Decoherence in supernova neutrino transformations suppressed by deleptonization

In the dense-neutrino region at 50-400 km above the neutrino sphere in a supernova, neutrino-neutrino interactions cause large flavor transformations. We study when the multi-angle nature of the neutrino trajectories leads to flavor decoherence between different angular modes. We consider a two-flavor mixing scenario between νe and another flavor νx and assume the usual hierarchy Fνc > Fνc > Fνx = Fνx for the number fluxes. We define ε = (Fνc - Fνe)/(Fνc - Fνx) as a measure for the deleptonization flux which is the one crucial parameter. The transition between the quasi single-angle behavior and multi-angle decoherence is abrupt as a function of e. For typical choices of other parameters, multi-angle decoherence is suppressed for ε ∼> 0.3, but a much smaller asymmetry suffices if the neutrino mass hierarchy is normal and the mixing angle small. The critical e depends logarithmically on the neutrino luminosity. In a realistic supernova scenario, the deleptonization flux is probably enough to suppress multi-angle decoherence.