Numerical Experimental Check of Lynden-Bell Statistics--II: The Core-Halo Structure and the Role of the Violent Relaxation

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Abstract
In a previous paper, Lynden-Bell's statistical mechanics of collisionless stellar systems was checked by numerical experiments on four initial configurations of a one-dimensional self-gravitating system. Three of the configurations reached a final state which differed from the predicted one: a relatively small fraction of the particles formed a high energy halo (which contained most of the energy of the system) around a strongly degenerate, low energy core (which contained most of the particles). In the present experiment the core-halo structure appearing in all four configurations considered by us was investigated; in addition, the fourth configuration was continued to a final state, and it was the state predicted by the statistics. A detailed analysis of the particle trajectories showed, that the configuration that reached the predicted final state, and one of those that did not, relaxed equally as violently. The other two configurations, by comparison, relaxed weakly. This limited experimental evidence does not support a strong correlation between the violence of the relaxation and the satisfaction of Lynden-Bell's statistics.

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