STABILITY AGAINST PHASE MIXING OF COLLISIONLESS SELF-GRAVITATING MATTER

It is suggested how to define a macroscopic steady state of a collisionless self-gravitating system with Newtonian interactions in terms of H-functions. A new condition for stability is formulated as a consequence thereof: Any single-variable distribution function, f = f (Q), which is a stationary point of some entropy-like functional, must have df/dQ less-than-or-equal-to 0 to be stable against phase mixing. For the special class of Osipkov-Merritt models, Q = E + L2/2r(a)2, this is found to agree with results of published numerical experiments. The stability criterion may have important implications for the equilibria of galaxies and dark-matter halos. One consequence is that stable spherical galaxies apparently have an anisotropy radius, r(a), greater than approximately 40% of the half-mass radius. This finding is consistent with dissipationless-collapse simulations.