Massive Perturbers and the Efficient Merger of Binary Massive Black Holes

We show that dynamical relaxation in the aftermath of a galactic merger and the ensuing formation and decay of a binary massive black hole (MBH) are dominated by massive perturbers (MPs) such as giant molecular clouds or clusters. MPs accelerate relaxation by orders of magnitude compared to two-body stellar relaxation alone, and efficiently scatter stars into the binary MBH’s orbit. The three-body star-binary MBH interactions shrink the binary MBH to the point where energy losses from the emission of gravitational waves (GWs) lead to rapid coalescence. We model this process based on observed and simulated MP distributions and take into account the decreased efficiency of the star-binary MBH interaction due to acceleration in the galactic potential. We show that mergers of gas-rich galactic nuclei lead to binary MBH coalescence well within the Hubble time. Moreover, lower mass binary MBHs (<108 M☉) require only a few percent of the typical gas mass in a postmerger nucleus to coalesce in a Hubble time. The fate of a binary MBH in a gas-poor galactic merger is less certain, although massive stellar structures (e.g., clusters, stellar rings) could likewise lead to efficient coalescence. These coalescence events are observable by their strong GW emission. MPs thus increase the cosmic rate of such GW events, lead to a higher mass deficit in the merged galactic core, and suppress the formation of triple-MBH systems and the resulting ejection of MBHs into intergalactic space.