Self-Similar Approach to Violent Relaxation

Abstract

We consider the evolution of an initially cold, spherically symmetric system of self-gravitating particles. At early times the system undergoes self-similar collapse of the type described by Fillmore & Goldreich and Bertschinger. This stage of phase mixing soon gives way to a period of violent relaxation driven by an instability in the similarity solution. The onset of violent relaxation is illustrated by numerical simulations and supported by non-linear analysis of the ``scaled'' collisionless Boltzmann and Poisson equations.