Statistical mechanics of violent relaxation in stellar systems
Abstract
Description
We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small-scales and describe the ``coarse-grained'' dynamics. In a coarse-grained sense, the system is expected to reach an equilibrium state of a Fermi-Dirac type within a few dynamical times. We describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self-gravitating systems. Then, we introduce a small-scale parametrization of the Vlasov equation and propose a set of relaxation equations for the coarse-grained dynamics. These relaxation equations, of a generalized Fokker-Planck type, are derived from a Maximum Entropy Production Principle (MEPP). We make a link with the quasilinear theory of the Vlasov-Poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces. With the aid of this kinetic theory, we qualitatively discuss the concept of ``incomplete relaxation'' and the limitations of Lynden-Bell's theory.
In Proceedings of the Conference on Multiscale Problems in Science and Technology, edited by N. Antonic, C.J. van Duijn, W. Jager, and A. Mikelic (Springer, Berlin, 2002)
In Proceedings of the Conference on Multiscale Problems in Science and Technology, edited by N. Antonic, C.J. van Duijn, W. Jager, and A. Mikelic (Springer, Berlin, 2002)