ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2The structure of the paper is as follows.,The structure of the paper is as follows.3 In Section 2 we describe our set of simulated clusters;, In Section 2 we describe our set of simulated clusters.4 After describing the procedure to compute the svuthetic spectra. we preseut i Section 3 our results on the excess. its origin and a comparison with observations.," After describing the procedure to compute the synthetic spectra, we present in Section 3 our results on the excess, its origin and a comparison with observations."5 We draw our main conclusions in Section L., We draw our main conclusions in Section 4.6" We analyze a representative sot of 20 simulated clusters. which are extracted from a cosmological box for a standard flat ACDAL cosmological model. with ο=0.3.04.= 0.7. IIubble constant fy=1007 lau IMpe 14)=0.7. barvou density Q,=0.0 Laud σε=US for the nommalization of the power spectrum."," We analyze a representative set of 20 simulated clusters, which are extracted from a cosmological box for a standard flat $\Lambda$ CDM cosmological model, with $\Omega_m=0.3, \Omega_\Lambda=0.7$ , Hubble constant $H_0=100h$ km $^{-1}$ $^{-1}$ $h=0.7$, baryon density $\Omega_b=0.04$ and $\sigma_8=0.8$ for the normalization of the power spectrum."7 The box has side-leugth of 1927.1MIpe and coutaius. INO? dark matter particles and an initially equal προς of gas particles. thus resulting iu smpap=L6&105TAL. aud ma=6.9«10572.TAL. for the mass of the two particle species.," The box has side-length of $192h^{-1}\rm Mpc$ and contains $480^3$ dark matter particles and an initially equal number of gas particles, thus resulting in $m_{\rm DM}=4.6\times 10^9 h^{-1}M_\odot$ and $m_{\rm gas}=6.9\times 10^8 h^{-1}M_\odot$ for the mass of the two particle species."8 The Pliununerequivaleut eravitational force softening is set to 7.5h Aspe im plwsical units from 2= to.=0. while it is kept fixed in comoving uuits at higher redshift.," The Plummer–equivalent gravitational force softening is set to $7.5\,h^{-1}$ kpc in physical units from $z=2$ to $z=0$, while it is kept fixed in comoving units at higher redshift."9 The SPIT soothing scale is allowee to decrease at most to onefourth of the eravitational softening (sce Paper 1. for a more detailed description of this simulation).," The SPH smoothing scale is allowed to decrease at most to one–fourth of the gravitational softening (see Paper I, for a more detailed description of this simulation)."10 The ruu has been evolved usingP-GADGET2. a massively parallel TreeSPII code (Sprinecl ο al.," The run has been evolved using, a massively parallel Tree–SPH code (Springel et al."11 2001) with fully adaptive time-step iutegration., 2001) with fully adaptive time-step integration.12 The Huplementation of SPIT adopted im the code follows the chtropycouscrving formulation by Springel Teruquist (2002)., The implementation of SPH adopted in the code follows the entropy–conserving formulation by Springel Hernquist (2002).13 The simulation includes a treatment of star ornmation sed on a subresolution model of the interstellar iuediuni and the effect of galactic winds oowered by SN-II explosions (Springel Ieruquist 2003. S03).," The simulation includes a treatment of star formation based on a sub–resolution model of the interstellar medium and the effect of galactic winds powered by SN-II explosions (Springel Hernquist 2003, SH03)."14 The code also includes a treatinent of metal xoduction from: SN-IL., The code also includes a treatment of metal production from SN-II.15 The resulting metallicity value. which is assigned to cach eas and star particle. has to ο iuterpreted as a global value which is coutributed by different heavy elements with solar relative abuucdauces.," The resulting metallicity value, which is assigned to each gas and star particle, has to be interpreted as a global value which is contributed by different heavy elements with solar relative abundances."16 We exclude those particles from the computation of X.rav emissivity having temperature below 3Pa«10! Is and gas density above 500ppar. being phar the wean barvon density.," We exclude those particles from the computation of X–ray emissivity having temperature below $3\times 10^4$ K and gas density above $500\bar\rho_{\rm bar}$, being $\bar\rho_{\rm bar}$ the mean baryon density."17 Furthermore. following SIIO3. cach gas particle which lies above a limiting density threshold is assumed to be composed of a hot ionized phase aud a cold neutral phase. whose relative amounts depend on the local conditions of density aud temperature.," Furthermore, following SH03, each gas particle which lies above a limiting density threshold is assumed to be composed of a hot ionized phase and a cold neutral phase, whose relative amounts depend on the local conditions of density and temperature."18 Since such particles are aimed at describing the multiiphase nature of the inter-stellar medium. we decided to exclude also their contribution iu the computation of the ICM. X.rav. cinissivity.," Since such particles are aimed at describing the multi-phase nature of the inter-stellar medium, we decided to exclude also their contribution in the computation of the ICM X–ray emissivity."19 Although the nuuber of such particles is always verv simall. their lieh density may cause a sizable. although spurious. contribution to the soft Norav eimission.," Although the number of such particles is always very small, their high density may cause a sizable, although spurious, contribution to the soft X–ray emission."20" The selected clusters have virial masses spannius about a decade from ~Lot!)TAL. to —1005141, (see Table 1).", The selected clusters have virial masses spanning about a decade from $\sim 10^{14}h^{-1}M_\odot$ to $\sim 10^{15}h^{-1}M_\odot$ (see Table 1).21 We did uot apply any particular criterion to select the clusters to be analysed aud. therefore. our set is representative of the whole cluster population iu our simulation within this mass range.," We did not apply any particular criterion to select the clusters to be analysed and, therefore, our set is representative of the whole cluster population in our simulation within this mass range."22 For each cluster. We Lnieasure the viral radius. Rey. as the cistauce from the mostbound DAL particle. which euconipasses an average density equal to the virial deusitv for our cosinological model (c.g. Eke et al.," For each cluster, we measure the virial radius, $R_{\rm vir}$, as the distance from the most–bound DM particle, which encompasses an average density equal to the virial density for our cosmological model (e.g., Eke et al."23 1996)., 1996).24 Accordingly. the virial mass. AM. is defined as the mass contained within Ri.," Accordingly, the virial mass, $M_{\rm vir}$, is defined as the mass contained within $R_{\rm vir}$."25 We τος to Paper 1 for a description of the cluster identification aleorithiu hat we have applied., We refer to Paper I for a description of the cluster identification algorithm that we have applied.26 The cussionweielted temperature and ietallicity iu a eiven enerev baud used to model the hot ICAL also are listed in Table 1., The emission–weighted temperature and metallicity in a given energy band used to model the hot ICM also are listed in Table 1.27 Around each chuster we extract a spherical region extending out to 64.," Around each cluster we extract a spherical region extending out to $6\,R_{\rm vir}$."28 This region is then observed in projection. bv extracting a cylinder with axis ou the ceuter of each cluster.," This region is then observed in projection, by extracting a cylinder with axis on the center of each cluster."29 This allows us to account for the contribution of the surrouudiug largescale structure to the Nray emission of cach cluster., This allows us to account for the contribution of the surrounding large–scale structure to the X–ray emission of each cluster.30 As we will show below. taking the fore/background structure out to ORay is sufficient. to obtain converged estimates of this contribution.," As we will show below, taking the fore/back–ground structure out to $6R_{\rm vir}$ is sufficient to obtain converged estimates of this contribution."31 The Xrav huuinositv contributed by the / th gas particle in the simulation is computed according to where Hg aud pi are the nass are the density of the hot phase of that particle. respectively. jp is the mean molecular weight. ο and ayy are the πανο deusities of clectrous aud protous. respectively.," The X–ray luminosity contributed by the $i$ –th gas particle in the simulation is computed according to where $m_i$ and $\rho_i$ are the mass and the density of the hot phase of that particle, respectively, $\mu$ is the mean molecular weight, $n_e$ and $n_H$ are the number densities of electrons and protons, respectively."32 The cooling fuuctiou ACT.ZiEy.E») is calculated within the cucrey band £4 Το] using the plasima cussion model bv BRavmnond Suüth (1977). where Z is the eas metallicity.," The cooling function $\Lambda(T,Z;E_1,E_2)$ is calculated within the energy band $E_1$ $E_2$ ] using the plasma emission model by Raymond Smith (1977), where $Z$ is the gas metallicity."33 Using this cooling function. the spectra are computed by binning the chussivity within cucrey intervals. so as to have an energy resolution AlogE= 0.01.," Using this cooling function, the spectra are computed by binning the emissivity within energy intervals, so as to have an energy resolution $\Delta \log34E=0.01$ ."35 Iu their analysis of the soft Norav excess of the Coma cluster from ROSATPSPC data. Bouamente et al. (," In their analysis of the soft X–ray excess of the Coma cluster from ROSAT–PSPC data, Bonamente et al. ("362003) apply a MERKAL model to fit the highenergy ([1.2] keV) portion of the spectrmu.,2003) apply a MEKAL model to fit the high–energy ([1–2] keV) portion of the spectrum.37 Then they extrapolate the bestfitting model to a lower energy (0.2.1] keV) baud. where the predicted spectrum is compared with the actually observed one.," Then they extrapolate the best--fitting model to a lower energy ([0.2–1] keV) band, where the predicted spectrum is compared with the actually observed one."38 Iu order to reproduce this same procedure. we would be required to simulate mock observations of our sinulated clusters. aud extract a spectrum withsignaltonoise appropriate for a realistic exposure time and using the appropriate response function.," In order to reproduce this same procedure, we would be required to simulate mock observations of our simulated clusters, and extract a spectrum withsignal--to--noise appropriate for a realistic exposure time and using the appropriate response function."39 Since reproducing iu detail the observational setup is beyond the scope of this paper. we adopt the approach ofcomputing for cach cluster the emission.weighted temperature.," Since reproducing in detail the observational setup is beyond the scope of this paper, we adopt the approach ofcomputing for each cluster the emission–weighted temperature,"40upper klIz QPO detected rises to 4.8 σ (single (rial significance). For a frequency separation of 266.5+13.1 Iz. consistent with the value of Sannaetal.(2010)..,"upper kHz QPO detected rises to 4.8 $\sigma$ (single trial significance), for a frequency separation of $266.5\pm13.1$ Hz, consistent with the value of \citet{sanna10mnras}."41 At the same time. the significance of the main peak increased [rom 300 (0 more (han 500 in our analvsis (see Figure 5)).," At the same time, the significance of the main peak increased from $30\sigma$ to more than $50\sigma$ in our analysis (see Figure \ref{fig5}) )."42 In the wo ObsIDs of the Z phase. in which the simultaneous twin klIz QPOs are the most significant. (2>3) (92405-01-40-04 ancl 92405-01-40-05). we have measured a frequency difference of 280.3617.6 and 276.1+18.8 Iz respectively. ie. consistent within errors with the frequeney difference we have measured in the Atoll phase.," In the two ObsIDs of the Z phase, in which the simultaneous twin kHz QPOs are the most significant $R \ge 3$ ) (92405-01-40-04 and 92405-01-40-05), we have measured a frequency difference of $280.8\pm17.6$ and $276.1\pm18.8$ Hz respectively, i.e. consistent within errors with the frequency difference we have measured in the Atoll phase."43 Based on the observations reported here. our main findines can be summarized as follows:," Based on the observations reported here, our main findings can be summarized as follows:"44most of the line emission is indeed produced in a pro-gracely rotating disc that extends from close to the white cwarl to he outer regions of the primary Roche lobe.,most of the line emission is indeed produced in a pro-gradely rotating disc that extends from close to the white dwarf to the outer regions of the primary Roche lobe.45 We dsolated. the mid-eclipse. spectrum. (Figure 2.. middle) by averaging all spectra. between orbital phases 1.995 and 1.005.," We isolated the mid-eclipse spectrum (Figure \ref{specs}, middle) by averaging all spectra between orbital phases 0.995 and 1.005."46 As the relatively blue continuum from the inner disc is eclipsed. the cool companion star makes a larger ractional contribution. resulting in a sliehtly recedenecl continuum slope.," As the relatively blue continuum from the inner disc is eclipsed, the cool companion star makes a larger fractional contribution, resulting in a slightly reddened continuum slope."47 Weak emission lines with a very strong due shifted emission component are present. indicating that he eclipse is not total and some (outer) disc emission is still visible around these phases.," Weak emission lines with a very strong blue shifted emission component are present, indicating that the eclipse is not total and some (outer) disc emission is still visible around these phases."48 The fact that the blue-shifted side is much stronger than the red-shifted peak. points to an asymmetry in the outer disc that was already. visible as a persistent asvmmoetry. in the out-of-eclipse line profiles.," The fact that the blue-shifted side is much stronger than the red-shifted peak, points to an asymmetry in the outer disc that was already visible as a persistent asymmetry in the out-of-eclipse line profiles."49 ]Zither there is excess line Hux produced in the blue-shifted side of the disc. or part of the red-shifted. side is absorbed by a geometrically (ancl optically) thick structure.," Either there is excess line flux produced in the blue-shifted side of the disc, or part of the red-shifted side is absorbed by a geometrically (and optically) thick structure."50 1n order to isolate the contribution from the white cwarl we subtracted the spectra [rom either side of white dwarf ingress and egress (Figure 2.. bottom).," In order to isolate the contribution from the white dwarf we subtracted the spectra from either side of white dwarf ingress and egress (Figure \ref{specs}, bottom)."51 To correct. to firs order. for the changing contribution [rom the disc. we performed a linear fit to cach wavelength pixel on a shor section just before and. after ingress.," To correct, to first order, for the changing contribution from the disc, we performed a linear fit to each wavelength pixel on a short section just before and after ingress."52 This fit was used to extrapolate the spectrum just before and alter white dwarf ingress. and the white cwarl spectrum was obtained by taking the difference.," This fit was used to extrapolate the spectrum just before and after white dwarf ingress, and the white dwarf spectrum was obtained by taking the difference."53 The same procedure was applied. at white dwarf egress. and the two derived white dwarf spectra. identical within the error bars. were averaged to derive our final white dwarl spectrum as plotted in Figure 2..," The same procedure was applied at white dwarf egress, and the two derived white dwarf spectra, identical within the error bars, were averaged to derive our final white dwarf spectrum as plotted in Figure \ref{specs}."54 Some emission line contribution from the cise is still. present. although strong absorption cores of the Balmer lines are due to the white dwarf absorption line spectrum.," Some emission line contribution from the disc is still present, although strong absorption cores of the Balmer lines are due to the white dwarf absorption line spectrum."55 The blue slope reflects. the continuum contribution expected. from a hot white dwarf., The blue slope reflects the continuum contribution expected from a hot white dwarf.56 Its relative contribution to the out-of-eclipse spectrum. increases from ~ a up to ~ at4000A., Its relative contribution to the out-of-eclipse spectrum increases from $\sim$ at up to $\sim$ at.57. Black-body fits. to the continuum shape indicates a white cwarf temperature around 15000 + 2000 Ix. Catalan et al., Black-body fits to the continuum shape indicates a white dwarf temperature around 15000 $\pm$ 2000 K. Catalan et al.58 also clerivec a white dwarf temperature of 150001Ix. (rom LIST FOS data., \nocite{cat98} also derived a white dwarf temperature of 15000K from HST FOS data.59 In order to measure the contact phases of the white dwarl accurately. we applied. the conventional method. of using the derivative of the continuum light curve (e.g. Woo: et al. 1986)).," In order to measure the contact phases of the white dwarf accurately, we applied the conventional method of using the derivative of the continuum light curve (e.g. Wood et al. \nocite{wood86}) )."60 The light curve was first filtered with a running mean filter using a width of one third of the expectec duration of the ingress ancl egress features., The light curve was first filtered with a running mean filter using a width of one third of the expected duration of the ingress and egress features.61" The numerica derivative was then calculated. and the ingress (6,5) ane egress (Oe) are defined as the orbital phases of minimum and maximum derivative (Figure 4))."," The numerical derivative was then calculated, and the ingress $\phi_{wi}$ ) and egress $\phi_{we}$ ) are defined as the orbital phases of minimum and maximum derivative (Figure \ref{wdphases}) )."62 In order to determine these extrema. the derivative light curve was fitted with a Gaussian near the white dwarl features.," In order to determine these extrema, the derivative light curve was fitted with a Gaussian near the white dwarf features."63 The fitted centroids of these Gaussians are marked by vertical dashed lines., The fitted centroids of these Gaussians are marked by vertical dashed lines.64 To exploit the available spectral information. we also," To exploit the available spectral information, we also"65In this paper. we assume that the PW'N is a uniform sphere expanding al a constant velocily epus.,"In this paper, we assume that the PWN is a uniform sphere expanding at a constant velocity $v_{\rm{PWN}}$."66 The assumption of the constant. velocity is the easiest wav to take into account the expansion of the PWN. although the real behavior of the expansion must be more complex.," The assumption of the constant velocity is the easiest way to take into account the expansion of the PWN, although the real behavior of the expansion must be more complex."67" Gelhuxletal.(2009) investigated the dynamical evolution of the PWN surrounded by supernova ejecta,", \citet{get09} investigated the dynamical evolution of the PWN surrounded by supernova ejecta.68 μον showed that the PWN expands at an almost constant velocily at first ancl then it (rus to shrink and bounces in a late phase of the evolution alter about. LOkvr from birth., They showed that the PWN expands at an almost constant velocity at first and then it turns to shrink and bounces in a late phase of the evolution after about 10kyr from birth.69 We consider that the age of the PWN is vounger than LOkvr in this paper aud that the constant velocity is a good assumption in (his range., We consider that the age of the PWN is younger than 10kyr in this paper and that the constant velocity is a good assumption in this range.70 The radius ol the PWN HRpwx() at a time / is given by For the components inside the PWN. we assume that the PWN is composed of the magnetic field and (he relativistic electron-positron plasma. both of which are injected from (he pulsar inside the PWN.," The radius of the PWN $R_{\rm{PWN}}(t)$ at a time $t$ is given by For the components inside the PWN, we assume that the PWN is composed of the magnetic field and the relativistic electron-positron plasma, both of which are injected from the pulsar inside the PWN."71" The evolution of the spin-down power L(/) is given by where Ly is the initial spin-down power and 7, is the initial spin-down time.", The evolution of the spin-down power $L(t)$ is given by where $L_0$ is the initial spin-down power and $\tau_0$ is the initial spin-down time.72 Both parameters are fixed. if (he current pulsar period P. its lime derivative P. braking index η and age of the pulsar fas. ave known. assuming that the moment of inertia of the pulsar is 11ο.cm.," Both parameters are fixed, if the current pulsar period $P$, its time derivative $\dot{P}$, braking index $n$ and age of the pulsar $t_{\rm{age}}$ are known, assuming that the moment of inertia of the pulsar is $10^{45}\rm g \cdot \rm cm^2$."73 We divide the energy injection from the pulsar into the magnetic field energy. £y ancl the relativistic particle energy {ες using the tme independent parameter 5 (0<7€ 1)., We divide the energy injection from the pulsar into the magnetic field energy $\dot{E}_{\rm{B}}$ and the relativistic particle energy $\dot{E}_{\rm{e}}$ using the time independent parameter $\eta$ $0 \leq \eta \leq 1$ ).74 The fraction parameter + is the ratio of (he magnetic field energv injection to the spin-down, The fraction parameter $\eta$ is the ratio of the magnetic field energy injection to the spin-down75Withoout Event Horizon lez-Diaaz! Madrid. Spain. ,"out Event Horizon $^{1}$ Madrid, Spain. }"76Perhaps oue of the bigeest problems of nowadays plivsies is the possible incompatibility between the recently discovered accelerated expansion of the nuiverse and a consistent mathematical formulation of string or AL theories based on the existence of a Sauatrix or S-vector. provided the universe would accelerate eternally due to the existence of a positive cosmological coustaut or quintessence scalar field with coustaut parameter for its equation of state. aud hence shows a future event horizon [5]..|9]..," Perhaps one of the biggest problems of nowadays physics is the possible incompatibility between the recently discovered accelerated expansion of the universe and a consistent mathematical formulation of string or M theories based on the existence of a S-matrix or S-vector, provided the universe would accelerate eternally due to the existence of a positive cosmological constant or quintessence scalar field with constant parameter for its equation of state, and hence shows a future event horizon \cite{FKMP}, \cite{HKS}."77 Solutious to this problem have been considered only at the cost of allowing loss of quautum coherence | or the existence of real light signals traveling backward in time [6].., Solutions to this problem have been considered only at the cost of allowing loss of quantum coherence \cite{EMN} or the existence of real light signals traveling backward in time \cite{Gon1}.78 In. this report we present a very simple solution to the problemi which is based ou the siuultaneous existence of both a quiutesseutial slowly-varving scalar field o and a negative cosmological coustaut A [2] whose absolute value is very sinall. so that the deceleration parameter keeps negative along the eutire evolution after coincidence tine.," In this report we present a very simple solution to the problem which is based on the simultaneous existence of both a quintessential slowly-varying scalar field $\phi$ and a negative cosmological constant $\Lambda$ \cite{CGOQ} whose absolute value is very small, so that the deceleration parameter keeps negative along the entire evolution after coincidence time."79" Disreearding the effects of any matter field (see later ou). let us then use the action all svinbols have their conveutional meaning.aud £,, is the Lagrangian for the quintessence field. £.,=0,0""Wo}. Vto) being thequintessence poteutial whose explicit fori is not of interest for our present purposes [7].."," Disregarding the effects of any matter field (see later on), let us then use the action where all symbols have their conventionalmeaning, and $L_{\phi}$ is the Lagrangian for the quintessence field, $L_{\phi}=-\phi_{,n}\phi^{,n}-V(\phi)$, $V(\phi)$ being thequintessence potential whose explicit form is not of interest for our present purposes \cite{Gon}."80" Iu the most observationally favored case of a spatially flat universe |3].. if we use the customary definitionEAS of+ the quintesseuce. field.d 8x6Gp/p*E=o7D|V(o)- (with &= defdf) a state equation p= wp. with 1/3«w1 being constant. and the couservatiou uv p,καDbgue) |7|.. then we obtain the"," In the most observationally favored case of a spatially flat universe \cite{Deb}, if we use the customary definition of the quintessence field, $8\pi81G\rho/p=\dot{\phi}^2+/-V(\phi)$ (with $\dot{x}=dx/dt$ ), a state equation $p=\omega\rho$ , with $-1/3 <\omega < -1$ being constant, and the conservation law $\rho_{\phi}\propto a^{-3(1+\omega)}$ \cite{Gon}, , then we obtain the"82conical volumes also has peaks ancl valleys. but these peaks and valleys are distributed: randomly and have random amplitudes.,"conical volumes also has peaks and valleys, but these peaks and valleys are distributed randomly and have random amplitudes."83 “Phe probability that a model with a broad-banc power spectrum has parameters of oscillations of the correlation function similar to observed parameters is very low (<< ο)., The probability that a model with a broad-band power spectrum has parameters of oscillations of the correlation function similar to observed parameters is very low $\ll 1$ ).84 Analytical calculations show that oscillations of the correlation function appear only in case that the power spectrum has a peak at the wavelength equal to the period of oscillations., Analytical calculations show that oscillations of the correlation function appear only in case that the power spectrum has a peak at the wavelength equal to the period of oscillations.85 We have compared. spectra ancl correlation functions of models with various heights of the peak in the spectrum., We have compared spectra and correlation functions of models with various heights of the peak in the spectrum.86 These caleulations show that it is possible to e&enerate an oscillating correlation function for clusters in rich superclusters if the height of the peak is of the order of a factor of at least 1.25r in amplitude over the conventional smooth spectrum., These calculations show that it is possible to generate an oscillating correlation function for clusters in rich superclusters if the height of the peak is of the order of a factor of at least 1.25 in amplitude over the conventional smooth spectrum.87 The fact that the ampliude of oscillations near the Last maximum is still rather large suggests tha the coherence of positions of high-density regions extends over very large separations (at least 10‘ of the diameter of the observable Universe)., The fact that the amplitude of oscillations near the last maximum is still rather large suggests that the coherence of positions of high-density regions extends over very large separations (at least 10 of the diameter of the observable Universe).88 This work Νας supported. by Estonian Science Foundation grant 182 and International Science Foundation erant LLE100., This work was supported by Estonian Science Foundation grant 182 and International Science Foundation grant LLF100.89 We thank Bernard Jones. Jerry Ostriker and Jim Peebles for discussions.," We thank Bernard Jones, Jerry Ostriker and Jim Peebles for discussions."90 JE and AS were supported by the Deutsche Forschungsgemeinschaft in. Potscam: AS was partially supported. by the Russian Foundation for. Basic Research uncer Grant 96-02-1759, JE and AS were supported by the Deutsche Forschungsgemeinschaft in Potsdam; AS was partially supported by the Russian Foundation for Basic Research under Grant 96-02-17591.91" ~1076 ~10°Mo tremendously (forareview,seee.g.,[Barack]2009)."," $\sim 10^{5-6}$ $\sim 10^6 \ M_\odot$ \citep{pau07,hughes09}. \citep[for a review, see92e.g.,][]{barack09}."93". provided that accretion on to the black hole occurs in a low density, radiatively inefficient flow 2000)."," provided that accretion on to the black hole occurs in a low density, radiatively inefficient flow \citep{narayan00}."94". Such flows are much more common than(Narayan| dense accretion discs, whichwould yield observable phase shifts during inspiral (Kocsis at least at the relatively low redshifts where EMRIset al2011),,may be observed."," Such flows are much more common than dense accretion discs, which yield observable phase shifts during inspiral \citep{KocsisEtAl11}, at least at the relatively low redshifts where EMRIs may be observed."95" In this Letter, we quantify the nature and strength of possible perturbations from point mass perturbers: low mass stars or compact objects in tight orbits around the supermassive black hole."," In this Letter, we quantify the nature and strength of possible perturbations from point mass perturbers: low mass stars or compact objects in tight orbits around the supermassive black hole."96" Any perturbers are unlikely to orbit close enough to the EMRI to undergo strong interactions, so the regime of interest is one where the third body is relatively distant and the interaction weak."," Any perturbers are unlikely to orbit close enough to the EMRI to undergo strong interactions, so the regime of interest is one where the third body is relatively distant and the interaction weak."97" The Newtonian analog of this problem has been studied extensively in the context both of Solar System satellite evolution, and for transit timing variations of extrasolar planets (Dermott,Mal-hotra⋅&Murray||I988;|Ag ."," The Newtonian analog of this problem has been studied extensively in the context both of Solar System satellite evolution, and for transit timing variations of extrasolar planets \citep{dermott88,agol05,holman05,veras11}."98" In Newtonian& gravity, perturbations are strong only at the location of mean motion resonances, and these have the effect of inducing small jumps in eccentricity upon divergent resonance crossing."," In Newtonian gravity, perturbations are strong only at the location of mean motion resonances, and these have the effect of inducing small jumps in eccentricity upon divergent resonance crossing."99" This would be interesting for the EMRI problem, since the jumps in alreadyeccentricity would result in a perturbation to the gravitational wave decay rate, and an eventual dephasing of the waveform."," This would already be interesting for the EMRI problem, since the jumps in eccentricity would result in a perturbation to the gravitational wave decay rate, and an eventual dephasing of the waveform."100" However, as we will see, the inclusion of post-Newtonian corrections changes the evolution qualitatively."," However, as we will see, the inclusion of post-Newtonian corrections changes the evolution qualitatively."101" Computing trajectories that include the two first-order non-dissipative post-Newtonian corrections, we find evidence of on initial conditions in the evolution of the perturbed dependenceinner binary, such that arbitrarily small variations in the initial orbit lead to significantly different future behaviour."," Computing trajectories that include the two first-order non-dissipative post-Newtonian corrections, we find evidence of dependence on initial conditions in the evolution of the perturbed inner binary, such that arbitrarily small variations in the initial orbit lead to significantly different future behaviour."102"Tn particular for the νι ας, we can remark that up to redshift 2.=3 the A aud A|uu-corrections are nearly independcut on the spectral type and small.","In particular for the $K_s$ -band, we can remark that up to redshift $z=3$ the $k$ and $k_{\rm evol}$ -corrections are nearly independent on the spectral type and small."103" For these reasons we considered reliable the extrapolation of absolute magnitudes up to at least redshift ~2 in the A, filter and. with some caution. upto.~3."," For these reasons we considered reliable the extrapolation of absolute magnitudes up to at least redshift $\sim1042$ in the $K_s$ filter and, with some caution, up to $z \sim 3$."105 The advantage of using a photometric catalogue is that it is less subject to iuconipleteness then spectroscopic redshift surveys., The advantage of using a photometric catalogue is that it is less subject to incompleteness then spectroscopic redshift surveys.106" The incompleteness in redshift survevs. hat cal affect the LF estimate, can be not only uaenuitude-depeudoeut. but it can also arise as a function of ealaxy type or redshift. aud iu some cases it is iupossible o take it iuto account."," The incompleteness in redshift surveys, that can affect the LF estimate, can be not only magnitude-dependent, but it can also arise as a function of galaxy type or redshift, and in some cases it is impossible to take it into account."107 Obvioush also photometric surveys are affected by incompleteness.," Obviously, also photometric surveys are affected by incompleteness."108 The SUNY catalogue iu the ITIDE-N is. X construction. an Za; baud selected sample (Fernaudez-Soto et al. 1999)).," The SUNY catalogue in the HDF-N is, by construction, an $I_{814}$ band selected sample (Fernandez-Soto et al. \cite{fsoto}) ),"109 whereas objects in the ISAAC IIDE-S catalog are detected on the Vou|fxr) image., whereas objects in the ISAAC HDF-S catalog are detected on the $V_{606}+I_{814}$ image.110" Eveu though we use a Jv, limited sample in the subsequent calculations. it is worth to check ou the possible color-sclectiou effects which could affect the two fields in differeut wavs."," Even though we use a $K_s$ limited sample in the subsequent calculations, it is worth to check on the possible color-selection effects which could affect the two fields in different ways."111 Figures 5H and 9 display the color-redshift aud color-magnitude diagrams., Figures \ref{z_ik} and \ref{kik} display the color-redshift and color-magnitude diagrams.112 As shown in Fie. 9..," As shown in Fig. \ref{kik},"113 very red objects inA. with faint Wy=2[.5 magnitudes. could be missed due to selection criteria.," very red objects in, with faint $K_s \ge 24.5$ magnitudes, could be missed due to selection criteria."114" To avoid such effects of colour selection. we adopted a Μαιος magnitude A,=2[. correspondiug to S/N ~ 3."," To avoid such effects of colour selection, we adopted a limiting magnitude $K_s=24$, corresponding to S/N $\sim$ 3."115" Moreover. this selection allows us to use the whole area of 5.31 απο in the HIDE-N. conmibiuation of the Zl aud Z2 zones. because a this nm he colour distributions of objects with redshifts between band 2 have a sinular average: (a,Woy=1.28 in Zl alu 0.95 in Z2. with a large dispersion iu both zones."," Moreover, this selection allows us to use the whole area of $5.31$ $^2$ in the HDF-N, combination of the Z1 and Z2 zones, because at this limit the colour distributions of objects with redshifts between $0$ and $2$ have a similar average: $\left<I_{814}-K_s\right> = 1.28$ in Z1 and $0.95$ in Z2, with a large dispersion in both zones."116 Iu he Z2 zone. even for the faintest objects in Avy. the colours upto2 25 are allowed: iu the Zl zone most objects have colours below this value. thus we do not mtroduce any bias w comibiuiug the data belonging to the two zones.," In the Z2 zone, even for the faintest objects in $K_s$, the colours up to $2$ – $2.5$ are allowed: in the Z1 zone most objects have colours below this value, thus we do not introduce any bias by combining the data belonging to the two zones."117 At the selectec lit in magnitude. blue ealaxies have about the same chance to be observed than the reddest oues in the A-baud selected subsamples iu both fields.," At the selected limit in magnitude, blue galaxies have about the same chance to be observed than the reddest ones in the $K_s$ -band selected subsamples in both fields."118 Another type of incompleteness could arise from the surface brigltuess effect: when objects are detected at melt surface brightuess limit. then the LF estimate could © affected. with AL” becoming fainter. o πιαοι iuda slightly flatter (Cross Driver 2002 and references therein).," Another type of incompleteness could arise from the surface brightness effect: when objects are detected at bright surface brightness limit, then the LF estimate could be affected, with $M^*$ becoming fainter, $\phi^*$ smaller and $\alpha$ slightly flatter (Cross Driver \cite{cross} and references therein)."119 In our case. 16 detection up to faint surface brightness used by the authors of the catalogues (μμκ)~26aaresee ? in th. the IIDE-N and IHIDE-S) will not iuduce siguificaut effects ou the LE estimates.," In our case, the detection up to faint surface brightness used by the authors of the catalogues $\mu_{\rm lim} (I_814) \simeq 26$ $^{-2}$ in both the HDF-N and HDF-S) will not induce significant effects on the LF estimates."120 Ii particular. the bright cud of 1ο LF. on which we base our conclusions. will not suffer strougly from the mentioned effect.," In particular, the bright end of the LF, on which we base our conclusions, will not suffer strongly from the mentioned effect."121" The same inference can be demonstrated for other types of inconipleteness. such as the detection aud measurement algorithii. or the cosmological dining of surface brighltucss, discussed by Yoshii (1993)) aud Totani Yoshii (20003). affecting the very faint part of the sample at the lut of the sclection aud then unable to invalidate our conclusions."," The same inference can be demonstrated for other types of incompleteness, such as the detection and measurement algorithm, or the cosmological dimming of surface brightness, discussed by Yoshii \cite{yoshii}) ) and Totani Yoshii \cite{totani}) ), affecting the very faint part of the sample at the limit of the selection and then unable to invalidate our conclusions."122 The quantity Vi used in the ως ucthod to compute LEs cau also be used to test the completeness of the sample: if the set of observed galaxies is complete. we expect that they populate unifoiulv the volune of the survey. tthat the ealaxies are raudonlv distributed inside their Vi; volume.," The quantity $V_{\rm max}$ used in the $1/V_{\rm max}$ method to compute LFs can also be used to test the completeness of the sample: if the set of observed galaxies is complete, we expect that they populate uniformly the volume of the survey, that the galaxies are randomly distributed inside their $V_{\rm max}$ volume."123 This corresponds to the condition (VT;=0.5. where V is the volue characteristic of cach galaxy. given its redshift aud the Πιο magnitude of the survey.," This corresponds to the condition $\left<V/V_{\rm max}\right> = 0.5$, where $V$ is the volume characteristic of each galaxy, given its redshift and the limiting magnitude of the survey."124 However. this line X reasoning is valid only if the population does not evolve in huninosity and if is spatially homogencous.," However, this line of reasoning is valid only if the population does not evolve in luminosity and it is spatially homogeneous."125 Larger or sinaller values can have different origins., Larger or smaller values can have different origins.126 When the sunuple is subject to magnuitude completeness to the Huitine magnitude (the more distant galaxies become undetectable). he volume Vyas becomes too big aud we rave (V1wan/«0.5.," When the sample is subject to magnitude incompleteness to the limiting magnitude (the more distant galaxies become undetectable), the volume $V_{\rm max}$ becomes too big and we have $\left<V/V_{\rm max}\right> < 0.5$."127 The same effect can be the result 6 luminosity evolution. if the nearest objects are also the intrinsically brightest ones.," The same effect can be the result of luminosity evolution, if the nearest objects are also the intrinsically brightest ones."128 A value (V/V)>0.5 could v the effect of luminosity evolution. with the brightest jects beiug the most distant oues.," A value $\left<V/V_{\rm max}\right> >1290.5$ could be the effect of luminosity evolution, with the brightest objects being the most distant ones."130 In Sect., In Sect.131 5 πο list re values of ρω averaged over 100 Monte Carlo, \ref{resu} we list the values of $\left<V/V_{\rm max}\right>$ averaged over $100$ Monte Carlo132the ISO catalogue.,the ISO catalogue.133 The X-ray light curve shows a short-lasting. impulsive flare.," The X-ray light curve shows a short-lasting, impulsive flare."134 The spectrum has a best fit temperature of KT=1.0 keV and and a typical absorption value of NCH)=0.8x107 em’., The spectrum has a best fit temperature of $kT = 1.0$ keV and and a typical absorption value of $\nh = 0.8 \times 10^{22}$ $^{-2}$.135 A Class II object identified both in the ISO and ddata., A Class II object identified both in the ISO and data.136 It has an absorption value below the average (N(H)=0.5x107 em) for this sample and a relatively high plasma temperature (k7=2.8 keV)., It has an absorption value below the average $\nh = 0.5 \times 10^{22}$ $^{-2}$ ) for this sample and a relatively high plasma temperature $kT = 2.8$ keV).137Tustitutions. the National Science Foundation. the U.S. Departinent of Encrev. the National Acrouautics aud Space Administration. the Japanese Aloubukasakusho. the Max Planck Society. and the Higher Education Fuudiug Council for Euglaud.,"Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."138 The SDSS Web Site is http:/fwww.sdss.ore/. The SDSS is managed by the Astrophysical Research Consortium for the Participating lIustitutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.139 The Participating Institutions are the American Asem of Natural History. Astrophysical Institute Potsdam. University of Basel. Cuiversity of Cambridec. Case Western Reserve University. Uiiversity of Chicago. Drexel University. Fermilab. the Iustitute for Advanced Study. the Japan Participation Group. Johus Wopkins University. the Jott Tustitute for Nuclear Astrophysics. the Kavli Iustitute for Particle Astrophysics aud Cosimologv. the orca Scientist Group. the Chinese Academy of Sciences (LAMOST). Los Alamos National Laboratory. the Max-Plauck-Institute for Astronomy (MPIA). New Mexico State Uuiversitv. Olio State University. Universitv of Pittsburgh. Universitv of Portsmouth. Priucetou University. the United States Naval