Statistics – Computation
Scientific paper
Nov 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984a%26a...140...82s&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 140, no. 1, Nov. 1984, p. 82-90.
Statistics
Computation
11
Computational Astrophysics, Star Clusters, Stellar Motions, Stellar Oscillations, Stellar Systems, Systems Stability, Boltzmann Transport Equation, Density Wave Model, Liouville Equations, Motion Stability, Star Distribution, Stellar Gravitation
Scientific paper
Linear perturbations of stellar systems with step-like distributions of the form F(E)H(-E) are studied, where E is the energy integral, and H is Heaviside's step-function. If (1) dF/dE > 0 and (2) F|dF/dE|-1/2 = 0 at E = 0, then the operator generating the self gravitation term in Antonov's equation is positive. Then the system is stable against all infinitesimal perturbations of the Boltzmann-Liouville equation. Polytropes with index 0.5 < n < 1.5 satisfy conditions (1) and (2) and are stable. If (1) is satisfied and (2) is not satisfied, instability is possible. Polytropes with n < 0.5 are examples of such systems. If dF/dE < 0, the operator generating the self gravitation term is negative and contributes negatively to the stability of the system.
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