| Summary: | Ultralight bosons can form clouds around rotating black holes if their
Compton wavelength is comparable to the black hole size. The boson cloud spins
down the black hole through a process called superradiance, lowering the black
hole spin to a characteristic value. It has been suggested that spin
measurements of the black holes detected by ground-based gravitational-wave
detectors can be used to constrain the mass of ultralight bosons.
Unfortunately, a measurement of the individual black hole spins is often
uncertain, resulting in inconclusive results. Instead, we use hierarchical
Bayesian inference to combine information from multiple gravitational-wave
sources and obtain stronger constraints. We show that hundreds of high
signal-to-noise ratio gravitational-wave detections are enough to exclude
(confirm) the existence of non-interacting bosons in the mass range
$\left[10^{-13},3\times 10^{-12}\right]~\rm{eV}$
$\left([10^{-13},10^{-12}]~\rm{eV}\right)$. The precise number depends on the
distribution of black hole spins at formation and the mass of the boson. From
the few uninformative spin measurements of binary black hole mergers detected
by LIGO and Virgo in their first two observing runs, we cannot draw
statistically significant conclusions.
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