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 . (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.

Using high-resolution hydrodynamics simulations, we show that equal-mass binaries accreting from a circumbinary disk evolve toward an orbital eccentricity of e ≃ 0.45, unless they are initialized on a nearly circular orbit with e ≲ 0.08, in which case they further circularize. The implied bi-modal eccentricity distribution resembles that seen in post-AGB stellar binaries. Large accretion spikes around periapse impart a tell-tale, quasiperiodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at z ≲ 10 entering the LISA band will have measurable eccentricities in the range of e ≃ 10−3 − 10−2, if they have experienced a gas-driven phase. On the other hand, GW190521 would have entered the LIGO/Virgo band with undetectable eccentricity ∼10−6 if it had been driven into the gravitational-wave regime by a gas disk.

Linear analysis of gas flows around orbiting binaries suggests that a centrifugal barrier ought to clear a low-density cavity around the binary and inhibit mass transfer onto it. Modern hydrodynamics simulations have confirmed the low-density cavity, but show that any mass flowing from large scales into the circumbinary disk is eventually transferred onto the binary components. Even though many numerical studies confirm this picture, it is still not understood precisely how gas parcels overcome the centrifugal barrier and ultimately accrete. We present a detailed analysis of the binary accretion process, using an accurate prescription for evolving grid-based hydrodynamics with Lagrangian tracer particles that track the trajectories of individual gas parcels. We find that binary accretion can be described in four phases: (1) gas is viscously transported through the circumbinary disk up to the centrifugal barrier at the cavity wall, (2) the cavity wall is tidally distorted into accretion streams consisting of near-ballistic gas parcels on eccentric orbits, (3) the portion of each stream moving inwards of an accretion horizon radius r ¯ ≃ a —the radius beyond which no material is returned to the cavity wall—becomes bound to a minidisk orbiting an individual binary component, and (4) the minidisk gas accretes onto the binary component through the combined effect of viscous and tidal stresses.