Relaxation of a Collisionless System and the Transition to a New Equilibrium Velocity Distribution

In this paper, we present our conclusions from the numerical study of thecollapse of a destabilized collisionless stellar system. We use both directintegration of the Vlasov-Poisson equations and an N-body tree code to obtainour results, which are mutually confirmed. We find that spherical andmoderately nonspherical collapse configurations evolve to new equilibriumconfigurations in which the velocity distribution approaches a Gaussian form,at least in the central regions. The evolution to this state has long been anopen question, and in this work we are able to clarify the process responsibleand to support predictions made from statistical considerations (Lynden-Bell1967; Nakamura 2000). The simulations of merging N-body systems show atransition to a Gaussian velocity distribution that is increasingly suppressedas the initial separation of centres is increased. Possible reasons for thisare discussed.Comment: 25 pages, LaTeX. Accepted for publication in Ap