Astronomy and Astrophysics – Astrophysics
Scientific paper
Feb 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...243.1013s&link_type=abstract
Astrophysical Journal, Part 1, vol. 243, Feb. 1, 1981, p. 1013-1029. Research supported by the Deutsche Forschungsgemeinschaft.
Astronomy and Astrophysics
Astrophysics
7
Astrophysics, Dynamic Stability, Quasi-Steady States, Stellar Gravitation, Stellar Systems, Systems Stability, Variational Principles, Domains, Eigenvalues, Inhomogeneity, Perturbation Theory, Symmetry
Scientific paper
This paper deals with the stability of two-dimensional collision-free self-gravitating equilibria. Interest is focused on rotational symmetry with an equilibrium distribution function monotonically decreasing with energy and depending on the stars' angular momentum. Other simple geometries are also briefly discussed. It is demonstrated that under well defined conditions Lynden-Bell's variational principle provides necessary and sufficient stability criteria for two-dimensional perturbations. Additional variational principles are derived; they give further insight into the stability properties of stellar systems. The stability of elliptical equilibria is treated in a simplified way. The results support the conjecture that there is a transition from stability to instability at a sufficiently large ellipticity.
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