Observatory. and the University of Washington: and 5) [TwperLeda database (lttp://leda.univ-Ivonl.fr).," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington; and 5) HyperLeda database (http://leda.univ-lyon1.fr)."140speed.,speed.141 “Phe net effect is that particles orbiting outside the Ccorotation radius gain angular momentum from the field. and can be pushed outwards. while particles orbiting inside the corotation radius lose angular momentum to the field and so acerete onto the white dwarf.," The net effect is that particles orbiting outside the corotation radius gain angular momentum from the field, and can be pushed outwards, while particles orbiting inside the corotation radius lose angular momentum to the field and so accrete onto the white dwarf."142 lxing WWvnn (1999). proposed that this model can explain the anomalously long spin periods of LEX IIya andCen.. suggesting that the svstems are in an equilibrium. where z b.," King Wynn (1999) proposed that this model can explain the anomalously long spin periods of EX Hya and, suggesting that the systems are in an equilibrium where $\approx$ $b$."143 Using this mocel we have computed simulations of the accretion Low appropriate toCen., Using this model we have computed simulations of the accretion flow appropriate to.144.. We assume white-cdwarl ancl rec-cdwart masses of 0.7 and 0.1 respectively., We assume white-dwarf and red-dwarf masses of 0.7 and 0.1 respectively.145 Using an orbital period of 5077 s we then tweak the & parameter until we get a spin period of 2147 s. This requires a magnetic timescale. &JL. of a few seconds.," Using an orbital period of 5077 s we then tweak the $k$ parameter until we get a spin period of 2147 s. This requires a magnetic timescale, $k^{-1}$, of a few seconds."146" We can combine this with estimates for the density aad blob- in the stream 10 ""gem * ane LO"" respectively. sce lxing WWvnn (1999)] to find a magnetic moment of G en? (equating to a field of z 1 MC)."," We can combine this with estimates for the density and blob-length in the stream $^{-9}$ g $^{-3}$ and $^{9}$ respectively, see King Wynn (1999)] to find a magnetic moment of G $^{3}$ (equating to a field of $\approx$ 1 MG)."147 1n this model the [ow alternates between episodes of accretion and ejection. according to the beat phase between the orbital evele and the white-dwarl rotation.," In this model the flow alternates between episodes of accretion and ejection, according to the beat phase between the orbital cycle and the white-dwarf rotation."148 Accretion events occur when one of the magnetic poles points towards the accretion How. allowing the blobs to How down field lines: they thus occur twice per beat evcle.," Accretion events occur when one of the magnetic poles points towards the accretion flow, allowing the blobs to flow down field lines; they thus occur twice per beat cycle."149 Between cach accretion event. when the magnetic poles are on the white-dwarl limb as seen from the approaching flow. the blobs are expelled outwards. and may be swept up by the secondary.," Between each accretion event, when the magnetic poles are on the white-dwarf limb as seen from the approaching flow, the blobs are expelled outwards, and may be swept up by the secondary."150 Most of he flow (290 per cent) accretes. but the expulsion of he remaining 1) per cent. with a high specific angular momentum. allows the svstem to maintain equilibrium. at. a far longer spin. period than would. be possible in a disc-fed svstem.," Most of the flow 90 per cent) accretes, but the expulsion of the remaining 10 per cent, with a high specific angular momentum, allows the system to maintain equilibrium at a far longer spin period than would be possible in a disc-fed system."151 Hlustrations of the How in this model are presented in Fig., Illustrations of the flow in this model are presented in Fig.152 5., 5.153 Perhaps the biggest dillicultv in applying this model to EX Iva and lis that it predicts an aceretion rate modulated on the beat evele Hig., Perhaps the biggest difficulty in applying this model to EX Hya and is that it predicts an accretion rate modulated on the beat cycle fig.154 3 of Wing WWvnn 1999). whereas the hard-N-rav lighteurves of both stars are modulated: only at. the spin. frequencies. CCorrdova. VNason IxIxahn 1985: Lellicr 11998).," 3 of King Wynn 1999), whereas the hard-X-ray lightcurves of both stars are modulated only at the spin frequencies Córrdova, Mason Kahn 1985; Hellier 1998)."155 Phe euwrent moclels calculate only the blob-accretion rate and don? vet predict. X-ray lightcurves this would involve factors such as the optical depth in the accreting regions. which could modulate the Dux at the spin frequency.," The current models calculate only the blob-accretion rate and don't yet predict X-ray lightcurves — this would involve factors such as the optical depth in the accreting regions, which could modulate the flux at the spin frequency."156 llowever. the ightcurve would still be expected to show the hallmarks of «iscless accretion. namely. pulsations at Q. and/or δω € (oe. Wvnn ας 1992). whereas none of these are seen in the > 22 XXA-ray lightcurves of either star.," However, the lightcurve would still be expected to show the hallmarks of discless accretion, namely pulsations at $\Omega$, and/or $2\omega$ $\Omega$ (e.g. Wynn King 1992), whereas none of these are seen in the $>$ 2 X-ray lightcurves of either star."157 This argument is supported. by V2400 Oph. an LP which is almost certainly discless. whose X-ray lishteurve is dominated by the beat xulse (Bucklev 1997: LLellier DDeardmore 2002).," This argument is supported by V2400 Oph, an IP which is almost certainly discless, whose X-ray lightcurve is dominated by the beat pulse (Buckley 1997; Hellier Beardmore 2002)."158 llaving said the above. the simple magnetic-drag »escription adopted. in the current model may not. be appropriate ¢jose to the white cwarl since it ignores magnetic pressure and Ixelvin.Helmholtz instabilities.," Having said the above, the simple magnetic-drag prescription adopted in the current model may not be appropriate close to the white dwarf, since it ignores magnetic pressure and Kelvin–Helmholtz instabilities."159 Also. he equilibria of EX Iva and rrequire only 10 per cent of the Dow to be ejected. back," Also, the equilibria of EX Hya and require only 10 per cent of the flow to be ejected back"160where (he change occurs on the aperture. the resulting anele of high contrast in the imagine plane is given bv By placing a mask into the pupil plane with a Gaussian aperture. one can (transform a traditional circular aperture telescope into one with a diffraction pattern better suited for hieh contrast imagine.,"where the change occurs on the aperture, the resulting angle of high contrast in the imaging plane is given by By placing a mask into the pupil plane with a Gaussian aperture, one can transform a traditional circular aperture telescope into one with a diffraction pattern better suited for high contrast imaging."161 Using a mask represents a quick. efficient. and economical wav {ο test (his emerging imaging method to determine its advantages and (racleolls ancl compare them to the performance of other existing techniques.," Using a mask represents a quick, efficient, and economical way to test this emerging imaging method to determine its advantages and tradeoffs and compare them to the performance of other existing techniques."162 More subtle phenomena (hat limit contrast ean also be studied aud removed wilh a well-known svstem whose ideal performance and performance under non-ileal conditions can be easily modeled., More subtle phenomena that limit contrast can also be studied and removed with a well-known system whose ideal performance and performance under non-ideal conditions can be easily modeled.163 Scattered light. from microroughness or polarization effects can be more reliably studied and verified experimentally rather (han with completely theoretical treatments., Scattered light from microroughness or polarization effects can be more reliably studied and verified experimentally rather than with completely theoretical treatments.164 We have endeavored to begin anwerine the question of which design ultimatelv will be useful in the search for extrasolar planets. or which will be most useful lor other areas of astrononiv where less stringent tolerances are present.," We have endeavored to begin anwering the question of which design ultimately will be useful in the search for extrasolar planets, or which will be most useful for other areas of astronomy where less stringent tolerances are present."165 To (hat end we have designed. fabricated. and tested several GAPM designs for use with the Penn State near-IR Dnager and Spectrograph (PIRIS)(2)..," To that end we have designed, fabricated, and tested several GAPM designs for use with the Penn State near-IR Imager and Spectrograph \citep{ge03}."166 In Section 2 we explore what the best design for a telescope would be., In Section \ref{design} we explore what the best design for a telescope would be.167" In Section 3. we briefly. discuss the process of fabrication of the GAPAIs. while Π we discuss (he various tests we performed in the lab and on the ground at the Mt. Wilson 100"" telescope."," In Section \ref{fab} we briefly discuss the process of fabrication of the GAPMs, while in \ref{test} we discuss the various tests we performed in the lab and on the ground at the Mt. Wilson $^{\prime\prime}$ telescope."168 Finally in Section 5Hr we diseuss what role GAPAIs have for future high contrast imaging., Finally in Section \ref{concl} we discuss what role GAPMs have for future high contrast imaging.169 The idealized desien of a single gaussian aperture in practice cannot be used on current telescopes due to their circular secondary obstructions and (he presence of the support structure., The idealized design of a single gaussian aperture in practice cannot be used on current telescopes due to their circular secondary obstructions and the presence of the support structure.170 These two additions serve to moclily the resulting diffraction pattern and destroy the advantages of the single aperture., These two additions serve to modify the resulting diffraction pattern and destroy the advantages of the single aperture.171 Therefore. a new design that avoids or minimizes their effect is necessary (0 retain high contrast.," Therefore, a new design that avoids or minimizes their effect is necessary to retain high contrast."172 There are (wo possible solutions: multiple apertures (hat avoid the structure completely. or a wav of blocking the structure without changing the diffraction pattern in the imaging plane. such as with another gaussian curve.," There are two possible solutions: multiple apertures that avoid the structure completely, or a way of blocking the structure without changing the diffraction pattern in the imaging plane, such as with another gaussian curve."173Similar expression hold for the second survey and the cross terms for product of two surveys are also needed to derive the error covariance matrices.,Similar expression hold for the second survey and the cross terms for product of two surveys are also needed to derive the error covariance matrices.174 Finally the error covariances associated with deconvolved estimators C'; can be expressed in terms of that of the convolved estimators Cas follows: In deriving these results it is assumed that the coverage of the sky is near complete., Finally the error covariances associated with deconvolved estimators $\hat C_l$ can be expressed in terms of that of the convolved estimators $\tilde C_l$ as follows: In deriving these results it is assumed that the coverage of the sky is near complete.175 This will mean that the windows associated. with the various couplings are sharper than any features in the power spectra., This will mean that the windows associated with the various couplings are sharper than any features in the power spectra.176 The shape of the mask and the noise covariance properties are quite general at this stage, The shape of the mask and the noise covariance properties are quite general at this stage.177Tf the ) Cys of ↔∡∡individual data sets are known .from .independent estimations. then cross spectra deconvolution. of. the cross-spectra C5NON can be simply. written as: In the limiting situation when the survey area covers almost the entire sky these equation takes a much simpler form which are in common use in the literature.,"If the $C_l$ s of individual data sets are known from independent estimations then cross spectra deconvolution of the cross-spectra $C_l^{X,X}$ can be simply written as: In the limiting situation when the survey area covers almost the entire sky these equation takes a much simpler form which are in common use in the literature."178" If fo), is the fraction of the sky covered then one can write: The Cys toein these expression. are the total Cj=Ci|Cr7N which. takes contribution. from5 both signal. and noise. Cys. The statistics of temperature fluctuations in the sky are very nearly Gaussian. but small departures from Gaussianity can put constraints on early universe scenarios."," If $f_{sky}$ is the fraction of the sky covered then one can write: The $C_l$ s in these expression are the total ${\cal C}_l = {\cal C}_l^S + {\cal C}_l^N$ which takes contribution from both signal and noise ${\cal C}_l$ s. The statistics of temperature fluctuations in the sky are very nearly Gaussian, but small departures from Gaussianity can put constraints on early universe scenarios."179 Secondary non-Gaussianity on the other hand ean provide valuable information to distinguish structure formation scenarios. and when used with constraints from the power spectrum it can be a very valuable tool.," Secondary non-Gaussianity on the other hand can provide valuable information to distinguish structure formation scenarios, and when used with constraints from the power spectrum it can be a very valuable tool."180 However estimation of the bispectrum for each triplet of harmonies modes can be difficult to perform numerically., However estimation of the bispectrum for each triplet of harmonics modes can be difficult to perform numerically.181 Munshi&Heavens(2009). introduced a limited data compression method for 3-point functions which reduces the data to a single function (the skew spectrum). and which ean be made optimal for estimating a bispectrum form.," \cite{MuHe09} introduced a limited data compression method for 3-point functions which reduces the data to a single function (the skew spectrum), and which can be made optimal for estimating a bispectrum form."182 In the same spirit. we detine a pseudo-skew spectrum for three arbitrary fields defined on a cut sky. and show how it is related to the skew spectrum on the uncut sky.," In the same spirit, we define a pseudo-skew spectrum for three arbitrary fields defined on a cut sky, and show how it is related to the skew spectrum on the uncut sky."183 The PCL-based approach deseribed here is not optimal. however. it ean be made optimal with suitable choice of weights.," The PCL-based approach described here is not optimal, however, it can be made optimal with suitable choice of weights."184 Let us assume that we have three fields which are defined over the observed sky., Let us assume that we have three fields which are defined over the observed sky.185 The product of two of these fields as X(OYY(OS has an associated mask which. we denote as iw4(O). and which is a product of two masks associated with the individual fields.," The product of two of these fields as $\rX(\hat \Omega)\rY(\hat \Omega)$ has an associated mask which, we denote as $w_A(\Omega)$, and which is a product of two masks associated with the individual fields."186 Analogously. the third field Z(Q) is observed with a mask wg(Q).," Analogously, the third field $\rZ(\Omega)$ is observed with a mask $w_B(\Omega)$."187 From the harmonie transforms of these fields we study the skew spectrum and express it in terms of the mixed bispectra of fields X. Y and Z. Dif.," From the harmonic transforms of these fields we study the skew spectrum and express it in terms of the mixed bispectra of fields X, Y and Z, $B_{l_1l_2l_3}^{XYZ}$."188 We develop this generally. but the results we derive will be useful for the study of primordial non-Gaussianity.," We develop this generally, but the results we derive will be useful for the study of primordial non-Gaussianity."189 Here we consider a single field, Here we consider a single field1900.035. 0.1. Οι.,", 0.1, $R_s$."191 With regards to our own Solar svstem. Jupiter is ~OLR. while Uranus aud Neptune are ~O.O386R.: these would induce a transit. dinunine of theSun of 1% and 0.1354 respectively.," With regards to our own Solar system, Jupiter is $\sim0.1R_s$, while Uranus and Neptune are $\sim0.036R_s$; these would induce a transit dimming of theSun of $1\%$ and $0.13\%$ respectively."192 it is assuned that the time scale for the caustic crossing the stellar surface is small compared to the orbital motion of the plauet can be neglected., it is assumed that the time scale for the caustic crossing the stellar surface is small compared to the orbital motion of the planet can be neglected.193We have shown that six of the IIUVIS have periocicities of significance greater than 99% in the pulse arrival times.,We have shown that six of the RRATs have periodicities of significance greater than $\%$ in the pulse arrival times.194 The »eriods of the most significant peak range from. 1.4 hours (lor PSR. 30) to 2102 davs (for PSR. JISIO 1458)., The periods of the most significant peak range from 1.4 hours (for PSR $-$ 30) to 2102 days (for PSR $-$ 1458).195 o significant. periodicities were detected upon randomizing he time series. showing that these periodicities are real.," No significant periodicities were detected upon randomizing the time series, showing that these periodicities are real."196 We do not find any relationship between the number and significance of detected: periodicities ane spindown ooperties such as period or characteristic age., We do not find any relationship between the number and significance of detected periodicities and spin–down properties such as period or characteristic age.197 I (is possible hat some of the periodic behavior is due to refractive scintillation., It is possible that some of the periodic behavior is due to refractive scintillation.198 However. the number and wide range of imeseales of the periodicities are impossible to exjain with refractive scintillation alone.," However, the number and wide range of timescales of the periodicities are impossible to explain with refractive scintillation alone."199 The shorter timescale periodicities in pulse arrival times are similar to typically observed. nulling timescales. which range from minutes to days (7)..," The shorter timescale periodicities in pulse arrival times are similar to typically observed nulling timescales, which range from minutes to days \citep{wmj+06}."200 Explanations for pulsar πιπο incluce an empty sight.line passing through the subbeam structure (7)... a reversal of the emission. direction (?).. pulsar emission ceasing temporarily cue to intermittent failuwe of pair. production (Zhang et al.," Explanations for pulsar nulling include an empty sight–line passing through the sub--beam structure \citep{dr01}, , a reversal of the emission direction \citep{mg+06}, pulsar emission ceasing temporarily due to intermittent failure of pair production (Zhang et al."201 20Nr). an asteroid belt of material (2). or changese in magnetospherico currents (??7)..," 2007), an asteroid belt of material \citep{cs08} or changes in magnetospheric currents \citep{lhk+10,wmj+06}."202 Any combination of these could explain the extreme pulse-to-pulse variability of the RATS anc also the longer term perioclicities., Any combination of these could explain the extreme pulse-to-pulse variability of the RRATs and also the longer term periodicities.203 The significant periocdicities found in the RRAT pulse arrival times may suggest a relationshi» with pulsars whose spindown rates ancl pulse shapes un- dergo periodic variations. with implied changes in magnetospheric particle density (2)..," The significant periodicities found in the RRAT pulse arrival times may suggest a relationship with pulsars whose spin–down rates and pulse shapes un- dergo periodic variations, with implied changes in magnetospheric particle density \citep{lhk+10}."204 The prototype of this source class is 31931|24 (Ixramer οἱ al., The prototype of this source class is B1931+24 (Kramer et al.205 2006)., 2006).206 The asteroid belt model of (7) attributes the 40-day on/oll timescale of this. pulsar lo an asteroid with eccentric 40-day orbit., The asteroid belt model of \citep{cs08} attributes the 40-day on/off timescale of this pulsar to an asteroid with eccentric 40-day orbit.207 lt may be t the pulseto variability of the RIRATS is. due a similar process happening on very short timesca, It may be that the pulse–to–pulse variability of the RRATs is due to a similar process happening on very short timescales.208 llowever. because the on states of the RRATLS are so short. it is impossible to measure period derivatives during the on ancl olf states.," However, because the on states of the RRATs are so short, it is impossible to measure period derivatives during the on and off states."209 Lt could also be that a similar process is causing the longer term. periodicities in pulse arrival times., It could also be that a similar process is causing the longer term periodicities in pulse arrival times.210 If we apply the model of (?) to the RIGVES. multie asteroids of an asteroid belt. could. be responsible [or he observed. periodicities in the arrival times.," If we apply the model of \citep{cs08} to the RRATs, multiple asteroids of an asteroid belt could be responsible for the observed periodicities in the arrival times."211 This is consistent with the large root mean square timing resicluals which range from 11 ms (for PSR. J1913]1330) to 11.2 ms (for PSR JOS47 4816) of these RRATS as an earth.sized asteroid woulcl induce residuals of the order of 1 ms (?).., This is consistent with the large root mean square timing residuals which range from 1.1 ms (for PSR $+$ 1330) to 11.2 ms (for PSR $-$ 4316) of these RRATs as an earth–sized asteroid would induce residuals of the order of 1 ms \citep{cs08}.212 Llowever it is possible that much of these large residuals are due to pulseto jitter. indicating that the true asteroid mass cannot be determined by the residuals only.," However it is possible that much of these large residuals are due to pulse–to–pulse jitter, indicating that the true asteroid mass cannot be determined by the residuals only."213 The periodic Huctuations in. pulse arrival times could also bedue to non.racial oscillations whic1 drive dillerent emission modes. as often seen in white cwarl stars (?)..," The periodic fluctuations in pulse arrival times could also bedue to non–radial oscillations which drive different emission modes, as often seen in white dwarf stars \citep{rr11}. ."214 The fundamental oscillation periods for neutron stars are expected to be on the order of milliseconds (2). to seconds (2) [or οmodes., The fundamental oscillation periods for neutron stars are expected to be on the order of milliseconds \citep{rg92} to seconds \citep{mh88} for g–modes.215" ""These. are far too short. to explain the multiple periodiciles seen. but it is possible that we are observing the beat frequency between a nonracial oscillation period and that from a longer timescale process like those observed in ?.."," These are far too short to explain the multiple periodicities seen, but it is possible that we are observing the beat frequency between a non–radial oscillation period and that from a longer timescale process like those observed in \citet{lhk+10}."216 We also searched. for periodicities in the daily pulse detection rates., We also searched for periodicities in the daily pulse detection rates.217 Six of the RRATs do not show any significant periodicities in their claily pulse detection rates over timescales of months to vears., Six of the RRATs do not show any significant periodicities in their daily pulse detection rates over timescales of months to years.218 The exceptions are PSK. 1458. which exhibits a 1260 day period. with a significance ofO7%.. and PSR 30. which exibits a 994 day period. with significance of4.," The exceptions are PSR $-$ 1458, which exhibits a 1260 day period with a significance of, and PSR $-$ 30, which exibits a 994 day period with significance of."219". We detect a peak of higher significance only and of the time in 1000 trials in which the rates were randomly assigned to the ALJDs for PSRs JISI9. 1458 and 30 respectively, sugeesting that the significance of the peak may be underesimatecd by the LombScargle algorithm."," We detect a peak of higher significance only and of the time in 1000 trials in which the rates were randomly assigned to the MJDs for PSRs $-$ 1458 and $-$ 30 respectively, suggesting that the significance of the peak may be underestimated by the Lomb–Scargle algorithm."220 Given eight. trials. if all of the RRATs had. no. periodicities. we would. exOC to lind one periodicity with significance. greater. thanSS%.," Given eight trials, if all of the RRATs had no periodicities, we would expect to find one periodicity with significance greater than."221. Llowever. two RRATS with significances greater than are not expected.," However, two RRATs with significances greater than are not expected."222 “Phe predicted. timescales for reractive interstellar scintillation of 117 davs for PSR 1458 and 21 cays for PSR 30 are much smaller than the reported periodicities in pulse detecjon rates. indicating that these periodicities are not. likely due to scintillation.," The predicted timescales for refractive interstellar scintillation of 117 days for PSR $-$ 1458 and 21 days for PSR $-$ 30 are much smaller than the reported periodicities in pulse detection rates, indicating that these periodicities are not likely due to scintillation."223 Llowever. these periodicities are roughly half of he total data span.," However, these periodicities are roughly half of the total data span."224 “Pherefore. a longer time sxui of observaions is necessary to confirm them as significant.," Therefore, a longer time span of observations is necessary to confirm them as significant."225 There is evidence for changes in period cerivative associated with changes in pulse detection rate for PSR 91819 1458 (2).., There is evidence for changes in period derivative associated with changes in pulse detection rate for PSR $-$ 1458 \citep{lmk09}.226 The peak in the rate inuccliately ollowing the first (and largest) eliteh at ALJD 53926 (?) hints at a correlation between elitches ancl emission. properties., The peak in the rate immediately following the first (and largest) glitch at MJD 53926 \citep{lmk09} hints at a correlation between glitches and emission properties.227 Lf confirmed in future elitches. this correlation might suggest a link with the magnetars. for which radiative changes often accompany elitches (e.g.2). or the class of mode changing pulsars whoseperiod derivative. undergoes quasiporiocic changes (7)..," If confirmed in future glitches, this correlation might suggest a link with the magnetars, for which radiative changes often accompany glitches \citep[e.g.][]{dkg+08} or the class of mode changing pulsars whoseperiod derivative undergoes quasi–periodic changes \citep{lhk+10}. ."228 Allof the sources exhibit random pulse distributions on, Allof the sources exhibit random pulse distributions on229In this scenario. the initial angular momentum of the central hole shall be very close to the maximum value (sav. αcm where e is the Werr parameter and m is the mass of the hole) which the Ixerr hole can hold.,"In this scenario, the initial angular momentum of the central hole shall be very close to the maximum value (say, $a \sim m$ where $a$ is the Kerr parameter and $m$ is the mass of the hole) which the Kerr hole can hold."230 Hence it seems reasonable to suppose that the central blackhole is similar o the extreme Ixerr hole at the formation stage., Hence it seems reasonable to suppose that the central blackhole is similar to the extreme Kerr hole at the formation stage.231 Such holes lave an enormous rotation. energy (~107uu~I07MFM100sr or the hole with mass 107AZ. )., Such holes have an enormous rotation energy $\sim 10^{54} \mbox{J} \sim 10^{39} \mbox{W} \times 10^9 \mbox{yr}$ for the hole with mass $\sim 10^8 M_\odot$ ).232 This is enough to explain he total energy. release of Αλ»., This is enough to explain the total energy release of AGNs.233 There are two cdillerent. tvpes of engines for energv ooduction at. the blackhole-aceretion disk. svstems., There are two different types of engines for energy production at the blackhole-accretion disk systems.234 The irst is the well-known “fuel engine. which is the accretion »owered engine.," The first is the well-known “fuel engine”, which is the accretion powered engine."235 This is the major one which has been requenthy adopted to explain the ACGN activities., This is the major one which has been frequently adopted to explain the AGN activities.236 Lhe fuel engine acts by a process to convert the gravitational energy released. from the infalling matter to the radiation., The fuel engine acts by a process to convert the gravitational energy released from the infalling matter to the radiation.237 The standard: disk. model (Shakura Sunvaey 1973). is the representative of this model., The standard disk model (Shakura Sunyaev 1973) is the representative of this model.238 The second is the cHv-wheel engine”., The second is the “fly-wheel engine”.239 This is the rotation powered engine., This is the rotation powered engine.240 While the Ηνπου engine is not so Familiar in the field of XGNs. this engine is as powerful as the fucl engine. and has very interesting features as discussed in the following sections.," While the fly-wheel engine is not so familiar in the field of AGNs, this engine is as powerful as the fuel engine, and has very interesting features as discussed in the following sections."241 In contrast with the fuel engines. the energy. source is the rotation of the Kerr DII itself.," In contrast with the fuel engines, the energy source is the rotation of the Kerr BH itself."242 Of course. the rotation of the accretion disk also can be another energy source.," Of course, the rotation of the accretion disk also can be another energy source."243 However our scope is focused to the case in which the rotation of the DII is energy source. because. the rotation energy of the disk is supplied by accretion. so that there is an apprehension of confusion of two engines.," However our scope is focused to the case in which the rotation of the BH is energy source, because, the rotation energy of the disk is supplied by accretion, so that there is an apprehension of confusion of two engines."244 The author strongly hopes to introduce this fascinating engine to researchers working in the field of ACGNs., The author strongly hopes to introduce this fascinating engine to researchers working in the field of AGNs.245 The comparison of the Us-wheel engine and the fuel engine is discussed in section 2., The comparison of the fly-wheel engine and the fuel engine is discussed in section 2.246 Let us summarize the properties of the Ηννου engine., Let us summarize the properties of the fly-wheel engine.247 The idea to extract the rotation encrey of the Ixerr. holes is firstly proposed. by Penrose (1969)., The idea to extract the rotation energy of the Kerr holes is firstly proposed by Penrose (1969).248 When an incident xwticle into the Ixerr hole splits into two parts inside the ergo-sphere with a very large relative velocity. one particle can be thrown into the negative energv orbit falling to the 10le and another particle escapes outward with larger energy han the initial energy of the incident. particle.," When an incident particle into the Kerr hole splits into two parts inside the ergo-sphere with a very large relative velocity, one particle can be thrown into the negative energy orbit falling to the hole and another particle escapes outward with larger energy than the initial energy of the incident particle."249 In this case. he rotation energy of the hole is reduced by the infall of the negative energy particle. and. reduced. energy. is carried by he escaping particle.," In this case, the rotation energy of the hole is reduced by the infall of the negative energy particle, and reduced energy is carried by the escaping particle."250" his is well-known “Penrose process"".", This is well-known “Penrose process”.251 Unfortunately it is pointed out that the Penrose process is not ellective for astrophysical problems (see. Bardeen οἱ al., Unfortunately it is pointed out that the Penrose process is not effective for astrophysical problems (see Bardeen et al.252 1972) »ecause the critical value of the relative velocity in order o realize the negative energy. orbit is close to one half of the light velocity., 1972) because the critical value of the relative velocity in order to realize the negative energy orbit is close to one half of the light velocity.253 Such a laree relative velocity can be realized. only by nuclear reactions of particles and may not be achieved by usual dynamical processes. c.g.. the tidal disruption of the accreting matter.," Such a large relative velocity can be realized only by nuclear reactions of particles and may not be achieved by usual dynamical processes, e.g., the tidal disruption of the accreting matter."254 The clectromagnetic mechanism extracting the rotation enerev of the Werr 1115 is firstly proposed. by Blandford Znajek (19717)., The electromagnetic mechanism extracting the rotation energy of the Kerr BHs is firstly proposed by Blandford Znajek (1977).255 This is well known as the “magnetic breaking process” or the “BZ process”., This is well known as the “magnetic breaking process” or the “BZ process”.256" 1n thei stuck. the magnetosphere is supposed to be “force-free” (strictly saving. this is “magnetically dominated""). and they clearly showed the energy. extraction in the form of the Poynting lux when the rotation speed. of BIL is greater han it of he magnetosphere."," In their study, the magnetosphere is supposed to be “force-free” (strictly saying, this is “magnetically dominated”), and they clearly showed the energy extraction in the form of the Poynting flux when the rotation speed of BH is greater than it of the magnetosphere."257 An extension of the magnetic breaking xocess to the full MIID. (magnetohvdrodynamic) system was performed by Takahashi et al. (, An extension of the magnetic breaking process to the full MHD (magnetohydrodynamic) system was performed by Takahashi et al. (2581990) as an elementary oocess of the DII engines.,1990) as an elementary process of the BH engines.259 By precise analysis of the MIID accretion [low onto the Kerr DIL. they succeeded to clarity he condition to realize the “negative energv. MIID inflow”.," By precise analysis of the MHD accretion flow onto the Kerr BH, they succeeded to clarify the condition to realize the “negative energy MHD inflow”."260 This process is named as the ΑΗΙΟ Penrose process”., This process is named as the “MHD Penrose process”.261 Nitta et al. (, Nitta et al. (2621991) studied the magnetospheric structure filled with he trans-magnetosonic ΑΠ) inflow onto the herr hole. and applied the MILD. Penrose process to the problem of the individual evolution of AGNs.,"1991) studied the magnetospheric structure filled with the trans-magnetosonic MHD inflow onto the Kerr hole, and applied the MHD Penrose process to the problem of the individual evolution of AGNs."263 Phe result. of this work is xielly reviewed in section 3., The result of this work is briefly reviewed in section 3.264 ltecentIs. the BZ process is speculatively staged again as the elementary. process of the 5-rav. burst. (CRB. see Paczvuski 1998).," Recently, the BZ process is speculatively staged again as the elementary process of the $\gamma$ -ray burst (GRB, see Paczynski 1998)."265 In this case. the rotation energy ~1071 J] o£ nearly maximum rotating Ixerr DII of mass ~10M. is considered to be extracted by very strong magnetic field ~qo A] in a few seconds.," In this case, the rotation energy $\sim 10^{47}$ [J] of nearly maximum rotating Kerr BH of mass $\sim 10 M_\odot$ is considered to be extracted by very strong magnetic field $\sim 10^{11}$ [T] in a few seconds."266 The extracted Povnting energy is expected to produce the ultra relativistic wind with the [actor Lorentz 107., The extracted Poynting energy is expected to produce the ultra relativistic wind with the Lorentz factor $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$ $}}}\hbox{$ $}}} 10^2$.267 Of course. “magnetically dominated? assumption o ," Of course, “magnetically dominated” assumption of original BZ process is too simple to treat the wind acceleration, and it should be extended to full MHD fly-wheel model."268," The fly-wheel model is still unclear, but it should be one of fascinating process to unify physics of quasars and micro-quasars."269," In this paper, the result of Nitta et al. ("270,1991) for individual evolution of fly-wheel engine is applied to the statistics of ensemble of QSOs/AGNs and compared with the observation.271Ll, Figure \ref{fig:LFO} shows observation of the luminosity function (LF) of QSOs.272ere we , Figure \ref{fig:popO} shows observation of the evolution of the spatial number density of QSOs.273comp, Our attention will be focused to explain the evolution of QSOs/AGNs in a range $0 \leq z \leq 5$ by a mechanical process.274are the ," In order to discuss the physical process of the plasma inflows and the magnetospheric structure of the Kerr BH, we suppose general relativistic, stationary and axisymmetric ideal cold MHD flows."275Iv," In this case, MHD equations reduce to well-known basic equations: the Bernoulli equation and the Grad-Shafranov equation (see Takahashi et al."276, 1990 and Nitta et al.277, 1991) with constants of the motion.278," By using these basic equations, we discuss the properties of the fly-wheel engine and apply it to the evolution of ensemble of QSOs/AGNs in section 4."279-wv, We should note again that our primary purpose is to demonstrate the fascinating properties of the fly-wheel model and not to produce a serious model for evolution and statistics of QSOs/AGNs.280heel model with the fuel mocel. and clarify the cillerences between them.," Here we compare the fly-wheel model with the fuel model, and clarify the differences between them."281 Our attention is [ocused to the energy source. the power output and the form of the energy transfer.," Our attention is focused to the energy source, the power output and the form of the energy transfer."282 The most fundamental cillerence is in the energy source ol them., The most fundamental difference is in the energy source of them.283 The energy source of the fuel engine is gravitational enerey of infalling matter released through some dissipation process like a-viscosity (Shakra Sunvacy 1973)., The energy source of the fuel engine is gravitational energy of infalling matter released through some dissipation process like $\alpha$ -viscosity (Shakra Sunyaev 1973).284 Hence this engine can act while the aceretion is continued., Hence this engine can act while the accretion is continued.285 The energy source of the [Iv-wheel engine is the rotation energy of the central spinning DIT itself which can be extracted through an electromagnetic process (the magnetic breaking)., The energy source of the fly-wheel engine is the rotation energy of the central spinning BH itself which can be extracted through an electromagnetic process (the magnetic breaking).286 We should note that the rotation energy. of he BLT is obtained at the formation stage. and is finite.," We should note that the rotation energy of the BH is obtained at the formation stage, and is finite."287 Vhus the lifetime of the wheel engine. on the contrary. must be finite.," Thus the lifetime of the fly-wheel engine, on the contrary, must be finite."288 The output power of the fuel engine essentially depends upon the mass aceretion rate of the infalling matter. and is widely variable.," The output power of the fuel engine essentially depends upon the mass accretion rate of the infalling matter, and is widely variable."289 Upper boundary of the power approximately corresponds to the Eedcington luminosity., Upper boundary of the power approximately corresponds to the Eddington luminosity.290 On he contrary. the output power of the Div-wheel engine is determined by the magnetospheric equilibrium.," On the contrary, the output power of the fly-wheel engine is determined by the magnetospheric equilibrium."291 In a tvpica case. the power — 107W] for the BLE mass ~105 M. (sco the next. section) and is enough to explain actua QSOs/AGNs.," In a typical case, the power $\sim 10^{39}$ [W] for the BH mass $\sim 10^8$ $_\odot$ (see the next section), and is enough to explain actual QSOs/AGNs."292 In the fuel engine. generated. power is in a therma orm (e.g. the standard. disk model) ancl is immediately converted to the radiation from the central region.," In the fuel engine, generated power is in a thermal form (e.g., the standard disk model) and is immediately converted to the radiation from the central region."293 The mechanical process of the fucling is so complicated., The mechanical process of the fueling is so complicated.294 We rece several mocdels of the angular momentum extraction for each decade of distance from the BLL., We need several models of the angular momentum extraction for each decade of distance from the BH.295 ποσο mechanisms must be matched consistently. however. this is very. düllicult.," These mechanisms must be matched consistently, however, this is very difficult."296 In the Uv-wheel engine. the extracted. rotation energy from the BL is once stored. in the form of the Maxwell," In the fly-wheel engine, the extracted rotation energy from the BH is once stored in the form of the Maxwell"297Dwarf nova oscillations (DNOs) and quasi-perioclic oscillations (QPOs) in cataclysmic variables (CVs). have been observed for thirty vears the DNOs were discovered in 1972 (Warner Robinson 1972). the QPOs were first recognised in 1977 (Patterson. Robinson Nather 1977) and were found to be clearly discernable in some earlier light curves.,"Dwarf nova oscillations (DNOs) and quasi-periodic oscillations (QPOs) in cataclysmic variables (CVs) have been observed for thirty years – the DNOs were discovered in 1972 (Warner Robinson 1972), the QPOs were first recognised in 1977 (Patterson, Robinson Nather 1977) and were found to be clearly discernable in some