Geometric Approach to Secular and Nonlinear Stability for Spherical Star Clusters
Abstract
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 cocallesd Casimirs C. For a plasma, powerful 'energyCasimir' 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 selfgravitating 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1990
 DOI:
 10.1086/168449
 Bibcode:
 1990ApJ...351..104K
 Keywords:

 Computational Astrophysics;
 Secular Variations;
 Star Clusters;
 Stellar Physics;
 Cosmic Plasma;
 Gravitational Effects;
 Vlasov Equations;
 Astrophysics;
 CLUSTERS: GLOBULAR;
 HYDRODYNAMICS;
 STARS: STELLAR DYNAMICS