#
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

## 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 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.