  The superradiant instability of black hole space-times has been used to place
limits on ultra-light bosonic particles. We show that these limits are model
dependent. While the initial growth of the mode is gravitational and thus model
independent, the ability to place a limit on new particles requires the mode to
grow unhindered to a large number density. Non-linear interactions between the
particle and other light degrees of freedom that are mediated through higher
dimension operators can damp this growth, eliminating the limit. However, these
non-linearities may also destroy a cosmic abundance of these light particles,
an attractive avenue for their discovery in several experiments. We study the
specific example of the QCD axion and show that it is easy to construct models
where these non-linearities eliminate limits from superradiance while
preserving their cosmic abundance.
