Collisionless relaxation in gravitational systems From violent relaxation to gravothermal c.pdfVIP

a r X i v : 0 8 0 8 .3 0 9 2 v 1 [ c o n d - m a t .s t a t - m e c h ] 2 2 A u g 2 0 0 8 Collisionless relaxation in gravitational systems: From violent relaxation to gravothermal collapse Yan Levin, Renato Pakter, and Felipe B. Rizzato Instituto de F??sica, UFRGS, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil (Dated: August 22, 2008) 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 τG ～ N collisionless relaxation leads to a gravothermal collapse. Since the pioneering works of Boltzmann and Gibbs, systems with long range interactions have been a ma- jor stumbling block to the development of statistical me- chanics [1]. The difficulty was already well appreciated by Gibbs, who has noted that the equivalence between statistical ensembles breaks down when the interparti- cle potentials decay with exponents smaller than the dimensionality of the embedding space [2]. When this happens, systems exhibit some very unusual properties which appear to violate the second law of thermodynam- ics. For example, confined non-neutral plasmas are found to phase separate into coexisting phases of different tem- peratures [3], while the self-gravitating systems, such as elliptical galaxies, are characterized by a negative specific heat [4].