Statistical Mechanics of Violent Relaxation in Stellar Systems

By Pierre-Henri Chavanis. 2002

229 citations recorded by the source corpus.

We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of (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.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e0ad85fabc5c676afa3a22fb2fdc96ed62e6577e

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In Astronomy and Astrophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems (2002, methodology): “A similar kinetic confinement can be advocated in the case of stellar systems [54,42] to account for incomplete relaxation [90] and solve the infinite mass problem.”
Galactic Searches for Dark Matter (2012, background): “The above paradox led to the development of the theory of ‘violent relaxation’ by Lynden-Bell (1967).”
On Landau damping (2009, background): “11In Lynden-Bell’s appealing words [52, p.295], “a system whose density has achieved a steady state will have information about its birth still stored in the peculiar velocities of its stars.” it may be a good illustration of what happens in phase mixing.)”
Landau Damping: Paraproducts and Gevrey Regularity (2013, background): “It was later “exported” to galactic dynamics by Lynden-Bell [55,56] where it is thought to play a key role in the stability of galaxies.”
Gravitational N-Body Simulations (2003, background): “The concept of violent relaxation [Lynden-Bell, 1967] was introduced to describe galaxy formation but is equally relevant for star clusters.”
Nonequilibrium statistical mechanics of systems with long-range interactions (2013, methodology): “Lynden-Bell Statistics In a seminal work, Lynden-Bell (LB) proposed a statistical approach for calculating f̄(q,p) for the final stationary state [104].”