  We obtain constraints from black hole superradiance in an ensemble of
compactifications of type IIB string theory. The constraints require knowing
only the axion masses and self-interactions, and are insensitive to the
cosmological model. We study more than $2 \cdot 10^5$ Calabi-Yau manifolds with
Hodge numbers $1\leq h^{1,1}\leq 491$ and compute the axion spectrum at two
reference points in moduli space for each geometry. Our computation of the
classical theory is explicit, while for the instanton-generated axion potential
we use a conservative model. The measured properties of astrophysical black
holes exclude parts of our dataset. At the point in moduli space corresponding
to the tip of the stretched K\"{a}hler cone, we exclude $\approx 50\%$ of
manifolds in our sample at 95% C.L., while further inside the K\"{a}hler cone,
at an extremal point for realising the Standard Model, we exclude a maximum of
$\approx 7\%$ of manifolds at $h^{1,1}=11$, falling to nearly zero by
$h^{1,1}=100$.
