Discovering the QCD axion with black holes and gravitational waves

Advanced LIGO may be the first experiment to detect gravitational waves. Through superradiance of stellar black holes, it may also be the first experiment to discover the QCD axion with decay constant above the grand unification scale. When an axion's Compton wavelength is comparable to the size of a black hole, the axion binds to the black hole, forming a ``gravitational atom.'' Through the superradiance process, the number of axions occupying the bound levels grows exponentially, extracting energy and angular momentum from the black hole. Axions transitioning between levels of the gravitational atom and axions annihilating to gravitons can produce observable gravitational wave signals. The signals are long lasting, monochromatic, and can be distinguished from ordinary astrophysical sources. We estimate up to $\mathcal{O}(1)$ transition events at aLIGO for an axion between $1{0}^{\ensuremath{-}11}$ and $1{0}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{eV}$ and up to $1{0}^{4}$ annihilation events for an axion between $1{0}^{\ensuremath{-}13}$ and $1{0}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$. In the event of a null search, aLIGO can constrain the axion mass for a range of rapidly spinning black hole formation rates. Axion annihilations are also promising for much lighter masses at future lower-frequency gravitational wave observatories; the rates have large uncertainties, dominated by supermassive black hole spin distributions. Our projections for aLIGO are robust against perturbations from the black hole environment and account for our updated exclusion on the QCD axion of $6\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}<{\ensuremath{\mu}}_{a}<2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$ suggested by stellar black hole spin measurements.