Star distribution around a massive black hole in a globular cluster

To predict the likely distribution of stars around a massive black hole in the core of a cluster of stars, an equation of the Fokker-Planck type is derived that describes the diffusion of stars in the 1/r gravitational well of the black hole, by star-star gravitational collisions. The main assumptions are: (1) the distribution of stars is described by a single-particle distribution function that is shperically symmetric in coordinate space and approximately isotropic in velocity space; (2) the stars have equal masses; (3) star mass very-much-less-thanblack-hole massvery-much-less-thancluster-core mass; (4) a star is destroyed by star-star collisions or by tidal forces when its binding energy in the well exceeds a specified large value; (5) binaries are unimportant. Numerical solutions for the time-dependent equations indicate that the equilibrium star density, closely approached within a collision time, approximates an r/sup -7///sup 4/ power law throughout most of the well. The same equilibrium power law obtains for nonisotropic distribution functions whose anisotropy is independent of r. Stars in bound orbits about a black hole diffuse slowly into its gravitational well under equilibrium conditions. A black hole of approximately-less-than10/sup 3/ M/sub sun/ may accrete stars primarily by capture from unbound orbits.Theshape of the star distribution more » near the cluster center observed with small diaphragms is predicted. As a function of diaphragm size, the velocity dispersion and line profile that might be measured spectroscopically is calculated. Some calculations are also presented for an open slit configuration. For globular clusters in our Galaxy, one might be able to detect black holes with masses approximately-greater-than5 x 10/sup 3/ M/sub sun/ and, with a large space telescope, masses approximately-greater-than10/sup 3/ M/sub sun/. An approximate formula for the mean distance of a massive black hole from the center of mass of the unbound stars is also presented. (AIP) « less