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 nu(e) and another flavor nu(x) and assume the usual hierarchy F-nu e > F-(nu) over bare > F-nu x = F-(nu) over barx for the number fluxes. We define epsilon = (F-nu e - F-(nu) over bare)/(F-(nu) over bare - F-(nu) over barx) 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 epsilon. For typical choices of other parameters, multiangle decoherence is suppressed for epsilon greater than or similar to 0.3, but a much smaller asymmetry suffices if the neutrino mass hierarchy is normal and the mixing angle small. The critical epsilon depends logarithmically on the neutrino luminosity. In a realistic supernova scenario, the deleptonization flux is probably enough to suppress multiangle decoherence.