Detectability of gravitational atoms in black hole binaries with the Einstein Telescope

Rotating black holes can amplify ultralight bosonic fields through superradiance, forming macroscopic clouds known as gravitational atoms. When the cloud forms around one of the components of a binary system, it can undergo a series of distinctive interactions, comprising both secular effects, such as dynamical friction or accretion, and resonant behaviour. These processes are expected to leave a distinctive signature on the gravitational waveform emitted by the binary, whose detectability we investigate in this paper. To do so, we implement a numerical code that integrates these effects, computed within a Newtonian approximation, for intermediate-to-high mass-ratio binaries on circular equatorial orbits. Realistic waveforms incorporating these environmental influences are generated and analyzed using the Fisher matrix formalism to evaluate the detectability of bosonic clouds with current and next-generation ground-based gravitational wave observatories. Our results demonstrate the potential for gravitational wave astronomy to probe the existence and properties of ultralight bosons.