Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

We present a study of the secular evolution of a spherical stellar system with a central star-accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker-Planck equation, with Boltzmann-Vlasov terms on the left-hand side and collisional terms on the right-hand side. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post-collapse evolution of the surrounding stellar cluster in a self-consistent manner. Diffusion in velocity space into the loss cone is approximated by a simple model. The results show that the self-regulated growth of the BH reaches a certain fraction of the total mass cluster and agrees with other methods. Our approach is much faster than competing ones (Monte Carlo, N-body) and provides detailed information about the time- and space-dependent evolution of all relevant properties of the system. In this paper we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). None the less, a generalization to include such effects is conceptually simple and under way.