Orbital fingerprints of ultralight scalar fields around black holes

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.