency. and maprobable that all have even achieved a 0.5% efficiency.," However, it is highly unlikely that all of these surveys have achieved the optimistic $1.0\%$ detection efficiency, and improbable that all have even achieved a $0.5\%$ efficiency."438 We therefore conclude that ueelecting these other surveys does not qualitativev chauge our primarily conclusion. that the lack of detections is consistent with the hypothesis that cluster anc field stars host the same planet population.," We therefore conclude that neglecting these other surveys does not qualitatively change our primarily conclusion, that the lack of detections is consistent with the hypothesis that cluster and field stars host the same planet population."439 We do note that. had each of these surveys carefully quantified heir detection efficiencies. the coustraiuts on the umber of short-period plauets in open clusters could have been roticeably tighter.," We do note that, had each of these surveys carefully quantified their detection efficiencies, the constraints on the number of short-period planets in open clusters could have been noticeably tighter."440 Tt is useful to ask. even our results. how may more cluster stars ust be observed nh surevs with null results before the combined upper lit derived using all extant surveys becomes meonsisteut wit1 the observed frequency of plaucts around field stars.," It is useful to ask, given our results, how many more cluster stars must be observed in surveys with null results before the combined upper limit derived using all extant surveys becomes inconsistent with the observed frequency of planets around field stars."441 Because of the low detection efficiencies and relatively fevsuitable open clusters iu our ealaxy. it is wnlikely that upper linits derived from transit surveys in open custers will he inconsistent with the resuts of CUS and €06 in the rear future. even if it is the case that the frequency : plauets in open clusters is significanlv lower than hat of the field.," Because of the low detection efficiencies and relatively few suitable open clusters in our galaxy, it is unlikely that upper limits derived from transit surveys in open clusters will be inconsistent with the results of C08 and G06 in the near future, even if it is the case that the frequency of planets in open clusters is significantly lower than that of the field."442" For the €JS result. a combined upper (at coufidenuce) would be inconsistent with confidence lower ]und on the COs frequency yaction of stars wih planets was found to he f,<0.0076 for 1.2 Ry plaucts in the 3<P5 day veriod range."," For the C08 result, a combined upper limit (at confidence) would be inconsistent with the confidence lower bound on the C08 frequency of the fraction of stars with planets was found to be $f_p \le 0.0076$ for 1.2 $R_J$ planets in the $3<P<5$ day period range."443" The six-survey"" upper limit is f,<0.019. which 1uplies that ~Ls.00! inore cluster stars lust be observed (with null results) at a detection ¢LCICLCY efore he Tait is in conflict with COs (currently. 1300) stars have Όσοι observed at ~0.55 efficiency)."," The six-survey upper limit is $f_p \le 0.019$, which implies that $\sim 48,000$ more cluster stars must be observed (with null results) at a detection efficiency before the limit is in conflict with C08 (currently, $\sim13000$ stars have been observed at $\sim0.5\%$ efficiency)."444 This 111iiber drops to 9000 with a detection eLCICLCY O|Cu., This number drops to 9000 with a detection efficiency of.445 Given that there are about 1200 known open clusters iu the ealaxy (WEDDA). ouly a handful of whicji are rich enough to contain thousands ft stars. the «mlv wav to make the upper limits onu the plauct freqicacy in open clusters derived from trausit surveys competitive with field surveys is to drastically 1lcrease the detection efficiency of the surveys imuuber of clusters observed.," Given that there are about 1200 known open clusters in the galaxy (WEBDA), only a handful of which are rich enough to contain thousands of stars, the only way to make the upper limits on the planet frequency in open clusters derived from transit surveys competitive with field surveys is to drastically increase the detection efficiency of the surveys number of clusters observed."446 When we ask how many stars would, When we ask how many stars would447topological statistic. (he genus number.,"topological statistic, the genus number."448 By doing so. we can identify the central period οἱ (he reionization process.," By doing so, we can identify the central period of the reionization process."449 The topological signature of overlap will work whether reionization proceeds from high- to low-densityv regions or vice versa., The topological signature of overlap will work whether reionization proceeds from high- to low-density regions or vice versa.450 Topological tests could be applied using anv method that allows mapping ionized and neutral regions during the epoch of reionization., Topological tests could be applied using any method that allows mapping ionized and neutral regions during the epoch of reionization.451 Both 21cm emission [rom neutral gas and obscuration of eoalaxies by neutral gas could provide such maps., Both 21cm emission from neutral gas and obscuration of galaxies by neutral gas could provide such maps.452 Each tool has its own strengths: The 21cm maps can in principle map smaller bubbles. but diffieulties associated with foreground removal will not be fully resolved. before the first test data [rom new experiments becomes available.," Each tool has its own strengths: The 21cm maps can in principle map smaller bubbles, but difficulties associated with foreground removal will not be fully resolved before the first test data from new experiments becomes available."453 We have given particular attention to applications of (his test based on mapping the distribution of eenulling galaxies., We have given particular attention to applications of this test based on mapping the distribution of emitting galaxies.454 For reasonable expectations. the ionized bubbles during overlap will be large enough to permit transmission of Iflux through an otherwise neutral medium.," For reasonable expectations, the ionized bubbles during overlap will be large enough to permit transmission of flux through an otherwise neutral medium."455 Moreover. the number density of emitting galaxies provides a sample of several objects per bubble.," Moreover, the number density of emitting galaxies provides a sample of several objects per bubble."456 Complementary survevs for Lyman break selected: ealaxies can provide control samples to separate the topological signature of structure lormation from that of reionization., Complementary surveys for Lyman break selected galaxies can provide control samples to separate the topological signature of structure formation from that of reionization.457 Applications of this test are practical at redshilts up to 6.9 with CCD cameras. and at least to z~10 with the new generation of large format near-inlrared detectors now becoming available.," Applications of this test are practical at redshifts up to $6.9$ with CCD cameras, and at least to $z\sim 10$ with the new generation of large format near-infrared detectors now becoming available."458 Indeed. several survevs for eealaxies al 2Z8 are already underway.," Indeed, several surveys for galaxies at $z\ga 8$ are already underway."459 Thus. egalaxies could well provide our first direct evidence for individual ionized bubbles in the epoch of reionization.," Thus, galaxies could well provide our first direct evidence for individual ionized bubbles in the epoch of reionization."460 Topological tests lor the overlap phase would be practical once a contiguous volume corresponding to several bubbles had been mapped., Topological tests for the overlap phase would be practical once a contiguous volume corresponding to several bubbles had been mapped.461 IT thank Steven Furlanetto. Benedetta Ciardi. Michael Strauss. and Sangeeta Malhotra for helpful discussions on various aspects of this idea over the last few vears.," I thank Steven Furlanetto, Benedetta Ciardi, Michael Strauss, and Sangeeta Malhotra for helpful discussions on various aspects of this idea over the last few years."462Observations of the inner regions (X 5 AU) of circustellar disks are esseutial for obtaining a comete undersandiug of star aud planet formation.,Observations of the inner regions $\lesssim$ 5 AU) of circumstellar disks are essential for obtaining a complete understanding of star and planet formation.463 The iuner disk iucracts with the central star. thereby controlling he ac‘cretion aud ejection of material :uid. setting he timescale for star formation aud disk evolution.," The inner disk interacts with the central star, thereby controlling the accretion and ejection of material and setting the timescale for star formation and disk evolution."464 lu adition. inuer disks are the likely birthplace of orrestyjal planets.," In addition, inner disks are the likely birthplace of terrestrial planets."465 However. these regions ax» iticult to study. )ecause of their small angular size at the distance of nearw ostar-foriuing regions aud the proximity to hei xweut stars.," However, these regions are difficult to study, because of their small angular size at the distance of nearby star-forming regions and the proximity to their parent stars."466 Receitly. sieuificaut advancements iu our πο.anding of inner disks have Όσοι made with Wo Coniementarv techniques IR interferometry and high-esolutiou spectroscopy.," Recently, significant advancements in our understanding of inner disks have been made with two complementary techniques: IR interferometry and high-resolution spectroscopy."467 IR interferonetrv ds capable of observing thermal ciission from the clusty COMpPoOlrent of disks with resolutions of a few las (probing size scales down to a few huudyrect o ean AU: Alillan-Ciavot et 11999: Eisner et 22003:ls Akesou et 22005b. Monnicr et 22005).," IR interferometry is capable of observing thermal emission from the dusty component of disks with resolutions of a few mas (probing size scales down to a few hundredths of an AU; Millan-Gabet et 1999; Eisner et 2003; Akeson et 2005b, Monnier et 2005)."468 These observatious have shown that standard. optically thick accretion dis- models (such as outlined bv IHilleubraud 19923) fail to sinultaueouslv fit spectral energy. distributious (SEDs) and visibilities (Millau-Ciabetetal.2001:AXeson 2002).," These observations have shown that standard, optically thick accretion disk models (such as outlined by \citealt{Hillenbrand92}) ) fail to simultaneously fit spectral energy distributions (SEDs) and visibilities \citep{Millan-Gabet01, Akeson02}."469. Better fits to visibilities were obtained with a- optically thin iuner eas disk iuterior to a hot. putffed-u wall of dust (Dullemondetal.2001:Natta2001).. with the dust wall located where temperatures are hnieh cnough to sublimate silicate erains (Monnierctal. 2005).," Better fits to visibilities were obtained with an optically thin inner gas disk interior to a hot, puffed-up wall of dust \citep{Dullemond01, Natta01}, with the dust wall located where temperatures are high enough to sublimate silicate grains \citep{Monnier05}."470. Recent observations and modeling efforts have introduced complications to this simple picture. including a significant source of ciissiou of uuknowu origi the dust sublimation radius (foranexten-sivereview.seeDullemoud&Mounier 2010).," Recent observations and modeling efforts have introduced complications to this simple picture, including a significant source of emission of unknown origin the dust sublimation radius \citep[for an extensive review, see][]{Dullemond10}."471.. ILosvever. the major conclusion that there is a defined ier radius consistent with dust sublimation Sill holds true.," However, the major conclusion — that there is a defined inner radius consistent with dust sublimation — still holds true."472 The complementary technique of high-resolutiou spectroscopy has been— used to study rovibrational cnussion from hot gaseous moleciles. specifically IT20 and CO (e.g...Brittainetal.2003:Najita2001:Salvketal. 2008).. that originate im the iuncer disk atinosphere.," The complementary technique of high-resolution spectroscopy has been used to study rovibrational emission from hot gaseous molecules, specifically $_2$ O and CO \citep[e.g.,][]{Brittain03,Najita03, Blake04, Carr04, Rettig04, Salyk08}, that originate in the inner disk atmosphere."473 Because of the high temperatures (21000 IX) required to populate vibrationally excited states. CO vibrational cinission originates at disk radi similar to those probed by IR interferometry <a few AU).," Because of the high temperatures $\gtrsim 1000$ K) required to populate vibrationally excited states, CO vibrational emission originates at disk radii similar to those probed by IR interferometry $\lesssim$ a few AU)."474 When the spectral resolution is high cuouerh that the emission lines are spectrally resolved. the li1e profile acts asx a proxy for the spatial location of he eus.ons under the assuniptiou that the enüssion origilates In a rotating Keplerian disk.," When the spectral resolution is high enough that the emission lines are spectrally resolved, the line profile acts as a proxy for the spatial location of the gas, under the assumption that the emission originates in a rotating Keplerian disk."475 Siuce the emission ine wings represent the highest observed velocities. the fux in the line wines originates at the inner edge of the ujolecular disk.," Since the emission line wings represent the highest observed velocities, the flux in the line wings originates at the inner edge of the molecular disk."476 Thus. Cluission lines (after a correction for disk inclination) eau," Thus, emission lines (after a correction for disk inclination) can"477((r)) for different epochs «irectly using spectroscopic redshifts (LeFevreefαἱ.1996:Carlbere«al.1997.1999:Sinallefal. 1999).,"$\xi(r)$ ) for different epochs directly using spectroscopic redshifts \citep{leFevre96,carlberg97,carlberg99,small99}."478. These two techuiques. however. sulfer from. cliferent limitations that have resricted their uility.," These two techniques, however, suffer from different limitations that have restricted their utility."479 Sttdies which utilize cli[Iereut magnittide ittervals are limiecd in that au apο maguitude selection samsles galaxies of ¢illerent intrinsic |uninosities al cifferent redsifts. complicating the analysis. considerably.," Studies which utilize different magnitude intervals are limited in that an apparent magnitude selection samples galaxies of different intrinsic luminosities at different redshifts, complicating the analysis considerably."480 Furtjerigore. the clustering of galaxies Ol stuall scales is the result of a highly ou-linear. complex p'Ocess: acl. therefore. the actual validity- of he power law model for the evoluion of the spatial clustering fuuction is uot guvanteec. altlough it is at least useful ¢lagnostic.," Furthermore, the clustering of galaxies on small scales is the result of a highly non-linear, complex process; and, therefore, the actual validity of the power law model for the evolution of the spatial clustering function is not guaranteed, although it is at least a useful diagnostic."481 Finally. this approach is also lunited by the ayplicability of the asstumecl recdshi clistribtjon. which cau heaviM7 influence the theoretical conversion [rom aigular coordiuates to spatial coordinates.," Finally, this approach is also limited by the applicability of the assumed redshift distribution, which can heavily influence the theoretical conversion from angular coordinates to spatial coordinates."482 The spectroscopic approach. on the other haud. is hindered either by tte size of the available samples. especially when the data is binued into clistinet redshift intervals. or by the depth or wiclt1 of the survey. (which implies either a redshift variable. intrinsic bumiuosity selection efTect or possible contamination [rou strong clusteriug).," The spectroscopic approach, on the other hand, is hindered either by the size of the available samples, especially when the data is binned into distinct redshift intervals, or by the depth or width of the survey (which implies either a redshift variable, intrinsic luminosity selection effect or possible contamination from strong clustering)."483 For example. LeFevreetal(11996) analyze the spatial clustering for 591 galaxies iu the CFRS with J«22.5. Siuallefal.(1909) analyze the spatial clustering of 831 galaxies with rpom o lneasure the evolutiou in the correlation length for 0.2<2<cU0.5. auc Carlbergefal.(1JOT) use a sample of 218 galaxies wih A«uw21.5 while Carlergefab(1999) use 2300 high intri uniiosity galaxies distributed over a wide area. to clete‘mune tje spatial correlation fujcton Tereit epochs.," For example, \citet{leFevre96} analyze the spatial clustering for 591 galaxies in the CFRS with $I < 22.5$, \citet{small99} analyze the spatial clustering of 831 galaxies with $r \leq 21^m$ to measure the evolution in the correlation length for $0.2 \leq z \leq 0.5$, and \citet{carlberg97} use a sample of 248 galaxies with $K < 21.5$ while \citet{carlberg99} use 2300 high intrinsic luminosity galaxies distributed over a wide area, to determine the spatial correlation function for different epochs."484 In this yaper. we continue our developi falew technique which uses photometric redshifts O lease the angular correlation functiOl ln reshift shells (Bruner1997:Connollyefad.1998:Brueretal. 1999b).," In this paper, we continue our development of a new technique which uses photometric redshifts to measure the angular correlation function in redshift shells \citep{myThesis,connolly98,brunner99c}."485. This j0vel adproach nMinimizes the galaxs: projection ellect inherent in standard augular correlation measureurents. wlile utilizing a signiicantly large sample that nininizes tje. effects of shot nolse i1 OUP alalysis.," This novel approach minimizes the galaxy projection effect inherent in standard angular correlation measurements, while utilizing a significantly large sample that minimizes the effects of shot noise in our analysis."486 By adoptiug au etserible approach. we are able ο Weastlre he evolution of clustering with both redshift aud intrinsic luuiuosity.," By adopting an ensemble approach, we are able to measure the evolution of clustering with both redshift and intrinsic luminosity."487" Unless otherwise i0ted. we assume /;=1.0. Qa,=0.3. and Q4=0.7. throughout this pagel."," Unless otherwise noted, we assume $h = 1.0$, $\Omega_M =4880.3$, and $\Omega_\Lambda = 0.7$, throughout this paper."489 The observations aud reduction of the data used in this analysis have been extensively detailed elsewhere (Brunuer1997:Brunuerefaf.1997.1999a).," The observations and reduction of the data used in this analysis have been extensively detailed elsewhere \citep{myThesis,brunner97,brunner99}."490. In this section. we discuss the importaut poiuts which impact the rest of our ciscussiou.," In this section, we discuss the important points which impact the rest of our discussion."491 The photometric data analyzed in this paper are located at 1120. +E9:30 covering approximately," The photometric data analyzed in this paper are located at 14:20, +52:30 covering approximately"492Charlot Bruzual 2007 models with the Padova 1994 evolutionary tracks (7) anda? mass function.,Charlot Bruzual 2007 models with the Padova 1994 evolutionary tracks \citep{bertelli1994} and a \citet{chabrier2003} mass function.493" We use a ? extinction law to estimate the internal extinction, and fit the photometry at observed wavelengths A« Ίθμπι to exclude PAH emission."," We use a \citet{calzetti2000}494 extinction law to estimate the internal extinction, and fit the photometry at observed wavelengths $\lambda<10\mu$ m to exclude PAH emission."495 We refer the reader to ffor further details., We refer the reader to for further details.496" In deriving confidence intervals on the age and extinction, we find that the data are best fit by a 10 Myr population."," In deriving confidence intervals on the age and extinction, we find that the data are best fit by a 10 Myr population."497" The solutions for the emission-weighted age bifurcate though, permitting both very young templates and solutions with ages of a few Gyrs."," The solutions for the emission-weighted age bifurcate though, permitting both very young templates and solutions with ages of a few Gyrs."498 The confidence intervals on the age are t«90 Myrs and 1.4«t2.6 Gyrs., The confidence intervals on the age are $t<90$ Myrs and $1.4<t<2.6$ Gyrs.499 We note however that strong observed submillimeter emission provides a compelling argument for a very young stellar population., We note however that strong observed submillimeter emission provides a compelling argument for a very young stellar population.500 The extinction meanwhile is constrained to be Ay=3.8*0 confidence)., The extinction meanwhile is constrained to be $A_V=3.8^{+0.5}_{-1.0}$ confidence).501 The confidence interval reduces to Ay=3.8793 if one considers only the younger age solutions., The confidence interval reduces to $A_V=3.8^{+0.5}_{-0.2}$ if one considers only the younger age solutions.502" Next, we update our estimate of the stellar mass using the code (?),, as inI."," Next, we update our estimate of the stellar mass using the code \citep{blanton2007}, as in."503" We fit the combined flux from images A and B, using the data at observed wavelengths of -8um."," We fit the combined flux from images A and B, using the data at observed wavelengths of $-$."504".Forz=2.79andAy =3.8, we obtain a stellar mass M.=4x10°(uap/100)-! Μο. This value is roughly a factor of 3 lower than the previously published result."," For $z=2.79$ and $A_V=3.8$, we obtain a stellar mass $M_*=4\times10^{9}$ $M_\sun$ This value is roughly a factor of 3 lower than the previously published result."505" The added leverage from the ddata point is the largest factor in the decrease, with the addition of this data point accounting for roughly a factor of 2."," The added leverage from the data point is the largest factor in the decrease, with the addition of this data point accounting for roughly a factor of 2."506" The revised magnification estimates account for the remainder of the change, while the changes in redshift and extinction have only a minor impact."," The revised magnification estimates account for the remainder of the change, while the changes in redshift and extinction have only a minor impact."507 The updated stellar mass implies that the target is a low-mass dwarf galaxy., The updated stellar mass implies that the target is a low-mass dwarf galaxy.508 There exist multiple different techniques for estimating the total infrared luminosity for a galaxy where the infrared emission is dominated by star formation., There exist multiple different techniques for estimating the total infrared luminosity for a galaxy where the infrared emission is dominated by star formation.509 The preferred technique is to use data spanning the peak of the far-infrared (FIR) spectral energy distribution and directly fit a modified blackbody to the far-infrared emission., The preferred technique is to use data spanning the peak of the far-infrared (FIR) spectral energy distribution and directly fit a modified blackbody to the far-infrared emission.510" This technique, which should now become the default method in the era ofHerschel,, provides the most straightforward constraint on DyR with the added advantage of directly yielding the temperature of the dust if the redshift is known."," This technique, which should now become the default method in the era of, provides the most straightforward constraint on $L_{IR}$ with the added advantage of directly yielding the temperature of the dust if the redshift is known."511" Many past studies, in the absence of the requisite ΕΤΗ, data, have instead utilized either 24 eemission or PAH luminosities to estimate L;g."," Many past studies, in the absence of the requisite FIR data, have instead utilized either 24 emission or PAH luminosities to estimate $L_{IR}$."512" With the unique data sets available for our lensed galaxy behind the Bullet Cluster, we are able to compare estimates via all three approaches and assess the level of consistency for this particular dusty starburst."," With the unique data sets available for our lensed galaxy behind the Bullet Cluster, we are able to compare estimates via all three approaches and assess the level of consistency for this particular dusty starburst."513steeper slope.,steeper slope.514 The upper-mass slope only matches the slope of the CMP if fragmentation is independent of mass for cores above the knee in the IMF at 0.5M..., The upper-mass slope only matches the slope of the CMF if fragmentation is independent of mass for cores above the knee in the IMF at $0.5 M_\odot$.515 The problem with the upper-mass slope can be alleviated somewhat by assuming that all stars form with the field binary fraction (rising from for M-dwarfs to for G-dwarts)., The problem with the upper-mass slope can be alleviated somewhat by assuming that all stars form with the field binary fraction (rising from for M-dwarfs to for G-dwarfs).516 However. this solution conflicts with observations that the initial binary fraction for stars >1M. is consistent with unity (Goodwin Kroupa 2005: Duchénne et al.," However, this solution conflicts with observations that the initial binary fraction for stars $>1 M_\odot$ is consistent with unity (Goodwin Kroupa 2005; Duchênne et al."517 2007: Goodwin et al., 2007; Goodwin et al.518 2007)., 2007).519 These observations suggest that there must be a fairly rapid transition between 0.5 and 1M. from a low to a high primordial binary fraction which will result in too-steep an upper-mass slope of the IMF., These observations suggest that there must be a fairly rapid transition between $0.5$ and $1 M_\odot$ from a low to a high primordial binary fraction which will result in too-steep an upper-mass slope of the IMF.520 We have assumed that the mass ratio of binaries Is a flat distribution., We have assumed that the mass ratio of binaries is a flat distribution.521 Biasing the mass ratio distribution to low-g (1e., Biasing the mass ratio distribution to $q$ (ie.522 highly unequal mass systems) improves the problems at the high-mass end of the IMF slightly., highly unequal mass systems) improves the problems at the high-mass end of the IMF slightly.523 If most high-mass cores produce one large star and one or two very low-mass stars. then the IMF at the high-mass end becomes more similar to the MSMF (as this is dominated by