{ "0212/astro-ph0212491_arXiv.txt": { "abstract": " ", "introduction": "Since 1985~\\cite{bib-witten}, various experimental techniques have been proposed to detect the nuclear recoils that would be produced by the scattering of WIMP dark matter particles from our galactic halo (for a recent review of experimental searches, see e.g. Ref.~\\cite{bib-expreview}). The goal is to be sensitive to recoil energies down to 10 keV~\\cite{bib-lewin}, at event rates well below one per kilogram of detector material per day~\\cite{bib-rate}. For this, the detector response to low-energy nuclear recoils must be well known. Depending on the detection process (ionization, scintillation or heat), this response may differ significantly from that inferred from calibration with electron or gamma-ray sources. A quantity of interest is thus the {\\em quenching factor}, defined as the ratio of the signal amplitudes induced by a nuclear recoil and an electron of the same energy. This factor depends mainly on the detector material, the energy of the recoil and the detection process, although temperature and alignment effects may play a role (see e.g. Ref.~\\cite{bib-align}). Quenching factor measurements have been made on scintillation detectors such as NaI~\\cite{bib-nai}, CsI~\\cite{bib-csi}, CaF$_2$~\\cite{bib-caf2} and Xe~\\cite{bib-xe}, leading to values ranging from 4 to 30\\% depending on the recoil nucleus and its energy. The measured quenching factors of ionization detectors such as Si~\\cite{bib-si} or Ge~\\cite{bib-chasman,bib-jones,bib-shutt,bib-messous} vary between 25 and 40\\% and appear to follow the recoil energy dependence predicted by the Lindhart theory~\\cite{bib-lindh}. More recently, the thermal detection efficiency for recoiling nuclei has been measured for the first time in a TeO$_{2}$ cryogenic detector, giving a thermal quenching factor slightly above unity\\cite{bib-aless}. The purpose of the SICANE facility (SIte de CAlibration NEutron) is the measurement of quenching factors of cryogenic detectors using nuclear recoils induced by monoenergetic neutron beams. The facility has been commissioned with tests using scintillation in a NaI(Tl) crystal and measurements of quenching factors for ionization and heat signals in a germanium cryogenic detector developed by the EDELWEISS collaboration. ", "conclusions": "The commissioning tests of the SICANE array and its setup confirm its high relevance for the calibration of the response of cryogenic detectors to nuclear recoils. Using inverse reactions to produce a highly collimated neutron beam, no massive shielding of the neutron detectors is necessary, giving more freedom in their spatial setup. Competitive results have been obtained in a short running time (less than a day) for the quenching of scintillation in NaI(Tl) and of ionization in Ge. The array also makes possible a deeper investigation of the effect of inelastic scattering on the measurement. The powerful diagnostic tools provided by the array (simultaneous measurements at different angles, neutron identification and time-of-flight measurements) are ideally suited for the study of cryogenic detectors. For such measurements, important factors that require proper attention are: {\\em i)\\/} the slow response of the detector, and how it compares with the single rate in the cryogenic detector and the rate in coincidence with the neutron array; {\\em ii)\\/} the rate in the neutron detector array due to neutron scattering in the material in the vicinity of the detector and {\\em iii)\\/} the ability to resolve inelastic and elastic events, either using the energy or the time-of-flight measurements. In addition, for the first time, it was directly verified that the ionization quenching factor of Ge at 35 mK is very close to that at liquid nitrogen temperature. This is consistent with the fact that the CDMS and EDELWEISS collaborations~\\cite{bib-shutt,bib-benoit} obtain $Q/Q'$ ratios compatible with the $Q$ values measured at liquid nitrogen temperature~\\cite{bib-chasman,bib-messous} under the assumption that $Q'$=1. Conversely, this last hypothesis is verified for the first time in the present work, albeit at a 15\\% level." }, "0212/astro-ph0212172_arXiv.txt": { "abstract": "Millimeter and mid-infrared observations have been made of the dense clumps of dust and gas and of young stellar objects (YSOs) associated with the bright, compact submillimeter source G79.3+0.3~P1 in the relatively nearby MSX infrared-dark cloud G79.3+0.3. The Gemini mid-infrared observations reported here indicate the presence of three YSOs within the cloud. BIMA 3~mm continuum observations show that the brightest of the YSOs is likely to be a Herbig Ae/Be star. High-angular-resolution molecular-line observations suggest that a wind from this star may be triggering collapse in the adjacent molecular cloud. The submillimeter source G79.3+0.3~P1 itself does not contain infrared sources and may represent an earlier stage of star formation. ", "introduction": "\\citet{ega98} have identified a large population of cold dust clouds in images of the Galactic Plane made with the MSX satellite \\citep{pri01}. These clouds appear as dark patches of absorbing material against a background of mid-infrared emission bands and emission from warm, small dust grains. Egan et al. defined the infrared-dark clouds (IRDCs) as having one to several magnitudes of extinction at 8~\\micron\\ and no obvious emission in any of the 8 to 25~\\micron\\ bands observed by the MSX satellite. They concluded that the IRDCs possess hundreds of magnitudes of visual extinction and contain large column densities of cold dust. Observations of a selection of these clouds in H$_2$CO by \\citet{car98} revealed that much of the gas inside the IRDCs has T$_{\\rm K}$~$\\approx$~10-20~K and n(H$_2$)~$\\gtrsim$~10$^6$~cm$^{-3}$, with H$_2$ column densities ranging up to 10$^{23}$~cm$^{-2}$. Most of these objects are quite distant, with kinematic distances between 1 and 8.5 kpc. The IRDCs appear to be a very interesting population of molecular clouds. On theoretical grounds, we expect that molecular clouds on the verge of star formation will contain extremely cold and dense condensations, which will show up as IRDCs if they are favourably located in front of a region of extended mid-IR emission. The selection criteria for the MSX IRDCs \\citep{car98} ensures that they do not yet contain high-mass main-sequence stars and HII regions. Trying to relate the physical properties of this selection of dust clouds to those of better-studied nearby molecular clouds, such as those in the Orion-Taurus region, is problematic. Most of the best studied clouds lie in the outer Galaxy where there is insufficient background emission for IRDCs to be identifiable. By contrast, the large distances of many MSX IRDCs make them difficult to detect at visible and near-infrared wavelengths, and difficult to pick out from the surrounding clutter of lower density clouds in molecular-line surveys. A notable exception is the cloud G79.3+0.3, located in the Cygnus Rift at an estimated distance of 800~pc \\citep{mil37, ikh61, wen91}, close enough to the Sun that it can be seen at visible wavelengths \\citep{red00b}. Figure~\\ref{g79} and Figure~\\ref{8mic} show our JCMT SCUBA 850~\\micron\\ image of the G79.3+0.3 IRDC and the MSX 8~\\micron\\ image of the same region, respectively. Unlike the other IRDCs we have observed, this cloud exhibits a variety of indicators of star formation. Most prominently, the HII region DR15 (G79.307+0.277) lies behind and slightly south of the IRDC, between P4 and P5 in the figure. It is not immediately obvious whether the IRDC is part of a larger complex including DR15 or is an unrelated foreground cloud. In visible and near-IR images of the region \\citep{red00b}, there is an association of stars (to the west of DR15) whose northern boundary is defined by the southern edge of the IRDC. If DR15 is related to this association, it suggests that both DR15 and the association lie beyond the IRDC. In the 8~\\micron\\ MSX image (Figure~\\ref{8mic}), the dark filament of the IRDC (whose dust content is traced by the SCUBA 850~\\micron\\ emission in Figure~\\ref{g79}) is interrupted between P1 and P3 by a bright patch of warm dust emission which is suggestive of deeply embedded hot stars. Because of this, the eastern and western parts of the IRDC were initially assigned different designations in the MSX catalog (G79.34+0.33 and G79.27+0.38, labeled G79.34 and G79.27 in Figure~\\ref{g79}), although the figure clearly shows them to comprise a single, connected filament. A Herbig-Haro jet that appears to be driven by a YSO at RA(2000) = 20~31~45.5, Dec(2000) = +40~18~44 (see Figure~\\ref{8mic}) has been discovered in front of the IRDC at visible wavelengths \\citep{red00b}. In this paper we focus our attention on the star-forming activity in the vicinity of its most prominent condensation, G79.3+0.3~P1. This region was selected for closer study because comparison of the SCUBA and MSX images discussed below showed the presence of a faint, point-like emission source MSX5C G079.3398+00.3415 in the MSX image that was nearly coincident with the brightest compact source of emission at 850 and 450~\\micron . This suggested the presence of a deeply embedded star interacting with the cold dust cloud, but the relatively coarse resolution of both the MSX and SCUBA images hampered a more detailed interpretation. To address these issues, we combined JCMT observations at 450~\\micron , BIMA interferometry at 3~mm, and Gemini North imaging at 10.75~\\micron , together with archival data from the MSX satellite and the 2MASS survey. ", "conclusions": "Our Gemini N-band observations demonstrate that the MSX 8~\\micron\\ source MSX5C G079.3398+00.3415 associated with G79.3+0.3~P1 is dominated by a single compact object that we identify with the star 2MASSI~2032220+402017. This object is a luminous YSO with a strong IR excess that will likely become an early-B star when it reaches the main sequence. Two nearby, fainter YSOs were discovered in our N-band images, and a cluster of faint, heavily reddened stars are visible in the 2MASS K-band images of the region. This concentration of stars and YSOs indicates that the IRDC is actively forming low-mass stars, with the 2MASS star as the most massive star that has formed from it to date. There are a variety of unusual features in the region around G79.3+0.3~P1 that suggest 2MASSI~2032220+402017 is interacting with the foreground IRDC. Most directly, the BIMA HCO$^+(1-0)$ line has a strongly enhanced blue wing in the velocity range $-1.5$ to 0~km/s, as well as a slight enhancement on the red wing, in a region immediately to the southeast of the 2MASS star. The emission in the blue wing shows considerable structure on small angular scales. The unusual nature of this structure is highlighted by the fact that the rest of the cloud shows little emission in the blue wing and very modest small-scale structure in the velocity range $[-0.25, +2.25]$~km/s that traces most of the mass of the cloud. The presence of small-scale structure close to the 2MASS star is confirmed by CS$~(5-4)$ observations with even higher angular resolution. The simplest interpretation of these data is that the 2MASS star is a Herbig Ae/Be star that is forming on the far side of the IRDC. This star must have a warm disk that is the source of the N-band emission, but the disk cannot produce the observed reddening at K. Hence the star must lie behind a lot of extinction from the IRDC. The strong wind that would be expected from such a star is probably impacting the back of the IRDC, exciting the blue wing of the HCO$^+$ line. Although it appears to be massive, the 2MASS star is still too young to have disrupted the IRDC. We speculate that in another million years or so this region may resemble a smaller version of DR15 to the south, appearing as an HII region partially obscured by foreground dust left over from the IRDC. It is, at the very least, a striking coincidence that the two condensations of dust and gas that comprise the G79.3+0.3~P1 SCUBA source (the A and B components in the BIMA data) lie immediately adjacent in the plane of the sky to the most massive YSO in the cloud, and are apparently being impacted by the same wind that is exciting the blue wing in the HCO$^+(1-0)$ line in the rest of the IRDC. The combined masses of the two components are comparable to the mass of the Herbig Ae/Be star. These two objects are the obvious candidates for the next generation of stars to form in the vicinity of the 2MASS star. Further observations may reveal whether the wind from the 2MASS star has played a role in forming the A and B components, or is just now impacting these two pre-existing clumps, possibly driving them into collapse." }, "0212/astro-ph0212458_arXiv.txt": { "abstract": "Motivated by the recent direct detection of cosmological gas infall, we develop an analytical model for calculating the mean density profile around an initial overdensity that later forms a dark matter halo. We account for the problem of peaks within peaks; when considering a halo of a given mass we ensure that this halo is not a part of a larger virialized halo. For halos that represent high-sigma fluctuations we recover the usual result that such halos preferentially lie within highly overdense regions; in the limit of very low-sigma fluctuations, on the other hand, we show that halos tend to lie within voids. Combined with spherical collapse, our results yield the typical density and velocity profiles of the gas and dark matter that surround virialized halos. ", "introduction": "\\label{sec:Intro} Numerical simulations of hierarchical halo formation indicate a roughly universal spherically-averaged density profile within virialized dark matter halos \\citep{NFW}. Such profiles are generated by complicated processes that involve violent relaxation and multiple shell crossing; the great interest in them results from the possibility of a direct comparison to the profiles inferred from galactic rotation curves \\citep[e.g.,][]{sb00,dmr01,vs01} and from lensing in clusters \\citep[e.g.,][]{ste02,dhs02}. However, the analogous question of what is the typical density profile outside the virial radius has received relatively little attention, because of the difficulty of directly observing density profiles even out to the halo virial radius; this difficulty results from the rapid decrease in the gas and dark matter densities with distance from the halo center. However, the theoretical description is simpler for infall outside the virialization radius, since in cold dark matter (hereafter CDM) models there is no shell crossing until the final non-linear collapse. The gas around halos can only be detected using physical effects that are very sensitive to low-density gas. One such phenomenon is resonant \\Lya absorption; \\citet{GP} first noted that even an H I neutral fraction $\\sim 10^{-5}$ suffices to make gas at the cosmic mean density strongly absorb photons at the \\Lya resonance. Thus, the pattern of gas infall around halos may affect observable properties of the \\Lya absorption in these regions. At moderate redshifts, these regions near halos play a prominent role in measurements of the proximity effect of quasars \\citep[e.g.,][]{prox1, prox2}. In these measurements, the effect of the high quasar intensity on the statistics of \\Lya absorption is analyzed and used to infer the mean ionizing background, since the quasar intensity dominates only as long as it is significantly stronger than the background. A different application may be possible at very high redshifts, corresponding to the time before the universe was fully reionized; the presence of the fully neutral IGM could be detected through absorption of a bright source by the \\Lya damping wing of the IGM \\citep{jordi98}. However, every bright source creates a surrounding H II region which complicated the interpretation \\citep{CH00,MR00}. The properties of the gas in the regions that lie just outside the host halo of the source galaxy or quasar should play a major role in these various applications of the observed absorption. The various calculations of absorption cited above neglected the enhanced densities and the negative (i.e., infall) velocities expected for the gas surrounding a massive halo at high redshift. This infall, however, may be an essential component of any correct interpretation of observations; \\citet{le95} applied it to the proximity effect and showed that neglecting infall can lead to an overestimate of the ionizing background flux by up to a factor of three. Applying the same infall profile, \\citet{nature} have recently revealed the signature of infalling gas around high redshift quasars. The spectral pattern due to \\Lya absorption by the infalling gas can be used to estimate the quasar's ionizing intensity and the total mass of its host halo. While the spectra of individual objects are marked by the large density fluctuations expected in the intergalactic medium (hereafter IGM), if this pattern is averaged over many objects then the resulting mean profile could be compared directly with an accurate theoretical prediction for the density and velocity profile of the infalling gas. \\citet{le95} defined a halo in the same way as halos were defined in the classic model of \\citet{PS}. In this approach, halos on a given scale are defined as forming when the initial density averaged on this scale is higher than a threshold that depends on the collapse redshift and is fixed using spherical collapse. The halo mass function derived from this assumption, when multiplied by an ad-hoc correction factor of two, provides a reasonable match to the results of numerical simulations \\citep[e.g.,][]{katz93}. The same mass function was later derived by \\citet{bc91} using a self-consistent approach, with no need for external factors. In their derivation, the factor of two has a more satisfactory origin, namely the so-called ``cloud-in-cloud'' problem: if the average initial density on a certain scale is above the collapse threshold, this region may be contained within a larger region that is itself also denser than the collapse threshold; in this case the original region should be counted as belonging to the halo with mass corresponding to the larger collapsed region. \\citet{bc91} and \\citet{PS} both give the same halo mass function and thus appear to be at least statistically valid given the agreement with the mass function seen in numerical simulations. However, the \\citet{bc91} model is more satisfactory since it accounts for the cloud-in-cloud problem and, more importantly, allows for calculations of other halo properties in addition to simple mass functions, all in an approach that is more self-consistent. The \\citet{bc91} approach (also known as extended Press-Schechter) has been used to calculate halo merger histories \\citep{lc93}, halo mass functions in models with warm dark matter \\citep{wdm}, halo mass functions in a model with ellipsoidal collapse \\citep{ellipse}, and the nonlinear biasing of halos \\citep{porciani,evan}. In this paper, we present a new application of this approach in which we obtain the expected profile of infalling matter around virialized halos. The rest of this paper is organized as follows. In \\S~2.1 we establish our notation and review the \\citet{bc91} derivation of the \\citet{PS} halo mass function. In \\S~2.2 we review the infall profile used by \\citet{le95} and also derive an alternative model based on similar assumptions but carried out in Fourier space. In \\S~2.3 we derive our model based on the extended Press-Schechter formalism. In \\S~2.4 we then discuss the modified picture of halo virialization once infall is included. In \\S~3 we illustrate the predictions of our model for the initial and final density profiles surrounding halos. Finally in \\S~4 we give our conclusions. ", "conclusions": "We have developed a model for calculating the initial density profile around overdensities that later collapse to form virialized halos. This is the first such model to account for the possibility that an overdensity on a given scale may be contained inside a large overdensity on an even bigger scale. As a result, we have found that the mean expected profile [eqs.~(\\ref{eq:ePSk}) and (\\ref{eq:final})] depends on both the mass of the halo and its formation redshift. Starting from this mean initial profile, we have used spherical collapse to obtain the final density profile surrounding the virialized halo. In reality, there will be some variation in the initial profiles, with each leading to a different final profile. We have estimated the scatter within our spherical model, and found that a sample of around a few dozen halos is required in order to obtain an accurate mean profile by averaging. Halo samples derived from numerical simulations or from observations can be used to test our predictions for the mean and for the scatter of the density and velocity profiles of infalling matter around virialized halos. Once infall is included, the standard derivation of the mean density enclosed within the virial radius fails. Redefining the virial radius as the radius enclosing a density higher than the cosmic mean by the standard value of $18 \\pi^2$, we have found that the initial overdensity needed for a halo to form at some final redshift is lower than it would have to be for an isolated tophat perturbation [compare eqs.~(\\ref{eq:delc}) and (\\ref{eq:delv})]. Therefore, accounting for infall increases the predicted abundance of rare halos for a given initial power spectrum, but the increase is too small to fully explain the discrepancy between the Press-Schechter prediction for the number of high-mass halos and the number seen in numerical simulations. We have confirmed that rare halos at a given redshift are surrounded by large, overdense regions of infall, but we have found that the more numerous halos that correspond to low-sigma peaks are surrounded by small infall regions that lie within large voids. However, the infalling gas just beyond the cosmological accretion shock is in general much denser than the cosmic mean; a density larger by a factor of at least 10 occurs around the most massive halos at $z \\ga 2$. Possible applications of our results include the Lyman-$\\alpha$ absorption profiles of high-redshift objects and the proximity effect of quasars at all redshifts." }, "0212/astro-ph0212202_arXiv.txt": { "abstract": "AGILE is a small gamma-ray astronomy satellite, with good spatial resolution, excellent timing capabilities and an unprecedented large field of view ($\\sim$1/5 of the sky). It will be the next mission dedicated to high energy astrophysics in the range 30 MeV-50 GeV, and will be launched in 2005. Pulsars are a major topic of investigation of AGILE and, besides studying the small sample of known objects, AGILE will offer the first possibility of detecting several young and energetic radio pulsars that have been discovered since the end of the CGRO mission. We provide an estimate of the expected number of detectable gamma-ray pulsars and present AGILE capabilities for timing analysis with small counting statistics, based on the analysis of data from simulations, from the EGRET archive, and from radio pulsar catalogs. ", "introduction": " ", "conclusions": "" }, "0212/astro-ph0212034_arXiv.txt": { "abstract": "Absorption and Reprocessing of Gamma-ray burst radiation in the environment of cosmological GRBs can be used as a powerful probe of the elusive nature of their progenitors. In particular, transient X-ray emission line and absorption features in the prompt and early afterglows of GRBs are sensitive to details of the location and density structure of the reprocessing and/or absorbing material. To date, there have been only rather few detections of such features, and the significance is marginal in most individual cases. However, transient X-ray emission lines in GRB afterglows have now been found by four different X-ray satellites, which may justify a more detailed theoretical investigation of their origin. In this paper, I will first present a brief review of the status of observations of transient X-ray emission line and absorption features. I will then discuss general physics constraints which those results impose on isotropy, homogeneity, and location of the reprocessing material with respect to the GRB source, and review the various currently discussed, specific models of GRBs and their environments in which the required conditions could arise. ", "introduction": " ", "conclusions": "" }, "0212/hep-th0212290_arXiv.txt": { "abstract": "Recent cosmological observations suggest the existence of a positive \\cc\\ $\\Lambda$ with the magnitude $\\Lambda(G\\hbar/c^3) \\approx 10^{-123}$. This review discusses several aspects of the \\cc\\ both from the cosmological (sections \\ref{intro}--\\ref{cmbrani}) and field theoretical (sections \\ref{interpretcc}--\\ref{ccstring}) perspectives. After a brief introduction to the key issues related to cosmological constant and a historical overview, a summary of the kinematics and dynamics of the standard Friedmann model of the universe is provided. The observational evidence for cosmological constant, especially from the supernova results, and the constraints from the age of the universe, structure formation, Cosmic Microwave Background Radiation (CMBR) anisotropies and a few others are described in detail, followed by a discussion of the theoretical models (quintessence, tachyonic scalar field, ...) from different perspectives. The latter part of the review (sections \\ref{interpretcc}--\\ref{ccstring}) concentrates on more conceptual and fundamental aspects of the \\cc\\ like some alternative interpretations of the \\cc, relaxation mechanisms to reduce the cosmological constant to the currently observed value, the geometrical structure of the de Sitter spacetime, thermodynamics of the de Sitter universe and the role of string theory in the \\cc\\ problem. ", "introduction": "This review discusses several aspects of the \\cc\\ both from the cosmological and field theoretical perspectives with the emphasis on conceptual and fundamental issues rather than on observational details. The plan of the review is as follows: This section introduces the key issues related to cosmological constant and provides a brief historical overview. (For previous reviews of this subject, from cosmological point of view, see \\cite{jpbr,carolcomb1,carolcomb3,carolcomb2}.) Section \\ref{framework} summarizes the kinematics and dynamics of the standard Friedmann model of the universe paying special attention to features involving the cosmological constant. Section \\ref{evidencecc} reviews the observational evidence for cosmological constant, especially the supernova results, constraints from the age of the universe and a few others. We next study models with evolving cosmological `constant' from different perspectives. (In this review, we shall use the term \\cc\\ in a generalized sense including the scenarios in which cosmological ``constant'' is actually varying in time.) A phenomenological parameterization is introduced in section \\ref{paraeqn} to compare theory with observation and is followed up with explicit models involving scalar fields in section \\ref{theorydark}. The emphasis is on quintessence and tachyonic scalar field models and the cosmic degeneracies introduced by them. Section \\ref{sfinuniv} discusses cosmological constant and dark energy in the context of models for structure formation and section \\ref{cmbrani} describes the constraints arising from CMBR anisotropies. The latter part of the review concentrates on more conceptual and fundamental aspects of the \\cc. ( For previous reviews of this subject, from a theoretical physics perspective, see \\cite{swlambda,weincomb1,weincomb2}.) Section \\ref{interpretcc} provides some alternative interpretations of the \\cc\\ which might have a bearing on the possible solution to the problem. Several relaxation mechanisms have been suggested in the literature to reduce the cosmological constant to the currently observed value and some of these attempts are described in section \\ref{relaxcc}. Section \\ref{desittergeom} gives a brief description of the geometrical structure of the de Sitter spacetime and the thermodynamics of the de Sitter universe is taken up in section \\ref{horizons}. The relation between horizons, temperature and entropy are presented at one go in this section and the last section deals with the role of string theory in the \\cc\\ problem. \\subsection{The many faces of the cosmological constant}\\label{facescc} Einstein's equations, which determine the dynamics of the spacetime, can be derived from the action (see, eg. \\cite{LL2}): \\begin{equation} A = \\frac{1}{16\\pi G} \\int R \\sqrt{-g} d^4 x + \\int L_{\\rm matter}(\\phi, \\partial \\phi) \\sqrt{-g} d^4x \\label{one} \\end{equation} where $L_{\\rm matter}$ is the Lagrangian for matter depending on some dynamical variables generically denoted as $\\phi$. (We are using units with $c=1$.) The variation of this action with respect to $\\phi$ will lead to the equation of motion for matter $ (\\delta L_{\\rm matter}/\\delta \\phi) =0 $, in a given background geometry, while the variation of the action with respect to the metric tensor $g_{ik}$ leads to the Einstein's equation \\begin{equation} R_{ik} - \\frac{1}{2} g_{ik} R = 16 \\pi G \\frac{\\delta L_{\\rm matter}}{\\delta g^{ik}} \\equiv 8 \\pi G T_{ik} \\label{three} \\end{equation} where the last equation defines the energy momentum tensor of matter to be $T_{ik} \\equiv 2(\\delta L_{\\rm matter}/\\delta g^{ik})$. Let us now consider a new matter action $L'_{\\rm matter}=L_{\\rm matter} -(\\Lambda/8\\pi G)$ where $\\Lambda$ is a real constant. Equation of motion for the matter $ (\\delta L_{\\rm matter}/\\delta \\phi) =0 $, does not change under this transformation since $\\Lambda $ is a constant; but the action now picks up an extra term proportional to $\\Lambda$ \\begin{eqnarray} A &=& \\frac{1}{16\\pi G} \\int R \\sqrt{-g} d^4 x + \\int \\left(L_{\\rm matter} -\\frac{\\Lambda}{8\\pi G}\\right) \\sqrt{-g} d^4x\\nonumber \\\\ &=& \\frac{1}{16\\pi G} \\int (R-2\\Lambda) \\sqrt{-g} d^4 x+ \\int L_{\\rm matter} \\sqrt{-g} d^4x \\label{four} \\end{eqnarray} and equation (\\ref{three}) gets modified. This innocuous looking addition of a constant to the matter Lagrangian leads to one of the most fundamental and fascinating problems of theoretical physics. The nature of this problem and its theoretical backdrop acquires different shades of meaning depending which of the two forms of equations in (\\ref{four}) is used. The first interpretation, based on the first line of equation (\\ref{four}), treats $\\Lambda $ as the shift in the matter Lagrangian which, in turn, will lead to a shift in the matter Hamiltonian. This could be thought of as a shift in the zero point energy of the matter system. Such a constant shift in the energy does not affect the dynamics of matter while gravity --- which couples to the total energy of the system --- picks up an extra contribution in the form of a new term $Q_{ik}$ in the energy-momentum tensor, leading to: \\begin{equation} R^i_k - \\frac{1}{2} \\delta^i_k R = 8\\pi G (T^i_k + Q^i_k); \\qquad Q^i_k \\equiv \\frac{\\Lambda}{8 \\pi G} \\delta^i_k \\equiv \\rho_\\Lambda \\delta^i_k \\label{six} \\end{equation} The second line in equation (\\ref{four}) can be interpreted as gravitational field, described by the Lagrangian of the form $L_{\\rm grav} \\propto (1/G) (R-2\\Lambda)$, interacting with matter described by the Lagrangian $L_{\\rm matter}$. In this interpretation, gravity is described by two constants, the Newton's constant $G$ and the {\\it \\cc}\\ $\\Lambda$. It is then natural to modify the {\\it left hand side} of Einstein's equations and write (\\ref{six}) as: \\begin{equation} R^i_k - \\frac{1}{2} \\delta^i_k R - \\delta^i_k \\Lambda = 8\\pi G T^i_k \\label{five} \\end{equation} In this interpretation, the spacetime is treated as curved even in the absence of matter ($T_{ik} =0$) since the equation $R_{ik} - (1/2) g_{ik}R -\\Lambda g_{ik} =0$ does not admit flat spacetime as a solution. (This situation is rather unusual and is related to the fact that symmetries of the theory with and without a \\cc\\ are drastically different; the original symmetry of general covariance cannot be naturally broken in such a way as to preserve the sub group of spacetime translations.) In fact, it is possible to consider a situation in which both effects can occur. If the gravitational interaction is actually described by the Lagrangian of the form $(R-2\\Lambda)$, then there is an intrinsic cosmological constant in nature just as there is a Newtonian gravitational constant in nature. If the matter Lagrangian contains energy densities which change due to dynamics, then $L_{\\rm matter}$ can pick up constant shifts during dynamical evolution. For example, consider a scalar field with the Lagrangian $L_{\\rm matter} =(1/2) \\partial_i\\phi \\partial^i\\phi - V(\\phi)$ which has the energy momentum tensor \\begin{equation} T^a_b = \\partial^a\\phi \\partial_b \\phi - \\delta^a_b \\left( \\frac{1}{2} \\partial^i\\phi\\partial_i\\phi - V(\\phi)\\right) \\label{scalartab} \\end{equation} For field configurations which are constant [occurring, for example, at the minima of the potential $V(\\phi)$], this contributes an energy momentum tensor $T^a_b = \\delta^a_b V(\\phi_{\\rm min})$ which has exactly the same form as a \\cc. As far as gravity is concerned, it is the combination of these two effects --- {\\it of very different nature} --- which is relevant and the source will be $T_{ab}^{\\rm eff} = [V(\\phi_{\\rm min}) + (\\Lambda/8\\pi G)]g_{ab}$, corresponding to an effective gravitational constant \\begin{equation} \\Lambda_{\\rm eff} = \\Lambda + 8\\pi G V(\\phi_{\\rm min}) \\label{nine} \\end{equation} If $\\phi_{\\rm min}$ and hence $V(\\phi_{\\rm min})$ changes during dynamical evolution, the value of $\\Lambda_{\\rm eff}$ can also change in course of time. More generally, any field configuration which is varying slowly in time will lead to a slowly varying $\\Lambda_{\\rm eff}$. The extra term $Q_{ik}$ in Einstein's equation behaves in a manner which is very peculiar compared to the energy momentum tensor of normal matter. The term $Q^i_k = \\rho_\\Lambda \\delta^i_k$ is in the form of the energy momentum tensor of an ideal fluid with energy density $\\rho_\\Lambda$ and pressure $P_\\Lambda = - \\rho_\\Lambda$; obviously, either the pressure or the energy density of this ``fluid'' must be negative, which is unlike conventional laboratory systems. (See, however, reference \\cite{volovik}.) Such an equation of state, $\\rho = -P $ also has another important implication in general relativity. The spatial part ${\\bf g}$ of the geodesic acceleration (which measures the relative acceleration of two geodesics in the spacetime) satisfies the following exact equation in general relativity (see e.g., page 332 of \\cite{probbook}): \\begin{equation} \\nabla \\cdot {\\bf g} = - 4\\pi G (\\rho + 3P) \\label{nextnine} \\end{equation} showing that the source of geodesic acceleration is $(\\rho + 3P)$ and not $\\rho$. As long as $(\\rho + 3P) > 0$, gravity remains attractive while $(\\rho + 3P) <0$ can lead to repulsive gravitational effects. Since the \\cc\\ has $(\\rho_\\Lambda + 3P_\\Lambda) = -2\\rho_\\Lambda$, a positive \\cc\\ (with $\\Lambda >0$) can lead to {\\it repulsive} gravity. For example, if the energy density of normal, non-relativistic matter with zero pressure is $\\rho_{\\rm NR}$, then equation (\\ref{nextnine}) shows that the geodesics will accelerate away from each other due to the repulsion of \\cc\\ when $\\rho_{\\rm NR} < 2\\rho_\\Lambda$. A related feature, which makes the above conclusion practically relevant is the fact that, in an expanding universe, $\\rho_\\Lambda$ remains constant while $\\rho_{\\rm NR}$ decreases. (More formally, the equation of motion, $d(\\rho_\\Lambda V) = - P_\\Lambda dV$ for the cosmological constant, treated as an ideal fluid, is identically satisfied with constant $\\rho_\\Lambda, P_\\Lambda$.) Therefore, $\\rho_\\Lambda $ will eventually dominate over $\\rho_{\\rm NR}$ if the universe expands sufficiently. Since $|\\Lambda|^{1/2}$ has the dimensions of inverse length, it will set the scale for the universe when cosmological constant dominates. It follows that the most stringent bounds on $\\Lambda$ will arise from cosmology when the expansion of the universe has diluted the matter energy density sufficiently. The rate of expansion of the universe today is usually expressed in terms of the Hubble constant: $H_0 = 100 h $ km s$^{-1}$ Mpc$^{-1}$ where 1 Mpc $ \\approx 3\\times 10^{24}$ cm and $h$ is a dimensionless parameter in the range $0.62\\lesssim h \\lesssim 0.82$ (see section \\ref{ageuniv}). From $ H_0$ we can form the time scale $t_{\\rm univ}\\equiv H_0^{-1}\\approx 10^{10} h^{-1}$ yr and the length scale $ cH_0^{-1} \\approx 3000 h^{-1}$ Mpc; $t_{\\rm univ}$ characterizes the evolutionary time scale of the universe and $H_0^{-1}$ is of the order of the largest length scales currently accessible in cosmological observations. From the observation that the universe is at least of the size $H_0^{-1}$, we can set a bound on $\\Lambda $ to be $|\\Lambda| < 10^{-56}$ cm$^{-2}$. This stringent bound leads to several issues which have been debated for decades without satisfactory solutions. \\begin{itemize} \\item In classical general relativity, based on the constants $G, c $ and $\\Lambda$, it is not possible to construct any dimensionless combination from these constants. Nevertheless, it is clear that $\\Lambda$ is extremely tiny compared to any other physical scale in the universe, suggesting that $\\Lambda$ is probably zero. We, however, do not know of any symmetry mechanism or invariance principle which requires $\\Lambda$ to vanish. Supersymmetry does require the vanishing of the ground state energy; however, supersymmetry is so badly broken in nature that this is not of any practical use \\cite{supersym1,supersym2}. \\item We mentioned above that observations actually constrain $\\Lambda_{\\rm eff}$ in equation (\\ref{nine}), rather than $\\Lambda$. This requires $\\Lambda$ and $V(\\phi_{\\rm min})$ to be fine tuned to an enormous accuracy for the bound, $|\\Lambda_{\\rm eff}| < 10^{-56} \\ {\\rm cm}^{-2}$, to be satisfied. This becomes more mysterious when we realize that $V(\\phi_{\\rm min})$ itself could change by several orders of magnitude during the evolution of the universe. \\item When quantum fields in a given curved spacetime are considered (even without invoking any quantum gravitational effects) one introduces the Planck constant, $\\hbar$, in the description of the physical system. It is then possible to form the dimensionless combination $\\Lambda (G\\hbar/c^3) \\equiv \\Lambda L_P^2$. (This equation also defines the quantity $L_P^2$; throughout the review we use the symbol `$\\equiv$' to define variables.) The bound on $\\Lambda$ translates into the condition $\\Lambda L_P^2 \\lesssim 10^{-123}$. As has been mentioned several times in literature, this will require enormous fine tuning. \\item All the above questions could have been satisfactorily answered if we take $\\Lambda_{\\rm eff}$ to be zero and assume that the correct theory of quantum gravity will provide an explanation for the vanishing of \\cc. Such a view was held by several people (including the author) until very recently. Current cosmological observations however suggests that $\\Lambda_{\\rm eff}$ is actually non zero and $\\Lambda_{\\rm eff} L_P^2$ is indeed of order ${\\mathcal O}(10^{-123})$. In some sense, this is the cosmologist's worst nightmare come true. {\\it If the observations are correct, then $\\Lambda_{\\rm eff}$ is non zero, very tiny and its value is extremely fine tuned for no good reason}. This is a concrete statement of the first of the two `\\cc\\ problems'. \\item The bound on $\\Lambda L_P^2$ arises from the expansion rate of the universe or --- equivalently --- from the energy density which is present in the universe today. The observations require the energy density of normal, non relativistic matter to be of the same order of magnitude as the energy density contributed by the cosmological constant. But in the past, when the universe was smaller, the energy density of normal matter would have been higher while the energy density of \\cc\\ does not change. Hence we need to adjust the energy densities of normal matter and \\cc\\ in the early epoch very carefully so that $\\rho_\\Lambda\\gtrsim \\rho_{\\rm NR}$ around the current epoch. If this had happened very early in the evolution of the universe, then the repulsive nature of a positive cosmological constant would have initiated a rapid expansion of the universe, preventing the formation of galaxies, stars etc. If the epoch of $\\rho_\\Lambda \\approx \\rho_{\\rm NR}$ occurs much later in the future, then the current observations would not have revealed the presence of non zero \\cc. This raises the second of the two \\cc\\ problems: Why is it that $(\\rho_\\Lambda/ \\rho_{\\rm NR}) = \\mathcal{O} (1)$ at the {\\it current} phase of the universe ? \\item The sign of $\\Lambda$ determines the nature of solutions to Einstein's equations as well as the sign of $(\\rho_\\Lambda + 3P_\\Lambda)$. Hence the spacetime geometry with $\\Lambda L_P^2 = 10^{-123}$ is very different from the one with $\\Lambda L_P^2 = - 10^{-123}$. Any theoretical principle which explains the near zero value of $\\Lambda L_P^2$ must also explain why the observed value of $\\Lambda$ is positive. \\end{itemize} At present we have no clue as to what the above questions mean and how they need to be addressed. This review summarizes different attempts to understand the above questions from various perspectives. \\subsection{A brief history of \\cc} \\label{history} Originally, Einstein introduced the \\cc\\ $\\Lambda$ in the field equation for gravity (as in equation (\\ref{five})) with the motivation that it allows for a finite, closed, static universe in which the energy density of matter determines the geometry. The spatial sections of such a universe are closed 3-spheres with radius $l = (8\\pi G \\rho_{\\rm NR})^{-1/2} = \\Lambda^{-1/2}$ where $\\rho_{\\rm NR}$ is the energy density of pressureless matter (see section \\ref{geometry}) Einstein had hoped that normal matter is {\\it needed} to curve the geometry; a demand, which --- to him --- was closely related to the Mach's principle. This hope, however, was soon shattered when de Sitter produced a solution to Einstein's equations with \\cc\\ containing no matter \\cite{desitter}. However, in spite of two fundamental papers by Friedmann and one by Lemaitre \\cite{F1,F2}, most workers did not catch on with the idea of an expanding universe. In fact, Einstein originally thought Friedmann's work was in error but later published a retraction of his comment; similarly, in the Solvay meeting in 1927, Einstein was arguing against the solutions describing expanding universe. Nevertheless, the Einstein archives do contain a postcard from Einstein to Weyl in 1923 in which he says: ``If there is no quasi-static world, then away with the cosmological term''. The early history following de Sitter's discovery (see, for example, \\cite{north}) is clearly somewhat confused, to say the least. It appears that the community accepted the concept of an expanding universe largely due to the work of Lemaitre. By 1931, Einstein himself had rejected the cosmological term as superflous and unjustified (see reference \\cite{einstein}, which is a single authored paper; this paper has been mis-cited in literature often, eventually converting part of the journal name ``preuss'' to a co-author ``Preuss, S. B''!; see \\cite{history}). There is no direct record that Einstein ever called \\cc\\ his biggest blunder. It is possible that this often repeated ``quote'' arises from Gamow's recollection \\cite{gamow}: ``When I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life.'' By 1950's the view was decidedly against $\\Lambda$ and the authors of several classic texts ( like Landau and Liftshitz\\cite{LL2}, Pauli \\cite{pauli} and Einstein \\cite{meaning}) argued against the \\cc. In later years, \\cc\\ had a chequered history and was often accepted or rejected for wrong or insufficient reasons. For example, the original value of the Hubble constant was nearly an order of magnitude higher \\cite{hubble29} than the currently accepted value thereby reducing the age of the universe by a similar factor. At this stage, as well as on several later occasions (eg., \\cite{sandage61,gunntinsley}), cosmologists have invoked \\cc\\ to reconcile the age of the universe with observations (see section \\ref{ageuniv}). Similar attempts have been made in the past when it was felt that counts of quasars peak at a given phase in the expansion of the universe \\cite{petro,shklov,kardash}. These reasons, for the introduction of something as fundamental as \\cc, seem inadequate at present. However, these attempts clearly showed that sensible cosmology can only be obtained if the energy density contributed by \\cc\\ is comparable to the energy density of matter at the present epoch. This remarkable property was probably noticed first by Bondi \\cite{bondi} and has been discussed by McCrea \\cite{mccrea}. It is mentioned in \\cite{jpbr} that such coincidences were discussed in Dicke's gravity research group in the sixties; it is almost certain that this must have been noticed by several other workers in the subject. The first cosmological model to make central use of the \\cc was the steady state model \\cite{steady1,steady2,steady3}. It made use of the fact that a universe with a cosmological constant has a time translational invariance in a particular coordinate system. The model also used a scalar field with negative energy field to continuously create matter while maintaining energy conservation. While modern approaches to cosmology invokes negative energies or pressure without hesitation, steady state cosmology was discarded by most workers after the discovery of CMBR. The discussion so far has been purely classical. The introduction of quantum theory adds a new dimension to this problem. Much of the early work \\cite{earlywork1a,earlywork1b} as well as the definitive work by Pauli \\cite{earlywork2a,earlywork2b} involved evaluating the sum of the zero point energies of a quantum field (with some cut-off) in order to estimate the vacuum contribution to the \\cc. Such an argument, however, is hopelessly naive (inspite of the fact that it is often repeated even today). In fact, Pauli himself was aware of the fact that one must {\\it exclude} the zero point contribution from such a calculation. The first paper to stress this clearly and carry out a {\\it second order} calculation was probably the one by Zeldovich \\cite{zeldo} though the connection between vacuum energy density and cosmological constant had been noted earlier by Gliner \\cite{gliner} and even by Lemaitre \\cite{earlywork3}. Zeldovich assumed that the lowest order zero point energy should be subtracted out in quantum field theory and went on to compute the gravitational force between particles in the vacuum fluctuations. If $E$ is an energy scale of a virtual process corresponding to a length scale $l=\\hbar c/E$, then $l^{-3}=(E/\\hbar c)^3$ particles per unit volume of energy $E$ will lead to the gravitational self energy density of the order of \\begin{equation} \\rho_\\Lambda \\approx \\frac{G(E/c^2)^2}{l}l^{-3} = \\frac{GE^6}{c^8\\hbar^4} \\end{equation} This will correspond to $\\Lambda L_P^2\\approx (E/E_P)^6$ where $E_P=(\\hbar c^5/G)^{1/2}\\approx 10^{19}$GeV is the Planck energy. Zeldovich took $E\\approx 1$ GeV (without any clear reason) and obtained a $\\rho_\\Lambda$ which contradicted the observational bound ``only'' by nine orders of magnitude. The first serious symmetry principle which had implications for \\cc\\ was supersymmetry and it was realized early on \\cite{supersym1,supersym2} that the contributions to vacuum energy from fermions and bosons will cancel in a supersymmetric theory. This, however, is not of much help since supersymmetry is badly broken in nature at sufficiently high energies (at $E_{\\rm SS} > 10^2$ Gev). In general, one would expect the vacuum energy density to be comparable to the that corresponding to the supersymmetry braking scale, $E_{\\rm SS}$. This will, again, lead to an unacceptably large value for $\\rho_\\Lambda$. In fact the situation is more complex and one has to take into account the coupling of matter sector and gravitation --- which invariably leads to a supergravity theory. The description of \\cc\\ in such models is more complex, though none of the attempts have provided a clear direction of attack (see e.g, \\cite{swlambda} for a review of early attempts). The situation becomes more complicated when the quantum field theory admits more than one ground state or even more than one local minima for the potentials. For example, the spontaneous symmetry breaking in the electro-weak theory arises from a potential of the form \\begin{equation} V = V_0 - \\mu^2 \\phi^2 + g \\phi^4 \\qquad (\\mu^2, g>0) \\end{equation} At the minimum, this leads to an energy density $V_{\\rm min} = V_0 - (\\mu^4/4g)$. If we take $V_0 =0$ then $(V_{\\rm min}/g) \\approx -(300\\ {\\rm GeV})^4$. For an estimate, we will assume that the gauge coupling constant $g$ is comparable to the electromagnetic coupling constant: $g ={\\mathcal O}(\\alpha^2)$, where $\\alpha \\equiv (e^2/\\hbar c)$ is the fine structure constant. Then, we get $|V_{\\rm min}| \\sim 10^6\\ {\\rm GeV}^4$ which misses the bound on $\\Lambda$ by a factor of $10^{53}$. It is really of no help to set $V_{\\rm min}=0$ by hand. At early epochs of the universe, the temperature dependent effective potential \\cite{thermo1,thermo2} will change minimum to $\\phi =0$ with $V(\\phi) = V_0$. In other words, the ground state energy changes by several orders of magnitude during the electro-weak and other phase transitions. Another facet is added to the discussion by the currently popular models of quantum gravity based on string theory \\cite{stringtext1,stringtext2}. The currently accepted paradigm of string theory encompasses several ground states of the same underlying theory (in a manner which is as yet unknown). This could lead to the possibility that the final theory of quantum gravity might allow different ground states for nature and we may need an {\\it extra} prescription to choose the actual state in which we live in. The different ground states can also have different values for \\cc\\ and we need to invoke a separate (again, as yet unknown) principle to choose the ground state in which $\\Lambda L_P^2 \\approx 10^{-123}$ (see section \\ref{ccstring}). ", "conclusions": "" }, "0212/astro-ph0212278_arXiv.txt": { "abstract": "This poster discusses a possible explanation for the relationship between the mass of the central supermassive black hole and the velocity dispersion in the bulge of the host galaxy. We suppose that the black hole and the dark matter halo are forming simultaneously as matter falls in, and a self-similar system then exists in which the mass and the velocities of the system evolve as power-law functions of time. This leads naturally to a relationship between the black hole mass and the velocities in the halo which, with a reasonable choice of cosmological parameters, is in good agreement with the observed relationship. We also confirm this relationship with more robust numerical results. ", "introduction": "Supermassive black holes (BHs) are now considered to be a common feature of galaxies which have a bulge. Furthermore, a number of observational properties of the host galaxy correlate with the BH mass. Among the strongest of these correlations is the relationship between the BH mass and velocity dispersion within the galactic bulge (Ferrarese \\& Merritt 2000; Gebhardt et al. 2000): $M_{\\rm BH} \\propto \\sigma^a$, where $a = 4.02 \\pm 0.32$ (Tremaine et al. 2002). Since the velocity dispersion is measured well outside of the BH ``influence,'' this correlation indicates that an intimate relationship exists between the BH and the dynamical structure of the host galaxy. We assume that a galaxy forms by the extended collapse of a ``halo'' composed of collisionless matter and that simultaneously the central black hole is growing proportionally to the halo as matter continues to fall in. This is equivalent to the assumption of multidimensional self-similarity (Carter \\& Henriksen 1991; Henriksen 1997), and MacMillan \\& Henriksen (2002) show that, in this case, the mass $M$ inside any surface in the halo is related to the velocity of the particles by \\begin{equation} \\log{ M}\\propto \\left(\\frac{3\\delta/\\alpha-2}{\\delta/\\alpha-1}\\right) \\log{\\sigma}, \\label{eq:predict} \\end{equation} where $\\sigma$ is the averaged velocity. Since the system is self-similar, this relation will apply at both the ``bulge'' mass scale as well as the BH mass scale. The quantities $\\delta$ and $\\alpha$ are scales in space and time, respectively, and are related to the power-law index of the initial density perturbation $\\epsilon$ in spherical infall models of halo growth (Henriksen \\& Widrow 1999): \\begin{equation} \\frac{\\delta}{\\alpha}=\\frac{2}{3}\\left(1+\\frac{1}{\\epsilon}\\right). \\label{eq:relate} \\end{equation} This power-law index $\\epsilon$ depends on the spectral index $n$ of the primordial power spectrum, $P(k) \\propto k^n$, by $n = 2\\epsilon - 3$. There is therefore a direct link between the initial power spectrum and the predicted relationship between the BH mass and the velocity dispersion; for agreement with observations, we must have $n = -2$, so that $\\epsilon = 1/2$ and $\\delta/\\alpha = 2$. We determine below that the addition of sufficient angular momentum breaks the self-similarity in the central regions. This creates a ``mass reservoir'' around the BH that does grow in proportion to the galaxy mass, and from which the BH grows more slowly by collisional interactions between clumps of matter. Provided most of this mass may be absorbed by the BH on a cosmic timescale, the proposed relation should still hold. ", "conclusions": "For systems in which there is no angular momentum or deviation from spherical symmetry initially, the numerical work, with both the spherical shell code and the more general n-body code, confirms the predicted black hole growth: $M_{\\rm BH} \\propto t^4$. However, for the simulations in which there was some deviation from a simple spherical infall of matter, results were contrary to what was expected. In particular, the n-body results show a black hole growth approximately proportional to the time. However, it is apparent from the simulations that the black hole growth in these cases is not dominated by the infalling matter, as it is in the initially spherical case. Rather, the particles form a ``core'' about the centre, and so the growth is fed in a different manner. Dimensional arguments suggest that the Schwarzschild radius should scale with time as $R_s \\propto ct$, where $c$ is the speed of light, a constant of the system. If this is the case, then we get that the black hole mass will grow as $M_{\\rm BH} \\propto R_s \\propto t$, which is approximately what is observed. Note, however, that this breaks the symmetry of the system, since the mass on a larger scale is predicted to grow as $t^{3\\delta - 2\\alpha}$. The numerically derived $M_{\\rm BH} - \\sigma$ relationship, which here compared the black hole growth with the average velocity of particles within some radius $r$, only gave the expected relation, $M_{\\rm BH} \\propto \\sigma^4$, when a fixed, rather than comoving radius was considered. Furthermore, the cases for which the growth rate was much shallower than expected still showed the same trend as the other case; that is, $M_{\\rm BH} \\propto \\sigma^4$ regardless of how the black hole grew with time. As stated above, however, this result is for a fixed radius. From the definition of $\\mathbf{X}$ and $T$ in MacMillan \\& Henriksen (2002), we see that $r = \\mathbf{X} t^{\\delta / \\alpha}$. Fixing $r$ requires $\\mathbf{X}$ to then depend on time. Recalling that we're considering a density profile that goes as $X^{-\\epsilon}$, and $\\epsilon$ is related to the quantity $\\delta / \\alpha$ by equation (\\ref{eq:relate}), we can write the mass as a function of $X$: \\begin{equation} \\mathcal{M}(X) \\propto X^{3 - 2 \\alpha / \\delta}. \\end{equation} Thus, as a function of the (fixed) radius, we have $M(r) \\propto r^{3 - 2 \\alpha / \\delta}$. Similarly, we can write the self-similar velocity, assuming it is in its virialized state, as a function of $X$: \\begin{equation} Y(X) \\propto \\sqrt{\\bar{\\Phi}} \\propto X^{1 - \\alpha / \\delta}, \\end{equation} so that the radial dependence of the velocity takes the form $v(r) \\propto r^{1 - \\alpha / \\delta}$. Combining these two equations for mass and velocity and eliminating $r$ gives us the familiar relation given by equation (\\ref{eq:predict}). Thus, taking the mass and velocity at a fixed radius $r$ gives the same relation regardless of the time dependence of either." }, "0212/astro-ph0212087_arXiv.txt": { "abstract": "We combine Sloan Digital Sky Survey spectra of 22,000 luminous, red, bulge-dominated galaxies to get high $S/N$ average spectra in the rest-frame optical and ultraviolet (2600\\,\\AA\\ to 7000\\,\\AA). The average spectra of these massive, quiescent galaxies are early-type with weak emission lines and with absorption lines indicating an apparent excess of $\\alpha$ elements over solar abundance ratios. We make average spectra of subsamples selected by luminosity, environment and redshift. The average spectra are remarkable in their similarity. What variations do exist in the average spectra as a function of luminosity and environment are found to form a nearly one-parameter family in spectrum space. We present a high signal-to-noise ratio spectrum of the variation. We measure the properties of the variation with a modified version of the Lick index system and compare to model spectra from stellar population syntheses. The variation may be a combination of age and chemical abundance differences, but the conservative conclusion is that the quality of the data considerably exceeds the current state of the models. ", "introduction": "Luminous elliptical and bulge-dominated galaxies are the most massive galaxies in the Universe. These objects show little rotation, have smooth radial profiles, are massive and kinematically hot, have a narrow range of stellar-mass-to-light ratios, show high metallicities, and reside preferentially in the Universe's denser environments \\citep[e.g.,][]{Kor89,Rob94,Ben98}. These galaxies are also the most intrinsically luminous galaxies in the Universe \\citep[e.g.,][]{Tam79,Bla01a}. That the most optically luminous galaxies are red is remarkable, given that unextincted red stellar populations generally have higher stellar mass than blue populations at constant luminosity; it means that they are considerably more massive than their bluer, fainter spiral neighbors. A common paradigm for the formation of bulge-domi\\-nated systems is hierarchical merging of smaller, star-forming progenitors \\citep{Bar92,Kau96,Bau96}. In this model, the systems appear old and metal-rich because the merging is more common at high redshift and because the resulting starburst consumes or expels the remaining gas, thereby ending star formation \\citep{Kau98}. This dependence upon cosmological merger rates and feedback suggests that the stellar populations of bulges should display subtle but important dependencies on mass and environment. In this paper, we study the aggregate stellar populations of luminous, red, bulge-dominated galaxies using averaged spectra from the Sloan Digital Sky Survey \\citep[SDSS;][]{Yor00} We select these galaxies because we know that they dominate the stellar mass density of the Universe \\citep{Fuk98,Hog02} and because they show great regularities in their properties \\citep[e.g.,][]{Fab73,Vis77,Djo87,Dre87,Kor89,Bow92,Rob94, Ber01}. In addition, the great age of their stellar populations ease some, but not all, of the difficulties in understanding superimposed younger populations \\citep{Fab72,OCo76,Gun81,Cha96}. As the luminosity-weighted average spectrum does measure the total stellar population of an entire sample of galaxies, it is a well-defined mean property that can be compared to theoretical models of galaxy formation \\citep[][e.g.,]{Bal02}. We focus not on the interpretations of the average spectrum itself, but rather on the variations of this average with luminosity, environment, and redshift. These variations should be able to test predictions that more luminous (or massive) galaxies have higher metallicity and galaxies in clusters have older stellar populations. Previous observational studies \\citep[e.g.,][]{Bow90,Guz91,Ros94,Jam99,Ter99,Pog01} comparing spectra of individual galaxies have found evidence to support these hypotheses. Of course, one would also expect to find that galaxies at high redshift should have younger stellar populations than similar galaxies at low redshift, but even this trend can be altered if massive, bulge-dominated galaxies are still forming at low redshift \\citep{Fra95, van01}. Because we are interested in comparing the average spectra of samples, it is critical that the samples be selected so that the variation between the samples is as controlled as possible. With SDSS data, we can select uniform samples according to rest-frame photometry and morphological properties across a wide range of environments and redshifts, allowing trends in the data to be attributed to astrophysics rather than selection biases. The average spectra are of extremely high signal-to-noise ratio, thereby allowing analyses that would be impractical on individual SDSS spectra. Over 100 absorption lines are apparent in the composite. Indeed, the resulting spectra exceed the ability of the best spectral models of stellar populations to interpret, especially given the non-solar ratio of $\\alpha$-element to iron-peak abundances \\citep{Wor92,Gon93,Dav93,Paq94,Wor98,Pro02} apparent in the data. The outline of this paper is as follows. In \\S~2, we describe the relevant aspects of SDSS data and introduce the methods for our analysis, including principal component analysis (PCA) and a modification of the Lick absorption line index system. In \\S~3, we describe our sample selection and environment estimation. We present a general analysis of the average spectra in \\S~4 and analysis of the variations with luminosity and environment in \\S~5. Variations with redshift are presented in \\S~6. In \\S~7, we use the highest redshift sample to determine the average spectrum in the mid-ultraviolet. We conclude in \\S~8. Except where noted otherwise, we adopt a conventional cosmological world model with $H_0=100\\,h~{\\rm km\\,s^{-1}\\,Mpc^{-1}}$ and $(\\Omega_M,\\Omega_{\\Lambda})=(1/3,2/3)$. ", "conclusions": "" }, "0212/astro-ph0212108_arXiv.txt": { "abstract": "The origin of large scale cosmological magnetic fields remains a mystery, despite the continuous efforts devoted to that problem. We present a new model of magnetic field generation, based on local charge separation provided by an anisotropic and inhomogeneous radiation pressure. In the cosmological context, the processes we explore take place at the epoch of the reionisation of the Universe. Under simple assumptions, we obtain results (i) in terms of the order of magnitude of the field generated at large scales and (ii) in terms of its power spectrum. The amplitudes obtained ($B\\sim 8.~10^{-6} ~\\mu{\\rm G}$) are considerably higher than those obtained in usual magnetogenesis models and provide suitable seeds for amplification by adiabatic collapse and/or dynamo during structure formation. % ", "introduction": "According to observations, magnetic fields are pervading the whole Universe. In particular, both synchrotron emission and Faraday rotation measurements reveal a magnetic field present on large scales. On galactic scales \\cite{beck}, on galaxy cluster scales \\cite{eo} and even on larger scales \\cite{kronberg}, the observed magnetic field strengths range from $0.1$ micro-Gauss to a few tens of micro-Gauss. The origin of the magnetic field is, however, still a mystery. Clearly, the fields cannot be generated directly with the observed amplitudes since, in that case, they would strongly affect the formation of structures \\cite{rr}. Therefore, the fields must arise in the form of weak seeds which are subsequently, in some way, strongly amplified after the onset of structure formation. Various mechanisms have been proposed for the generation of such seeds. Basically, they can be sorted in two types. In cosmology, the mechanisms of the first type operate before matter-radiation decoupling. They take advantage of high energy physics processes such as inflation \\cite{ratra,dimo,maroto} or phase transitions in the early Universe \\cite{sigl,grario}. However, these mechanisms are still unsatisfactory in two respects. First, they do not provide a real prediction since the generated fields can be as weak as $10^{-65}$ Gauss and as strong as $10^{-9}$ Gauss. Moreover, a property shared by fields created before decoupling is that the stronger their amplitude, the smaller the scale on which they are generated (see Battaner \\& Lesch~\\cite{bl}, and references therein). Furthermore, under the assumption of \\textit{frozen magnetic flux}, these fields decay following cosmological expansion as $(1+z)^2$. Therefore, fields of primordial origins (generated before nucleosynthesis, say) are extremely weak on galactic scales and are very strong on much smaller scales. Finally, extremely tight constraints on pre-BBN magnetic fields from gravity wave production have been recently derived \\cite{chiara}, possibly ruling out a majority of the proposed models. The mechanisms of the second type produce magnetic fields after matter-radiation decoupling. They rely essentially on the battery effect \\cite{battery} which was first introduced to explain stellar magnetic fields and is basically a consequence of charge separation. Several authors explored the same mechanism in various cosmological contexts \\cite{lazarian,lc,khanna}. The intensity of the fields generated is found to be roughly of the order of $10^{-20}$ Gauss. These weak seeds are then amplified on galactic scales by a dynamo sustained by turbulence and differential rotation in protogalaxies. As noticed by Grasso \\& Rubinstein \\cite{GR}, this type of mechanism can hardly be responsible for magnetic fields on galaxy cluster scales. Consequently, we would have to deal with different mechanisms to explain the origin of fields in galaxies and clusters, which exhibit similar properties. Moreover, this mechanism cannot really account for the strong fields observed in objects at high redshifts where galaxies did not have enough time to rotate and amplify the seeds efficiently. Finally, whatever the problems of each type of mechanisms, the seeds produced are generally small. As such, they require the action of a strong process capable of amplifying the magnetic amplitudes up to the values observed in galaxies. The dynamo mechanism evoked above has long been considered suitable for that purpose but it is, however, subject to controversy nowadays. In fact, it has recently been pointed out \\cite{ketal} that dynamo tends to amplify the small scale magnetic fields in a more efficient way than fields on large scales. The consequence of this is that small scale fields reach rapidly dynamically important strengths and stop, in back-reaction, the dynamo mechanism itself. This happens long before large scale fields can reach the observed equipartition values. Significant progress has been achieved very recently and the back-reaction of small scale fields is now better understood. In particular, the importance of magnetic helicity conservation in dynamo quenching has been demonstrated in ideal cases \\cite{fb02,blackman,branden}. However, for their application to real astrophysical systems such as galaxies, these theories require further developments. Small scale fields thus remain a possible threat to dynamo amplification mechanisms. In this paper, we propose a mechanism which appears to be relatively free of the problems outlined above. Applied to cosmology, it operates after decoupling in the natural context of inhomogeneous reionisation, for a redshift $z$ between 6 and 7 \\cite{becker, go}. Similarly to the battery effect, it relies upon local charge separation provided in our case by radiation pressure. The physics involved is fairly simple and was nevertheless left aside until now, surprisingly enough. Notice however that Subramanian \\textit{et. al.}~\\cite{subra} proposed a mechanism (which has been explored numerically by Gnedin \\textit{et. al.}~\\cite{gnedin}) for the generation of magnetic field seeds at reionisation, and obtained magnetic fields of the order of $10^{-20} - 10^{-19}$ Gauss on galactic scales. Their solution for magnetogenesis relies explicitly on the actual battery effect which requires non-parallel temperature and electron density gradients. While exploring the physics at a comparable epoch, we consider here a different and more efficient process, as will appear below. In the following section, we describe in details the mechanism of our model. Then, in Sect. 3, we present the results obtained for the cosmological case, emphasising on the magnetic field power spectrum and its order of magnitude at protogalactic and galactic scales. We also apply our mechanism to the case of interstellar magnetic fields. Finally, we discuss the model and its limitations in Sect. 4. ", "conclusions": "We presented a new model for the generation of large scale magnetic fields. The mechanism proposed relies upon the simple physics of local charge separation which occurs naturally in the cosmological context of reionisation, at a redshift $z \\sim 7$. As we have seen, the first luminous objects, such as quasars, emit a radiation which ionises the gas filling the Universe. The anisotropy of the ionising flux leads to the generation of electrical fields. The distribution of the ionising sources together with the gas density inhomogeneities imply that the ionising flux is inhomogeneous. The fluctuations in the flux generate electric currents which in turn induce a magnetic field on the scale of the fluctuations. With only a couple of simple initial assumptions, we could derive interesting properties for the generated magnetic fields. In particular, the fields produced in our model have amplitudes several orders of magnitude higher than in usual plasma physics magnetogenesis models. These fields are therefore suitable to serve as seeds on large scales for adiabatic collapse amplification up to $10^{-10}$ Gauss in galaxies. Such large values represent an improvement for further amplification by dynamo mechanisms since less time is required in order to account for magnetic fields observed in high redshift galaxies. Furthermore, relating the magnetic field power spectrum to the matter density power spectrum, we have shown that magnetic fields are generated in our model preferably on large scales, whereas small scale fields are strongly suppressed. This result is true at least in the non-saturated regime and we are currently exploring the saturated case. Such a property is highly interesting again with respect to dynamo amplification theories: the small scale fields are weak and therefore their amplification by dynamo represent a less crucial threat. We showed also that, in the context of the ISM, our mechanism is negligible as a source of magnetic fields when compared to usual effects such as dynamo and turbulence. As we mentioned earlier, Subramanian \\textit{et. al.}~\\cite{subra} and Gnedin \\textit{et. al.}~\\cite{gnedin} explored the generation of magnetic field seeds in the context of reionisation. In their model, the magnetic field source term is the Battery effect relying on charge separation. The latter is obtained when ionisation fronts either break out from protogalaxies or propagate past overdense regions of the Universe. Across an ionising front, the temperature varies sharply by several orders of magnitude. The driving physical process for charge separation is the thermal pressure of the gas, acting in the same way on electrons and ions. Since their mass is far smaller than the ion mass, electrons are more accelerated by the pressure force than ions and this provides charge separation. However, the mechanism we presented in this paper relies on a quite different process: The source of charge separation is not differential thermal pressure but differential radiation pressure. For a particle $i=e,p$, the acceleration due to thermal pressure is $a^\\text{t}_i \\propto m_i^{-1}$ whereas radiation pressure provides an acceleration $a^\\text{r}_i \\propto m_i^{-3}$. Radiation pressure is therefore more efficient by a factor of \\beq \\frac{a^\\text{r}_\\text{e}/a^\\text{r}_\\text{p}}{a^\\text{t}_\\text{e}/a^\\text{t}_\\text{p}} = \\left(\\frac{m_\\text{p}}{m_\\text{e}}\\right)^2 \\approx 3. ~10^6 \\eeq than thermal pressure for accelerating electrons and creating electrical fields. This explains why our model leads to orders of magnitude higher predictions than in \\cite{subra}. Thus, the mechanism we described in this paper is likely to be dominant in cosmological situations where strong anisotropic and inhomogeneous radiation pressure exists. Further developments of the model presented in this paper, relaxing our geometrical assumptions and addressing the magnetic field power spectrum in the saturated regime will appear in a forthcoming paper.\\\\" }, "0212/astro-ph0212422_arXiv.txt": { "abstract": "We have investigated the X-ray spectral properties of a collection of low-mass X-ray binaries (LMXBs) within a sample of 15 nearby early-type galaxies using proprietary and archival data from the {\\it Chandra X-ray Observatory}. We find that the spectrum of the sum of the sources in a given galaxy is remarkably similar from galaxy to galaxy when only sources with X-ray luminosities less than $10^{39}$ ergs s$^{-1}$ (0.3--10 keV) are considered. Fitting these lower luminosity sources in all galaxies simultaneously with a power law model led to a best-fit power law exponent of $\\Gamma = 1.56 \\pm 0.02$ (90\\% confidence), and using a thermal bremsstrahlung model yielded $kT_{brem} = 7.3 \\pm 0.3$ keV. This is the tightest constraint to date on the spectral properties of LMXBs in external galaxies. The spectral properties of the LMXBs do not vary with galactic radius out to three effective radii. There is also no apparent difference in the spectral properties of LMXBs that reside within globular clusters and those that do not. We demonstrate how the uniformity of the spectral properties of LMXBs can lead to more accurate determinations of the temperature and metallicity of the hot gas in galaxies that have comparable amounts of X-ray emission from hot gas and LMXBs. Although few in number in any given galaxy, sources with luminosities of $1-2 \\times 10^{39}$ ergs s$^{-1}$ are present in 10 of the galaxies. The spectra of these luminous sources are softer than the spectra of the rest of the sources, and are consistent with the spectra of Galactic black hole X-ray binary candidates when they are in their very high state. The spatial distribution of these sources is much flatter than the optical light distribution, suggesting that a significant portion of them must reside within globular clusters. The simplest explanation of these sources is that they are $\\sim 10-15$ M$_{\\odot}$ black holes accreting near their Eddington limit. The spectra of these sources are very different than those of ultraluminous X-ray sources (ULXs) that have been found within spiral galaxies, suggesting that the two populations of X-ray luminous objects have different formation mechanisms. The number of sources with apparent luminosities above $2 \\times10^{39}$ ergs s$^{-1}$ when determined using the distance of the galaxy is equal to the number of expected background AGN and thus appear to not be associated with the galaxy, indicating that very luminous sources are absent or very rare in early-type galaxies. The lack of ULXs within elliptical galaxies strengthens the argument that ULXs are associated with recent star formation. ", "introduction": "\\label{sec:intro} The {\\it Chandra X-ray Observatory} has made it possible to resolve dozens if not hundreds of individual X-ray point sources in nearby galaxies owing to its sub-arcsecond spatial resolution (Sarazin, Irwin, \\& Bregman 2000; Angelini, Loewenstein, \\& Mushotzky 2001; Kraft et al.\\ 2001; Bauer et al.\\ 2001; Soria \\& Wu 2002). While spiral galaxies contain a variety of types of X-ray point sources (high- and low-mass X-ray binaries, supernovae remnants), elliptical and S0 galaxies, as well as the bulges of spiral galaxies contain almost exclusively low-mass X-ray binaries (LMXBs). LMXBs are believed to be composed of a compact accreting primary (a neutron star or a black hole) and a low-mass main sequence or red giant secondary that is losing material to the primary as a result of Roche lobe overflow. Although LMXBs have been studied extensively in our Galaxy, resolving them and determining their spatial distribution and spectral characteristics in external galaxies has only recently become feasible. \\begin{table*}[t] \\scriptsize \\caption{Sample of Galaxies} \\label{tab:sample} \\begin{center} \\begin{tabular}{lcccccccccc} \\multicolumn{10}{c}{} \\cr \\tableline \\tableline Galaxy & Galaxy &Type & Obs. & Distance & Semimajor & Semiminor & $N_H$ & Exposure & Luminosity \\cr Number &&&ID & (Mpc) & Axis ($^{\\prime\\prime}$) & Axis ($^{\\prime\\prime}$) & ($10^{20}$ cm$^{-2}$) & (seconds) & Limit (ergs s$^{-1}$)\\cr \\tableline \\phn\\phn1 & NGC~1291 & Sa & 795 & 8.9 & \\ldots & \\ldots &2.12 & 37,406 & $2.0 \\times 10^{37}$ \\\\ \\phn\\phn2 & NGC~1316 & S0 & 2022 & 21.5 & 132.2\\tablenotemark{a} & 90.5\\tablenotemark{a} & 1.88 & 24,478 & $1.7 \\times 10^{38}$ \\\\ \\phn\\phn3 & NGC~1399 & E1 & 319 & 20.0 & 44.6\\tablenotemark{b} & 40.5\\tablenotemark{b} & 1.34 & 54,540 & $5.7 \\times 10^{37}$ \\\\ \\phn\\phn4 & NGC~1407 & E0 & 791 & 28.8 & 73.9\\tablenotemark{b} & 68.7\\tablenotemark{b} & 5.42 & 33,763 & $2.8 \\times 10^{38}$ \\\\ \\phn\\phn5 & NGC~1549 & E0 & 2077 & 19.7 & 51.0\\tablenotemark{b} & 44.7\\tablenotemark{b} & 1.46 & 21,892 & $1.8 \\times 10^{38}$ \\\\ \\phn\\phn6 & NGC~1553 & S0 & 783 & 18.5 & 78\\tablenotemark{c} & 51\\tablenotemark{c} & 1.50 & 16,361 & $1.6 \\times 10^{38}$ \\\\ \\phn\\phn7 & NGC~3115 & S0 & 2040 & 9.7 & 93\\tablenotemark{d} & 35\\tablenotemark{d} & 4.32 & 36,979 & $2.6 \\times 10^{37}$ \\\\ \\phn\\phn8 & NGC~3585 & E/S0 & 2078 & 20.0 & 56\\tablenotemark{e} & 28\\tablenotemark{e} & 5.57 & 33,706 & $1.7 \\times 10^{38}$ \\\\ \\phn\\phn9 & NGC~4374 & E1 & 803 & 18.4 &58.2\\tablenotemark{b} & 53.3\\tablenotemark{b} & 2.60 & 28,049 & $9.8 \\times 10^{37}$ \\\\ \\phn\\phn10 & NGC~4472 & E2 & 321 & 16.3 & 114.0\\tablenotemark{f} & 95.6\\tablenotemark{f} & 1.66 & 26,326 & $9.5 \\times 10^{37}$ \\\\ \\phn\\phn11 & NGC~4494 & E1 & 2079 & 17.1 & 49.3\\tablenotemark{b} & 42.2\\tablenotemark{b} & 1.52 & 18,254 & $1.3 \\times 10^{38}$ \\\\ \\phn\\phn12 & NGC~4636 & E/S0 & 323 & 14.7 & 117.0\\tablenotemark{f} & 85.6\\tablenotemark{f} & 1.81 & 42,686 & $5.2 \\times 10^{37}$ \\\\ \\phn\\phn13 & NGC~4649 & E2 & 785 & 16.8 & 82.0\\tablenotemark{f} & 66.2\\tablenotemark{f} & 2.20 & 18,401 & $1.4 \\times 10^{38}$ \\\\ \\phn\\phn14 & NGC~4697 & E6 & 784 & 11.8 & 97.3\\tablenotemark{b} & 60.2\\tablenotemark{b} & 2.12 & 39,063 & $3.1 \\times 10^{37}$ \\\\ \\phn\\phn15 & M31 & Sb & 309 & 0.76 & \\ldots & \\ldots & 6.66 & 5,089 & $1.2 \\times 10^{36}$ \\\\ \\tableline \\end{tabular} \\end{center} \\tablenotetext{a}{Caon, Capaccioli, \\& D'Onofrio (1994)} \\tablenotetext{b}{Goudfrooij et al.\\ (1994)} \\tablenotetext{c}{Kormendy (1984) and Jorgensen, Franx, \\& Kjaergaard (1995)} \\tablenotetext{d}{Capaccioli, Held, \\& Nieto (1987)} \\tablenotetext{e}{Ryden, Forbes, \\& Terlevich (2001)} \\tablenotetext{f}{Peletier et al.\\ (1990)} \\end{table*} Initial work on the LMXB population of early-type galaxies has led to several interesting results. Sarazin, Irwin, \\& Bregman (2000, 2001) detected 90 X-ray sources in a {\\it Chandra} observation of the elliptical galaxy NGC~4697, and found a break in the luminosity function of the sources at a luminosity of $\\sim3 \\times 10^{38}$ ergs s$^{-1}$, intriguingly close to the Eddington luminosity of an accreting 1.4 M$_{\\odot}$ neutron star. One interpretation of this break is that it represents a division between black hole X-ray binaries and neutron star X-ray binaries, with only black hole binaries more luminous than the break, and a mixture of neutron star and black hole binaries less luminous than the break. Such breaks have also been found in other early-type galaxies (Blanton, Sarazin, \\& Irwin 2001; Finoguenov \\& Jones 2002; Randall, Sarazin, \\& Irwin 2002; Kundu, Maccarone, \\& Zepf 2002). Recent studies have also found that a significant fraction (40\\%--70\\%) of the X-rays binaries reside in globular clusters of the host galaxy (Angelini et al.\\ 2001; Randall et al.\\ 2002; Kundu et al.\\ 2002), in marked contrast to the $\\sim10\\%$ of Galactic and M31 LMXBs that reside within globular clusters. In addition, when the spectra of all the resolved LMXBs of a given galaxy were added together and fit with a power law spectral model, an index ranging from 1.5--2.0 has been obtained (Sarazin et al.\\ 2001; Randall et al.\\ 2001; Kim \\& Fabbiano 2002; Irwin, Sarazin, \\& Bregman 2002). Previous X-ray satellites lacked the needed spatial resolution and bandpass coverage to separate cleanly the LMXB component from the hot gas component in early-type galaxies. While recent progress has been made from the study of the luminosity functions and host environment of LMXBs in early-type galaxies, a detailed analysis of the spectral properties of LMXBs with a large sample of galaxies has not yet been attempted with {\\it Chandra}. With {\\it Chandra} we are now in a position to determine the spectral properties of individual bright sources in galaxies or add up the spectra of the fainter sources to determine the bulk spectral properties of the LMXBs. A more thorough understanding of the X-ray spectral properties of LMXBs in early-type galaxies is critical for the study of the hot, X-ray--emitting gas within these systems. Although the LMXB contribution to the X-ray emission from gas-rich galaxies is negligible, this is not the case for galaxies with moderate to low amounts of X-ray--emitting gas. In these galaxies, the LMXB contribution can be the dominant X-ray emission mechanism. Quantifying the spectral properties of LMXBs in nearby galaxies where the LMXBs are resolvable will allow for a more accurate separation of the gaseous and stellar X-ray components in galaxies too distant for the individual LMXBs to be detected. In this paper we use both proprietary and archival {\\it Chandra} data for 15 early-type systems (consisting of eight elliptical galaxies, two transitional E/S0 galaxies, three S0 galaxies, and two spiral bulges) to determine the spectral characteristics of LMXBs over a range of X-ray luminosity classes, as well as a function of galactic radius. Unless otherwise stated, all uncertainties are 90\\% confidence levels, and all X-ray luminosities are in the 0.3--10 keV energy band. ", "conclusions": "\\label{sec:conclusions} We have used {\\it Chandra} data for 15 early-type systems to constrain the spectral and spatial properties of LMXBs in these galaxies. We have found that once the most luminous ($> 10^{39}$ ergs s$^{-1}$) sources are removed from the combined spectra of the sources, the spectra of the sum of the sources are very similar values among the galaxies. When all the galaxies are fit simultaneously with a power law spectral model, the best-fit power law exponent is $\\Gamma = 1.56 \\pm 0.02$. Even faint sources as dim as $10^{36}$ ergs s$^{-1}$ in the bulge of M31 have similar spectral properties as the more luminous sources. There was no apparent difference in the spectral properties of LMXBs as a function of galactic radius. Nor was there a significant difference in the spectral properties of sources based on their presence within or outside a globular cluster. A significant number of sources with luminosities of $1-2 \\times 10^{39}$ ergs s$^{-1}$ were found within the galaxies, and they exhibited significantly softer spectral properties than the fainter sources. The disk blackbody + power law model used to model their spectra is very reminiscent of Galactic black hole X-ray binaries when they are in their very high state. Their spectra were also quite different from ULXs found within spiral galaxies. The simplest explanation of these sources is that they are $\\sim7-15$ M$_{\\odot}$ accreting near their Eddington limit. The spatial distribution of these sources is significantly more extended than the optical light. With rare exception, sources more luminous than $2 \\times 10^{39}$ ergs s$^{-1}$ are absent from early-type galaxies. The number and spatial distribution of the sources with fluxes corresponding to $2 \\times 10^{39}$ ergs s$^{-1}$ or greater if they are at the distance of the galaxy is consistent with them being unrelated background/foreground sources. The only exceptions to this seems to be two $\\sim 4\\times 10^{39}$ ergs s$^{-1}$ sources found within globular clusters of NGC~1399. Their spectra are also quite different than that of a typical spiral galaxy ULX. Their presence within a globular cluster suggests that globular clusters might harbor intermediate mass black holes that are accreting at a few percent of their Eddington limit. Finally, we have discussed how these constraints on the spectral properties of LMXBs, especially the fainter ones, can lead to better constraints to the luminosity, temperature, and metallicity of the hot gas within early-type galaxies that contain little gas." }, "0212/astro-ph0212570_arXiv.txt": { "abstract": "{ Low cooling plasmas associated with large kinetic energies are likely to be the origin of the kpc-extended and well collimated extra-galactic jets. It is proposed that jets are launched from a layer, governed by a highly diffusive, super-Keplerian rotating and thermally dominated by virial-hot and magnetized ion-plasma. The launching layer is located between the accretion disk and the corona surrounding the nucleus. The matter in the layer is causally connected to both the disk and to the central engine. Moreover we find that coronae, in the absence of heating from below, are dynamically unstable to thermal ion-conduction, and that accretion disks become intrinsically advection-dominated. We confirm the capability of this multi-layer model to form jets by carrying out 3D axisymmetric quasi-stationary MHD calculations with high spatial resolution, and taking into account turbulent and magnetic diffusion. The new multi-layer topology accommodates several previously proposed elements for jet-initiation, in particular the ion-torus, the magneto-centrifugal and the truncated disk - advective tori models. ", "introduction": "\\label{intro} Jets have been observed in many systems including active galaxies, X-ray binaries, black holes X-ray transients, supersoft X-ray sources and young stellar objects (K\\\"onigl 1997, Livio 1999, Mirabel 2001). Each of these systems is considered to contain an accretion disk, while jet-speeds have been verified to be of the order of the escape velocity at the vicinity of the central object (Mirabel 1999, Livio 1999 and the references therein). Recent observations of the M87 galaxy reveal a significant jet-collimation already at 100 gravitational radii from the central engine, and that jet-launching should occur close to the last stable orbit (Biretta et al. 2002). Several scenarios have been suggested to uncover the mechanisms underlying jet-initiations and their connection to accretion disks (Pudritz \\& Norman 1986). In most of these models magnetic fields (-MFs) are considered to play the major role in powering and collimating jets (e.g., the magneto-centrifugal acceleration model of Blandford \\& Payne 1982, the ion-torus model of Rees et al. 1982, X-point model of Shu et al. 1995, ADAF and ADIOS models of Narayan \\& Yi 1995 and Blandford \\& Begelman 1999). Previous radiative hydrodynamical studies without magnetic fields have confirmed the formation of a transition layer (-TL) between the disk and the corona, governed by thermally-induced outflows (Hujeirat \\& Camenzind 2000). The aim of this paper is show that incorporating large scale magnetic fields (-MFs) manifests such formation and dramatically strengthen the dynamic of the in- and out-flows. Moreover, the TL is shown to be an optimal runaway region where highly energetic ion-jets start off. The back reaction of jet-flows on the structure of the disk and on the corona surrounding the nucleus is investigated also. The study is based on self-consistent 3D axi-symmetric quasi-stationary MHD calculations, taking into account magnetic and hydro-turbulent diffusion, and adopting the two-temperature description (Shapiro et al. 1976). This adaptation is fundamental as 1) the dynamical time scale around the last stable orbit may become shorter than the Coulomb-coupling time. Therefore turbulent dissipation, adiabatic or shock compression preferentially heat up the ions rather than electrons ($T_\\mathrm{i} \\propto \\rho^{2/3}_\\mathrm{i}$, while $T_\\mathrm{e} \\propto \\rho^{1/3}_\\mathrm{i}$). 2) Taking into account that ions radiate inefficiently, having virial-heated ions in the vicinity of the last stable orbit is essential for the total energy-budget of large scale jets. \\begin{figure}[htb] \\centering {\\hspace*{-0.1cm} \\includegraphics*[width=8.0cm, bb=0 0 392 194,clip] {Eg221_f1.eps} } {\\vspace*{-0.1cm}} \\caption{ The model consists of $10^8M_{\\odot}$ Schwarzschild BH at the center (its gravity is described in terms of the quasi--Newtonian potential of Paczynski\\,\\&\\,Wiita 1980), and an SS-disk (blue color, extending from r=1 to r=20 in units of the radius of the last stable orbit i.e., in $3\\times R_\\mathrm{Schwarzschild}$, thickness $H_\\mathrm{d} = 0.1 r,$ an accretion rate of $\\Mdot = 0.01\\times \\Mdot_\\mathrm{Edd},$ and a central disk temperature of $T=10^{-3} T_\\mathrm{virial}$ at the outer radius). The ion-temperature $\\rm T_\\mathrm{i}$ is set to be equal to the electron temperature $\\rm T_\\mathrm{e}$ initially.) The low-density hot corona ($T=T_\\mathrm{virial}$, and density $\\rho(t=0,r,\\theta)=10^{-4}\\rho(t=0,r,\\theta=0$) is set to envelope the disk. A large scale magnetic field is set to thread the disk and the overlying corona (blue lines, $\\beta = P_\\mathrm{mag}/P_\\mathrm{gas} = 1/4$ at the outer radius, where $P_\\mathrm{gas}$ is the ion-pressure, $P_\\mathrm{mag} = B\\cdot B/8 \\pi$ is the magnetic pressure, and $\\rm B$ is the magnetic field whose components are $(B_\\mathrm{P}, B_\\mathrm{T})= (B1,B2,B_\\mathrm{T})$.) The low-density hot corona ($T=T_\\mathrm{virial}$, and density $\\rho(t=0,r,\\theta)=10^{-4}\\rho(t=0,r,\\theta=0$) is set to envelope the disk. A large scale magnetic field is set to thread the disk and the overlying corona (blue lines, $\\beta = P_\\mathrm{mag}/P_\\mathrm{gas} = 1/4$ at the outer radius, where $P_\\mathrm{gas}$ is the ion-pressure, $P_\\mathrm{mag} = B\\cdot B/8 \\pi$ is the magnetic pressure, and $\\rm B$ is the magnetic field whose components are $(B_\\mathrm{P}, B_\\mathrm{T})= (B1,B2,B_\\mathrm{T})$.) The numerical procedure is based on using the implicit solver IRMHD3 to search steady-state solution for the 3D axi-symmetric two-temperature diffusive MHD equations in spherical geometry (for further clarifications about the equations and the numerical method see Hujeirat \\& Rannacher 2001, Hujeirat \\& Camenzind 2000). The ion-pressure is used to describe the turbulent viscosity: $\\nu_\\mathrm{turb} = \\alpha P_\\mathrm{gas}/\\Omega$, where $\\alpha$ is the usual viscosity coefficient, and $\\Omega$ is the angular frequency. The magnetic diffusivity is taken to be equal to $\\nu_\\mathrm{turb}.$ $250\\times80$ strongly stretched finite volume cells in the radial and vertical direction have been used. Normal symmetry and anti-symmetry boundary conditions have been imposed along the equator and the rotation axis. Extrapolation has been adopted to fix down-stream values at the inner boundary. Non-dimensional formulation is adopted, using the reference scaling variables: $\\rm{\\tilde{\\rho}= 2.5 \\times 10^{-12} {\\rm g\\, cm^{-3}}, \\tilde{T}= 5 \\times 10^7 K},$ $\\tilde{U}=\\tilde{V_\\mathrm{S}} = \\gamma {\\cal R}_\\mathrm{g} \\tilde{T}/ \\mu_\\mathrm{i},$ $(\\mu_\\mathrm{i}=1.23)$. $\\tilde{B}=\\tilde{V_\\mathrm{S}} \\sqrt{4 \\pi \\tilde{\\rho}}.$ The location of the transition layer (-TL), where the ion-dominated plasma is expected to rotate super-Keplerian and being accelerated into jets, is shown for clarity. } \\end{figure} ", "conclusions": "We have presented a multi-layer model for initiating ion-jets in AGNs. The model agrees with a previous numerical study which confirmed the formation of thermally-induced outflows in the transition layer (Hujeirat \\& Camenzind 2000). Here we have shown that incorporating the effects of MFs manifests their formation and dramatically strengthen their dynamics. Three ingredients for initiating winds have been detected: 1) a highly diffusive plasma dominated by virial-hot ions, 2) large scale magnetic fields that efficiently transport angular momentum from the disk into the TL, where the plasma rotates super-Keplerian, and 3) an underlying advection-dominated accretion disk. Taking into account that the corona is dynamically unstable, adopting a large scale magnetic topology, and allowing ion-electron thermal decoupling appear to force accretion flows to undergo a global energy re-distribution: confined inflows (negative Bernoulli number) in the equatorial region and in the corona, and thermally and magneto-centrifugally-driven outflows in the TL characterized through a positive Bernoulli number. This feature may survive under different conditions: strong MFs suppress turbulence, weakening thereby the effect of the turbulent-viscosity and dominate the transport of angular momentum. On the other hand weak MFs in rotating stratified flows would be amplified via dynamo-action and reach equipartition, beyond which turbulence is again suppressed. This interplay between MFs and turbulent-viscosity, Balbus-Hawley and Parker instabilities may settle into an equilibrium state, in which inflows are simultaneously associated with low-cooling out-flowing ion-plasma. We note that in the absence of thermal conduction and adopting the one-temperature description, low-viscosity radiatively inefficient HD and MHD accretion flows become inevitably convection-dominated. Therefore, in the early phases of jet-initiation, CDAFs may play an important role in powering the jets in AGNs and microquasars (Abramowicz et al. 2002). The multi-layer model presented here accommodates some elements of BP82. In particular, we agree with BP82 about the necessity for a super-Keplerian rotation of the plasma overlying the accretion disk. However, the plasma here is dominated by highly-diffusive and virial-hot ions; it does not require a special $\\rm{B_\\mathrm{P}}-$alignment with respect to the disk-normal to enable jet-launching, as ideal-MHD treatment requires. While our results agrees with the ion-torus model with respect to the necessity of 2T-plasma to maintain the ions hot for a significant time of their propagation-life in the ISM, no signatures for the formation of ion-supported tori have been detected (Rees et al. 1982).\\\\ Our results differ from ADAF and ADIOs in several issues, and in particular with respect to 1) the existence of a layer adjusting to the disk, where the plasma is found to rotate super-Keplerian, 2) the configurations of the in- and the out-flows, 3) stability of the corona in the vicinity of the BH, 4) the transition from SS-disk to advection-dominated disks and 5) with respect to the essence of Bernoulli number in dissipative flows, i.e., a positive Bernoulli number is necessary but not sufficient for outflows (Abramowicz et al. 2000).