Monte Carlo simulations of the evolution of galactic nuclei containing massive, central black holes

Several Monte Carlo simulations of the dynamical evolution of dense galactic nuclei containing massive central black holes have been performed. The initial conditions used in the simulations are discussed and the numerical methods used to incorporate stellar collisions into the Monte Carlo scheme are described. Various analytic results and scaling laws for the collision rates in certain limiting cases are derived and used to test the Monte Carlo code. The Monte Carlo results are presented for cluster evolution without physical collisions, and simulations dominated by physical collisions are treated. Simple analytic scaling laws are derived for the evolutionary time scales, mass accretion rates, and late-time evolution of galactic nuclei. Finally, the relationship between the results and the observed magnitudes and redshifts of quasars is addressed.