one of the stars).," If most high-mass cores produce one large star and one or two very low-mass stars, then the IMF at the high-mass end becomes more similar to the MSMF (as this is dominated by one of the stars)."524 However. the mass ratio distribution needs to be very biased for this to have a significant effect.," However, the mass ratio distribution needs to be very biased for this to have a significant effect."525 The too-steep slope of the upper-end of the IMF can also be solved by assuming that the SFE increases with increasing core mass (in just the right way)., The too-steep slope of the upper-end of the IMF can also be solved by assuming that the SFE increases with increasing core mass (in just the right way).526 However. we feel this solution is unlikely as the SFE would have to be fine-tuned to give the correct slope and it would seem peculiar to postulate that low-mass cores produce stars at very low efficiencies (~ 10%)). whilst higher-mass cores are able to convert more of their gas (~ 30%)) into stars (the opposite of what might be expected from arguments based on feedback).," However, we feel this solution is unlikely as the SFE would have to be fine-tuned to give the correct slope and it would seem peculiar to postulate that low-mass cores produce stars at very low efficiencies $\sim 10$ ), whilst higher-mass cores are able to convert more of their gas $\sim 30$ ) into stars (the opposite of what might be expected from arguments based on feedback)."527 We have shown that the observed mass functions of cores in Orion B (Nutter Ward-Thompson 2007) can give rise to the IMF of stars., We have shown that the observed mass functions of cores in Orion B (Nutter Ward-Thompson 2007) can give rise to the IMF of stars.528 In particular we have shown that. to produce the stellarsub-stellar IMF. the majority of these cores must fragment into multiple systems.," In particular we have shown that, to produce the stellar IMF, the majority of these cores must fragment into multiple systems."529 However. there are a number of issues about cores and the CMF that are worth discussing in this context.," However, there are a number of issues about cores and the CMF that are worth discussing in this context."530" It should be noted that it may not be fragmentation into ""cores! in clusters that sets the IMF of stars.", It should be noted that it may not be fragmentation into `cores' in clusters that sets the IMF of stars.531 If competitive accretion (see Bonnell et al., If competitive accretion (see Bonnell et al.532 2007 and references therein) is the dominant process. then the CMF at best acts to set the initial masses upon which competitive accretion begins to work.," 2007 and references therein) is the dominant process, then the CMF at best acts to set the initial masses upon which competitive accretion begins to work."533 In such a scenario there would be little or no relationship between the CMF and the IMF., In such a scenario there would be little or no relationship between the CMF and the IMF.534 However. we would argue that the form of the CMF in diffuse star forming regions have a direct relevance to the origin and form of the IMF.," However, we would argue that the form of the CMF in diffuse star forming regions have a direct relevance to the origin and form of the IMF."535 Given the apparent universality of the IMF across a wide range of star forming environments (e.g. Kroupa 2002) we are presented with two options., Given the apparent universality of the IMF across a wide range of star forming environments (e.g. Kroupa 2002) we are presented with two options.536 Firstly. that the mechanism(s) that produce the IMF are fundamentally different in different environments. but they always produce the same outcome.," Firstly, that the mechanism(s) that produce the IMF are fundamentally different in different environments, but they always produce the same outcome."537 Or. secondly. that there is a single. underlying. mechanism that produces the IMF i all environments.," Or, secondly, that there is a single, underlying, mechanism that produces the IMF in all environments."538 The latter possibility appeals due to its simplicity. and would suggest that the form of the CMF is the driving factor in establishing the form of the IMF. and that the form of the CMF is roughly the same in diffuse and clustered regions (even if the cores themselves are different in. spacial size).," The latter possibility appeals due to its simplicity, and would suggest that the form of the CMF is the driving factor in establishing the form of the IMF, and that the form of the CMF is roughly the same in diffuse and clustered regions (even if the cores themselves are different in spacial size)."539 Indeed. simulations of turbulence always seem to produce roughly normal CMFs whatever the environment.," Indeed, simulations of turbulence always seem to produce roughly log-normal CMFs whatever the environment."540 We have examined the relationship between the core mass function (CMF) and the stellar initial mass function (IMF)., We have examined the relationship between the core mass function (CMF) and the stellar initial mass function (IMF).541 We use the Orion CMF from Nutter Ward-Thompson (2007) as a ‘standard’ which we fit using a log-normal distribution., We use the Orion CMF from Nutter Ward-Thompson (2007) as a `standard' which we fit using a log-normal distribution.542 We note that this CMF is not dissimilar to the stellar (Kroupa 2002) IMF shifted upwards in mass by a factor of 8 (see also Alves 2007)., We note that this CMF is not dissimilar to the stellar (Kroupa 2002) IMF shifted upwards in mass by a factor of $8$ (see also Alves 2007).543 We randomly sample cores from the CMF and assumed that each core produces a certain number of stars with à random distribution of masses between the components., We randomly sample cores from the CMF and assumed that each core produces a certain number of stars with a random distribution of masses between the components.544 The canonical IMF is reproduced very well by à scenario in which every low-mass cores fragment into binartes. and high-mass cores fragment into a multiple system with a ratio of binaries-to-triples of 3:1 (see e.g. Goodwin Kroupa 2005) and a star formation efficiency (SFE) of ~30%.," The canonical IMF is reproduced very well by a scenario in which every low-mass cores fragment into binaries, and high-mass cores fragment into a multiple system with a ratio of binaries-to-triples of $3\!:\!1$ (see e.g. Goodwin Kroupa 2005) and a star formation efficiency (SFE) of $\sim\! 30$."545. Dynamical disruption (Kroupa 1995a.b: Goodwin Whitworth 2007) of systems then evolves the initial binary fraction of unity into the field population.," Dynamical disruption (Kroupa 1995a,b; Goodwin Whitworth 2007) of systems then evolves the initial binary fraction of unity into the field population."546 We find that a scenario in which low-mass stars preferentially form single systems (e.g. Lada 2006) cannot reproduce the observed IMF from a log-normal CMF., We find that a scenario in which low-mass stars preferentially form single systems (e.g. Lada 2006) cannot reproduce the observed IMF from a log-normal CMF.547 Firstly. the slope of the high-mass IMF ts too steep.," Firstly, the slope of the high-mass IMF is too steep."548 Secondly. and most seriously. this model cannot reproduce the correct numbers of brown dwarfs to high-mass stars.," Secondly, and most seriously, this model cannot reproduce the correct numbers of brown dwarfs to high-mass stars."549 The best-fit to the canonical IMF is found when the SFE is only -15%., The best-fit to the canonical IMF is found when the SFE is only $\sim\! 15$.550. Such a low SFE is required. as the only way in which brown dwarfs may be produced in significant numbers is through the formation of a single brown dwarf from à core.," Such a low SFE is required, as the only way in which brown dwarfs may be produced in significant numbers is through the formation of a single brown dwarf from a core."551 Higher SFEs are required to produce sufficient. high-mass stars. however such SFEs significantly under-produce brown dwarfs and low-mass stars.," Higher SFEs are required to produce sufficient high-mass stars, however such SFEs significantly under-produce brown dwarfs and low-mass stars."552 A lingering question is the value of the star formation efficiency that must be applied to fit the IMF., A lingering question is the value of the star formation efficiency that must be applied to fit the IMF.553 The best-fit value of € in the fully multiple model suggest that only ~30% of the mass in a core ends-up in the stars which that core forms (a similar value for the SFE is found by Alves et al., The best-fit value of $\epsilon$ in the fully multiple model suggest that only $\sim\! 30$ of the mass in a core ends-up in the stars which that core forms (a similar value for the SFE is found by Alves et al.554 2007)., 2007).555 This seems a very low value and may suggest that the determinations of the absolute core masses are wrong., This seems a very low value and may suggest that the determinations of the absolute core masses are wrong.556 Another possibility i5 that feedback from jets is far more efficient than previously thought and manages to disperse most of the gas initially in the core., Another possibility is that feedback from jets is far more efficient than previously thought and manages to disperse most of the gas initially in the core.557" A final possibility ts that we are not observing ""typical cores which produce the IMF and that the observed CMFS will produce somewhat top-heavy IMFs (cf.", A final possibility is that we are not observing `typical' cores which produce the IMF and that the observed CMFs will produce somewhat top-heavy IMFs (cf.558 Taurus. Goodwin et al.," Taurus, Goodwin et al."559 200450., 2004c).560 We conclude that a model in which«// stars and brown dwarfs form in multiple systems from a log-normal core mass distribution provides a very good fit the observed IMF., We conclude that a model in which stars and brown dwarfs form in multiple systems from a log-normal core mass distribution provides a very good fit the observed IMF.561" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ "562" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $"563" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—1"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^"564" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{"565" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10."," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{1"566" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13"567" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 "," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}"568" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$"569" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +)"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$"570" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) "," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^"571" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) I"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{"572" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) II"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+"573" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) IIC"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+}"574" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) IICO"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+}$"575The resulting fit NOT aud ALO pressure profiles are used to solve for the radial profile of Vandre} (Equation 5).,The resulting fit N07 and A10 pressure profiles are used to solve for the radial profile of $\Ysph(r)$ (Equation \ref{eq:Ysph}) ).576 For cach acceted. link in the AICAIC. we fit the function described x Equation 19 assmuineg a coustaut fas0.12 and pa.=1.17.," For each accepted link in the MCMC, we fit the function described by Equation \ref{eq:YsphNFW}577 assuming a constant $\fgas=0.13$ and $\mu_{\rm e}=1.17$."578 The resulting mass profiles. computed using Ixuation 12.. are used to fud ra ancl Αν). which arc- respectively the radius within which the average deusity is A times greater than the critical density of the uuiverse at that redshift. aud the total lass contained witvin thatradius.," The resulting mass profiles, computed using Equation \ref{eq:Mtot}, , are used to find $r_{\Delta}$ and $\Mtot(r_{\Delta})$, which are respectively the radius within which the average density is $\Delta$ times greater than the critical density of the universe at that redshift, and the total mass contained within thatradius."579 As in M09. we report ry. Ανν). aud for A= with statistical error bars. in Your)Table 1..," As in M09, we report $r_{\Delta}$, $\Mtot(r_{\Delta})$, and $\Ysph(r_{\Delta})$ for $\Delta=[2500,500]$, with statistical error bars, in Table \ref{table:derivedQuants}."580 We discuss [2500.systematics500). along with our co1cTusious iu Section ??.., We discuss systematics along with our conclusions in Section \ref{conc}.581 We conclude that this method is remarkably consistcut eiven the simplifving assumptions required to derive total nass using the virial relation and SZE data alone with the X-ray ouly aud N-ray|SZE mass determination methods in MO (see Table 1)5, We conclude that this method is remarkably consistent — given the simplifying assumptions required to derive total mass using the virial relation and SZE data alone — with the X-ray only and X-ray+SZE mass determination methods in M09 (see Table \ref{table:derivedQuants}) ).582 The assumption of constant f=0.13 has perhaps tje largest systematic iupact on the derived values of Mr) and ra for overdeusitv A., The assumption of constant $\fgas=0.13$ has perhaps the largest systematic impact on the derived values of $\Mtot(r_{\Delta})$ and $r_{\Delta}$ for overdensity $\Delta$.583 Thο radial lass xofile ALG) is x Vas can ])j6 seen by examine he relation between the NEW 4xuanneter py aud in Equation 11..," The radial mass profile $\Mtot(r)$ is $\propto \fgas^{-1/2}$ , as can be seen by examining the relation between the NFW parameter $\rho_0$ and in Equation \ref{eq:UgravNFW}."584 Ikvever. any change in Afar(re) atfects ry and therefore Myr). so the systematic change iu the ass at fixed overdensity ds arecr than a simple rescaling by the inverse square root of the ratio of the correct to the assumed.fos...," However, any change in $\Mtot(r)$ affects $r_{\Delta}$ and therefore $\Mtot(r_{\Delta})$, so the systematic change in the mass at fixed overdensity is larger than a simple rescaling by the inverse square root of the ratio of the correct to the assumed."585 Fitting the same data with an assumed for.=11. for example. increases Mr) by an average of (rather than the change in the profile Af (r7).," Fitting the same data with an assumed $\fgas=0.11$, for example, increases $\Mtot(r_{\Delta})$ by an average of (rather than the change in the profile $\Mtot(r)$ )."586 The assmuption that 44.LAT. bv contrast. can be expected to have a much smaller impact on the mass determination method preseuted here.," The assumption that $\mu_{\rm e}=1.17$, by contrast, can be expected to have a much smaller impact on the mass determination method presented here."587For typical abundance eradients due to inetal euriclunent. pi varies ou the ~| levelwhich οjuges the (1|1/44) factor in Equatio1 15 on the ~0.5% level.,"For typical abundance gradients due to metal enrichment, $\mu_{\rm e}$ varies on the $\sim 1\%$ level, which changes the $(1 + 1/\mu_{\rm e})$ factor in Equation \ref{eq:YsphNFW} on the $\sim 0.5\%$ level."588 Large systematic deviations in metalicity therefore affect the fit Aro(ir) at the (25% level., Large systematic deviations in metallicity therefore affect the fit $\Mtot(r)$ at the $\sim 0.25\%$ level.589 The assmuptiou of a single. constant metallicity is also common in X-rav studies of hieh recshift chsters. where the limited πο of N-rav counts is iusufficieu to constrain more than a sinee spectroscoplc biu.," The assumption of a single, constant metallicity is also common in X-ray studies of high redshift clusters, where the limited number of X-ray counts is insufficient to constrain more than a single spectroscopic bin."590 Ou the other haud. helium sediucutatio iint1 abseice of magnetic fields. in a cluser unudisturbec for 5 Cars. could increase ji. du the core region by ~n. (Peng&Nagai2009).," On the other hand, helium sedimentation in the absence of magnetic fields, in a cluster undisturbed for 3 Gyrs, could increase $\mu_{\rm e}$ in the core region by $\sim 5\%$ \citep{peng2009}."591. Using the results of Peuο&Nagai(2009).. we note that the sedinentatio1i of helimm has litte effect ou the average Ho OV On fdr) at laree The expectation is that merecrs and magnetic fields wil both suppress holiuu secimenutation (Pe1ο&Nagai2009).," Using the results of \citet{peng2009}, we note that the sedimentation of helium has little effect on the average $\mu_{\rm e}$ or on $\mu_{\rm e}(r)$ at large The expectation is that mergers and magnetic fields will both suppress helium sedimentation \citep{peng2009}."592. Another poteuti:d source of bias is due to uncertainties iu the calibration of the SZE data., Another potential source of bias is due to uncertainties in the calibration of the SZE data.593 As discussed. iu Achovejetal.(207).. the absolute calibration of SZA da ais knownto better than aud the variation TOi observation ο observation in amplitude of a fiux calibrator (in this case Mars) is $5 5%. Calibration errors would result iu scaiar svsteniatic errors 1 ithe fit pressure xofile aud. have a linear inpact ou," As discussed in \citet{muchovej2007}, the absolute calibration of SZA data is knownto better than , and the variation from observation to observation in amplitude of a flux calibrator (in this case Mars) is $\lesssim 5 \%$ Calibration errors would result in scalar systematic errors in the fit pressure profile and have a linear impact on"594a stun of three components: bulge. disk. and dark matter halo.,"a sum of three components: bulge, disk, and dark matter halo."595 A convenient way to cleseribe the Galactic potential has been proposed by (MiyamotoanclNagai.1975).. while a series of more detailed models were constructed by (IxuijkenandGilmore.1989). and used in modeling the galactic halo population of neutron stars1998).," A convenient way to describe the Galactic potential has been proposed by \cite{1975PASJ...27..533M}, while a series of more detailed models were constructed by \cite{1989MNRAS.239..571K}596 and used in modeling the galactic halo population of neutron stars."597. The (AlivamotoandNagai.1975) potential for a galactic disk and bulee is where e; and 6; are the parameters. M is the mass. and /?=[usmag.," The \cite{1975PASJ...27..533M} potential for a galactic disk and bulge is where $a_i$ and $b_i$ are the parameters, $M$ is the mass, and $R=\sqrt{x^2 = y^2}$ ."598 he dark matter halo potential is spherically symmetric corresponds to a mass distribution. p—p.f71|(rr)].," The dark matter halo potential is spherically symmetric corresponds to a mass distribution $\rho = \rho_c/[1 +599(r/r_c)^2]$."600"2 The mass of such halo is infinite. so we introduce a cutoll value 724,=I00kpc above which the density of the halo falls to zero."," The mass of such halo is infinite, so we introduce a cutoff value $r_{cut} = 100\,$ kpc above which the density of the halo falls to zero."601 While the details of the model of galactic potential are not important for this study we have to adopt a particular value of the masses ancl sizes of cach of the components., While the details of the model of galactic potential are not important for this study we have to adopt a particular value of the masses and sizes of each of the components.602 We use the values of the parameters asdetermined by (BlaesancRajagopal.L991) for the Alilky Wav: e;=Okpe. bj=O.277 kpc. ae4.2kpe. by—0.198 kpe. A4;=112.1017AZ. Als—SOS101AL... ro=60kpe. and Adj—5.01077 AL.," We use the values of the parameters asdetermined by \cite{1991ApJ...381..210B} for the Milky Way: $a_1 =0\,$ kpc, $b_1 = 0.277\,$ kpc, $a_2 = 4.2\,$ kpc, $b_2 = 0.198\,$ kpc, $M_1 =6031.12\times 10 ^{10}\,M_\odot$, $M_2 = 8.78\times60410^{10}\,M_\odot$, $r_c = 6.0\,$ kpc, and $M_h = 5.0 \times60510^{10}\,M_\odot$ ."606" We assume that the distribution of binaries in. our model galaxy follows the mass distribution in the voung disk (Paczváski.1990).. that is The raclial distribution is exponential with with Row,= 4.5kpe and extends to Rie= 20kpc."," We assume that the distribution of binaries in our model galaxy follows the mass distribution in the young disk \cite{1990ApJ...348..485P}, that is The radial distribution is exponential with with $R_{exp} =6074.5\,$ kpc and extends to $R_{max}= 20\,$ kpc."608 The vertical distribution is pls)xe and no= 75pc.," The vertical distribution is $p(z) \propto e^{-z/z_{exp}}$ and $z_{exp} =60975\,$ pc."610 We note that this is not à self. consistent approach: the density inferred. [rom the disk potential is not the same as the clensity of binaries., We note that this is not a self consistent approach: the density inferred from the disk potential is not the same as the density of binaries.611 However in this work we are not interested in determining high accuracy positions around the host galaxy. and rather with an estimate of the eeneral properties of the distribution of compact object mergers.," However in this work we are not interested in determining high accuracy positions around the host galaxy, and rather with an estimate of the general properties of the distribution of compact object mergers."612 Each binary moves initially with the local rotational velocity in the galactic disk., Each binary moves initially with the local rotational velocity in the galactic disk.613 After each supernova explosion we add an appropriate velocity. provided that the svsten survives the explosion.," After each supernova explosion we add an appropriate velocity, provided that the system survives the explosion."614 We calculate the orbit of each system until it merger time provided that the merger time is smaller than the Hubble time (15 Caves here)., We calculate the orbit of each system until it merger time provided that the merger time is smaller than the Hubble time (15 Gyrs here).615 The kick velocity distribution is not very well known., The kick velocity distribution is not very well known.616" Therefore. we use the population svnthesis code. with four values of the kick. velocity. distribution width: with no kick velocities o= Okm s +. and with o,=200.400.SOO km |."," Therefore, we use the population synthesis code with four values of the kick velocity distribution width: with no kick velocities $\sigma_v =0\,$ km $^{-1}$ , and with $\sigma_v = 200,\, 400,\,617800\,$ km $^{-1}$."618 This covers the range of values this distribution is likely to have., This covers the range of values this distribution is likely to have.619 This the same approach as acloptecl in our previous work (BelezvnskiandBulik. 1999).., This the same approach as adopted in our previous work \cite{BB1998}. .620 The binaries receive kicks for two reasons., The binaries receive kicks for two reasons.621 First. the envelope of the supernovaislost. [rom the system ancl it," First, the envelope of the supernovaislost from the system and it"622The effect. of euvironmeut on galaxy evolution bas long been a subject of intense research aud debate cliscussion).,The effect of environment on galaxy evolution has long been a subject of intense research and debate .623. Kuown environmental effects include tidal eucounters aix mereers. altered Morj»holoegies. alc st‘ipping of gas from disks.," Known environmental effects include tidal encounters and mergers, altered morphologies, and stripping of gas from disks."624 A natiral question is whether the clister environment has signifiaut ellects of the chemical evolution of sealaxies., A natural question is whether the cluster environment has significant effects of the chemical evolution of galaxies.625 This topic has received increasing attention i the last few years., This topic has received increasing attention in the last few years.626 explore the effect of environment on chemical evolutiou Or spirals in the Virgo cluster., explore the effect of environment on chemical evolution for spirals in the Virgo cluster.627 Ενα]ug H II region spectra [rom 9 Vireo spirals. they find e three most H I deficient objects lolave O/H aouucdauces 0.3-0.5 dex higher thau their gas-1ια counterparts.," Examining H II region spectra from 9 Virgo spirals, they find the three most H I deficient objects to have O/H abundances 0.3-0.5 dex higher than their gas-normal counterparts."628 They suggest that |he abuudaice differential results in part. from a lack of iall of metal-poor eas into the spirals in the cluster core., They suggest that the abundance differential results in part from a lack of infall of metal-poor gas into the spirals in the cluster core.629 fit phoolonizzion models to the Virgo data. c«firmiug the alindauce excess lor O/H aud N/O. Other stucles. involviug large-scale spectrose¢yple surveys 2000).. see a qualitatively simiar galactic metalicity depeudence on local galaxy density or eas [raction.," fit photoionization models to the Virgo data, confirming the abundance excess for O/H and N/O. Other studies, involving large-scale spectroscopic surveys , see a qualitatively similar galactic metallicity dependence on local galaxy density or gas fraction."630 analvze a sample οἱ 5060 galaxies in the HyperLeda catalog. concludiug gas-poor galaxies clisplay |igher heavy-eleiuent couteut [or a given stellar πάς».," analyze a sample of 800 galaxies in the HyperLeda catalog, concluding gas-poor galaxies display higher heavy-element content for a given stellar mass."631and the Cepheids (larrisetal.1999:Rejkuba2004;Ferrarese2006).,"and the Cepheids \citep{hhp99,rejkuba04,ferr06}."632. IICIII5 and R122 have not been included in our kinematic study. as our study was completed before publication of these velocities.," HCH15 and R122 have not been included in our kinematic study, as our study was completed before publication of these velocities."633 The weighted velocities used in (his kinematic study do not include (he most recent 25 velocities of previously known GC's published in Rejkubaetal.(2007)., The weighted velocities used in this kinematic study do not include the most recent 25 velocities of previously known GCs published in \cite{rejkuba07}.634. Note that the velocities published in Table 1. do. however. include the Rejkubaetal.