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Massive black hole and gas dynamics in mergers of galaxy nuclei - II. Black hole sinking in star-forming nuclear discs

Mergers of gas-rich galaxies are key events in the hierarchical built-up of cosmic structures, and can lead to the formation of massive black hole binaries. By means of high-resolution hydrodynamical simulations we consider the late stages of a gas-rich major merger, detailing the dynamics of two circumnuclear discs, and of the hosted massive black holes during their pairing phase. During the merger gas clumps with masses of a fraction of the black hole mass form because of fragmentation. Such high-density gas is very effective in forming stars, and the most massive clumps can substantially perturb the black hole orbits. After $\sim 10$ Myr from the start of the merger a gravitationally bound black hole binary forms at a separation of a few parsecs, and soon after, the separation falls below our resolution limit of $0.39$ pc. At the time of binary formation the original discs are almost completely disrupted because of SNa feedback, while on pc scales the residual gas settles in a circumbinary disc with mass $\sim 10^5 M_\odot$. We also test that binary dynamics is robust against the details of the SNa feedback employed in the simulations, while gas dynamics is not. We finally highlight the importance of the SNa time-scale on our results.