Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986ap%26ss.125..361k&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 125, no. 2, Aug. 1986, p. 361-374. Research supported by the University of
Astronomy and Astrophysics
Astrophysics
1
Boltzmann Transport Equation, Dynamic Stability, Gravitation Theory, Jeans Theory, Momentum Theory, Secular Variations, Star Clusters
Scientific paper
This paper uses existing techniques developed by Ipser, Thorne, and Kandrup (Ipser and Kandrup, 1980, and Ipser and Thorne, 1968) to examine the stability of multicomponent systems, with a distribution of masses, whose evolution is described by the 'collisionless' or 'collisional' Boltzmann equation. The principal conclusions are as follows: (1) all static, spherically-symmetric solutions to the collisionless equations, appropriate for a star cluster, are guaranteed to be stable with respect to spherically-symmetric disturbances, provided only that the population of stars is, for fixed mass, a decreasing function of the mean field energy; (2) if, furthermore, the static configuration has an isotropic distribution of momenta, it will also be stable toward nonradial perturbations; (3) the unique static solution to the collisional equations for a spherically-symmetric spatially truncated configuration can be stable only if that configuration is a local entropy maximum; and (4) a simple expression is obtained for the Jeans length for a system with an arbitrary isotropic distribution of momenta.
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