(2007) velocities in the quoted final weighted radial velocities Lor completeness.," Note that the velocities published in Table \ref{tab:cat_GC} do, however, include the \cite{rejkuba07} velocities in the quoted final weighted radial velocities for completeness."635 The velocity distribution of the entire sample of 340 is shown in Figure 2. leff). binned in 50 kins ! intervals.," The velocity distribution of the entire sample of 340 is shown in Figure \ref{fig:gausfit_all} ), binned in 50 km $^{-1}$ intervals."636 A fit with a single Gaussian vields a mean velocity of 54647 lan 1 ft. nicely matching the known svstemic velocity of 54147 kms | (Huietal.1995).," A fit with a single Gaussian yields a mean velocity of $546\pm7$ km $^{-1}$ , nicely matching the known systemic velocity of $541\pm7$ km $^{-1}$ \citep{hui95}."637. There is a slight asvmunetiv at the low-velocitv end that is likely due to contamination by a few metal-poor Milkv Way halo stars (also seen in (he metal-poor subpopulation in the bottom left panel. which has a mean velocity determined by (he Gaussian fit as 532413 kin LH.," There is a slight asymmetry at the low-velocity end that is likely due to contamination by a few metal-poor Milky Way halo stars (also seen in the metal-poor subpopulation in the bottom left panel, which has a mean velocity determined by the Gaussian fit as $532\pm13$ km $^{-1}$ )."638 Selecting the clusters with radial velocity uncertainties less than 50 kins ! leaves 226 clusters. plotted in Fig.," Selecting the clusters with radial velocity uncertainties less than 50 km $^{-1}$ leaves 226 clusters, plotted in Fig."639 2. right)., \ref{fig:gausfit_all} ).640 The close fit toa single Gaussian is consistent wilh an isotropic distribution of orbits: the mean velocity is 55445 km |., The close fit toa single Gaussian is consistent with an isotropic distribution of orbits; the mean velocity is $554\pm5$ km $^{-1}$.641 The metal-rich population. with a mean velocity determined by the Gaussian fit of 565411 km b. is plotted in the bottom right panel. and also shows no strong asvimnmetries.," The metal-rich population, with a mean velocity determined by the Gaussian fit of $565\pm11$ km $^{-1}$, is plotted in the bottom right panel, and also shows no strong asymmetries."642 Looking closer at the metal-poor velocity asymmetry. we note (hat the 15 metal-poor clusters between 250 and 300 km 1 (in the region where contamination by Milky Way field stars could occur) are balanced by only two GCs at the high-velocity end on reflection across the svstemic velocitv.," Looking closer at the metal-poor velocity asymmetry, we note that the 15 metal-poor clusters between 250 and 300 km $^{-1}$ (in the region where contamination by Milky Way field stars could occur) are balanced by only two GCs at the high-velocity end on reflection across the systemic velocity."643 The same velocity regions in the metal-rich. population are nearly equally balanced. with low clusters between 250 and 300 km 1 with three clusters αἱ the reflected high-velocity range., The same velocity regions in the metal-rich population are nearly equally balanced with four clusters between 250 and 300 km $^{-1}$ with three clusters at the reflected high-velocity range.644 Interestingly. the four metal-rich clusters between 250 and 300 km ! have projected radii >17 kpe even though the metal-rich population is more centrallv. concentrated (han the metal-poor (seePene.Ford&Freeman2000:Woodley.lluris.&LHlarris2005.among others).," Interestingly, the four metal-rich clusters between 250 and 300 km $^{-1}$ have projected radii $> 17$ kpc even though the metal-rich population is more centrally concentrated than the metal-poor \citep[see][among others]{pff04II,whh05}."645 The metal-poor clusters between 250 and 300 km LH. conversely. are more evenly distributed. with five clusters between projected radii of 5 and 10 kpc. five clusters between 10 and 20 κρο and five clusters bevond 20 kpe from the center of NGC 5128.," The metal-poor clusters between 250 and 300 km $^{-1}$, conversely, are more evenly distributed, with five clusters between projected radii of 5 and 10 kpc, five clusters between 10 and 20 kpc, and five clusters beyond 20 kpc from the center of NGC 5128."646 Some of these low-velocitv. metal-poor objects could be foreground stars with velocities in the realm of GCs in NGC 5128 (ο>250 kins !).," Some of these low-velocity, metal-poor objects could be foreground stars with velocities in the realm of GCs in NGC 5128 $v_r \gtrsim 250$ km $^{-1}$ )."647 However. with only 340 GCs currently confirmed within ~ 45° trom the center of NGC 5128. out of an estimated ~1500 total clusters within 25° (ILarrisetal.2006).. these metal-poor. low-velocily objects could simply be part of a very incomplete GC sample that is also spatially biased.," However, with only 340 GCs currently confirmed within $\sim45$ ' from the center of NGC 5128, out of an estimated $\simeq6481500$ total clusters within 25' \citep{harris06}, these metal-poor, low-velocity objects could simply be part of a very incomplete GC sample that is also spatially biased."649 This potential bias is clearlyshown in Figure 3.. which shows the projected radial distribution as a function of azimuthal angle for our GC sample.," This potential bias is clearlyshown in Figure \ref{fig:gc_thetar}, , which shows the projected radial distribution as a function of azimuthal angle for our GC sample."650 Devond 12 kpe. the two “voids” coincide," Beyond 12 kpc, the two ”voids” coincide"651507 independent measurements of ο in this wav. we arrive al an average value of 0.0011.,"507 independent measurements of $\beta$ in this way, we arrive at an average value of $\beta_{ave} = 0.254 \pm6520.0011$ ."653 While Chis value is only ~4% lower than the value given in Table 1. the difference is statistically significant at the 7.90 level.," While this value is only $\sim 4 \%$ lower than the value given in Table 1, the difference is statistically significant at the $7.9 \sigma$ level."654 This may indicate that “noise” in the Doppler shilts may in fact be impacting Che parameter estimates for the kinematic moclel in a svstemalic wav. as cliscussecl in Section 3.1.," This may indicate that “noise” in the Doppler shifts may in fact be impacting the parameter estimates for the kinematic model in a systematic way, as discussed in Section 3.1."655 As noted above. the upper limit on precessional period derivative of P<5x10? shows that there is no large long-term ο in (he precessional timing properties of 55433.," 	As noted above, the upper limit on precessional period derivative of $\dot P < 5 \times 10^{-5}$ shows that there is no large long-term drift in the precessional timing properties of SS433."656" The presence of jitter in (he svstem implies some ""torque noise"" in the process driving the precession. according to the phase noise model."," The presence of jitter in the system implies some “torque noise” in the process driving the precession, according to the phase noise model."657 However. il this were the case. (hiat noise must average oul over timescales of ~20 vears.," However, if this were the case, that noise must average out over timescales of $\sim 20$ years."658 We can also see from Figure 7 that there are fairly large phase deviations of «Ao~0.1 eveles over limescales as short as ~10 davs., We can also see from Figure 7 that there are fairly large phase deviations of $\Delta \phi \sim 0.1$ cycles over timescales as short as $\sim 10$ days.659 This implies that the torque noise Av has a maximum relative amplitude of al least Thus. the variation in torque can in [act exceed the time-averaged torque driving the precession.," This implies that the torque noise $\Delta \tau$ has a maximum relative amplitude of at least Thus, the variation in torque can in fact exceed the time-averaged torque driving the precession."660 This may be a problem lor certain plvsical models of the precession and timing noise in 55433., This may be a problem for certain physical models of the precession and timing noise in SS433.661 Finally. we note that the phase noise model is incapable of producing the observed Doppler shifts which exceed the maximum amplitude predicted by the kinematic model.," 	Finally, we note that the phase noise model is incapable of producing the observed Doppler shifts which exceed the maximum amplitude predicted by the kinematic model."662 We have considered (he possibility that (he phase noise itself causes (he \-squarecl fitting procedure used to determine the model parameters to svstematically underestimate the true jet velocity. and thus undershoot the maxima.," We have considered the possibility that the phase noise itself causes the $\chi$ -squared fitting procedure used to determine the model parameters to systematically underestimate the true jet velocity, and thus “undershoot” the maxima."663 Iowever. Monte Carlo simulations of data sets with higher (rue velocities and phase noise identical to that observed here fail to produce such undershooting.," However, Monte Carlo simulations of data sets with higher true velocities and phase noise identical to that observed here fail to produce such undershooting."664 Therefore. we conclude that phase noise model cannot reproduce the observed Doppler shift residuals near the maximum projected velocities.," Therefore, we conclude that phase noise model cannot reproduce the observed Doppler shift residuals near the maximum projected velocities."665improve the accuracy of the spectral measurement.,improve the accuracy of the spectral measurement.666" Given this and the brightness of the BAT data, if a spectral break is present, the XRT+BAT data are not sensitive to it."," Given this and the brightness of the BAT data, if a spectral break is present, the $+$ BAT data are not sensitive to it."667" The expected Galactic line-of-sight absorption for MAXI J1659—152 is 1.7x10?! ccm""? etal.2005), however the fitted absorption(Kalberla column is higher and variable, indicating an additional intrinsic absorption component."," The expected Galactic line-of-sight absorption for MAXI $-$ 152 is $1.7668\times 10^{21}$ $^{-2}$ \citep{Kalberla05}, however the fitted absorption column is higher and variable, indicating an additional intrinsic absorption component."669" The fitted Ny increases rapidly during the initial stages of the outburst, beginning at Ng=2.440.3x10?!cm?! on MJD 55464 and rising to a mean value of Ny=5x10?!cm? on MJD 55465."," The fitted $N_\mathrm{H}$ increases rapidly during the initial stages of the outburst, beginning at $N_\mathrm{H} = 2.4670\pm 0.3 \times 10^{21}\ \mathrm{cm^{21}}$ on MJD 55464 and rising to a mean value of $N_\mathrm{H} = 5 \times 10^{21}\ \mathrm{cm^{2}}$ on MJD 55465."671 Measured absorption remains consistent with this value until observations ceased on MJD 55491., Measured absorption remains consistent with this value until observations ceased on MJD 55491.672" Fitting more complex models for absorption such as a warm absorber or partial covering model, with a fixed Galactic absorption also provide good fits to the increasing absorption, although given the spectral resolution of the XRT data, these more complex models are not required over a simple single-parameter variable absorption model."," Fitting more complex models for absorption such as a warm absorber or partial covering model, with a fixed Galactic absorption also provide good fits to the increasing absorption, although given the spectral resolution of the XRT data, these more complex models are not required over a simple single-parameter variable absorption model."673" A later follow-up observation taken on MJD 55598 after MAXI J1659—152 had faded significantly to a flux of 2.4+0.1x107ergs~!cm""? (0.5-10 keV) and entered the Hard State (Τ=1.81+0.1, no significantly detected disk component), gives a fitted absorption of Ny=4.2+0.6x10?!cm-?, consistent with the post-outburst value, suggesting that the additional absorption component is still present despite the lowered X-ray flux."," A later follow-up observation taken on MJD 55598 after MAXI $-$ 152 had faded significantly to a flux of $2.4 \pm 0.1 \times 10^{-11}\ \mathrm{erg\674 s^{-1}\ cm^{-2}}$ (0.5-10 keV) and entered the Hard State $\Gamma =6751.81\pm0.1$, no significantly detected disk component), gives a fitted absorption of $N_\mathrm{H} = 4.2 \pm 0.6 \times 10^{21}\676\mathrm{cm^{-2}}$, consistent with the post-outburst value, suggesting that the additional absorption component is still present despite the lowered X-ray flux."677" With moderate resolution spectral fitting, variable absorption may be due to a statistical correlation between spectral parameters."," With moderate resolution spectral fitting, variable absorption may be due to a statistical correlation between spectral parameters."678" To investigate this we examined confidence contours in T) parameter space, and find that the low Ny spectra (Ng,(MJD 55464) are distinct from the higher Ny spectra (MJD 55465) with 5c confidence."," To investigate this we examined confidence contours in $N_\mathrm{H}$, $\Gamma$ ) parameter space, and find that the low $N_\mathrm{H}$ spectra (MJD 55464) are distinct from the higher $N_\mathrm{H}$ spectra (MJD 55465) with $5\sigma$ confidence."679 Joint BAT and XRT spectral fits allow to constrain I and Ny more independently than by fitting XRT alone., Joint BAT and XRT spectral fits allow to constrain $\Gamma$ and $N_\mathrm{H}$ more independently than by fitting XRT alone.680" Care was taken to remove the effects of pile-up from the spectra, as pile-up can considerably affect continuum spectra fitting (Milleretal."," Care was taken to remove the effects of pile-up from the spectra, as pile-up can considerably affect continuum spectra fitting \citep{Miller10}."681" The fitted values of Ny and T do not vary in lock-step 2010)..either, given the fast initial rise in Ng between MJD 55464 and MJD 55465, compared with an linear rise in I ending around MJD 55470."," The fitted values of $N_\mathrm{H}$ and $\Gamma$ do not vary in lock-step either, given the fast initial rise in $N_\mathrm{H}$ between MJD 55464 and MJD 55465, compared with an linear rise in $\Gamma$ ending around MJD 55470."682 The consistency of the measured absorption in the later follow-up observation of MAXI J1659—152 provides further evidence that the measured Ny is not related to the fitted model or source brightness., The consistency of the measured absorption in the later follow-up observation of MAXI $-$ 152 provides further evidence that the measured $N_\mathrm{H}$ is not related to the fitted model or source brightness.683 We therefore conclude that the variable absorption is physical and not an artifact of the fit., We therefore conclude that the variable absorption is physical and not an artifact of the fit.684" We searched for QPOs using a fast Fourier transform method, adopting the power-spectral normalization of Leahyetal. and the search technique described by vanderKlis(1983)(1989)."," We searched for QPOs using a fast Fourier transform method, adopting the power-spectral normalization of \cite{Leahy83} and the search technique described by \cite{vanderKlis89}."685". For each orbit of XRT data, power density spectra (PDS) were generated for M continuous sections of data of 4096 bins duration, with a bin size of 0.01 s, and averaged."," For each orbit of XRT data, power density spectra (PDS) were generated for $M$ continuous sections of data of 4096 bins duration, with a bin size of 0.01 s, and averaged."686" The averaged PDS from each orbit was then rebinned in frequency so that W continuous frequencies were averaged, using a geometrical series binning scheme."," The averaged PDS from each orbit was then rebinned in frequency so that $W$ continuous frequencies were averaged, using a geometrical series binning scheme."687" Each rebinned/averaged PDS was fit with a model consisting of a power-law for the low frequency noise, a Lorentzian for the QPO (whose width was fixed to preserve a quality factor Q= of 5) and a constant for the Poisson noise level."," Each rebinned/averaged PDS was fit with a model consisting of a power-law for the low frequency noise, a Lorentzian for the QPO (whose width was fixed to preserve a quality factor $Q = \nu / \Delta\nu$ of 5) and a constant for the Poisson noise level."688" The ν/ΔνQPO was considered detected if the Lorentzian amplitude exceeded the local detection level, Puctect(MW) (given by the integral probability of a chi-squared distribution for 2MW d.o.f,."," The QPO was considered detected if the Lorentzian amplitude exceeded the local detection level, $P_\mathrm{detect}(MW)$ (given by the integral probability of a chi-squared distribution for $2MW$ d.o.f,."689" scaled by a factor of minus the mean noise level, which is 2 for the Leahy1/MW)etal.(1983) normalization."," scaled by a factor of 1/MW) minus the mean noise level, which is 2 for the \cite{Leahy83}690 normalization."691 Example PDS for 4 epochs are shown in Figure 4.., Example PDS for 4 epochs are shown in Figure \ref{fig:4_pspe}.692" Figure 5 shows in two energy bands (0.3— 2kkeV and 2—10 kkeV), the QPO frequency, the fractional rms variability of the fitted Lorentzian for PDS in which QPO were detected at greater than 50, and the broadband continuum rms for 0.02—10 HHz, including the QPO and low-frequency noise components."," Figure \ref{fig:qpo_freq} shows in two energy bands $0.3-2$ keV and $2-10$ keV), the QPO frequency, the fractional rms variability of the fitted Lorentzian for PDS in which QPO were detected at greater than $5\sigma$, and the broadband continuum rms for $0.02-10$ Hz, including the QPO and low-frequency noise components."693 The QPO frequency and detection energy evolves with the QPO peak frequency increasing approximately linearly with time., The QPO frequency and detection energy evolves with the QPO peak frequency increasing approximately linearly with time.694" After MJD 55466 QPOs are not detected in the 0.3— 2kkeV band, but are still detected in the 2— 10kkeV band until MJD 55472."," After MJD 55466 QPOs are not detected in the $0.3-2$ keV band, but are still detected in the $2-10$ keV band until MJD 55472."695 The QPO, The QPO696residuals are minimized in the least square sense by y7E which. can be expressed in. terms of the data (V)EI and the model data (V ) as Often. this results in complex and non-linear algorithms but these seem to work well most of the time.,"residuals are minimized in the least square sense by $\chi^2$ which can be expressed in terms of the data $\vec{V}$ ) and the model data $\vec{V^M}$ ) as Often, this results in complex and non-linear algorithms but these seem to work well most of the time."697 To make a practical algorithm. it is ecessary to find efficient ways of calculating the gradients of y with respect to the unknowns.," To make a practical algorithm, it is necessary to find efficient ways of calculating the gradients of $\chi^2$ with respect to the unknowns."698 In this paper. we consider the case of estimating the sky brightness in the presence of directionally dependent gain terms.," In this paper, we consider the case of estimating the sky brightness in the presence of directionally dependent gain terms."699 In a subsequent paper. we will consider the estimation of parameters describing gain terms.," In a subsequent paper, we will consider the estimation of parameters describing gain terms."700 There are cases in which the deconvolution and correction for the Mueller matrix can be decoupled., There are cases in which the deconvolution and correction for the Mueller matrix can be decoupled.701 For example. direction dependent effects which are identical for all the measurements can be removed by dividing the deconvolved image byΜ," For example, direction dependent effects which are identical for all the measurements can be removed by dividing the deconvolved image by."702"Υ, The correction for an azimuthally symmetric and time-constant antenna power pattern provides one such example.", The correction for an azimuthally symmetric and time-constant antenna power pattern provides one such example.703 The deconvolution is then performed on the entire data set. ignoring the antenna power pattern. whose inverse function is applied to the image only after the deconvolution and self-calibration have been completed.," The deconvolution is then performed on the entire data set, ignoring the antenna power pattern, whose inverse function is applied to the image only after the deconvolution and self-calibration have been completed."704 However. this assumption often breaks down.," However, this assumption often breaks down."705 In such case. processing time slices of the data independently might lower the range of the gain variations in each subset.," In such case, processing time slices of the data independently might lower the range of the gain variations in each subset."706 The final deconvolved images for each subset are averaged post-deconvolution., The final deconvolved images for each subset are averaged post-deconvolution.707 This is straightforward and often used. but can be expected to be sub-optimal because the deconvolution step is inherently non-linear and higher PSF sidelobes for individual subsets increase the level of (non-symmetric) deconvolution errors in each sub-image.," This is straightforward and often used, but can be expected to be sub-optimal because the deconvolution step is inherently non-linear and higher PSF sidelobes for individual subsets increase the level of (non-symmetric) deconvolution errors in each sub-image."708 Hence it would seem preferable to follow a procedure that applied the corrections while imaging the full data set., Hence it would seem preferable to follow a procedure that applied the corrections while imaging the full data set.709 In this seetion. we consider in detail an example of directionally dependent gains - the antenna far-field voltage pattern.," In this section, we consider in detail an example of directionally dependent gains - the antenna far-field voltage pattern."710 The far-field voltage pattern ts the Fourier transform of the antenna illumination function (?).., The far-field voltage pattern is the Fourier transform of the antenna illumination function \citep{KRAUS}.711 Thus it is typically the case that because of the details of the antenna geometry (such as quadrupod legs) and feed design. the antenna voltage patterns are azimuthally asymmetric.," Thus it is typically the case that because of the details of the antenna geometry (such as quadrupod legs) and feed design, the antenna voltage patterns are azimuthally asymmetric."712 Furthermore. the polarization response of the antenna will vary away from the antenna optical axis due to antenna geometry and the physics of the reflection of electromagnetic waves from curved surfaces.," Furthermore, the polarization response of the antenna will vary away from the antenna optical axis due to antenna geometry and the physics of the reflection of electromagnetic waves from curved surfaces."713 In addition. as an interferometric array composed of altitude-elevation mounted antenas tracks a region of the sky. these asymmetrical antenna voltage patterns rotate on the sky.," In addition, as an interferometric array composed of altitude-elevation mounted antennas tracks a region of the sky, these asymmetrical antenna voltage patterns rotate on the sky."714 This. along with significant time varying antenna pointing errors. makes time varying and different for each antenna pur (interferometric baseline).," This, along with significant time varying antenna pointing errors, makes time varying and different for each antenna pair (interferometric baseline)."715 Even equatorially mounted antennas share in this problem to the extent that changes in elevation (temperature) might deform the antennas due to gravity (dilation)., Even equatorially mounted antennas share in this problem to the extent that changes in elevation (temperature) might deform the antennas due to gravity (dilation).716 The Mueller matrix is an outer product of the two antenna based Jones matrices. (22)...," The Mueller matrix is an outer product of the two antenna based Jones matrices \citep{Jones,HBS1}."717 A’ full direction-dependent polarimetric description requires a Jones matrix per pixel in the image., A full direction-dependent polarimetric description requires a Jones matrix per pixel in the image.718 For the two orthogonal polarizations. labeled p and q. the Sky Jones matrix as a function of direction is given by: The super-scripts pg and gp represent leakage of the g- polarization signal to p-polarization signal and vice-versa.," For the two orthogonal polarizations, labeled $p$ and $q$, the Sky Jones matrix as a function of direction is given by: The super-scripts $pq$ and $qp$ represent leakage of the $q$ -polarization signal to $p$ -polarization signal and vice-versa."719 The diagonal elements correspond to the antenna voltage patterns on the sky while the off-diagonal elements correspond to the polarization leakage terms (p—g and g-p) due to instrumental leakage (antenna geometry. electronics) and/or atmospheric. ionospheric or other transmission effects such as Faraday rotation.," The diagonal elements correspond to the antenna voltage patterns on the sky while the off-diagonal elements correspond to the polarization leakage terms $p\rightarrow q$ and $q\rightarrow p$ ) due to instrumental leakage (antenna geometry, electronics) and/or atmospheric, ionospheric or other transmission effects such as Faraday rotation."720 The full direction-dependent Sky Mueller matrix Mj for baseline i-/ is a 4x matrix: The diagonalJ elementsJ of thisJ matrix areJ the antenna power patterns for the four polarization products. whereas the off-diagonal products incorporate the cross-polarization leakage terms.," The full direction-dependent Sky Mueller matrix $\MS{ij}{Sky}{}$ for baseline $i$ $j$ is a $4\times 4$ matrix: The diagonal elements of this matrix are the antenna power patterns for the four polarization products, whereas the off-diagonal products incorporate the cross-polarization leakage terms."721 For the VLA antennas. where the two circular polarization power patterns are squinted with respect to each other. the power pattern for the parallel hand (J ο. and the difference between a parallel hanc and a cross hand product (PAP- JE are shown in Fig.," For the VLA antennas, where the two circular polarization power patterns are squinted with respect to each other, the power pattern for the parallel hand $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{}$ ) and the difference between a parallel hand and a cross hand product $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{} - \JS{i}{R}{}\JS{j}{L^{\textstyle *}}{}$ ) are shown in Fig."722 1. (super-seript R and L denotes the right- and left-circular polarizations respectively)., \ref{JONES_DIAG} (super-script $\tens{R}$ and $\tens{L}$ denotes the right- and left-circular polarizations respectively).723 The main lobe of the power patterr is azimuthally asymmetric and. clearly. highly asymmetric in the first sidelobe.," The main lobe of the power pattern is azimuthally asymmetric and, clearly, highly asymmetric in the first sidelobe."724 This asymmetry is due to aperture blockage by the feed and the feed-legs., This asymmetry is due to aperture blockage by the feed and the feed-legs.725 The two parallel-hand power patterns ων. and JJ diagonal terms) are also not identical because of differences between the power patterns for the two orthogonal, The two parallel-hand power patterns $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{}$ and $\JS{i}{L}{}\JS{j}{L^{\textstyle *}}{}$ diagonal terms) are also not identical because of differences between the power patterns for the two orthogonal726To calculate the influence of the gravitational microlensing magnification upon the BLR. each image of the source (as a unction of velocity) was convolved with the magnification maps.,"To calculate the influence of the gravitational microlensing magnification upon the BLR, each image of the source (as a function of velocity) was convolved with the magnification maps."727 For the larger BLR models. the source size becomes comparable to he scale of the magnification maps.," For the larger BLR models, the source size becomes comparable to the scale of the magnification maps."728 Hence. appropriate regions are rimmed from the convolved maps to negate edge effects.," Hence, appropriate regions are trimmed from the convolved maps to negate edge effects."729 For the smaller sources. this means that the central 187 ER were employed or analysis. whereas the larger sources yielded a region 12? ER.," For the smaller sources, this means that the central $^2$ ER were employed for analysis, whereas the larger sources yielded a region $^2$ ER."730 ote that for the purposes of this study. all models are oriented yerpendicular to the shear field.," Note that for the purposes of this study, all models are oriented perpendicular to the shear field."731 Random orientations of the BLR models with respect to the microlensing structure is reserved to a ‘uture contribution., Random orientations of the BLR models with respect to the microlensing structure is reserved to a future contribution.732shows the error in the numerical frequency. (shown as a fractional deviation from the exact value) in each case.,shows the error in the numerical frequency (shown as a fractional deviation from the exact value) in each case.733 The unequal particle mass simulations at this resolution show CLEOLS © 2% for all modes up to jf=Ls., The unequal particle mass simulations at this resolution show errors of $\lesssim 2\%$ for all modes up to $j=18$.734 The results using equal mass particles have comparable accuracy up to the 7=6 mode but thereafter show errors of ~10., The results using equal mass particles have comparable accuracy up to the $j=6$ mode but thereafter show errors of $\sim 10\%$.735 One interesting point to note in the equal particle mass case is that the 7=10 mode seems to ἄοσαν to the j=δ mode and correspondingly the j=20 mode seems to decay to the j=16 mode., One interesting point to note in the equal particle mass case is that the $j=10$ mode seems to decay to the $j=8$ mode and correspondingly the $j=20$ mode seems to decay to the $j=16$ mode.736 The frequencies obtained with the time-reversible integrator are indistinguishable from those obtained using the predicetor-corrector. method. provided that the timestep does not change rapidly between timesteps as discussed in re[secistatic..," The frequencies obtained with the time-reversible integrator are indistinguishable from those obtained using the predictor-corrector method, provided that the timestep does not change rapidly between timesteps as discussed in \\ref{sec:static}."737 The two dimensional. Vor Star can also oscillate non-axisvmmetricallv., The two dimensional Toy Star can also oscillate non-axisymmetrically.738 Phe frequencies in the numerical solutions at a resolution of 1000 particles for the j=0 modes (j—0. s=2.4.6 etc) are shown in Figure 11..," The frequencies in the numerical solutions at a resolution of 1000 particles for the $j=0$ modes (j=0, s=2,4,6 etc) are shown in Figure \ref{fig:phifreq}."739 As in Figure 10. the absolute frequencies are shown in the top panel whilst the [ractional error is shown in the bottom panel., As in Figure \ref{fig:rfreq} the absolute frequencies are shown in the top panel whilst the fractional error is shown in the bottom panel.740 Using unequal mass particles (filled circles. dashed line) the frequencies in the numerical solutions show good agreement with the exact solutions (errors 2%) for modes up to s=16. above which the modes are damped out.," Using unequal mass particles (filled circles, dashed line) the frequencies in the numerical solutions show good agreement with the exact solutions (errors $\lesssim 2\%$ ) for modes up to $s=16$, above which the modes are damped out."741 The results using equal mass particles (open circles. dotted line) show somewhat lower errors C50.64) but only the modes up tos =S are captured in this case.," The results using equal mass particles (open circles, dotted line) show somewhat lower errors $\lesssim 0.6\%$ ) but only the modes up to $s=8$ are captured in this case."742 Finally the Tov Star can oscillate with modes which have both jz0 and sz0., Finally the Toy Star can oscillate with modes which have both $j\neq 0$ and $s\neq 0$.743 Phe density perturbation in the modes with 2—j<12 and 2<s12 is shown in Ligure 12.., The density perturbation in the modes with $2\le j \le 12$ and $2\le s \le 12$ is shown in Figure \ref{fig:mixedmodes_deltarho}.744 The numerical frequencies of the perturbations show similar accuracy to the svmmetric modes., The numerical frequencies of the perturbations show similar accuracy to the symmetric modes.745 As mentioned earlier. one of the most useful features of the ‘Tow Star is that it is possible to get exact. or very accurate solutions of the full non linear equations.," As mentioned earlier, one of the most useful features of the Toy Star is that it is possible to get exact, or very accurate solutions of the full non linear equations."746 These. provide excellent tests of the ability of a numerical code to follow a surface into à region devoid of matter., These provide excellent tests of the ability of a numerical code to follow a surface into a region devoid of matter.747 We assume that the velocity Ποια is a linear function of the cartesian coordinates and that the density is given. by the following second degree function of the coordinates Lor. this. case we choose |Zu=\cAa(f) and |ud=11-030) in which case the velocity field can be written where the first. term produces. an axisvnunetric expansion or contraction. and the second term gives a rigid rotation with angular velocity S3(/)z where @ is à unit vector in the z direction.," We assume that the velocity field is a linear function of the cartesian coordinates and that the density is given by the following second degree function of the coordinates For this case we choose $V^{11} = V^{22} = \alpha(t)$ and $V^{12} = - V^{21} = - \beta(t)$ in which case the velocity field can be written where the first term produces an axisymmetric expansion or contraction, and the second term gives a rigid rotation with angular velocity $\beta(t) \hat{\bf z}$ where $\hat{\bf z}$ is a unit vector in the z direction."748 The motion takes place so that. ab any time. each clement of ης has the same angular velocity.," The motion takes place so that, at any time, each element of fluid has the same angular velocity."749 The reader will appreciate that the solution has many features in common with the svmmetric pulsation of a polvtropic star. for example a model White Dwarf. under gravity.," The reader will appreciate that the solution has many features in common with the symmetric pulsation of a polytropic star, for example a model White Dwarf, under gravity."750 For this axisvmmetric case Co=D. D— 0. so that Substitution of the assumed. forms for v and. p into the acceleration and. continuity equations. with P—Αρ and replacing the Lagrangian derivative by the Eulerian accordingto and equating powers of wv and y we get," For this axisymmetric case $C=D$, $B=0$ , so that Substitution of the assumed forms for ${\bf v}$ and $\rho$ into the acceleration and continuity equations, with $P = K \rho^\gamma$ and replacing the Lagrangian derivative by the Eulerian accordingto and equating powers of $x$ and $y$ we get"751reproduce the observed A sstellar P-Cveni absorption feature and A sstellar emission line.,reproduce the observed $\lambda$ stellar P-Cygni absorption feature and $\lambda$ stellar emission line.752 The shape and strength of these broad ines are determined primarily by the stellar content of a ealaxv. in combination with a relatively narrow nebular component.," The shape and strength of these broad lines are determined primarily by the stellar content of a galaxy, in combination with a relatively narrow nebular component."753 Massive. main-sequence OB stars. dominate he line (with a small contribution from highly stripped WC \Woll-Ravet stars). while the line emission owimarilv arises from. evolved. hydrogen. poor. Wolf-Iavet (WR) stars (with a small. contribution from rare but uminous Of stars).," Massive main-sequence OB stars dominate the line (with a small contribution from highly stripped WC Wolf-Rayet stars), while the line emission primarily arises from evolved, hydrogen poor, Wolf-Rayet (WR) stars (with a small contribution from rare but luminous Of stars)."754 Recently Drinchmann.Petting&Char-ot(2008). revised. predictions for the line strengths expected from a stellar population by including updated Wolf-Itavet. star line equivalent widths. (EWs) in the population svnthesis code., Recently \citet{brinchmann1} revised predictions for the line strengths expected from a stellar population by including updated Wolf-Rayet star line equivalent widths (EWs) in the population synthesis code.755 From this the authors were able to predict a EW that was in agreement with that observed in the Shapleyetal.(2003). spectrum. suggesting that careful consideration of these massive stars and their evolutionary pathways is vital in the interpretation of these distant. sources.," From this the authors were able to predict a EW that was in agreement with that observed in the \citet{shapley} spectrum, suggesting that careful consideration of these massive stars and their evolutionary pathways is vital in the interpretation of these distant sources."756 While the use of composite spectra is necessary to study the majority of distant sources. there are now a small but. &rowing number of individual. Lyman-break galaxies for which high signal-to-noise rest-UV. spectra have been obtained.," While the use of composite spectra is necessary to study the majority of distant sources, there are now a small but growing number of individual Lyman-break galaxies for which high signal-to-noise rest-UV spectra have been obtained."757 The majority of these observations are made possible by high magnification due to strong lensing by intervening material along the line of sight., The majority of these observations are made possible by high magnification due to strong lensing by intervening material along the line of sight.758 They have highlighted a diversity in the population that is obscured by use of a composite. with some galaxies having extremely strong. emission and others. vanishinely weak. undetectable lines.," They have highlighted a diversity in the population that is obscured by use of a composite, with some galaxies having extremely strong emission and others vanishingly weak, undetectable lines."759 Phis variety leacs to a dilemma in its interpretation., This variety leads to a dilemma in its interpretation.760 While strong lines indicate the presence of massive O stars. a weak line would suggest a surprising absence of WR stars in the same galaxies.," While strong lines indicate the presence of massive O stars, a weak line would suggest a surprising absence of WR stars in the same galaxies."761 This dichotomy suggests that a reexamination of the spectral synthesis predictions of these and. features. is DOCOCSSÜAV., This dichotomy suggests that a reexamination of the spectral synthesis predictions of these and features is necessary.762 Aluch work has been done over the past few vears improving stellar. population ancl spectral svnthesis. and cquantifving the uncertainties of these models (c.g.LeithererConroy.White&Gunn2010:Conroy 2010)..," Much work has been done over the past few years improving stellar population and spectral synthesis and quantifying the uncertainties of these models \citep[e.g.][]{1999ApJS..123....3L,2003MNRAS.344.1000B,2004A&A...425..881L,2005MNRAS.362..799M,2007ASPC..374..303B,uncertain,uncertain1,uncertain2}."763 Our approach has been to consider the uncertainties inherent in the use of only single-star evolution models as the building blocks of svnthesis codes., Our approach has been to consider the uncertainties inherent in the use of only single-star evolution models as the building blocks of synthesis codes.764 We have expanded: our. input stellar. evolution models to take account. of binary stars and the many new evolutionary paths wavs this entails., We have expanded our input stellar evolution models to take account of binary stars and the many new evolutionary paths ways this entails.765 In Eldridge&Stanway(2009) we showed that when recent single star stellar models are used to predict the line strength. the measured line equivalent width (EW) is very small. ancl that binary evolution mocels are a better match for the observed. strength (and for other spectral Wh population indicators) in star-forming galaxies.," In \citet{ES09} we showed that when recent single star stellar models are used to predict the line strength, the measured line equivalent width (EW) is very small, and that binary evolution models are a better match for the observed strength (and for other spectral WR population indicators) in star-forming galaxies."766 Ilere we build on that work. ancl consider two uncertainties in the stellar evolution models in an elfort to interpret both the Shapleyetal.(2003). composite spectrum and those of individual lensed LBGs at 2=3.," Here we build on that work, and consider two uncertainties in the stellar evolution models in an effort to interpret both the \citet{shapley} composite spectrum and those of individual lensed LBGs at $z=2-3$."767 First. we investigate the οσοι of variation in the surface carbon abundance of OB stars on the derived stellar spectra.," First, we investigate the effect of variation in the surface carbon abundance of OB stars on the derived stellar spectra."768 Erbοἱal.(2010) show that the amount of carbon in high redshift ealaxies. as measured by nebular emission lines. decreases more rapidlv than their O/I]-derived. metallicity. at low abundances.," \citet{erb} show that the amount of carbon in high redshift galaxies, as measured by nebular emission lines, decreases more rapidly than their [O/H]-derived metallicity at low abundances."769 Pherefore we investigate the ellect ofdecreasing the relative abundance of carbon on the absorption line. in order to examine and mocel this trend.," Therefore we investigate the effect of decreasing the relative abundance of carbon on the absorption line, in order to examine and model this trend."770 Second. we further investigate the importance. of duplicity in. a synthesised.— stellar population when determining the line equivalent width. assuming both instantaneous burst and. constant. star-formation histories.," Second, we further investigate the importance of duplicity in a synthesised stellar population when determining the line equivalent width, assuming both instantaneous burst and constant star-formation histories."771 We now include a new evolutionary process that may only be possible at. low metallicities., We now include a new evolutionary process that may only be possible at low metallicities.772 Quasi-homogeneous evolution (OLI) occurs when a massive star rotates sullicientIv rapidly that the star becomes fully mixed. during its main-sequence Lifetime (AlaederLOST:Yoon&Langer2005:AMevnet&Maeder2007).," Quasi-homogeneous evolution (QHE) occurs when a massive star rotates sufficiently rapidly that the star becomes fully mixed during its main-sequence lifetime \citep{maeder87,yoon1,2007A&A...464L..11M}."773. While it is difficult for a single star to be born rapidly rotating. cllicient mass-transfer in massive binaries can spin up secondary stars to high rotation rates with case (Cantielloetal.2007)..," While it is difficult for a single star to be born rapidly rotating, efficient mass-transfer in massive binaries can spin up secondary stars to high rotation rates with ease \citep{cantiello}."774. At Solar metallicities such stars are likely to spin down quickly due to strong stellar winds., At Solar metallicities such stars are likely to spin down quickly due to strong stellar winds.775 However with the weakening of stellar winds at lower metallicities. elficient rotational mixing can occur.," However with the weakening of stellar winds at lower metallicities, efficient rotational mixing can occur."776 In. this paper we model the elect of this unusual form of evolution on stars that acerete material during a nmiass-transfer event. and investigate the dramatic elect such stars would have on the integrated: spectrum. of a stellar population.," In this paper we model the effect of this unusual form of evolution on stars that accrete material during a mass-transfer event, and investigate the dramatic effect such stars would have on the integrated spectrum of a stellar population."777 This paper is organised. as follows., This paper is organised as follows.778 In Section 2. we discuss the moclilications mace to our. Binary Population and Spectral Synthesis (BPASS) code in order to investigate the phenomena outlined above., In Section \ref{sec:synthetic_spectra} we discuss the modifications made to our Binary Population and Spectral Synthesis (BPASS) code in order to investigate the phenomena outlined above.779 In Section 3. we describe the ellects of these phenomena on the strength of the diagnostic aad spectral features., In Section \ref{sec:pred-equiv-widths} we describe the effects of these phenomena on the strength of the diagnostic and spectral features.780 In Section 4d. we go on to compare our predicted spectra to a composite spectrum constructed from ~900 Lyman-break galaxies by Shapleyetal.(2003). and to various individual examples of z~203 Lyman-break ealaxies., In Section \ref{sec:comp_spect} we go on to compare our predicted spectra to a composite spectrum constructed from $\sim$ 900 Lyman-break galaxies by \citet{shapley} and to various individual examples of $z\sim2-3$ Lyman-break galaxies.781 Finally. in Section 5 we brielly cliscuss our results and outline our conclusions.," Finally, in Section \ref{sec:conclusions} we briefly discuss our results and outline our conclusions."782 Thesvnthetic spectra used in this paper are created: using the Binary Population and Spectral Synthesis. (BASS) codel., Thesynthetic spectra used in this paper are created using the Binary Population and Spectral Synthesis (BPASS) .783. LU is described in detail in Eldridge. (2008).. ElLdridge&Stanway(2009) and. Eldridge.Langer.Tout (2011)..," It is described in detail in \citet{EIT}, \citet{ES09} and \citet{2011arXiv1103.1877E}."784" We use stellar models from the Cambridge STATS code (Eeeleton1971:Eldridege.Γκαν&""Tout.2008.ences therein).. specifically those calculated in IEldridge.Lz-zard&""Tout."," We use stellar models from the Cambridge STARS code \citep[][ and785 references therein]{egg,EIT}, specifically those calculated in \citet{EIT}."786 (2008).. Their kev feature is an extensive set of detailed binary star models (in addition to the detailed single star models) which are kev to producing a realistic svnthetie stellar population., Their key feature is an extensive set of detailed binary star models (in addition to the detailed single star models) which are key to producing a realistic synthetic stellar population.787 We consider stellar models at live dillerent metallicities: Z= 0.001. 0.004. 0.008. 0.020 and 0.040 (where a metallicity of Z=0.020 is conventionally considered Solar). with hyerogen massfraction.," We consider stellar models at five different metallicities: $Z=0.001$ , 0.004, 0.008, 0.020 and 0.040 (where a metallicity of $Z=0.020$ is conventionally considered Solar), with hydrogen massfraction,"788b; and of the Levi-Civita symbol when contracting one obtains the result. that the expression given in equation (X1)) vanishes in case of toroidal modes. (seeMaggiore 2008).,"$\ddot{h}_{ij}$ and of the Levi-Civita symbol when contracting one obtains the result, that the expression given in equation \ref{eq:integral}) ) vanishes in case of toroidal modes \citep[see][]{Mag}."789. Therefore. toroidal modes do not couple to external &ravitational waves.," Therefore, toroidal modes do not couple to external gravitational waves."790 For spheroidal modes one has to consider the expression which is obtained byinserting (17)) into equation considerCX1)), For spheroidal modes one has to consider the expression which is obtained byinserting \ref{eq:sphmodes}) ) into equation \ref{eq:integral}) ).791 ‘The solid angle is denoted by ©., The solid angle is denoted by $\Omega$.792 1n the following. we the contributions from the two terms in brackets separately: the expressions arising from the first and second. term. are denoted by Land LE. respectively.," In the following, we consider the contributions from the two terms in brackets separately; the expressions arising from the first and second term are denoted by I and II, respectively."793" ὃν making use of equation (6)). the first contribution (1) can be rewritten as In this expression the contribution arising from the first terni in. brackets since with the help of equation (1) one has 5;;$;;∕∕vanishes.=hi,im"," By making use of equation \ref{eq:rel_2}) ), the first contribution (I) can be rewritten as In this expression the contribution arising from the first term in brackets vanishes, since with the help of equation \ref{eq:tt_gauge}) ) one has $\ddot{h}_{ij}\delta_{ij}=\ddot{h}^i_{\phantom{i}i}=0$."794 The contribution arising5 from the second term is seen to be non-vanishing only for /=2 due to the orthogonality property of the spherical harmonics., The contribution arising from the second term is easily seen to be non-vanishing only for $l=2$ due to the orthogonality property of the spherical harmonics.795 Consequently. in order to obtain a simple analvtical expression for Ll. we again start with the original expression but now setting /—2 and substitute equation (5)) therein.," Consequently, in order to obtain a simple analytical expression for I, we again start with the original expression but now setting $l=2$, and substitute equation \ref{eq:rel_1}) ) therein."796 Then. again using the orthogonality property of the spherical harmonics. one is left with Finally we define a new variable. z=H. such that the integral is independent of the stellar radius Ze.," Then, again using the orthogonality property of the spherical harmonics, one is left with Finally we define a new variable, $z\equiv r/R$, such that the integral is independent of the stellar radius $R$."797" Fhis vields Proceeding as in the former case. we employ. equation (60) to gain the [following expression. for the second contribution (LL): since Lia, gives a linear combination of spherical harmonics with the same value of /. the contribution [roni the first term in brackets vanishes unless /=0 due to the orthogonality property of the spherical harmonics."," This yields Proceeding as in the former case, we employ equation \ref{eq:rel_2}) ) to gain the following expression for the second contribution (II): Since $L_q Y_{lm}$ gives a linear combination of spherical harmonics with the same value of $l$, the contribution from the first term in brackets vanishes unless $l=0$ due to the orthogonality property of the spherical harmonics."798" Lowever. for /=0 the coellicient function 6,07) is zero. b,o(r)=0 (sce Section 4)."," However, for $l=0$ the coefficient function $b_{nl}(r)$ is zero, $b_{n0}(r)=0$ (see Section 4)."799 Likewise. the contribution arising from the second term in brackets is seen to vanish unless /=2," Likewise, the contribution arising from the second term in brackets is seen to vanish unless $l=2$."800 Ixnowing that Ll is non-vanishing only for /=2. we start again with the original expression. where ωρα has already been inserted.," Knowing that II is non-vanishing only for $l=2$, we start again with the original expression, where $L_q=-\rmn{i}\epsilon_{qab}x_a\partial_b$ has already been inserted."801 Making use of the evclic property of the Levi-Civita symbol and contracting the epsilon tensors vielcds where the n term in brackets M since ↔⊔∣⋡≱∖⋯⋯↓⊔⋏∙≟_," Making use of the cyclic property of the Levi-Civita symbol and contracting the epsilon tensors yields where the second term in brackets vanishes, since $x_p\partial_p Y_{2m}^*=r\frac{\partial}{\partial r}Y_{2m}^*=0$ ."802≼∍↗⊓∕⋟∣≼∙↗⊔∪↓((A2 1: ntSTET ⋅⋅ ∩≖RETI ine quation dus (3))). (2)). (3)) (5)): (+) CX1)), Substituting $\left(\mathcal{Y}_{pq}^{2m}\right)^*\partial_i\left(\frac{x_px_q}{r^2}\right)$ for $\partial_i Y_{2m}^*$ in equation \ref{eq:int_sph_1}) \ref{eq:sph.harm}) \ref{eq:expan.sph.harm.