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.