Numerical Experimental Check of Lynden-Bell Statistics for a Collisionless One-Dimensional Stellar System

Abstract

Lynden-Bell's statistical mechanics of violent relaxation in stellar systems was checked by numerical experiments on one-dimensional collisionless self-gravitating systems. All the free parameters of the statistics (the initial fine grained phase space density, the total energy and the total mass) were kept constant, while the configuration in phase space was varied. Three cases did reach the same final state. In all three cases, the distribution of the low energy particles (about 6o per cent of the particles) resembled Lynden-Bell's prediction, but the high energy tail containing the bulk of the total energy was not in accord with the statistics. It is not known what fraction of the tail was formed dynamically or was left behind from the initial distribution and failed to interact with the bulk of the particles.