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By means of 3D hydrodynamical simulations, in a separate paper we have discussed the properties of non-axisymmetric density wave trains in the outermost regions of galaxy disks, based on the picture that self-excited global spiral modes in the bright optical stellar disk are accompanied by low-amplitude short trailing wave signals outside corotation; in the gas, such wave trains can penetrate through the outer Lindblad resonance and propagate outwards, forming prominent spiral patterns. In this paper we present the synthetic 21~cm velocity maps expected from simulated models of the outer gaseous disk, focusing on the case when the disk is dominated by a two-armed spiral pattern, but considering also other more complex situations. We discuss some aspects of the spiral pattern in the gaseous periphery of galaxy disks noted in our simulations that might be interesting to compare with specific observed cases., Comment: 14 pages, 7 figures, accepted for publication in Journal of Plasma Physics

Deep HI observations of the outer parts of disc galaxies demonstrate the frequent presence of extended, well-developed spiral arms far beyond the optical radius. To understand the nature and the origin of such outer spiral structure, we investigate the propagation in the outer gaseous disc of large-scale spiral waves excited in the bright optical disc. Using hydrodynamical simulations, we show that non-axisymmetric density waves, penetrating in the gas through the outer Lindblad resonance, can exhibit relatively regular spiral structures outside the bright optical stellar disc. For low-amplitude structures, the results of numerical simulations match the predictions of a simple WKB linear theory. The amplitude of spiral structure increases rapidly with radius. Beyond $\approx 2$ optical radii, spirals become nonlinear (the linear theory becomes quantitatively and qualitatively inadequate) and unstable to Kelvin-Helmholtz instability. In numerical simulations, in models for which gas is available very far out, spiral arms can extend out to 25 disc scale-lengths. A comparison between the properties of the models we have investigated and the observed properties of individual galaxies may shed light into the problem of the amount and distribution of dark matter in the outer halo., Comment: 12 pages, 13 figures (accepted for publication in MNRAS)

Internal rotation is considered to play a major role in the dynamics of some globular clusters. However, in only few cases it has been studied by quantitative application of realistic and physically justified global models. Here we present a dynamical analysis of the photometry and three-dimensional kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is very well interpreted by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster omega Cen, the selected model reproduces the complex three-dimensional kinematics; in particular the observed anisotropy profile, characterized by a transition from isotropy, to weakly-radial anisotropy, and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy., Comment: 19 pages, 14 figures, accepted for publication in the Astrophysical Journal

We present new number density and surface brightness profiles for the globular cluster M92 (NGC 6341). These profiles are calculated from optical images collected with the CCD mosaic camera MegaCam at the Canada-France-Hawaii-Telescope and with the Advanced Camera for Surveys on the Hubble Space Telescope. The ground-based data were supplemented with the Sloan Digital Sky Survey photometric catalog. Special care was taken to discriminate candidate cluster stars from field stars and to subtract the background contamination from both profiles. By examining the contour levels of the number density, we found that the stellar distribution becomes clumpy at radial distances larger than about 13 arcminutes, and there is no preferred orientation of contours in space. We performed detailed fits of King and Wilson models to the observed profiles. The best-fit models underestimate the number density inside the core radius. Wilson models better represent the observations, in particular in the outermost cluster regions: the good global agreement of these models with the observations suggests that there is no need to introduce an extra-tidal halo to explain the radial distribution of stars at large radial distances. The best-fit models for the number density and the surface brightness profiles are different, even though they are based on the same observations. Additional tests support the evidence that this fact reflects the difference in the radial distribution of the stellar tracers that determine the observed profiles (main sequence stars for the number density, bright evolved stars for the surface brightness)., Comment: 18 pages, 10 figures, Accepted by AJ

A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for the onset of the gravothermal catastrophe, under different external conditions, coincide with those obtained from thermodynamical arguments. This suggests that the gravothermal catastrophe may reduce to Jeans instability, rediscovered in an inhomogeneous framework. We find normal modes and frequencies for the fluid system and show that instability develops on the dynamical time scale. We then discuss several related issues. In particular: (1) For perturbations at constant total energy and constant volume, we introduce a simple heuristic term in the energy budget to mimic the role of binaries. (2) We outline the analysis of the two-component case and show how linear perturbation analysis can be carried out also in this more complex context in a relatively straightforward way. (3) We compare the behavior of the fluid model with that of the collisionless sphere. In the collisionless case the instability seems to disappear, which is at variance with the linear Jeans stability analysis in the homogeneous case; we argue that a key ingredient to understand the difference (a spherical stellar system is expected to undergo the gravothermal catastrophe only in the presence of some collisionality, which suggests that the instability is dissipative and not dynamical) lies in the role of the detailed angular momentum in a collisionless system. Finally, we briefly comment on the meaning of the Boltzmann entropy and its applicability to the study of the dynamics of self- gravitating inhomogeneous gaseous systems., Comment: accepted for publication in Astronomy & Astrophysics

Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The second is characterized by differential rotation, designed to be rigid in the central regions and to vanish in the outer parts, where the energy truncation becomes effective. The models are constructed by solving the nonlinear Poisson equation for the self-consistent mean-field potential. For rigidly rotating configurations, the solutions are obtained by an asymptotic expansion on the rotation strength parameter. The differentially rotating models are constructed by means of an iterative approach based on a Legendre series expansion of the density and the potential. The two classes of models exhibit complementary properties. The rigidly rotating configurations are flattened toward the equatorial plane, with deviations from spherical symmetry that increase with the distance from the center. For models of the second family, the deviations from spherical symmetry are strongest in the central region, whereas the outer parts tend to be quasi-spherical. The relevant parameter spaces are explored and the intrinsic and projected structural properties are described. Special attention is given to the effect of different options for the truncation of the distribution function in phase space. Models in the moderate rotation regime are best suited to applications to globular clusters. For general interest in stellar dynamics, at high values of the rotation strength the differentially rotating models exhibit a toroidal core embedded in a quasi-spherical configuration. Physically simple analytical models of the kind presented here provide insights into dynamical mechanisms and may be a basis for more realistic investigations with the help of N-body simulations., Comment: 24 pages, 26 figures. To appear in Astronomy and Astrophysics

We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^(\nu) models, originally designed to represent stellar systems produced by a violent relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^(\nu) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field., Comment: 18 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_{\Omega} and h, respectively characterizing the rise of the rotation curve and the luminosity profile of the disk, which surprisingly applies to both high surface brightness and low surface brightness galaxies. This empirical correlation identifies a much stronger conspiracy than the one required by the smoothness and flatness of the rotation curve (disk-halo conspiracy). The self-consistent models are characterized by smooth and flat rotation curves for very different disk-to-halo mass ratios, hence suggesting that conspiracy is not as dramatic as often imagined. For a typical rotation curve, with asymptotically flat rotation curve at V_{\infty} (the precise value of which can also be treated as a free parameter), and a typical density profile of the disk, self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. We show that if the rotation curve is decomposed by means of our self-consistent models, the disk-halo degeneracy is removed and typical rotation curves are fitted by models that are below the maximum-disk prescription. Similar results are obtained from a study of NGC 3198. Finally, we quantify the flattening of the spheroidal halo, which is significant, especially on the scale of the visible disk., Comment: accepted for publication in A&A

Context: Several spiral galaxies, as beautifully exhibited by the case of NGC 6946, display a prominent large-scale spiral structure in their gaseous outer disk. Such structure is often thought to pose a dynamical puzzle, because grand-design spiral structure is traditionally interpreted as the result of density waves carried mostly in the stellar disk. Aims. Here we argue that the outer spiral arms in the cold gas outside the bright optical disk actually have a natural interpretation as the manifestation of the mechanism that excites grand-design spiral structure in the main, star-dominated body of the disk: the excitation is driven by angular momentum transport to the outer regions, through trailing density waves outside the corotation circle that can penetrate beyond the Outer Lindblad Resonance in the gaseous component of the disk. Methods: Because of conservation of the density wave action, these outgoing waves are likely to become more prominent in the outer disk and eventually reach non-linear amplitudes. To calculate the desired amplitude profiles, we make use of the theory of dispersive waves. Results: If the conditions beyond the optical radius allow for an approximate treatment in terms of a linear theory, we show that fitting the observed amplitude profiles leads to a quantitative test on the density of the disk material and thus on the dark matter distribution in the outer parts of the galaxy. Conclusions: This study is thus of interest to the general problem of the disk-halo decomposition of rotation curves., Comment: accepted for publication in Astronomy & Astrophysics

In a previous paper, we have constructed a family of self-consistent triaxial models of quasi-relaxed stellar systems, shaped by the tidal field of the hosting galaxy, as an extension of the well-known spherical King models. For a given tidal field, the models are characterized by two physical scales (such as total mass and central velocity dispersion) and two dimensionless parameters (the concentration parameter and the tidal strength). The most significant departure from spherical symmetry occurs when the truncation radius of the corresponding spherical King model is of the order of the tidal radius, which, for a given tidal strength, is set by the maximum concentration value admitted. For such maximally extended (or "critical") models the outer boundary has a generally triaxial shape, given by the zero-velocity surface of the relevant Jacobi integral, which is basically independent of the concentration parameter. In turn, the external tidal field can give rise to significant global departures from spherical symmetry (as measured, for example, by the quadrupole of the mass distribution of the stellar system) only for low-concentration models, for which the allowed maximal value of the tidal strength can be relatively high. In this paper we describe in detail the intrinsic and the projected structure and kinematics of the models, covering the entire parameter space, from the case of sub-critical (characterized by "underfilling" of the relevant Roche volume) to that of critical models. The intrinsic properties can be a useful starting point for numerical simulations and other investigations that require initialization of a stellar system in dynamical equilibrium. The projected properties are a key step in the direction of a comparison with observed globular clusters and other candidate stellar systems., Comment: 13 pages, 11 figures, uses emulateapj.cls with apjfonts.sty. Accepted for publication in The Astrophysical Journal

Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a "frozen" external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to two orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified non-spherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the non-spherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy., Comment: AASTeX v5.2, 37 pages with 2 figures, accepted for publication in The Astrophysical Journal

