The Dynamical Evolution of Dense Rotating Systems: Paper I. Two-Body Relaxation Effects

This paper, and its companion, investigate the evolution of dense stellar systems due to the influence of two-body gravitational encounters, physical collisions and stellar evolution. Our goal is the simulation of the densest centers of galaxies, like M32, which reach stellar densities near a million solar masses per cubic parsec and which may harbor black holes. These systems have a different Safronov number (the dimensionless ratio of stellar binding energy to mean stellar kinetic energy) than globular clusters, substantially increasing the importance of physical collisions relative to gravitational encounters. In this paper, we focus only on the gravitational encounters. We demonstrate, first, that our simulations with small N with a Hernquist tree code yield results basically in accord with years of effort studying globular clusters. Second, we investigate (crudely) core collapse in rotating systems with mass segregation, to separate out the effects purely due to two-body encounters from those seen in the more complex second paper. Consistent with previous studies, we find that systems whose constituent particles follow the Salpeter initial mass function rapidly undergo core collapse through Spitzer's mass segregation instability. All rotationally flattened systems show a decrease in flattening with time, consistent with Fokker-Planck calculations. An interesting new result concerns the well-established inability of simulators to identify a static center in their simulations of collisional systems. We find that the lump of high mass stars which condenses at the center wanders about the core in Brownian motion.