Hydrodynamics of Circumbinary Accretion: Angular Momentum Transfer and Binary Orbital Evolution

We carry out 2D viscous hydrodynamical simulations of circumbinary accretion using the moving-mesh code AREPO. We self-consistently compute the accretion flow over a wide range of spatial scales, from the circumbinary disk (CBD) far from the central binary, through accretion streamers, to the disks around individual binary components, resolving the flow down to 2% of the binary separation. We focus on equal-mass binaries with arbitrary eccentricities. We evolve the flow over long (viscous) timescales until a quasi-steady state is reached, in which the mass supply rate at large distances {\dot{M}}₀ (assumed constant) equals the time-averaged mass transfer rate across the disk and the total mass accretion rate onto the binary components. This quasi-steady state allows us to compute the secular angular momentum transfer rate onto the binary, < {\dot{J}}_{{b}}> , and the resulting orbital evolution. Through direct computation of the gravitational and accretional torques on the binary, we find that < {\dot{J}}_{{b}}> is consistently positive (i.e., the binary gains angular momentum), with {l}₀\equiv < {\dot{J}}_{{b}}> /{\dot{M}}₀ in the range of (0.4-0.8){a}_{{b}}²{{{Ω }}}_{{b}}, depending on the binary eccentricity (where {a}_{{b}}, {{{Ω }}}_{{b}} are the binary semimajor axis and angular frequency); we also find that this < {\dot{J}}_{{b}}> is equal to the net angular momentum current across the CBD, indicating that global angular momentum balance is achieved in our simulations. In addition, we compute the time-averaged rate of change of the binary orbital energy for eccentric binaries and thus obtain the secular rates < {\dot{a}}_{{b}}> and < {\dot{e}}_{{b}}> . In all cases, < {\dot{a}}_{{b}}> is positive; that is, the binary expands while accreting. We discuss the implications of our results for the merger of supermassive binary black holes and for the formation of close stellar binaries.