Simulating the Galactic population of axion clouds around stellar-origin black holes: Gravitational wave signals in the 10–100 kHz band

Ultralight scalar fields can experience runaway ``superradiant'' amplification near spinning black holes, resulting in a macroscopic ``axion cloud,'' which slowly dissipates via continuous monochromatic gravitational waves. For a particular range of boson masses, $\mathcal{O}({10}^{\ensuremath{-}11}--{10}^{\ensuremath{-}10})\text{ }\text{ }\mathrm{eV}$, an axion cloud will radiate in the 10--100 kHz band of the levitated sensor detector (LSD). Using fiducial models of the mass, spin, and age distributions of stellar-origin black holes, we simulate the present-day Milky Way population of these hypothetical objects. As a first step toward assessing the LSD's sensitivity to the resultant ensemble of gravitational wave signals, we compute the corresponding signal-to-noise ratios which build up over a nominal integration time of ${10}^{7}\text{ }\text{ }\mathrm{s}$, assuming the projected sensitivity of the 1 m LSD prototype currently under construction, as well as for future 10 m and 100 m concepts. For a 100 m cryogenic instrument, hundreds of resolvable signals could be expected if the boson mass $\ensuremath{\mu}$ is around $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$, and this number diminishes with increasing $\ensuremath{\mu}$ up to $\ensuremath{\approx}5.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$. The much larger population of unresolved sources will produce a confusion foreground which could be detectable by a 10-m instrument if $\ensuremath{\mu}\ensuremath{\in}(3--4.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$ or by a 100-m instrument if $\ensuremath{\mu}\ensuremath{\in}(3--6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$.