Multi-angle effects in self-induced oscillations for different supernova neutrino fluxes

The non-isotropic nature of the neutrino emission from a supernova (SN) core might potentially affect the flavor evolution of the neutrino ensemble, via neutrino-neutrino interactions in the deepest SN regions. We investigate the dependence of these "multi-angle effects" on the original SN neutrino fluxes in a three-flavor framework. We show that the pattern of the spectral crossings (energies where F_\nu_e= F_\nu_x, and F_\bar\nu_e= F_\bar\nu_x) is crucial in determining the impact of multi-angle effects on the flavor evolution. For neutrino spectra presenting only a single-crossing, synchronization of different angular modes prevails over multi-angle effects, producing the known "quasi single-angle" evolution. Conversely, in the presence of spectra with multiple crossing energies, synchronization is not stable. In this situation, multi-angle effects would produce a sizable delay in the onset of the flavor conversions, as recently observed. We show that, due to the only partial adiabaticity of the evolution at large radii, the multi-angle suppression can be so strong to dramatically affect the final oscillated neutrino spectra. In particular three-flavor effects, associated with the solar parameters, could be washed-out in multi-angle simulations.