2001ApJ...563...34M

We investigate a model in which galactic nuclei form via the coalescence of preexisting stellar systems containing supermassive black holes. Merger simulations are carried out using N-body algorithms that can follow the formation and decay of a black hole binary and its effect on the surrounding stars down to subparsec scales. Our initial stellar systems have steep central density cusps similar to those in low-luminosity elliptical galaxies. Immediately following the merger, the density profile of the remnant is homologous with the initial density profile and the steep nuclear cusp is preserved. However, the formation of a black hole binary transfers energy to the stars and lowers the central density; continued decay of the binary creates a ρ∼r^–1 density cusp similar to those observed in bright elliptical galaxies, with a break radius that extends well beyond the sphere of gravitational influence of the black holes. Our simulations are the first to successfully produce shallow power-law cusps from mergers of galaxies with steep cusps, and our results support a picture in which the observed dependence of nuclear cusp slope on galaxy luminosity is a consequence of galaxy interactions. We follow the decay of the black hole binary over a factor of ∼20 in separation after formation of a hard binary, considerably farther than in previous simulations. We see almost no dependence of the binary's decay rate on number of particles in the simulation, contrary to earlier studies in which a lower initial density of stars led to a more rapid depletion of the binary's loss cone. We nevertheless argue that the decay of a black hole binary in a real galaxy would be expected to stall at separations of 0.01-1 pc unless some additional mechanism is able to extract energy from the binary. We discuss the implications of our results for the survivability of dark matter cusps.