}) \ref{eq:sph.harm}) \ref{eq:rel_1}) \ref{eq:orth.rel}) \ref{eq:integral})803al. (,al. (8042004) model with all three sources.,2004) model with all three sources.805 The low values of [F/O] in the w Cen stars were discussed by both Cunhla et al. (, The low values of [F/O] in the $\omega$ Cen stars were discussed by both Cunha et al. (8062003) and Renda οἱ al. (,2003) and Renda et al. (8072004) in the context of the unusual star formation history and chemical evolution within this sell-enriched stellar svstem that has been captured by the Galaxy.,2004) in the context of the unusual star formation history and chemical evolution within this self-enriched stellar system that has been captured by the Galaxy.808 We detect the HF molecular line at iin WAL dwarls and present the first fiaorine abundance measurements in young stars still in (he pre-anain sequence phase of evolution., We detect the HF molecular line at in K-M dwarfs and present the first fluorine abundance measurements in young stars still in the pre-main sequence phase of evolution.809 These (targets are members of the Orion association. in particular [rom the Orion Nebula cluster. will masses around 0.4-0.5 M...," These targets are members of the Orion association, in particular from the Orion Nebula cluster, with masses around 0.4-0.8 $_{\odot}$."810 Our results for JW433 and JW?22. which do not show substantial emission from a cireumstellar disk. reveal abundances of C and O that are in excellent agreement with those Chat are found in B-type stellar members of Orion Id (Cunha Lambert 1994).," Our results for JW433 and JW22, which do not show substantial emission from a circumstellar disk, reveal abundances of C and O that are in excellent agreement with those that are found in B-type stellar members of Orion Id (Cunha Lambert 1994)."811 This agreement bolsters confidence in the «quantitative spectroscopic abundance analyses techniques used in the hotter D. stars. as well as the eool IX and AL dwarfs.," This agreement bolsters confidence in the quantitative spectroscopic abundance analyses techniques used in the hotter B stars, as well as the cool K and M dwarfs."812 Moreover. JW433 and JW22 also clisplay abundance patterns in agreement. wilh the general behavior of fhiorine versus oxvgen for the Milkv Way disk that has been established [rom stars in a distinctly different evolutionary state.," Moreover, JW433 and JW22 also display abundance patterns in agreement with the general behavior of fluorine versus oxygen for the Milky Way disk that has been established from stars in a distinctly different evolutionary state."813 All previous F abundances had been derived from studies of red giants., All previous F abundances had been derived from studies of red giants.814 The overlap in these abundances provides an important confirmation for the relation of the fluorine abundance with oxveen in the Disk., The overlap in these abundances provides an important confirmation for the relation of the fluorine abundance with oxygen in the Disk.815 In the future. larger samples of Ix aud AI cias. as well as L aud T clwarls. can be used {ο measure f[Inorine and oxvgen abundances both in the field and in (he nearer star-forming regions.," In the future, larger samples of K and M dwarfs, as well as L and T dwarfs, can be used to measure fluorine and oxygen abundances both in the field and in the nearer star-forming regions."816 Based on observations obtained at the Gemini Observatory. which is operated by the Association of Universities for Research in Astronomy. Inc.. under a cooperative agreement with (he NSF on behalf of the Gemini partnership: the National Science Foundation (United States). the Particle Physics and Astronomy Research Couneil (United Ixingdom). the National Research Council (Canada). CONICYT (Chile). the Australian Research Couneil (Australia). CNPq (Brazil). and CONICRT (Argentina). as program GS-2002D-Q-2.," Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil), and CONICRT (Argentina), as program GS-2002B-Q-2."817 This work is also supported in part bv the National Science Foundation through ASTO3-07534 (VVS) and NASA through NAG5-9213 (VV$)., This work is also supported in part by the National Science Foundation through AST03-07534 (VVS) and NASA through NAG5-9213 (VVS).818Ol course. (he terminology “texture matter” does not seem to be perfectly apposite because (he real e-nodel textures are ονποσα] defects ancl the equation of state above is not. valid in general case.,"Of course, the terminology ""texture matter"" does not seem to be perfectly apposite because the real $\sigma$ -model textures are dynamical defects and the equation of state above is not valid in general case."819 However. in numerous papers such a terminology was fixedly settled (see [1] and references therein) thus we will follow it in present paper as Some known properties of textures sav that it is probably another kind of vacuum similar to the de Sitter vacuum =+p0 (the latter is known also as the bubble matter).," However, in numerous papers such a terminology was fixedly settled (see \cite{dn} and references therein) thus we will follow it in present paper as Some known properties of textures say that it is probably another kind of vacuum similar to the de Sitter vacuum $\varepsilon + p = 0$ (the latter is known also as the bubble matter)."820 Let us consider. for instance. the O(4)—O(3) textures arising in the scalar fourplet theory described by the action in a closed FRW universe (0<€< x) Then the texture solution of winding number one. has the following stvess-enerey tensor. which evidently satisfies with the above-mentioned equation of state.," Let us consider, for instance, the $\to$ O(3) textures arising in the scalar fourplet theory described by the action in a closed FRW universe $0\leq\xi\leq\pi$ ) Then the texture solution of winding number one, has the following stress-energy tensor, which evidently satisfies with the above-mentioned equation of state."821 The zero-zero component of (his tensor will be compared in Sec., The zero-zero component of this tensor will be compared in Sec.822 3 wilh a surface case., 3 with a surface case.823 The gravitational effects caused by 3D texture matter were intensively studied in many works 1.2]..," The gravitational effects caused by 3D texture matter were intensively studied in many works \cite{dn,texture}."824 The main aim of present paper is to study the 2D fluid of global textures which forms spherically svinmetrie singular bypersurlaces (surfaces of discontinuities of second kind)., The main aim of present paper is to study the 2D fluid of global textures which forms spherically symmetric singular hypersurfaces (surfaces of discontinuities of second kind).825 These hypersurfaces can be interpreted both as the (hin-wall approximation of the laver of bulk matter and as the brane-like objects embedded in spacetime of higher dimensionality., These hypersurfaces can be interpreted both as the thin-wall approximation of the layer of bulk matter and as the brane-like objects embedded in spacetime of higher dimensionality.826 As such. the singular model (turns to be simple enough to obtain important and instructive exact results not only when studsyiug classical dynamics but also when considering quantum aspects.," As such, the singular model turns to be simple enough to obtain important and instructive exact results not only when studying classical dynamics but also when considering quantum aspects."827 With respect to the 3D case this model appears to be the thin-wall approximation. which can elicit main features common for 2D ancl 3D cases.," With respect to the 3D case this model appears to be the thin-wall approximation, which can elicit main features common for 2D and 3D cases."828 The paper is organized as follows., The paper is organized as follows.829 In section 2 we give a comparative description of thermodynamics of 2D and 3D texture matter al [finite temperature wilh respect to each other ancl with respect to bubble matter ancl ordinary matter represented by radiation fluid., In section 2 we give a comparative description of thermodynamics of 2D and 3D texture matter at finite temperature with respect to each other and with respect to bubble matter and ordinary matter represented by radiation fluid.830" Section 3 is devoted to Classical οναός of (he isentropic singular shells ""made"" from 2D texture fluid.", Section 3 is devoted to classical dynamics of the isentropic singular shells “made” from 2D texture fluid.831 In section 4 we perform minisuperspace quantization of the singular model with provision lor both the through (wormhole-like) ancl ordinary topology., In section 4 we perform minisuperspace quantization of the singular model with provision for both the through (wormhole-like) and ordinary topology.832 Conclusions are made in section 5., Conclusions are made in section 5.833simulations of convection (e.g..Si-—eh.Boxburgh&Chan1998).,"simulations of convection \citep[e.g.,][]{singh}."834. The extent to which overshooting actually occurs in stars. however. is unclear.," The extent to which overshooting actually occurs in stars, however, is unclear."835 Since the stars in our simulation do not have convective cores. we are coucerned ouly with overshooting at the base of the surface convection zone.," Since the stars in our simulation do not have convective cores, we are concerned only with overshooting at the base of the surface convection zone."836 The stellar evolution calculations moclel convective overshooting by assuming that the region in which the chemical composition is homogenized by convective mixing extends some cdistauce below the Schwartzschild boundary into the stable radiative region., The stellar evolution calculations model convective overshooting by assuming that the region in which the chemical composition is homogenized by convective mixing extends some distance below the Schwartzschild boundary into the stable radiative region.837 Temperature gradients. however. are taken to be unaffected by overshooting.," Temperature gradients, however, are taken to be unaffected by overshooting."838 The single parameter iu this treatment is the depth by which convective mining reaches into the radiative region. and this distauce is expressed as a fraction of the pressure scale height at the Scliwartzschild boundary.," The single parameter in this treatment is the depth by which convective mixing reaches into the radiative region, and this distance is expressed as a fraction of the pressure scale height at the Schwartzschild boundary."839 Au upper limit on convective overshooting in metal-poor stars is set by observed. lithium abundauces., An upper limit on convective overshooting in metal-poor stars is set by observed lithium abundances.840 Lithium breaks down iu the high temperatures of stellar interiors. beginuiug near the bottom of the surface convection zone.," Lithium breaks down in the high temperatures of stellar interiors, beginning near the bottom of the surface convection zone."841 A large amount of convective overshooting would carry lithium more quickly from the surface to the ---interior. aud lithium depletion would occur at a faster rate.," A large amount of convective overshooting would carry lithium more quickly from the surface to the interior, and lithium depletion would occur at a faster rate."842" Overshooting depths greater than about 0.2 4, would be inconsistent with the relatively high lithium abuucauces observed in metal-poor stars.", Overshooting depths greater than about 0.2 $H_p$ would be inconsistent with the relatively high lithium abundances observed in metal-poor stars.843 Iu our simulation. therefore. we draw. values [or the overshooting depth frou the uniform distribution 0.0 — 0.2 Ap.coefficients.," In our simulation, therefore, we draw values for the overshooting depth from the uniform distribution 0.0 – 0.2 $H_p.$."844. Models of stable astrophysical plasinas predict that heliuui aud heavy elements in a stars radiative regions should settle toward the center of the star over time. while hydrogen rises toward the sur(ace.," Models of stable astrophysical plasmas predict that helium and heavy elements in a star's radiative regions should settle toward the center of the star over time, while hydrogen rises toward the surface."845 The extent to which this actually occurs. however. is subject to considerable uncertainty.," The extent to which this actually occurs, however, is subject to considerable uncertainty."846 There is clear evidence from belioseismology that element cliffusiou occurs inthe sun (Christenseu-Dalsgaard.Proffitt&Thompson1993:Basu.Pinsouneault 2000).," There is clear evidence from helioseismology that element diffusion occurs in the sun \citep{dals,basu}."847. Studies of surface abuudauces in metal-poor stars. though. iudicate that in these stars (illusion for some reason does uot occur in the outer layers (Chaboveretal.2001).," Studies of surface abundances in metal-poor stars, though, indicate that in these stars diffusion for some reason does not occur in the outer layers \citep{chab01}."848. Our stellar evolution calculations incorporate element diffusion using the treatment of &Loeb (1991)., Our stellar evolution calculations incorporate element diffusion using the treatment of \citet{thoul}.849. Because cdiffusiou is uot seen in the outer layers of metal-poor stars. we include a modification introduced by Chaboyveretal.(2001) which suppresses diffusion near he surface.," Because diffusion is not seen in the outer layers of metal-poor stars, we include a modification introduced by \citet{chab01} which suppresses diffusion near the surface."850 By comparing observed iron abuudances in globular clusters to the iron abundance oedieted by their stellar evolution models. Chaboyerοἱal.(2001) estimate that whatever process inhibits cdiffusiou in metal-poor stars must act over an outer regiou of at least 0.005 AL..," By comparing observed iron abundances in globular clusters to the iron abundance predicted by their stellar evolution models, \citet{chab01} estimate that whatever process inhibits diffusion in metal-poor stars must act over an outer region of at least 0.005 $M_\odot$."851 Ou the her hand. the fact that diffusion is not found to be inhibited in the sun suggests that the process inhibiting diffusion extends no lower than the bottom of the solar surface couvection zone. whicl las a Luass of O.O2AL..," On the other hand, the fact that diffusion is not found to be inhibited in the sun suggests that the process inhibiting diffusion extends no lower than the bottom of the solar surface convection zone, which has a mass of $0.02852M_\odot$."853 Therefore Chaboveretal. couclude that the process inhibiting clilfusion ikely acts over a surlace region with mass somewhere between 0.005 aud 0.02 AL.., Therefore \citeauthor{chab01} conclude that the process inhibiting diffusion likely acts over a surface region with mass somewhere between 0.005 and 0.02 $M_\odot$.854 To reflect this in our calculatious we follow Chaboveretal.(2001) in setting the ciffusioi coellicients to zero in the outer 0.005 AL. layer of the star.," To reflect this in our calculations we follow \citet{chab01}855 in setting the diffusion coefficients to zero in the outer 0.005 $M_\odot$ layer of the star."856" In the interior region delined by where M, is the star's total mass. the clilfusion coellicients are set to the standar values of Thoul.Bahcall&Loeb(199 1)."," In the interior region defined by$M_* - M(r) > 0.02\,M_\odot$ where $M_*$ is the star's total mass, the diffusion coefficients are set to the standard values of \citet{thoul}. ."857". In the middle region 0.005AL.<AL,—M(r)0.02 M..."," In the middle region $0.005\,M_\odot < M_* - M(r) < 0.02\,M_\odot$ ,"858factor of ~3 with respect to that of The possibility that space weatlering is responsible for the spectral müsmiateh is also reinforced ly the few experiments published to date of iou bombarcdianeut of Bercha eucrite and Johustown diogeuite (Troi&Pieters1998:Veruazzaotal. 2006).,"factor of $\sim$ 3 with respect to that of The possibility that space weathering is responsible for the spectral mismatch is also reinforced by the few experiments published to date of ion bombardment of Bereba eucrite and Johnstown diogenite \citep{hir98,ver06}."859. They both exhibit reddening (aud darkening)., They both exhibit reddening (and darkening).860 Note tha these experiments also confiui a slower timescale with respect to The true nature of the spectral mismatch still relains elusive iu several aspects: uevertheless sole noteworthy characteristics have been identified., Note that these experiments also confirm a slower timescale with respect to The true nature of the spectral mismatch still remains elusive in several aspects; nevertheless some noteworthy characteristics have been identified.861 Iu particular. we explore m detail the possibility that the spectral mismatch is due to space weathering Fist of all. the spectral slope auti-correlates with exposure to solar wind.," In particular, we explore in detail the possibility that the spectral mismatch is due to space weathering First of all, the spectral slope anti-correlates with exposure to solar wind."862 This is the opposite of what was found. for S-tvpes aud other spectral vpes (Lazzarinetal.2006)., This is the opposite of what was found for S-types and other spectral types \citep{laz06}.863. Therefore. if some sud of Suuaclated space weathering is operating ou V-tvpes. either it behaves in a different niuimner with respect to S-tvpes or other factors wipe out je reddenimg-exposure relation.," Therefore, if some kind of Sun-related space weathering is operating on V-types, either it behaves in a different manner with respect to S-types or other factors wipe out the reddening-exposure relation."864" Concerning the atter. a possibility is represcuted by a composition eradieut across προς, frou eucrite-like for the smallest imuenmibers (1 kin) to diogenite-like for he largest members (—10 kin)."," Concerning the latter, a possibility is represented by a composition gradient across V-types, from eucrite-like for the smallest members $\sim$ 1 km) to diogenite-like for the largest members $\sim$ 10 km)."865 This putative conrposition eradieut would help to explain the observed slope-exposure trend for two reasons: 1) diogenites are bluer. on average. than eucrites: Hxd ii) according to the few experiuents available. the reddening of dioseuites seen less pronounced than for eucrites. although the space parameters of TED compositions aud alteration processes are far frou being exhaustively investigated.," This putative composition gradient would help to explain the observed slope-exposure trend for two reasons: i) diogenites are bluer, on average, than eucrites; and ii) according to the few experiments available, the reddening of diogenites seem less pronounced than for eucrites, although the space parameters of HED compositions and alteration processes are far from being exhaustively investigated."866 Note that the above explanation is preferred with respect to other possibilities. e$. grain size variation. since the latter would require a erain size fuer than ~25 ((i.c. higher slope) for smaller objects.," Note that the above explanation is preferred with respect to other possibilities, e.g. grain size variation, since the latter would require a grain size finer than $\sim25$ (i.e. higher slope) for smaller objects."867 This is the opposite of what is expected. since smaller objects tend to have a larger grain size due to the low eravitv.," This is the opposite of what is expected, since smaller objects tend to have a larger grain size due to the low gravity."868 Also. the substantial presence of S-type interlopors amoung the red W-types would not ereatlv affect the observed slope-exposure trend since they are nearly equally distributed iu terms of E (see Fig. 3))," Also, the substantial presence of S-type interlopers among the red V-types would not greatly affect the observed slope-exposure trend since they are nearly equally distributed in terms of $E$ (see Fig. \ref{f1})"869. If coufirmed. the above conrpositional trend amone family V-tvpes could be the result of cratering ejecta frou various depths in Vesta's crust (eucrite is expected in the upper crust. while ciogenite is expected in the lower crust): or nav be due to different episodes of cratering occurrnue im regions with different compositions.," If confirmed, the above compositional trend among family V-types could be the result of cratering ejecta from various depths in Vesta's crust (eucrite is expected in the upper crust, while diogenite is expected in the lower crust); or may be due to different episodes of cratering occurring in regions with different compositions."870 However. since huge fragnmieuts are expected to originate iu the near-surface spall region. the second lypothesis seems more xobaljle.," However, since large fragments are expected to originate in the near-surface spall region, the second hypothesis seems more probable."871 This inv also be confirmed by the variety 7041-19 Ar shock ages of WEDs (Bogard&Carrison2003)., This may also be confirmed by the variety $^{39}$ $^{40}$ Ar shock ages of HEDs \citep{bog03}.872 Furthermore. the spectral data of V-tvpes seca to imdicate that both nuünceralogies are preseut (αναotal.2001).. but the Ini5 salple prevents a firma The proposed scenario could be tesdoas SOOM as lnore venir spectra of small V-types would become available.," Furthermore, the spectral data of V-types seem to indicate that both mineralogies are present \citep{duf04}, but the limited sample prevents a firm The proposed scenario could be tested as soon as more v-nir spectra of small V-types would become available."873 Note that the above discussion holds for both famuly aud non-fuuiv V-types., Note that the above discussion holds for both family and non-family V-types.874 For the latter. however. the auti-correlation is less xononunced. aud it becomes nearly flat if the outlicrs (red aud blue) are excluded.," For the latter, however, the anti-correlation is less pronounced, and it becomes nearly flat if the outliers (red and blue) are excluded."875" This could be an indication that most nou-funilv V-tvpes have a differcut orieiu with respect to family The NASA Dawn mission will aid iu uudoerstaulue the weatheriug process on Vesta, thanks to spectral dmaging and global mapping."," This could be an indication that most non-family V-types have a different origin with respect to family The NASA Dawn mission will aid in understanding the weathering process on Vesta, thanks to spectral imaging and global mapping."876 Therefore. the possibility to have detailed spectral informatio of specific areas of differcut conrposition ας texture will shed light ou the differcut effects of space weathering on basaltic asteroids.," Therefore, the possibility to have detailed spectral information of specific areas of different composition and texture will shed light on the different effects of space weathering on basaltic asteroids."877 We thank the anonymous referee for the holptu conumnents on the manuscript., We thank the anonymous referee for the helpful comments on the manuscript.878a resolution of 173x035 at 1.3 maim.,a resolution of $1''\!.3\times0''\!.85$ at 1.3 mm.879 For both sources. the peak positions al 1.3 mm and 3.4 mim coincide well with each other.," For both sources, the peak positions at 1.3 mm and 3.4 mm coincide well with each other."880 In 123151. a fan-shaped structure opening to the east can be roughly identified in the 3.4 mm continuum emission.," In I23151, a fan-shaped structure opening to the east can be roughly identified in the 3.4 mm continuum emission."881 In the 1.3 mm continuum enission. (here is a clisconlinuous arch structure at the lowest contour level which goes from a little bit northeast to the southeast of the mm contünuum peak.," In the 1.3 mm continuum emission, there is a discontinuous arch structure at the lowest contour level which goes from a little bit northeast to the southeast of the mm continuum peak."882 We will further discuss these features in Sect. 3.2.., We will further discuss these features in Sect. \ref{sio}.883 Because the weather conditions were only adequate for 1ο 2. mm. wave band during the observing seasons. we use the 3.4 mm continuum data lor quantitative analvsis.," Because the weather conditions were only adequate for the 3 mm wave band during the observing seasons, we use the 3.4 mm continuum data for quantitative analysis."884" Asstunine that the 3.4 mam continuum is mainly produced by optically (hin dust emission. we can calculate (he masses of the dense cores following the relation Algasdust=ΕΙ] (Hildebrand1983).. where £5 is the flux density of the dust enussion. D is the clistance to (he source. ancl D, is the Plank function at a dust temperature of Ty."," Assuming that the 3.4 mm continuum is mainly produced by optically thin dust emission, we can calculate the masses of the dense cores following the relation $M_{gas+dust}=F_{\nu}D^2/B_{\nu}(T_d)\kappa{_\nu}$ \citep{Hildebrand83}, where $F_\nu$ is the flux density of the dust emission, D is the distance to the source, and $B_\nu$ is the Plank function at a dust temperature of $T_d$."885 Sridharanetal.(2002) derive dust temperatures of 35 Ix for 118264 and 6&8 Ix. [or 123151 by eravbody fits to the IRAS and mim data., \citet{Sridharan02} derive dust temperatures of 35 K for I18264 and 68 K for I23151 by graybody fits to the IRAS and mm data.886" Here the dust opacity per eram is taken to her,= 0.1(r/I.2TIIz) 'engg! (Hildebrand.1983).. where the opacity index 3 is set to be 1.5."," Here the dust opacity per gram is taken to be $\kappa_\nu=0.1(\nu/1.2$ $)^{\beta}$ $^2$ $^{-1}$ \citep{Hildebrand83}, where the opacity index $\beta$ is set to be 1.5."887 The results of the ealeulations (M) ave listed in Table. 1.., The results of the calculations $M_{core}$ ) are listed in Table. \ref{table1}.888 The uncertainty of this estimation mainly comes from the determinations of ? and Z7., The uncertainty of this estimation mainly comes from the determinations of $\beta$ and $T_d$.889 The masses will decrease by a [actor of 4 il 7=1. and increase by a [actor of 2 if T; decreases to 17/2.," The masses will decrease by a factor of 4 if $\beta=1$, and increase by a factor of 2 if $T_d$ decreases to $T_d/2$."890 The integrated fIux al 3.4 nun ds 0.13 Jv for 118264 and 0.029 Jv lor 123151., The integrated flux at 3.4 mm is 0.13 Jy for I18264 and 0.029 Jy for I23151.891 When compared with the 1.2 nun sinele-clish flux (Beutheretal. 2002a).. the total flux [rom PdBI amounts to for 118264 and for 23151 of the single-dish flux extrapolated from 1.2 mm using S(v)xi|i with >=]1.5.," When compared with the 1.2 mm single-dish flux \citep{Beuther02a}, , the total flux from PdBI amounts to for I18264 and for I23151 of the single-dish flux extrapolated from 1.2 mm using $S({\nu})\,{\propto}\,{\nu}^{2+{\beta}}$ with $\beta=1.5$."892 Some extended emission is not recovered by (he interferometer., Some extended emission is not recovered by the interferometer.893 Fig., Fig.894 2 presents the channel maps in SiO (2-1) in 118264. where the velocity resolution is smoothed to 5 !