  For dark matter to be detectable with gravitational waves from binary black
holes, it must reach higher than average densities in their vicinity. In the
case of light (wave-like) dark matter, the density of dark matter between the
binary can be significantly enhanced by accretion from the surrounding
environment. Here we show that the resulting dephasing effect on the last ten
orbits of an equal mass binary is maximized when the Compton wavelength of the
scalar particle is comparable to the orbital separation, $2\pi/\mu\sim d$. The
phenomenology of the effect is different from the channels that are usually
discussed, where dynamical friction (along the orbital path) and radiation of
energy and angular momentum drive the dephasing, and is rather dominated by the
radial force (the spacetime curvature in the radial direction) towards the
overdensity between the black holes. Whilst our numerical studies limit us to
scales of the same order, this effect may persist at larger separations and/or
particle masses, playing a significant role in the merger history of binaries.