earlier light curves."298 The accumulated observations of DNOs and QPOs have been Listed in Warner (1995a) and. discussed there ancl in the first two papers of this series (Woudt Warner 2002: Paper E: Warner Woudt 2002a: Paper HH: see also Warner Woucdt 2002b. 2003).," The accumulated observations of DNOs and QPOs have been listed in Warner (1995a) and discussed there and in the first two papers of this series (Woudt Warner 2002: Paper I; Warner Woudt 2002a: Paper II; see also Warner Woudt 2002b, 2003)."299 Phe observations of VW Livi presented and analysed in Paper . and the discussion given in Paper Η. led to the realization that in that star the period ratio £ = PopofPpxo remains approximately constant at a value  15 during the rapid increases in these periods seen near the end of VW Elvi outbursts.," The observations of VW Hyi presented and analysed in Paper I, and the discussion given in Paper II, led to the realization that in that star the period ratio $R$ = $P_{QPO}$ $P_{DNO}$ remains approximately constant at a value $\sim$ 15 during the rapid increases in these periods seen near the end of VW Hyi outbursts."300 We pointed out that not only is # similar to that found for the high. and low frequency QPOs observed in N-IHav binaries (Psaltis. Belloni van der Ixlis 1999). the VW. Livi relationship in fact appears to be an extension of the X-Ray binary correlation to frequencies two orders of magnitude lower.," We pointed out that not only is $R$ similar to that found for the high and low frequency QPOs observed in X-Ray binaries (Psaltis, Belloni van der Klis 1999), the VW Hyi relationship in fact appears to be an extension of the X-Ray binary correlation to frequencies two orders of magnitude lower."301 Subsequently. Mauche. (2002). discovered. that DNOs and. QPOs observed. in the EUW and. soft. X-Ray regions," Subsequently, Mauche (2002) discovered that DNOs and QPOs observed in the EUV and soft X-Ray regions"302 , 303The spectroscopic observations of ESO 139-C:009. LC S74. NGC 1308 and NGC 1440. were carried oul with NTT at ESO in La Silla in May ancl November 2001.,"The spectroscopic observations of ESO 139-G009, IC 874, NGC 1308 and NGC 1440 were carried out with NTT at ESO in La Silla in May and November 2001."304 The NTT mounted EMAL in. red meciumedispersion spectroscopic (RIEATD) mode. using the grating No.," The NTT mounted EMMI in red medium-dispersion spectroscopic (REMD) mode, using the grating No."305 6 with 1200 eroovesmm+ in first order with a 1.0 arcsec 5.5 arcmin slit.," 6 with 1200 $\rm306grooves\,mm^{-1}$ in first order with a $1.0$ arcsec $\times$ $5.5$ arcmin slit."307 Phe detector was the No., The detector was the No.308 36 Tektronix FIx2045 EB CCD with 2048 pixels of 24 µην”.," 36 Tektronix TK2048 EB CCD with $2048\,\times\,2048$ pixels of $24\,\times\,24$ $\rm \mu m^2$."309 Lt vielded a wavelength coverage between about 4840 aanel 5490 with a reciprocal dispersion of 0.320 Apixel !..," It yielded a wavelength coverage between about 4840 and 5490 with a reciprocal dispersion of 0.320 $\rm \AA\,pixel^{-1}$ ."310 Lhe instrumental resolution was 1.19 Ελ corresponding to m~30 aat 5170A., The instrumental resolution was $1.19$ (FWHM) corresponding to $\sigma_{\it inst}\approx30$ at 5170.311 The spatial scale was 0.27 )uwrcsec 1., The spatial scale was $0.270$ arcsec $^{-1}$.312 We observed NGC 3412 with the 3.6-m Telescopio razionale Galileo. (ΤΝ) at the ORAL in La Palma in February 2001., We observed NGC 3412 with the 3.6-m Telescopio Nazionale Galileo (TNG) at the ORM in La Palma in February 2001.313 The TNG was equipped. with the Low tesolution Spectrograph (DOLORES): we usedthe LIV ο No., The TNG was equipped with the Low Resolution Spectrograph (DOLORES); we usedthe HR-V grism No.314 6 with 600 groovesmim.! in combination with he 0.7 aresec S.] avemin slit and the Loral CCD with 2048. pixels of 15 pP.," 6 with 600 $\rm grooves\,mm^{-1}$ in combination with the $0.7$ arcsec $\times$ $8.1$ arcmin slit and the Loral CCD with $2048\,\times\,2048$ pixels of $15\,\times\,15$ $\rm \mu m^2$."315 The wavelength range xtween about 4700 and 6840 wwas covered with a reciprocaldispersion of 1.055 opxel ., The wavelength range between about 4700 and 6840 was covered with a reciprocaldispersion of 1.055 $^{-1}$ .316" ""Phe instrumental resolution (obtained by", The instrumental resolution (obtained by317clusters.,clusters.318 Finally. Sect.," Finally, Sect."319 5. is dedicated to the discussion of the results and conclusions., \ref{discu} is dedicated to the discussion of the results and conclusions.320 The four main targets are the clusters B058. B292. B337. and B350.," The four main targets are the clusters B058, B292, B337, and B350."321 They were selected from Table A.3 of POS as candidate intermediate-age GCs., They were selected from Table A.3 of P05 as candidate intermediate-age GCs.322The observations were performed under program GO-10631 (P.L: Thomas Puzia). using the ACS on board HST. and the filters F435W (similar to Johnson B: four images with a total exposition time of 4800 sec for BOSS. and 4900 sec for the other three targets) and F606W (similar to Johnson Vi; six images with a total exposition time of 7500 sec for each target).,"The observations were performed under program GO-10631 (P.I.: Thomas Puzia), using the ACS on board HST, and the filters F435W (similar to Johnson B; four images with a total exposition time of 4800 sec for B058, and 4900 sec for the other three targets) and F606W (similar to Johnson V; six images with a total exposition time of 7500 sec for each target)."323 Fig., Fig.324 1. shows the location of the four target fields on the body of M31., \ref{fig:map} shows the location of the four target fields on the body of M31.325 In Table | we give the basic parameters of the target clusters., In Table \ref{tab:targets} we give the basic parameters of the target clusters.326 Their images in the F606W band are shown in Fig. 2.., Their images in the F606W band are shown in Fig. \ref{fig:targets}.327 The pointings were arranged to contain as many clusters or candidate clusters as possible because other confirmed or candidate GCs are present in the proximity of the targets., The pointings were arranged to contain as many clusters or candidate clusters as possible because other confirmed or candidate GCs are present in the proximity of the targets.328 This optimized the scientific output of the images., This optimized the scientific output of the images.329 For the fields with multiple objects. orientation requirements were set to guarantee the best coverage of all targets. and additional orientational constraints were added to the B292 pointing to avoid a bright star in the field of view.," For the fields with multiple objects, orientation requirements were set to guarantee the best coverage of all targets, and additional orientational constraints were added to the B292 pointing to avoid a bright star in the field of view."330 The field of BOSS also contains BO49 (already studied in. Perina et al., The field of B058 also contains B049 (already studied in Perina et al.331 2009b); the field of B33 also contains B336 and in the field of B292 we discovered anew cluster that was never detected before (dubbed B53]. according to the RBC nomenclature).," 2009b); the field of B337 also contains B336 and in the field of B292 we discovered a new cluster that was never detected before (dubbed B531, according to the RBC nomenclature)."332 For these clusters it was possible to obtain meaningful CMD that are presented and discussed below., For these clusters it was possible to obtain meaningful CMD that are presented and discussed below.333 In the field of BOSS we identified another three candidate GCs listed in the RBC (SKO87B. SKOSSB. SKO89B).," In the field of B058 we identified another three candidate GCs listed in the RBC (SK087B, SK088B, SK089B)."334 These are faint and very compact objects for which we provide only a re-classification based on visual inspection of the ACS images., These are faint and very compact objects for which we provide only a re-classification based on visual inspection of the ACS images.335 In Table 4. are listed some basic parameters of these additional objects. and their images in the Fo06W band are show! in Fig. 3..," In Table \ref{tab:others} are listed some basic parameters of these additional objects, and their images in the F606W band are shown in Fig. \ref{fig:others}."336 The data reduction was performed in the same way as in Perma et al. (2009b:;, The data reduction was performed in the same way as in Perina et al. \cite{P09b};337 PO9b hereafter) on the pre-reduced images provided by STScI. using the ACS module of DOLPHOT? (Dolphin 20004). a point-spread function fitting package specifically devoted to stellar photometry from HST images.," P09b hereafter) on the pre-reduced images provided by STScI, using the ACS module of DOLPHOT (Dolphin \cite{dol_a}) ), a point-spread function fitting package specifically devoted to stellar photometry from HST images."338 The package identifies the sources above a fixed flux threshold on a stacked image and performs the photometry on individual frames. accounts for the hot-pixel and cosmic-ray," The package identifies the sources above a fixed flux threshold on a stacked image and performs the photometry on individual frames, accounts for the hot-pixel and cosmic-ray"339and positive colour eradieuts. while the Wari Sevfert 2 aud the Cold galaxies show the exact opposite trends.,"and positive colour gradients, while the Warm Seyfert 2 and the Cold galaxies show the exact opposite trends."340 Most likely. these aperture eradieuts reflect the contamination of unclear colours by the AGN iu Sevtert Ls aud by dust extinction in Sevfert 2s.," Most likely, these aperture gradients reflect the contamination of nuclear colours by the AGN in Seyfert 1s and by dust extinction in Seyfert 2s."341 In the Wari Sevfert 2 and Cold samples. the colour aud enission Lue distributions are more couples than iu the Wari Sevfert ls. showiug evidence for patchy dust extinction and intense star formation mostly associated with spiral and. tidal features.," In the Warm Seyfert 2 and Cold samples, the colour and emission line distributions are more complex than in the Warm Seyfert 1s, showing evidence for patchy dust extinction and intense star formation mostly associated with spiral and tidal features."342 2., 2.343 Surface colour eradieuts at radii 2 kpc. indicate a clear distinction between the Wari Sevfert 1 aud 2 ealaxies: For the Sevtert Ls. positive colour gradients persist even at larec disk radii (225 kpc} where contamination by the uucleus is minimal. most likely indicative of (increasing outwards) age eraclicuts.," Surface colour gradients at radii $\geq$ 2 kpc, indicate a clear distinction between the Warm Seyfert 1 and 2 galaxies: For the Seyfert 1s, positive colour gradients persist even at large disk radii $\geq$ 5 kpc) where contamination by the nucleus is minimal, most likely indicative of (increasing outwards) age gradients."344 In Sevfert 2s. any nuclear exctinction should uot affect seriously the colour eradicuts at radic2 kpe. which are thus dominated by (decreasing outwards} metallicity aud stellar age effects.," In Seyfert 2s, any nuclear exctinction should not affect seriously the colour gradients at $\geq$ 2 kpc, which are thus dominated by (decreasing outwards) metallicity and stellar age effects."345 There is an overall similarity between Wari Sevfert 2 aud Cold galaxy colour eracdicuts. which indicates that similar (external) processes. sucli as strong interactions. must dominate their disk properties.," There is an overall similarity between Warm Seyfert 2 and Cold galaxy colour gradients, which indicates that similar (external) processes, such as strong interactions, must dominate their disk properties."346 3., 3.347 Sevfert 2 (bluer) colour exadieuts correlate witli (larger) IR luminosities. mdicatiug centrally concentrated dust and stroug disk star formation.," Seyfert 2 (bluer) colour gradients correlate with (larger) IR luminosities, indicating centrally concentrated dust and strong disk star formation."348 Iu fact. we fud that both these observed quantities scale witli interaction streneth. a result that will be further explored in Paper IV.," In fact, we find that both these observed quantities scale with interaction strength, a result that will be further explored in Paper IV."349 ., 4.350" The Cold sample shows larger SFRs (as deduced roni their IR cussion lougword of G0 jnu) by factors of 2-3 compared to the Wari Sevtert samples,", The Cold sample shows larger SFRs (as deduced from their IR emission longword of 60 $\mu$ m) by factors of 2-3 compared to the Warm Seyfert samples.351 However. if in the Sevfert 2 subsample we inchide the ultra-tninous (Loy 21013) Gitronely interacting) members. it becomes statistically comparable to the Cold sample.," However, if in the Seyfert 2 subsample we include the ultra-luminous $L_{60}\geq$ $^{11}$ ) (strongly interacting) members, it becomes statistically comparable to the Cold sample."352 Galactic interactions seeni again to be the issue here. or the euliaunced far-IR cussion aud SFRs.," Galactic interactions seem again to be the issue here, for the enhanced far-IR emission and SFRs."353 5., 5.354 The radial colour-colow profiles show that the Wari Sevtert 1 aud Sevtert 2 ealaxies occupy cdiffercut reeions (the first bluer. the second redder) iu these diagranis.," The radial colour-colour profiles show that the Warm Seyfert 1 and Seyfert 2 galaxies occupy different regions (the first bluer, the second redder) in these diagrams."355 For each sample the galaxies can be erouped in three classes: (a) Early-tvpe galaxies with mean disk stell ages z5 Cyr (b) Early or intermeciate-type galaxies with colours indicating starbursts —1 Cyr or vounger. superposed ou the older underlviug ealaxv population.," For each sample the galaxies can be grouped in three classes: (a) Early-type galaxies with mean disk stellar ages $\geq$ 5 Gyr (b) Early or intermediate-type galaxies with colours indicating starbursts $\sim$ 1 Gyr or younger, superposed on the older underlying galaxy population."356 Within this class. the Sevfert 1s are isolated objects while the Sevfert 23 are mostly interacting with a companion galaxy. (," Within this class, the Seyfert 1s are isolated objects while the Seyfert 2s are mostly interacting with a companion galaxy. ("3570) Objects with conrplex profiles aud. in the case of Sevfert 2s. also complex inorphologies.,"c) Objects with complex profiles and, in the case of Seyfert 2s, also complex morphologies."358 The Seyfert Is are mostlv suele carly-tvpe systems with strong cireummnuclear Ilo enisionu and colours indicating a very voung starburst <0.5 Civr superposed ou the redder galaxy xo»pulation., The Seyfert 1s are mostly single early-type systems with strong circumnuclear $\alpha$ emission and colours indicating a very young starburst $\leq$ 0.5 Gyr superposed on the redder galaxy population.359 The Sevtert 2s m this class. are all extreme cases of stronely interacting. tidally distorted and double nucleus merge svstenis. that le way off he normal sequence. with extremely red (V.R) colours.," The Seyfert 2s in this class, are all extreme cases of strongly interacting, tidally distorted and double nucleus merging systems, that lie way off the normal sequence, with extremely red $(V-R)$ colours."360 The only two Cold galaxies with available hree-colour information. belong also to this latter class of extreme profiles.," The only two Cold galaxies with available three-colour information, belong also to this latter class of extreme profiles."361 We conclude that. for all lice classes. the observed colour profiles can be deseribed by age and dust effects within simpele-burst. solar metallicitv models.," We conclude that, for all three classes, the observed colour profiles can be described by age and dust effects within single-burst, solar metallicity models."362 Motallicitv changes within OY almoug the galaxies and differing star formation histories do not secin to affect significantly the above conclusions., Metallicity changes within or among the galaxies and differing star formation histories do not seem to affect significantly the above conclusions.363 6., 6.364 Iu double nucleus svsteiis one of the two nuclei is activated aud becomes the main source of optical and IR endüssion. ioudizius the eas auisotropically.," In double nucleus systems one of the two nuclei is activated and becomes the main source of optical and IR emission, ionizing the gas anisotropically."365 These characteristics are strikingly simular for the four mergers that we have observed. independently of which sample they belong to.," These characteristics are strikingly similar for the four mergers that we have observed, independently of which sample they belong to."366 In the present Paper IV we have shown significant cüffereuces iu the host Sevfert 1 aud 2 colour distributions. that caunot be attributed to simple oricutation effects.," In the present Paper IV we have shown significant differences in the host Seyfert 1 and 2 colour distributions, that cannot be attributed to simple orientation effects."367 Iu turn. they secur to be related to the interaction stage of the host galaxy. at least for the Warm Sevtert 2 ealaxics which in this respect are simular to the Cold galaxies.," In turn, they seem to be related to the interaction stage of the host galaxy, at least for the Warm Seyfert 2 galaxies which in this respect are similar to the Cold galaxies."368 Through aperture photometry (Paper ID) and decomposition of the host light profiles (Paper HI) we have reached simular conclusious., Through aperture photometry (Paper II) and decomposition of the host light profiles (Paper III) we have reached similar conclusions.369" Iu the forthcoming. last in this series, Paper TV we will comnbiue all these results within the contest of au evolutionary sccuario for the Warn Seyfert galaxies."," In the forthcoming, last in this series, Paper IV we will combine all these results within the context of an evolutionary scenario for the Warm Seyfert galaxies."370 T am erateful to my thesis advisors George. Milev and Walter Jaffe for providing me with stinulatiou and support throughout the completion ofthis project., I am grateful to my thesis advisors George Miley and Walter Jaffe for providing me with stimulation and support throughout the completion of this project.371 This research has mace use of the NASA/TPAC Extragalactic Database (NED) which is operatedby the Jet Propulsion Laboratory. California Iustitute of Technology. uuder contract with the National Aeronautics iud Space Adininistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."372 Part of this work was completed while the author held a National Research Council - NASA GSFC Research Associateship., Part of this work was completed while the author held a National Research Council - NASA GSFC Research Associateship.373contanunated 2036 MeV region cau be seen clearly from a comparison of Fies,contaminated 20–36 MeV region can be seen clearly from a comparison of Figs.374 2 aud 3.., \ref{fig:2} and \ref{fig:3}. .375 Fieure 2. made using data with e! euereyv between 20 and GU. MeV. seenis to show that other experiments exclude most of the LSND region. whereas Fig. 3.," Figure \ref{fig:2}, made using data with $e^+$ energy between 20 and 60 MeV, seems to show that other experiments exclude most of the LSND region, whereas Fig. \ref{fig:3},"376 which uses the cleaner data with e! energv between 36 aud GO MeV. shows that there is a wide range of Am? not in coutzadictionwith other experiments.," which uses the cleaner data with $e^+$ energy between 36 and 60 MeV, shows that there is a wide range of $\Delta m^2$ not in contradictionwith other experiments."377 Also shown in Fig., Also shown in Fig.378" 2 is the LSND vy,>v, result! which although quite broad tends to favor Ligher Am? values.", \ref{fig:3} is the LSND $\nu_\mu\to\nu_e$ \cite{ref:23} which although quite broad tends to favor higher $\Delta m^2$ values.379" This broaduess results from the ereater backeround in this case. primarily because the observed process (4CΣο X) gives only one signal instead of the two available in the My$e case,"," This broadness results from the greater background in this case, primarily because the observed process $\nu_eC\to e^-X$ ) gives only one signal instead of the two available in the $\bar\nu_\mu\to\bar\nu_e$ case."380" While-4e the fluctuation. probabilityEM for. vy,>vis + only ~+10Di7. the two wavs of detecting oscillations are essentially. independent. providing sole coufirlation that a real effect isbeiug observed."," While the fluctuation probability for $\nu_\mu\to\nu_e$ is only $\sim10^{-2}$, the two ways of detecting oscillations are essentially independent, providing some confirmation that a real effect isbeing observed."381" If neutrino dark matter were due to oue neutrino. that would presumably be ve. aud this would be ruled out if. as fits the Super-Namiokaude data? best. the atinospherie anomalous 74/17. ratio is due to vy,5» rj; snce the ass difference required is Am.~10? eV?, andthe needed. neutrino lnass is 91,57~5 eV(for ucutrinos andQ,,= 1. h=0.5 or Q,,= 0.6."," If neutrino dark matter were due to one neutrino, that would presumably be $\nu_\tau$ , and this would be ruled out if, as fits the Super-Kamiokande \cite{ref:19} best, the atmospheric anomalous $\nu_\mu/\nu_e$ ratio is due to $\nu_\mu\to\nu_\tau$ , since the mass-squared difference required is $\Delta m^2_{\mu\tau}\sim10^{-3}$ $^2$ , andthe needed neutrino mass is $94\Omega_\nu h^2\sim5$ eV(for neutrinos and$\Omega_m=1$ , $h=0.5$ or $\Omega_m=0.6$ ,"382the disk with a 10 AU radius. possibly caused by a Jupiter- planet?).,"the disk with a 10 AU radius, possibly caused by a Jupiter-sized planet."383". Direct evidence of cold dise material at larger radit is provided by ATCA observations of at 89 GHz (3.4 mm) and 2"" resolution. withthe flux of 3643 mJy. values consistent. with the. 1.3 mm observations of?."," Direct evidence of cold disc material at larger radii is provided by ATCA observations of at 89 GHz (3.4 mm) and $\arcsec$ resolution, withthe flux of $\pm$ 3 mJy, values consistent with the 1.3 mm observations of."384. They do not detect HCO / z1-0 line emission and speculate that photodissociation of its progenitor species 'CO. in the upper disc layers or an overall gas depletion may be the reason for this.," They do not detect $^+$ $J=$ 1–0 line emission and speculate that photodissociation of its progenitor species $^{12}$ CO, in the upper disc layers or an overall gas depletion may be the reason for this."385" Recent spectroastrometric observations of rovibrational ""CO transitions by suggest that this molecular species is missing from the inner disc. at least up to 8 AU from the star?)."," Recent spectroastrometric observations of rovibrational $^{12}$ CO transitions by suggest that this molecular species is missing from the inner disc, at least up to 8 AU from the star."386. Scattered light imaging of HD 100546 reveals the disc extending up to 4” from the star viewed at an inclination of 50°. and an interesting disc structure resembling spiral arms).," Scattered light imaging of HD 100546 reveals the disc extending up to $\arcsec$ from the star viewed at an inclination of $\degr$, and an interesting disc structure resembling spiral arms."387. This structure was interpreted as due to dise perturbation by a companion or a warped dise structure(?)., This structure was interpreted as due to disc perturbation by a companion or a warped disc structure.388". Coronographic imaging by shows steep surface brightness profiles in the environment of HD 100546 indicative of optically thin emission in the near-infrared. with surface densities as low as 107 g em""."," Coronographic imaging by shows steep surface brightness profiles in the environment of HD 100546 indicative of optically thin emission in the near-infrared, with surface densities as low as $^{-3}$ g $^{-2}$."389 Their images trace the emission of small dust (< Sym). extending out to 800 AU from the star.," Their images trace the emission of small dust $<5\,\mu$ m), extending out to 800 AU from the star."390 The authors suggest the presence of an optically thick dise with à 400 AU radius. and an optically thin flattened halo or envelope farther from the star.," The authors suggest the presence of an optically thick disc with a 400 AU radius, and an optically thin flattened halo or envelope farther from the star."391 The scattered light mages hint at the presence of gas in the disc that supports the disc vertical structure., The scattered light images hint at the presence of gas in the disc that supports the disc vertical structure.392" In this work. we detect and study the molecular gas. its kinematics and temperature. in the disce at spatial resolution from 777 to 18.9""."," In this work, we detect and study the molecular gas, its kinematics and temperature, in the disc at spatial resolution from $\farcs$ 7 to $\farcs$ ."393 In Sect., In Sect.394" 22. we present our observations of ""CO. CO and |C IJ lines."," \ref{s:obs&res} we present our observations of $^{12}$ CO, $^{13}$ CO and [C I] lines."395" All ""CO lines are detected. there is a tentative detection of the 'CO line. while [C I] emission is not detected."," All $^{12}$ CO lines are detected, there is a tentative detection of the $^{13}$ CO line, while [C I] emission is not detected."396 We model the spectra in Sect., We model the spectra in Sect.397 ??. discussing the implications for the dise size. mass and kinematics.," \ref{s:discussion} discussing the implications for the disc size, mass and kinematics."398 We identify the regions dominating the observed lines. and derive their temperatures.," We identify the regions dominating the observed lines, and derive their temperatures."399 Section 22 summarises our results., Section \ref{s:conclusions} summarises our results.400" The observations of '""*CO J 26-5 at 691.472 GHz and [C Πρ.P, (C I] J 22-1 hereafter) at 809.344 GHz towards HD 100546 at R.A.21133""2$4 and Dee= -70*11'41 (J2000) were obtained simultaneously. using the CHAMP- heterodyne array receiver on APEX on 2008 November 11."," The observations of $^{12}$ CO $J=$ 6–5 at 691.472 GHz and [C I] $^3$ $_2$ $^3$ $_1$ ([C I] $J=$ 2–1 hereafter) at 809.344 GHz towards HD 100546 at $=$ $^\mathrm{h}$ $^\mathrm{m}$ $\fs$ 4 and $=-$ $\degr$ $\arcmin$ $\arcsec$ (J2000) were obtained simultaneously, using the $^+$ heterodyne array receiver on APEX on 2008 November 11."401" The 7 pixels in each wavelength band are arranged in a hexagon of 6 pixels around one central pixel pointed towards the source. with beam sizes of 9"" at 691 GHz and 7/7 at 809 GHz."," The 7 pixels in each wavelength band are arranged in a hexagon of 6 pixels around one central pixel pointed towards the source, with beam sizes of $\arcsec$ at 691 GHz and $\farcs$ 7 at 809 GHz."402 The backend consisting of the Fast Fourier Transform Spectrometer unit was used o all pixels. providing a spectral resolution of 0.37 MHz or 0.14-0.16 km s! at these frequencies. and covering a bandwidth of 1.5 GHz or 4096 channels.," The backend consisting of the Fast Fourier Transform Spectrometer unit was used on all pixels, providing a spectral resolution of 0.37 MHz or 0.14-0.16 km $^{-1}$ at these frequencies, and covering a bandwidth of 1.5 GHz or 4096 channels."403 Main beam efficiencies are 0.40 at 691 GHz and 0.37 at 809 GHz., Main beam efficiencies are 0.40 at 691 GHz and 0.37 at 809 GHz.404 Calibration is uncertain by =30% at both frequencies., Calibration is uncertain by $\approx$ $\%$ at both frequencies.405 Pointing was performed directly prior to. and after the on-source integration providing an accuracy better than 3.," Pointing was performed directly prior to, and after the on-source integration providing an accuracy better than $\arcsec$."406 The pointing source was 07454-7112. about 20° away from HD 100546. at the same airmass.," The pointing source was 07454-7112, about $\degr$ away from HD 100546, at the same airmass."407 The CO /26-5 line was also observed on 2008 November 10 injiggle mode and its intensity and spectral profile were found to be the same within20%., The CO $J=$ 6–5 line was also observed on 2008 November 10 in jiggle mode and its intensity and spectral profile were found to be the same within.408. Since these data are noisier. the data sets taken on different dates were not combined.," Since these data are noisier, the data sets taken on different dates were not combined."409 During this latter observation. the high band was tuned to 'CO J27-6 at 806.665 GHz. with the beam efficiency of 0.37.," During this latter observation, the high band was tuned to $^{12}$ CO $J=$ 7–6 at 806.665 GHz, with the beam efficiency of 0.37."410" Only the high S/N ""CO J26-5 data taken on 2008 November 11 are used in the further analysis.", Only the high S/N $^{12}$ CO $J=$ 6–5 data taken on 2008 November 11 are used in the further analysis.411" The ""CO J 23-2 line at 345.796 GHz. and the CO J=3- line at 330.588 GHz. were observed on 2005 July 27 and 28 with the APEX-2a receiver using a single pointing."," The $^{12}$ CO $J=$ 3–2 line at 345.796 GHz, and the $^{13}$ CO $J=$ 3--2 line at 330.588 GHz, were observed on 2005 July 27 and 28 with the APEX-2a receiver using a single pointing."412 The channel spacing of these data is 61 KHz or 0.05-0.06 km s. and the spectral resolution 98 kHz or 0.09 km s!(2)..," The channel spacing of these data is 61 kHz or 0.05-0.06 km $^{-1}$, and the spectral resolution 98 kHz or 0.09 km $^{-1}$."413 The main beam efficiency of APEX at 346 GHz is 0.73. and the beam sizes are 181 and 1879 at 345.796 GHz and 330.588 GHz. respectively.," The main beam efficiency of APEX at 346 GHz is 0.73, and the beam sizes are $\farcs$ 1 and $\farcs$ 9 at 345.796 GHz and 330.588 GHz, respectively."414 Our CO J =3-2 line data were presented in ?., Our $^{12}$ CO $J=$ 3–2 line data were presented in .415 In all our observations. APEX forward efficiency of 0.95 was taken into account.," In all our observations, APEX forward efficiency of 0.95 was taken into account."416 The data were reduced and analysed using the CLASS and STARLINK software., The data were reduced and analysed using the CLASS and STARLINK software.417" We detect all the observed ""CO line transitions at 7-20 im terms of the integrated intensity.", We detect all the observed $^{12}$ CO line transitions at $\sigma$ in terms of the integrated intensity.418 The CO J23-2 line is marginally detected at 2c. and the [C I] J =2-] line is not detected.," The $^{13}$ CO $=$ 3–2 line is marginally detected at $\sigma$, and the [C I] $J=$ 2–1 line is not detected."419" The 'CO J=3- and J 26-5 lines are detected at the highest signal to noise ratio, and show a double peaked profile characteristic of disc rotation."," The $^{12}$ CO $J=$ 3--2 and $J=$ 6–5 lines are detected at the highest signal to noise ratio, and show a double peaked profile characteristic of disc rotation."420 The intensities integrated over the velocity range 10 km s!. over which line emission is detected. are listed in Table | together with thefull width at half-maximum (FWHM) of the lines with sufficiently well defined profiles.," The intensities integrated over the velocity range 0-10 km $^{-1}$ , over which line emission is detected, are listed in Table \ref{tab2} together with thefull width at half-maximum (FWHM) of the lines with sufficiently well defined profiles."421 In addition to the observations towards the source. the CHAMP? array provides measurements at nearby offsets.," In addition to the observations towards the source, the $^+$ array provides measurements at nearby offsets."422 This setup provides an excellent way to discern the emission from the disc. with an estimated size of at least 400 AU in radius from the surrounding material known tobe present further," This setup provides an excellent way to discern the emission from the disc, with an estimated size of at least 400 AU in radius from the surrounding material known tobe present further"423"hole svstem. in which each hole possesses its own μα,","hole system, in which each hole possesses its own BLR."424 For the wide separation of the peaks in SDSS J09424-0900. there are additional problems for the model besides (hose listed by EMO3.," For the wide separation of the peaks in SDSS J0942+0900, there are additional problems for the model besides those listed by EH03."425 First. the profile is not consistent with the combination of two broad emission lines. which should show two well defined peaks.," First, the profile is not consistent with the combination of two broad emission lines, which should show two well defined peaks."426" Second. the very wide separation of the (wo peaks requires the separation of the binary to be order of 100r,. and the size of each DLR should be even smaller."," Second, the very wide separation of the two peaks requires the separation of the binary to be order of $r_g$, and the size of each BLR should be even smaller."427 Such a small BLBR. would be unprecedented., Such a small BLR would be unprecedented.428 Furthermore. equal mass binary of black holes at this separation will merge on a (ine scale of dotie-l! Gal vis de Lo gravitational radiation (Misner. Thorne Wheeler 1972). which makes the probability to see such objects extremely low.," Furthermore, equal mass binary of black holes at this separation will merge on a time scale of $\frac{5}{256}\frac{a_0^4} {\mu M^2}$ $^4$ $\frac{M}429{10^8M_\odot})^2$ yrs due to gravitational radiation (Misner, Thorne Wheeler 1973), which makes the probability to see such objects extremely low."430 If the line is emitted from a disk. what makes the line-emitting region so small?," If the line is emitted from a disk, what makes the line-emitting region so small?"431 From the consideration of energv balance. CIIS9 argued (that double-peaked lines originate from a iyineated disk. with an outer thin disk and an inner thick. Low BRadiative Efficiency Accretion Flow (LRAF). presumably with a very low mass accretion rate (Quataert οἱ al.," From the consideration of energy balance, CH89 argued that double-peaked lines originate from a truncated disk, with an outer thin disk and an inner thick, Low Radiative Efficiency Accretion Flow (LRAF), presumably with a very low mass accretion rate (Quataert et al."432 1999) and iluminating the outer thin disk., 1999) and illuminating the outer thin disk.433 Within this scenario. we night expect that the truncation radius depends on the mass accretion rate: al very low accretion rate. (he iruncation radius is large and the disk is neutral: as the rate increases. the truncation radius decreases but the (hin disk is still not ionized: but if (he accretion rate increases further. the inner part of thin disk becomes ionized. which sets the smallest possible disk radius that can produce significant Balmer line emission even if the truncation radius shifts inwards.," Within this scenario, we might expect that the truncation radius depends on the mass accretion rate: at very low accretion rate, the truncation radius is large and the disk is neutral; as the rate increases, the truncation radius decreases but the thin disk is still not ionized; but if the accretion rate increases further, the inner part of thin disk becomes ionized, which sets the smallest possible disk radius that can produce significant Balmer line emission even if the truncation radius shifts inwards."434 IIence there may exist a sequence of objects from very low-luminosity AGNs with a narrow line profile. to normal double-peaked line emitters. aud to extremely broad double-peaked line emitters. depencine on one intrinsic parameter. the accretion rate.," Hence there may exist a sequence of objects from very low-luminosity AGNs with a narrow line profile, to normal double-peaked line emitters, and to extremely broad double-peaked line emitters, depending on one intrinsic parameter, the accretion rate."435 SDSS JO94L2+0900 may be a fortuitous object that at the right accretion rate. possessing a disk wilh a small (runcation radius vel partially ionized.," SDSS J0942+0900 may be a fortuitous object that at the right accretion rate, possessing a disk with a small truncation radius yet partially ionized."436" With a truncation radius of order 50—100r,. the thermal emission from the disk (turns down in (he optical or near UV."," With a truncation radius of order $-$ $r_g$, the thermal emission from the disk turns down in the optical or near UV."437 The spectrum steepening in the near UV in SDSS JO942-+0900 mav be an indication of this., The spectrum steepening in the near UV in SDSS J0942+0900 may be an indication of this.438 A further prediction of the truncated disk model is an iron Α line component will a profile similar to that of the optical Wa line and with an EW of a few tens of eV lor the fraction of N-ravs intercepted by the disk as estimated in CIIS9., A further prediction of the truncated disk model is an iron K line component with a profile similar to that of the optical $\alpha$ line and with an EW of a few tens of eV for the fraction of X-rays intercepted by the disk as estimated in CH89.439 The radiative efficiency. of such a disk in the optical/UV is on Che order of 0.01. and the presence of an LRAF in these objects requires the accretion rate considerably lower than the Edington accretion rate.," The radiative efficiency of such a disk in the optical/UV is on the order of 0.01, and the presence of an LRAF in these objects requires the accretion rate considerably lower than the Edington accretion rate."440 Thus. to explain the optical luminosity of 1.9x107! eres 1 in 5D55 JO942+0900. as well as many other double-peaked line emitters in the SDSS. a black hole mass of at least 105 is required.," Thus, to explain the optical luminosity of $\times 10^{44}$ ergs $^{-1}$ in SDSS J0942+0900, as well as many other double-peaked line emitters in the SDSS, a black hole mass of at least $^8$ is required."441 llowever. local viscous heating seems sufficient to power the Ila emission in SDSS J0942--0900.," However, local viscous heating seems sufficient to power the $\alpha$ emission in SDSS J0942+0900."442 We carry out an analysis similar (o that presented in CIIS9 as follows., We carry out an analysis similar to that presented in CH89 as follows.443 The, The444from the non-local moment equations.,from the non-local moment equations.445 For the latter we used the prescription described iu CD9s., For the latter we used the prescription described in CD98.446 As c is an inτσortant topological quautity describing the inhomogenous nature of convection. the reasonable aegrecicut found here is a very pronusing result.," As $\sigma$ is an important topological quantity describing the inhomogenous nature of convection, the reasonable agreement found here is a very promising result."447 It illustrates the mnuportauce of improving the TOMSs. because the DOA used in Iupka(1999a) onlv indicated a correct trend. while the more complete ΤΟΝΙ used here also provides a closer quiititative agreement.," It illustrates the importance of improving the TOMs, because the DGA used in \citet{Kup99a} only indicated a correct trend, while the more complete TOM used here also provides a closer quantitative agreement."448 The local convection model predicts a structureless 9—(0.5., The local convection model predicts a structureless $\sigma=0.5$.449 Fig., Fig.450 3) compares the conuvective fux from numerical simulations for model 3.3 with solutions from the moment equations using the itermeciate TOM., \ref{Fig3} compares the convective flux from numerical simulations for model 3J with solutions from the moment equations using the intermediate TOM.451 Clearly. the latter has improved over the DCA (Iupka1999a) both qualitatively anc quantitatively.," Clearly, the latter has improved over the DGA \citep{Kup99a} both qualitatively and quantitatively."452 Except for the overshooting region the DGA barely differed from the local mode which is shown here for comparison., Except for the overshooting region the DGA barely differed from the local model which is shown here for comparison.453 Though the preseut convection model provides a substautia iuproveient. the couvective flux still falls short in the muddle of the convection zone of 3J iux the extent of the lower overshooting zoue ids underestimated.," Though the present convection model provides a substantial improvement, the convective flux still falls short in the middle of the convection zone of 3J and the extent of the lower overshooting zone is underestimated."454" This may be due to uecelecting effects of radiative losses on the time scales το aud t,o as well as because several contributions to the TOMs are neglected in our “intermediate model”. or due to the Doussinesq treatiucut of the 'TOMSs in (Cauuto1992.1993).. or iuconupletenuess of equation (5])."," This may be due to neglecting effects of radiative losses on the time scales $\tau_{\theta}$ and $\tau_{p\theta}$ as well as because several contributions to the TOMs are neglected in our “intermediate model”, or due to the Boussinesq treatment of the TOMs in \citep{Can92,Can93}, or incompleteness of equation \ref{eq_epsilon}) )."455 Fie., Fig.456" L comwes local leugth scales A=of, as used in WuNine cheth theory with the leneth scale A=Nise ohained with the non-local moment equations for tie case of model 2111. Obviously. there is no à that brines the leneth scales iu agrecinent."," \ref{Fig4} compares local length scales $\Lambda =457\alpha H_{\rm p}$ as used in mixing length theory with the length scale $\Lambda = K^{1.5}/\epsilon$ obtained with the non-local moment equations for the case of model 211P. Obviously, there is no $\alpha$ that brings the length scales in agreement."458" Thus. there is no alternative but to solve at least the full equatious (5)) (6)) to obtain 6,"," Thus, there is no alternative but to solve at least the full equations \ref{eq_epsilon}) \ref{eq_diffeps}) ) to obtain $\epsilon$."459 Iu conclusion. we have found uot only qualitative. but also quantitative agreement between nuuerical sinulations aud the non-local 1io1ieut equations. provided one avoids the DCA for the TOMS and cluplovs the stationary solution of their dvuauiic equations as sugeested in appendix D of (Canuto1993) aud neglects Boussinesq type factors Guvolving JJ.," In conclusion, we have found not only qualitative, but also quantitative agreement between numerical simulations and the non-local moment equations, provided one avoids the DGA for the TOMs and employs the stationary solution of their dynamic equations as suggested in appendix B of \citep{Can93} and neglects Boussinesq type factors (involving $\beta$ )."460 Moreover. we have found the mean values for T. P. and p to be accurate to within in comparison with found for local models