|.," \ref{siochan1} presents the channel maps in SiO (2-1) in I18264, where the velocity resolution is smoothed to 5 $^{-1}$."895 The SiO emission mostly appears in the redshifted channels in Fig. 2..," The SiO emission mostly appears in the redshifted channels in Fig. \ref{siochan1},"896 and only the 38.6 ! channel shows prominent blueshifted emission., and only the 38.6 $^{-1}$ channel shows prominent blueshifted emission.897 The most remarkable feature in the channel maps is an elongated structure in the southeast., The most remarkable feature in the channel maps is an elongated structure in the southeast.898 This redshifted emission has verv high velocities up to Ac ~60 kms+ with respect to the svstemic velocity (ος) 43.6 |., This redshifted emission has very high velocities up to $\Delta{v}\sim$ 60 $^{-1}$ with respect to the systemic velocity $v_{LSR}$ ) 43.6 $^{-1}$.899" We have examined the data from the 320 MlIz band and [found that there is no detectable SiO emission bevond eps, of 110 !.", We have examined the data from the 320 MHz band and found that there is no detectable SiO emission beyond $v_{LSR}$ of 110 $^{-1}$.900 The integrated blue- and redshilted SiO emission is shown in Fig., The integrated blue- and redshifted SiO emission is shown in Fig.901 3aa. where (he sinele-dish bipolar CO outflow is resolved into (wo quasi-perpendicular outflows: The southeast to northwest (SE-NW) outflow and (he northeast (NE) outflow.," \ref{sioint1}a a, where the single-dish bipolar CO outflow is resolved into two quasi-perpendicular outflows: The southeast to northwest (SE-NW) outflow and the northeast (NE) outflow."902 Both outflows seem to originate from the western peak of the mm continu., Both outflows seem to originate from the western peak of the mm continuum.903 Along the SE-NW outflow. both red- ancl blueshifted emission can be found. which is a tvpical feature for expanding bow shocks near the plane ofthe sky.," Along the SE-NW outflow, both red- and blueshifted emission can be found, which is a typical feature for expanding bow shocks near the plane ofthe sky."904 From its alienment wilh the SE jet-like outflow. (he bipolar emission in the northwest seems {ο," From its alignment with the SE jet-like outflow, the bipolar emission in the northwest seems to"905wavelength range to fit (heFUSE spectirun.,wavelength range to fit the spectrum.906" The model with M5x10""M. {νι glves a distance of 666pc. too large to be acceptable. and with M=1xLOSAL. /vr the distance becomes twice the value found in the low state."," The model with $\dot{M}=5 \times 10^{-9}M_{\odot}$ /yr gives a distance of 666pc, too large to be acceptable, and with $\dot{M}=1 \times 10^{-8}M_{\odot}$ /yr the distance becomes twice the value found in the low state."907 As an example. a model with /vr is shown in Figure I. giving a distance of 557pe.," As an example, a model with $\dot{M} = 3.5 \times 10^{-9}M_{\odot}$ /yr is shown in Figure 1, giving a distance of 557pc."908 The flux deficiency in the shorter wavelengths is clearly seen., The flux deficiency in the shorter wavelengths is clearly seen.909 The inclusion of a hotter WD does not provide a significant improvement of the mocdel fit., The inclusion of a hotter WD does not provide a significant improvement of the model fit.910 In order to increase the flux in (he shorter wavelengths. the (temperatures of (he two inner rines of the standard disk model are modified to represent the DL.," In order to increase the flux in the shorter wavelengths, the temperatures of the two inner rings of the standard disk model are modified to represent the BL."911" The first ring is located at ry=1.0522, aud the second is al ro=1.2042,. The temperatures of the rings (Lj T5 respectively) are listed in Table 2.", The first ring is located at $r_1=1.05 R_*$ and the second is at $r_2=1.20R_*$ The temperatures of the rings $T_1$ $T_2$ respectively) are listed in Table 2.912 In the standard disk model these temperatures are below 50.000Ix [or the aceretion rate considered here.," In the standard disk model these temperatures are below 50,000K for the accretion rate considered here."913 For the modeling of the DL. rings are computed with temperatures between. 100.0001. and175.000Ix. in agreement with the BL models of Godonetal.(1995). (~125. 000Ix) and Popham&Naravan(1995) (ου180.000) for the mass aceretion rates considered here.," For the modeling of the BL, rings are computed with temperatures between 100,000K and175,000K, in agreement with the BL models of \citet{god95} $\sim 125,000$ K) and \citet{pop95} $\sim 180,000$ K) for the mass accretion rates considered here."914 In doing so. one is able to construct two models ol BL: thin (first ring only) and extended (first two rings).," In doing so, one is able to construct two models of BL: thin (first ring only) and extended (first two rings)."915 The standard disk model with a mass accretion rate of 3xLOM. /vr fits the long wavelength: end of the.FUSE spectrum using the assumed distance to MV. Lyr., The standard disk model with a mass accretion rate of $3 \times 10^{-9}M_{\odot}$ /yr fits the long wavelength end of the spectrum using the assumed distance to MV Lyr.916 For this reason models with M>3x10?M. /vr are nol considered when including the DL. since ihe DL increases the this of the model and therefore its distance becomes too large.," For this reason models with $\dot{M} \ge 3 \times 10^{-9}M_{\odot}$ /yr are not considered when including the BL, since the BL increases the flux of the model and therefore its distance becomes too large."917 Also. since MV Lyris in a high state. mass accretion rates below 1x10.M. /vr are not considered (these points are discussed in (lie section 5).," Also, since MV Lyr is in a high state, mass accretion rates below $1 \times 10^{-9}M_{\odot}$ /yr are not considered (these points are discussed in the section 5)."918" First. an accretion disk with a mass accretion rate of 1x10.9A, /vr is considered. and the DL temperature and size are then varied."," First, an accretion disk with a mass accretion rate of $1 \times 10^{-9}M_{\odot}$ /yr is considered, and the BL temperature and size are then varied."919 It is found that the best model fits lead to a distance of only 350pc-400pc., It is found that the best model fits lead to a distance of only 350pc-400pc.920 Since the mass accretion rate is fixed to κLOM. /vr. the only wav to increase the distance is to increase the contribution of the BL. bv increasing its temperature and/or size.," Since the mass accretion rate is fixed to $1 \times 10^{-9}M_{\odot}$ /yr, the only way to increase the distance is to increase the contribution of the BL, by increasing its temperature and/or size."921 In cloing so. the models that give an acceptable distance (of sav αἱ least » 430pc) have actually too much flux in the shorter wavelengths. a sign that the BL contributes too much flix.," In doing so, the models that give an acceptable distance (of say at least $\sim 430$ pc) have actually too much flux in the shorter wavelengths, a sign that the BL contributes too much flux."922 Only a few of these models are listed in Table 2., Only a few of these models are listed in Table 2.923 These models are not better than the standard disk models: their AZ is as large and/or their distance is too short., These models are not better than the standard disk models: their $\chi^2_{\nu}$ is as large and/or their distance is too short.924 The best fit models are obtained for a thin (one ring) BL with a temperature of ~150.000K-175.000K. The distance for these models is. however. far too short.," The best fit models are obtained for a thin (one ring) BL with a temperature of $\sim$ 150,000K-175,000K. The distance for these models is, however, far too short."925 The inclusion of a heated WD does not improve the models aud produces only a small increase in the distance., The inclusion of a heated WD does not improve the models and produces only a small increase in the distance.926 Next. to obtain models with a larger distance. (he mass aceretion rate is increased to 2xLOΑΙ. νο.," Next, to obtain models with a larger distance, the mass accretion rate is increased to $2 \times 10^{-9}M_{\odot}$ /yr."927 This has the elfect of decreasing the relative flux contributed bv the BL.These models agree with the assumed distance and have a lower V7. especially the two-ring," This has the effect of decreasing the relative flux contributed by the BL.These models agree with the assumed distance and have a lower $\chi^2_{\nu}$ , especially the two-ring"928inclination. and that the bulks of the H and of the K-banc emissions are unlikely to originate in the same physical region.,"inclination, and that the bulks of the $H$ and of the $K$ -band emissions are unlikely to originate in the same physical region."929 The model of a rim of dust grains directly. irradiated by the star cannot fit our data., The model of a rim of dust grains directly irradiated by the star cannot fit our data.930 However. we find that. for various dust grain properties. the silicate sublimation occurs around ~0.65 AU. a distance similar to the sharp transitior in surface brightness seen in the K-band image.," However, we find that, for various dust grain properties, the silicate sublimation occurs around $\sim$ 0.65 AU, a distance similar to the sharp transition in surface brightness seen in the $K$ -band image."931 We therefore interpret the ring-like feature in the K-band image as tracing the emission from dust at ~ 1500 K. Le.. at the transition radius where silicate The previous simple models suggest that the H-band emission is more compact than the K-band emission. and indicate that there is material located inside the silicate sublimation radius. as already found in other Herbig Ae stars.," We therefore interpret the ring-like feature in the $K$ -band image as tracing the emission from dust at $\sim$ 1500 K, i.e., at the transition radius where silicate The previous simple models suggest that the $H$ -band emission is more compact than the $K$ -band emission, and indicate that there is material located inside the silicate sublimation radius, as already found in other Herbig Ae stars."932 Assuming that the ring-like feature in the K- image is related to silicate sublimation. we compose a model made of three elements: a star. a ring at the silicate sublimation radius. and an inner disk.," Assuming that the ring-like feature in the $K$ -band image is related to silicate sublimation, we compose a model made of three elements: a star, a ring at the silicate sublimation radius, and an inner disk."933 This inner and compact emission Is expected to modify the shape of the visibility curves and to smooth the closure phases predicted by à very asymmetric component such as the puffed-up rim., This inner and compact emission is expected to modify the shape of the visibility curves and to smooth the closure phases predicted by a very asymmetric component such as the puffed-up rim.934 In this section. we attempt to derive the main characteristics of these three components. Le.. their extents and contributions to the NIR emission.," In this section, we attempt to derive the main characteristics of these three components, i.e., their extents and contributions to the NIR emission."935 Since it is unclear whether a rim would puff up in the way computed in ? 1f inside matter is blocking part of the stellar emission. we refer to the inner edge of the dusty disk as instead ofrim.," Since it is unclear whether a rim would puff up in the way computed in \citet{isella05} if inside matter is blocking part of the stellar emission, we refer to the inner edge of the dusty disk as instead of."936. Determining its exact structure is beyond the scope of this paper., Determining its exact structure is beyond the scope of this paper.937 This ring traces dust condensation and provides some asymmetric emission. as indicated by the non-zero closure phases.," This ring traces dust condensation and provides some asymmetric emission, as indicated by the non-zero closure phases."938" We compute its emission using the rim model at R;,,,20.65 AU. but where its luminosity is treated as a free parameter to enable SED fitting with an additional inner component."," We compute its emission using the rim model at $_{\rm{sub}}$ =0.65 AU, but where its luminosity is treated as a free parameter to enable SED fitting with an additional inner component."939 We describe the inner disk using a radial temperature profile T«r as expected in a circumstellar disk. and a vertical optical depth τ.," We describe the inner disk using a radial temperature profile $\propto$ $^{-\alpha}$ as expected in a circumstellar disk, and a vertical optical depth $\tau$."940" We find an acceptable fit to the SED. the visibilities. and the closure phases in the H and K bands using a model where the inner disk extends from R;,20.1 AU to Ry. with T;,=2400 K. «0.4. and a vertical optical depth +~0.4."," We find an acceptable fit to the SED, the visibilities, and the closure phases in the $H$ and $K$ bands using a model where the inner disk extends from $_{\rm{in}}$ =0.1 AU to $_{\rm{sub}}$, with $_{\rm{in}}$ =2400 K, $\alpha$ =0.4, and a vertical optical depth $\tau\sim0.4$."941 In this model. the ring contributes of the K-band flux. while the inner disk provides of it.," In this model, the ring contributes of the $K$ -band flux, while the inner disk provides of it."942 In the H-band. the ring is responsible for of the emission. the inner disk for 34%.. leaving the star as the major contributor at 1.6 jm. The parameters of the model are summarized m Tab. 1..," In the $H$ -band, the ring is responsible for of the emission, the inner disk for , leaving the star as the major contributor at 1.6 $\mu$ m. The parameters of the model are summarized in Tab. \ref{tab:bestmodels}."943 We show in Figs., We show in Figs.944 3 and 4 the model predictions for the SED. the broad-band visibilities and closure phases (full black lines).," \ref{fig:sedv2} and \ref{fig:2} the model predictions for the SED, the broad-band visibilities and closure phases (full black lines)."945 By spreading the NIR emission across a broader range of radii (compared to the puffed-up rim). re.. from Εως to R;j. the shape of the visibility-versus-baseline curve is well reproduced and the high closure phases predicted by the model of the puffed-up rim are smoothed out. resulting in values close to the observations (from 0 to 207)).," By spreading the NIR emission across a broader range of radii (compared to the puffed-up rim), i.e., from $_{\rm{sub}}$ to $_{\rm{in}}$, the shape of the visibility-versus-baseline curve is well reproduced and the high closure phases predicted by the model of the puffed-up rim are smoothed out, resulting in values close to the observations (from 0 to )."946 A temperature gradient within the inner disk is needed to reproduce the H and K band visibilities together. as a single temperature disk at a specific τ cannot.," A temperature gradient within the inner disk is needed to reproduce the $H$ and $K$ band visibilities together, as a single temperature disk at a specific $\tau$ cannot."947 The model is shown in Fig. 5..," The model is shown in Fig. \ref{fig:imagemodel},"948 right., right.949 Considering the large scatter in the observations. we do not claim the uniqueness of the parameters of our model (7. Τμ. α). although they provide a qualitatively good fit to the observations. and the extents and flux ratio of each component are well constrained and in agreement with the images.," Considering the large scatter in the observations, we do not claim the uniqueness of the parameters of our model $\tau$, $_{\rm{in}}$, $\alpha$ ), although they provide a qualitatively good fit to the observations, and the extents and flux ratio of each component are well constrained and in agreement with the images."950 Our model produces a strong variation in surface brightness in the first AU. from the star to the ring.," Our model produces a strong variation in surface brightness in the first AU, from the star to the ring."951 To better interpret the reconstructed image presented in Fig. 2..," To better interpret the reconstructed image presented in Fig. \ref{fig:image},"952 we performed an image reconstruction from the visibilities and closure phases of our model., we performed an image reconstruction from the visibilities and closure phases of our model.953 To do so. we computed synthetic data sets from the model image. with an identical coverage as the observations. the same errors. and a similar scatter in the visibility measurements.," To do so, we computed synthetic data sets from the model image, with an identical coverage as the observations, the same errors, and a similar scatter in the visibility measurements."954 We present an example of a reconstructed image from the model in Fig. 5.. ," We present an example of a reconstructed image from the model in Fig. \ref{fig:imagemodel}, ,"955middle. compared to the real image (left).," middle, compared to the real image (left)."956 The image reconstructed from the model shares the same characteristics as the real image. Le.. an incomplete ring-like feature in the K-band oriented along PA~135° and inclined by ~45°.. with an inner diameter of ~5.5 mas. and an extended central spot.," The image reconstructed from the model shares the same characteristics as the real image, i.e., an incomplete ring-like feature in the $K$ -band oriented along $\sim$ and inclined by $\sim$, with an inner diameter of $\sim$ 5.5 mas, and an extended central spot."957 This confirms that our model provides a qualitatively good description of our data., This confirms that our model provides a qualitatively good description of our data.958 In particular. the missing part of the ring-like feature can be explained by the low-brightness edge of an inclined rim (while the other edge ts much brighter).," In particular, the missing part of the ring-like feature can be explained by the low-brightness edge of an inclined rim (while the other edge is much brighter)."959 It also shows that although the star is unresolved in the model with a diameter of ~0.2 mas (r.e.. inside the central pixel). the central spot in the reconstructed Image is much more extended (~2.] màs; similar to the real image).," It also shows that although the star is unresolved in the model with a diameter of $\sim$ 0.2 mas (i.e., inside the central pixel), the central spot in the reconstructed image is much more extended $\sim$ 2.1 mas; similar to the real image)."960 Its size is about the interferometric beam size. but in the model image. it has much more flux than the star's. due to the inner disk emission on unresolved scales as small as 0.1 AU.," Its size is about the interferometric beam size, but in the model image, it has much more flux than the star's, due to the inner disk emission on unresolved scales as small as 0.1 AU."961 This could indicate that the central spot in the real image also includes an additional emission to the star's., This could indicate that the central spot in the real image also includes an additional emission to the star's.962 Several tests have led us to conclude that the scatter in the visibility measurements lowers the achievable dynamics which canresult in an image that has low or no emission insidethe, Several tests have led us to conclude that the scatter in the visibility measurements lowers the achievable dynamics which canresult in an image that has low or no emission insidethe963iu the same sense as one introduces anomalous resistivity and anomalous diffusion iu plasma plivsics: The origin of this viscosity is in fully developed turbulence which is established in the saturation regime described above.,in the same sense as one introduces anomalous resistivity and anomalous diffusion in plasma physics: The origin of this viscosity is in fully developed turbulence which is established in the saturation regime described above.964 Eq. (, Eq. (9653.15) or (3.16) could be derived frou dimensional arguments (of course. without the nuuerical coefficieut) as an estimation of viscosity in a rotating disk with turbulent motions.,"3.15) or (3.16) could be derived from dimensional arguments (of course, without the numerical coefficient) as an estimation of viscosity in a rotating disk with turbulent motions."966 Towever. we should emphasize that without au analysis such as one given above it would be impossible to reveal an underline plivsical mechauisin for the origin of such turbulence.," However, we should emphasize that without an analysis such as one given above it would be impossible to reveal an underlying physical mechanism for the origin of such turbulence."967 It is iuportaut to test whether the necessary condition for developing of zinall-scale turbulence is met., It is important to test whether the necessary condition for developing of small-scale turbulence is met.968 To this end. let us find the ratio vVenue as a function of 7=Of; of the basic parameter that characterizes the umuber of interactions per one revolution: mn both hmnüts. 7 laud rX1. the viscosity coefficient is mich less than the critical value giveu by Eqs. (," To this end, let us find the ratio $\nu/\nu_{\rm turb}$ as a function of $\tau=\Omega t_i$, of the basic parameter that characterizes the number of interactions per one revolution: Asymptotically, in both limits, $\tau\ll 1$ and $\tau \gg 1$, the viscosity coefficient is much less than the critical value given by Eqs. ("9693.15) or (3.16).,3.15) or (3.16).970" The fuuction (3.18) reaches its masta at 7=B,*. and this maxima is eiven by Even in this. the least favorable case [when 72:0.5 as one cau see from Eq. ("," The function (3.18) reaches its maximum at $\tau971=B_i^{-1}$, and this maximum is given by Even in this, the least favorable case [when $\tau \simeq 0.5$ as one can see from Eq. ("9722.1)] iis less than 144 by a factor of2 or so. Which is enough for small-scale turbulence to appear.,"2.4)] $\nu$ is less than $\nu_{\rm cr}$ by a factor of 2 or so, which is enough for small-scale turbulence to appear."973 Therefore the range of physical conditious under which the viscosity due to fully developed turbulence should donunate is indeed very broad., Therefore the range of physical conditions under which the viscosity due to fully developed turbulence should dominate is indeed very broad.974 Uulike the classical example of gravitational iustabilitv. our mechanism for the erowtl of shortwave perturbations bas a much higher level of VISCOUS stabilization. as it follows from the value of critical viscosity calculated above in comparison with that for a sclberavitatingo disk.," Unlike the classical example of gravitational instability, our mechanism for the growth of shortwave perturbations has a much higher level of viscous stabilization, as it follows from the value of critical viscosity calculated above in comparison with that for a self-gravitating disk."975 DIudeed. the erowth of shortwave perturbations leads to the increase of the amplitude by a factor of This strong imequality follows from the fact that [eQD)I|~FT. where f is the characteristic time of the erowth of perturbations and T is the period of the disk revolution.," Indeed, the growth of shortwave perturbations leads to the increase of the amplitude by a factor of This strong inequality follows from the fact that $|k_r(0)/ k_\varphi| \sim t_*/T,$ where $t_*$ is the characteristic time of the growth of perturbations and $T$ is the period of the disk revolution."976 According to the perturbation theory implemented to cxamune instability. the condition LT>>1 holds (otherwise the zero-approxinatiou of perturbation theorv is uot fulfilled: the equilibria condition is broken for the time less then that of one revolution of the disk).," According to the perturbation theory implemented to examine instability, the condition $t_*/T >> 1$ holds (otherwise the zero-approximation of perturbation theory is not fulfilled: the equilibrium condition is broken for the time less then that of one revolution of the disk)."977 As a result of the above inequality. a strong growth of perturbation takes place. which leads to the development of short-scale turbulence ar the appearance of turbulent viscosity.," As a result of the above inequality, a strong growth of perturbation takes place, which leads to the development of short-scale turbulence and the appearance of turbulent viscosity."978" A very laree factor of the erowth given above explains why the value of the critical turbulent viscosity. which stops the growth of perturbations. turus out to be much larger than that for the instability of a sclteravitating disk (οιο,, Fridian Polvacheuko 1981. p. 1)."," A very large factor of the growth given above explains why the value of the critical turbulent viscosity, which stops the growth of perturbations, turns out to be much larger than that for the instability of a self-gravitating disk (e.g., Fridman Polyachenko 1984, p. 41)."979 Before making nunercal estimates. we dist the basic parameters of the chuupy eas in the circumuuclear rine (CNR). such as the inferred clump size e. the volume filling factor F. aud velocity dispersion of the chumps σι. taken from Jacksou et al. (," Before making numerical estimates, we list the basic parameters of the clumpy gas in the circumnuclear ring (CNR), such as the inferred clump size $a$, the volume filling factor $F$, and velocity dispersion of the clumps $\sigma_v$, taken from Jackson et al. ("9801993) and Caissten at al. (,1993) and Güssten at al. (9811987): Adoptingc» the average[m] C»gas deusitv iu the clumps η=cu? one fiuds the average clin mass mn=5M.,1987): Adopting the average gas density in the clumps $n=10^5~{\rm cm^{-3}}$ one finds the average clump mass $m=5$.982 This gives the ratio ία2107. which iuplies that clastic (eravitational) imteractions between the chumps are ueelieible conrpared to melastie ones. chuup-chuup collisions.," This gives the ratio $a_G/a\simeq 10^{-3}$, which implies that elastic (gravitational) interactions between the clumps are negligible compared to inelastic ones, clump-clump collisions."983 Iu other words. ogravitation plavs no role in the interactions between the CNR clamps.," In other words, gravitation plays no role in the interactions between the CNR clumps."984 The mean free path ofthe chuups given by is rather laree (even in a nuuginal conflict with the siuplifvine asstuuption (3.1) that / hj., The mean free path of the clumps given by is rather large (even in a marginal conflict with the simplifying assumption (3.1) that $l\ll h$ ).985 The chup collision rate in the CNR is giveu by: welQs2.10324? nuplving less than one collision per revolution., The clump-clump collision rate in the CNR is given by: $\omega_c\lax\Omega\simeq 2\cdot 10^{-12}~{\rm s}^{-1}$ implying less than one collision per revolution.986 The auticipated optical depth is T=ει0.5. which. according to Eq. (," The anticipated optical depth is $\tau\simeq 0.1~-~0.5$, which, according to Eq. ("9873.17). results in<My.,"3.17), results in $\nu < \nu_{\rm cr}$."988 Therefore. the conditions for fully developed turbuleuce to appear. which are described at the cud of Sec.," Therefore, the conditions for fully developed turbulence to appear, which are described at the end of Sec."989 3. are met to vield the viscosity coefficieut It is iustructive to compare this result with the upper lait to viscosity derived by von Linden et al. (," 3, are met to yield the viscosity coefficient It is instructive