Brownian Motion of a Massive Binary

Abstract

The dynamical friction and diffusion coefficients are derived for a massive binary that moves against a uniform background of stars. The random impulses exerted on the binary's center of mass by the field stars are greater than those exerted on a point particle due to inelastic scattering. The frictional force acting on the binary is less than that acting on a point particle due to randomization of the trajectories of field stars that pass near the binary. Both effects tend to increase the random motion of a binary compared with that of a point mass. If the maximum effective impact parameter for gravitational encounters is comparable to the radius of gravitational influence of the binary, its Brownian velocity can be increased by a modest factor compared with that of a single particle. This condition is probably fulfilled in the case of binary supermassive black holes in galactic nuclei.

27 pages, 11 postscript figures, uses emulateapj.sty. Accepted for publication in The Astrophysical Journal