The globular clusters (GC) of our Galaxy have been found to lie close to a plane in the log(R_e), log(sigma), SB_e space, on the continuation of the Fundamental Plane (FP) known to characterize the properties of early-type galaxies. We reexamine the issue on a sample of 48 GCs selected in terms of homogeneity criteria for the photometric data available from the literature and perform a model-independent analysis of surface brightness profiles (SBP) and distance moduli, estimating error bars and studying selection effects with non-parametric statistical tests. We determine the coefficients of the FP and their error bars. The scatter from the FP relation is likely to be intrinsic, i.e. not due to measurement errors only. We find that in the standard FP coordinates our sample occupies a slim, axisymmetric region of parameter space, suggesting that the scaling relation might be around a Fundamental Line, rather than a plane, confirming a result noted earlier. This is likely to be the origin of the difficulties in the fit by a plane mentioned in previous investigations. Such FL relation would imply a pure photometric scaling law, which might be tested on wider samples and on extra-galactic GC systems. We find a correlation of the residuals from the FP relation with the central slope of the SBP. No other correlations are found. Finally, we reconstruct the distribution of the values of the quantity log(K_V/(M/L)) (virial coefficient divided by the mass-to-light ratio) through kernel density estimation and find evidence for bimodality, which suggests that the galactic GC system may be composed of at least two dynamically different populations. Yet, these populations do not reflect the standard dichotomy between disk and halo clusters. (abridged)., Comment: 11 pages, 4 figures, accepted for publication in A&A, no boldface text

Gravitational lens modeling is presented for the first discovered example of a three-component source for which each component is quadruply imaged. The lens is a massive galaxy member of the cluster Cl J0152.7-1357 at z ~ 0.84. Taking advantage of this exceptional configuration and of the excellent angular resolution of the HST/ACS, we measure the properties of the lens. Several parametric macroscopic models were developed for the lens galaxy, starting from pointlike to extended image models. For a lens model in terms of a singular isothermal sphere with external shear, the Einstein radius is found to be R_{E} = (9.54 +/- 0.15) kpc. The external shear points to the cluster's northern mass peak. The unknown redshift of the source is determined to be higher than 1.9 and lower than 2.9. Our estimate of the lensing projected total mass inside the Einstein radius, M_{len}(R < 9.54 kpc), depends on the source distance and lies between 4.6 and 6.2 x 10^{11} M_{Sun}. This result turns out to be compatible with the dynamical estimate based on an isothermal model. By considering the constraint on the stellar mass-to-light ratio that comes from the evolution of the Fundamental Plane, we can exclude the possibility that at more than 4 sigma level the total mass enclosed inside the Einstein ring is only luminous matter. Moreover, the photometric-stellar mass measurement within the Einstein radius gives a minimum value of 50% (1 sigma) for the dark-to-total matter fraction. The lensing analysis has allowed us to investigate the distribution of mass of the deflector, also providing some interesting indications on scales that are larger and smaller than the Einstein radius of the lens galaxy. The combination of different diagnostics has proved to be essential in determining quantities that otherwise would have not been directly measurable with the current data., Comment: 10 pages, 9 figures, accepted by Astronomy & Astrophysics

[Abridged] We consider two clusters (A496 and Coma) that are representative of the two classes of cool-core and non-cool-core clusters. We first refer to a two-component dynamical model that ignores the contribution from the galaxy density distribution and study the condition of hydrostatic equilibrium for the hot intracluster medium (ICM) under the assumption of spherical symmetry, in the presence of dark matter. We model the ICM density distribution in terms of a standard $\beta$-model with $\beta=2/3$, i.e. with a distribution similar to that of a regular isothermal sphere (RIS), and fit the observed X-ray brightness profiles. With the explicit purpose of ignoring cosmological arguments, we na\"ively assume that dark matter, if present, has an analogous density distribution, with the freedom of two different density and length scales. The relative distribution of visible and dark matter is then derived by fitting the temperature data for the ICM under conditions of hydrostatic equilibrium. For both clusters, we find that dark matter is more concentrated with respect to visible matter. We then test whether the conclusion changes significantly when dark matter is taken to be distributed according to cosmologically favored density profiles and when the contribution of the mass contained in galaxies is taken into account. Although the qualitative conclusions remain unchanged, we find that the contribution of galaxies to the mass budget is more important than generally assumed. We also show that, without resorting to additional information on the small scale, it is not possible to tell whether a density cusp is present or absent in these systems. [Abridged], Comment: 13 pages, 3 figures, accepted for publication in Il Nuovo Cimento B

