Star clusters containing massive, central black holes: Monte Carlo simulations in two-dimensional phase space.

It is pointed out that the approximations employed by previous authors regarding the two-dimensionality of the distribution function and the process of consumption in the case of the problem of a massive black hole residing at the center of a star cluster have not been very precise. A new analysis is, therefore, conducted, involving the construction of a two-dimensional, Monte Carlo dynamical simulation scheme and its application to solve the Fokker-Planck equation in E- and J-space for the steady distribution and consumption of stars around a massive black hole. The key features of the Monte Carlo method used include a 'step adjustment algorithm', used to reconcile the very short dynamical time scales, associated with loss-cone consumption, with the rather long relaxation time scales found deep in the cusp. Another feature is a star 'creation-annihilation scheme' which ensures that the results of the simulation remain statistically accurate even at large absolute values of E, deep in the cusp where the actual number of stars decreases rapidly and becomes small.