with optimized ήπιο leneth paramcter.," Moreover, we have found the mean values for T, P, and $\rho$ to be accurate to within in comparison with found for local models with optimized mixing length parameter."461 Couvective and radiative flux are typically accurate to within., Convective and radiative flux are typically accurate to within.462 The improvements are largest in regious of weak convection and in stably stratified Lbdwers., The improvements are largest in regions of weak convection and in stably stratified layers.463 We lave used the closure coustauts sugeested πι Canuto(1993) and CDOS except for eq. which was increased from 0.2 to 0.5. because this nuproved the results for the planetary boundary laver (Canto ccommuuication) aud enhanced the numerical stability.," We have used the closure constants suggested in \citet{Can93} and CD98 except for $c_{11}$, which was increased from 0.2 to 0.5, because this improved the results for the planetary boundary layer (Canuto communication) and enhanced the numerical stability."464" We lave uot found the DGAÀ to he able to vield a similar agreement for both 23J aud 211P even when tunius the closure constants individually for 3J aud 9111, The situation is even worse for the local model.", We have not found the DGA to be able to yield a similar agreement for both 3J and 211P even when tuning the closure constants individually for 3J and 211P. The situation is even worse for the local model.465 Tn lkupka(19995). we will deal with this problem in detail., In \citet{Kup99b} we will deal with this problem in detail.466" Finally, while cach 3D simulation took vetween several davs aud several weeks ou a nodern workstation to obtain a thermally relaxed solution. the moment equations took a couple of uinutes to half aun low."," Finally, while each 3D simulation took between several days and several weeks on a modern workstation to obtain a thermally relaxed solution, the moment equations took a couple of minutes to half an hour."467 This holds true already or a low ummerical resolution aud for an explicit ine inteeration method., This holds true already for a low numerical resolution and for an explicit time integration method.468" The results found here are promising for the application of the uou-local convection model iu xwtieular to envelope couvection zones of A aud F stars. because they feature a simular range of convective efficiency. thickness iu terms of IT, and interaction amone uciehbowing convection zoues."," The results found here are promising for the application of the non-local convection model in particular to envelope convection zones of A and F stars, because they feature a similar range of convective efficiency, thickness in terms of $H_p$, and interaction among neighbouring convection zones."469 For A aud F stars the thermal structure is rot known in advance., For A and F stars the thermal structure is not known in advance.470 Heuce. thermal relaxation and thus the eain on speed in comparison with Munerical simulations is esseutial.," Hence, thermal relaxation and thus the gain on speed in comparison with numerical simulations is essential."471 The computational savings are very attractive also for problems studied on lydrostatic time scales. whenever the ull information provided by a simulation is nof receded.," The computational savings are very attractive also for problems studied on hydrostatic time scales, whenever the full information provided by a simulation is not needed."472 huprovemieuts of the convection model studied are possible. nevertheless it is a more o»oniüsng basis for asteroscismological studies of pulsating A auc F stars (0 Set. + Dor. roAp. ete.)," Improvements of the convection model studied are possible, nevertheless it is a more promising basis for asteroseismological studies of pulsating A and F stars $\delta$ Sct, $\gamma$ Dor, roAp, etc.)"473 iiu local convection mocels aud also a new basis or related work such as diffusion calculations., than local convection models and also a new basis for related work such as diffusion calculations.474" Detailed results for a broader range of physical »uwanieters, in particular for efficient convection and deeper convection zones. and thus of high iuportauce also for other types of stars. have vet o corroborate this study."," Detailed results for a broader range of physical parameters, in particular for efficient convection and deeper convection zones, and thus of high importance also for other types of stars, have yet to corroborate this study."475 Tam indebted to IT.J. Muthsun for permission oO use lis simulation code aud data., I am indebted to H.J. Muthsam for permission to use his simulation code and data.476 I am erateful to V.M. Cauuto and ALS. Dubovikov for discussions on turbulent convection models., I am grateful to V.M. Canuto and M.S. Dubovikov for discussions on turbulent convection models.477 The, The4781n magnetic cataclysmic variables (mC'Vs) the accreting material from the secondary. star is entrained onto magnetic field lines and aceretes onto the surface of the white dwarf.,In magnetic cataclysmic variables (mCVs) the accreting material from the secondary star is entrained onto magnetic field lines and accretes onto the surface of the white dwarf.479 Phere it forms a standolf shock. followed by a hot post-shock region of plasma settling onto the white dwarf surface as it cools. principally by bremsstrahlung X-ray radiation. and by optical/Lh evelotron radiation if the magnetic field is sullicienthy strong (see Cropper 1990 and Warner 1995 for reviews of mC’V's).," There it forms a standoff shock, followed by a hot post-shock region of plasma settling onto the white dwarf surface as it cools, principally by bremsstrahlung X-ray radiation, and by optical/IR cyclotron radiation if the magnetic field is sufficiently strong (see Cropper 1990 and Warner 1995 for reviews of mCVs)."480 There have been a number of studies of the post-shock accretion How Xizu 1973: Langer. Chanmugam Shaviv 1981: Chevalier Imamura 1982: WKylalis Lamb 1982: Chanmugam. Langer Shaviv LOSS: Imamura 11987: Wu 1904: Wu. Chanmugam Shaviv 1994: Woelk Beucrmann 1996: Ixocabivik 19907: Cropper 11909: Saxton Wu 1999). investigating dillerent aspects of the region. both analytically and numerically (see Wu 2000 for a review).," There have been a number of studies of the post-shock accretion flow Aizu 1973; Langer, Chanmugam Shaviv 1981; Chevalier Imamura 1982; Kylafis Lamb 1982; Chanmugam, Langer Shaviv 1985; Imamura 1987; Wu 1994; Wu, Chanmugam Shaviv 1994; Woelk Beuermann 1996; Kocabiyik 1997; Cropper 1999; Saxton Wu 1999), investigating different aspects of the region, both analytically and numerically (see Wu 2000 for a review)."481 Despite the [act that substantial progress has been made. the existing studies generally. assume that the velocity and the temperature drop to zero at the base of the accretion column.," Despite the fact that substantial progress has been made, the existing studies generally assume that the velocity and the temperature drop to zero at the base of the accretion column."482 The assumption of zero How velocity and the strict requirement of mass continuity along the field lines immediately implies that the matter density at the base of the accretion column must reach infinity., The assumption of zero flow velocity and the strict requirement of mass continuity along the field lines immediately implies that the matter density at the base of the accretion column must reach infinity.483 Reeent work by Cropper. Wu Ramsay (2000) has highlighted the consequences of an infinite density at the base of the accretion column: the X-ravs from the shock-heated region is emitted mostly from its base where the density is rising steeply.," Recent work by Cropper, Wu Ramsay (2000) has highlighted the consequences of an infinite density at the base of the accretion column: the X-rays from the shock-heated region is emitted mostly from its base where the density is rising steeply."484 This is true at energies up to approximately that of the shock temperature. which is in the ~LO60 keV range higher than most imaging or CCD-based X-ray. instruments.," This is true at energies up to approximately that of the shock temperature, which is in the $\sim 10-60$ keV range — higher than most imaging or CCD-based X-ray instruments."485 Ehe preponderance of emission from the base of the accretion column has made a more in-depth understanding of the physical conditions in shock-heatecl emission regions essential. no only from the theoretical point of view but also for mocelling and extracting information from the observed. X-ray spectra.," The preponderance of emission from the base of the accretion column has made a more in-depth understanding of the physical conditions in shock-heated emission regions essential, not only from the theoretical point of view but also for modelling and extracting information from the observed X-ray spectra."486 Several aspects have to be considered in order to derive a self-consistent formulation of the aceretion flow. especially a the boundary [aver where the hyvdrodsnamic How. merges into a hvedrostatie white-dwarl atmosphere.," Several aspects have to be considered in order to derive a self-consistent formulation of the accretion flow, especially at the boundary layer where the hydrodynamic flow merges into a hydrostatic white-dwarf atmosphere."487 In the stationary-state case. the hydrodynamic variables at the base of the accretion column should match smoothly to the corresponding variables at the white-dwarl atmosphere.," In the stationary-state case, the hydrodynamic variables at the base of the accretion column should match smoothly to the corresponding variables at the white-dwarf atmosphere."488 In addition. the energy deposition due to the heat Dux emerging from below the white-dwarl atmosphere should be considered.," In addition, the energy deposition due to the heat flux emerging from below the white-dwarf atmosphere should be considered."489 Moreover. at some point in the post-shock region. material may become sulliciently. col that a fraction becomes neutral and cannot be elliciently confined by the magnetic field.," Moreover, at some point in the post-shock region, material may become sufficiently cold that a fraction becomes neutral and cannot be efficiently confined by the magnetic field."490 In the time-dependent. situation. i is necessary to consider the response of the white-dwarl atmosphere to changes in the local mass-aceretion rate and its effects on the stability of the accretion How.," In the time-dependent situation, it is necessary to consider the response of the white-dwarf atmosphere to changes in the local mass-accretion rate and its effects on the stability of the accretion flow."491"where the epicyclic frequency & is defined as py is the perturbation of the pressure. aud &=VIE|A is total wave ΠΙΟΣ, respectively,","where the epicyclic frequency $\kappa$ is defined as $p_1$ is the perturbation of the pressure, and $k=\sqrt{k_z^2+k_r^2}$ is total wave number, respectively."492 Note that & cau be expressed through ο aud b in Eq. (3)), Note that $\kappa$ can be expressed through $a$ and $b$ in Eq. \ref{ab}) )493" as which vanishes when velocity shear is maxi («e=0. b= ο], "," as which vanishes when velocity shear is maximum $a=0$, $b=r^2\Omega$ )."494These equations lead to the following local dispersion relation . Neglecting all 1/r ternis compared to & vields the following dispersion relation. which is identical to the dispersion relation derived by Jietal.(2001) Iu the case of iiaxininun shear flow. ¢=0. aud heuce. &=0. the dispersion relation siniplifies to which imunediately vields the following solutions for + Oulv when we take the plus sien for the square root teri and the ninus sien for the last terii in eq. (12)).," These equations lead to the following local dispersion relation where Neglecting all $1/r$ terms compared to $k$ yields the following dispersion relation, which is identical to the dispersion relation derived by \citet{ji01}495 In the case of maximum shear flow, $a=0$, and hence, $\kappa=0$, the dispersion relation simplifies to which immediately yields the following solutions for $\gamma$ Only when we take the plus sign for the square root term and the minus sign for the last term in eq. \ref{sol}) ),"496 docs it eive the unstable solution. and all the other three solutions are stable.," does it give the unstable solution, and all the other three solutions are stable."497" The MBI occurs only when the secoud term inside the square root of (12)) is negative. Lec. where w,=nk. Ly=yh? aud wy=Wyk..."," The MRI occurs only when the second term inside the square root of \ref{sol}) ) is negative, i.e., where ${\omega_\nu}=\nu{k^2}$, ${\omega_\eta}=\eta{k^2}$ and ${\omega_A}={V_A}{k_z}$."498 Thus. viscosity. maeuetic diffusion aud magnetic tension stabilize the MBRI whereas the shear flow destabilizes it.," Thus, viscosity, magnetic diffusion and magnetic tension stabilize the MRI, whereas the shear flow destabilizes it."499" The coudition for neglecting v aud 1 cau be derived from (12)) by evaluating the expression under the square root. 1.6.. For ky,=0. eq. CL1))"," The condition for neglecting $\nu$ and $\eta$ can be derived from \ref{sol}) ) by evaluating the expression under the square root, i.e., For ${k_r}=0$, eq. \ref{sol2}) )"500 further reduces to Thus it ds apparent that maeuetic diffusivity ancl οποιαο viscosity ouly affect high &; modes.," further reduces to Thus, it is apparent that magnetic diffusivity and kinematic viscosity only affect high ${k_z}$ modes."501 If the magnetic diffusivity is large aud the applied naenetic field is weak. eq. (12))," If the magnetic diffusivity is large and the applied magnetic field is weak, eq. \ref{sol}) )"502 reduces to two roots ~=phe aud~= yh?., reduces to two roots ${\gamma=-\nu{k^2}}$ and ${\gamma=-\eta{k^2}}$.503 The former root correspouds to a warodvuamical brauch i which the fiuid is disconnected roni the clectromaguetic force auc behaves as a pure thud., The former root corresponds to a hydrodynamical branch in which the fluid is disconnected from the electromagnetic force and behaves as a pure fluid.504 The latter root is an clectromaguetic brauch. iu which the magnetic field diffuses as in vactuun.," The latter root is an electromagnetic branch, in which the magnetic field diffuses as in vacuum."505 With an increasing magnetic field. bifurcations occur in which the ivdrodyuauic aud electromagnetic branches are split iuto our branches.," With an increasing magnetic field, bifurcations occur in which the hydrodynamic and electromagnetic branches are split into four branches."506 When uy~uamwy the unstable solution of (L1)) is given bx showing that the unstable solution cimerecs from the lydrodvnamical brauch., When $\omega_\nu\sim\omega_A\ll\omega_\eta$ the unstable solution of \ref{dis2}) ) is given by showing that the unstable solution emerges from the hydrodynamical branch.507 Though imaenetic diffusion dimimishes the MBI. the brauch remains unstable if the," Though magnetic diffusion diminishes the MRI, the branch remains unstable if the"508ohysies affeets the satellite population strongly. with respect o quantities sueh as luminosity function. scaling relations. or star formation histories.,"physics affects the satellite population strongly, with respect to quantities such as luminosity function, scaling relations, or star formation histories."509" Εις emphasizes the significant potential of ""near-Hield cosmology within our Local Croup o inform the general theory of galaxy. formation.", This emphasizes the significant potential of “near-field cosmology” within our Local Group to inform the general theory of galaxy formation.510 Our work vas also shown that it is not necessarily the physics of cosmic reionization ancl supernova feedback. alone that is responsible for resolving the missing satellite problem., Our work has also shown that it is not necessarily the physics of cosmic reionization and supernova feedback alone that is responsible for resolving the missing satellite problem.511 In act. the role of reionization has probably been grossly overstated in many previous works. while other important eedback. such as cosmic ravs. has been ignored.," In fact, the role of reionization has probably been grossly overstated in many previous works, while other important feedback, such as cosmic rays, has been ignored."512 Le will herefore be very interesting to refine the hydrodynamical simulations further in future work. and to make them more πιΠΠ in capturing all the relevant physics.," It will therefore be very interesting to refine the hydrodynamical simulations further in future work, and to make them more faithful in capturing all the relevant physics."513" This research was supported. by the DEC: cluster of exccllence ""Origin and Structure of the Universe’.", This research was supported by the DFG cluster of excellence `Origin and Structure of the Universe'.514The Chandra sources wilh optical counterparts are sources #11. 36533. 4655. #66. #111. and #2113.,"The Chandra sources with optical counterparts are sources 1, 3, 5, 6, 11, and 13."515 The [ist (wo sources are the X-aayv emitüng quasars discussed: earlier., The first two sources are the X-ray emitting quasars discussed earlier.516 Source 3233 lies on the ACTS-S2 chip rather than the 53 chip where the bright X-ray source is located and we chose not to use it for the astrometric solution., Source 3 lies on the ACIS-S2 chip rather than the S3 chip where the bright X-ray source is located and we chose not to use it for the astrometric solution.517 Source 4266 is ihe nucleus of the galaxy and is unsuitable for astrometry., Source 6 is the nucleus of the galaxy and is unsuitable for astrometry.518 We used the remaining four sources (S411. 3655. 4111. and #113) io align the Chandra astrometry (ο that of the HST image (which had previously been aligned with ihe USNO 1.0 catalog).," We used the remaining four sources 1, 5, 11, and 13) to align the Chandra astrometry to that of the HST image (which had previously been aligned with the USNO B1.0 catalog)."519" We estimate that the relative alignment is accurate to better than 0.3"",", We estimate that the relative alignment is accurate to better than $0.3\arcsec$.520 An optical image of the region near LINO 5 is shown in Fig. 2.., An optical image of the region near IXO 5 is shown in Fig. \ref{sb_image}.521 INO 5 appears to lie near a star-lormine ring., IXO 5 appears to lie near a star-forming ring.522 We performed photometry of the entire field shown in Fig., We performed photometry of the entire field shown in Fig.523 2 using DAOPIIOT Classic (Stetson1987) as translated into the Interactive Data Language (IDL) by W.B. Landsman., \ref{sb_image} using DAOPHOT Classic \citep{stetson87} as translated into the Interactive Data Language (IDL) by W.B. Landsman.524 We applied an intensity threshold somewhat above the limiting magnitude of the images in order to select only sources [or which eood photometry could be obtained., We applied an intensity threshold somewhat above the limiting magnitude of the images in order to select only sources for which good photometry could be obtained.525 We selected only sources for which the absolute value of the DAOPIIOT peak parameter was less than 0.75 ilo remove extended sources and image defects and also recquired that the fit of the model point spread function to source intensity profile have ox3., We selected only sources for which the absolute value of the DAOPHOT peak parameter was less than 0.75 to remove extended sources and image defects and also required that the fit of the model point spread function to source intensity profile have $\chi^2 < 3$.526 These cuts remove a number of sources. including some with A4.——10 which are likely regions.," These cuts remove a number of sources, including some with $M_V \sim -10$ which are likely regions."527 llowever. some unresolved or marginally resolved regions or star clusters may remain.," However, some unresolved or marginally resolved regions or star clusters may remain."528 To enable direct comparison with theoretical stellar isochrones. see below. we calculated SI magnitudes in the F439W and F606W filter bandpasses of the HST Wide-Field Planetary Camera 2 (WEDPC2).," To enable direct comparison with theoretical stellar isochrones, see below, we calculated ST magnitudes in the F439W and F606W filter bandpasses of the HST Wide-Field Planetary Camera 2 (WFPC2)."529 The reddening along the line of sight to NGC 1013 calculated. from dust maps derived. from COBE data (Schlegel.Finkbeiner.&Davis1993) gives an extinction E(B—V)=0.039.," The reddening along the line of sight to NGC 1073 calculated from dust maps derived from COBE data \citep{schlegel98} gives an extinction $\rm530E(B-V) = 0.039$ ."531 Using this extinction. a Galactic reddening law. and the package which is part of theSTSDAS IST data analvsis software under(AF. we calculated reddening corrected magnitudes [rom the count rates measured in (he F435W ancl F606W fillers using the specirum of a AOV star taken [rom the Druzual stellar spectrum atlas available insynpholf.," Using this extinction, a Galactic reddening law, and the package which is part of the HST data analysis software under, we calculated reddening corrected magnitudes from the count rates measured in the F435W and F606W filters using the spectrum of a A0V star taken from the Bruzual stellar spectrum atlas available in."532 Because the WEPC2 F439W filler is well matched io the ACS/WFC F435W filter and the ΛΕΡΟΣ F606W filler is well matched to ihe ACS/WFC FG606W filler. translation of the ACS/WFC count rates into ST magnitudes for the WEPC2 filler bandpasses is nol stronglv. dependent on color.," Because the WFPC2 F439W filter is well matched to the ACS/WFC F435W filter and the WFPC2 F606W filter is well matched to the ACS/WFC F606W filter, translation of the ACS/WFC count rates into ST magnitudes for the WFPC2 filter bandpasses is not strongly dependent on color."533 From the resulis presented. by Siriannietal.( 2005).. we estimate that (he maximum error on the ST magnitudes induced. by the transformation is 0.14 [or mgpqiow and 0.11 for pcos.," From the results presented by \citet{sirianni05}, we estimate that the maximum error on the ST magnitudes induced by the transformation is 0.14 for $m_{\rm F439W}$ and 0.11 for $m_{\rm F606W}$ ."534 A color-magnitude diagram. of Mypgogw versus Mpjgow—Mypsogw. lor the field of Fig.," A color-magnitude diagram of $M_{\rm F606W}$ versus $M_{\rm F439W} -535M_{\rm F606W}$ for the field of Fig."536 2 is shown in Fig. 3.., \ref{sb_image} is shown in Fig. \ref{sb_hr}.537 The magnitudes are ST magnitudes. calenlated for the bandpasses of the IST/WPFC2 F439W and FOOGW filters., The magnitudes are ST magnitudes calculated for the bandpasses of the HST/WPFC2 F439W and F606W filters.538 The colors are tvpically accurate to within 40.4., The colors are typically accurate to within $\pm 0.4$.539 There may be additional reddening within NGC 1073 or internal to the source which would allect ihe magnitudes ancl colors., There may be additional reddening within NGC 1073 or internal to the source which would affect the magnitudes and colors.540 Shown on the ligure are isochrones for stellar populations for a metallicity of z=0.019with ages of 8 and 16 Myr 2002)..," Shown on the figure are isochrones for stellar populations for a metallicity of $z = 0.019$with ages of 8 and 16 Myr \citep{bertelli94,girardi02}. ."541"In Case A, the temperatures of the SPH particles are set as described in refgivetemp,, and therefore there is an abrupt decrease in temperature across the ionization front.","In Case A, the temperatures of the SPH particles are set as described in \\ref{givetemp}, and therefore there is an abrupt decrease in temperature across the ionization front."542 The simulation is terminated once the ionization front reaches the edge of the cloud., The simulation is terminated once the ionization front reaches the edge of the cloud.543 In Fig., In Fig.544 5 the smoothing lengths of all SPH particles are plotted against their distance from the ionizing source at time t=0.14Myr.," \ref{fig.hnosm} the smoothing lengths of all SPH particles are plotted against their distance from the ionizing source at time $t\,=\,0.14\,{\rm Myr}$."545 Due to the abrupt temperature and pressure, Due to the abrupt temperature and pressure546It is believed that new stars are born in dense molecular cloud cores.,It is believed that new stars are born in dense molecular cloud cores.547" Therefore, the physical properties of the dense cores are thought to be closely related to the masses of new stars to form within them."," Therefore, the physical properties of the dense cores are thought to be closely related to the masses of new stars to form within them."548" Particularly, the dense core mass function (DCMF) has been considered as a key to understanding the stellar initial mass function (IMF)."," Particularly, the dense core mass function (DCMF) has been considered as a key to understanding the stellar initial mass function (IMF)."549" Many authors have investigated the DCMFs by using dense (710*? cm?) gas tracers such as (sub)millimeter dust continuum emission, infrared visual extinction, and molecular line emissions having high critical densities, for example, the(J—1-0) and(J—1-0) lines (e.g.,Motteetal.1998;Reid&Wilson2006;NutterWard-ThompsonRathborneetal.2009;Ikeda2007;WalshEnoch 2008).."," Many authors have investigated the DCMFs by using dense $\geq 10^{4\mbox{\scriptsize --}5}$ ) gas tracers such as (sub)millimeter dust continuum emission, infrared visual extinction, and molecular line emissions having high critical densities, for example, the and lines \citep[e.g.,][]{mot98,rei06,nut07,rat09,ike07,wal07,eno08}. ."550" In nearby (X 500 pc) star forming regions such as Orion, Ophiuchus, the Pipe Nebula, Perseus, and Serpens, they found that the DCMFs seem to have power-law-like behaviors in high-mass parts as dN/dMοςM, whose * values are very similar to that of the IMF."," In nearby $\leq$ 500 pc) star forming regions such as Orion, Ophiuchus, the Pipe Nebula, Perseus, and Serpens, they found that the DCMFs seem to have power-law-like behaviors in high-mass parts as $dN/dM \propto M^{-\gamma}$, whose $\gamma$ values are very similar to that of the IMF."551" Based on these observational facts, they propose a hypothesis that the power-law form of the IMF has been already determined at the formation stage of the dense cores."," Based on these observational facts, they propose a hypothesis that the power-law form of the IMF has been already determined at the formation stage of the dense cores."552 Ikeda&Kitamura(2009) have recently discovered a similarity between the power-law forms of the IMF and the core mass function (CMF) even in the tenuous (1033 οπι5) cloud structures., \citet{ike09b} have recently discovered a similarity between the power-law forms of the IMF and the core mass function (CMF) even in the tenuous $10^{3\mbox{\scriptsize --}4}$ ) cloud structures.553" They carried out mapping observations by using the (J=1-0) line, whose critical density is (Yoshidaetal.2010),, toward the OMC-1 region in the Orion A cloud."," They carried out mapping observations by using the line, whose critical density is \citep{yos10}, toward the OMC-1 region in the Orion A cloud."554 They found the  value of the CMF of 2.3 - 2.4., They found the $\gamma$ value of the CMF of 2.3 – 2.4.555" The  value is not only similar to those of the H'CO* DCMF (2.2+0.1;Ikedaetal.2007) and the 850um dust continuum DCMF (2.20.2;Nutter&Ward-Thompson2007) within the uncertainties, but also quite consistent with that of the IMF of the Orion Nebula Cluster 2002),, which is associated with the OMC-1 region."," The $\gamma$ value is not only similar to those of the $^{13}$ $^{+}$ DCMF \citep[$2.2\pm0.1$;][]{ike07}556 and the 850 dust continuum DCMF \citep[2.2$\pm$0.2;][]{nut07} within the uncertainties, but also quite consistent with that of the IMF of the Orion Nebula Cluster \citep[2.2;][]{mue02}, which is associated with the OMC-1 region."557" The agreement between the C150CMF and IMF 7 values suggests that, at least in theOMC-1 region, the power-law form of"," The agreement between the $^{18}$ OCMF and IMF $\gamma$ values suggests that, at least in theOMC-1 region, the power-law form of"558The detailed analysis of the arrival time of Cherenkov light from EM. component aud frou. nimous was performed by MonteCarlo simulations of EAS development in the atmosphere. light txausiuission. niürror reflection. photomultiplier efficiency. aud signal To simulate EAS development in the atinosphere we used the CORSINA code v. 150 ,"The detailed analysis of the arrival time of Cherenkov light from E–M component and from muons was performed by Monte–Carlo simulations of EAS development in the atmosphere, light transmission, mirror reflection, photomultiplier efficiency and signal To simulate EAS development in the atmosphere we used the CORSIKA code v. 4.50 ."559A, This is a current version of detailed simulation program for EAS developed in Forschungszentrum Karlsruhe (Germany).560PPLE MacintoshandtransputcrsuscdinE ZN).," It uses FORTRAN77, and different CMZ selections give the versions for different computer systems (IBM M3090, VMS, DEC-Unix, APPLE Macintosh and transputers used in FZK)."561TheDEC UnivoptionhasbeenadaptedtoAMpha XPeomputersu 0.2. TheprimnargC ," The DEC-Unix option has been adapted to Alpha XP computers using Digital FORTRAN at Perpignan, and GNU's f2c converter at Alpha XP, PC 486 with Linux, and PC 486 with DOS in óddź.. The CORSIKA program has been used to study different aspects of Cherenkov radiation in EAS."562Rparticleen, Results presented in this work are extracted for further processing from simulations of 10 showers generated by vertical 6 TeV CR gamma and 10 showers by 10 TeV CR proton.563ergicshadbecusc," We used the program option with GHEISHA code for low energy interactions, EGS electromagnetic interaction code, the Cherenkov light bunch size' of 1 photon per bunch, and CORSIKA Coulomb scattering parameter STEPFC = 0.2."564lectedtogicesiimilurCherenkoephoton(300 150 iin. nolossesylensitic: ," The primary CR particle energies had been selected to give similar Cherenkov photon (300–450 nm, no losses) densities at 50 m from EAS core, equal to about 1000 $^{2}$."565The simulation time using Alpha NP 175 MITz station was about 60 iin., The simulation time using Alpha XP 175 MHz station was about 60 min.566 per gama shower aud about 10 ain., per gamma shower and about 40 min.567 per proton shower., per proton shower.568 The total (10 EAS) CORSIKA output have more than 105 Mb (for σας) and more than 80 Mb (for protons) Gmostly due to Chereukov photon information. despite the fact that only photous pointed to preselected detector areas. 729 mw? in total. were memorized: 28 bytes per The standard CORSISA output for Cherenkov light coutains seven 1byte real uuubers por registered Cherenkov light bunch.," The total (10 EAS) CORSIKA output have more than 105 Mb (for gammas) and more than 80 Mb (for protons) (mostly due to Cherenkov photon information, despite the fact that only photons pointed to preselected detector areas, 729 $^{2}$ in total, were memorized; 28 bytes per The standard CORSIKA output for Cherenkov light contains seven 4–byte real numbers per registered Cherenkov light bunch."569 These provide information ou muuber of Cherenkov photons im a buuch. x position of buuch at registration level. v position. direction cosine to the xaxis. direction cosine to the v.axis. altitude of buuch production. time of buuch arrival with respect to the time of the first interaction in the EAS.," These provide information on number of Cherenkov photons in a bunch, x position of bunch at registration level, y position, direction cosine to the x–axis, direction cosine to the y–axis, altitude of bunch production, time of bunch arrival with respect to the time of the first interaction in the EAS."570 The program produces the buuch of Cherenkov photons. all iu the same direction (on the cone surface). instead of generating cach photon at the cone surface.," The program produces the bunch of Cherenkov photons, all in the same direction (on the cone surface), instead of generating each photon at the cone surface."571 The average bunch size can be selected as an input parameter., The average bunch size can be selected as an input parameter.572 In the default the plotous have wavelength range 300 150, In the default the photons have wavelength range 300 – 450573amount of small-scale structure in a section of forest is measured by computing the mean absolute curvature. aamong pixels within a fixed range range in Lux (see section ??)).,"amount of small-scale structure in a section of forest is measured by computing the mean absolute curvature, among pixels within a fixed range range in flux (see Section \ref{sec:continuum}) )."574 Simulations are then used to convert. iinto a temperature. as described in Section ?7?..," Simulations are then used to convert into a temperature, as described in Section \ref{sec:overdensities}."575 Several issues must be adcdressed before the curvature can be used as a reliable probe of the IGM temperature., Several issues must be addressed before the curvature can be used as a reliable probe of the IGM temperature.576 Phe first of these is noise in the Dux spectra. which will dominate the curvature measurement i£ it is caleulated cirectlv from even very high-quality data.," The first of these is noise in the flux spectra, which will dominate the curvature measurement if it is calculated directly from even very high-quality data."577 Rather than compute the curvature from the raw spectra. therefore. we first. Gt a smoothly varying b-spline to the flux.," Rather than compute the curvature from the raw spectra, therefore, we first fit a smoothly varying b-spline to the flux."578 The curvature is then computed from the fit., The curvature is then computed from the fit.579 We use cubic. polynomials for the piece-wise fits. such that the curvature is continuous across the break points.," We use cubic polynomials for the piece-wise fits, such that the curvature is continuous across the break points."580 The b-spline if fit adaptively. with the break points initially separated by 50+.," The b-spline if fit adaptively, with the break points initially separated by 50."581 Ehe fit is then evaluated around each break point. anc additional points are added where the fit is poor in à chi-squared. sense.," The fit is then evaluated around each break point, and additional points are added where the fit is poor in a chi-squared sense."582 Εις process is repeated until the fit converges. or until the break point spacing reaches a minimum value (6.7 Tor the LILRES data. 13.6 for the ALINE cata).," This process is repeated until the fit converges, or until the break point spacing reaches a minimum value (6.7 for the HIRES data, 13.6 for the MIKE data)."583 Figure 3. shows examples of the b-spline fits to the data., Figure \ref{fig:bspline_example} shows examples of the b-spline fits to the data.584 The fits are naturally more highly constrained [or ligh signal-to-noise data., The fits are naturally more highly constrained for high signal-to-noise data.585 In order to compare with the simulations. therefore. we add the same level of the noise to he simulated spectra as we find in the data. and compute he b-splines using the same method.," In order to compare with the simulations, therefore, we add the same level of the noise to the simulated spectra as we find in the data, and compute the b-splines using the same method."586 A significant benelit of our adaptive fitting scheme is that the curvature of the inal Gt is only moderately sensitive to the amount of noise in the spectrum., A significant benefit of our adaptive fitting scheme is that the curvature of the final fit is only moderately sensitive to the amount of noise in the spectrum.587 We estimate that our [lux error arrays are wencrally accurate to., We estimate that our flux error arrays are generally accurate to.58810-204... Tests using simulations indicated that uncertainties in the flux error at this level will translate into errors in the temperature measurements that are smaller than our statistical errors., Tests using simulations indicated that uncertainties in the flux error at this level will translate into errors in the temperature measurements that are smaller than our statistical errors.589 We have also verified that the measured curvature is not. highly sensitive to moderate correlations in the [ux errors. and that a constant error is an adequate approximation in cases where the error scales with the flux. as expected for bright sources.," We have also verified that the measured curvature is not highly sensitive to moderate correlations in the flux errors, and that a constant error is an adequate approximation in cases where the error scales with the flux, as expected for bright sources."590 We found hat useful curvation informaiton could be extracted. [rom data with errors in the normalized Lux as large as ~O.1 per bin., We found that useful curvation informaiton could be extracted from data with errors in the normalized flux as large as $\sim$ 0.1 per bin.591 NEMTo be conservative.. however. we have limited.s our analysis to regions of the data where the mean error within a .MMpe section is less than 0.06 perκας.," To be conservative, however, we have limited our analysis to regions of the data where the mean error within a Mpc section is less than 0.06 per."592.. This was done to maximize the contrast in curvature tween simulation runs with different temperatures. which ends to diminish as sharp features become washed out by noise. and to make it easier to identify metal lines (sec Section ??))," This was done to maximize the contrast in curvature between simulation runs with different temperatures, which tends to diminish as sharp features become washed out by noise, and to make it easier to identify metal lines (see Section \ref{sec:metals}) )."593 The curvature as defined by Eq. (1)), The curvature as defined by Eq. \ref{eq:curvature}) )594 depends linearly on 1e amplitude of the Dux. which in turn will depend on the 'ontinuum level.," depends linearly on the amplitude of the flux, which in turn will depend on the continuum level."595 Unfortunately. the high levels of absorption in the forest make it dillicult to reliably establish the continuum in 1 real cata. especially at 4. where even the voids may tbsorb z10 per cent of the flux.," Unfortunately, the high levels of absorption in the forest make it difficult to reliably establish the continuum in the real data, especially at $z \gtrsim 4$ , where even the voids may absorb $\gtrsim 10$ per cent of the flux."596 This issue has recently been cdaressed in the context of measuring the mean transmitted ux in the forest., This issue has recently been addressed in the context of measuring the mean transmitted flux in the forest.597 7. used simulations to estimate their. likely error in the continuum. placement as a function of redshift. and 1en applied a correction to their measured mean flux.," \citet{fg2008} used simulations to estimate their likely error in the continuum placement as a function of redshift, and then applied a correction to their measured mean flux."598 This approach will work so long as the optical depth of the voids is consistent., This approach will work so long as the optical depth of the voids is consistent.599 We wishto allow for changes in the, We wishto allow for changes in the600aand oobservations make it possible to systematically discover and study very soft X-ray sources (VSSs) in external galaxies.,and observations make it possible to systematically discover and study very soft X-ray sources (VSSs) in external galaxies.601 Until now. the canonical examples of VSSs were luminous supersoft X-ray sources (SSS).," Until now, the canonical examples of VSSs were luminous supersoft X-ray sources (SSS)."602 The SSSs that established the class lie in the Magellanic Clouds and in the Milky Way: they have AT in the range of tens of eV and luminosities between roughly 1097 erg s! and a few times 10 erg s7!., The SSSs that established the class lie in the Magellanic Clouds and in the Milky Way; they have $kT$ in the range of tens of eV and luminosities between roughly $10^{37}$ erg $^{-1}$ and a few times $10^{38}$ erg $^{-1}$.603 aand ssurveys in other galaxies are important. since gas obscures more than of the Milky Way's SSSs. so that direct studies of the size and characterics of galactic populations of SSSs can be carried out only in other galaxies.," and surveys in other galaxies are important, since gas obscures more than of the Milky Way's SSSs, so that direct studies of the size and characterics of galactic populations of SSSs can be carried out only in other galaxies."604 This paper is the third is a series on the selection of VSSs in external galaxies., This paper is the third is a series on the selection of VSSs in external galaxies.605" In paper | (Di Stefano Kong 2003a). we presented a set of strict hardness ratio conditions (the ""HR conditions) to select only the softest sources."," In paper 1 (Di Stefano Kong 2003a), we presented a set of strict hardness ratio conditions (the “HR conditions) to select only the softest sources."606 Sources selected by the HR conditions are likely to have spectra very similar to those of the SSSs observed in the Galaxy and Magellanic Clouds., Sources selected by the HR conditions are likely to have spectra very similar to those of the SSSs observed in the Galaxy and Magellanic Clouds.607 Also in paper | we tested the HR conditions. by applying them to data from 4+ galaxies., Also in paper 1 we tested the HR conditions by applying them to data from $4$ galaxies.608 In. paper 2 (Di Stefano Kong 2003b). we presented an algorithm that starts with the HR conditions. but which then proceeds to progressively relax them.," In paper 2 (Di Stefano Kong 2003b), we presented an algorithm that starts with the HR conditions, but which then proceeds to progressively relax them."609 Each set of relaxed conditions chooses sources that deviate from the expected broadband spectra of SSSs in some way., Each set of relaxed conditions chooses sources that deviate from the expected broadband spectra of SSSs in some way.610 For example. the 30 conditions select sources that may be as soft as SSS-HRs. but which provide too few photons to satisfy the stronger HR conditions.," For example, the $3\sigma$ conditions select sources that may be as soft as SSS-HRs, but which provide too few photons to satisfy the stronger HR conditions."611 Any source satisfying either the HR or 3¢ conditions is called a classical supersoft source. or simply an SSS (SSS-HR or 30).," Any source satisfying either the HR or $3\sigma$ conditions is called a classical supersoft source, or simply an SSS (SSS-HR or $3\sigma$ )."612 In addition. there is a set of 7 conditions which can select either highly absorbed SSSs. or sources that are genuinely harder than the SSSs studied in the Galaxy and Magellanic Clouds.," In addition, there is a set of $7$ conditions which can select either highly absorbed SSSs, or sources that are genuinely harder than the SSSs studied in the Galaxy and Magellanic Clouds."613 We refer to any source which satisfies one of these weaker conditions as a quasisoft source (QSS)., We refer to any source which satisfies one of these weaker conditions as a quasisoft source (QSS).614" For example. the ""NOH"" conditions can select quasisoft sources (QSS-NOH) located behind large gas columns."," For example, the “NOH” conditions can select quasisoft sources (QSS-NOH) located behind large gas columns."615 Other conditions (e.g.. the “a” conditions) select sources (QSS-7) which may have a dominant component as soft as SSSs. but which also include asmall hard component.," Other conditions (e.g., the $\sigma$ ” conditions) select sources $\sigma$ ) which may have a dominant component as soft as SSSs, but which also include a small hard component."616 All sources selected by the algorithm. whether they are supersoft or quasisoft. are referred to as very soft sources (VSSs).," All sources selected by the algorithm, whether they are supersoft or quasisoft, are referred to as very soft sources (VSSs)."617 In this paper. we apply the full algorithm to data from the same 4 galaxies considered in paper 1: MIOI. M83. ΜΟΙ. and NGC 4472.," In this paper, we apply the full algorithm to data from the same $4$ galaxies considered in paper 1: M101, M83, M51, and NGC 4472."618 Because the HR conditions have already been applied. we could have left SSS-HR sources out of this analysis.," Because the HR conditions have already been applied, we could have left SSS-HR sources out of this analysis."619 We decided however. to include them. because it is useful to explicitly compare their properties with those of the other soft sources identified by higher steps in the algorithm.," We decided however, to include them, because it is useful to explicitly compare their properties with those of the other soft sources identified by higher steps in the algorithm."620 For M101 and M51. we generated our own source lists with the CLAO tool WAVDETECT.," For M101 and M51, we generated our own source lists with the CIAO tool WAVDETECT."621 For M83 we used a source list, For M83 we used a source list622Jaxis; anef ectreinf orcedbysaturationof thepowerLLz; due to the limited output extractable from a rotating SMBH via the Blanford-Znajek mechanism (Vittorinietal.,"axis; an effect reinforced by saturation of the power due to the limited output extractable from a rotating SMBH via the Blanford-Znajek mechanism \citep{vittorini,paggi2}."623"2009;etal. 2009b).. So we the for blazar flareshere: proposeflaring spectral followingchanges patternrelate to the pre-flare of BL Lacs and FSRQs on the - plane, specifically, to their respective branch of the bright gamma,blazar strip; this is because the constraints that set such positions are retained or reinforced during the flares."," So we propose the following pattern for blazar flares: flaring spectral changes relate to the pre-flare of BL Lacs and FSRQs on the - plane, specifically, to their respective branch of the bright blazar strip; this is because the constraints that set such positions are retained or reinforced during the flares."624" To wit: bright sources lying in the upper branch of the strip flare up almost as expected from the cooling constraint to, while source sinthelowerrightbranchmovealmosthorizontallywhen]Wriaoksowmedpecisdfinowmmheabits trestins by entheir BH massMMo."," To wit: bright sources lying in the upper branch of the strip flare up almost as expected from the cooling constraint to, while sources in the lower right branch move almost when luminous, as expected from the BZ constraint to output given their BH masses."625". Such a may be tested on more sources with and multi-wavelengthpicture data; in particular, it will be fruitful to study any interlopers between gas-rich powerful FSRQs and gas-poor BL Lacs (that is, lower-luminosity FSRQs and the LBLs, low-peaked BL Lacs) during their flares on the - plane in search of any divide or smooth rotation gamma,between these patterns."," Such a picture may be tested on more sources with and multi-wavelength data; in particular, it will be fruitful to study any interlopers between gas-rich powerful FSRQs and gas-poor BL Lacs (that is, lower-luminosity FSRQs and the LBLs, low-peaked BL Lacs) during their flares on the - plane in search of any divide or smooth rotation between these patterns."626" This may be the case for the BL Lac sources PKS 0537-441, AO 02354164 and PKS 0426-380; with their weak broad lines and with (seeGhisellinietal.2009)they may constitute transitional objects between FSRQs and BL Lacs."," This may be the case for the BL Lac sources PKS 0537-441, AO 0235+164 and PKS 0426-380; with their weak broad lines and with \citep[see][]{ghisellini2009} may constitute transitional objects between FSRQs and BL Lacs."627 Further investigation of such objects will help understanding their nature and their stance in the above picture., Further investigation of such objects will help understanding their nature and their stance in the above picture.628 anonymous referee., We acknowledge useful comments and suggestions by our anonymous referee.629" A. P. thanks the andHarvard-Smithsonianag Center for for hospitality, and F. Massaro in particular for useful Astrophysicsdiscussions during completion of the present work."," A. P. thanks the Harvard-Smithsonian Center for Astrophysics for hospitality, and F. Massaro in particular for useful discussions during completion of the present work."630NGC 6810. is à earlv-tvpe spiral galaxy (morphological tvpe Sab(sXEsp.