Collisional Stellar Dynamics around Massive Black Holes in Active Galactic Nuclei

Abstract

The dynamical evolution of nuclear star clusters containing a massive black hole is examined in the region in which physical collisions dominate other processes and the black hole dominates the potential. The numerical method features a discrete cluster of stars, fully relativistic calculation of the orbital trajectories (including an algorithm that searches for individual collisions between pairs of orbits), and the use of a series of smooth particle hydrodynamics simulations of high-velocity stellar impacts (computed independently of this work) to determine collision outcomes. In contrast to a Fokker-Planck analysis, this approach allows small-number statistics, relativistic effects, and collision dynamics to be accounted for directly and accurately. The versatility of the simulation techniques makes them usable in a range of problems; useful by-products of the routines include a simple, exact procedure for computing the integrals of motion of Kerr geodesics given their Keplerian orbital elements and a generalized form of Kepler's equation that is (asymptotically) valid in the Kerr geometry. We find that many grazing collisions produce very little mass loss—even when a head-on collision would lead to complete disruption—thereby creating an extended distribution of low-mass remnants. Collisional refilling of the loss cone is seen and generally dominates relaxation-induced disruptions in these systems. It is found that collisions preferentially produce a constant density core in the collisionally dominated region of the cusp, as opposed to the ρ∝r−½ profile found in Fokker-Planck studies; the discrepancy can be traced to the simplifying assumptions typically employed by the latter approach.