Numerical experiments on stationary, oscillating, and damped spherical galaxy models

We numerically analyse solutions of the spherically symmetric gravitational Vlasov-Poisson system close to compactly supported stable steady states. We observe either partially undamped oscillations or macroscopically damped solutions. We investigate for many steady states to which of these behaviours they correspond. A linear relation between the exponents of polytropic steady states and the qualitative behaviour close to them is identified. Undamped oscillations are also observed around not too concentrated King models and around all shells with a sufficiently large vacuum region. We analyse all solutions both at the non-linear and linearised level and find that the qualitative behaviours are identical at both. To relate the observed phenomena to theoretical results, we further include a comprehensive numerical study of the radial particle periods in the equilibria.