  Sterile neutrinos with masses up to $\mathcal{O} (100)$ MeV can be copiously
produced in a supernova (SN) core, through the mixing with active neutrinos. In
this regard the SN 1987A detection of neutrino events has been used to put
constraints on active-sterile neutrino mixing, exploiting the well-known SN
cooling argument. We refine the calculation of this limit including neutral
current interactions with nucleons, that constitute the dominant channel for
sterile neutrino production. We also include, for the first time, the charged
current interactions between sterile neutrinos and muons, relevant for the
production of sterile neutrinos mixed with muon neutrinos in the SN core. Using
the recent modified luminosity criterion, we extend the bounds to the case
where sterile states are trapped in the stellar core. Additionally, we study
the decays of heavy sterile neutrinos, affecting the SN explosion energy and
possibly producing a gamma-ray signal. We also illustrate the complementarity
of our new bounds with cosmological bounds and laboratory searches.
