Effects of Wandering on the Coalescence of Black Hole Binaries in Galactic Centers

We examine whether massive binary black holes in spherically symmetric bulges of galaxies can achieve coalescence through the emission of gravitational radiation under the action of stellar dynamical processes alone. In particular, we address the importance of the Brownian motion of a binary's center-of-mass to its continued interaction with stellar orbits that allows it to keep hardening: the restoring force holding the binary at the center decreases as it depletes the central stellar density, causing the amplitude of wandering to increase. We use an analytical model and N-body simulations to calculate the time required to reach the gravitational-radiation dominated stage. We find that a substantial fraction of all massive binaries in galaxies can coalesce within a Hubble time.