Astrophysical observations of spinning BHs, which span $ 5M_odotlesssim M_{rm BH}lesssim 5times 10^8 M_odot$, can be used to exclude the existence of certain massive bosons via the superradiance phenomenon. In this work, we explore for the first time how these measurements can be used to constrain properties of statistical distributions for the masses of multiple bosonic fields. Quite generally, our methodology excludes $N_{rm ax}gtrsim 30$ scalar fields with a range of mass distribution widths and central values spanning many orders of magnitude. We demonstrate this for the specific example of axions in string theory and M-theory, where the mass distributions in certain cases take universal forms. We place upper bounds on $N_{rm ax}$ for certain scenarios of interest realised approximately as mass distributions in M-theory, including the QCD axion, grand unified theories, and fuzzy dark matter.
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