\\\\ Finally, we note that since the flow in the TL is highly dissipative (strengthen thermal and rotational coupling with the central nucleus), the innermost region of the disk rotates synchronously with Kerr black holes (due to the frame dragging effect), and since $\\tau_\\mathrm{rem}$ decreases with radius and depends inversely on $\\rm{B_\\mathrm{T}}$ and $\\rm{B_\\mathrm{P}}$, we think that the plasma attached to the poloidal magnetic field would be forced to deposit its angular momentum to the plasma in the TL, thereby considerably enhancing the centrifugal power and ejecting the ion-plasma into space with relativistic speeds. \\small" }, "0212/astro-ph0212020_arXiv.txt": { "abstract": "A technique of timescale analysis performed directly in the time domain has been developed recently. We have applied the technique to study rapid variabilities of hard X-rays from neutron star and black hole binaries, $\\gamma$-ray bursts and terrestrial $\\gamma$-ray flashes. The results indicate that the time domain method of spectral analysis is a powerful tool in revealing the underlying physics in high-energy processes in objects. ", "introduction": "The widely used Fourier analysis method in temporal analysis is to derive frequency spectra from a time series. After the Fourier transform of a light curve $x(t_k)$ \\begin{equation} X(f_j)=\\sum_k x(t_k) e^{-i2\\pi f_jk\\Delta t}, \\hspace{5mm} f_j=j/T \\end{equation} we can get the power density spectrum \\begin{equation} P_j=|X(f_j)|^2 \\end{equation} From two light curves, $x_1(t_k)$ and $x_2(t_k)$, observed simultaneously in two energy bands at times $t_k$, and their Fourier transforms $X_1(f_j)$ and $X_2(f_j)$, we can construct the cross spectrum \\begin{equation}C(f_j)=X_1^*(f_j)X_2(f_j) \\end{equation} and then the time lag spectrum \\begin{equation} \\Lambda (f_j)=\\arg [C(f_j)]/2\\pi f_j \\end{equation} and the coherence coefficient spectrum \\begin{equation} r(f)=\\frac{||}{\\sqrt{<|X_1(f)|^2><|X_2(f)|^2>}} \\end{equation} People usually take a Fourier period $1/f$ as a timescale and use the Fourier power spectrum to describe the distribution of variation amplitude at different timescales, the time lag spectrum to describe the distribution of the emission time difference between two energy bands at different timescales and the coherence coefficient spectrum to describe the distribution of degree of linear correlation between high and low energy processes at different timescales. But it is not correct to equate the Fourier period with the timescale; a Fourier component with a certain frequency $f$ of a light curve is not equal to the real process with the timescale $1/f$. For some important high-energy emission processes the Fourier spectra distort the timescale distribution of real physical processes seriously. It is needed to derive timescale spectra from observed light curves directly in the time domain without through Fourier transforms. ", "conclusions": "" }, "0212/astro-ph0212216_arXiv.txt": { "abstract": "Weak gravitational lensing of background galaxies by intervening matter directly probes the mass distribution in the universe. This distribution, and its evolution at late times, is sensitive to both the dark energy, a negative pressure energy density component, and neutrino mass. We examine the potential of lensing experiments to measure features of both simultaneously. Focusing on the radial information contained in a future deep $4000$ square degree survey, we find that the expected ($1$-$\\sigma$) error on a neutrino mass is $0.1$ eV, if the dark energy parameters are allowed to vary. The constraints on dark energy parameters are similarly restrictive, with errors on $w$ of $0.09$. Much of the restrictive power on the dark energy comes not from the evolution of the gravitational potential but rather from how distances vary as a function of redshift in different cosmologies. ", "introduction": " ", "conclusions": "" }, "0212/astro-ph0212166_arXiv.txt": { "abstract": "Gas processes affecting star formation are reviewed with an emphasis on gravitational and magnetic instabilities as a source of turbulence. Gravitational instabilities are pervasive in a multi-phase medium, even for sub-threshold column densities, suggesting that only an ISM with a pure-warm phase can stop star formation. The instabilities generate turbulence, and this turbulence influences the structure and timing of star formation through its effect on the gas distribution and density. The final trigger for star formation is usually direct compression by another star or cluster. The star formation rate is apparently independent of the detailed mechanisms for star formation, and determined primarily by the total mass of gas in a dense form. If the density distribution function is a log-normal, as suggested by turbulence simulations, then this dense gas mass can be calculated and the star formation rate determined from first principles. The results suggest that only $10^{-4}$ of the ISM mass actively participates in the star formation process and that this fraction does so because its density is larger than $10^5$ cm$^{-3}$, at which point several key processes affecting dynamical equilibrium begin to break down. ", "introduction": "Gas processes in the interstellar medium (ISM) are varied and complex. This review is limited to those most closely involved with precursors to star formation. Other talks at this conference cover the high energy phase and the dispersal of gas after star formation. Some ideas expressed here are considered in more detail in Elmegreen (2002). At the beginning of star formation is cloud formation, but stars are also triggered in pre-existing clouds by processes unrelated to cloud formation (e.g., by supernovae), and many clouds are formed that do not produce new stars (e.g., diffuse clouds). Thus star formation is distinct from cloud formation. Figure 1 shows a diagram of the flow of energy into ISM structure, starting with sources dominated by young stars, gaseous self-gravity, and magnetism (which derives its energy from galactic rotation via the dynamo). The stellar sources tend to produce expanding regions and cosmic rays, turning their energy into radiation behind shock fronts and turbulent motions that also decay into radiation. Gravity produces contracting regions by swing amplified instabilities and collapse along spiral arms. This contraction releases more gravitational energy as the density increases, and again much of this energy goes into turbulence and ultimately radiation. The shells produced by stellar pressures and the turbulence produced in these shells and by various instabilities makes the observed cloudy structure of the ISM. Other stellar pressures, along with continued self-gravity and magnetic forces, then modify these clouds and eventually produce individual and binary stars on very small scales. \\begin{figure} \\centerline{\\includegraphics[width=28pc]{elmegreen.fig1.eps}} \\caption{Schematic diagram showing paths from the main energy sources, which are self-gravity, magnetic fields, and stars, to the formation of cloudy structure, going through intermediate steps of explosions, instabilities, and turbulence. The cloudy structure that is formed by these processes is modified further by stars, gravity and magnetic fields.} \\end{figure} ", "conclusions": "Instabilities involving gravity, magnetism, and pressure lead to spirals, accretion, clouds, and turbulence. Stellar pressures produce bubbles, more turbulence, and triggered star formation in clouds that already formed. Self-gravity and turbulence combine to structure the ISM, giving self-correlated properties for the gas and young stars with respect to size, velocity dispersion, and crossing time or duration of star formation. Turbulence also gives power law mass functions for clouds and clusters. The turbulence generated by gravitational instabilities can maintain the ISM in a state of quasi-equilibrium where $\\Sigma\\sim\\Sigma_{\\rm crit}$. If small scale instabilities continue in the cool component of the gas even when the average rms speed is large enough to give global stability, then star formation cannot regulate the $\\Sigma/\\Sigma_{\\rm crit}>1$ threshold. In this case, there is no self-regulation of star formation involving $\\Sigma_{\\rm crit}$ on a galactic scale. This will be true even if young stellar pressures agitate the ISM locally. They can blow the gas out into the halo and stop star formation locally, but young stars probably cannot fine-tune or moderate their own formation rate so that it stays near the historical or Hubble-type average. Young stars commonly trigger other stars anyway, so the feedback they produce should de-stabilize, not stabilize, the star formation rate, unless the entire local ISM is removed. The star formation rate depends on the mass fraction in dense gas. Turbulence may determine this mass fraction, independent of the sources for the turbulence. The global SFR is then independent of the detailed triggering mechanisms. Then again there would be no self-regulation of star formation, only a star formation {\\it saturated} to its maximum possible value, as determined by the open and tenuous geometry of the gas. In this case, star formation can be halted only by a dominance of the warm phase of the ISM." }, "0212/astro-ph0212485_arXiv.txt": { "abstract": "s{ I discuss anew how arguments about the internal dynamics of galactic disks set constraints on the otherwise ambiguous decomposition of the rotation curves of spiral galaxies into the contributions by the various constituents of the galaxies. Analyzing the two sample galaxies NGC\\,3198 and NGC\\,2985 I conclude from the multiplicities of the spiral arms and the values of the $Q$ disk stability parameters that the disks of both galaxies are `maximum disks'.} ", "introduction": "The rotation curves of spiral galaxies provide the most direct evidence for the presence of dark matter in galaxies. However, taken alone they do not discriminate luminous from dark matter because their decomposition into the contributions from the various constituents of the galaxies is highly ambiguous. Thus further constraints are needed. Considerations of the dynamical state of the resulting disk models can provide such constraints (Bosma 1999, Fuchs 1999). Of particular interest is the question if the much discussed `maximum--disk' models, i.e.~disks with their masses chosen at the maximum allowed by the data, are dynamical viable disk models. The degeneracy of the decomposition problem is illustrated in Fig.~1 for the example of NGC\\,3198. The rotation curve is modelled as \\begin{equation} v_{\\rm c}^2(R) = v_{\\rm c, disk}^2(R) + v_{\\rm c, halo}^2(R) + v_{\\rm c, is\\,gas}^2(R)\\,, \\end{equation} where $v_{\\rm c, disk}$, $v_{\\rm c, halo}$, and $v_{\\rm c, is\\,gas}$ denote the contributions due to the stellar disk, the dark halo, and the interstellar gas, respectively. The disk is modelled as an exponential disk and the dark halo is described by a quasi--isothermal sphere. In the left panel of Fig.~1 the maximum--disk model of Broeils (1992) is reproduced, while the right panel shows a submaximal disk model. The halo model parameters have been changed so that both fits to the observed rotation curve are of the same quality. \\begin{center} \\hbox{ \\epsfclipon \\epsfxsize=5.4cm \\epsffile{york_f1.eps} \\hspace{0.2cm} \\epsfclipon \\epsfxsize=5.4cm \\epsffile{york_f2.eps} } \\end{center} \\vspace{- 0.5cm} {\\footnotesize Figure 1. Maximum and submaximal disk models of the rotation curve of NGC\\,3198.} ", "conclusions": "Arguments for and against maximum disks have been discussed at length in the literature and are reviewed in detail, for instance, by Bosma (1999) or Sellwood (1999). One of the major consequences of maximum disks are the implied large core radii of the dark halos. These challenge the contemporary theory of the formation of galaxies according to CDM cosmology. Obviously the dynamical constraints on the decomposition of rotation curves must be tried out on a much larger data set than here in order to test the maximum disk hypothesis. This can be easily done with the density wave theory criterion by inspecting images of galaxies for which rotation curves are available. I have, for instance, analyzed a set of low surface brightness galaxies and found again indications for maximum disks (Fuchs 2003a, b). However, velocity dispersions have been measured in very few galaxies. Thus the $Q$ stability parameter criterion, which is an independent consistency check on the density wave theory criterion, can be applied only in deplorably few cases." }, "0212/gr-qc0212121_arXiv.txt": { "abstract": "Gravitational physics of VLBI experiment conducted on September 8, 2002 and dedicated to measure the speed of gravity (a fundamental constant in the Einstein equations) is treated in the first post-Newtonian approximation. Explicit speed-of-gravity parameterization is introduced to the Einstein equations to single out the retardation effect caused by the finite speed of gravity in the relativistic time delay of light, passing through the variable gravitational field of the solar system. The speed-of-gravity 1.5 post-Newtonian correction to the Shapiro time delay is derived and compared with our previous result obtained by making use of the post-Minkowskian approximation. We confirm that the 1.5 post-Newtonian correction to the Shapiro delay depends on the speed of gravity $c_g$ that is a directly measurable parameter in the VLBI experiment. ", "introduction": "The gravitational VLBI experiment for measuring the relativistic effect of propagation of gravity field of orbiting Jupiter was conducted on September 8, 2002 by the National Radio Astronomical Observatory (USA) and the Max Plank Institute for Radio Astronomy (Germany). The idea of the experiment was proposed by Kopeikin \\cite{2} who had noted that an arbitrary-moving gravitating body deflects light not instantaneously but with retardation caused by the finite speed of gravity propagating from the body to the light ray. This is because positions of the gravitating bodies are connected to the light-ray particle by the gravity null cone which is defined by the equation for the retarded time in the gravitational {\\it Li\\'enard-Wiechert} potentials being solutions of the Einstein equations. The goal of the experiment was to confirm this prediction by making use of the close celestial alignment of Jupiter and the quasar J0842+1835. The goal of this paper is to make use of the parameterized post-Newtonian technique to reveal how the gravity propagation affects the light-ray trajectory. This approach allows us to confirm our previous theoretical results \\cite{2} by looking at the problem from different position. The problem is formulated as follows. Light ray is emitted by a quasar (QSO J0842+1835) at the time $t_0$ and moves to the network of VLBI stations located on the Earth. As light moves, it passes through the variable gravitational field of the solar system, created by the orbital motion of Sun and other massive planets, and is received by the first and second VLBI stations at the times $t_1$ and $t_2$ respectively. Gravitational field of the solar system causes delay in the time of propagation of radio signals -- the effect discovered by \\cite{6} in static gravitational field approximation. We noted \\cite{2} that the present-day accuracy of phase-reference VLBI measurements is sufficient to detect a 1.5 post-Newtonian\\footnote{The first 1.0 post-Newtonian approximation is of order $c^{-2}$, and 1.5 post-Newtonian correction to the Newtonian gravity is of order $c^{-3}$. } correction to the Shapiro time delay incorporated implicitly into position of the light-ray deflecting body (see Fig.\\ref{fig1}) which must be taken at the retarded instant of time related to the time of observation by the equation of the gravity null-cone. We solved the Einstein-Maxwell system of differential equations and calculated this correction for Jupiter by making use of the post-Minkowskian approximation \\cite{2} with the retarded {\\it Li\\'enard-Wiechert} solutions of the Einstein equations. The retardation is caused by the finite speed of propagation of gravity $c_g=c$ which, as we have revealed in \\cite{2}, enters the 1.5 post-Newtonian correction to the Shapiro time delay. Hence, we concluded that the VLBI experiment on September 8, 2002 is sensitive to the effect of the {\\it propagation of gravity} and can be used to measure its speed. Our primary paper \\cite{2} has given no particular details on the parameterization of the gravity propagation effect the amplitude of which was characterized by the parameter $\\delta$. For this reason the physical meaning of the gravity propagation effect was not understood adequately by some researchers \\cite{1,w-astro}. By scrutiny inspection we found that \\cite{1} made an erroneous use of insufficient 1.0 post-Newtonian (static) approximation to discuss the high-order 1.5 post-Newtonian (dynamic) correction to the Shapiro time delay while \\cite{w-astro} gave analysis of the problem of propagation of light ray in the time-dependent gravitational field of the solar system on the basis of the PPN formalism which was not sufficiently elaborated to tackle properly the 1.5 post-Newtonian approximation to general relativity (see appendix \\ref{a2}). In this paper we extend our theoretical analysis of the VLBI experiment by proving that the parameter $\\delta=c/c_g-1$, where $c$ is the speed of light and $c_g$ is the speed of gravity. Parameter $\\delta$ is a measurable quantity and its determination will provided us with the numerical estimate of the magnitude of the propagation of gravity effect in terms of the speed of gravity $c_g$. The spectrum of plausible values of $c_g$ ranges from $c_g=c$ in general relativity to $c_g=\\infty$ as advocated by \\cite{tvf}. The VLBI experiment gives $c_g/c=1.06\\pm 0.21$ \\cite{apj}. The values $c_g4.5$ galaxies. The resulting integral surface density of the $Z_{AB}<25$ candidates at $z>4.5$ is in the range $0.13-0.44$ arcmin$^{-2}$ and that in the highest redshift bin $54.5$ has been so far serendipitous. There are obvious difficulties to tackle: first, the objects become progressively fainter and rarer. Second, the multicolor ``drop--out'' criteria used to select high--$z$ galaxies must be shifted from the UV-visual into the near-IR bands to follow the rest--frame UV. For the same reasons, the spectroscopic follow--up is progressively harder. Besides this, the number of possible interlopers increases, with early--type galaxies and late--type stars progressively entering in the selection criteria. The current statistics of high--$z$ galaxies reflects these problems. Few serendipitous objects have been identified (e.g. Spinrad et al 1998), mostly because of a large EW emission line identified as Ly$\\alpha$, (e.g. Chen et al 1999; Hu et al. 1998, 1999, 2002). Some identification have been later disputed on the basis of deep imaging shortward of the (presumed) Lyman Limit (Chen et al 2000, Stern et al 2000). In general, the search of $z\\geq5$ emission line galaxies has been shown to suffer from the strong contamination by OII emitters at $z\\simeq 1.4$ (Stern et al 2000). Thus, the conclusions that can be drawn from the few objects observed so far are that {\\it a)} spectroscopy is by itself not conclusive at these redshifts to derive a firm estimate of the average cosmic star formation rate, firstly because it mostly requires the existence of a strong Ly$\\alpha$ emission line, and because of the contamination from OII emitters; and {\\it b)} deep imaging observations are required in any case not only to select the objects but also to validate the spectroscopic identifications. Previous color selections at $z>4.5$ based on the photometric redshift technique (Fontana et al. 1999, 2002) took advantage of the very deep HST North and South samples, discovering 4 $z>5.5$ candidates in each field down to $I_{AB}<27.5$. Evidence has come up for a comoving UV luminosity density at $z\\simeq 5$ lower by a factor of 5 than at $z\\simeq3$. However, this estimate is based on a sample of very faint sources selected in a small area and could be strongly affected by the presence of large-scale structure in the ``pencil'' beams. For this reason, we have started a relatively deep survey of galaxies selected in the Z band to search for galaxies at $4.5 \\leq z \\leq 6.2$, covering two well known fields where broad band multicolor imaging is available, namely the extended ESO Imaging Survey (EIS) Hubble Deep Field South and the NTT Deep Field. We have designed a strategy based on a combination of intermediate and broad band filters to identify high--$z$ galaxies against the increasingly large number of interlopers. We emphasize that this is not a ``pre--selection'' survey, but it is designed to provide by itself a reliable identification for the bulk of the galaxy population at $z\\geq 5$. To increase the accuracy of the photometric estimate of the redshift and to minimize the presence of interlopers (mainly intermediate redshift early--type galaxies and late type stars) in our high $z$ sample, we have included a set of intermediate band filters namely IB691, IB834 and IB915, available at the ESO/VLT FORS imager. These filters, although of intermediate width, are relatively efficient since they sample spectral regions devoid of strong sky emission lines. The adopted filter set is thus tailored to trace the peculiar spectral features of the extremely high redshift galaxies, i.e. the flat rest--frame UV continuum that even at $z\\sim 6$ can be sampled by the Z-IB915 color and the very abrupt change of the shape due to the hydrogen absorption spectral breaks by the intergalactic and interstellar medium sampled by the bluer bands. In the following, we will adopt a $\\Lambda$CDM cosmology with $\\Omega_\\Lambda=0.7$, $\\Omega=1$ and $H_0=70$ km/s/Mpc. All magnitudes will be given in the AB system. ", "conclusions": "In this work we have presented the results of a pilot survey aimed at detecting $z>4.5$ galaxies with deep multicolor images. The key features of our approach are {\\it a)} the use of an extended set of broad (UBVRIZJK) and intermediate band ($\\Delta \\lambda \\simeq 400$~\\AA) filters centered at 6900 and 8340~\\AA, {\\it b)} the adoption of conservative thresholds on the S/N for object detection and {\\it c)} the application morphological and spectral criteria: all these aspects improve the estimates of the redshifts, and help exclude or minimize the number of lower $z$ interlopers. When applied to the present data set, these criteria make it possible to reject all the brightest interlopers, that would dominate the LD, and to select a ``minimal'' sample of 4 high--confidence candidates at $z>4.5$, and a sample of 9 additional candidates where the stellar contamination is uncertain. This ambiguity depends on the relative depth of our data set: it is well within the possibilities of red--enhanced imagers at 8--m class telescope or of ACS to extend this kind of analysis 1-2 magnitudes fainter, so that the stellar contamination to the LD can be lowered by a large amount, as in the case of deeper but smaller WFPC2-HDF data that we present here. Even with this ambiguity, the two selected datasets constrain the $z>4.5$ UV LD with sufficient accuracy to show that the {\\it observed} $Z_{AB}<25$ UV LD drops by about one order of magnitude from $z\\simeq 3$ to $z\\simeq 6$. This drop is largely due to the progressively brighter cutoff in the rest frame luminosity function: if we correct for this incompleteness, the UV LD appears to be roughly constant from $z \\simeq 2.5$ up to $z\\simeq 6$. The present results are apparently in contrast with recent findings by Lanzetta et al (2002), who make use of the same WFPC2--HDF data and apply photometric redshifts, that claim the global SFR to steadily increase up to $z=12$. Unfortunately, the overall approach and techniques adopted are so different that it is difficult to make a clean comparison. First, we note that the use of wide aperture magnitude and the adoption of a much higher S/N threshold to the catalog strongly reduce the systematics in the WFPC2 data induced by surface brightness dimming, that otherwise require the complex and model--dependent correction applied by Lanzetta et al (2002). Besides, we draw our conclusions from a homogeneous sample, that includes only objects selected down to the same absolute magnitude limit, rather than correcting for the incomplete coverage of the luminosity function, as done by Lanzetta et al (2002). Finally, the photometric redshift distribution obtained by Lanzetta et al (2002) is markedly different from our own, and peaks at $z\\simeq 0$, a factor that may lead to an overestimate of the faint end of the SFR distribution function that is used to correct the high--$z$ data. Despite all these differences, it is to be noted that the two results are still consistent when the more conservative estimate of Lanzetta et al (2002) is compared with our data in the appropriate redshift range $z\\simeq 3$ to $z\\simeq 6$: given the overall uncertainties both analyses suggest that UV LD is roughly constant in this redshift range. The question that naturally arises is whether a constant UV LD up to $z\\simeq 6$ may be compatible with the hierarchical scenario of galaxy formation. To discuss this point, we present in both panels of fig. 3 the UV LD predicted by the CDM semianalytic model described in Menci et al. (2002). This model is based on the Cole et al (2000) recipes, with an additional improved treatment of aggregation of satellite galaxies in common DM haloes. We first show that the {\\it total} SFR derived from this model (thin solid lines) is nearly constant from $z\\simeq 2$ to about $z\\simeq 5$, and then fades by only a factor about 5 at $z=6$. To allow a fair comparison with our data, we have applied the effects of magnitude limit cut and dust extinction directly to the theoretical model. The effect is shown by the thick solid lines in Fig3a and Fig3b. The shaded area show the possible effects of dust extinction, ranging from no dust (upper lines) to SMC-like extinction curve (lower lines). Please note that the inclusion of dust correction effects in the theoretical model decreases the average UV LD respect to the unextincted amount. It appears that while the CDM model broadly encompasses the observed values, it progressively under-predicts the LD observed in the bright $Z_{AB}<25$ sample, while over-predicts the LD observed in the faintest $I_{AB}<27.2$ sample. This behavior can be understood in term of a poor match to the slope of the UV luminosity function. At the brightest magnitudes, the CDM model under-predicts the number of bright sources, while it over-predicts the number of fainter sources dominating the deeper sample. This is analogous to what already found at $z\\simeq 3$ and confirms a general trend of this version of CDM models to under-predict the amount of star--formation rate in high redshift massive objects (Somerville and Primack 2001, Poli et al 2001 and Menci et al 2002, Cimatti et al 2002). The origin of this discrepancy is likely tied to the lack or to the oversimplified treatment of fundamental physical process. Indeed, we remark that the basic recipes adopted in this model already concur to enhance the SFR in high redshift massive objects, and that these aspects are further boosted with respect to the models that we used in Fontana et al (1999). The star formation rate is computed as $\\dot M_*=M_g/\\tau_*$, where $M_g$ is the amount of cool gas and the time-scale $\\tau_*$ is proportional to the dynamical time $\\tau_{dyn}$ and to the galaxy circular velocity $V_c$ as $\\tau_*=\\epsilon_*^{-1}\\,\\tau_{dyn}\\,\\big(V_c/200\\,{\\rm km/s}\\big)^{\\alpha_*}$. Since both $M_g$ and $1/\\tau_{dyn}$ increase with redshift, and $\\alpha_*=-1.5$, these models naturally predict that the star-formation rate increases with redshift (for a given galaxy mass), and is more efficient in massive galaxies (at a given redshift). In addition, feedback effects are also a strong function of $V_c$, since they scale as $\\big(V_c\\big)^{-5.5}$, and again strongly favor the more massive objects. These basic recipes, combined with the effects of the biased process of galaxy formation induced by hierarchical merging, already conspire to boost at high $z$ the SFR in massive objects, with respect to the less massive one. In the present context, it is not possible to flatten the high--$z$ luminosity function by simply changing the free parameters of the model, since one rapidly worsens the fit to the local observables (Cole et al 2000). Other physical processes that are important in the high--$z$ Universe are not included in our model. On the one hand, mechanical and ionizational feedback on the intergalactic medium by early galaxy and QSO formation is not included in our rendition, a process that is expected to quench the SFR in low mass objects and hereby to flatten the low luminosity side of the LF. On the other hand, molecular cooling is efficient at high $z$ and not included here. Another possibility that has been proposed is that the starburst efficiency increases during major mergers. These ``starburst'' models are known to increase the bright side of the LF at $z=3-4$ (Somerville and Primack 1999), but require new additional free parameters to be introduced in the models, and may become less efficient at $z>5$, when major merging events are very rare. The challenge of the next years is to include all these processes in a self consistent picture that reproduce the high--$z$ observables." }, "0212/astro-ph0212399_arXiv.txt": { "abstract": "The current status of our efforts to trace cosmic structure with $10^6$ galaxies (2MASS), $10^3$ galaxy clusters (NORAS\\,II cluster survey), and precision measurements for $10^2$ galaxy clusters (\\gcss) is given. The latter is illustrated in more detail with results on the gas temperature and metal abundance structure for $10^0$ cluster (A1644) obtained with XMM-Newton. ", "introduction": " ", "conclusions": "" }, "0212/nucl-th0212065_arXiv.txt": { "abstract": "In this paper an equation of state of neutron star matter which includes strange baryons in the framework of Zimanyi and Moszkowski (ZM) model has been obtained. We concentrate on the effects of the isospin dependence of the equation of state constructing for the appropriate choices of parameters the hyperons star model. Numerous neutron star models show that the appearance of hyperons is connected with the increasing density in neutron star interiors. Various studies have indicated that the inclusion of $\\delta$ meson mainly affects the symmetry energy and through this the chemical composition of a neutron star. As the effective nucleon mass contributes to hadron chemical potentials it alters the chemical composition of the star. In the result the obtained model of the star not only excludes large population of hadrons but also does not reduce significantly lepton contents in the star interior. ", "introduction": "Compact stars which are known from observations can be classified into two distinctive groups. The first one is exemplified by white dwarfs and the second by neutron stars. Neutron stars themselves are identify with pulsars and compact X-ray sources \\cite{weber}. At the core of a neutron star the density of matter ranges from a few times of the density of normal nuclear matter to about an order of magnitude higher. Thus various exotic forms of matter such as hyperons or quark-hadron mix phase are expected to emerge in the interior of a neutron star \\cite{weber}. The appearance of these additional degrees of freedom and their impact not only on neutron stars but on proto-neutron stars structure and evolution as well has been the subject of extensive studies \\cite{glen}. Properties of matter at such extreme densities are of particular importance in determining forms of equations of state relevant for neutron stars and in examining their global parameters \\cite{bema}. Theoretical description of hadronic systems should be performed with the use of quantum chromodynamics (QCD) as it is the fundamental theory of strong interactions. However, at the hadronic energy scale where the observed experimentally degrees of freedom are not quarks but hadrons the direct description of nuclei in terms of QCD become inadequate. Other alternative approach has to be formulated one of which is quantum hadrodynamics (QHD) \\cite{walecka} giving quantitative description of the nuclear many body problem. QHD is a relativistic quantum field theory in which nuclear matter description in terms of baryons and mesons is provided. The original model (QHD-I) contains nucleons interacting through the exchange of simulating medium range attraction $\\sigma$ meson and $\\omega$ meson responsible for short range repulsion. Extension (QHD-II) of this theory \\cite{bog77,bodmer,gmuca} includes also the isovector meson $\\rho $. Nonlinear terms in the scalar and vector fields were added in order to get the correct value of the compressibility of nuclear matter and the proper density dependence in the vector self-energy. The variation of nucleon properties in nuclear medium is the key problem in nuclear physics. In order to incorporate quark degrees of freedom in the analysis of nuclear many-body system Guichon \\cite{qmc1} provides a quark-meson coupling model (QMC). The extension of the QMC theory namely the quark mean field model (QMF), describing a nucleon with the use of the constituent quark model, has been successfully applied to study the properties of both nuclear matter and finite nuclei. The model considered in this paper is an alternative version of the Walecka approach with enlarged meson sector. In the interior of neutron stars the density of matter could exceed normal nuclear matter density up to a few times, in such high density regime nucleon Fermi energies exceed the value of hyperon masses and thus the new hadronic degrees of freedom are expected to emerge. The higher the density the more various hadronic species are expected to populate. The onset of hyperon formation depends on the hyperon-nucleon and hyperon-hyperon interactions. Hyperons can be formed both in leptonic and baryonic processes. Several relevant strong interaction processes proceed and establish the hyperon population in the neutron star matter. Neutron star models are constructed at different levels of complexity starting from the most elementary one which assumes that neutrons are the only component. The more sophisticated version is formulated under the assumption that the neutron star matter has to obey the constrains of charge neutrality and $\\beta$ equilibrium. Thus the model considered describes high isospin asymmetric matter and it has to be extended by the inclusion of isovector-scalar meson $a_{0}(980)$ ($\\delta $ meson)\\cite{delta}. For the sake of completness additional nonlinear vector meson interactions are included. When strange hadrons are taken into account uncertainties which are present in the description of nuclear matter are intensified due to the incompleteness of the available experimental data. The standard approach does not reproduce the strongly attractive hyperon-hyperon interaction seen in double $\\Lambda$ hypernuclei. In order to construct a proper model which do include hyperons the effects of hyperon-hyperon interactions have to be taken into account. These interactions are simulated via (hidden) strange meson exchange: scalar meson $f_0 (975)$ ($\\sigma^*$ meson) and vector meson $\\phi (1020)$ ($\\phi $ meson) and influence the form of the equation of state and neutron stars properties. \\newline The solution of the presented model is gained with the mean field approximation in which meson fields are replaced by their expectation values. The parameters used are adjusted in the limiting density range around saturation density $\\rho_0$ and in this density range give very good description in finite nuclei. However, incorporation of this theory to higher density require an extrapolation which in turn leads to some uncertainties and suffers of several shortcomings. The standard TM1 parameter set for high density range reveals an instability of neutron star matter which is connected with the appearance of negative nucleon effective mass due to the presence of hyperons. The Zimanyi-Moszkowski (ZM) \\cite{zima} model in which the Yukawa type interaction $g_{sN}\\varphi$ is replaced by the derivative one $(g_{sN}\\varphi/M_N)\\bar{\\psi}_N\\gamma_{\\nu}\\partial^{\\nu}\\psi$ exemplifies an alternative version of the Walecka model which improves the behaviour of the nucleon effective masses. It also influences the value of the incompressibility $K$ of neutron star matter. The derivative coupling effectively introduces the density dependence of the scalar and vector coupling constants. Knowing the form of the equation of state (EOS) is the decisive factor in determining properties of neutron stars such as: central density, mass-radius relation, crust extent or the moment of inertia.\\\\ The essential goal of this paper is to obtain within the described above model the equation of state for the neutron star matter on the basis of calculations carried out for asymmetric nuclear matter in the relativistic mean field approach (RMF) and to compare the obtained results with ones that are relevant for high density calculations - namely with a quark star. The inclusion of $\\delta$ meson affects the neutron stars chemical composition changing the proton fraction which in turn affects the cooling mechanism. If the proton fraction is higher than the critical value of about $Y_p \\sim 0.11$ \\cite{lat} the direct URCA processes can proceed and this enhances the rate of neutron star cooling. Whether the proton fraction can exceed the critical value and at what density it occurs depends on the model. The proton fraction is almost entirely determined by the isospin-dependent part of the EOS thus the inclusion of $\\delta$ meson and nonlinear vector meson interactions influence the neutron star structure and properties.\\newline This paper is organized as follows. Section 2 outlines the extended model with derivative coupling including hyperons and additional mesons, together with the collected equations of motions. Their solutions enable the construction of the equation of state . In section 3 the equilibrium conditions leading to the relevant hyperon star composition are presented together with the chosen values of parameters. Section 4 contains numerical results and the discussion of their influence on neutron stars properties. ", "conclusions": "In this paper the complete form of the equation of state of hyperon matter has been obtained with the use of the derivative coupling model in the framework of an extended RMF theory which besides hyperons and leptons includes the extended meson sector with additional $\\delta$ meson and hidden strange mesons $\\sigma^*$ and $\\phi$. The model considered is also supplemented with nonlinear vector meson interactions. This enlargement alters the symmetry properties of neutron star matter and through this neutron stars parameters. The value of baryon effective masses depend on the scalar meson condensates and at high densities when hyperon species appear the possibility of negative nucleon masses emerges. The derivative coupling model allows to avoid this difficulty reproducing reasonable value of baryon effective masses for densities relevant for neutron stars. The inclusion of $\\delta$ meson and nonlinear vector meson interactions influences the chemical composition of a neutron star. This is especially evident comparing the effective baryon masses in the density span $(3-4)\\times \\rho_0 $ and equilibrium compositions of the star. For the third group of parameters the higher value of asymmetry has been obtained. This changes the properties of a neutron star diminishing the hyperon core extent. The asymmetry of the system also influence the star radius, for the third group of parameters the one can obtain the lower value of the star radius. There is also possible a configuration representing a star with lower densities (a maximum radius configuration) which excluded the existence of a hyperon core. The model considered excludes a large hyperon fraction which can be connected with thermal properties of a hot neutron star. As the most populated strange baryon is the $\\Lambda$ hyperon it does not reduce significantly number of leptons in the star interior and thus the models calculated with the use of the parameter set I and II do not exclude rapid cooling rate of the star. This is even more evident analyzing the proton fractions obtained for all parameter groups. The equilibrium proton fraction is also determined by the nuclear symmetry energy. The parameter sets I and II permit higher values of proton fraction which is indispensable for URCA processes to proceed. However, the equilibrium proton fraction $Y_p$ is significantly reduced for the third group of parameter.\\\\ Analyzing the gravitational binding energy one can come to the conclusion that configurations with hyperons are energetically favorable than the one obtained with the use of TM1 parameter set for higher densities.\\\\ All assumption which have been made namely: the derivative coupling model being connected with the higher effective baryon masses, the inclusion of $\\delta$ meson and nonlinear vector meson interactions, and the repulsive nucleon-hyperon $\\Sigma$ interaction lead to the neutron star model with the value of maximum mass close to $1.5 \\ M_{\\odot}$ with the reduced value of proton fraction and very compact hyperon core. The calculation of the quark matter equation of state. allows to construct the mass-radius relation for the quark star. Comparing gravitational binding energies one can come to the conclusion that the addition of hyperons to the model shifts the stable hyperon matter configuration towards higher densities even to the density range which is relevant for a quark star and at the same time makes the existence of a pure quark star more problematic." }, "0212/astro-ph0212284_arXiv.txt": { "abstract": "We derive constraints on the mass-temperature relation of galaxy clusters from their observed luminosity-temperature relation and X-ray temperature function. Adopting the isothermal gas in hydrostatic equilibrium embedded in the universal density profile of dark matter halos, we compute the X-ray luminosity for clusters as a function of their hosting halo mass. We find that in order to reproduce the two observational statistics, the mass-temperature relation is fairly well constrained as $T_{\\rm gas} =(1.5\\sim 2.0)\\; {\\rm keV} (M_{\\rm vir}/10^{14}h_{70}^{-1}M_\\odot)^{0.5\\sim 0.55}$, and a simple self-similar evolution model ($T_{\\rm gas} \\propto M_{\\rm vir}^{2/3}$) is strongly disfavored. In the cosmological model that we assume (a $\\Lambda$CDM universe with $\\Omega_0=0.3$, $\\lambda_0=0.7$ and $h_{70}=1$), the derived mass-temperature relation suggests that the mass fluctuation amplitude $\\sigma_8$ is 0.7--0.8. ", "introduction": "While clusters of galaxies are relatively simple dynamical systems that consist of dark matter, stars, and X-ray--emitting hot gas, their thermal evolution is not yet fully understood. This is clearly illustrated by the well-known inconsistency of the observed X-ray luminosity-temperature ($\\Lx$-$T$) relation, $\\Lx \\propto T^3$ \\citep[e.g., ][]{david93, markevitch98, ae99} against the simple self-similar prediction $\\Lx \\propto T^2$ \\citep{kaiser86}. Conventionally this is interpreted as evidence for preheating of intracluster gas; additional heating tends to increase the temperature and the core size of the cluster, and to decrease the central density and the luminosity. Since the effect is stronger for less massive systems, the slope of $\\Lx$-$T$ relation becomes steeper than that of the self-similar prediction \\citep{eh91, kaiser91}. In addition, the mass-temperature ($M$-$T$) relation of clusters is also poorly determined. Although it is conventionally assumed that the gas shock heating is efficient enough and the temperature of the intracluster gas reaches the corresponding virial temperature of the hosting halos, this should be regarded as a simple working hypothesis. Nevertheless, the cosmological parameters derived from the cluster abundances are sensitive to the adopted $M$-$T$ relation. While this has already been recognized for some time (e.g., Figs.5d and 6d of Kitayama \\& Suto 1997), \\citet{seljak02} recently showed in a quantitative manner that the use of the observed $M$-$T$ relation by \\citet*{finogu} decreases the value of the mass fluctuation amplitude at $8\\; h^{-1}\\;$Mpc, $\\sigma_8$, by $\\sim 20\\%$ where $h$ is the Hubble constant $H_0$ in units of 100 km s$^{-1}$ Mpc$^{-1}$ [we use, however, the dimensionless Hubble constant $h_{70} \\equiv H_{0}/(70\\;\\mathrm{km}\\; \\mathrm{s}^{-1}\\; \\mathrm{Mpc}^{-1})$ in the following analysis]. Therefore, the independent derivation of the cluster $M$-$T$ relation is important both in understanding the thermal history of the intracluster gas and in determining the cosmological parameters. Our primary aim in this paper is to find the $M$-$T$ relation of clusters that reproduces the observed $\\Lx$-$T$ relation and X-ray temperature function (XTF). The reason we focus on $M$-$T$ relation is as follows: since recent $N$-body simulations strongly indicate the universality of the density profile of the hosting halos of clusters (\\citealt*{nfw96}; \\citealt{moore98, js00}), the intracluster gas density profile in hydrostatic equilibrium with the underlying dark matter can be computed \\citep*{MSS98, SSM98} for a given mass of the halo. This enables one to make a reliable prediction for the $\\Lx$-$T$ relation once the $M$-$T$ relation is specified. In turn, one can obtain the $M$-$T$ relation that reproduces the observed $\\Lx$-$T$ relation without assuming an ad hoc model for the thermal evolution of intracluster gas. In what follows, we parameterize the $M$-$T$ relation as a single power law, and derive the best-fit values of their amplitude and slope from the observed $\\Lx$-$T$ relation and the XTF. The result is compared with the recent observational studies by \\citet{finogu} and \\citet*{allen}. We also discuss the implications for the value of $\\sigma_8$ from cluster abundances. Throughout the paper, we adopt a conventional $\\Lambda$CDM model with density parameter $\\Omega_{0}=0.3$, cosmological constant $\\lambda_{0}=0.7$, dimensionless Hubble constant $h_{70}=1$, and baryon density parameter $\\Omega_{{B}}=0.04\\;h_{70}^{-2}$. ", "conclusions": "We have presented the constraints on the (empirically parameterized) mass-temperature relation of galaxy clusters from the two different observational data, the luminosity-temperature relation and the temperature function. We summarize in Figure~\\ref{fig:f08} our constraints on the $T_{\\rm gas, 0}$-$p_\\mathit{MT}$ plane, adopting the observed gas mass fraction (eq.~[\\ref{eq:fhotobs500}]). The fact that the simple self-similar evolution model $T_{\\rm gas} \\propto M_{\\rm vir}^{2/3}$ fails to explain the observed $\\Lx$-$T$ relation is well known and not at all new. Rather, it should be noted that the mass-temperature relation of galaxy clusters is fairly well constrained by combining the observed $\\Lx$-$T$ relation and XTF. It is encouraging that $T_{\\rm gas} =(1.5\\sim 2.0)\\; {\\rm keV} (M_{\\rm vir}/10^{14}\\;h_{70}^{-1}\\;M_\\odot)^{0.5\\sim 0.55}$ barely satisfy the two constraints simultaneously. This conclusion applies for $1\\le \\alpha \\le 3/2$ as long as the dark halo density profile is described by equation (\\ref{eq:nfw}). In addition, our analysis implies that the amplitude of the mass variance $\\sigma_8$ in the standard $\\Lambda$CDM model should be 0.7--0.8. These values are significantly smaller than the previous estimates \\citep{vl96, eke96, KS97} but in better agreement with more recent results \\citep{seljak02, efsta}. Since our current analysis has adopted a simple parameterized model for the mass-temperature relation, the result should be understood by a physical model of the thermal evolution of the intracluster gas. For instance, our result may be qualitatively explained by a kind of phenomenological heating of $T_{\\rm gas}(M_{\\rm vir}) = T_{\\rm vir}(M_{\\rm vir}) + 1\\; $keV. We plan to examine the implications for the possible heating sources from the derived mass-temperature relation of galaxy clusters using the Monte-Carlo modeling of merger trees." }, "0212/astro-ph0212237_arXiv.txt": { "abstract": "{ We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation. Due to the conditions of charge neutrality and $\\beta$-equilibrium the flavor asymmetry increases with the number density of trapped antineutrinos. Above a critical value of the antineutrino chemical potential of $30$ MeV diquark condensation is inhibited at low densities and a two-phase structure emerges: a superconducting quark matter core surrounded by a shell of normal quark matter. When the quark star cools down below a temperature $T \\sim 1$ MeV, the mean free path of antineutrinos becomes larger than the thickness of the normal quark matter shell so that they get untrapped within a sudden process. By comparing the masses of configurations with the same baryon number we estimate that the release of energy due to the antineutrino untrapping transition can be in the range of $10^{51} \\div 10^{52}$ erg. ", "introduction": "\\label{sec:intro} The engine which drives supernova explosions and gamma ray bursts being among the most energetic phenomena in the universe remains still puzzling [\\cite{Piran:2001da}]. The phase transition to a quark matter phase may be a mechanism that could release such an amount of energy [\\cite{Drago:1997tn}, \\cite{Berezhiani:2002ea}]. It has been proposed that due to the Cooper instability in dense Fermi gases cold dense quark matter shall be in the color superconducting state with a nonvanishing diquark condensate [\\cite{Alford:2000sx}, \\cite{Blaschke:2001uj}]. The consequences of diquark condensation for the cooling of compact stars due to changes in the transport properties and neutrino emissivities have been investigated much in detail, see [\\cite{Blaschke:1999qx}, \\cite{Page:2000wt}, \\cite{Blaschke:2000dy}, \\cite{Blaschke:2003yn}], and may even contribute to the explanation of the relative low temperature of the pulsar in the supernova remmant 3C58 [\\cite{cooling}]. Unlike the case of normal (electronic) superconductors, the pairing energy gap in quark matter is of the order of the Fermi energy so that diquark condensation gives considerable contributions to the equation of state (EoS) of the order of $({\\Delta}/{\\mu})^2$. Therefore, it has been suggested that there might be scenarios which identify the unknown source of the energy of $~10^{53}$ erg with a release of binding energy due to Cooper pairing of quarks in the core of a cooling protoneutron star [\\cite{Hong:2001gt}]. In that work the total diquark condensation energy released in a bounce of the core is estimated as $({\\Delta}/{\\mu})^2M_{{\\rm core}}$ corresponding to a few percent of a solar mass, that is $~10^{52}$ erg. In this estimate, general relativistic effects have been disregarded. It has been shown in [\\cite{Blaschke:2003yn}] by solving the selfconsistent problem of the star configurations, however, that these effects due to the stiffening of the EoS in the diquark condensation transition lead to an increase in the gravitational mass of the star contrary to the naive estimates. It has also been demonstrated [\\cite{Blaschke:2003yn}] that the energy release due to cooling of a quark core in a protoneutron star does not occur whithin an explosive process, since the diquark condensation is a second order phase transition. In the present work, we propose a new mechanism of energy release which involves a first order phase transition induced by antineutrino untrapping. (Anti-)neutrino trapping occurs in hot compact star configurations at temperatures $T\\geq 1$ MeV where the mean free path of (anti-)neutrinos is smaller than the typical size of a star [\\cite{Prakash:2001rx} and references therein]. During the collapse in the hot era of protoneutron star evolution, antineutrinos are produced due to the $\\beta$-processes. Since they have a small mean free path, they cannot escape and the asymmetry in the system is increased. This entails that the formation of the diquark condensate is shifted to higher densities or even inhibited depending on the fraction of trapped antineutrinos. As the quark star cools, a two-phase structure will occur. Despite the asymmetry, the interior of the quark star (because of its large density) could consist of color superconducting quark matter, whereas in the more dilute outer shell, diquark condensation cannot occur and quark matter remains in the normal state, opaque to antineutrinos for $T\\geq 1$ MeV. When in the continued cooling process the antineutrino mean free path increases above the size of this normal matter shell, an outburst of neutrinos occurs and gives rise to an energy release of the order of $10^{51}-10^{52}$ erg. This untrapping transition is of first order and could lead to an explosive phenomenon. The scenario to be detailed in the present paper suggests that the first pulse of neutrinos emitted in the deleptonization stage of the core collapse, after a cooling time scale, shall be followed by a second pulse of antineutrinos as an observable characteristics of the present scenario. ", "conclusions": "We have investigated the effects of trapped antineutrinos on the asymmetry and diquark condensates in a quark star configurations. By comparing configurations with fixed baryon number the release of energy in an antineutrino untrapping transition is estimated to be of the order of $10^{52}$ erg. Such a transition is of first order so that antineutrinos can be released in a sudden process (burst). This scenario could play an important r\\^ole to solve the problem of the engine of supernova explosions and gamma ray bursts. A second antineutrino pulse is suggested as an observable characteristics of the present scenario." }, "0212/astro-ph0212371_arXiv.txt": { "abstract": "Within the framework of a model Universe with time variable space dimensions (TVSD), known as decrumpling or TVSD model, we study TVSD chaotic inflation and obtain dynamics of the inflaton, scale factor and spatial dimension. We also study the quantum fluctuations of the inflaton field and obtain the spectral index and its running in this model. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. We compare our results with the recent Wilkinson Microwave Anisotropy Probe (WMAP) data. ", "introduction": "One of the most intriguing challenges in modern physics is to find observable consequences of different kinds of theories in higher dimensions. We here present an inflationary model, known as decrumpling inflation model in which the number of spatial dimension has a dynamical behavior and decreases during the expansion of the Universe with a rate to be less than about $10^{-14} {\\rm yr}^{-1}$.\\cite{1} Our motivation to study decrumpling inflation is to investigate cosmological implications of time variability of the number of spatial dimensions. To do so, we compute the spectral index and its running within the framework of decrumpling inflation. For more details about a model Universe with time variable space dimensions (TVSD), known as TVSD or decrumpling model, see Refs. [1-6]. To do this research an important conceptual issue is properly dealt with the meaning of time variability of the number of spatial dimensions. In Ref. [5], this conceptual issue has been discussed in detail. Although time variability of spatial dimensions have not been firmly achieved in experiments and theories, such dynamical behavior of the spatial dimensions should not be ruled out in the context of cosmology and astroparticle physics. Here, we will be concerened with the approaches proposed in the pioneer paper\\cite{12} where the cosmic expansion of the Universe is named decrumpling expansion and is due to decrease of the number of spatial dimensions. The most important difference between decrumpling model and other attempts about the time evolution of spatial dimension is that in this model the number of extra spatial dimensions changes with time while in other theories the size of extra spatial dimensions is a dynamical parameter. Based on time variability of the size of spatial dimensions it has been reported\\cite{1} that the present rate of change of the mean radius of any additional spatial dimensions to be less than about $10^{-19} {\\rm yr^{-1}}$. It is worth mentioning that this result is based on dynamical behavior of the size of extra spatial dimensions while in decrumpling model we take the size of extra spatial dimensions to be constant and the number of spatial dimensions decreases continuously as the Universe expands. The present rate of time variation of the number of the spatial dimensions in decrumpling or TVSD model is about $10^{-13} {\\rm yr^{-1}}$.\\cite{1} Another subject which lately has attracted much attention is the scalar spectral index and its running. Primordial perturbations from inflation currently provide our only complete model for the generation of structure in the Universe. It is commonly stated that a generic prediction of inflationary models is a scale-invariant spectrum of adiabatic perturbations, characterized by a scalar spectral index $n_S$ that obeys $n_S-1=0$. However, this statement is only true for very special spacetimes like a pure de Sitter spacetime, which does not describe our cosmological history. For nearly all realistic inflationary models, the value of $n_S$ will vary with the wave number $k$. Typically, since $n_S-1\\simeq 0$ on the scales probed by the cosmic microwave background (CMB), the deviations from a constant $n_S$ must be small. Nevertheless, increasingly accurate cosmological observations provide information about the scalar spectral index on scales below those accessible to anisotropy measurements of the CMB. Our such a wide range of scales, it is entirely possible that $n_S$ will exhibit significant running, a value that depends on the scale on which it is measured. Such running is quantified by the derivative $dn_S/d\\ln k$ and, in fact, recently released data from the WMAP satellite indicates that\\cite{7} \\begin{eqnarray} \\label{1} n_S\\;(k_0=0.05\\;\\;{\\rm Mpc}^{-1})&=&0.93^{+0.03}_{-0.03},\\\\ \\label{2} \\frac{dn_S}{d\\ln k}\\;(k_0=0.05\\;\\;{\\rm Mpc}^{-1})&=& -0.031^{+0.016}_{-0.018}. \\end{eqnarray} The limits on the $n_S$ and its running using WMAP data alone are\\cite{8} \\begin{eqnarray} \\label{3} n_S\\;(k_0=0.002\\;\\;{\\rm Mpc}^{-1})&=&1.20^{+0.12}_{-0.11},\\\\ \\label{4} \\frac{dn_S}{d\\ln k}\\;(k_0=0.002\\;\\;{\\rm Mpc}^{-1})&=& -0.077^{+0.050}_{-0.052}, \\end{eqnarray} where $k_0$ is some pivot wave number. Recent data, including that from the WMAP data satellite, show some evidence that the index runs (changes as a function of the scale $k$ at which it is measured) from $n_S>1$ (blue) on long scales to $n_S<1$ (red) on short scales. The authors of Ref.[9] investigated the extent to which inflationary models can accommodate such significant running of $n_S$. They show that within the slow-roll approximation, the fact that $n_S-1$ changes sign from blue to red forces the slope of the potential to reach a minimum at a similar field location. Chaotic inflation models are usually based upon potentials of the form $V(\\phi)=a \\phi^b$ ($a$ is a constant and $b=2,4,...$ is an even integer). For the interesting cases of $b=2$ and $4$, it has been shown that\\cite{10} \\begin{eqnarray} \\label{5} \\frac{dn_S}{d\\ln k}=-0.8\\times 10^{-3}\\;(b=2,\\;{\\cal{N}}=50),\\\\ \\label{6} \\frac{dn_S}{d\\ln k}=-1.2\\times 10^{-3}\\;(b=4,\\;{\\cal{N}}=50), \\end{eqnarray} where ${\\cal{N}}$ is the e-folding number. We will use the natural units system that sets $k_B$, $c$, and $\\hbar$ all equal to one, so that $\\ell_P=M_P^{-1}=\\sqrt{G}$. To read easily this article we also use the notation $D_t$ instead of $D(t)$ that means the space dimension $D$ is as a function of time. The plan of this article is as follows. In section 2, we give a brief review of decrumpling or TVSD model. In section 3, we present the dynamical solutions of $\\phi(t)$, $a(t)$ and $D_t(t)$. In section 4, we first present the explicit and general formulae for the spectral index and its running within the framework of decrumpling or TVSD inflation and then apply them to two classes of examples of the inflaton potential. Finally, we discuss our results and conclude in section 5. ", "conclusions": "In previous our studies about time variable spatial dimension model\\cite{1} we showed that based on observational bounds on the present-day variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was at the Planck length to be less than or equal to $3.09$. In [1] we concluded that if the dimension of space when the Universe was at the Planck scale is constrained to be fractional and very close to $3$, then the whole edifice of TVSD model loses credibility.\\cite{1} In this paper, we have studied the effects of time variability of the spatial dimension on the time evolution of inflaton field, space dimension and scale factor for the potential $m^2\\phi^2/2$. We have also obtained general and explicit formulae for the scalar spectral index and its running in TVSD or decrumpling model and then applied them to two classes of examples of the inflaton potential. The correction terms due to time variability of space dimension depend on the e-folding number and the universal constant of TVSD model which is $C$. The numerical calculations for the spectral index and its running have been done for two classes of examples. We have also discussed on dynamical solutions of inflaton field, scale factor and space dimension in TVSD or decrumpling chaotic inflation model. The outline of results has been shown in Figs. 1, 2 and 3. Fig.1 compares inflaton field within the framework of TVSD model and the constant three-space chaotic inflation. It is seen time variability of space dimension causes that inflaton field evolves slowly. This behavior of the scalar field can be seen by Eq. (\\ref{15}) where the effect of time variable dimension is like decreasing friction term in this equation, or subsequently causes that the scalar field changes slowly. In Fig. 2 the evolution of space dimension has been obtained. It is seen from Eq. (\\ref{11}) that temporal rate of space dimension is proportional to the square of space dimension. So during the inflationary epoch the Universe with $D_{P} = 10$ loses $6$ dimensions in comparison to $D_{P} = 4$ which loses less than one. In other words, $\\Delta D_{\\rm inflation}^{D_{P} = 10} = 6$ and $\\Delta D_{\\rm inflation}^{D_{P} = 4} <1 $. From Fig.3 it is seen that dynamical character of the space dimension increases the e-folding number.\\cite{4} Starting an Universe with higher dimensions at the Planck epoch, it leaves inflationary phase later.\\cite{3} The final point that must be emphasized is about decrumpling model in cosmology. The original motivation of this model presented in the pioneer paper\\cite{12} was based on an {\\it ad hoc} assumption inspired from polymer physics. It is quite possible that this part of decrumpling model should be revised. However, just how this should be done is far from obvious. The progress in decrumpling model can only be made if there is a breakthrough in terms of finding a natural mechanism for varying the spatial dimension in some alternative fashion to that which we have considered." }, "0212/astro-ph0212479_arXiv.txt": { "abstract": "The spectra of stars with the B[e] phenomenon are dominated by features that are related to physical conditions of circumstellar material around these objects and are not intrinsic to the stars. Because of this, they form a very heterogeneous group. This group contains objects with different evolutionary stages. Lamers et al. (1998) have suggested a new designation with five sub-groups, which indicate the evolutionary stage. They are: supergiants, pre-main sequence or Herbig Ae/Be, compact planetary nebulae, symbiotic and unclassified. The unclassified group has many objects that need a better study to resolve their evolutionary status. Forbidden lines can be a useful tool to solve this problem. They can give informations about chemical composition, ionization and density of the circunstellar medium and probably the evolutionary phase of these objects. We analize spectra of some galactic objects, obtained with FEROS and B\\&C spectrograph at 1.52 telescope in ESO (La Silla-Chile), with a special focus on the forbidden lines. We have studied the spectra of 5 B[e] stars of uncertain evolutionary stage. We find that one of them is a pre-WN star, the other four are supergiant B[e] stars. ", "introduction": "The presence of some forbidden lines is a criterion to distinguish differents groups of massive stars. For example, LBV and sgB[e] have similar spectral characteristics, however, [OI] lines are present only in the sgB[e] (Zickgraf, 1989). Below, we have a table showing the presence (Yes) or not (No) of some important forbidden lines. Figure 1 shows the profiles of forbidden and permitted NII lines in the spectra of HD 326823. \\vskip 0.4truecm \\begin{center} {\\small \\begin{tabular}{|c|c|c|c|c|c|c|} \\hline \\multicolumn{1}{|c|}{ Objects } & \\multicolumn{1}{|c|}{ [OI] } & \\multicolumn{1}{|c|}{ [OII] } & \\multicolumn{1}{|c|}{ [OIII] } & \\multicolumn{1}{|c|}{ [SII] } & \\multicolumn{1}{|c|}{ [NII] } & \\multicolumn{1}{|c|}{ [FeII] } \\\\ \\hline \\hline HD 87643 & Yes & No & No & Yes & No & Yes\\\\ Hen 3-847 & Yes & No & No & Yes & Yes & Yes \\\\ GG Car & Yes & No & No & No & Yes & Yes \\\\ MWC 300 & Yes & No & No & Yes & Yes & Yes \\\\ HD 326823 & No & No & No & Yes & Yes & Yes \\\\ \\cline{1-3} \\hline \\end{tabular} } \\end{center} \\vskip 60truecm \\vbox{\\special{psfile=fig1.ps angle=0 vscale=27 hscale=37 voffset=-190 hoffset=65}} \\vskip 5.5truecm \\noindent {\\footnotesize {\\bf \\it Figure 1 -}Profiles of NII lines in the high resolution spectrum (FEROS-agreement ESO/ON) of HD 326823. The permitted lines are in absorption, indicating a photospheric origin, and the forbidden are in emission, indicating a circumstellar origin. } ", "conclusions": "" }, "0212/astro-ph0212153_arXiv.txt": { "abstract": " ", "introduction": "Extremely Red Objects (EROs), which have optical-to-infrared colors which differ significantly from typical field sources, encompass a wide variety of phenomen\\ae. Galaxies of assorted types make up the dominant component of ERO samples, but one can also find low mass stars, gravitationally lensed sources, and transient sources such as variable stars, asteroids or supernovae which may not be initially recognized as such. The term Extremely Red Galaxies (ERGs) is also commonly used, sometimes interchangeably, but usually refers to a sample of EROs which has been cleaned of the objects which are not galaxies. ERGs are therefore a subset of the EROs. We adopt the more general term ERO throughout this paper. Both the definition and interpretation of EROs has evolved somewhat since their initial discovery, and it is useful to review the subject here for some historical perspective. When first identified as a distinct population of sources ~\\citep{ERR88}, EROs were thought to be good candidates for primeval galaxies. Subsequent observations ~\\citep{ERR89}, however, showed these early EROs to be $z \\sim 0.8$ elliptical galaxies. Additional EROs were noted in the following years \\citep{MPW92,ED92,Pea93,Graham94,HR94,Sea94,DSD95,Dj95,Treu98,Im02}. Most of these were serendipitous detections, identified on images targeting known, high-redshift radio galaxies or other active galactic nuclei. Little or no followup work was done on these objects at the time, which to some extent reflected the limited capabilities of existing instruments and telescopes. These EROs were identified with colors spanning a wide range: ($R-K$)\\,$\\geq$\\,5--7, or ($I-K$)\\,$\\geq$\\,4--6. A resurging interest in EROs accompanied the development of the Submillimeter Common User Bolometer Array \\citep[SCUBA]{SCUBA}, and the subsequent detection of the extremely red galaxy HR\\,10 ~\\citep[this source is also known as HR94\\,10 or ERO\\,J164502+4626.4]{HR94} at 850\\,$\\mu$m ~\\citep{cim98,dey99}. At a redshift of 1.44 ~\\citep{GD96}, the detection of HR\\,10 in the submillimeter implied the presence of massive quantities of dust accompanied by very high star formation rates. The ERO population was thought to provide fertile hunting grounds for more submillimeter-bright galaxies at high redshift. Additional observations have not supported this idea, however, with only a relatively small fraction, on the order of 20\\% ~\\citep[Thompson, priv. comm.]{and99,mohan02}, of the bright EROs ($K < 19.5$) showing strong submillimeter emission. The development of larger-format infrared arrays and wider field instrumentation enabled subsequent field surveys to cover enough area to assemble significant samples of systematically selected EROs for further study, in blank fields ~\\citep{tho99,daddi00a,LCIR01} as well as targeted surveys ~\\citep{Chap00,Cim00,Liu00}. \\citet{tho99} adopted a color selection for EROs of ($R-K$)\\,$>$\\,6\\fm0. The motivation was that this color was redder than the expected colors of elliptical galaxies with anything but the highest formation redshifts ($z_f > 10$), and thus represents an extreme color for any normal galaxy. The assumption at the time was that the extremely red galaxy population consisted of either old ellipticals or young, dusty starbursts ~\\citep{cim98,tho99,dey99}. The relative contribution of these two types of galaxies would have a bearing on the timing of massive galaxy formation and their subsequent evolution. It is important to emphasize that, at that time, the term ``young, dusty starbursts'' referred specifically to massive starbursts like that seen in HR\\,10 or luminous infrared galaxies. Multi-band photometry could potentially distinguish between ellipticals and starbursts ~\\citep{PM00}, but this technique requires very low photometric uncertainties to work well (see, for example, ~\\citet{Mea02}). In order to better study the $z \\sim 1$ elliptical galaxy population, \\citet{daddi00a} adopted a bluer color selection limit, ($R-K$)\\,$>$\\,5.3, set by the expected colors of a $z = 1$ passively evolving old stellar population. This definition, or the roughly equivalent ($I-K$)\\,$>$\\,4.0, for the ERO color selection criterion has generally been adopted in the majority of subsequent work. While there are a number of redshifts now known for EROs ~\\citep{GD96,Sea99,Liu00,afonso01,smith02b}, systematic redshift surveys of complete samples are only now becoming available ~\\citep{cim02}. Morphological information based on high-resolution HST imaging for complete samples of EROs are also only now starting to appear ~\\citep[this work]{smith02a}. Without similar spectroscopic or morphological information, earlier ERO surveys divided the ERO population into two components: old, evolved systems or dusty, massive starbursts. But the true nature of K-selected EROs is likely to be much more complex, as suggested by recent work ~\\citep{LCIR01,cim02}. ~\\citet{LCIR01} find a large scatter in the $(V - I)$ colors of their ERO sample, best fit by passive evolution models with extended star formation ($\\tau = 1$~Gyr). This implies that the star formation history of EROs is more complex than a binary division into evolved ellipticals or dusty, massive starbursts implies. From their K20 survey, ~\\citet{cim02} found that about half of their spectroscopic sample of $\\sim$30 EROs are dusty star-forming galaxies with emission lines, while the remaining half are old stellar populations with absorption line spectra. However, the simple presence of line emission could span a wide range of galaxy types, from bulge-dominated, late type spiral galaxies with a small amount of star formation through the more massive starbursts like HR\\,10. Dust could also completely obscure any on-going star formation, to the point that the optical and UV emission lines are not seen ~\\citep{PW00}. Examples of what appear to be quiescent disks at $z \\sim 1.5$ exist ~\\citep{dokk01,smith02b}. There are important differences in the formation and evolution of quiescent normal galaxies and young, dusty, massive starbursts. Morphologies have the potential to distinguish between the various interpretations, which motivated this work. In this paper, we present the high resolution morphologies derived from HST WFPC2 images for a large sample of K-selected EROs. Our results reveal for the first time a new type of ERO which dominates the population and is neither an early-type galaxy nor a dusty, massive star forming galaxy. We will also discuss the implications of our results for the past and future evolution of massive galaxies at $z \\sim 1$. ", "conclusions": "\\subsection{Morphological Distribution} Our morphologies are based on F814W images. Assuming the median redshift of one for EROs from the ~\\citet{cim02} sample with K$ \\leq 19.2$, the WFPC2 data sample a rest-frame wavelength of 4100\\,\\AA. The F814W images thus represent a compromise between sensitivity to star formation at shorter restframe wavelengths and better probing any extended old stellar populations at longer restframe wavelengths. As shown in simulations by ~\\citet{hibvac97}, morphological classifications using F814W images do not show any significant biases at $z \\sim 1$. Using the results from our visual classification, we find that 30$\\pm$5\\% of our EROs have morphologies consistent with spheroidal (B and BD) galaxies. Disks (D and DB) dominate the EROs at 64$\\pm$7\\%\\ of the sample. Only 6\\% of the EROs were unclassifiable, due primarily to low SNR on the WFPC images. The uncertainties are derived simply from the square root of the number of EROs in that subset, and does not try to include the unclassifiable sources. We plot in Figure~\\ref{relfrac} the relative fractions of spheroids and disks in our visual classification as well as from the MDS profile fitting. \\begin{figure}[!ht] \\plotone{f7.eps} \\caption{Relative fraction of spheroidal galaxies vs. disks as classified in this survey (gray bars) and by the MDS automated profile fitting (white bars). Not included in this plot are the 6\\% of sources unclassifiable by us or the 14\\% unclassified by the MDS. \\label{relfrac}} \\end{figure} We find that the relative morphological mix of EROs in subsets constructed of the EROs in known foreground galaxy cluster fields vs. those selected in the remaining ``blank'' fields is consistent to within the uncertainties. Since any lensing should be unbiased with respect to background galaxy morphologies, we do not differentiate between cluster and field sources in the remaining analysis. Some of the EROs, including both disks and spheroids, appear to be involved in recent mergers or show evidence of strong interactions (e.g. tidal tails, strong asymmetries). These comprise 17$\\pm$4\\% of the sample. Without additional information, these systems represent the most likely source of possible large-scale starbursts. This is consistent with the observation that among {\\it bright} EROs, roughly 20\\% have 850$\\mu$m detections ~\\citep{and99}. One third of the galaxies we classed as spheroids have one or more faint companions or show signs of recent interaction, suggesting that a significant fraction of otherwise old stellar populations may not be in purely passively evolving systems. The morphological classifications derived from the MDS profile fitting are largely consistent with our visual results, but show a slightly higher fraction of spheroidal galaxies, with 37$\\pm$6\\% of the sample classed as B or BD (with a bulge fraction larger than 50\\%). There is a corresponding drop in the disk fraction, with 50$\\pm$7\\% classed as DB or D, but disks still dominate the overall $\\rm (I-K)\\geq 4$ ERO population. A larger fraction of the sample, 14$\\pm$3\\%, were not fit with the bulge$+$disk models due to low SNR or a more conservative avoidance of the CCD edges in the WFPC2 data. We find that our ERO sample selected with $(F814W - Ks) \\geq 4$ is dominated by disk galaxies, and not by spheroids or strongly interacting systems. The star formation rates in these disks could span a wide range, including normal galaxies with fairly quiescent star formation. HR\\,10 type systems, with mostly young stars and undergoing massive starbursts, may comprise only a small fraction of the sample. The origins of their red colors may be traced to a significant old stellar population combined with some dust extinction, especially considering the edge-on orientation of many of the disks in our sample of EROs. Even though most of the stellar mass may already be in place by $ z \\sim 1 - 2$ for these EROs, such a large fraction of disk galaxies implies that there is still a substantial amount of gas available to feed on-going star formation. The existence of such a large fraction of disk galaxies and interacting systems in our sample suggests that hierarchical merging may be an important mechanism for the formation and evolution of the ERO population. However, the scenario in which ellipticals were formed in a ``monolithic collapse'' at high redshifts and evolve passively thereafter cannot be excluded. While 30\\% of our ERO sample are clearly early type galaxies, whose colors are consistent with old stellar populations formed at high redshifts. We also found that one-third of the spheroids in our sample have faint companions or signs of interaction. This suggests that although a majority of their mass could be assembled rapidly at high redshift, these systems are not simply isolated, passively evolving old stellar populations, and continuing accretion of gas or merger events plays a significant role in their evolution. Examples of secondary star formation in field E/S0s ($z \\sim 0.1 - 0.73$) can be found in ~\\citet{treu02}. Our results contradict those of ~\\citet{mor00}, which are also based on HST morphologies. They find that 50--80\\%\\ of their sample have E/S0 morphologies on the basis of one-component exponential model fits. However, we note that their ERO sample was assembled from the published literature, with the corresponding heterogeneous selection functions of the original surveys. In addition, the morphologies were determined on HST images from both WFPC2 and NICMOS, probing widely different rest-frame wavelengths and thus differing sensitivities to star formation or old stellar population. \\subsection{Surface Density} \\label{SDsect} The integrated surface density of EROs, is defined as total number of EROs brighter than a given magnitude per unit area on the sky. Because the area covered in this survey is a function of the magnitude, the differential number of EROs selected in each magnitude bin is a function of both the magnitude and the area surveyed. Calculating the integrated surface density thus required rescaling the number of EROs in each of the brighter bins by the appropriate area ratio prior to integration. We plot the resulting surface density of EROs from our survey derived by this method in Figure~\\ref{surfdens} (filled diamonds). The uncertainties were derived simply from the square root of the rescaled number of EROs. \\begin{figure}[!ht] \\plotone{f8.eps} \\caption{Cumulative ERO surface density from this work (filled diamonds), as well as several other surveys for comparison. The uncertainties are derived assuming only Poisson counting statistics in each bin. \\label{surfdens}} \\end{figure} For comparison, we also plot in Figure~\\ref{surfdens} the results from other recent surveys ~\\citep{tho99,smith02a,daddi00a,LCIR01,cim02,barg99}. The primary difficulty in making such comparisons is that each survey used a different set of filters and different selection criteria for identifying EROs. In order to make a general comparison between these disparate surveys, we make several simplifying assumptions. First, we treat all K filters as functionally equivalent (e.g. $K == K^\\prime == K_s$), so no color terms are applied to convert magnitudes between them. The same is true for the several different I filters and R filters used. We note that these assumptions are generally made in most recent published ERO surveys unless the color selection limit is explicitly tied to some fiducial model SED, typically a passively evolving $z=1$ old stellar population (i.e. elliptical galaxies), {\\em and} the specific filters used for the survey. Second, we adopt the generic colors of ($R-I$)$=$1\\fm3 and ($H-K$)$=$1\\fm0 to convert the surveys based on R band or H band data to our $I-K$ colors. Third, we plot without additional correction the ~\\citet{cim02} results, even though they select EROs at a bluer limit: ($R-K_s$)$\\geq$5\\fm0. Finally, we adopt the ~\\citet{barg99} results directly for ($I_c-HK^\\prime$)$\\geq$3\\fm7, which they show to be equivalent to ($I-K$)$\\geq$4\\fm0 for that filter set. While the generic color conversions we adopt obviate the possibility of more detailed comparisons between the different ERO surveys, they do allow us to consider broad trends in the surface densities as a function of the selection filters. First, the two I-band based surveys (this work and ~\\citet{LCIR01}) agree quite well over the region $17^{\\rm m} \\leq K_s \\leq 19^{\\rm m}$. This suggests that our sample is neither significantly inhomogeneous nor incomplete over this range, although the turnover in counts to fainter magnitudes suggests incompleteness in our sample for $K>19^{\\rm m}$. The two larger R-band based surveys ~\\citep{tho99,daddi00a} also agree with each other over this same range in K-band magnitude, but are systematically about a factor of three lower than the I-band surveys. The lensing-corrected surface density of EROs from the cluster-pointed survey of ~\\citet{smith02a}, despite using an R-band filter, agrees well with the I-band based surveys at brighter magnitudes ($K<19^{\\rm m}$). The other two surveys, ~\\citet{cim02,barg99}, differ from the other results. Aside from the uncertainties in converting from one filter system to another, there are two primary effects which can qualitatively account for the similarities and differences in the surface densities of EROs from these different surveys: cosmic variance, and color selection effects. Both the ~\\citet{cim02} and ~\\citet{barg99} surveys cover relatively small, connected areas on the sky, and are thus more subject to cosmic variance, especially considering the strong clustering seen in ~\\citet{daddi00a}. The ~\\citet{smith02a} survey is composed of 10 widely-separated sight lines and thus should be less sensitive to cosmic variance, but their sample does show a wide field-to-field variation in the number of EROs. ~\\citet{cim02} selects EROs at a bluer limit, ($R-K_s$)$\\geq$5\\fm0, which likely contributes to their higher ERO surface density. A color selection effect may contribute to the apparent differences in surface density between R-band based ~\\citep{tho99,daddi00a} and I-band based (this work and ~\\citet{LCIR01}) ERO surveys. We offer below (see \\S\\ref{ColSel}) a qualitative argument on this, as we do not have a proper multiband deep survey to address this with real data. \\subsection{Volume Density} We can make an estimate of the volume density of EROs with some assumptions on the range of redshifts at which they may be found, and compare these results with the local density of massive galaxies. The color selection limit of ($I-K$)\\,$\\geq$\\,4\\fm0 sets the lower redshift bound to $z = 1$, which is appropriate for passively evolving old stellar populations. However, photometric uncertainties could make this $z = 1$ boundary somewhat fuzzy. Galaxies with significant dust extinction (see the following section) could also lie at lower redshifts. \\citet{cim02} obtained spectroscopic redshifts for a sample of EROs with ($R-K$)$>$5 which includes sources of both types down to $z \\sim 0.7$. We adopt an upper cutoff to the assumed redshift range of $z = 2$, as higher redshift EROs would be anomalously luminous given their bright $K$-band magnitudes. Under the above assumptions, we derive a co-moving volume covered by our survey to be $4\\times10^5\\,h_{70}^{-3}$\\,Mpc$^3$. This volume is only weakly dependent on the assumed redshift range, and only changes by a factor of two if the redshift range is narrowed to $z \\sim 1.0 - 1.5$ or broadened to $z \\sim 0.7 - 2.8$. This volume was derived from the total survey area of 409 square arcminutes, and does not take into account the variable survey depth with magnitude. The galaxies classed as spheroids in our survey have a co-moving volume density of $1\\times10^{-4}\\,h_{70}^3$\\,Mpc$^{-3}$. The disks have a co-moving volume density about twice as large, and the total ERO sample (115 EROs) reach a density of $3\\times10^{-4}\\,h_{70}^3$\\,Mpc$^{-3}$. To compare with nearby massive galaxies, we adopt the local K-band luminosity functions for early-type and late type galaxies from ~\\citet{Kochanek01}. We integrate from 10L$^*$ down to 1L$^*$, which corresponds to our K-band limit at $z = 1$ after correcting for passive evolution and cosmological K-corrections. We find that the EROs can account for only one-third of the local massive galaxies, and that the relative morphological mix is about the same in the two samples. This is reasonable, but should be considered only an order-of-magnitude agreement given the factors of $\\sim$2 uncertainties in the volume densities arising from the assumptions on the redshift distributions, area surveyed as a function of depth (\\S\\ref{sec:area}), and contamination (\\S\\ref{sec:eodisks}). \\subsection{Dust Extinction in Disky EROs} \\label{sec:eodisks} While classifying the EROs, we also noted that 40\\% of the disky systems (DB and D) appeared to be sufficiently edge-on that even small amounts of dust in a disk could have a disproportionately large effect on the overall system color. These systems are noted in Table~\\ref{ERO_tab} with italicized entries under morphology: {\\em DB} and {\\em D}, and we show two examples of edge-on EROs in Figure~\\ref{edgeon}. This is far more than expected from a set of randomly oriented galaxies, suggesting that orientation effects are responsible for their inclusion in the ERO sample. \\begin{figure}[!ht] \\plotone{f9.eps} \\caption{Examples of two edge-on disks where dust extinction may contribute significantly to their overall ($I-K_s$) color. Each image is 8'' square. The labels correspond to their source numbers from Table~\\ref{ERO_tab}. \\label{edgeon}} \\end{figure} Given the potentially large extinctions possible from dust in otherwise normal disk galaxies, it is possible that the edge-on systems are at lower redshift ($z < 1$). Several of these show extended disks of large apparent size (several arcseconds), which would be unusually large (tens of kiloparsecs) if at $z \\sim 1$ or more. The edge-on systems comprise half of the disky EROs, or one-third of the total ($I-K$) selected ERO sample. They thus represent a large and previously unanticipated source of contamination in the ERO population. \\subsection{Color Selection Effects} \\label{ColSel} How comparable are ERO samples selected using an $(R - K) \\ge 5.3$ color versus an $(I - K) \\ge 4$ color? This important issue has never been clearly addressed. We investigated this issue using model spectral energy distributions, but lack the necessary multiband data to compare to the models. Deep, wide-field infrared/optical surveys should be able to address this point in more detail. In Figure~\\ref{modelRIK} we plot the ($R-K$) vs. ($I-K$) colors for a ~\\citet{BC96} model approximating an old stellar population (OSP, $\\tau = 0.1, z_f=30$) or passively evolving elliptical galaxy. We also plot two models with longer exponential decay times ($\\tau = 1.0$) but differing formation redshifts ($z_f = 30, 5$), which should contain a significant fraction of old stars in the range of $1 < z < 2$, but still have some residual star formation. A similar plot covering the $VIH$ color-color plane can be found in ~\\citep[their Figure 2]{LCIR01}. Their data show that EROs selected with ($I - H$)\\,$\\geq$\\,3 have a wide scatter in the $(V - I)$ color, which the authors interpreted as due to prolonged star formation. \\begin{figure}[!th] \\plotone{f10.eps} \\caption{$RIK$ colors for a ~\\citet{BC96} model approximating an old stellar population (OSP, $\\tau = 0.1, z_f=30$), as well as two models with longer exponential decay times ($\\tau = 1.0$) but differing formation redshifts ($z_f = 30, 5$). All three curves are marked with squares at $z \\sim 1$. Note that that pure, passively-evolving OSPs would be selected in either an ($R-K$) or ($I-K$) survey for EROs, but that any residual star formation, such as from a disk, would quickly drop objects out of the ($R-K$) sample. Reducing the redshift of formation much below five, or increasing the residual star formation rates ($\\tau > 1$) would drop objects out of both samples. Dust counteracts these effects somewhat, shifting objects towards the upper right of this plot. \\label{modelRIK}} \\end{figure} The two dotted lines in Figure~\\ref{modelRIK} mark the fiducial colors ($R - K$)\\,$=$\\,5\\fm3 and ($I - K$)\\,$=$\\,4\\fm0, representing the colors of a $z = 1$ passively-evolving elliptical galaxy used by most surveys to select EROs. The squares mark the $z \\sim 1$ points in each model curve. Assumptions on the models used, as well as the assumed cosmology and the specific filter bandpasses used for ERO surveys can account for several tenths of a magnitude variation in the expected colors of a $z = 1$ passively-evolving elliptical galaxy. Several predictions can be made from this color selection effect. First, is that both R-band and I-band based ERO surveys should select the {\\em same population} of passively-evolving old stellar populations (elliptical galaxies). Second, I-band based ERO surveys should preferentially include disk galaxies. Light from a bulge comprised of older stars would dominate the ($I-K$) color, while even small amounts of residual star formation in the disk keeps them too blue in ($R-I$) to be included in an ($R-K$) selected sample. Other factors, such as dust extinction, may counteract the star-formation and contribute significantly to their overall color. This implies that ERO samples selected on their ($R - K$) color may not be comparable to samples selected on their ($I - K$) color. Figure~\\ref{modelRIK} can also be used to set some constraints on the formation redshift for the EROs. Models with exponential decay times longer than about 1.5\\,Gyr ($\\tau \\geq 1.5$), or with a formation redshift lower than five ($z \\leq 5$) simply have too much residual star formation. Without any reddening from dust, the blue light from a young population of stars would be sufficient to drop these galaxies out of either ($R-K$) or ($I-K$) samples of EROs. Thus, the brighter EROs classed as spheroids, especially those without any evidence of a disk or ongoing star formation, are likely to have formed a majority of their stars at relatively high redshift ($z > 5$). The morphological mix in our sample of relatively bright, ($I-K$)-selected EROs is similar to that of ~\\citet{smith02a} among a sample of fainter EROs ($K \\leq 20.6$, $R-K \\geq 5.3$) identified in the fields of foreground clusters massive enough to gravitationally lens the higher redshift EROs. They classify 18\\% of their sample as compact, and 50\\% as irregulars (including disk-like systems), while 32\\% are too faint to be classified. Considering redder subsamples from both this work ($F814W - K_s \\geq 5$) and ~\\citet{smith02a} ($R - K \\geq 6.0$), we again find similar results. Of the 11 redder EROs in our sample, nine were classifiable. Of these nine, 89$\\pm$31\\% have disk morphologies, a much higher fraction than in the full sample. The redder ~\\citet{smith02a} subsample has $\\sim$90\\% with disk/irregular morphologies. The expectation from the color selection effect is that (R-K) samples should contain a higher fraction of spheroids at a given $K$ magnitude limit. However, the fainter ~\\citet{smith02a} sample, about three magnitudes deeper than our ERO sample, is composed primarily of irregulars and disks. This suggests that the morphological mix of EROs does change at fainter magnitudes, and ~\\citet{smith02a} conclusion that fainter and redder samples are dominated by massive, dusty starbursts does not contradict our findings. Clearly, this color selection effect needs to be investigated further, with larger and deeper samples of EROs with both (R-K) and (I-K) selection on the same area of sky, so that a proper comparison can be made." }, "0212/astro-ph0212365_arXiv.txt": { "abstract": "The wealth of high quality data now available on the M87 jet inspired us to carry out a detailed analysis of the plasma physical conditions in the jet. In a companion paper (Lobanov, Hardee \\& Eilek, this proceedings) we identify a double-helix structure within the jet, and apply Kelvin-Helmholtz stability analysis to determine the physical state of the jet plasma. In this paper we treat the jet as a test case for {\\it in situ} particle acceleration. We find that plasma turbulence is likely to exist at levels which can maintain the energy of electrons radiating in the radio to optical range, consistent with the broadband spectrum of the jet. ", "introduction": "We know a great deal about the jet in M87. Radio \\citep{OHC} and optical \\citep{HST} images reveal ordered, filamentary structures whose synchrotron emission extends from radio at least to optical frequencies, and probably up to X-rays \\citep{Xray}. Multi-epoch studies detect relativistic proper motion, at $\\gamma$ of a few\\citep{Biretta}. The jet begins by expanding uniformly, out to $\\sim 2$ kpc (we assume an angle $\\sim 40^{\\circ}$ to the line of sight, and a distance of 17 Mpc). At that point, the location of the bright knot A, it recollimates, and continues for another 1-2 kpc before disrupting strongly and depositing its matter and energy in the larger radio halo. The minimum pressure required to produce the synchrotron emission remains approximately constant during the expansion. Because $p_{min}$ measures the energy density in relativistic electrons and magnetic field, $p_{min} \\propto u_e^{4/7} u_B^{3/7}$, we know that these quantities do not decay adiabatically during the expansion. This is clear evidence that {\\it in situ} energization is occuring. The broadband, slice-integrated synchrotron spectrum is nearly constant along the jet. This suggests that the electron energy distribution is also nearly constant along the jet, and supports the idea that it is maintained against losses by {\\it in situ} energization. We must recall, however, that the jet is not internally homogeneous. The radio-bright filaments probably show us high-field regions. In addition, resolved two-dimensional images show that the optical knots are more concentrated than the radio knots. We have enough information about this jet to justify detailed modelling of the turbulence and its effect on the particles. To be specific, we consider particle acceleration by Alfvenic turbulence. In this paper we summarize our analysis, which will be published elsewhere in more detailed form. ", "conclusions": "" }, "0212/astro-ph0212492.txt": { "abstract": "Improving our understanding of the initial conditions and earliest stages of protostellar collapse is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. Observationally, there are two complementary approaches to this problem: (1) studying the structure and kinematics of prestellar cores observed prior to protostar formation, and (2) studying the structure of young (e.g. Class 0) accreting protostars observed soon after point mass formation. We discuss recent advances made in this area thanks to (sub)millimeter mapping observations with large single-dish telescopes and interferometers. %Two results have emer-ged. First, In particular, we argue that the beginning of protostellar collapse is much more violent in cluster-forming clouds than in regions of distributed star formation. %Second, protostars in clusters seem to originate from %finite, detached reservoirs of mass, suggesting the IMF is largely %determined by pre-collapse cloud fragmentation. Major breakthroughs are expected in this field from future large submillimeter instruments such as Herschel and ALMA. ", "introduction": "Although the formation of low-mass stars is now reasonably well understood in outline (see, e.g., Mannings, Boss, \\& Russell 2000 for recent reviews), several important aspects remain poorly known, such as the initial stages of the collapse process, the mechanism(s) selecting stellar masses, or the formation of multiple systems. Some progress on the earliest stages of star formation was achieved over the last decade thanks to the use of sensitive receivers on large (sub)millimeter radiotelescopes such as JCMT, CSO, and the IRAM 30m. Young protostars were identified at the beginning of the main accretion phase (Class 0 objects -- Andr\\'e, Ward-Thompson, \\& Barsony 1993), and the starless dense cores extensively studied in NH$_3$ by Myers and collaborators (e.g. Benson \\& Myers 1989) were found to be characterized by flat inner density gradients (Ward-Thompson et al. 1994). Direct evidence for infall motions was observed toward a large number of Class~0 protostars and prestellar cores (e.g. Gregersen et al. 1997 -- see \\S ~3 below and Evans, this volume). Class~0 objects were also found to drive more powerful outflows than more evolved (Class~I) protostars, suggesting a marked decrease of the mass accretion/ejection rates in the course of protostellar evolution (Bontemps et al. 1996). As advocated by Henriksen, Andr\\'e, \\& Bontemps (1997), there may be a causal relationship between these results, in the sense that the accretion/ejection decline during the protostellar phase may be a direct consequence of the form of the density profile at the prestellar stage.