Inverting a Supernova: Neutrino Mixing, Temperatures and Binding Energy

We show that the temperatures of the emergent non-electron neutrinos and the binding energy released by a galactic Type II supernova are determinable, assuming the Large Mixing Angle (LMA) solution is correct, from observations at the Sudbury Neutrino Observatory (SNO) and at Super-Kamiokande (SK). If the neutrino mass hierarchy is inverted, either a lower or upper bound can be placed on the neutrino mixing angle $\theta_{13}$, and the hierarchy can be deduced for adiabatic transitions. For the normal hierarchy, neither can $\theta_{13}$ be constrained nor can the hierarchy be determined. Our conclusions are qualitatively unchanged for the proposed Hyper-Kamiokande detector.