Merging of Galaxies with Central Black Holes. II. Evolution of the Black Hole Binary and the Structure of the Core

We investigated the evolution of the black hole binary formed by the merging of two galaxies, each containing a central massive black hole. Our main goal here is to determine if the black hole binary can merge through the hardening by dynamical friction and the gravitational wave radiation. We performed N-body simulations of the merging of two galaxies with a wide range of the total number of particles to investigate the effect of the number of particles on the evolution of the black hole binary. We found that the evolution timescale was independent of the number of particles in the galaxy N until the semimajor axis reached a critical value. After the semimajor axis became smaller than this critical value, the evolution timescale was longer for larger numbers of particles. Qualitatively, this behavior is understood naturally as the result of the "loss cone" effect. However, the dependence of the timescale on N is noticeably weaker than the theoretical prediction. In addition, the critical semimajor axis is smaller than the theoretical prediction. The timescale of evolution through gravitational radiation at this critical semimajor axis is longer than the Hubble time. We discuss the reason of this discrepancy and the implication of the present result on the structure of the elliptical galaxies and QSO activities.