Evolution of Supermassive Black Hole Pairs on Inclined Orbits in Post-Merger Galaxies

Theoretical models of the evolution of supermassive black hole (SMBH) pairs in post-merger remnant galaxies are necessary to motivate observational searches for dual active galactic nuclei (AGN) and gravitational wave sources. Studies have explored the dynamical evolution of SMBH pairs under the influence of dynamical friction to calculate pairing times and predict the expected population of dual-AGNs at various redshifts. We formulate a three-dimensional dynamical model of SMBH pairs in the innermost kiloparsec of a post-merger galaxy to investigate the impact of orbital inclination with respect to the galactic disk on pairing times. The SMBH pairs are evolved in 81 different galaxy configurations initialized using a Gauss-Seidel Poisson solver. The dynamics are calculated for 12 distinct initial inclinations ranging from 0 to 75 degrees in each of the galaxies to gauge the impact of inclination on pairing time. Orbits characterized by initial inclinations greater than 20 degrees frequently require longer pairing times when compared to uninclined orbits. Pairing times for orbits with inclinations $\gtrsim 45$ degrees often exceed 14 Gyr. Galaxies with higher mass SMBH pairs and faster rotating disks generally shorten pairing times relative to galaxies with less massive or slower rotating disks when the inclination is $\lesssim 45$ degrees. The model suggests that SMBH pairs that form from mergers at inclinations $\lesssim 20$ degrees are likely progenitors of dual-AGN and gravitational wave sources.