to compare this result with the upper limit to viscosity derived by von Linden et al. ("9901993a.)).,"1993a,b)."991 Their results were obtained by fitting an accretion disk model with arbitrary viscosity to the velocity fields of various molecular clouds. auc then inferring the required kinematic viscosity from the fit.," Their results were obtained by fitting an accretion disk model with arbitrary viscosity to the velocity fields of various molecular clouds, and then inferring the required kinematic viscosity from the fit."992 Successful fits were made in the radial rauge from 10 to 100 pe. with an implied," Successful fits were made in the radial range from 10 to 100 pc, with an implied"993Another potentially interesting population is that defined by objects in region II of figure 3..,Another potentially interesting population is that defined by objects in region II of figure \ref{fig:coltheory}.994 These objects are clearly visible in figure | at magnitudes V.719.5., These objects are clearly visible in figure \ref{fig:color-mag} at magnitudes $V \gsim 19.5$.995 These blue objects could be either relatively hot (young) disk white dwarfs or blue horizontal branch (HB). low-metallicity halo stars.," These blue objects could be either relatively hot (young) disk white dwarfs or blue horizontal branch (HB), low-metallicity halo stars."996 However. for V220 HB stars would be located at 7100 kpc. where the density should be extremely small for standard galactic structure models.," However, for $V \gsim 20$ HB stars would be located at $\gsim100$ kpc, where the density should be extremely small for standard galactic structure models."997 There are 32 objects in region IL which are listed in table 5.., There are 32 objects in region II which are listed in table \ref{tab:wd}.998 The adopted cut-off in (VY7) (see table 1)) was chosen based on cooling sequence of disk white dwarfs (Bergeron. Wesemael. Beauchamp 1995) shown in figure 3..," The adopted cut-off in $(V-I)$ (see table \ref{tab:scheme}) ) was chosen based on cooling sequence of disk white dwarfs (Bergeron, Wesemael, Beauchamp 1995) shown in figure \ref{fig:coltheory}."999 We emphasize that the criterion adopted is somewhat arbitrary and it is used simply to illustrate the possible identification of these objects., We emphasize that the criterion adopted is somewhat arbitrary and it is used simply to illustrate the possible identification of these objects.1000 As can be seen from figure 3.. this sample can be contaminated by low redshift quasars.," As can be seen from figure \ref{fig:coltheory}, this sample can be contaminated by low redshift quasars."1001 In fact table 5 contains 2 already known quasar which are identified (name and redshift from the Simbad database)., In fact table \ref{tab:wd} contains 2 already known quasar which are identified (name and redshift from the Simbad database).1002 The U-band data will be useful to sort out these cases., The $U$ -band data will be useful to sort out these cases.1003 Finally. figure + shows the spatial distribution of these various candidates.," Finally, figure \ref{fig:starsdist} shows the spatial distribution of these various candidates."1004 Note that the northeast edge of the patch has been removed because of the incompleteness of the B-band catalogs., Note that the northeast edge of the patch has been removed because of the incompleteness of the B-band catalogs.1005 Similarly. a region along the southern edge was removed because of the incompleteness in the I-band catalog.," Similarly, a region along the southern edge was removed because of the incompleteness in the I-band catalog."1006 A small trimming of the whole region has also been done yielding a total area of 1.27 square degrees., A small trimming of the whole region has also been done yielding a total area of 1.27 square degrees.1007 From simulations of QSO tracks (figure 3)) high redshift QSOs (3«z 5) can be found in region III of the color-color diagram. while the available sample of known low redshift QSOs populate region IV (see figure 3.. Osmer 1998).," From simulations of QSO tracks (figure \ref{fig:coltheory}) ) high redshift QSOs $3<z<5$ ) can be found in region III of the color-color diagram, while the available sample of known low redshift QSOs populate region IV (see figure \ref{fig:coltheory}, Osmer 1998)."1008 The rough criteria used to define region III (table 1)) were chosen based on the simulated QSO track., The rough criteria used to define region III (table \ref{tab:scheme}) ) were chosen based on the simulated QSO track.1009 The blue part was chosen to be parallel to the stellar locus but shifted to minimize the contamination by stars., The blue part was chosen to be parallel to the stellar locus but shifted to minimize the contamination by stars.1010 Several improvements in the selection can be made to take into account the errors in colors. as a function of the magnitude. and to optimize the yield based on the expected density of objects of different types.," Several improvements in the selection can be made to take into account the errors in colors, as a function of the magnitude, and to optimize the yield based on the expected density of objects of different types."1011 Since the parent sample is public. interested groups are likely to make significant refinements to the selection eriteria adopted here.," Since the parent sample is public, interested groups are likely to make significant refinements to the selection criteria adopted here."1012 In region III there are 70 objects detected in all three passbands., In region III there are 70 objects detected in all three passbands.1013 These are listed in table 6.., These are listed in table \ref{tab:qsocand}.1014 In addition. there are 126 objects that are detected in V and / but not detected in B (hence have lower limits in (B.— VJ) that could also lie in region IV.," In addition, there are 126 objects that are detected in $V$ and $I$ but not detected in B (hence have lower limits in $(B-V)$ ) that could also lie in region IV."1015 These objects are listed in table 7.., These objects are listed in table \ref{tab:qsobdrop}.1016 Note that. since the depth of the B images varies across the patch. the limits on (BV) are more meaningful in some areas than others.," Note that, since the depth of the B images varies across the patch, the limits on $(B-V)$ are more meaningful in some areas than others."1017 The depth of the B frames corresponding to each object can be calculated from the V magnitude and the (BV) limits given in table 6.., The depth of the $B$ frames corresponding to each object can be calculated from the $V$ magnitude and the $(B-V)$ limits given in table \ref{tab:qsocand}.1018 In the tables the following naming convention has been adopted: QSO and QSOB stand for objects in region III detected in all three bands 73.0) and B-dropouts candidates. respectively.," In the tables the following naming convention has been adopted: QSO and QSOB stand for objects in region III detected in all three bands $\gsim3.0$ ) and B-dropouts candidates, respectively."1019 Adopting the criteria given in table | for region IV. where QSOs with z<3 are likely to be found. one finds 48 stellar objects which are listed in table 8..," Adopting the criteria given in table \ref{tab:scheme} for region IV, where QSOs with $z\lsim3$ are likely to be found, one finds 48 stellar objects which are listed in table \ref{tab:qsolowz}."1020 This table includes 6 known QSOs. as indicated (name and redshift are from the Simbad database).," This table includes 6 known QSOs, as indicated (name and redshift are from the Simbad database)."1021 In the table QLZ stands for low redshift (z <3.0) quasars., In the table QLZ stands for low redshift $z\lsim3.0$ ) quasars.1022 Note. however. that with the follow-up observations in U band to be carried out later this year. 1t will be possible to select low-z QSOs more efficiently.," Note, however, that with the follow-up observations in $U-$ band to be carried out later this year, it will be possible to select low-z QSOs more efficiently."1023 Figure 5. show the projected sky distribution of the QSO candidates., Figure \ref{fig:qsodist} show the projected sky distribution of the QSO candidates.1024 This figure should be compared with those for the seeing and the limiting magnitudes presented in paper III to investigate possible correlations between the QSO candidates and the quality of the data. especially the B-dropouts or those detected only in the /-band.," This figure should be compared with those for the seeing and the limiting magnitudes presented in paper III to investigate possible correlations between the QSO candidates and the quality of the data, especially the B-dropouts or those detected only in the $I$ -band."1025 At first glance there is no obvious correlation as the QSO candidates seem to be uniformly distributed over the surveyed area., At first glance there is no obvious correlation as the QSO candidates seem to be uniformly distributed over the surveyed area.1026noted in WOO. IH» has a cross-section that is approximately larger (per IE nucleus) than atomic IH. We adopt the enhanced Is cross-section and assume the gas is fully molecular (i.e. ΠΟ)ΓΗ= 0.5).,"noted in W00, $_2$ has a cross-section that is approximately larger (per H nucleus) than atomic H. We adopt the enhanced $_2$ cross-section and assume the gas is fully molecular (i.e. $n(\textrm{H}_2 )/n_{\textrm{H}} = 0.5$ )."1027 Relative to earlier work focusing on the largely atomic ISM. the inclusion of the molecular enhancement increases the cross-section most signicantlv ad extreme ultraviolet wavelengths where hydrogen opacity dominates.," Relative to earlier work focusing on the largely atomic ISM, the inclusion of the molecular enhancement increases the cross-section most signiÞcantly at extreme ultraviolet wavelengths where hydrogen opacity dominates."1028 The well-tested IDL (line routines POLY_FFIT and SVD were used to evaluate aud test the uniqueness of the ts., The well-tested IDL Þtting routines FIT and SVD were used to evaluate and test the uniqueness of the Þts.1029 The fitting coellicients are given in Table 1.., The fitting coefficients are given in Table \ref{table_fits}.1030 The resulting opacily curves are shown in Figure 2.., The resulting opacity curves are shown in Figure \ref{fig:cross}.1031 By comparison wilh a gas of pure IE ancl Ile. Figure 2 clearly shows that C. O and Noble gases Ne and Ar. contribute signicantlv to the gas opacity at energies > Q.3keV. Away from photoelectric edges the fitting errors are (vpically al the level. which is small compared to the compositional uncertainties of gas and dust.," By comparison with a gas of pure H and He, Figure \ref{fig:cross} clearly shows that C, O and Noble gases Ne and Ar, contribute signiÞcantly to the gas opacity at energies $E > 0.3$ keV. Away from photoelectric edges the fitting errors are typically at the level, which is small compared to the compositional uncertainties of gas and dust."1032 Noticeable in the dust component are significant (~1054) error spikes near to metal Ix-edge thresholds., Noticeable in the dust component are significant $(\sim10\%)$ error spikes near to metal K-edge thresholds.1033 These errors (consistent with those in WOO) arise from the numerical discretization of the elemental cross-sections. and trom the fundamental limitations of a low-order fit.," These errors (consistent with those in W00) arise from the numerical discretization of the elemental cross-sections, and from the fundamental limitations of a low-order fit."1034 It is important to note that striving lor a more accurate polvnomial Lit ad Ix-shell edges is not entirely meaningful unless we include actual solid-state effects. which in general are too complex for a low order polvnomial fit (Draine2003)..," It is important to note that striving for a more accurate polynomial fit at K-shell edges is not entirely meaningful unless we include actual solid-state effects, which in general are too complex for a low order polynomial fit \citep{Draine:2003fk}."1035" The derivation of the sell-blanketing factor. {η} for spherical. homogeneous grains is described in Appendix A. Plots of /5,CE) versus X-ray energy for a range of grain sizes are shown in Figure 3..."," The derivation of the self-blanketing factor $\fb$ for spherical, homogeneous grains is described in Appendix A. Plots of $\fb$ versus X-ray energy for a range of grain sizes are shown in Figure \ref{fig:self_blanket}. ."1036" As a function of energy it bears the imprintof 64,44 since f;(E) depends", As a function of energy it bears the imprintof $\sxdust$ since $\fb$ depends1037Normal form theory is one of the most effective tools for the local study of nonlinear dynamical systems.,Normal form theory is one of the most effective tools for the local study of nonlinear dynamical systems.1038 The basic idea is to use permissible transformations and obtain a simplified vector field., The basic idea is to use permissible transformations and obtain a simplified vector field.1039 Transformations are permissible that preserve certain dynamical features of the original system., Transformations are permissible that preserve certain dynamical features of the original system.1040 The space of all permissible transformations form a group and acts on vector fields like an action of a group on a vector space., The space of all permissible transformations form a group and acts on vector fields like an action of a group on a vector space.1041 Consider a set of vector fields generated by the group acting on a given vector field., Consider a set of vector fields generated by the group acting on a given vector field.1042" Then, the infinite level normal form of the vector field is to find a unique representative from this set."," Then, the infinite level normal form of the vector field is to find a unique representative from this set."1043" Thereby, the computation of infinite level normal forms is an important tool for classification of vector fields."," Thereby, the computation of infinite level normal forms is an important tool for classification of vector fields."1044 The uniqueness of a normal form computation is determined by the (infinite) level of normal form through an specifically chosen normal form style and costyle., The uniqueness of a normal form computation is determined by the (infinite) level of normal form through an specifically chosen normal form style and costyle.1045" The level of a normal form assesses the remaining spectral data at our disposal in the permissible transformation space for further simplification of the system while a normal form style and costyle makes a unique choice for the normal form vector field in each level of normal form computation, see (0,(21∙∙"," The level of a normal form assesses the remaining spectral data at our disposal in the permissible transformation space for further simplification of the system while a normal form style and costyle makes a unique choice for the normal form vector field in each level of normal form computation, see \cite{baiderchurch,Gazor,GazorYuSpec,MurdBook,Sanders03}."1046" Therefore, the infinite level normal form is sometimes called the simplest normal form or unique normal form when a normal form style have already been fixed."," Therefore, the infinite level normal form is sometimes called the simplest normal form or unique normal form when a normal form style have already been fixed."1047" When a system has some symmetries, it is important that its normal form would preserve the symmetries."," When a system has some symmetries, it is important that its normal form would preserve the symmetries."1048 Although there are research results on the simplest normal forms of symmetric systems but they are considerably less than the existing results on normal forms without symmetry., Although there are research results on the simplest normal forms of symmetric systems but they are considerably less than the existing results on normal forms without symmetry.1049 There are several reasons for this., There are several reasons for this.1050" The first difficulty is to recognize the symmetries and then, to find the group of transformations preserving the symmetries."," The first difficulty is to recognize the symmetries and then, to find the group of transformations preserving the symmetries."1051" Therefore, one is also concerned with the space of the symmetric vector fields invariant under the group action."," Therefore, one is also concerned with the space of the symmetric vector fields invariant under the group action."1052 This needs a good understanding on the algebraic interactions of the symmetric and nonsymmetric vector fields with the transformation groups., This needs a good understanding on the algebraic interactions of the symmetric and nonsymmetric vector fields with the transformation groups.1053" Once all these are successfully accomplished, in most cases the normal form computation is more difficult in systems with symmetry than in systems without symmetry."," Once all these are successfully accomplished, in most cases the normal form computation is more difficult in systems with symmetry than in systems without symmetry."1054 Normal form decomposition of a nonsymmetric vector field into two symmetric vector fields can have many important potential applications., Normal form decomposition of a nonsymmetric vector field into two symmetric vector fields can have many important potential applications.1055 For example Eulerian and Hamiltonian vector fields are two important families of vector fields., For example Eulerian and Hamiltonian vector fields are two important families of vector fields.1056" Therefore, the study of their dynamics is important."," Therefore, the study of their dynamics is important."1057 Normal form decomposition of arbitrary vector fields into Eulerian (nonconservative or dissipative) and Hamiltonian (conservative) vector fields are also important in both theory and applications., Normal form decomposition of arbitrary vector fields into Eulerian (nonconservative or dissipative) and Hamiltonian (conservative) vector fields are also important in both theory and applications.1058" Wiggins (0,Chapter33] remarks that transforming a system into an integrable Hamiltonian system plus a nonconservative perturbation facilitates “a wealth of techniques for the global analysis of nonlinear dynamical systems such as Melnikov theory, perturbation theory for normally hyperbolic invariant manifolds, and Kolmogorov, Arnold, and Moser (KAM) theory”."," Wiggins \cite[Chapter 33]{Wiggins} remarks that transforming a system into an integrable Hamiltonian system plus a nonconservative perturbation facilitates “a wealth of techniques for the global analysis of nonlinear dynamical systems such as Melnikov theory, perturbation theory for normally hyperbolic invariant manifolds, and Kolmogorov, Arnold, and Moser (KAM) theory”."1059" Furthermore, )nn1001 [OJindicatedthatsuchkindo| decompositioncanbeusedindevelopinganO D Esolver."," Furthermore, n \cite{PalacChaos05} indicated that such kind of decomposition can be used in developing an ODE solver."1060F orexampleusin fusionte," For example using the obtained scalar function as the integral of a piece of the vector field in an ODE solver, can enhance its efficiency."1061rmsandit, These signify the importance of developing methods for such kind of decomposition.1062sdynamiccsiswellunder stoodasacom Section5.5].," Recently, some researchers have paid attention to this theory and have made important contributions to the subject, see cs is well understood as a combination/competition of the dynamics associated with the advection and diffusion terms, see \cite[Section 5.5]{Logan}."1063".Therefore, thestudyof eachcomponentsof adecomposedvector fieldmayhelptobettert oris"," Therefore, the study of each components of a decomposed vector field may help to better understand the dynamics of the full system as a combined dynamics or as a competing behavior between its components."1064"aconservativevector see1001]12, [[4]."," Thus, it is important to individually deal with the cases that the vector field is a quasi-Eulerian, or is a conservative vector field, see \cite{GazorMoazeni,GazorMokhtari1st}."1065.Inthispaperavector f ieldiscalledconservativewh , In this paper a vector field is called when it has a first integral and is called when it does not have any first integral.1066"This paper deals with the nonconservativefield, family of our upcoming results on such decomposition for Hopf-Zero singular vector fields.", This paper deals with the nonconservative family of our upcoming results on such decomposition for Hopf-Zero singular vector fields.1067 Systems with Hopf-Zero singularity are important in applications., Systems with Hopf-Zero singularity are important in applications.1068" There are several important research results on the simplest normal forms of Hopf-Zero singularity, see .."," There are several important research results on the simplest normal forms of Hopf-Zero singularity, see \cite{AlgabaHopfZ,ChenHopfZ03,ChenHopfZ,YuHopfZero}."1069" However, there does not seem to exist any result on such kind of normal form decomposition(ums for Hopf-Zero singularity."," However, there does not seem to exist any result on such kind of normal form decomposition for Hopf-Zero singularity."1070" Although the Hamiltonian vector fields (symplectic structures) require an even dimensionality, the decomposition idea still can work."," Although the Hamiltonian vector fields (symplectic structures) require an even dimensionality, the decomposition idea still can work."1071" Indeed we instead work with conservative and nonconservative family of vector fields, see |13].."," Indeed we instead work with conservative and nonconservative family of vector fields, see \cite{GazorMokhtari}."1072 In this paper we are concerned with the study of nonconservative family., In this paper we are concerned with the study of nonconservative family.1073" Indeed, we consider the family of Hopf-Zero singularities given by"," Indeed, we consider the family of Hopf-Zero singularities given by"1074bv the effects of the orbit of the Sun around the Galactic Center. while the motion out of the plane should contain only small terms from (he Z-component of the Solar Motion aud a possible peculiar motion ofÀ*.,"by the effects of the orbit of the Sun around the Galactic Center, while the motion out of the plane should contain only small terms from the Z-component of the Solar Motion and a possible peculiar motion of."1075. In the following subsections. we investigate the various components of the apparent velocity and acceleration ofA*.," In the following subsections, we investigate the various components of the apparent velocity and acceleration of."1076. lt is clear [rom Fie., It is clear from Fig.1077 1 that the apparent motion of is almost entirely in the Galactic plane., 1 that the apparent motion of is almost entirely in the Galactic plane.1078 Thus. we convert the positions [rom equatorial to Galactic coordinates and determine motions in Galactic coordinates. (," Thus, we convert the positions from equatorial to Galactic coordinates and determine motions in Galactic coordinates. ("1079Because of the high accuracy of our observations. some pitfalls in the implementation of the equatorial to Galactic coordinate conversion (Lane 1979). and the need to transfer the LAUdefined plane [rom D1950 to J2000 coordinates. we document the procedures involved in the Appendix.),"Because of the high accuracy of our observations, some pitfalls in the implementation of the equatorial to Galactic coordinate conversion (Lane 1979), and the need to transfer the IAU–defined plane from B1950 to J2000 coordinates, we document the procedures involved in the Appendix.)"1080 Fig., Fig.1081 4 is a plot the position of relative to J1745.283 in Galactic coordinates., 4 is a plot the position of relative to J1745–283 in Galactic coordinates.1082 Variance-weighted least-squares fits of straight lines to these data are indicated bv dashed lines., Variance-weighted least-squares fits of straight lines to these data are indicated by dashed lines.1083 The apparent motion of is —6.379£0.026 and —0.2024:0.019 mas in Galactic longitude and latitude. respectively.," The apparent motion of is $-6.379\pm0.026$ and $-0.202\pm0.019$ mas in Galactic longitude and latitude, respectively."1084 Assuming a distance to the Galactie center (£24) of 8.040.5 kpe (Reid 1993). the apparent angular motion of in the plane of the Galaxy translates to —2412:15..," Assuming a distance to the Galactic center$\rnot$ ) of $8.0\pm0.5$ kpc (Reid 1993), the apparent angular motion of in the plane of the Galaxy translates to $-241\pm15$."1085 The uncertainty [rom measurement error alone is only 1.. and the quoted value is dominated by the 0.5 kpe uncertainty in.," The uncertainty from measurement error alone is only $1$, and the quoted value is dominated by the 0.5 kpc uncertainty in."1086. Provided that the peculiar motion of is small (see 83.2). this corresponds to the reflex of (rue orbital motion of the Sun around the Galactic Center.," Provided that the peculiar motion of is small (see 3.2), this corresponds to the reflex of true orbital motion of the Sun around the Galactic Center."1087 This reflex motion can be parameterized as a combination of a circular orbit of the LSR) and the deviation of the Sun from that cireular orbit. (the Solar Motion)., This reflex motion can be parameterized as a combination of a circular orbit of the LSR) and the deviation of the Sun from that circular orbit (the Solar Motion).1088 The Solar Motion. determined from Iipparcos data by Dehnen Binney (1993). is 5.25+0.62 iin (he direction of Galactic rotation.," The Solar Motion, determined from Hipparcos data by Dehnen Binney (1998), is $5.25\pm0.62$ in the direction of Galactic rotation."1089 Removing this component of the Solar Motion from thereffer of the apparent motion of vields an estimate for oof 236415 Note that other definitions and measurements of this component of the Solar Motion have resulted in somewhat greater values. 12 (Cox2000).. which if adopted would reduce our value of to 229.," Removing this component of the Solar Motion from the of the apparent motion of yields an estimate for of $236\pm15$ Note that other definitions and measurements of this component of the Solar Motion have resulted in somewhat greater values, 12 \citep{Allen00}, which if adopted would reduce our value of to 229."1090. Should be determined independently to high accuracy. then our measurement of the apparent motion of would eive with corresponding accuracy.," Should be determined independently to high accuracy, then our measurement of the apparent motion of would give with corresponding accuracy."1091 Orbital solutions for stars near that combine proper motions and radial velocities have great potential to accomplish this 2003:Ghezetal. 