  An extension of the Standard Model is studied, in which two new vector bosons
are introduced, a first boson $Z'$ coupled to the SM by the usual minimal
coupling, producing an enlarged gauge sector in the SM. The second boson $A'$
field, in the dark sector of the model, remains massless and originates a dark
photon $\gamma'$. A hybrid mixing scenario is considered based on a combined
Higgs and Stueckelberg mechanisms. In a Compton-like process a photon scattered
by a WIMP is converted into a dark photon. This process is studied, in an
astrophysical application obtaining an estimate of the impact on stellar
cooling of white dwarfs and neutron stars.
