Self-refraction of supernova neutrinos: mixed spectra and three-flavor instabilities

Neutrinos in a core-collapse supernova undergo coherent flavor transformations in their own background. We explore this phenomenon during the cooling stage of the explosion. Our three-flavor calculations reveal qualitatively new effects compared to a two-flavor analysis. These effects are especially clearly seen for the inverted mass hierarchy: we find a different pattern of spectral "swaps" in the neutrino spectrum and a novel "mixed" spectrum for the antineutrinos. A brief discussion of the relevant physics is presented, including the instability of the two-flavor evolution trajectory, the 3-flavor pattern of spectral "swaps," and partial nonadiabaticity of the evolution.