A Survey of Disc Thickness and Viscosity in Circumbinary Accretion: Binary Evolution, Variability, and Disc Morphology

Much of the parameter space relevant to the evolution of astrophysical circumbinary accretion discs remains unexplored. We have carried out a suite of circumbinary disc simulations surveying both disc thickness and kinematic viscosity, using both constant-$\nu$ and constant-$\alpha$ prescriptions. We focus primarily on disc aspect ratios between $0.1$ and $0.033$, and on viscosities between $\nu=0.0005$ and $\nu=0.008$ (in units of binary semi-major axis and orbital frequency), and specialise to circular equal-mass binaries. Both factors strongly influence the evolution of the binary semi-major axis: at $\nu=0.0005,$ inspirals occur at aspect ratios $\lesssim0.059$, while at $\nu=0.004$ inspirals occur only at aspect ratios $\lesssim0.04$. Inspirals occur largely because of the increasingly strong negative torque on the binary by streams of material which lag the binary, with negligible contributions from resonant torques excited in the circumbinary disc. We find that reductions in accretion rate occur when simulations are initialised too far from the eventual quasi-steady state driven by interaction with the binary, rather than being intrinsically linked to the disc aspect ratio. We find not only that the cavity size increases as viscosity is decreased, but that thinner circumbinary discs become more eccentric. Our results suggest that supermassive black hole binaries should be driven, more rapidly than previous estimates, from $\sim$parsec separations to distances where gravitational waves drive their inspiral, potentially reducing the number of binaries observable by pulsar timing arrays.