2003).," Orbital solutions for stars near that combine proper motions and radial velocities have great potential to accomplish this \citep{E03,Ghez03}."1092. A direct comparison of our measurement of the angular rotation rate of the LSR at the, A direct comparison of our measurement of the rotation rate of the LSR at the1093the Galactic field. ancl are being found in ever-increasing numbers with the Chandra X-ray observatory (Grindlay et al.,"the Galactic field, and are being found in ever-increasing numbers with the Chandra X-ray observatory (Grindlay et al."1094 2001)., 2001).1095 Milliseconcl pulsars. including some in binaries or wilh planets (D'Amico οἱ al.," Millisecond pulsars, including some in binaries or with planets (D'Amico et al."1096 2001) are prevalent in cluster cores., 2001) are prevalent in cluster cores.1097 Cataclysmic binaries in clusters have been predicted ancl are also being found. (Shara et al., Cataclysmic binaries in clusters have been predicted and are also being found (Shara et al.1098 1996: Crinclay et al., 1996; Grindlay et al.1099 2001)., 2001).1100 A few sdD stars have been located and characterized (Aloehler et al., A few sdB stars have been located and characterized (Moehler et al.1101 1997)., 1997).1102 Even though the stellar neighbourhood within an open cluster is less dense (han that of a elobular cluster it is still capable of producing exotic objects., Even though the stellar neighbourhood within an open cluster is less dense than that of a globular cluster it is still capable of producing exotic objects.1103 The number of BSs found in the open cluster M61 is much greater (han we would expect if they are simply produced via mass transfer in binaries exhibiting the same distribution of orbital characteristics as binary stars founcl in the field., The number of BSs found in the open cluster M67 is much greater than we would expect if they are simply produced via mass transfer in binaries exhibiting the same distribution of orbital characteristics as binary stars found in the field.1104 Furthermore. these BSs have a variety of living arrangements (Leonard 1996. and references within).," Furthermore, these BSs have a variety of living arrangements (Leonard 1996, and references within)."1105 Some are single while others are [ound with a companion., Some are single while others are found with a companion.1106 In some cases the DS and the companion star interact in an intimate and regular manner (short-period circular orbit). in other cases the relationship is distant (long-period orbit) aud Nav even appear eccentric.," In some cases the BS and the companion star interact in an intimate and regular manner (short-period circular orbit), in other cases the relationship is distant (long-period orbit) and may even appear eccentric."1107 One of the BSs is so massive. a super-D5. that it must represent the merger of three stars. ancl another is observed in an active triple-svsteni. a (van den Bere et al.," One of the BSs is so massive, a super-BS, that it must represent the merger of three stars, and another is observed in an active triple-system, a menage-a-trois (van den Berg et al."1108 2001)., 2001).1109 All of (his suggests that the BSs have varied formation histories ancl (hat no one mechanism is responsible for their production (Leonard 1996)., All of this suggests that the BSs have varied formation histories and that no one mechanism is responsible for their production (Leonard 1996).1110 In parücular. (he presence of a super-D5 and of Bss in eccentric binaries is not. predicted by standard binary evolution and points to dynamical interactions (ampering will (he destinies ol stars.," In particular, the presence of a super-BS and of BSs in eccentric binaries is not predicted by standard binary evolution and points to dynamical interactions tampering with the destinies of stars."1111 On a basic dvnamical level a star cluster is composed of No bodies interacting wilh each other due to the gravitational lorce of everv other body in the svstem., On a basic dynamical level a star cluster is composed of $N$ bodies interacting with each other due to the gravitational force of every other body in the system.1112 The ideal method [or following the evolution of such a svstenm is to integrate directly the NV individual equations of motion. the N-body approach.," The ideal method for following the evolution of such a system is to integrate directly the $N$ individual equations of motion, the $N$ -body approach."1113 However. the cost of integrating the cluster for a scales as ο ΑΔ per force caleulation. V7 to integrate No bodies for one crossing (dynamical) üme. and there are of order No crossing (mes per relaxation (ime — so the method is computationally expensive.," However, the cost of integrating the cluster for a relaxation-time scales as $N^3$ – $N$ per force calculation, $N^2$ to integrate $N$ bodies for one crossing (dynamical) time, and there are of order $N$ crossing times per relaxation time – so the method is computationally expensive."1114 As a result most N-bocly simulations performed until recently. alühough state-ol-the-art at the (time. have involved a varying nunber of simplified and unrealistic conditions. such as including only single stus. using only equal-mass stars. neglecting stellar evolution or assuming no external tidal field (MeMillan. Hut Makino 1991: llegeie Aarseth 1992).," As a result most $N$ -body simulations performed until recently, although state-of-the-art at the time, have involved a varying number of simplified and unrealistic conditions, such as including only single stars, using only equal-mass stars, neglecting stellar evolution or assuming no external tidal field (McMillan, Hut Makino 1991; Heggie Aarseth 1992)."1115 Performance has been enhanced by the development οἱ improved computational algorithms., Performance has been enhanced by the development of improved computational algorithms.1116 For example. the use of individual time-steps (Aarseth 1963) enables each star to evolve on iis own natural dvnamical timescale rather rather," For example, the use of individual time-steps (Aarseth 1963) enables each star to evolve on its own natural dynamical timescale rather rather"1117component is very uncertain. as discussed below.,"component is very uncertain, as discussed below."1118 The peak redshifts for the different spectral Classes reflect (heir vvalues., The peak redshifts for the different spectral classes reflect their values.1119 This illustrates clearly that the Euclidean lis a cosmological distance indicator., This illustrates clearly that the Euclidean is a cosmological distance indicator.1120 In Figure 11 we show the huninositv. function for ease A. as well as the luminosity distribution for the 1319 GUSBAD sources with P>0.5 ph ? !.," In Figure 11 we show the luminosity function for case A, as well as the luminosity distribution for the 1319 GUSBAD sources with $P > 0.5$ ph $^{-2}$ $^{-1}$."1121 Also shown are the individual luminosity functions for the five spectral classes., Also shown are the individual luminosity functions for the five spectral classes.1122 The first peak of the Iuminosity funelion is contributed by spectral class 1., The first peak of the luminosity function is contributed by spectral class 1.1123 The lower half of ils gaussiuir clearly plays no role. as il produces no objects in the Iuminosity distribution.," The lower half of its gaussian clearly plays no role, as it produces no objects in the luminosity distribution."1124 The Iuminosity assigned to this class is uncertain. since the slope of the curve in Figure 9 is relatively shallow.," The luminosity assigned to this class is uncertain, since the slope of the curve in Figure 9 is relatively shallow."1125 Actually. if the [for sp=1 were only 1.20 larger. it could not be reproduced by any value of £L...," Actually, if the for $sp=1$ were only $1.2\sigma$ larger, it could not be reproduced by any value of $L_c$."1126" Altogether. (his suggests that the (large) z=0 density rates fy for sp=1 given in Table 4 are very uncertain,"," Altogether, this suggests that the (large) $z=0$ density rates $R_0$ for $sp = 1$ given in Table 4 are very uncertain."1127 The second peak in the huninosity [unction is contributed by the large number of GRBs in spectral classes 2-5., The second peak in the luminosity function is contributed by the large number of GRBs in spectral classes 2-5.1128 Their combined :=0 rate is 0.09—0.22 ? |. for models A and D. respectively.," Their combined $z=0$ rate is $0.09 - 0.22$ $^{-3}$ $^{-1}$, for models A and B, respectively."1129 ecorrelations with radiated energy or Iuminosity are of interest in exploring (he mechanism for the prompt emission of GRBs., correlations with radiated energy or luminosity are of interest in exploring the mechanism for the prompt emission of GRBs.1130" They are also of practical interest in allowing an estimation of the redshift of GRBs with measured,,.", They are also of practical interest in allowing an estimation of the redshift of GRBs with measured.1131. In this section. we discuss the derivation of the relevant isotropic-equivalent Iuminositv.Lj... present the aand ccorrelations and briefly mention the problem of extracting individual redshilts from ccorrelations.," In this section, we discuss the derivation of the relevant isotropic-equivalent luminosity, present the and correlations and briefly mention the problem of extracting individual redshifts from correlations."1132 As discussed in Section 3.the derivation of the huninosity function involves an iteration of the central luminosity L(sp). where each spectral component is a gaussian wilh dispersionAix.," As discussed in Section 3,the derivation of the luminosity function involves an iteration of the central luminosity $L_c(sp)$, where each spectral component is a gaussian with dispersion."1133 We chose a dispersion p=0.5 that produces a reasonably smooth overall Iuminosity function., We chose a dispersion $= 0.5$ that produces a reasonably smooth overall luminosity function.1134 We want to use the £.(sp) Iuminosities in deriving the isotropic-equivalent. peak huminosities uused in the correlations., We want to use the $L_c(sp)$ luminosities in deriving the isotropic-equivalent peak luminosities used in the correlations.1135 It turns out. however. that £.(sp) varies considerably with oie...," It turns out, however, that $L_c(sp)$ varies considerably with ."1136 We explored using, We explored using1137(Hammel&Lockwood1997).,\citep{ham97}.1138. ΗΕ wind speed is a function of latitude as on all the giant planets of our solar svstem. (hen spots al different. latitudes will circle the object with different periods.," If wind speed is a function of latitude as on all the giant planets of our solar system, then spots at different latitudes will circle the object with different periods."1139 Observations taken several months apart will show periodic variations wilh different periods as is reported for the L-dwarf 2\TASS 1145423., Observations taken several months apart will show periodic variations with different periods as is reported for the L-dwarf 2MASS 1145+23.1140 Finally. L dwarls whose clouds change on time scales of a few days or less or whose cloudy spots are distributed at several latitudes with different wind speeds could still produce a photometric signal. but the signal might not be periodic.," Finally, L dwarfs whose clouds change on time scales of a few days or less or whose cloudy spots are distributed at several latitudes with different wind speeds could still produce a photometric signal, but the signal might not be periodic."1141 Clearly. more observations aud modeling are required to better characterize atmospheric circulation and weather in L-dwarl alinospheres.," Clearly, more observations and modeling are required to better characterize atmospheric circulation and weather in L-dwarf atmospheres."1142 There is little doubt that some L dwarls are photometrically variable., There is little doubt that some L dwarfs are photometrically variable.1143 Although most authors suggest that the variations are caused by clouds. the possibility of magnetic spots is often mentioned (e.g.Dailer-Jones&Mundi.1999.2001:Martínetal.2001).," Although most authors suggest that the variations are caused by clouds, the possibility of magnetic spots is often mentioned \citep[e.g.][]{bai99,bai01,mart01}."1144. We have shown that the low ionization fraction predicted by L-cdwarf models and the accompanvinely low magnetic Revnolds numbers stronglv argue against spots as a possible cause lor the photometric variations., We have shown that the low ionization fraction predicted by L-dwarf models and the accompanyingly low magnetic Reynolds numbers strongly argue against spots as a possible cause for the photometric variations.1145 On (he other hand silicate and iron grains condense im L-cwarl ablmospheres within (he photosphere., On the other hand silicate and iron grains condense in L-dwarf atmospheres within the photosphere.1146 These clouds are likely responsible for the photometric variations discovered in (he various studies. particularly for the later L cdwarls (about L2 and later).," These clouds are likely responsible for the photometric variations discovered in the various studies, particularly for the later L dwarfs (about L2 and later)."1147 Since the thermal emission of T cdwarfs is also influenced by clouds (Marley. et al., Since the thermal emission of T dwarfs is also influenced by clouds (Marley et al.1148 2001) we predict that. variability will also be found in the opacity window regions of these objects., 2001) we predict that variability will also be found in the opacity window regions of these objects.1149 Further work with models ancl more observations are clearly needed to better understand cloud composition ancl dvnanmics., Further work with models and more observations are clearly needed to better understand cloud composition and dynamics.1150High luminosity aud massive high redshift clusters of galaxies are crucially inuportant tools in cosinology.,High luminosity and massive high redshift clusters of galaxies are crucially important tools in cosmology.1151 Their distribution aud evolution is fully determined by the spectrum of primordial perturbations aud cosmological parameters Q0 aud A (e.g. Press Schechter 1971)., Their distribution and evolution is fully determined by the spectrum of primordial perturbations and cosmological parameters $\Omega_0$ and $\Lambda$ (e.g. Press Schechter 1974).1152 In particular. the moclels of low £2 universe (witli or without cosmological coustant) (e.g. Henry 2000. Borgani Guzzo 2001) predict a higher deusity of massive clusters at high redshifts than the bieh © A sample of high redshift clusters is essential in determining the evolution of the clusters X-ray luminosity functiou (e.g. Rosati et al..," In particular, the models of low $\Omega$ universe (with or without cosmological constant) (e.g. Henry 2000, Borgani Guzzo 2001) predict a higher density of massive clusters at high redshifts than the high $\Omega$ A sample of high redshift clusters is essential in determining the evolution of the clusters X-ray luminosity function (e.g. Rosati et al.,"1153 1998). aud also would allow us to determine if there is evolution in the |=uinuositv-teruperature (Ly— T) relation.," 1998), and also would allow us to determine if there is evolution in the luminosity-temperature $L_X-T$ ) relation."1154 The evolution of the Ly—TF is very iniportant since it is related to plivsical mmechauisins of cooling auc heating in the central cluster region (e.g. Tozzi Norman. 2001).," The evolution of the $L_X-T$ is very important since it is related to physical mechanisms of cooling and heating in the central cluster region (e.g. Tozzi Norman, 2001)."1155 Ouly a few bright high redshift clusters have been found so far (e.g. in the EMSS. Gioia Luppino 1991: in the RDCS Rosati et al.," Only a few bright high redshift clusters have been found so far (e.g. in the EMSS, Gioia Luppino 1994; in the RDCS Rosati et al."1156 1999. Della Ceca et al.," 1999, Della Ceca et al."1157 2000: in the WARPS Ebeling et al., 2000; in the WARPS Ebeling et al.1158 1005: 2000) and only 9 of them at 2>0.5 have a measure of their temperature (e.g. Della Ceca et al., 1998; 2000) and only 9 of them at $z>0.5$ have a measure of their temperature (e.g. Della Ceca et al.1159 2001. Cagnoni et al.," 2001, Cagnoni et al."1160 2001. Stauford et al.," 2001, Stanford et al."1161 2001)., 2001).1162 Siuce the statistics is very scanty. the search for high redshift aud bieh luminosity clusters is the ouly meaus to improve such studies.," Since the statistics is very scanty, the search for high redshift and high luminosity clusters is the only means to improve such studies."1163 Two high redshift (2> 0.15) clusters of galaxies have been already found zunoug the 16ROSAT blank field sources and other cau be present in the remaining 11 unidentified sources., Two high redshift $z \geq 0.45$ ) clusters of galaxies have been already found among the 16 blank field sources and other can be present in the remaining 11 unidentified sources.1164 We will describe the selection iuethod in Section 2. aud cliscuss the possibilities regarding the uature of the blauks aud the presence of high redshift clusters of ealaxies among them in Section 3.," We will describe the selection method in Section 2, and discuss the possibilities regarding the nature of the blanks and the presence of high redshift clusters of galaxies among them in Section 3."1165" We call blank field sources"" (blanks) all the bright X-ray sources (Fx>10.P! erg 7s 4) with no optical counterpart on the Palomar Sky survey (ο O=21.5) within their 39"" ))", We call `blank field sources' (blanks) all the bright X-ray sources $F_X > 10^{-13}$ erg $^{-2}$ $^{-1}$ ) with no optical counterpart on the Palomar Sky survey (to O=21.5) within their $39^{\prime \prime}$ )1166Pin,2in1167and AT); (the interval between the minimal points of the Av eveles) ancl the eliteh number.,and $\Delta{T_{min}}$ (the interval between the minimal points of the $\Delta\nu$ cycles) and the glitch number.1168" This plot shows that the indicated intervals are approximately equal to 580 and GOO davs. respectively,"," This plot shows that the indicated intervals are approximately equal to 580 and 600 days, respectively."1169 The bottom panel shows the relation between the glitch parameters .A4 (the relaxation time interval) and «ως (the rise time interval) and the eliteh number and defines the average values of these parameters equal to 400 and 180 days. respectively.," The bottom panel shows the relation between the glitch parameters $\Delta{T_{rel}}$ (the relaxation time interval) and $\Delta{T_{ris}}$ (the rise time interval) and the glitch number and defines the average values of these parameters equal to 400 and 180 days, respectively."1170 These three relations indicate that all the slow elitches observed have similar properties which can be described by the following average parameters., These three relations indicate that all the slow glitches observed have similar properties which can be described by the following average parameters.1171 The elitches have a small absolute amplitude equal to 3.5x10? Iz., The glitches have a small absolute amplitude equal to $3.5\times 10^{-9}$ Hz.1172" Thev are characterized by the identical intervals AT), and approximately the same width of the intervals «Αρ. equal to ~ 600 davs."," They are characterized by the identical inter-glitch intervals $\Delta{T_{max}}$ and approximately the same width of the intervals $\Delta{T_{min}}$, equal to $\sim$ 600 days."1173 The glitehes have similar signature related to a slow increase in the rotation frequency during ~ 200 davs and the subsequent relaxation back to (he pre-elitch value during ο” 400 days., The glitches have similar signature related to a slow increase in the rotation frequency during $\sim$ 200 days and the subsequent relaxation back to the pre-glitch value during $\sim$ 400 days.1174 The relaxation after all the glitches can be described by a linear curve as is seen [rom Figure 4((a)., The relaxation after all the glitches can be described by a linear curve as is seen from Figure \ref{form}( (a).1175 These properties suggest that the sequence of (he slow elitches observed can be approximated by a sawtooth-like function., These properties suggest that the sequence of the slow glitches observed can be approximated by a sawtooth-like function.1176 We created the model sawtooth-like curve using the indicated average parameters., We created the model sawtooth-like curve using the indicated average parameters.1177 This model curve has the starting point NJD 48350 and includes 10 eveles consisting of two stages the stage of a linear gliteh arising with a timescale of 200 davs and the stage of a linear post-elitch relaxation with a timescale of 400 days., This model curve has the starting point MJD 48350 and includes 10 cycles consisting of two stages – the stage of a linear glitch arising with a timescale of 200 days and the stage of a linear post-glitch relaxation with a timescale of 400 days.1178 Only two eglitches observed. 2 and 3. (take off from this sequence.," Only two glitches observed, 2 and 3, take off from this sequence."1179 An analvsis of the Av eveles showed that event 2 represents (he sum of two partially overlapping glitches 2 and 3., An analysis of the $\Delta\nu$ cycles showed that event 2 represents the sum of two partially overlapping glitches 2 and 3.1180 Glitch 3 defines the starting point of a new phase in (he sequence of the slow glitches., Glitch 3 defines the starting point of a new phase in the sequence of the slow glitches.1181" Therefore. event 2 should be described by three stages the stage of a linear gliteh arising with a timescale of 200 days is followed by the stage in which the eliteh amplitude keeps constant within 400 davs (the duration of this interval corresponds to the duration of the relaxation time interval AZ,,;) and only then is Iollowed by a Inear post-eliteh relaxation wilh a timescale of 400 days."," Therefore, event 2 should be described by three stages – the stage of a linear glitch arising with a timescale of 200 days is followed by the stage in which the glitch amplitude keeps constant within 400 days (the duration of this interval corresponds to the duration of the relaxation time interval $\Delta{T_{rel}}$ ) and only then is followed by a linear post-glitch relaxation with a timescale of 400 days."1182 The derived values for this model sawtooth-like curve are given in Table 4.., The derived values for this model sawtooth-like curve are given in Table \ref{sawt}.1183 Figure 4((b) shows a model sawtooth-like curve with a period of GOO days which is superimposed on the eliteh sequence observed., Figure \ref{form}( (b) shows a model sawtooth-like curve with a period of 600 days which is superimposed on the glitch sequence observed.1184 It is seen that (he maxima of the model curve well coincide with the maxima of nearly all the slow glitches., It is seen that the maxima of the model curve well coincide with the maxima of nearly all the slow glitches.1185 Only the maxima of glitehes 8 and 9 slightly do not correspond to the model curve., Only the maxima of glitches 8 and 9 slightly do not correspond to the model curve.1186 However. as is seen [rom the plot. the slight deviations of the amplitude and phase of these evcles [rom a model curve do not change a phase of the next eveles of the sequence.," However, as is seen from the plot, the slight deviations of the amplitude and phase of these cycles from a model curve do not change a phase of the next cycles of the sequence."1187" Probably. the shape of these elitches was nol restored. precisely,"," Probably, the shape of these glitches was not restored precisely."1188 The model curve very. well describes partially overlapping glitches 2 and 3., The model curve very well describes partially overlapping glitches 2 and 3.1189 It is seen that in this range there was a phase shift lor 400 days. exactly equal to relAT.," It is seen that in this range there was a phase shift for 400 days, exactly equal to $\Delta{T_{rel}}$."1190 After that. point 3 started marking5 the starting5 point of a new phase in the sequence ol the slow elitches.," After that, point 3 started marking the starting point of a new phase in the sequence of the slow glitches."1191 Despite the phase shift between points 2 and 3. we suppose that the," Despite the phase shift between points 2 and 3, we suppose that the"1192we are simply looking at a field star Our analysis suggests that Bochum 10 is a very voung and poorly populated open cluster.,we are simply looking at a field star Our analysis suggests that Bochum 10 is a very young and poorly populated open cluster.1193 As many other voung poor clusters. it is certainly an unbounded: objects and will gradually disrupt.," As many other young poor clusters, it is certainly an unbounded objects and will gradually disrupt."1194 We provide estimates of interstellar reddening and distance compatible with previous studies., We provide estimates of interstellar reddening and distance compatible with previous studies.1195 As for Bochum 11. we find that it is a voung open cluster. less than 4«10? ves old. and. confirm previous estimates for the cluster mean reddening and From our photometry we find. indications of possible pre AIS candidates in Bochum 9 and. 11.," As for Bochum 11, we find that it is a young open cluster, less than $4 \times 10^{6}$ yrs old, and confirm previous estimates for the cluster mean reddening and From our photometry we find indications of possible pre MS candidates in Bochum 9 and 11."1196 This issue will be addressed in a forthcoming paper (Itomaniello et al 2001). where CDVI photometry for all the other star clusterings known to lie in the Carina spiral feature will be presented and. compared with theoretical moclels.," This issue will be addressed in a forthcoming paper (Romaniello et al 2001), where $UBVRI$ photometry for all the other star clusterings known to lie in the Carina spiral feature will be presented and compared with theoretical models."1197 This paper was based on observations made at ESO-La Sila., This paper was based on observations made at ESO-La Silla.1198 We acknowledge: useful discussions with M. Zoceali. M. Rejkuba and A. Brown.," We acknowledge useful discussions with M. Zoccali, M. Rejkuba and A. Brown."1199 GC thanks ESO for the kind hospitality., GC thanks ESO for the kind hospitality.1200 We are grateful to Drs., We are grateful to Drs.

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