  Ultralight scalars can extract rotational energy from astrophysical black
holes through superradiant instabilities, forming macroscopic boson clouds.
This process is most efficient when the Compton wavelength of the boson is
comparable to the size of the black hole horizon, i.e. when the "gravitational
fine structure constant" $\alpha\equiv G \mu M/\hbar c\sim 1$. If the black
hole/cloud system is in a binary, tidal perturbations from the companion can
produce resonant transitions between the energy levels of the cloud, depleting
it by an amount that depends on the nature of the transition and on the
parameters of the binary. Previous cloud depletion estimates considered
binaries in circular orbit and made the approximation $\alpha\ll 1$. Here we
use black hole perturbation theory to compute instability rates and decay
widths for generic values of $\alpha$, and we show that this leads to much
larger cloud depletion estimates when $\alpha \gtrsim 0.1$. We also study
eccentric binary orbits. We show that in this case resonances can occur at all
harmonics of the orbital frequency, significantly extending the range of
frequencies where cloud depletion may be observable with gravitational wave
interferometers.
