Clockwork mechanism to remove superradiance limits

The superradiant instability of black hole space-times has been used to place limits on ultra-light bosonic particles. 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. Nonlinear 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 nonlinearities 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 nonlinearities eliminate limits from superradiance while preserving their cosmic abundance.