Triggering collective oscillations by three-flavor effects

Collective flavor transformations in supernovae, caused by neutrino-neutrino interactions, are essentially a two-flavor phenomenon driven by the atmospheric mass difference and the small mixing angle θ₁₃. In the two-flavor approximation, the initial evolution depends logarithmically on θ₁₃ and the system remains trapped in an unstable fixed point for θ₁₃=0. However, any effect breaking exact ν_μ-ν_τ equivalence triggers the conversion. Such three-flavor perturbations include radiative corrections to weak interactions, small differences between the ν_μ and ν_τ fluxes, or nonstandard interactions. Therefore, extremely small values of θ₁₃ are in practice equivalent, the fate of the system depending only on the neutrino spectra and their mass ordering.