\\\\ Further studying the detailed properties of prestellar cores and young protostars is of prime importance to distinguish between collapse models and shed light on the origin of stellar masses. Indeed, the effective reservoirs of mass available for the formation of individual stars may be largely determined at the prestellar stage, and it is during the main protostellar accretion phase that stars accrete some fraction of these reservoirs and build up the masses they will have on the zero-age main sequence. \\begin{figure}[ht] %\\resizebox{\\hsize}{!}{\\includegraphics{/home/storage/pandre/tmp3/fig/l1544_iram%04191.ps}} \\resizebox{\\hsize}{!}{\\includegraphics{andrep1_rev.ps}} \\caption{Dust continuum maps of L1544 (a) and IRAM~04191 (b) at 1.3~mm taken with the IRAM 30~m telescope and the MPIfR bolometer array (from Ward-Thompson et al. 1999 and Andr\\'e et al. 1999, respectively). Effective resolution: 13\\arcsec ; base contour and contour step: 20~mJy/beam. The direction of the magnetic field measured in L1544 with the SCUBA polarimeter on JCMT (Ward-Thompson et al. 2000) and the collimated CO(2-1) bipolar flow emanating from IRAM~04191 are shown. \\label{fig-intro}} \\end{figure} After a brief introduction of the theoretical background (\\S ~1.1), we review recent observational advances concerning the density and velocity structure of cloud cores in \\S ~2 and \\S ~3, respectively. We conclude in \\S ~4 with a comparison between observations and theoretical models. %\\vskip 0.3cm \\subsection{Collapse Initial Conditions: Theory} The inside-out collapse model of Shu (1977), starting from a singular isothermal sphere (SIS) or toroid (cf. Li \\& Shu 1996, 1997), is well known and underlies the `standard' picture of isolated, low-mass star formation (e.g. Shu, Adams, \\& Lizano 1987).\\\\ Other collapse models exist, however, which adopt different initial conditions. In particular, Whitworth \\& Summers (1985) have shown that there is a two-parameter continuum of similarity solutions to the problem of isothermal spherical collapse. One of the parameters measures how close to hydrostatic equilibrium the system is initially, while the other parameter reflects how important external compression is in initiating the collapse. In this continuum, the solutions proposed by Shu (1977) and Larson (1969)-Penston (1969) represent two extreme limits. All of the similarity solutions share a universal evolutionary pattern. At early times ($t < 0$), a compression wave (initiated by, e.g., an external disturbance) propagates inward %at the sound speed, leaving behind it a $\\rho(r) \\propto r^{-2}$ density profile. At $t = 0$, the compression wave reaches the center and a point mass forms which subsequently grows by accretion. At later times ($t > 0$), this wave is reflected into a rarefaction or expansion wave, propagating outward through the infalling gas (at the isothermal sound speed $a_s$), and leaving behind it a free-fall $\\rho(r) \\propto r^{-1.5}$ density distribution. Several well-known features of the Shu model (such as the expansion wave) are thus in fact common to all solutions. The various solutions can be distinguished by the {\\it absolute} values of the density and velocity at $t \\sim 0$. In particular, the Shu (1977) solution has $\\rho(r) = (\\as^2/2\\pi\\,G)\\ r^{-2}$ and is static ($v = 0$) at $t = 0$, while the Larson-Penston (1969) solution is $\\sim 4.4$ times denser and far from equilibrium ($v \\approx -3.3\\ \\as$). During the accretion phase ($t > 0$), the infall envelope is a factor $\\sim 7$ denser in the Larson-Penston solution. %than in the Shu model. Accordingly, the mass infall rate is also much larger in the Larson-Penston case ($\\sim 47\\, \\as^3/G$) than in the Shu case ($\\sim \\as^3/G$). In practice, however, protostellar collapse is unlikely to be strictly self-similar, and the above similarity solutions can only be taken as plausible asymptotes. More realistic initial conditions than the SIS are provided by the so-called `Bonnor-Ebert' spheres (e.g. Bonnor~1956), which represent the equilibrium states for self-gravitating isothermal spheres and have a flat density profile in their central $\\sim $ Jeans length region. Such spheres are stable for a center-to-edge density contrast $< 14.3$ and unstable for a density contrast $> 14.3$ (e.g. Bonnor~1956). Numerical hydrodynamic simulations of cloud collapse starting from such initial conditions (e.g. Foster \\& Chevalier 1993, Hennebelle et al. 2002) find that the Larson-Penston similarity solution is generally a good approximation near point-mass formation ($t= 0$) {\\it at small radii}, but that the Shu solution is more adequate at intermediate $t \\geq 0$ times, before the expansion wave reaches the edge of the initial, pre-collapse dense core. In general, the mass accretion rate is thus expected to be time-dependent. Observationally, it is by comparing the (density and velocity) structure of prestellar cores such as L1544 (see Fig.~\\ref{fig-intro}a) with the structure of the envelopes surrounding Class~0 protostars such as IRAM~04191 (cf. Fig.~\\ref{fig-intro}b) that one may hope to constrain the initial conditions for collapse and to discriminate between the various existing models. %In the following, we discuss these two aspects in turn. ", "conclusions": "In the case of low-mass, isolated dense cores, the SIS model of Shu~(1977) describes global features of the collapse (e.g. the mass infall rate) reasonably well and thus remains a useful, approximate guide. In detail, however, the extended infall velocity profiles observed in prestellar cores (e.g. Lee et al. 2001) and in the very young Class~0 object IRAM~04191 (\\S ~3.2 above) are inconsistent with the pure inside-out collapse picture of Shu (1977). The {\\it shape} of the density profiles observed in prestellar cores are well fitted by purely thermal Bonnor-Ebert sphere models, but the {\\it absolute} values of the densities are suggestive of some additional magnetic support (\\S ~2.2). The observed infall velocities are also marginally consistent with isothermal collapse models starting from %marginally stable equilibrium Bonnor-Ebert spheres (e.g. Foster \\& Chevalier 1993, Hennebelle et al. 2002), as such models tend to produce somewhat faster velocities. This suggests that the collapse of `isolated' cores is essentially {\\it spontaneous} and somehow moderated by magnetic effects in magnetized, probably not strictly isothermal Bonnor-Ebert cloudlets. Furthermore, the contrast seen in Fig.~\\ref{iram04191_model} between a steeply declining rotation velocity profile and a flat infall velocity profile beyond $\\sim 3500$~AU suggests that angular momentum is {\\it not} conserved in the outer envelope of IRAM~04191. Such a behavior is very difficult to explain in the context of non-magnetic collapse models. In the presence of a relatively strong ($\\sim 60\\, \\mu$G) magnetic field, on the other hand, the outer envelope can be coupled to, and spun down by, the (large moment of inertia of the) ambient cloud (e.g. Basu \\& Mouschovias 1994). Based on a qualitative comparison with the ambipolar diffusion models of Basu \\& Mouschovias, Belloche et al. (2002) propose that the rapidly rotating inner envelope of IRAM~04191 corresponds to a magnetically supercritical core decoupling from an environment still supported by magnetic fields and strongly affected by magnetic braking. (Quantitatively, however, the models published so far are rotating too slowly to fit the observations.) In this view, the inner $\\sim 3500$~AU radius envelope of IRAM~04191 would correspond to the effective mass reservoir ($\\sim 0.5\\, M_\\odot $) from which the central star is being built. Moreover, comparison of these results with the rotational characteristics of other %(prestellar and protostellar) objects in Taurus (Ohashi et al. 1997) suggests that IRAM~04191 behaves in a typical manner and is simply observed particularly soon after point mass formation (i.e., at $t \\simgt 0$). If this is correct, {\\it the masses of the stars forming in clouds such as Taurus may be largely determined by magnetic decoupling effects}. \\begin{figure}[ht] %\\resizebox{\\hsize}{!}{\\includegraphics{/home/storage/pandre/tmp3/waterloo/phen_%waterloo.ps}} \\resizebox{\\hsize}{!}{\\includegraphics{andrep9_rev.ps}} \\caption{Density profiles (solid curves) obtained slightly after point mass formation ($t \\simlt 10^4$~yr) in SPH numerical simulations of the collapse of a nearly critical [$(\\rho_c/\\rho_{out})_{init} \\sim 12$] %initially stable isothermal ($T= 10$~K) Bonnor-Ebert sphere induced by external compression (Hennebelle et al. 2002). For comparison, the dotted line shows the $\\rho \\propto r^{-2}$ profile of a SIS at 10~K. In (a), the collapse was initiated quasi-statically (by very slow compression with $P_{ext}/\\dot{P}_{ext} = 20\\ \\times$ the initial sound crossing time $R_{init}/\\as $) and the density profile at $t \\simgt 0$ is very similar to that of the SIS. By contrast, in (b), the collapse was induced by a very rapid increase in external pressure (with $P_{ext}/\\dot{P}_{ext} = 0.03 \\times R_{init}/\\as$), resulting in much larger densities around $t \\sim 0$. \\label{hennebelle}} \\end{figure} In protoclusters, by contrast, the large overdensity factors measured for Class~0 envelopes compared to hydrostatic isothermal structures (cf. \\S ~2.4), as well as the fast supersonic infall velocities and very large infall rates observed in some cases (e.g. \\S ~3.2), are inconsistent with self-initiated forms of collapse and require a {\\it strong external influence}. This point is illustrated in Fig.~\\ref{hennebelle} with the results of recent SPH simulations by Hennebelle et al. (2002). These simulations follow the evolution of a Bonnor-Ebert sphere whose collapse has been induced by an increase in external pressure $P_{ext}$. Large overdensity factors (compared to a SIS), together with supersonic infall velocities, and large infall rates ($\\simgt 10\\, \\as^3/G$) are found near $t = 0$ when (and only when) the increase in $P_{ext}$ is strong and very rapid (e.g. Fig.~\\ref{hennebelle}b), resulting in a violent compression wave. Such a violent collapse may be conducive to the formation of both massive stars (through higher accretion rates) and multiple systems (when realistic, non-isotropic compressions are considered). Future high-resolution studies with the next generation of (sub)millimeter instruments (e.g., ALMA) will greatly help test this view and shed further light on the physics of collapse in cluster-forming regions." }, "0212/astro-ph0212015_arXiv.txt": { "abstract": "Extensive observational campaigns of afterglow hunting have greatly enriched our understanding of the gamma-ray burst (GRB) phenomenon. Efforts have been made recently to explore some afterglow properties or signatures that will be tested by the on-going or the future observational campaigns yet come. These include the properties of GRB early afterglows in the temporal domain; the GeV-TeV afterglow signatures in the spectral domain; as well as a global view about the GRB universal structured jet configuration. These recent efforts are reviewed. Within the standard cosmological fireball model, the very model(s) responsible for the GRB prompt emission is (are) not identified. These models are critically reviewed and confronted with the current data. ", "introduction": "Gamma-ray bursts (GRBs) belong to one of those classes of mysterious objects whose nature took great efforts to identify. For years after their discovery, our knowledge about the objects had been limited to the ``gamma-ray'' in the spectral domain, and the ``burst'' in the temporal domain. The revolutionary discovery and the extensive hunting and monitoring of the broadband afterglows for dozens of GRBs greatly extended our knowledge about the events both in the spectral domain (from radio to X-rays) and in the temporal domain (from minutes to years). We now have some good knowledge about at least one subset of GRBs, i.e. the so-called long GRBs whose durations are longer than 2 seconds. These include that they are originated from cosmological distances, likely associated with the deaths of massive stars; that the afterglow is emission from the external forward shock when the fireball impacts the ambient interstellar medium (ISM); and that the fireballs are likely collimated at least for some GRBs (e.g., Piran 1999; van Paradjis, Kouveliotou, \\& Wijers 2000; M\\'esz\\'aros 2002). It is expected that some new progress will be made in the GRB study in the coming years, thanks to the observational advances led by some future space and ground-based multi-wavelength telescopes, especially by the two NASA missions, Swift and GLAST. Among others, the very early afterglows including the bridge between the GRB prompt phase and the afterglow phase will be carefully studied; the broad-band afterglow campaign will be extended to high energy (GeV-TeV) regimes; and a large sample of dataset combining the redshifts and the GRB prompt emission \\& afterglow properties will be available, leading to a global view of the GRB jet configuration and the identification of the GRB prompt emission site(s) and mechanism(s). Below we will review some recent theoretical efforts in anticipation of these upcoming observational breakthroughs. ", "conclusions": "A new epoch for the GRB study is coming within the next several years, especially following the launches of Swift and GLAST, and the utilization of some other broad-band advanced facilities. It is optimistic to expect the following breakthroughs in the coming years: \\ref $\\bullet$ Early afterglows will be carefully studied. The missing link between the prompt emission and the afterglow will be identified, including the detailed reverse shock information. The information from the central engine may be retrievable through well-modeled injection signatures. \\ref $\\bullet$ High energy afterglows will be monitored and studied in conjunction with the low energy afterglows, which will bring invaluable information about the unknown shock physics and the GRB environments. \\ref $\\bullet$ The GRB jet configuration will be identified. We expect the universal structured jet model will be validated by future data. \\ref $\\bullet$ With accumulation of a large sample of the redshift and spectral information for GRBs/XRFs in the Swift era, the right emission site(s) and mechanism(s) for the prompt emission may be identified (or at least strongly constrained). The fireball content and the nature of the relativistic wind from the central engine may be also understood." }, "0212/astro-ph0212223_arXiv.txt": { "abstract": "This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multi-connected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps. \\vspace*{0.35cm} \\noindent {\\footnotesize Preprint numbers: SPhT-T02/182, LPT-02/123, {\\tt astro-ph/0212223}} ", "introduction": "\\label{sec_intro} Future cosmic microwave background (CMB) experiments such as the MAP~\\cite{map} and later the Planck satellites~\\cite{planck} will provide full sky maps of CMB anisotropies (up to the galactic cut). These datasets offer the opportunity to probe the topological properties of our universe. A series of tests to detect the topology, including the use of the angular power spectrum~\\cite{sokolov93,staro93,stevens93,costa95}, the distribution of matched patterns such as circles~\\cite{cornish98}, correlation of antipodal points~\\cite{levin98} and non Gaussianity~\\cite{inoue00} have been proposed (see Refs.~\\cite{lachieze95,uzan99,levin02} for reviews of CMB methods to search for the topology). The study of the detectability of the topology by any of these methods first requires simulating maps with the topological signature for a large set of topologies. These maps will allow one to test the detection methods, estimate their run time, and, once all sources of noise are added, determine to what extent a given method detects the topological signal (in the same spirit as the investigation of the ``crystallographic'' methods based on galaxy catalogs~\\cite{us3}). In a simply connected\\footnote{Geometers and cosmologists often refer to simple-connectedness as the ``trivial topology''. However, trivial topology has a different meaning in the context of point-set topology: in that formalism, the trivial topology is the smallest topology on a set $X$, namely the one in which the only open sets are the empty set and the entire set $X$.}, spatially homogeneous and isotropic universe, the angular correlation function depends only on the angle between the two directions and the coefficients $\\ALM{\\ell}{m}$ of the decomposition of the temperature fluctuation in spherical harmonics, which are uncorrelated for different sets of $\\ell$ and $m$. Multi-connectedness breaks the global isotropy and sometimes the global homogeneity of the universe, except in projective space (see, e.g., Ref.~\\cite{lwugl}). Consequently, the CMB temperature angular correlation function will depend on the two directions of observation, not only on their relative angle, and possibly on the position of the observer. This induces correlations between the $\\ALM{\\ell}{m}$ of different $\\ell$ and $m$. Such correlations are hidden when one considers only the angular correlation function and its coefficients, the so-called $C_\\ell$, in a Legendre polynomial decomposition, because they pick up only the isotropic part of the information and are therefore a poor indicator of the topology. This work aims to detail the whole computation of the correlation matrix \\begin{equation} \\label{eq:I:1} \\CLMLPMP{\\ell}{m}{\\ell'}{m'} \\equiv \\left< \\ALM{\\ell}{m} \\ALM{\\ell'}{m'}^* \\right> , \\end{equation} which encodes all the topological properties of the CMB, and from which one can compute the usual $C_\\ell$, simulate maps, and so on. The study of the detectability of a topological signal (if it exists) in forthcoming CMB datasets requires simulating high quality maps containing the topological signature for a wide class of topologies. Up to now, most CMB studies considered only compact Euclidean spaces~\\cite{sokolov93,staro93,stevens93,costa95,levin99,inoue01} and some compact hyperbolic spaces~\\cite{aurich00,inoue00b,cornish00,bond1,bond2,bond3}, and focused mainly on the $C_\\ell$. The approach developed in this article, and first introduced in Ref.~\\cite{lwugl}, is well suited to simulate the required CMB maps in any topology once the eigenmodes of the Laplacian have been determined. It paves the way to the simulation of maps for a wide range of topologies, particularly spherical ones. Recent measurements of the density parameter $\\Omega$ imply that the observable universe is ``approximately flat''\\footnote{The popular expression ``flat universe'' is misleading, because in General Relativity the ``universe'' is not three-, but four-dimensional and the Friedmann-Lema\\^{\\i}tre solutions are dynamical, so that the universe is not flat --- only its spatial section may be flat or nearly so. In what follows, we will implicitly assume we are talking about the {\\em three-dimensional spacelike sections} of the universe when talking about flat, hyperbolic, or spherical spaces/universes.}, perhaps with a slight curvature. The exact constraint on the total density parameter obtained from CMB experiments depends on the priors used during the data analysis. For example with a prior on the nature of the initial conditions, the Hubble parameter and the age of the universe, recent analysis of the DASI, BOOMERanG, MAXIMA and DMR data~\\cite{sievers,netterfield,archeops2} lead to $\\Omega = 0.99 \\pm 0.12$ at $1\\sigma$ level, and to $\\Omega = 1.04 \\pm 0.05$ at $1\\sigma$ level if one takes into account only the DASI, BOOMERanG and CBI data. Including stronger priors can indeed sharpen the bound. For instance, including information respectively on large scale structure and on supernovae data leads to $\\Omega = 1.01_{- 0.06}^{+ 0.09}$ and $\\Omega = 1.02_{- 0.08}^{+ 0.09}$ at $1\\sigma$ level while including both finally leads to $\\Omega = 1.00_{- 0.06}^{+ 0.10}$. This has been recently improved by the Archeops balloon experiments~\\cite{archeops2,archeops1} which get, with a prior on the Hubble constant, $\\Omega = 1.00_{- 0.02}^{+ 0.03}$. In conclusion, it is fair to assert that current cosmological observations set a reliable bound $0.9 < \\Omega < 1.1$. These results are consistent with Friedmann-Lema\\^{\\i}tre universe models with spherical, flat or hyperbolic spatial sections. In the spherical and hyperbolic cases, $\\Omega \\simeq 1$ implies that the curvature radius must be larger than the horizon radius. In all three cases --- spherical, flat, and hyperbolic --- the universe may be simply connected or multiply connected.\\\\ The possibility of detecting the topology of a nearly flat universe was discussed in Ref.~\\cite{wlu02}. It was noted that the chances of detecting a multiply connected topology are worst in a large hyperbolic universe. The reason is that the typical translation distance between a cosmic source and its nearest topological image seems to be on the order of the curvature radius, and that when $\\Omega \\simeq 1$ the distance to the last scattering surface is less than the half of that distance. See Refs.~\\cite{gomero1,aurichsteiner,inoue3,gomero3,weeks} for some studies on detectability of nearly flat hyperbolic universes. In a multiply connected flat universe the topology scale is completely independent of the horizon radius, because Euclidean geometry --- unlike spherical and hyperbolic geometry --- has no preferred scale and admits similarities. Note that in the Euclidean case, there are only ten compact topologies, which reduces and simplifies the analysis (in particular regarding the computation of the eigenmodes of the Laplacian). In a spherical universe the topology scale depends on the curvature radius, but, in contrast to the hyperbolic case, as the topology of a spherical manifold gets more complicated, the typical distance between two images of a single cosmic source decreases. No matter how close $\\Omega$ is to $1$, only a finite number of spherical topologies are excluded from detection. The particular case of the detectability of lens spaces was studied in Ref.~\\cite{gomero2}, which also considers the detectability of hyperbolic topologies.\\\\ At present, the status of the constraints on the topology of the universe is still very preliminary. Regarding locally Euclidean spaces, it was shown on the basis of the COBE data that in the case of a vanishing cosmological constant the size of the fundamental domain of a 3-torus has to be larger than $L \\geq 4800 \\,h ^{-1} \\UUNIT{Mpc}{}$~\\cite{sokolov93,staro93,stevens93,costa95}, where the length $L$ is related to the smallest wavenumber $2 \\pi / L$ of the fundamental domain, which induces a suppression of fluctuations on scales beyond the size $L$ of the fundamental domain. This constraint does not exclude a toroidal universe since there can be up to eight copies of the fundamental cell within our horizon. This constraint relies mainly on the fact that the smallest wavenumber is $2 \\pi / L$, which induces a suppression of fluctuations on scales beyond the size of the fundamental domain. This result was generalized to all Euclidean manifolds in Ref.~\\cite{levin99}. A non-vanishing cosmological constant induces more power on large scales, via the integrated Sachs-Wolfe effect. For instance if $\\Omega_\\Lambda = 0.9$ and $\\Omega_\\MAT = 0.1$, the constraint is relaxed to allow for 49 copies of the fundamental cell within our horizon. The constraint is also milder in the case of compact hyperbolic manifolds and it was shown~\\cite{aurich00,inoue00b,cornish00} that the angular power spectrum was consistent with the COBE data on multipoles ranging from 2 to 20 for the Weeks and Thurston manifolds. Another approach, based on the method of images, was developed in~\\cite{bond1,bond2,bond3}. Only one spherical space using this method of images was considered in the literature, namely projective space~\\cite{souradeep}. The tools developed in this article, as well as in our preceding works~\\cite{lwugl,glluw,luw02}, will let us fill the gap regarding the simulation of CMB maps in spherical universes. Technically, in standard relativistic cosmology, the universe is described by a Friedmann-Lema\\^{\\i}tre spacetime with locally isotropic and homogeneous spatial sections. These spatial sections can be defined as constant density or time hypersurfaces. With such a splitting, the equations of evolution of the cosmological perturbations, which give birth to the large scale structures of the universe, reduce to a set of coupled differential equations involving the Laplacian. This system is conveniently solved in Fourier space. In the case of a multiply connected universe, we visualize space as the quotient $X / \\Gamma$ of a simply connected space $X$ (which is just a $3$-sphere $\\STR$, a Euclidean space $\\RTR$, or a hyperbolic space $\\HTR$, depending on the curvature) by a group $\\Gamma$ of symmetries of $X$ that is discrete and fixed point free. The group $\\Gamma$ is called the holonomy group. To solve the evolution equations we must first determine the eigenmodes $\\UPSTKS{\\Gamma}{k}{}$ and eigenvalues $- \\kappa_k^2$ of the Laplacian on $X / \\Gamma$ through the generalized Helmholtz equation \\begin{equation} \\label{Helmotz1} \\Delta \\UPSTKS{\\Gamma}{k}{} = -\\kappa_k^2 \\UPSTKS{\\Gamma}{k}{} , \\end{equation} with \\begin{equation} \\kappa_k^2 = k^2 - K , \\end{equation} where $k$ indexes the set of eigenmodes, the constant $K$ is positive, zero or negative according to whether the space is spherical, flat or hyperbolic, respectively,\\footnote{We work here in comoving units, but when spatial section are not flat, the curvature of the comoving space is {\\em not} normalized: it is not assumed to be $+ 1$ in the spherical case nor is it assumed to be $- 1$ in the hyperbolic case. Thus our eigenvalues may differ numerically from those found in the mathematical literature, although of course they agree up to a fixed constant multiple $|K|^{-\\frac{1}{2}}$.} and the boundary conditions are compatible with the given topology. The Laplacian in Eq.~(\\ref{Helmotz1}) is defined as $\\Delta \\equiv D^i D_i$, $D_i$ being the covariant derivative associated with the metric $\\gamma_{i j}$ of the spatial sections ($i$, $j = 1$, $2$, $3$). The eigenmodes of $X / \\Gamma$, on which any function on $X / \\Gamma$ can be developed, respect the boundary conditions imposed by the topology. That is, the eigenmodes of $X / \\Gamma$ correspond precisely to those eigenmodes of $X$ that are invariant under the action of the holonomy group $\\Gamma$. Thus any linear combination of such eigenmodes will satisfy, by construction, the required boundary conditions. In this way we visualize the space of eigenmodes of $X / \\Gamma$ as a subspace of the space of eigenmodes of $X$, namely the subspace that is invariant under the action of $\\Gamma$. The computational challenge is to find this $\\Gamma$-invariant subspace and construct an orthonormal basis for it. In the case of flat manifolds the eigenmodes of $X / \\Gamma = \\RTR / \\Gamma$ can be found analytically. In the case of hyperbolic manifolds, many numerical investigations of the eigenmodes of $X / \\Gamma = \\HTR / \\Gamma$ have been performed~\\cite{inoue00b,aurich89a,aurich89b,inoue99,aurich96,cornish99}. In the case of spherical manifolds, the eigenmodes of $X / \\Gamma = \\STR / \\Gamma$ have been found analytically for lens and prism spaces~\\cite{luw02} and otherwise can be found numerically~\\cite{lwugl}. In the following, we will develop the eigenmodes of $X / \\Gamma$ on the basis $\\YXKLM{X}{k}{\\ell}{m}$ of the eigenmodes of the universal covering space as \\begin{equation} \\label{eq:1} \\UPSTKS{\\Gamma}{k}{s} = \\sum_{\\ell = 0}^\\infty \\sum_{m = -\\ell}^{\\ell} \\XITKSLM{\\Gamma}{k}{s}{\\ell}{m} \\YXKLM{X}{k}{\\ell}{m} , \\end{equation} so that all the topological information is encoded in the coefficients $\\XITKSLM{\\Gamma}{k}{s}{\\ell}{m}$, where $s$ labels the various eigenmodes sharing the same eigenvalue $-\\kappa_k^2$, both of which are discrete numbers\\footnote{The spectrum is discrete when the space is compact, e.g. the torus or any spherical space. In a non-compact multi-connected space such as a cylinder it will have a continuous component.}. The sum over $\\ell$ runs from $0$ to infinity if the universal covering space is non-compact (i.e., hyperbolic or Euclidean). The $\\XITKSLM{\\Gamma}{k}{s}{\\ell}{m}$ coefficients can be determined analytically for Euclidean manifolds. In the case of a spherical manifold, the modes are discrete, \\begin{equation} \\label{knu} k = (\\nu + 1) \\sqrt{K} \\end{equation} where $\\nu$ is a nonnegative integer (the cases $\\nu = 0$ and $\\nu = 1$ correspond to pure gauge modes~\\cite{abott86}), so that $\\kappa_k^2 = \\nu (\\nu + 2) K$, and the sum over $\\ell$ is finite and runs from 0 to $\\nu$ since the multiplicity of a mode $k$ is at most its multiplicity in the universal cover, which is $(\\nu + 1)^2$. Among spherical spaces, the case of prism and lens spaces are the simplest since one can determine these coefficients analytically~\\cite{luw02}. The worst situation is that of compact hyperbolic manifolds, which is analogous to the Euclidean case since the universal covering $\\RTR$ is not compact but for which no analytical forms are known for the eigenmodes. One then needs to rely on numerical computations (see, e.g., Refs.~\\cite{cornish99,glluw}). Our preceding works provided a full classification of spherical manifolds~\\cite{glluw} and developed methods to compute the eigenmodes of the Laplacian in them~\\cite{lwugl}. Among all spherical manifolds, we were able to obtain analytically the spectrum of the Laplacian for lens and prism spaces~\\cite{luw02} which form two countable families of spherical manifolds. The goal of the present article is to simulate CMB maps for these two families of spherical topologies, as well as for the Euclidean topologies. We first review briefly the physics of CMB anisotropies (Sec.~\\ref{sec_cmb}) mainly to explain how to take into account the topology (Sec.~\\ref{subsec_implement}) once the coefficients $\\XITKSLM{\\Gamma}{k}{s}{\\ell}{m}$ are determined. We then detail the computation of these coefficients, focusing on the cases where it can be performed analytically, that is for flat spaces and lens and prism spaces. We then present results of numerical simulations (Sec.~\\ref{sec_simulation}) as well as simulated maps. We discuss these maps qualitatively and confirm that the expected topological correlations (namely matching circles~\\cite{cornish98}) are indeed present. The effects of the integrated Sachs-Wolfe and Doppler terms, as well as the thickness of the last scattering surface, are discussed in order to give some insight into the possible detectability of these correlations. Figure~\\ref{method} summarizes the different independent steps of the computation as well as their interplay. \\section*{Notations} The local geometry of the universe is described by a Friedmann-Lema\\^{\\i}tre metric \\begin{equation} \\label{fl_metric} \\ddd s^2 = - c^2 \\ddd t^2 + a^2 (t) \\left[\\ddd \\CHU^2 + \\SK{K}^2 (\\CHU) \\ddd \\Omega^2 \\right] , \\end{equation} where $a(t)$ is the scale factor, $t$ the cosmic time, $\\ddd \\Omega^2 \\equiv \\ddd \\theta^2 + \\sin^2 \\theta \\, \\ddd \\varphi^2$ the infinitesimal solid angle, $\\CHU$ is the comoving radial distance, and where \\begin{equation} \\label{def_sk} \\SK{K}(\\CHU) = \\left\\lbrace \\begin{array}{ll} \\sinh (\\sqrt{|K|}\\;\\CHU) / \\sqrt{|K|} & \\quad {\\rm (hyperbolic \\, case)} \\\\ \\CHU & \\quad {\\rm (flat \\, case) } \\\\ \\sin (\\sqrt{K}\\;\\CHU) / \\sqrt{K} & \\quad {\\rm (spherical \\, case) } \\end{array} \\right. \\end{equation} In the case of spherical and hyperbolic spatial sections, we also introduce the dimensionless coordinate \\begin{equation}\\label{def_chn} \\CHN=\\sqrt{|K|}\\CHU, \\end{equation} which expresses radial distances in units of the curvature radius. \\begin{center} \\begin{figure} \\unitlength=1cm \\begin{picture}(18,18) \\thicklines \\put(0,0) {\\framebox(9.5,8){}} \\put(0.25,7.5) {\\SZFIG III: Eigenmodes of $X / \\Gamma$} \\put(0.5,6.75) {\\circle{0.8} \\makebox(0,0) {\\SZFIG$\\Gamma$}} \\put(0.9,6.7) {\\vector(1,0){3}} \\thinlines \\put(4,6.35) {\\framebox(4.25,.8){}} \\thicklines \\put(4.25,6.6) {\\SZFIG $\\UPSTKS{\\Gamma}{k}{s} = \\sum_{\\ell, m} \\XITKSLM{\\Gamma}{k}{s}{\\ell}{m} \\YXKLM{X}{k}{\\ell}{m}$} \\put(0.5,3.25) {\\circle{0.8} \\makebox(0,0) {\\SZFIG$K$}} \\put(0.7,3.6) {\\vector(2,3){0.9}} \\put(0.9,3.2) {\\vector(1,0){0.7}} \\put(0.7,2.8) {\\vector(2,-3){0.9}} \\put(1.6,5) {\\dashbox{0.05}(0.8,0.8) {\\SZFIG$< 0$}} \\put(2.75,5.25) {\\SZFIG numerical~\\cite{cornish99,glluw}} \\put(1.6,2.85) {\\dashbox{0.05}(0.8,0.8) {\\SZFIG$= 0$}} \\put(2.75,3.1) {\\SZFIG analytical~\\cite{lachieze95,levin02}\\ldots} \\put(1.6,0.6) {\\dashbox{0.05}(0.8,0.8) {\\SZFIG$> 0$}} \\put(2.75,1.2) {\\SZFIG general case: numerical~\\cite{glluw}} \\put(2.75,0.5) {\\SZFIG lens and prism: analytical~\\cite{luw02,glluw}} \\put(7.1,0.15) {(see Sec.~\\ref{subsubsec_lens})} \\put(0,10) {\\framebox(9.5,8){}} \\put(0.25,17.5) {\\SZFIG I: Universal cover ($X$) eigenmodes} \\thinlines \\put(0.1,16.5) {\\framebox(9.25,.75){}} \\thicklines \\put(0.25,16.75) {$\\Delta \\YXKLM{X}{k}{\\ell}{m} = - (k^2 - K) \\YXKLM{X}{k}{\\ell}{m} \\;;\\quad \\YXKLM{X}{k}{\\ell}{m} = \\RXKL{X}{k}{\\ell} (\\CHU) \\YLM{\\ell}{m} (\\theta, \\varphi)$} \\put(0.5,13.25) {\\circle{0.8} \\makebox(0,0){$K$}} \\put(0.7,13.6) {\\vector(2,3){0.9}} \\put(0.9,13.2) {\\vector(1,0){0.7}} \\put(0.7,12.8) {\\vector(2,-3){0.9}} \\put(1.6,15) {\\dashbox{0.05}(0.8,0.8) {$< 0$}} \\put(2.75,15.25) {$X = \\HTR:\\, \\RXKL{X}{k}{\\ell} = \\sqrt{\\frac{N_{k \\ell}}{k \\SK{K} (\\CHU)}} \\PLM{- 1 / 2 + i \\omega}{-1 / 2 - \\ell} \\left(\\cosh\\CHN \\right)$} \\put(4.25,14.6) {$\\omega \\in[0,\\infty[\\quad\\hbox{or}\\quad i \\omega \\in[0,1]$} \\put(1.6,12.85) {\\dashbox{0.05}(0.8,0.8) {$0$}} \\put(2.75,13.1) {$X = \\RTR:\\, \\RXKL{X}{k}{\\ell} = \\sqrt{\\frac{2}{\\pi}} j_\\ell(k \\CHU)$} \\put(4.25,12.45) {$k\\in[0,\\infty[$} \\put(1.6,10.6) {\\dashbox{0.05}(0.8,0.8) {$> 0$}} \\put(2.75,10.85) {$X = \\STR:\\, \\RXKL{X}{k}{\\ell} = \\sqrt{\\frac{M_{k \\ell}}{k \\SK{K} (\\CHU)}} \\PLM{1 / 2 + \\nu}{- 1 / 2 - \\ell} \\left(\\cos\\CHN \\right)$} \\put(4.25,10.2) {$\\nu=2,3,\\ldots$} \\put(7.5,10.15) {(see App.~\\ref{app_A})} \\put(11,8.5) {\\framebox(7,1){}} \\put(11.25,8.9) {\\SZFIG V: Output: $\\ALM{\\ell}{m}$, maps, $C_\\ell$\\ldots} \\put(16.1,8.65) {(see Sec.~\\ref{sec_simulation})} \\put(11,10) {\\framebox(7,8){}} \\put(11.25,17.5) {\\SZFIG II: CMB in $X$} \\thinlines \\put(11.25,16.5) {Perturbation equations} \\put(11.8,16.2) {(local physics)} \\put(15.25,16.5) {Initial conditions} \\put(12,15) {\\SZFIG $O_k^{[X]} \\left(\\RXKL{X}{k}{\\ell}\\right)$} \\put(12.25,14) {\\SZFIG $G_\\ell(k)$} \\put(15.9,14) {\\SZFIG $\\PS (k)$} \\put(12.5,12) {\\SZFIG $\\left<\\ALM{\\ell}{m} \\ALM{\\ell'}{m'}^* \\right> = C_\\ell \\KRON{\\ell}{\\ell'} \\KRON{m}{m'}, $} \\put(12.5,11) {\\SZFIG $C_\\ell = \\frac{2}{\\pi} \\int k^2 \\ddd k G_\\ell^2(k) \\PS (k)$} \\put(15.9,10.15) {(see Sec.~\\ref{subsec_local})} \\thicklines \\put(12.25,10.75) {\\dashbox{0.05}(4.75,1.75){}} \\put(12.8,16){\\vector(0,-1){.6}} \\put(12.8,14.8){\\vector(0,-1){.5}} \\put(16.2,16.3){\\vector(0,-1){2}} \\put(13.2,14.15){\\framebox(2.6,0){}} \\put(14.5,14.15){\\vector(0,-1){1.6}} \\put(11,0) {\\framebox(7,8){}} \\put(11.25,7.5) {\\SZFIG IV: CMB in $X / \\Gamma$} \\put(15.9,0.15) {(see Sec.~\\ref{subsec_implement})} \\put(12.75,6.5) {\\SZFIG $\\left<\\ALM{\\ell}{m} \\ALM{\\ell'}{m'}^* \\right> = \\CLMLPMP{\\ell}{m}{\\ell'}{m'} ,$} \\put(11.75,5.5) {\\SZFIG $\\CLMLPMP{\\ell}{m}{\\ell'}{m'} = \\frac{2}{\\pi} \\sum_{k, s} \\XITKSLM{\\Gamma}{k}{s}{\\ell}{m} \\XITKSLM{\\Gamma}{k}{s \\; *}{\\ell'}{m'}$} \\put(14.14,4.9) {\\SZFIG $\\quad G_\\ell(k) G_{\\ell'}(k) \\PS (k)$} \\put(11.6,4.65) {\\dashbox{0.05}(5.9,2.4){}} \\thinlines \\put(11.4,1) {Perturbation equations} \\put(11.15,0.7) {(local physics, unchanged)} \\put(15.25,1) {Initial conditions} \\put(15.5,0.7) {(unchanged)} \\put(12,2) {\\SZFIG $O_k^{[X]} \\left(\\UPSTKS{\\Gamma}{k}{s}\\right)$} \\put(12.25,3.5) {\\SZFIG $G_\\ell(k)$} \\put(15.9,3.5) {\\SZFIG $\\PS (k)$} \\thicklines \\put(12.7,1.3){\\vector(0,1){.6}} \\put(12.7,2.4){\\vector(0,1){1}} \\put(16.2,1.3){\\vector(0,1){2.05}} \\put(13.2,3.6){\\framebox(2.6,0){}} \\put(14.5,3.6){\\vector(0,1){1.0}} \\put(4.75,10) {\\vector(0,-1){2}} \\put(9.5,14) {\\vector(1,0){1.5}} \\put(9.5,4) {\\vector(1,0){1.5}} \\put(14.5,10) {\\vector(0,-1){0.5}} \\put(14.5,8) {\\vector(0,1){0.5}} \\end{picture} \\caption{The computation of CMB anisotropies in multi-connected spaces follows a series of independent steps. From the knowledge of the spatial curvature $K$, one determines the universal covering space, $X$, as well as the eigenmodes of the Laplacian in this simply-connected space (upper left box); these functions are well-known and frequently used in standard cosmology computations, and are recalled in Appendix~\\ref{app_A} [we have introduced $\\omega = k / \\sqrt{|K|}$ for the hyperbolic case and $\\nu = k / \\sqrt{K} - 1$ for the spherical case [recall Eq.~(\\ref{knu})], and used $\\CHN$ defined by Eq.~(\\ref{def_chn})]. Once some cosmological parameters and a scenario of structure formation has been chosen (upper right box), the CMB anisotropies in the universal covering space can be computed. This step is also a standard step that can be achieved numerically by a number of codes (see Sec.~\\ref{subsec_local}). An independent computation (lower left box) is the determination of the eigenmodes of the Laplacian compatible with the topology of space, specified by the choice of the holonomy group $\\Gamma$. Our approach is to encode all the topological information in a set of parameters $\\XITKSLM{\\Gamma}{k}{s}{\\ell}{m}$. Their computation is described in Sec.~\\ref{subsubsec_lens} and can be performed either numerically or analytically according to the case at hand. The implementation of the topology in a standard CMB code (lower right box) is described in Sec.~\\ref{subsec_implement} and yields the complete correlation matrix of the $\\ALM{\\ell}{m}$ from which one can (center right box) compute $C_\\ell$, simulate maps, etc.} \\label{method} \\end{figure} \\end{center} ", "conclusions": "\\label{sec_conclusion} This articles describes the implementation of topology in CMB codes and gives explicitly the required tools to perform such an implementation in flat and spherical spaces. As emphasized in the Introduction, these two cases are observationally the most relevant for an almost flat universe. Examples of simulated maps were given in the two cases. Here we presented only low resolution maps due to the computational time limitation but higher resolution maps will be presented elsewhere. It was checked that the expected topological correlations (the matched circles) were present, confirming the quality of our simulations. Our method relies on the computation of the correlation matrix of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics. This matrix encodes all the topological information. We emphasize that, due to the breakdown of global isotropy, this matrix is not purely diagonal. This also offers a working example to construct tests for the detection of deviation from global isotropy. We have illustrated the influence of different effects that will tend to blur these patterns and affect the perfect circle matching, namely the Doppler effect and the integrated Sachs-Wolfe effect. We also considered the effect of the thickness of the last scattering surface, but found it to be negligible on the scales considered here. A more detailed quantitative analysis of these effects on the detectability of the topological signal is left for future studies~\\cite{future}. A complete investigation of the detectability of the topology in coming CMB data requires the construction of reliable simulation tools. Besides the quantification of the amplitude of the effects cited above, one would also need to include all other observational effects such as instrumental noise, foreground contamination, etc. The present work paves the way to all these essential studies." }, "0212/astro-ph0212545_arXiv.txt": { "abstract": "Recent {\\it Hubble Space Telescope} photometry in the nearby elliptical galaxy NGC 5128 shows that its halo field star population is dominated by moderately metal-rich stars, with a peak at [m/H] $\\simeq$ $-0.4$ and with a very small fraction of metal-poor ([m/H] $<$ $-1.0$) stars. In order to investigate the physical processes which may have produced this metallicity distribution function (MDF), we consider a model in which NGC 5128 is formed by merging of two major spiral galaxies. We find that the halo of an elliptical formed this way is predominantly populated by moderately metal-rich stars with [m/H] $\\sim$ $-0.4$ which were initially within the outer parts of the two merging discs and were tidally stripped during the merger. To match the NGC 5128 data, we find that the progenitor spiral discs must have rather steep metallicity gradients similar to the one defined by the Milky Way open clusters, as well as sparse metal-poor haloes (5\\% or less of the disc mass). Very few stars from the central bulges of the spiral galaxies end up in the halo, so the results are not sensitive to the relative sizes (bulge-to-disc ratios) or metallicities of the initial bulges. Finally, we discuss the effects on the globular cluster system (GCS). The emergent elliptical will end up with metal-poor halo clusters from the original spiral haloes, but with moderately metal-rich halo stars from the progenitor discs, thus creating a mean offset between the MDFs of the halo stars and the GCS. Remaining questions yet to be answered concern the total size of the GCS population (the ``specific frequency problem'') and the observed existence of metal-rich globular clusters in large numbers in the outer haloes of giant ellipticals. We also discuss possible differences in the MDFs of stellar haloes of galaxies of different Hubble type. ", "introduction": "Physical properties of metal-deficient stellar haloes in galaxies are considered to provide vital clues to the understanding of early dynamical and chemical evolution of galaxies. In particular, the detailed investigation of structural, kinematic, and chemical properties of such a ``fossil record'' component (i.e., stellar halo) of the Galaxy has revealed a possible scenario as to how the Galaxy has developed its dynamical structures such as bulge, thin and thick discs (e.g., Freeman 1987; Majewski 1993; van den Bergh 1996). Because of the observational difficulties in revealing three dimensional structure and kinematics of halo stars (with respect to their host galaxy) in each of the Local Group galaxies other than the Milky Way, the metallicity distribution function (hereafter MDF) of halo stars in these galaxies has served to give some constraints on the past star formation and chemical evolution histories of these systems (Mould \\& Kristian 1986; Durrell, Harris, \\& Pritchet 1994, 2001; Pritchet \\& van den Bergh 1998; Christian \\& Heasley 1986: Reitzel, Guhathakurta, \\& Gould 1998; Grillmair et al. 1996; Han et al. 1997; Martinez-Delagado \\& Aparicio 1998). The stellar halo of M31 appears to be dominated by a moderately high-metallicity population with [m/H] $\\sim$ $-0.5$ (cf.~the references cited above), a strikingly different enrichment level than in the Milky Way stellar halo, and a strong indicator of a different formation history (e.g.~Durrell, Harris, \\& Pritchet 2001). Although there have been many MDF studies of halo stars in Local Group members, galaxies beyond the Local Group have only recently been investigated through {\\it HST}/WFPC2 photometry and for only a small number of cases: the giant E/S0 NGC 5128 (Soria et al. 1996; Harris, Harris, \\& Poole 1999 hereafter referred to as HHP; Harris \\& Harris 2000, HH00; Harris \\& Harris 2002, HH02; Marleau et al. 2000), the edge-on S0 NGC 3115 (Elson 1997; Kundu \\& Whitmore 1998), and two dwarf ellipticals in the M81 group (Caldwell et al. 1998). Furthermore, Rejkuba et al. (2002) have demonstrated the existence of a significant intermediate-age AGB population in parts of the NGC 5128 halo, based on deep $U$, $V$, and $K_{s}$ color-magnitude and color-color diagrams of halo stars resolved by VLT. A remarkable result emerging from the {\\it HST}/WFPC2 photometry of the old-halo red giant stars in NGC 5128 is the dominance of moderately metal-rich stars in the range $-1$ $<$ [m/H] $<$ 0.0 (HHP, HH00, and HH02). HH00 and HH02 suggested that the relatively high mean abundance and small fraction ($\\sim$ 10\\%) of metal-poor stars with [m/H] $<$ $-1$ can give strong constraints on the total mass of dwarf galaxies that could be accreted by NGC 5128 and then disrupted to form its faint stellar halo. To date, however, there are only a few attempts at physical interpretation of this material. HH00 discussed a one-zone model of chemical evolution of this galaxy and suggested that it experienced two fairly distinct stages of halo formation: an early ``accreting box'' stage when the galaxy is assembling through infall of star-forming gas clumps, and then a major stage of ``closed-box'' evolution when the star formation proceeds in the galaxy with little gas infall. HH02 extended this basic picture further to a more generalized accreting-box formation model, in which the infall rate of unenriched gas is envisaged to start at a high rate and then dies away exponentially, while star formation continues throughout until the gas supply is exhausted. With appropriate choices of gas infall rate and the effective chemical yield, excellent overall matches to the observed MDFs can be obtained. Recently, Beasley et al. (2002a, b) have further discussed the origin of the stellar halo MDF within the context of a semi-analytic model of galaxy formation (GALFORM), based on the Cold Dark Matter (CDM) picture. In this model, star formation can take place in two modes, a ``quiescent'' mode within the relatively unenriched pregalactic clouds, and a ``starburst'' mode whenever two roughly equal clouds suddenly merge. They demonstrated that the global metallicity distribution within model galaxies comparable to NGC 5128 in size is broadly consistent with the observed MDF, although the model is unable to provide any information on the spatial distribution or radial change in the MDF. These previous studies are based on one-zone models of chemical evolution and thus cannot spatially resolve the various distinct stellar components (i.e., halo, bulge, and disc) in a galaxy. Accordingly, comparisons of these models with the MDFs observed at different places in NGC 5128 have limited value. Numerical simulations which enable us to resolve spatially the halo, bulge, and disc components and thereby to investigate the MDF for each of these components should be very helpful for better understanding the formation of galactic stellar haloes. The purpose of this paper is to investigate the origin of the MDF of the stellar halo of NGC 5128 based on numerical simulations of elliptical galaxy formation. We here adopt the basic ``merger'' approach (Toomre 1977) in which elliptical galaxies are proposed to be formed by major merging of two spiral galaxies. Within the context of this assumption, we investigate the final MDF of the outer halo component of the merger remnant (i.e., the giant E galaxy) as well as its dependence on the input parameters of the progenitor discs (e.g., the MDFs of discs, bulge-to-disc-ratio, and halo mass fraction of the disc). Comparing the simulated MDFs with the observed ones for NGC 5128, we discuss the following points: (1) how the dynamics of galaxy merging is important for the formation of the gE stellar halo, (2) how the initial MDF of a disc (or bulge) in a merger controls the final MDF of the stellar halo, (3) whether the bulge-to-disc ratio of a merger progenitor spiral is important for the determination of the stellar halo's MDF, (4) what initial conditions of galaxy mergers in the present simulations can best give the MDF similar to the observed one, (5) the relevance of the MDF for the globular cluster system, which is different from the field-halo stars, and (6) whether, on the grounds of the merger picture, we should always expect the MDFs of stellar haloes in elliptical galaxies (E) to be systematically different (more metal-rich) from those in late-type spirals (Sp). The plan of the paper is as follows: In the next section, we describe our numerical models for stellar halo formation in galaxy mergers. In \\S 3, we present the numerical results mainly on the final MDFs of merger remnants (i.e., elliptical galaxies) for variously different merger models. In \\S 4, we predict a possible relationship between MDFs of stellar haloes and physical properties of their host elliptical galaxies. In this section, we also discuss the origin of M31's metal-rich stellar halo. We summarize our conclusions in \\S 5. ", "conclusions": "We have numerically investigated MDFs of stellar haloes of elliptical galaxies formed by major merging in order to elucidate the origin of the observed MDF of NGC 5128. We mainly investigated the MDF of halo stars with $R$ $>R_{\\rm d}$ (where $R$ and $R_{\\rm d}$ are the radius from the center of a merger remnant and the initial size of the merger progenitor spiral) in the merger remnant for several models with different physical parameters of the progenitor spirals. Our numerical study clearly demonstrates the importance of {\\it dynamical processes of galaxy merging} (i.e., tidal stripping of metal-poor disc stars) in determining MDFs of stellar haloes of elliptical galaxies. We summarize our principal results as follows. (1) The stellar halo of an elliptical galaxy formed by major merging is predominantly populated by moderately metal-rich stars with [m/H] $\\sim$ $-0.4$, which come from the outer parts of the discs of the merging spirals. Furthermore, the fraction of metal-poor stars with [m/H] $<$ $-1.0$ in the halo is very small ($\\sim$ 17 \\%). The MDF of the merger remnant does not show a strong radial dependence for 0.5 $<$ $R$ $<$ 2.0 (in our units). These results are broadly consistent with recent {\\it HST} observations on MDFs of the stellar halo of NGC 5128. (2) Irrespective of the physical parameters of merger progenitor discs, the MDFs of stellar haloes of merger remnants show both the dominant moderately metal-rich populations and the minor metal-poor ones. Thus future systematic observations on MDFs of elliptical galaxies can assess the relative importance of major galaxy merging in the formation of elliptical galaxies by confirming the above generic trend of MDFs. (3) The MDFs of elliptical galaxies formed by major merging depend strongly on the initial MDFs of merger progenitor discs, because halo stars are dominated by those which are initially in the outer part of the discs and tidally stripped during merging. (4) MDFs of stellar haloes do not depend so strongly on the MDFs of the progenitor spiral bulges, essentially because bulge stars are not be tidally stripped so efficiently during merging owing to bulge's compact configuration. However, the shapes of MDFs of a merger remnant at $-0.2$ $\\le$ [m/H] $\\le$ 0 can be affected by the bulge-to-disc-ratio of the merger progenitor spiral. (5) The shape of the halo MDF of a merger remnant at [m/H] $\\le$ $-1.0$ depends on the mass fraction and the mean metallicity of the progenitor spiral's halo. Therefore the observed shape of the halo MDF at [m/H] $\\le$ $-1.0$ in NGC 5128 can give some constraints on the stellar populations of the progenitor spiral's stellar halo. (6) The observed similarity in MDFs of stellar haloes between M31 and NGC 5128 can be naturally explained, if the M31 bulge was also formed by major merging between two spirals with the masses (a factor of $2-4$) smaller than those that are assumed to merge to from NGC 5128 in the present study. The observed markable difference in MDFs between stellar haloes and GCs for NGC 5128 and M31 can be also explained by the merger scenario. (7) Our simulations predict that if most elliptical galaxies are formed by major merging, the photometric properties (e.g., colors and magnitudes) of a stellar halo in an elliptical galaxy can correlate with those of the galaxy (i.e., redder Es have redder stellar haloes). Also our study predicts that there can be CM relations in stellar haloes of elliptical galaxies." }, "0212/astro-ph0212290_arXiv.txt": { "abstract": "We present results from a detailed dynamical analysis of five high surface brightness, late type spiral galaxies NGC 3810, NGC 3893, NGC 4254, NGC 5676, and NGC 6643 which were studied with the aim to quantify the luminous-to-dark matter ratio inside their optical radii. The galaxies' stellar light distribution and gas kinematics have been observed and compared to hydrodynamic gas simulations which predict the gas dynamics arising in response to empirical gravitational potentials, which are combinations of differing stellar disk and dark halo contributions. The gravitational potential of the stellar disk was derived from near-infrared photometry, color-corrected to yield a constant stellar mass-to-light ratio (M/L); for the dark halo, the mass density distribution of an axisymmetric isothermal sphere with a core was chosen. Hydrodynamic gas simulations were performed for each galaxy for a sequence of five different mass fractions of the stellar disk and for a wide range of spiral pattern speeds. These two parameters mainly determine the modelled gas distribution and kinematics. The agreement between the simulated and observed gas kinematics permitted us to conclude that the galaxies with the highest rotation velocities tend to possess very massive stellar disks which dominate the gas dynamics within the optical radius. In less massive galaxies, with a maximal rotation velocity of $<$\\,200\\,km\\,s$^{-1}$, the mass of the dark halo at least equals the stellar mass within 2 -- 3 disk scale lengths. The maximal disk stellar mass-to-light ratio in the $K$-band was found to lie at about M/L$_K \\approx 0.6$. Furthermore, the gas dynamic simulations provide a powerful tool to accurately determine the dominant spiral pattern speed for galaxies, independent of a specific density wave theory. It was found that the location of the corotation resonance falls into a narrow range of around three exponential disk scale lengths for all galaxies from the sample. The corotation resonance encloses the strong part of the stellar spiral in all cases. Based on the experience gained from this project, the use of a color-correction to account for local stellar population differences is strongly encouraged when properties of galactic disks are studied that rely on their stellar mass distributions. ", "introduction": "Much evidence has accumulated in recent years that the stellar disks of high surface brightness spiral galaxies dominate the mass budget of the inner regions. Most of the studies arguing for a maximal disk scenario, are based on the detailed analysis of high resolution rotation curve measurements \\citep{bla99,pal00,rat00,sal01}. These studies, however, generally derive the rotational support of the stellar disk from an axisymmetric disk mass model and allow no consideration of non-circular rotation components. More sophisticated modelling strategies have been applied to spiral galaxies with variable significance \\citep{eri99,pig01}. For the most part those studies also support heavy disks for high surface brightness galaxies, but they also find candidates for which lower disk mass fractions are more likely. The most convincing direct arguments for the maximal disk scenario come from the studies of strong bars in spiral galaxies. These features induce a strong dynamic trace in the velocity field and provide a good laboratory for estimating the stellar mass component. Based on fluid dynamic modelling, a maximal disk solution is found by \\citet{eng99} for the Milky Way and by \\citet{wei01} for NGC 4123. Furthermore, theoretical considerations hint for the requirement of a non-massive halo contribution in the central regions of strongly barred galaxies with a very cold disk, because otherwise dynamical friction would slow down the bar very quickly, leading to its destruction \\citet{deb98,deb00}. On the other hand, for initially hotter disks, this effect is largely reduced \\citet{ath02} and references therein. However, there is also evidence that even high surface brightness spiral galaxies might be dominated by the dark matter mass component in their central disk regions as suggested by high resolution simulations of cosmological dark matter halos \\citep[e.g.]{moo99a,ghi00,fuk01}. \\citet{bot93} inferred from stellar velocity dispersions in spiral galaxy disks that a more massive halo component is needed to explain the findings. There are recent studies that argue for lighter disk models by making use of previously hardly exploited relations. \\citet{CR99} applied a statistical Tully-Fisher relation analysis to a large sample of galaxies trying to relate the maximal rotation velocity of a galaxy to its disk size. \\citet{mal00}, and more recently \\citet{tro02} used the geometry of gravitationally lensed systems to disentangle the effects of the stellar disk and the halo masses. These groups found that the dark halo also dynamically plays an important role in the galaxies' inner regions. In the present study, we quantify the relative mass fractions of the stellar disk and the inner dark halo by analyzing the non-axisymmetric force component in the gravitational force field that arises in response to the spiral structure of the observable stellar mass distribution. We address this issue by exploring the influence of the spiral arms on the gas velocity field that builds up in response to the total gravitational potential of the galaxy. We model the gravitational potential from a mass map of the stellar distribution and a dark halo model. With the use of hydrodynamical gas simulations, we predict the gas velocity fields for different empirical mass models of the sample galaxies, assembled from a variety of stellar disk and dark matter mass components. The two parameters that dominate the resulting forces in the disk are the stellar disk mass contribution and the pattern speed of the stellar spiral, $\\Omega_{\\rm p}$. Thus, in this study we explore the effects of those parameters and compare the simulated gas morphology and velocity wiggles with our observations, enabling the identification of the best fitting scenario for each individual galaxy. Comparable studies have been applied to barred spiral galaxies taking advantage of the strong dynamical trace of the bar in the velocity field \\citep{wei01}. First results from our study have been presented already in \\citet{kra01}, (hereafter, KSR01) for NGC 4254 where it was proven that this strategy yields valuable information which allows us to constrain disk and halo fractions also for spiral galaxies without a strong bar. In the present paper we only briefly discuss the modelling and comparison strategies involved (Section~\\ref{modelling}) but instead focus on the conclusions of the analysis. More details about the modelling issues can be found in KSR01, \\citet{sly02b} and \\citet{kra02}. ", "conclusions": "We have presented a new, direct and independent estimate of the stellar mass fraction in a small sample of spiral galaxies. With respect to ratio of luminous and dark matter in their inner parts, the population of high surface brightness spiral galaxies does not seem to comprise an entirely homogeneous class of objects. Combining the maximum rotation velocity, presented in Table~\\ref{properties}, with the estimates for the galaxies' most probable fractions of the stellar disk mass, reveals an intriguing trend: the most massive of the analyzed galaxies, NGC 3893 and NGC 5676, tend to also possess the most massive stellar disks which dominate the dynamics of the central regions. The other galaxies from the sample are less massive systems that exhibit a maximum rotation velocity $v_c$\\,$<$\\,200\\,km\\,s$^{-1}$. For those objects the total mass of the dark halo within the optical radius is higher and was found to, at least, equal the stellar mass. This trend is graphically presented in Figure~\\ref{vc2fdcomp}. Our results can be compared to \\citet{ath87}. These authors inferred disk and halo mass fractions from spiral structure constraints. The small points displayed in Figure~\\ref{vc2fdcomp} represent a subsample of the total sample (given in Athanassoula et al.~1987, Table A2), selected for late type galaxies with a bulge mass $M_{\\rm bulge} < 20$\\,\\% $M_{\\rm disk}$ and a maximum rotation velocity of more than 100\\,km\\,s$^{-1}$. For comparison the stated disk-to-halo mass ratio was converted into our scheme of quantifying the disk mass fraction ${\\rm f_d}$. It can be clearly seen that the trend that emerged from our small dataset is supported by the results from \\citet{ath87}. In this sample there is no late type spiral galaxy with a maximum rotation velocity of over 200\\,km\\,s$^{-1}$ that seems to be in agreement with a substantially submaximal stellar disk. For less massive systems this is not the case anymore. Apparently galaxies with a wide range of dark halo and disk mass decompositions can exist and maintain spiral structure. In light of this, the results from \\citet{CR99} might be explained that in a statistical sample of spiral galaxies the heavy and clearly maximum disk galaxies could account for only a relatively small fraction and most of the ``lighter'' high surface brightness galaxies exhibit already a considerable dark mass fraction. Indeed, in the Courteau \\& Rix sample, only roughly a third of the galaxies exhibit maximal rotation velocities $v_c$\\,$>$\\,200\\,km\\,s$^{-1}$. However, beyond the discussion of the disk mass fraction in spiral galaxies, at present there is growing evidence that galaxy size dark halos are not cuspy in their centers, as claimed by standard cold dark matter (CDM) models. \\citep{moo94,flo94,moo99b,sal00,bor01,deb01,vdb01}. This circumstance was first found for low surface brightness and dwarf galaxies, that supposedly are comprised of a massive dark halo. Most of the authors argued that this also applies to high surface brightness galaxies. For the present analysis, the functional form of the dark halo profile has only a second order effect on the results as long as the models describe well the overall shape of the observed rotation curves. Thus, we decided not to distinguish between different dark halo profiles. However, the results from this study, which mostly confirm the strong dynamic influence of the stellar disk in massive high surface brightness spiral galaxies within the optical radius, provide very little room for a strongly cusped halo core." }, "0212/astro-ph0212259_arXiv.txt": { "abstract": "We have found for the first time a Balmer edge feature in the Big Blue Bump emission of a quasar. The feature is seen in the polarized flux spectrum of the quasar, where all the emissions from outside the nucleus are scraped off and removed. The existence of the Balmer-edge absorption feature directly indicates that the Big Blue Bump is indeed thermal and optically-thick. ", "introduction": "Among the various components of a quasar emission, the optical/UV component, called Big Blue Bump (BBB), is energetically the most dominant. The BBB is often assumed to be from optically-thick thermal emission from an accretion flow, such as an accretion disk. However, this fundamental issue (i.e. the emission mechanism of the BBB) is actually very far from being solved, since observations are hardly said to be well described by disk models. Among several serious problems are the continuum slope and apparent lack of continuum edges. In order to explain the observed optical/UV slope (e.g. $F_{\\nu} \\propto \\nu^{-0.3}$, Francis et al. 1991), the disk has to be rather cool. However, naively, in a cool disk, its atmosphere would show large continuum edges (but see below). Apparently, we do not see such features. ", "conclusions": "Figure~1 shows our recent Keck spectropolarimetry data of a quasar. Thick line is the polarized flux spectrum, while the dotted line is the total flux spectrum scaled to roughly match the polarized flux at the red side. Emission lines are essentially all absent in the polarized flux (see Fig.2 which shows that the polarization clearly decreases at the line wavelengths). The slope of the polarized flux at the red side is roughly the same as that of the total flux. However, we find that the slope changes at the bluer side of $\\sim$4000\\AA\\ in the rest frame, just where the 3000\\AA\\ bump starts in the total flux (there might also be a possible up-turn at the bluer side of $\\sim$3600\\AA). This is an expected Balmer-edge absorption feature, and directly indicates that the Big Blue Bump is indeed thermal and optically thick, without involving any particular model of the nucleus. \\bigskip \\unitlength 1cm \\begin{figure} \\hbox to \\textwidth{\\hfil \\begin{minipage}{7cm} \\begin{picture}(5,5) \\put(0,0){\\psfig{figure=kishimoto_fig1.ps,width=6cm}} \\end{picture} \\caption{{\\footnotesize The polarized flux and total flux of Ton202, taken at Keck in May 2002.}} \\end{minipage} \\hfil \\begin{minipage}{7cm} \\begin{picture}(5,5) \\put(0,0){\\psfig{figure=kishimoto_fig2.ps,width=6cm}} \\end{picture} \\caption{{\\footnotesize The normalized Stokes $q$ and $u$, with the scaled total flux at the bottom for reference.}} \\end{minipage} \\hfil} \\end{figure}" }, "0212/astro-ph0212403_arXiv.txt": { "abstract": "We present results from the first hydrodynamical star formation calculation to demonstrate that close binary stellar systems (separations $\\lsim 10$ AU) need not be formed directly by fragmentation. Instead, a high frequency of close binaries can be produced through a combination of dynamical interactions in unstable multiple systems and the orbital decay of initially wider binaries. Orbital decay may occur due to gas accretion and/or the interaction of a binary with its circumbinary disc. These three mechanisms avoid the problems associated with the fragmentation of optically-thick gas to form close systems directly. They also result in a preference for close binaries to have roughly equal-mass components because dynamical exchange interactions and the accretion of gas with high specific angular momentum drive mass ratios towards unity. Furthermore, due to the importance of dynamical interactions, we find that stars with greater masses ought to have a higher frequency of close companions, and that many close binaries ought to have wide companions. These properties are in good agreement with the results of observational surveys. ", "introduction": "The process of star formation preferentially produces binary stellar systems (e.g.\\ Duquennoy \\& Mayor 1991). The favoured mechanism for explaining this high frequency of binaries is the collapse and fragmentation of molecular cloud cores (e.g.\\ Boss \\& Bodenheimer 1979; Boss 1986; Bonnell et al.\\ 1991; Nelson \\& Papaloizou 1993; Burkert \\& Bodenheimer 1993; Bate, Bonnell \\& Price 1995). However, while fragmentation can readily create wide binary systems (separations $\\gsim 10$ AU), there are severe difficulties with fragmentation producing close binaries directly. This is a significant deficiency since approximately 20\\% of solar-type stars have main-sequence companions that orbit closer than 10 AU (Duquennoy \\& Mayor 1991), and the frequency of massive spectroscopic binaries appears to be even higher (Garmany, Conti \\& Massey 1980; Abt et al.\\ 1990; Morrell \\& Levato 1991; Mason et al.\\ 1998). As a molecular cloud core begins to collapse, the formation of wide binaries through fragmentation is possible because the gas easily radiates away the gavitational potential energy that is released. The gas remains approximately isothermal and, thus, the Jeans mass decreases with density as $\\rho^{-1/2}$. However, at densities of $\\gsim 10^{-13}$ g~cm$^{-3}$ or $n({\\rm H}_2)\\gsim 10^{10}$ cm$^{-3}$ (Larson 1969; Masunaga \\& Inutsuka 2000) the rate of heating from dynamical collapse exceeds the rate at which the gas can cool. The gas heats up, and the Jeans mass begins to increase so that a Jeans-unstable region of gas becomes Jeans-stable. This results in the formation of a pressure-supported fragment with a mass of several Jupiter-masses and a radius of $\\approx 5$ AU (Larson 1969). Fragmentation on smaller scales is inhibited by thermal pressure. Therefore, initial binary separations must be $\\gsim 10$ AU. The formation of such pressure-supported fragments is frequently refered to as the opacity limit for fragmentation (Low \\& Lynden-Bell 1976; Rees 1976) and may set a lower limit to the mass of brown dwarfs (Boss 1988; Bate, Bonnell \\& Bromm 2002). A possibility for fragmentation at higher densities (hence on smaller length scales) exists when the pressure-supported fragment has accreted enough material for its central temperature to exceed 2000 K. At this temperature, molecular hydrogen begins to dissociate, which provides a way for the release of gravitational energy to be absorbed without significantly increasing the temperature of the gas. Thus, a nearly isothermal second collapse occurs within the fragment that ultimately results in the formation of a stellar core with radius $\\approx 1 R_\\odot$ \\cite{Larson1969}. Several studies have investigated the possibility that fragmentation during this second collapse forms close binary systems directly (Boss 1989; Bonnell \\& Bate 1994; Bate 1998, 2002). Boss \\shortcite{Boss1989} found that fragmentation was possible during this second collapse, but that the fragments spiralled together due to gravitational torques and did not survive. Bonnell \\& Bate \\shortcite{BonBat1994} found that fragmentation to form close binaries and multiple systems could occur in a disc that forms around the stellar core. However, both these studies began with somewhat arbitrary initial conditions for the pressure-supported fragment. Bate \\shortcite{Bate1998} performed the first three-dimensional calculations to follow the collapse of a molecular cloud core through the formation of the pressure-supported fragment, the second collapse, and the formation of the stellar core and its surrounding disc. In these and subsequent calculations (Bate 2002), Bate found that the second collapse did not result in sub-fragmentation due to the high thermal pressure and angular momentum transport via gravitational torques. In this paper, we present results from the first hydrodynamical star formation calculation to produce dozens of stars and brown dwarfs while simultaneously resolving beyond the opacity limit for fragmentation. Despite the fact that no close binaries (separations $\\lsim 10$ AU) are formed by direct fragmentation, we find that the calculation eventually produces several close binary systems through a combination of dynamical interactions in multiple systems, and the orbital decay of wide binaries via gas accretion and their interactions with circumbinary discs. The paper is structured as follows. In section 2, we briefly describe the numerical method and the initial conditions for our calculation. In section 3, we present results from our calculation and compare them with observations. Finally, in section 4, we give our conclusions. ", "conclusions": "We have presented results from a hydrodynamic calculation of the collapse and fragmentation of a turbulent molecular cloud to form 50 stars and brown dwarfs. The calculation mimics the opacity limit for fragmentation by using a barotropic equation of state to model the heating of collapsing gas at high densities. This results in a minimum mass of $\\approx 10$ Jupiter masses for the lowest-mass brown dwarfs (see Bate et al.\\ 2002) and prevents fragmentation on scales smaller than $\\approx 10$ AU. Despite this lower limit on the initial minimum separation between fragments, we find that as the stellar groups and unstable multiple systems evolve in the gas-rich environment, a high frequency of close binary systems (separations $\\lsim 10$ AU) is produced. Examining the history of these close binary systems, we find that they are formed through a combination of dynamical interactions in unstable multiple systems, and orbital decay due to accretion and/or the interaction of binary and triple systems with circumbinary and circumtriple discs. These formation mechanisms allow realistic numbers of close binary systems to be produced without the need for fragmentation on length scales $<10$ AU. This avoids the difficulties associated with the fragmentation of optically-thick gas during the collapse initiated by the dissociation of molecular hydrogen (Boss 1989; Bonnell \\& Bate 1994; Bate 1998, 2002). As a consequence of the dependence of close binary formation on dynamical exchange interactions and the accretion of material with high specific angular momentum, we find that close binaries tend not to have extreme mass ratios. All of our systems have mass ratios $q \\gsim 0.3$. Furthermore, the frequency of close binaries is dependent on mass in that massive stars are more likely to have close companions than lower mass stars. These properties are in good agreement with the results of observational surveys. At the end of our calculation, many of the close binaries are members of hierarchical triple systems. Although these systems may not yet have finished evolving, the implication is that many close binaries ought to have wider companions. Recent observations support this hypothesis, but larger surveys to determine the frequency of wide companions to close binary systems are necessary to demonstrate it conclusively." }, "0212/astro-ph0212129_arXiv.txt": { "abstract": "We present a detailed analysis of the error budget for the TreePM method for doing cosmological N-Body simulations. It is shown that the choice of filter for splitting the inverse square force into short and long range components suggested in Bagla (2002) is close to optimum. We show that the error in the long range component of the force contributes very little to the total error in force. Errors introduced by the tree approximation for the short range force are different from those for the inverse square force, and these errors dominate the total error in force. We calculate the distribution function for error in force for clustered and unclustered particle distributions. This gives an idea of the error in realistic situations for different choices of parameters of the TreePM algorithm. We test the code by simulating a few power law models and checking for scale invariance. ", "introduction": "Cosmological N-Body simulations have played a crucial role in improving our understanding of formation of large scale structure. These have filled large gaps in a domain where analytical solutions do not exist. N-Body simulations have also played a useful role by testing scaling relations derived from physically motivated ansatze. Limitations of computing resources and our ability to simulate physical processes numerically have meant that N-Body simulations give only approximate solutions. It is possible to test whether the approximations in evolution of the system affects estimation of physical quantities of interest so the results are generally more reliable than those based on approximate evolution of the system. A large number of methods have been used for doing Cosmological N-Body simulations \\citep{edbert_araa}. All of these use some approximation for calculation of force. Approximations are used because direct summation over all pairs of particles scales as $O(N^2)$, where $N$ is the number of particles, making the calculation very time consuming for large $N$. The use of these approximations reduces the number of calculations required to $O(N\\ln{N})$ or less. These approximations also introduce inaccuracies in the computed force. The TreePM code \\citep{treepm}, that we study here, is a hybrid technique for carrying out large N-Body simulations to study formation and evolution of large scale structures in the universe. It is a combination of the \\citet{bh86} Tree code and a Particle-Mesh code \\citep{sim_book}. The TreePM method combines high resolution of tree codes with the ability of PM codes to compute the long range force with periodic boundary conditions. In this paper we carry out a comprehensive study of the TreePM code. We analyse errors in estimation of force in both the tree and the PM components, and also study the distribution of errors for different distributions of particles. We also study the variation of CPU time required for the TreePM code as we vary parameters describing the mathematical model of this method. ", "conclusions": "In this paper we have presented a detailed study of performance characteristics of the TreePM method. We have analysed different sources of error and suggested remedies for the main source of errors. The analysis of errors in realistic situations shows that the TreePM method performs very well and gives acceptably small errors. This method compares favourably with other comparable methods such as implementations of the tree code like GADGET \\citep{gadget} and hybrid methods such as the TPM \\citep{tpm,tpm2}. From the numbers available in these papers, we find that the errors in the recommended configuration of the TreePM method are comparable with those in GADGET and lower than those in the TPM method. In terms of CPU time taken per step per particle, we again find that the numbers are comparable. Of course, it is not possible to make a detailed comparison of this quantity as the whole approach is different. E.g., we do not use multiple time steps whereas GADGET relies heavily on these to optimise the speed. On the other hand GADGET and TreePM have a uniform force resolution whereas TPM does not and hence the time taken is likely to vary more strongly with the amplitude of clustering for the TPM code as compared to the other two. Splitting of force into a short range and a long range part has a useful implication in terms of parallel implementation. Unlike the tree methods, the TreePM method involves a considerably smaller overhead in terms of inter-process communication and hence is likely to score over other methods in terms of scaling for a very large number of CPUs. In summary we can state that TreePM is a competitive method for doing Cosmological N-Body simulations. Explicit use of three parameters gives users control over errors and CPU time required." }, "0212/hep-th0212312_arXiv.txt": { "abstract": "The possibility of obtaining singularity free cosmological solutions in four dimensional effective actions motivated by string theory is investigated. In these effective actions, in addition to the Einstein-Hilbert term, the dilatonic and the axionic fields are also considered as well as terms coming from the Ramond-Ramond sector. A radiation fluid is coupled to the field equations, which appears as a consequence of the Maxwellian terms in the Ramond-Ramond sector. Singularity free bouncing solutions in which the dilaton is finite and strictly positive are obtained for models with flat or negative curvature spatial sections when the dilatonic coupling constant is such that $\\omega < - 3/2$, which may appear in the so called $F$ theory in 12 dimensions. These bouncing phases are smoothly connected to the radiation dominated expansion phase of the standard cosmological model, and the asymptotic pasts correspond to very large flat spacetimes. ", "introduction": "Superstring is the most promising candidate to describe a unified theory of all interactions, gravity included. There are five consistent superstring theories in 10 dimensions, which are connected among themselves through duality transformations. To each superstring theory, there is a corresponding supergravity theory in 10 dimensions. All of them can be obtained from the 11 dimensional supergravity theory. This indicates that those superstring theories are different manifestations of a unique 11 dimensional framework, that has been named $M$ theory~\\cite{polchinski,green,kiritsis}. Moreover, the superstring type-IIB can be recast in a more geometrical form in a 12 dimensional model, suggesting that perhaps a yet more fundamental framework may exist in 12 dimensions, which has been called $F$ theory~\\cite{pope}. The physical properties of superstring theories become relevant at energy scales comparable with the Planck scale. This renders very improbable that superstring phenomenology may be tested in the near future in some laboratory experiment (see, however, Ref.~\\cite{randal} in which the Planck mass is lowered to TeV scale by accounting for large extra dimensions). According to the hot big bang scenario, however, energy scales even as high as the usual Planck scale ($\\mP\\sim 10^{19}$GeV) may have been reached in the very early universe. Hence, for the moment, cosmology seems to be the most natural arena where the consequences of superstring theories may be tested. The pre-big bang paradigm~\\cite{PBB} was one of the first ideas to implement superstring theories in this framework. Some relics of a cosmological string phase may also be identified~\\cite{bdp}, opening perhaps the possibility of testing superstring models. Furthermore, superstring theories open the possibility that some typical drawbacks of the standard cosmological model, such as the existence of an initial singularity, may be solved in the context of superstring cosmological models. The goal of the present paper is to show that, under certain conditions, it is possible to obtain completely regular bouncing cosmological models in the context of effective actions constructed from superstring theories (not involving, in particular, negative energies~\\cite{ppnpn2}), for which, moreover, the dilaton is strictly positive (nonvanishing) at all times and never diverges. String cosmology is based on the low energy limit of string or superstring theories. In the most general case of the supersymmetric string theory, there are two sectors, related with the choice of periodic or antiperiodic boundary conditions on the spinor fields, namely the Ramond and Neveu-Schwarz (NS) sectors~\\cite{polchinski,green}. Since fermions can be either left or right moving, this leads to four possible combinations of these sectors. The bosonic fields arise both from the NS-NS and Ramond-Ramond (RR) sectors. The NS-NS sector provides the Einstein-Hilbert term, as well as a three-form, called the axionic field, and the dilaton. The latter is directly related with the string perturbative expansion parameter and takes the form of a Brans-Dicke-like scalar field, nonminimally coupled to both the Einstein-Hilbert and the axionic fields. In the RR sector, $p$ forms appear, which are minimally coupled to the dilaton field. The dimensions of the $p$ forms depend on the specific superstring theory which is under consideration. In cosmological applications, we are interested in scalar fields that emerge from these different $p$ forms. They differ by the way they couple with the dilatonic field and between themselves. Out of the many different possibilities stemming from string theory, one can construct in general an effective action suitable for cosmological applications with two main features: scalar fields coming from the NS-NS sector and nonminimally coupled to the dilaton, and scalar fields from the RR sector which are minimally coupled to the dilaton. All the possibilities are not exhausted by these two frameworks, but they summarize the general aspects of what has been proposed in the literature as far as effective actions coming from string theory are concerned. One can also obtain phenomenological matter fields by averaging on some components of those original $p$ forms. This brief description explicits the great richness of the string effective action procedure, which implies a large variety of possible cosmological models. Notice that these effective actions exhibit great similarities with those that can be obtained from multidimensional and supergravity theories. To select one cosmological model that could be a candidate to describe the physical world, two possible prescriptions are: either the cosmological model is completely regular, with no curvature or expansion parameter singularity, or it is compatible with observation; ultimately, both criteria should be satisfied. In the present work we will concentrate on the first. The second criterion, which presents some specific challenges, will be treated in the future~\\cite{future}. The search for singularity free cosmology in string theories is not a new subject~\\cite{lidsey,vasquez,picco,kirill,branden}. The string action at tree level does not lead in general to singularity free cosmological solutions, at least when the strict string case ($\\omega = - 1$, $\\omega$ being the dilatonic coupling parameter) is considered. The pre-big bang model~\\cite{PBB}, which is an example of a string cosmology, requires the introduction of nonlinear curvature terms in order to achieve a smooth transition from a curvature growing phase to a curvature decreasing phase. If large negative values of the dilatonic coupling parameter $\\omega$ are allowed, it is possible, in some cases, to obtain completely regular models, including in the dilatonic sector~\\cite{kirill}. This may be achieved mainly in models with spatial sections with negative curvature. Here, it will be shown that regular cosmological models may also be obtained if a radiation fluid is coupled to the string action at the tree level. Such a radiation fluid can have a fundamental motivation, for example, in the case of the superstring type IIB theory, where a 5-form appears in the RR sector. Truncation and dimensional reduction of this 5-form lead to a Maxwell term in four dimensions with the desired features~\\cite{fabris}. Hence, the model to be studied here is totally based on superstring theories. The string motivated phenomenological term included under the form of a radiation fluid makes it possible to connect smoothly such string cosmological models to the radiation phase of the standard cosmological model before nucleosynthesis. In Ref.