Long-term evolution of massive black hole binaries. IV. Mergers of
  galaxies with collisionally relaxed nuclei
  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 black
holes 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 time-scale, the BH density can be much smaller than in those models.
We discuss the implications of our results for the EMRI problem and for the
existence of Bahcall-Wolf cusps.
