The study of anomalous electromagnetic emission in the sky is the basis of indirect searches for dark matter. It is also a powerful tool to constrain the radiative decay of active neutrinos. Until now, quantitative analyses have focused on the flux and energy spectrum of such an emission; polarisation has never been considered. Here we show that we could be missing out on an essential piece of information. The radiative decay of neutrinos, as well as the interactions of dark matter and neutrinos with Standard Model particles can generate a circular polarisation signal in X-rays or γ -rays. If observed, this could reveal important information about their spatial distribution and particle-antiparticle ratio, and could even reveal the nature of the high-energy particle physics processes taking place in astrophysical sites. The question of the observability of these polarised signatures and their separation from background astrophysical sources is left for future work.