~\\cite{picco}, models motivated by string theory similarly including a radiation fluid have been studied, restricted to flat spatial sections and $\\omega > -3/2$. In such cases, bouncing solutions have been obtained only for $\\omega < -4/3$. Furthermore, for these solutions, the dilaton vanishes in the infinite past, raising doubts on the validity of the tree level action in such a region. In the present paper, the curvature of the spatial sections and the value of $\\omega$ are kept arbitrary. New bouncing regular solutions are then obtained, for which, as mentioned above, the dilaton remains finite and nonvanishing at all times. When $\\omega > -3/2$, which includes the strict string case ($\\omega = -1$), the solutions can only be bouncing provided the spatial sections have negative curvature and if the dilaton is always negative, which is not consistent with the higher dimensional framework of stringlike theories, and implies a repulsive gravity. We shall henceforth disregard such solutions. When $\\omega < -3/2$, the bouncing solutions are obtained for models with flat or negative curvature, and the dilaton is strictly positive at all times. In the following section, we derive effective string motivated actions in four dimensions. In particular, we show how to obtain an effective string action in four dimensions with $\\omega < -3/2$ in the context of the so-called $F$ theory in twelve dimensions. In Sec. III we derive nonsingular cosmological solutions from these effective theories, which are thoroughly discussed in Sec. IV from the point of view of violation of energy conditions. We end up with the conclusions in Sec. V. ", "conclusions": "We have constructed fully regular cosmological solutions in the framework of effective actions derived from string theory principles. These solutions present bouncing behaviors for a wide range of parameters ($\\omega < -3/2$), and are singularity free; furthermore, the spacetimes they lead to are geodesically complete, thereby improving the so-called horizon problem of standard cosmology. Stemming from string theory in the context of the so-called $F$ theory in twelve dimensions, where it is possible to have $\\omega < -3/2$, they have a reasonably sound basis as long as the dilaton is strictly positive and finite in such a case. As a consequence, it is not necessary to go beyond the tree level approximation in any part of their histories: the analytic solutions exhibited above can describe the whole history of the cosmological models they represent. Their consequences may, in turn, be used as cosmological tests. Remembering that the radiation fluid included here also has a motivation in the superstring type IIB action, this turns out to be, to our knowledge, the first case where a complete regular bouncing cosmological solution is obtained in the string framework and related theories, which moreover is smoothly connected with the standard cosmological model radiation dominated phase. This solution may have flat or negative curvature spatial sections. In the axionic and RR cases with $k=0$ or $k=-1$, there are nonsingular bouncing solutions for $-3/2<\\omega<-4/3$ but with vanishing dilaton in the beginning, where the tree level action cannot be trusted, and bouncing solutions with an initial curvature singularity if $-4/3<\\omega<0$. If $k = - 1$ and $-3/2<\\omega<0$ (normal, including the pure string case), one can have singularity free bouncing solutions with, however, a negative definite dilaton field. As all the models with $\\omega<-3/2$ have the interesting feature to approach flat spacetime in the infinite past (either in Milne coordinates for $k=-1$, or the infinitely large radiation dominated standard model with $k=0$), there is the possibility to implement a quantum spectrum of perturbations in the initial asymptotics without any trans-Planckian problem~\\cite{transP}, and, at the same time, to accomplish a smooth transition to the standard cosmological model when, after the bounce, a standard radiation dominated phase is recovered (asymptotically in the $k=0$ case), preserving some of its main achievements like, \\eg primordial nucleosynthesis. The bouncing solutions with $\\omega>-3/2$ and positive dilaton still present some sort of trans-Planckian problem as long as the string expansion parameter diverges initially and one must go beyond the tree level action in such cases. Notice that, in the cases where the dilaton is strictly positive, the initial value of the dilatonic field can be made smaller than its final value. Hence, the gravitational coupling can be initially given a much greater value than it would have today. This opens the possibility to solve the hierarchical problem of the gravitational coupling, in a spirit similar to the so-called brane cosmology~\\cite{langlois}." }, "0212/astro-ph0212513_arXiv.txt": { "abstract": "The variability of gamma-ray burst (GRB) is thought to be correlated with its absolute peak luminosity, and this relation had been used to derive an estimate of the redshifts of GRBs. Recently Amati et al. presented the results of spectral and energetic properties of several GRBs with known redshifts. Here we analyse the properties of two group GRBs, one group with known redshift from afterglow observation, and another group with redshift derived from the luminosity - variability relation. We study the redshift dependence of various GRBs features in their cosmological rest frames, including the burst duration, the isotropic luminosity and radiated energy, and the peak energy $E_p$ of $\\nu F_\\nu$ spectra. We find that, for these two group GRBs, their properties are all redshift dependent, i.e. their intrinsic duration, luminosity, radiated energy and peak energy $E_p$, are all correlated with the redshift, which means that there are cosmological evolution effects on gamma-ray bursts features, and this can provide an interesting clue to the nature of GRBs. If this is true, then the results also imply that the redshift derived from the luminosity - variability relation may be reliable. ", "introduction": "The study of gamma-ray bursts (GRBs) afterglows has enable the measurement of their distances, so far GRBs are known as an explosive phenomenon occurring at cosmological distances, emitting large amount of energy mostly in the gamma-ray range (see, e.g. Piran 1999; Cheng \\& Lu 2001 for a review). So GRBs can provide useful information about the early epochs in the history of the universe. Although a great achievements have been made about the GRB afterglows, we still know little about the origin of gamma-ray bursts, the reason is that the GRBs with known redshifts are relatively rare, now there are only about 20 GRBs with known redshifts, so it is difficult to do some statistics about GRBs features, such as their luminosity function, duration distribution, etc.. However, two important correlations have been discovered, i.e. between the degree of variability of the gamma-ray burst light curve and the GRB luminosity (Ramirez-Ruiz \\& Fenimore 1999; Feminore \\& Ramirez-Ruiz 2001), and between the differential time lags for the arrival of burst pulses at different energies and the GRB luminosity (Norris, Marani \\& Bonnell 2000), although these correlations are still tentative, they offer the possibility to derive independent estimates of the redshifts of GRBs. Recently Amati et al. (2002) have reported the spectral and energetic properties of several GRBs with known redshifts, these bursts were all detected by BeppoSAX and have good-quality time-integrated spectra. In addition, Lloyd-Ronning \\& Ramirez-Ruiz (2002) have found that bursts with highly variable light curves have greater $\\nu F_\\nu$ spectral peak energies in their cosmological rest frames. These results reinforce the validity of the redshift estimates derived from the luminosity - variability relation. Here we will discuss the properties of two group GRBs, one group includes the bursts with known redshifts and well-defined spectra detected by BeppoSAX, and another group consists of bursts whose redshifts are derived from the luminosity - variability relation. We will show that the properties of these two group GRBs are all correlated with redshift, which suggests that the luminosity - variability relation may be reliable, and furthermore the GRBs' features are redshift dependent. ", "conclusions": "In previous section we have shown that the properties of our two group GRBs, one group includes 9 GRBs with secure redshifts derived from the afterglow observation, another group consists of 159 GRBs with known peak energy and their redshifts are derived from the luminosity - variability relation, are all correlated with the redshifts, which reinforces the validity of the luminosity - variability distance indicator. Our results further support the conclusion obtained by Lloyd-Ronning \\& Ramirez-Ruiz (2002), they found that there is positive correlation between the peak energy in the cosmological rest frame and the variability for gamma-ray bursts whose redshifts are derived either from optical spectral features or from the luminosity - variability distance indicator. Since the BATSE GRB sample is flux truncated, i.e. only those bursts with flux exceeding the threshold flux can be detected, so it is necessary to discuss this selection effects on the statistical results. Here we use the Monte Carlo simulation method. We find that, after correcting the selection effects, the cosmological evolution trends are still exist, although they are much shallower than the trends found in the face values of the data. For example, if ignored the flux truncation effect, we obtained the relation $L \\propto (1+z)^{2.5\\pm 0.1}$, while when the selection effects are taken into account, we got the relation $L \\propto (1+z)^{1.7\\pm 0.5}$, which is consistent with the value $L \\propto (1+z)^{1.4\\pm 0.5}$ obtained by Lloyd-Ronning et al. (2002). Fig.5 illustrates our simulated results, where the circles are the 300 bursts produced by the simulation, the solid line is the flux threshold for BATSE, and the dashed line is the flux threshold for Swift. From this figure it is obvious that the property of the \"observed\" sample should depend on the adopted flux threshold, for different flux threshold their statistical properties are different. For example, when taking the BATSE flux threshold, there are 100 bursts with flux lower than the threshold, while when taking the Swift flux threshold, there are only 7 bursts with flux lower than the threshold, so in this case the observed $L-z$ relation should close to the true $L-z$ relation. Therefore we expect that the luminosity - redshift relation for bursts observed by Swift should be shallower than that for bursts observed by BATSE. Fig.6 and Fig.7 show that there is a good correlation between the peak energy and luminosity for both group GRBs, and the relation $E_p \\propto L^{1/2}$ can account for the observed data quite well. Up to now the location of the GRB emission site is still unsettled, although the internal shock model is thought to be more reasonable than the external shock model. Zhang \\& Meszaros (2002b) analysed various fireball models within a unified picture and investigated the $E_p$ predictions of different models. It is known that for internal shock model, if the GRB bulk Lorentz factors are not correlated with the luminosities, then there is the relation $E_p \\propto L^{1/2}$, while for external shock model $E_p \\propto \\Gamma ^4$, where $\\Gamma$ is the shock Lorentz factor. So our results suggest that the gamma-ray burst emission are more likely from the internal shock. Frail et al. have discussed the afterglow properties of several GRBs with known redshifts, they assumed that the breaks in the afterglow light curves are caused by the sideways expansion of the jet, and then they concluded that the GRB emission energy is nearly a constant, $E\\sim 5\\times 10^{50}$ ergs (Frail et al. 2001). However, Fig.3 shows that the isotropic radiated energy increases with redshift, so if the conclusion of Frail et al. is true, then we notice that the jet opening angle must decrease with the redshift, as shown by Fig.8, where the data points are taken from the paper of Frail et al. (2001). This point is very interesting, since it can put constraints on the central engines of GRBs. Of course, this phenomena can also be explained within the framework of a structured universal jet model (Zhang \\& Meszaros 2002a; Rossi et al. 2002). In this model, an observer closer to the jet axis would detect a higher luminosity, thus at higher redshift, smaller viewing angle detections are preferred due to luminosity selection effect. \\begin{figure} \\centerline{\\psfig{file=fig8.eps,width=0.6\\textwidth}} \\caption{The relation between the jet opening angle and redshift. The data are taken from the paper of Frail et al. (2001). } \\end{figure} It should be noted that in our analysis we have not considered the errors coming from the luminosity - variability relation. We know that the relation between luminosity and variability is somewhat scatter, the correlation coefficient $n$ ($L\\propto V^n$) can be range from 2.2 to 5.8 (the best value is 3.3, see Fenimore \\& Ramirez-Ruiz 2001), so it is natural that the redshifts and luminosities inferred from this luminosity - variability relation should have large errors, and these errors should be somehow transferred to the final errors in the correlation indices. However this effect is very complicated, we hope that this effect can be taken into account in the future work. In summary, in this paper we discuss the properties of two group GRBs, one group with known redshift from afterglow observation, and another group with redshift derived from the luminosity - variability relation. We find that the properties of these two group GRBs are all correlated with the redshifts, which reinforces the validity of the redshift estimates derived from the luminosity - variability relation. If this is true, then we see that the burst features, such as their intrinsic duration, luminosity, radiated energy and peak energy $E_p$, are all redshift dependent, which means that there are cosmological evolution effects on gamma-ray bursts features, and this can provide an interesting clue to the nature of GRBs." }, "0212/astro-ph0212039_arXiv.txt": { "abstract": "We present the first results obtained at CFHT with the TRIDENT infrared camera, dedicated to the detection of faint companions close to bright nearby stars. The camera's main feature is the acquisition of three simultaneous images in three wavelengths (simultaneous differential imaging) across the methane absorption bandhead at 1.6~$\\mu $m, that enables a precise subtraction of the primary star PSF while keeping the companion signal. The main limitation is non-common path aberrations between the three optical paths that slightly decorrelate the PSFs. Two types of PSF calibrations are combined with the differential simultaneous imaging technique to further attenuate the PSF: reference star subtraction and instrument rotation to smooth aberrations. It is shown that a faint companion with a $\\Delta H$ of 10 magnitudes would be detected at $0.5^{\\prime \\prime}$ from the primary. ", "introduction": "The next generation high order adaptive optics (NGAO) systems that are currently in development will produce high Strehl ratio images in the infrared on 10~m class telescopes. If those NGAO systems are to be used to search for very faint companions (brown dwarfs and exoplanets), it is of great importance to understand the limits for high contrast imaging on current adaptive optics (AO) systems and see how they would affect NGAO systems performances. Static aberrations have long been known to be the limiting factor for space-based telescopes when attempting high contrast imaging for faint companion detection (\\cite{Brown90}). If the telescope physical conditions change in time (like point spread function (PSF) breathing for HST), the structure becomes quasi-static and produces PSF structures that evolve slowly in time, making difficult a good PSF calibration when using reference stars. Long AO corrected exposures have shown that ground-based imaging is not free from this problem. When using an AO system that delivers partially diffracted PSFs, the final wavefront is an interference between the AO wavefront residuals and the optical path wavefront aberrations to the detector. If enough random aberrations are removed by the AO system, a coherent PSF starts to appear. This is also true for the quasi-static portion of the wavefront. As more turbulence is removed, the quasi-static wavefront errors not corrected by the AO system will introduce coherent structures that will not average out in time and will mask faint companions. A partially-corrected long exposure AO observation thus suffers from the same problem that limits space telescopes. The current limit for detecting faint companions with existing AO systems is not the atmospheric turbulence correction efficiency but rather a quasi-static PSF calibration problem. \\vspace{0.3cm} In the past few years, our group has developed a specialized infrared camera, TRIDENT (\\cite{Marois2000a,Marois2002}), to overcome the PSF calibration problem. The main feature of TRIDENT is to acquire three simultaneous images in three distinct narrow spectral bands. It is possible to enhance the star/companion contrast after image combinations by selecting special spectral features that are typical of the companion and not of the star (\\cite{Smith87,Rosen87,Racine99,Marois2000b}). In TRIDENT, the three wavelengths (1.567~$\\mu$m, 1.625~$\\mu$m and 1.680~$\\mu$m, 1\\% bandwidth) have been selected across the 1.6 $\\mu$m methane absorption bandhead that is only present in the spectrum of cold ($T_{\\rm{eff}}$ $<$ 1470~K, \\cite{Feg96}) substellar objects. The 1.567~$\\mu$m image ($I_{\\lambda_1}$) shows the star and companion while the 1.625 and 1.680~$\\mu$m images ($I_{\\lambda_2}$ and $I_{\\lambda_3}$) show the star with a fainter companion due to the methane absorption bandhead. The 1.625 and 1.680~$\\mu$m images can thus be used as reference PSFs to correct the first and second order PSF structure evolution with wavelength. Since the three wavelengths are simultaneous, each observed wavelength sees the same PSF atmospheric distortion, a good PSF correlation between the three wavelengths can thus be achieved. This concept would remove atmospheric speckles and problems associated with the PSF evolution with telescope pointing, thermal changes and atmospheric r$_0$ variations. PSF subtraction is achieved by calculating simple and double image differences (SD and DD) obtained with the following algorithms (\\cite{Marois2000b}): \\begin{center} $sd_{1-2} = I_{\\lambda_1} - I_{\\lambda_2}$ and $dd = sd_{1-2} - $k$*sd_{1-3}$ \\end{center} The DD can bring the atmospheric speckle noise below the level of the photon noise and remove the PSF quasi-static structure to its second order evolution with wavelength. \\clearpage ", "conclusions": "Quasi-static aberrations in AO corrected images are the main problem when attempting high contrast imaging for faint companion searches. If quasi-static aberrations cannot be minimized or removed in NGAO systems, an optimized camera will be essential to calibrate and subtract them. If a multiple optical path camera is considered, non-common path aberrations need to be minimized to avoid PSF decorrelation. Reference star subtraction and aberration smoothing by instrument rotation improve by one order of magnitude the faint companion detection threshold. Typical attenuation in good seeing conditions are 10 magnitudes in $H$ band at $0.5^{\\prime \\prime}$ on a 3.6~m telescope. \\vspace{0.5cm} This work is supported in part through grants from NSERC, Canada and from Fonds FQRNT, Qu\\'{e}bec." }, "0212/astro-ph0212455_arXiv.txt": { "abstract": "A comprehensive study on compactness has been carried out on the 2dF Galaxy Group Catalogue constructed by Merch\\'an \\& Zandivarez. The compactness indexes defined in this work take into account different geometrical constraints in order to explore a wide range of possibilities. Our results show that there is no clear distinction between groups with high and low level of compactness when considering particular properties as the radial velocity dispersion, the relative fraction of galaxies per spectral type and luminosity functions of their galaxy members. Studying the trend of the fraction of galaxies per spectral type as a function of the dimensionless crossing time some signs of dynamical evolution are observed. From the comparison with previous works on compactness we realize that special care should be taken into account for some compactness criteria definitions in order to avoid possible biases in the identification. ", "introduction": "Compact groups (CGs) are small systems of a few galaxies which are in close proximity one another. Their are excellent laboratories for studying galaxy interactions and, in particular, merging processes. Given their high galaxy density (equivalent to those at the centers of rich clusters) and small velocity dispersion ($\\sim 200 \\kms$), CG members are expected to finally merge into one giant elliptical galaxy within a few short crossing times. Historically, CGs were of interest because of the obvious distortion of many of their member galaxies. The first systematic seek for CGs was pioneered by Rose (1977), using a surface number density contrast procedure. The most widely analysed samples are the Hickson Compact Groups (HCGs) (Hickson 1982, Hickson 1997), which have been selected on the basis of population, isolation (avoiding cores of rich clusters) and compactness. Their compactness criteria involve the computation of the mean surface brightness of a group which should be lesser than a maximun limit. This mean was calculated distributing the flux of the member galaxies over the circular area containing their geometric centers. Previous samples have been visually selected, and thus reflect some of the systematic biases intrinsic to bidimensional identification of systems. A geometric bias arise because prolate systems along the line of sight will be preferentially selected. A kinematic bias could enhance the selection of systems which are in a transient compact configuration due to galaxy internal motions. Mamon (1986) has suggested that about half of HCGs are superpositions of galaxies within loose groups (hereafter LGs). This suggestion could imply that groups properties in any particular sample may be strongly influenced by the criteria used to define the sample. Another important clue in order to test the compact groups environment is the color of their galaxy members. It is well known that elliptical galaxies recently formed from mergers of spiral galaxies should be bluer than normal elliptical galaxies. This kind of interactions should be more frecuently observed in a compact group environment. Nervertheless, a study on galaxy members of HCGs made by Zepf, Whitmore \\& Levinson (1991) have show that most of the early-type galaxies have optical colors indistinguishable form those of elliptical galaxies in other environments. Furthermore, there is evidence of a strange absence of strong signs of interactions, strong radio sources or far infrared radiation emission, etc. (Menon 1995, Pildis, Bregman \\& Schombert 1995, Sulentic 1997). Recently, Tovmassian, Yam \\& Tiersch (2001) and Tovmassian (2001) presents new evidence that indicates that almost all HCGs are dynamically associated generally with elongated LGs which are distributed along the elongation of the corresponding groups, suggesting that the HCGs are the compact cores of the latter. Consequently, an important question about the real nature of CGs arise: are CGs a distinct class by themselves or are extreme examples of systems having a particular range of galaxy density and population. This question can be addressed studying the spatial distribution and environment of CGs. However, estimating the velocity dispersion and physical separations of galaxies in groups with a small number of galaxies is highly uncertain. Meaningful conclusions on dynamical properties about systems containing only four or five galaxies requires statistical analysis of large homogeneous samples. \\begin{figure} \\epsfxsize=0.5\\textwidth \\hspace*{-0.5cm} \\centerline{\\epsffile{figzzz.ps}} \\caption{ The median mean nearest neighbour separation $\\langle R_{nn}\\rangle$ (upper panel) and the median virial radius $\\langle R_{vir}\\rangle$ (lower panel) as a function of redshift (filled circles) superimposed to the real data (dots) distribution. } \\label{fig0} \\end{figure} \\begin{figure} \\epsfxsize=0.5\\textwidth \\hspace*{-0.5cm} \\centerline{\\epsffile{graf1.ps}} \\caption{ Example (a): Possible configuration of binary galaxy members of a group separated one another by large distances. Example (b): Configuration of the group galaxy members showing the possibility to find a loose group with a central concentration of galaxies. } \\label{fig00} \\end{figure} \\begin{figure} \\epsfxsize=0.5\\textwidth \\hspace*{-0.5cm} \\centerline{\\epsffile{fig1.ps}} \\caption{ Upper left panel: Scatter plot of the normalized mean nearest neighbour separation of group members in the 2dFGGC versus the normalized virial radius. Upper right panel: Distribution of the normalized mean nearest neighbour separation. Lower right panel: Distribution of the normalized virial radius. Lower left panel: Distribution of the compactness index 1 ($CI_1$) defined in section 3 for groups in the 2dFGGC. } \\label{fig1} \\end{figure} In order to overcome these biases, it has recently become feasible to find CGs using automatic identification. Such a procedure has the advantage of generate a sample that is homogeneous and complete within the criteria specified for the search. Barton et al. (1996) have used a selection criteria (friends-of-friends algorithm) based only on physical extent and association in redshift space. Eventhough Hickson's isolation criteria is not present at all in Barton's work, this technique is more effective in finding groups in regions of higher galaxy density because foreground and background galaxies are automatically eliminated by the velocity selection criteria. Other automatic algorithm for the selection of CGs from large galaxy catalogues has been developed by Iovino et al. (1999). The algorithm is such as to maximize the probability that the groups selected are physically related and partially reproduces the criteria used in the visual search by Hickson (1982), where his isolation criteria is slightly relaxed.\\\\ Since it is very difficult to identify compact groups at high redshifts, more reliable results can be obtained restricting the analysis to low redshift samples. Under this constraint applied on the Updated Zwicky Catalogue, Focardi \\& Kelm (2002) have shown that triplets are characterized by different properties than that obtained for higher order compact groups suggesting the existence of two different galaxy systems in the compact group samples. It is therefore of great interest to obtain larger and deeper samples of CGs, in order to put the CGs properties on a statistical basis. This will help to work out the controversy around the properties of CGs, contradictions that may only be apparent, given our still limited knowledge of the nature of these structures. Currently, one of the largest group catalogues (hereafter 2dFGGC) was constructed by Merch\\'an \\& Zandivarez (2002). They have identified groups in the 2dF public 100K data release using a modified Huchra \\& Geller (1982) group finding algorithm that takes into account 2dF magnitude limit and redshift completeness masks. This catalogue constitutes a large and suitable sample for the study of both, processes in group environments and the properties of the group population itself. The global effects of group environment on star formation was analysed by Mart\\'{\\i}nez et al (2002a) using this catalogue. Dom\\'{\\i}nguez et al (2002) presented hints toward understanding local environment effects on the spectral types of galaxies in groups by studying the relative fractions of different spectral types as a function of the projected local galaxy density and the group-centric distance. Recently, an extensive statistical analysis on galaxy luminosity function in groups was carried out by Mart\\'{\\i}nez et al (2002b). The aim of this work is to perform an analysis on the groups in the 2dFGGC by defining new compactness indexes which are assigned to every group in the sample. Several studies have been made using galaxy spectral type, velocity dispersion, luminosity and crossing time as a function of the compactness indexes. The outline of this paper is as follows. In section 2, we present the 2dF Galaxy Group Catalogue (2dFGGC) used throughout this work. Section 3 describes the compactness indexes definitions while in section 4 we analyse the possible dependence of our indexes with group and galaxy properties. Finally, in section 5 we summarize our conclusions. ", "conclusions": "In this work we report a statistical compactness analysis using the catalogue of galaxy groups constructed by Merch\\'an \\& Zandivarez (2002). Given the size of the original sample and 3-dimensional information our study intend to characterize groups of galaxies according to the level of compactness and analyse its influence on groups and galaxy members. For this purpose, we define two new compactness indexes based on geometrical criteria. Whereas index $CI_1$ prioritizes the distance to the nearest neighbour and the size of the system (eq. 1), index $CI_2$ enhances a possible core concentration in the system (eq. 2). Special cares have been taken over the construction of these indexes in order to avoid possible dependences on redshift and redshift completeness of the parent catalogue (Figures \\ref{fig2} and \\ref{fig3}). With this characterization, we develop a wide analysis over many physical properties of groups and galaxy members. First, we observe that the compactness indexes distribution shows identical behaviours when the group sample is split for low ($\\sigma_r < 300 \\kms$) and high ($\\sigma_r \\ge 300 \\kms$) velocity dispersion. Furthermore, we observe that groups with high and low levels of compactness show the same normalized radial velocity dispersion distributions with a mean of $\\sim 200 \\kms$. This result is consistent with previous ones which reflect that the mean velocity dispersion of compact groups is quite similar to that found for loose groups (Hickson et al. 1992). Analysing the dependence of group compactness with numerical richness we observe that groups with high level of compactness have typically a low number of galaxy members, while most of the loose groups are characterized by a larger number of galaxy members. On the other hand, another study has been made about the fraction of galaxies per spectral type and luminosity as a function of the two compactness indexes (Figures \\ref{fig8}, \\ref{fig9} and \\ref{fig10}). Our results do not show any particular correlation between the above parameters and the compactness level for groups in the sample. The similar behaviour observed in groups with high level of compactness and loose ones probably suggests that this distinction is not fundamental. This result is supported by previous works which state an indistinguishable behaviour between compact and loose groups showing that many compact groups are located within overdense environments (de Carvalho et al. 1997, Barton et al. 1998, Zabludoff \\& Mulchaey 1998). Furthermore, an analysis on X-ray properties of groups shows that it is impossible to separate loose and compact groups on the luminosity-temperature relation, the luminosity-velocity dispersion relation or in the velocity dispersion-temperature relation stating that a more useful distinction is that between X-ray bright and X-ray faint systems (Helsdon \\& Ponman 2000). The mean dimensionless crossing times obtained for a sample with high level of compactness is shifted toward higher values when comparing to the obtained for a sample of compact groups constructed by Hickson et al. (1992). This shift could be due to some biases in the compact group identification criteria. These biases could imply the detection of the cores of larger systems generating smaller dimensionless crossing times determinations. The last correlation we studied is the fraction of galaxies per spectral type as a function of the dimensionless crossing time. Eventhough the correlations we found are not significant, it is worth to mention that for Type 2 galaxies, smaller is the fraction when higher is the dimensionless crossing time and the opposite trend is maintained for Type 4 galaxies. This latter result is consistent with the stated by Hickson et al. (1992) about groups with smaller crossing times typically containing fewer late-type galaxies." }, "0212/astro-ph0212380_arXiv.txt": { "abstract": "We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process. Star formation occurs in localised bursts within the cloud via the fragmentation both of dense molecular cloud cores and of massive circumstellar discs. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. We find that the observed statistical properties of stars are a natural consequence of star formation in such a dynamical environment. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation ($\\approx 5$ Jupiter masses). The initial mass function is consistent with a Salpeter slope ($\\Gamma=-1.35$) above 0.5 M$_\\odot$, a roughly flat distribution ($\\Gamma=0$) in the range $0.006-0.5$ M$_\\odot$, and a sharp cutoff below $\\approx 0.005$ M$_\\odot$. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations $\\lsim 10$ AU) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 AU due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium Cluster and implies that most stars and brown dwarfs do not form large planetary systems. ", "introduction": "The collapse and fragmentation of molecular cloud cores to form bound multiple stellar systems has been the subject of many numerical studies (e.g.\\ Boss \\& Bodenheimer 1979; Boss 1986; Bonnell et al.\\ 1991; Nelson \\& Papaloizou 1993; Bonnell 1994; Burkert \\& Bodenheimer 1993; Bate, Bonnell \\& Price 1995; Truelove et al.\\ 1998). These calculations have resulted in the adoption of fragmentation as the favoured mechanism for the formation of binary and multiple stars, since it can produce a wide range of binary properties through simple variations of the pre-collapse initial conditions. However, while individual binary systems can be reproduced by such fragmentation calculations, it is extremely difficult to use these calculations to predict the statistical properties of the stellar systems that should result from the fragmentation model. Quantities that we may wish to determine include the initial mass function (IMF), the relative frequencies of single, binary and multiple stars, the properties of multiple stars, the properties of circumstellar discs, and the efficiency of star formation. In order to predict these statistical properties, we need to produce a large sample of stars. There are two possibilities. We could perform many calculations of isolated cloud cores using a representative sample of initial conditions. However, this has two disadvantages. First, the conditions in molecular clouds are not sufficiently well understood to be able to select a representative sample of cloud cores for the initial conditions. Second, the production of isolated stellar systems neglects interactions between systems that may be important in determining stellar properties, especially in young star clusters. Examples of such interactions include binary formation via star-disc capture (Larson 1990; Clarke \\& Pringle 1991a,b; Heller 1995; McDonald \\& Clarke 1995; Hall, Clarke \\& Pringle 1996), truncation of protostellar discs (Heller 1995; Hall 1997), and competitive accretion leading to a range of stellar masses (Larson 1978; Zinnecker 1982; Bonnell et al. 1997, 2001a,b). The second possibility is to perform a calculation of the collapse and fragmentation of a large-scale molecular cloud to form many stars simultaneously. This is the approach taken in this paper. Interactions between stars are automatically allowed for. We must still specify global initial conditions, but the formation of individual cores within the cloud occurs self-consistently; we do not have to select initial conditions for each core arbitrarily. The only disadvantage is that such a calculation is extremely computationally intensive. Several such global calculations have been performed in the past. The earliest was that of Chapman et al.\\ \\shortcite{Chapmanetal1992} who followed the collapse and fragmentation of a shock-compressed layer of molecular gas between two colliding clouds. The calculation produced many single, binary, and multiple protostars, but there was no attempt to derive the statistical properties of these systems. Klessen, Burkert \\& Bate \\shortcite{KleBurBat1998} followed the collapse of a large-scale clumpy molecular cloud to form $\\sim 60$ protostars. They found that the mass function of the protostars could be fit by a lognormal mass function that has a similar width to the observed stellar initial mass function. The protostellar masses were set by a combination of the initial density structure, competitive accretion, and dynamical interactions. Further calculations in which the global initial conditions were varied confirmed the lognormal form of the mass function and showed that the mean mass of the protostars was similar to the mean initial Jeans mass in the cloud (Klessen \\& Burkert 2000, 2001; Klessen 2001). These calculations enabled us to identify some of the processes that may help to determine the initial mass function. However, they did not have the resolution to follow the collapsing molecular gas all the way down to the opacity limit for fragmentation (Low \\& Lynden-Bell 1976; Rees 1976; Silk 1977a), or even to resolve the median separation of binary systems of $\\approx 30$ AU \\cite{DuqMay1991}. Thus, we cannot determine the total number of stars that will form or the stellar initial mass function from these calculations, let alone the frequency of binary stars or the importance of star-disc encounters. This paper presents results from the first calculation to follow the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster while resolving beyond the opacity limit for fragmentation. Thus, assuming that fragmentation does not occur at densities greater than those at which the opacity limit sets in (Section \\ref{opacitysec}), it resolves all potential fragmentation, including that which produces binary systems. This allows us to predict a wide variety of stellar properties. Two papers that contain results from this calculation have already been published. They concentrate on the formation mechanisms of brown dwarfs (Bate, Bonnell \\& Bromm 2002a) and close binaries (Bate, Bonnell \\& Bromm 2002b). In this paper, we consider how the dynamics of star formation determine the properties of stars and brown dwarfs, and we compare these properties with observations. The outline of this paper is as follows. In Section 2, we briefly review the opacity limit for fragmentation. The computational method and the initial conditions for our calculation are described in Section 3. Section 4 discusses the evolution of the cloud and the star formation that occurs during the calculation. The properties of the resulting stars and brown dwarfs are compared with observations of star-forming regions in Section 5. Finally, in section 6, we give our conclusions ", "conclusions": "We have presented the results from one of the most complex hydrodynamical star formation calculations to date. The calculation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster consisting of 50 stars and brown dwarfs. The opacity limit for fragmentation is mimicked by the use of a non-isothermal equation of state and the resolution is sufficient to resolve all fragmentation before this physical limit is reached. Binary stars with separations as small as 1 AU and circumstellar discs with radii down to $\\approx 10$ AU are resolved. The calculation allows us to study the formation mechanisms of stars and brown dwarfs and to determine a wide range of statistical properties for comparison with observation. We find that star formation is a highly dynamic and chaotic process. A true appreciation of the process can only be obtained from examining an animation of the calculation. These can be downloaded from http://www.astro.ex.ac.uk/people/mbate or http://www.ukaff.ac.uk/starcluster. Fragmentation occurs both in dense molecular cloud cores and in massive circumstellar discs. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. The star formation occurs on the dynamical timescale of the cloud and the star formation efficiency across the cloud is variable with a low global efficiency ($\\approx 12$\\% when we stop the calculation) but local efficiencies as high as $\\approx 50$\\%. The high local efficiencies in dense molecular cores result in bursts of star formation because the rapid conversion of gas into stars depletes the high-density gas to such an extent that the star formation essentially comes to a halt until more gas has fallen into the core. When enough new gas has accumulated, another burst of star formation occurs. We find that the opacity limit for fragmentation sets an initial mass for all fragments of $\\approx 0.005$ M$_\\odot$. Subsequently, the fragments accrete from the surrounding gas. Those that manage to accrete enough mass become stars ($M\\gsim 0.075$ M$_\\odot$), while the rest are left as brown dwarfs. We propose that the initial mass function results from this accretion process, with each fragment accreting according to the conditions in which it is formed. The calculation produces a mass function that is consistent with a Salpeter slope ($\\Gamma=-1.35$) above 0.5 M$_\\odot$, a roughly flat distribution ($\\Gamma=0$) in the range $0.006-0.5$ M$_\\odot$, and a sharp cutoff below $\\approx 0.005$ M$_\\odot$. This is consistent with observational surveys. Those objects that end up as brown dwarfs stop accreting before they reach stellar masses because they are ejected from the dense gas soon after their formation by dynamical interactions in unstable multiple systems. Thus, they can be viewed as `failed stars'. This ejection mechanism is very efficient, producing roughly equal numbers of stars and brown dwarfs (see also Bate et al.\\ 2002a). However, the close interactions that occur during these dynamical ejections results in a low frequencies ($\\sim 5$\\%) of binary brown dwarf systems. Similarly, the fraction of brown dwarfs with large (radii $\\gsim 20$ AU) circumstellar discs is $\\sim 5$\\%. The accuracy of these frequencies is limited by our small number statistics (for example, we can only exclude a binary brown dwarf frequency of 20\\% at the 94\\% confidence level). However, further simulations will increase the significance of the predictions. Therefore, observational surveys to determine accurately the frequencies of binary brown dwarfs and the sizes of discs around brown dwarfs should be performed now so that we can test the models. The calculation produces several binary and higher-order multiple systems. The opacity limit for fragmentation results in an initial minimum binary separation of $\\approx 10$ AU. Despite this, we find that 7 close binary systems (separations $< 10$ AU) exist when the calculation is stopped. These systems are produced by the hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs (see also Bate et al.\\ 2002b). These mechanisms lead to close binaries having a bias towards equal-mass systems and a higher frequency of close binaries for higher-mass stars. Many of the close binaries also have wider companions. The resulting frequency of close binary systems is $\\approx 16$\\%, consistent with observations. Thus, close binary systems need not be formed by fragmentation in situ. Perhaps the most surprising result of this calculation is that most of the circumstellar discs in the calculation are severely truncated by dynamical encounters. Most young brown dwarfs should have discs with radii of $\\approx 10$ AU, with large discs ($\\gsim 20$ AU) occurring around only $\\sim 5$\\% of brown dwarfs. The discs around many stars are also severely truncated with the majority having radii $\\lsim 20$ AU (i.e.\\ too small to form our solar system). Such severe disc truncation, and the associated low masses, may explain the observation that approximately 1/3 of the young stars in Taurus have lost their discs when they are only $\\approx 1$ Myr old (Armitage et al.\\ 2002). Currently, the only star-forming region in which we have information on the size distribution of circumstellar discs is the Orion Trapezium Cluster thanks to the silhouette discs. Our results are consistent with the sizes of discs in the Trapezium Cluster. However, massive stars are known to be evaporating discs in the Trapezium Cluster and the cluster is much larger than the system we are able to model. Thus, we strongly encourage observations to determine the size distribution of discs in low-mass star-forming regions such as $\\rho$ Ophiuchus. This is the first of a new generation of star-formation calculations that resolves all fragmentation and allows us to compare a wide range of statistical properties of stars and brown dwarfs with observations. Future calculations will determine the dependence of these properties on the initial Jeans mass in the cloud, the properties of the turbulence, and will improve the statistical significance of the results. In this way, we hope to understand better the origin of stars and brown dwarfs." }, "0212/astro-ph0212105_arXiv.txt": { "abstract": "We use the time-dependent photoionization and dust destruction code developed by Perna \\& Lazzati (2002) to study the time evolution of the medium in a dusty gaseous cloud illuminated by a bright central source that sets on at time zero. We study the case of a bright source, which lasts for a time scale much smaller than the recombination and dust creation time scales. For this reason an equilibrium is never reached. We show that the presence of dust and its properties, such as its composition, can have a big effect on the time scale for the evaporation of the soft X-ray absorption, in particular for ionizing sources with hard spectra. We discuss the profile of evaporation of the soft X-ray absorbing column, as well as how the apparent ionization state of the cloud evolves in time. We finally consider the apparent metallicity of the cloud that is left behind as a function of the cloud and ionizing source properties. ", "introduction": "The measurement of the amount of absorption in the soft X-ray band is highly informative about the amount and physical state (e.g. temperature, ionization parameter) of the material that lies along the line of sight between a source and an observer. Observed spectra are usually analyzed under the assumption that the absorber is in equilibrium, either a thermal or photoionization equilibrium (Morrison \\& McCammon 1983; Done et al. 1992; Zdziarski et al. 1995). This assumption is justified if the source that is studied is constant or if its variability time scale is much longer than the electron recombination time scale of the absorbing material. There are however many variable sources in the universe that do not fulfill this condition. Among them it is worth mentioning X-ray transients (see e.g. Schwarz 1973), variable AGNs (see, e.g. Risaliti, Elvis \\& Nicastro 2002) and especially gamma-ray bursts (Perna \\& Loeb 1998; Lazzati \\& Perna 2002, hereafter LP02). In all these cases, out to a certain distance, photoionization acts as a destructive mechanism: each time a photon is absorbed an electron is stripped, and therefore the state of the absorber and its absorption properties are modified. LP02 (see also Schwarz 1973) analyzed by means of numerical simulations the absorption properties of a gaseous medium suddenly illuminated by a strong photon source with a power-law spectrum. They followed the ionization state of the 12 astrophysically relevant elements and hydrogen producing time resolved transmittance spectra to be compared with the data. In many cases, however, assuming that all the interstellar medium (ISM) is in a gaseous phase is not accurate. There can be molecules (that do not have sizable affect on the X-ray opacity of the medium, see Perna, Lazzati \\& Fiore 2002, hereafter Paper II) and, most importantly, there can be dust grains. These in particular are relevant to X-ray absorption since a large fraction of heavy metals can be condensed in silicate dust grains (Savage \\& Mathis 1979; Laor \\& Draine 1993). The presence of dust grains in the ISM modifies the X-ray absorption properties in two main ways. First, the presence of dust increases the opacity for UV photons, that cannot therefore contribute to the ionization of metals by stripping their external electrons. Most importantly, the metals contained into a dust grain are shielded to photoionization, so that they can survive in an almost neutral state for a much longer time than the same atom in gaseous phase. We (Perna \\& Lazzati 2002, hereafter Paper I) have developed a code that computes the time-dependent absorption properties of a dusty ISM (possibly enriched with $H_2$ molecules) as a function of time under the illumination of a power-law ionizing continuum that evaporates dust grains, dissociates molecules and ionizes atoms. The code and the physical processes considered are fully described in Paper I. The properties of absorption in the optical range are analyzed in a second paper (Paper II). Here, we focus on the properties of the absorber in the X-ray range, and on how the presence of dust influences the evolution of the opacity under different conditions. In \\S~2, we briefly introduce the code and describe the outputs that will be used here, in \\S~3 we discuss the main effects of the presence of dust while in \\S~4 we study how these effects depend on the spectrum of the central ionizing source. In \\S~5 we study how the residual column density can be quantified with a single parameter and in \\S~6 we consider the shape of the transmitted spectrum and in particular whether a high ionization parameter can be detected at intermediate stages. In \\S~7, we consider the different ionization time scales of the various elements and the possible effects that this can have on the estimate of metallicity derived from the fit of the relative opacities. Finally, in \\S~8, we summarize and discuss our results. \\begin{figure} \\psfig{file=f1.eps,width=0.48\\textwidth} \\caption{{The opacity as a function of frequency from optical to X-rays in several time shots after the ionizing continuum onset. The absorbing medium is a spherical cloud with radius $R=10^{18}$~cm and uniform density $n=10^4$~cm$^{-3}$ ($N_H=10^{22}$~cm$^{-2}$) with the source at its centre. Abundances are set to the solar value and the dust-to-gas mass fraction is 0.01 (the average Galactic value).} \\label{fig:sim1}} \\end{figure} ", "conclusions": "We have analyzed with a dedicated code the time-dependent absorption properties of a cloud subject to a strong photon source that sets in at time $t=0$ at its centre. The novelty of this paper consists in the fact that the presence of dust and its evaporation is fully taken into account by the code, allowing us to study if and how the presence of dust grains can affect the evolution of ionization and vice versa. This has great importance for variable sources such as GRBs and Seyfert galaxies, which are sometimes associated with unusual dust-to-gas ratios (Galama \\& Wijers 2001; Stratta et al. 2002), with variations of the column density (Risaliti et al. 2002; LP02) and with unusual extinction curves (Maiolino et al. 2001). In this work we concentrated on the X-ray part of the spectrum, since the optical and infrared bands were addressed in a companion paper (Paper II). We study the evolution (evaporation) of the absorption in X-rays of a uniform cloud with solar metallicity for different dust contents, initial column density, cloud radius and hardness of the ionizing spectrum. A source of [1~eV--100~keV] luminosity $L=10^{50}$~erg~s$^{-1}$ is turned on at time $t=0$ at the centre of the cloud. We first concentrated on the effects that the presence of dust can have on the photoionization rate of metals. We find that, for hard spectrum sources, the presence of dust grains can have a big effect on the photoionization of metals (Fig.~\\ref{fig:dnd}). In fact, if the soft photon flux is not large enough to destroy the dust grain by thermal sublimation, the surviving grains will effectively shield the entrained metals from photoionization (Fig~\\ref{fig:sef}), allowing them to survive in their neutral state for a long time (Fig~\\ref{fig:sim1}). In the more extreme cases, it is possible that the ionizing flux completely ionizes all the atoms in the gaseous phase, leaving behind preferentially large graphite grains, that can contribute a sizable amount of absorption both at optical and X-ray wavelengths. The final conditions of the cloud depend on both the spectrum, luminosity and variability of the ionizing source as well as on the cloud size and column density (Fig~\\ref{fig:sim1}, \\ref{fig:var}, \\ref{fig:sima}). We then study two issues related to observations and their modelling. It is in fact customary to model the absorption in the soft X-ray regime by means of equilibrium model for the absorbing medium. In the case we discuss, equilibrium is far from being reached, nevertheless it is useful, in order to exploit real observations, to understand if the predicted spectra look similar to those in equilibrium and how the column density of the absorbing material that would be measured does compare to the real one. We discuss the results of a fit with a cold absorber to our time dependent absorbed spectra (Fig~\\ref{fig:nhs}, \\ref{fig:nhsa}), and then show that a condition in which the absorber seems warm is never reached (Fig~\\ref{fig:xi}, \\ref{fig:xia}). We finally consider the observed column densities of the various elements, which are time dependent, since atoms completely stripped off their electrons do not contribute to the absorption and are therefore ``invisible''. We find that these ratios are strong functions of time and that as a consequence the metallicities inferred from opacity ratios are not indicative of the pristine composition of the cloud (Fig~\\ref{fig:col}, \\ref{fig:cola}). Present data do not allow for a detailed comparison with our numerical spectra. The only evidence of spectral evolution in the early phase of GRBs and afterglows comes from two detections of decreasing column density (Connors \\& Hueter 1998; Frontera et al. 2000), one variable absorption edge (Amati et al. 2000) and a puzzling evidence of variable (but not monotonic) column density (in't Zand et al. 2001). All these detections belong to the $3\\sigma$ realm and do not give much more information than their mere existence. In the near future, thanks to the launch of the Swift satellite in 2003, higher quality spectra will be available, allowing for a more secure detection of transient features and a more meaningful comparison with theoretical spectra." }, "0212/astro-ph0212043_arXiv.txt": { "abstract": "We investigate a stationary pair production cascade in the outer magnetosphere of a spinning neutron star. The charge depletion due to global flows of charged particles, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate gamma-rays via curvature and inverse-Compton processes. Some of such gamma-rays collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the energy distribution of particles and gamma-rays at each point along the field lines. By solving the set of Maxwell and Boltzmann equations, we demonstrate that an external injection of charged particles at nearly Goldreich-Julian rate does not quench the gap but shifts its position and that the particle energy distribution cannot be described by a power-law. The injected particles are accelerated in the gap and escape from it with large Lorentz factors. We show that such escaping particles migrating outside of the gap contribute significantly to the gamma-ray luminosity for young pulsars and that the soft gamma-ray spectrum between 100~MeV and 3~GeV observed for the Vela pulsar can be explained by this component. We also discuss that the luminosity of the gamma-rays emitted by the escaping particles is naturally proportional to the square root of the spin-down luminosity. ", "introduction": "\\label{sec:intro} Recent years have seen a renewal of interest in the theory of particle acceleration in pulsar magnetospheres, after the launch of the {\\it Compton Gamma-ray Observatory} (e.g., for the Vela pulsar, Kanbach et al. 1994, Fierro et al. 1998; for PSR B1706--44, Thompson et al. 1996; for Geminga, Mayer-Hasselwander et al. 1994, Fierro et al. 1998; for PSR B1055--52, Thompson et al. 1999). The modulation of the $\\gamma$-ray light curves testifies to the particle acceleration either at the polar cap (Harding, Tademaru, \\& Esposito 1978; Daugherty \\& Harding 1982, 1996; Sturner, Dermer, \\& Michel 1995), or at the vacuum gaps in the outer magnetosphere (Cheng, Ho, \\& Ruderman 1986a,b, hereafter CHR; Chiang \\& Romani 1992, 1994; Romani \\& Yadigaroglu 1995; Higgins \\& Henriksen 1997, 1998). Both models predict that electrons and positrons are accelerated in a charge depletion region, a potential gap, by the electric field along the magnetic field lines to radiate high-energy $\\gamma$-rays via the curvature process. However, there is an important difference between these two models: An polar-gap accelerator releases very little angular momenta, while an outer-gap one could radiate them efficiently. In addition, three-dimensional outer-gap models commonly explain double-peak light curves with strong bridges observed for $\\gamma$-ray pulsars. On these grounds, the purpose of the present paper is to explore further into the analysis of the outer-gap accelerator. In the CHR picture, the gap is assumed to be geometrically thin in the transfield direction on the poloidal plane in the sense $D_\\perp \\ll W$, where $D_\\perp$ represents the typical transfield thickness of the gap, while $W$ does the width along the magnetic field lines. In this limit, the acceleration electric field is partially screened by the zero-potential walls separated with a small distance $D_\\perp$; as a result, the gap, which is assumed to be vacuum, extends from the null surface to (the vicinity of) the light cylinder. Here, the null surface is defined as the place on which the local Goldreich-Julian charge density \\begin{equation} \\rhoGJ \\equiv -\\frac{\\Omega B_z(s,z)}{2\\pi c} \\label{eq:def_rhoGJ} \\end{equation} vanishes, where $\\Omega$ refers to the angular frequency of the neutron star, $B_z$ the magnetic field component projected along the rotational axis, and $c$ the velocity of light; $s$ and $z$ refer to the coordinates parallel and perpendicular, respectively, to the poloidal magnetic field. The star surface corresponds to $s=0$; $s$ increases outwardly along the field lines. The last-open field line corresponds to $z=0$; $z$ increases towards the magnetic axis (in the same hemisphere). If $B_z>0$ holds in the starward side of the null surface, a positive acceleration field arises in the gap. The light cylinder is defined as the surface where the azimuthal velocity of a plasma would coincide with $c$ if it corotated with the magnetosphere. Its radius from the rotational axis becomes the so-called \\lq light cylinder radius', $\\rlc \\equiv c / \\Omega$. Particles are not allowed to migrate inwards beyond this surface because of the causality in special relativity. It should be noted that the null surface is not a special place for the gap electrodynamics in the sense that the plasmas are not completely charge-separated in general and that the particles freely pass through this surface inwards and outwards. Therefore, the gap inner boundary is located near to the null surface, not because particle injection is impossible across this surface (as previously discussed), but because the gap is vacuum and transversely thin. Then what occurs in the CHR picture if the gap becomes no longer vacuum? To consider this problem rigorously, we have to examine the Poisson equation for the electrostatic potential. In fact, as will be explicitly demonstrated in the next section, the original vacuum solution obtained in the pioneering work by CHR cannot be applied to a non-vacuum CHR picture. We are, therefore, motivated by the need to solve self-consistently the Poisson equation together with the Boltzmann equations for particles and $\\gamma$-rays. Although the ultimate goal is to solve three-dimensional issues, a good place to start is to examine one-dimensional problems. In this context, Hirotani and Shibata (1999a,~b,~c; hereafter Papers~I,~II,~III) first solved the Boltzmann equations together with the Maxwell equations one-dimensionally along the field lines, extending the idea originally developed for black-hole magnetospheres by Beskin et al. (1992). In Paper~I, II, and III, they assumed that the gap is geometrically thick in the transfield direction in the sense $D_\\perp \\gg W$. There is one important finding in this second picture: The gap position shifts if there is a particle injection across either of the boundaries (Hirotani \\& Shibata 2001, 2002a,b; hereafter Papers~VII, VIII, IX). For example, when the injection rate across the outer (or inner) boundary becomes comparable to the typical Goldreich-Julian value, the gap is located close to the neutron star surface (or to the light cylinder). In other words, an outer gap is not quenched even when the injection rate of a completely charge-separated plasma across the boundaries approaches the typical Goldreich-Julian value. Thus, an outer gap can coexist with a polar-cap accelerator; this forms a striking contrast to the first, CHR picture. It is also found in the second picture that an outer gap is quenched if the {\\it created} particle density within the gap exceeds several percent of the Goldreich-Julian value. That is, the {\\it discharge} of created pairs is essential to screen the acceleration field. The purpose of this paper is to examine the second picture more closely. In all the previous works in the second picture, the particle energy distribution has been assumed to be mono-energetic in the sense that the particles attain the equilibrium Lorentz factor at each point, in a balance between the electrostatic acceleration and the radiation-reaction forces. In the present paper, we discard this assumption and explicitly consider the energy dependence of particles by solving the Boltzmann equations for positrons and electrons. We will demonstrate that the particle energy distribution cannot be represented either by a power law or by the mono-energetic approximation. We will further show that a soft power-law spectrum is generally formed in 100~MeV-GeV energies as a result of the superposition of the curvature spectra emitted by particles migrating at different positions. In the next section, we describe the difficulties of electrodynamics found in the first picture. We then present the basic equations in \\S~\\ref{sec:basic}. and apply the theory to four $\\gamma$-ray pulsars and compare the predictions with observations in \\S~\\ref{sec:app}. In the final section, we discuss the possibilities of the unification of our picture with the CHR picture, as well as the unification of the outer-gap and polar-cap models. ", "conclusions": "\\label{sec:discussion} In summary, we have quantitatively examined the stationary pair-production cascade in an outer magnetosphere, by solving the set of Maxwell and Boltzmann equations one-dimensionally along the magnetic field. We revealed that an accelerator (or a potential gap) is quenched by the created pairs in the gap but is {\\it not} quenched by the injected particles from outside of the gap, and that the gap position shifts as a function of the injected particle fluxes: If the injection rate across the inner (or outer) boundary approaches the typical Goldreich-Julian value, the gap is located near to the light cylinder (or the star surface). It should be emphasized that the particle energy distribution is not represented by a power law, as assumed in some of previous outer-gap models. The particles escape from the gap with sufficient Lorentz factors and emit significant photons in 100~MeV--3~GeV energies via curvature radiation outside of the gap. The $\\gamma$-ray spectrum including this component explains the phase-averaged EGRET spectra for the Vela pulsar, the Geminga pulsar and PSR~B1055-52 between 100~MeV and 6~GeV. TeV fluxes are unobservable with current ground-based telescopes for these pulsars. We show that synchro-curvature process can be approximated by the pure-curvature one in the next subsection. We then point out an implication to the $\\gamma$-ray luminosity versus the spin-down luminosity in \\S~\\ref{sec:lumin}, and discuss future extensions of the present method in \\S\\S~\\ref{sec:return}--\\ref{sec:unif_pol}. \\subsection{Synchrotron vs. Curvature Processes} \\label{sec:small_pitch} Let us first examine the pitch angles of particles injected across the inner boundary. Imposing that the synchrotron cooling length scale, \\begin{equation} l_{\\rm sync} \\equiv \\frac{\\Gamma m_{\\rm e} c^2}{P_{\\rm sync}/c} = \\frac{3 m_{\\rm e}^3 c^6}{2 e^4 B^2 \\Gamma \\sin^2\\chi} \\label{eq:cool_sync} \\end{equation} is greater than the distance, $\\varepsilon \\rlc$, for the particles to migrate before arriving the outer gap, we obtain \\begin{equation} \\sin\\chi < 7.2 \\times 10^{-6} \\left( \\frac{\\Omega_2}{\\varepsilon_{0.1}\\Gamma_2} \\right)^{1/2} B_{10}^{-1}, \\label{eq:cool_pitch} \\end{equation} where $\\varepsilon_{0.1}\\equiv \\varepsilon/0.1$, $\\Gamma_2 \\equiv \\Gamma/10^2$, $\\Omega_2 \\equiv \\Omega/(10^2 \\mbox{rad s}^{-1})$, and $B_{10} \\equiv B/(10^{10} \\mbox{G})$. Particles having initial pitch angles greater than this value will lose transverse momentum to reduce the pitch angles below this value, while migrating the distance $\\varepsilon \\rlc$. Therefore, if the particles are supplied from the polar cap with $\\Gamma \\sim 10^2$ for instance, we can safely state that the the pitch angles are less than $10^{-5}$ rad. If a particle having such a small pitch angle is accelerated to $\\Gamma=10^7$ in a weak magnetic field region $B=10^6$~G, the ratio between the synchrotron and the curvature radiation rate becomes \\begin{eqnarray} \\lefteqn{ \\frac{P_{\\rm sync}}{\\Pcv} = \\left( \\frac{\\rho_{\\rm c} \\sin\\chi} {\\Gamma m_{\\rm e}c^2/eB} \\right)^2} \\nonumber\\\\ &=& 7.7 \\times 10^{-3} \\Omega_2^{-2} B_6^2 \\Gamma_7^{-2} \\left(\\frac{\\rho_{\\rm c}}{0.5\\rlc} \\cdot \\frac{\\sin\\chi}{10^{-5}} \\right)^2, \\label{eq:PsyPcv} \\end{eqnarray} where $B_6 \\equiv B/10^6 \\mbox{G}$, $\\Gamma_7 \\equiv \\Gamma/10^7$. It follows that the synchro-curvature radiation can be approximated by a pure-curvature one for the particles injected across the inner boundary. It is noteworthy that the density of created particles is much less than that of injected ones (i.e., $j_{\\rm gap} \\ll j^{\\rm in}$); therefore, the synchro-curvature effects for the created particles, which have much greater pitch angles compared with the injected ones, are negligibly small for the gap electrodynamics as well for the resultant $\\gamma$-ray spectrum. \\subsection{Gamma-ray vs. Spin-down Luminosities} \\label{sec:lumin} It should be noted that the emission from the escaping particles attain typically $40\\%$ of the total $\\gamma$-ray luminosity for young pulsars. Thus, it is worth mentioning its relationship with the spin-down luminosity, \\begin{equation} L_{\\rm spin}= -I \\Omega \\dot{\\Omega} \\propto \\Omega^{n+1}, \\label{eq:spindown} \\end{equation} where the braking index $n$ is related to the spin-down rate as \\begin{equation} \\dot{\\Omega}= -k \\Omega^n. \\label{eq:braking} \\end{equation} If the spin down is due to the magnetic dipole radiation, we obtain $n=3$. The outwardly propagating particles escape from the gap with spatial number density (eq.~[\\ref{eq:def-n}]) \\begin{equation} N_{\\rm out} = (j^{\\rm in}+j_{\\rm gap})\\frac{\\Omega B^{\\rm out}}{2\\pi ce}, \\label{eq:NeOUT} \\end{equation} where $B^{\\rm out}=B(\\xi^{\\rm out})$. Therefore, the energy carried by the escaping particles per unit time is given by \\begin{equation} L_{\\rm esc} = D_\\perp^2 c N_{\\rm out} \\Gamma_{\\rm esc} m_{\\rm e}c^2, \\label{eq:def_Lesc} \\end{equation} where $\\Gamma_{\\rm esc} (\\sim 10^{7.5})$ refers to the Lorentz factor of escaping particles. Note that $\\Gamma_{\\rm esc}$ is essentially determined by the equilibrium Lorentz factor (dotted line in fig.~\\ref{fig:EVela_75a}) near the gap center. Since the equilibrium Lorentz factor depends on the one-fourth power of $\\Ell$, the variation of $\\Gamma_{\\rm esc}$ on pulsar parameters is small. We can approximate $B^{\\rm out}$ as \\begin{equation} B^{\\rm out} \\sim \\frac{\\mu}{\\rlc^3} \\left( \\frac{\\rlc}{r^{\\rm out}} \\right)^3, \\label{eq:Bout} \\end{equation} where $r^{\\rm out}$ refers to the distance of the outer boundary of the gap from the star center. Let us assume that the position of the gap with respect to the light cylinder radius, $r^{\\rm out}/\\rlc$, does not change as the pulsar evolves; this situation can be realized if $j^{\\rm in}-j^{\\rm out}$ is unchanged. Evaluating $B$ at $r=0.5\\rlc$, we obtain \\begin{eqnarray} L_{\\rm esc} &=& \\frac{4 \\Gamma_{\\rm esc} m_{\\rm e}c}{\\pi e} \\mu \\Omega^2 \\left(\\frac{D_\\perp}{\\rlc}\\right)^2 \\nonumber\\\\ &\\propto& L_{\\rm spin}{}^{0.5}, \\label{eq:Lesc} \\end{eqnarray} where $n=3$ is assumed in the second line. To derive this conclusion, it is essential that the particles are not saturated at the equilibrium Lorentz factor. Thus, the same discussion can be applied irrespective of the gap position or the detailed physical processes involved. For example, an analogous conclusion was derived for a polar-cap model by Harding, Muslimov, and Zhang (2002). It is, therefore, concluded that the observed relationship $L_\\gamma \\propto L_{\\rm spin}{}^{0.5}$ merely reflects the fact that the particles are unsaturated in the gap and does not discriminate the gap position. Let us compare this result with what would be expected in the CHR picture. Since the gap is extended significantly along the field lines in the CHR picture, particles are saturated at the equilibrium Lorentz factor to lose most of their energies within the gap, rather than after escaping from it. We can therefore estimate the $\\gamma$-ray luminosity as \\begin{equation} L_{\\rm gap} = (D_\\perp D_\\phi W) \\cdot N_{\\rm out} \\cdot \\Pcv \\label{eq:def_Lgap} \\end{equation} where $D_\\phi$ refers to the azimuthal thickness of the gap, $\\Pcv$ [ergs s$^{-1}$ (particle)$^{-1}$] represents the curvature radiation rate. Noting that the particle motion saturates at the equilibrium Lorentz factor satisfying $\\Pcv/c=e(-d\\Psi/ds)$, recalling that the acceleration field is given by $-d\\Psi/ds \\approx \\Omega B D_\\perp^2 / 4\\rho_{\\rm c}c$ in the CHR picture, and evaluating $B$ at $r=\\rlc$, we obtain \\begin{eqnarray} L_{\\rm gap} &=& \\frac{\\mu^2 \\Omega^4}{4\\pi c^3} \\frac{D_\\perp^3 D_\\phi W}{\\rlc^5} \\left(\\frac{\\rho_{\\rm c}}{0.5\\rlc}\\right)^{-1} \\nonumber\\\\ &\\propto& L_{\\rm spin} \\label{eq:Lgap}, \\end{eqnarray} where $n=3$ is assumed again in the second line. Even though the escaping particles little contribute to the $\\gamma$-ray luminosity in the CHR picture, it is worth mentioning the work done by Crusius--W$\\ddot{\\rm a}$tzel and Lesch (2002), who accurately pointed out the importance of the escaping particles in the CHR picture, when we interpret $L_\\gamma \\propto L_{\\rm spin}^{0.5}$ relation. As we have seen, the particles being no longer accelerated contribute for the $\\gamma$-ray luminosity that is proportional to $L_{\\rm spin}^{0.5}$. Reminding that the particles migrate with larger Lorentz factors than the equilibrium value in the outer part of the gap (see fig.~\\ref{fig:EVela_75a}), we can expect roughly half of the $\\gamma$-ray luminosity is proportional to $L_{\\rm spin}^{0.5}$ (mainly between 100~MeV and 1~GeV), and the rest of the half to $L_{\\rm spin}$ (mainly above 1~GeV). As a pulsar ages, its declined surface emission results in a large pair-production mean free path, and hence $W$. Because $\\vert \\rhoGJ \\vert \\propto r^{-3}$ becomes small in the outer part of such an extended gap, $\\Ell(\\xi)$ deviates from quadratic distribution to decline gradually in the outer part (fig.~\\ref{fig:EGemi_60}). As a result, particles tend to be saturated at the equilibrium value. On these grounds, we can predict that the $\\gamma$-ray luminosity tends to be proportional to $L_{\\rm spin}$ with age, deviating from $L_{\\rm spin}^{0.5}$ dependence for young pulsars. In the present paper, we have examined the set of Maxwell and Boltzmann equations one-dimensionally both in the configuration and the momentum spaces (i.e., only $\\xi$ and $\\Gamma$ dependences are considered.) In the next three sections, we discuss the extension of the present method into higher dimensions \\subsection{Returning Particles} \\label{sec:return} If we consider the pitch-angle dependence of particle distribution functions, we can compute the radiation spectrum with synchro-curvature formula (Cheng and Zhang 1996). Moreover, we can also consider the returning motion of particles inside and outside of the gap. The returning motion becomes particularly important when both signs of charge are injected across the boundary. For example, not only positrons but also electrons could be injected across the inner boundary from the polar-cap accelerator. If $\\Ell>0$ for instance, the injected electrons return in the gap. This returning motion significantly affects the Poisson equation, if their injection rate is a good fraction of the Goldreich-Julian value. It remains an unsettled issue whether an outer-gap accelerator resides on the field lines on which a polar-cap accelerator exists. To begin with, let us consider the case when the plasma flowing between the polar cap and the outer-gap accelerator is completely charge separated. Such a situation can be realized, for instance, if only positively charged particles are ejected outwardly from the polar cap while there is virtually no electrons ejected inwardly from the outer gap. Neglecting the pair production, current conservation law gives the charge density, $\\rho_{\\rm e}$, per unit magnetic flux tube as \\begin{equation} \\frac{\\rho_{\\rm e}}{B} \\propto \\frac{j_{\\rm tot}}{v}, \\label{eq:sep_flow} \\end{equation} where $v$ refers to the particle velocity along the field line, and $j_{\\rm tot}$ the conserved current density per magnetic flux tube. At each point along the field line, $\\rho_{\\rm e}$ should match $\\rho_{\\rm GJ}$. If the field line intersects the null surface, $\\rho_{\\rm e}$ must vanish there; this obviously violates the causality in special relativity. Therefore, a stationary ejection of a completely charge-separated plasma from the polar cap can be realized only along the field lines between the magnetic axis and those intersecting the null surface at the light cylinder. On these grounds, it was argued that an outer-gap accelerator, which is formed close to the last-open field line, may not resides on the same field lines on which a polar-cap accelerator resides. This has been, in fact, the basic idea that an outer gap will not be quenched, because the particles ejected from the polar cap will flow along the different field lines. This idea was welcomed in outer-gap models, because a gap has been considered to be quenched if the external particle injection rate becomes comparable to the Goldreich-Julian value, which was proved to be incorrect in this paper. In general, however, the plasmas are not completely charge separated and consist of both signs of charge (e.g., positrons and electrons). Such a situation can be realized, for instance, if both charges are ejected outwardly from a polar-cap accelerator, or if positively charged particles are ejected outwardly from the polar cap while electrons are ejected inwardly from the outer gap, or if there is a pair production between the two accelerators. In these cases, the velocities of both charges will be adjusted so that both the current conservation and $\\rho_{\\rm e}=\\rho_{\\rm GJ}$ are satisfied at each point along the field lines. Therefore, it seems likely that a polar-cap accelerator and an outer-gap accelerator reside on the same field lines. To examine if there is a stationary plasma flow between the polar cap and the outer gap, we must extend the present analysis into two dimensional momentum space in the sense that the pitch-angle dependence of the particle distribution functions is taken into account in addition to the Lorentz factor dependence. For example, if both charges are ejected from the polar-cap accelerator, electrons will return in the outer gap, screening the original acceleration field in the gap, and violating the original balance of $\\rho_{\\rm e}=\\rhoGJ$ outside of the gap. Because the returning motion of particles can be treated correctly if we consider the pitch-angle evolution of the distribution functions, and because the pair production is already taken into account, our present method is ideally suited to investigate the plasma flows and $\\Ell$ distribution self-consistently inside and outside of the gap. \\subsection{Unification of Outer-gap Models} \\label{sec:unif_out} In addition to the extension into a higher dimensional momentum space, it is also important to extend the present method into a two- or three-dimensional configuration space. In particular, determination of the perpendicular thickness, $D_\\perp$, is important to constrain gap activities. There have been, in fact, some attempts to constrain $D_\\perp$ in the CHR picture. Since $-d\\Psi/ds$ is proportional to $B D_\\perp^2$, particles energies, and hence the $\\gamma$-ray energies increase with increasing $D_\\perp$ (for a fixed $B$). Zhang and Cheng (1997) constrained $D_\\perp$, by considering the condition that the $\\gamma$-rays cause photon-photon pair production in the gap. Subsequently, Cheng, Ruderman, and Zhang (2000) extended this idea into three-dimensional magnetosphere and discussed phase-resolved $\\gamma$-ray spectra for the Crab pulsar. In addition, Romani (1996) discussed the evolution of the $\\gamma$-ray emission efficiency and computed the phase-resolved spectra for the Vela pulsar, by assuming that $BD_\\perp^2$ declines as $r^{-1}$. However, in these works, screening effects due to pair production has not been considered; thus, the obtained $D_\\perp$, as well as the assumed gap position along the magnetic field, are still uncertain. On the other hand, in our approach (picture), $D_\\perp$ is not solved but only adjusted so that the $\\gamma$-ray flux may match the observations. Therefore, the question we must consider next is to solve such geometrical and electrodynamical discrepancies between these two pictures. We can investigate this issue by extending the present method into higher spatial dimensions. \\subsection{Unification of Outer-gap and Polar-cap Models} \\label{sec:unif_pol} Electrodynamically speaking, the essential difference between outer-gap and polar-cap accelerators is the value of the optical depth for pair production. In an outer-gap accelerator, pair production takes place via $\\gamma$-$\\gamma$ collisions and its mean-free path is much greater than the light cylinder radius. Therefore, a pair production cascade takes place gradually in the gap. In such a gap, $\\Ell$ is screened out by the \\lq generalized Goldreich-Julian charge density', $f_{\\rm null}$ (eq.~[\\ref{eq:def_fnull}]), which increases outwards if $\\mbox{\\boldmath$\\Omega$}\\cdot\\mbox{\\boldmath$B$}>0$. Since $f_{\\rm null}$ is negative (or positive) in the inner (or outer) part of the gap, there is a surface on which the right-hand side of equation~(\\ref{eq:Poisson_1Db}) vanishes, as long as the injected current density is less than the Goldreich-Julian value. The gap is located around this \\lq generalized null surface', which is explicitly defined in \\S~2 of Paper~VII. On the contrary, in a polar-cap accelerator, pair production takes place mainly via magnetic pair production, of which mean free path is much less than the star radius for a typical magnetic field strength ($B \\sim 10^{12}$~G, say). As a result, a pair production avalanche takes place in a limited region, which is called as the \\lq pair formation front', in the gap (Fawley, Arons, \\& Sharlemann 1977; Harding \\& Muslimov 1998, 2001, 2002; Shibata, Miyazaki, Takahara 1998, 2002; Harding, Muslimov, Zhang 2002). In the pair formation front, a small portion of the particles return to screen out $\\Ell$. Such a returning motion can be self-consistently solved together with $\\Ell$ by our present method, if we implement the magnetic pair production and the resonant IC scattering redistribution functions in the source terms of the particles' and $\\gamma$-rays' Boltzmann equations. We can execute the same advection-phase computation in CIP scheme; thus, all we have to do is to add these source terms in the non-advection-phase computation, which is not very difficult. Since analogous boundary conditions (e.g., $\\Ell=0$ for a space-charge limited flow) will be applied, we expect the present method is also applicable to a polar-cap accelerator. This is an issue to be examined in our subsequent papers. \\par \\vspace{1pc}\\par One of the authors (K. H.) wishes to express his gratitude to Drs. K. Shibata and A. Figueroa-Vin{$\\bar{\\rm a}$}s for valuable advice on numerical analysis, and to Drs. K.~S.~Cheng and C. Thompson for fruitful discussion on theoretical aspects. He also thanks Canadian Institute for Theoretical Astrophysics for welcoming him as a visiting researcher." }, "0212/astro-ph0212261_arXiv.txt": { "abstract": "This study calls attention to the importance of properly coupling the molecular opacities to the actual surface abundances of TP-AGB stars that experience the third dredge-up and/or hot-bottom burning, i.e. with surface abundances of carbon and oxygen varying with time. New TP-AGB calculations with variable opacities -- replacing the usually adopted solar-scaled opacity tables -- have proven to reproduce, for the first time, basic observables of carbon stars, like their effective temperatures, C/O ratios, and near-infrared colours. Moreover, it turns out that the effect of envelope cooling -- due to the increase in molecular opacities -- may cause other important effects, namely: i) shortening of the C-star phase; ii) possible reduction or shut-down of the third dredge-up in low-mass carbon stars; and iii) weakening or even extinction of hot-bottom burning in intermediate-mass stars. ", "introduction": "The observed spectral dichotomy between M-type (with C/O$<1$) and C-type (with C/O$>1$) stars was first explained by Russell (1934) on the basis of of molecular equilibria calculations. It was pointed out that the C/O ratio plays the key-role in determining the different patterns of molecular abundances, hence different dominant molecular bands, characterising the two classes of giant stars. Despite this basic fact, the description of molecular opacities is still improper in most evolution models of AGB stars. In fact, the usually adopted opacity tables (e.g. Alexander \\& Ferguson 1994) are strictly valid for solar-scaled abundances of elements heavier than helium, corresponding to C/O$ = 0.48$ (hereinafter also $\\kappa_{\\rm fix}$ prescription). Therefore, it is already clear that the inadequacy of the opacity prescription becomes particularly serious when modelling carbon stars, characterised by surface C/O$ > 1$ as a consequence of recurrent third dredge-up episodes during the TP-AGB evolution. Marigo (2002) investigates the effects on the AGB evolution due to variable molecular opacities (hereinafter also $\\kappa_{\\rm var}$ prescription), that are now computed consistently to the current envelope chemical composition of TP-AGB models experiencing the third dredge-up and hot-bottom burning (HBB). As illustrated in the following, from comparing the new $\\kappa_{\\rm var}$ with the standard $\\kappa_{\\rm fix}$ results, the impact turns out indeed significant. \\begin{figure} \\plotfiddle{marigof1.ps}{2.8in}{0.}{42.}{42.}{-135}{-75} \\caption{Molecular abundances (in terms of partial pressures) of a few atomic and molecular species as a function of the C/O ratio, assuming a gas pressure $P_{\\rm gas} = 10^3$ dyne cm$^{-2}$, and a temperature $T = 2500$ K. The vertical line marks the molecular concentrations for a solar composition, with C/O$\\sim 0.48$ } \\label{fig_molcovar} \\end{figure} ", "conclusions": "This explorative study has shown how large is the impact of introducing variable molecular opacities in AGB models. This has improved the comparison with observations and brought many new results, which may critically change and revitalise, in various aspects, the present scenario of AGB evolution." }, "0212/astro-ph0212057_arXiv.txt": { "abstract": "{ We present evolutionary models of zero-metallicity very massive objects, with initial masses in the range 120 $M_{\\odot}$ -- 1000 $M_{\\odot}$, covering their quiescent evolution up to central carbon ignition. In the attempt of exploring the possible occurrence of mass loss by stellar winds, calculations are carried out with recently-developed formalisms for the mass-loss rates driven by radiation pressure (Kudritzki 2002) and stellar rotation (Maeder \\& Meynet 2000). The study completes the previous analysis by Marigo et al. (2001) on the constant-mass evolution of primordial stars. Our results indicate that radiation pressure (assuming a minimum metallicity $Z = 10^{-4}\\times Z_{\\odot}$) is not an efficient driving force of mass loss, except for very massive stars with $M \\ga 750 \\, M_{\\odot}$. On the other hand, stellar rotation might play a crucial role in triggering powerful stellar winds, once the $\\Omega\\Gamma$-limit is approached. However, this critical condition of intense mass loss can be maintained just for short, as the loss of angular momentum due to mass ejection quickly leads to the spinning down of the star. As by-product to the present work, the wind chemical yields from massive zero-metallicity stars are presented. The helium and metal enrichments, and the resulting $\\Delta Y/\\Delta Z$ ratio are briefly discussed. ", "introduction": "\\label{sec_intro} The first generation of stars ever born in the Universe (Population III) is assigned a role of paramount importance for several astrophysical issues. In particular, the formation of a primeval population of very massive objects (VMOs, with initial masses in the range $10^2-10^5 \\, M_{\\odot}$) was invoked in the '80s to explain several questions, such as the observed metallicities of Population II stars, the primordial helium abundance, the re-ionisation of cosmic matter after the Big-Bang, the missing mass in clusters of galaxies and galactic haloes, the G-dwarf problem (see Carr et al. 1984 for an extensive review). In those years a few evolutionary calculations of zero-metallicity VMOs were carried out (e.g. Bond et al. 1984, El Eid et al. 1983, Ober et al. 1983, Klapp 1984ab), but afterwards the scientific production on the evolution of the first stars dropped off. The recently renewed interest in Pop-III stars, essentially driven by the nowadays flourishing of observations at very low metallicity and/or high redshift (refer to e.g. the proceedings of the ESO symposium edit by Weiss et al. (2000); see also Kudritzki et al. (2000), Bromm et al. (2001), Schaerer (2002), Panagia (2002) for extensive analyses on the expected observable properties of primordial stellar populations) has again stimulated the calculation of stellar structures made evolve with initial metal-free chemical composition (e.g. Cassisi et al. 2001; Marigo et al. 2001 and references therein). Marigo et al. (2001; thereinafter Paper I) presented an extensive study of the evolutionary properties of zero-metallicity stars over a wide range of initial masses ($0.7 \\, M_{\\odot} \\la M \\la 100 M_{\\odot}$). In that work -- to which the reader is referred for all the details -- we calculated all stellar tracks at constant mass. Our study on Pop-III stars is now extended to very massive objects (VMOs), with initial masses in the range $120-1000\\, M_{\\odot}$, that is chosen not only for continuity with Paper I, but also in consideration of current theoretical indications that the primordial initial mass function (IMF) might have peaked in the (very) high-mass domain (with $M \\ga 100 \\, M_{\\odot}$; see e.g. Bromm et al. 1999, 2002; Nakamura \\& Umemura 2001; Abel et al. 2000). To this aim we calculate evolutionary models for zero-metallicity VMOs that cover the major core-burning phases, extending from hydrogen to carbon ignition. With aid of available analytic formalisms, we address the question of the possible occurrence of mass loss via stellar winds, which is an important, but still problematic, aspect of stellar evolution at zero metallicity. In massive stars with ``normal'' chemical composition the principal driving force resides in the capability of metallic ions, present in the atmosphere, to absorb radiative momentum and transfer it to the outermost layers, that can be then accelerated beyond their escape velocity (Castor et al. 1975; Pauldrach et al. 1986). In a gas composed only of hydrogen and helium, like the primordial one, the lack of metallic ions sets the first important difference and the question arises: Is the radiative acceleration due to the H and He lines strong enough to trigger significant mass loss ? Furthermore, may other possible processes -- e.g. related to pulsation instability and stellar rotation -- be efficient mechanisms to drive mass loss from Pop-III massive stars ? Some of these questions have already been addressed by other investigations, others still deserve to be quantitatively analysed and discussed. There are few studies in the literature that present evolutionary models of very massive zero-metallicity stars with mass loss during the pre-supernova phases. In the very massive domain ($500-1000\\, M_{\\odot}$) Klapp (1983, 1984) carried out evolutionary calculations by adopting a simple empirical law for mass-loss (Barlow \\& Cohen 1977) -- based on Galactic observations -- that linearly scales with the stellar luminosity. On the basis of semi-analytical models of very massive objects (with masses $10^2 -10^5\\, M_{\\odot}$), Bond et al. (1984) argued that the same kind of dynamical instability arising in the H-burning shell of Population I models -- which should cause the ejection of the entire envelope -- might also affect Population III VMOs, depending on the actual abundance of the CNO catalysts in the H-shell. The evolution of zero-metallicity stars (with masses $80 - 500\\, M_{\\odot}$) during the nuclear phases of H- and He-burning was calculated by El Eid et al. (1983) with the adoption of a semi-empirical relation to derive the mass loss rate (Chiosi 1981). Recently Baraffe et al. (2001, see also Heger et al. 2001) performed a linear stability analysis on metal-free very massive models (with masses $120-500\\, M_{\\odot}$), and investigated the related possibility that mass loss may characterise the pulsation-unstable stages. Heger \\& Woosley (2002) calculated the evolution and nucleosynthesis of quite massive Population III stars (with masses $\\sim 100 - 300\\, M_{\\odot}$) including the final fate of the supernova event, but no mass-loss is assumed to occur during the hydrostatic phases of major nuclear burnings. In the present work we attempt to further explore the issue of mass loss in primordial conditions, by carrying out new evolutionary calculations of zero-metallicity VMO with recently developed mass-loss formalisms, related to radiation pressure and stellar rotation. The paper is organised as follows. Section \\ref{sec_evolcalc} introduces new evolutionary calculations for zero-metallicity VMOs, having initial masses of 120, 250, 500, 750, and 1000 $M_{\\odot}$. Mass loss is included with the adoption of recent analytic formalisms, namely: Kudritzki (2002) for radiation-driven mass loss, and Maeder \\& Meynet (2000) for the additional effect of stellar rotation. General characteristics of the models are analysed in relation to energetics, nuclear lifetimes, internal structure, surface and chemical properties. The efficiency of mass loss is discussed on the basis of the adopted formalisms. The corresponding predictions for the chemical yields, ejected via stellar winds, are given in Sect.~\\ref{sec_yields}. In particular, the expected helium and metal enrichment, produced by a hypothetical burst of Pop-III star formation, is derived and discussed as a function of the involved parameters. In Sect.~\\ref{sec_concl} we express a few concluding remarks. Finally, stellar isochrones for very young ages are presented in Sect.~\\ref{sec_tableisoc}. ", "conclusions": "\\label{sec_concl} In this work we have discussed the evolutionary properties of zero-metallicity very massive objects ($120\\, M_{\\odot} \\le M \\le 1000\\, M_{\\odot}$), on the basis of new calculations that extend the work presented in Paper I. Stellar isochrones (see Appendix A) for ages from 16~Gyr down to $10^{4}$~yr are available at the web-address http://pleiadi.pd astro.it. In the attempt to estimate the possible effects produced by stellar winds from primordial VMOs, we adopt recent formalisms that describe the role of radiation pressure and stellar rotation as mass-loss driving factors. The emerging picture is the following: \\begin{itemize} \\item At extremely low metallicity ($Z \\approx 10^{-6}$), the mechanism of line-radiation transfer should be scarcely efficient, except for very large masses, say $\\ga 750 M_{\\odot}$. We also find that, as long as the mass loss front penetrates into the chemical profile left by the convective core during the H-burning phase, the maximum CNO abundance exposed at the surface does not exceed $\\approx 10^{-9}-10^{-8}$, which are typical values required by the CNO-cycle operating in stars with original metal-free composition. Such degree of chemical self-pollution is also too low to trigger efficient radiation-driven winds from zero-metallicity massive stars. Instead, much larger surface enrichment may be attained whenever the nuclear products of He-burning, like carbon and oxygen -- potentially able to produce large mass-loss rates -- were brought up to the surface by either the penetrating mass-loss front, or some dredge-up process. In our computations this occurs only for the $1000\\, M_{\\odot}$ model. \\item Our calculations also indicate that rotating very massive stars may actually reach the critical condition defined as the $\\Omega\\Gamma$-limit, which should be likely accompanied by large mass-ejection rates (here taken as large as $\\dot M_{\\rm crit} = 10^{-3}$ yr$^{-1}$). However, the net impact on mass loss should be quite limited, given the extremely short time during which these critical regimes can be maintained. To this respect, we remind these results are obtained in the context of a simplified description of stellar rotation, and the reader should consider the remarks expressed in Sect.~\\ref{ssec_cautr}. \\item Finally we recall that, according to a recent analysis by Baraffe et al. (2001), another possible mass-loss driving mechanism, namely the pulsation instability -- usually at work in VMO models with ``normal'' chemical composition -- has been found of modest potential efficiency at zero metallicity, at least for masses $M \\la 500\\, M_{\\odot}$. \\end{itemize} By combining the supernova yields available in the literature with our predicted wind contributions, we also evaluate, in a simple way, the chemical enrichment produced by a primeval population of (very) massive stars. It is found that a significant helium enrichment, $\\Delta Y \\sim 0.01$, may be reached by assuming that the primordial conditions in the Universe were such that only very massive stars could form, with typical masses of $\\approx 1000\\, M_{\\odot}$, or extending into the super-massive domain (up to $\\approx 10^{5} M_{\\odot}$). In the former case the implied efficiency of gas-to-star conversion should be of the order of $10 \\%$, and the first metal enrichment should be in the form of CNO elements (no iron-group elements). On the other side, under the assumption of the standard Salpeter IMF, the resulting $\\Delta Y$ is indeed negligible over the maximum allowed enrichment in metals, $10^{-5} \\la \\Delta Z_{\\rm max} \\la 10^{-3}$. The corresponding star formation efficiency should be also be quite small, $\\approx 0.01-0.1 \\%$. In any case, as already pointed out long ago by Bond et al. (1983) and Carr (1994), the interesting possibility arises that the first generation of stars could mask the true (somewhat lower) primordial abundance of helium as predicted by the standard Big Bang Nucleosynthesis (e.g. Olive et al. 1997). The question and its implications have been recently addressed by Salvaterra \\& Ferrara (2002) on the base of the present results. \\appendix" }, "0212/astro-ph0212327_arXiv.txt": { "abstract": "{ We calculate the luminosity function of galaxies of the Early Data Release of the Sloan Digital Sky Survey (SDSS) and the Las Campanas Redshift Survey (LCRS). The luminosity function depends on redshift, density of the environment and is different for the Northern and Southern slice of SDSS. We use luminosity functions to derive the number and luminosity density fields of galaxies of the SDSS and LCRS surveys with a grid size of 1~$h^{-1}$ Mpc for flat cosmological models with $\\Omega _m=0.3$ and $\\Omega _\\Lambda =0.7.$ We investigate the properties of these density fields, their dependence on parameters of the luminosity function and selection effects. We find that the luminosity function depends on the distance and the density of the environment. The last dependence is strong: in high-density regions brightest galaxies are more luminous than in low-density regions by a factor up to 5 (1.7 magnitudes). ", "introduction": "The study of the distribution of matter on large scales is usually based on the distribution of individual galaxies or clusters of galaxies. An alternative is to use the density field applying smoothing of galaxy or cluster distribution with a suitable kernel and smoothing length. This approach is customary in N-body simulations, where in each step a smoothed density field is evaluated. To the real cosmological data the smoothed density method has been applied in the study of the topology of the galaxy distribution by Gott et al. (\\cite{gmd86}). The IRAS redshift survey was used by Saunders et al. (\\cite{sfr91}) to calculate the density field up to a distance 140~$h^{-1}$\\thinspace Mpc. Recently Basilakos et al. (\\cite{bpr00}) applied the same method using the PSCz-IRAS redshift survey by Saunders et al. (\\cite{s00}). In all three studies a 3-dimensional spatial distribution was found. Due to the small volume density of galaxies with known redshifts a rather large smoothing length was used. This was sufficient to investigate topological properties of the galaxy distribution in the first case, and to detect superclusters of galaxies and voids in other cases. In this paper, we shall calculate the number and luminosity density fields based upon the Early Data Release (EDR) of the Sloan Digital Sky Survey (SDSS) by Stoughton et al. (\\cite{s02}) and the Las Campanas Redshift Survey (LCRS) by Shectman et al. (\\cite{Shec96}). The SDSS Early Data Release consists of two slices of about 2.5 degrees thickness and $65-90$ degrees width, centred on celestial equator, LCRS consists of six slices of 1.5 degrees thickness and about 80 degrees width. The number of galaxies observed per slice (over 10.000 in the SDSS slices and about 4,000 in LCRS slices) and their depth (almost 600~$h^{-1}$\\thinspace Mpc) are sufficient to calculate the 2-dimensional density fields with a high resolution (here $h$ is the Hubble constant in units of 100~km~s$^{-1}$~Mpc$^{-1}$). Using high-resolution number or luminosity density maps with smoothing scale of the order of 1~$ h^{-1}$\\thinspace Mpc\\ it is possible to find density enhancements in the field, which correspond to groups and clusters of galaxies. Using a larger smoothing length we can extract superclusters of galaxies as done by Basilakos et al. (\\cite{bpr00}). In calculating the density fields we can take into account most of the known selection effects, thus we hope that the density field approach gives additional information on the structure of the Universe on large scales. Clusters of galaxies from the SDSS were extracted previously by \\cite{2002PASJ...54..515G} using the cut and enhance method. Loose groups of galaxies from LCRS were found by Tucker et al. (\\cite{Tucker00}). In accompanying papers by Einasto et al. (\\cite{e02a}, \\cite{e02b}, papers II and III, respectively) we use the density fields of SDSS and LCRS galaxies to derive catalogues of clusters and superclusters and to compare samples of density-field defined clusters and superclusters with clusters and superclusters found with conventional methods. In the next section we describe the Early Data Release of the SDSS, and the LCRS samples of galaxies used. In section 3 we derive the luminosity function for the SDSS and LCRS galaxies using distances found for a cosmological model with dark matter and energy. In section 4 we calculate the density fields using SDSS and LCRS galaxy samples. We analyse our results in section 5, section 6 brings conclusions. ", "conclusions": "In this paper we have calculated the galaxy luminosity function for the SDSS EDR and LCRS samples and used it to construct the number and luminosity density fields (smoothed on $0.8\\ h^{-1}$ Mpc scale) assuming flat underlying cosmologies with $\\Omega _m=0.3$ and $\\Omega _\\Lambda =0.7.$ The analysis presented here is rather simple and serves as a first step in the study of the distribution of galaxies in SDSS and LCRS samples. The principal conclusion from our study is: parameters of the galaxy luminosity function depend on the distance from the observer, density of the environment, they are different for the Northern and Southern slice. The largest effect is the dependence on the density of the environment: in high-density regions brightest galaxies are more luminous than in low-density regions by a factor up to 5 (1.7 magnitudes). Some of these effects suggest that it is not yet possible to find an universal set of parameters of the luminosity function valid for a fair sample of the Universe. In other words, presently available samples are still too small to be considered as candidates for the fair sample." }, "0212/astro-ph0212111_arXiv.txt": { "abstract": " ", "introduction": "\\label{sec:intro} Most of the available information about matter in our Universe, and in our Galaxy in particular, comes indirectly from the collection of the electromagnetic radiation (from meter waves to $\\gamma$ rays) that was emitted or absorbed by this matter. A completely different information is provided by the cosmic ray nuclei, which constitute a genuine sample of galactic matter. Many different nuclei species are observed, in a wide range of energy, and with different origins. Some of them come unaltered from the sources (they are called {\\em primaries}\\/), others ({\\em secondaries}\\/) come from nuclear reactions between the primaries and the interstellar medium, or from the disintegration of unstable species. Moreover, the trajectories of these nuclei from creation to detection are rather erratic, due to the influence of the galactic magnetic field on all the charged particles, and it is generally not possible to follow the direction of an incoming nucleus back to the source. If we were able to understand clearly the processes by which all these nuclei are produced, accelerated and propagated in the Galaxy, the wealth of data available now or in the near future would yield most valuable information about the matter content and magneto-hydrodynamical properties of our Galaxy. In principle, it would even be possible to discover some evidence for new physics (e.g. supersymmetry) or new objects (e.g. primordial black holes or stars made of antimatter) as they can give rise to the emission of charged antinuclei and make an extra contribution to the observed cosmic ray fluxes. This review presents a summary of the work made in this direction by the authors from 1999 to 2002, in a {\\sc lapth-isn-iap} collaboration. As a first step, we tried to reach a {\\em quantitative}\\/ understanding of the propagation of cosmic ray nuclei in the energy range 100~MeV/nuc-100~GeV/nuc. More precisely, we described propagation with a diffusion model, in which the free parameters are adjusted to account for the available data on cosmic rays. This provides the regions of the parameter space allowed by the data. As a second step, we took advantage of this model to investigate several points concerning astrophysics and astroparticle physics. During this study, various aspects related to the ``standard\" or to more speculative processes were examined in detail. These may be summarized as follows: \\begin{itemize} \\item Standard cosmic rays \\begin{itemize} \\item Diffusion parameters from secondary-to-primary ratio \\item The flux of standard secondary antiprotons and antideuterons \\item Spatial origin \\item Radioactive species and the local bubble \\item Evolution of composition with energy \\end{itemize} \\item Exotic cosmic rays \\begin{itemize} \\item Baryonic Dark Matter \\item Antimatter \\item Supersymmetric particles \\item Primordial Black Holes \\end{itemize} \\end{itemize} The extraction of the diffusion parameters is the central goal since all conclusions follow from their values. ", "conclusions": "\\label{sec:concl} A consistent framework to understand the propagation of CR nuclei in the energy range 100 MeV--100 GeV was presented in this paper. The observed fluxes of most species can be explained by assuming that once emitted from some sources located in the galactic disc, these nuclei undergo a diffusive propagation altered by escape through the boundaries, spallations, reacceleration, energy losses and galactic wind. The magnitude of these effects has been constrained using the B/C data, and the consistency of the model has been tested against the observed antiproton flux and by the study of radioactive species. This well-tested model has then been used to study the propagation of cosmic rays of a more hypothetical origin, such as light antinuclei produced by SUSY galactic Dark Matter or Primordial Black Holes. In particular, limits on the abundance of primordial black holes in the galactic halo could be set. There are several directions in which this work may be extended. First, the constraints on the propagation parameters could be refined by considering other species, stable or secondary. However, this approach is currently limited by the accuracy of the available data on cosmic ray fluxes and on the nuclear cross sections. Second, a specific study of the EC unstable species could provide valuable information about the processes responsible for the acceleration of cosmic rays. Third, the existing limits on the SUSY induced antiproton signal can be bettered by using the constraints on the propagation parameters in a fully consistent way. Finally, the propagation code we use should ultimately be able to yield the flux of all cosmic ray species (including gamma rays, electrons and positrons) at every position in the Galaxy. \\begin{figure}[hbt!] \\includegraphics[width=\\columnwidth]{organigramme_an.ps} \\caption{Schematic view of the subjects discussed in this paper. The stars indicate collaborations of {\\sc lapth} (Annecy-le-Vieux, France) members with {\\sc isn} ($\\star$, Grenoble, France), {\\sc iap} ($\\star \\star$, Paris, France) or {\\sc infn} ($\\star \\star \\star$, Turin, Italy). Dashed boxes represent future projects. The numbers in parenthesis represent the publications. The starting point (1) is the first use of the elaborate propagation model presented here \\cite{Maurin01}, (2) is \\cite{Donato02} (3) is \\cite{Donato01}, (4) is \\cite{barrau01}, (5) is \\cite{Maurin03}, (6) is \\cite{Maurin02}, (7) is \\cite{barrau02} and (8) is \\cite{Taillet01,Maurin04}. The pre-\\cite{Maurin01} works are labelled as (-1) for \\cite{Bottino_Salati} (-2) for \\cite{Orloff} and (-3) for \\cite{chardonnet96}.