We show how the combination of observations related to strong gravitational lensing and stellar dynamics in ellipticals offers a new way to measure the cosmological matter and dark-energy density parameters. A gravitational lensing estimate of the mass enclosed inside the Einstein circle can be obtained by measuring the Einstein angle, once the critical density of the system is known. A model-dependent dynamical estimate of this mass can also be obtained by measuring the central velocity dispersion of the stellar component. By assuming the well-tested homologous 1/r^{2} profile for the total density distribution in the lens elliptical galaxies, these two mass measurements can be properly compared. Thus, a relation between the Einstein angle and the central stellar velocity dispersion is derived, and the cosmological matter and the dark-energy density parameters can be estimated from this. We determined the accuracy of the cosmological parameter estimates by means of simulations that include realistic measurement uncertainties on the relevant quantities. Interestingly, the expected constraints on the cosmological parameter plane are complementary to those coming from other observational techniques. Then, we applied the method to the data sets of the Sloan Lens ACS and the Lenses Structure and Dynamics Surveys, and showed that the concordance value between 0.7 and 0.8 for the dark-energy density parameter is included in our 99% confidence regions. The small number of lenses available to date prevents us from precisely determining the cosmological parameters, but it still proves the feasibility of the method. When applied to samples made of hundreds of lenses that are expected to become available from forthcoming surveys, this technique will be an important tool for measuring the geometry of the Universe., Comment: 11 pages, 9 figures, accepted by Astronomy & Astrophysics

In this paper we study the infall, by dynamical friction, of rigid "satellites" taken in a variety of initial configurations and models. We thus measure how dynamical friction depends on the density concentration and on the pressure anisotropy of the host galaxy and, separately, the response of the galaxy during the process. The investigation is carried out by using a numerical laboratory set up in previous papers of this series. We find that the pressure anisotropy present in the host galaxy has little effect on dynamical friction. Instead, the shape of the galaxy density profile is very important. The classical idealized description appears to be applicable to galaxy models characterized by a small density gradient but not to concentrated models. In contrast to the behavior found in small density gradient models, the orbits of satellites captured in concentrated models are not circularized by dynamical friction. The induced evolution in the host galaxy reflects the initial conditions adopted for the captured satellite. Satellites spiraling in on quasi-circular orbits tend to modify the pressure tensor of the host galaxy in the tangential direction and the galaxy shape from spherical to oblate, while satellites captured along quasi-radial orbits tend to induce pressure anisotropy in the radial direction and to generate a prolate shape. This result suggests that the shape of early-type galaxies may result from occasional mergers rather than being directly related to the effectiveness of the radial-orbit instability during the process of formation via collisionless collapse, as often argued in the past., Comment: 16 pages, 18 figures, accepted by Astronomy & Astrophysics

Many astrophysical problems, ranging from structure formation in cosmology to dynamics of elliptical galaxies, refer to slow processes of evolution of essentially collisionless self-gravitating systems. In order to determine the relevant quasi-equilibrium configuration at time t from given initial conditions, it is often argued that such slow evolution may be approximated in terms of adiabatic evolution, for the calculation of which efficient semi--analytical techniques are available. Here we focus on the slow process of evolution, induced by dynamical friction of a host stellar system on a minority component of "satellites", that we have investigated in a previous paper, to determine to what extent an adiabatic description might be applied. The study is realized by comparing directly N--body simulations of the stellar system evolution (in two significantly different models) from initial to final conditions in a controlled numerical environment. We demonstrate that for the examined process the adiabatic description is going to provide incorrect answers, not only quantitatively, but also qualitatively. The two classes of models considered exhibit generally similar trends in evolution, with one exception noted in relation to the evolution of the total density profile. This simple conclusion should be taken as a warning against the indiscriminate use of adiabatic growth prescriptions in studies of structure of galaxies., Comment: 13 pages, 5 figures, Accepted for publication in A&A

It is well known that the simple criterion proposed originally by Polyachenko and Shukhman (1981) for the onset of the radial orbit instability, although being generally a useful tool, faces significant exceptions both on the side of mildly anisotropic systems (with some that can be proved to be unstable) and on the side of strongly anisotropic models (with some that can be shown to be stable). In this paper we address two issues: Are there processes of collisionless collapse that can lead to equilibria of the exceptional type? What is the intrinsic structural property that is responsible for the sometimes noted exceptional stability behavior? To clarify these issues, we have performed a series of simulations of collisionless collapse that start from homogeneous, highly symmetrized, cold initial conditions and, because of such special conditions, are characterized by very little mixing. For these runs, the end-states can be associated with large values of the global pressure anisotropy parameter up to 2K_r/K_T \approx 2.75. The highly anisotropic equilibrium states thus constructed show no significant traces of radial anisotropy in their central region, with a very sharp transition to a radially anisotropic envelope occurring well inside the half-mass radius (around 0.2 r_M). To check whether the existence of such almost perfectly isotropic "nucleus" might be responsible for the apparent suppression of the radial orbit instability, we could not resort to equilibrium models with the above characteristics and with analytically available distribution function; instead, we studied and confirmed the stability of configurations with those characteristics by initializing N-body approximate equilibria (with given density and pressure anisotropy profiles) with the help of the Jeans equations., Comment: 26 pages, 9 figures, accepted for publication in The Astrophysical Journal

