Production of unstable heavy neutrinos in proto-neutron stars

We discuss the production of a class of heavy sterile neutrinos $\nu_h$ in proto-neutron stars. The neutrinos, of mass around $50$ MeV, have a negligible mixing with the active species but relatively large dimension-5 electromagnetic couplings. In particular, a magnetic dipole moment $\mu\approx 10^{-6}$ GeV$^{-1}$ implies that they are thermally produced through $e^+ e^-\to \bar \nu_h \nu_h$ in the early phase of the core collapse, whereas a heavy--light transition moment $\mu_{\rm tr}\approx 10^{-8}$ GeV$^{-1}$ allows their decay $\nu_h\to \nu_i \gamma$ with a lifetime around $10^{-3}$ s. This type of electromagnetic couplings has been recently proposed to explain the excess of electron-like events in baseline experiments. We show that the production and decay of these heavy neutrinos would transport energy from the central regions of the star to distances $d\approx 400$ km, providing a very efficient mechanism to enhance the supernova shock front and heat the material behind it.