Gravitational Waves from Resonant Transitions of Tidally Perturbed Gravitational Atoms

Abstract

Light bosons can form a gravitational atom (GA) around a spinning black hole through the superradiance process. Considering the black hole to be part of a binary system, the tidal potential of the companion periodically perturbs the GA such that an ``atomic'' transition occurs between two of its energy eigenstates. The resonant transition is modeled by the Landau-Zener system, where the orbital frequency of the companion determines the relevant transition. In this work, we study a novel quasi-monochromatic gravitational wave signal originating directly from the level transition of the GA in a binary system. We derive the analytical formulae of both the strain waveform and frequency spectrum of the signal. We further investigate the GA-binary systems that can have a large signal-to-noise ratio in the milli-Hz to deci-Hz frequency band. Using the future space-based gravitational wave observatory DECIGO, we find the signal-to-noise ratio is $\mathcal{O}(10-200)$ for the fine-structure constant $\alpha\simeq 0.3$, host black hole mass $M= 150M_\odot$ and boson mass $\mu \simeq 10^{-13} \rm eV$ at a distance within 100 kpc. Given astrophysical uncertainties about the black hole's initial spin, the degeneracy with other monochromatic signals and the small merger rate at those distances, we conclude that the detection of the signal would be challenging.