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 nu(e) and nu(mu,tau) energy spectra below (above) energy E(C) 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, E(C) decreases as the assumed effective 2x2 vacuum nu(e)<==>nu(mu,tau) mixing angle (approximately theta13) is decreased. In contrast, these calculations indicate that E(C) 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 theta13 is too small to be measured by terrestrial neutrino oscillation experiments.