The dynamical evolution of massive black hole binaries — II. Self-consistent N-body integrations

We use a hybrid N-body program to study the evolution of massive black hole binaries in the centers of galaxies, mainly to understand the factors affecting the binary eccentricity, the response of the galaxy to the binary merger, and the effect of loss-cone depletion on the merger time. The scattering experiments from paper I (Quinlan, 1996)[NewA, 1, 35] showed that the merger time is not sensitive to the eccentricity growth unless a binary forms with at least a moderate eccentricity. We find here that the eccentricity can become large under some conditions if a binary forms in a galaxy with a flat core or with a radial bias in its velocity distribution, especially if the dynamical friction is enhanced by resonances as suggested by Rauch & Tremaine (1996)[NewA, 1, 149]. But the necessary conditions seem unlikely, and our prediction from paper I remains unchanged: in most cases the eccentricity will start and remain small. The ejection of stars caused by the hardening of a binary may explain why large elliptical galaxies have weaker density cusps than smaller galaxies. If so, the central velocity distributions in those galaxies should have strong tangential anisotropies. The wandering of a binary from the center of a galaxy counteracts the effects of loss-cone depletion and helps the binary merge.