1,721,105 research outputs found
Introduction to Stellar Dynamics
No full textThe study of stellar dynamics is experiencing an exciting new wave of interest thanks to observational campaigns and the ready availability of powerful computers. Whilst its relevance includes many areas of astrophysics, from the structure of the Milky Way to dark matter halos, few texts are suited to advanced students. This volume provides a broad overview of the key concepts beyond the elementary level, bridging the gap between the standard texts and specialist literature. The author reviews Newtonian gravity in depth before examining the dynamical properties of collisional and collisionless stellar-dynamical systems that result from gravitational interactions. Guided examples and exercises ensure a thorough grounding in the mathematics, while discussions of important practical applications give a complete picture of the subject. Readers are given a sound working knowledge of the fundamental ideas and techniques employed in the field and the conceptual background needed to progress to more advanced graduate-level treatises
Nagai discs
Full text linkThe face-on projected density profile of the Miyamoto & Nagai discs of arbitrary flattening is obtained analytically in terms of incomplete elliptic integrals of first and second type, by using two complementary approaches, and then checked against the results of numerical integration. As computer algebra systems do not seem able to obtain the resulting formula in any straightforward way, the relevant mathematical steps are provided. During this study, three wrong identities in the Byrd & Friedman tables of elliptic integrals have been identified, and their correct expression is given
Isothermal Bondi Accretion in Two-component Jaffe Galaxies with a Central Black Hole
Full text linkThe fully analytical solution for isothermal Bondi accretion onto a black hole (MBH) at the center of two-component Jaffe galaxy models is presented. In a previous work, we provided the analytical expressions for the critical accretion parameter and the radial profile of the Mach number in the case of accretion onto an MBH at the center of a spherically symmetric one-component Jaffe galaxy model. Here we apply this solution to galaxy models where both the stellar and total mass density distributions are described by the Jaffe profile with different scale lengths and masses and to which a central MBH is added. For such galaxy models, all the relevant stellar dynamical properties can also be derived analytically. In these new models, the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the galaxy stellar component. The formulae that are provided allow one to evaluate all flow properties and are then useful for estimates of the scale radius and mass flow rate when modeling accretion onto MBHs at the center of galaxies. As an application, we quantify the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the MBH, under the hypothesis of classical Bondi accretion
Regular and chaotic orbits in axisymmetric stellar systems
Full text linkThe gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper, we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (non-Stäckel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in Miyamoto-Nagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic (ξc) and resonantly trapped (ξt) orbits to a stellar system of given distribution function (DF), which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure ξc and ξt in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic DF, finding ξc ~ 10-4 - 10-3 and ξt ~ 10-2 - 10-1
Miyamoto-Nagai discs embedded in the Binney logarithmic potential: analytical solution of the two-integrals Jeans equations
No full textWe present the analytical solution of the two-integrals Jeans equations for Miyamoto-
Nagai discs embedded in Binney logarithmic dark matter haloes. The equations can be solved
(both with standard methods and with the Residue Theorem) for arbitrary choices of the parameters,
thus providing a very flexible two-component galaxy model, ranging from flattened
discs to spherical systems. A particularly interesting case is obtained when the dark matter
halo reduces to the Singular Isothermal Sphere. Azimuthal motions are separated in the ordered
and velocity dispersion components by using the Satoh decomposition. The obtained
formulae can be used in numerical simulations of galactic gas flows, for testing codes of
stellar dynamics, and to study the dependence of the stellar velocity dispersion and of the
asymmetric drift in the equatorial plane as a function of disc and halo flattenings. Here, we
estimate the inflow radial velocities of the interstellar medium, expected by the mixing of the
stellar mass losses of the lagging stars in the disc with a pre-existing gas in circular orbit
Fidelity and Reversibility in the Three Body Problem
No full textWe use the Reversibility Error Method and the Fidelity to analyze the global effects of a small
perturbation in a non-integrable system. Both methods have already been proposed and used
in the literature but the aim of this paper is to compare them in a physically significant example
adding some considerations on the equivalence, observed in this case, between round-off and random
perturbations.
