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 mergingof two galaxies each containing a central massive black hole. Our main goalhere is to determine if the black hole binary can merge through the hardeningby dynamical friction and the gravitational wave radiation. We performed$N$-body simulations of merging of two galaxies with wide range of total numberof particles to investigate the effect of the number of particles on theevolution of the black hole binary. We found that the evolution timescale wasindependent of the number of particles in the galaxy $N$ until the separationreaches a critical value. After the separation became smaller than thiscritical value, the evolution timescale was longer for larger number ofparticles. Qualitatively, this behavior is understood naturally the result the``loss-cone'' effect. However, the dependence of the timescale on $N$ isnoticeably weaker than the theoretical prediction. In addition, the criticalseparation is smaller than the theoretical prediction. The timescale ofevolution through gravitational radiation at this critical separation is longerthan the Hubble time. We discuss the reason of these discrepancy and theimplication of the present result on the structure of the ellipticals and QSOactivities.