ANISOTROPIC GASEOUS MODELS FOR THE EVOLUTION OF STAR-CLUSTERS

We present two anisotropic gaseous models for star clusters. Both are extensions of the standard isotropic gaseous model where the heat flux is proportional to the local temperature gradient and the coefficient of thermal conductivity is a function of the local Jeans length and the local relaxation time, but they differ in the relation between the third-order moments of the velocity distribution. We derive self-similar pre-collapse solutions for both models. We find that, in both solutions, the power-law index is alpha congruent-to 2.23 and the ratio of the radial and tangential mean-square velocity dispersion grows to sigma-r2/sigma-t2 congruent-to 1.30 in the outer parts of the halo which is in excellent agreement with higher order fluid-dynamical models including anisotropy. We demonstrate that these results do not depend sensitively on the assumptions in the models. We then show that, for the boundary conditions of a growing singular isothermal sphere with a central energy source, only one of the models has a self-similar post-collapse solution. The implications of this fact for future time-dependent calculations through core collapse are discussed.