On the statistical mechanics of violent relaxation

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[[abstract]]This paper reexamines the foundations of Lynden-Bell's (1967) statistical-mechanical discussion of violent relaxation in collisionless stellar systems. It is argued that Lynden-Bell's formulation in terms of a continuum description introduces unnecessary complications, and a more conventional formulation in terms of particles is considered. The exclusion principle discovered by Lynden-Bell is found to be quantitatively important only at phase densities where two-body encounters are no longer negligible. Since the dynamical basis for the exclusion principle vanishes in such cases anyway, Lynden-Bell statistics always reduces in practice to Maxwell-Boltzmann statistics when applied to stellar systems. Lynden-Bell also found the equilibrium distribution function generally to be a sum of Maxwellians with velocity dispersions dependent on the phase density at star formation. It is shown that this difficulty vanishes in the particulate description for an encounterless stellar system as long as stars of different masses are initially well mixed in phase space. --------------------------------------------------------------------------------[[fileno]]2010118010117[[department]]物理

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