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 $\Delta \phi_\text{\tiny{FC}}$ 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 $\theta^2\lesssim 10^{-2}$ motivated by models with a hidden sector coupled to the sterile neutrino, the Faraday conversion can be estimated as $\Delta \phi_\text{\tiny{FC}}\lesssim 10^{-3}-10^{-18}$ rad for GRB, $\Delta \phi_\text{\tiny{FC}}\lesssim 10^{-6}-10^{-11}$ rad for radio emission source from our galaxy and $\Delta \phi_\text{\tiny{FC}}\lesssim 10^{-6}-10^{-15}$ rad for extra-galactic sources. We also examine the V-mode power spectrum $C_{Vl}$ 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 $C_{pl}$ and the mixing angle where for $\theta^2\lesssim 10^{-2}$ leads to $C_{Vl}\lesssim 0.01$ Nano-Kelvin squared.