Binary orbital evolution driven by a circumbinary disc

The question whether the interaction of a circumbinary disc with the central binary system leads to a shrinking or to an expansion of the binary orbit has attracted considerable interest as it impacts the evolution of binary black holes and stellar binary stars in their formation phase. We performed two-dimensional hydrodynamical simulations of circumbinary discs for a large parameter set of disc viscosities and thicknesses and for two different binary mass ratios for binaries on circular orbits. We measured the net angular momentum and mass transfer between disc and binary system, and evaluated the normalised specific angular momentum accretion, j s . This was compared to the theoretical, critical specific angular momentum change j s,crit that separates contracting from expanding cases, which depends on the binary mass ratio and on the relative accretion onto the two stars. Using finite and infinite disc models, we show that the inferred binary evolution is very similar for both setups, and we confirm that j s can be measured accurately with cylindrical simulations that do not include the central binary. However, to obtain the relative accretion onto the stars for non-equal mass binaries, simulations that cover the whole domain including the binary are required. We find that for thick discs with aspect ratio h = 0.1, the binaries expand for all viscosities, while discs with h = 0.05 lead to an expansion only for higher viscosities with α exceeding ∼0.005. Overall, the regime of binary expansion extends to a much wider parameter space than previously anticipated, but for thin, low-viscosity discs, the orbits shrink.