} \\label{fig:organigram} \\end{figure}" }, "0212/astro-ph0212394_arXiv.txt": { "abstract": "We present a 40GHz (7.5 mm) raster scan image of a $3.6\\arcdeg\\times2\\arcdeg$ region centered on the low redshift ($z=0.055$) cluster of galaxies Abell 3667. The cluster was observed during the Antarctic winter of 1999 using the Corona instrument ($15.7\\arcmin$ FWHM beam) on the Viper Telescope at the South Pole. The Corona image of A3667 is one of the first direct ({\\it i.e.} rather than interferometer) thermal Sunyaev-Zel'dovich effect images of a low redshift cluster. The brightness temperature decrement at the X-ray centroid ($20^h 12^m 28.9^s, -56\\arcdeg 49\\arcmin 51\\arcsec$ J2000) was measured to be $\\Delta T_{\\rm CMB}=-154\\mu K$. We have used the 40GHz map of A3667 in conjunction with a deep ROSAT PSPC (X-ray) image of the cluster, to make a measurement of the Hubble Constant. We find $H_0= 64^{+96}_{-30}$ km s$^{-1}$ Mpc$^{-1}$ (68\\% confidence interval). Our $H_0$ calculation assumes that the cluster can be described using an isothermal, tri-axial ellipsoidal, $\\beta$-model and includes several new analysis techniques including an automated method to remove point sources from X-ray images with variable point spread functions, and an efficient method for determining the errors in multi-parameter maximum likelihood analyzes. The large errors on the $H_0$ measurement are primarily due to the statistical noise in the Corona image. We plan to increase the precision of our measurement by including additional clusters in our analysis and by increasing the sensitivity of the Viper SZE maps. ", "introduction": "\\label{sec:intro} The Sunyaev-Zel'dovich effect (Sunyaev \\& Zel'dovich 1972, SZE hereafter) describes the inverse Compton scattering of cosmic microwave background (CMB) photons by energetic free electrons. For instance, the random thermal motions of electrons trapped in the potential wells of clusters of galaxies result in a frequency dependent change in CMB intensity known as the thermal SZE. Similarly, the bulk peculiar motion of these electrons results in frequency independent change known as the kinetic SZE. Observations of the thermal and kinetic SZE using either single dish telescopes ({\\it e.g.} Mason, Myers \\& Readhead 2001; Pointecouteau et al. 2001 \\& 2002; De Petris et al. 2002 or interferometric techniques ({\\it e.g.} Jones et al. 2001; Reese et al. 2001 \\& 2002; Udomprasert, Mason \\& Readhead 2001) have improved dramatically in recent years (see Birkinshaw 1999 for a recent review). Measurements of the SZE have been used for a variety of scientific applications, including the estimation of the Hubble Constant (e.g. Mason, Myers, \\& Readhead 2001; Jones et al. 2001; Reese et al. 2002); determinations of the fraction, by mass, of baryons in the Universe (e.g. Grego et al. 2001); X-ray independent measurements of cluster temperatures (e.g. Pointecouteau et al. 2002); and constraints on cluster peculiar velocities (Holzapfel et al. 1997b, LaRoque et al. 2002). The technique of interferometric SZE imaging is now well established. By contrast, only recently has it become possible to generate direct (rather than aperture synthesis) SZE images using single dish telescopes. To date, only two clusters, RX J1347-1145 \\& RX J2228+2037, both at $z\\simeq0.4$, have published direct SZE images (Pointecouteau et al. 1999, 2001 \\& 2002; Komatsu et al. 2001). We report here a third direct SZE image. This 40 GHz (7.5 mm) image of the ($z=0.055$, Sodre et al. 1992) Abell cluster (Abell, Corwin, \\& Olowin 1989) A3667 was made using the Viper telescope at the South Pole as part of the Viper Sunyaev-Zel'dovich Survey (VSZS). The VSZS aims to study a complete sample of southern clusters at radio/microwave, optical and X-ray wavelengths and it goals include the measurement of the Hubble Constant. We chose to study A3667 as our initial VSZS target because, as one of the brightest X-ray ($L_{0.5-2.0 {\\rm keV}} = 4.1\\times10^{44}$ ergs $s^{-1}$, David et al. 1999) clusters in the REFLEX catalog (B\\\"ohringer et al. 2001), A3667 is expected to have a strong SZE signal. A3667 is also one of the best studied clusters in the sky. Supporting data at other wavelengths include: X-ray imaging and spectroscopy (ROSAT: Knopp, Henry \\& Briel 1996; ASCA: Markevitch, Sarazin, Vikhlinin 1999; White et al. 2000; BeppoSAX: Fusco-Femiano et al. 2001; Chandra: Vikhlinin, Markevitch \\& Murray 2001 a\\& b; XMM), optical data in the form of images, weak lensing mass maps and multi-object spectroscopy ({\\it e.g.} Joffre et al. 2000; Katgert et al. 1998), and radio maps (R\\\"ottgering et al. 1997; Hunstead et al. 1999). In addition, A3667 has been the focus of three-dimensional MDH/N-body numerical simulations (Roettiger, Burns \\& Stone 1999). An outline of the paper is as follows. In section~\\ref{sec:viper-data} we review our observing strategy and data reduction methods. We also present the Corona map of the area around A3667. In section~\\ref{sec:Ho} we describe a joint fit, to an isothermal, tri-axial ellipsoidal $\\beta$-model, to the ROSAT Position Sensitive Proportional Counter (PSPC) and Corona images of A3667 and present an estimate of the Hubble Constant. In section~\\ref{sec:conclusions}, we present conclusions and discuss future plans for cluster observations with Viper. ", "conclusions": "\\label{sec:conclusions} As the first stage of the Viper Sunyaev-Zel'dovich Survey (VSZS), we have presented a 40 GHz raster scan map of the region surrounding the $z=0.055$ cluster A3667. The cluster was observed during the Antarctic winter of 1999 using the Corona instrument ($15.7\\arcmin$ FWHM beam) on the Viper Telescope at the South Pole. The Corona image of A3667 is one of the first Sunyaev-Zel'dovich effect (SZE) images of a low redshift cluster. Currently, only the Viper telescope and the Cosmic Background Imager interferometer (Udomprasert, Mason \\& Readhead 2001) are able to make SZE images of low redshift clusters. One of the advantages of low redshift observations of the SZE is that complimentary data at other wavelengths, for example those necessary to make Hubble Constant estimates, are comparatively easy to obtain. The Corona image of A3367 is also one of the first direct ({\\it i.e.} rather than interferometer) SZE images; only two other clusters have published direct SZE images. We have used the 40GHz map of A3667 in conjunction with a deep ROSAT PSPC (X-ray) image to make a maximum likelihood fit to an isothermal tri-axial ellipsoidal $\\beta$ model. We have determined 68\\% confidence regions for nine of the eleven free parameters in the model using a modified Likelihood Ratio Test. Our analysis method includes new approaches to point source detection in X-ray images with varying point spread functions and also to error estimation in multi-dimensional parameter space. These innovations will be applied during the analysis of other VSZS clusters, but are also relevant to other SZE experiments. Our measurement of the Hubble Constant, $H_0= 64^{+96}_{-30}$ km s$^{-1}$ Mpc$^{-1}$, is in good agreement with previous, SZE determined, measurements. The error on this measurement is large, but not atypical for single dish experiments, and is being driven by instrument noise in the Corona map. Other parameters in the fit have been determined to much higher precision (1-3\\%). The Corona instrument was retired at the end of 2000 and replaced with the ACBAR instrument (Runyan et al. 2002). ACBAR offers both improved spatial resolution ($5\\arcmin$ FWHM beam) compared to Corona and simultaneous multi-wavelength (150, 220, 280 GHz) capabilities. Using ACBAR, in combination with data from CTIO, XMM-Newton and Chandra, we have continued the VSZS and are working toward completion of the SZE, X-ray and weak lensing observations of a complete, luminosity limited, sample of $\\simeq10$ clusters. These observations will improve our $H_0$ measurement in several ways. First, long duration ACBAR observations produce more sensitive maps than was possible with Corona (see Kuo et al. 2002). Second, we can minimize the contribution of primary CMB anisotropies in our SZE images by combining data at the three ACBAR observing frequencies (Gomez et al. 2002). This feature becomes important when the instrument noise gets down to the level of the CMB noise and it is noteworthy that most other SZE experiments only operate at a single frequency; Diabolo (Pointecouteau 1999, 2001 \\& 2002), BOLOCAM (Mauskopf et al. 2000b) and SuZIE (Holzapfel 1997 a\\&b) are exceptions, but these are not optimized to image low redshift clusters. Third, combining observations of several clusters drawn from a statistically complete sample reduces both random errors and systematic errors associated with orientation bias ({\\it e.g.} Grainger 2001). Finally, the improved spatial resolution of ACBAR over Corona, means that we will be able to use independent beams to probe different lines of the sight through each cluster. We only used data from the central beam of the A3667 Corona image for the analysis above, but by using multiple lines of sight we can reduce the error on the overall measurement. Together, these improvements will allow us to measure the Hubble constant with significantly higher precision than was possible with the Corona observation of A3667 presented herein. \\paragraph" }, "0212/astro-ph0212441_arXiv.txt": { "abstract": "We are modeling the spectra of dwarf galaxies from infrared to submillimeter wavelengths to understand the nature of the various dust components in low-metallicity environments, which may be comparable to the ISM of galaxies in their early evolutionary state. The overall nature of the dust in these environments appears to differ from those of higher metallicity starbursting systems. Here, we present a study of one of our sample of dwarf galaxies, NGC~1569, which is a nearby, well-studied starbursting dwarf. Using ISOCAM, IRAS, ISOPHOT and SCUBA data with the D\\'esert et al (1990) model, we find consistency with little contribution from PAHs and Very Small Grains and a relative abundance of bigger colder grains, which dominate the FIR and submillimeter wavelengths. We are compelled to use 4 dust components, adding a very cold dust component, to reproduce the submillimetre excess of our observations. ", "introduction": "Dwarf galaxies in our local universe are ideal laboratories for studying the interplay between the ISM and star formation in low-metallicity environments (Hunter \\& Gallagher 1989). They are at relatively early epochs of their chemical evolution, possibly resembling distant protogalaxies in their early stages of star formation. Although only a few metal-poor galaxies have been observed in the MIR using ISO, the characteristics of the MIR dust components appear to differ remarkably from those of normal-metallicity starbursts (Madden 2000). Whether this is an abundance or composition effect is not yet clear. For this reason, we are studying their detailed luminosity budget by modeling their spectral energy distributions (SEDs) from optical to millimeter wavelengths, thereby constructing templates to study conditions in primordial galaxies to help to constrain galaxy evolution models. The galaxy we present here is NGC~1569. It is a HI-rich, metal-poor ($Z=0.25\\;\\rm Z_\\odot$) dwarf irregular galaxy which lies near the galactic plane at a distance of $(2.2 \\pm 0.6)\\;\\rm Mpc$ (Israel 1988). NGC~1569 is presently in the aftermath of a massive burst of star formation (Israel 1988, Israel \\& De Bruyn 1988, Waller 1991) and exhibits very compact HII regions and 2 super-star-clusters (Hunter et al 2000). ", "conclusions": "The dust masses deduced from our modeling are $m_{\\rm PAH}\\sim 3 \\msol$, $m_{\\rm VSG}\\sim 600 \\msol$, $m_{\\rm BG}\\sim 2.5\\, 10^5 \\msol$, $m_{\\rm VCG}\\sim 2.7\\, 10^5 \\msol$ and the gas-to-dust mass ratio is $\\sim 400$. % The dust mass deduce from the extinction is $\\sim 2.2\\, 10^5 \\msol$ which is the same order of magnitude as the mass deduced from the model. Our results seem to show that the dust mass in NGC~1569 is mainly concentrated in cold dust: big grains and very cold grains which both have roughly the same mass abundance. The PAHs as well as the VSGs are very sparse, while the SED is dominated by bigger grains." }, "0212/astro-ph0212507_arXiv.txt": { "abstract": "We present interplanetary network localization, spectral, and time history information for 7 episodes of exceptionally intense gamma-ray emission from Cygnus X-1. The outbursts occurred between 1995 and 2003, with durations up to $\\thicksim$28000 seconds. The observed 15 - 300 keV peak fluxes and fluences reached $\\rm3 \\times 10^{-7}\\, erg \\, cm^{-2} s^{-1} \\, and \\, 8 \\times 10^{-4}\\, erg \\,cm^{-2}$ respectively. By combining the triangulations of these outbursts we derive an $\\thicksim$ 1700 square arcminute (3 $\\sigma$) error ellipse which contains Cygnus X-1 and no other known high energy sources. The outbursts reported here occurred both when Cyg X-1 was in the hard state as well as in the soft one, and at various orbital phases. The spectral data indicate that these outbursts display the same parameters as those of the underlying hard and soft states, suggesting that they represent another manifestation of these states. ", "introduction": "The X-ray source Cygnus X-1 was discovered by Bowyer et al (1965), and its optical counterpart, a spectroscopic binary at a distance of $\\sim$ 2 kpc with a 5.6 day period (HDE226868), was identified by Webster and Murdin (1972) and Bolton (1972). The primary is a supergiant, and the mass of the secondary is at least $\\rm 7 M_{\\sun}$ (Gies \\& Bolton 1986), making it a black hole candidate and a high mass X-ray binary. The X-ray source, which has been observed from keV to MeV energies, is thought to be powered by accretion (e.g. Petterson 1978). Soft X-radiation may be produced in an accretion disk close to the black hole, and hard X-rays by inverse Compton scattering in a separate hot plasma; see Liang and Nolan (1984) for a review. Recently, a relativistic jet has been detected in the radio (Stirling et al. 2001), and Romero et al. (2002) have suggested that Cygnus X-1 is a microblazar, that is, that we are observing it close to the axis of the jet. Cygnus X-1 is known to exhibit two states of X-ray emission, which are thought to depend on the accretion rate (Esin et al. 1998). The first, more common one, is the hard state, in which the 20 - 200 keV flux is roughly one Crab, and the $<$10 keV emission is about 0.5 Crab. The second is the soft state, in which the low energy X-ray flux increases by a factor of 2 - 4, while the high energy flux decreases by a factor of about 2. Transitions between the two states and flaring have been documented extensively (Ling et al. 1997; Zhang et al. 1997; Cui et al. 2002; McConnell et al. 2002), and both states exhibit variability of a factor of two or so on all timescales. In this paper we report on seven episodes of long, intense gamma-ray emission from this source; we refer to them as \\it outbursts \\rm (and identify them by their dates), to distinguish them from the shorter, less intense flaring which has been documented previously. One of these outbursts, 950325, was found by Mazets et al. (1995) and initially thought to be a gamma-ray burst; subsequently, however, its source was found to be Cygnus X-1 by M. Briggs (private communication, 1995). Later, Stern et al. (2001) called attention to five outbursts on 1999 April 19-21. During the two brightest events, the hard X-ray flux increased by over an order of magnitude for $\\sim$ 1000 s. Observations by \\it Ulysses \\rm and Konus - \\it Wind \\rm of still three more outbursts in 2002 - 2003 have prompted us to reanalyze all the available data in order to obtain better energy spectra and a more precise source location as well. ", "conclusions": "The outbursts reported here have durations comparable to the period of a low Earth-orbiting spacecraft, making them difficult to detect and follow from experiments aboard such spacecraft, but relatively easy for experiments which are far from Earth and do not undergo occultation and orbital background variations. Indeed, our observations of 990421A show that it continues well beyond the point at which it was Earth-occulted to BATSE, and our observations of 990421B indicate that it commenced several hundred seconds before it rose on BATSE (Stern et al. 2001). These observations point to a new use for the IPN, namely tracking long, intense flares from Galactic transients. The data from a single experiment which has little or no directional and/or spectral information are easily confused with solar X-ray and particle events, which explains why it has taken so long to determine the origin of some of the outbursts presented here. However, confirmation by a second spacecraft solves this problem and gives an annulus of position which in many cases may be sufficient to determine the origin of the emission. For several outbursts, the BATSE observations alone yield source directions which are only accurate to 17$\\degr$ , leaving the possibility that the source could have been Cygnus X-3. However, relatively small error ellipses may be obtained from multiple observations, and our localizations rule this possibility out conclusively. The histories of Cygnus X-1 and GRBs have been curiously intertwined over the decades. In the early days of X-ray astronomy, the use of interplanetary spacecraft was suggested to localize sources with rapid time variations such as Cyg X-1 (Giacconi 1972). Although, to our knowledge, such measurements were never carried out on persistent X-ray sources, today the technique is the basis of the IPN, and the present observations demonstrate the feasibility of this suggestion. Later, Mason et al. (1997) pointed out that bursts from Cyg X-1 could appear in the BATSE database; BATSE has indeed triggered many times on this source. Some of the long outbursts presented here have time histories which, if compressed in time, would be virtually impossible to distinguish from those of GRBs, and their spectra are hard. These similarities suggest that accretion onto a black hole, which is believed to power both Cyg X-1 and GRBs albeit under very different circumstances, may manifest itself in similar ways in very different settings." }, "0212/astro-ph0212076_arXiv.txt": { "abstract": "The evolution of the magnetorotational instability (MRI) during the transition from outburst to quiescence in a dwarf nova disk is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted for the analysis, so that the efficiency of angular momentum transport is studied in a small local patch of the disk: this is usually referred as to a one-zone model. To take account of the low ionization fraction of the disk, the induction equation includes both ohmic dissipation and the Hall effect. We induce a transition from outburst to quiescence by an instantaneous decrease of the temperature. The evolution of the MRI during the transition is found to be very sensitive to the temperature of the quiescent disk. As long as the temperature is higher than a critical value of about 2000 K, MHD turbulence and angular momentum transport is sustained by the MRI. However, MHD turbulence dies away within an orbital time if the temperature falls below this critical value. In this case, the stress drops off by more than 2 orders of magnitude, and is dominated by the Reynolds stress associated with the remnant motions from the outburst. The critical temperature depends slightly on the distance from the central star and the local density of the disk. ", "introduction": "Dwarf novae are close binary systems that consist of a white dwarf and a Roche-lobe-filling secondary star. The matter overflowing from the secondary star forms an accretion disk around the white dwarf. Dwarf nova systems show repetitive outbursts in which the luminosity of the disks increase rapidly. The duration of the outbursts ranges from a few to 20 days, and the recurrence time is about 20 -- 300 days. The disk instability model (Osaki 1974), in which the evolution of the disk is regulated by changes in the rate of angular momentum transport, is generally accepted as the explanation of the outbursts (Cannizzo 1993; and references therein). Since ordinary molecular viscosity is too low to explain the evolutionary timescale of the disks, an anomalous stress associated with turbulence and characterized by the $\\alpha$ parameter (Shakura \\& Sunyaev 1973), is thought to be the source of angular momentum transport. Detailed comparisons between observed light curves of dwarf novae and the theoretical disk models suggest that the viscous parameter $\\alpha$ must vary between the hot (outburst) and cold (quiescent) state, and the amplitude of $\\alpha_{\\rm hot}$ and $\\alpha_{\\rm cold}$ is typically of the order of 0.1 and 0.01, respectively. However, while the origin of the anomalous stress has become better understood in recent years (see below), the reasons for the difference between $\\alpha_{\\rm hot}$ and $\\alpha_{\\rm cold}$ are still unclear. The magnetorotational instability (MRI; Balbus \\& Hawley 1991) is the most promising source of the anomalous stress. MHD turbulence driven by the MRI can transport angular momentum by the Maxwell (magnetic) stress. During the hot state, the disk gas is fully ionized so that the ideal MHD approximation is appropriate. Numerical simulations that adopt ideal MHD have shown that the Maxwell stress caused by the MRI can give $\\alpha \\sim 0.1$ to 0.01, where the saturation level is determined by the geometry and strength of the magnetic field (e.g., Hawley, Gammie, \\& Balbus 1995; 1996). Therefore, MHD turbulence can be the primary mechanism of angular momentum transport at least during outbursts, that is it can account for $\\alpha_{\\rm hot}$. During the cold state, on the other hand, the gas is only weakly ionized. Gammie \\& Menou (1998) have pointed out that ohmic dissipation could modify the nature of the MHD turbulence at quiescence, and this could make the difference between $\\alpha_{\\rm hot}$ and $\\alpha_{\\rm cold}$. Calculations of the ionization fraction in dwarf nova disks reveal that the Hall effect as well as ohmic dissipation must be considered if the temperature is $T \\lesssim 2000$ K (Sano \\& Stone 2002a). At low temperatures, ohmic dissipation can suppress the growth of the MRI (Jin 1996; Sano \\& Miyama 1999). If turbulence dies away completely as a result of ohmic dissipation, the Maxwell stress cannot provide the required anomalous stress during quiescence (Menou 2000). Thus, it is important to calculate numerically the amplitude of the Maxwell stress at the cold state. In this paper, we examine the behavior of MHD turbulence during the transition from an outburst to quiescence using local three-dimensional MHD simulations. These simulations include the dominant non-ideal MHD effects as determined from a self-consistent calculation of the ionization state in the disk. Since we adopt a local approximation to study the turbulent stresses (usually referred to as a one-zone model, e.g., Mineshige \\& Osaki 1983; Cannizzo \\& Wheeler 1984), our calculations do not include global effects (such as spiral shocks in the disk, Sawada, Matsuda, \\& Hachisu 1986) which may contribute to angular momentum transport. The plan of this paper is as follows. In \\S~2, we calculate the ionization fraction in dwarf nova disks by solving the Saha equation to estimate the magnitude of nonideal MHD effects at quiescence. Our numerical method is described in \\S~3. The results of numerical simulations which examine the dependence of the stress on the geometry of magnetic field and the decay timescale of turbulence are presented in \\S~4. In \\S~5, we discuss the activity of MHD turbulence and the source of angular momentum transport during quiescence. ", "conclusions": "\\subsection{The Critical Temperature and Transition Timescale} When the magnetic Reynolds number falls to unity, MHD turbulence is suppressed by ohmic dissipation independent of the amplitude of the Hall term (Sano \\& Stone 2002a,b). The critical temperature corresponding to $Re_{M} = 1$ is about 2000 K for our model. As seen from equation~(\\ref{eqn:rem}), however, the critical temperature depends on the neutral density $n_n$ and the distance from the central star $r$. Figure~\\ref{fig:tcrit} shows the critical temperature $T_{\\rm crit}$ as a function of $r$ for the cases of the neutral density $n_n = 10^{17}$, $10^{18}$, and $10^{19}$ cm$^{-3}$. We assume the Alfv{\\'e}n speed $v_{A} = 10^5$ cm s$^{-1}$ and the mass of the central star $M = M_{\\odot}$. At a given temperature, the electron abundance decreases as the neutral density increases, so that the critical temperature is slightly higher when the density is higher. The MRI wavelength ($\\sim v_{\\rm A} / \\Omega$) is shorter at a smaller radius, because the angular velocity is larger. Therefore, the MRI can be suppressed with a smaller amount of diffusivity $\\eta$ in the inner regions of the disk. The critical temperature is about 2500 and 1500 K at $r = 10^9$ and $10^{11}$ cm, respectively. Since the magnetic Reynolds number, or the electron abundance, has a steep dependence on the temperature, the range of the critical temperature is quite narrow and the difference is at most a factor of 2 over the entire disk. In our numerical analysis, we assume a fixed temperature during quiescence. Thus the electron abundance at quiescence is assumed to be constant. In a real disk, the critical temperature could be a little higher due to a runaway decay of MHD turbulence (Menou 2000). The decrease of the temperature makes both the electron abundance lower and nonideal MHD effects more important. The turbulent stress is therefore suppressed further, so that the temperature falls even more. However, a very weak dependence of the stress on the temperature can be seen in our models when $T \\gtrsim 3000$ K. This indicates that the runaway temperature should be less then 3000 K. Although a self-consistent study of the evolution of the temperature and electron abundance is needed to obtain a real $T_{\\rm crit}$, Figure~\\ref{fig:tcrit} may give a fairly good estimate of the critical temperature in dwarf nova disks. We also assume the transition to quiescence occurs instantaneously. In actual systems, however, this may proceed at the thermal timescale $t_{\\rm th}$, where $t_{\\rm th}/t_{\\rm rot} \\sim 1 / \\alpha \\gtrsim 100$ (Frank, King, \\& Raine 1992). Suppose the temperature decreases gradually. As long as the temperature is higher than the critical value, we have shown that the accretion stress is nearly constant. But, once the temperature drops below this critical value, the MRI is suppressed, the turbulence decays within an orbit, and the $\\alpha$ parameter drops by more than 2 orders of magnitude. Therefore, even though the decrease of the temperature is gradual, the transition timescale of the stress may be very much shorter. \\subsection{Onset of the Next Outburst} Dwarf nova systems undergo recurrent outbursts. The matter from the secondary star accumulates in the disk during quiescence. When the surface density exceeds a critical value at some region in the disk, the thermal instability sets in and the temperature goes up. Here we examine the behavior of the MRI at the transition to the hot state. Figure~\\ref{fig:w-t100-z} shows the time evolution of the Maxwell and Reynolds stress for model ZC until 100 orbits. After 100 orbits, the induction equation for the ideal MHD is used in order to imitate the onset of the next outburst. As seen from the figure, the growth of the MRI starts immediately at the transition to the outburst and the magnetic field is amplified exponentially. In a few orbits, the Maxwell stress reaches the same saturation level as that before 50 orbits. The key to this evolution is the existence of a net vertical flux. During quiescence (from 50 to 100 orbits), MHD turbulence is suppressed, but the magnetic flux within the shearing box is conserved throughout the evolution. Thus the field geometry at 100 orbits is a nearly uniform vertical field. When the nonideal MHD effects are turned off, the linear growth of the MRI starts and MHD turbulence is initiated. This evolution may be different if the system has no net magnetic flux. For example, if the magnetic field is {\\em completely} dissipated during quiescence (e.g., model SD), MHD-driven activity cannot occur during the next outburst. However, if enough magnetic field remains for there to be unstable modes even in a small region of the disk, MHD turbulence develops in that region and finally may spread over a large part of the disk (Hawley \\& Balbus 1991). Therefore, it is quite important to understand the global structure of the magnetic field during quiescence, including the magnetosphere of the white dwarf and the magnetic field supplied by accreting material from the secondary star (Meyer \\& Meyer-Hofmeister 1999). \\subsection{Beyond the Local Model} Since we focus on the local behavior of MHD turbulence in this paper, neither global structural effects nor global instabilities have been considered. In real disks, global effects such as spiral shocks (Sawada et al. 1986) may also transport angular momentum. From our numerical results, the dependence of the $\\alpha$ parameter associated with local turbulence on temperature in a dwarf nova disk can be summarized as follows. The contribution of the MRI to the $\\alpha$ parameter is significant during outburst. When the temperature is higher than the critical value $T_{\\rm crit} \\sim 2000$~ K, the accretion stress is dominated by the Maxwell stress, with $\\alpha \\sim 0.1$ and 0.01 for the cases with and without net vertical flux, respectively. At quiescence, on the other hand, $\\alpha$ is very sensitive to the temperature of the disk. If $T \\lesssim T_{\\rm crit}$, the stress is more than 2 orders of magnitude smaller than that during outburst. There are several reasons why global effects may influence these results. Firstly, the presence of a net vertical flux can affect the amplitude of the turbulence stress during outburst, that is $\\alpha_{\\rm hot}$. In agree with the previous works using the local shearing box (e.g., Hawley et al. 1995; 1996), our simulations have shown that an sufficient amount of angular momentum transport in the hot state requires the existence of a net vertical field. On the other hand, recent global simulations obtained a higher stress ($\\alpha \\sim 0.1$) even without a net magnetic flux (Stone \\& Pringle 2001; Hawley, Balbus, \\& Stone 2001). There is no observational constraint yet in the structure and strength of the magnetic field in dwarf nova disks. Thus, theoretical modeling of the global structure of the magnetic field is quite important for a more detailed analysis of $\\alpha$ at the hot state. Secondly, the ionization fraction of the disk gas, and therefore the importance of non-ideal MHD effects, is extremely sensitive to temperature. Thus global models in which the radial and vertical temperature profiles in the disk are calculated self-consistently with the local heating rate due to turbulent stresses and cooling rate due to radiation are required. Furthermore, at the surface of the disk, the radiation from a hot white dwarf could be important source of heating and ionization (Hameury, Lasota, \\& Dubus 1999; Menou 2002). Finally, even when Ohmic dissipation completely suppresses the MRI, small amplitude motions remain in the disk and can give a non-zero Reynolds stress. In the local model, these motions are damped on a viscous timescale, which may be very long. However, they may be affected by global density waves in the disk or tidally induced spiral shocks. Thus, global MHD simulations are an important next step for understanding the dynamics of dwarf nova disks." }, "0212/astro-ph0212240_arXiv.txt": { "abstract": "We present optical and near--infrared Keck spectroscopy of CXOHDFN J123635.6$+$621424 (hereafter HDFX28), a hard X--ray source at a redshift of $z = 2.011$ in the flanking fields of the Hubble Deep Field--North (HDF--N). HDFX28 is a red source (${\\cal R} - K_s = 4.74$) with extended steep--spectrum ($\\alpha^{\\mbox{\\tiny 8.4 GHz}}_{\\mbox{\\tiny 1.4 GHz}} > 0.87$) microjansky radio emission and significant emission (441 $\\mu$Jy) at 15 $\\mu$m. Accordingly, initial investigations prompted the interpretation that HDFX28 is powered by star formation. Subsequent {\\it Chandra} imaging, however, revealed hard ($\\Gamma = 0.30$) X--ray emission indicative of absorbed AGN activity, implying that HDFX28 is an obscured, Type II AGN. The optical and near--infrared spectra presented herein corroborate this result; the near--infrared emission lines cannot be powered by star formation alone, and the optical emission lines indicate a buried AGN. HDFX28 is identified with a face--on, moderately late--type spiral galaxy. Multi--wavelength morphological studies of the HDF--N have heretofore revealed no galaxies with any kind of recognizable spiral structure beyond $z > 2$. We present a quantitative analysis of the morphology of HDFX28, and we find the measures of central concentration and asymmetry to be indeed consistent with those expected for a rare high--redshift spiral galaxy. ", "introduction": "\\label{introduction} The origin of the X--ray background (XRB) remains an enduring puzzle for X--ray astronomy. Great progress has been made during the last four years: {\\it ROSAT} surveys successfully resolved $\\sim$80\\% of the soft XRB (0.5--2 keV) into discrete sources \\citep[e.g.][]{hasinger98} and current work with the {\\it Chandra X--ray Observatory} (hereafter, {\\it Chandra}) has successfully resolved a similar fraction of the hard XRB \\citep[2--8 keV;][]{brandt01, giacconi01, giacconi02, hornschemeier01, rosati02}. Nonetheless, a coherent understanding of the physical and evolutionary properties of the sources which comprise the XRB is only just now emerging. Although much of this population appears to be the nuclei of otherwise normal bright galaxies ($I < 23.5$) or typical active galactic nuclei (AGNs), a significant fraction of the discrete sources is optically faint ($I > 23.5$), and therefore not easily identified \\citep[e.g.][]{alexander01, barger02}. {\\it Type II quasars}, for instance, are thought to be AGNs viewed edge--on through an obscuring torus \\citep{antonucci93} and are deemed an essential component of the XRB--producing population \\citep{moran01}. However, few well--studied examples of such systems are known at high redshift, and owing in part to their lack of relativistic brightening, they are not easily identified in shallow, large--area surveys \\citep{norman02, stern02q}. Type II quasars represent just one of several diverse classes of objects emerging in follow--up work to deep {\\it Chandra} fields \\citep[e.g.][]{hornschemeier01, schreier01, stern02}. On the extra--galactic side, we find X-ray--loud composite galaxies typified by starburst or early--type optical spectra which bear no signature of their buried AGN \\citep[e.g.][]{moran96, levenson01, stern02}. Additionally, we find X--ray sources whose optical counterparts belong to the class of faint, extremely red objects (EROs), the nature of which has remained uncertain owing to the difficulty in spectroscopic follow--up \\citep[e.g.][]{alexander02, elston88, elston89, hu94, graham96, liu00, hornschemeier01, stern02}. On the Galactic side, we find late--type dwarfs emitting soft X--rays originating in chromospheric activity \\citep[e.g.][]{hornschemeier01}, and very low mass binary systems emitting hard X--rays driven by accretion \\citep[e.g.][]{stern02}. Amidst the emergence of this menagerie of objects, optical and near--infrared spectroscopic follow--up has become increasingly vital not only to identifying the source population of the XRB, but also to elucidating the physics of X--ray sources in general, and to delineating their evolution with redshift. One critical facet of this endeavor is simply to distinguish between objects powered by mass accretion onto supermassive black holes (quasars and other AGNs) and those powered by nuclear fusion in stars (normal and starburst galaxies). To this end, we present optical and near--infrared spectra of CXOHDFN J123635.6$+$621424 (hereafter HDFX28), a hard X--ray source identified with a face--on spiral galaxy at redshift $z = 2.011$ (Figure~\\ref{flank}). HDFX28 is fortuitously located in the Hubble Deep Field--North inner west (HDF--N IW) flanking field, and was therefore subject to a vast array of follow--up imaging. As such, HDFX28 was initially identified as an extended microjansky radio source with a comparatively steep spectral index ($S_{\\nu} \\propto \\nu^{-\\alpha}$; $\\alpha^{\\mbox{\\tiny 8.4 GHz}}_{\\mbox{\\tiny 1.4 GHz}} > 0.87$). Together with its detection by the {\\em Infrared Space Observatory} Camera (ISOCAM) and its pronounced optical spatial extent ($\\sim 1\\farcs6$), the radio data for HDFX28 prompted an initial interpretation as a galaxy powered by star formation \\citep[e.g.][]{richards00}. However, as we discuss below, the detection of HDFX28 as a hard X--ray source in the deep {\\it Chandra} survey of the HDF--N \\citep{hornschemeier01, brandt01}, corroborated by the spectroscopy presented herein, demonstrates that this galaxy in fact harbors an obscured, Type II AGN. In addition to confirming its AGN status, the spectroscopy of HDFX28 indicates a surprisingly high redshift for an object with identifiable spiral structure. \\citet{dickinson00} summarizes the results of morphological studies of the HDF--N by reporting a total lack of even plausible candidates for spiral galaxies at $z>2$. Prompted by this lack of precedent for high--redshift spirals, we present a quantitative study of central concentration and asymmetry in HDFX28 based on the scheme devised by \\citet{abraham96} for the analysis of large CCD imaging surveys. With the application of a modest morphological $k$--correction, we find HDFX28 to have morphological parameters consistent with those derived from catalogs of both artificially redshifted nearby spirals, as well as catalogs of {\\it HST} imaging of spirals out to $z \\sim 1$ \\citep{abraham96}. In short, HDFX28 is intriguing both for its membership in the emerging class of X--ray--selected Type II AGN, and for possessing a morphology which is unprecedented at its redshift. We describe the optical and near--infrared spectroscopy of HDFX28 in section \\S \\ref{observations}, and we present the results of the spectroscopy and the classification of the source as an obscured, Type II AGN in \\S \\ref{as_an_agn}. We report on our quantitative analysis of its morphology in \\S \\ref{as_a_spiral}, and we summarize our results in \\S \\ref{conclusion}. Throughout this paper we adopt the currently favored $\\Lambda$--cosmology of $\\Omega_{\\mbox{\\tiny M}} = 0.35$ and $\\Omega_\\Lambda = 0.65$, with $H_0 = 65$ km s$^{-1}$ Mpc$^{-1}$ \\citep[e.g.][]{riess01}. At $z=2.011$, such a universe is 3.22 Gyr old, the lookback time is 76.9\\% of the total age of the Universe, and an angular size of 1\\farcs0 corresponds to 8.66 kpc. \\bigskip \\bigskip \\bigskip ", "conclusions": "\\label{conclusion} We have reported on two aspects of the high--redshift, hard X--ray emitting spiral galaxy HDFX28: (1) its classification as a Type II AGN, a population recently attracting renewed interest due to deep X--ray surveys, and for which few {\\it HST} images are available, and (2) its unprecedented redshift for a galaxy with spiral morphology. As for HDFX28 as a Type II AGN, the canonical wisdom regarding weak, extended radio sources with spectral indices steeper than $\\alpha^{\\mbox{\\tiny 8.4 GHz}}_{\\mbox{\\tiny 1.4 GHz}} > 0.5$ dictates that such sources are driven by star formation. Nonetheless, the combined weight of evidence from X--ray, optical, and near--infrared observations of HDFX28 indicates the presence of obscured AGN activity. It is instructive to note that when re--interpreted in light of the spectroscopic redshift, even the mid--infrared data for HDFX28 corroborates this result. At $z = 2.011$, the ISOCAM LW3 filter samples rest wavelengths spanning only 4 $\\mu$m to 5 $\\mu$m. Here, the contribution to the mid--IR spectral energy distribution made by UIB emission and by dust at 200 K is severely attenuated \\citep[see][Figure 1]{aussel99}. Hence, the ISOCAM detection of this source is far more plausibly explained by the hot, $\\sim 10^3$ K dust found in the central region of an AGN \\citep[e.g.\\ see][]{aussel98} than it is by star formation alone. As to the precise nature of the central engine in HDFX28, we conclude from the comparatively narrow emission lines in the spectroscopy and from the heavy obscuration evident in the X--ray data that HDFX28 is far more like an obscured Type II system than an unobscured Type I system. Though this conclusion is slightly at odds with the presence of weak, broad \\hal\\ emission, all remaining aspects of the source are entirely consonant with observations of other Type II AGN at moderate--to--high redshifts \\citep[e.g.][]{kleinmann88, norman02, stern02q} and with HzRGs \\citep[e.g.][]{larkin00, mccarthy93, stern99hzrg, vernet01}. \\citet{norman02} describe a very similar situation in which their source CDF--S 202 shows both the narrow ($\\sim 1000$ km s$^{-1}$) emission lines in its optical spectrum and the heavy obscuration in its X--ray emission typical of a Type II system, but also shows emission line flux ratios intermediate between Type I and Type II systems. As noted by \\citet{stern02q}, it is conceivable that longer--wavelength spectra of CDF--S 202 and other sources like it would also reveal broad \\hal, though they in every other way give evidence of the heavy obscuration considered to be emblematic of Type II AGN. Separately, the spectroscopy presented herein shows HDFX28 to be at an unprecedented redshift for a galaxy with identifiably spiral structure. Nevertheless, with the application of a modest morphological $k$--correction, our quantitative analysis of its central concentration and asymmetry is consistent with the interpretation that HDFX28 is a rare example of a high--redshift spiral galaxy. Owing to its proximity to the HDF--N, HDFX28 will be subject to deep, space--based $B$, $V$, $i$, and $z$ imaging with the Advanced Camera for Surveys as part of the upcoming GOODS {\\it HST} Treasury Program (M.\\ Giavalisco, PI), as well as to infrared imaging at $\\lambda > 3$ $\\mu$m with the Infrared Array Camera as part of the GOODS {\\it SIRTF} Legacy project (M.\\ Dickinson, PI). At a minimum, the availability of multi--wavelength imaging will provide a powerful additional lever arm on the issue of the morphology of HDFX28 \\citep[e.g.][]{conselice97,conselice00}. As such, we eagerly look forward to these expansive datasets." }, "0212/astro-ph0212289_arXiv.txt": { "abstract": "We report the first measurements of anisotropy in the cosmic microwave background (CMB) radiation with the Arcminute Cosmology Bolometer Array Receiver ({\\sc Acbar}). The instrument was installed on the $2.1\\,$m Viper telescope at the South Pole in January 2001; the data presented here are the product of observations up to and including July 2002. The two deep fields presented here, have had offsets removed by subtracting lead and trail observations and cover approximately $24\\,{\\rm deg}^2$ of sky selected for low dust contrast. These results represent the highest signal to noise observations of CMB anisotropy to date; in the deepest $150\\,$GHz band map, we reached an RMS of $\\sim8.0\\,\\mu$K per $5^{\\prime}$ beam. The 3 degree extent of the maps, and small beamsize of the experiment allow the measurement of the CMB anisotropy power spectrum over the range $\\ell = 150-3000$ with resolution of $\\Delta \\ell=150$. The contributions of galactic dust and radio sources to the observed anisotropy are negligible and are removed in the analysis. The resulting power spectrum is found to be consistent with the primary anisotropy expected in a concordance $\\Lambda$CDM Universe. ", "introduction": "\\ln{\\cal L}({\\bf q}) = \\ln{\\cal L}(\\overline{{\\bf q}})-\\frac{1}{2} \\sum\\limits_{B}\\frac{(Z_B - \\overline{Z}_B)^2}{\\sigma_B^2}e^{2{\\overline Z}_B}, \\end{equation} where the offset log-normal parameters ${\\bf Z}$ are defined as \\begin{equation}\\label{lognorm} Z_B = \\ln{(q_B + x_B)}. \\end{equation} Even to the quadratic order, the Fisher matrix is only an approximation to the curvature matrix of the likelihood function near the extrema. To examine the real shape of the likelihood function, we explicitly fit the curvature $\\sigma_B$ and log-normal offset $x_B$ and compared the results with the Fisher matrix (now diagonal) and the offsets suggested by \\citet{bond2000} (see their eq. [28]). In general we found very good agreement. In a few bands, however, the uncertainty indicated by the true likelihood function is $\\sim 15\\%$ larger than that derived from the Fisher matrix. The uncertainty and log-normal offsets reported in this paper are determined from fits to the likelihood function. \\subsubsection{Window Functions}\\label{subsubsec:window} Our goal is to produce a CMB power spectrum that can be used to constrain cosmological models. Window functions are used to convert a given model power spectrum to quantities directly comparable to the band-power measurements of the experiment. A window function $W_{B\\ell}$ for band ``$B$'' should have the following property: $$ \\langle q_B \\rangle=\\sum_\\ell (W_{B\\ell}/\\ell)D_\\ell\\,, $$ where $q_B$ is the experimental band-power measurement. \\citet{knox99} derived the appropriate window function for the band-power quadratic estimator \\citep{tegmark97b}, $$ W_{B\\ell}/\\ell=\\frac{1}{2}\\sum_{B'} (F^{-1})_{BB'}{\\rm Tr}\\left( \\frac{\\partial C_T}{\\partial D_\\ell}C^{-1}C_{T,B'}C^{-1}\\right)\\,. $$ This form of window function has been used in several other experiments \\citep{halverson_thesis,pryke02,myers02}, and should serve as a good approximation for maximum likelihood band-power. Making use of eqs.~[\\ref{fish}][\\ref{ctb}], it can be shown that the pre-decorrelation window functions satisfy the following normalization condition, \\begin{equation} \\sum_\\ell \\chi_{B\\ell}W_{B'\\ell}/\\ell=\\delta_{BB'}\\,.\\label{norm} \\end{equation} In Section~\\S\\ref{subsubsec:decorr}, we described the computation of a set of decorrelated band-powers from the Fisher matrix of the raw band-powers. This same linear transformation is applied to the window functions to produce a set of decorrelated window functions. It is not necessary to calculate the window functions for all $\\ell$. However, we would like to sub-divide the $q_B$ bands into bins with finer $\\ell$ space resolution than the $q_B$ themselves. Otherwise in order to satisfy the normalization condition eq.~[\\ref{norm}], the pre-decorrelation window function reduces to a Kronecker-$\\delta$ in band index ``$B$'', or the tophat function given by $\\chi_{B\\ell}$. This is a reasonable approximation for experiments like BOOMERANG where the sky coverage, and therefore intrinsic $\\ell$ resolution, is large enough to resolve all the structures in the power spectrum. For {\\sc Acbar}, the $\\ell$ resolution of the experiment is comparable to the expected structure in $D_\\ell$ and it is essential to precisely characterize the dependence of each band power on the details of the power spectrum. The decorrelated window functions shown in Figure~\\ref{fig:window} were calculated with a resolution in $\\ell$ space of $\\Delta \\ell =30$. The first window function has significant oscillations with $\\Delta \\ell \\sim 110$. This appears to be an result of the close spacing of the fields in the LMT subtraction. For sufficiently smooth theoretical models these oscillations will average to a mean value, however, the exact dependence of the first band power on arbitrary input models could be complex. Numerical tabulations of the window functions are available on the {\\sc Acbar} public web site. \\begin{figure*}[t] \\centerline{ \\psfig{figure=window_joint_pq_c3_14.ps,width=5in,height=3in,angle=0}} \\caption{The window functions ($W_{B\\ell}/\\ell$) for the decorrelated {\\sc Acbar} band powers. The vertical lines show the band boundaries. Numerical tabulations of these functions are given on the {\\sc Acbar} website. } \\label{fig:window} \\end{figure*} \\subsubsection{Monte Carlo Simulations} In order to test our analysis technique, we performed 300 Monte Carlo realizations of CMB2 and CMB5 maps that are consistent with our observed noise statistics and the same underlying $\\Lambda$CDM model. These maps were processed exactly as the real data, including using the same projection of corrupted modes, in order to test the ability of our pipeline to accurately determine the input CMB power spectrum. A quadratic estimator technique \\citep{tegmark97b} is used to rapidly determine the power spectrum for each of 300 realizations. In Figure~\\ref{fig:montecarlo}, we show the resulting average power spectrum overlaid on the input model. It is clear that the input model is recovered without bias, even in the low $\\ell$ bins that are sensitive to the angular scales on which the mode removal is occurring. \\begin{figure*}[t] \\centerline{ \\psfig{figure=cl_joint_pq_c3_montecarlo.ps,width=6in,height=3in,angle=0}} \\caption{The results of 300 Monte Carlo runs using the measured {\\sc Acbar} noise correlation. The solid line is the input fiducial $\\Lambda$CDM model. It is clear that the analysis method accurately reproduces the input power spectrum.} \\label{fig:montecarlo} \\end{figure*} ", "conclusions": "\\label{sec:conclusion} We have used the {\\sc Acbar} receiver to measure the angular power spectrum of the CMB at a frequency of $150\\,$GHz over the multipole range $\\ell = 100-3000$. The power spectrum we present is derived from approximately 21 weeks of Austral winter observations with {\\sc Acbar} installed on the $2.1\\,$m Viper telescope at the South Pole. In the course of analyzing this data, we have employed new analysis techniques designed specifically for high sensitivity ground based CMB observations. Monte Carlo simulations are used to verify that the analysis method accurately recovers the power spectrum without bias. The power spectrum we present is robust and has passed stringent tests for systematic errors. Galactic dust emission and radio point sources do not contribute significantly to the observed power and are projected out in the final analysis. Although dusty protogalaxies cannot be ruled out as a source of confusion, the expected contribution to the measured power is negligible. Overall, the resulting power spectrum appears to be consistent with the damped acoustic oscillations expected in standard cosmological models. In a companion paper \\citep{goldstein02}, the {\\sc Acbar} power spectrum is used to place constraints on cosmological models. The power in the highest $\\ell$ {\\sc Acbar} bin is consistent with the excess power measured in the Deep CBI pointings. At this point, the {\\sc Acbar} data lack the sensitivity to place significant constraints on the origin of the excess power observed by CBI. We acknowledge assistance in the design and construction of {\\sc Acbar} by the UC Berkeley machine and electronics shop staff. The support of Center for Astrophysics Research in Antarctica (CARA) polar operations has been essential in the installation and operation of the telescope. Percy Gomez, Kathy Romer, and Kim Coble are thanked for their assistance in monitoring the observations and telescope pointing. We thank Nils Halverson, Julian Borrill, and Radek Stompor for a careful reading of the draft and useful comments on analysis algorithms. Finally, we would like to thank John Carlstrom, the director of CARA, for his early and continued support of the project. The ACBAR program has been primarily supported by NSF office of polar programs grants OPP-8920223 and OPP-0091840. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. Chao-Lin Kuo acknowledges support from a Dr. and Mrs. CY Soong fellowship and Marcus Runyan acknowledges support from a NASA Graduate Student Researchers Program fellowship. Chris Cantalupo, Matthew Newcomb and Jeff Peterson acknowledge partial financial support from NASA LTSA grant NAG5-7926. \\appendix" }, "0212/astro-ph0212130_arXiv.txt": { "abstract": "{ A new, momentum preserving fast Poisson solver for N-body systems sharing effective $O(N)$ computational complexity, has been recently developed by Dehnen (2000, 2002). We have implemented the proposed algorithms in a Fortran-90 code, and parallelized it by a domain decomposition using the MPI routines. The code has been applied to intensive numerical investigations of galaxy mergers, in particular focusing on the possible origin of some of the observed scaling relations of elliptical galaxies. We found that the Fundamental Plane is preserved by an equal mass merging hierarchy, while it is {\\it not} in a scenario where galaxies grow by accretion of smaller stellar systems. In addition, both the Faber-Jackson and Kormendy relations are {\\it not} reproduced by our simulations. ", "introduction": "In the last few years, fast algorithms for computing N-body interactions relying on the general multipole expansion techniques have been developed. These schemes, usually referred to as Fast Multipole Methods (FMMs, see, e.g., Greengard \\& Rokhlin 1987, 1997), are designed to have $O(N)$ computational complexity. However, it has been noted that only $O(N{\\rm log}N)$ scaling is usually achieved in numerical implementation (see, e.g., Capuzzo-Dolcetta \\& Miocchi 1998, hereafter CM98). The $O(N{\\rm log}N)$ operation count also characterizes the N-body codes based on tree algorithms, originally proposed by Barnes \\& Hut (1986, hereafter BH86). In addition, it has been shown by direct numerical tests that, for given accuracy, tree-codes are faster than the FMMs by a factor of $\\sim 4$ (CM98). For this reason, most of the N-body codes currently used for astrophysical applications are based on the classical BH86 tree scheme, where the particle data are organized into a nested oct-tree cell structure. Interactions between distant particles are approximated by cell--particle interactions, and the distribution of the particles on each cell is represented by a multipole expansion, usually truncated to the quadrupole term. Recently, a new scheme has been introduced (Dehnen 2000, 2002, hereafter D02), which can be seen as an original combination of the tree-based BH86 scheme and of the FMMs multipole expansion, truncated at a fixed low order level (the proposed $p=3$ order results the optimal one). This scheme, implemented by the Author in a C++ code [named falcON, Force Algorithm with Complexity $O(N)$], results in a significant improvement over the existing BH86 tree-codes, in terms of uniform accuracy, linear momentum conservation, and CPU time performances. Moreover, the numerical tests presented in the D02 paper show that for an accuracy level $\\epsilon \\simeq 10^{-3}$, for the first time an {\\it effective} $O(N)$ scaling in operation count, as predicted by the FMM theory, is in fact obtained. For these reasons two of us (P.L. and C.N.) have implemented this scheme in a new Fortran-90 code (FVFPS, a Fortran Version of a Fast Poisson Solver), and have then parallelized it by using the MPI procedures. A completion of the code to handle gas-dynamics using Euler equations and the AMR (Adaptive Mesh Refinement) techniques is under development. Here we briefly describe the main characteristics of Dehnen's algorithm, and we present our FVFPS implementation and its parallelization. The achieved accuracy level, the performances in terms of operation count speed-up, the effective $O(N)$ scaling, as well as the parallel scaling with the processors number, are then documented in numerical tests. Finally, we describe some interesting astrophysical applications of the code, in the context of the study of galaxy merging. Our version of the code is available upon request. ", "conclusions": "The main results of our work can be summarized as follows: \\begin{itemize} \\item Our implementation of the D02 scheme in a F-90 N-body code (FVFPS) has effective $O(N)$ complexity for number of particles $N \\gsim 10^4$, though its time efficiency is lower by a factor of $\\sim 1.5$ than Dehnen's C++ implementation. \\item As shown by numerical tests, the parallelized version of the FVFPS code has good scaling with the number of processors (for example for numbers of particles $N \\simeq 10^6$, at least up to 16 processors). \\item We found very good agreement between the results of merging simulations performed with our FVFPS code and with the GADGET code. \\item From an astrophysical point of view, our high resolution simulations of hierarchies of {\\it dissipationless} galaxy mergers indicate that {\\it equal mass} merging is compatible with the existence of the FP relation. On the other hand, when an {\\it accretion} scenario is considered, the merger remnants deviate significantly from the observed edge--on FP (see also NLC02). \\item The different behavior with respect to the FP of the merger remnants in the two scenarios is a consequence of structural non--homology, as shown by the analysis of their projected stellar density profiles. \\item In any case, the end--products of our simulations fail to reproduce both the FJ and Kormendy relations. In the case of equal mass merging, the combination of large effective radii and low central velocity dispersions maintains the remnants near the edge--on FP. \\end{itemize}" }, "0212/astro-ph0212306_arXiv.txt": { "abstract": "Magnetic elements on the quiet sun are buffeted by convective flows that cause lateral motions on timescales of minutes. The magnetic elements can be observed as bright points (BPs) in the G band at 4305 {\\AA}. We present observations of BPs based on a long sequence of G-band images recorded with the Dutch Open Telescope (DOT) and post-processed using speckle masking techniques. From these images we measured the proper motions of isolated BPs and derived the auto-correlation function of their velocity relative to the solar granulation pattern. The accuracy of BP position measurements is estimated to be less than 23 km on the Sun. The rms velocity of BPs (corrected for measurement errors) is about 0.89 km s$^{-1}$, and the correlation time of BP motions is about 60 s. This rms velocity is about 3 times the velocity measured using cork tracking, almost certainly due to the fact that isolated BPs move more rapidly than clusters of BPs. We also searched for evidence of vorticity in the motions of G band BPs. ", "introduction": "Observations of the Sun with high spatial resolution show network bright points (Muller 1983, 1985, 1994; Muller \\& Keil 1983; Muller \\& Roudier 1984, 1992) and ``filigree'' (Dunn \\& Zirker 1973; Mehltretter 1974; Berger et al 1995), which are chains of bright features located within the intergranular lanes. The bright points and filigree are seen in the wings of strong spectral lines such as H$\\alpha$ and Ca II H \\& K, in lines formed in the photosphere, and even at continuum wavelengths (with reduced contrast). The widths of these structures is 100 to 200 km, at the limit of resolution of ground-based solar telescopes. In the following we collectively refer to these bright structures as bright points (BPs). The BPs are associated with regions of strong magnetic field (Chapman \\& Sheeley 1968; Title, Tarbell \\& Topka 1987; Simon et al 1988; Title et al 1989, 1992; Keller 1992) and correspond to magnetic flux tubes of kilogauss field strength that stand nearly vertically in the solar atmosphere (Stenflo 1973; Stenflo \\& Harvey 1985; S\\'{a}nchez Almeida \\& Mart\\'{i}nez Pillet 1994; see review by Solanki 1993). The dynamical behavior of BPs has been studied by a number of authors. Muller (1983) found that facular points on the quiet sun are predominantly located in patches at the periphery of supergranule cells, indicating that the magnetic elements are advected by the supergranular flow. The BPs always first appear in the dark spaces at the junction of several granules, never inside a granule nor in the space between only two granules. As the granulation pattern evolves, the BPs remain in the intergranular spaces throughout their lifetime, but not necessarily at the junction of several granules like at the time of their first appearance. New BPs have a tendency to appear adjacent to existing points, and 15 \\% of the BPs seem to split into two points which move apart until a separation of 1 to {1.5\\arcsec} is reached. Muller et al (1994) measured velocities of 29 isolated BPs and found a mean speed of 1.33 km s$^{-1}$. Strous (1994) studied BPs in a growing active region. Using line-center images taken in Fe~I (5576~{\\AA}), he found velocities between 0.26 km s$^{-1}$ and 0.62 km s$^{-1}$. Berger \\& Title (1996) measured velocities of 1 to 5 km s$^{-1}$ for G-band (4305~{\\AA}) BPs in the ``moat'' around a sunspot; they showed that the motions are constrained to the intergranular lanes and are primarily driven by the evolution of the granulation pattern. They found that the BPs continually split up and merge, with a mean time between splitting events of few hundred seconds. L\\\"{o}fdahl et al (1998) and Berger et al (1998) analyzed G-band and continuum images obtained at the Swedish Vacuum Solar Telescope (SVST) on La Palma and found rapid splitting and merging of BPs in an enhanced network region. Van Ballegooijen et al (1998) used a ``cork tracking'' method to measure the proper motions of G-band BPs and found that BPs appear to be passively advected by the granulation flow. The filigree are known to be associated with abnormal granulation patterns (Dunn \\& Zirker 1973), and the granules near network BPs are smaller and more numerous than near a normal intergranular space (Muller, Hulot \\& Roudier 1989), suggesting that the magnetic field has some effect on the granulation flow. Little is known about the small-scale dynamics of flows in intergranular lanes and the interaction of magnetic elements with such flows. Theoretical models (e.g.,~Stein \\& Nordlund 2000; Emonet \\& Cattaneo 2001) predict that vorticity is concentrated in the lanes and that magnetic elements exhibit rapid rotational motions. At present, there is no direct observational evidence for vorticity in intergranular lanes. More detailed measurements of vorticity are needed for testing magneto-convection models, and as input for models of flux-tube waves that heat the upper solar atmosphere (Hasan et al 2002). In this paper we present measurements of BP proper motions within the intergranular lanes. In particular, we look for evidence of vortical motions. Tracking BPs is a difficult task. Long sequences of images with very good seeing (or corrections of seeing) are needed. Image jitter due to residual atmospheric effects needs to be reduced as much as possible. The measurements of BP positions need to be made with respect to some frame of reference. The solar granulation is used as a reference, and the motion of this reference frame is determined by correlation tracking on the granulation pattern. We also tested measuring the BPs with respect to the average position of the bright points in each field, but found that the result is nearly identical to the result from correlation tracking. BPs vary widely in lifetime and contrast, so it is very difficult to automate the process of tracking them. In this paper, we use manual selection of BPs followed by fitting the peaks. ", "conclusions": "We have shown that with good enough data we can precisely measure positions for isolated BPs, obtaining both their linear and angular motions. The errors due to image jitter have been reduced to levels of 25 km (0.5~pixels) or less. This allows us to measure the motions of individual BPs to a precision of less than 1 km s$^{-1}$ for each 30 second time interval, which will be important for studying the generation of MHD waves in flux tubes. We also track BPs for sufficiently long times that we can see the regularity in their motions. The rms velocities we measured for isolated BPs were almost a factor of three higher than velocities measured using cork tracking (van Ballegooijen et al 1998). We believe this is due to a selection effect. By only measuring isolated BPs we measure the fastest-moving features. Once BPs cluster with other BPs, mostly at lane interstices, they seem to be ``captured'' by the group and their motions are reduced. There are many more BPs in these clusters than there are isolated BPs so the cluster statistics dominate when measurements are made with cork tracking and the average velocity is reduced. In measuring the motions of BPs, we have found that they move in somewhat circular paths. Combining the angular change of their motions with the distance they travel is a potential way of estimating the (vertical) vorticity in the flow field, assuming the BPs act as test particles. While performing the tracking of individual BPs, we saw little evidence of vorticity other than the tracks of the BPs themselves. We looked for, but did not find, pairs of BPs that orbited one another; in fact, BPs that came in close proximity to other BPs tended to have reduced motion. We also saw little evidence of swirling motions in the granules or granular lanes that would correspond to the observed BP motions. This might indicate that BPs are affected not only by surface flows associated with the solar granulation, but also by other flows that occur at larger depth below the photosphere. Further modeling will be required to establish whether or not the BPs move passively with the surface flow, and to determine whether the observed BP motions are consistent with models of flux tube waves and heating of the upper solar atmosphere." }, "0212/astro-ph0212183_arXiv.txt": { "abstract": "We discuss in detail the pulsation properties of variable stars in globular clusters (GCs) and in Local Group (LG) dwarf galaxies. Data available in the literature strongly support the evidence that we still lack a complete census of variable stars in these stellar systems. This selection bias is even more severe for small-amplitude variables such as Oscillating Blue Stragglers (OBSs) and new exotic groups of variable stars located in crowded cluster regions. The same outcome applies to large-amplitude, long-period variables as well as to RR Lyrae and Anomalous Cepheids in dwarf galaxies. ", "introduction": "Variable stars in stellar systems such as GCs and dwarf galaxies have played a fundamental role in improving our knowledge on stellar populations (Baade 1958) as well as on the physical mechanism that drive the pulsation instability (Schwarzschild 1942). The main advantage of cluster variables when compared with field ones is that they are located at the same distance, and possibly the same reddening. Moreover, they formed from the same proto-globular cloud and therefore they have the same age, and chemical composition. Even though cluster variables present several undoubted advantages current knowledge concerning the pulsation properties of these objects is still limited. Recent estimates based on new data reduction procedures to perform differential photometry (ISIS, Alard 2000) suggest that the incompleteness factor in the detection of RR Lyrae stars is at least of the order of 30\\% (Kaluzny et al. 2001; Corwin \\& Carney 2001) in Galactic GCs characterized by high central densities. This limit is even more severe for OBSs, since the luminosity amplitude range from hundredths of a magnitude to a few tenths. Moreover, their radial distribution peaks toward the center of the cluster, and therefore ground based observations are strongly limited by crowding (Gilliland et al. 1998; Santolamazza et al. 2001). The same outcome applies to Miras and to Semi-Regular variables in GGCs, but for a different reason, quite often they are saturated in current CCD chips. This is a real limit for metal-rich clusters of the Galactic bulge, since they lack of RR Lyrae stars or host a few of them (Pritzl et al. 2002), and the detection of Miras could supply an independent distance estimate (Feast et al. 2002). Variable stars in dwarf spheroidal (dSph) galaxies presents several pros and cons when compared with variables in GGCs. The star formation history as well as the dynamical evolution of dSph galaxies is much more complex than for GGCs. Typically the age of stellar populations in LG dSphs ranges from a few Gyr to 12-13 Gyr, i.e. as old as stars in GGCs (Da Costa 1999). Wide photometric surveys strongly support the evidence of extra-tidal stars near several dSphs (Irwin \\& Hatzidimitriou 1995; Martinez-Delgado et al. 2001). The observation of these stellar debris resembles the tidal tails detected in several GGCs (Leon et al. 2000). On the other hand, dSph galaxies apparently host large amounts of Dark Matter (DM), and indeed the mass-to-light ratios in these systems range from $(M/L)_V\\sim 5$ (Fornax) to $\\sim100$ (Ursa Minor). However, the scenario is still quite controversial and the evidence that dSphs present large DM central densities would suggest that they are not a large version of GGCs, since the latter present M/L ratios $\\approx1-2$. Photometric and spectroscopic data on variable stars in dSphs might supply new insights on the impact that environmental effects have on their evolutionary and pulsation properties. Unfortunately, data available in the literature are limited, since these stellar systems cover wide sky regions. The use of wide field imagers and wide field, multifiber spectrographs might overcome these problems. In the following we discuss the impact that variables in stellar systems might have on cosmic distances and on stellar populations. ", "conclusions": "The results presented in the previous sections bring forward the evidence that the empirical scenario for variable stars in stellar systems such as GCs and LG dwarf galaxies is far from being complete. The limit applies not only to aperiodic variables but also to long-period variables such as Miras and Semi-Regulars. The same outcome applies to RR Lyrae stars affected by the Blazhko effect. Even though several LG dSphs present stellar populations with chemical compositions and stellar ages quite similar to stars in GCs, the RR Lyrae variables present pulsation properties that are a {\\em bridge} between Oosterhoff type I and Oosterhoff type II clusters. This preliminary evidence seems to suggest that either the dynamical history and/or the chemical evolution in these stellar systems might play a role to explain this difference. In this context the use of the new wide field imagers will supply the unique opportunity to investigate on a star-by-star basis the stars and the variables in LG dwarf galaxies. Although new theoretical frameworks have been developed to account for the occurrence of mixed-mode pulsators among RR Lyrae and OBSs we still lack a comprehensive explanation of the physical mechanisms that drive the occurrence of such a phenomena. It goes without saying that new sets of full amplitude nonlinear, convective models tightly connected with evolutionary models are highly requested to constrain the region of the instability strip where these pulsators present this intriguing behavior." }, "0212/astro-ph0212460_arXiv.txt": { "abstract": "Experience with core-collapse supernova simulations shows that accurate accounting of total particle number and 4-momentum can be a challenge for computational radiative transfer. This accurate accounting would be facilitated by the use of particle number and 4-momentum transport equations that allow transparent conversion between volume and surface integrals in both configuration and momentum space. Such conservative formulations of general relativistic kinetic theory in multiple spatial dimensions are presented in this paper, and their relevance to core-collapse supernova simulations is described. ", "introduction": "\\label{sec:introduction} The state of the art in core-collapse supernova simulations now includes energy- and angle-dependent neutrino transport \\cite{rampp00,mezzacappa01,liebendoerfer01b,rampp02,liebendoerfer02,thompson02,janka02,janka02b}. However, experience shows that simultaneous conservation of both energy and lepton number is difficult numerically \\cite{mezzacappa93b,liebendoerfer02}. This challenge motivates us to develop new conservative formulations of relativistic kinetic theory that are specifically attuned to the need for accurate accounting of particle number and energy in numerical simulations of radiative transfer problems. Before describing the conservative formulations of kinetic theory we seek, we explain why energy- and angle-dependent neutrino transport is necessary in supernova simulations and detail the magnitude of the challenge of energy conservation. Sophisticated treatments of neutrino transport are necessary because the ultimate energy source of the supernova explosion---the gravitational potential energy of the stellar progenitor's core---is eventually converted almost completely into neutrinos. Some of the gravitational potential energy is lost to escaping neutrinos during core collapse, but most of it is converted into a thermal bath of dense nuclear matter, photons, electron/positron pairs, and trapped neutrinos deep inside the nascent neutron star. Neutrinos, having the weakest interactions, are the most efficient means of cooling; they diffuse outward on a time scale of seconds towards a semi-transparent region near the surface of the newly forming neutron star, and eventually escape with about 99\\% of the released gravitational energy. In modeling the conversion of gravitational potential energy into neutrino fluxes, energy- and angle-dependent neutrino transport is necessary to accurately follow the transition from quasi-isotropic diffusion to forward-peaked free streaming. In this transition region energy is transferred from the neutrino radiation to the matter behind a stalled shock wave, and this energy transfer may be necessary to propel the shock through the outer layers in an explosion \\cite{colgate66,bethe85}. But whether or not such neutrino heating is the proximate cause of explosion, the fact that neutrinos dominate the energetics implies that accurate neutrino transport is integral to any realistic and comprehensive study of the explosion mechanism. The importance of accurate neutrino transport is a lesson learned from experience with supernova simulations. Parametrized studies \\cite{janka96} highlight the sensitivity of explosions to neutrino luminosities and to conditions in the semi-transparent region near the nascent neutron star's surface (see also Ref. \\cite{janka01})---precisely the region where neutrino energy and angle dependence must be tracked carefully. Moreover, there remains a nagging qualititative uncertainty in simulations with multidimensional hydrodynamics: Those with neutrino transport that depends on direction in configuration space but is averaged over energy and angles exhibit explosions \\cite{herant94,burrows95,fryer02}, while those with neutrino transport that depends on energy but is averaged over angles in both configuration and momentum space do not show explosions \\cite{mezzacappa98,mezzacappa98b}. It may be that these differing outcomes are due to the different neutrino transport schemes, both of which are ultimately inadequate. Moving beyond these general arguments for the necessity of accurate neutrino transport, quantitative consideration of the energetics shows how severe the requirements are on one aspect of accuracy: energy conservation. As mentioned above, virtually all of the gravitational potential energy (\\inlineSFinmath${\\Tilde {{10}^{53}}\\multsp\\ \\Mvariable{\\rm erg}}$) released during collapse is eventually converted into intense neutrino fluxes lasting several seconds. However, supernova explosion energies (the kinetic energy of the ejecta) are observed to be only \\inlineSFinmath${\\Tilde {{10}^{51}}\\Mvariable\\ {\\rm erg}}$. Now, because it is difficult to argue with any rigor about the physical impact of any energy lost or gained due to numerical error, the total energy should be conserved to a precision corresponding to the phenomena of interest in the problem. Hence a simulation's result for explosion energy accurate to, say, \\inlineSFinmath${10\\InvisibleSpace \\%}$ would require total energy conservation to an accuracy of about \\inlineSFinmath${0.1\\InvisibleSpace \\%}$. Allowing for systematic error accrual, the total energy would have to be conserved at a level of \\inlineSFinmath${0.1\\InvisibleSpace \\%/N}$ per time step, where \\inlineSFinmath${N\\Tilde {{10}^5}}$ is the total number of time steps in the simulation. Conservative formulations of kinetic theory would help to meet the numerical challenge of particle number and energy conservation in core-collapse supernova simulations. To give an idea of the kind of formulation of kinetic theory that we seek, we first review familiar descriptions of the dynamics of a fluid medium. The dynamics can be described in two different ways, which might be called {\\em elemental} and {\\em conservative}. The elemental formulation expresses the evolution of the fluid in terms of equations of motion for the velocity and some independent set of quantities (e.g. temperature, densities of various species comprising the fluid, etc.) measured by an observer moving along with the fluid (``comoving observer''). For example, consider a spacetime with metric components $\\{g_{\\mu\\nu}\\}$ and metric determinant $g\\equiv \\det(g_{\\mu\\nu})$, containing a perfect fluid with 4-velocity components $\\{u^\\mu\\}$ and comoving frame total energy density $\\rho$, pressure $p$, and baryon density $n$. Iin the absence of radiative transfer and significant energy input from nuclear reactions, the perfect fluid evolves according to \\begin{eqnarray} (\\rho +p){u^{\\mu }}\\Big(\\frac{\\partial {u^{i }}}{\\partial {x^{\\mu }}}+{{{{\\Gamma }^{i }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}{u^{\\rho }}\\Big)+({g^{\\Mvariable{i \\mu }}}+{u^{i }}{u^{\\mu }})\\frac{\\partial p}{\\partial {x^{\\mu }}}&=&0, \\label{euler} \\\\ \\dispSFNumberedEquationmath{u^{\\mu }}\\frac{\\partial \\rho }{\\partial {x^{\\mu }}}+\\frac{(\\rho +p)}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{u^{\\mu }}\\big)&=&0, \\label{energy} \\\\ \\dispSFNumberedEquationmath{u^{\\mu }}\\frac{\\partial n}{\\partial {x^{\\mu }}}+\\frac{n}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{u^{\\mu }}\\big)&=&0.\\label{baryon} \\end{eqnarray} (Greek and latin letters are spacetime and space indices respectively.) Supplementary relations between \\inlineSFinmath${\\rho }$, \\inlineSFinmath${p}$, and \\inlineSFinmath${n}$---referred to as the {\\em equation of state}---are determined by the microphysics of the fluid. The name {\\em elemental} denotes the fact that by writing down separate equations of motion for the velocity and comoving-frame quantities, the kinetic and ``intrinsic'' fluid energies---two ``elements'' of the system---are analytically separated. The conservative approach expresses the evolution of the system in terms of the divergence of the stress-energy tensor \\inlineSFinmath${{T^{\\Mvariable{\\mu \\nu }}}}$. For a perfect fluid, $T^{\\mu\\nu}\\inlineSFinmath{=(\\rho +p){u^{\\mu }}{u^{\\nu }}+p {g^{\\Mvariable{\\mu \\nu }}}}$, and Eqs. (\\ref{euler}) and (\\ref{energy}) are replaced by \\begin{equation} \\dispSFNumberedEquationmath{\\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{T^{\\Mvariable{\\nu \\mu }}}\\big)=-{{{{\\Gamma }^{\\nu }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}{T^{\\Mvariable{\\rho \\mu}}},}\\label{divergence} \\end{equation} while Eq. (\\ref{baryon}) is replaced by \\begin{equation} \\dispSFNumberedEquationmath{\\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}n\\multsp {u^{\\mu }}\\big)=0.}\\label{baryon2} \\end{equation} Volume integrals of the left-hand sides of Eqs. (\\ref{divergence}) and (\\ref{baryon2})---obtained by multiplying by the invariant spacetime volume element $\\sqrt{-g}\\,d^4x$ and integrating---are related to surface integrals in an obvious manner. Physically, this relates the time rates of change of 4-momentum and baryon number in a volume to fluxes through a surface surrounding that volume; hence the labeling of Eqs. (\\ref{divergence}) and (\\ref{baryon2}) as {\\em conservative}. The right-hand side of Eq. (\\ref{divergence}) deserves note. After discussing the % reasons for this term's existence, we comment on what it means for conservation issues. There are several important cases where the connection coefficients ${{{{\\Gamma }^{\\nu }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}$ on the right-hand side of Eq. (\\ref{divergence}) might not vanish. They are present in curved spacetime, where (at least in part) they embody gravitational forces. But even in flat spacetime, coordinates employed by accelerated observers give rise to connection coefficients. And even without spacetime curvature or accelerated reference frames, connection coefficients arise from the use of curvilinear coordinates. What does the right-hand side of Eq. (\\ref{divergence}) mean for 4-momentum conservation? Only when it vanishes---that is, only for inertial observers in flat spacetime employing rectilinear coordinates---are the components of total 4-momentum constant in time (``conserved''). For only in this case do the coordinates reflect the translation invariance of flat spacetime, the physical origin of 4-momentum conservation. (Curved spacetime lacks translation invariance, so there is no 4-momentum conservation.) Because the presence, for whatever reason, of a source term like the right-hand side of Eq. (\\ref{divergence}) means that the 4-momentum components in such a basis are not conserved, it might more properly be called a ``balance equation'' than a ``conservation law''. But because the volume integral of the left-hand side easily translates into a surface integral, we still call it a ``conservative'' formulation. There are some special cases in which a conserved quantity associated with the time coordinate $t$ can be found, however. For unaccelerated observers in flat spacetime, ${{{{\\Gamma }^{t }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}=0$, even in curvilinear coordinates. This means that energy is conserved, though the 3-momentum components in cuvilinear coordinates are not. Another special case is the restriction to spherical symmetry in general relativity: Here certain coordinate choices allow the non-vanishing ${{{{\\Gamma }^{t }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}$ terms to be absorbed into the left-hand aside, leading to the identification of a conserved energy-like quantity (see e.g. Ref. \\cite{liebendoerfer01}). Having used the familiar example of a perfect fluid to discuss what we mean by ``elemental'' and ``conservative'' formulations, we now consider kinetic theory in terms of these categories. The evolution of a particle type described by kinetic theory is often expressed as an equation of motion for the distribution function \\inlineSFinmath${f}$, the ensemble-averaged density of a given particle type in phase space. (These concepts will be defined with greater precision in subsequent sections; for the present discussion it is sufficient to understand that phase space is the combination of configuration space and momentum space, and that multiplying $f$ by the volume of an infinitesimal cell in phase space gives the number of particles having positions and momenta within the ranges defined by that cell.) The distribution function evolves due to advection through phase space and particle interactions. Advection through phase space gives rise to derivatives of $f$ with respect to the components of the position vector $x$ and the momentum vector $p$. For numerical evolution it is convenient to parametrize the distribution function in terms of $\\{x^\\mu\\}$, the components of $x$ in a global ``coordinate basis'' \\footnote{In a ``coordinate basis'' the basis vectors are $\\vec{e}_\\mu = {\\partial\\over \\partial x^\\mu}$. These basis vectors ``commute'' because the order of partial derivatives can be interchanged freely. The connection coefficients in a coordinate basis are given by ${{{{\\Gamma }^{\\mu }}\\InvisibleSpace }_{\\Mvariable{\\nu \\rho }}}=\\frac{1}{2}{g^{\\Mvariable{\\mu \\sigma }}}\\Big(\\frac{\\partial {g_{\\Mvariable{\\sigma \\nu }}}}{\\partial {x^{\\rho }}}+\\frac{\\partial {g_{\\Mvariable{\\sigma \\rho }}}}{\\partial {x^{\\nu }}}-\\frac{\\partial {g_{\\Mvariable{\\nu \\rho }}}}{\\partial {x^{\\sigma }}}\\Big).$ In a ``non-coordinate basis'' obtained from the coordinate basis by a transformation $\\vec{e}_{\\mu'} = {L^\\mu}_{\\mu'}\\vec{e}_\\mu$, the basis vectors $\\vec{e}_{\\mu'} = {L^\\mu}_{\\mu'}{\\partial\\over \\partial x^\\mu}$ do not commute if ${L^\\mu}_{\\mu'}$ depends on position in spacetime. The connection coefficients in a non-coordinate basis have extra terms associated with the non-vanishing commutators of the basis vectors. In this paper, the connection coefficients in a non-coordinate basis are obtained from those of a coordinate basis via the transformation ${{{{\\Gamma }^{{\\mu' }}}}_{{\\nu' }{\\rho' }}}={{{{L }^{{\\mu' }}}}_{\\mu }}{{{{L }^{\\nu }}}_{{\\nu' }}}{{{{L }^{\\rho }}}_{{\\rho' }}}{{{{\\Gamma }^{\\mu }}}_{\\Mvariable{\\nu \\rho }}}+{{{{L }^{{\\mu' }}}}_{\\mu }}{{{{L }^{\\rho }}}_{{\\rho' }}}\\frac{\\partial {{{{L }^{\\mu }}}_{{\\nu' }}}}{\\partial {x^{\\rho }}}$. }. (Here and throughout this paper, quantities defined with respect to the coordinate basis have % indices without accents.) For momentum we make a different choice of basis, because interactions with a fluid are most easily described---and best handled numerically---in terms of momentum components measured by a comoving observer. The change from the coordinate basis to an orthonormal basis associated with the comoving observer (a ``non-coordinate basis'') has two parts. First there is a transformation \\inlineSFinmath${{{\\Mvariable{dx}}^{\\overvar{\\mu }{\\_}}}={{{e^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\mu }}{{\\Mvariable{dx}}^{\\mu }}}$ to an (in general non-comoving) orthonormal basis. (Here and throughout this paper, quantities defined with respect to the non-comoving orthonormal basis have indices accented with a bar.) This is followed by a Lorentz transformation \\inlineSFinmath${{{\\Mvariable{dx}}^{\\overvar{\\mu }{\\RawWedge }}}={{{{\\Lambda }^{\\overvar{\\mu }{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}{{\\Mvariable{dx}}^{\\overvar{\\mu }{\\_}}}}$ to a comoving orthonormal basis. (Here and throughout this paper, quantities defined with respect to the comoving orthonormal basis have indices accented with a hat.) Hence advection through phase space will involve derivatives of $f$ with respect to the coordinate basis position components $\\{x^\\mu\\}$ and the comoving orthonormal basis momentum components $\\{p^{\\overvar{\\mu}{\\RawWedge}}\\}$. Turning from advection to particle interactions, we consider the case where the particle species are sufficiently dilute that the interactions can be described in terms of a collision integral \\inlineSFinmath${\\mathbb{C}[f]}$ depending only on % the distribution functions $f$ of the individual particle species. (This approximation ignores correlations between particles; that is, the number of instances of finding particles at the same position is obtained from the product of their distribution functions.) In this case, the equation of motion for the distribution function \\inlineSFinmath${f}$ is \\cite{lindquist66,mezzacappa89} \\begin{equation} \\dispSFNumberedEquationmath{{p^{\\overvar{\\mu }{\\RawWedge }}}\\bigg({{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{e^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}\\frac{\\partial f}{\\partial {x^{\\mu }}}-{{{{\\Gamma }^{\\overvar{\\nu }{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\rho }{\\RawWedge }\\overvar{\\mu }{\\RawWedge }}}{p^{\\overvar{\\rho }{\\RawWedge }}}\\frac{\\partial f}{\\partial {p^{\\overvar{\\nu }{\\RawWedge }}}}\\bigg)=\\mathbb{C}[f].