Circular polarization of cosmic photons due to their interactions with sterile neutrino dark matter

In this paper, we explore the possibility of the polarization conversion of a wide energy range of cosmic photons to the circular polarization through their interactions with right handed sterile neutrinos as a candidate for dark matter. By considering the sterile neutrino in the seesaw mechanism framework and right-handed current model, we examine the Faraday conversion ΔϕFC of gamma ray burst (GRB) photons at both the prompt and afterglow emission levels as well as the radio photons emitted from our galaxy and extra-galactic sources interacting with the sterile neutrinos. Consequently, for the sterile neutrino with mixing angle θ2 ≲ 10−2 motivated by models with a hidden sector coupled to the sterile neutrino, the Faraday conversion can be estimated as ΔϕFC ≲ 10−3 – 10−18 rad for GRB, ΔϕFC ≲ 10−6 – 10−11 rad for radio emission source from our galaxy and ΔϕFC ≲ 10−6 – 10−15 rad for extragalactic sources. We also examine the V-mode power spectrum CVl of the cosmic microwave background (CMB) at the last scattering surface. We show that the circular polarization power spectrum at the leading order is proportional to the linear polarization power spectrum Cpl and the mixing angle where for θ2 ≲ 10−2 leads to CVl ≲ 0.01 nano-Kelvin squared.