Supernova Neutrinos and the LSND Evidence for Neutrino Oscillations

The observation of the $\bar{\nu}_e$ energy spectrum from a supernova burst can provide constraints on neutrino oscillations. We derive formulas for adiabatic oscillations of supernova antineutrinos for a variety of 3- and 4-neutrino mixing schemes and mass hierarchies which are consistent with the LSND evidence for $\bar{\nu}_{\mu}\to \bar{\nu}_e$ oscillations. Finally, we explore the constraints on these models and LSND given by the supernova SN1987A $\bar{\nu}_e$'s observed by the Kamiokande-2 and IMB-3 detectors.