  Ultralight degrees of freedom coupled to matter lead to resonances, which can
be excited when the Compton wavelength of the field equals a dynamical scale in
the problem. For binaries composed of a star orbiting a supermassive black
hole, these resonances lead to a smoking-gun effect: a periastron distance
which {\it stalls}, even in the presence of gravitational-wave dissipation.
This effect, also called a {\it floating orbit}, occurs for generic equatorial
but eccentric orbits and we argue that finite-size effects are not enough to
suppress it.