“Lully 1988)). also. classified as a Sevfert 2 (NASAExtragalacticDatabaset:: see 19000).,"NGC 6810 is a early-type spiral galaxy (morphological type Sab(s):sp,\citealt{rc3}) ) also classified as a Seyfert 2 \citep[NASA Extragalactic 631Database\footnote{NED: http://nedwww.ipac.caltech.edu/}; see ."632 Despite being relatively nearby. (2~27 Alpe. see below) it has not been the target of much observational study.," Despite being relatively nearby $D\sim 27$ Mpc, see below) it has not been the target of much observational study."633 What little literature on NGC 6810 exists suggests that a powerful. galactic-scale ομον (or superwind. Leckmanetal. 1990)) emanates from it.," What little literature on NGC 6810 exists suggests that a powerful galactic-scale outflow (or superwind, \citealt{ham90}) ) emanates from it."634 Hamoeed&Devereux(1999). present a image of NGC 6810 as part ofa study of star formation rates in carly type spirals. but do not comment on the ~5 kpc-long emission line filament rising at an angle of 45° out of the plane of the ealaxy that is visible in their image.," \citet{hameed99} present a image of NGC 6810 as part of a study of star formation rates in early type spirals, but do not comment on the $\sim 5$ kpc-long emission line filament rising at an angle of $\sim 45\degr$ out of the plane of the galaxy that is visible in their image."635 Coceatoetal.(2004) observed NGC 6810 in a survey of ionized gas along the minor axes of spiral galaxies. noting that the high minor axis velocity dispersion and kinematics were suggestive of an outflow.," \citet{coccato04} observed NGC 6810 in a survey of ionized gas along the minor axes of spiral galaxies, noting that the high minor axis velocity dispersion and kinematics were suggestive of an outflow."636" The moderately high of NGC 6810. i=7S"". djs advantageous for studies of extra-planar emission and is similar to other galaxies with well-studied superwinds such as NGC 253. NGC 3079 and MS2 (7;~το18.85. respectively. using averages of the values given in Stricklandetal. 2004)."," The moderately high of NGC 6810, $i = 78\degr$, is advantageous for studies of extra-planar emission and is similar to other galaxies with well-studied superwinds such as NGC 253, NGC 3079 and M82 $i \sim 76, 78, 85\degr$ respectively, using averages of the values given in \citealt{strickland04a}) )."637 Superwinds may play important roles in. galaxy formation and evolution (seec.g.Heckman2003:Veilleux therein). but examples. of starburst-driven winds that are nearby. bright enough," Superwinds may play important roles in galaxy formation and evolution \citep[see \eg][and references therein]{heckman03,veilleux05}, but examples of starburst-driven winds that are nearby, bright enough"638the asteroseismic data may become more difficult for this and other sub-giant stars with similar magnetic properties.,the asteroseismic data may become more difficult for this and other sub-giant stars with similar magnetic properties.639 A longer time series is required in order to obtain quantitative results., A longer time series is required in order to obtain quantitative results.640 For reference purposes. having accurate oscillation data for a active star at the position in the HR diagram of EK Eri would be highly desirable.," For reference purposes, having accurate oscillation data for a non-active star at the position in the HR diagram of EK Eri would be highly desirable."641 Unfortunately. neither CoRoT nor Kepler apparently covers this.," Unfortunately, neither CoRoT nor Kepler apparently covers this."642 Based on the roughly sinusoidal shape of the light curve. the likely very high inclination. the field geometry suggested by ?.. and the behavior of the activity indicators as function of RV. we suggest a conceptual model of EK Eri with two large low-latitude spot covered areas approximately [80° apart on a star viewed equator-on.," Based on the roughly sinusoidal shape of the light curve, the likely very high inclination, the field geometry suggested by \citet{auriere+2008}, and the behavior of the activity indicators as function of RV, we suggest a conceptual model of EK Eri with two large low-latitude spot covered areas approximately $180^\circ$ apart on a star viewed equator-on."643 In this scenario. the rotational period is twice the photometric period. thus Py=2Ppno617.6 d. We note however. that a simple two-spot model is not able to account for all the seasonal light variations observed. mostly due to the unknown spot lifetimes. sizes and longitudes.," In this scenario, the rotational period is twice the photometric period, thus $P_\mathrm{rot} = 2P_\mathrm{phot} = 617.6$ d. We note however, that a simple two-spot model is not able to account for all the seasonal light variations observed, mostly due to the unknown spot lifetimes, sizes and longitudes."644 Regardless of the rotation period. the measured values of vsiné both from this work and from the literature are inconsistent with the derived radius of the star.," Regardless of the rotation period, the measured values of $v\sin i$ both from this work and from the literature are inconsistent with the derived radius of the star."645 Both the radius derived from asteroseismology and from the spectral analysis set strict upper limits on vsin/ which are lower than previous estimates., Both the radius derived from asteroseismology and from the spectral analysis set strict upper limits on $v\sin i$ which are lower than previous estimates.646 We thus conclude that the vsini is too low to be reliably measured with available spectrographs., We thus conclude that the $v\sin i$ is too low to be reliably measured with available spectrographs.647 Based on high-quality HARPS spectra we have derived the atmospheric parameters of EK Eri to very high precision., Based on high-quality HARPS spectra we have derived the atmospheric parameters of EK Eri to very high precision.648 The abundance pattern for 17 analysed elements is very similar to the Sun. and we detect no anomalies that could otherwise be attributed to an earlier evolutionary state às a magnetic Ap star.," The abundance pattern for 17 analysed elements is very similar to the Sun, and we detect no anomalies that could otherwise be attributed to an earlier evolutionary state as a magnetic Ap star."649 However. in order to argue for or against EK Eri being a descendant of a magnetic Ap star. stronger constraints on the mass and evolutionary. state are needed.," However, in order to argue for or against EK Eri being a descendant of a magnetic Ap star, stronger constraints on the mass and evolutionary state are needed."650 Further seismic studies. preferably at varying rotational phases. may deliver such constraints in terms of accurate asteroseismic mass and radius measurements. and are also needed to probe the possible link between solar-like oscillations and the magnetic field.," Further seismic studies, preferably at varying rotational phases, may deliver such constraints in terms of accurate asteroseismic mass and radius measurements, and are also needed to probe the possible link between solar-like oscillations and the magnetic field."651development which resulted in a peak of interest for stereoscopy that started iu the 70.,development which resulted in a peak of interest for stereoscopy that started in the 70'.652 Severa] viewing devices have also been developed over the voeurs. with one common aiu: ducreasing the comfort aud simplicity of stereoscopyv for the viewer.," Several viewing devices have also been developed over the years, with one common aim: increasing the comfort and simplicity of stereoscopy for the viewer."653 Iu comparison to individual stercographs. the development of specialized glasses (ved-blic. polarised. shutter-tvpe) made stereo pairs easier to visualise.," In comparison to individual stereographs, the development of specialized glasses (red-blue, polarised, shutter-type) made stereo pairs easier to visualise."654 Lately. new stereoscopic techuologics are being integrated inte constuner products at a fast pace: movies. televisious canus οςxisoles. cell phones. advertisement paucls. aud so on.," Lately, new stereoscopic technologies are being integrated into consumer products at a fast pace; movies, televisions, gaming consoles, cell phones, advertisement panels, and so on."655" SStercoscopy has ecole especially popular iu the movie iunustrv in he past few vears with the advent of dieial 3D cuxquas,", Stereoscopy has become especially popular in the movie industry in the past few years with the advent of digital 3D cinemas.656 One should nonetheless not forge that stereo movies themselves are not recent: iiaiielvph 3D. first aired in 1922 (Zone2007).," One should nonetheless not forget that stereo movies themselves are not recent:, in anaglyph 3D, first aired in 1922 \citep[]{Zone07}."657. Tn the scientific comuunity. stereoscopy has Ὃςren shown aand used in the vast. but the exten to which it has been exploited in the preseutation of«ata differs youn field to field.," In the scientific community, stereoscopy has been known and used in the past, but the extent to which it has been exploited in the presentation of data differs from field to field."658 In Astroplivsies. stereoscoyw has not )oen used exteusively. «lespite the inulti-dimenusional ure of many data sets;," In Astrophysics, stereoscopy has not been used extensively, despite the multi-dimensional nature of many data sets."659 Often. a data cube is sliced or projected in order to ¢tain 2D publishabe pictures and erapls.," Often, a data cube is sliced or projected in order to obtain 2D publishable pictures and graphs."660 The issue of displaving and iblishius 111Iti-dinensional data sets has heen ideutified iu the vast. and some interesting (non-stereoscopic) solutious wave been proposed.," The issue of displaying and publishing multi-dimensional data sets has been identified in the past, and some interesting (non-stereoscopic) solutions have been proposed."661" Cosinologists working οi the time evolutioi of the large scale sti1ctures in the Universe using 3D movies to illustrate thei simulations restIts 1s one example οιο,Tolliman2 Hn0)..", Cosmologists working on the time evolution of the large scale structures in the Universe using 3D movies to illustrate their simulations results is one example \citep[e.g.][]{Holliman10}. .662" Recently, BarnesandFluke(2008) descyibed how documents iu ali (pdt) are now ae to contain amunaed 3D nodels, and described how this can be used to create diteractive 3D erap"," Recently, \cite{Barnes08} described how documents in an (.pdf) are now able to contain animated 3D models, and described how this can be used to create interactive 3D graphs."663 lu addition. Diunesetal.(2006) developed a plotting Library specific:dlv tailored to the needs the Astrophysics community.," In addition, \cite{Barnes06} developed a 3D plotting library specifically tailored to the needs of the Astrophysics community."664 Flukeetal.(2006) a discuss aud presen alterjafive advanced image displays which might poteulally talse Oll nore significant place within the AstropWsics COMMuty in the future., \cite{Fluke06} also discuss and present alternative advanced image displays which might potentially take on a more significant place within the Astrophysics community in the future.665 Yot. 8ercoscopic fecinques are not uukuownu to Astroplvsicists.," Yet, stereoscopic techniques are not unknown to Astrophysicists."666 Panctary scientists. for example. use red-blue anaglvphlis.," Planetary scientists, for example, use red-blue anaglyphs."667" Tn t1C CüsC ο [Mars (οι,Newstinetal.2001:Ixeszthelvi 2008). several prolIOS and remote scusing satellites were equipped with special stereo caucras. for example the European Space Agency satellite aud its Teh Resolutioi Stereo Camera Experiment (Jaunuumnctal. 2007).. the aud its Ilieh Resolution huaging Science Experiuent (IBRISE) calnera CMeEwenetal.2007).. the lander aud its Surface Stereo Tuaeger (SST) or the nuager for the Mars Patifinder (MPI) mission (Sinithetal.1997)."," In the case of Mars \citep[e.g.][]{Neukum04,Keszthelyi08}, several probes and remote sensing satellites were equipped with special stereo cameras, for example the European Space Agency satellite and its High Resolution Stereo Camera Experiment \citep[][]{Jaumann07}, the and its High Resolution Imaging Science Experiment (HiRISE) camera \citep[][]{McEwen07}, the lander and its Surface Stereo Imager (SSI) or the imager for the Mars Pathfinder (MPI) mission \citep[][]{Smith97}."668. Ste‘oO pairs are another type cof stereoscopic solution that has been emiploved to accomnodate 1multi-diumeusionall data sets in publications., Stereo pairs are another type of stereoscopic solution that has been employed to accommodate multi-dimensional data sets in publications.669 One of the first Astronomical stereo pairs published depicte the Aloon and was created as carly as 1862 bv L.A. Rutherford (Darrah1977)., One of the first Astronomical stereo pairs published depicted the Moon and was created as early as 1862 by L.M. Rutherford \citep{Darrah77}.670. By taking two subsequent images of the Moon with a six days interval. he obtained a strong cuouel change in orientation to induce a reasonable fecliug of deph.," By taking two subsequent images of the Moon with a six days interval, he obtained a strong enough change in orientation to induce a reasonable feeling of depth."671 More veceuth. the adveut of computers expanded the possible ayplications of stereo pairs in Astrophysics.," More recently, the advent of computers expanded the possible applications of stereo pairs in Astrophysics."672" For exiuuple. Yalul(1980) used theli to display the position othe galaxies iu the Revised Shaplev-Aes Catalog: ÀartinctandMagnenat(19587) and Martinet.ctal.(]981) used stereo pairs to illustrae the shape of invariant surfaces in their stiv of dynamical problems with 3H degrees of freedom: va11deWeveaertaudIcke(1989) aud IckeaudvaneWeveacrt(1991) created stereo pairs to illustrate he Voronol model they use to describe the asviupttic distributio1i of the cosmic mass on 10-200 Mpc scaCR Rheeetal.(1991) procuced stereo pairs to show a 3D imap o their sample of Abell clusters: IoutcluuvandMoloxenskii(1992) mublished a stereo pair of he Solar Coroa caving the 1991 Solar eclipse: Sofue(1991) ---Hustrate> the stripping «f the LAIC aud moleclar clouds: Selnanetal.(1999a.b) created stereo pairs of the colom-iuaguituce diagrauus of the ionizing cluster 30 Doracdus: Sirkoetal.(2001) usec stereo pairs to display the 3D posiion of the blue horizoutal-brauch (BIIB) stars discovered iu the SDSS (Yorketal.2000) spectroscopic Survey: and VostikDopita(2010) and VostaulDorita(2011) used stereo pairs ju complement to fan iuter:ictive 3D maos of the oxvecu-rich material in SNR 1Et)1102.2-7219 aid SNR N132D. These exiuupCR do AC tox""preseif an exhaustive list of all the work tha has beo1 published 1sing stereo pairs in Astrophysics. but illustrate f10 weah of topics that can profi alc make 1πο ο ‘this technique."," For example, \cite{Yahil80} used them to display the position of the galaxies in the Revised Shapley-Ames Catalog; \cite{Martinet81} and \cite{Martinet81b} used stereo pairs to illustrate the shape of invariant surfaces in their study of dynamical problems with 3 degrees of freedom; \cite{Weygaert89} and \cite{Icke91} created stereo pairs to illustrate the Voronoi model they used to describe the asymptotic distribution of the cosmic mass on 10-200 Mpc scales; \cite{Rhee91} produced stereo pairs to show a 3D map of their sample of Abell clusters; \cite{Koutchmy92} published a stereo pair of the Solar Corona during the 1991 Solar eclipse; \cite{Sofue94} illustrated the stripping of the LMC and molecular clouds; \cite{Selman99,Selman99-3} created stereo pairs of the colour-magnitude diagrams of the ionizing cluster 30 Doradus; \cite{Sirko04} used stereo pairs to display the 3D position of the blue horizontal-branch (BHB) stars discovered in the SDSS \citep[][]{York00} spectroscopic survey; and \cite{Vogt10a} and \cite{Vogt10c} used stereo pairs in complement to their interactive 3D maps of the oxygen-rich material in SNR 1E 0102.2-7219 and SNR N132D. These examples do not represent an exhaustive list of all the work that has been published using stereo pairs in Astrophysics, but illustrate the wealth of topics that can profit and make use of this technique."673 Nonotjoless. he use of stereo pairs in AstroplivsicE is less prevalent than iu ¢ther fields.," Nonetheless, the use of stereo pairs in Astrophysics is less prevalent than in other fields."674 In Biocj0nistrv. for example. they lave CCL an 1111yortaut tool to publish t16 3D shapes of molecues frou the ]cee of the computer-era (e.g.Taiilt«πι197ΠαςlanAinsworth1973) until texlav (0.8PujadasaudPalau2001:Landsbereetal.201G:Niaie 2010).," In Biochemistry, for example, they have been an important tool to publish the 3D shapes of molecules from the beginning of the computer-era \citep[e.g.][]{Hamilton70,Hardman73} until today \citep[e.g][]{Pujadas01,Landsberg06, Xiang10}."675. We believe that stereo pairs are a valuabe tool in Astrophysics too. which recent 3D innovations iav help renew.," We believe that stereo pairs are a valuable tool in Astrophysics too, which recent 3D innovations may help renew."676 Iu other words. we areue thatstereoscopy las a ereat but uuder-exploited potential for the yrblicatiou of multi-dineusional Astrophysical data sets aud cau be a valuabe complement to more standard plotting," In other words, we argue thatstereoscopy has a great but under-exploited potential for the publication of multi-dimensional Astrophysical data sets and can be a valuable complement to more standard plotting"677Although the main purpose of this paper is not to discuss the dependences of tidal stripping processes on CC mass Adve. it is important to confirm whether the present numerical,"Although the main purpose of this paper is not to discuss the dependences of tidal stripping processes on GC mass $M_{\rm gc}$, it is important to confirm whether the present numerical"678and medium resolution spectra were obtained with Double Beam Spectrograph (DBS) on the Nasmyth-A focus of the Australian National University’s 2.3. πι telescope.,and medium resolution spectra were obtained with Double Beam Spectrograph (DBS) on the Nasmyth-A focus of the Australian National University's 2.3 m telescope.679 The red channel of the DBS covered the spectral range 6500—7450 aat a measured resolution of AA//pixel)., The red channel of the DBS covered the spectral range $6500-7450$ at a measured resolution of /pixel).680 DBS spectra. displayed in Figure .. have ~5000 counts per pixel in the vicinity ofAA.," DBS spectra, displayed in Figure \ref{spectrum}, , have $\sim5000$ counts per pixel in the vicinity of."681. From these spectra. one can clearly see the non-detection and detection of the Li aabsorption feature from the primary and secondary. respectively. and strong Ha emission from both stars.," From these spectra, one can clearly see the non-detection and detection of the Li absorption feature from the primary and secondary, respectively, and strong $\alpha$ emission from both stars."682 Eight orders of the echelle covered portions of the spectra between 5800 andAA., Eight orders of the echelle covered portions of the spectra between 5800 and.683. At orders containing the Ho and Li llines. the measured resolution was AA//pixel).," At orders containing the $\alpha$ and Li lines, the measured resolution was /pixel)."684 All spectra were reduced following standard procedure using ΠΑΕ., All spectra were reduced following standard procedure using IRAF.685 We also obtained photometric magnitudes of the binary as part of a larger photometry program (Shobbrook et aL.," We also obtained photometric magnitudes of the binary as part of a larger photometry program (Shobbrook et al.,"686 in preparation) for young stars identified in our on-going spectroscopy program., in preparation) for young stars identified in our on-going spectroscopy program.687" The HIP 112312 components haveK, magnitudes from the 2MASS 2nd release database.", The HIP 112312 components have magnitudes from the 2MASS 2nd release database.688 Spectroscopic and photometric data are summarized in Table 2.., Spectroscopic and photometric data are summarized in Table \ref{data}.689 Some colors of the HIP 112312 binary from are slightly inconsistent compared to normal M. dwarfs., Some colors of the HIP 112312 binary from are slightly inconsistent compared to normal M dwarfs.690 For example. the B-V of the two stars are bluer by about 0.1 mag than normal M dwarfs.," For example, the B-V of the two stars are bluer by about 0.1 mag than normal M dwarfs."691 The lower gravity of a young M dwarf compared to the mean gravities of ZAMS M dwarfs could account for much of this difference and a few stars in the Taurus-Auriga region studied by Kenyon&Hartmann(1995) have similarly blue B—V colors for their V—/ colors.," The lower gravity of a young M dwarf compared to the mean gravities of ZAMS M dwarfs could account for much of this difference and a few stars in the Taurus-Auriga region studied by \citet{KH95}692 have similarly blue B-V colors for their V-I colors."693 The Pleiades M dwarfs are also bluer in B—V than one would expect for their V-/ or V-K colors (Stauffer et al., The Pleiades M dwarfs are also bluer in $B-V$ than one would expect for their $V-I$ or $V-K$ colors (Stauffer et al.694 2002. in prep.).," 2002, in prep.)."695 This ts probably just a feature of young K and M dwarfs., This is probably just a feature of young K and M dwarfs.696 The V—/ and V—K colors are quite consistent and correspond to spectral types around M4 and M4.5 for HIP 112312 A and B. respectively.," The V-I and V-K colors are quite consistent and correspond to spectral types around M4 and M4.5 for HIP 112312 A and B, respectively."697 We also measured the TiOS spectral index F[7126-7135[/F|7042-7046] )) for HIP 112312 A and B together with that for GJ 644 (an M3 standard) following etal. (1995)., We also measured the TiO5 spectral index F[7126-7135]/F[7042-7046] ) for HIP 112312 A and B together with that for GJ 644 (an M3 standard) following \citet{TiO5}.698. The measured TIOS index for GJ 644 00.48) was in good agreement with its standard value and with its V—7 color., The measured TiO5 index for GJ 644 = 0.48) was in good agreement with its standard value and with its V-I color.699 Based on the TIO5 and spectral type relation of Reidetal... T1055€8.2)). the TIOS indices for HIPtype 112312 A B again indicate MA.| and M4.5 spectral types. respectively.," Based on the TiO5 and spectral type relation of \citeauthor{TiO5}700 5+8.2 ), the TiO5 indices for HIP 112312 A B again indicate M4.1 and M4.5 spectral types, respectively."701 From colors and ΠΟΣ indices. we assign M4 and M4.5 spectral types to the primary and secondary. respectively.," From colors and TiO5 indices, we assign M4 and M4.5 spectral types to the primary and secondary, respectively."702 The effective temperatures of HIP 112312 A and B from their V-I and V—K colors using an empirical temperature calibration and model colors (Bessell1991) are estimated to be 3150 K and 3030 K respectively. and their uncertainties are not larger than 100 K. Estimation of Li abundances from observed Li 6708 equivalent width requires information on Li curves of growth.," The effective temperatures of HIP 112312 A and B from their V-I and V-K colors using an empirical temperature calibration and model colors \citep{Bessell-Mstars} are estimated to be 3150 K and 3030 K respectively, and their uncertainties are not larger than 100 K. Estimation of Li abundances from observed Li 6708 equivalent width requires information on Li curves of growth."703 From synthetic model spectra (Allardetal.2001. and private communication with P. Hauschildt for updates) for 7;;;23000. 3100. 3200 K and logg=4.0 4.5 with a range of Li abundances (logN(Li)= —99. 0.05. 0.1. 0.3. 0.5. 0.75. 1.0. 1.3). we constructed a set of Li curves of growth (Figure 2).," From synthetic model spectra \citealt{PHEONIX} and private communication with P. Hauschildt for updates) for $T_{eff}$ =3000, 3100, 3200 K and $\log g$ =4.0 4.5 with a range of Li abundances $\log N(Li)=-$ 99, 0.05, 0.1, 0.3, 0.5, 0.75, 1.0, 1.3), we constructed a set of Li curves of growth (Figure \ref{LiCurve}) )."704 We note that the indicated.curves of growth take into account the effect of strong TIO band absorption features around which can alter the lithium equivalent, We note that the indicatedcurves of growth take into account the effect of strong TiO band absorption features around which can alter the lithium equivalent705"breakup speed, given by 2008b)), where Equation (12)) assumes that the truncation radius is always near the corotation radius, which turns out to be true in the models with non-zero magnetic field presented in this paper.","breakup speed, given by ), where Equation \ref{eq_feq}) ) assumes that the truncation radius is always near the corotation radius, which turns out to be true in the models with non-zero magnetic field presented in this paper."706" Below, we will use the predicted equilibrium spin rate of equation to compare with the results of our spin evolution models."," Below, we will use the predicted equilibrium spin rate of equation \ref{eq_feq}) ) to compare with the results of our spin evolution models."707"(12)) The coupled equations (3)), (4)), and (5)) describe the evolution of the system in time."," The coupled equations \ref{eq_mdotstar}) ), \ref{eq_rstar}) ), and \ref{eq_angmom}) ) describe the evolution of the system in time."708" We wrote a computational code that solves these simultaneously, using the fourth-order Runge-Kutta scheme of Pressetal. (1994),, starting from tg=3x10* yr and ending at 3 Myr."," We wrote a computational code that solves these simultaneously, using the fourth-order Runge-Kutta scheme of \citet{pressea94}, starting from $t_0=3\times10^4$ yr and ending at 3 Myr."709" The code is described in more detail in Paper I. Table 1 contains the parameters for each case presented in this section, listed in order of their presentation and grouped by the figures in which the results appear."," The code is described in more detail in Paper I. Table \ref{tab_parms} contains the parameters for each case presented in this section, listed in order of their presentation and grouped by the figures in which the results appear."710" For each case, we present the evolution of the system for the 4 possible combinations of 2 different initial mass accretion rates (parameterized by Mao) and 2 different initial spin rates (fo)."," For each case, we present the evolution of the system for the 4 possible combinations of 2 different initial mass accretion rates (parameterized by $\dot M_{a0}$ ) and 2 different initial spin rates $f_0$ )."711" The “B,= 0"" case is identical to that of Paper I, and we include it here to facilitate comparison with the new results (cases W1-W3)."," The $B_*=0$ ” case is identical to that of Paper I, and we include it here to facilitate comparison with the new results (cases W1--W3)."712" It is instructive first to examine the non-magnetic case, DB,=0, in which there are no magnetic fields."," It is instructive first to examine the non-magnetic case, $B_*=0$, in which there are no magnetic fields."713" Figure 1 illustrates the evolution of the spin rate—expressed as the spin period (panel (a)) and as a fraction of breakup speed (b))—the total torque experienced by the star (panel and the radial locations of the disk inner edge (11) (paneland (c)),corotation radius (R.o) (panel (d))."," Figure \ref{fig_b0} illustrates the evolution of the spin rate—expressed as the spin period (panel (a)) and as a fraction of breakup speed (panel (b))—the total torque experienced by the star (panel (c)), and the radial locations of the disk inner edge $R_t$ ) and corotation radius $R_{\rm co}$ ) (panel (d))."714" In the B,=0 case, the disk extends all the way to the surface"," In the $B_*=0$ case, the disk extends all the way to the surface"715Large scale structures in the universe like galaxies and clusters of galaxies are believed to have formed by gravitational amplitication of small perturbations (Peebles1980:Shandarin&Zeldovich1989:Peacock1999:Padmanabhan2002:Bernardeauetal. 2002)..,"Large scale structures in the universe like galaxies and clusters of galaxies are believed to have formed by gravitational amplification of small perturbations \citep{1980lssu.book.....P, 1989RvMP...61..185S,7161999coph.book.....P, 2002tagc.book.....P, 2002PhR...367....1B}."717 Much of the matter in galaxies and clusters of galaxies is the so called dark matter that is believed to be weaklyinteracting and non-relativistic (Trimble1987:Komatsuetal.2008)...," Much of the matter in galaxies and clusters of galaxies is the so called dark matter that is believed to be weaklyinteracting and non-relativistic \citep{1987ARA&A..25..425T, 2008arXiv0803.0547K}."718 Dark matter responds mainly to gravitational forces. and by virtue of larger density than baryonic matter. assembly of matter into haloes and large scale structure is driven by gravitational instability of initial perturbations.," Dark matter responds mainly to gravitational forces, and by virtue of larger density than baryonic matter, assembly of matter into haloes and large scale structure is driven by gravitational instability of initial perturbations."719 Galaxies are believed to form when gas in highly over-dense haloes cools and collapses to form stars in significant numbers (Hoyle1953:Rees&Ostriker 1977)..," Galaxies are believed to form when gas in highly over-dense haloes cools and collapses to form stars in significant numbers \citep{1953ApJ...118..513H, 1977MNRAS.179..541R, 1977ApJ...211..638S,7201977ApJ...215..483B}."721" The formation of first stars in turn leads to emission of UV radiation that starts to ionize the inter-galactic medium (IGM),", The formation of first stars in turn leads to emission of UV radiation that starts to ionize the inter-galactic medium (IGM).722 The period of transition of the IGM from a completely neutral to a completely ionized state is known as the epoch of reionization (EoR). e.g.. see Loeb&Barkana(2001)..," The period of transition of the IGM from a completely neutral to a completely ionized state is known as the epoch of reionization (EoR), e.g., see \citet{2001ARA&A..39...19L}."723 The study of EoR has been an active area of research in recent yeurs., The study of EoR has been an active area of research in recent years.724 Theoretical ideas about the reionization history have been constrained by a variety of observations (Fan.Carilli.&Keat-ing 2006)., Theoretical ideas about the reionization history have been constrained by a variety of observations \citep{2006ARA&A..44..415F}.725. For example. observations of Gunn-Peterson troughs in AGN spectra at 2.~6 (Beckeretal.2001:Fan2006) indicate that the process of reionization was nearly complete by that redshift.," For example, observations of Gunn-Peterson troughs in AGN spectra at $z \sim 6$ \citep{2001AJ....122.2850B, 2006AJ....132..117F} indicate that the process of reionization was nearly complete by that redshift."726 Bounds on luminosity function of Lya galaxies at high redshifts (Malhotra&Rhoads2004:Sternetal.2005:Bouwensal.2008) also constrain the ΕΟΚ. These bounds are consistent with the conclusion that the IGM was completely ionized by 2~ 6.," Bounds on luminosity function of $\alpha$ galaxies at high redshifts \citep{2004ApJ...617L...5M, 2005ApJ...619...12S,2008ApJ...686..230B} also constrain the EoR. These bounds are consistent with the conclusion that the IGM was completely ionized by $z \sim 6$ ."727 Furthermore. Thomson scattering by free electrons in the IGM," Furthermore, Thomson scattering by free electrons in the IGM"728The spectroscopic study of globular cluster (G:C) systems las made great progress in the past few vears.,The spectroscopic study of globular cluster (GC) systems has made great progress in the past few years.729 The availability. of 10. metre. class telescopes. and ellicient spectrographs. has meant that it is now possible to obtain ow-resolution spectra of individual GCs of sullicient quality o derive reliable abundance and age information (in addition to valuable kinematic information) out to Virgo cluster distances.," The availability of 10 metre class telescopes, and efficient spectrographs, has meant that it is now possible to obtain low-resolution spectra of individual GCs of sufficient quality to derive reliable abundance and age information (in addition to valuable kinematic information) out to Virgo cluster distances."730 However. such studies still only number a 1ancdful. and have largely focused on the rich cluster svstemis of giant elliptical galaxies NGC 1998: NGC 1399:]xissler-Patigetal. 1998: Forbes 2001: NCC 4472:Deaslevetal. 2000: Cohen.Blakeslee.Coté 2003. see also Peng.Ford.