When First Beats Fast: Early Neutrino-Mass-Driven Flavor Instabilities in Supernovae

Collective neutrino flavor conversions in core-collapse supernovae (SNe) begin with instabilities, initially triggered when the dominant $ν_e$ outflow concurs with a small flux of antineutrinos with the opposite lepton number, with $\overlineν_e$ dominating over $\overlineν_μ$. 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 $20~\mathrm{ms}$ of collapse, i.e., local spectral excesses of $\overlineν_e$ over $\overlineν_μ$ along some direction. Therefore, post-processing SN simulations cannot consistently capture later fast instabilities because the early slow ones have already altered the conditions.