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Gravitational wave observation has the potential of probing ultralightbosonic fields such as axion. Axion forms a cloud around a rotating black hole(BH) by superradiant instability and should affect the gravitational waveformfrom binary BHs. On the other hand, considering the cloud associated with a BHin a binary system, tidal interaction depletes the cloud in some cases duringthe inspiral phase. We made the exhaustive study of cloud depletion numericallyin a wide parameter range for equal mass binaries, assuming only thequadrupolar tidal perturbation is at work. We found that clouds can avoiddisappearing due to the tidal effect only when $l=1$ mode is the fastestgrowing mode and when the binary orbit is counter-rotating in thenon-relativistic parameter region.

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