} \\label{boltzmann} \\end{equation} This is the {\\em Boltzmann equation}. In terms of the categories described above in connection with fluid evolution, the Boltzmann equation is ``elemental'': The most fundamental quantity---the distribution function---is the evolved variable, and volume integrals of the equation in both configuration space and momentum space are not obviously related to surface integrals. This ``non-conservative'' character is present even in flat spacetime and rectangular coordinates. The first term of Eq. (\\ref{boltzmann}) is non-conservative even in flat spacetime and rectilinear coordinates because the boost \\inlineSFinmath${{{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}}$---which depends on the coordinates $\\{x^\\mu\\}$---sits outside the derivative $\\partial f/\\partial x^\\mu$. The spatial dependence of the boost also gives rise to non-vanishing ${{{{\\Gamma }^{\\overvar{\\nu }{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\rho }{\\RawWedge }\\overvar{\\mu }{\\RawWedge }}}$, even in flat spacetime and rectilinear coordinates; therefore the second term of Eq. (\\ref{boltzmann}) does not vanish. This second term is non-conservative because the factor $p^{\\overvar{\\rho }{\\RawWedge }}$ sits outside the derivative ${\\partial f}/{\\partial {p^{\\overvar{\\nu }{\\RawWedge }}}}$. While the Boltzmann equation is ``elemental'' or ``non-conservative'', it is well known (e.g., see Refs. \\cite{lindquist66,ehlers71,israel72}) the first two momentum moments of the distribution function (integrated over a suitable invariant momentum space volume element \\inlineSFinmath${\\Mvariable{dP}}$) constitute a particle number current \\inlineSFinmath${{N^{\\mu }}}$ and particle stress-energy tensor \\inlineSFinmath${{T^{\\Mvariable{\\mu \\nu }}}}$, \\begin{eqnarray} \\dispSFNumberedEquationmath{N^{\\mu }}&=&\\int f\\multsp {p^{\\mu }}\\Mvariable{dP} =\\int f\\multsp \\,{p^{\\overvar{\\mu }{\\RawWedge }}}{{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{e^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}\\, \\Mvariable{dP}, \\label{particleNumberCurrent} \\\\ \\dispSFNumberedEquationmath{T^{\\Mvariable{\\mu \\nu }}}&=&\\int f\\multsp {p^{\\mu }}{p^{\\nu }}\\Mvariable{dP} = \\int f\\multsp \\, {p^{\\overvar{\\mu }{\\RawWedge }}}{{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{e^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}\\, {p^{\\overvar{\\nu }{\\RawWedge }}}{{{{\\Lambda }^{\\overvar{\\nu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\nu }{\\RawWedge }}}{{{e^{\\nu }}\\InvisibleSpace }_{\\overvar{\\nu }{\\_}}}\\, \\Mvariable{dP}, \\label{particleStressEnergy} \\end{eqnarray} which (for electrically neutral particles) obey the balance equations \\begin{eqnarray} \\dispSFNumberedEquationmath\\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{N^{\\mu }}\\big)&=&\\int \\mathbb{C}[f]\\Mvariable{dP}, \\label{particleNumberConservation} \\\\ \\dispSFNumberedEquationmath\\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{T^{\\Mvariable{\\nu \\mu }}}\\big) &=& -{{{{\\Gamma }^{\\nu }}\\InvisibleSpace }_{\\Mvariable{\\rho \\mu }}}{T^{\\Mvariable{\\rho \\mu }}} + \\int \\mathbb{C}[f]{p^{\\nu }}\\Mvariable{dP}. \\label{particleEnergyConservation} \\end{eqnarray} While this result is often stated in the literature (e.g., see Refs. \\cite{lindquist66,ehlers71,israel72}), because of the non-conservative character of Eq. (\\ref{boltzmann}) it is not obvious how its momentum moments give rise to Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation}). Equation (\\ref{boltzmann}) contains factors ${{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{e^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}$ outside ${\\partial f}/{\\partial {x^{\\mu }}}$; but from Eqs. (\\ref{particleNumberCurrent})-(\\ref{particleEnergyConservation}) we see that these factors have come inside the derivative with respect to $x^\\mu$. What happens to the spacetime derivatives of ${{{{\\Lambda }^{\\overvar{\\mu }{\\_}}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{e^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\_}}}$ that are generated in taking these factors inside the derivative? Furthermore, according to Eqs. (\\ref{particleNumberCurrent}) and (\\ref{particleStressEnergy}), the quantities \\inlineSFinmath${{N^{\\mu }}}$ and \\inlineSFinmath${{T^{\\Mvariable{\\mu \\nu }}}}$ involve no momentum derivatives of $f$. But the second term of Eq. (\\ref{boltzmann}) contains a factor $p^{\\overvar{\\rho }{\\RawWedge }}({\\partial f}/{\\partial {p^{\\overvar{\\nu }{\\RawWedge }}}})$. Because of the momentum factor outside the momentum derivative it is not obvious how this term will contribute to Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation}) when integrated over momentum space. How, then, is the connection between Eq. (\\ref{boltzmann}) and Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation}) established in detail? The reviews of relativistic kinetic theory by Lindquist \\cite{lindquist66} and Israel \\cite{israel72} do not provide detailed proofs. As discussed in Sec. \\ref{sec:distribution}, an explicit proof by Ehlers \\cite{ehlers71} relies on the fact that \\inlineSFinmath${{N^{\\mu }}}$ and \\inlineSFinmath${{T^{\\Mvariable{\\mu \\nu }}}}$ are momentum-integrated quantities, and no direct insight is gained into what happens to the momentum derivatives of $f$ in the integration over momentum space. For those interested in computer models of radiative transfer problems, these are not idle academic questions; they are issues that must be faced in order to build simulations capable of making meaningful scientific statements about the core-collapse supernova explosion mechanism. Experience with supernova simulations in spherical symmetry shows that understanding the detailed connection between the Boltzmann equation and the particle number and 4-momentum balance equations has important consequences for how well these quantities are conserved in a simulation \\cite{mezzacappa93,liebendoerfer02}. While a discretization of the Boltzmann equation is a natural numerical method of evolving the neutrino species, na\\\"{\\i}ve differencings of the various terms in Eq. (\\ref{boltzmann}) generally will not be consistent with a straightfoward differencing of Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation}), leading to unacceptable numerical errors in particle number and energy conservation. % In Lagrangian (or ``comoving'') coordinates in spherical symmetry, Mezzacappa and Bruenn \\cite{mezzacappa93} derive a conservative formulation of the Boltzmann equation transparently related to particle number balance as expressed in Eq. (\\ref{particleNumberConservation}). They also devise methods of handling momentum derivatives that are consistent with both number and energy conservation \\cite{mezzacappa93b}. Liebend\\\"orfer et al. \\cite{liebendoerfer02} went a step further in this spherically symmetric case, deducing the connnection between the Mezzacappa and Bruenn ``number conservative'' Boltzmann equation in comoving coordinates and energy conservation as represented by an Eulerian (or ``lab frame'') version of Eq. (\\ref{particleEnergyConservation}). Using complicated, non-intuitive differencings of hydrodynamic and gravitational variables, they construct a numerical implementation of % the Mezzacappa and Bruenn ``number conservative'' Boltzmann equation that is stable and faithful to its analytic connection to the lab frame version of Eq. (\\ref{particleEnergyConservation}) to the accuracy necessary to make solid scientific statements about the neutrino-driven explosion mechanism in spherical symmetry \\cite{mezzacappa01,liebendoerfer01b,liebendoerfer02}. Because spherically symmetric models with Boltzmann transport fail to reproduce some important observable characteristics of core-collapse supernovae (e.g. the launch of an explosion \\cite{mezzacappa01,liebendoerfer01b,liebendoerfer02,rampp00,rampp02,thompson02}), this work must be followed up in multiple spatial dimensions (see Refs. \\cite{janka02,janka02b} for some early efforts). In this paper we develop---allowing for full relativity and multiple spatial dimensions---conservative formulations of kinetic theory, such that volume integrals in both configuration and momentum space are {\\em trivially related} to surface integrals. These conservative expressions {\\em make transparent} the connection between Eq. (\\ref{boltzmann}) and Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation}). They can be used to deduce the term-by-term cancellations involved in this connection, thereby illuminating the complicated differencings required to achieve the cancellations numerically. Our conservative formulations also suggest new primary variables of radiation transport: particle number and energy variables describing the contribution of each {\\em comoving orthonormal basis} momentum bin to the {\\em coordinate basis} number and energy densities. It may be that the use of these new radiation variables could provide a simpler path to an accurate accounting of particle number and energy in simulations of radiative transfer problems. The organization of this paper is as follows. Differential forms and exterior calculus are natural mathematical tools for handling the volume elements and integrations needed in relativistic kinetic theory. We closely follow (and slightly extend) Ehlers' work \\cite{ehlers71} in reviewing their use in the description of phase space for particles of definite mass (Sec. \\ref{sec:phaseSpace}) and the derivation of the Boltzmann equation (Sec. \\ref{sec:distribution}). The centerpieces of this paper---two conservative reformulations of the Boltzmann equation, which provide transparent connections to particle number and energy-momentum balance as expressed in Eqs. (\\ref{particleNumberConservation}) and (\\ref{particleEnergyConservation})---are presented in Sec. \\ref{sec:conservative}. Because differential forms and exterior calculus may be unfamiliar to those whose primary interests are radiation transport, in general, or supernova science, in particular, Secs. \\ref{sec:phaseSpace}-\\ref{sec:conservative} each will contain two subsections: one containing a general derivation, and a second that explicitly demonstrates aspects of the derivation in the familiar case of the $O(v)$ limit in Lagrangian coordinates in spherical symmetry. (While we review some aspects of exterior calculus in our presentation, these are mostly in endnotes, and are more in the character of reminders than a self-contained introduction. For the latter we refer the reader to Refs. \\cite{ehlers71,mtw}.) A conclusion (Sec. \\ref{sec:conclusion}) summarizes our results, comments on their connection to moment formalisms, and discusses the utility of these formulations for supernova simulations. As an application of our formalism, an appendix contains \\inlineSFinmath{$O (v)$} equations in flat spacetime, but in coordinates sufficiently general to represent rectangular, spherical, and cylindrical coordinate systems. ", "conclusions": "\\label{sec:conclusion} In this section we summarize our conservative formulations of kinetic theory, comment on their relation to moment formalisms, and discuss their possible application in the core-collapse supernova environment. Having in mind computational radiative transfer in astrophysical environments, we have sought formulations of relativistic kinetic theory with the following properties: (1) they are expressed in terms of global, Eulerian (or ``lab-frame'') spacetime coordinates \\inlineSFinmath${\\{{x^{\\mu }}\\}}$; (2) they are expressed in terms of convenient three-momentum coordinates \\inlineSFinmath${\\big\\{{u^{\\overvar{i}{\\RawWedge }}}\\big\\}}$ (e.g. spherical polar), which are taken from the orthonormal momentum components \\inlineSFinmath${\\big\\{{p^{\\overvar{i}{\\RawWedge }}}\\big\\}}$ measured by an observer comoving with the medium; and (3) they are ``conservative'', having transparent connections to total particle number and 4-momentum balance as expressed in Eqs. (\\ref{numberConservation}) and (\\ref{energyConservation}). To express our formulations having these properties, we here introduce the {\\itshape specific particle number flux vector } \\begin{equation} \\dispSFNumberedEquationmath{{{\\ScriptCapitalN }^{\\mu }}\\equiv {{{{\\ScriptCapitalL }^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{p^{\\overvar{\\mu }{\\RawWedge }}}f} \\end{equation} and the {\\itshape specific particle stress-energy tensor} \\begin{equation} \\dispSFNumberedEquationmath{{{\\ScriptCapitalT }^{\\Mvariable{\\mu \\nu }}}\\equiv {{{{\\ScriptCapitalL }^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{{{{\\ScriptCapitalL }^{\\nu }}\\InvisibleSpace }_{\\overvar{\\nu }{\\RawWedge }}}{p^{\\overvar{\\mu }{\\RawWedge }}}{p^{\\overvar{\\nu }{\\RawWedge }}}f,} \\end{equation} where the transformation to the comoving frame \\inlineSFinmath${{{{{\\ScriptCapitalL }^{\\overvar{\\mu }{\\RawWedge }}}\\InvisibleSpace }_{\\mu }}}$ is given by equation (\\ref{compositeTransformation}). (While the adjective ``specific'' often denotes a quantity measured per unit mass, in this context we use it to denote the particle flux and stress-energy in a given invariant momentum space volume element.) While the distribution function \\inlineSFinmath${f}$ of a given particle type of mass \\inlineSFinmath${m}$ and charge \\inlineSFinmath${e}$ obeys the Boltzmann equation (Eq. (\\ref{fullBoltzmann})), the specific particle number flux and stress-energy satisfy the conservative equations \\begin{eqnarray} \\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\mu }}}\\big({\\sqrt{-g}}{{\\ScriptCapitalN }^{\\mu }}\\multsp \\big)+\\nonumber \\\\ E({\\bf p})\\Bigg|\\det \\big[\\frac{\\partial {\\bf p}}{\\partial {\\bf u}}\\big]{{\\Bigg|}^{-1}} \\frac{\\partial }{\\partial {u^{\\overvar{i}{\\RawWedge }}}}\\Bigg(\\frac{1}{{E({\\bf p})}}\\Bigg|\\det \\big[\\frac{\\partial {\\bf p}}{\\partial {\\bf u}}\\big]\\Bigg|\\big(e\\multsp {{{F^{\\overvar{j}{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}-{{{{\\Gamma }^{\\overvar{j}{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }\\overvar{\\nu }{\\RawWedge }}}{p^{\\overvar{\\nu }{\\RawWedge }}}\\big)\\frac{\\partial {u^{\\overvar{i}{\\RawWedge }}}}{\\partial {p^{\\overvar{j}{\\RawWedge }}}}{{{{\\ScriptCapitalL }^{\\overvar{\\mu }{\\RawWedge }}}\\InvisibleSpace }_{\\mu }}{{\\ScriptCapitalN }^{\\mu }}\\Bigg)\\IndentingNewLine \\nonumber\\\\ = \\mathbb{C}[f], \\label{conservative1} \\\\ \\frac{1}{{\\sqrt{-g}}}\\frac{\\partial }{\\partial {x^{\\nu }}}\\big({\\sqrt{-g}}{{\\ScriptCapitalT }^{\\Mvariable{\\mu \\nu }}}\\big)+ \\nonumber \\\\ {E({\\bf p})}\\Bigg|\\det \\big[\\frac{\\partial {\\bf p}}{\\partial {\\bf u}}\\big]{{\\Bigg|}^{-1}} \\frac{\\partial }{\\partial {u^{\\overvar{i}{\\RawWedge }}}}\\Bigg(\\frac{1}{{E({\\bf p})}}\\Bigg|\\det \\big[\\frac{\\partial {\\bf p}}{\\partial {\\bf u}}\\big]\\Bigg|\\big(e\\multsp {{{F^{\\overvar{j}{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\nu }{\\RawWedge }}}-{{{{\\Gamma }^{\\overvar{j}{\\RawWedge }}}\\InvisibleSpace }_{\\overvar{\\nu }{\\RawWedge }\\overvar{\\rho }{\\RawWedge }}}{p^{\\overvar{\\rho }{\\RawWedge }}}\\big)\\frac{\\partial {u^{\\overvar{i}{\\RawWedge }}}}{\\partial {p^{\\overvar{j}{\\RawWedge }}}}{{{{\\ScriptCapitalL }^{\\overvar{\\nu }{\\RawWedge }}}\\InvisibleSpace }_{\\nu }}{{\\ScriptCapitalT }^{\\Mvariable{\\mu \\nu }}}\\Bigg)\\IndentingNewLine \\nonumber\\\\ = {{{F^{\\mu }}\\InvisibleSpace }_{\\nu }}{{\\ScriptCapitalN }^{\\nu }} - {{{{\\Gamma }^{\\mu }}\\InvisibleSpace }_{\\Mvariable{\\nu \\rho }}}{{\\ScriptCapitalT }^{\\Mvariable{\\nu \\rho }}} + {{{{\\ScriptCapitalL }^{\\mu }}\\InvisibleSpace }_{\\overvar{\\mu }{\\RawWedge }}}{p^{\\overvar{\\mu }{\\RawWedge }}}\\mathbb{C}[f].\\label{conservative2} \\end{eqnarray} In stating that Eqs. (\\ref{conservative1}) and (\\ref{conservative2}) constitute conservative formulations of particle kinetics, we mean that the connection to the balance equations of Eqs. (\\ref{numberConservation}) and (\\ref{energyConservation}) is transparent, in the following sense. We can use elementary calculus to form the familiar invariant momentum space volume element \\begin{equation} \\dispSFNumberedEquationmath{\\frac{{d^3}p}{E({\\bf p})}=\\frac{1}{{E({\\bf p})}}\\Bigg|\\det \\big[\\frac{\\partial {\\bf p}}{\\partial {\\bf u}}\\big]\\Bigg|{d^3}u,}\\label{momentumElement2} \\end{equation} where a transformation from orthonormal momentum components \\inlineSFinmath${\\big\\{{p^{\\overvar{i}{\\RawWedge }}}\\big\\}}$ to some other set of coordinates (e.g. momentum space spherical coordinates \\inlineSFinmath${\\big\\{{u^{\\overvar{i}{\\RawWedge }}}\\big\\}=\\{|{\\bf p}|,\\vartheta ,\\varphi \\}}$) has been performed. Multiplying Eqs. (\\ref{conservative1}) and (\\ref{conservative2}) by Eq. (\\ref{momentumElement2}) and integrating, the terms with momentum space derivatives are obviously transformed into vanishing surface terms; the results are Eqs. (\\ref{numberConservation}) and (\\ref{energyConservation}) for total particle number and 4-momentum balance. In terms of differential forms, the procedure for obtaining the conservative formulations of kinetic theory is straightforward. First, express the volume element \\inlineSFinmath${\\Omega }$ in the phase space for particles of definite mass in terms of the desired spacetime and 3-momentum coordinates. Next, by contraction with the Liouville vector, form the hypersurface element \\inlineSFinmath${\\omega ={L_m}\\cdot \\Omega }$. Then bring the exterior derivative \\inlineSFinmath${d(f\\multsp \\omega )}$ into the form \\inlineSFinmath${\\mathbb{N} [f]\\Omega }$ by direct computation; Eq. (\\ref{conservative1}) results on comparison with the Boltzmann equation. This result can then be used in conjunction with an evaluation of \\inlineSFinmath${d({v_{\\mu }}{p^{\\mu }}f\\multsp \\omega )}$ for arbitrary \\inlineSFinmath${{v_{\\mu }}}$ to obtain Eq. (\\ref{conservative2}). The reason the procedure is straightforward is that the ``heavy lifting'' of transforming the Boltzmann equation into conservative forms is handled by two ``levers'' of considerable power: the generalized Stokes theorem, and the key relation \\inlineSFinmath${\\Mvariable{d\\omega }=0}$, which is closely related to the relativistic Liouville theorem. A concrete example of our formalism is provided in the appendix, which contains \\inlineSFinmath{$O (v)$} equations for the specific particle number density, specific particle energy density, and their angular moments---all in flat spacetime, but in coordinates sufficiently general to represent rectangular, spherical, and cylindrical coordinate systems. We now comment on the connection of Eqs. (\\ref{conservative1}) and (\\ref{conservative2}) to moment formalisms. In the usual treatments, if one writes the distribution function as a function of momentum variables as measured in a given frame (lab or comoving), it is natural to form moments by multiplying the distribution function by, for example, energies and angles measured in that frame, and integrating. Lo and behold, it turns out that these moments are number densities and fluxes, and energy/momentum densities and fluxes: components of a particle number flux vector and stress-energy tensor, measured in the same frame chosen to measure angles and energies. Traditional, then, are treatments in which the components of conserved tensors as measured in a given frame are expressed as functions of momentum variables as measured in that same frame. But this traditional approach to moments may not be the most convenient, and Eqs. (\\ref{conservative1}) and (\\ref{conservative2}) provide an attractive alternative. For example, Liebend\\\"orfer et al. \\cite{liebendoerfer01,liebendoerfer02} form moments in the traditional way, resulting in components of conserved tensors as measured in an {\\em orthonormal comoving frame.} But it is the tensor components in the {\\em lab frame} that one would like to check, either because it is the coordinate basis (at least in a spatially multidimensional simulation) and therefore natural to deal with, or because it is the basis in which energy is conserved (in a simulation in comoving coordinates in spherical symmetry). The required transformation of the tensor components between these frames leads to the numerical complexity mentioned in Sec. \\ref{sec:introduction}, and discussed further in the latter parts of Subsecs. \\ref{subsec:conservativeGeneral} and \\ref{subsec:conservativeComoving}. In contrast, when the coordinate basis is in the lab frame as expected in spatially multidimensional simulations, {\\itshape integration of Eqs. (\\ref{conservative1}) and (\\ref{conservative2}) over momentum variables leads directly to the tensor components in the desired coordinate basis, even though the specific particle number and stress-energy are functions of comoving frame momentum variables.} The insight here is that the frame in which the tensor components are measured need not be the same as that employed to obtain the momentum variables used to parametrize the particle distributions. The appendix provides an example of a moment formalism of this kind. In simulations of systems like core-collapse supernovae---in which careful attention to energetics is critical---a number of possible approaches, based on the conservative formulations of kinetic theory presented in this paper, might be suggested. First, the general approach of, for example, Refs. \\cite{mezzacappa01,liebendoerfer01b,liebendoerfer02} could be followed, in which the conservative particle number distribution equation (Eq. (\\ref{conservative1})) is solved, and the conservative particle energy equation (the time component of Eq. (\\ref{conservative2})) is used as a consistency check. The quantitiy $\\sqrt{-g}\\,{\\cal N}^0$, which might be called the {\\em specific particle number density}, would be the primary neutrino distribution variable: It is the contribution of each {\\em comoving frame} momentum bin to the {\\em lab frame} particle number density. This approach makes number conservation a somewhat natural outcome, but energy conservation would require finite-differenced representations of various quantities to be ``matched'' in order that Eq. (\\ref{matching}) be satisified numerically. This might be considered the most rigorous and self-consistent method. (Note that if one solves the ``plain'', non-conservative Boltzmann equation---Eq. (\\ref{fullBoltzmann})---for the scalar distribution function $f$ as a function of comoving frame momentum variables, conservation of {\\em neither} lab frame particle number or energy is straightforward. The same is true of methods (e.g., Ref. \\cite{burrows00}) based on a non-conservative form of the transport equation for the comoving frame specific intensity.) In order to avoid the intricate finite differencing of numerous terms demanded by this method, a second option would be the use of \\inlineSFinmath$\\sqrt{-g}\\, {{{\\ScriptCapitalT }^{00}}}$, which might be called the {\\itshape specific particle energy density, }as the primary neutrino distribution variable. Designing a code around a differenced version of the \\inlineSFinmath${\\mu =0}$ component of Eq. (\\ref{conservative2}) would make accurate accounting of total neutrino energy (as represented by the \\inlineSFinmath${\\mu =0}$ component of Eq. (\\ref{energyConservation})) relatively straightfoward. Of course, the neutrino number balance equation expressed in terms of \\inlineSFinmath$\\sqrt{-g}\\,{{{\\ScriptCapitalT }^{00}}}$ would have numerical errors unless certain finite differencings were carefully designed. But with respect to the crucial energetics of the physical system, it is worth noting that there are a couple of factors mitigating the impact of errors in number conservation in comparison with errors in energy conservation. Errors in number conservation translate into errors in the electron fraction \\inlineSFinmath${{Y_e}}$, which affect energy conservation through the equation of state, but: (1) Only \\inlineSFinmath${{{\\nu }_e}}$ and \\inlineSFinmath${{{\\left( \\overvar{\\nu }{\\_} \\right) }_e}}$ affect \\inlineSFinmath${{Y_e}}$, while all species impact the energy budget. Better to have two species contributing to error rather than six! (2) The effects of \\inlineSFinmath${{{\\nu }_e}}$ and \\inlineSFinmath${{{\\left( \\overvar{\\nu }{\\_} \\right) }_e}}$ on \\inlineSFinmath${{Y_e}}$ are opposite in sign (unlike their contributions to energy), so that to the extent that their distributions are similar, the impact of their errors on \\inlineSFinmath${{Y_e}}$ may approximately cancel. A third possibility would be to solve for {\\itshape both} the specific particle energy density \\inlineSFinmath$\\sqrt{-g}\\,{{{\\ScriptCapitalT }^{00}}}$ and the specific particle number density \\inlineSFinmath$\\sqrt{-g}\\,{{{\\ScriptCapitalN }^0}}$. (Rampp and Janka \\cite{rampp02} solve for both number and energy distributions, but in the comoving frame; this limits the utility of their approach with respect to accurate tracking of lab frame quantities.) Instead of pre-defining both the boundaries and center values of bins in energy space, one could define the boundaries only and use the values of $\\sqrt{-g}\\,{{{\\ScriptCapitalT }^{00}}}$ and $\\sqrt{-g}\\,{{\\ScriptCapitalN }^0}$ (along with the transformation \\inlineSFinmath${{{{{\\ScriptCapitalL }^{\\overvar{\\mu }{\\RawWedge }}}\\InvisibleSpace }_{\\mu }}}$) to obtain center values of the energy bins in each spatial zone and each time step. The consistency of the solutions would be arguably reasonable as long as the derived center values of the energy bins do not wander outside the pre-defined bin boundaries. \\appendix*" }, "0212/astro-ph0212526_arXiv.txt": { "abstract": "{We derive the galaxy luminosity functions in V-, R-, I-, and K-bands of the cluster EIS\\,0048 at $z \\sim 0.64$ from data taken at the ESO Very Large Telescope. The data span the restframe wavelength range from UV, which is sensitive to even low rates of star formation, to the NIR, which maps the bulk of the stellar mass. By comparing our data and previous results with pure luminosity evolution models, we conclude that bright ($M \\leq M^*+1$) cluster galaxies are already assembled at $z \\sim 1$ and that star formation is almost completed at $z \\sim 1.5$. ", "introduction": "One of the main issues in theoretical and observational research is to understand the physical processes driving the formation and evolution of bright massive galaxies in clusters, and to constrain the relative time scales. The evolution of the cluster galaxy sequence (the colour--magnitude relation) has been studied for large cluster samples up to redshift $z \\sim 1$ (Aragon--Salamanca et al. \\cite{AEC93}; Lubin \\cite{LUB96}; Ellis et al. \\cite{ESD97}; Stanford et al. \\cite{SED98}, hereafter SED98; Nelson et al. \\cite{NGZ01}, hereafter NGZ01). The results are consistent with a monolithic collapse scenario (see e.g. Larson \\cite{L74}) in which galaxies form at high redshifts and subsequently undergo passive evolution. However, the evolution of colours only inform on the epoch when the bulk of stellar mass formed, while cluster bright galaxies ($M \\leq M^*+1$, mostly early--type) could have been also assembled recently ($z < 1$) from mergers of smaller units, at least as long as the merging processes do not induce strong star formation. A different approach consists in the study of the evolution of the cluster luminosity function (CLF). In particular, the near--infrared (NIR) CLF can be used to assess the assembly history of galaxies, because the NIR light mainly informs on galaxy mass. From the analysis of the values of $M^*$ in the K-band as a function of redshift for a sample of 38 clusters in the range $0.1 < z < 1$, De Propris et al. (\\cite{DPSE99}, hereafter DPSE99) found a trend consistent with passive luminosity evolution (PLE) (see also Nakata et al. \\cite{NAK01}, hereafter NKY01). DPSE99 conclude that the mass function of bright cluster galaxies is invariant at $z < 1$, and that the assembly of those galaxies is largely complete by $z \\sim 1$. Spectroscopic data also show that massive galaxies already exist at least up to $z=0.83$ (van Dokkum et al. \\cite{vDF98}). In this work we derive the CLFs for EIS\\,0048 at $z \\sim 0.64$ in the V-, R-, I-, and K-band (UV to NIR restframe). The cluster membership has been assessed with the photometric redshift technique up to $M-M^* \\sim 1.5-2.5$ (according to the different depth of each band). Since no other selection has been applied, the samples are not biased toward a particular galaxy population. The paper is organized as follows. In Sect. 2 we introduce the photometric data, discuss the background subtraction, the selection of cluster members, the completeness of the samples, and obtain the CLFs. In Sect. 3 we discuss the results in terms of galaxy formation and evolution. In Sect. 4 we give a summary of the paper. In this work we assume H$_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\\Omega_M=0.3$ and $\\Omega_{\\Lambda} = 0.7$. ", "conclusions": "\\label{CONC} We derived the galaxy LF in V-, R-, I-, and K-bands of the cluster EIS\\,0048 at $z \\sim 0.64$ from new photometric observations carried out at ESO VLT with FORS2 and ISAAC. Cluster members have been selected with the photometric redshift technique in order to enhance the contrast among cluster- and background--foreground galaxies. The remaining field contamination has been estimated as detailed in LBMI03. The CLFs have been obtained up to $M-M^* \\sim 1.5-2.5$ (according to the waveband). We modelled the CLFs with a weighted parametric fit of the Schechter function, fixing the faint end slope to be $\\alpha = -0.9$. The values of $M^*$ obtained in I- and K-bands are in agreement with the analysis of DPSE99 and NGZ01 at similar redshifts. We collected results from literature and introduced PLE models with different formation redshifts in order to discuss the evolution of $M^*$ in the V- and K-bands. The key factors driving the evolution of bright galaxies in the scenario of hierarchical structure formation are the epoch when the bulk of stellar populations is formed, the cosmological time when mergers are effective to assemble the galaxies, the amount of star formation induced by mergers, and the age of the youngest stars. Since the evolution of $K^*$ is consistent with a PLE scenario at least up to $z \\sim 1$, we can conclude that mergers must have already assembled bright ($M \\leq M^*+1$) cluster galaxies at this redshift (see also DPSE99 for a thorough discussion). At $z = 0.64$ the V-band samples the UV restframe wavelength region and is sensitive to even low levels of SF. We find that the SF in bright cluster galaxies has to be almost completed at $z \\sim 1.5$, whereas the formation redshift is $z_f \\geq 3$ assuming $\\tau \\sim 1$ Gyr as the time scale for SF. These results lead to conclude that the structure and the stars of bright cluster galaxies must have been formed between $z=4\\pm 1$ and $z=1.2\\pm0.2$." }, "0212/hep-th0212327_arXiv.txt": { "abstract": "We consider the quasi-de Sitter geometry of the inflationary universe. We calculate the energy flux of the slowly rolling background scalar field through the quasi-de Sitter apparent horizon and set it equal to the change of the entropy (1/4 of the area) multiplied by the temperature, $dE=T dS$. Remarkably, this thermodynamic law reproduces the Friedmann equation for the rolling scalar field. The flux of the slowly rolling field through the horizon of the quasi-de Sitter geometry is similar to the accretion of a rolling scalar field onto a black hole, which we also analyze. Next we add inflaton fluctuations which generate scalar metric perturbations. Metric perturbations result in a variation of the area entropy. Again, the equation $dE=T dS$ with fluctuations reproduces the linearized Einstein equations. In this picture as long as the Einstein equations hold, holography does not put limits on the quantum field theory during inflation. Due to the accumulating metric perturbations, the horizon area during inflation randomly wiggles with dispersion increasing with time. We discuss this in connection with the stochastic decsription of inflation. We also address the issue of the instability of inflaton fluctuations in the ``hot tin can'' picture of de Sitter horizon. ", "introduction": "\\label{sec:intr} The inflationary paradigm established during the last 20 years assumes that the primordial equation of state is almost vacuum-like: $p\\approx -\\epsilon$. To realize this equation of state, most models deal with a scalar field $\\phi(t)$ (or other fields which in combination act as an effective scalar field) slowly rolling to the minimum of its potential $V(\\phi)$. During the slow roll regime the homogeneous scalar field produces geometry which can be well approximated by the quasi-de~Sitter metric. The full pure de~Sitter spacetime, which corresponds to a 4d hyperboloid of constant curvature, can be compactly represented by its Penrose diagram, given by the full square in Fig. \\ref{fig:penrose}. It can be covered by different coordinates. Cosmologists most often use coordinates in which the metric is time-dependent and corresponds to an expanding flat universe \\begin{equation}\\label{flat} ds^2= -dt^2 + e^{ 2Ht} \\left(dr^2+r^2 d\\Omega^2 \\right) \\ , \\end{equation} where $d\\Omega^2=d \\theta^2+\\sin^2 \\theta d \\phi^2$. This coordinate system covers the upper half of the hyperboloid, which corresponds to the expansion branch. The Penrose diagram of de Sitter spacetime in flat FRW coordinates is shown on the left panel of Fig.~\\ref{fig:penrose}. Quasi-de~Sitter geometry is described by the scale factor $a(t)=a_0 \\, e^{\\int dt H(t)}$, where the Hubble parameter $H$ is a slowly varying function of time, $\\dot H \\ll H^2$. \\begin{figure}[b] \\centerline{\\epsfig{file=ds2b.eps, height=5cm}\\hspace{2cm} \\epsfig{file=ds3.eps, height=4.5cm}} \\medskip \\caption{ Penrose diagram of de~Sitter spacetime in the flat FRW coordinates (left) and the static coordinates (right). Each point represent a sphere $S^2$. Its radius at the horizon (dashed line on the left, edge of diamond on the right) is equal to $\\frac{1}{H}$. } \\label{fig:penrose} \\end{figure} The time-dependent form of the metric (\\ref{flat}) is very convenient for investigating the dynamics of a scalar field with the equation \\begin{equation}\\label{scalar} \\Box \\phi=V_{,\\phi} \\end{equation} and for quantizing this field in the de~Sitter spacetime \\cite{bd}. Among quantum scalar fields with mass $m$ and conformal coupling $\\xi$ in de~Sitter geometry, the case of minimal coupling $\\xi=0$ and very small mass $m \\ll H$ plays an especially important role. Indeed, the regularized vacuum expectation value is $\\langle \\delta \\phi^2\\rangle =\\frac{3H^4}{8\\pi^2 m^2}$. Formally, as was noted before the discovery of inflation, this is an odd case since its eigen-spectrum contains an infrared divergent term: $\\langle \\delta \\phi^2\\rangle \\to \\infty$ as $m \\to 0$. On the other hand, this is the most interesting case for application to inflation, since the theory of inflaton (as well as tensor) fluctuations is reduced exactly to this case. Following the time evolution of individual fluctuations, it was found that the infrared divergence can be interpreted as the instability of quantum fluctuations of a very light scalar field, which are accumulated with time $\\langle \\delta \\phi^2 \\rangle =\\frac{H^3}{4\\pi} \\, t$ \\cite{fluc,linde,star}. Fluctuations of $\\delta \\phi$ induce scalar metric perturbations \\cite{metr,star,hawking,guth,bardeen}. This picture is a basis of the inflationary paradigm so successfully confirmed observationally. Notice that heavy or conformal fields are not produced by inflation. Further, backreaction of fluctuations $\\delta \\phi$ leads to the picture of stochastic evolution of quasi-de~Sitter geometry \\cite{stoch1,stoch2}, and at large values of $H$ even to self-reproduction (eternal) of the inflationary universe \\cite{self}. Scalar field in the eternal inflationary universe is described naturally in terms of the probability distribution function $P(\\phi, t)$ \\cite{stoch2,stoch3}. Recently, de~Sitter spacetime and inflation have drawn significant attention in the theoretical physics/superstring community. Some of the most interesting topics are holography and the thermodynamics associated with the de~Sitter horizon. In this context, the static form of the metric of the de Sitter spacetime \\begin{equation}\\label{static} ds^2=-(1-H^2 \\, R^2)d\\tau^2+ {{dR^2} \\over{(1-H^2 \\, R^2)}}+R^2 d\\Omega^2 \\ \\end{equation} is commonly used. The Penrose diagram of de Sitter spacetime in static coordinates is plotted on the right panel of Fig.~\\ref{fig:penrose}. The classical result of \\cite{GH} is that observer at the origin detects a thermal radiation from the de Sitter horizon at $R=\\frac{1}{H}$ with the temperature $T=\\frac{H}{2\\pi}$, and the horizon area $A=\\frac{4\\pi}{H^2}$ is associated with the huge (geometrical) entropy $S=\\frac{A}{4G}$. Thermal vacuum in the causal patch (``hot tin can'') corresponds to the Bunch-Davies vacuum of the metric (\\ref{flat}) \\cite{BMS,kleban} and gives a complementary picture of scalar field(s) fluctuations. It is not clear to us, however, how quantum fluctuations in the ``hot tin can'' picture correspond to the instability of quantum inflaton fluctuations $\\delta \\phi$ and generation of metric perturbations. We will return to this point at the end of the paper. One of the issues in the holographic approach is the bookkeeping of entropy of de~Sitter spacetime. The holography bound declares that the geometrical entropy of the horizon exceeds the entropy of quantum states (of fields and particles) within the volume surrounded by the horizon. It was recently claimed that counting the entropy of quantum fluctuations generated during inflation in the ``hot tin can'' and comparing it to the change of the apparent horizon entropy violates the holography bound unless an ultra-violet cutoff of order of $\\sim 10^{16}$ GeV in the momenta of fluctuations is imposed \\cite{kaloper}. While it is expected that the approaches based on the time-dependent form of the de Sitter metric with unstable fluctuations and the static form of the de Sitter metric with thermal flux should give us complementary insights, their languages are apparently different. This is partly due to the difference between quasi-de~Sitter and pure de~Sitter geometries, and partly because different questions are addressed. However, we have to understand how these two different approaches to (quasi-)de~Sitter geometry with a scalar field are compatible with each other with respect to such important issues as the generation of fluctuations, entropy and global geometry. In this paper we consider a particular question of how the apparent horizon area $A$, or the entropy $S=\\frac{A}{4G}$, vary due to the slow roll of the background scalar field and the generation of scalar metric perturbations during inflation. A novel element here is that we combine the concepts of a dynamical, slowly rolling background field and the instability of its fluctuations, with the concept of geometrical, holographic entropy. In Section \\ref{sec:geom}, we will calculate a variation of the geometrical entropy due to the energy flux through the apparent horizon area. We find that, remarkably, the thermodynamical relation $\\delta E=TdS$ is equivalent to the Einstein equation for the rolling inflaton field. In a sense, our derivation of a correspondence between thermodynamics and the Einstein equations for inflation is a realization of such a correspondence found in an inspiring paper \\cite{jacob} for local accelerating observers. However, we introduce a technique to treat the apparent horizon of $R \\times S^2$ topology which is different from the description \\cite{jacob} of a local Rindler horizon for an accelerating observer. As we will see, a non-vanishing flux is generated by the kinetic term $\\dot \\phi^2$ of the slowly rolling inflaton field. It turns out that this problem is very similar to the problem of the interaction of a homogeneous rolling scalar field with a runaway potential $V(\\phi)$ and a black hole. In Section \\ref{sec:bh}, we switch our attention from inflation to black holes. A rolling scalar field interacting with a black hole is a transparent illustration of the energy flow of a light scalar field through a horizon. In Section \\ref{sec:fluc1}, we return to inflation. On top of the rolling background inflaton, we consider inflaton fluctuations $\\delta \\phi$, which generate scalar metric perturbations $\\Phi$. We study the energy flux through the horizon including inhomogeneous $\\delta \\phi$ fluctuations and corresponding variations in the area of the horizon, or entropy $dS$, which are sensitive to the scalar metric perturbations $\\Phi$. In this case, the calculations are more involved than the calculations for the homogeneous time dependent background field in Section \\ref{sec:geom}. This happens because there is no exact Killing vector generating the horizon. However, for metric perturbations which preserve spherical symmetry we still can define $TdS$ and compare it with the energy flux through the horizon. In Section \\ref{sec:fluc2}, we argue that the metric perturbations generated from inflaton quantum fluctuations can indeed be treated as (locally) spherically symmetric. We apply the general formalism for spherically symmetric non-static geometry of Section \\ref{sec:fluc1} to fluctuations from inflation. Again, we find that the thermodynamical relation $\\delta E=TdS$ leads to equations connecting $\\Phi$ and $\\delta \\phi$ which are in exact agreement with the linearized Einstein equations for the fluctuations from inflation. This allows us to give new insights into the entropy of cosmological fluctuations, as we will discuss in Section \\ref{sec:disc}. ", "conclusions": "\\label{sec:disc} In this paper we calculated the apparent horizon area and geometrical entropy of quasi-de~Sitter geometry, which describes an inflationary stage, and the energy flux of the scalar fields through the apparent horizon. Issues related to de Sitter thermodynamics are commonly considered in the static de Sitter coordinates, where an observer at the origin is surrounded by the event horizon and detects a thermal flux of temperature $T=\\frac{H}{2\\pi}$. We work with the geometrical entropy $S$ of the apparent horizon in the time-dependent planar de-Sitter coordinates adopted in inflationary cosmology, which admit a simple generalization to the quasi-de~Sitter geometry and, most importantly, admit a clear interpretation of fluctuations generated from inflation. The slow roll of the inflaton field leads to slow change in the horizon radius. Assuming that the energy flux of the rolling scalar field through the horizon changes the geometrical entropy $\\delta E=TdS$, we reproduce the Einstein equation (\\ref{einst}) which relates $\\dot H$ and $\\dot \\phi^2$. Other background scalars $\\chi$ which are subdominant during inflation give similar contributions to the energy flux $\\dot \\chi^2$, independent of their potentials. This change of the quasi-de~Sitter horizon radius due to the rolling scalar field is very similar to the increase of the mass of a black hole due to the accretion of a background scalar field rolling towards the minimum of its potential $\\dot M \\sim \\dot \\phi^2$. This type of accretion, which can be described analytically with the delayed field approximation, can be realized for runaway potentials of the background scalar field or for very light massive fields. We present this material here mainly to illustrate similar calculations for rolling scalars in quasi-de~Sitter geometry, as the astrophysical effects of accretion of a rolling scalar onto a black hole that we considered (say quintessence and astrophysical-size black holes) are negligibly small. Oscillating heavy scalar field accretes onto black hole very differently as quasi-particles. Inflationary, quasi-de~Sitter stage erases classical inhomogeneities which could exist prior to it. However, quantum fluctuations of the inflaton field (as well as other light scalars minimally coupled to gravity) are unstable and produce long-wavelength fluctuations of the inflaton field $\\delta \\phi$ which behave as classical inhomogeneities at scales larger than the Hubble patch of size $H^{-1}$. Fluctuations $\\delta \\phi$ generate long-wavelength scalar metric perturbations $\\Phi$. Geometrical quantities, like an area of the apparent horizon, acquire corrections due to the scalar metric perturbations. We calculate the energy flux of the inhomogeneous scalar field $\\phi(t)+\\delta \\phi(t, \\vec x)$ through the apparent horizon and the change in the apparent horizon area of the perturbed metric multiplied by its (geometrical) temperature $T dS$. Again, equating $\\delta E=TdS$, we show that this thermodynamics relation is compatible with the linearized Einstein equations which relate $\\Phi$ and $\\delta \\phi$. Thus, as long as the Einstein equations hold, generation of the inflaton fluctuations is in full agreement with the variation of the entropy of the quasi-de~Sitter horizon. Therefore, in the picture of rolling inflaton with quantum fluctuations generated with time, we did not find that quantum fluctuations may violate holographic bound during inflation. (Notice that the fluctuations from inflation are described by squeezed states, which do not carry entropy \\cite{bpm,Kiefer}. In simple terms, locally the effect of fluctuations is just a wiggling of the local Hubble parameter). It was suggested in \\cite{kaloper} that in the ``hot tin can'' picture the entropy of fluctuations may violate holographic bound during inflation.\\footnote{If frozen fluctuations from inflation were carrying large entropy, then a number $N$ of free light scalars produced during inflation would have $N$ times bigger entropy and UV cutoff proposed in \\cite{kaloper} would depend on $N$.} The issue of inflaton fluctuations in the ``hot tin can'' picture is not clear to us. In theory of inflation, scalar field fluctuations are usually considered in the time dependent metric (\\ref{flat}), as it was described in Section \\ref{sec:fluc2}. Bunch-Davies vacuum corresponds to the thermal state in the static coordinates. On the other hand, in the static de~Sitter coordinates, discussion of the quantum field theory is usually restricted to thermal radiation from the horizon, usually in terms of the detector response. Thermal radiation associated with the de~Sitter horizon is related to any free quantum field, scalar fields with mass $m$ and any coupling to gravity, vector fields etc., the difference will be only in the radial dependence of the wave functions (``gray-body factor''). On the other hand, instability of quantum fluctuations from inflation occurs only for very light minimally coupled scalar fields. It will be interesting to understand what is relation of the quantum field theory in the ``hot tin can'' picture, and the instability of fluctuations from inflation. For this it will be essential to work with regularized VEV $<\\delta \\phi^2>$. As we already mentioned, in the picture of rolling scalar field with accumulating inflaton fluctuations, which we adopt in the paper, holographic bound and quantum fluctuations from inflation are compatible. A lesson from our calculations is that in the quasi-de~Sitter geometry with slowly rolling scalar field, the horizon area, or geometrical entropy, are perturbed by the scalar metric fluctuations according to the formulas (\\ref{wiggles}), (\\ref{wiggles2}). This means that the area of the horizon for an ensemble of the different Hubble patches is not the same but is a statistical variable by itself. For small metric perturbations (of order of $\\Phi \\sim \\frac{H}{M_p}$), its mean value is $\\bar A=\\frac{4\\pi}{H^2}$, where $H(t)$ is slowly decreasing background value, but dispersion around the mean value is defined by $\\langle\\Phi^2\\rangle$, which growth with time. Equivalently, we can talk about statistical properties of the local Hubble values $\\tilde H$ \\cite{star,stoch3}. Notably, this picture is converging with the stochastic description of inflation in terms of the probability distribution of the inflaton field \\cite{stoch1,stoch2,stoch3}. Probability to have the value of inflaton field $\\phi$ in quasi-static regime is $P(\\phi)\\sim \\exp{ \\left(-\\frac{3M_p^4}{8V(\\phi)}\\right)}$ and can be interpreted in terms of entropy $S=\\log P(\\phi)$ \\cite{entr}. Remarkably, this entropy is identical to the geometrical entropy $\\frac{A}{4G}$. During inflation and rolling of $\\phi$ the Wiener process of accumulating fluctuations $\\delta \\phi$ (or similarly perturbations of $\\Phi$) changes distribution of $P(\\phi)$. Distribution of the horizon areas of different Hubble patches, defined by the local values of the Hubble parameters, depends on the background slow roll regime and the regime of accumulation of fluctuations, both of which depend on the model of inflation \\cite{stoch1,stoch2,stoch3}. It would be interesting to understand further the correspondence between stochastic approach to inflation and geometrical entropy (\\ref{wiggles}), (\\ref{wiggles2}). So far we discussed small metric fluctuations $\\Phi$ or small local variations of $H$. However, in the chaotic inflationary scenario for large enough values of $\\phi$, variations of $H$ due to the quantum jumps of $\\delta \\phi$ can be large and lead to the self-reproducing inflationary universe \\cite{self}. We would like to draw attention to this regime (which is still below the Planck energy density) and to note that ``adiabatic'' geometrical thermodynamics which we considered in this paper is not applicable here. Indeed, consider the Hubble patch where $H$ is increasing due to the quantum jumps. Increase of $H$ is not compatible with the classical Einstein equation (\\ref{einst}). Consequently, quantum jumps are not compatible with the horizon thermodynamics (of a single Hubble patch) since $\\delta E=TdS$ does not hold either. Geometrical entropy of the local Hubble patch is decreasing. However, we have to take into account the entropy of all Hubble patches. Self-reproduction of inflating regions looks like a chain reaction, which is described by the branching diffusion process \\cite{branch}." }, "0212/astro-ph0212018_arXiv.txt": { "abstract": "A new hybrid approach to air shower simulations is described. At highest energies, each particle is followed individually using the traditional Monte Carlo method; this initializes a system of cascade equations which are applicable for energies such that the shower is one-dimensional. The cascade equations are solved numerically down to energies at which lateral spreading becomes significant, then their output serves as a source function for a 3-dimensional Monte Carlo simulation of the final stage of the shower. This simulation procedure reproduces the natural fluctuations in the initial stages of the shower, gives accurate lateral distribution functions, and provides detailed information about all low energy particles on an event-by-event basis. It is quite efficient in computation time. ", "introduction": "The field of highest energy cosmic rays is an exciting subject with many open questions: What is the nature of the primary cosmic ray? What are the highest energies? What are possible sources/acceleration mechanisms? Is there clustering of events? Is there a GZK cutoff due to the microwave background? Ongoing (HIRES, AGASA) and future (Auger, OWL, EUSO) cosmic ray experiments aim to shed light on these mysteries. At these high energies, direct measurement of the primary cosmic ray is impossible due to the low flux, which is only of order one event per square-kilometer per century at the highest observed energies. But cosmic rays initiate showers in the atmosphere, a cascade of secondary particles from collisions with air molecules, which themselves collide and so on. Experiments measure these air showers and reconstruct from their properties information about the primary ray at the beginning of the reaction. Air shower models are of crucial importance for the reconstruction of the energy and primary type. The straightforward approach is to model each possible interaction of hadrons, leptons and photons with air molecules, and trace all secondary particles. At high energies this leads quickly to unpractical computation times, since the time grows with the number of particles in the shower and therefore increases rapidly with the primary energy. A shower of even \\( 10^{19}eV \\) has more than $10^{10}$ particles at its maximum and would take months to compute. The thinning algorithm proposed by Hillas \\cite{Hillas1985} tries to solves this problem: below a fraction \\( f_{\\mathrm{thin}} \\) of the primary energy only a small sample of the particles is actually followed in detail, attributing them a higher weight. This procedure introduces artificial fluctuations and one must compromise between these and computation time. People have tried to overcome these difficulties by defining systems of (mostly one-dimensional) transport equations which describe air showers \\cite{Kalmykov:1986ii,GaisserBook}. The numerical solutions of these equations can then be combined with a Monte-Carlo in order to account for natural fluctuations due to the first interactions and for lateral spread of low-energy particles \\cite{Dedenko1968,Lagutin:1999xh}. This is the principle of the hybrid method. Another realization of the hybrid approach is to use shower libraries in which presimulated longitudinal profiles are combined to compute the one-dimensional properties of air showers \\cite{Gaisser1997,Alvarez-Muniz:2002ne}. In a recent paper \\cite{Bossard:2000jh}, a new approach to an old idea was introduced: the method of cascade equations, which allows one to compute longitudinal characteristics of air showers numerically in a very short time. In this paper we introduce the further development of this approach. Traditional Monte-Carlo methods are combined with cascade equations in a hybrid approach. This allows to construct an efficient model which accounts not only for natural fluctuations due to the first interactions but also for the correct 3-dimensional spreading of low-energy secondary particles. In reasonable computing time it is possible to calculate longitudinal profiles and lateral distribution functions with detailed knowledge about particle momenta and arrival-times, which are reliable on an event-by-event basis. ", "conclusions": "" }, "0212/astro-ph0212532_arXiv.txt": { "abstract": "{ We present the results of a search for globular clusters in the surroundings of 15 low surface brightness dwarf galaxies belonging to the Fornax Cluster, which was carried out on CCD images obtained with the $C$ and $T_1$ filters of the Washington photometric system. The globular cluster candidates show an extended and probably bimodal $(C-T_1)$ color distribution, which is inconsistent with the presence of a single population of metal-poor clusters detected in several dwarf galaxies. The surface number density of these candidates shows no concentration towards the respective dwarf galaxies, in whose outskirts they have been identified. On the contrary, if we split the candidates in two groups according to their projected distances to the center of the Fornax Cluster, those located closer to the center show a higher projected density than those located farther from it. These results suggest that the potential globular clusters might not be bound to the dwarf galaxies. Alternatively, these globulars could form part of the very peripheral regions of \\object{NGC 1399} (the central galaxy of the Fornax Cluster) or even belong to the intracluster medium. ", "introduction": "The Fornax Cluster is an excellent target for studying globular clusters: it is very rich, contains different types of galaxies and the globular cluster candidates can be detected at least as unresolved sources. There are numerous photometric studies of globular cluster systems in selected Fornax galaxies, particularly the central one \\object{NGC 1399} as well as other early-type galaxies. Most of these studies show that the color distribution of the globular clusters is bimodal due to the presence of two globular cluster populations, ``red\" and ``blue\"; these integrated colors are mainly driven by metallicity in objects as old as these ones. With regard to the globular cluster system of \\object{NGC 1399}, the Washington photometry by \\citet{ost93} confirmed the existence of a color gradient that had been detected earlier by \\citet{bri91}, and suggested that the color distribution was multimodal, as was also supported by the V,I photometry by \\citet{kis97}. The HST imaging by \\citet{for98} and \\citet{gri99}, and a refined analysis of their previous Washington photometry by \\citet{ost98}, pointed to the bimodal character of the color distribution. More recently, the wide-field study by \\citet{di02a,di02b} showed that globular custers with a broad metallicity distribution -- that cannot be fitted with a single Gaussian -- extend further than 100 kpc from \\object{NGC 1399} center. There are fewer investigations of globular cluster systems in dwarf galaxies that are not in the Local Group. Miller and collaborators \\citep{mi98a,mi98b,mil99,lot01} carried out a survey with images from the Wide Field Planetary Camera 2 of the Hubble Space Telescope (FOV $\\approx$ 6~arcmin$^2$) to analyze the properties of globular clusters and nuclei of dwarf elliptical galaxies (dEs) in the Fornax and Virgo Clusters and the Leo Group. They include about 20 dEs from the Fornax Cluster but none of them are in common with the present work. They show that the globular cluster specific frequency $S_\\mathrm{N}$ (number of globular clusters with respect to the parent galaxy's luminosity) of the dEs is in the range 2--6; the luminosity function of the globular cluster candidates is consistent with a Gaussian with peak at $M_V^0 \\approx - 7$ mag and dispersion $\\sigma_V \\approx~1.4$ mag (assuming a distance modulus of 31.4 for the Fornax Cluster); and most of the globular cluster $(V-I)$ colors are similar to those of the metal-poor globular cluster population \\citep[also][]{ash93}. The globular cluster system of the luminous dE,N galaxy \\object{NGC 3115 DW1} was studied by \\citet{du96a} and \\citet{puz00} who obtained mean metallicities $[Fe/H]= -1.2$ and $-1$, respectively, and they both agreed on a specific frequency $S_\\mathrm{N}$ = 4.9. \\citet{du96b} obtained, on the basis of Washington photometry, a low mean metallicity, $[Fe/H]= -1.45$, for the globular cluster systems of two dE galaxies in the Virgo Cluster and they suggested that the dwarf galaxies globular cluster systems present a similar range of metallicities ($[Fe/H] = -2$ to $-1$) as globular clusters in the halos of spiral galaxies, in agreement with \\citet{ash93}. Turning to the Local Group, \\citet{min96} constructed a master-dE galaxy combining the data from globular cluster systems of several dEs in this Group; they found an old and metal-poor globular cluster population whose metallicity distribution matched the one of the Milky Way halo globulars. The abovementioned bimodality in the color distribution of globular clusters in elliptical galaxies, is closely related to the formation of the globular clusters and a variety of scenarios have been proposed (for reviews on the subject see, e.g., \\citealt{ash98} or \\citealt{har01}). \\citet{ash92} and \\citet{zep93} predicted this bimodal metallicity distribution of globulars in elliptical galaxies as a result of gas-rich mergers; they proposed that the blue population originally belonged to the progenitor galaxies and the red population formed during the merger. The numerical simulations from \\citet{bek02} showed that dissipative mergers create new globular clusters but they were not able to reproduce properly the bimodal metallicity distribution observed in elliptical galaxies. A different point of view was exposed, e.g., by \\citet{for97} who found a correlation between the mean metallicity of the metal-rich globular clusters and the parent galaxy luminosity, which suggested that they share the same chemical enrichment process, while the mean metallicity of the metal-poor ones seems to be independent of the galaxy luminosity. They proposed that the bimodality originated in two phases of globular cluster formation from gas with different metallicities, and that most of them formed \"in situ\". The HST study of 17 early-type galaxies by \\citet{lar01} showed a correlation between the colors of both, blue and red globular clusters populations, with the B-luminosity and central velocity dispersion of the host galaxy, and concluded that their observations support globular cluster formation \"in situ\", in the protogalaxy potential well. Alternatively, \\citet{for01} analyzed the relation between the mean color of blue and red globulars with the galaxy velocity dispersion and suggested that red globular clusters share a common origin with the host galaxy and blue ones seem to have formed quite independently; according to \\citet{cot98} these blue globular clusters may have been captured from other galaxies by merger processes or tidal stripping. The idea of the accretion of dwarf galaxies into the cD halo of \\object{NGC 1399}, the stripping of their gas and globular clusters and the formation of new clusters from this gas poses a different origin for the red globular clusters \\citep{hil99}. \\citet{bur01} analyzed the blue globular cluster populations from 47 galaxies and found no correlation between their mean metallicity, which is very similar for all these systems, and the galaxy properties (luminosity, velocity dispersion, etc); they proposed that the metal-poor globular clusters may have formed from gas fragments of similar metallicity, as already suggested by \\citet{ash93}, and located within the dark halo of the galaxy. More recently, the semianalytic model by \\citet{bea02} assumed that the metal-poor globular clusters formed in protogalactic fragments and the metal-rich ones originated in the gas-rich mergers of such fragments that occurred later. Assuming the presence of globular clusters inside clusters of galaxies, an alternative scenario is proposed by \\citet{whi87} and \\citet{wes95}, who pointed to the possible existence of a population of globular clusters that are not bound to individual galaxies; instead, they are supposed to move freely in the central regions of the galaxy clusters. These intracluster globular clusters may be the result of interactions or mergers between the galaxies, or they may have formed precisely in the environment of a galaxy cluster without any parent galaxy. The kinematic analysis by \\citet{min98} and by \\citet{kis99} also suggested that some globular clusters may be associated with the gravitational potential of the galaxy cluster and not solely with \\object{NGC 1399}. On the other hand, \\citet{gri99} found no evidence of intergalactic globular clusters in an HST/WFPC image at a radial distance of about $1\\,\\fdg4$ from \\object{NGC 1399}, but due to the small field of view, they were not able to rule out their existence. Several objections against the intraclusters were raised by \\citet{har98} who tried to explain by means of their existence the supposed high specific frequency of M87, the central Virgo galaxy; but the latest values of $S_\\mathrm{N}$ obtained for NGC 1399 by \\citet{ost98} and \\citet{di02b} showed that it is not so high ($S_\\mathrm{N}$ = 5.6 and 5.1, respectively). In favor of the existence of intergalactic material, \\citet{the97}, \\citet{men97}, and \\citet{cia98} presented evidence for the presence of intergalactic planetary nebulae within the Fornax and Virgo Clusters, while \\citet{fer98} reported several hundred of intracluster red giants in Virgo. Some globular clusters may have been stripped with them from other cluster galaxies if this is their origin \\citep{har01}. In this paper, we analyze the characteristics of globular cluster candidates found near dwarf galaxies in the Fornax Cluster and its connection with the above mentioned scenarios. It is organized as follows: Section 2 describes the observations and the adopted criteria for the globular cluster candidates' selection. In Sect. 3 we analyze the color distribution, luminosity function and spatial distribution of the candidates. Finally, a summary of the results and a discussion on their implications are provided in Sect. 4. Preliminary results of this work have been presented by \\citet{bas02}. ", "conclusions": "With regard to the color distribution of the globular cluster candidates, it is interesting to note that we do not find a single population, the metal-poor one, as seems to be the common case for dwarf galaxies \\citep{du96b,mi98a,mi98b,mil99}, but an extended distribution, which appears to be bimodal though we cannot prove it statistically due to the small sample involved. In addition, if we take into account the specific frequency estimated for dwarf galaxies \\citep{mi98a,elm99} and the luminosity function of the globular cluster candidates, we should have found significantly fewer globular cluster candidates than we actually do. According to the projected density of the potential globular clusters, they show no concentration towards the dwarfs while they do show concentration with respect to the center of the cluster. These results led us to speculate that the globular cluster candidates may not be associated to the dwarf galaxies themselves. We are then left with three possibilities: first, that these globular cluster candidates belong to the globular cluster system of \\object{NGC 1399}; second, they may be moving freely throughout the potential well of the cluster, without being bound to any galaxy in particular; or third, that they are a mix of both. In the first case, we should be accepting that the globular cluster system of \\object{NGC 1399} is much more extended and numerous than previously thought. According to this hypothesis, Figure\\,\\ref{f6} suggests that there should be clusters up to at least an intermediate angular distance of 80\\arcmin~(a projected distance of about 430 kpc) from the central galaxy; the CCD study over the largest area around \\object{NGC 1399} was performed by \\citet{di02b}, which extends up to 22\\arcmin, and showed that the globular cluster system extends over a radial projected distance of more than 100 kpc. The total number (background corrected) of globular clusters within the area covered by our observations can be roughly estimated as about 550 clusters, by extrapolating their luminosity function over the whole range of $T_1$ magnitudes. Thus, the number of clusters that should be distributed within a circular area of radius 80\\arcmin around \\object{NGC 1399} may be calculated, just taking into account the ratio of the areas, as several $10^4$ clusters. For comparison, the total number of globular clusters associated with galaxies in the Fornax Cluster may also be roughly estimated as follows. The blue magnitude of all the galaxies included in the \\citet{fer89} catalogue is $B = 8.3$ mag; adopting for them a mean color index $B-V \\approx 0.8$ mag and the distance modulus mentioned above, we obtain an absolute visual magnitude $M_V = -23.8$. If we assume a \"typical\" specific frequency $S_\\mathrm{N}=5$ we conclude that about $1.6\\times 10^4$ globular clusters should be associated with galaxies in Fornax. It is interesting to note that the number of globular clusters that we found within a circular area of radius 80\\arcmin around \\object{NGC 1399} is of the same order o larger than the estimated number of globulars associated to galaxies in the whole Fornax Cluster. It is also likely that some globular clusters might have escaped from its parent galaxies and, after that, remained within the potential well of the Fornax Cluster as a whole \\citep[see, for instance,][]{kis99}. \\citet{whi87} propose that the distribution of the stripped globular clusters within the cluster will follow the same density profile as the galaxies and they might form a kind of envelope around the central galaxy. Alternative origins for the intraclusters are mentioned by \\citet{wes95}, who speculate that they might have formed ``in situ\", without a parent galaxy, or during mergers of sub-systems with a high gas content. Deeper images are required to clarify this picture and a new survey in the Fornax Cluster is in progress. The true nature of these candidates might be confirmed by means of spectra." }, "0212/gr-qc0212105.txt": { "abstract": "s{ Recent developments on the rotational instabilities of relativistic stars are reviewed. The article provides an account of the theory of stellar instabilities with emphasis on the rotational ones. Special attention is being paid to the study of these instabilities in the general relativistic regime. Issues such as the existence relativistic r-modes, the existence of a continuous spectrum and the CFS instability of the w-modes are discussed in the second half of the article.} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ", "introduction": "The oscillations and instabilities of relativistic stars gained a lot of interest in the last decades because of the possible detection of their associated gravitational waves. It is not impossible that every compact star in a specific period of its life will undergo an oscillatory phase, in which it becomes unstable. Only the dynamical instabilities were thought to be a relevant source of gravitational waves, whereas instabilities due to dissipation mechanisms were believed to be only of academic interest. This belief has been dramatically altered during the last five years after it was discovered that for a specific class of rotational perturbations, the so called r-modes\\cite{Nils98,FM98}, the instability due to gravitational radiation\\cite{Chandra70a,Chandra70b,FS78a,FS78b} has the potential of being a prime source for gravitational waves. It was subsequently shown that this instability has many interesting astrophysical implications, which attracted the attention of both relativists and astrophysicists. In the first section of this review we shortly describe the various stellar instabilities and how they operate, for a more detailed review one can refer to a recent article by Stergioulas\\cite{Nick98}. The second section is devoted to the r-mode instability with the focus on its application to gravitational-wave research and astrophysics, for more details see a recent review by Andersson and Kokkotas\\cite{AK01}. The last section is devoted to an analysis of new features brought about by the relativistic treatment of the problem. Questions on the existence relativistic r-modes and a continuous spectrum are discussed in detail. A new result that is presented is the existence of the w-mode instability in ultra-compact stars, i.e.~the instability due to the existence of an ergosphere of the spacetime or w-modes\\cite{KRA02}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ", "conclusions": "" }, "0212/astro-ph0212368_arXiv.txt": { "abstract": "We present optical and infrared spectra of SN~1999ex, which are characterized by the lack of strong hydrogen lines, weak optical He I lines, and strong He I $\\lambda$10830,20581. SN~1999ex provides a clear example of an intermediate case between pure Ib and Ic supernovae, which suggests a continuous spectroscopic sequence between SNe~Ic to SNe~Ib. Our $UBVRIz$ photometric observations of SN~1999ex started only one day after explosion, which permitted us to witness an elusive transient cooling phase that lasted 4 days. The initial cooling and subsequent heating due to $^{56}$Ni$\\rightarrow$$^{56}$Co$\\rightarrow$$^{56}$Fe produced a dip in the lightcurve which is consistent with explosion models involving core collapse of evolved massive helium stars, and not consistent with lightcurves resulting from the thermonuclear runaway of compact white dwarfs. ", "introduction": "In a rare occurrence the spiral galaxy IC~5179 ($cz$=3,498 $km$ $s^{-1}$) produced two supernovae (SNe) in an interval of only three weeks. The first object (SN~1999ee) was a Type Ia event discovered by us 10 days before maximum \\cite{maza99}. The early discovery motivated us to use the YALO and 0.9-m telescopes at the Cerro Tololo Inter-American Observatory in order to secure nightly $UBVRIz$ photometric observations of this event, and the YALO and Las Campanas 1-m and 2.5-m telescopes to obtain $JHK$ photometry. Although the second object (SN~1999ex) exploded three weeks later and was promptly present in our CCD images we did not notice its presence. Its discovery had to await independent observations obtained at Perth Observatory \\cite{martin99}. Once SN~1999ex was reported to the IAU Circulars we initiated an optical and infrared (IR) spectroscopic followup using the European Southern Observatory NTT and Danish 1.5-m telescope at La Silla, and the VLT at Cerro Paranal. Our spectroscopic and photometric observations of SN~1999ex constitute an unprecedented dataset which provides support to our understanding of the nature of core collapse SNe. In this paper we show some of our observations and their interpretation. For a detailed report of our observations the reader is referred to \\cite{hamuy02}, \\cite{stritzinger02}, and \\cite{krisciunas02}. ", "conclusions": "" }, "0212/astro-ph0212474_arXiv.txt": { "abstract": "{Optical spectral variability of quasars and BL Lac Objects is compared by means of the spectral variability parameter $\\beta$ \\citep{tre02}. Both kinds of objects change their spectral slopes $\\alpha$, becoming bluer when brighter, but BL Lac Objects have smaller $\\beta$ values and are clearly separated from quasars in the $\\alpha-\\beta$ plane. Models accounting for the origin of the variability are discussed for both classes of objects. ", "introduction": "Variability of the spectral energy distribution (SED) of Active Galactic Nuclei (AGNs) is a powerful tool to investigate the role of the main emission processes in different AGN classes, and the origin of their variations. The most common behavior in the optical band is that AGNs become bluer, i.e. their spectrum becomes harder, when brighter. This has been shown for individual Quasi Stellar Objects (QSOs) and Seyferts \\citep{cut85,ede90,kin91,pal94} and for one complete sample, i.e. for the 42 PG QSOs monitored by \\citet{giv99} in B and R for 7 years. Evidence based on two epochs has been found also for the faint QSO sample in the SA 57 \\citep{tre01}. The same trend is apparently shared by BL Lac Objects, as shown by \\citet{dam02}, who present 5-year long B, V, R, I light curves for eight objects. A quantitative estimate of color variability is necessary to compare the observational data with emission models and to compare different AGN classes. In a previous paper \\citep{tre02}, we introduced the spectral variability parameter $\\beta \\equiv \\Delta \\alpha / \\Delta \\log f_{\\nu}$, $f_{\\nu}$ being the specific flux and $\\alpha\\equiv\\partial\\log f_{\\nu}/\\partial\\log\\nu$ the spectral slope. From the average $\\alpha$ and $\\beta$ values, it was possible to derive constraints on the variability mechanisms. The spectral variability parameter was then estimated \\citep{vag02} for the BL Lac Objects of \\citet{dam02}. Observations and models can be compared in the $\\alpha-\\beta$ plane, which is reported in Fig. 1 for both the PG QSOs and the BL Lac Objects. ", "conclusions": "We show that the spectral variability parameter $\\beta$ is a powerful tool to discriminate between different models of the variability of AGNs. Hot spots on the disk, likely produced by local instabilities, are able to account for the observed spectral variability of QSOs. We show that BL Lacs clearly differ from QSOs in their $\\alpha,\\beta$ distribution. A simple model representing the variability of a synchrotron component can account for the observed $\\alpha$ and $\\beta$ values. In the framework of wide field variability studies, we stress that observations in at least two photometric bands, repeated on the same field at many epochs, would allow a detailed test of variability models, extending our knowledge of the emission processes in AGNs." }, "0212/astro-ph0212197_arXiv.txt": { "abstract": "We present results from a {\\it Chandra} observation of the NGC\\,346 cluster, which is the ionizing source of N66, the most luminous \\hii\\ region and the largest star formation region in the SMC. In the first part of this investigation, we have analysed the X-ray properties of the cluster itself and the remarkable star \\hd. But the field contains additional objects of interest. In total, 75 X-ray point sources were detected in the {\\it Chandra} observation: this is five times the number of sources detected by previous X-ray surveys. We investigate here their characteristics in detail. Due to high foreground absorption, the sources possess rather high hardness ratios. Their cumulative luminosity function appears generally steeper than that for the rest of the SMC at higher luminosities. Their absorption columns suggest that most of the sources belong to NGC\\,346. Using DSS data and new $UBVRI$ imaging with the ESO 2.2m telescope, we also discovered possible counterparts for 32 of these X-ray sources and estimated a B spectral type for a large number of these counterparts. This tends to suggest that most of the X-ray sources in the field are in fact X-ray binaries. Finally, some objects show X-ray and/or optical variability, with a need for further monitoring. ", "introduction": "The launch of the {\\it Chandra} satellite provides an opportunity to explore the X-ray sky with a far greater sensitivity and spatial resolution than ever before. In a given field of interest, these characteristics enable the discovery of numerous X-ray sources in addition to the main target(s). Although often regarded as secondary, these sources provide important information which can improve our knowledge of the X-ray emission mechanisms in the Universe.\\\\ These serendipitous discoveries also enable us to study the source distribution in galaxies, especially Magellanic dwarf galaxies in our case. Most of the dwarf galaxies studied are at a distance of a few Mpc (e.g. Martin, Kobulnicky, \\& Heckman 2002), and their X-ray observations only sample the population with L$_X$ $>$ 10$^{36}$ erg s$^{-1}$. On the other hand, the relative closeness of the Magellanic Clouds enable us to probe the X-ray sources with luminosities as low as 10$^{32}$ erg s$^{-1}$. Putting together the informations on faint and bright X-ray sources will ultimately lead to a better understanding of this type of galaxies.\\\\ We have obtained a deep {\\it Chandra} observation of the giant \\hii\\ region N66 \\citep{he56}, the largest star formation region in the Small Magellanic Cloud (SMC). The large number of massive stars and the presence of the remarkable star \\hd\\ make the NGC\\,346 field one of the best opportunities to conduct an investigation of the X-ray domain. \\\\ In the first part of this analysis (Naz\\'e et al. 2002, paper I), we have presented the characteristics of the cluster, the star \\hd\\ and its close neighborhood. The cluster itself is relatively faint and most of its emission seems correlated with the location of the brightest stars in the core. However, the level of X-ray emission could not be explained solely by the emission from individual stars. The {\\it Chandra} observation also provides the first X-ray detection of \\hd. In X-rays, the star, that underwent a LBV-type eruption in 1994, appears very bright, comparable only to the brightest WR stars in the Galaxy. This high luminosity could be explained either by colliding winds in the binary system or by post-eruption effects. Finally, a bright, extended X-ray emission seems to surround this star. It is probably due to a SNR which may or may not be related to \\hd\\ itself (see paper I). \\\\ In this second paper, we will focus on the other X-ray sources present in the field. First, we will describe in \\S~2 the observations used in this study. The detected sources, their hardness ratios (HRs), and their spectral characteristics will then be discussed in \\S~3, 4, and 5, respectively. Next, we will describe the overall properties of the point sources' population in \\S~6, present their possible counterparts in \\S~7 and investigate their variability in \\S~8. Finally, we will give a summary in \\S~9.\\\\ ", "conclusions": "In this series of articles, we report the analysis of the {\\it Chandra} data of N66, the largest star formation region of the SMC. In this second article, we have focused on the other sources detected in the field. The X-ray properties of 75 point sources, of which 32 may possess an optical counterpart, have been analysed. Their cumulative luminosity function is steeper than the global one of the SMC at higher luminosities. Using new photometry of the NGC\\,346 field, we estimate that a large number of the counterparts are B-type stars, suggesting that many of the X-ray sources may be X-ray binaries. Considering their absorption column and the photometry of their counterparts, we also conclude that most of these X-ray sources probably belong to NGC\\,346. Finally, due to their variability, some of the objects should be monitored in the future, both in the visible and X-ray wavebands.\\\\" }, "0212/astro-ph0212312_arXiv.txt": { "abstract": "{ We apply the 2-dimensional high-resolution density field of galaxies of the Early Data Release of the Sloan Digital Sky Survey with a smoothing lengths 0.8~\\Mpc\\ to extract clusters and groups of galaxies, and a low-resolution field with smoothing lengths 10~\\Mpc\\ to extract superclusters of galaxies. We investigate properties of density field clusters and superclusters and compare properties of these clusters and superclusters with Abell clusters, and superclusters found on the basis of Abell clusters. We found that clusters in high-density environment have a luminosity a factor of $\\sim 5$ higher than in low-density environment. There exists a large anisotropy between the SDSS Northern and Southern sample in the properties of clusters and superclusters: most luminous clusters and superclusters in the Northern sample are a factor of 2 more luminous than the respective systems in the Southern sample. ", "introduction": "Clusters and groups of galaxies are the basic building blocks of the Universe on cosmological scales. The first catalogues of clusters of galaxies (Abell \\cite{abell}, Zwicky et al. \\cite{zwicky}) were constructed by visual inspection of the Palomar Observatory Sky Survey plates. More recent catalogues of clusters, as well as catalogues of groups of galaxies, have been derived using catalogues of galaxies (\\cite{1983ApJS...52...89H}, \\cite{1997MNRAS.289..263D}). Moving up the hierarchy of large-scale structure, galaxy cluster catalogues themselves have been used to define still larger systems such as superclusters of galaxies (Einasto et al. \\cite{e1994},~\\cite{e1997}, ~\\cite{e2001}, hereafter E94, E97 and E01). The goal of the present paper is to map the Universe up to redshift $z=0.2$ and to find galaxy clusters and superclusters using the density field method. The application of the density field is not new. In the pioneering study by \\cite{1982ApJ...254..437D} the density field was used to calculate the gravitational field of the nearby Universe. Gott, Melott \\& Dickinson ~(\\cite{gmd86}) used the density field to investigate topological properties of the Universe. \\cite{1990ApJ...364..370B} calculated the potential, velocity, and density fields from redshift-distance data. Saunders et al. (\\cite{s91}) applied the density field to map the Universe, to find superclusters and voids, and calculated moments of the density field. Marinoni et al. (\\cite{mar99}) reconstructed real space local density field. In these studies nearby optical or infrared galaxy samples were used. More recently, Hoyle et al. (\\cite{h2002}) used smoothed 2-dimensional density fields from volume limited subsamples of SDSS EDR galaxies to discuss the 2-dimensional geometry of the large-scale matter distribution in comparison with $\\Lambda$CDM simulations, and Sheth et al. (\\cite{s2002}) advertised a new method of evaluating isodensity contours of smoothed 3-dimensional density fields from simulations for characterizing topological properties of the supercluster-void network. \\begin{table*} \\caption[]{Data on SDSS EDR galaxies, clusters and superclusters} \\label{Tab1} \\[ \\begin{tabular}{cccccccccccc} \\hline \\noalign{\\smallskip} Sample& DEC & RA & $\\Delta$RA & $\\alpha_1$&$M_1^{\\ast}$&$\\alpha_2$&$M_2^{\\ast}$& $N_{\\rm gal}$&$N_{\\rm cl}$&$N_{\\rm ACO}$& $N_{\\rm scl}$\\\\ \\noalign{\\smallskip} \\hline \\noalign{\\smallskip} SDSS.N& $0^{\\circ}$&$190.25^{\\circ}$&$90.5^{\\circ}$ & $-1.06$&$-21.55$&$-1.22$&$-20.80$& 15209& 2868&22&24 \\\\ SDSS.S& $0^{\\circ}$&$23.25^{\\circ}$&$65.5^{\\circ}$& $-1.06$&$-21.40$&$-1.10$&$-20.71$&11882&2287&16&16\\\\ \\\\ \\noalign{\\smallskip} \\hline \\end{tabular} \\] \\end{table*} We calculate the density field of the Sloan Digital Sky Survey Early Data Release (SDSS EDR) by Stoughton et al. (\\cite{s02}), as described by H\\\"utsi et al. (\\cite{hytsi02}, hereafter Paper I), to find clusters and superclusters of galaxies, and to investigate their properties. Clusters of galaxies from the SDSS were extracted previously by \\cite{2002PASJ...54..515G} using the cut and enhance method; \\cite{2002AJ....123...20K} compared various cluster detection algorithms based on SDSS data. In this paper we define clusters as enhancements of the density field and use various smoothing lengths to separate systems of galaxies of different size and luminosity. We use a high-resolution density field to find clusters and groups of galaxies. For simplicity, we use the term ``DF-clusters'' for both groups and clusters found in the high-resolution density field of galaxies. Similarly, we use a low-resolution density field to construct a catalogue of superclusters of galaxies, and denote them as ``DF-superclusters''. DF-clusters and superclusters are defined as enhancements of the density field, DF-clusters in a fixed volume ($\\pm 2.5$~\\Mpc\\ from the centre), and DF-superclusters as high-density regions surrounded by a fixed isodensity contour. In determining DF-clusters and superclusters we take into account known selection effects. We shall investigate some properties of DF-clusters and superclusters, and study these clusters and superclusters as tracers of the structure of the local Universe. This study is of exploratory character to find the potential of SDSS data to analyse the structure of the Universe both on small and large scales. In this stage we use the fact that SDSS EDR covers only relatively thin slices; thus we calculate the density field in 2 dimensions only. As more data will be made available we plan to use a full 3-dimensional data set to detect clusters and superclusters of galaxies. In this exploratory stage of the study we will make no attempt to convert distances of galaxies and systems of galaxies from redshift space to true space. This correction applies only to positions of galaxies and clusters, not to their luminosity. Due to smoothing of the density field, small-scale corrections (e.g., the ``Finger-of-God'' Effect) are practically flattened out. Although there are large-scale corrections due to the apparent contraction of superclusters in redshift space (the Kaiser Effect, \\cite{1984ApJ...284L...9K}), the actual positional shifts of supercluster centres are very small; furthermore, they do not alter cluster and galaxy positions in tangential direction. The only large-scale redshift distortion is the radial contraction of superclusters, not the number and luminosity of clusters within superclusters. Since supercluster shapes are not the main target of this present study, we may ignore this effect for now. In Section 2 we give an overview of the observational data. In Section 3 we find DF-clusters and investigate their properties. Similarly, in Section 4 we compose a catalogue of DF-superclusters, identify them with conventional superclusters, and study their properties. In Section 5 we continue the study of DF-clusters and superclusters, derive the luminosity function of DF-clusters, and analyse these systems as tracers of the large-scale structure of the universe. Section 6 brings our conclusions. The three-dimensional distribution of DF-clusters and superclusters in comparison with Abell clusters and superclusters is shown on the web-site of Tartu Observatory. The analysis of the density field of LCRS shall be published by Einasto et al. (\\cite{e02b}). ", "conclusions": "Results of this paper and Paper I are of a methodical and quantitative character. Methodical aspects concern the application of the density field method with various smoothing lengths to display and describe systems of galaxies of various scales. We calculated density field for a number of smoothing lengths from 0.8 to 16~\\Mpc. In this way systems of galaxies on various scales could be visualised and their mutual relationship could be studied. The high-resolution density field, with dispersion 0.8~\\Mpc\\, was used to define density field clusters and to investigate the structure of superclusters. The low-resolution density field, with dispersion 10~\\Mpc\\, was used to define superclusters of galaxies and to study global properties of clusters and superclusters. The inspection of the distribution of clusters in superclusters and voids suggests that galaxy systems have in both regions similar shape in that the dominant structural elements are single or multi-branching filaments. Massive superclusters have dominantly a multi-branching morphology; less massive superclusters have various morphologies, including compact, filamentary, multi-branching, and diffuse systems. Quantitative results concern the luminosity function of galaxies and properties of clusters and superclusters. We have found in Paper I and confirmed in this paper that it is impossible to find a global set of parameters of the luminosity function which can be applied in all cases. We found that parameters of the luminosity function are different for high- and low-density regions: galaxies in high-density regions are more luminous. This result confirms earlier findings by Lindner et al. (\\cite{l95}): bright galaxies define larger voids than faint ones. More recently this conclusion was obtained by \\cite{1998ApJ...505...25B}, \\cite{2000ApJ...545....6B}, and by \\cite{2001MNRAS.328...64N}. The present study indicates that the effect is larger than previously suspected: luminosities of the brightest galaxies in high-density regions exceed the luminosities of the brightest galaxies in low-density regions by a factor of about 5. The values of the parameters of the luminosity function are also different for nearby and distant parts of the survey and for the Northern and Southern slices. A distance dependence of parameters of the luminosity function has been found for deeper surveys spanning redshift interval up to $z=1$ by \\cite{1999ApJ...518..533L} and by \\cite{2001ApJ...560...72S} in the Canadian Network for Observational Cosmology Redshift Survey. However, in this survey the distance dependence appears only by comparison of nearby ($z \\sim0$) and distant ($z > 0.2$) parts of the survey. Thus it seems improbable that this effect can explain our results on the distance dependence in a relatively small redshift interval $0 < z \\leq 0.2$. Parameters of the luminosity function depend also on the density of the environment. This dependence influences properties of the density field. High-density regions contain brighter galaxies than do low-density ones. This difference leads to different selection effects for galaxies in high- and low-density environments. In a high-density environment, due to selection effects, faint galaxies in clusters cannot be observed, but clusters themselves are visible (since they contain at least one galaxy bright enough) and the total luminosity of clusters can be estimated to take into account unobserved galaxies. In a low-density environment all galaxies of the cluster may be too faint, and the cluster may not be seen at all. In another words, distance-dependent selection effects influence clusters and superclusters in different ways. The density field was calculated using the expected total luminosities of clusters of galaxies, including the expected luminosities of galaxies too faint or too bright to be included in the redshift survey. The correction for unobserved galaxies was made assuming a Schechter luminosity function for galaxies. Our analysis shows that it is impossible to correct the density field so that general properties of the density field and properties of clusters of galaxies are correct for the same set of parameters of the galaxy luminosity function. For this reason we have used two sets of parameters of the luminosity function. Parameter set 1 has a strong bright-end (parameter $M^{\\star} = -21.55$) and corresponds to galaxies in a high-density environment which dominate clusters observed at large distance; this set yields correct properties of clusters of galaxies, but does not include faint clusters at large distances, and thus gives too low of a density for distant superclusters. Parameter set 2 was obtained for the whole region under study, and it has moderate bright-end (parameter $M^{\\star} = -20.80$). In this parameter set ALL faint invisible galaxies at large distance are included within visible clusters, including galaxies that belong to non-detected clusters; thus clusters themselves become too luminous with increasing distance, but supercluster properties are correct. Comparing clusters in different environments we have found that there exists a strong dependence of cluster properties on the density of the large-scale environment: clusters located in high-density environments are a factor of $5 \\pm 2$ more luminous than clusters in low-density environments. Finally we found that there exists a large difference between properties of clusters and superclusters in the Northern and Southern slices of the SDSS EDR survey: clusters and superclusters in the Northern slice are more luminous than those in the Southern slice by a factor of 2. This difference may be due to differences in the location of slices with respect to the very large-scale environment. If this conclusion is confirmed by future observations one must conclude that the formation and evolution of galaxies and systems of galaxies of various scales depends on the nearby as well as on the large-scale environment. Richer superclusters have more luminous galaxies and clusters. On smaller scales this tendency has been observed as a difference between properties of clusters within superclusters and in voids. Now we see that a similar difference may be observed on much larger scales." }, "0212/astro-ph0212124_arXiv.txt": { "abstract": "Bose-Einstein condensation (BEC) and evaporation of transverse photons from the Bose condensate is studied in the case when the density of plasma does not change. The generation of the longitudinal photons (photonikos) by the transverse photons (photons) in terms of the Cherenkov type of radiation in a uniform plasma is demonstrated. The Bogoliubov energy spectrum is derived for photonikos. A new physical phenomena of the \"Compton\" scattering type in nonlinear photon gas is discussed. To this end, a new version of the Pauli equation in the wavevector representation is derived. The formation of Bose-Einstein condensate and evaporation of photons from the condensate is investigated by means of the newly derived Fokker-Planck equation for photonikos. The relevance of this work to recent discovery of black hole X-ray jets is pointed out. ", "introduction": "An immense amount of research has been carried out on propagation of relativistically intense electromagnetic (EM) waves into an isotropic plasma demonstrating that the relativistic oscillatory motion of electrons causes a whole set of interesting and salient phenomena \\cite{shu}-\\cite{kiv}, relevant to the study of laser accelerators of electrons, ions and photons, laser fusion, nonlinear optics, etc. Some of them have already been confirmed by experiments due to the recent progress in compact, high-power, short pulse laser technology. In our previous paper \\cite{tsin} we have suggested a new mechanism for ultrahigh gradient electron and ion acceleration. In addition we have shown over $10^7G$ generated magnetic fields by the nonpotential ponderomotive force. The above treatments were restricted to the case of monochromatic EM waves. However, the interaction of relativistically intense radiation with a plasma leads to several kinds of instabilities and the initially coherent spectrum may eventually broaden, and naturally for ultrashort pulses the initial bandwidth is increasingly broad. Moreover, in astronomical plasmas there are a variety of sources of radiation, and in this case we speak about the average density of radiation from all the sources and their spectral distribution. Hence, the natural state of the strong radiation of EM field is with a broad spectrum. In order to study the interaction of spectrally broad and relativistically intense EM waves with a plasma, it was necessary to derive a general equation for the EM spectral intensity. Such an investigation was reported recently \\cite{ltsin98}, \\cite{ntsin98}, where the authors derived a general kinetic equation for the photons in a plasma. It should be emphasized that the radiation can be in two distinct states. Namely, one is when the total number of photons is not conserved. A good example is a black-body radiation. Another situation is when the total number of photons is conserved. Both these states have been studied in several aspects, mostly for the weak radiation. It is well known that the nature of EM waves in a vacuum is quit different from the one in a medium. In the vacuum EM wave exists only in motion, however the light can be stopped (wavevector $\\vec{k}=0,\\ \\omega=\\omega(0)\\neq 0$) in different mediums and wave-guides. As was shown in Ref.\\cite{ltsin96} the photons acquire the rest mass and become one of the Bosons in plasmas and posses all characteristics of nonzero rest mass, i.e., we may say that the photon is the elementary particle of the optical field. Besides, a several reviews and books have been published on theory of Bose-Einstein condensation (BEC) in a quantum Bose liquid \\cite{lif} and in trapped gases \\cite{dal},\\cite{ant}. Kompaneets \\cite{kom} has shown that the establishment of equilibrium between the photons and the electrons is possible through the Compton effect. In his consideration, since the free electron does not absorb and emit, but only scatters the photon, the total number of photons is conserved. Using the kinetic equation of Kompaneets, Zel'dovich and Levich \\cite{zel} have shown that in the absence of absorption the photons undergo BEC. Such a possibility of the BEC occurs in the case, when the processes of change of energy and momentum in scattering dominates over the processes involving change of the photon number in their emission and absorption. Very recently it was shown that exists an another new mechanism of the creation of equilibrium state and Bose-Einstein condensation in a nonideal dense photon gas \\cite{ltsin02}. More importantly a new effect was predicted in the same paper, namely that the inhomogeneous dense photon gas can be found in the intermediate state. In the present paper, we consider the BEC and evaporation of the transverse photons (photons) from the Bose condensate. In our study we assume that the intensity of radiation (strong and super-strong laser pulse, non-thermal equilibrium cosmic field radiation, etc.) is sufficiently large, so that the photon-photon interaction can become more likely than the photon-electron interaction. We will show that for certain conditions the variation of the plasma density can be neglected in comparison with the variation of the photon density. In such case the elementary excitations represent the longitudinal photons (photonikos), for which we will derive the well known Bogoliubov's energy spectrum. The paper is organized as follows. First in Sec.II a basic equations, describing the relativistic photon-plasma interactions, is presented. The problem of stability of the photon flow is discussed in Sec.III. The derivation of the Bogoliubov energy spectrum for the photonikos is given in the same section. Then in Sec.IV, we derive the Pauli kinetic equation from the Wigner-Moyal equation. Section V is devoted to BEC. The Fokker-Planck equation for photonikos, by which we discuss the possibility of the creation of Bose-Einstein condensate and evaporation of the photons from the condensate, is obtained in the same section. Finally, a brief summary and discussion of our results are given in the last section. ", "conclusions": "We have investigated a class of problems involving the interaction of spectrally broad and relativistically intense EM radiation with a plasma in the case when the photon-photon interaction dominates the photon-particle interactions. We have presented a new concept of the establishment of equilibrium between the photon and the wavepacket of EM field (the dense photon bunch). This is a fully relativistic effect due to the strong EM radiation. We have established the condition under which the variation of the plasma density can be neglected in comparison with the variation of the photon density. In such case the elementary excitations represent the photonikos, for which we have derived the well known Bogoliubov energy spectrum. We have studied the BEC and evaporation of the photons from the Bose condensate in the case when the density of plasma does not change. To this end, from the Wigner-Moyal-Tsintsadze equation \\cite{ltsin98},\\cite{ntsin98},\\cite{men} we have derived a new version of the Pauli kinetic equation for the photon gas. For the case, when the wavevector and frequency of the photoniko is small in comparison with the wavevector and frequency of the photon, we have derived the Fokker-Planck equation for photonikos. We have presented a simple model, which exhibits the possibility of the creation of Bose-Einstein condensate and evaporation of photons from the condensate. We think that these processes can be detectable in next generation experiments with appropriate instrumentation. In fact, a number of experiments have been carried out in which plasmas are irradiated by laser beams with intensities up to $3\\cdot 10^{20}W/cm^2$. At such intensities the photon density is of the order of $n_\\gamma\\sim 10^{29}cm^{-3}.