#
Dynamical Evolution of Star Clusters Around a
Rotating Black Hole With an Accretion Disk

*Kevin P. Rauch*

Theoretical Astrophysics 130-33,

California Institute of Technology,

Pasadena, CA 91125.

## Abstract

The dynamical evolution of relativistic star clusters around a massive
Kerr black hole with an accretion disk
is examined, in the regime where the black hole dominates the
potential and star-disk interactions dominate the evolution.
A set of diagrams exhibiting the time development of the
energy-dependent distribution function, *f*(*E*), and the
distributions of semi-major axes, *a*, eccentricities, *e*,
and inclinations, *i*, of the model system
are presented; plots of the latter three quantities over time for a few
illustrative orbits are also given.
A simple approximation for the final radius of an orbit brought into
the disk under star-disk interactions, namely
*a*_{f} =
*a*_{0}(1-*e*_{0}^{2})
cos^{4}(*i*_{0}/2)
(or, in terms of angular momentum,
*L*_{f} =
(*L*_{0}+*L*_{z,0})/2), is derived.
It is found that the main effect of star-disk interactions on an
isotropic cluster, besides the circularization and alignment of orbits,
is to steepen an initial density profile
ρ_{*} ∝ *r*^{-n}
to the approximate `asymptotic' profile
ρ_{*} ∝ *r*^{-2.5}
when *n* < 2.5, to leave the profile
unchanged when *n* > 2.5,
and in both cases to increase the central density (by several hundred
very close to the black hole); initially anisotropic clusters are found
to exhibit similar patterns. The numerical results can be explained
in terms of a simple analytic model. Relativistic effects are found
to affect the cluster properties significantly only at very small radii
(< 10*GM/c*^{2});
in particular, the location of the last stable orbit limits the
cluster's inner extent. By significantly
increasing the central stellar density, star-disk interactions could
self-limit themselves by causing stellar collisions to become
important; the future
evolution of the cluster in this case will depend on the relative
balance of the collisional, alignment, and stellar evolutionary
timescales.

**Keywords:**
accretion disks --- black hole physics --- galaxies: nuclei ---
stellar dynamics

**Status:** Appeared in *MNRAS*, **275**, 628 (1995).