&Freeman (2003) for à recent study of NGC 5128).," However, such studies still only number a handful, and have largely focused on the rich cluster systems of giant elliptical galaxies NGC 1998; NGC \citeANP{KisslerPatig98} 1998; \citeANP{Forbes01} 2001; NGC \citeANP{Beasley00} 2000; \citeANP{Cohen03} 2003, see also \citeANP{Peng03} (2003) for a recent study of NGC 5128)."731 Such studies have alloreed unique insights into both he individual properties of GC svstemis associated with ellipticals. and the relation between GCs and the formation of their host. galaxies.," Such studies have afforded unique insights into both the individual properties of GC systems associated with ellipticals, and the relation between GCs and the formation of their host galaxies."732 The results of these previous works we shown that the GC's possess metallicities ranging rom 1/400 to approximately solar values. with these most metal-rich GCs comparable to the integrated bulge starlight of their host. galaxies.," The results of these previous works have shown that the GCs possess metallicities ranging from 1/400 to approximately solar values, with these most metal-rich GCs comparable to the integrated bulge starlight of their host galaxies."733 Moreover. within the uncertainties (which remain necessarily mocdel-dependent). many of GC's in these galaxies appear old and coeval.," Moreover, within the uncertainties (which remain necessarily model-dependent), many of GCs in these galaxies appear old and coeval."734 Recent spectroscopic, Recent spectroscopic735only marginally significant) inflow for the low ionization. low column density absorber. and an outflow velocity (very poorly determined. with confidence level range between 1800 and 12000 km/s) for the high ionization. high column density absorber.,"only marginally significant) inflow for the low ionization, low column density absorber, and an outflow velocity (very poorly determined, with confidence level range between 1800 and 12000 km/s) for the high ionization, high column density absorber."736 An ionized and unstable torus wind. as suggested by Smith et al..," An ionized and unstable torus wind, as suggested by Smith et al.,"737 may indeed provide an explanation for the latter zone., may indeed provide an explanation for the latter zone.738 No significant inflow/outflow is instead found. for both absorbers. in the second observation.," No significant inflow/outflow is instead found, for both absorbers, in the second observation."739 The partial covering scenario. even if providing better fits. Is more demanding geometrically. requiring a size of the obscuring clouds of the same order of the size of the emitting region.," The partial covering scenario, even if providing better fits, is more demanding geometrically, requiring a size of the obscuring clouds of the same order of the size of the emitting region."740 This naturally points to a much closer location of the obscuring clouds. as e.g. due to a radiatively-driven accretior disk wind (e.g. Proga 2003).," This naturally points to a much closer location of the obscuring clouds, as e.g. due to a radiatively-driven accretion disk wind (e.g. Proga 2003)."741 Interestingly. the variability behaviour of Mrk 704 closely resemble that of mini-BAL QSOs (Giustini et al.," Interestingly, the variability behaviour of Mrk 704 closely resemble that of mini-BAL QSOs (Giustini et al."742 2010). strengthening the disk win scenario. at least for the more tonized absorber (the colder absorber may be composed of orbiting clouds as those founc in NGC 1365. Risaliti et al.," 2010), strengthening the disk wind scenario, at least for the more ionized absorber (the colder absorber may be composed of orbiting clouds as those found in NGC 1365, Risaliti et al."743 2009)., 2009).744 Interestingly. a possible outflow has been detected in the first observation (but not in the second. despite very similar column densities and ionization parameters).," Interestingly, a possible outflow has been detected in the first observation (but not in the second, despite very similar column densities and ionization parameters)."745 The alternative hypothesis. that the partial covering is mimicking the presence of a scattering component originating outside the absorbing region. is ruled out by the short term variability of the X-ray emission.," The alternative hypothesis, that the partial covering is mimicking the presence of a scattering component originating outside the absorbing region, is ruled out by the short term variability of the X-ray emission."746 Mrk 704 was also observed four times by Swift/XRT between January 2006 and January 2007., Mrk 704 was also observed four times by Swift/XRT between January 2006 and January 2007.747 Spectral and flux variability 15 apparent between the observations. but the quality of the spectra is not sufficient to establish the nature of the variations.," Spectral and flux variability is apparent between the observations, but the quality of the spectra is not sufficient to establish the nature of the variations."748 The iron Ka line. studied with XMM. is broad. much broader than the optical broad lines but narrower than expected if the entire line would be originated in the innermost accretion disk.," The iron $\alpha$ line, studied with XMM, is broad, much broader than the optical broad lines but narrower than expected if the entire line would be originated in the innermost accretion disk."749 However. if a narrow component (which seems to be almost ubiquitous in Seyfert galaxies) is. added. then the remaining broad component is consistent with emission down to the innermost stable orbit. even if the quality of the data in not good enough to constrain the spin of the black hole.," However, if a narrow component (which seems to be almost ubiquitous in Seyfert galaxies) is added, then the remaining broad component is consistent with emission down to the innermost stable orbit, even if the quality of the data in not good enough to constrain the spin of the black hole."750 We thank the anonymous referee for her/his suggestions which helped improving the clarity of the paper., We thank the anonymous referee for her/his suggestions which helped improving the clarity of the paper.751" We thank all the members of the FERO collaboration for useful discussions,", We thank all the members of the $FERO$ collaboration for useful discussions.752 GM. SB and EP acknowledge financial support from ASI under grant L/088/06/0. and [/090/10/0/. POP. acknowledges financial support from CNES and French GDR PCHE.," GM, SB and EP acknowledge financial support from ASI under grant I/088/06/0 and I/090/10/0/. POP acknowledges financial support from CNES and French GDR PCHE."753 GP acknowledges support from an EU Marie Curie. European Fellowship under contract no. FP7-PEOPLE-2009-, GP acknowledges support from an EU Marie Curie Intra-European Fellowship under contract no. FP7-PEOPLE-2009-IEF-254279.754"paper, but the FM provides a new constraint.","paper, but the FM provides a new constraint."755" The FM-derived values of Y, suggest that all currently popular stellar population model variants over-predict the stellar mass-to-light ratio of old populations (seeMieskeetal. Stellar conclusion).", The FM-derived values of $\Upsilon_*$ suggest that all currently popular stellar population model variants over-predict the stellar mass-to-light ratio of old populations \citep[see][for an alternate approach that results in the same conclusion]{mieske}.756.population models that provide accurate stellar mass-to-light ratios are manifestly important for a variety of uses., Stellar population models that provide accurate stellar mass-to-light ratios are manifestly important for a variety of uses.757" However, star clusters on the FM provide a new way to estimate Y, for large sets of galaxies."," However, star clusters on the FM provide a new way to estimate $\Upsilon_e$ for large sets of ."758" Currently, the FM zero point (C in Equation (1)) is calibrated using the results for Y, from detailed dynamical studies of several tens of early-type galaxies (Cappellarietal."," Currently, the FM zero point $C$ in Equation (1)) is calibrated using the results for $\Upsilon_e$ from detailed dynamical studies of several tens of early-type galaxies \citep{cappellari}."759" If we knew, from stellar models, the values of T,, and 2007)..hence Ύς, for star clusters, we could use them instead to calibrate the FM."," If we knew, from stellar models, the values of $\Upsilon_*$, and hence $\Upsilon_e$, for star clusters, we could use them instead to calibrate the FM."760" Once the FM is accurately calibrated, one can use it to solve for Y, for any galaxy with measured V, Το, and I<."," Once the FM is accurately calibrated, one can use it to solve for $\Upsilon_e$ for any galaxy with measured $V$, $r_e$, and $I_e$."761" We apply the FM to derive empirical relationships between parameters such as main sequence turn-off age and color, and Y,."," We apply the FM to derive empirical relationships between parameters such as main sequence turn-off age and color, and $\Upsilon_*$."762" Figure 12 shows our crude fits to the age- (Table 2)) and (Β-Ν)-Ύ, (Table 3;; the fit is valid for T,B—V<0.75,for>0.75useY,= relationships."," Figure \ref{fig:independent}763 shows our crude fits to the $\Upsilon_*$ (Table \ref{tb:fitage}) ) and $\Upsilon_*$ (Table \ref{tb:fitbmv}; the fit is valid for $B-V \le 0.75, {\rm \ for\ } B-V > 0.75 {\rm \ use\ } \Upsilon_* = 1.13$ ) relationships."764" Neither 1-D relationship appears satisfactory1.13) for the full range of clusters, and certain populations, such as young and metal-poor populations, are completely unconstrained."," Neither 1-D relationship appears satisfactory for the full range of clusters, and certain populations, such as young and metal-poor populations, are completely unconstrained."765" More sophisticated and well-constrained fits will be possible once more data become available for intermediate age clusters, providing an alternative to Y, estimates that depend on stellar populations models."," More sophisticated and well-constrained fits will be possible once more data become available for intermediate age clusters, providing an alternative to $\Upsilon_*$ estimates that depend on stellar populations models."766" We find the following: 1) On average, star clusters fall along the extrapolation of the Fundamental Manifold (FM) defined by spheroidal galaxies."," We find the following: 1) On average, star clusters fall along the extrapolation of the Fundamental Manifold (FM) defined by spheroidal galaxies."767 Their larger scatter is consistent with the proportionally larger uncertainties in their velocity dispersion measurements., Their larger scatter is consistent with the proportionally larger uncertainties in their velocity dispersion measurements.768 Even extreme clusters such as Pal 5 and 14 fall on the relationship when precise velocity dispersions are available., Even extreme clusters such as Pal 5 and 14 fall on the relationship when precise velocity dispersions are available.769 2) Individual clusters are offset from the FM in proportion to their age: older clusters fall on the manifold and younger clusters do not., 2) Individual clusters are offset from the FM in proportion to their age: older clusters fall on the manifold and younger clusters do not.770" Unfortunately, the sample of clusters with measured velocity dispersions does not include many clusters with [yr]<10, so we apply the FM relationship log(ageto infer σ and Y. simultaneously for the remainder."," Unfortunately, the sample of clusters with measured velocity dispersions does not include many clusters with $\log ({\rm age\ [yr]}) < 10$, so we apply the FM relationship to infer $\sigma$ and $\Upsilon_e$ simultaneously for the remainder."771 This procedure works faithfully for those with measured o., This procedure works faithfully for those with measured $\sigma$.772" 3) Aside from the trend with age, deviations from the FM do not correlate measurably with metallicity, dynamical state, or galactocentric distance."," 3) Aside from the trend with age, deviations from the FM do not correlate measurably with metallicity, dynamical state, or galactocentric distance."773" 4) The sense of the evolution of mass-to-light ratio with age is as predicted by stellar population synthesis models, but currently popular models fail to reproduce the estimates from the FM (seealsoMieskeetal."," 4) The sense of the evolution of mass-to-light ratio with age is as predicted by stellar population synthesis models, but currently popular models fail to reproduce the estimates from the FM \citep[see also][]{mieske}."774"2008).. Specifically, the models over-predict the mass-to-light ratio of old, metal-rich populations."," Specifically, the models over-predict the mass-to-light ratio of old, metal-rich populations."775 We provide empirical formulae with which to estimate the stellar mass-to-light ratios of certain cluster populations derived from the estimated mass-to-light ratios., We provide empirical formulae with which to estimate the stellar mass-to-light ratios of certain cluster populations derived from the FM-estimated mass-to-light ratios.776" All stellar systems that we have examined in detail so far— brightest cluster galaxies (Zaritskyetal.2006a),, various galaxy types and luminosity classes (Zaritskyetal.2008;Mieskeet 2008),, and now star clusters — satisfy a simple, 3-parameter (2-dimensional, but not planar) scaling relation."," All stellar systems that we have examined in detail so far— brightest cluster galaxies \citep{zgz}, various galaxy types and luminosity classes \citep{zzg, mieske}, and now star clusters --- satisfy a simple, 3-parameter (2-dimensional, but not planar) scaling relation."777" For star clusters, deviations from the scaling law are age dependent, which is qualitatively consistent with the expectation for passive stellar evolution of the population."," For star clusters, deviations from the scaling law are age dependent, which is qualitatively consistent with the expectation for passive stellar evolution of the population."778" Quantitatively, however, this description fails."," Quantitatively, however, this description fails."779" We suggest, but have not definitively demonstrated, that this disagreement arises from systematic errors in the stellar population models that lead to an overestimation of the V-band mass-to-light ratio of old stellar populations."," We suggest, but have not definitively demonstrated, that this disagreement arises from systematic errors in the stellar population models that lead to an overestimation of the V-band mass-to-light ratio of old stellar populations."780 The sense and magnitude of the effect are consistent with conclusions reached by others investigating stellar evolution models in detail (Toninietal.2008;Maraston2006) and at the very least suggest that a factor of two uncertainty remains in modeling stellar populations.," The sense and magnitude of the effect are consistent with conclusions reached by others investigating stellar evolution models in detail \citep{tonini, maraston}781 and at the very least suggest that a factor of two uncertainty remains in modeling stellar populations."782" As stressed by others (cf.Marastonetal.2006;Conroy,Gunn,&White 2008),, this uncertainty propagates in complicated ways, particularly for composite populations of unknown age distributions, in analyses of galaxy evolution."," As stressed by others \citep[cf.][]{maraston,conroy}, this uncertainty propagates in complicated ways, particularly for composite populations of unknown age distributions, in analyses of galaxy evolution."783" We conclude that there are no evident structural differences, in either stellar spatial distribution or kinematics, between galaxies and star clusters beyond those of scale and those captured in the mass-to-light ratios within Τε."," We conclude that there are no evident structural differences, in either stellar spatial distribution or kinematics, between galaxies and star clusters beyond those of scale and those captured in the mass-to-light ratios within $r_e$."784" Star clusters appear to be baryon-dominated versions of highly-compact, low-mass galaxies."," Star clusters appear to be baryon-dominated versions of highly-compact, low-mass galaxies."785" As such, we are not surprised by the difficulties encountered by others in distinguishing clusters from ultra-compact galaxies."," As such, we are not surprised by the difficulties encountered by others in distinguishing clusters from ultra-compact galaxies."786" If there are wholesale differences between the formation process evolution of star clusters and galaxies, they do not and/ormanifest themselvesdirectly in the gross physical properties."," If there are wholesale differences between the formation process and/or evolution of star clusters and galaxies, they do not manifest themselvesdirectly in the gross physical properties."787" We conclude that even if significant differences exist between the populations, due to the existence or lack of a dark matter halo, simple measurements will not reveal them."," We conclude that even if significant differences exist between the populations, due to the existence or lack of a dark matter halo, simple measurements will not reveal them."788 Projections of parameter space in which these, Projections of parameter space in which these789 (Zhang&Liu2002).. (Scluneja&Ixinieswenger2001).," \citep{ZL02}, \citep{SK01}, \citep{LM83,MW85}."790. (López&Moeaburu1983:MoeaburnWalsh1985). Redianetal.(2000) (Lopez&Moeaburu Πα. 1.0. AG583. Πα Πα IL) ," \citet{Retal00} \citep{LM83,MW85}, $\alpha$ $\beta$ $\lambda$ $\alpha$ $\alpha$ $\beta$ "791hydrogen is almost completely depleted [ον the more massive parent star. which is very close to iis TAAIS: the low-mass parent star. at early stages of its M5 evolution. still has a large fraction of hydrogen.,"hydrogen is almost completely depleted for the more massive parent star, which is very close to its TAMS; the low-mass parent star, at early stages of its MS evolution, still has a large fraction of hydrogen."792 Already a decade ago ? began investigating evolutionary scenarios of collisionally merged stars. with the aim of examining possible formation channels and properties of blue strageler stars in elobular clusters.," Already a decade ago \cite{1997ApJ...487..290S} began investigating evolutionary scenarios of collisionally merged stars, with the aim of examining possible formation channels and properties of blue straggler stars in globular clusters."793 They present results of evolutionary calculations for seven head-on collisions., They present results of evolutionary calculations for seven head-on collisions.794" Among their results. we find for instance a MS duration of 3.74xLO"" vr for their 0.80+0.60AZ. merger: although details of the collision. including abundances. might not be exactly comparable. (is result seems to be in very g00d agreement will our derived MS duration of 3.75x105 vr for our 0.854-0.60AL. similar merger."," Among their results, we find for instance a MS duration of $3.74\times10^8$ yr for their $0.80+0.60\ \Msun$ merger; although details of the collision, including abundances, might not be exactly comparable, this result seems to be in very good agreement with our derived MS duration of $3.75\times10^8$ yr for our $0.85+0.60\ \Msun$ similar merger."795 As mentioned. more extensive evolutionary caleulations for collision products have recently been performed by ?.. 2..," As mentioned, more extensive evolutionary calculations for collision products have recently been performed by \citet{2008A&A...488.1007G}, \citet{2008A&A...488.1017G}."796 Nowaclavs. several procedures for performing calculations of stellar collisions. such as the mentioned MMAS by 2 or MMAMS (make me a massive star) by ? are available.," Nowadays, several procedures for performing calculations of stellar collisions, such as the mentioned MMAS by \cite{2002ApJ...568..939L}797 or MMAMS (`make me a massive star') by \cite{2008MNRAS.383L...5G} are available."798 As illustrated by the foregoing three examples. our eode is able to import and initiate evolution for merger-products created by either of the above procedures.," As illustrated by the foregoing three examples, our code is able to import and initiate evolution for merger-products created by either of the above procedures."799 In future. it will be interesting to study non-canonical evolution merger-productis over a wider range of masses and initial compositions (outcomes of various combinations of the parent stars). as well as mergers involving other (vpes of stars. such as compact objectsthe merging of WD-MS or WD-WD.," In future, it will be interesting to study non-canonical evolution merger-products over a wider range of masses and initial compositions (outcomes of various combinations of the parent stars), as well as mergers involving other types of stars, such as compact objects—the merging of WD-MS or WD-WD."800 We have developed a stellar evolution code that is capable of caleulating full evolutionary tracks without interruption or intervention., We have developed a stellar evolution code that is capable of calculating full evolutionary tracks without interruption or intervention.801 The implicit numerical scheme is based on simultaneous solution of the thermodynamic and composition equations on an adaptive exid., The implicit numerical scheme is based on simultaneous solution of the thermodynamic and composition equations on an adaptive grid.802 Time steps are sell-adjusting according to numerical as well as evolutionary. (ünie-scale criteria., Time steps are self-adjusting according to numerical as well as evolutionary time-scale criteria.803 The code was applied to a laree variety of examples: full evolutionary tracks [or stars of a wide range of masses ancl metallicities. ancl non-canonical stars obtained from," The code was applied to a large variety of examples: full evolutionary tracks for stars of a wide range of masses and metallicities, and non-canonical stars obtained from"8041998: hereafter Paper D.,1998; hereafter Paper I).805 Although the data are still iu a prelininary form. wich cau already be learned regarding the characteristics of the sample of candidate clusters that can be detected using he EIS data.," Although the data are still in a preliminary form, much can already be learned regarding the characteristics of the sample of candidate clusters that can be detected using the EIS data."806 In this paper prelaminary catalogs of objects detected ou single 150 sec., In this paper preliminary catalogs of objects detected on single 150 sec.807 T baud frames are used (see Sects., I band frames are used (see Sects.808 2 and 3)) mainly to assess the capability of the EIS to detect clusters of galaxies at 220.5., \ref{sec:obs_and_data} and \ref{sec:gal_cat}) ) mainly to assess the capability of the EIS to detect clusters of galaxies at $z \gsim 0.5$.809 A discussion of a full cluster sample based on the ealaxy caalog extracted from the coadded EIS inages. is postponed to a future paper (Scodegeio 1998).," A discussion of a full cluster sample based on the galaxy catalog extracted from the coadded EIS images, is postponed to a future paper (Scodeggio 1998)."810 The reason for using here the sinele-fraime catalogs is that they provide two independent datasets for the same area of the sky., The reason for using here the single-frame catalogs is that they provide two independent datasets for the same area of the sky.811 The comparison between the cluster detections obtained using the two catalogs separately. cau be used to quautify the reliability of the cluster detection procedure.," The comparison between the cluster detections obtained using the two catalogs separately, can be used to quantify the reliability of the cluster detection procedure."812" When the haudliug of catalogs extracted from the coadded nuages is fully implemented in the EIS data reduction pipeline. the cluster search will be carried out usiug those catalogs. iustead of the single-framie oues. to benefit from the deeper limiting magnitude of the coadded images,"," When the handling of catalogs extracted from the coadded images is fully implemented in the EIS data reduction pipeline, the cluster search will be carried out using those catalogs, instead of the single-frame ones, to benefit from the deeper limiting magnitude of the coadded images."813 Iu the meanwhile a better quantification of the detection inits for distant clusters of galaxies within the EIS data could be obtained bv comparing the results presented here with those obtained using iudependoeut cluster search methods., In the meanwhile a better quantification of the detection limits for distant clusters of galaxies within the EIS data could be obtained by comparing the results presented here with those obtained using independent cluster search methods.814 Iu Sects., In Sects.815 2 aud 3 the observations. data reduction aud the object catalogs. that are used for the cluster search. are briefly discussed.," \ref{sec:obs_and_data} and \ref{sec:gal_cat} the observations, data reduction and the object catalogs, that are used for the cluster search, are briefly discussed."816 The cluster finding procedure. based ou the matched-filter aleorithiu proposed by P96. is deseribed iu Sect. «," The cluster finding procedure, based on the matched-filter algorithm proposed by P96, is described in Sect. \ref{sec:cluster_finding}."817 Iu Sect., In Sect.818 Ὁ the preliminary cluster catalog is presented. and the properties of the detected candidates are discussed.," \ref{sec:results} the preliminary cluster catalog is presented, and the properties of the detected candidates are discussed."819 Tn Sect., In Sect.820" 6 conclusions of this work are μπασος, aud its possible exteusious to the search for clusters using the coadded EIS images discussed."," \ref{sec:future} conclusions of this work are summarized, and its possible extensions to the search for clusters using the coadded EIS images discussed."821 The observations for the EIS are being conducted. using he EMAIL camera (D'Odorico 1990) on the ESO 3.51 New Technology Telescope., The observations for the EIS are being conducted using the EMMI camera (D'Odorico 1990) on the ESO 3.5m New Technology Telescope.822" The effective field-of-view of the camera is about 9%ος8.5"". with a pixel size of 42667."," The effective field-of-view of the camera is about $9' \times 8.5'$, with a pixel size of 0.266""."823 Observations are being carried. out over four pre-selected patches of the sky spanning a wide range iu right asceusion.," Observations are being carried out over four pre-selected patches of the sky, spanning a wide range in right ascension."824" In this paper ouly the data obtained in he first of these patches. at a~22/15"" and à = 107 (hereafter Patch A) are used."," In this paper only the data obtained in the first of these patches, at $\alpha \sim 22^h 45^m$ and $\delta$ = $^\circ$ (hereafter Patch A) are used."825 Observations in this vatch were obtained during six different rus. from Julv o Noveniber 1997. aud cover a total area of 3.2 square degrees in I baud.," Observations in this patch were obtained during six different runs, from July to November 1997, and cover a total area of 3.2 square degrees in I band."826 The I filter that is beiug used has4. a wide waveleneth coverage. aud the response function can e found in Paper 1. The EIS magnitude svstei is defined o correspond to the Johnsou-Cousius svstem. for zero-color stars.," The I filter that is being used has a wide wavelength coverage, and the response function can be found in Paper I. The EIS magnitude system is defined to correspond to the Johnson-Cousins system, for zero-color stars."827" The EIS observations cousist of a sequence of 150 sec exposures,", The EIS observations consist of a sequence of 150 sec exposures.828 Each point of a patch is imaged twice (except at the edees of the patch). for a total iuteeration time of 300 sec. using two frames shifted by half au EMMIÁ-fine both in right asceusion aud dechnation.," Each point of a patch is imaged twice (except at the edges of the patch), for a total integration time of 300 sec, using two frames shifted by half an EMMI-frame both in right ascension and declination."829 The easiest wav of visualizing the elobal geometry of this mosaic of frames is to consider two indepeudent sets of thon. fornung contiguous erids (n the following referred to as odd aud even frames}. superposed aud shifted by half a frame both iu right ascension aud declination.," The easiest way of visualizing the global geometry of this mosaic of frames is to consider two independent sets of them, forming contiguous grids (in the following referred to as odd and even frames), superposed and shifted by half a frame both in right ascension and declination."830 Observations were carried out in regular visitor modo. and observing conditions varied quite siguificautlv from. run to run. and also from night to nieht within a single run.," Observations were carried out in regular visitor mode, and observing conditions varied quite significantly from run to run, and also from night to night within a single run."831 This fact translates into a considerable spread iu he data-quality of differcut EIS frames., This fact translates into a considerable spread in the data-quality of different EIS frames.832 The secing aud uniting Lo isoplote iu one arcsec? distributions for Patch A observatious are shown in Fig., The seeing and limiting $\sigma$ isophote in one $^2$ distributions for Patch A observations are shown in Fig.833 1. for the odd and even yanes., \ref{fig:qual_distr} for the odd and even frames.834", The median values for the combined sample are 1.107 aud 23.9 limae/aresec*. respectively."," The median values for the combined sample are 1.10"" and 23.94 $^2$, respectively."835 The data reduction is carried out automatically woueh the EIS upeliue. described in Paper L Eveu rough the pipeline was desigued to xoducee: coacded oeuages. it also produces fully corrected single frames. sing the astrometric aud photometric solution derived roni the global data reduction process.," The data reduction is carried out automatically through the EIS pipeline, described in Paper I. Even though the pipeline was designed to produce coadded images, it also produces fully corrected single frames, using the astrometric and photometric solution derived from the global data reduction process."836 The astrometric solution is found rclative to the USNO-AT catalog., The astrometric solution is found relative to the USNO-A1 catalog.837 The oeternal accuracy ο ‘the astrometric solution is better than 1.03 arcsec. although the absolute calibration suffers from," The internal accuracy of the astrometric solution is better than 0.03 arcsec, although the absolute calibration suffers from"838"the IMF, set at m,=25 Mo..","the IMF, set at $m_u$ =25."839" In addition another setting is required for the model; that is, a relatively efficient star formation is demanded in order to prevent an increase in [Ba/Fe] from occurring at a lower metallicity than observed."," In addition another setting is required for the model; that is, a relatively efficient star formation is demanded in order to prevent an increase in [Ba/Fe] from occurring at a lower metallicity than observed."840" This view is compatible with the observed ADF of stars that are older than 10 Gyr, which extends to the metal-rich end around (Coleman& 2008).."," This view is compatible with the observed ADF of stars that are older than 10 Gyr, which extends to the metal-rich end around[Fe/H]=-0.5 \citep{Coleman_08}. ."841" Here, v=2 Gyr[Fe/H]=-0.5! and 74,20.1 Gyr are chosen with Agp—1.5 Gyr."," Here, $\nu$ =2 $^{-1}$ and $\tau_{\rm in}$ =0.1 Gyr are chosen with $\Delta_{\rm SF}$ =1.5 Gyr."842" The fraction of SNe Ia is determined to be fi,—0.03 by the late evolution of Ba and Eu against Fe.", The fraction of SNe Ia is determined to be $f_{\rm Ia}$ =0.03 by the late evolution of Ba and Eu against Fe.843" We refer to this model as model Fnx1, since we will prepare for another two models in order to understand the chemical evolution of the Fnx dSph in 83."," We refer to this model as model Fnx1, since we will prepare for another two models in order to understand the chemical evolution of the Fnx dSph in 3."844 The results are indicated by the red curves in each panel., The results are indicated by the red curves in each panel.845 Each predicted curve passes through the GC data and broadly fits the observed trend at a late phase for Our study will be put forward to the examination into the nucleosynthesis of some other elements in the framework that connects their elemental features to our proposed view., Each predicted curve passes through the GC data and broadly fits the observed trend at a late phase for Our study will be put forward to the examination into the nucleosynthesis of some other elements in the framework that connects their elemental features to our proposed view.846" Here we discuss the nucleosynthesis site of the light s-process element Y. Regarding a-elements, detailed discussion will be presented in §4."," Here we discuss the nucleosynthesis site of the light $s$ -process element Y. Regarding $\alpha$ -elements, detailed discussion will be presented in 4."847" Yttrium (A=89) has been well observed in dSphs (e.g.,Shetroneetal.2001),, including the Fnx dSph (Letarteetal. 2010)."," Yttrium $A$ =89) has been well observed in dSphs \citep[e.g.,][]{Shetrone_01}, including the Fnx dSph \citep{Letarte_10}."848". In regard to the s-process for the light s-elements with mass number A 90, the core He-burning in massive stars, the so-called weak S-process, is considered to be more important than the s-process operating in AGB stars."," In regard to the $s$ -process for the light $s$ -elements with mass number $A$ 90, the core He-burning in massive stars, the so-called weak $s$ -process, is considered to be more important than the $s$ -process operating in AGB stars."849 The weak s-process yield is found to increase with stellar mass (Pumoetal.2010)., The weak $s$ -process yield is found to increase with stellar mass \citep{Pumo_10}.850". Moreover, a recent study claims that the r-process for A ~90-110 is produced by a charged particle reaction (CPR) and shares the same site with Fe production in massive stars (Qian&Wasser-burg 2007)."," Moreover, a recent study claims that the $r$ -process for $A\sim$ 90-110 is produced by a charged particle reaction (CPR) and shares the same site with Fe production in massive stars \citep{Qian_07}."851". These theoretical results, together with the additional assumption of a similar mass-dependence between the r-process Y and Fe yields, provide a consistent interpretation of the Y feature present in the middle and lower panels."," These theoretical results, together with the additional assumption of a similar mass-dependence between the $r$ -process Y and Fe yields, provide a consistent interpretation of the Y feature present in the middle and lower panels."852" T'here is a broad coincidence of the [Y/Fe] value at the same [Fe/H] between the Galaxy and the Fnx dSph over an entire metallicity range, while there is a large deviation of [Ba/Y] between two galaxies in the late evolution."," There is a broad coincidence of the [Y/Fe] value at the same [Fe/H] between the Galaxy and the Fnx dSph over an entire metallicity range, while there is a large deviation of [Ba/Y] between two galaxies in the late evolution."853" In Figure 3, the model results for the two galaxies are superimposed."," In Figure 3, the model results for the two galaxies are superimposed."854" Here we adopt the Y yields which have a mass-dependence similar to Fe in massive stars for both r- and s- processes, and ignore the AGB contribution for Y. The model presented in 82.2 (i.e., model Fnx1) that reproduces the observed Ba feature is equipped with a rather short timescale (—1.5 Gyr) for star formation."," Here we adopt the Y yields which have a mass-dependence similar to Fe in massive stars for both $r$ - and $s$ - processes, and ignore the AGB contribution for Y. The model presented in 2.2 (i.e., model Fnx1) that reproduces the observed Ba feature is equipped with a rather short timescale (=1.5 Gyr) for star formation."855 Such rapid enrichment is observationally supported by the presence of old (710 Gyr) stars having metallicity up to [Fe/H]~-0.5 (Coleman&deJong2008)., Such rapid enrichment is observationally supported by the presence of old $>$ 10 Gyr) stars having metallicity up to $\sim$ -0.5 \citep{Coleman_08}.856". On the other hand, the Fnx dSph has a much longer star formation history on the whole etal.2006;Coleman&deJong 2008)."," On the other hand, the Fnx dSph has a much longer star formation history on the whole \citep{Battaglia_06, Coleman_08}."857. These (Battagliatwo aspects seem to require the introduction of the complex model into the framework to consistently explain both the elemental feature and the overall star formation history., These two aspects seem to require the introduction of the complex model into the framework to consistently explain both the elemental feature and the overall star formation history.858" As a likely case, we can raise the possibility that different paths of chemical enrichment exist leading to a large variation in the abundances of the present-day Fnx dSh stars."," As a likely case, we can raise the possibility that different paths of chemical enrichment exist leading to a large variation in the abundances of the present-day Fnx dSh stars."859" It is, at least in part, inclined to result from the different speeds of star formation depending on the distance from the galaxy center, that wil appear as an observed radial metallicity gradient (Battagliaetal.2006;ColemandeJong 2008)."," It is, at least in part, inclined to result from the different speeds of star formation depending on the distance from the galaxy center, that will appear as an observed radial metallicity gradient \citep{Battaglia_06, Coleman_08}."860". In fact, a close look at the [Ba/Fe] evolution in Figure 1 shows that some stars in the Fnx dSph are located right on the predicted path for the Galaxy."," In fact, a close look at the [Ba/Fe] evolution in Figure 1 shows that some stars in the Fnx dSph are located right on the predicted path for the Galaxy."861" This implied channel is modeled by (v, Asr)=(0.08, 5) with a normal IMF, i.e., m,=50Mo."," This implied channel is modeled by $\nu$, $\Delta_{\rm SF}$ )=(0.08, 5) with a normal IMF, i.e., $m_u$ =50."862. This case is referred to as model Fnx2., This case is referred to as model Fnx2.863" In addition, the presence of the age-metallicity relation in the Fnx dSph (Battagliaetal.2006;Coleman&deJong2008) implies that a large proportion of the metal-rich starsleading to an increasing Ba/Fe trend are relatively young."," In addition, the presence of the age-metallicity relation in the Fnx dSph \citep{Battaglia_06, Coleman_08} implies that a large proportion of the metal-rich starsleading to an increasing Ba/Fe trend are relatively young."864"Incorporating the observed finding of an enhanced star formation at a very late epoch (Coleman into the model, we set (v, Asp)—(1, 2) with m,—25 and an initial metallicity of","Incorporating the observed finding of an enhanced star formation at a very late epoch \citep{Coleman_08} into the model, we set $\nu$ , $\Delta_{\rm SF}$ )=(1, 2) with $m_u$ =25 and an initial metallicity of"865field perturbations. the existence and extension of the tails depends on how much wave energy is contained in long-wave perturbations.,"field perturbations, the existence and extension of the tails depends on how much wave energy is contained in long-wave perturbations."866 For the flat wave power spectrum (wilh the spectral index q=1: Fig. 14), For the flat wave power spectrum (with the spectral index $q = 1$; Fig. \ref{wobl1}{ )867 the tails are steep and the resulting spectra of accelerated. particles do not differ significantly from (he pure compressed ones formed without any turbulence., the tails are steep and the resulting spectra of accelerated particles do not differ significantly from the pure compressed ones formed without any turbulence.868 For the high-amplitude Ixolmogorov. turbulence. with most power in long waves (q=5/3: Fie. L5).," For the high-amplitude Kolmogorov turbulence, with most power in long waves $q=5/3$; Fig. \ref{wobl1}{ ),"869 much flatter hieh-enerev tails are formed. which contain a substantial part of the accelerated. particles energy. densitv.," much flatter high-energy tails are formed, which contain a substantial part of the accelerated particles energy density."870 These (ails diverge [rom the power-law [orm bv exhibiting a continuous steepening., These tails diverge from the power-law form by exhibiting a continuous steepening.871 For both tvpes of wave spectra the cutolls appear within ihe resonance energv range., For both types of wave spectra the cutoffs appear within the resonance energy range.872 To be noted from Figure 2. is that the eutoff energy cdlecreases with growing shock Lorentz factor., To be noted from Figure \ref{wobl2} is that the cutoff energy decreases with growing shock Lorentz factor.873 To understand these spectral features one has to consider the influence of the turbulence characteristics al energetic particle trajectories near the shock (see.e.g..Degelman&Ixirk1990:Ostrowski1991.1993:Bednarz&1996:Nieniec 2004).," To understand these spectral features one has to consider the influence of the turbulence characteristics at energetic particle trajectories near the shock \citep[see, e.g.,][]{beg90,ost91,ost93,bed96,nie04}."874. For the superluminal shock parameters considered here. with the projected velocity uyfeosey&1ο in each case. a low amplitude of magnetic field perturbations leads to the accelerated. particle spectrum being just the anisolropically compressed upstream injected distribution.," For the superluminal shock parameters considered here, with the projected velocity $u_{B,1} \equiv u_1/\cos{\psi_1} \approx 1.4c$ in each case, a low amplitude of magnetic field perturbations leads to the accelerated particle spectrum being just the anisotropically compressed upstream injected distribution."875 In our approach. with approximately monoenergetic particle injection. this process can be seen in Figures 1 and 2 as a step-like spectral component at low energies.," In our approach, with approximately monoenergetic particle injection, this process can be seen in Figures \ref{wobl1} and \ref{wobl2} as a step-like spectral component at low energies."876 To enable the formation of a power-law tail at higher energies. some downstream particles nist succeed in being transported back to the shock for continued energization alter the initial compression phase.," To enable the formation of a power-law tail at higher energies, some downstream particles must succeed in being transported back to the shock for continued energization after the initial compression phase."877 There are (wo features of the perturbed magnetic field which can provide a backward transport., There are two features of the perturbed magnetic field which can provide a backward transport.878 Either (he resonant waves wilh a substantial ampliticle are present. which enable particle cross-field diffusion backward to the mean plasma flow. or long-wave perturbations form locally subliminal field configurations near the shock aud some particles propagating in (hese regions succeed in reaching the shock again.," Either the resonant waves with a substantial amplitude are present, which enable particle cross-field diffusion backward to the mean plasma flow, or long-wave perturbations form locally subluminal field configurations near the shock and some particles propagating in these regions succeed in reaching the shock again."879 To better understand how these two factors can inlluence the acceleration process let us analvze (hem separately., To better understand how these two factors can influence the acceleration process let us analyze them separately.880 Toenable efficient. cross-lield diffusion behind the shock. three-dimensional resonant MILD. perturbations (see.e.g..Giacalone&JokipiiMichalek&Ostrowski1997:Jonesetal.1998) must be present.," Toenable efficient cross-field diffusion behind the shock, large-amplitude three-dimensional resonant MHD perturbations \citep[see, e.g.,][]{gia94,mich97,jon98} must be present."881 In the case of relativistic shock waves. the shock moves in the downstream plasma rest frame with velocity ue&6/3 and the cross-field diffusion must approach its upper limit the Bohm diffusion efficiency — in order to allow a sullicient fraction of downstream particles to remain continuously aclive in (he enereizalion process.," In the case of relativistic shock waves, the shock moves in the downstream plasma rest frame with velocity $u_2\approx c/3$ and the cross-field diffusion must approach its upper limit — the Bohm diffusion efficiency — in order to allow a sufficient fraction of downstream particles to remain continuously active in the energization process."882 This can be achieved in a relatively easy wav bv applying simplified turbulence modeling similar to those proposed in Ostrowski(1991).. Ellisonetal.(1990) or Dednarz&Ostrowski(1996.1993).. where bv selecting specific parameters for small-;umnplitude. particle pitch-angle scattering one allows for conditions with nearly isolropic particle diffusion. or the modeling of Ostrowski (1993).. where upstream sinusoidal," This can be achieved in a relatively easy way by applying simplified turbulence modeling similar to those proposed in \citet{ost91}, \citet{ell90} or \citet{bed96,bed98}, where by selecting specific parameters for small-amplitude particle pitch-angle scattering one allows for conditions with nearly isotropic particle diffusion, or the modeling of \citet{ost93}, , where upstream sinusoidal"883main difference is the absence of the last peak in. 2003-2006 (expected maximum in 2005.9 at 4.8 GHz. 2002.9 at 8 GHz. and 2004.1 at 14.5 GHz). which ts predicted by the periodicity analysis. but is not observed.,"main difference is the absence of the last peak in 2003–2006 (expected maximum in 2005.9 at 4.8 GHz, 2002.9 at 8 GHz, and 2004.1 at 14.5 GHz), which is predicted by the periodicity analysis, but is not observed."884 Both methods give similar results and one can calculate an average period of 7.9+0.5 years for all three frequencies and for the two methods., Both methods give similar results and one can calculate an average period of $7.9\pm0.5$ years for all three frequencies and for the two methods.885 The four main peaks in the total flux-density light curve indicate a periodical behavior of about 8 years., The four main peaks in the total flux-density light curve indicate a periodical behavior of about 8 years.886 If the period preserves over time. we would expect a powerful outburst in ~ 2004.," If the period preserves over time, we would expect a powerful outburst in $\sim$ 2004."887 However. after year 2000. the flux-density of B0605—085 stayed at the same flux level of about 1.7 Jy at all five frequencies.," However, after year 2000, the flux-density of $-$ 085 stayed at the same flux level of about 1.7 Jy at all five frequencies."888 In case of variability caused solely by jet precession we can expect that the flares will appear simultaneously at all frequencies., In case of variability caused solely by jet precession we can expect that the flares will appear simultaneously at all frequencies.889 In order to check whether the peaks at different frequencies reach a maximum at the same time. we calculated frequency-dependent time delays.," In order to check whether the peaks at different frequencies reach a maximum at the same time, we calculated frequency-dependent time delays."890 The Gaussian functions were fitted to the light curves at 4.8 GHz. 8 GHz. 14.5 GHz. 22 GHz. 37 GHz. and 90 GHz as was described in Pyatunina et al. (," The Gaussian functions were fitted to the light curves at 4.8 GHz, 8 GHz, 14.5 GHz, 22 GHz, 37 GHz, and 90 GHz as was described in Pyatunina et al. ("8912006. 