Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse

Theory and simulations are used to study collisionless relaxation of a gravitational N-body system. It is shown that when the initial one-particle distribution function satisfies the virial condition-potential energy is minus twice the kinetic energy-the system quickly relaxes to a metastable state described quantitatively by the Lynden-Bell distribution with a cutoff. If the initial distribution function does not meet the virial requirement, the system undergoes violent oscillations, resulting in a partial evaporation of mass. The leftover particles phase-separate into a core-halo structure. The theory presented allows us to quantitatively predict the amount and the distribution of mass left in the central core, without any adjustable parameters. On a longer time scale tau(G) similar to N, collisionless relaxation leads to a gravothermal collapse.