Neutrino mass hierarchy and three-flavor spectral splits of supernova neutrinos

It was recently realized that three-flavor effects could peculiarly modify the development of spectral splits induced by collective oscillations, for supernova neutrinos emitted during the cooling phase of a protoneutron star. We systematically explore this case, explaining how the impact of these three-flavor effects depends on the ordering of the neutrino masses. In inverted mass hierarchy, the solar mass splitting gives rise to instabilities in regions of the (anti) neutrino energy spectra that were otherwise stable under the leading two-flavor evolution governed by the atmospheric mass splitting and by the 1-3 mixing angle. As a consequence, the high-energy spectral splits found in the electron (anti) neutrino spectra disappear, and are transferred to other flavors. Imperfect adiabaticity leads to smearing of spectral swap features. In normal mass hierarchy, the three-flavor and the two-flavor instabilities act in the same region of the neutrino energy spectrum, leading to only minor departures from the two-flavor treatment.