Related papers: How general is the global density slope-anisotropy…
Starting from the central density slope-anisotropy theorem of An and Evans (2006), recent investigations have shown that the involved density slope-anisotropy inequality holds not only at the center, but at all radii (i.e. globally) in a…
Recently, some intriguing results have lead to speculations whether the central density slope -- velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by…
General criteria to check the positivity of the distribution function (phase-space consistency) of stellar systems of assigned density and anisotropy profile are useful starting points in Jeans-based modeling. Here we substantially extend…
It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function are not fully independent. Here we study the interplay between density profile and orbital…
Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditions the distribution constructed as such is…
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy…
Following earlier authors, we re-examine constraints on the radial velocity anisotropy of generic stellar systems using arguments for phase space density positivity, stability, and separability. It is known that although the majority of…
We study a new class of equilibrium two-parametric distribution functions of spherical stellar systems with radially anisotropic velocity distribution of stars. The models are less singular counterparts of the so called generalized…
We identify a universal relation between the radial density slope \alpha (r) and the velocity anisotropy \beta (r) for equilibrated structures. This relation holds for a variety of systems, including disk galaxy mergers, spherical…
One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that…
For a wide class of self-gravitating systems, we show that if the density is cusped like 1/r^{gamma} near the center, then the limiting value of the anisotropy parameter beta = 1 - <v_T^2>/(2<v_r^2>) at the center may not be greater than…
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the…
Modern cosmology rests on the cosmological principle, that on large enough scales the Universe is both homogeneous and isotropic. A corollary is that galaxies' spin vectors should be isotropically distributed on the sky. This has been…
A widely employed method for estimating the mass of stellar systems with apparent spherical symmetry is dynamical modelling using the spherically symmetric Jeans equation. Unfortunately this approach suffers from a degeneracy between the…
We discuss some contradictions found in the literature concerning the problem of stability of collisionless spherical stellar systems which are the simplest anisotropic generalization of the well-known polytrope models. Their distribution…
We add to the lore of spherical, stellar-system models a two-parameter family with an anisotropic velocity dispersion, and a central point mass (``black hole''). The ratio of the tangential to radial dispersions, is constant--and…
Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high resolution cosmological N-body simulations by…
The cosmological principle is fundamental to the standard cosmological model. It assumes that the Universe is homogeneous and isotropic on very large scales. As the basic assumption, it must stand the test of various observations. In this…