Self-Similar Relaxation of Self-Gravitating Collisionless Particles

Abstract

We study the evolution of an initially cold, spherically symmetric system of self-gravitating particles. This is done through numerical simulation using a simple shell code and through an analysis of the ``scaled'' collisionless Boltzmann and Poisson equations. At early times the system undergoes self-similar collapse of the type described by Fillmore and Goldreich and by Bertschinger. This stage of what is essentially phase mixing soon gives way to a period of more efficient relaxation driven by an instability in the similarity solution. We also discuss the connection between initial conditions and the final distribution function.