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

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|(γ N)| and the conductivity coefficient C in the gas model of Lynden-Bell & Eggleton. These are |γ 0.11| and |C 0.104|⁠, respectively.