Gas-driven Inspiral of Binaries in Thin Accretion Disks

Numerical studies of gas accretion onto supermassive black hole binaries have generally been limited to conditions where the circumbinary disk (CBD) is 10-100 times thicker than expected for disks in active galactic nuclei. This discrepancy arises from technical limitations, and also from publication bias toward replicating fiducial numerical models. Here we present the first systematic study of how the binary's orbital evolution varies with disk scale height. We report three key results: (1) binary orbital evolution switches from outspiraling for warm disks (aspect ratio h/r ∼ 0.1), to inspiraling for more realistic cooler, thinner disks at a critical value of h/r ∼ 0.04, corresponding to orbital Mach number ${{ \mathcal M }}_{\mathrm{crit}}\approx 25$ . (2) The net torque on the binary arises from a competition between positive torque from gas orbiting close to the black holes, and negative torque from the inner edge of the CBD, which is denser for thinner disks. This leads to increasingly negative net torques on the binary for increasingly thin disks. (3) The accretion rate is modestly suppressed with increasing Mach number. We discuss how our results may influence modeling of the nano-Hz gravitational-wave background, as well as estimates of the Laser Interferometer Space Antenna merger event rate.