Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors

We examine a phenomenon recently predicted by numerical simulations of supernova neutrino flavor evolution: the swapping of supernova ₄ and, energy spectra below (above) energy E₂ for the normal (inverted) neutrino mass hierarchy. We present the results of large-scale numerical calculations which show that in the normal neutrino mass hierarchy case, E₂ decreases as the assumed effective 22 vacuum ₄, mixing angle (₁₃) is decreased. In contrast, these calculations indicate that E₂ is essentially independent of the vacuum mixing angle in the inverted neutrino mass hierarchy case. With a good neutrino signal from a future galactic supernova, the above results could be used to determine the neutrino mass hierarchy even if ₁₃ is too small to be measured by terrestrial neutrino oscillation experiments.