2007).,"2006, 2007)."892 The frequency-dependent time delays were estimated as the time difference between the Gaussian peaks at different frequencies., The frequency-dependent time delays were estimated as the time difference between the Gaussian peaks at different frequencies.893 Due to insufficient data. it was possible to calculate frequency-dependent time delays only for the outbursts happened in 1988 and 1995-1996.," Due to insufficient data, it was possible to calculate frequency-dependent time delays only for the outbursts happened in 1988 and 1995-1996."894 However. from Fig.," However, from Fig."895 |. it is seen that the 1973 flare appeared almost simultaneously at 8 GHz and 14.5 GHz., \ref{0605_hist_lcurve} it is seen that the 1973 flare appeared almost simultaneously at 8 GHz and 14.5 GHz.896 We were not able to get reliable fits for the frequencies 22 GHz and 37 GHz due to sparse observations., We were not able to get reliable fits for the frequencies 22 GHz and 37 GHz due to sparse observations.897 The parameters of the Gaussians. fitted to the light curves. are shown in Table 2.. where frequency. amplitude of a flare. time of the maximum. width of a flare O. and time delay are listed.," The parameters of the Gaussians, fitted to the light curves, are shown in Table \ref{0605outbursts}, where frequency, amplitude of a flare, time of the maximum, width of a flare $\Theta$, and time delay are listed."898 We calculated frequency-dependent time delays with respect to the position of the peak at the highest frequency (22 GHz for the 1995-1996 flare and at 90 GHz for the 1988 flare)., We calculated frequency-dependent time delays with respect to the position of the peak at the highest frequency (22 GHz for the 1995-1996 flare and at 90 GHz for the 1988 flare).899 It is clearly seen that the C outburst in 1988 appeared almost simultaneously at all four frequencies with the negligible difference in time between individual frequencies of about 0.08+0.05 years., It is clearly seen that the $C$ outburst in 1988 appeared almost simultaneously at all four frequencies with the negligible difference in time between individual frequencies of about $\pm$ 0.05 years.900 The 1995-1996 flare D shows similar properties. the light curves at all frequencies have reached the maxima almost simultaneously in about 1995.9. except for 4.8 GHz. which has a delay of 0.43+40.07 years.," The 1995-1996 flare $D$ shows similar properties, the light curves at all frequencies have reached the maxima almost simultaneously in about 1995.9, except for 4.8 GHz, which has a delay of $\pm$ 0.07 years."901 On the other hand. the data at 4.8 GHz are poorly sampled during the flare rise. which could shift the Gaussian peak.," On the other hand, the data at 4.8 GHz are poorly sampled during the flare rise, which could shift the Gaussian peak."902 We have also caleulated frequency-dependent time lags using the cross-correlation function., We have also calculated frequency-dependent time lags using the cross-correlation function.903 Table 3. shows delays between various frequencies for C and D flares., Table \ref{0605dcftdel} shows delays between various frequencies for $C$ and $D$ flares.904 The delays for the C flare are zero within the error bars., The delays for the $C$ flare are zero within the error bars.905 The D flare has shown the large time delay of 0.69+0.05 years between 4.8 GHz and 22.0 GHz. whereas the lags at all other frequencies are much shorter. from 0.08+0.02 to 0.19+0.03 years.," The $D$ flare has shown the large time delay of $0.69\pm0.05$ years between 4.8 GHz and 22.0 GHz, whereas the lags at all other frequencies are much shorter, from $0.08\pm0.02$ to $0.19\pm0.03$ years."906 These values are consistent with the lags obtained from the Gaussian fitting. especially that we obtained the larger time delay at 4.8 GHz and lower lags at other frequencies.," These values are consistent with the lags obtained from the Gaussian fitting, especially that we obtained the larger time delay at 4.8 GHz and lower lags at other frequencies."907 The 1982 flare 1s poorly sampled. but it is seen from the plot in Fig.," The 1982 flare is poorly sampled, but it is seen from the plot in Fig."908 | that it appeared almost simultaneously at 5 GHz and at low frequency 408 MHz., \ref{0605_hist_lcurve} that it appeared almost simultaneously at 8 GHz and at low frequency 408 MHz.909 The 1973 flare was observed only at 8 GHz and 14.5 GHz., The 1973 flare was observed only at 8 GHz and 14.5 GHz.910 There is not enough data for this flare to fit Gaussian functions. but it is seen from Fig.," There is not enough data for this flare to fit Gaussian functions, but it is seen from Fig."911 |. that rising of the flare appear simultaneously at two frequencies., \ref{0605_hist_lcurve} that rising of the flare appear simultaneously at two frequencies.912 Therefore. we can conclude from the Gaussian fitting and from the visual analysis of the flares. that the 1973. 1988. and 1995-1996 outbursts appeared almost simultaneously at different frequencies.," Therefore, we can conclude from the Gaussian fitting and from the visual analysis of the flares, that the 1973, 1988, and 1995-1996 outbursts appeared almost simultaneously at different frequencies."913 The bright outbursts appearing simultaneously at all frequencies can be an evidence for a periodic total flux-density variability caused by the jet precession., The bright outbursts appearing simultaneously at all frequencies can be an evidence for a periodic total flux-density variability caused by the jet precession.914" We would expect that if the total flux-density variability is solely due to changes in the Doppler factor. then the peaks of Hares should appear at the same time at various frequencies. since the flux-density 5; is changing like Sj=500.yy"", where c is the spectral index (Lind Blandford 1985)."," We would expect that if the total flux-density variability is solely due to changes in the Doppler factor, then the peaks of flares should appear at the same time at various frequencies, since the flux-density $S_{j}$ is changing like $S_{j} = S_{j}' \delta (\phi,915\gamma)^{p+\alpha}$, where $\alpha$ is the spectral index (Lind Blandford 1985)."916 In order to check whether all outbursts in the total flux-density light curves have similar spectral properties. we constructed the quasi-simultaneous spectra for all available frequencies.," In order to check whether all outbursts in the total flux-density light curves have similar spectral properties, we constructed the quasi-simultaneous spectra for all available frequencies."917 We have selected and plotted spectra for various states of variability of B0605—085. such as ninimum. rising. maximum and falling states.," We have selected and plotted spectra for various states of variability of $-$ 085, such as minimum, rising, maximum and falling states."918 Figure 7 shows the spectral evolution observed for the 1988 (Left) and 1995-1996 (Right) bright outbursts., Figure \ref{0605_spectra} shows the spectral evolution observed for the 1988 (Left) and 1995-1996 (Right) bright outbursts.919 The 1988 flare starts from a steep spectrum in 1983 and 1984. that then changes its turnover frequency in. 1986.," The 1988 flare starts from a steep spectrum in 1983 and 1984, that then changes its turnover frequency in 1986."920 During the maximum of the 1988 flare. the spectrum becomes flat and then steepens again during the minimum state after the flare.," During the maximum of the 1988 flare, the spectrum becomes flat and then steepens again during the minimum state after the flare."921 The 1995-1996 flare shows similar spectral evolution.," The 1995-1996 flare shows similar spectral evolution,"922 , 923Type Ta supernovae |12]..,Type Ia supernovae \cite{Perl96}.924" The analvsis of the data from the first 7 of the Type Ta superuovae from the LBL group [13]. gave Qy=|OQ,0.01PR. Or equivalently Q4—0.06!Wal (0.51 at the coufidence level)."," The analysis of the data from the first 7 of the Type Ia supernovae from the LBL group \cite{Perl96b} gave $\Omega_0=1-\Omega_\Lambda=9250.94^{+0.34}_{-0.28}$ , or equivalently $\Omega_\Lambda=9260.06^{+0.28}_{-0.34}$ $<0.51$ at the confidence level)."927 It is instructive to compare the Qy=0.3. fh=0.7 model that we have been considering with standard CDM and with CIIDAL," It is instructive to compare the $\Omega_0=0.3$, $h=0.7$ model that we have been considering with standard CDM and with CHDM."928 At k=0.5h +. Figs," At $k=0.5 h$ $^{-1}$, Figs."929 5 and 6 of Ref., 5 and 6 of Ref.930" [15| show that the Q,=0.3 CITDM spectrum and that of a biased CDM model with the same a,=0.67 are both iu good agrecinent with the values imdicated for the power spectrum {0} by the APM and CfA data. while the CDAI spectra with es=1 is higher by about a factor of two."," \cite{KNP96} show that the $\Omega_\nu=0.3$ CHDM spectrum and that of a biased CDM model with the same $\sigma_8=0.67$ are both in good agreement with the values indicated for the power spectrum $P(k)$ by the APM and CfA data, while the CDM spectrum with $\sigma_8=1$ is higher by about a factor of two."931" As Figure 2 shows. CIIDM with 9,=0.2in two ucutrino species [5| also gives nonlinear P(E) consistent with the APM data."," As Figure 2 shows, CHDM with $\Omega_\nu=0.2$in two neutrino species \cite{PHKC95} also gives nonlinear $P(k)$ consistent with the APM data."932CGIIz observed at NoRID just one aud a half minutes before ZP1. aud ouly two miuutes after the onset of the flare.,"GHz observed at NoRH just one and a half minutes before ZP1, and only two minutes after the onset of the flare."933 From this figure. we find that fare eruptive process started frou several separated siunall roegious which behave as several simall discrete bright points ou the image at extreme ultraviolet 171 observed at SDO/ATA.," From this figure, we find that flare eruptive process started from several separated small regions which behave as several small discrete bright points on the image at extreme ultraviolet 171 observed at SDO/AIA."934 Aud the microwave emission with masxinuun intensity at 17 GIIz also distributed close to the sanall discrete bright poiuts., And the microwave emission with maximum intensity at 17 GHz also distributed close to the small discrete bright points.935 These facts indicate that the magnetic reconnection aud the energy release may break out from several places with simall size., These facts indicate that the magnetic reconnection and the energy release may break out from several places with small size.936 ZP1 just times at this visine phase. where most of the stored magnetic enerev has not released. aud the maguetic field in the active region keeps in stroug status.," ZP1 just times at this rising phase, where most of the stored magnetic energy has not released, and the magnetic field in the active region keeps in strong status."937 The plasina in the maguetic loops may become very dense because of the confinement of strong magnetic field., The plasma in the magnetic loops may become very dense because of the confinement of strong magnetic field.938 The magneticOo reconnection accelerates electrous to form auisotropic energetico clectron beams. this electrou beau can excite low frequency clectrostatic waves. then couple with the upper-liybrid plasma waves. aud forms the ZP structures.," The magnetic reconnection accelerates electrons to form anisotropic energetic electron beams, this electron beam can excite low frequency electrostatic waves, then couple with the upper-hybrid plasma waves, and forms the ZP structures."939 Additionally. from Fig.l we may fiud that the temperature associated with the source region plasimia is about 22 MI. 16 ME. and 15 MES corresponding to the ZP structures occurred at frequency of 6.10. 7.00 CIIz. 2.60 2.75 CGHIz. aud 10f 1.13 CdIz. respectively.," Additionally, from Fig.1 we may find that the temperature associated with the source region plasma is about 22 MK, 16 MK, and 15 MK corresponding to the ZP structures occurred at frequency of 6.40 – 7.00 GHz, 2.60 – 2.75 GHz, and 1.04 – 1.13 GHz, respectively."940 Table 1 is the brief sumunary of the ZP structures observed in tlis flare events., Table 1 is the brief summary of the ZP structures observed in this flare events.941 Tere. the method of derived plasina density will be introduced in uext section.," Here, the method of derived plasma density will be introduced in next section."942 We find that the frequency separation between zebra stripes increases with respect to the central ciission frequency. and the umuber of zebra stripes decreases with respect to the ceutral cuission frequency.," We find that the frequency separation between zebra stripes increases with respect to the central emission frequency, and the number of zebra stripes decreases with respect to the central emission frequency."943 Iu an ordinary ZP structure. the frequency separation between the adjacent stripes grows with the enission frequency: from 17 5 MIIz at 200 MITz to about sO ΑΠΣ at 3.0 GIIz. aud to about 150 ~ 200 AMIIz at 5.70 CIIz. anc the relative frequency separation of stripes is about acoustaut: Af/fz 2 ~ 3.5," In an ordinary ZP structure, the frequency separation between the adjacent stripes grows with the emission frequency: from 4 $\sim$ 5 MHz at 200 MHz to about 80 MHz at 3.0 GHz, and to about 150 $\sim$ 200 MHz at 5.70 GHz, and the relative frequency separation of stripes is about aconstant: $\Delta f/f\simeq$ 2 $\sim$ 3.5."944 However. in this N2.2 flare event. we find that ZP1 aud. ZP3 has a narrow relative frequency separation of the zebra stripes. which is smaller than1.8%... although the relative frequency. separation of ZP2 stripes is very close to the above gcucral ZP structure.," However, in this X2.2 flare event, we find that ZP1 and ZP3 has a narrow relative frequency separation of the zebra stripes, which is smaller than, although the relative frequency separation of ZP2 stripes is very close to the above general ZP structure."945 Table 2 preseuts the frequency ratio of the adjacent zebra stripes in each ZP structure., Table 2 presents the frequency ratio of the adjacent zebra stripes in each ZP structure.946 We fiud. that the frequency ratios of the adjacent zebra stripes are approximated to a coustaut of about 1.020 in ZP1. aud 1.013 in ZP3.," We find that the frequency ratios of the adjacent zebra stripes are approximated to a constant of about 1.020 in ZP1, and 1.013 in ZP3."947 This feature is much more obvious iu ZP3 where there are 5 zebra stripes. the maxima ratio is 1.015 while the minima ratio is 1.012. all of them are very close to 1.013.," This feature is much more obvious in ZP3 where there are 5 zebra stripes, the maximum ratio is 1.015 while the minimum ratio is 1.012, all of them are very close to 1.013."948 This fact indicates that the Ledeuev's model is not suitable to interpret the formation of the ZP structures observed in this work., This fact indicates that the Ledenev's model is not suitable to interpret the formation of the ZP structures observed in this work.949 At first. almost all the theoretical models (BAT model. WW 120del. or DPR model) for the generation of ZP structures indicate that the ZP cussion frequeucies are approximately around the plasma frequency or its second harmonics.," At first, almost all the theoretical models (BM model, WW model, or DPR model) for the generation of ZP structures indicate that the ZP emission frequencies are approximately around the plasma frequency or its second harmonics."950" With this poiut. the plana density iu the ZP source regious cau be estimated: ny,fefSls?."," With this point, the plasma density in the ZP source regions can be estimated: $n_{e}\approx951f^{2}/81s^{2}$."952 As ZPL and ZP2 have stronglv polarization. s=1.," As ZP1 and ZP2 have strongly polarization, $s=1$."953 As for ZP3. its has moderate polarization deeree (35 1056).," As for ZP3, its has moderate polarization degree (35 – )."954 According to the calenlation of Dulk (1985). the polarization degree of the secoud harmouic plasma cussion is only LO ," According to the calculation of Dulk (1985), the polarization degree of the second harmonic plasma emission is only 10 –."955So. ZP3 also possibly beloues to the fuudameutal emission s=|.," So, ZP3 also possibly belongs to the fundamental emission $s=1$."956" Substituting the cussion frequencies of ZP structures into this expression. the range of plasma density in the ZP source regions cau be obtained. respectively: ZP1.5.410% 6.0.1013 7, the averaged value is 5.5«Lott oem ZP2. 8.3«101. ος1079 7. the averaged value js 8.8<1010 οι7:"," Substituting the emission frequencies of ZP structures into this expression, the range of plasma density in the ZP source regions can be obtained, respectively: ZP1, $5.1\times10^{11}$ – $6.0\times10^{11}$ $^{-3}$, the averaged value is $5.5\times10^{11}$ $^{-3}$ ; ZP2, $8.3\times10^{10}$ – $9.3\times10^{10}$ $^{-3}$, the averaged value is $8.8\times10^{10}$ $^{-3}$;"957Ψε.,.958" Instead of solving the transport equations for vz, we employ the so-called light-bulb approximation and focus on the optically thin region outside the neutrinosophere (e.g.,Janka&Mueller1996;Ohnishietal.2006)."," Instead of solving the transport equations for $\nu_x$, we employ the so-called light-bulb approximation and focus on the optically thin region outside the neutrinosophere \citep[e.g.,][]{jank96,ohni06}."959". According to Duanetal.(2010),, we set the threshold energy, €:5, to be 9 MeV, above which the spectral swap takes place."," According to \cite{duan10}, we set the threshold energy, $\epsilon_{th}$, to be 9 MeV, above which the spectral swap takes place."960" Below the threshold, the neutrino heating is estimated by the spectral transport via the IDSA scheme."," Below the threshold, the neutrino heating is estimated by the spectral transport via the IDSA scheme."961" Above the threshold, the heating rate is replaced by where j and x are the neutrino emissivity and absorptivity, respectively, and f,(r,e,) corresponds to the neutrino distribution function for v, with e, being energies of electron neutrinos and antineutrinos."," Above the threshold, the heating rate is replaced by where $j$ and $\chi$ are the neutrino emissivity and absorptivity, respectively, and $f_{\nu}(r,\epsilon_\nu)$ corresponds to the neutrino distribution function for $\nu_x$ with $\epsilon_\nu$ being energies of electron neutrinos and antineutrinos."962" In the light-bulb approach, it is often approximated by the Fermi-Dirac distribution with a vanishing chemical potential (e.g.,Ohnishietal.2006) as, where k, are the Boltzmann constatn and the neutrino temperature,T,, respectively."," In the light-bulb approach, it is often approximated by the Fermi-Dirac distribution with a vanishing chemical potential \citep[e.g.,][]{ohni06} as, where $k$, $T_{\nu_x}$ are the Boltzmann constatn and the neutrino temperature, respectively."963" g(r) is the geometric factor, g(r)=1—[1—? which is taken into account for the normalization, (R,,,/r)2]with being the radius of the neutrinosphere."," $g(r)$ is the geometric factor, $g(r)=1-\left[1-(R_{\nu_x}/r)^2\right]^{1/2}$ which is taken into account for the normalization, with $R_{\nu_x}$ being the radius of the neutrinosphere."964" The neutrino R,,luminosity of v4 at the infinity is the given as where (εν)=Jn""dev,fulev.)/fu(ev,) is the average energy of emitted neutrinos."," The neutrino luminosity of $\nu_x$ at the infinity is the given as where $\bracket{\epsilon_{\nu_x}}=\int^\infty_0965d\epsilon_{\nu_x}\epsilon_{\nu_x}^3966f_\nu(\epsilon_{\nu_x})/\int^\infty_0967d\epsilon_{\nu_x}\epsilon_{\nu_x}^2 f_\nu(\epsilon_{\nu_x})$ is the average energy of emitted neutrinos."968"[ο Theεν, position where the spectral swapping sets in is fixed at 100 km the gain and the onset time is varied as a (aroundparameter, £, =100, radius)200, and 300 ms after bounce."," The position where the spectral swapping sets in is fixed at 100 km (around the gain radius) and the onset time is varied as a parameter, $t_s=$ 100, 200, and 300 ms after bounce."969" In fact, the threshold energy depends on the neutrino luminosities, spectra and oscillation parameters (see,e.g.,Duanetal.2010,andreferencestherein) with conserved net rv, flux (ie., the lepton number conservation)."," In fact, the threshold energy depends on the neutrino luminosities, spectra and oscillation parameters \cite[see, e.g.,][and references970 therein]{duan10} with conserved net $\nu_e$ flux (i.e., the lepton number conservation)."971" However, the conservation of lepton number is too complicated to satisfy in the dynamical simulation because the neutrino spectrum and the luminosity evolve with time."," However, the conservation of lepton number is too complicated to satisfy in the dynamical simulation because the neutrino spectrum and the luminosity evolve with time."972" In order to focus on the hydrodynamic features affected by the spectral modulation induced by the swapping, we simplify just a single threshold energy in this work."," In order to focus on the hydrodynamic features affected by the spectral modulation induced by the swapping, we simplify just a single threshold energy in this work."973" To summarize, the parameters that we use to mimic the spectral swapping are the following three items, (i) which is the radius of the neutrinosphere of v,, (ii) Ry,(e,,) which is the average energy of v,, and (iii) t, which is the time when the spectral swapping sets in."," To summarize, the parameters that we use to mimic the spectral swapping are the following three items, (i) $R_{\nu_x}$ which is the radius of the neutrinosphere of $\nu_x$, (ii) $\bracket{\epsilon_{\nu_x}}$ which is the average energy of $\nu_x$, and (iii) $t_s$ which is the time when the spectral swapping sets in."974" In this subsection, we first outline the 1D collapse dynamics without spectral swapping."," In this subsection, we first outline the 1D collapse dynamics without spectral swapping."975 We take a 13 Mo progenitor (Nomoto&Hashimoto1988) as a reference.," We take a 13 $M_{\odot}$ progenitor \citep{nomo88}976 as a reference."977" At around 112 ms after the onset of gravitational collapse, the bounce shock forms at a radius of ~ 10 km with an enclosed mass of ~0.7Mo"".."," At around 112 ms after the onset of gravitational collapse, the bounce shock forms at a radius of $\sim$ 10 km with an enclosed mass of $\sim9780.7M_\odot$."979 The central density at this time is p.=3.6x1014 g cm-?., The central density at this time is $\rho_c=3.6\times 10^{14}$ g $^{-3}$.980 The shock propagates outwards but finally stalls at a radius of ~ 100 km., The shock propagates outwards but finally stalls at a radius of $\sim$ 100 km.981" Due to the decreasing accretion rate through the stalled shock, the shock can be still pushed outward."," Due to the decreasing accretion rate through the stalled shock, the shock can be still pushed outward."982" However, after some time, the shock radius begins to shrink."," However, after some time, the shock radius begins to shrink."983" The ratio of the advection timescale, Taqy, and the heating timescale, Theat, is an important indicator for the criteria of neutrino driven explosion etal.2006;Marek&Janka2009;Suwaetal. 2010)."," The ratio of the advection timescale, $\tau_\mathrm{adv}$, and the heating timescale, $\tau_\mathrm{heat}$, is an important indicator for the criteria of neutrino driven explosion \citep{bura06,mare09,suwa10}."984".(Buras In our 1D simulations, Ταν/Tneac is generally smaller than unity in the postbounce phase."," In our 1D simulations, $\tau_\mathrm{adv}/\tau_\mathrm{heat}$ is generally smaller than unity in the postbounce phase."985 This is the reason why our 1D simulations do not yield a delayed explosion., This is the reason why our 1D simulations do not yield a delayed explosion.986" This also the case for the other progenitors (15, 20, and 25 Mo) investigated in this study."," This also the case for the other progenitors (15, 20, and 25 $M_\odot$ ) investigated in this study."987" As for the accretion phase than ~ 50 ms after the the typical neutrino (laterluminosity at r=5000 kmbounce), is 3x10?? erg s! for both rv, and r,, and the typical average energy is (ev,)&:9 MeV and (εν)712 MeV as shown in Figure 1.."," As for the accretion phase (later than $\sim$ 50 ms after the bounce), the typical neutrino luminosity at $r=5000$ km is $3\times 10^{52}$ erg $^{-1}$ for both $\nu_e$ and $\bar\nu_e$, and the typical average energy is $\bracket{\epsilon_{\nu_e}}\approx 9$ MeV and $\bracket{\epsilon_{\bar\nu_e}}\approx 12$ MeV as shown in Figure \ref{fig:neu_lum}."988 Figure 2 indicates the resultant neutrino luminosity spectrum at 100 ms after the bounce., Figure \ref{fig:spec} indicates the resultant neutrino luminosity spectrum at 100 ms after the bounce.989 The investigated models with the spectral swapping are summarized in Table 1.., The investigated models with the spectral swapping are summarized in Table \ref{tab:models}. .990" As already mentioned, the model parameters are the neutrinosphere radius (19), the average energy of neutrinos ((e,,)), and the onset time of the spectral swapping (ές)."," As already mentioned, the model parameters are the neutrinosphere radius $R_{\nu_x}$ ), the average energy of neutrinos $\bracket{\epsilon_{\nu_x}}$ ), and the onset time of the spectral swapping $t_s$ )."991" The model names include these parameters; “NH13” represents the progenitor model, “R..” represents R,, in units of km, “E..” represents (ce,,) in MeV, “T..” represents ἐν in ms, and the last letter ""S"" represents 1D (spherical symmetry)."," The model names include these parameters; “NH13” represents the progenitor model, “R..” represents $R_{\nu_x}$ in units of km, “E..” represents $\bracket{\epsilon_{\nu_x}}$ in MeV, “T..” represents $t_s$ in ms, and the last letter “S” represents 1D (spherical symmetry)."992 Figure 3 presentsthe time evolution of the mass shells for models NH13R30E12T100S and NH13R30E13T100S., Figure \ref{fig:mass_shell} presentsthe time evolution of the mass shells for models NH13R30E12T100S and NH13R30E13T100S.993Given the large sensitivity of c/« to sample size. we prefer to use the A measure in what follows.,"Given the large sensitivity of $c/a$ to sample size, we prefer to use the $\Delta$ measure in what follows."994 This measure intuitively appears to be more robust since it derives from a simple plane-fit to a distribution of points., This measure intuitively appears to be more robust since it derives from a simple plane-fit to a distribution of points.995 Of the 3.246 subhalos within 300 kpe from the centre of the MW-like halo that have survived until the present-day. 505 subhalos fell in as part of a group.," Of the $3,246$ subhalos within $300$ kpc from the centre of the MW-like halo that have survived until the present-day, $898$ subhalos fell in as part of a group."996 321 different groups have contributed to the present-day population of subhalos. of which the earliest two were accreted at >=3.05.," $321$ different groups have contributed to the present-day population of subhalos, of which the earliest two were accreted at $z=3.05$."997" From now on. subhalos identitied to be part of a group are referred to as ""grouped"". while those which are not are termed ""field"" subhalos."," From now on, subhalos identified to be part of a group are referred to as “grouped”, while those which are not are termed “field” subhalos."998" We first test how often a disk-like structure is obtained when selecting a set of 11 subhalos consisting of a certain number JN; of subhalos from one group GV,= 1)while the rest /Vy;4, are from the ""field"".", We first test how often a disk-like structure is obtained when selecting a set of $11$ subhalos consisting of a certain number $N_{sub}$ of subhalos from one group $N_{group} = 1$ ) while the rest $N_{field}$ are from the “field”.999" Note that Niu,=2.3.....11. and the condition Now=Nquaa|Noe11 has to be satistied."," Note that $N_{sub} = 2, 3,1000\ldots, 11$, and the condition $N_{sat} = N_{field} + N_{sub} =100111$ has to be satisfied."1002 We make 10 realisations of such subsets and compute the fraction that gives rise to a configuration as flat as observed. ie. A0.23.," We make $10^{5}$ realisations of such subsets and compute the fraction that gives rise to a configuration as flat as observed, i.e. $\Delta \le 0.23$."1003 The result is shown in the left panel of Fig., The result is shown in the left panel of Fig.1004 9 where the disk fraction increases from to as the number of selected subhalos INus Increases from 2 to 11., \ref{diskness_from_1grp} where the disk fraction increases from to as the number of selected subhalos $N_{sub}$ increases from $2$ to $11$.1005 In comparison. IH1-randomly selected subhalos €within 300 kpc) gives rise to flattened configurations 2.2% of the time.," In comparison, 11-randomly selected subhalos (within $300$ kpc) gives rise to flattened configurations $\sim10062.2\%$ of the time."1007 This shows that if the Milky Way satellites fell in together. it would not be very surprising that they would be in a planar configuration at the present-day.," This shows that if the Milky Way satellites fell in together, it would not be very surprising that they would be in a planar configuration at the present-day."1008" It is important to note that when No,=6. we select predominantly from just two groups accreted at relatively high redshift (2.=1.08 and 2= 0.843."," It is important to note that when $N_{sub} \ge 6$, we select predominantly from just two groups accreted at relatively high redshift $z=1.08$ and $z=0.84$ )."1009 Other large groups accreted more recently are still strongly clustered in space. and hence are discarded in this exercise since they cannot be considered as a valid representation of the MW satellite population.," Other large groups accreted more recently are still strongly clustered in space, and hence are discarded in this exercise since they cannot be considered as a valid representation of the MW satellite population."1010 Furthermore. although there is a relatively high chance of obtaining a value of A as low as observed. this is driven more by the large median distance of the subhalos than by their RMS distance to the best fit plane.," Furthermore, although there is a relatively high chance of obtaining a value of $\Delta$ as low as observed, this is driven more by the large median distance of the subhalos than by their RMS distance to the best fit plane."1011" A second possibility is to consider only ""grouped"" subhalos.", A second possibility is to consider only “grouped” subhalos.1012" That is. we select randomly 11 subhalos from ;V,.,,,,,, different groups where JN,1...5."," That is, we select randomly $11$ subhalos from $N_{group}$ different groups where $N_{group} = 1...5$."1013 The panel on the right of Fig., The panel on the right of Fig.1014 9 shows the fraction of disk-like configurations obtained in this way as a function of the number of groups considered., \ref{diskness_from_1grp} shows the fraction of disk-like configurations obtained in this way as a function of the number of groups considered.1015 This fraction can be as high as 40% when the subhalos come from only two groups. and of course reaches when they come from just one group.," This fraction can be as high as $\sim 40\%$ when the subhalos come from only two groups, and of course reaches when they come from just one group."1016 Note that the fraction when selecting from 5 different groups is still much higher than if one selects 11 subhalos randomly., Note that the fraction when selecting from $5$ different groups is still much higher than if one selects $11$ subhalos randomly.1017 The reason for the larger number of disk-like configurations when selecting subhalos from several groups as in the right of Fig. 9..," The reason for the larger number of disk-like configurations when selecting subhalos from several groups as in the right of Fig. \ref{diskness_from_1grp},"1018 rather than from just one group and the field. may be understood by examining Fig. 10..," rather than from just one group and the field, may be understood by examining Fig. \ref{orbitalpoles_of_grp_nongrp}."1019" This shows the present-day angular momentum orientations for ""grouped"" (left panel) anc ""field"" tright panel) subhalos.", This shows the present-day angular momentum orientations for “grouped” (left panel) and “field” (right panel) subhalos.1020 The two distributions differ clearly in the sense that the “grouped” subhalos are generally more clustered (see also Sec. 2.2).," The two distributions differ clearly in the sense that the “grouped” subhalos are generally more clustered (see also Sec. \ref{group_infall_sec}) ),"1021 also on larger scales., also on larger scales.1022" On the contrary. ""field"" subhalos tend to have their angular momenta more isotropically distributed."," On the contrary, “field” subhalos tend to have their angular momenta more isotropically distributed."1023" Therefore. when selecting 11 subhalos purely from groups. the chance of picking up subhalos with similar angular momentum orientations. is higher than when selecting also from the ""field""."," Therefore, when selecting $11$ subhalos purely from groups, the chance of picking up subhalos with similar angular momentum orientations, is higher than when selecting also from the “field”."1024" The more isotropically distributed orbits of ""field"" subhalos essentially add noise to the highly correlated orbits of subhalos originating in just one group.", The more isotropically distributed orbits of “field” subhalos essentially add noise to the highly correlated orbits of subhalos originating in just one group.1025 Therefore the disk signal gets smeared out quite significantly when more than half of the subhalos are in the field in one realisation. as shown on the left of Fig. 9..," Therefore the disk signal gets smeared out quite significantly when more than half of the subhalos are in the field in one realisation, as shown on the left of Fig. \ref{diskness_from_1grp}."1026 Given the large fraction of flattened contigurations found in our simulations. we conclude that the spatial distribution of the 1l Milky Way satellites can be reproduced within . XCDM.," Given the large fraction of flattened configurations found in our simulations, we conclude that the spatial distribution of the $11$ Milky Way satellites can be reproduced within $\Lambda$ CDM."1027 The requirement is that these satellites fell onto the Galactic halo in groups., The requirement is that these satellites fell onto the Galactic halo in groups.1028where 0 is the inchnation angle of the (taken equal to 27 degrees). 2 is niieasured aloug the line-of-sight. aud pa is the mass deusitv of the deflectors.,"where $\theta$ is the inclination angle of the (taken equal to 27 degrees), $z$ is measured along the line-of-sight, and $\rho_d$ is the mass density of the deflectors."1029 The velocities ος and ce; of the objects are supposed to be Caussian-distributed with a mass-cdepeudent velocity dispersion. as explained in section 2.1..," The velocities $v_s$ and $v_d$ of the objects are supposed to be Gaussian-distributed with a mass-dependent velocity dispersion, as explained in section \ref{ssec:descript_dsk}."1030 The term <|eye in equation (1 6)) represents the average of the relative velocity between the deflector aud the source over all possible velocities of these two objects: where fe Qesp., The term $<\!|v_{\rm rel}|\!>$ in equation \ref{eq_dgamma1}) ) represents the average of the relative velocity between the deflector and the source over all possible velocities of these two objects: where $f_s$ (resp.1031 fu) is the source (resp., $f_d$ ) is the source (resp.1032 deflector) velocity distribution function projection effects are neelected since i<oDste., deflector) velocity distribution function — projection effects are neglected since $z \ll \DLMC$.1033" Let p, be the mass density of the sources.", Let $\rho_s$ be the mass density of the sources.1034 The mass density at a given coordinate only depends on the mass of the object., The mass density at a given coordinate only depends on the mass of the object.1035 Iuteerating equations (15)) and (16)) over all source positions viclds: The values obtained with the equatious (18)) aud (191) must then be stmuned on all the deflector species. aud averaged on all the source species.," Integrating equations \ref{eq_dtau1}) ) and \ref{eq_dgamma1}) ) over all source positions yields: The values obtained with the equations \ref{eq_dtau}) ) and \ref{eq_dgamma}) ) must then be summed on all the deflector species, and averaged on all the source species."1036 Ouly the uppermost nass bin will be considered. as possible sources (d.e. HuC[1.92.0] M...) iu agreement with the mass of the faintest stars that are reconstructed in miücroleusimg surveys. whereas all the mass bius are of course taken iuto account when sunumiue for all possible defectors.," Only the uppermost mass bin will be considered as possible sources (i.e. $m_s \in [1.9--2.0]\, M_\odot$ ) in agreement with the mass of the faintest stars that are reconstructed in microlensing surveys, whereas all the mass bins are of course taken into account when summing for all possible deflectors."1037 The elobal optical depth and event rate due to the eutire stellar population are therefore given by: The first mass bin has iu practice to be treated specially. since it is not thin.," The global optical depth and event rate due to the entire stellar population are therefore given by: The first mass bin has in practice to be treated specially, since it is not thin."1038 The deflector masses in this biu follow the Salpeter law eiven in Eq. (7))., The deflector masses in this bin follow the Salpeter law given in Eq. \ref{eq:Salpeter}) ).1039 These results depend on the maxinuun dispersion velocity of the stars (i.e. ou the dispersion velocity of the lightest population). as illustrated in figures 1. aud 2..," These results depend on the maximum dispersion velocity of the stars (i.e. on the dispersion velocity of the lightest population), as illustrated in figures \ref{fig1} and \ref{fig2}."1040 The confieurationC» where all the stellar populations have the sue velocity dispersion (ie. when (ag=20 km/s) vields the same results as the calculations done by Gould (Could 1995)., The configuration where all the stellar populations have the same velocity dispersion (i.e. when $v_{\rm max} = 20$ km/s) yields the same results as the calculations done by Gould (Gould 1995).1041 The slower increase i the optical depth with the maximum velocity for a radial distance of 5 kpe as compared to that observed at a distance of 1 kpc is due to the 10 kpe vertical cut-off we have imposed ou the stars to © considered: as objects (sce comment at the end o| section. 2.1)). since the disk gets wider ou the edges.," The slower increase in the optical depth with the maximum velocity for a radial distance of 5 kpc as compared to that observed at a distance of 1 kpc is due to the 10 kpc vertical cut-off we have imposed on the stars to be considered as objects (see comment at the end of section \ref{ssec:descript_dsk}) ), since the disk gets wider on the edges."1042 As expected. the optica depth aud event rate decrease as one goes to larger aud larger radii from the ealactic ceuter.," As expected, the optical depth and event rate decrease as one goes to larger and larger radii from the galactic center."1043 For Όμως=80 kms. there is a factor of," For $v_{\rm1044max} = 80$ km/s, there is a factor of"1045"for the distances of these stars the reddening will also be of the order of E(J—K)~0.02, which does not effect the plot significantly and is neglected.","for the distances of these stars the reddening will also be of the order of $E(J-K)\sim0.02$, which does not effect the plot significantly and is neglected."1046" The isochrone from Figure 4 is over-plotted, where we find that a large tangential velocity of vr=150kms to 350kms'! is required to shift the isochrone to a reasonable! fit, which compare to vp~2304100kms""! for the halo for bb)=(55°, —60°)."," The isochrone from Figure \ref{f4} is over-plotted, where we find that a large tangential velocity of $v_T=150\,\kms$ to $350\,\kms$ is required to shift the isochrone to a reasonable fit, which compare to $v_T\sim230\pm100\,\kms$ for the halo for $55^\circ,\ -60^\circ$ )."1047" Once again, the group is consistent with a halo stream."," Once again, the group is consistent with a halo stream."1048 We will see in Section 6 that the tangential velocity for the stream is indeed within a relatively narrow range as shown in Figure 5.., We will see in Section \ref{sec:Nat} that the tangential velocity for the stream is indeed within a relatively narrow range as shown in Figure \ref{f5}.1049" A few of the redder, more-distant giants deviate from the rest of the group but they also have larger errors in their proper motions, which translates into larger RPM errors as shown: they are within 2c of the group fit."," A few of the redder, more-distant giants deviate from the rest of the group but they also have larger errors in their proper motions, which translates into larger RPM errors as shown: they are within $2\sigma$ of the group fit."1050" The consistency of the fit for the bluer stars supports their inclusion in the candidate list, (nearer)though the range in values for the RPM of halo stars means that we cannot exclude contamination from the halo."," The consistency of the fit for the bluer (nearer) stars supports their inclusion in the candidate list, though the range in values for the RPM of halo stars means that we cannot exclude contamination from the halo."1051" Indeed, from Figure 1 it is clear that we expect a few of the stars to be non-members."," Indeed, from Figure \ref{f1} it is clear that we expect a few of the stars to be non-members."1052 We therefore take the consistency of the RPMD to be a good indication of the consistency of the Aquarius member selection but not absolute proof of membership., We therefore take the consistency of the RPMD to be a good indication of the consistency of the Aquarius member selection but not absolute proof of membership.1053" If we accept the group's tangential velocity of υγ.