On the orbital evolution of supermassive black hole binaries with circumbinary accretion discs

Gaseous circumbinary accretion discs provide a promising mechanism to facilitate the mergers of supermassive black holes (SMBHs) in galactic nuclei. We measure the torques exerted on accreting SMBH binaries, using 2D, isothermal, moving-mesh, viscous hydrodynamical simulations of circumbinary accretion discs. Our computational domain includes the entire inner region of the circumbinary disc, with the individual black holes (BHs) treated as point masses on the grid. A sink prescription is used to account for accretion on to each BH through well-resolved minidiscs. We explore a range of mass-removal rates for the sinks. We find that the torque exerted on the binary is primarily gravitational, and dominated by the gas orbiting close behind and ahead of the individual BHs. The torques are sensitive to the sink prescription: slower sinks result in more gas accumulating near the BHs and more negative torques, driving more rapid binary merger. For faster sinks, the torques are less negative, and eventually turn positive (for unphysically fast sinks). When the minidiscs are modelled as standard α discs, our results are insensitive to the chosen sink radius. When scaled to \dot{M}/\dot{M}_Edd=0.3, the implied residence time-scale is ≈3 × 10⁶ yr, independent of the SMBH masses and orbital separation. For binaries with total mass ≲ 10⁷ M_⊙, this is shorter than the inspiral time due to gravitational wave (GW) emission alone, implying that gas discs will have a significant impact on the SMBH binary population and can affect the GW signal for pulsar timing arrays.