Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 0.4 * 10^6 are considered. The results are compared with the predictions of loss-cone theory under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binaryʹs influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify a recent claim that the hardening rate of the binary stabilizes when N exceeds a particular value or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational wave coalescence in a Hubble time.