Numerical Experiments on the Stability of Spherical Stellar Systems

Abstract

The concentric shell model is used to investigate numerically the stability of spherical steady-state stellar systems. Polytropic models with an isotropic velocity distribution are found to be stable almost down to the limiting index n =1/2. ‘Generalized polytropes’, with a distribution function depending on energy and angular momentum, show instability when n is low and the velocity distribution is radially elongated.