Self-similar relaxation of self-gravitating collisionless particles

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 selfsimilar 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.