The imprint of superradiance on hierarchical black hole mergers

Ultralight bosons are a proposed solution to outstanding problems in cosmology and particle physics: they provide a dark-matter candidate while potentially explaining the strong charge-parity problem. If they exist, ultralight bosons can interact with black holes through the superradiant instability. In this work we explore the consequences of this instability on the evolution of hierarchical black holes within dense stellar clusters. By reducing the spin of individual black holes, superradiance reduce the recoil velocity of merging binary black holes, which, in turn, increases the retention fraction of hierarchical merger remnants. We show that the existence of ultralight bosons with mass $ 2\times10^{-14}\lesssim \mu/\textrm{eV} \lesssim2\times10^{-13}$ would lead to an increased rate of hierarchical black hole mergers in nuclear star clusters. An ultralight boson in this energy range would result in up to $\approx60\%$ more present-day nuclear star clusters supporting hierarchical growth. The presence of an ultralight boson can also double the rate of intermediate mass black hole mergers to $\approx0.08$\,Gpc$^{-3}$\,yr$^{-1}$ in the local Universe. These results imply that a select range of ultralight boson mass can have far-reaching consequences for the population of black holes in dense stellar environments. Future studies into black hole cluster populations and the spin distribution of hierarchically formed black holes will test this scenario.