As a paradigmatic example we adopt the restricted planar circular three body problem. The
cumulative effect of random perturbations or round-off leads to a divergence of the perturbed
orbit from the reference one. Rather than computing the distance of the perturbed orbit from
the reference one, after a given number n of iterations, a procedure we name the Forward Error
Method (FEM), we measure the distance of the reversed orbit (n periods forward and backward)
from the initial point. This approach, that we name Reversibility Error Method (REM), does
not require the computation of the unperturbed map. The loss of memory of the perturbed map
is quantified by the Fidelity decay rate whose computation requires a statistical average over an
invariant region. Two distinct definitions of Fidelity are given. The asymptotic equivalence of
REM and FEM is analytically proved for linear symplectic maps with random perturbations. For
a given map, the REM plot provides a picture of the dynamic stability regions in the phase space,
very easy to obtain for any kind of perturbation and very simple to implement numerically. The
REM and FEM for linear symplectic maps are proved to be asymptotically equivalent. The global
error growth follows a power law in the regions of integrable (or quasi integrable) motion and an
exponential law in the regions of chaotic motion. We prove that the power law exponent is 3/2 for a
generic anisochronous system, but drops down to 1/2 if the system is isochronous. Correspondingly
the Fidelity F(t) exhibits an exponential decay and −ln F(t) grows just as the square of the FEM
or REM error. The Reversibility Error and Fidelity can be used for a quantitative analysis of
dynamical systems and are suited to investigate the transition regions from chaotic to regular
motion even for Hamiltonian systems with many degrees of freedom such as the N-body problem
Reasoning from fossils: learning from the local black hole population about the evolution of quasars''
No full textX-ray properties of elliptical galaxies as determined by feedback from their central black holes
No full textThe centers of elliptical galaxies host supermassive black holes that - through feedback resulting from the accretion process - are believed to significantly affect their hot interstellar medium. The evolution of this hot gas together with that of the nuclear emission during the whole galaxies lifetime has been studied with the aid of high-resolution hydrodynamical simulations, with cooling and heating functions including photoionization plus Compton process, and specific for an average AGN spectral energy distribution
A new class of galaxy models with a central BH - I. The spherical case
No full textThe dynamical properties of spherically symmetric galaxy models, where a Jaffe stellar density profile is embedded in a total mass density decreasing as r-3 at large radii, are presented. The orbital structure of the stellar component is described by the Osipkov-Merritt anisotropy; the dark matter halo is isotropic, and a black hole is added at the centre of the galaxy. First, the conditions for a nowhere negative and monotonically decreasing dark matter halo density profile are derived; this profile can be made asymptotically coincident with an NFW profile at the centre and large radii. Then, the minimum value of the anisotropy radius for phase-space consistency is derived as a function of the galaxy parameters. The Jeans equations for the stellar component are solved analytically; the projected velocity dispersion at the centre and large radii is also obtained, for generic values of the anisotropy radius. Finally, analytical expressions for the terms entering the Virial Theorem are derived, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, built following an approach already adopted in our previous works, can be a useful starting point for a more advanced modelling of the dynamics of elliptical galaxies, and can be easily implemented in numerical simulations requiring a realistic dynamical model of a galaxy
Two-body relaxation in modified Newtonian dynamics
No full textA naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t 2b implies that 2b is comparable to the crossing time regardless of the number W of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of t 2b is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case, we find that in the deep-MOND regime t 2b scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Near the centre of a spherical system that is in the deep-MOND regime, we show that the fluctuating component of the gravitational force is never small compared to the mean-field force; this conclusion surprisingly even applies to systems with a density cusp that keeps the mean-field force constant to arbitrarily small radius, and suggests that a cuspy centre can never be in the deep-MOND regime. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two-body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ∼10 M⊙ should have spiralled to the centres of dwarf galaxies
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