Dynamical Theory of Collisionless Relaxation
Abstract
In his theory of violent relaxation, LyndenBell gave a rigorous derivation of the equilibrium distribution, but only a qualitative discussion of the manner in which equilibrium is attained Here we present a fully explicit dynamical theory of collisionless relaxation towards LyndenBel equilibrium. The analysis proceeds from the coarsegraining in phase space of the collisionless Boltzmann equation the mesh size being determined by the precision of the observational data. The theoretical developmen leads to a kinetic equation generalizing that obtained by Kadomtsev and Pogutse in the rather differen context of homogeneous plasma turbulence. The ‘collision’ integral differs from the classical Fokker Planck type essentially by the appearance of products of three distribution functions. It drives th systems towards the LyndenBell equilibrium state, on a timescale which is inversely proportional to th coarsegraining mesh and, in the nondegenerate limit, to the finegrained phase density. Owing to th various approximations introduced, the theory does not, however, describe the violent relaxation proces itself, but rather its late quiescent phases.
 Publication:

Astrophysics and Space Science
 Pub Date:
 October 1980
 DOI:
 10.1007/BF00639139
 Bibcode:
 1980Ap&SS..72..293S
 Keywords:

 Astrophysics;
 Collision Parameters;
 Dynamic Models;
 Gravitational Effects;
 Relaxation (Mechanics);
 Boltzmann Transport Equation;
 Correlation;
 Integral Equations;
 Kinetic Equations;
 Vlasov Equations;
 Astrophysics