The distribution of stars around a massive black hole

The stellar density distribution around a massive black hole at the centre of a spherical star cluster is determined from a simple scaling argument. The distribution is obtained by examining the net diffusion timescales associated with star and energy transport in a spherical, N -body system in dynamic equilibrium. The same analysis is also used to determine the stellar density profile in the halo of a star cluster. The approximate distribution obtained here for a relaxed, N -body system with (or without) a central, massive black hole agrees qualitatively with the results of detailed numerical calculations.