Production of keV Sterile Neutrinos in Supernovae: New Constraints and Gamma Ray Observables

We study the production of sterile neutrinos in supernovae, focusing in particular on the keV--MeV mass range, which is the most interesting range if sterile neutrinos are to account for the dark matter in the Universe. Focusing on the simplest scenario in which sterile neutrinos mixes only with muon or tau neutrino, we argue that the production of keV--MeV sterile neutrinos can be strongly enhanced by a Mikheyev--Smirnov--Wolfenstein (MSW) resonance, so that a substantial flux is expected to emerge from a supernova, even if vacuum mixing angles between active and sterile neutrinos are tiny. Using energetics arguments, this yields limits on the sterile neutrino parameter space that reach down to mixing angles of the order of $\sin^2 2\theta \lesssim 10^{-14}$ and are up to an order of magnitude stronger than those from X-ray observations. While supernova limits suffer from larger systematic uncertainties than X-ray limits they apply also to scenarios in which sterile neutrinos are not abundantly produced in the early Universe. We also compute the flux of $\mathcal{O}(\text{MeV})$ photons expected from the decay of sterile neutrinos produced in supernovae, but find that it is beyond current observational reach even for a nearby supernova.