Common envelope evolution of ultralight boson clouds

Ultralight bosons can be excited around spinning black holes via black hole superradiance. These boson clouds may play an important role in the orbital evolution of binary black holes. In this work, we investigate the formation and evolution of common envelopes of ultralight boson clouds in comparable mass-ratio black hole binaries. We describe the cloud evolution using gravitational molecular eigenstates and analyze the possible level transitions during orbital decay, as well as the impact on orbital dynamics. We find that the cloud can generally lead to eccentricity growth. In particular, the eccentricity may vary significantly during level transition, leaving an eccentricity of ${\cal O}(0.1)$ within the detection band of ground-based gravitational wave detectors.