Resonant motions of supermassive black hole triples

Triple supermassive black holes (SMBH) can form during the hierarchical mergers of massive galaxies with an existing binary. Perturbations by a third black hole may accelerate the merging process of an inner binary, for example through the Kozai mechanism. We analyze the evolution of simulated hierarchical triple SMBHs in galactic centers, and find resonances in the evolution of the semi-major axis, the eccentricity and the inclination, for both the inner and the outer orbits of the triple system, which are not only Kozai like. Through resonant oscillations, SMBH can trigger a significant increase of the inner SMBH binary eccentricity shortening the merger timescale expected from gravitational wave (GW) emission. As hierarchical triple SMBHs may be frequent in massive galaxies, the influence of orbital resonances is of great importance to our understanding of black hole coalescence and gravitational wave detection. Although Kozai mechanism is believed to play an important role in this process, detailed studies on the pattern of these resonances is necessary.