A class of self-gravitating accretion disks

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&

Dynamical properties of a family of collisionless models of elliptical galaxies

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. YY

Dynamical models and numerical simulations of incomplete violent relaxation

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, 200

The relative concentration of visible and dark matter in clusters of galaxies

[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

Spiral density waves in the outer galactic gaseous discs

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

Relaxation of spherical systems with long-range interactions: a numerical investigation

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of Physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of 1/r^2 force law. However, recently the interest in alternative gravities emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an 1/r^alpha force law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent alpha, with small values of alpha corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.Comment: 6 pages, 3 figures, accepted in the International Journal of Bifurcation and Chao

Properties of quasi-relaxed stellar systems in an external tidal field

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 Journa

A dynamical study of Galactic globular clusters under different relaxation conditions

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 & Astrophysic

On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the 'off' periods has as a power-law tail with an exponent varying continuously between -1 and -2, at odds with standard on-off intermittency which occurs at a specific value of the control parameter, and leads to the exponent -3/2. This non-trivial behavior results from the competition between a strong slowing down of the dynamics at small values of the observable, and a systematic drift toward large values.Comment: 4 pages, 3 figure