Neutrino-Mass-Driven Instabilities as the Earliest Flavor Conversion in Supernovae

Collective neutrino flavor conversions in core-collapse supernovae begin with instabilities, initially triggered when the dominant νe outflow concurs with a small antineutrino flux of opposite lepton number, with $\bar{ν}_e$ dominating over $\bar{ν}_μ$. When these “flipped” neutrinos emerge in the energy-integrated angular distribution (angular crossing), they initiate a fast instability. However, before such conditions arise, spectral crossings typically appear within 20 ms of collapse, i.e., local spectral excesses of $\bar{ν}_e$ over $\bar{ν}_μ$ along some direction. Therefore, postprocessing supernova simulations cannot consistently capture later fast instabilities because the early slow ones have already altered the conditions.