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.
