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, $\mathcal{O}({10}^{-11}$ – ${10}^{-10})$ 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 towards assessing the LSD’s sensitivity to the resultant ensemble of GW signals, we compute the corresponding signal-to-noise ratios which build up over a nominal integration time of ${10}^7$ 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 $\mu$ is around $3\times {10}^{-11}$ eV, and this number diminishes with increasing $\mu$ up to $\approx 5.5\times {10}^{-11}$ eV. The much larger population of unresolved sources will produce a confusion foreground which could be detectable by a $10$-m instrument if $\mu \in (3-4.5)\times {10}^{-11}$ eV, or by a $100$-m instrument if $\mu \in (3-6)\times {10}^{-11}$ eV.