Inert neutrinos in supernovae

We study the constraints the observations of the supernova SN1987A impose on the mixing of the electron neutrino with an inert neutrino. A part of the electron neutrinos produced in the core of the star convert themselves into inert neutrinos as a result of the mixing. They would then escape the core and cool the star very rapidly in contrast to the observations. We show that due to matter effects the mixing of relatively light states propagating in the core is strongly suppressed, so that essentially no bounds exist if the mass of the inert neutrino is less than 200 eV. We also give a wave packet treatment of the propagation and the mixing of a neutrino state in matter, and find a condition for the ceasing of the oscillations due to the separation of the wave packets. (orig.)