=250kms !, we can use the RPM to establish a second estimate of the distance to the stars."," If we accept the group's tangential velocity of $v_T=250\,\kms$ , we can use the RPM to establish a second estimate of the distance to the stars."1054 From Equation 2 we have the distance modulus From this we have distance moduli ranging from 8.5 to 16 for the group members., From Equation \ref{Eqn1} we have the distance modulus From this we have distance moduli ranging from 8.5 to 16 for the group members.1055" The corresponding distances are listed in Table 3 as dp, with the errors calculated using the upper and lower tangential velocity bounds as well as the proper motion errors in Hj."," The corresponding distances are listed in Table \ref{tab3} as $d_\mathrm{R}$, with the errors calculated using the upper and lower tangential velocity bounds as well as the proper motion errors in $H_J$."1056" These distances differ somewhat from those calculated using the isochrones in Section 4.2 but are of the same order of magnitude, with an average value of da,=4.5X:4.6kpc (4=13.2)."," These distances differ somewhat from those calculated using the isochrones in Section \ref{subsec:iso} but are of the same order of magnitude, with an average value of $d_\mathrm{av}=4.5\pm4.6\,\kpc$ $\mu=13.2$ )."1057 Two stars (C2222241-094912 and C2242408-024953) have very large distances but the errors are also large., Two stars (C2222241-094912 and C2242408-024953) have very large distances but the errors are also large.1058" If we exclude the largest of these but retain the other for consistency with the isochrone distance average, the mean distance reduces to day=3.64:3.4kpc (u=12.8), which is very similar to the value found for the isochrones."," If we exclude the largest of these but retain the other for consistency with the isochrone distance average, the mean distance reduces to $d_\mathrm{av}=3.6\pm3.4\,\kpc$ $\mu=12.8$ ), which is very similar to the value found for the isochrones."1059" In Table 3 we also list distances derived in Breddelsal.(2010) (dg), Zwitteretal.(2010) (dz) and Burnett&Binney(2010) (dgg), where these distances are all derived from RAVE stellar parameters, employing various methodology."," In Table \ref{tab3} we also list distances derived in \citet{Breddels2010} $d_\mathrm{B}$ ), \citet{Zwitter2010} $d_\mathrm{Z}$ ) and \citet{Burnett2010} $d_\mathrm{BB}$ ), where these distances are all derived from RAVE stellar parameters, employing various methodology."1060" Comparing the above d; and dg to the distancescalculated in Zwitteretal.(2010),, for which 11 of the 15 Aquarius stars have an entry, we find that the isochrone distances agree better with a utc for the difference —dr)/dz of 23%+2096, while for (dz—dg)/dz we have(dz —1096+100%."," Comparing the above $d_\mathrm{I}$ and $d_\mathrm{R}$ to the distancescalculated in \citet{Zwitter2010}, for which 11 of the 15 Aquarius stars have an entry, we find that the isochrone distances agree better with a $\mu\pm\sigma$ for the difference $(d_\mathrm{Z} - d_\mathrm{I})/d_\mathrm{Z}$ of $23\%\pm20\%$, while for $(d_\mathrm{Z} - d_\mathrm{R})/d_\mathrm{Z}$ we have $-10\%\pm100\%$."1061 Thisis somewhat unsurprising given that theZwitter distances and the isochrone distances are both based on RAVE stellar parameters., Thisis somewhat unsurprising given that theZwitter distances and the isochrone distances are both based on RAVE stellar parameters.1062" Interestingly, however, for 6 stars that have distances calculated by the method of Burnett&Binney(2010),, the RPM distances fare better: (dgp—di)/dpn gives —100%+170% while (dpp—dr)/dep yields —30%+70%."," Interestingly, however, for 6 stars that have distances calculated by the method of \citet{Burnett2010}, the RPM distances fare better: $(d_\mathrm{BB} - d_\mathrm{I})/d_\mathrm{BB}$ gives $-100\%\pm170\%$ while $(d_\mathrm{BB} - d_\mathrm{R})/d_\mathrm{BB}$ yields $-30\%\pm70\%$ ."1063 For the 6 Breddelsetal.(2010) entires we have much larger discrepancies of (dg—di)/dg of —200%+40% and (dg—dg)/dg of 330%+60%., For the 6 \citet{Breddels2010} entires we have much larger discrepancies of $(d_\mathrm{B} - d_\mathrm{I})/d_\mathrm{B}$ of $-200\%\pm40\%$ and $(d_\mathrm{B} - d_\mathrm{R})/d_\mathrm{B}$ of $330\%\pm60\%$.1064" Clearly, all these discrepancies imply that the individual distances listed in Table 3 have large uncertainties."," Clearly, all these discrepancies imply that the individual distances listed in Table \ref{tab3} have large uncertainties."1065" In general, however, the RPM distances give more consistent kinematics than the isochrone distances as we will see below in Section 5.."," In general, however, the RPM distances give more consistent kinematics than the isochrone distances as we will see below in Section \ref{sec:Pos}."1066 In this section we seek connections between the Aquarius stream and other known kinematic and spatial substructures nearby in the Galaxy., In this section we seek connections between the Aquarius stream and other known kinematic and spatial substructures nearby in the Galaxy.1067 We start with the spatially detected substructures before returning to kinematically detected solar neighbourhood features., We start with the spatially detected substructures before returning to kinematically detected solar neighbourhood features.1068" The nearest companion of the Milky Way, the Sgr dSph (Ibata,Gilmore&Irwin1994),, has shed significant debris on its polar orbit around our Galaxy."," The nearest companion of the Milky Way, the Sgr dSph \citep{Ibata1994}, has shed significant debris on its polar orbit around our Galaxy."1069 The all-sky mapping of this debris by Majewskietal. using 2MASS M-giants clearly showed the plane (2003)of the Sgr debris., The all-sky mapping of this debris by \citet{Majewski2003} using 2MASS M-giants clearly showed the plane of the Sgr debris.1070 Further studies such as those by Newberg have (2003);revealed further branches(2004); and details within the (2006)debris wraps.," Further studies such as those by \citet{Newberg2003, Martinez2004, Belokurov2006} have revealed further branches and details within the debris wraps."1071" Recently, Yannyetal.(20098) used M and K giants selected from SDSS and SEGUE data Yannyetal. to provide additional observational constraints on the (2009b)stream."," Recently, \citet{Yanny2009a} used M and K giants selected from SDSS and SEGUE data \citet{Yanny2009b} to provide additional observational constraints on the stream."1072 'The Aquarius stars fall fairly close to the orbital plane of the Sgr dwarf., The Aquarius stars fall fairly close to the orbital plane of the Sgr dwarf.1073" Also, the isochrone fit from Section 4 is consistent with a population of 10 Gyr, [M/H]= —1."," Also, the isochrone fit from Section \ref{sec:Pop} is consistent with a population of $10\,\gyr$ , $\mh=-1$ ."1074" Layden&Sarajedini(2000) obtain CMDs of Sgr field populations, finding a dominant old and intermediate age population of 11Gyr, [M/H]=—1.3 and 5 Gyr, [M/H]= —0.7."," \citet{Layden2000} obtain CMDs of Sgr field populations, finding a dominant old and intermediate age population of 11Gyr, $\mh=-1.3$ and 5 Gyr, $\mh=-0.7$ ."1075" Giuffridaetal. find a range of populations in the periphery of Sagittarius,(2010) with [M/H]=—2.34 to -0.6, while the dominant population has a similar"," \citet{Giuffrida2010} find a range of populations in the periphery of Sagittarius, with $\mh=-2.34$ to -0.6, while the dominant population has a similar"1076In Fig.,In Fig.1077 | the distribution of X-ray surface brightness is shown for the studied galaxies., \ref{fig:profiles} the distribution of X-ray surface brightness is shown for the studied galaxies.1078 The profiles were extracted in the 0.5—2 keV energy band using circular annuli. centered on the center of the galaxy.," The profiles were extracted in the $ 0.5-2 $ keV energy band using circular annuli, centered on the center of the galaxy."1079 The data was corrected for vignetting. and all background components were subtracted.," The data was corrected for vignetting, and all background components were subtracted."1080 The contribution of resolved compact sources was removed as deseribed in the previous section., The contribution of resolved compact sources was removed as described in the previous section.1081 It is known that the distribution of unresolved compact objects follows the stellar mass (Revnivtsevetal.2006:Bogdán&Gilfanov.2008;Revnivtsevetal.. 2008).," It is known that the distribution of unresolved compact objects follows the stellar mass \citep{revnivtsev2,bogdan,revnivtsevm105}."1082. Therefore. we looked for deviations in the X-ray profile from the distribution of the K-band light as an indication. of an additional emission. component. presumably the emission. of warm 1onized gas.," Therefore, we looked for deviations in the X-ray profile from the distribution of the K-band light as an indication of an additional emission component, presumably the emission of warm ionized gas."1083 There are five galaxies. M32. ΜΙΟ5. NGC3377. NGC3585. and Sagittarius in. which the X-ray brightness closely follows the stellar light distribution at all central distances.," There are five galaxies, M32, M105, NGC3377, NGC3585, and Sagittarius in which the X-ray brightness closely follows the stellar light distribution at all central distances."1084 In several others - M31. M60. NGC1291. and NGC4278 the X-ray emission follows the near-infrared light only in the outer regions.," In several others – M31, M60, NGC1291, and NGC4278 the X-ray emission follows the near-infrared light only in the outer regions."1085 In the inner parts of these galaxies. an additional X-ray emitting component is present and often dominates.," In the inner parts of these galaxies, an additional X-ray emitting component is present and often dominates."1086 In all other cases. the X-ray surface brightness strikingly deviates from the near-infrared light. distribution. indicating the presence of strong additional X-ray emitting components.," In all other cases, the X-ray surface brightness strikingly deviates from the near-infrared light distribution, indicating the presence of strong additional X-ray emitting components."1087 The largest difference between the X-ray and K-band profiles are observed in M84. NGC4636. and NGC5128.," The largest difference between the X-ray and K-band profiles are observed in M84, NGC4636, and NGC5128."1088 These galaxies are known to show recent activity in their nuclei (e.g.Finugenovetal..2008:Kraft2005:Baldi 2009).," These galaxies are known to show recent activity in their nuclei \citep[e.g.][]{finugenov,kraft,baldi}."1089. To confirm that there is emissior from tonized gas. we investigated the spectra of unresolved emission (Fig. 2)).," To confirm that there is emission from ionized gas, we investigated the spectra of unresolved emission (Fig. \ref{fig:spectra}) )."1090 As the gas emission Is more centrally concentrated in some of the galaxies. we distinguished between inner and outer regions.," As the gas emission is more centrally concentrated in some of the galaxies, we distinguished between inner and outer regions."1091 The dividing radii are listed in Table 1.., The dividing radii are listed in Table \ref{tab:list2}.1092 Similar to the radial profiles. we excluded the contribution of resolved compact sources.," Similar to the radial profiles, we excluded the contribution of resolved compact sources."1093 To facilitate the comparison. all spectra. shown in Fig. 2..," To facilitate the comparison, all spectra, shown in Fig. \ref{fig:spectra},"1094" were normalized to the same K-band luminosity of Ly=10""! and projected to a distance of 10 Mpe."," were normalized to the same K-band luminosity of $ L_{K} = 10^{11} \ \mathrm{L_{K,\odot}} $ and projected to a distance of $ 10 $ Mpc."1095 In the case of Sagittarius and NGC3377. we only show the spectrum of the entire galaxy due to the relatively low number of counts.," In the case of Sagittarius and NGC3377, we only show the spectrum of the entire galaxy due to the relatively low number of counts."1096 The emission from the hot ISM reveals itself as a soft component. clearly visible in the spectra of many of the galaxies.," The emission from the hot ISM reveals itself as a soft component, clearly visible in the spectra of many of the galaxies."1097 To quantitatively characterize its contribution. we performed fits to the spectra of unresolved emission (Table 3)). using the MEKAL model in XSPEC to represent the emission from ionized gas and a power-law spectrum for the contribution of unresolved compact sources.," To quantitatively characterize its contribution, we performed fits to the spectra of unresolved emission (Table \ref{tab:fit}) ), using the MEKAL model in XSPEC to represent the emission from ionized gas and a power-law spectrum for the contribution of unresolved compact sources."1098 The spectra were derived from full regions whose parameters are presented in the Table |.. the metal abundances for the thermal component were fixed at solar values (Anders&Grevesse.1989). and the hydrogen column density was fixed at the Galactic value (Dickey&Lockman.," The spectra were derived from full regions whose parameters are presented in the Table \ref{tab:list2}, the metal abundances for the thermal component were fixed at solar values \citep{anders}, and the hydrogen column density was fixed at the Galactic value \citep{dickey}."10991990).. Such a simple model does not always describe the observed spectra well from the statistical point of view. as illustrated by the high y values given in the last column of Table 3..," Such a simple model does not always describe the observed spectra well from the statistical point of view, as illustrated by the high $ \chi^2 $ values given in the last column of Table \ref{tab:fit}."1100 However. it does describe the spectra with relative accuracy better than <10%. which is entirely sufficient. for the purpose of this calculation.," However, it does describe the spectra with relative accuracy better than $\lesssim 10 \%$, which is entirely sufficient for the purpose of this calculation."1101" The contribution of the hot ISM ts. in principle. characterized by the ratio of luminosities of thermal and power-law components,"," The contribution of the hot ISM is, in principle, characterized by the ratio of luminosities of thermal and power-law components."1102 The latter. however. includes the contribution of unresolved LMXBs. which may be dominant for galaxies. with. point source detection sensitivity that is too high. 210°ergs7!. making the luminosity ratios also depend on the sensitivity of the available Chandra data.," The latter, however, includes the contribution of unresolved LMXBs, which may be dominant for galaxies with point source detection sensitivity that is too high, $\ga 10^{36} \ \mathrm{erg \ s^{-1}}$, making the luminosity ratios also depend on the sensitivity of the available Chandra data."1103 To compensate for this. we estimated the contribution of unresolved LMXBs using the average LMXB X-ray luminosity function of Gilfanov(2004) and subtracted their contribution from the luminosity of the power-law component.," To compensate for this, we estimated the contribution of unresolved LMXBs using the average LMXB X-ray luminosity function of \citet{gilfanov} and subtracted their contribution from the luminosity of the power-law component."1104 These corrected values are shown in the column labeled L4;νι—Lig) in Table 3.., These corrected values are shown in the column labeled $L_{MKL}/(L_{PL}-L_{LMXB})$ in Table \ref{tab:fit}.1105 The spectral analysis results presented in Table 3. lead to the conclusions consistent with the brightness profile analysis., The spectral analysis results presented in Table \ref{tab:fit} lead to the conclusions consistent with the brightness profile analysis.1106 As expected from surface brightness profiles. M32. M105. NGC3377. NGC3585. and Sagittarius show the same spectral properties at all central radii. they all have a rather weak soft component.," As expected from surface brightness profiles, M32, M105, NGC3377, NGC3585, and Sagittarius show the same spectral properties at all central radii, they all have a rather weak soft component."1107 In M3] and NGC4278. the significant difference between the spectra is that the luminous soft component is present only in the inner region. not the outer ones. suggesting that the hot gas is centrally concentrated (Bogdán&Gilfanov.," In M31 and NGC4278, the significant difference between the spectra is that the luminous soft component is present only in the inner region, not the outer ones, suggesting that the hot gas is centrally concentrated \citep{bogdan}."11082008).. In all other galaxies. the soft component dominates at all central radii and can be well-fitted with an optically-thin thermal plasma emission model with temperature in the range of ATx0.3—0.8 keV. in good agreement with previous studies (Sarazinetal..2001:Irwin2002;Sivakoff2003;Randalletal.," In all other galaxies, the soft component dominates at all central radii and can be well-fitted with an optically-thin thermal plasma emission model with temperature in the range of $ kT \approx 0.3-0.8 $ keV, in good agreement with previous studies \citep{sarazin,irwin1,sivakoff,randall}."1109. 2004). Based on radial profiles and spectral analysis. we conclude that the following seven galaxies are relatively gas-poor and may be suitable for our analysis: the bulge of M31. M32. M105. NGC3377. NGC3585. NGC4278. and Sagittarius.," Based on radial profiles and spectral analysis, we conclude that the following seven galaxies are relatively gas-poor and may be suitable for our analysis: the bulge of M31, M32, M105, NGC3377, NGC3585, NGC4278, and Sagittarius."1110 In all other cases. the signatures of recent activity of the galactic nucleus and/or large amount of hot gas make the galaxies unsuitable for our study.," In all other cases, the signatures of recent activity of the galactic nucleus and/or large amount of hot gas make the galaxies unsuitable for our study."1111 The high bolometric luminosity. ~105—10°°eresv! means that some (generally speaking unknown) fraction. of the nuclear-burning white dwarfs is detected by as supersoft sources. despite the low color temperature of their emission.," The high bolometric luminosity, $\sim 10^{37}-10^{38} \ \mathrm{erg \ s^{-1}}$, means that some (generally speaking unknown) fraction of the nuclear-burning white dwarfs is detected by as supersoft sources, despite the low color temperature of their emission."1112 These sources obviously should be included in computing the final X/K ratios., These sources obviously should be included in computing the final X/K ratios.1113 To separate them from LMXBs. we used the spectral properties of compact sources.," To separate them from LMXBs, we used the spectral properties of compact sources."1114" The temperature of the hydrogen burning layer ts in the range of Tay~30—100 eV. but we conservatively included. all resolved sources with hardness ratios corresponding to the blackbody temperature lower than £7),<200 eV. We used this method for all galaxies. except for M31. where we relied on the catalog of supersoft sources from DiStefanoetal.(2004)."," The temperature of the hydrogen burning layer is in the range of $ T_{\mathrm{eff}} \sim 30-100 $ eV, but we conservatively included all resolved sources with hardness ratios corresponding to the blackbody temperature lower than $ kT_{\mathrm{bb}} <200 $ eV. We used this method for all galaxies, except for M31, where we relied on the catalog of supersoft sources from \citet{distefano}."1115. Because of the increased source cell size (Sect. 2.1)).," Because of the increased source cell size (Sect. \ref{sec:sample}) ),"1116 some of the sources are merged into one., some of the sources are merged into one.1117 This may compromise identification of supersoft sources. because some of them could be confused with harder sources and missed in our analysts.," This may compromise identification of supersoft sources, because some of them could be confused with harder sources and missed in our analysis."1118We have conducted a more detailed analysis of &rain clisalignment associated. with the time-varving electric dipole moment than was attenipted. in. WO06. focusing on suprathcrmally rotating silicate grains.,"We have conducted a more detailed analysis of grain disalignment associated with the time-varying electric dipole moment than was attempted in W06, focusing on suprathermally rotating silicate grains."1119 We considered. 4 idealized: models for how charge is transported. within the erain (83.1)): a perfect insulator. 2 models involving special sites in the grain (deep traps’) where electrons or holes are effectively trapped. aid a perfect. conductor.," We considered 4 idealized models for how charge is transported within the grain \ref{sec:idealizations}) ): a perfect insulator, 2 models involving special sites in the grain (`deep traps') where electrons or holes are effectively trapped, and a perfect conductor."1120 “Phe resulting disalignment times mu. for the first 3 models are. highly. consistent (Fig. 8)), The resulting disalignment times $\tau_{\mathrm{dis}}$ for the first 3 models are highly consistent (Fig. \ref{fig:ratio_a0.1}) )1121 and substantially shorter (up to 2 orders of magnitude) than those obtained by WNO0G6 (ο, and substantially shorter (up to 2 orders of magnitude) than those obtained by W06 (cf.1122 Fig., Fig.1123 7 here with figs., \ref{fig:tau_dis_ins} here with figs.1124 2 and 3 in W06)., 2 and 3 in W06).1125 We expect the behavior of real grains to be bracketed by these 3 models., We expect the behavior of real grains to be bracketed by these 3 models.1126 Disalignment proceeds more slowly (up to 2 orders of magnitude: Fig. 9)), Disalignment proceeds more slowly (up to 2 orders of magnitude; Fig. \ref{fig:ratio_cond}) )1127 [or conducting erains. but we do not expect this idealization to be realistic for interstellar &rains.," for conducting grains, but we do not expect this idealization to be realistic for interstellar grains."1128 1n treating the collisional charging. we neglected. the eas-erain drift.," In treating the collisional charging, we neglected the gas-grain drift."1129 Drift can. in principle. allect the time variation of the electric dipole moment.," Drift can, in principle, affect the time variation of the electric dipole moment."1130 For a non-rotating erain. there may be a stable contribution to p directed along the drift. velocity.," For a non-rotating grain, there may be a stable contribution to $\bmath{p}$ directed along the drift velocity."1131 For a grain rotating uniformly about &4. the charging rate may have some dependence on [atitude on the grain. suppressing (ips in p..," For a grain rotating uniformly about $\bmath{\hat{a}_1}$, the charging rate may have some dependence on latitude on the grain, suppressing flips in $p_z$."1132 We examine this possibility in Appendix A ancl conclude that Hipping is not suppressed., We examine this possibility in Appendix \ref{app:drift} and conclude that flipping is not suppressed.1133 1n the radiative torque alignment scenario. suprathermal rotation with— way—x=100 and —alignment times ο)10°vr appear to be typical (Draine Weingartner 1997: Lazarian lIloang 2007: Hoang Lazarian 9005). though additional studies are needed to confirm these results.," In the radiative torque alignment scenario, suprathermal rotation with $\omega / \omega_T \approx 100$ and alignment times $\ga 10^5 \ \mathrm{yr}$ appear to be typical (Draine Weingartner 1997; Lazarian Hoang 2007; Hoang Lazarian 2008), though additional studies are needed to confirm these results."1134" We have found. cisalignment times =10""vr when wary=100 (Figs.", We have found disalignment times $\la 10^5 \ \mathrm{yr}$ when $\omega / \omega_T \approx 100$ (Figs.1135" 7 and 8)). presenting a severe challenge to the radiative torque model,"," \ref{fig:tau_dis_ins} and \ref{fig:ratio_a0.1}) ), presenting a severe challenge to the radiative torque model."1136 Aluch of the physics involved. in the clisalignment mechanism has not been directly verified. including the details of the charging and the turbulence-incduced grain acceleration. (Yan ct al.," Much of the physics involved in the disalignment mechanism has not been directly verified, including the details of the charging and the turbulence-induced grain acceleration (Yan et al."1137 2004)., 2004).1138 Perhaps current models of these processes are incomplete in such a way as to overestimate the magnitude of the disalignment., Perhaps current models of these processes are incomplete in such a way as to overestimate the magnitude of the disalignment.1139" Alternatively, interstellar grains might contain superparamagnetic inclusions. (Jones Spitzer 1967). which could increase the magnetic susceptibility by orders of magnitude."," Alternatively, interstellar grains might contain superparamagnetic inclusions (Jones Spitzer 1967), which could increase the magnetic susceptibility by orders of magnitude."1140 The parameter Y would. be decreased. by the same factor. and the disalignment time xY7 when Y« l(eqs.," The parameter $\Upsilon$ would be decreased by the same factor, and the disalignment time $\propto \Upsilon^{-2}$ when $\Upsilon \ll 1$ (eqs."1141 7 and 8))., \ref{eq:tau_dis1} and \ref{eq:tau_dis2}) ).1142 Iecently. Lazarian Hoang (2008) found that the presence. of superparamagnetic inclusions can modifv alignment by. radiative torques. vielding a higher degree of alignment than experienced. by grains [ree of inclusions.," Recently, Lazarian Hoang (2008) found that the presence of superparamagnetic inclusions can modify alignment by radiative torques, yielding a higher degree of alignment than experienced by grains free of inclusions."1143 Perhaps superparamagnetie inclusions also suppress crift-induced disalignmoent., Perhaps superparamagnetic inclusions also suppress drift-induced disalignment.1144 We are grateful to. Yuri Alishin for valuable: cliscussions and an anonymous referee for helpful comments., We are grateful to Yuri Mishin for valuable discussions and an anonymous referee for helpful comments.1145 JOW is a Cottrell Scholar of Research Corporation., JCW is a Cottrell Scholar of Research Corporation.1146 Consider a grain drifting with velocity vg with respect to the gas., Consider a grain drifting with velocity $\bmath{v_{\rm gr}}$ with respect to the gas.1147 The grain rotates uniformly about &4. which is inclined at angle 67. relative to Vey.," The grain rotates uniformly about $\bmath{\hat{a}_1}$, which is inclined at angle $\theta_{Jv}$ relative to $\bmath{v_{\rm gr}}$."1148 To treat the collisional charging in this case. we first construct a large sphere with radius mig instantaneouslvy centercd on the grain.," To treat the collisional charging in this case, we first construct a large sphere with radius $r_{\mathrm{big}}$ instantaneously centered on the grain."1149 Adopting the rest. [rame of the gas and taking the direction of the drift velocity Gey as the polar, Adopting the rest frame of the gas and taking the direction of the drift velocity $\bmath{{v}_{\mathrm{gr}}}$ as the polar1150Iu Paper 1. we concluded that the lack of high |OII| EW Abell 551 cluster galaxies was evidence for the suppression of starbursts in Abell 851 relative to the ficld galaxy population.,"In Paper 1, we concluded that the lack of high [OII] EW Abell 851 cluster galaxies was evidence for the suppression of starbursts in Abell 851 relative to the field galaxy population."1151 Infalling galaxies are predicted to have their eaxcous reservolrs removed by the cluster cuviroument on timescales of 1-3 ανν (Balogh et al., Infalling galaxies are predicted to have their gaseous reservoirs removed by the cluster environment on timescales of 1-3 Gyr (Balogh et al.1152 2000)., 2000).1153 If star-formation in field. galaxies is eradually suppressed as they enter the cluster euvironmnoeut. one may expect to find a population of cluster galaxies with slowly facing star-formation.," If star-formation in field galaxies is gradually suppressed as they enter the cluster environment, one may expect to find a population of cluster galaxies with slowly fading star-formation."1154 The deficit of intermediate color. 7> 100 My objects iu the AMS1512.1]3617 and the foreground field of Abell 55] implies that relatively few cuuission-line galaxies have beeu accreted and “strangled” by the MS1512.1123617 cluster within the previous few Covrs.," The deficit of intermediate color, $\tau > $ 100 Myr objects in the MS1512.4+3647 and the foreground field of Abell 851 implies that relatively few emission-line galaxies have been accreted and “strangled” by the MS1512.4+3647 cluster within the previous few Gyrs."1155 The suppression of star-formation within the cluster core should be evident as a dependence on star-formation rate (and [OTL] emission) on cluster-centric radius., The suppression of star-formation within the cluster core should be evident as a dependence on star-formation rate (and [OII] emission) on cluster-centric radius.1156 Iu Figure 13. we plot the average SER and ΠΟΠ of the MS81512.112617. and Abell 851. [OTI]. euiission-line candidates with projected radius.," In Figure 13, we plot the average SFR and L[OII] of the MS1512.4+3647 and Abell 851 [OII] emission-line candidates with projected radius."1157" The average SER of the central regions (r « 100"") of both clusters is dominated by the central cluster galaxies. which appear to be uudereoiug nunor mergers."," The average SFR of the central regions (r $<$ ) of both clusters is dominated by the central cluster galaxies, which appear to be undergoing minor mergers."1158 Otherwise. the mean star-formation rate is approximately coustaut with projected radius out to ~ 3 ooo iu MS1512.113617 and ~ 1 Πο ma Abell 551.," Otherwise, the mean star-formation rate is approximately constant with projected radius out to $\sim$ 3 $_{200}$ in MS1512.4+3647 and $\sim$ 1 $_{200}$ in Abell 851."1159 If the AIS1512.1136.17 sauuple is dominated by field galaxies. we would not expect to see any radial treud.," If the MS1512.4+3647 sample is dominated by field galaxies, we would not expect to see any radial trend."1160 Also. the effect ofthe cluster enviroment on infalliug galaxies is believed to be strongest outside of the virial radius (Ellingson ct al.," Also, the effect of the cluster environment on infalling galaxies is believed to be strongest outside of the virial radius (Ellingson et al."1161 2001. Diaferio et al.," 2001, Diaferio et al."1162 2001) aud therefore outside of our field of view for Abell 851., 2001) and therefore outside of our field of view for Abell 851.1163" Therefore it is difficult to rule out salaxv ""straugulation in these two clusters. despite the lack of racial dependence ou the observed average star-formation rate."," Therefore it is difficult to rule out galaxy “strangulation” in these two clusters, despite the lack of radial dependence on the observed average star-formation rate."1164 Most of the faint star-forming galaxies in the field strounding MS$1512.L12617 are best described bv low-luass star-buurwts with τς 100 Myr. as are the off-hand excess objects in the field in frout of Abell 851 (Figure 11 and 12).," Most of the faint star-forming galaxies in the field surrounding MS1512.4+3647 are best described by low-mass star-bursts with $\tau <$ 100 Myr, as are the off-band excess objects in the field in front of Abell 851 (Figure 11 and 12)."1165 Galaxies with longer star-formation timescales above our detection limit of 0.13. AL. | are abseut your our “field” ealaxv samples. nuplviug that short musts dominate the star-formation m imauy field ealaxies.," Galaxies with longer star-formation timescales above our detection limit of 0.13 $\Msun$ $^{-1}$ are absent from our “field” galaxy samples, implying that short bursts dominate the star-formation in many field galaxies."1166 Both the derived star-formation histories of local irregular ealaxies (Cirebel 1997) aud the lack of red. faded. low-mass Bold galaxies iu the Uubble Deep Field at τς0.5 sugees hat field dwarf galaxies (Lotz 2003: Ferguson Babu 1998) uudergo multiple bursts throughout their evolution.," Both the derived star-formation histories of local irregular galaxies (Grebel 1997) and the lack of red, faded, low-mass field galaxies in the Hubble Deep Field at $z < 0.5$ suggest that field dwarf galaxies (Lotz 2003; Ferguson Babul 1998) undergo multiple bursts throughout their evolution."1167 ILowever. further star-formation nav be suppressed if he ealaxy falls iuto a rich cluster environnmieut.," However, further star-formation may be suppressed if the galaxy falls into a rich cluster environment."1168 Loca clusters are filled with thousauds of dwarf galaxies which are gas-poor and no longer forming stars., Local clusters are filled with thousands of dwarf galaxies which are gas-poor and no longer forming stars.1169 If the observe OI ciuiission-line galaxies fade quickly aud do not undergo another episode of star-formation. many couk ecole as faint as preseut dav dEs.," If the observed [OII] emission-line galaxies fade quickly and do not undergo another episode of star-formation, many could become as faint as present day dEs."1170 A ealaxy with an τ 10 Myr exponentially decaving burst. au age = LO AIvr. and an observed / maenitude ~ 22 at 2=0.37 woul ade into a Mj ~ 16 by 2=0.," A galaxy with an $\tau$ = 10 Myr exponentially decaying burst, an age = 40 Myr, and an observed $i$ magnitude $\sim$ 22 at $z=0.37$ would fade into a $_R$ $\sim$ $-16$ by $z=0$."1171 A ealaxy with 7 = 100 Abvr. age = 300 Myr. aud an observed / magnitude ~ 22 at 2=0.37 would fade into a Mg ~ -I8 by 2=0.," A galaxy with $\tau$ = 100 Myr, age = 300 Myr, and an observed $i$ magnitude $\sim$ 22 at $z=0.37$ would fade into a $_R$ $\sim$ -18 by $z=0$."1172 At lo 0.1. we are only able to observe the progenitors of cluster dEs brighter than Aly=15.0. which munber ~ 300 in Vireo.," At $z \sim$ 0.4, we are only able to observe the progenitors of cluster dEs brighter than $_R = -15.0$, which number $\sim$ 300 in Virgo."1173 To produce this number of faded emission-liune galaxies in MS1512.1123617. over four times the umuber of [OTL candidates observed iu the AIS1512.113617 field iust acerete onto the cluster bv the present dav.," To produce this number of faded emission-line galaxies in MS1512.4+3647, over four times the number of [OII] candidates observed in the MS1512.4+3647 field must accrete onto the cluster by the present day."1174 Correcting the observed density of field enüssion-liue galaxies for the duty evcle. this requires a field voluue infall rate greater than 50 Mpe? tin order to accrete simular nuinubers of bright dEs iu the 1-5 Cyr suce τ=0.4.," Correcting the observed density of field emission-line galaxies for the duty cycle, this requires a field volume infall rate greater than 50 $^{3}$ $^{-1}$ in order to accrete similar numbers of bright dEs in the 4-5 Gyr since $z= 0.4$."1175 Our observations of MS1512.1123617 sugecsts a ΛΑΣΠΗ iufall rate for enüssion-liue. ealaxies of a few Mpe? | if recently accreted galaxies are able to form stars aud have [OT] cussion visible for ~ 1 Cyr.," Our observations of MS1512.4+3647 suggests a maximum infall rate for emission-line galaxies of a few $^{3}$ $^{-1}$, if recently accreted galaxies are able to form stars and have [OII] emission visible for $\sim$ 1 Gyr."1176 Therefore it is unlikely that most bright dEs in typical clusters were acquired by the eradual infall of star-forming field galaxies since 2~0.1., Therefore it is unlikely that most bright dEs in typical clusters were acquired by the gradual infall of star-forming field galaxies since $z \sim 0.4$.1177 But if most dE progenitors are accreted iu clumps as eroups ineree intermittently: with the cluster. as is the case for Abell 851. then one or two such major merecrs could account for the majority of the dE population observed in local clusters.," But if most dE progenitors are accreted in clumps as groups merge intermittently with the cluster, as is the case for Abell 851, then one or two such major mergers could account for the majority of the dE population observed in local clusters."1178 Iu this case. clusters which have asseiibled: more receutlv would have significantly: τοσο dE populations.," In this case, clusters which have assembled more recently would have significantly younger dE populations."1179 Tn the Virgo cluster. bright uucleated dE (dE.N) aud faint dSph/dEs are as spatially clustered. as the eiaut ellipticals (Ferguson Sandage 1989).," In the Virgo cluster, bright nucleated dE (dE,N) and faint dSph/dEs are as spatially clustered as the giant ellipticals (Ferguson Sandage 1989)."1180 Could a z<0.1 intalling ealaxy population become as clustered by 2=0 as local dE populations?, Could a $z \leq 0.4$ infalling galaxy population become as clustered by $z=0$ as local dE populations?1181" Dynamical friction timescales erow louger with sialler satellite mass and x 10?AL, ealaxies would sink quite slowly iu the cluster potcutial dwart galaxies accreted 1-5 Cyr ago do not have enough time to become as spatially clustered as the local dE cluster population.", Dynamical friction timescales grow longer with smaller satellite mass and $\leq$ $^9 \Msun$ galaxies would sink quite slowly in the cluster potential $-$ dwarf galaxies accreted 4-5 Gyr ago do not have enough time to become as spatially clustered as the local dE cluster population.1182 However. the Fornax and Vireo dwarf ealaxy populations (which are dominated by dE.N) lave lugher velocity dispersions than the eiaut elliptical calaxy populations (Drinkwater. Grege Colless 2001: Cousclice. Gallagher. Wyse 2001). which is consistent with recent iufall.," However, the Fornax and Virgo dwarf galaxy populations (which are dominated by dE,N) have higher velocity dispersions than the giant elliptical galaxy populations (Drinkwater, Gregg Colless 2001; Conselice, Gallagher, Wyse 2001), which is consistent with recent infall."1183 One wav to reconcile the spatial distribution of dE.N with their high cluster velocities is to form the nuclei as je dwarfs pass through the cluster center on timescales ess than a fev Cor.," One way to reconcile the spatial distribution of dE,N with their high cluster velocities is to form the nuclei as the dwarfs pass through the cluster center on timescales less than a few Gyr."1184 Cas-rich cawarfs may form centralized stellar excesses via ealaxy harassincut in a few Cor aud ealaxies which form nuclei are more likely to survive within ie central reeious of clusters than those that do nof (Moore. Lake Katz 1998).," Gas-rich dwarfs may form centralized stellar excesses via galaxy harassment in a few Gyr and galaxies which form nuclei are more likely to survive within the central regions of clusters than those that do not (Moore, Lake Katz 1998)."1185 Most dE nuclei are compact. elobular cluster-like objects aud could also be formed by je decay of massive elobular clusters iuto the ceuter via dviauical friction (Lotz et al.," Most dE nuclei are compact, globular cluster-like objects and could also be formed by the decay of massive globular clusters into the center via dynamical friction (Lotz et al."1186 2001)., 2001).1187 The timescale for is process nav be shorter for dwarfs within the ceutral regions of clusters than those on the outskirts (Ol Lin 2000)., The timescale for this process may be shorter for dwarfs within the central regions of clusters than those on the outskirts (Oh Lin 2000).1188 We have presented the results of a deep narrow-band [OT eeniüssion-line survey for faint star-forming galaxies in the 2=0.37 MS1512.112617 cluster., We have presented the results of a deep narrow-band [OII] emission-line survey for faint star-forming galaxies in the $z = 0.37$ MS1512.4+3647 cluster.1189 Using broad-band vw/ and g ὁ colors. we are able to distinguish 2~ 0.37 [OT] emission-line candidates from 2~ (0.37 elliptical ealaxies which may produce false ou-baud excesses aud backeround :7 3.2 Exiuan o ciitters.," Using broad-band $u-i$ and $g-i$ colors, we are able to distinguish $z \sim$ 0.37 [OII] emission-line candidates from $z \sim$ 0.37 elliptical galaxies which may produce false on-band excesses and background $z \sim$ 3.2 Lyman $\alpha$ emitters."1190 We find two Lyman a candidates with EW > 300 aand undetected « fluxes., We find two Lyman $\alpha$ candidates with EW $>$ 300 and undetected $u$ fluxes.1191 We identify 66 [OTL candidates in the NS1512.1123617 field., We identify 66 [OII] emission-line candidates in the MS1512.4+3647 field.1192 The observed deusity of |OIT| ciissiou-line galaxies, The observed density of [OII] emission-line galaxies1193.117 18 My --6.28.,17 is $_{V}$ –6.28.1194 Of spectral type O5 III + OB. this is the brightest. star (V=14.96. B-V=-0.06 mag) apparently associated with the blob.," Of spectral type O5 III + OB, this is the brightest star $V=14.96$, $B-V=-0.06$ mag) apparently associated with the blob."1195 The doubled line profiles in its spectrogram suggest a spectroscopic binary with ó 5530 km s!., The doubled line profiles in its spectrogram suggest a spectroscopic binary with $\delta$ 530 km $^{-1}$.1196 The companion dominates at 44471 but the primary at 44026., The companion dominates at 4471 but the primary at 4026.1197 The i2 region 2214C lies in the OB association 1110 of size .(2).. in which the latter authors detected seven OB candidates.," The 2 region 214C lies in the OB association 110 of size \citep{lh}, in which the latter authors detected seven OB candidates."1198 The color-magnitude diagram obtained for 2341 stars of the OB association is displayed in refcol-mag.., The color-magnitude diagram obtained for 2341 stars of the OB association is displayed in \\ref{col-mag}.1199 Overplotted are also the isochrones with ages | Myr. | Gyr. and 10 Gyr for metallicity Z = 0.008 obtained by ?..," Overplotted are also the isochrones with ages 1 Myr, 1 Gyr, and 10 Gyr for metallicity Z = 0.008 obtained by \citet{lejeune01}."1200 Two main stellar populations show up in this diagram: a main sequence and an evolved component., Two main stellar populations show up in this diagram: a main sequence and an evolved component.

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