Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...424..106h&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 424, no. 1, p. 106-113
Astronomy and Astrophysics
Astrophysics
5
Boltzmann Transport Equation, Dark Matter, Galactic Evolution, Galactic Halos, Many Body Problem, Mathematical Models, Gravitational Effects, Hamiltonian Functions, Steady State
Scientific paper
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 + L2/2r2a, 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, ra, greater than approximately 40% of the half-mass radius. This finding is consistent with dissipationless-collapse simulations.
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