Dynamical evolution of star clusters around a rotating black hole with an accretion disc

Abstract

The dynamical evolution of relativistic star clusters around a massive Kerr black hole with an accretion disc is examined, in the regime where the black hole dominates the potential and star-disc interactions dominate the evolution. A set of diagrams exhibiting the time development of the energy-dependent distribution function, /(¿f), and the distributions of semimajor axes, a, eccentricities, e, and inclinations, /, 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 disc under star-disc interactions, namely a f ~a 0 {l-el) 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-disc interactions on an isotropic cluster, besides the circularization and alignment of orbits, is to steepen an initial density profile p*°c r~ n to the approximate 'asymptotic' profile jO*°cr~ 25 when 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 (^ 10GM/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-disc interactions could be self-limiting 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 .