We present 21-cm line observations of the spiral galaxy NGC 4559, made with the Westerbork Synthesis Radio Telescope. We have used them to study the HI distribution and kinematics, the relative amount and distribution of luminous and dark matter in this galaxy and, in particular, the presence of extra-planar gas. Our data do reveal the presence of such a component, in the form of a thick disk, with a mass of 5.9 x 10^8 Mo (one tenth of the total HI mass) and a mean rotation velocity 25-50 km/s lower than that of the thin disk. The extra-planar gas may be the result of galactic fountains but accretion from the IGM cannot be ruled out. With this study we confirm that lagging, thick HI layers are likely to be common in spiral galaxies., Comment: 17 pages, 10 figures. Accepted for publication in A&A

We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct a variety of exact density-potential pairs with spheroidal, toroidal, or triaxial shapes for which the deviation from spherical symmetry is finite. As concrete analytical applications, we describe: (1) The construction of a family of toroidal axisymmetric density-potential pairs one of which is associated with a perfectly flat rotation curve (for a member of this family, the supporting two-integral phase-space distribution function is obtained in closed form); (2) The determination of the aperture velocity dispersion in a wide class of two-integral axisymmetric models not stratified on homeoids with central black hole, which may be useful for the discussion of the dynamical contributions to the characteristics of the Fundamental Plane of early-type galaxies; and (3) For such class of models, the construction of the v/sigma-ellipticity relation, often considered to assess the role of rotation in the structure of elliptical galaxies., Comment: 22 pages, 3 figures, accepted by A&A

[Abridged] N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Understanding this idealized and relatively simple process, by which stellar systems can reach partially relaxed equilibrium configurations (characterized by isotropic central regions and radially anisotropic envelopes), is a prerequisite to more ambitious attempts at constructing physically justified models of elliptical galaxies in which the problem of galaxy formation is set in the generally accepted cosmological context of hierarchical clustering. In a previous paper, we have discussed the dynamical properties of a family of models of partially relaxed stellar systems (the f^{(\nu)} models), designed to incorporate the qualitative properties of the products of collisionless collapse at small and at large radii. Here we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of such family of models and those of the products of collisionless collapse found in N-body simulations that we have run for the purpose. Surprisingly, the models thus identified are able to match the simulated density distributions over nine orders of magnitude and also to provide an excellent fit to the anisotropy profiles and a good representation of the overall structure in phase space., Comment: 16 pages, 17 figures, accepted for publication in Astronomy & Astrophysics

[Abridged] Recently we have found that a family of models of partially relaxed, anisotropic stellar systems, inspired earlier by studies of incomplete violent relaxation, exhibits some interesting thermodynamic properties. Here we present a systematic investigation of its dynamical characteristics, in order to establish the basis for a detailed comparison with simulations of collisionless collapse, planned for a separate paper. For a full comparison with the observations of elliptical galaxies, the models should be extended to allow for the presence a sizable dark halo and of significant rotation. In the spherical limit, the family is characterized by two dimensionless parameters, i.e. \Psi, measuring the depth of the galaxy potential, and \nu, defining the form of a third global quantity Q, which is argued to be approximately conserved during collisionless collapse (in addition to the total energy and the total number of stars)., Comment: 12 pages, 15 figures, accepted for publication in Astronomy & Astrophysics

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation. In this paper we revisit the problem, by comparing the detailed properties of a family of distribution functions derived from statistical mechanics arguments to those of the products of collisionless collapse found in N-body simulations., Comment: 4 pages, 2 figures, to appear in the proceedings of the 39th Rencontres de Moriond, "Exploring the Universe," La Thuile, Italy, March 28 - April 4, 2004

We present preliminary results on a new family of distribution functions that are able to generate axisymmetric, truncated (i.e., finite size) stellar dynamical models characterized by toroidal shapes. The relevant distribution functions generalize those that are known to describe polytropic spheres, for which all the dynamical and structural properties of the system can be expressed in explicit form as elementary functions of the system gravitational potential. The model construction is then completed by a numerical study of the associated Poisson equation. We note that our axisymmetric models can also include the presence of an external gravitational field, such as that produced by a massive disk or by a central mass concentration (e.g., a supermassive black hole)., Comment: 4 pages, 2 figures, to appear in "Plasmas in the Laboratory and in the Universe: new insights and new challenges", G. Bertin, D. Farina, R. Pozzoli eds., AIP Conference Proceedings

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago (see Bertin et al. 1993 and references therein), the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations., Comment: to appear in "Plasmas in the Laboratory and in the Universe: new insights and new challenges", G. Bertin, D. Farina, R. Pozzoli eds., AIP Conference Proceedings, Vol. XXX, pp. YYY

The main goal of this paper is to set up a numerical laboratory for the study of the slow evolution of the density and of the pressure tensor profiles of an otherwise collisionless stellar system, as a result of the interactions with a minority component of heavier "particles".The effects that we would like to study are those attributed to slow collisional relaxation and generically called "dynamical friction". We start by revisiting the problem of the sinking of a satellite inside an initially isotropic, non-rotating, spherical galaxy, which we follow by means of N-body simulations using about one million particles. We then consider a quasi-spherical problem, in which the satellite is fragmented into a set of many smaller masses with a spherically symmetric initial density distribution. In a wide set of experiments, designed in order to bring out effects genuinely associated with dynamical friction, we are able to demonstrate the slow evolution of the density profile and the development of a tangentially biased pressure in the underlying stellar system, while we briefly address the issue of the circularization of orbits induced by dynamical friction on the population of fragments. The results of the simulations presented here and others planned for future investigations allow us to study the basic mechanisms of slow relaxation in stellar systems and thus may be of general interest for a variety of problems, especially in the cosmological context. Here our experiments are conceived with the specific goal to clarify some mechanisms that may play a role in the evolution of an elliptical galaxy as a result of the interaction between the stars and a significant population of globular clusters or of the merging of a large number of small satellites., Comment: 29 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

