Massive black hole binaries in gas-rich galaxy mergers; multiple regimes of orbital decay and interplay with gas inflows

We revisit the phases of the pairing and sinking of black holes (BHs) in galaxy mergers and circumnuclear discs in light of the results of recent simulations with massive BHs embedded in predominantly gaseous backgrounds. After a general overview we highlight for the first time the existence of a clear transition, for unequal mass BHs, between the regime in which the orbital decay is dominated by the conventional dynamical friction wake and one in which global disc torques associated with density waves launched by the secondary BH as well as co-orbital torques arising from gas gravitationally captured by the BH dominate and lead to faster decay. The new regime intervenes at BH binary separations of a few tens of parsecs and below, following a phase of orbital circularization driven dynamical friction. It bears some resemblance with planet migration in protoplanetary discs. While the orbital timescale is reasonably matched by the migration rate for the Type-I regime, the dominant negative torque arises near the co-rotation resonance, which is qualitatively similar to what is found in the so-called Type-III migration, the fastest migration regime identified so far for planets. This fast decay rate brings the BHs to separations of order 10^-1 pc, the resolution limit of our simulations, in less than ∼10⁷ yr in a smooth disc, while the decay timescale can increase to >10⁸ yr in clumpy discs due to gravitational scattering with molecular clouds. Eventual gap opening at sub-pc scale separations will slow down the orbital decay subsequently. How fast the binary BH can reach the separation at which gravitational waves take over will be determined by the nature of the interaction with the circumbinary disc and the complex torques exerted the gas flowing through the edge of such disc, the subject of many recent studies. We also present a new intriguing connection between the conditions required for rapid orbital decay of massive BH binaries and those required for prominent gas inflows in gas-rich galaxies undergoing major mergers. We derive a condition for the maximum inflow rate that a circumnuclear disc can host while still maintaining a sufficiently high gas density at large radii to sustain the decay of a BH binary. We find that gas inflows rates exceeding 10 M_⊙ yr^-1, postulated to form massive BH seeds in some direct collapse models, would stifle the sinking of massive BH binaries in gas-dominated galactic nuclei. Vice-versa, lower inflow rates, below a solar mass per year, as required to feed typical active galactic nuclei (AGNs), are compatible with a fast orbital decay of BH binaries across a wide range of masses.