Stability of nonrotating stellar systems. I - Oblate shell-orbit models

Abstract

The stability of perhaps the simplest family of nonspherical stellar system models with realistic density profiles, the oblate shell-orbit models first described by Bishop (1987), is investigated. The axisymmetric stability of these models is considered first by presenting an approximate criterion for short-wavelength stability and then by N-body integration. It is found that models flatter than about E6 are axisymmetrically unstable. The results of three-dimensional N-body simulations are presented which reveal that shell-orbit models of all flattenings - even nearly spherical - are subject to a dipole instability that gradually increases the radial velocity dispersion of these models. Thus, the results show that no radially cold oblate model can be stable even in the absence of rotation. The possible relevance of these results to real elliptical galaxies is discussed. 56 refs.