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Light bosonic fields are ubiquitous in extensions of the Standard Model. Evenwhen minimally coupled to gravity, these fields might evade the assumptions ofthe black-hole no-hair theorems and give rise to spinning black holes which canbe drastically different from the Kerr metric. Furthermore, they allow forself-gravitating compact solitons, known as (scalar or Proca) boson stars. Thequasi-periodic oscillations (QPOs) observed in the X-ray flux emitted byaccreting compact objects carry information about the strong-field region, thusproviding a powerful tool to constrain deviations from Kerr's geometry and tosearch for exotic compact objects. By using the relativistic precession modelas a proxy to interpret the QPOs in terms of geodesic frequencies, weinvestigate how the QPO frequencies could be used to test the no-hair theoremand the existence of light bosonic fields near accreting compact objects. Weshow that a detection of two QPO triplets with current sensitivity can alreadyconstrain these models, and that the future eXTP mission or a LOFT-like missioncan set very stringent constraints on black holes with bosonic hair and on(scalar or Proca) boson stars. The peculiar geodesic structure of compactscalar/Proca boson stars implies that these objects can easily be ruled out asalternative models for X-ray source GRO J1655-40.

Constraining Black Holes with Light Boson Hair and Boson Stars using Epicyclic Frequencies and QPOs