Globally stable equilibria of collisionless self-gravitating matter with nonvanishing total angular momentum

Astronomy and Astrophysics – Astrophysics

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Angular Momentum, Celestial Mechanics, Elliptical Galaxies, Galactic Evolution, Relaxation (Mechanics), Stellar Orbits

Scientific paper

We demonstrate how to determine globally stable equilibrium states of collisionless self-gravitating matter with nonvanishing total angular momentum by a suitable energy minimization procedure. The distribution functions of the resulting equilibria depend on Jacoby's integral. In the minimization procedure we consider explicitly that the systems should be gravitationally bound in all parts. With the help of a model relaxation this technique can be used to determine final states of collisionless relaxation. In our approach to that dissipationless (i.e., energy conserving) relaxation by mixing in phase space the final states are calculated as globally stable equilibria on macroscopic scales. The energy conserving model relaxation increases entropy but does not maximize entropy. This approach yields new aspects considering the dependence of the final states on the initial conditions.

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