Gravitational Waves from Resonant Transitions of Tidally Perturbed Gravitational Atoms

Abstract: Light bosons can form gravitational atoms (GA) around spinning black holes 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 gravitational wave signal originating directly from the atomic 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 present the GA-binary systems that can have a large signal-to-noise ratio in LISA's frequency band. Finally, we discuss the implications of detection of the signal:inferring model parameters,including the boson mass and black hole spin,and computing the phase shift and Doppler shift of the gravitational wave signal for equal mass binaries.