The nucleus of the Seyfert galaxy NGC 1068 is believed to host a supermassive black hole. Evidence for the presence of a massive central object is provided by water maser emission, which displays a linear pattern in the sky, suggestive of a rotating disk. The rotating disk hypothesis is further strengthened by the declining shape of the derived rotation curve. Similar maser emission from NGC 4258 has led to a reliable estimate of the mass of the central black hole, because in this case the rotation curve is Keplerian. In the case of NGC 1068 the rotation curve traced by the water maser is non-Keplerian. In this paper we provide an interpretation of the non-Keplerian rotation in NGC 1068 by means of a self-gravitating accretion disk model. We obtain a good fit to the available data and derive a black hole mass M_{bh}=(8.0\pm 0.3) 10^6M_{sun}. The resulting disk mass is comparable to the black hole mass. As an interesting by-product of our fitting procedure, we are able to estimate the viscosity parameter, which turns out to be \alpha\approx 10^{-2}, in line with some theoretical expectations., Comment: 9 pages, A&A in press

We examine the thermodynamical properties of a family of partially relaxed, anisotropic stellar systems, derived earlier from the Boltzmann entropy under the assumption that a third quantity Q is conserved in addition to the total energy and the total number of stars. We now show that the family of models conforms to the paradigm of the gravothermal catastrophe, which is expected to occur (in the presence of adequate energy transport mechanisms) when the one-parameter equilibrium sequence attains sufficiently high values of the concentration parameter; these are the values for which the models are well fitted by the R^(1/4) law. In the intermediate concentration regime the models belonging to the sequence exhibit significant deviations from the R^(1/4) law. Curiously, in the low-concentration regime, the global thermodynamical temperature associated with the models becomes negative when the models become too anisotropic so that they are unstable against the radial orbit instability; this latter behavior, while offering a new clue to the physical interpretation of the radial orbit instability, is at variance with respect to the low-concentration limit of the classical case of the isotropic, isothermal sphere investigated by Bonnor (1956) and Lynden-Bell & Wood (1968)., Comment: 16 pages, 4 figures, accepted for publication in The Astrophysical Journal (Part 1)

We start by studying a small set of objects characterized by photometric profiles that have been pointed out to deviate significantly from the standard R^{1/4} law. For these objects we confirm that a generic R^{1/n} law, with n a free parameter, can provide superior fits (the best-fit value of n can be lower than 2.5 or higher than 10), better than those that can be obtained by a pure R^{1/4} law, by an R^{1/4}+exponential model, and by other dynamically justified self--consistent models. Therefore, strictly speaking, elliptical galaxies should not be considered homologous dynamical systems. Still, a case for "weak homology", useful for the interpretation of the Fundamental Plane of elliptical galaxies, could be made if the best-fit parameter n, as often reported, correlates with galaxy luminosity L, provided the underlying dynamical structure also follows a systematic trend with luminosity. We demonstrate that this statement may be true even in the presence of significant scatter in the correlation n(L). Preliminary indications provided by a set of "data points" associated with a sample of 14 galaxies suggest that neither the strict homology nor the constant stellar mass--to--light solution are a satisfactory explanation of the observed Fundamental Plane (abridged)., Comment: 34 pages, 11 figures, accepted by Astronomy and Astrophysics

We have measured the Fundamental Plane (FP) parameters for a sample of 30 field early-type galaxies (E/S0) in the redshift range 0.15\AA in 22% of an enlarged sample of 42 massive E/S0 in the range 0.1

The long wavelength emission of protostellar objects is commonly attributed to a disk of gas and dust around the central protostar. In the first stages of disk accretion or in the case of high mass protostars, the disk mass is likely to be sufficiently large, so that the disk self-gravity may have an impact on the dynamics and the emission properties of the disk. In this paper we describe the spectral energy distribution (SED) produced by a simple, non-flaring, self-gravitating accretion disk model. Self-gravity is included in the calculation of the rotation curve of the disk and in the energy balance equation, as a term of effective heating related to Jeans instability. In order to quantify in detail the requirements on the mass of the disk and on the accretion rate posed on the models by realistic situations, we compare the SEDs produced by these models with the observed SEDs of a small sample of well-studied protostellar objects. We find that relatively modest disks - even lighter than the central star - can lead to an interesting fit to the infrared SED of the FU Orionis objects considered, while in the case of T Tauri stars the required parameters fall outside the range suggested as acceptable by the general theoretical and observational scenario. On the basis of the present results, we may conclude that the contribution of a self-gravitating disk is plausible in several cases (in particular, for FU Orionis objects) and that, in the standard irradiation dominated disk scenario, it would help softening the requirements encountered by Keplerian accretion models., Comment: 26 pages, 7 figures, accepted by A&A

