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Title:
A simple proof of dynamical stability for a class of spherical clusters
Authors:
Kandrup, H. E.; Sygnet, J. F.
Affiliation:
AA(CNRS, Institut d'Astrophysique, Paris, France; Maryland, University, College Park), AB(CNRS, Institut d'Astrophysique, Paris, France)
Publication:
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 298, Nov. 1, 1985, p. 27-33. Research supported by the University of Maryland and Institut d'Astrophysique. (ApJ Homepage)
Publication Date:
11/1985
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
Astronomical Models, Dynamic Stability, Globular Clusters, Perturbation Theory, Boundary Value Problems, Symmetry
DOI:
10.1086/163586
Bibliographic Code:
1985ApJ...298...27K

Abstract

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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