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 multiangle nature of the neutrino trajectories leads to flavor decoherence between different angular modes. We consider a two-flavor mixing scenario between ₄ and another flavor ₗ and assume the usual hierarchy F₄>F{₄}>Fₗ=F{ₗ} for the number fluxes. We define ϵ= (F₄-F{₄}) / (F{₄}-F{ₗ}) as a measure for the deleptonization flux which is the one crucial parameter. The transition between the quasi-single-angle behavior and multiangle decoherence is abrupt as a function of ϵ. For typical choices of other parameters, multiangle decoherence is suppressed for ϵ0. 3, but a much smaller asymmetry suffices if the neutrino mass hierarchy is normal and the mixing angle small. The critical ϵ depends logarithmically on the neutrino luminosity. In a realistic supernova scenario, the deleptonization flux is probably enough to suppress multiangle decoherence.