Long-term evolution of massive black hole binaries. IV. Mergers of galaxies with collisionally relaxed nuclei

Abstract

We simulate mergers between galaxies containing collisionally relaxed nuclei around massive black holes (MBHs). Our galaxies contain four mass groups, representative of old stellar populations; a primary goal is to understand the distribution of stellar-mass black holes (BHs) after the merger. Mergers are followed using direct-summation N-body simulations, assuming a mass ratio of 1:3 and two different orbits. Evolution of the binary MBH is followed until its separation has shrunk by a factor of 20 below the hard-binary separation. During the galaxy merger, large cores are carved out in the stellar distribution, with radii several times the influence radius of the massive binary. Much of the pre-existing mass segregation is erased during this phase. We follow the evolution of the merged galaxies for approximately three central relaxation times after coalescence of the massive binary; both standard and top-heavy mass functions are considered. The cores that were formed in the stellar distribution persist, and the distribution of the stellar-mass BHs evolves against this essentially fixed background. Even after one central relaxation time, these models look very different from the relaxed, multi-mass models that are often assumed to describe the distribution of stars and stellar remnants near a massive BH. While the stellar BHs do form a cusp on roughly a relaxation timescale, the BH density can be much smaller than in those models. We discuss the implications of our results for the extreme-mass-ratio inspiral problem and for the existence of Bahcall-Wolf cusps.