  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 GUT 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 O(1) transition events at
aLIGO for an axion between 10^-11 and 10^-10 eV and up to 10^4 annihilation
events for an axion between 10^-13 and 10^-11 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*10^-13 eV < ma < 2*10^-11 eV suggested by stellar black hole spin
measurements.
