Superradiant clouds may be relevant for close compact object binaries

Bosonic fields (within suitable mass range) may be collectively generated by rotating black holes through the black hole superradiance process. The resulting black hole is surrounded by a ``cloud" of particles whose wave function populates the superradiant energy level of the black hole. For comparable mass ratio binary black hole systems, it has been suggested that these clouds often deplete at large binary separations because of level mixing effects. As a result, these clouds may not be dynamically relevant for black hole and neutron star binaries that enter the LIGO-Virgo-KAGRA and LISA detection frequency band. In this work, we point out that the common envelope process during a compact binary evolution may bring the binary to $\sim 0.01$AU in hundreds to thousands of years, so that depletion caused by certain level mixings are no longer important. We derive a relevant regime of binary parameters where the clouds are still present for binary entering the LISA band, and show that common envelop process does enlarge such parameter regime. When the binary separation further decreases due to gravitational wave radiation, we discuss the impact of possible cloud mass transfer between the binary objects.