Dynamics of triple black hole systems in hierarchically merging massive galaxies

Galaxies with stellar bulges are generically observed to host supermassive black holes (SMBHs). The hierarchical merging of galaxies should therefore lead to the formation of SMBH binaries. Merging of old massive galaxies with little gas promotes the formation of low-density nuclei where SMBH binaries are expected to survive over long times. If the binary lifetime exceeds the typical time between mergers, then triple-black-hole systems may form. Such systems can lead to the ejection of one of the black holes (BHs) at a speed exceeding 1000 km/s, far greater than attainable through gravitational radiation recoil. We study the statistics of close triple-SMBH encounters in galactic nuclei by computing a series of three-body orbits with physically-motivated initial conditions appropriate for giant elliptical galaxies. Our simulations include a smooth background potential consisting of a stellar bulge plus a dark matter halo, drag forces due to gravitational radiation and dynamical friction on the stars and dark matter, and a simple model of the time evolution of the inner density profile under heating and mass ejection by the SMBHs. We find that the binary pair coalesces as a result of repeated close encounters in ~85% of our runs. In about 40% of the runs the lightest BH is left wandering through the galactic halo or escapes the galaxy altogether, but escape of all three SMBHs is exceedingly rare. The triple systems typically scour out cores with mass deficits ~1-2 times their total mass, which can help to account for the large cores observed in some massive elliptical galaxies, such as M87. The high coalescence rate, prevalence of very high-eccentricity orbits, and gravitational radiation ``spikes'' during close encounters may provide interesting signals for the future Laser Interferometer Space Antenna (LISA)