Neutrinos self interactions in Supernovae

Oscillations of neutrino emerging from a supernova core are studied. In this extremely high density region neutrino self interactions induce collective flavor transitions. When collective transitions are decoupled from matter oscillations, as for our chosen matter profile, an analytical interpretation of the collective effects is possible, by means of a mechanical analogy with a spherical pendulum. For inverted neutrino hierarchy the neutrino propagation can be divided in three regimes: synchronization, bipolar oscillations, and spectral split. Our simulation shows that averaging over neutrino trajectories does not alter the nature of these three regimes.