Heavy sterile neutrino emission in core-collapse supernovae: constraints and signatures

Heavy sterile neutrinos with masses $O\left(100\right)$ MeV mixing with active neutrinos can be produced in the core of a collapsing supernova (SN). In order to avoid an excessive energy loss, shortening the observed duration of the SN 1987A neutrino burst, we show that the active-sterile neutrino mixing angle should satisfy ${\sin }^2\theta \lesssim 5\times {10}^{-7}$. For a mixing with tau flavour, this bound is much stronger than the ones from laboratory searches. Moreover, we show that in the viable parameter space the decay of such "heavy" sterile neutrinos in the SN envelope would lead to a very energetic flux of daughter active neutrinos; if not too far below current limits, this would be detectable in large underground neutrino observatories, like Super-Kamiokande, as a (slightly time-delayed) high-energy bump in the spectrum of a forthcoming Galactic SN event.