Stability of Encounterless Spherical Stellar Systems

Physics

Scientific paper

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Scientific paper

We show that a sufficient condition for stability for the spherical modes of a stellar system is that the distribution function F(ɛ) decrease with the energy ɛ. For this demonstration we approximate the function F(ɛ) by a succession of steps corresponding to a multiple "water-bag" model. The total energy is shown to be an absolute minimum: The second variation δW of the energy is always strictly positive and there is no marginal mode.

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