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Supermassive black holes (SMBHs) are ubiquitous in galaxies with a sizablemass. It is expected that a pair of SMBHs originally in the nuclei of twomerging galaxies would form a binary and eventually coalesce via a burst ofgravitational waves. So far theoretical models and simulations have been unableto predict directly the SMBH merger timescale from ab-initio galaxy formationtheory, focusing only on limited phases of the orbital decay of SMBHs underidealized conditions of the galaxy hosts. The predicted SMBH merger timescalesare long, of order Gyrs, which could be problematic for future gravitationalwave searches. Here we present the first multi-scale $\Lambda$CDM cosmologicalsimulation that follows the orbital decay of a pair of SMBHs in a merger of twotypical massive galaxies at $z\sim3$, all the way to the final coalescencedriven by gravitational wave emission. The two SMBHs, with masses $\sim10^{8}$M$_{\odot}$, settle quickly in the nucleus of the merger remnant. The remnantis triaxial and extremely dense due to the dissipative nature of the merger andthe intrinsic compactness of galaxies at high redshift. Such propertiesnaturally allow a very efficient hardening of the SMBH binary. The SMBH mergeroccurs in only $\sim10$ Myr after the galactic cores have merged, which is twoorders of magnitude smaller than the Hubble time.

Swift coalescence of supermassive black holes in cosmological mergers of massive galaxies