Random Gravitational Encounters and the Evolution of Spherical Systems. IV Isolated Systems of Identical Stars

Abstract

Models of isolated stellar systems with stars all of the same mass have been recomputed, allowing for the exact dependence of the velocity diffusion coefficients on stellar velocity, and extending to later evolutionary phases than before. The results show that the inner 10 percent of the mass collapses to a singularity in a time about equal to 18 t , where is the dynamical relaxation time at the mean density inside the median radius rh during the early life of the system. This behavior is in general agreement with earlier results by Larson. Early in the evolution the energy released by the contracting core goes primarily into stars which accumulate in the outer halo, with some drain also into stars which escape from the system. Toward the end of the development the energy goes into a readjustment of the intermediate regions of the system; this later stage appears unrelated to buildup of the outer halo or to stellar escape but is similar to the "gravo-thermal instability" discussed by Lynden-Bell and Wood. These models permit a comparison of escape rates with a "local" theory, where the velocity distribution function at any point is arbitrarily assumed to be the same as that obtained from the Fokker-Planck equation for a homogeneous system, with a rectangular profile for the potential (r), and where , the overall probability of escape per star per interval of time, is computed by averaging over the entire system the local escape probability at each point. The "observed" for the isolated systems rises to about 0.3 percent per time interval t , as compared with about 0 8 to 1 percent predicted by the local theory. If escaping stars are taken to include those which accumulate in the outer halo, which outnumber the true escapers by about two to one at intermediate evolutionary phases, the results from the computer models are in reasonable agreement with the simple theory at these intermediate times.