Stability of spherical stellar systems -- II. Numerical results

We have performed a series of high resolution N-body experiments on aConnection Machine CM-5 in order to study the stability of collisionlessself-gravitating spherical systems. We interpret our results in the frameworkof symplectic mechanics, which provides the definition of a new class ofparticular perturbations: The preserving perturbations, which are ageneralization of the radial ones. Using models defined by the Ossipkov-Merrittalgorithm, we show that the stability of a spherical anisotropic system isdirectly related to the preserving or non-preserving nature of theperturbations acting on the system. We then generalize our results to allspherical systems. Since the ``isotropic component'' of the linear variation ofthe distribution function cannot be used to predict the stability orinstability of a spherical system, we propose a more useful stability parameterwhich is derived from the ``anisotropic'' component of the linear variation.Comment: uuencoded gzip compressed postscript file containing 14 pages, accepted for publication in MNRA