A simple proof of dynamical stability for a class of spherical clusters

Details A simple proof of dynamical stability for a class of spherical clusters A simple proof of dynamical stability for a class of spherical clusters

Nov 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985apj...298...27k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 298, Nov. 1, 1985, p. 27-33. Research supported by the University of Maryla

Astronomy and Astrophysics

Astrophysics

40

Astronomical Models, Dynamic Stability, Globular Clusters, Perturbation Theory, Boundary Value Problems, Symmetry

Scientific paper

This paper examines the dynamical stability of stationary, collisionless, spherically symmetric Newtonian clusters for which the population f0 of stars in phase space varies monotonically as a function of the energy E0. A pulsation equation is obtained for arbitrary linearized perturbations which, for some cases of physical interest, admits a symmetric operator formulation and, hence, an energy principle. This energy principle provides a simple proof that, at least when ∂f0/∂E0 < 0, (1) all these clusters are stable to radial perturbations, and (2) isotropic clusters are stable to all perturbations.

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