Self-gravity in superradiance clouds: Implications for binary dynamics and observational prospects

Spinning black holes could produce ultralight particles via the superradiance instability. These particles form a dense cloud around the host black hole, introducing new opportunities for the detection of ultralight new physics. When the black hole is part of a binary system, the binary can trigger transitions among different states of the cloud configuration. Such transitions backreact on the orbital dynamics, modifying the frequency evolution of the emitted gravitational waves. Based on this observation, black hole binaries were proposed as a way to test the existence of ultralight particles. We investigate the effects of the self-gravity of the cloud on the orbital evolution and on the gravitational wave emission. We find that cloud self-gravity could lead to a density-dependent modification of the energy levels of ultralight particles and that it could alter the order of hyperfine energy levels. The crossing of hyperfine levels prevents binaries from triggering resonant hyperfine transitions, and allows them to approach radii that could trigger resonant transitions of fine levels. We study the implications of these findings, especially in the context of future space-borne gravitational wave observatory, the Laser Interferometer Space Antenna (LISA). For quasicircular, prograde, and equatorial orbits, we find that LISA could probe ultralight particles in the mass range ${10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{eV}--{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$ through gravitational wave observations.