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 on to the binary, 〈 M˙ 〉, matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities (e_B). For e_B ≲ 0.05, the mass accretion rate of the binary is modulated at about five times the binary period; otherwise, it is modulated at the binary period. The inner part of the circumbinary disc (r ≲ 6a_B) generally becomes coherently eccentric. For low and high e_B, the disc line of apsides precesses around the binary, but for intermediate e_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, 〈J˙ 〉. The specific angular momentum, l₀ = 〈J˙〉/ 〈 M˙〉, depends nonmonotonically on e_B. Contrary to previous claims, we find that l₀ is positive for most e_B, implying that the binary receives net angular momentum, which may cause its separation to grow with time. The minimum l₀ occurs at intermediate e_B (0.2-0.4), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.