  We perform an extensive analysis of the statistics of axion masses and
interactions in compactifications of type IIB string theory, and we show that
black hole superradiance excludes some regions of Calabi-Yau moduli space.
Regardless of the cosmological model, a theory with an axion whose mass falls
in a superradiant band can be probed by the measured properties of
astrophysical black holes, unless the axion self-interaction is large enough to
disrupt formation of a condensate. We study a large ensemble of
compactifications on Calabi-Yau hypersurfaces, with $1 \leq h^{1,1} \leq 491$
closed string axions, and determine whether the superradiance conditions on the
masses and self-interactions are fulfilled. The axion mass spectrum is largely
determined by the K\"ahler parameters, for mild assumptions about the
contributing instantons, and takes a nearly-universal form when $h^{1,1} \gg
1$. When the K\"ahler moduli are taken at the tip of the stretched K\"ahler
cone, the fraction of geometries excluded initially grows with $h^{1,1}$, to a
maximum of $\approx 0.5$ at $h^{1,1} \approx 160$, and then falls for larger
$h^{1,1}$. Further inside the K\"ahler cone, the superradiance constraints are
far weaker, but for $h^{1,1} \gg 100$ the decay constants are so small that
these geometries may be in tension with astrophysical bounds, depending on the
realization of the Standard Model.
