Breaking the symmetries of the bulb model in two-dimensional self-induced supernova neutrino flavor conversions

Self-induced flavor conversions of supernova (SN) neutrinos have been characterized in the spherically symmetric "bulb model", reducing the neutrino evolution to a one dimensional problem along a radial direction. We lift this assumption, presenting a two-dimensional model where neutrinos are launched from a spherical neutrino-sphere with many zenithal angles and two azimuthal angles. We also assume that self-induced conversions are not suppressed by large matter effects. In this situation we find that self-interacting neutrinos spontaneously break axial and spherical symmetries. As a result the flavor content and the lepton number of the neutrino gas would acquire seizable direction-dependent variations, breaking the coherent behavior found in the spherically symmetric case. This finding would suggest that the previous results of the self-induced flavor evolution obtained in one-dimensional models should be critically re-examined