N-Body Evolution of Dense Clusters of Compact Stars

The dynamical evolution of dense clusters of compact stars is studied using direct N-body simulations. The formation of binaries and their subsequent merging by gravitational radiation emission is important to the evolution of such clusters. Aarseth's NBODY5 N-body simulation code is modified to include the lowest order gravitational radiation force during two-body encounters and to handle the decay and merger of radiating binaries. It is used to study the evolution of small-N (= 1000) clusters with different initial velocity dispersions. The initial evolution is similar to that obtained by Quinlan & Shapiro (1989) using a multimass Fokker-Planck code and shows orderly formation of heavy objects. However, the late evolution differs qualitatively from previous results. In particular, we find runaway growth for the most massive object in the cluster: it acquires a mass much larger than that of the other objects and is detached from the smooth mass spectrum of the rest of the objects. We discuss why the Fokker-Planck equation with a mean-rate approach to the merger process cannot model runaway growth, and we present arguments to show that merger by gravitational radiation is expected to be unstable to runaway growth. The results suggest that a seed massive black hole can be formed by runaway growth in a dense cluster of compact stars. The possibility of runaway growth in dense clusters of normal stars is also discussed.