On the Distribution of High Energy Stars in Spherical Stellar Systems

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Abstract
A distribution function f ( r, υ, µ; t ) for isolated spherical stellar systems is obtained from the Boltzmann equation with encounters described by the Fokker-Planck equation. The distribution function is believed to correspond rather closely to actual stellar systems since it is obtained from the Boltzmann equation, the potential is obtained from Poisson's equation, and the stellar orbits are not assumed to be isotropic everywhere but rather are more radial at greater distances from the centre. The paper emphasizes the importance of a careful analysis in the region of phase space at and near the energy of escape. In this region it is shown that the velocity space flux vector is constant, and it is this constancy which allows a solution for f . The distribution of high energy stars is depopulated for (i) those stars whose mass is small compared to the average stellar mass, (ii) regions close to the centre of the system, and (iii) large values of the model parameter C . It is proposed that the method of analysis presented in this study may be used for obtaining a distribution function for rotating stellar systems.

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