Constructing stable spherical galaxy models
Abstract
This paper extends a recent method of Gerhard for constructing spherical galaxy models with velocity anisotropy. The method develops the distribution function f( E, L) given the potential and density and a trial function g( E, L), by solving an integral equation, for which a suitable numerical algorithm is given. For any g( E, L) there is a unique f, though positivity is not guaranteed. The paper then picks a twoparameter family of models and studies the radial orbit instability by linear theory. The results indicate that the anisotropy of the core is important for the instability, but not independently of other features (such as the asymptotic smallE behaviour of f) and it appears that there is no simple general criterion for predicting instability.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 1992
 DOI:
 10.1093/mnras/254.1.132
 Bibcode:
 1992MNRAS.254..132S
 Keywords:

 Astronomical Models;
 Elliptical Galaxies;
 Galactic Structure;
 Orbital Mechanics;
 Velocity Distribution;
 Computational Astrophysics;
 Galactic Evolution;
 Kernel Functions;
 Spheres;
 Astrophysics