Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase

It has been recently pointed out that removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos, a new multi- azimuthal-angle (MAA) instability would arise. In particular, for a flux ordering Fe > Fe > Fx, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hier- archy. However, during this phase the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. At this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino non-linear evolution equations. We find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward- peaked neutrino angular distributions. As a result, in our model for a 10.8 M⊙ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a 8.8 M⊙ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.