Viscous hydrodynamics simulations of circumbinary accretion discs: variability, quasi-steady state and angular momentum transfer

We carry out numerical simulations of circumbinary discs, solving the viscous hydrodynamics equations on a polar grid covering an extended disc outside the binary co-orbital region. We use carefully controlled outer boundary conditions and long-term integrations to ensure that the disc reaches a quasi-steady state, in which the time-averaged mass accretion rate onto the binary, $\langle\dot{M}\rangle$, matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities ($e_\mathrm{B}$). For $e_\mathrm{B} \lesssim 0.05$, the mass accretion rate of the binary is modulated at about $5$ times the binary period; otherwise it is modulated at the binary period. The inner part of the circumbinary disc ($r \lesssim 6 a_\mathrm{B}$) generally becomes coherently eccentric. For low and high $e_\mathrm{B}$, the disc line of apsides precesses around the binary, but for intermediate $e_\mathrm{B}$ ($0.2 - 0.4$), it instead becomes locked with that of the binary. By considering the balance of angular momentum transport through the disc by advection, viscous stress, and gravitational torque, we determine the time-averaged net angular momentum transfer rate to the binary, $\langle\dot{J}\rangle$. The specific angular momentum, $l_0 = \langle\dot{J}\rangle/\langle\dot{M}\rangle$, depends non-monotonically on $e_\mathrm{B}$. Contrary to previous claims, we find that $l_0$ is positive for most $e_\mathrm{B}$, implying that the binary receives net angular momentum, which may cause its separation to grow with time. The minimum $l_0$ occurs at intermediate $e_\mathrm{B}$ ($0.2 - 0.4$), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.