SELF-SIMILAR RELAXATION OF SELF-GRAVITATING COLLISIONLESS PARTICLES

We study the evolution of an initially cold, spherically symmetric sys tem of self-gravitating particles. This is done through numerical simu lation using a simple shell code and through an analysis of the ''scal ed'' collisionless Boltzmann and Poisson equations. At early times the system undergoes selfsimilar collapse of the type described by Fillmo re and Goldreich and by Bertschinger. This stage of what is essentiall y 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 f unction.