  Recently, the Scalar Field Dark Matter (SFDM) model (also known as Fuzzy,
Wave, Bose-Einstein, Ultra-light Dark Matter) has gained a lot of attention
because it has provided simpler and more natural explanations for various
phenomena observed in galaxies, as a natural explanation for the center of
galaxies, the number of satellite galaxies around their host and, more
recently, a natural explanation for anomalous trajectories of satellite
galaxies called Vast Polar Orbits (VPO) observed in various galaxies. In the
present work we study the assumption that the SFDM is a type of charged dark
boson whose gauge charge is associated with the Dark Photon (DP). Inspired by
these results, we study the formation of compact bosonic objects, such as Boson
Stars (BS) and focus on the possibility that, due to spontaneous $U(1)$ SFDM
symmetry breaking, the DP may acquire mass and form compact objects like Proca
Stars (PS). If this is true, we can expect measurable effects on the
electromagnetic field of the Standard Model (SM) of particles due to their
interaction with the DP on the formation of compact objects.
