Gas-driven inspiral of binaries in thin accretion disks
  Numerical studies of gas accretion onto supermassive black hole binaries
(SMBHBs) have generally been limited to conditions where the circumbinary disk
(CBD) is 10-100 times thicker than expected for disks in active galactic nuclei
(AGN). 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 outspiralling for warm disks (aspect ratio ~0.1), to inspiralling
for more realistic cooler, thinner disks at a critical aspect ratio ~0.04,
corresponding to orbital Mach number ~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 LISA merger event rate.
