Evolution of Massive Black Hole Binaries

We present the result of large-scale N-body simulations of thestellar-dynamical evolution of a massive black-hole binary at the center of aspherical galaxy. We focus on the dependence of the hardening rate on therelaxation timescale of the parent galaxy. A simple theoretical argumentpredicts that a binary black hole creates the ``loss cone'' around it. Once theloss cone is formed, the hardening rate is determined by the rate at whichfield stars diffuse into the loss cone. Therefore the hardening timescalebecomes proportional to the relaxation timescale. Recent N-body simulations,however, have failed to confirm this theory and various explanations have beenproposed. By performing simulations with sufficiently large N (up to $10^6$)for sufficiently long time, we found that the hardening rate does depend on N.Our result is consistent with the simple theoretical prediction that thehardening timescale is proportional to the relaxation timescale. Thisdependence implies that most massive black hole binaries are unlikely to mergewithin the Hubble time through interaction with field stars and gravitationalwave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear in the February 10, 2004 issu