Merger Criteria of Multiple Massive Black Holes and the Impact on the Host Galaxy

Abstract: We perform N-body simulations on a multiple massive black hole (MBH) system in a host galaxy to derive the criteria for successive MBH merger. The calculations incorporate the dynamical friction by stars and general relativistic effects as pericentre shift and gravitational wave recoil. The orbits of MBHs are pursed down to ten Schwarzschild radii (~ 1 AU). As a result, it is shown that about a half of MBHs merge during 1 Gyr in a galaxy with mass $10^{11}M_{\odot}$ and stellar velocity dispersion 240 km/s, even if the recoil velocity is two times as high as the stellar velocity dispersion. The dynamical friction allows a binary MBH to interact frequently with other MBHs, and then the decay of the binary orbits leads to the merger through gravitational wave radiation, as shown by Tanikawa & Umemura (2011). We derive the MBH merger criteria for the masses, sizes, and luminosities of host galaxies. It is found that the successive MBH mergers are expected in bright galaxies, depending on redshifts. Furthermore, we find that the central stellar density is reduced by the sling-shot mechanism and that high-velocity stars with ~ 1000 km/s are generated intermittently in extremely radial orbits.