We report on the study of a sample of 25 field early-type galaxies, in the redshift range z~0.1-0.5, selected on the basis of colours and morphology from the HST-MDS. Field early-type galaxies define a tight Fundamental Plane (FP) out to z~0.4, with scatter unchanged with respect to local samples, within the observational errors. The intermediate redshift FP is offset with respect to the FP of the Coma Cluster. The offset of the FP is found to increase with redshift. The evolution of the FP is studied quantitatively with a Bayesian-Montecarlo technique. By applying this technique, we find that the offset of the intercept of the FP (\Delta \gamma) with respect to the local FP increases as \Delta \gamma = \tau z with the following 68 per cent limits: 0.33<\tau<0.44 (for \Omega=1, \Omega_{\Lambda}=0) or 0.44<\tau<0.56 (for \Omega=0.3,\Omega_{\Lambda}=0.7). In addition, we interpret the results in terms of the evolution of the stellar populations, under the assumption of passive evolution. In a single-burst scenario, the observed properties are consistent with those of a stellar population formed at z>2 (for \Omega=1, \Omega_{\Lambda}=0, H_0=50 \kms Mpc^{-1}) or 0.8

We have carried out a search for Lyman alpha emission from galaxies at z~=2.4 over a field of 1200 sq. arcmin using the CFH12K camera at the CFHT and a custom medium band filter. The search has uncovered 58 candidates, corresponding to a completeness-corrected source density of ~0.07 sq. arcmin^-2. Our sources have red colors (B-I~=1.8) which imply either that a large fraction of the light is highly reddened and we are detecting Lyman alpha through special lines of sight, or that these objects contain an underlying older stellar population. While for each individual object we cannot discriminate between these alternatives, we conclude that most of the objects actually contain an older component because the star formation rates inferred from the picture based on reddening, applied to all candidates, would imply an exceedingly high star formation rate, i.e. more than two orders of magnitude above the peak cosmic star formation rate (e.g. Lilly et al. 1996)., Comment: 9 pages plus 2 figures, ApJ Letters in press

A sample of field early-type galaxies (E/S0) at intermediate redshift ($z\sim0.1-0.6$) is selected, based on morphology and colours from HST-WFPC2 parallel images. Photometric structural parameters (effective radius $R_{\tx{e}}$ and effective surface brightness $SB_{\tx{e}}$) are derived through the F606W and F814W filters, using luminosity profile fitting and two-dimensional fitting techniques. The combined parameter that enters the Fundamental Plane ($\log R_{\tx{e}}-\beta SB_{\tx{e}}$, with $\beta\approx0.32$) is shown to suffer from significantly smaller uncertainties (r.m.s. 0.03) than the individual structural parameters (e.g. $\sim 15$ per cent r.m.s. on the effective radius). High signal-to-noise intermediate resolution spectra, taken at the ESO-3.6m, yield redshifts for 35 galaxies and central velocity dispersions for 22 galaxies. Central velocity dispersions are derived using a library of stellar templates covering a wide range of spectral types, in order to study the effects of templates mismatches. The average random error on the central velocity dispersion is found to be 8 per cent and the average systematic error due to template mismatch is found to be 5 per cent. The errors on velocity dispersion measurement and the effects of template mismatches are studied by means of extensive Montecarlo simulations. In addition, we investigate whether the determination of the velocity dispersion is sensitive to the spectral range used, finding that the value of velocity dispersion is unchanged when the spectral regions that include the absorption features Ca HK and NaD are masked out during the fit., Comment: 19 pages, 16 figures, MNRAS accepted

In the dynamics of accretion disks, the presence of collective effects associated with the self-gravity of the disk is expected to affect not only the momentum transport, but also the relevant energy balance equations, which could differ substantially from the non-self-gravitating case. Here we follow the picture that, when the disk is sufficiently cold, the stirring due to Jeans-related instabilities acts as a source of effective heating. The corresponding reformulation of the energy equations allows us to: ({\it i}) demonstrate how self-regulation can be established, so that the stability parameter $Q$ is maintained close to a threshold value, with weak dependence on radius; ({\it ii}) rediscuss the opacity properties in the self-gravitating regime. In particular, we show that, if cooling is dominated by {\it bremsstrahlung}, an optically thin stationary accretion solution is thermally stable, even in the non-advective case, provided the disk is self-gravitating. The details of the cooling function have little effect on the structure of such accretion disk, which is in any case brought by self-gravity to self-regulate. This condition of self-gravitating accretion is expected to be appropriate for the outer regions of many disks of astrophysical interest. With the reformulation of the energy equations described in this paper we have also secured: ({\it iii}) a starting point for the study of the emission properties of self-gravitating accretion disks; ({\it iv}) a tool to analyze the structure of the transition region, where the disk becomes self-gravitating., Comment: 9 pages, 5 figures, accepted by A&A

