Statistics of N-body simulations -I. Equal masses before core collapse

Abstract

We study the dynamical evolution of idealized stellar systems by averaging results from many N-body simulations, each having modest numbers of stars. For isolated systems with stars of uniform mass, we discuss aspects of evolution up to the point of core collapse: relaxation and its N-dependence, the evolution of the density profile, the development of the velocity dispersion and anisotropy, and the rate of stellar escape. We find that the continuum models (gas and Fokker-Planck) agree quite accurately with N-body simulations in which N is of order of a few hundred. Small deviations from these models are present at small radii and at radii from the half-mass radius outwards. They are probably associated with binary activity and with the development of anisotropy, respectively. As expected, the N-body systems are strongly anisotropic in the outer half of the mass, while in the core the velocity distribution is isotropic to good approximation. Anisotropy has a very important influence on the rate of escape of stars. We also estimate quite reliable values for the coefficient γ in the Coulomb logarithm ln(γV) and the conductivity coefficient C in the gas model of Lynden-Bell & Eggleton. These are γ ≈ 0.11 and C-0.104, respectively.