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Neutrinos from a supernova (SN) might undergo fast flavor conversions nearthe collapsed stellar core. We perform a detailed study of this intriguingpossibility, analyzing time-dependent state-of-the-art 3D SN models of 9 and 20Msun. Both models were computed with multi-D three-flavor neutrino transportbased on a two-moment solver, and both exhibit the presence of thelepton-number emission self-sustained asymmetry (LESA). The transport solutiondoes not provide the angular distributions of the neutrino fluxes, which arecrucial to track the fast flavor instability. To overcome this limitation, weuse a recently proposed approach based on the angular moments of theenergy-integrated electron lepton-number distribution. With this method we findthe possibility of fast neutrino flavor instability at radii <~20 km, which iswell interior to the neutrinosphere. Our results confirm recent observations ina 2D SN model and in 2D/3D models with fixed matter background, which werecomputed with Boltzmann neutrino transport. However, the flavor unstablelocations are not isolated points as discussed previously, but thin skinssurrounding volumes where electron antineutrinos are more abundant thanelectron neutrinos. These volumes grow with time and appear first in theconvective layer of the proto-neutron star (PNS), where a decreasing electronfraction (Ye) and high temperatures favor the occurrence of regions withnegative neutrino chemical potential. Since Ye remains higher in the LESAdipole direction, where convective lepton-number transport out from thenonconvective PNS core slows down the deleptonization, flavor unstableconditions become more widespread in the opposite hemisphere. This interestingphenomenon deserves further investigation, since its impact on SN modeling andpossible consequences for SN dynamics and neutrino observations are presentlyunclear. (abridged)

Fast Neutrino Flavor Instability in the Neutron-star Convection Layer of Three-dimensional Supernova Models