Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems

Abstract

ABSTRACT We investigate the evolution of the phase–space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating system. By means of the recently introduced symplectic coarse graining technique, we obtain an effective evolution equation that allows us to compute the scaling of the frequencies around a stationary state, as well as the damping times of Fourier modes of the distribution function, with the magnitude of the Fourier k −vectors themselves. We compare our analytical results with N-body simulations.