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, $⟨\dot{M}⟩$, 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}$$) generally becomes coherently eccentric. For low and high $e_{\mathrm{B}}$, the disc line of apsides precesses around the binary, but for intermediate $e_{\mathrm{B}}$ ($0.2-0.4$), it instead becomes locked with that of the binary. By considering the balance of angular momentum transport through the disc by advection, viscous stress, and gravitational torque, we determine the time-averaged net angular momentum transfer rate to the binary, $⟨\dot{J}⟩$. The specific angular momentum, $l_0 = \langle\dot{J}\rangle/\langle\dot{M}\rangle$,dependsnon-monotonicallyon$e_$\mathrm{B}$$\mathrm{.}Contrarytopreviousclaims,wefindthat$l_0$ 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.