$ For the plasma densities up to $n_e\\sim 10^{19}$, we should expect that the Bose-Einstein condensate becomes observable. The theory developed in this paper should also be the case for astrophysical objects, such as a black hole. In this connection we speculate that the recently observed radiation from the black hole may be attributed to the evaporated photons from the Bose condensate. That is initially all photons fall into Bose-Einstein condensate, and then after a certain time, as discussed in this paper, some photons undergo evaporation from the condensate. These processes may also explain the observable variation in radiation intensity, from being undetectable to one of the brightest sources on the sky. Note that these sources can turn off for decades, and new ones are always being found. In addition Universe is filled with a gas of photonikos. This gas may play the decisive role in the expansion of the Universe. Moreover, it may also be useful for explaining certain processes in supernovae explosion. Finally, the present theory may also find a valuable application in the future space technology, as well as in nonlinear optics." }, "0212/astro-ph0212254_arXiv.txt": { "abstract": "s{I discuss recent developments in the field of relativistic jets in AGNs. After a brief review of our current knowledge of emission from Blazars, I discuss some consequences of the recent detection made by {\\it Chandra} of X-ray emission from extended jets. Finally I report some recent results on the problem of the connection between accretion and jets, study that in principle could shed light on the important issue of jet formation.} ", "introduction": "Jets are ``pipelines'' through which energy and matter originating from the central region of AGNs can flow out from the galaxy and, as in FRII radio galaxies, reach the radio-lobes (e.g. Begelman, Blandford \\& Rees 1984). The comprehension of such structures represents a great challenge for Astrophysics: the ultimate goals include the understanding of the physical processes able to produce such energetics and collimated outlows and the complex dynamics of the jet and its interaction with the environment. In the last decade, thanks to new instruments (in particular the $\\gamma $-ray telescope EGRET, the TeV Cherenkov telescopes and {\\it Chandra}), this field has received a great impulse. In the following I briefly present our current view of the principal physical processes acting in jets, from the innermost portion of the jet close to the central ``engine'' to the external regions. Finally I discuss some works in progress regarding the connection between the inner portion of the jet and the outer regions. ", "conclusions": "" }, "0212/astro-ph0212062_arXiv.txt": { "abstract": "We present an equation of state and radiative opacities for a strongly magnetized hydrogen plasma at magnetic fields $B$, temperatures $T$, and densities $\\rho$ typical for atmospheres of isolated neutron stars. The first- and second-order thermodynamic functions, monochromatic radiative opacities, and Rosseland mean opacities are calculated and tabulated, taking account of partial ionization, for $8\\times10^{11}$ G $\\leq B\\leq 3\\times10^{13}$ G, $2\\times10^5$ K $\\leq T\\leq 10^7$ K, and a wide range of $\\rho$. We show that bound-bound and bound-free transitions give an important contribution to the opacities at $T \\la (1$---$5)\\times 10^6$ K in the considered range of $B$ in the outer neutron-star atmosphere layers, which may substantially modify the X-ray spectrum of a typical magnetized neutron star. In addition, we re-evaluate opacities due to free-free transitions, taking into account the motion of both interacting particles, electron and proton, in a strong magnetic field. Compared to the previous neutron-star atmosphere models, the free-free absorption is strongly suppressed at photon frequencies below the proton cyclotron frequency. The latter result holds for any field strength, which prompts a revision of existing theoretical models of X-ray spectra of magnetar atmospheres. ", "introduction": "\\label{sect-intro} Models of neutron star atmospheres are needed for interpretation of their spectra and cooling. These atmospheres differ from the atmospheres of ordinary stars because of the high gravity and magnetic fields (for review, see, e.g., \\citealp{Pavlov95,elounda}). A magnetic field is called \\emph{strong}\\ if the electron cyclotron energy $\\hbar\\omc=\\hbar eB/\\mel c$ exceeds 1 a.u. -- i.e., the field strength $B$ is higher than $B_0=\\mel^2 c\\, e^3/\\hbar^3 = 2.3505\\times10^9$~G, where $\\mel$ is the electron mass, $e$ the elementary charge, and $c$ the speed of light. Usually the field is called \\emph{superstrong} if $\\hbar\\omc > \\mel c^2$, that is $B > B_\\mathrm{r}=\\mel^2 c^3/e\\hbar = 4.414\\times10^{13}$~G. Most of the radio pulsars have magnetic fields $B \\sim 10^{12}$---$10^{13}$ G \\citep*{tml93}, whereas anomalous X-ray pulsars and soft gamma repeaters are thought to have superstrong fields (e.g., \\citealp{mereghetti01,thompson00}, and references therein). Non-negligible amount of neutral atoms can exist in the photosphere at typical neutron-star temperatures $T \\sim 10^6$ K (\\citealp*{PCS99}, hereafter Paper I). A strong magnetic field enhances atomic binding and makes the quantum-mechanical characteristics of an atom dependent on its motion across the field (see \\citealp{Lai01} for a recent review). In photospheres of the neutron stars, the field is, as a rule, \\emph{strongly quantizing}, i.e., it sets all the electrons on the ground Landau level. This occurs if $\\beta_\\mathrm{e} \\gg 1$ and $\\rho<\\rho_B$, where \\beq \\beta_\\mathrm{e} = \\hbar\\omc/\\kB T \\approx 134.3\\,B_{12}/T_6 , \\label{beta-e} \\eeq $\\rho$ is the density, and $\\rho_B = \\mH/(\\pi^2\\sqrt{2}\\,\\am^3) \\approx 7100\\,B_{12}^{3/2}$ \\gcc\\ (for the hydrogen plasma). Here and hereafter, $\\mH = \\mpr+\\mel$, $\\mpr$ is the proton mass, $\\am=(\\hbar c/eB)^{1/2}$ is the \\emph{magnetic length}, $\\kB$ is the Boltzmann constant, $B_{12}=B/10^{12}$~G, and $T_6=T/10^6$~K. Opacities for the two polarization modes of radiation are quite different in strongly magnetized plasmas (e.g., \\citealp{Pavlov95}, and references therein), which makes thermal emission of neutron stars polarized and anisotropic \\citep{Zavlin95}. The mean opacities are strongly reduced at $\\beta_\\mathrm{e}\\gg1$ (e.g., \\citealp{silyak}); thus the bottom of the photosphere is shifted to high densities (e.g., \\citealp{Pavlov95,LS97}). The chemical composition of neutron-star atmospheres is not precisely known. Just after the neutron star birth in a supernova explosion, the outer stellar envelope is most probably composed of iron. However, light elements may be brought to the surface later (e.g., by fallback, accretion, or encounters with comets). Because of rapid gravitational sedimentation, the lightest element will cover the surface (see \\citealp*{Brown02}). About $10^{12}$---$10^{14}$ grams of hydrogen ($<10^{-19}$ M$_\\odot$) is sufficient to fill the entire photosphere. \\citet{Shib92} presented the first model of hydrogen atmospheres with strong magnetic fields. Later it was developed beyond the diffusion approximation \\citep{SZ95} and used for astrophysical predictions (e.g., \\citealp{Zavlin95}; \\citealp*{Zane00,Zane01,HoLai,HoLai02,LaiHo02,Ozel01,Ozel02}) and for interpretation of observed neutron-star spectra (e.g., \\citealp*{PSZ95,PSZ96,Pavlov95,Ozel-ea}). The above studies assume that the atmosphere is fully ionized. Meanwhile, it was recognized long ago (e.g., \\citealp{Miller92}) that a significant contribution to the opacities of neutron-star photospheres with strong magnetic fields might come from bound-bound and bound-free absorption by atoms. Examples of monochromatic opacities in partially ionized iron \\citep*{RRM} and hydrogen \\citep*{PCS00} atmospheres confirmed this conjecture. In Paper I we have presented an equation of state (EOS) of a partially ionized hydrogen plasma for the values of $T$ and $B$ typical for atmospheres of the radio pulsars. Here we report results of extensive calculations of thermodynamic functions based on the theory developed in Paper~I, supplemented by calculations of the opacities (monochromatic and Rosseland mean). Partial ionization and plasma nonideality are taken into account for $11.9 \\leq \\log_{10} B/\\mathrm{G} \\leq 13.5$ and $5.3 \\leq \\log_{10} T/\\mathrm{K} \\leq 7.0$. Bound-bound and bound-free radiative transitions are treated within the framework of a previously developed theory \\citep{PP95,PP97}. The free-free absorption cross sections are re-evaluated. Whereas the previous authors considered photoabsorption by an electron scattered off a fixed Coulomb center, we take into account the finite proton mass, which has a nontrivial effect on the photoabsorption in a quantizing magnetic field. The paper is composed as follows. In Sect.\\ \\ref{sect-input} we formulate the main assumptions and give the basic formulae used in our work. Section \\ref{sect-EOS} presents the EOS of partially ionized hydrogen under conditions in neutron-star photospheres. In Sect.\\ \\ref{sect-cross} we discuss various contributions to the hydrogen photoabsorption cross sections in strong magnetic fields and derive a new formula for the free-free cross section. Opacities of hydrogen photospheres of the neutron stars are discussed in Sect.\\ \\ref{sect-opac}. Appendices give some detail of calculation of the free-free cross sections. ", "conclusions": "We have calculated the EOS and radiative opacities of fully and partially ionized hydrogen plasmas in a wide range of densities, temperatures, and magnetic fields typical for photospheres of the strongly magnetized neutron stars. The first- and second-order thermodynamic functions, non-ionized fractions, and effective Rosseland mean opacities are published in the electronic form. The opacities are calculated more accurately than in the previous publications. In particular, we take into account suppression of the free-free absorption below the proton cyclotron frequency, which was overlooked previously. This effect reduces the opacities of the ionized component of the plasma by orders of magnitude at photon energies $\\hbar\\omega\\lesssim0.3\\,\\hbar\\omp\\sim 0.02\\,B_{12}$ keV, which necessitates a revision of the previously published models of X-ray spectra of magnetars \\citep{Zane01,HoLai,HoLai02,Ozel01,Ozel02}. On the other hand, the bound-bound and bound-free absorption, neglected in the previous models of neutron-star atmospheres, increase the opacities by more than one order of magnitude at $\\hbar\\omega\\sim(0.1$--3) keV in the outer atmosphere layers of the ordinary neutron stars with $B\\sim10^{12}$--$10^{13.5}$ G and $T < (1$--$3)\\times10^6$ K, which can also significantly affect the spectra. One can expect that the effect of the bound species on the EOS and opacities is as important for magnetars (despite their supposedly higher temperatures) as for the ordinary neutron stars. To check this, we need to extend our model to higher $B$; preliminary high-$B$ results \\citep{CDP02} support this anticipation." }, "0212/astro-ph0212581_arXiv.txt": { "abstract": "We construct models of triaxial galactic nuclei containing central black holes using the method of orbital superposition, then verify their stability by advancing $N$-body realizations of the models forward in time. We assume a power-law form for the stellar density, $\\rho \\propto r^{-\\gamma}$, with $\\gamma=1$ and $\\gamma=2$; these values correspond approximately to the nuclear density profiles of bright and faint galaxies respectively. Equidensity surfaces are ellipsoids with fixed axis ratios. The central black hole is represented by a Newtonian point mass. We consider three triaxial shapes for each value of $\\gamma$: almost prolate, almost oblate and maximally triaxial. Two kinds of orbital solution are attempted for each mass model: the first including only regular orbits, the second including chaotic orbits as well. We find that stable configurations exist, for both values of $\\gamma$, in the maximally triaxial and nearly-oblate cases; however steady-state solutions in the nearly-prolate geometry could not be found. A large fraction of the mass, of order 50\\% or more, could be assigned to the chaotic orbits without inducing evolution. Our results demonstrate that triaxiality may persist even within the sphere of influence of the central black hole, and that chaotic orbits may constitute an important building block of galactic nuclei. ", "introduction": "Schwarzschild (1979) demonstrated how to construct self-consistent models of stellar systems in the absence of analytic expressions for the orbital integrals. His method consists of three steps. i) Represent the stellar system by a smooth density law and divide it into discrete cells; ii) compute a library of orbits in the potential corresponding to the assumed density law, and record the time spent by each orbit in the cells; iii) find a linear combination of orbits that reproduces the cell masses. Using his method, Schwarzschild (1979, 1982) demonstrated self-consistency of triaxial mass models with and without figure rotation. Most of the orbits in his solutions were regular, i.e. non-chaotic (Merritt 1980). Subsequently, Statler (1987) found a variety of self-consistent solutions for the integrable, or ``perfect,'' triaxial mass models in which all orbits are regular. Models like these with large, constant-density cores are now known to be poor representations of elliptical galaxies, almost all of which have high central densities (\\cite{cra93}; Ferrarese et al. 1994). Stellar densities rise toward the center approximately as power laws, $\\rho \\propto r^{-\\gamma}$. Fainter galaxies have steeper cusps, $\\gamma \\approx 2$, while brighter galaxies have weaker cusps, $0\\lap\\gamma\\lap 1$, and exhibit an obvious break in the surface brightness profile. Following this discovery, Schwarzschild (1993) investigated triaxial models with singular density profiles, $\\rho\\sim r^{-2}$, and Merritt \\& Fridman (1996) constructed self-consistent solutions for triaxial galaxies with both weak and strong central cusps. A significant portion of the phase space in these models was found to be occupied by stochastic orbits. Furthermore, triaxial self-consistency could sometimes only be achieved by including some stochastic orbits. Models containing stochastic orbits can represent bona-fide equilibria as long as the stochastic orbits are represented as fully-mixed ensembles (Merritt \\& Fridman 1996; Merritt \\& Valluri 1996). In the last decade, evidence has grown that supermassive black holes are generic components of galactic nuclei (Ho 1999). There are roughly a dozen galaxies in which a compelling case for the presence of a supermassive black hole can be made based on the kinematics of stars or gas (Merritt \\& Ferrarese 2001), as well as a number of active galactic nuclei in which the kinematics of the broad emission line region imply the existence of a supermassive black hole (Peterson 2002). Inferred masses range from $\\sim 10^{6}\\msun$ to $\\sim 10^{9.5}\\msun$ and correlate well with stellar velocity dispersions (e.g. \\cite{fer01}) and bulge luminosities (e.g. \\cite{mcd02}). The possibility of maintaining triaxiality within a galactic nucleus containing a supermassive black hole remains a topic of interest. Very close to the black hole, the gravitational force can be considered a perturbation to the Kepler problem and the phase space is essentially regular (\\cite{mev99}; \\cite{sas00}; \\cite{pom01}, hereafter Paper I). Farther from the black hole, the fraction of chaotic orbits increases, up to a radius where the enclosed stellar mass is a few times the black hole mass; beyond this radius essentially all centrophilic orbits are chaotic (Paper I). The tube orbits remain mostly regular since they avoid the destabilizing center. The persistence of regular orbits throughout the region where the gravitational force from the black hole dominates, leaves open the possibility of constructing self-consistent solutions. Furthermore there is growing observational evidence for the existence of bar-like distortions at the very centers of galaxies (e. g. \\cite{ers02}). In Paper II (Poon \\& Merritt 2002), we presented preliminary results showing that self-consistent and stable triaxial equilibria could be constructed for power-law nuclei with certain axis ratios. In this paper, we present a more detailed investigation of triaxial black-hole nuclei. We find that stationary solutions are possible only for certain shapes; mass models that are too near to prolate axisymmetry always evolve toward axisymmetry. The properties of the mass models are presented in \\S2. Orbital solutions for various shapes and density profiles are presented in \\S3 and their stability is tested by N-body simulation in \\S4 and \\S5. Limits on the chaotic mass fraction are discussed in \\S6. \\S7 discusses some implications for the nuclear dynamics of galaxies. ", "conclusions": "We have shown that long-lived triaxial configurations are possible for nuclei containing black holes. Models with $T=0.5$ (maximally triaxial) and $T=0.25$ (oblate/triaxial) were constructed and found to be stable, retaining their non-axisymmetric shapes until the end of the integration interval, equal to several crossing times. Models with $T=0.75$ (prolate/triaxial) were always found to evolve rapidly to axisymmetry; we speculate that prolate/triaxial nuclei do not exist. The evolution seen in the nearly-prolate models does not appear to be a consequence of orbital chaos; indeed, in our stable solutions, we were able to replace a surprisingly large fraction of the regular orbits by chaotic orbits without inducing noticeable evolution in their shapes. We found that at least 50\\%, and perhaps as much as 75\\%, of the mass could be placed on chaotic orbits in the maximally triaxial and oblate/triaxial solutions. Such models violate Jeans's theorem in its standard form (e.g. \\cite{bt87}) but are consistent with a generalized Jeans's theorem (\\cite{mer99}) if we assume that the chaotic building blocks are ``fully mixed,'' that is, that they approximate a uniform population of the accessible phase space. This appears to be the case for the chaotic orbits in our models which have a very short mixing time. While a sudden onset of chaos can effectively destroy triaxiality in models containing a large population of regular box orbits (\\cite{meq98}; \\cite{sel01}), our work shows that at least the central parts of galaxies containing black holes can remain triaxial even when dominated by chaotic orbits. Our results have possibly important implications for the rate at which stars are fed to supermassive black holes in galactic nuclei. In spherical or axisymmetric nuclei, the feeding rate is determined by the rate at which stars on eccentric orbits are scattered into the loss cone, the phase-space region defined by orbits with pericenters lying within the black hole's tidal disruption radius. In the case of chaotic orbits in a triaxial nucleus, each passage brings the star near to the center, and the time required for a star to pass within a distance $r_t$ of the black hole should scale roughly as $r_t^{-1}$ (e.g. \\cite{geb85}). Thus even in the absence of gravitational scattering, the loss cone would remain full and the feeding rate could be orders of magnitude higher than in axisymmetric nuclei. We will examine these ``chaotic loss cones'' in detail in an upcoming paper (Merritt \\& Poon 2003). While our results strengthen the case for triaxiality in galactic nuclei, the case for nuclear triaxiality could be made even more compelling by the detection of isophotal twists or minor-axis rotation at the very centers of galaxies. Such observations will be challenging, requiring two-dimensional data on an angular scale that resolves the black hole's sphere of influence. Existing integral-field spectrographs on ground-based telescopes (e.g. SAURON, \\cite{bac01}) can only achieve this resolution for the nearest galaxies. Equally valuable would be $N$-body studies demonstrating that triaxial nuclei can form in realistic mergers. M.Y. Poon would like to thank Andrew Mack for stimulating discussions and constructive comments. This work was supported by NSF grants AST 96-17088 and AST 00-71099 and by NASA grants NAG5-6037 and NAG5-9046. M.Y. Poon is grateful to the Croucher Foundation for a postdoctoral fellowship. \\clearpage" }, "0212/hep-ph0212018_arXiv.txt": { "abstract": "We have earlier shown that cosmic strings moving through the plasma at the time of a first order quark-hadron transition in the early universe can generate large scale baryon inhomogeneities. In this paper, we calculate detailed structure of these inhomogeneities at the quark-hadron transition. Our calculations show that the inhomogeneities generated by cosmic string wakes can strongly affect nucleosynthesis calculations. A comparison with observational data suggests that such baryon inhomogeneities should not have existed at the nucleosynthesis epoch. If this disagreement holds with more accurate observations, then it will lead to the conclusions that cosmic string formation scales above $10^{14} - 10^{15}$ GeV may not be consistent with nucleosynthesis and CMBR observations. Alternatively, some other input in our calculation should be constrained, for example, if the average string velocity remains sufficiently small so that significant density perturbations are never produced at the QCD scale, or if strings move ultra-relativistically so that string wakes are very thin, trapping negligible amount of baryons. Finally, if quark-hadron transition is not of first order then our calculations do not apply. ", "introduction": "Recent measurements of the cosmic microwave background radiation (CMBR) anisotropy have reached a sufficiently high level of precision that stringent bounds can be put on various cosmological parameters such as baryon to entropy ratio $\\eta$. It is certainly quite remarkable that the calculations of standard big-bang nucleosynthesis (SBBN) are reasonably consistent with these stringent bounds on $\\eta$. Though several modifications to SBBN are still being considered to better account for the abundances of light elements. One such possibility discussed extensively in the literature is the so called inhomogeneous big bang nucleosynthesis (IBBN) \\cite{ibbn1,ibbn2} where nucleosynthesis takes place in the presence of baryon number inhomogeneities. Various models have been worked out where inhomogeneities of a particular shape and size are taken and their effects on nucleosynthesis are calculated. Different values of the light elemental abundances are calculated and compared with the observed values \\cite{ibbn2}. These calculations are supplemented with the investigations of baryon inhomogeneity generation during a first order quark-hadron phase transition \\cite{bfluct,bfluct2}. Though, it is fair to say that current observations do not support any strong deviation from the SBBN calculations. Calculations of IBBN, such as those in ref. \\cite{ibbn1,ibbn2}, therefore, can be used to constrain the presence of baryon fluctuations in the early universe. In a previous paper \\cite{layek}, we had shown that baryon inhomogeneities on large-scales will be generated by cosmic string wakes during the quark-hadron transition. This arises due to the fact that when there are density fluctuations present in the universe, (for example, those which eventually lead to the formation of structure we see today), then resulting temperature fluctuations, even if they are of small magnitude, can affect the dynamics of a first order phase transition in crucial ways. There have been many discussions of the effects of inhomogeneities on the dynamics of a first order quark-hadron transition in the universe \\cite{impur,inhm}. For example, Christiansen and Madsen have discussed \\cite{impur} heterogeneous nucleation of hadronic bubbles due to presence of impurities. Hadronic bubbles are expected to nucleate at these impurities with enhanced rates. Recently, Ignatius and Schwarz have proposed \\cite{inhm} that the presence of density fluctuations (those arising from inflation) at quark-hadron transition will lead to splitting of the region in hot and cold regions with cold regions converting to hadronic phase first. Baryons will then get trapped in the (initially) hotter regions. Estimates of sizes and separations of such density fluctuations were made in ref.\\cite{inhm} using COBE measurements of the temperature fluctuations in CMBR. In ref. \\cite{layek}, we considered the effect of cosmic string induced density fluctuations on quark-hadron transition and showed that it can lead to formation of extended planar regions of baryon inhomogeneity. We mention here again, as discussed in ref.\\cite{layek}, that there has been extensive study of density fluctuations generated by cosmic strings from the point of view of structure formation \\cite{str1}, and it is reasonably clear that recent measurements of temperature anisotropies in the microwave background by BOOMERANG, and MAXIMA experiments \\cite{expt} at angular scales of $\\ell \\simeq$ 200 disfavor models of structure formation based exclusively on cosmic strings \\cite{str2,str3}. However, even with present models of cosmic string network evolution, it is not ruled out that cosmic strings may contribute to some part in the structure formation in the universe. Further, cosmic strings generically arise in many Grand Unified Theory (GUT) models. If the GUT scale is somewhat lower than $10^{16}$ GeV then the resulting cosmic strings will not be relevant for structure formation (for a discussion of these issues, see \\cite{str3}). However, they may still affect various stages of the evolution of the universe in important ways. Our study in ref.\\cite{layek} (see, also ref.\\cite{ew}), and the present study are motivated from this point of view. In this paper we determine the detailed structure of the baryon inhomogeneities created by the cosmic string wakes \\cite{layek}. We find that the magnitude and length scale of these inhomogeneities are such that they should survive until the stage of nucleosynthesis, affecting the calculations of abundances of light elements. A comparison with observational data suggests that such baryon inhomogeneities should not have existed at the nucleosynthesis epoch. If this disagreement holds with more accurate observations then it will lead to the conclusion that cosmic string formation scales above $10^{14} - 10^{15}$ GeV may not be consistent with nucleosynthesis and CMBR observations. Alternatively, some other input in our calculation should be constrained, for example, if the average string velocity remains sufficiently small so that significant density perturbations are never produced at the QCD scale, or if strings move ultra-relativistically so that string wakes are very thin, trapping negligible amount of baryons. Of course entire discussion of this paper is applicable only when quark-hadron transition is of first order. The paper is organized in the following manner. In section II, we briefly discuss the nature of density fluctuations as expected from cosmic strings moving through a relativistic fluid. In section III we discuss the dynamics of quark-hadron transition in the presence of string wakes, and discuss how baryons are concentrated in sheet like regions inside these wakes. Section IV discusses the results of our calculations where we present the detailed structure of the baryon inhomogeneities. In section V we discuss the effects, these baryon inhomogeneities surviving until the nucleosynthesis stage, can have on the abundances of light elements, and discuss the constraints on the cosmic string models arising from observations of various abundances. Conclusions are presented in section VI. ", "conclusions": "We have calculated the detailed structure of the baryon inhomogeneities created by the cosmic string wakes \\cite{layek}. We find that the magnitude and length scale of these inhomogeneities is such that they survive until the stage of nucleosynthesis, affecting the calculations of abundances of light elements. A comparison with observational data suggests that such baryon inhomogeneities should not have existed at the nucleosynthesis epoch. If this disagreement holds with more detailed calculations and more accurate observations, then it will lead to the conclusion that cosmic string formation scales above a value of about $10^{14} -10^{15}$ GeV are not consistent with nucleosynthesis and CMBR observations. Alternatively, some other input in our calculation should be constrained, for example, the average string velocity can be sufficiently small so that significant density perturbations are never produced at the QCD scale, or strings may move ultra-relativistically so that resulting wakes are very thin, and trap a negligible amount of baryon number. Finally, all these considerations are valid only when quark-hadron transition is of first order. There are many uncertainties in our model, for example treatment of multiple wakes is rather ad hoc. Similarly, we have tried to use results from ref.\\cite{ibbn2} adopting them for our case even though detailed geometry of baryon inhomogeneity in our case is different. A more careful, detailed calculation of abundances of elements is needed for the present case. The uncertainties in various observations of abundances of elements, as well as CMBR anisotropy will be reduced as precision of various measurements gets better. Then one will be able to say with a greater certainty whether IBBN results puts a strong restriction on the density fluctuations, and hence on cosmic string parameters, or the order of quark-hadron phase transition. \\vskip .2in \\centerline {\\bf ACKNOWLEDGMENTS} \\vskip .1in We are very thankful to Rajiv Gavai and Rajarshi Ray for many useful suggestions and comments. We also thank Mark Trodden for very useful discussions and suggestions." }, "0212/astro-ph0212188_arXiv.txt": { "abstract": "We present results of hydrodynamical simulations of young supernova remnants. To model the ejecta, we use several models (discussed in literature) of type Ia supernova explosions with different abundances. Our hydro models are one-dimensional and spherically symmetrical, but they take into account ionization kinetics with all important processes. We include detailed calculations for the X-ray emission, allowing for time-dependent ionization and recombination. In particular, we compare the computed X-ray spectra with recent XMM-Newton observations of the Tycho SN remnant. Our goal is to find the most viable thermonuclear SN model that gives good fits to both these X-ray observations and typical SN~Ia light curves. ", "introduction": " ", "conclusions": "" }, "0212/astro-ph0212141_arXiv.txt": { "abstract": "We present a method for the study of second order superhorizon perturbations in multi field inflationary models with non trivial kinetic terms. We utilise a change of coordinates in field space to separate isocurvature and adiabatic perturbations generalizing previous results. We also construct second order gauge invariant variables related to them. It is found that with an arbitrary metric in field space the isocurvature perturbation sources the gravitational potential on long wavelengths even for ``straight'' trajectories. The potential decouples from the isocurvature perturbations if the background fields' trajectory is a geodesic in field space. Taking nonlinear effects into account shows that, in general, the two types of perturbations couple to each other. This is an outline of a possible procedure to study nonlinear and non-Gaussian effects during multifield inflation. ", "introduction": "Cosmological perturbation theory is a rather arcane subject. The reason is that in a general perturbed spacetime there is no privileged coordinate system with respect to which one can define perturbations. So perturbations can change when we change the coordinates. The study of general relativistic perturbations was pioneered in \\cite{lifs} and studied by many authors since (see e.g \\cite{mfb} for a comprehensive review). Let us briefly recall a more formal presentation of what is usually meant when one talks of perturbations in general relativity \\cite{j.m.s}. One considers a five dimensional space composed of the background spacetime ${\\mathcal{M}}_0$ and, stacked above it, perturbed spacetimes ${\\mathcal{M}}_{\\epsilon}$ parametrized by the parameter $\\epsilon$. We implicitly assume some sort of differentiable structure on this 5-D space such that these perturbed spacetimes can be considered ``close'' to ${\\mathcal{M}}_0$. On these spacetimes live tensor fields $T$. One then defines a vector field $X$, the integral curves of which are used for identifying points on ${\\mathcal{M}}_{\\epsilon}$ with points on the background ${\\mathcal{M}}_0$. The choice of $X$ is completely arbitrary and is called a choice of {\\it{gauge}}. In general, any tensor $T$ can be expanded as a taylor series \\beq T_{0}+\\delta_{X}T=\\phi^{*}_{X\\epsilon}(T_{\\epsilon})=T_0+\\epsilon\\pounds_XT\\mid_0+\\frac{1}{2}\\epsilon^2\\pounds_X\\pounds_XT\\mid_0+...\\,, \\eeq or, calling the various terms the perturbations at various orders, \\beq \\phi^{*}_{X\\epsilon}(T_{\\epsilon})=T_0+{\\delta}T^{(1)}+{\\delta}T^{(2)}+...\\, , \\eeq where $\\phi^{*}_{X\\epsilon}$ is the pullback along $X$ on the background manifold ${\\mathcal{M}}_0$ of a tensor that lives on a perturbed spacetime $\\mathcal{M}_{\\epsilon}$ parameter distance $\\epsilon$ away from the background. Hence the vector field $X$ alows us to define perturbations in a meaningful way. The choice of another vector field $Y=(1,Y^{\\mu})$ defines a different gauge and one finds that perturbations differ when defined in different gauges: \\beq \\delta_YT-\\delta_XT=\\epsilon\\pounds_{\\xi^{(1)}}T\\mid_0+\\frac{1}{2}\\epsilon^2\\pounds_{\\xi^{(1)}}^2T\\mid_0+\\epsilon^2\\pounds_{\\xi^{(1)}}\\delta^{(1)}_XT+\\frac{1}{2}\\epsilon^2\\pounds_{\\xi^{(2)}}T\\mid_0+...\\,, \\eeq where $\\delta^{(1)}_XT\\equiv\\epsilon\\pounds_XT\\mid_0$ is the linear perturbation of $T$ in the ``$X$ gauge'' and $\\xi^{(1)}\\equiv{Y-X}$, $\\xi^{(2)}\\equiv{[X,Y]}$ are vector fields which lie on ${\\mathcal{M}}_0$ and are independent of each other. Hence, by a suitable choice of ${\\xi^{(1)}}$ and ${\\xi^{(2)}}$, a gauge condition can be imposed order by order. Expansion (3) also suggests a strategy for identifying gauge invariant quantities at second order. Observe that the first and fourth terms on th r.h.s of (3) are essentially the same (the transformations they define have the same functional form). This means that any linear combination $f(\\delta{T}^{(1)})$ of first order variables which is gauge invariant to first order will also be gauge invariant w.r.t that part of the second order transformation which corresponds to the $\\frac{1}{2}\\epsilon^2\\pounds_{\\xi^{(2)}}T\\mid_0$ term in (3). The remaining terms, $\\frac{1}{2}\\epsilon^2\\pounds_{\\xi^{(1)}}^2T\\mid_0+\\epsilon^2\\pounds_{\\xi^{(1)}}\\delta^{(1)}_XT$, are all composed of products of first order quantities. So in seeking gauge invariant combinations at second order we must look for appropriate quadratic terms of first order quantities that will cancel these quadratic terms in (3). If this can be done in a unique way then the form of a gauge invariant quantity at first order will dictate its form at second order. We will now give an explicit example of the construction of a second order gauge invariant variable corresponding to the well known first order gauge invariant quantity (first introduced in \\cite{luk}, see also \\cite{mfb}) \\beq \\cR=\\psi+\\frac{\\ch}{\\varphi_{0}'}\\delta\\varphi . \\eeq In general every quantity will be expanded in orders like in (2). For example \\bea g_{\\mu\\nu}&=&g^{(0)}_{\\mu\\nu}+{\\delta}g^{(1)}_{\\mu\\nu}+\\frac{1}{2}{\\delta}g^{(2)}_{\\mu\\nu}+...\\nonumber\\\\ \\varphi&=&\\varphi^{(0)}+{\\delta}\\varphi^{(1)}+\\frac{1}{2}{\\delta}\\varphi^{(2)}+... \\eea e.t.c. In particular, writing the general perturbed metric element as \\beq ds^2=a^2[(1+2\\phi)d\\tau^2-2B_{i}dx^id\\tau-[(1-2\\psi)\\gamma_{ij}+2E_{ij}]dx^idx^j] \\eeq we have \\bea g_{00}&=&a(\\tau)^2\\left(1+2\\phi^{(1)}+\\phi^{(2)}+...\\,\\right)\\\\ g_{0i}&=&a(\\tau)^2\\left(B_i^{(1)}+\\frac{1}{2}B_i^{(2)}+...\\,\\right)\\\\ g_{ij}&=&-a(\\tau)^2\\left[\\left(1-2\\psi^{(1)}-\\psi^{(2)}+...\\right)\\delta_{ij}+2E_{ij}^{(1)}+E_{ij}^{(2)}+...\\,\\right]. \\eea Then, from eqn. (3) one can calculate the formulae for the gauge transformations of the relevant quantities. For an extensive account of second order gauge transformations, explicit formulae and some specific examples the reader can see \\cite{bruni,bruni2} and references therein. In general, formulae for perturbations at second order can be complicated and calculations rather tedious. In this paper we will make a number of simplifying assumptions. We will ignore vectors (hence spatially indexed quantities are given by derivatives of scalars) and, mainly, we will drop terms containing more than one spatial gradients. They are expected to be unimportant on scales longer than the hubble radious. Although there is no rigorous justification for the latter approximation it is expected to capture the main affects on superhorizon scales \\cite{long}. Within such an approach, initial conditions at horizon crossing can be set by linear theory. Then, the long wavelength equations can be used to calculate the nonlinearities induced during the superhorizon evolution. The authors of \\cite{uzan} adopted such a procedure and showed that it is possible for significant nongaussianities to be generated in the adiabatic mode from the long wavelength evolution in multifield inflationary models. Their calculation ignored metric perturbations which are included here (see next section). With these approximations in mind we have the following formulae for a gauge transformation: At first order \\bea \\tilde\\phi_{(1)}&=&\\phi_{(1)}+{\\xi^0_{(1)}}'+\\ch\\xi_{(1)}^0,\\\\ \\tilde{B}_{(1)i}&=&{B}_{(1)i}-\\partial_i\\xi^0_{(1)}+\\xi_{i(1)}',\\\\ \\tilde\\psi_{(1)}&=&\\psi_{(1)}-\\ch\\xi_{(1)}^0,\\\\ \\tilde{E}_{(1)ij}&=&{E(1)}_{ij},\\\\ \\tilde\\delta\\varphi_{(1)}&=&\\delta\\varphi_{(1)}+\\varphi'\\xi^0_{(1)}, \\eea and at second order \\bea \\tilde\\phi_{(2)}=\\phi_{(2)}+{\\xi^0_{(2)}}'+\\ch\\xi_{(2)}^0 &+&\\xi_{(1)}^0\\left[2\\left(\\phi_{(1)}'+2\\ch\\phi_{(1)}\\right)+{\\xi_{(1)}^0}''+5\\ch{\\xi_{(1)}^0}'+\\left(\\ch'+2\\ch^2\\right)\\xi_{(1)}^0\\right]\\nonumber\\\\ &+&2{\\xi_{(1)}^0}'\\left(2\\phi_{(1)}+{\\xi_{(1)}^0}'\\right), \\eea \\bea \\tilde{B}_{(2)i}&=&{B}_{(2)i}-4\\phi_{(1)}\\partial_i\\xi_{(1)}^0+\\xi_{(1)}^0\\left[2\\left({B_i^{(1)}}'+2\\ch B_i^{(1)}\\right)-\\partial_i{\\xi^0_{(1)}}'+{\\xi_i^{(1)}}''-4\\ch\\left(\\partial_i\\xi_{(1)}^0-{\\xi_i^{(1)}}'\\right)\\right]\\nonumber\\\\ &+&{\\xi^0_{(1)}}'\\left(2B_i^{(1)}-3\\partial_i\\xi^0_{(1)}+{\\xi_{i(1)}}'\\right)+{\\xi_{(1)}^j}'\\left(-4\\psi_{(1)}\\delta_{ij}+2E_{(1)ij}\\right)-\\partial_i\\xi^0_{(2)}+\\xi_{i(2)}', \\eea \\beq \\tilde\\psi_{(2)}=\\psi_{(2)}-\\ch\\xi^0_{(2)}+\\xi_{(1)}^0\\left[2\\left(\\psi_{(1)}'+2\\ch\\psi_{(1)}\\right)-\\left(\\ch'+2\\ch^2\\right)\\xi_{(1)}^0-\\ch{\\xi_{(1)}^0}'\\right], \\eeq \\beq \\tilde{E}_{(2)ij}={E}_{(2)ij}+2\\xi^0_{(1)}\\left({E}_{(1)ij}'+2\\ch{E}_{(1)ij}\\right) \\eeq \\beq \\tilde\\delta\\varphi_{(2)}=\\delta\\varphi_{(2)}+\\varphi'\\xi_{(2)}^0+\\xi_{(1)}^0\\left(\\varphi''\\xi_{(1)}^0+\\varphi'{\\xi_{(1)}^0}'+2\\delta\\varphi_{(1)}'\\right). \\eeq Note that, as mentioned before, the part of the transformations in (15) - (19) containing the vector field $\\xi_{(2)}$ is exactly the same as the first order case, eqn's (10) - (14). From the above we see that the variable (4) at second order transforms like \\bea \\frac{\\ch}{\\varphi_0'}\\delta\\tilde\\varphi^{(2)}+\\tilde\\psi^{(2)}=\\frac{\\ch}{\\varphi_0'}\\delta\\varphi^{(2)}+\\psi^{(2)}&+&\\left[\\ch\\frac{\\varphi_0''}{\\varphi_0'}-\\left(\\ch'+2\\ch^2\\right)\\right](\\xi_{(1)}^0)^2\\nonumber\\\\ &+&2\\left(\\frac{\\ch}{\\varphi_0'}\\delta\\varphi_{(1)}'+\\psi_{(1)}'+2\\ch\\psi_{(1)}\\right)\\xi_{(1)}^0 \\eea As expected the transformation contains only products of first order quantities. Therefore we seek to construct a gauge invariant quantity at second order by adding a quadratic combination of first order quantities that will transform appropriately. By inspection we see that it must contain $\\psi$, $\\delta\\varphi'$ and $\\psi'$ and it must not contain $\\delta\\varphi$. So we must have \\beq \\left(A\\psi+C\\psi'+D\\delta\\varphi'\\right)\\left(E\\psi+G\\psi'+H\\delta\\varphi'\\right). \\eeq Noting that \\bea \\psi'\\,\\rightarrow\\,\\psi'-\\ch'\\xi^0-\\ch{\\xi^{0}}'\\\\ \\delta\\varphi'\\,\\rightarrow\\,\\delta\\varphi'+\\varphi_0''\\xi^0+\\varphi_0'{\\xi^{0}}' \\eea and that we must not have terms involving ${\\xi^{0}}'$ we see that we have 2 options. We either set \\bea D=C\\frac{\\ch}{\\varphi_0'}\\\\ H=G\\frac{\\ch}{\\varphi_0'} \\eea which eliminates the terms involving ${\\xi^{0}}'$ in the transformation or take \\bea D=H=\\frac{4\\pi}{m_p^2}\\ch\\varphi_0'\\\\ C=G=\\ch^2-\\ch'. \\eea and use the background equations of motion. In both cases we are forced to consider $A=E$, $C=G$ and $D=H$ and we end up with the same variable \\cite{mat} \\bea \\cR_{(2)}&=&\\left[\\psi_{(2)}+\\frac{\\ch}{\\varphi_{0}'}\\delta\\varphi_{(2)}\\right]\\nonumber\\\\ &+&\\frac{\\left[\\psi_{(1)}'+2\\ch\\psi_{(1)}+\\frac{\\ch}{\\varphi_0'}\\delta_{(1)}\\varphi'\\right]^2}{\\ch'+2\\ch^2-\\ch\\frac{\\varphi_0''}{\\varphi_0'}} \\eea which is invariant under the transformations (17) and (19). ", "conclusions": "We have touched upon the issue of studying second order perturbations in multifield inflationary models and defined gauge invariant variables - equations (102) and (103) - on supehorizon scales also to second order. The latter can be constructed given the solution to lowest non linear order in a given gauge. We have presented a more geometrical method for the splitting of isocurvature and adiabatic perturbations and applied it to a two field model with a diagonal but otherwise arbitrary metric. We showed that in this case naive ``straight'' trajectories do not lead to the decoupling of adiabatic from isocurvature perturbations. We identified the type of curves for which this happens. A perturbative approach by which one can study the nonlinear evolution of perturbations in such models to second order was suggested. The resulting equations have the same form as the first order linear ones but with new terms appearing on the right hand side. These new terms are quadratic in the first order perturbations and therefore they can be considered as known ``sources'' from the solution of the first order problem. Such a formalism can be used to calculate the amount of nongaussianity produced in such models by treating the perturbations as gaussian stochastic fields when they become superhorizon and then study their non linear evolution from that point. The resulting non gaussianity will be of the $\\chi^2$ type since we are considering quadratic products of gaussian fields. We have implicitly assumed a smoothing on scales larger than the horizon and dropped second order spatial gradients. Although straightforward to calculate, the resulting source terms, in principle known, are quite complicated. We will return to the issue of calculating non linear evolution in multifield inflationary models with a different approach in a future publication \\cite{gp}. {\\bf Acknowledgements:} Many thanks to Carsten van de Bruck and Christopher Gordon for useful discussions and comments, Marco Bruni for bringing to my attention other works related to second order perturbation theory, and especially Paul Shellard for discussions and generous support. \\appendix" }, "0212/astro-ph0212007_arXiv.txt": { "abstract": "A number of `modified' Newtonian potentials of various forms are available in the literature which accurately approximate some general relativistic effects important for studying accretion discs around a Schwarzschild black hole. Such potentials may be called `pseudo-Schwarzschild' potentials because they nicely mimic the space-time around a non-rotating/slowly rotating compact object. In this paper, we examine the validity of the application of some of these potentials to study the spherically symmetric, transonic, hydrodynamic accretion onto a Schwarzschild black hole. By comparing the values of various dynamical and thermodynamic accretion parameters obtained for flows using these potentials with full general relativistic calculations, we have shown that though the potentials discussed in this paper were originally proposed to mimic the relativistic effects manifested in disc accretion, it is quite reasonable to use most of the potentials in studying various dynamical as well as thermodynamic quantities for spherical accretion to compromise between the ease of handling of a Newtonian description of gravity and the realistic situations described by complicated general relativistic calculations. Also we have shown that depending on the chosen regions of parameter space spanned by specific energy ${\\cal E}$ and adiabatic index $\\gamma$ of the flow, one potential may have more importance than another and we could identify which potential is the best approximation for full general relativistic flow in Scwarzschild space-time for particular values of ${\\cal E}$ and $\\gamma$. \\keywords {accretion, accretion discs --- black hole physics --- hydrodynamics} ", "introduction": "Stationary, spherically symmetric and transonic hydrodynamic accretion of adiabatic fluid on to a gravitating astrophysical object at rest was studied in a seminal paper by Bondi (1952) using purely Newtonian Potential and by including the pressure effect of the accreting material. Later, Michel (1972) discussed fully general relativistic polytropic accretion on to a Schwarzschild black hole by formulating the governing equations for steady spherical flow of a perfect fluid in the Schwarzschild metric. Following Michel's relativistic generalization of Bondi's treatment, Begelman (1978) discussed some aspects of the critical (sonic) points of the flow for such an accretion. Using an unrelaxed mono-energetic particle distribution and assuming the fact that the relaxation time of such a particle distribution is very long compared to the typical flow time scale or dynamical time scale of steady accretion on to black holes, Blumenthal and Mathews (1976) developed a model where the connection between the nonrelativistic to the relativistic regime of the spherically accreting material could be established. Taking the fully ionized one-temperature ($T_{electron}=T_{proton}$) hydrogen gas (governed by an exact relativistic equation of state) to be the fundamental constituent of the accreting material, Brinkmann (1980) treated spherically symmetric stationary accretion in Schwarzschild space time and showed that the temperature of accreting material at the Schwarzschild radius is one order of magnitude smaller than the flow temperature obtained by using a simple polytropic equation of state. Recently, Malec (1999) provided the solution for general relativistic spherical accretion with and without back reaction and showed that relativistic effects enhance mass accretion when back reaction is neglected.\\\\ \\noindent Meanwhile, the theory of the accretion disc found prior importance because of the fact that disc accretion describes more realistic astrophysical situations found in nature. The beginning of modern accretion disc physics is traditionally attributed to the two classical articles by Shakura \\& Sunyaev (1973) and Novikov \\& Thorne(1973) . While Shakura \\& Sunyaev (1973) calculated the disk structure and related phenomena using purely Newtonian potential, Novikov \\& Thorne provided a fully general relativistic description of accretion discs around black holes; later on, some aspects of which were modified by Riffert and Herold(1995). However, rigorous investigation of transonic disc structure was found to be extremely complicated in full general relativistic space time (Chakrabarti (1996) and references therein). At the same time it was understood that as relativistic effects play an important role in the regions close to the accreting black hole (where most of the gravitational potential energy is released), purely Newtonian gravitational potential (in the form ${\\Phi}_{Newton}=-\\frac{GM}{r}$) cannot be a realistic choice to describe transonic black hole accretion in general. To compromise between the ease of handling of a Newtonian description of gravity and the realistic situations described by complicated general relativistic calculations, a series of `modified' Newtonian potentials have been introduced to describe the general relativistic effects that are most important for accretion disk structure around Schwarzschild and Kerr black holes ( see Artemova et. al.(1996) for further discussion). Introduction of such potentials allows one to investigate the complicated physical processes taking place in disc accretion in a semi-Newtonian framework by avoiding pure general relativistic calculations that most of the features of spacetime around a compact object are retained and some crucial properties of the analogous relativistic solutions of disc structure could be reproduced with high accuracy. Hence, those potentials might be designated as `pseudo-Kerr' or `pseudo- Schwarzschild' potentials, depending on whether they are used to mimic the space time around a rapidly rotating or non rotating/ slowly rotating (Kerr parameter $a\\sim0$) black hole respectively.\\\\ \\noindent It is important to note that although a number of such `pseudo' potentials are available in the literature to study various aspects of disc accretion, no such potentials are available which had been solely derived to describe spherically symmetric accretion on to a Schwarzschild (or Kerr) black hole. In this paper, we will concentrate on some of the `pseudo-Schwarzschild' {\\it disc} potentials (potentials introduced to study {\\it accretion discs} around a Schwarzschild black hole) to investigate whether those potentials could be used to study Spherical accretion, and if so, how `good' the choice would be for various such potentials. Also, we would like to check which potential among those would be the `best-fit' to approximate the full general relativistic description of transonic, spherically symmetric accretion on to a Schwarzschild black hole. In doing so, we solve the equations of motion of spherically accreting fluid in full Schwarzschild space-time as well as for motion under various `pseudo'-potentials, to study the variation of different dynamical and thermodynamic quantities (like Mach number of the flow, flow temperature etc.) with radial distance measured from the accreting black hole for the {\\it full general relativistic spherical flow} (hereafter FGRSF) as well as for accretion using various `pseudo- Schwarzschild' potentials. We then compare the results obtained using such potentials with the solutions of exact relativistic problems in a Schwarzschild metric. The plan of the paper is as follows: In next section, we will describe four `pseudo-Schwarzschild' disc potentials available in the literature and some of their basic features. In \\S 3, we will provide the basic equations governing spherically symmetric accretion in full relativistic as well as in various `pseudo'--relativistic spacetimes. In \\S 4 we will discuss how to solve those equations to find various dynamical quantities which are to be mutually compared and we present our results. Finally in \\S 5 we conclude by discussing the suitability of various `pseudo' potentials in approximating the results obtained from exact relativistic calculations. For the rest of this paper, we will use the terms `modified- Newtonian potential' and `pseudo (Schwarzschild) potentials' synonymously. \\section {Some basic features of various `pseudo-Schwarzschild' potentials} From now, we will define the Schwarzschild radius $r_g$ as $$ r_g=\\frac{2G{M_{BH}}}{c^2} $$ (where $M_{BH}$ is the mass of the black hole, $G$ is universal gravitational constant and $c$ is velocity of light in vacuum) so that the marginally bound circular orbit $r_b$ and the last stable circular orbit $r_s$ take the values $2r_g$ and $3r_g$ respectively for a typical Schwarzschild black hole. Also, total mechanical energy per unit mass on $r_s$ (sometimes called `efficiency' $e$) may be computed as $-0.057$ for this case. Also, we will use a simplified geometric unit throughout this paper where radial distance $r$ is be scaled in units of $r_g$, radial dynamical velocity $u$ and polytropic sound speed $a$ of the flow is scaled in units of $c$ (the velocity of light in vacuum), mass $m$ is scaled in units of $M_{BH}$ and all \\begin{figure} \\vbox{ \\vskip -5.8cm \\centerline{ \\psfig{file=MS1237f1.eps,height=15cm,width=15cm}}} \\noindent {{\\bf Fig. 1:} Newtonian potential $\\Phi_{Newton}(r)$ and other pseudo-potentials $\\Phi_i(r)$'s ($i=1,2,3,4$) are plotted as a function of the logarithmic radial distance from the accreting black hole. Except $\\Phi_2$, all other pseudo-potentials have a singularity at one Schwarzschild radius $r_g$. For $r~>~2r_g$, while the relative stiffness factor ${\\cal S}$ is maximum for $\\Phi_4$, it is minimum for $\\Phi_2$, see text for details.} \\end{figure} other derived quantities would be scaled accordingly. Also, for simplicity,we will use $G=c=M=1$. Below we would like to briefly describe four different `pseudo- Schwarzschild' potentials (expressed in the system of units discussed above) and to provide the `free fall' acceleration obtained using such potentials in compact form.\\\\ \\noindent Paczy\\'nski and Wiita (1980) introduced a `pseudo-schwarzschild' potential of the form $$ \\Phi_{1}=-\\frac{1}{2(r-1)} \\eqno{(1a)} $$ which accurately reproduces the positions of $r_s$ and $r_b$ and gives the value of efficiency to be $-0.0625$. Also the Keplarian distribution of angular momentum obtained using this potential is exactly same as that obtained in pure Schwarzschild geometry. Although this potential (as well as the other `pseudo' potentials available in the literature) does not satisfy the boundary condition exactly on the horizon, however, close to the horizon, accretion flows are supposed to be highly supersonic and the dynamical infall time scale becomes too small to allow significant radiation from infalling fluid. Even if there are significant amounts of radiation, it does not contribute too much to the overall radiation coming out from the disc, due to the fact that radiation emitted from the very close viscinity of the black hole is highly redshifted. Thus, errors in calculation close to the horizon may have very little impact on the emitted disc spectrum and for all practical purposes, the Paczy\\'nski and Wiita (1980) potential is considered to be the best approximation of pure Schwarzschild spacetime while treating the disc accretion (Artemova 1996) . It is worth mentioning here that this potential was first introduced to study a thick accretion disc with super Eddington Luminosity. Also, it is interesting to note that although it had been thought of in terms of disc accretion, it is spherically symmetric (with a scale shift of $r_g$). So in principle, it can definitely be used to study spherical accretion also on to a Schwarzschild black hole.\\\\ \\noindent To analyse the normal modes of accoustic oscillations within a thin accretion disc around a compact object (slowly rotating black hole or weakly magnetized neutron star), Nowak and Wagoner (1991) approximated some of the dominant relativistic effects of the accreting black hole (slowly rotating or nonrotating) via a modified Newtonian potential of the form $$ \\Phi_{2}=-\\frac{1}{2r}\\left[1-\\frac{3}{2r}+12{\\left(\\frac{1}{2r}\\right)}^2\\right ] \\eqno{(1b)} $$ $\\Phi_2$ has correct form of $r_s$ as in the Schwarzschild case but is unable to reproduce the value of $r_b$. This potential has the correct general relativistic value of the angular velocity (as measured at infinity) at $r_s$. Also it reproduces the radial epicyclic frequency $\\kappa$ (for $r>r_s$) close to its value obtained from general relativistic calculations. However, this potential gives the value of efficiency as $-0.064$ which is larger than that produced by $\\Phi_1$, hence the disc spectrum computed using $\\Phi_2$ would be more luminous compared to a disc structure studied using $\\Phi_1$.\\\\ \\noindent Remembering that the free-fall acceleration plays a very crucial role in Newtonian gravity, Artemova et. al. (1996) proposed two different `pseudo' potentials to study disc accretion around a non-rotating black hole. The first potential proposed by them produces exactly the same value of the free-fall acceleration of a test particle at a given value of $r$ as is obtained for a test particle at rest with respect to the Schwarzschild reference frame, and is given by $$ \\Phi_{3}=-1+{\\left(1-\\frac{1}{r}\\right)}^{\\frac{1}{2}} \\eqno{(1c)} $$ The second one gives the value of the free fall acceleration that is equal to the value of the covariant component of the three dimensional free-fall acceleration vector of a test particle that is at rest in the Schwarzschild reference frame and is given by $$ \\Phi_{4}=\\frac{1}{2}ln{\\left(1-\\frac{1}{r}\\right)} \\eqno{(1d)} $$ Efficiencies produced by $\\Phi_3$ and $\\Phi_4$ are $-0.081$ and $-0.078$ respectively.The magnitude of efficiency produced by $\\Phi_3$ being maximum,calculation of disc structure using $\\Phi_3$ will give the maximum amount of energy dissipation and the corresponding spectrum would be the most luminous one. However, as both $\\Phi_3$ and $\\Phi_4$ stems from the consideration of free fall acceleration and calculates the dependence of free fall accleration on radial distance in the Schwarzschild metric (which describes a spherically symmetric gravitational field in vacuum), it appears to be quite justified to use those potentials to study spherically symmetric accretion.\\\\ \\noindent From now we will refer to all these four potentials as $\\Phi_i$ in general where $\\left\\{i=1,2,3,4\\right\\}$ would correspond to $\\Phi_1$ (eqn. 1(a)), $\\Phi_2$ (eqn. 1(b)), $\\Phi_3$ (eqn. 1(c)) and $\\Phi_4$ (eqn. 1(d)) respectively. In Fig. 1, we plot various $\\Phi_i$'s as a function of the radial distance measured from the accreting black hole in units of $r_g$. Also in the same plot, purely Newtonian potential $\\Phi_{Newton}$ is plotted. If we now define a quantity ${\\cal S}_i$ to be the `relative stiffness' of a potential $\\Phi_i$ as: $$ {\\cal S}_i=\\frac{\\Phi_i}{r} $$ (that is, ${\\cal S}_i$ is a measure of the numerical value of any $i$th potential at a radial distance $r$), we find that for $r~>~2r_g$: $$ {\\cal S}_2~<~{\\cal S}_{Newton}~<~{\\cal S}_1~<~{\\cal S}_3~<~{\\cal S}_4 $$ which indicates that while $\\Phi_2$ is a `flatter' potential compared to the pure Newtonian potential $\\Phi_{Newton}$, all other `pseudo' potentials are `steeper' to $\\Phi_{Newton}$ for $r~>~2r_g$. \\\\ \\noindent One can write the modulus of free fall acceleration obtained from all `pseudo' potentials except for $\\Phi_2$ in a compact form as $$ \\left|{{{{{\\Phi}^{'}}_{i}}}}\\right|=\\frac{1}{2{r^{2-{\\delta}_{i}} {\\left(r-1\\right)}^{\\delta_{i}}}} \\eqno{(2a)} $$ where ${\\delta_{1}}=2$, $\\delta_3=\\frac{1}{2}$ and $\\delta_4=1$. $\\left|{{{{{\\Phi}^{'}}_{i}}}}\\right|$ denotes the absolute value of the {\\it space derivative} of $\\Phi_i$, i.e., $$ \\left|{{{{{\\Phi}^{'}}_{i}}}}\\right|=\\left|{\\frac{d{\\Phi_i}}{dr}}\\right| $$ whereas acceleration produced by $\\Phi_2$ can be computed as, $$ {\\Phi_2}^{'}=\\frac{1}{2r^2}\\left(1-\\frac{3}{r}+\\frac{9}{2r^2}\\right) \\eqno{(2b)} $$ In the next section,we would like to describe how one can investigate transonic spherical accretion using these potentials. Also, we will discuss how to calculate various dynamical quantities for full general relativistic bondi flow in a Schwarzschild metric. One standard method to investigate classical transonic bondi flow is to formulate the basic conservation equations, i.e.,conservation of baryon number (obtained by integrating continuity equation) and conservation of specific energy (obtained by integrating Euler's equation using a specific equation of state for accreting matter) and then to simultaneously solve these conservation equations to get critical (sonic) quantities as functions of various accretion parameters (like specific energy ${\\cal E}$, adiabatic index $\\gamma$ or accretion rate ${\\dot M}_{in}$ in the flow) and also to calculate the values of various dynamical and thermodynamic quantities (like Mach number $M$, of the flow, flow temperature, $T$, etc.) as functions of various accretion parameters (like ${\\cal E}, \\gamma, {\\dot M}_{in}$ etc.) or radial distance (measured from the central accretor in the unit of Schwarzschild radius $r_g$). Also a common practice is to study the variation of Mach number $M$ (ratio of the local dynamical velocity $u$ to the local sound velocity $a$; $M=\\frac{u}{a}$) with radial distance $r$ (measured in units of $r_g$) to investigate the `transonicity' of the flow for a fixed set of input parameters. We will perform the above mentioned calculations for accretion in pure Schwarzschild spacetime as well as for accretion in `pseudo-schwarzschild' space time using $\\Phi_i$'s and compare the results obtained for various $\\Phi_i$'s with exact relativistic calculations. As accretion onto a black hole is {\\it necessarily} transonic to satisfy the inner boundary condition at the event horizon, unlike Bondi's (1952) original work, here we will concentrate only on transonic solutions, i.e., we will deal with accretion (wind) which is subsonic (supersonic) far away from the black hole and approaches (moves away from) the hole supersonically (subsonically) after crossing a sonic point (the location of which can be determined as a function of ${\\cal E}$ and $\\gamma$, see \\S 3) on its way towards (away from) the accretor. ", "conclusions": "In this paper we have solved a set of algebraic and differential equations governing various dynamical and thermodynamic behaviouars of Bondi (1954) type accretion in a full Schwarzschild metric as well as for motion under a number of `pseudo-Schwarzschild' potentials, to examine the suitability in application of those potentials in investigating spherically symmetric transonic accretion onto a non- rotating black hole. We have shown that though the potentials discussed here were originally proposed to mimic the relativistic effects manifested in the disc accretion, it is quite reasonable to use most of the potentials in studying various dynamical as well as thermodynamic quantities for spherical accretion. Also, we have shown that depending on the chosen regions of parameter space spanned by specific energy ${\\cal E}$ and adiabatic index $\\gamma$ of the flow, one potential may be important than others and we could identify which potential is the best approximation for FGRSF for what values of ${\\cal E}$ and $\\gamma$. We have restricted ourselves to the study of simple polytropic flows only. However, the validity of using all these $\\Phi_i$s discussed here can easily be examined for isothermal accretion and wind as well as for flows with other equations of state. Work in this direction is reported elsewhere (Sarkar \\& Das, 2001).\\\\ \\noindent It is observed that among all pseudo potentials, $\\Phi_1$ (potential proposed by Paczy\\'nski and Wiita (1980)) and $\\Phi_4$ (one of the potentials proposed by Artemova et. al. (1996)) are in general the best in the sense that they provide very reasonable approximation to the full general relativistic solution. While $\\Phi_1$ is the best approximation for ultra-relativistic flow, $\\Phi_4$ happens to be the best approximation as the flow tends to be fully non relativistic, i.e, $\\gamma$ tends to have the value $\\frac{5}{3}$. Also we see that there are certain cases for which one or more of the pseudo potentials may give the exact match with FGRSF for a particular value of ${\\cal E}$ or $\\gamma$ (for a fixed $r$) in finding some dynamical ($r_c, M$ etc.) or thermodynamic (flow temperature $T$, for example) quantity.\\\\ \\noindent It is worth mentioning that as long as one is not interested in astrophysical processes extremely close (within $1-2~r_g$) to a black hole horizon, one may safely use the `pseudo' potentials discussed here to study spherically symmetric accretion on to a Schwarzschild black hole with the advantage that use of these potentials would simplify calculations by allowing one to use some basic features of flat geometry (additivity of energy or de-coupling of various energy components, i.e., thermal ($\\frac{a^2}{\\gamma-1}$) Kinetic ($\\frac{u^2}{2}$) or gravitational ($\\Phi$) etc.) which is not possible for calculations in a purely Schawarzschild metric. Also, one can study more complex many body problems such as accretion from an ensemble of companions or overall effeciency of accretion onto an ensemble of black holes in a galaxy or for studying numerical hydrodynamic or magnetohydrodynamic flows around a black hole etc. as simply as can be done in a Newtonian framework, but with far better accuracy. However, one should be careful in using these potentials to study spherically symmetric accretion because of the fact that none of the potentials discussed here are `exact' in a sense that they are not directly derivable from the Einstein equations. These potentials could only be used to obtain more accurate correction terms over and above the pure Newtonian results and any `radically' new results obtained using these potentials should be cross-checked very carefully with the exact general relativistic theory.\\\\ \\noindent Although the theory of disc accretion has priority over spherical accretion because of the fact that accretion discs describe more realistic situations found in nature, it is not unreasonable to concentrate on spherical accretion because for certain cases, that may be quite useful and use of these potentials makes a complicated problem simpler to study. For example, for a supermassive black hole immersed in intergalactic space in such a way that matter falling on to it has negligible intrinsic angular momentum, the accretion (at least close to the hole) is quasi spherical and transonic spherical accretion might be a good approximation to mimic the situation. Same sort of approximation is valid when an accreting black hole is embedded in a number of donor stars (or star clusters) where the angular momentum of the stars are randomly oriented in such a way that the vector sum of the intrinsic angular momentum carried by the accreting matter as a whole may be quite negligible, so as to make Bondi-type accretion a good approximation. In fact, a number of recent works (Coker \\& Markoff 2001 and references therein, Das, 1999, 2000, 2001a,b, Toropin, et. al, 1999, Kovalenko \\& Eremin 1998, Titarchuk, et. al. 1996, 1997, Wang \\& Sutherland 1997, Zampieri, et. al. 1996, Yim \\& Park 1995, Markovic 1995, Tsuribe, et. al. 1995, Kazhdan \\& Murzina 1994, Fortner 1993) still deal with spherical accretion to investigate some basic astrophysical processes the black holes and neutron stars. So we believe that work presented in this paper is relevant and will be useful in investigation of various aspects of accretion and wind around non-rotating and slowly rotating compact objects." }, "0212/astro-ph0212282_arXiv.txt": { "abstract": "We present a detailed analysis of the dynamical properties of a simulated disk galaxy assembled hierarchically in the $\\Lambda$CDM cosmogony. At $z=0$, two distinct dynamical components are easily identified solely on the basis of the orbital parameters of stars in the galaxy: a slowly rotating, centrally concentrated spheroid and a disk-like component largely supported by rotation. These components are also clearly recognized in the surface brightness profile of the galaxy, which can be very well approximated by the superposition of an $R^{1/4}$ spheroid and an exponential disk. However, neither does the dynamically-identified spheroid follow de Vaucouleurs' law nor is the disk purely exponential, a result which calls for caution when estimating the importance of the disk from traditional photometric decomposition techniques. The disk may be further decomposed into a thin, dynamically cold component with stars on nearly circular orbits and a hotter, thicker component with orbital parameters transitional between the thin disk and the spheroid. Supporting evidence for the presence of distinct thick and thin disk components is found, as in the Milky Way, in the double-exponential vertical structure of the disk and in abrupt changes in the vertical velocity distribution as a function of age. The dynamical origin of these components offers intriguing clues to the assembly of spheroids and disks in the Milky Way and other spirals. The spheroid is old, and has essentially no stars younger than the time elapsed since the last major accretion event; $\\sim 8$ Gyr ago for the system we consider here. The majority of thin disk stars, on the other hand, form after the merging activity is over, although a significant fraction ($\\sim 15\\%$) of thin-disk stars are old enough to predate the last major merger event. This unexpected population of old disk stars consists mainly of the tidal debris of satellites whose orbital plane was coincident with the disk and whose orbits were circularized by dynamical friction prior to full disruption. More than half of the stars in the thick disk share this origin, part of a trend that becomes more pronounced with age: nine out of ten stars presently in the old ($\\tau \\gsim \\, 10$ Gyr) disk component were actually brought into the disk by satellites. By contrast, only one in two stars belonging to the old spheroid are tidal debris; the rest may be traced to a major merger event that dispersed the luminous progenitor at $z\\sim 1.5$ and seeded the formation of the spheroid. Our results highlight the role of satellite accretion events in shaping the disk---as well as the spheroidal---component and reveal some of the clues to the assembly process of a galaxy preserved in the detailed dynamics of old stellar populations. ", "introduction": "\\label{sec:intro} Some of the observed properties of galactic disks seem at odds with many of the ``natural'' trends expected in hierarchically clustering models and present a significant challenge to the current paradigm of structure formation on small scales (see, e.g., Sellwood \\& Kosowsky 2001, Navarro \\& Steinmetz 2000, Moore 2001). Qualitatively, the main difficulty lies in reconciling the early collapse and eventful merging history characteristic of the buildup of galactic dark matter halos with the many dynamical clues which point to a smooth assembly of the luminous component of galactic disks. This difficulty has made it necessary to postulate a substantial role for complex astrophysical processes in order to overcome some of these trends and to bring models of hierarchical assembly into agreement with observation. The prime concern regards the fragility of centrifugally supported stellar disks to rapid fluctuations in the gravitational potential such as those stirred by mergers and satellite accretion events (Toth \\& Ostriker 1992, Quinn, Hernquist \\& Fullagar 1993, Velazquez \\& White 1999). As first computed in detail by T\\'oth \\& Ostriker (1992), the constraints on merger events undergone by a thin disk such as that of the Milky Way are very strict indeed. These authors find that less than $10\\%$ of the disk mass within the solar circle could have been accreted in the past $5$ Gyr in the form of clumps, limiting severely the role of merging in the recent mass accretion history of the Milky Way. Although these numbers might be relaxed somewhat by taking into account the coherent response of a self-gravitating disk to the accretion event (Huang \\& Carlberg 1997, Walker, Mihos \\& Hernquist 1996, Vel\\'azquez \\& White 1999), there is broad consensus that the presence of a dominant, thin, cold stellar disk points convincingly to a history of mass accretion where major mergers have played a minor role. Indeed, since the fragile circular orbits of disk stars are easily perturbed during mergers, the age of the oldest disk stars is often used to estimate the epoch of the last major merger. In the case of the Milky Way, stars as old as $\\sim 14$ Gyr are found in the solar neighborhood, suggesting a protracted (and perhaps episodic) history of star formation in the disk (Wyse 2000, Rocha-Pinto et al 2000, Liu \\& Chaboyer 2000) and, consequently, a paucity of merger events at odds with typical merging histories of dark halos in cosmogonies such as the $\\Lambda$CDM model. The need for ordered and smooth settling of gas into thin galactic disks leads to a few basic predictions of hierarchical scenarios that can be contrasted directly with observation. For example, because angular momentum results from torques operating before collapse, it correlates directly with the radius and time of turnaround (Navarro \\& Steinmetz 1997). Thus, material that turns around later is expected to have higher angular momentum, with two major implications: (i) disks are expected to be physically smaller in the past, compared with systems of similar rotation speed identified at present, and (ii) disks form from the inside out, as higher angular momentum material, which collapses later, should settle preferentially in the outer regions of the disk (Mo, Mao \\& White 1998). Although overall these expectations are not grossly inconsistent with current data, a number of well established observations are worryingly difficult to accommodate within this general scenario. One of these worries concerns the origin of the complex vertical structure of galactic disks. Current datasets suggest that most (if not all) galactic disks are built out of two major dynamical components, referred to generally as the ``thick'' and ``thin'' disks (Dalcanton \\& Bernstein 2002 and references therein). Although varying in importance from galaxy to galaxy, the thick disk appears to be old ($\\gsim 10$-$12$ Gyr in the case of the Milky Way, Gilmore, Wyse \\& Jones 1995), poor in metals (Prochaska et al 2000), and of similar radial extent as the thin disk component (Wyse 2000). These trends have led to the popular conjecture that the Milky Way's thick disk has its origin in an early thin disk of velocity and size comparable to today's but ``thickened'' by the accretion of a satellite $\\sim 10$-$12$ Gyr ago (Gilmore, Wyse \\& Norris 2002). Appealing as this idea may be from a dynamical standpoint, it is rather unattractive in a hierarchical scenario, where the mere existence of such large, fast-rotating disks at $z\\sim 2$ (corresponding to roughly $\\sim 12$ Gyr ago in the $\\Lambda$CDM scenario) counters the ``natural'' prediction of the model. A related difficulty concerns the presence of old disk stars in the vicinity of the Sun, which might be taken to imply that even at high redshift the thin disk already extended as far as the solar circle and has remained essentially undisturbed dynamically since. Such a long period of quiet dynamical evolution is difficult to reconcile with the active merging expected at early times in the $\\Lambda$CDM cosmogony, and perhaps even with the presence of the Galaxy's spheroidal component, which is typically ascribed to a relatively recent major merger event. The discussion above illustrates the still unsettled account of the origin of the Galactic disk(s) in the hierarchical formation paradigm, and draws notice to the fundamental role that accretion events, be they mergers or satellite disruptions, have played in determining the structure of galactic disks. In this paper---the second in a series analyzing the dynamical properties of galaxies simulated in the ``concordance'' $\\Lambda$CDM paradigm---we examine these issues using a numerical simulation with high numerical resolution. The simulation is the same as described by Abadi et al (2002) in Paper I of this series; that paper confronts the global dynamical and photometric properties of the simulated galaxy with normal spirals, while the present one concentrates on the multi-component nature of the stellar disk and on its dynamical origin. The paper is organized as follows. In section~\\ref{sec:numexp} we briefly discuss, for completeness, numerical details of the simulation; \\S~\\ref{sec:results} discusses the identification of distinct dynamical components in the simulated galaxy, as well as the implications of these results in the context of the formation of the thick and thin disks of the Milky Way. Finally, \\S~\\ref{sec:conc} summarizes our main conclusions. ", "conclusions": "\\label{sec:conc} We present a detailed analysis of the dynamical components of a galaxy simulated in the ``concordance'' $\\Lambda$CDM cosmogony. The galaxy forms in a dark matter halo chosen so that mergers and accretion events are unimportant dynamically after $z\\sim 1$. Star formation and feedback parameters are such that the star formation history of the galaxy is largely driven by the rate at which gas cools and collapses within dark halos: this is a conservative choice where feedback effects are relatively unimportant. The shortcomings of this assumption concerning the global photometric and structural properties of the simulated galaxy are discussed in Paper I. We focus here on the multi-component nature of the stellar disk and on their dynamical origin. Our main results can be summarized as follows. \\begin{itemize} \\item{At $z=0$, two separate stellar components are easily distinguishable solely on the basis of the orbital parameters of stars in the galaxy: a slowly rotating, centrally concentrated spheroid and an extended disk-like component largely supported by rotation. } \\item{These components are also recognized in the surface brightness profile of the galaxy, which can be very well approximated by the superposition of an $R^{1/4}$ spheroid and an exponential disk, in agreement with observations of early-type spirals.} \\item{ Neither does the dynamically identified spheroid follow closely de Vaucouleurs' law nor is the disk purely exponential, a result which calls for caution in the interpretation of estimates of the dynamical importance of the disk and spheroid in traditional photometric decomposition techniques.} \\item{The spheroid is old, and has essentially no stars younger than the last major accretion episode; $\\sim 8$ Gyr ago for the system we consider here. The majority of thin disk stars, on the other hand, form after the merging activity is over and have a mean age of $\\sim 5$ Gyr.} \\item{The disk may be further decomposed into two well defined subcomponents: a thin, dynamically cold disk of stars on nearly circular orbits and a thicker disk with orbital parameters transitional between the thin disk and the spheroid. Supporting evidence for the true presence of these two distinct components is found, as in the Milky Way, in the double-exponential vertical structure of the disk and in abrupt changes in the vertical velocity distribution as a function of age.} \\item{The bulk ($\\sim 60\\%$) of the thick disk consists of the tidal debris of satellites whose orbital plane was coincident with the disk and whose orbits were circularized by dynamical friction prior to full disruption. This trend becomes more pronounced with age; $\\sim 90\\%$ of stars older than $10$ Gyr and presently in the thick disk component were brought into the disk by satellites.} \\item{ A significant fraction ($\\sim 15\\%$) of thin-disk stars are old enough ($\\gsim \\, 10$ Gyr) to predate the last major accretion event. The bulk of this unexpected population of old stars on nearly circular orbits share a common origin with the old thick disk: they are the remains of the cores of disrupted satellites. Interestingly, only one in two stars belonging to the old spheroid are tidal debris; the rest may be traced to a major merger event that disperses the luminous progenitor at $z\\sim 1.5$ and seeds the formation of the spheroid.} \\end{itemize} Our results offer clues to understanding a number of observational trends that challenge the standard hierarchical disk assembly process. In particular, the presence of an old disk component made up primarily of tidal debris from disrupted satellites helps to explain: (i) the presence of a significant number of old stars on circular orbits in the outskirts of galaxies like the Milky Way, and (ii) why the specific angular momentum and radial extent of the thick and thin disk components are comparable in spite of the significantly different ages of their individual stars. It also offers a ``natural'' explanation for the clear dynamical and evolutionary distinction between the thin and thick disk components: the thick disk is mostly tidal debris from disrupted satellites whereas the young thin disk consists mostly of stars formed ``in situ'' after the merging activity abates. These findings highlight the role of satellite accretion events in shaping the disk---as well as the spheroidal---components of a galaxy and reveal some of the clues to the assembly process of the galaxy preserved within the detailed dynamics of old stellar populations. We emphasize that these conclusions are based on the detailed analysis of a single simulation and that further work is needed to put these results on a firmer basis as well as to establish their true applicability to the origin of the dynamical components of the Milky Way. We plan to explore these issues in detail in future papers of this series." }, "0212/astro-ph0212557_arXiv.txt": { "abstract": "The $\\VVM$ of the cosmological X-ray flashes detected by Wide Field Cameras on {\\it BeppoSAX} is calculated theoretically in a simple jet model. The total emission energy from the jet is assumed to be constant. We find that if the jet opening half-angle is smaller than 0.03 radian, the theoretical $\\VVM$ for fixed opening half-angle is less than $\\sim0.4$, which is consistent with the recently reported observational value of $0.27\\pm 0.16$ at the 1 $\\sigma$ level. This suggests that the off-axis GRB jet with the small opening half-angle at the cosmological distance can be identified as the cosmological X-ray flash. ", "introduction": "The X-ray flash (XRF) is a class of X-ray transients (Heise et al. 2001, see also Barraud et al. 2003). Some properties of XRFs, such as the observed event rate, the duration and the isotropic distribution, are similar to that of Gamma-Ray Bursts (GRBs), while the spectral hardness of XRFs characterized by the peak flux ratio, the fluence ratio and the photon index is softer than that of GRBs. This class represents a large portion of the whole GRB population. Recently, the observational value of $\\VVM$, which is the measure of the homogeneity of spatial distribution (Schmidt, Higdon, \\& Hueter 1988; see also Chang \\& Yi 2001; Kim, Chang, \\& Yi 2001), has been updated from $0.56\\pm0.12$ (J.~Heise 2000, talk given in 2nd workshop Gamma-Ray Bursts in the Afterglow Era) to $0.27\\pm0.16$ (J.~Heise 2002, talk given in 3rd workshop Gamma-Ray Bursts in the Afterglow Era). The updated value of $\\VVM$ suggests that XRFs take place at a cosmological distance. Various models accounting for the nature of the XRFs have been proposed (Yamazaki, Ioka, \\& Nakamura 2002; Heise et al. 2001; Dermer, Chiang, \\& B\\\"{o}ttcher 1999; Huang, Dai, \\& Lu 2002; M\\'{e}sz\\'{a}ros et al. 2002; Mochkovitch et al. 2003; Daigne \\& Mochkovitch 2003). Heise et al. (2001) proposed that XRFs could be {\\it GRBs at high redshift}. The redshifts of XRF011030 and XRF020427 have an upper limit of $z\\lesssim 3.5$ (Bloom et al. 2003; J.~Heise 2002, talk given in 3rd workshop Gamma-Ray Bursts in the Afterglow Era), which suggests that XRFs take place at not so high redshift but the same as that of GRBs. {\\it The photosphere-dominated fireball model} may account the nature of the XRFs with peak energy $E_p$ more than $\\sim20$ keV (M\\'{e}sz\\'{a}ros et al. 2002, Ramirez-Ruiz \\& Lloyd-Ronning 2002). However, further considerations are needed to explain the event with $E_p\\sim $ of approximately a few keV, such as XRF020427 (L.~Amati 2002, talk given in 3rd workshop Gamma-Ray Bursts in the Afterglow Era), XRF020903 and XRF010213 (N.~Kawai 2002, talk given in 3rd workshop Gamma-Ray Bursts in the Afterglow Era). The models with small Lorentz factors, such as {\\it the dirty fireball model} (Dermer, Chang, \\& B\\\"{o}ttcher 1999; Huang, Dai, \\& Lu 2002) or {\\it the structured-jet model} (Rossi, Lazzati, \\& Rees 2001; Woosley et al. 2002; Zhang \\& M\\'{e}sz\\'{a}ros 2002a) also have possibilities to explain the properties of the XRF, with the implicit assumption that the XRF arises not from internal shocks (Zhang \\& M\\'{e}sz\\'{a}ros 2002b). The models for internal shocks with {\\it small contrast of high Lorents factors} might be the origin of XRFs (Mochkovitch et al. 2003; Daigne \\& Mochkovitch 2003). For the other possibility, we have studied {\\it the off-axis jet model} and proposed that if we observe the GRB jet with a large viewing angle, it looks like an XRF (Yamazaki, Ioka, \\& Nakamura 2002, Yamazaki, Ioka, \\& Nakamura 2003). In Yamazaki, Ioka, \\& Nakamura (2002) the value of the jet opening half-angle was adopted as $\\Delta\\theta=0.1$. In this model the distance to the farthest XRF ever detected is about 2 Gpc ($z\\sim0.4$) so that the cosmological effect is small and $\\VVM\\sim 0.5$. Recent observations suggest that GRBs with relatively small opening angle exist, while the distribution of $\\Delta\\theta$ is not yet clear (Panaitescu \\& Kumar 2002). If we assume the total emission energy to be constant as in the previous paper, the intrinsic luminosity is larger for the smaller opening half-angle. Such GRBs at the cosmological distance observed from off-axis viewing angle may be seen as XRFs and $\\VVM$ is expected to be smaller than 0.5. In this paper, we will show that our off-axis model has a possibility of accounting for the observational value of $\\VVM$ if we change some of the model parameters in the previous paper (Yamazaki, Ioka, \\& Nakamura 2002). This paper is organized as follows. In \\S~\\ref{sec:model}, we describe a simple jet model including the effect of cosmological expansion. We assume the uniform jet with sharp edges. Although one may consider the structured jet motivated by the simulation of the collapsar model, we cannot conclude, both observationally and theoretically, which model is preferable. The $\\VVM$ for the XRFs detected by the Wide Field Cameras (WFCs) on {\\it BeppoSAX} is calculated in \\S~\\ref{sec:vvm}. Section~\\ref{sec:dis} is devoted to a discussion. Throughout this paper, we adopt the flat universe with $\\Omega_M=0.3$, $\\Omega_\\Lambda=0.7$ and $h=0.65$. ", "conclusions": "\\label{sec:dis} We have calculated $\\VVM_{\\Delta\\theta}$ for the emission from a simple jet model, and shown that when the jet opening half-angle $\\Delta\\theta$ is smaller than about 0.03, $\\VVM_{\\Delta\\theta}$ for the XRFs detected by WFCs on {\\it BeppoSAX} is smaller than 0.4. The value of $\\Delta\\theta\\sim0.03$ has been obtained from the fitting of the afterglow light curve (Panaitescu \\& Kumar 2002; Frail et al. 2001). Such a narrow jet which is inferred by afterglow observations is rare. However, following Eq.~(1) of Frail et al. (2001), the jet break time is given by $t_j\\sim 13(\\Delta\\theta/0.01)^{8/3}$~minutes and so it requires fast localization to observe the jet break for a narrow jet. Therefore, at present, the small number of GRBs with small $\\Delta\\theta$ may come from the observational selection effect. In the context of this scenario, we might be able to account for the fact that afterglows of XRFs have been rarely observed since the afterglow at a fixed time gets dimmer for an earlier break time. Furthermore, some ``dark GRBs'' might be such a small opening angle jet observed with an on-axis viewing angle for the same reason. We briefly comment on how the results obtained in this paper will depend on the Lorentz factor of the jet $\\gamma$. We see that when $\\gamma$ becomes large, $\\VVM_{\\Delta\\theta}$ becomes small. For example, when we fix $\\gamma=200$, we obtain $\\VVM_{\\Delta\\theta=0.03}=0.39$ and $\\VVM_{\\Delta\\theta=0.1}=0.43$. This implies that the limitation on $\\Delta\\theta$ can be relaxed. We can estimate the typical observed photon energy as $h\\nu_{obs}\\sim (1+z)^{-1}\\delta\\nu'_0,$ where $\\delta^{-1}=\\gamma[1-\\beta\\cos\\tilde{\\theta}]$ and $\\tilde{\\theta}={\\rm max}\\{0,\\,\\theta_v-\\Delta\\theta\\}$ (Yamazaki, Ioka, \\& Nakamura 2002). Since $\\gamma\\gg 1$ and $\\theta_v,\\,\\Delta\\theta\\ll 1$, we obtain \\begin{equation} h\\nu_{obs}\\sim \\f{2\\gamma\\nu'_0}{(1+z) [1+(\\gamma\\tilde{\\theta})^2]}. \\end{equation} In \\S~\\ref{sec:vvm}, we have shown that for fixed $\\Delta\\theta\\lesssim0.03$, the typical value of $\\theta_v$ is $\\sim\\Delta\\theta+0.02$. Therefore, for the adopted parameters $\\gamma\\nu'_0=200$keV and the typical redshift $z=z_p\\sim 1.5$, one can derive $h\\nu_{obs}\\sim 30$ keV, which is the typical observed peak energy of the XRFs (Kippen et al. 2002). We can propose from our argument that the emissions from the jets with a small opening half-angle such as $\\Delta\\theta\\lesssim0.03$ are observed as XRFs when they are seen from off-axis viewing angle. If one can detect the afterglow of the XRF, which has the maximum flux at about several hours after the XRF, the fitting of light curve may give us the key information about the jet opening angle (Granot et al. 2002). Therefore, our theoretical model can be tested by the near-future observations. We can estimate the observed event rate of the XRF for fixed $\\Delta\\theta$ as, \\begin{equation} R_{{\\rm XRF},\\,\\Delta\\theta}=\\f{1}{4\\pi}\\int W(\\theta_v)\\,d\\theta_v. \\end{equation} In order to calculate $R_{{\\rm XRF},\\,\\Delta\\theta}$, we consider the proportionality constant ${\\cal R}=n(z)/n_{SF}(z)$. One can write approximately as ${\\cal R}=r_{>8M_\\sun}k$, where $r_{>8M_\\sun}$ is the number of stars with masses $M>8M_\\sun$ per unit mass. Since we assume all stars with masses $M>8M_\\sun$ explode as core-collapse SNe, $k$ represents the ratio of the number of XRF sources to that of core-collapse SNe. We adopt the value $k=1\\times10^{-3}$, which is derived by the result of Porciani \\& Madau (2001) combined with the effect of the solid angle factor $(\\Delta\\theta)^2/2$. Using a Salpeter initial mass function $\\phi(M)$, we obtain $r_{>8M_\\sun}=(\\int_{8M_\\sun}^{125M_\\sun}\\phi(M)\\,dM)/ (\\int_0^{125M_\\sun}M\\phi(M)\\,dM) =1.2\\times10^{-2}M_\\sun^{-1}$. Then, in the case of $\\Delta\\theta=0.03$, we derive $R_{{\\rm XRF},\\,\\Delta\\theta}=1\\times 10^2 \\ {\\rm events} \\ {\\rm yr}^{-1} ({\\cal R}/1\\times10^{-5}M_\\sun^{-1})$, which is comparable to the observed event rate of the XRF (Heise et al. 2001). Note that the value of $R_{{\\rm XRF},\\,\\Delta\\theta}$ remains unchanged within a factor of 2 when we vary $\\Delta\\theta$ from 0.01 to 0.07. When the jet opening half-angle $\\Delta\\theta$ has a distribution $f_{\\Delta \\theta}$, we integrate $\\VVM_{\\Delta\\theta}$ and $R_{{\\rm XRF},\\,\\Delta\\theta}$ over the distribution of $\\Delta\\theta$ as \\begin{equation} \\VVM= \\f{\\int d(\\Delta\\theta)\\, f_{\\Delta\\theta}\\,R_{{\\rm XRF},\\,\\Delta\\theta}\\, \\VVM_{\\Delta\\theta}} {\\int d(\\Delta\\theta)\\,f_{\\Delta\\theta}\\, R_{{\\rm XRF},\\,\\Delta\\theta}} \\ \\ , \\end{equation} \\begin{equation} R_{{\\rm XRF}}=\\f{\\int d(\\Delta\\theta)\\,f_{\\Delta\\theta}\\, R_{{\\rm XRF},\\,\\Delta\\theta}} {\\int d(\\Delta\\theta)\\,f_{\\Delta\\theta}} \\ \\ , \\end{equation} respectively. We assume a power-low distribution as $f_{\\Delta\\theta}\\propto(\\Delta\\theta)^{-q}$. When we adopt $q=4.54$ (Frail et al. 2001), and integrate over $\\Delta\\theta$ from 0.01 to 0.2 rad, we find $\\VVM=0.36$ and $R_{{\\rm XRF}}=1\\times10^2$~events~yr$^{-1}$. These values mainly depend on the lower bound of the integration. For example, we obtain $\\VVM=0.43$ and $R_{{\\rm XRF}}=3$~events~yr$^{-1}$ if the integration is done over $\\Delta\\theta$ from 0.03 to 0.2 rad (Note that we may let the value of $R_{\\rm XRF}$ be consistent with observed value by adjusting ${\\cal R}$). Since the statistics of the observational data will increase in the near future owing to instruments such as {\\it HETE-2} and {\\it Swift}, we will be able to say more than above discussion, including more accurate functional form of $f_{\\Delta\\theta}$ than that we have considered above, as well as the relation to the GRB event rate." }, "0212/astro-ph0212411_arXiv.txt": { "abstract": "s{As part of a research of elusive AGN in a well defined sample of infrared selected galaxies (using {\\em Beppo}SAX, Chandra, {\\em XMM-Newton} and INTEGRAL data) we have observed with \\sax the merging starburst system Arp~299. The broad-band (0.1--40 keV) coverage of this observation clearly reveals, for the first time in this system, the presence of a deeply buried AGN having an intrinsic luminosity of $L_{0.5-100\\:\\kev} \\simeq 1.9 \\times 10^{43}\\:$\\lum .