CONSTRUCTING STABLE SPHERICAL GALAXY MODELS

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 two-parameter 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 small-E behaviour of f) and it appears that there is no simple general criterion for predicting instability.