Identifying the neutrino mass spectrum from a supernova neutrino burst

We study the role that the future detection of the neutrino burst from a galactic supernova can play in the reconstruction of the neutrino mass spectrum. We consider all possible 3$\nu$ mass and flavor spectra which describe the solar and atmospheric neutrino data. For each of these spectra we find the observable effects of the supernova neutrino conversions both in the matter of the star and the earth. We show that studies of the electron neutrino and anineutrino spectra as well as observations of the neutral current effects from supernova will allow us (i) to identify the solar neutrino solution, (ii) to determine the type of mass hierarchy (normal or inverted) and (iii) to probe the mixing $|U_{e3}|^2$ to values as low as $10^{-4} - 10^{-3}$.Comment: 53 pages, 13eps figures. Substantial changes made, new results, figures and tables adde