We present preliminary results on the evolution of the stellar populations of field early-type galaxies (E/S0) from z=0.4 to z=0. The diagnostic tool used in this study is the Fundamental Plane (FP), a tight empirical correlation between their central velocity dispersion (sigma), effective radius (Re), and effective surface brightness (SBe), which is observed to hold in the local Universe. Using HST-WFPC2 archive images and spectra obtained at the ESO-3.6m telescope we measured the FP parameters for a sample of ~30 field E/S0s at z=0.2-0.4. Remarkably, field E/S0s at intermediate redshift also define a tight FP, with scatter unchanged with respect to that of local samples. The intermediate redshift FP is offset from the local one, in the sense that, for given RE and sigma, galaxies are brighter at z=0.4 than at z=0. The implication of the offset of the FP in terms of passive evolution of the stellar population depends on its star formation history. In a single burst scenario, the stellar populations of field E/S0s were formed at z=0.8-1.6 (Omega=0.3; Omega_{Lambda}=0.7; H_0=50 km/s/Mpc). Alternatively, the bulk of stars (90% in mass) can be formed at high redshift (z~3), and the rest in a secondary burst occurred more recently (z~0.5-0.8)., Comment: 4 pages, including Figures. To appear in the proceedings of the "A Decade of HST Science", held at the Space Telescope Science Institute, April 11-14, 2000

In this paper we describe some analytical properties of the R^{1/m} law proposed by Sersic (1968) to categorize the photometric profiles of elliptical galaxies. In particular, we present the full asymptotic expansion for the dimensionless scale factor b(m) that is introduced when referring the profile to the standard effective radius. Surprisingly, our asymptotic analysis turns out to be useful even for values of m as low as unity, thus providing a unified analytical tool for observational and theoretical investigations based on the R^{1/m} law for the entire range of interesting photometric profiles, from spiral to elliptical galaxies., Comment: 9 pages, 1 figure, to be published in A&A (main journal)

In this paper we describe some analytical properties of the R^{1/m} law proposed by Sersic to categorize the photometric profiles of elliptical galaxies. In particular, we present the full asymptotic expansion for the dimensionless scale factor b(m) that is introduced when referring the profile to the standard effective radius. Surprisingly, our asymptotic analysis turns out to be useful even for values of m as low as unity, thus providing a unified analytical tool for observational and theoretical investigations based on the R^{1/m} law for the entire range of interesting photometric profiles, from spiral to elliptical galaxies., Comment: 2 pages, to appear in "Galaxy Dynamics: from the Early Universe to the Present", ASP Conf. Series, eds. F. Combes, G. Mamon, V. Charmandaris

We consider a class of steady-state self-gravitating accretion disks for which efficient cooling mechanisms are assumed to operate so that the disk is self-regulated at a condition of approximate marginal Jeans stability. In an earlier paper, this scenario had been shown to lead naturally, in the absence of a central point mass, to a self-similar solution characterized by a flat rotation curve. In this article we investigate the entire parameter space available for such self-regulated accretion disks and provide two non-trivial extensions of the model. The first extension is that of a bimodal disk, obtained by partially relaxing the self-regulation constraint, so that full matching with an inner "standard" Keplerian accretion disk takes place. The second extension is the construction of self-regulated accretion disks embedded in a diffuse spherical "halo". The analysis is further strengthened by a careful discussion of the vertical structure of the disk, in such a way that the transition from self-gravity dominated to non-gravitating disks is covered uniformly., Comment: To appear in A&A

We present measurements of the Fundamental Plane (FP) parameters (the effective radius, the mean effective surface brightness, and the central velocity dispersion) of six field elliptical galaxies at intermediate redshift. The imaging is taken from the Medium Deep Survey of the Hubble Space Telescope, while the kinematical data are obtained from long-slit spectroscopy using the 3.6-m ESO telescope. The Fundamental Plane appears well defined in the field even at redshift $\approx$ 0.3. The data show a shift in the FP zero point with respect to the local relation, possibly indicating modest evolution, consistent with the result found for intermediate redshift cluster samples. The FP slopes derived for our field data, plus other cluster ellipticals at intermediate redshift taken from the literature, differ from the local ones, but are still consistent with the interpretation of the FP as a result of homology, of the virial theorem and of the existence of a relation between luminosity and mass, $L \propto M^{\eta}$. We also derive the surface brightness vs. effective radius relation for nine galaxies with redshift up to $z \approx0.6$, and data from the literature; the evolution that can be inferred is consistent with what is found using the FP., Comment: 17 pages, including 9 figures, MNRAS, accepted

We consider a class of fully self-gravitating accretion disks, for which efficient cooling mechanisms are assumed to maintain the disk close to the margin of Jeans instability. For such self-regulated disks the equations become very simple in the outer regions, where the angular momentum convective transport approximately balances the viscous transport. These latter equations are shown to lead naturally to a self-similar solution with flat rotation curve, with circular velocity proportional to Mdot^(1/3) and essentially fixed opening angle., Comment: 14 pages, LaTeX, uses AASTeX v4.0, no figures; accepted for publication in The Astrophysical Journal Letters