Star distribution around a massive black hole in a globular cluster

Abstract

The distribution of solar-mass stars around a massive black hole in a globular star cluster is investigated using a basic physical picture in which stars in bound orbits in the gravitational potential well of the black hole diffuse from one bound orbit to another via star-star gravitational scattering. Detailed expressions are derived for the relevant diffusion coefficients, the time-dependent Boltzmann equation is solved numerically, and solutions are found which satisfy the boundary conditions at both zero and large binding energy. The results indicate that the distribution function is approximately a power law throughout most of the black hole's gravitational well, that stars in bound orbits diffuse slowly down the gravitational well under equilibrium conditions, and that a black hole of less than or approximately 1000 solar masses may accrete stars primarily by capture from unbound orbits. Several methods for detecting massive black holes in cores of globular clusters are discussed along with expected large statistical fluctuations close to the black hole and the possible relevance of various stellar accretion processes for globular-cluster X-ray sources.