Axion clouds may survive the perturbative tidal interaction over the early inspiral phase of black hole binaries

Abstract: Gravitational wave observation has the potential of probing ultralight bosonic fields such as axion. Axion forms a cloud around a rotating black hole (BH) by superradiant instability and should affect the gravitational waveform from binary BHs. On the other hand, considering the cloud associated with a BH in a binary system, tidal interaction depletes the cloud in some cases during the inspiral phase. We made the exhaustive study of cloud depletion numerically in a wide parameter range for equal mass binaries, assuming only the quadrupolar tidal perturbation is at work. We found that clouds can avoid disappearing due to the tidal effect only when $l=1$ mode is the fastest growing mode and when the binary orbit is counter-rotating in the non-relativistic parameter region.