} ", "introduction": "Studies of active objects at IR and X-ray wavelengths indicate that star-formation and AGN activity may be related (Fadda et al. 2002). The trigger mechanism for both phenomena could be the interaction or the merging of gas-rich galaxies. This generates fast compression of the available gas in the inner galactic regions, causing both the onset of a major starburst and the fueling of a central black hole raising the AGN activity. However the concomitant AGN and starburst activity is expected to happen in a high-density medium ($N_H \\geq 10^{23-24}\\:$\\nh), characterized by high dust extinction of the UV-optical flux and strong photoelectric absorption of the soft X-rays (e.g. Fabian et al. 1998). Thus the study of these active phases in galaxies becomes very difficult; optical and even mid-/far-IR spectroscopy may not be sufficient to disentangle starburst activity from AGN activity, which is actually best probed in the hard ($E > 6\\:$keV, in order to sample also the Fe K$\\alpha$ line) X-ray energy band. To search for hidden AGNs and to shed light on the starburst-AGN connection and its occurrence we have started a systematic and objective investigation in hard ($E >6\\:$keV) X-rays of {\\it a flux-limited sample of IRAS galaxies}. The sample consists of 28 galaxies selected from the {\\it IRAS Cataloged Galaxies and Quasars} (see http://irsa.ipac.caltech.edu/) as having $f_{60\\mum} > 50\\:$Jy or $f_{25\\mum} > 10\\:$Jy. We stress here that no other selection criteria (e.g. established presence of an AGN, luminosities, IR colours, etc.) have been applied to the sample definition. ", "conclusions": "" }, "0212/astro-ph0212405_arXiv.txt": { "abstract": "The morphological dependence of the luminosity function is studied using a sample containing approximately 1500 bright galaxies classified into Hubble types by visual inspections for a homogeneous sample obtained from the Sloan Digital Sky Survey (SDSS) northern equatorial stripes. Early-type galaxies are shown to have a characteristic magnitude by 0.45 mag brighter than spiral galaxies in the $r^{\\ast}$ band, consistent with the `universal characteristic luminosity' in the $B$ band. The shape of the luminosity function differs rather little among different morphological types: we do not see any symptoms of the sharp decline in the faint end for the luminosity function for early-type galaxies at least 2 mag fainter than the characteristic magnitude, although the faint end behaviour shows a slight decline ($\\alpha\\lsim -1$) compared with the total sample. We also show that a rather flat faint end slope for early-type galaxies is not due to an increasing mixture of the dwarf galaxies which have softer cores. This means that there are numerous faint early-type galaxies with highly concentrated cores. ", "introduction": "The origin of morphology of galaxies is a long-standing issue, which could provide a key to discerning among models of the formation of galaxies. How galaxy morphology changes as a function of the lookback time is perhaps the prime approach to this problem, and the knowledge of the morphological dependence of the local luminosity function at zero redshift is the baseline. One specific example of the issues is whether the luminosity function of elliptical galaxies obeys the Schechter-type function with a rather flat faint end (e.g., Marzke et al. 1994; Kochanek et al. 2001), or the Gaussian function as inferred by Binggeli, Sandage \\& Tammann (1988) and more recently by Bernardi et al. (2002a). If the latter is correct, one would envisage galaxy morphology as a bulge-luminosity sequence (Dressler \\& Sandage 1983; Meisels and Ostriker 1984), which in turn reveals a clue about the formation of elliptical galaxies and bulges. There are also a number of uses of the morphology-dependent luminosity function (MDLF). We mention only one example: the frequency of gravitational lensing of quasar images is approximately proportional to the luminosity density of early-type galaxies rather than that of all galaxies (Fukugita \\& Turner 1991). The uncertainty in the MDLF is the largest source of error in predicting the frequency of gravitational lenses, and thus in inferring the cosmological constant from such analyses. The understanding of the MDLF is significantly poorer than that of the luminosity function for galaxies in general, which has undergone substantial progress in the latest years (Folkes et al. 1999; Blanton et al. 2001) by virtue of large galaxy samples. The traditional way to obtain MDLF is to use morphological classification based on visual inspections of the images (Binggeli et al. 1988; Loveday et al. 1992; Marzke et al. 1994; 1998; Kochanek et al. 2001). Some modern studies attempt to use spectroscopic features to classify galaxies into morphological types (Bromley et al. 1998; % Folkes et al. 1999), which makes it possible to analyze large samples. Although a general correlation is known between spectroscopic and Hubble morphologies, the samples derived from the two methods are considerably different. In particular, the classification using spectroscopic features or colours is sensitive to small star formation activities now or in the near past in early-type galaxies, whilst Hubble morphology is insensitive to this process. The problem of automated classification always lies in the difficulty in finding quantitative measures that strongly correlate with the Hubble sequence based on visual inspections. In this paper we derive the MDLF based on visual classifications using a homogeneous bright galaxy sample from Sloan Digital Sky Survey (SDSS; York et al. 2000). The sample we use in this paper is small, but it is based on a homogeneous morphological classification with accurate photometry. The SDSS conducts both photometric (Gunn et al. 1998; Hogg et al. 2001; Pier et al. 2002) and spectroscopic surveys, and is producing a homogeneous data set, which is suitable to studies of galaxy statistics. The initial survey observations were made in the northern and southern equatorial stripes, and produced a galaxy catalogue to $r^{\\ast}=22.5$ mag in five colour bands (Fukugita et al. 1996) with a photometric calibration using a new standard star network observed at USNO (Smith et al. 2002). Spectroscopic follow-up is made to 17.8 mag with accurately defined criteria for target selection (Strauss et al. 2002). Our study is limited to bright galaxies with $r^{\\ast}\\leq 15.9$ mag after Galactic extinction correction, since visual classifications sometimes cannot be made confidently beyond this magnitude with the SDSS imaging data. We have classified all galaxies satisfying this magnitude criterion in the northern equatorial stripe. The total number of galaxies in our sample is 1875, of which 1600 have spectroscopic information. The dominant part of the data we used are already published as an {\\it Early Data Release} (EDR) (Stoughton et al. 2002). Our present work uses primarily the EDR but supplemented by observations which are not included in EDR to make the sample as complete as possible. Photometry of galaxies in this region is discussed in a galaxy number count paper of Yasuda et al. (2001), and the luminosity function is derived by Blanton et al. (2001), which also discuss spectroscopic details. ", "conclusions": "Our sample is small and we may not be able to extract quantitatively robust parameters, yet we obtain a number of useful conclusions. The most important feature with our analysis is that we have used a homogeneous photometric catalogue with sharply defined selection criteria and a homogeneously morphologically-classified sample based on Hubble morphology of galaxies, rather than a sample classified by indicators using spectroscopic features or colours, which are sensitive to small star formation activities in the present or the near past. The first conclusion we have obtained is that the shape of the MDLF does not depend too strongly on the Hubble types. The characteristic luminosity of elliptical and S0 galaxies is brighter than that of spiral galaxies in the $r^{\\ast}$ band. The amount of the difference in brightness is consistent with universal characteristic luminosity in the $B$ band, which was found by Tammann et al. (1979). The MDLF of early-type galaxies somewhat declines in the faint end, but does not exhibit a sharp decline, and this is not due to an increasing mixture of dwarf galaxies at least in the magnitude range we are concerned with. The conclusion is unchanged if we use the concentration index as a classifier of early-type galaxies. This indicates that there are many intrinsically faint elliptical galaxies, whose luminosities are fainter than those of bulges in spiral galaxies. The existence of numerous early-type galaxies with a hard core at small luminosities indicates that morphology is unlikely to be a sequence of the bulge luminosity as advocated by Dressler \\& Sandage (1983), and by Meisels and Ostriker (1984). Our conclusion also justifies the calculation of the strong gravitational lensing frequency of quasars using the standard Schechter function without introducing a cutoff in the luminosity function, which would affect the frequency of sub-arcsecond lensing. \\vspace{10pt} Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington. We would like to thank Sadanori Okamura for useful comments. MF is supported in part by the Grant in Aid of the Japanese Ministry of Education. \\clearpage" }, "0212/astro-ph0212319_arXiv.txt": { "abstract": "{First results from a deep XMM-Newton observation of a field in the Large Magellanic Cloud (LMC) near the northern rim of the supergiant shell LMC\\,4 are presented. Spectral and temporal analyses of a sample of selected X-ray sources yielded two new candidates for supernova remnants, a supersoft X-ray source and a likely high mass X-ray binary (HMXB) pulsar. From the fourteen brightest sources up to ten are active galactic nuclei in the background of the galaxy which can be used as probes for the interstellar medium in the LMC. From the three previously known HMXBs the Be/X-ray binary \\exo\\ was the brightest source in the field, allowing a more detailed analysis of its X-ray spectrum and pulse profile. During the pulse \\exo\\ shows eclipses of the X-ray emitting areas with increased photo-electric absorption before and after the eclipse. The detection of X-ray pulsations with a period of 69.2 s is confirmed for \\rxbe\\ and a possible period of 272 s is discovered from \\xmmbex. The results are discussed with respect to individual sources as well as in the view of source population studies in the vicinity of the supergiant shell LMC\\,4. ", "introduction": "Due to their proximity the Large and Small Magellanic Cloud (LMC, SMC) were always subject to X-ray surveys for satellites carrying imaging instruments. The most sensitive and most complete survey is available from ROSAT data obtained between 1990 and 1998 in the energy range 0.1--2.4 keV. In particular pointed observations with the PSPC detector with its large field of view covered in total $\\sim$59 and $\\sim$18 square degrees of the LMC and SMC regions on the sky \\citep{1999A&AS..139..277H,2000A&AS..142...41H}. The ROSAT PSPC and HRI observations revealed about 1000 and 750 X-ray sources in the direction of the LMC and SMC, respectively \\citep[see also][]{2000A&AS..143..391S,2000A&AS..147...75S}. The large number of X-ray sources in the Magellanic Cloud fields allows population studies on rich samples of various kinds of source types powered by different mechanisms. An unusually high concentration of Be/X-ray binary systems was found in the SMC \\citep{2000A&A...359..573H}. Detectors sensitive to higher energies on board ASCA and XTE detected pulsations from many new Be/X-ray transients during outburst \\citep{2002Yokogawa}. The high sensitivity of the XMM-Newton instruments promises the detection of pulsations to much lower X-ray fluxes \\citep{2001A&A...369L..29S} usually observed from Be/X-ray binaries in their low state. To study the source population in the LMC to flux limits below \\oergcm{-14} a deep $\\sim$60 ks XMM-Newton observation was performed as part of the telescope scientist guaranteed time. The selected field, aimed at RA = 05$^{\\rm h}$31$^{\\rm m}$20$^{\\rm s}$ and Dec = --65\\degr57\\arcmin38\\arcsec, was chosen because of its location on the rim of the supergiant shell (SGS) LMC\\,4 \\citep{1980MNRAS.192..365M} and the simultaneous coverage of three known high mass X-ray binaries (HMXBs). These are : 1) The Be/X-ray binary pulsar \\exo\\ discovered in outburst during EXOSAT observations of the LMC\\,X-4 region in 1983 \\citep{1985SSRv...40..379P}. X-ray pulsations with a pulse period of 13.7 s were detected for the first time in ROSAT data by \\citet{1996rftu.proc..131D}. 2) An outburst observed from \\rxbe\\ by ROSAT and the detection of 69 s X-ray pulsations led to the suggestion by \\citet{1997A&A...318..490H} that \\rxbe\\ is also a Be/X-ray binary. Optical spectroscopy by \\citet{2002A&A...385..517N} confirmed this. 3) The highly variable source \\rxob\\ proposed as first HMXB in the LMC powered by accretion from the wind of an OB supergiant companion \\citep{1995A&A...303L..49H} which is supported by optical spectroscopy \\citep{2002A&A...385..517N}. Active galactic nuclei (AGN) behind nearby galaxies are of interest for two main reasons. They can be used to define a precise reference coordinate system \\citep[e.g.][]{2000AJ....120..845A} and provide line of sight probes to study the interstellar medium in the galaxies \\citep[e.g.][]{2001A&A...371..816K,2001A&A...365L.208H}. The new X-ray observatories Chandra and XMM-Newton will largely increase the number of background AGN as first results from LMC observations demonstrate \\citep{2001A&A...365L.208H,2002ApJ...569L..15D}. In this article first results from the deep XMM-Newton observation are presented. The paper concentrates on spectral and temporal analyses of a selected sample of X-ray sources which includes the three known HMXBs and new candidates for supernova remnants (SNRs), a supersoft source (SSS), a likely Be/X-ray binary pulsar and ten candidates for background AGN. \\begin{figure*} \\resizebox{\\hsize}{!}{\\includegraphics[clip=]{rgb_final.ps}} \\caption{EPIC-pn RGB color image produced from data in three energy bands (red: 0.3--1.0 keV, green: 1.0--2.0 keV and blue: 2.0--7.5 keV). Each individual image was smoothed with an adaptive intensity filter. Instrumental background from an observation with closed filter wheel (from revolution 59) was subtracted before vignetting and exposure correction. The XMM-Newton pointing was aimed at RA = 05$^{\\rm h}$31$^{\\rm m}$20$^{\\rm s}$ and Dec = --65\\degr57\\arcmin38\\arcsec\\ and covers about 13\\arcmin\\ in radius. North is to the top and West to the right. The brightest source, located in the South, is the Be/X-ray binary system \\exo.} \\label{epic-ima} \\end{figure*} ", "conclusions": "The deep XMM-Newton observation of a northern field in the LMC allows to uniquely classify the detected X-ray sources to flux levels of $\\sim$\\oergcm{-14} from their X-ray properties alone. X-ray spectra obtained by the EPIC cameras over a relatively broad energy band (0.15--12.0 keV) emphasize the various energy distributions observed from the different types of X-ray sources. A first analysis of twenty selected sources, presented here, yielded the discovery of a previously undetected supersoft source, revealed two ROSAT sources with indication for spatial extent as supernova remnants and rendered the detection of a possible pulsation in the X-ray flux of a candidate HMXB in the LMC. This increases the number of known HMXBs in the observed field to four. Among the fourteen brightest sources three HMXBs, one foreground star and up to ten AGN were found. Particular results on individual objects are discussed in Sect.\\,3 while in Sect\\,4 the analyzed sample of X-ray sources is considered in the view of source population studies in the Magellanic Clouds and nearby galaxies in general." }, "0212/astro-ph0212543_arXiv.txt": { "abstract": "We present optical and infrared photometry of the unusual Type Ia supernova 2000cx. With the data of Li et al. (2001) and Jha (2002), this comprises the largest dataset ever assembled for a Type Ia SN, more than 600 points in $UBVRIJHK$. We confirm the finding of Li et al. regarding the unusually blue $B-V$ colors as SN 2000cx entered the nebular phase. Its $I$-band secondary hump was extremely weak given its $B$-band decline rate. The $V$ {\\em minus} near infrared colors likewise do not match loci based on other slowly declining Type Ia SNe, though $V-K$ is the least ``abnormal''. In several ways SN 2000cx resembles other slow decliners, given its $B$-band {\\em decline} rate ($\\Delta$m$_{15}$($B$) = 0.93), the appearance of Fe III lines and weakness of Si II in its pre-maximum spectrum, the $V-K$ colors and post-maximum $V-H$ colors. If the distance modulus derived from Surface Brightness Fluctuations of the host galaxy is correct, we find that the rate of light increase prior to maximum, the characteristics of the bolometric light curve, and the implied absolute magnitude at maximum are all consistent with a sub-luminous object with $\\Delta$m$_{15}$($B$) $\\approx$ 1.6-1.7 having a higher than normal kinetic energy. ", "introduction": "\\parindent = 9 mm Astronomers try to understand the universe by looking for patterns in observed phenomena. Often, the patterns themselves are reason to believe in underlying, understandable physical mechanisms, while at other times the exceptions to the rules provide the motivation to expand our conceptions of the physical makeup of cosmic objects. In this paper we present optical and infrared photometry of the very unusual supernova 2000cx. Previous optical data have been presented by Li et al. (2001), who describe SN 2000cx as ``unique''. SN 2000cx was discovered by Yu, Modjaz, \\& Li (2000) from images taken on 17.5 and 18.4 July 2000 UT as part of the Lick Observatory Supernova Search, using the 0.76-m Katzman Automatic Imaging Telescope (KAIT). This object was located at $\\alpha$ = 1:24:46.15, $\\delta$ = +9\\arcdeg ~30\\arcmin ~30\\farcs9 (equinox 2000.0), which is 23\\farcs0 west and 109\\farcs3 south of the nucleus of the S0 galaxy NGC 524. A spectrum taken on 23 July UT with the Nickel 1-m reflector at Lick Observatory (Chornock et al. 2000) revealed that the object was a peculiar Type Ia supernova, resembling SN 1991T a few days before maximum brightness, with prominent Fe III absorption lines near 430 and 490 nm but weak Si II at 612 nm. Optical photometry (Li et al. 2001) revealed that SN 2000cx is different from all known Type Ia SNe and that the light curves cannot be fitted well using the techniques currently available. The pre-maximum rise was relatively fast, similar to SN 1994D, but the post-maximum decline was relatively slow, similar to SN 1991T. We present optical and infrared photometry of SN 2000cx, initiated at CTIO with the Yale-AURA-Lisbon-Ohio (YALO) 1-m telescope on 19 July 2000 (UT), some 8 days before the time of $B$-band maximum. We include data taken with the 0.76-m Manastash Ridge Observatory (MRO) of the University of Washington (also begun on 19 July UT), the CTIO 0.9-m telescope, and the Apache Point Observatory 3.5-m telescope (APO). The calibration of the infrared light curves was primarily made possible with observations made with the Swope 1-m telescope at Las Campanas Observatory. ", "conclusions": "SN 2000cx, the brightest supernova discovered in the year 2000, occurred in the unobscured outer regions of an early-type galaxy and was well observed with multiple telescopes, allowing us to compile a datset of unprecedented size. While many Type Ia SNe have light curves that follow patterns that are now well established, SN 2000cx did not conform to these patterns. SN 2000cx was a reasonably fast riser in $B$ and $V$. From the pre-maximum photometry Li et al. (2001) obtain a stretch factor that corresponds to $\\Delta$m$_{15}$($B$) = 1.64 $\\pm$ 0.02. Based solely on its weak $I$-band secondary hump, we would have predicted $\\Delta$m$_{15}$($B$) $\\approx$ 1.7. If the distance modulus based on Surface Brightness Fluctuations of the host galaxy is correct (Tonry et al. 2001), the corresponding absolute magnitudes in $BVIH$ are comparable to fast decliners, with $\\Delta$m$_{15}$($B$) in the range 1.4 to 1.7. However, SN 2000cx was a slow {\\em decliner}, with $\\Delta$m$_{15}$($B$) = 0.93. Its pre-maximum spectrum showed strong Fe III and weak Si II, like other slow decliners such as SN 1991T. Its $V-K$ color evolution, both pre- and post-maximum, was very similar to that of other slow decliners. The bolometric behavior of SN~2000cx, when compared to the normal SNe 1999ee and 2001el, showed that this SN rose and fell from maximum light more rapidly, and that the magnitude difference between peak brightness and 90 days past peak was larger than normal. This behavior is consistent with the higher kinetic energies seen at maximum light and reported by Li et al. (2002), but it can also be explained by this event being sub-luminous. The distance modulus of SN 2000cx is somewhat problematic. We note, however, that MLCS (Riess et al. 1996, 1998), Hubble Law's (with H$_0$ = 74 km s$^{-1}$ Mpc$^{-1}$), and the method that uses the $H$-band absolute magnitude at $t$ = 10 d (Krisciunas et al. 2003) give just about the same value. The SBF method gives a distance modulus roughly 0.6 mag smaller. Given: 1) the accuracy of the photometry of SN~2000cx at maximum ($\\pm$ 0.03 mag); 2) the host extinction of SN~2000cx is minimal (or zero); 3) the uncertainty of the Galactic extinction correction is also small; and 4) the light curves cannot be fit by templates based on other objects, confidently placing this SN in a Hubble diagram depends significantly on a direct measure of the host galaxy's distance (such as with the SBF method) or on an absolute magnitude derived from an explosion model that can match the many unusual observed facts." }, "0212/astro-ph0212069_arXiv.txt": { "abstract": "{ Based on a detailed study of the temperature structure of the intracluster medium in the halo of M~87, abundance profiles of 7 elements, O, Mg, Si, S, Ar, Ca, and Fe are derived. In addition, abundance ratios are derived from the ratios of line strengths, whose temperature dependences are small within the temperature range of the ICM of M~87. The abundances of Si, S, Ar, Ca and Fe show strong decreasing gradients outside 2$'$ and become nearly constant within the radius at $\\sim1.5$ solar. The Fe/Si ratio is determined to be 0.9 solar with no radial gradient. In contrast, the O abundance is less than a half of the Si abundance at the center and has a flatter gradient. The Mg abundance is $\\sim$1 solar within 2$'$, which is close to stellar abundance within the same radius. The O/Si/Fe pattern of M~87 is located at the simple extension of that of Galactic stars. The observed Mg/O ratio is about 1.25 solar, which is also the same ratio as for Galactic stars. The O/Si/Fe ratio indicates that the SN Ia contribution to Si and Fe becomes important towards the center and SN Ia products have similar abundances of Si and Fe at least around M~87, which may reflect dimmer SN Ia observed in old stellar systems. The S abundance is similar to the Si abundance at the center, but has a steeper gradient. This result suggests that the S/Si ratio of SN II products is much smaller than the solar ratio. ", "introduction": "The intracluster medium (ICM) contains a large amount of metals, which are mainly synthesized in early-type galaxies (e.g. Arnaud et al. 1992; Renzini et al. 1993). Thus, abundances of the metals are tracers of chemical evolution of galaxies and clusters of galaxies. Based on the Si/Fe ratio observed with ASCA, a discussion on contributions from SN Ia and SN II to the metals has commenced. In a previous nucleosynthesis model of SN Ia, the Fe abundance is much larger than the Si abundance in the ejecta of SN Ia (Nomoto et al. 1984). Observations of metal poor Galactic stars indicate that average products of SN II have a factor of 2--3 larger abundance of $\\alpha$-elements than Fe (e.g. Edvardsson et al. 1993; Nissen et al. 1994; Thielemann et al. 1996), although this ratio may depend on the initial mass function (IMF) of stars. From elemental abundance ratios in the ICM of four clusters of galaxies observed with ASCA, Mushotzky et al. (1996) suggested that the metals in the ICM were mainly produced by SN II. Since stars in early-type galaxies in galaxy clusters are very old (e.g. Stanford et al. 1995; Kodama et al. 1998), this means that most of the metals in the ICM are produced through star formations at high $z$. Fukazawa et al. (1998) systematically studied 40 nearby clusters and found that the Si/Fe ratio is lower among the low-temperature clusters, which indicates that SNe Ia products are also important among these clusters. From the observed radial dependence of the abundances, Finoguenov et al. (2000) found that the SNe II ejecta have been widely distributed in the ICM. In the ICM, around a cD galaxy, the contribution of metals from the galaxy becomes important. Fukazawa et al. (2000) found a central increment of Fe and Si abundances around cD galaxies, which is due to SNe Ia from the cD galaxies. The supply of metals by stellar mass loss must be also considered (e.g. Matsushita et al. 2000) In addition to the Si and Fe abundances, the XMM-Newton observatory enables us to obtain $\\alpha$-element abundances such as for O and Mg, which are not synthesized by SN Ia. B\\\"ohringer et al. (2001) and Finoguenov et al. (2002) analyzed annular spectra of M~87 observed by XMM-Newton, and found a flatter abundance gradient of O compared to steep gradients of Si, S, Ar, Ca, and Fe. The stronger abundance increase of Fe compared to that of O indicates an enhanced SN Ia contribution in the central regions (in disagreement with our findings, Gastaldello and Molendi (2002) claim a similar gradient for O and Fe, which would not support this conclusion). The observed similar abundance gradients of Fe and Si and the large Si/O ratio at the center imply a significant contribution of Si by SN Ia that is a larger Si/Fe abundance ratio by SN Ia than obtained by the classical model of Nomoto et al. (1984). The larger Si/Fe ratio and the implication that the Si/Fe ratio supplied by SN Ia may change with radius in the M~87 halo may indicate a diversity of SN Ia explosions also reflected in a diversity of the light curves as discussed by Finoguenov et al. (2002). A similar abundance pattern of O, Si and Fe is observed around center of A 496 (Tamura et al. 2001). A prerequisite of the abundance determination is a precise knowledge of the temperature structure of the ICM. Based on the XMM-Newton observation of M~87, Matsushita et al. (2002; hereafter Paper I) found that the intracluster medium has a single phase structure locally, except for the regions associated with radio jets and lobes (B\\\"ohringer et al. 1995; Belsole et al. 2001), where there is an additional $\\sim$ 1 keV temperature component. The signature of gas cooling below 0.8 keV to zero temperature is not observed as expected for a cooling flow (e.g Fabian et al. 1984). The fact that the thermal structure of the intracluster medium is fairly simple and the plasma is almost locally isothermal facilitates the abundance determination enormously and helps to make the spectral modeling almost unique. In this paper, based on the detailed study of the temperature structure, abundances of various elements are discussed. In section 2, we summarize the observation and data preperation. Sections 3 and 4 deal with the MEKAL (Mewe et al. 1995, 1996; Kaastra 1992; Liedahl et al. 1994) and the APEC model (Smith et al. 2001) fits to the deprojected spectra, and in section 5, abundance ratios are determined directly from the line ratios, considering their temperature dependences. In section 6, we evaluate an effect of resonant line scattering. Section 7 gives a discussion of the obtained results, and Section 8 summarizes the paper. We adopt for the solar abundances the values given by Feldman (1992), where the solar Ar and Fe abundances relative to H are 4.47$\\times10^{-6}$ and 3.24$\\times10^{-5}$ in number, respectively. These values are different from the ``photospheric'' values of Anders \\& Grevesse (1989), where the solar Ar and Fe abundances are 3.63$\\times10^{-6}$ and 4.68$\\times10^{-5}$, respectively. The solar abundances of the other elements are consistent with each other. Unless otherwise specified, we use 90\\% confidence error regions. ", "conclusions": "Based on the temperature structure studied in Paper I, abundance profiles of 7 elements of the ICM around M~87 are obtained using the deprojected spectra. We have discussed the use of one- and two-temperature models in the fit and the application of the MEKAL and APEC codes. Two temperature models are only important in the region, R$<2$ arcmin. The previous problems with an earlier version of the APEC code are now resolved in the present version and this code provides now better fitting solutions in general. In addition, using line ratio profiles of the projected and deprojected data, the abundance ratio profiles are obtained with smaller uncertainties, considering the temperature dependence of the line ratio, The main results obtained are as follows, \\begin{itemize} \\item Abundance profiles of 7 elements are obtained with high accuracy (e.g. $\\delta$Fe$\\sim\\delta$Si$\\sim$5\\%, $\\delta$O$\\sim$10\\%). \\item The Si and Fe abundance profiles have steep gradients at $>2'$ with a Fe/Si ratio of $0.9\\pm0.1$ solar, and become constant within this radius at 1.5--1.7 solar. \\item The S/Si ratio is about 1 solar at $r<$ 4$'$ and decreases to $\\sim$ 0.7 solar at $r>10'$. \\item The Ar/Si and Ca/Si are about 0.8 solar and 1.5 solar, respectively, although errors are relatively large. \\item The O and Mg abundances are smaller than the abundances of Fe and the intermediate elements. The O/Si ratio is less than half solar at the center and increases with radius. The Mg/O ratio is 1.25 solar and consistent with no radial gradients at least at $r>0.5'$. \\item The observed abundance pattern among O, Mg, Si, Ca and Fe of the ICM is located at an extension of that of Galactic stars. Therefore, the abundance pattern of the ICM is not peculiar and it should strongly constrain the products of SN Ia and SN II of early-type and late-type galaxies. \\item The Si/O/Fe diagnostics shows large Si contributions by SN Ia, which may reflect the observational finding that SN Ia in old stellar systems are fainter. \\item The observed Mg abundance of the ICM is consistent with the stellar metallicity profile from the Mg$_2$ index at the same radius. This result is consistent with stellar mass loss as the source of the gas in the very central region of M~87. \\item The central abundance can be explained with the observed SN Ia rate and SN Ia model yields. \\item The different radial profiles between Si and S suggest that the S/Si ratio synthesized from SN II is much smaller than the solar ratio. Then, the S/Si ratio may be a better indicator of the relative contribution from SN Ia and SN II, when O and Mg abundances cannot be observed. \\end{itemize} We are actually very fortunate to have M~87 and the Virgo cluster as the closest galaxy cluster in our neighborhood, since it offers an ICM in just this low temperature range where the spectra are richest in spectral lines for this type of abundance diagnostics. Therefore it would be worthwhile to use this unique case for even deeper observations and more detailed investigations by X-ray spectroscopy in the future." }, "0212/astro-ph0212296_arXiv.txt": { "abstract": "This paper describes a series of 3D simulations of shallow inefficient convection in the outer layers of the Sun. The computational domain is a closed box containing the convection-radiation transition layer, located at the top of the solar convection zone. The most salient features of the simulations are that: i)The position of the lower boundary can have a major effect on the characteristics of solar surface convection (thermal structure, kinetic energy and turbulent pressure). ii)The width of the box has only a minor effect on the thermal structure, but a more significant effect on the dynamics (rms velocities). iii)Between the surface and a depth of 1 Mm, even though the density and pressure increase by an order of magnitude, the vertical correlation length of vertical velocity is always close to 600 km. iv) In this region the vertical velocity cannot be scaled by the pressure or the density scale height. This casts doubt on the applicability of the mixing length theory, not only in the superadiabatic layer, but also in the adjacent underlying layers. v) The final statistically steady state is not strictly dependent on the initial atmospheric stratification. ", "introduction": "It is now just possible to perform physically realistic 3D simulations of the surface layers of the Sun which take into account the complex interaction between radiative and convective energy transports (Stein \\& Nordlund 1998, Kim \\& Chan 1998 hereafter denoted SN and KC, respectively, Stein \\& Nordlund 2000). There have also been a number of 2D simulations of the surface layers (Steffen et al. 1990 and Gadun et al. 2000). To model solar convection realistically, requires a realistic equation of state, realistic opacities and proper treatment of radiative transfer in the shallow layers. SN and KC are the two most freqently cited 3D models of this type of stratified convection. As their approaches differ considerably, both in numerical methods and in input model physics, it is important to find out, what particular aspect of the respective simulations, caused their results to be different. The aim of this paper is to describe solar surface convection which not only has the KC realistic physics, but also has a realistic (as is presently possible) geometry. To achieve this we had to increase both the depth and width of the original KC model, until the side walls and the horizontal boundaries had only a minimal effect on the flow. The simulations themselves model a region less than a few thousand kilometers in depth, as measured inwards from the visible solar surface. In the deep regions of the solar convection zone, the turbulent velocity is subsonic and the superadiabaticity is close to zero. However, within a few hundred kilometers of the solar surface, the convective flux starts to decrease. As the total flux is constant, the radiative flux must increase to offset the drop in the convective flux. This is achieved by a rise in the local temperature gradient $\\na$. This region of inefficient convection is called the superadiabatic layer (SAL). In the SAL, the superadiabaticity $\\na -\\na_{\\rm ad}$ is positive and of order unity (Demarque, Guenther \\& Kim 1997, 1999). As the buoyancy force is large in the SAL, the region is characterised by highly turbulent velocities and large relative thermodynamic fluctuations. The turbulent velocity also gives rise to a significant turbulent pressure (approximately 15 \\% of the gas pressure). This moves out the convection surface, modifying the SAL and the stratification. In one-dimensional (1D) models of the solar convection zone based on the mixing length theory (MLT)(B\\\"ohm-Vitense 1958), the velocity is set to zero above the convection boundary. However, three-dimensional (3D) numerical simulations described in Cattaneo et al. (1990), have shown that just above the top of the convection layer the turbulent velocities are still high. There are several motivations for such simulations among stellar physicists. One is to understand the effects of turbulence on the structure of the outer solar layers as revealed by the observed frequencies of solar {\\it p}-modes. Another is to explain the excitation mechanism of the {\\it p}-modes. Still another is to derive more realistic surface boundaries for stars with convection zones from first physical principles, free of the arbitrary assumptions of the mixing length theory. And finally, such simulations may be of help in investigations of the solar dynamo. Over the last few years, the science of helioseismology has provided some very precise measurements of the {\\it p}-mode oscillation frequencies (to within one part in a thousand) in the surface layers of the Sun \\cite{harvey1996}. The discrepancy between the observed {\\it p}-mode frequencies and those calculated from solar models, is known to be primarily due to the approximations made in modelling the surface layers, where turbulent and radiative losses are significant (Balmforth 1992; Guenther1994). In the 3D simulation described in KC, the turbulent pressure pushed the convective boundary radially outwards from its original position (that was computed using the MLT). This situation was mimicked in the 1D solar model by tweaking the opacity in the outer layers \\cite{demarque1999}. This resulted in improved {\\it p}-mode frequencies for low and intermediate degrees. However, Demarque et al. also showed that the mixing length prescription of Canuto \\& Mazzitelli (1991), which had a completely different SAL structure than KC, could produce a similar improvement of the {\\it p}-mode frequencies for the same $l$-values. Full details of the different approaches, the contrasting SAL structures and the resulting {\\it p}-modes, are described in Demarque et al. (1997, 1999). Later, Rosenthal et al (1999) used another approach to compute the {\\it p}-mode frequencies. These authors patched the mean stratification (horizontal average) of a 3D hydrodynamical simulation, onto a 1D MLT envelope model. In order to get a smooth 1D model, they adjusted the mixing length and the amplitude of the turbulent pressure to match the 3D simulation. The computed frequencies were closer to the observed frequencies than if a standard solar model is used, thus showing the importance of including turbulence in modeling the outer layers of the Sun. More recently, Li et al. (2002) found similar results to Rosenthal et al. by inserting the averaged turbulent pressure and turbulent kinetic energy directly into the 1D stellar model. Their method is applied to two of the simulations described in this paper (see section 4.3). As the turbulent kinetic energy and turbulent pressure were very small at the base of the 3D model, they were set to zero in regions of the 1D stellar model that lay below the 3D model domain. This required the usual adjustment of the mixing length parameter and the helium abundance to calibrate the perturbed stellar model. No other adjustable parameters were employed. The improvement in the eigenfrequencies was found to be primarily due to the inclusion of turbulent kinetic energy flux in the 1D stellar model. After extensive testing, we found that our simulations are in good agreement with other numerical studies of the surface layers (e.g. Rosenthal et al. 1999, Asplund et al. 2000). In addition, by incorporating the computed 3D turbulence into a 1D stellar model, we were able to produce solar surface eigenfrequencies ({\\it p}-modes) that were very close to the observed frequencies. As our eventual goal is to simulate the SAL in stars other than the Sun, it is vital to be sure we are modelling the Sun as correctly as possible. ", "conclusions": "As we intend to use our code to model the SAL in other stars, this paper is an important benchmark for future studies. From these simulations of the Sun, we found that: \\begin{enumerate} \\item The impenetrable lower boundary needs to be far enough away from the SAL so that by the time the fluid reaches the boundary, the velocities have become both weak and uncorrelated from velocities in the SAL. If the lower boundary is too close to the SAL, the kinetic energy will be overestimated. \\item The horizontal cross section needs to be large enough so that the side-walls do not restrict the movement of the granules. If the box width is too small then the kinetic energy will be underestimated. \\item There is a region close to the surface in which the vertical correlation length remains constant, even though the density and pressure vary by an order of magnitude. \\item In that region the mixing length theory, which assumes the correlation length to be a constant multiple of the pressure scale height, will not work. \\item The final equilibrium state is not strictly dependent on the initial model atmosphere (see appendix, section \\ref{initial}). \\end{enumerate} While these results have been found in a simulation of the Sun, it is reasonable to assume that similar criteria would apply to the convection-radiation transition layers in other stars. The effect of the boundaries should certainly be considered when simulating other convection-radiation layers. The correlation length (half-width) seems to be a very robust feature of the solar granules and could easily be measured in other computations. For example, in a recent proceedings (Robinson et al 2002) we describe the application of this model to the Sun at the sub-giant and the start of the red giant branch. Preliminary results indicate that, near the surface of each convection zone, the ratio of the half-width to the stellar radius depends directly on the surface gravity. \\vspace{3mm} This research is supported in part by NASA grant NAG5-8406 (FJR, PD, SS). YCK is supported by a Department of Astronomy, Yonsei University grant (2001-1-0134). DBG's research is supported in part by a grant from NSERC of Canada. We also would like to acknowledge computer support from the Centre for High Performance Computing at Saint Mary's University in Canada. Finally, we thank H.-G. Ludwig for helpful comments." }, "0212/hep-ph0212240_arXiv.txt": { "abstract": "In the light of KamLAND data just released, we reanalyze and update the constraints on neutrino masses and mixing parameters, the most general ones that can be derived in three-flavor mixing scheme of neutrinos with use of the bounds imposed by neutrinoless double beta decay search and reactor experiments. We point out that with KamLAND data and assuming Majorana neutrinos one can derive, for the first time, an upper bound on neutrino contribution to the cosmological $\\Omega$ parameter, $\\Omega_{\\nu} \\leq 0.070 h^{-2}$, by using the current upper bound on mass parameters obtained by Heidelberg-Moscow group, $\\langle m \\rangle_{\\beta \\beta} < 0.35$ eV (90 \\% CL). If the bound is tighten to $\\langle m \\rangle_{\\beta \\beta} < 0.1$ eV by future experiments, it would lead to a far severer bound $\\Omega_{\\nu} \\lsim 0.01 h^{-2}$. ", "introduction": "The solar neutrino problem is finally solved by the KamLAND experiment \\cite {KamLAND}, which observed a clear deficit of about 40 \\% in $\\bar{\\nu}_e$ flux from reactors located in all over Japan. It pin-points the Large-Mixing-Angle (LMA) region as the unique solution of the solar neutrino problem based on the MSW matter enhanced neutrino flavor transformation \\cite{MSW}, excluding the remaining LOW and the vacuum (VAC) solutions. While the LMA solution was preferred over others on statistical ground in combined analyses of solar neutrino data \\cite{solar} it is by no means true that it was selected out as the unique solution. It is because the values of $\\chi^2$ of the LOW and the VAC solutions, $\\sim$ unity per degrees of freedom\\cite{solaranalysis}, were acceptable and hence it was not possible with only solar neutrino data to uniquely idetify the LMA solution. It implies, first of all, that the three-flavor mixing scheme of neutrinos had further support by the experiments, and the structure of lepton flavor mixing is established together with the existing evidences which come from the atmospheric \\cite{SKatm} and the long-baseline accelerator experiments \\cite{K2K}. Given our above understanding of the KamLAND result it also means that the experiment gave the first direct proof of (almost) pure vacuum neutrino oscillation, the fascinating phenomenon first predicted by Maki, Nakagawa, and Sakata \\cite{MNS}, and first applied to the solar neutrino problem by Pontecorvo \\cite{pontecorvo}. The resolution of the solar neutrino problem implies that we now know within certain uncertainties the values of $\\Delta m^2_{12}$ and $\\sin^2{2\\theta_{12}}$. It is an urgent task to uncover the all possible implications of the far more constrained values of these mixing parameters. We address in this paper the impact of the KamLAND result on masses and possible mass patterns of neutrinos. We re-analyze the constraints on neutrino masses and mixing parameters imposed by neutrinoless double beta decay experiments in the light of the first results of KamLAND experiment under the assumption of Majorana neutrinos. See ref.~\\cite{vogel} for the present status of the double beta decay experiments. The constraints we will derive \\cite {mina-hiro02} are the maximal ones that can be derived in a model-independent way (and assuming ignorance of the CP violating phases) in a general framework of three-flavor mixing scheme of neutrinos. It utilizes the bounds imposed by neutrinoless double beta decay search and the CHOOZ reactor experiment \\cite{CHOOZ}. A natural question would be \"what is the impact of the KamLAND data on the double beta decay bound on neutrino mass and mixing parameters?\". The answer is that it allows us to derive, for the first time, an upper bound on the neutrino contribution to the cosmological $\\Omega$ parameter, the energy density normalized by the critical density in the present universe. It is not because the parameter region for the LMA solution becomes narrower (in fact, the region for $\\theta_{12}$ is virtually identical with that before KamLAND), but because the LOW and the VAC solutions which allow maximal or almost maximal mixing are eliminated by the KamLAND data at 99.95~\\% CL \\cite{KamLAND}. ", "conclusions": "In the light of the KamLAND data we reanalyzed the constraint on neutrino masses and mixing imposed by neutrinoless double beta decay search and the CHOOZ reactor experiment. We have shown that by now the absolute mass scale for neutrinos is bounded from above by the ``conspiracy'' of KamLAND and double beta decay experiments. This conclusion and our whole analysis in this paper are valid under the assumption that neutrinos are Majorana particles. In closer detail, allowed regions on a plane spanned by the lowest neutrino mass versus the solar mixing angle $\\theta_{12}$ were obtained by using $\\mbb^\\ma$ ($\\mbb^\\mi$), the experimental upper (lower) bound obtained and to be obtained in the ongoing and the future double beta decay experiments. For given $\\theta_{12}$, these become constraints on neutrino mass, the lightest mass $m_l$ (or the heaviest one though we did not give them explicitly). Roughly speaking, $\\mbb^\\mi \\leq m_l \\leq 3 [6]\\times\\mbb^\\ma$ for the LMA best fit parameters and for the most conservative case in square parenthesis, respectively. It was made clear that the condition $|\\cos{2\\theta_{12}}| > t_\\CH^2 \\simeq 0.03$ was necessary for the upper bound on $m_l$ to exist. On the other hand, the condition $\\mbb^\\mi \\geq 0.0056\\,\\eV (0.048\\,\\eV)$ needs to be satisfied for the normal (inverted) mass hierarchy, for the lower bound on $m_l$ to exist. For example, $0.05\\,\\eV \\le \\mbb \\le 0.84\\,\\eV$ gives $0.05\\,\\eV (0.005\\,\\eV) \\leq m_l \\leq 2.5 [5.0]\\,\\eV$ for the normal (inverted) hierarchy. \\vskip0.5cm \\noindent {\\bf Note added}: While this paper was in the revision process, we became aware of the report by the Wilkinson Microwave Anisotropy Probe (WMAP) \\cite{WMAP} in which a severe constraint on omega parameter $\\Omega_{\\nu} h^2 < 0.0076$ (95 \\% CL) is placed. It means that double beta decay searches must have the sensitivity in the region $\\mbb \\lsim 0.1\\,\\eV$ to be competitive, as one can see from Fig.~2." }, "0212/astro-ph0212539_arXiv.txt": { "abstract": "Significant gravitational wave emission is expected from gamma-ray bursts arising from compact stellar mergers, and possibly also from bursts associated with fast-rotating massive stellar core collapses. These models have in common a high angular rotation rate, and observations provide evidence for jet collimation of the photon emission, with properties depending on the polar angle. Here we consider the gravitational wave emission and its polarization as a function of angle which is expected from such sources. We discuss possible correlations between the burst photon luminosity, or the delay between gravitational wave bursts and X-ray flashes, and the polarization degree of the gravitational waves. ", "introduction": "\\label{sec:intro} The observations of gamma-ray burst (GRB) afterglows at energies ranging from X-rays to radio have lead to an increased understanding of the possible geometry of the inferred relativistic outflow or ejecta (see van Paradijs, Kouveliotou \\& Wijers 2000 for a review; also Rhoads 1999; Sari, Piran \\& Halpern 1999). At least for the class of long bursts (durations $\\gtrsim$ 10 s) there is now significant evidence that the ejecta is collimated in a jet. The evidence for jets is based on a change of the GRB light curve time-dependence power law index, and there appears to be a correlation in the sense that bursts with the largest gamma-ray fluences have the narrowest implied opening angles. Frail et al. (2001), Piran et al. (2001) and Panaitescu \\& Kumar (2002) reported that the total gamma-ray energy release, after correcting for the collimation and distance determined by the afterglow observations, are narrowly clustered around $5 \\times 10^{50}$erg, and suggested that the broad distribution in fluence and luminosity for GRBs is largely the result of a wide variation of the opening angles. This result can be obtained assuming that the jet emission inside some angle $\\theta_j$ is approximately uniform and then drops off abruptly beyond that. However, Rossi, Lazzati \\& Rees (2002) and Zhang \\& M\\'{e}sz\\'{a}ros (2002) showed that the observations can also be interpreted in terms of an alternative model where the jet, rather than having a uniform profile out to some definite cone angle, has a universal angle-dependent beam pattern with a luminosity per unit solid angle which is maximal along the axis, and drops off gradually away from the axis. In this model, it is the difference of viewing angles $\\theta$ which causes a wide variation in the apparent luminosity of GRBs, $L \\propto \\theta^{-2}$. Gravitational waves (GW) are also expected from some types of GRB (e.g. Kobayashi \\& M\\'{e}sz\\'{a}ros 2002). The GW emissivity and its polarization are angle-dependent, and may in principle be measurable, depending on the signal to noise ratio and on the detector alignments. In this Letter we discuss the prospects of exploiting measurements of the gravitational polarization degree to obtain information on the nature and orientation of the GRB system, providing additional constraints on the luminosity of the bursts, and we mention possible implications for the interpretation of dark GRB and X-ray flashes. ", "conclusions": "" }, "0212/astro-ph0212013_arXiv.txt": { "abstract": "The observables in a strong gravitational lens are usually just the image positions and sometimes the flux ratios. We develop a new and simple algorithm which allows a set of models to be fitted exactly to the observations. Taking our cue from the strong body of evidence that early-type galaxies are close to isothermal, we assume that the lens is scale-free with a flat rotation curve. External shear can be easily included. Our algorithm allows full flexibility as regards the angular structure of the lensing potential. Importantly, all the free parameters enter linearly into the model and so {\\it the lens and flux ratio equations can always be solved by straightforward matrix inversion}. The models are only restricted by the fact that the surface mass density must be positive. We use this new algorithm to examine some of the claims made for anomalous flux ratios. It has been argued that such anomalies betray the presence of substantial amounts of substructure in the lensing galaxy. We demonstrate by explicit construction that some of the lens systems for which substructure has been claimed can be well-fit by smooth lens models. This is especially the case when the systematic errors in the flux ratios (caused by microlensing or differential extinction) are taken into account. However, there is certainly one system (B\\,1422+231) for which the existing smooth models are definitely inadequate and for which substructure may be implicated. Within a few tens of kpc of the lensing galaxy centre, dynamical friction and tidal disruption are known to be very efficient at dissolving any substructure. Very little substructure is projected within the Einstein radius. The numbers of strong lenses for which substructure is currently being claimed may be so large that this contradicts rather than supports cold dark matter theories. ", "introduction": "The fitting of models to observational data has always been a major concern in strong gravitational lensing (e.g., Schechter 2000). In most cases, the lens is only composed of 2 (a ``doublet'') or 4 (a ``quadruplet'') point-like images. For the doublets, the observable constraints are the four relative coordinates of the images with respect to the lensing galaxy, together with the one flux ratio of the first image to the second. For the quadruplets, this becomes eight relative coordinates and three flux ratios. Only for a handful of lens systems are time delays available. It therefore happens very frequently that lens models have more degrees of freedom than the number of constraining observations. In fact, the situation is often even worse than we have just described. Sometimes the centre of the lensing galaxy itself cannot be reliably identified. Sometimes a lens system is complicated by the possible effects of nearby bright galaxies. Very often, the flux ratios are untrustworthy, either because of differential extinction in the optical bands (e.g., Falco et al. 1999) or because of microlensing in the optical and radio (e.g., Irwin et al. 1989; Koopmans \\& de Bruyn 2000) or because of scintillation, scatter-broadening and free-free absorption in the radio (e.g., Patnaik et al. 1992, Jones et al. 1996, Winn, Rusin \\& Kochanek 2003). It is therefore already clear that considerable caution must be exercised in interpreting the results of fits to gravitational lens systems. The approach of modellers has been largely two-pronged. First, general non-parametric methods have been developed (e.g., Saha \\& Wiliams 1997). These have proved powerful in exploring the range of degeneracies in the lensing mass that can give rise to a particular image configuration. For example, in the case of PG\\,1115+080, Saha \\& Williams present three different models obeying the lensing constraints, but for which the lensing mass distribution resembles a face-on spiral, an edge-on disk or a flattened elliptical galaxy respectively. Second, many simple parametric models have been thoroughly explored, such as those based on elliptically stratified potentials (e.g., Witt 1996; Witt \\& Mao 1997) or densities (e.g., Kassiola \\& Kovner 1993; Mu{\\~n}oz, Kochanek \\& Keeton 2001). The advantage of this is that the models may already incorporate some of the known properties of nearby galaxies. However, this approach may also be dangerous because simple ansatze like elliptical potentials or surface mass densities can introduce unexpected properties. These properties may be so severe that, for example, the flux ratios may not be well fitted and wrong conclusions may be drawn. This can be seen most clearly in the case of elliptical potentials, in which there are strong constraints on the flux ratios (e.g., Witt \\& Mao 2000; Hunter \\& Evans 2001). All this attains added significance in the light of recent claims of evidence for substructure from ``anomalous flux ratios'' in strong lensing. Mao \\& Schneider (1998) were the first to point out that substructure may be needed to explain the flux ratios in some cases. The instance that they selected, the quadruplet B\\,1422+231, has three highly magnified bright images and one much fainter image. Three highly magnified images occur generically near a cusp, and a Taylor expansion gives a universal relationship that the sum of the fluxes of the two outer images should equal the flux of the middle image. This is strongly violated in B\\,1422+231 leaving substructure on top of the smooth model as the believable culprit. This result is supported by the detailed models of B\\,1422+231 by Bradac et al. (2002) which find that the discrepancy requires substructure on the mass scale $\\sim 10^6 \\msun$. Recently, Dalal \\& Kochanek (2002) looked at seven predominantly radio quadruplets and argued that the flux ratios were anomalous by comparison with those expected for simple isothermal lenses with external shear. They claimed that the anomalous flux ratios implied the existence of $\\sim 2$ per cent of the mass of the lensing galaxy in substructure. Metcalf \\& Zhao (2002) looked at five optical quadruplets and similarly claimed evidence for anomalous flux ratios on comparison with those expected for simple elliptical power-law potentials with shear. The problem with this procedure is, of course, that anomalous flux ratios may not be the result of substructure at all, but may simply reflect deficiencies in the modelling. This motivates us to introduce in sections 2 and 3 a new approach for fitting which can incorporate the flux ratios at outset and which can permit an arbitrary azimuthal dependence for the surface density. Importantly, all the free parameters enter linearly into the models and so {\\it the lens and flux ratio equations can always be solved by straightforward matrix inversion}. The models are only restricted by the fact that the surface mass density must be positive. This algorithm is used in section 4 to assess the evidence for anomalous flux ratios. Readers who are mainly interested in this application may skip section 3 entirely on the first reading. This section is rather mathematical and explicitly derives the linear equations for the parameters to be fitted. \\begin{figure*} \\epsfysize=7.5cm \\centerline{\\epsfbox{fig1.ps}} \\caption{The two plots show truncated Fourier series approximations to the equidensity contours of an exactly elliptical E3 (left panel) and an E7 (right) galaxy. For moderate flattenings such as E3, excellent results are obtained with only the first three non-vanishing terms in the expansion. Even for the most highly flattened configurations such as E7, the approximation becomes very accurate when the first seven non-vanishing terms are included. } \\label{fig:sample} \\end{figure*} ", "conclusions": "The main aim of this paper is to present a new, simple approach to fitting a model to the data on a gravitational lens. Given the image positions and the flux ratios (if available), a model that exactly fits that data can be constructed by a simple matrix inversion (preferably by singular value decomposition, available in standard numerical libraries). All the fitting parameters enter linearly into the equation. No complicated non-linear $\\chi^2$-fitting needs to be done. The lensing galaxy is always assumed to be scale-free with a flat rotation curve. There is already a substantial body of evidence from fitting of lenses that early-type galaxies have nearly isothermal profiles (Kochanek 1995; Mu{\\~n}oz et al. 2001; Cohn et al. 2001; Rusin et al. 2002). In particular, the absence of central images strongly constrains the lensing potential of early-type galaxies to be isothermal or steeper and the size of any core region to be small (e.g., Rusin \\& Ma 2001; Evans \\& Hunter 2002). There is both stellar dynamical (e.g., Gerhard et al. 2001) and X-ray (Fabbiano 1997) evidence that early-type galaxies have flat rotation curves out to at least 4 effective radii. Hence, our assumption of a flat rotation curve seems exactly what the data require. Unusually, our algorithm allows full flexibility as regards the angular structure of the lensing potential. Earlier fitting procedures have allowed the lensing potential to have different radial structure (for example, different power-law profiles), but usually only simple forms of angular structure (for example, constant external shear). In our models, the radial structure is always fixed as isothermal, but the shape of the density contours is completely arbitrary. The lens model has a flexible number of free parameters, and of course includes the isothermal elliptic density and potential models which have a distinguished history in gravitational lens modelling. The fit allows direct deduction of the mass contour of the lensing galaxy. Although we have presented examples based on quadruplet lens systems, the algorithm can be adapted for a two image or a higher image model. A higher image model might be needed, for example, in Q\\,0957+561, where 10 sub-image positions can be detected in the radio band. Another good application might be MG\\,0414+0534, where some substructure of the images are detected (cf. Trotter, Winn \\& Hewitt 2000 and their fitting approach). Both lenses seem heavily distorted by external shear. A shear term can be added to our algorithm. If the shear is known, then the lens and flux ratio equations remain linear. The flux ratios may enter directly into the fit depending on whether they are available or trustworthy. We stress that flux ratios often do not provide good model constraints. The reason for this is easy to understand. The flux ratios depend on the second derivatives of the lensing potential, whereas time delays and image positions are proportional to the potential and its first derivative respectively. Therefore, flux ratios are particularly sensitive to graininess in the gravitational potential. This often manifests itself as microlensing. The flux ratios are also affected by the uncertain differential extinction corrections that must be applied to each image. Radio and mid-infrared fluxes are generally more reliable than optical. However, effects such as scintillation, scatter-broadening and free-free absorption may affect the radio fluxes in some of the lenses. If flux ratios are incorporated into a fit, it is vital that there is a realistic treatment of the errors. Our fitting algorithm permits the construction of a whole class of degenerate models all of which can fit the image position and flux ratios exactly. In addition, the models are also degenerate in the time delay since the delay depends only on the distance of the image positions to the centre of the lensing galaxy (cf. Witt, Mao \\& Keeton 2000). Such degeneracy is easy to understand pictorially. Given a Fermat time delay surface, we need only keep the values, the derivatives and the second derivatives of the surface at the image positions fixed. We then have enormous freedom to move the surface (subject only to the constraints that no additional images are introduced and that no negative mass density is produced). We have used our new fitting algorithm to examine critically some of the claims made recently for anomalous flux ratios. The procedure used by both Dalal \\& Kochanek (2002) and Metcalf \\& Zhao (2002) was to show that a family of simple models did not reproduce the flux ratios. However, it does not follow from this that substructure is necessary; it may just be that the simple model did not have enough flexibility to provide a good match. For example, of the five lenses studied by Metcalf \\& Zhao (2002), they themselves concluded that one (MG\\,0414+0534) could be satisfactorily explained by a smooth model. In this paper, we have demonstrated that the data on two others (PG\\,1115+080, Q\\,2237+030) are consistent with smooth galaxy-like models, especially when a realistic treatment of the errors in the flux ratios is incorporated. We note that the fraction of mass in substructure expected in galaxy haloes is very small ($\\lta 5$ per cent) and it occurs overwhelmingly in the outlying portions (e.g., Moore et al. 1999; Ghigna et al. 2000). Substructure evolves as it is subjected to tides, impulsive collisions and dynamical friction. Tidal disruption becomes important as soon as the mean density of the galaxy is equal to the density of the substructure. Similarly, the dynamical friction timescale scales with the square of the galactocentric radius (see e.g., Binney \\& Tremaine 1987). So, both tides and dynamical friction are efficient at erasing substructure in the inner parts. This effect is referred to as ``anti-biasing'' by Ghigna et al. (2000). So, on dynamical grounds, little substructure is projected within the Einstein radius. Taking the example of PG\\,1115+080, the projected Einstein radius is just $\\sim 3.6$ kpc. The fraction of mass in substructure projected within a cylinder of radius $\\sim 3.6$ kpc is clearly much lower than the global fraction of $5$ per cent, which pertains to the entire dark halo of total extent $\\sim 200$ kpc. It is crucial that lensing calculations do not assume an everywhere uniform fraction of substructure in the halo, as this does not take into account the ``anti-biased'' spatial distribution of substructure and therefore necessarily over-emphasises the importance of the effects of substructure on flux ratios. Notice that an interesting consequence of the spatial distribution is that anomalous flux ratios are more likely to occur for lenses with larger angular separation, as these have larger Einstein radii. The real question at issue is the following. Suppose a simple lens model (such as a simple isothermal ellipsoid plus shear) does not adequately fit the data on positions and flux ratios. What can be legitimately deduced? The difficulty is that there are many modifications of the simple model that remove the discrepancy. One of these is substructure, as pointed out by Dalal \\& Kochanek and Metcalf \\& Zhao. As shown in this paper, another is higher order multipoles in the lensing mass, such as diskiness, boxiness, lopsidedness and barredness (see also M\\\"oller, Hewett \\& Blain 2003, who make a similar point). It is crucial to develop techniques to distinguish between higher order quadrupoles on the one hand and substructure on the other. From our modelling, we tend to agree that the substructure candidate B\\,1422+231 originally pointed out by Mao \\& Schneider (1998) is strong. Using a novel application of the cusp relation, Keeton, Gaudi \\& Petters (2002) have argued that B\\,2045+265 and RX J\\,0911+0551 may be two further good candidates. It is an outstanding problem to predict -- for different cosmologies -- how many quadruplets may have anomalous flux ratios. Accurate calculations will become possible only when distributions of mass and position of substructure become available from high resolution simulations. It will be interesting to see whether the numbers of lenses for which substructure is currently being claimed are compatible with cold dark matter theories." }, "0212/astro-ph0212155_arXiv.txt": { "abstract": "{Compressible turbulence, especially the magnetized version of it, traditionally has a bad reputation with researchers. However, recent progress in theoretical understanding of incompressible MHD as well as that in computational capabilities enabled researchers to obtain scaling relations for compressible MHD turbulence. We discuss scalings of Alfven, fast, and slow modes in both magnetically dominated (low $\\beta$) and gas pressure dominated (high $\\beta$) plasmas. We also show that the new regime of MHD turbulence below viscous cutoff reported earlier for incompressible flows persists for compressible turbulence. Our recent results show that this leads to density fluctuations. New understanding of MHD turbulence is likely to influence many key astrophysical problems. } ", "introduction": " ", "conclusions": "In this paper we have discussed the new outlook onto compressible MHD turbulence. Contrary to common beliefs the compressible MHD turbulence does not present a complete mess, but demonstrates nice scaling relations for its modes. A peculiar feature is that those relations should be studied locally, i.e. in the frame related to the local magnetic field. However, such a system of reference is natural for many phenomena, e.g. for cosmic ray propagation. Recent application of the scalings obtained for compressible turbulence have shown that fundamental revisions are necessary for the field of high energy astrophysics. For instance, Yan \\& Lazarian (2002) demonstrated that fast modes dominate cosmic ray scattering even in spite of the fact that they are subjected to collisional and collisionless damping. This entails consequences for models of cosmic ray propagation, acceleration, elemental abundances etc. Advances in understanding of MHD turbulence have very broad astrophysical implications. The fields affected span from accretion disks and stars to the ISM and the intergalactic medium in clusters. Turbulence is known to hold the key to many astrophysical processes. It was considered too messy by many researchers who consciously or subconsciously tried to avoid dealing with it. Others, more brave types, used Kolmogorov scalings for compressible strongly magnetized gas, although they did understand that those relations could not be true. \\adjustfinalcols Recent research in the field provides the scaling relations and insights that will contribute to many areas of research." }, "0212/astro-ph0212363_arXiv.txt": { "abstract": "We determine the linear amplitude of mass fluctuations in the universe, $\\sigma_8$, from the abundance of massive clusters at redshifts $z=0.5-0.8$. The evolution of massive clusters depends exponentially on the amplitude of mass fluctuations and thus provides a powerful measure of this important cosmological parameter. The relatively high abundance of massive clusters observed at $z>0.5$, and the relatively slow evolution of their abundance with time, suggest a high amplitude of mass fluctuations: $\\sigma_8 =0.9\\pm 10$\\% for $\\Omega_m =0.4$, increasing slightly to $\\sigma_8 =0.95$ for $\\Omega_m =0.25$ and $\\sigma_8 =1.0$ for $\\Omega_m =0.1$ (flat CDM models). We use the cluster abundance observed at $z=0.5-0.8$ to derive a normalization relation from the high-redshift clusters, which is only weakly dependent on $\\Omega_m$: $\\sigma_8 \\Omega_m^{0.14}=0.78\\pm 0.08$. When combined with recent constraints from the present-day cluster mass function, $\\sigma_8 \\Omega_m^{0.6}=0.33\\pm 0.03$, we find $\\sigma_8 =0.98\\pm 0.1$ and $\\Omega_m =0.17\\pm 0.05$. Low $\\sigma_8$ values ($\\la 0.7$) are unlikely; they produce an order of magnitude fewer massive clusters than observed. ", "introduction": "\\label{sec:intro} The amplitude of mass fluctuations is a fundamental cosmological parameter that describes the normalization of the linear spectrum of mass fluctuations in the early universe -- the spectrum that seeded galaxy formation. The abundance of massive clusters depends exponentially on this parameter (assuming Gaussian initial fluctuations), because a high amplitude of mass fluctuations forms structure rapidly at early times, while a lower amplitude forms structure more slowly. The most massive systems ($\\sim 10^{15}h^{-1}M_\\odot$), which take the longest time to form and grow, did not exist at early times if the initial amplitude of mass fluctuations is low, but rather formed only recently. The amplitude parameter, denoted $\\sigma_8$ when referring to the {\\it rms} linear density fluctuation in spheres of radius $8h^{-1}$Mpc at $z=0$, is not easily determined since the mass distribution cannot be directly observed. As a result, this parameter is not yet accurately known. Recent observations suggest an amplitude that ranges in value from $\\sigma_8\\sim 0.7$ to a `high' value of $\\sigma_8\\sim 0.9-1$. While the difference in the reported values is only around 50\\%, the impact on structure formation and evolution is much larger, since the latter depends exponentially on $\\sigma_8^2$. The low amplitude values are suggested by current observations of the CMB spectrum of fluctuations \\citep{netterfield, sievers02, bondea02, ruhlea02}. However, this $\\sigma_8$ determination is degenerate with the unknown optical depth at reionization: if the optical depth were underestimated, then $\\sigma_8$ would be as well\\footnote{See note at end of paper}. Recent observations of the present-day cluster abundance as well as cosmic shear lensing measurements have also suggested that $\\sigma_8\\sim 0.7$ \\citep[e.g.][]{jarvis03, hamana02, sel01}. However, these measures provide a degenerate relation between the amplitude $\\sigma_8$ and the mass-density parameter $\\Omega_m$: $\\sigma_8 \\Omega_m^{0.6}\\approx 0.33$ \\citep{ike02, SDSSmf03, jarvis03, sel01}. The amplitude $\\sigma_8\\sim 0.7$ is implied only if $\\Omega_m \\sim 0.3$. If $\\Omega_m \\sim 0.2$, as is suggested by some observations \\citep[e.g.][]{CYE97, bah98, bah00, wklc01, ike02, rei02}, then the amplitude is $\\sigma_8\\sim 0.9-1$. Early results from the Sloan Digital Sky Survey (SDSS) cluster data \\citep{SDSSmf03} use the shape of the observed cluster mass function to break the degeneracy between the parameters and find $\\sigma_8 =0.9^{+0.3}_{-0.2}$ and $\\Omega_m =0.19^{+0.08}_{-0.07}$. Similar results have recently been obtained from the temperature function of a large sample of X-ray clusters \\citep{ike02, rei02}. Most of the recent cluster normalization observations, as well as cosmic shear lensing measurements suggest $\\sigma_8\\simeq 0.9-1$ if $\\Omega_m \\simeq 0.2$ \\citep[][and the references above]{jarvis03, hamana02}. Combining current CMB measurements with the SDSS cluster mass function yields intermediate values of $\\sigma_8 =0.76\\pm 0.09$ and $\\Omega_m =0.26^{+0.06}_{-0.07}$ \\citep{MBBS03}. The evolution of cluster abundance with time, especially for the most massive clusters, breaks the degeneracy between $\\sigma_8$ and $\\Omega_m$ \\citep[e.g.][]{PDJ89, ECF96, OB97, BFC97, CMYE97, bah98, DV99, Henry00}. This evolution depends strongly on $\\sigma_8$, and only weakly on $\\Omega_m$ or other parameters. The expected abundance of massive clusters at $z\\sim 0.5-1$ differs between Gaussian models with $\\sigma_8=0.6$ and $\\sigma_8=1$ by orders-of-magnitude, nearly independently of other parameters \\citep[e.g.]{FBC97}. Therefore, this method provides a uniquely powerful tool in estimating the amplitude $\\sigma_8$. In this paper we use the abundance of the most massive clusters observed at $z\\sim 0.5-0.8$ to place a strong limit on $\\sigma_8$. ", "conclusions": "\\label{sec:disc} We use the observed abundance of high-mass clusters of galaxies at $z=0.5-0.8$ to determine the linear amplitude of mass fluctuations, $\\sigma_8$. The cluster abundance depends exponentially on this amplitude, and only weakly on other parameters; it therefore provides a powerful method for measuring this important parameter. We show that the relatively high abundance of massive clusters observed at $z \\gtrsim 0.5$, as well as their relatively slow evolution with time, requires a high amplitude of mass fluctuations, $\\sigma_8 \\sim 0.9-1$. This conclusion is nearly independent of the exact value of $\\Omega_m$ (in the typical range of $\\Omega_m \\sim 0.1-0.4$). We use the observed abundance at $z\\gtrsim 0.5$ to determine a normalization relation from high redshift clusters. The relation depends only weakly on $\\Omega_m$: $\\sigma_8\\Omega_m^{0.14} = 0.78\\pm 0.08$; alternatively, a linear relation of the form $\\sigma_8 =1.03-0.3\\Omega_m$ ($\\pm$10\\%) provides a similarly good fit to the data. These fits illustrate that $\\sigma_8 \\gtrsim 0.8$ for any $\\Omega_m \\leq 0.4$. For the typical observationally suggested value of $\\Omega_m \\simeq 0.2-0.3$, the amplitude is $\\sigma_8 =0.95\\pm 0.1$. We emphasize that this high $\\sigma_8$ value indicated by the cluster abundance at high redshift is nearly independent of the exact value of $\\Omega_m$. We combine the high redshift constraint above with the independent normalization relation obtained from low redshift cluster abundance--- a relation that is steeper in $\\Omega_m$ ($\\sim \\Omega_m^{0.6}$; equation [\\ref{eqn:sdssfit}]). The combination breaks the degeneracy between the two parameters. We find $\\sigma_8 =0.98\\pm 0.1$ and $\\Omega_m =0.17\\pm 0.05$ (Figure \\ref{fig:hizont}; equation [\\ref{eqn:bestpar}]). The high value of $\\sigma_8$ required to explain the high abundance of the most massive clusters at $z \\gtrsim 0.5$ is consistent with the present day cluster mass function if the mass density parameter is low, $\\Omega_m \\sim 0.2$. If $\\Omega_m$=0.3, then the high redshift clusters still require a high amplitude ($\\sigma_8 =0.92 \\pm 0.1$), since this constraint is nearly independent of $\\Omega_m$; the low redshift cluster abundance is consistent with this value at the 2-sigma level. These results improve upon \\citet{bah98} by using improvements over the standard Press-Schechter formula (which does not accurately reproduce results from cosmological simulations at high redshift), allowing for changes in $h$ and $n$, and by using a more recent cluster normalization relation at low redshift. The current results yield slightly lower values for the cosmological parameters than the previous work (the latter suggested $\\sigma_8 =1.2\\pm 0.22$ and $\\Omega_m =0.2^{+0.13}_{-0.07}$ (68\\%) when using the most massive clusters) but are consistent with the new values within the error-bars \\citep{bah98,FBC97}. The excess CMB fluctuations detected on small scales by the CBI \\citep{mason02} and the BIMA \\citep{dawsea02} experiments implies (if correctly interpreted as being due to the S-Z effect from distant clusters) that $\\sigma_8 =1.04 \\pm 0.12$ \\citep[95\\%;][]{komsel02}. This is in excellent agreement with our current conclusions. We note, however, that this high amplitude is inconsistent with the lower value of $\\sigma_8\\approx 0.7$ suggested by current CMB data on large scales (which is degenerate with the unknown optical depth). Future CMB observations should clarify this current inconsistency. If massive clusters exist with relatively high abundance at high redshifts, as suggested by the data used here \\citep[as well as by deep X-ray surveys, e.g.][]{RBN02}, then these clusters should indeed produce the excess S-Z fluctuations observed by the CMB data. The relatively high abundance of massive clusters observed at $z\\gtrsim 0.5$ provides one of the strongest arguments for a high amplitude of mass fluctuations, $\\sigma_8\\simeq 1$. {\\bf Note added March 7, 2003:} The recent CMB anisotropy spectrum released by the WMAP team in February 2003 nicely confirms the results presented here. The constraint from the CMB alone is $\\sigma_8 =0.9\\pm 0.1$ \\citep{SpergWMAP}, in full agreement with the current high redshift cluster constraint." }, "0212/astro-ph0212424_arXiv.txt": { "abstract": "{ We describe an automatic procedure for determining abundances from high resolution spectra. Such procedures are becoming increasingly important as large amounts of data are delivered from 8m telescopes and their high-multiplexing fiber facilities, such as FLAMES on ESO-VLT. The present procedure is specifically targeted for the analysis of spectra of giants in the Sgr dSph; however, the procedure may be, in principle, tailored to analyse stars of any type. Emphasis is placed on the algorithms and on the stability of the method; the external accuracy rests, ultimately, on the reliability of the theoretical models (model-atmospheres, synthetic spectra) used to interpret the data. Comparison of the results of the procedure with the results of a traditional analysis for 12 Sgr giants shows that abundances accurate at the level of 0.2 dex, comparable with that of traditional analysis of the same spectra, may be derived in a fast and efficient way. Such automatic procedures are not meant to replace the traditional abundance analysis, but as an aid to extract rapidly a good deal of the information contained in the spectra. ", "introduction": "In recent years considerable attention has been devoted to full or partial automation of the process of abundance determination from high resolution spectra \\citep{Katz98,KatzT,EN02,EN02b}. One of the main thrusts behind these attempts is the increasingly large amount of data delivered by modern instrumentation. It is well known that astronomical archives are full of good quality high resolution spectra which have not been analysed, or only partially analysed, due to lack of manpower. In spite of the complexity of data reduction, this is not the bottleneck, thanks to the efficient software and instrument-dedicated pipelines that are available. The real bottleneck is the data analysis which, for abundances, is still done more or less in the same way as twenty years ago. The situation is going to become even more critical as high-multiplex instruments, such as FLAMES on ESO-VLT \\citep{Pasquini}, become fully operative. In the last years we have devoted special interest to the determination of abundances in giants of the Sgr dSph \\citep{B99,bonivlt,B00}. Such an astrophysical problem is ideal for the capabilities of FLAMES. It has also the advantage that two of the key parameters in the interpretation of stellar spectra, effective temperature and surface gravity, may be conveniently constrained. If we pick stars of roughly the same apparent magnitude, if they belong to Sgr, they will have the same luminosity and therefore surface gravity. At a given luminosity the RGB of Sgr spans a limited range in effective temperature, in fact less than 1000 K, and in the case of our sample less than 250 K. We had already attempted to develop a procedure to analyse the low resolution spectra which we obtained from EMMI-NTT \\citep{B99,bonivlt}, however the procedure, based on spectral indices, provided unsatisfactory results, essentially because of the combination of low resolution and low S/N ratios. Furthermore it was apparent that at low resolution we had no handle on the microturbulent velocity, and since the abundances relied only on strong lines (the only ones available at low resolution, whichever the S/N ratio), the result was strongly dependent on the unknown microturbulent velocity. Having in mind the future use of FLAMES and having available a few UVES spectra, obtained in slit-mode, we decided to concentrate on a procedure capable of analysing spectra from UVES and Giraffe. We have developed a procedure which is very efficient and stable, at least on the real UVES spectra. In spite of the fact that it is highly targeted (it will deal only with stars of a given luminosity and a limited range of effective temperatures), it has been written in such a way that it may be modified to deal with other types of stars. In this paper we describe the procedure placing our emphasis on the algorithms and on the stability of the method. The procedure rests on synthetic spectra computed from 1D LTE model atmospheres. In this paper we do not question the reliability of the input synthetic spectra, since it is straightforward to replace the existing grid with a better one, when available. \\begin{table} \\caption{Algorithm meta-code} \\label{algorithm} \\begin{center} \\begin{tabular}{lll} \\hline \\\\ \\\\ BEGIN &\\\\ & $\\xi$;\\\\ && pseudo-normalize;\\\\ && find [Fe/H] for each FeI feature;\\\\ && find slope A(FeI) vs. EW;\\\\ && if slope$<$ threshold, go to $\\alpha$;\\\\ && find a $\\xi$ to make slope smaller;\\\\ & goto $\\xi$;\\\\ & $\\alpha$;\\\\ && find [Mg/H] for each Mg I feature;\\\\ && find [Ca/H] for each Ca I feature;\\\\ && [$\\alpha$/Fe] = mean of [Mg/Fe] and [Ca/Fe];\\\\ && if $\\Delta$[$\\alpha$/Fe] $<$ threshold1 goto END;\\\\ & goto $\\xi$;\\\\ END \\\\ \\\\ \\hline \\\\ \\end{tabular} \\end{center} \\end{table} \\begin{figure} \\centering \\resizebox{\\hsize}{!}{\\includegraphics[clip=true]{histomet.eps}} \\caption{Histogram of the derived [Fe/H] for Monte Carlo simulations with different S/N ratios and a resolving power of 7 kms$^{-1}$} \\label{histo} \\end{figure} \\begin{figure} \\centering \\resizebox{\\hsize}{!}{\\includegraphics[clip=true]{fig_mc.eps}} \\caption{ Monte Carlo simulations corresponding to a resolving power of 7 kms$^{-1}$: [Fe/H], [$\\alpha$/Fe] and microturbulence velocity as a function of S/N for input spectrum at $\\xi =1.$Km/s, [$\\alpha $/Fe]=0.4 and [Fe/H]=--0.5 on the left panel and [Fe/H]=--1.5 on the right panel. For both the [Fe/H] vs S/N plots the smaller error bars correspond to Monte Carlo simulation dispersion, the bigger one to the [Fe/H] dispersion over the all Fe\\,\\textsc{i} features.} \\label{snplot} \\end{figure} \\begin{figure*} \\centering \\resizebox{16cm}{!}{\\includegraphics[clip=true]{code_vs_trad.eps}} \\caption{Comparison of [Fe/H], [$\\alpha$/Fe] and $\\xi$ from the traditional analysis and the automatic analysis for the 12 stars of Sgr observed with UVES. The left panels display the results from the UVES spectra, i.e. at a resolving power of $\\sim 7\\rm kms^{-1}$; the right panels display the results from the UVES spectra convolved with a gaussian profile, obtaining a resolving power of $\\sim 20 \\rm kms^{-1}$. The two points, in each of the eight panels, shown as crossed squares, identify the two stars for which the log g adopted in the traditional analysis is not 2.5.} \\label{conf} \\end{figure*} \\begin{figure} \\centering \\resizebox{8.5cm}{!}{\\includegraphics[clip=true]{pl_br7_br20.eps}} \\caption{Comparison of [Fe/H], [$\\alpha $/Fe] and $\\xi$ obtained for the 12 Sgr giants observed with UVES directly from the UVES spectra (resolving power $\\sim \\rm 7 kms^{-1}$) and UVES spectra broadened to a resolving power of $\\sim \\rm 20kms^{-1} $.} \\label{br7_20} \\end{figure} ", "conclusions": "" }, "0212/astro-ph0212048_arXiv.txt": { "abstract": "We present an analysis method that allows us to estimate the Galactic formation of radio pulsar populations based on their observed properties and our understanding of survey selection effects. More importantly, this method allows us to assign a statistical significance to such rate estimates and calculate the allowed ranges of values at various confidence levels. Here, we apply the method to the question of the double neutron star (NS--NS) coalescence rate using the current observed sample, and we find calculate the most likely value for the total Galactic coalescence rate to lie in the range $3-22$ Myr$^{-1}$, for different pulsar population models. The corresponding range of expected detection rates of NS--NS inspiral are $(1-9) \\times 10^{-3}$ yr$^{-1}$ for the initial LIGO, and $6-50$ yr$^{-1}$ for the advanced LIGO. Based on this newly developed statistical method, we also calculate the probability distribution for the expected number of pulsars that could be observed by the Parkes Multibeam survey, when acceleration searches will alleviate the effects of Doppler smearing due to orbital motions. We suggest that the Parkes survey will probably detect $1-2$ new binary pulsars like PSRs~B1913+16 and/or B1534+12. ", "introduction": "The detection of the double neutron star (NS--NS) prototype PSR~B1913+16 as a binary pulsar (Hulse \\& Taylor 1975) and its orbital decay due to emission of gravitational waves have inspired a number of quantitative estimates of the coalescence rate, $\\cal{R}$, of NS--NS binaries (Clark et al.\\ 1979; Narayan et al.\\ 1991; Phinney 1991; Curran \\& Lorimer 1995). Significant interest derives from their importance as gravitational-wave sources for the upcoming ground-based laser interferometers (such as LIGO). We present a newly developed statistical analysis that allows the calculation of statistical confidence levels associated with rate estimates. The method can be applied to any radio pulsar population. Here, we consider PSR~B1913+16 (Hulse \\& Taylor 1975) and PSR~B1534+12 (Wolszczan 1991). For different assumed distributions of pulsar properties (luminosities, Galactic positions), we derive the probability distribution function of the total Galactic coalescence rate weighted by the two observed binary systems. The method involves the simulation of selection effects inherent in all relevant radio pulsar surveys and a Bayesian statistical analysis for the probability distribution of ${\\cal R}$. The small-number bias and the effect of the faint-end of the luminosity function, previously identified as the main sources of uncertainty in rate estimates (Kalogera et al.\\ 2001) are {\\it implicitly included} in this analysis. We extrapolate the Galactic rate to cover the detection volume of LIGO and estimate the most likely detection rates of NS--NS inspiral events for the initial and advanced LIGO. Details of this work are given in Kim et al.\\ (2003; hereafter KKL). In the second part of this paper, we modify our statistical method in a way that allows us to calculate the probability distribution for the number of pulsars that could be detected by the Parkes Multibeam survey (hereafter PMB survey; Lyne et al.\\ 2000; Manchester et al.\\ 2001) PMB, when the effects of Doppler smearing due to orbital motions are corrected with acceleration searches. ", "conclusions": "We have recently developed a new method for estimating the total number of pulsars in our Galaxy and have applied it to the calculation of the coalescence rate of double neutron star systems in the Galactic field (for more details see KKL). Here, we extend this method to obtain a prediction for the average number of observed pulsars that the PMB survey could detect when acceleration searches are used to correct for the Doppler smearing due to orbital motions. The modeling of pulsar survey selection effects is formulated in a ``forward'' way, by populating the Galaxy with model pulsar populations and calculating the likelihood of the real observed sample. This is in contrast to the ``inverse'' way of the calculation of scale factors used in previous studies. We note that this method could be further extended to account for distributions of pulsar populations in pulse periods, widths, and orbital periods. It is important to note that both our rate estimates and the predictions for detections from the PMB survey do not apply to binary pulsars that are significantly different from with such properties that are significantly different PSRs~B1913+16 and B1534+12 in terms of pulse shapes and orbital properties. Most importantly the method can be applied to any type of pulsar population with appropriate modifications of the modeling of survey selection effects. Currently we are working on assessing the contribution of double neutron stars formed in globular clusters as well as the formation rate of binary pulsars with white dwarf companions that are important for gravitational-wave detection by LISA, the space-based interferometer planned by NASA and ESA for the end of this decade." }, "0212/astro-ph0212562_arXiv.txt": { "abstract": "We have determined the composite luminosity function (LF) for galaxies in 60 clusters from the 2dF Galaxy Redshift Survey. The LF spans the range $-22.510^{19}$ eV) energies have been recently proved to be a new powerful amplifier in Neutrino Astronomy \\cite{Fargion et all 1999}, \\cite{Fargion 2000-2002},\\cite{Bertou et all 2002},\\cite{Hou Huang 2002},\\cite{Feng et al 2002}. This new Neutrino $\\tau$ detector will be (at least) complementary to present and future, lower energy, $\\nu$ underground $km^3$ telescope projects (from AMANDA,Baikal, ANTARES, NESTOR, NEMO, IceCube). In particular Horizontal Tau Air shower may be naturally originated by UHE $\\nu_{\\tau}$ at GZK energies crossing the thin Earth Crust at the Horizon showering far and high in the atmosphere \\cite{Fargion 2000-2002},\\cite{Fargion2001a}, \\cite{Fargion2001b},\\cite{Bertou et all 2002},\\cite{Feng et al 2002}. UHE $\\nu_{\\tau}$ are abundantly produced by flavour oscillation and mixing from muon (or electron) neutrinos, because of the large galactic and cosmic distances respect to the neutrino oscillation ones (for already known neutrino mass splitting). Therefore EUSO may observe many of the above behaviours and it may constrains among models and fluxes and it may also answer open standing questions. I will briefly enlist, in this first preliminary presentation, the main different signatures and rates of UHECR versus UHE $\\nu$ shower observable by EUSO at 10\\% duty cycle time within a 3 year record period, offering a first estimate of their signals. Part of the results on UHECR are probably well known, even here it is re-estimated. Part of the results, regarding the UPTAUs and HORTAUs, are new and they rule the UHE $\\nu$ Astronomy in EUSO. \\begin{figure}\\centering\\includegraphics[width=8cm]{Fig001HIAS.eps} \\vspace{-1.5cm} \\caption {A very schematic Horizontal High Altitude Shower (HIAS); its fan-like imprint is due to geo-magnetic bending of charged particles at high quota ($\\sim 44 km$). The Shower may point to an satellite as old gamma GRO-BATSE detectors or very recent Beppo-Sax,Integral, HETE, Chandra or future Agile and Swift ones. \\cite{Fargion 2000-2002},\\cite{Fargion2001a},\\cite{Fargion2001b}. The HIAS Showers is open and forked in five (or three or at least two main component): ($e^+,e^-,\\mu^+,\\mu^-, \\gamma $, or just positive-negative); these multi-finger tails may be seen as split tails by EUSO. } \\label{fig:fig1} \\vspace{-0.3cm} \\end{figure} \\begin{figure} \\vspace{- 0.2cm} \\centering\\includegraphics[width=8cm]{Fig002HORTAUS.eps} \\vspace{-1cm} \\caption { As above Horizontal Upward Tau Air-Shower (HORTAUS) originated by UHE neutrino skimming the Earth: fan-like jets due to geo-magnetic bending shower at high quota ($\\sim 23-40 km$): they may be pointing to an orbital satellite detector \\cite{Fargion 2000-2002}, \\cite{Fargion2001a}, \\cite{Fargion2001b}. The Shower tails may be also observable by EUSO just above it.} \\label{fig:fig2} \\end{figure} \\begin{figure} \\vspace{-0.5cm} \\centering\\includegraphics[width=8cm]{Fig003EusoUPTAUS.eps} \\caption {A very schematic Upward Tau Air-Shower (UPTAUs) and its open fan-like jets due to geo-magnetic bending at high quota ($\\sim 20-30 km$). The gamma Shower may be pointing to an orbital detector \\cite{Fargion 2000-2002}, \\cite{Fargion2001a}, \\cite{Fargion2001b}. Its vertical Shower tail may be spread by geo-magnetic field into a thin eight-shape beam observable by EUSO as a small blazing oval (few dot-pixels) aligned orthogonal to the local magnetic field .} \\label{fig:fig3} \\vspace{-0.9cm} \\end{figure} ", "conclusions": "Highest Energy Neutrino signals may be well observable by next generation satellite as EUSO: the main source of such neutrino traces are UPTAUs (Upward Tau blazing the telescope born in Earth Crust) and mainly HORTAUs (Horizontal Tau Air-Showers originated by an Earth-Skimming UHE $\\nu_{\\tau}$). These showers will be opened in a characteristic thin fan-jet ovals like the $8$-shape horizontal cosmic ray observed on Earth. The UPTAUs will arise mainly at PeV energies (because the Earth neutrino opacity at higher energies and because the shorter $\\tau$ boosted lenght , at lower energies)\\cite{Fargion 2000-2002}; UPTAUs will be detected as a thin stretched multi-pixel event by EUSO, whose orientation is polarized orthogonal to local geo-magnetic field. The EUSO sensibility (effective volume ($V_{eff}$$\\sim 0.1 km^3$) for 3 years of detection) will be deeper an order of magnitude below present AMANDA-Baikal bounds. Horizontal Tau Air-Shower at GZK energies will be better searched and revealed. They are originated along huge Volumes around the EUSO Area. Their horizontal skimming secondary $\\tau$ decay occur far away $\\geq 500$ km, at high altitude ($\\geq 20-40$ km) and it will give clear signals distinguished from downward horizontal UHECR. HORTAUs are grown by UHE neutrino interactions inside huge volumes ($V_{eff}$$\\geq 5130-6250 km^3$) respectively for incoming neutrino energy $E_{\\nu_{\\tau}}$ $\\simeq 10^{19}$ eV and $3 \\cdot10^{19}$ eV. To obtain these results we applied the procedure described in recent articles \\cite{Fargion 2002b},\\cite{Fargion 2002c},\\cite{Fargion 2002d}. As summirized in last Figures the expected UHE fluence $$\\Phi_{\\nu}\\simeq 10^{3} eV cm^{-2} s^{-1}$$ needed in most Z-Shower models (as well as in most topological relic scenario) to solve GZK puzzles, will lead to nearly a hundred of horizontal events a year comparable to UHECR ones. Even in the most conservative scenario where a minimal GZK-$\\nu$ fluence must take place (at least at $$\\Phi_{\\nu} \\simeq 10 eV cm^{-2} s^{-1}$$ ,just comparable to well observed Cosmic Ray fluence), a few or a ten of such UHE astrophysical neutrino must be observed (respectively at $10^{19}$ eV and $3 \\cdot10^{19}$ eV energy windows) during three year of EUSO data recording. To improve their visibility EUSO must, in our opinion one may:\\\\ a) Improve the fast pattern recognition of Horizontal Shower Tracks with their few distant dots with forking signature.\\\\ b) Enlarge the Telescope Radius to embrace also lower $10^{19}$ eV energy thresholds where UHE neutrino signals are enhanced.\\\\ c) Consider a detection at angular $\\Delta\\theta$ and at height $\\Delta h$ level within an accuracy $\\Delta\\theta \\leq 0.2^o$,$\\Delta h \\leq 2$ km.\\\\ Even all the above results have been derived carefully following \\cite{Fargion 2002b},\\cite{Fargion 2002c},\\cite{Fargion 2002d} in a minimal realistic framework they may be used within $10\\%$ nominal value due to the present uncertain in EUSO detection capabilities. \\subsection*{Acknowledgment} The author wish to thank Prof. Livio Scarsi for inspiring the present search as well as the EUSO collaboration for the exciting discussion during November workshop in Rome; the author thanks also C.Leto and P.G.De Sanctis Lucentini and M.Teshima for support and technical suggestions." }, "0212/astro-ph0212497_arXiv.txt": { "abstract": "We constrain the basic comological parameters using the first observations by the Very Small Array (VSA) in its extended configuration, together with existing cosmic microwave background data and other cosmological observations. We estimate cosmological parameters for four different models of increasing complexity. In each case, careful consideration is given to implied priors and the Bayesian evidence is calculated in order to perform model selection. We find that the data are most convincingly explained by a simple flat $\\Lambda\\rm{CDM}$ cosmology without tensor modes. In this case, combining just the VSA and COBE data sets yields the 68 per cent confidence intervals $\\Omega_{\\rm{b}}h^2=0.034 ^{+0.007} _{-0.007}$, $\\Omega_{\\rm{dm}}h^2=0.18 ^{+0.06}_{-0.04}$, $h=0.72^{+0.15}_{-0.13} $, $n_s=1.07 ^{+0.06 }_{-0.06}$ and $\\sigma_8=1.17 ^{ +0.25 }_{ -0.20}$. The most general model considered includes spatial curvature, tensor modes, massive neutrinos and a parameterised equation of state for the dark energy. In this case, by combining all recent cosmological data, we find, in particular, 95 percent limit on the tensor-to-scalar ratio $R < 0.63$ and on the fraction of massive neutrinos $f_\\nu < 0.11$; we also obtain the 68 per cent confidence interval $w=-1.06^{+0.20}_{-0.25}$ on the equation of state of dark energy. ", "introduction": "In the past two years, a number of experiments have produced accurate measurements of the power spectrum of anisotropies in the cosmic microwave background (CMB) radiation on a range of angular scales (Hanany et al. 2002; Netterfield et al. 2002; Halverson et al. 2002; Sievers et al. 2002; Benoit et al. 2002). These data, together with other cosmological observations, have been used to place increasingly tight constraints on the values of cosmological parameters in current models of the formation and evolution of structure in the Universe. In this letter, we repeat this process with the inclusion of the latest observations from the Very Small Array (VSA) in its extended configuration. Results from the VSA in its compact configuration have already been presented in Watson et al. (2002), Taylor et al. (2002), Scott et al. (2002) and Rubi\\~no-Martin et al. (2002) (hereafter Papers I - IV). In Grainge et al. (2002, hereafter Paper V) these data are combined with the new extended configuration observations to produce a combined power spectrum with 16 spectral bins spanning the range $\\ell=160-1400$. This joint set of observed band-powers provides powerful new constraints on cosmological parameters. In this letter we extend the traditional likelihood approach of previous analyses to a fully Bayesian treatment, including careful consideration of our knowledge of cosmological parameters prior to the inclusion of any data, and the calculation of Bayesian evidences to perform model comparisons. \\begin{table} \\begin{center} \\caption{The priors assumed for the basic parameters common to all four cosmological models under consideration. The notation $(a,b)$ for parameter $x$ denotes a top-hat prior in the range $a