Unstable modes of a spherical stellar system

This work studies the radial orbit instability for a family of anisotropic isochrone spheres by a numerical linear stability analysis, and then compares the results with N-body simulations. A new way of choosing basis functions for the modes is introduced that allows spatially infinite systems to be handled without truncation. For the more unstable models, the shapes and growth rates of the modes are fairly well reproduced in N-body simulations. These results suggest that spherical models are unstable over a wider range of anisotropies than previously supposed.