  Ultralight scalars have been predicted in a variety of scenarios, and
advocated as a possible component of dark matter. These fields can form compact
regular structures known as boson stars, or---in the presence of
horizons---give rise to nontrivial time-dependent scalar hair and a stationary
geometry. Because these fields can be coherent over large spatial extents,
their interaction with "regular" matter can lead to very peculiar effects, most
notably resonances. Here we study the motion of stars in a background
describing black holes surrounded by non-axially symmetric scalar field
profiles. By analyzing the system in a weak-field approach, we find that the
presence of a scalar field gives rise to secular effects akin to ones existing
in planetary and accretion disks. Particularly, the existence of resonances
between the orbiting stars and the scalar field may enable angular momentum
exchange between them, providing mechanisms similar to planetary migration.
Additionally, these mechanisms may allow \textit{floating orbits}, which are
stable radiating orbits. We also show, in the full relativistic case, that
these effects also appear when there is a direct coupling between the scalar
field and the stellar matter, which can arise due to the presence of a scalar
core in the star or in alternative theories of gravity.
