Collisional Stellar Dynamics Around Massive Black Holes in Active Galactic Nuclei

Kevin P. Rauch
California Institute of Technology,
Canadian Institute for Theoretical Astrophysics, and
University of Maryland


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 independent 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-1/2 profile found in Fokker-Planck studies; the discrepancy can be traced to the simplifying assumptions typically employed by the latter approach.

Keywords: black hole physics --- celestial mechanics, stellar dynamics --- galaxies: active --- galaxies: nuclei

Status: Appeared in The Astrophysical Journal, 514,725.