Numerical models of star clusters with a central black hole. I - Adiabatic models

Numerical models of star clusters containing a massive black hole are computed for the case of a black hole which grows adiabatically in the cluster center. The growth of the hole is assumed to be at a rate longer than the cluster dynamical time scale but shorter than the relaxation time scale. The angular momentum and radial action of each star in the cluster are conserved during the adiabatic variations. This leads to the invariance of the distribution function in (E, J) space which is used to facilitate the numerical calculations. A power-law density cusp forms near the black hole. When the hole has grown to exceed the core mass of the cluster, this cusp joins smoothly onto the isothermal density law.