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 h / r \sim 0.1 ) , to inspiralling for more realistic cooler , thinner disks at a critical value of h / r \sim 0.04 , corresponding to orbital Mach number \mathcal { M } _ { 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 LISA merger event rate .