Inward Bound: The incredible journey of massive black holes as they pair and merge; I. The effect of mass ratio in flattened rotating galactic nuclei

Understanding how supermassive black holes (SMBHs) pair and merge helps to inform predictions of off-center, dual, and binary AGN, and provides key insights into how SMBHs grow and co-evolve with their galaxy hosts. As the loudest known gravitational wave source, binary SMBH mergers also hold centerstage for the Laser Interferometer Space Antenna (LISA), a joint ESA/NASA gravitational wave observatory set to launch in 2034. Here, we continue our work to characterize SMBH binary formation and evolution through increasingly more realistic high resolution direct $N$-body simulations, focusing on the effect of SMBH mass ratio, orientation, and eccentricity within a rotating and flattened stellar host. During the dynamical friction phase, we found a prolonged orbital decay for retrograde SMBHs and swift pairing timescales for prograde SMBHs compared to their counterparts in non-rotating models, an effect that becomes more pronounced for smaller mass ratios $M_{\rm sec}/M_{\rm prim} = q$. During this pairing phase, the eccentricity dramatically increases for retrograde configurations, but as the binary forms, the orbital plane flips so that it is almost perfectly prograde, which stifles the rapid eccentricity growth. In prograde configurations, SMBH binaries form and remain at comparatively low eccentricities. As in our prior work, we note that the center of mass of a prograde SMBH binary itself settles into an orbit about the center of the galaxy. Since even the initially retrograde binaries flip their orbital plane, we expect few binaries in rotating systems to reside at rest in the dynamic center of the host galaxy, though this effect is smaller as $q$ decreases.