Statistics – Computation
Scientific paper
Mar 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990apj...351..104k&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 351, March 1, 1990, p. 104-113.
Statistics
Computation
25
Computational Astrophysics, Secular Variations, Star Clusters, Stellar Physics, Cosmic Plasma, Gravitational Effects, Vlasov Equations
Scientific paper
This paper focuses on the secular and nonlinear stability of spherical star clusters, modeled as static solutions f(0) to the collisionless Boltzmann, or Vlasov, equation. As for the corresponding case of an electrostatic plasma, this Vlasov equation can be viewed as a Hamiltonian system with respect to a noncanonical generalization of the Poisson bracket, the Hamiltonian H being determined up to the addition of conserved co-callesd Casimirs C. For a plasma, powerful 'energy-Casimir' techniques may then be used to prove that many linearly stable configurations are also secularly and nonlinearly stable. Because of the sign of the gravitational potential, this proof fails for a self-gravitating system, but these techniques are still useful in that they make clear precisely why gravity is pathological and in that they serve to clarify the geometric meaning of earlier analyses.
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