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, ̇, matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities (eB). For eB 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 6 aB) generally becomes coherently eccentric. For low and high eB, the disc line of apsides precesses around the binary, but for intermediate eB (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, ̇. The specific angular momentum, l₀ = ̇/̇, depends non-monotonically on eB. Contrary to previous claims, we find that l₀ is positive for most eB, implying that the binary receives net angular momentum, which may cause its separation to grow with time. The minimum l₀ occurs at intermediate eB (0. 2 - 0. 4), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.