Relaxation with close encounters in stellar systems

Previous applications of the Kolomogorov-Feller (KF; 1940) equation to the problem of the relaxation of the velocity distribution in a star cluster are reviewed. Solutions to the KF equation are presented in which earlier shortcomings concerning encounters with a small velocity increment are corrected. Results are reported for calculations of steady-state velocity distributions, theoretical estimates of the number of stars that escape due to sudden energy gains during close encounters, and a theoretical estimate of the fraction of kinetic energy carried away by escaping stars. These results are compared with corresponding solutions to the Fokker-Planck equation.

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