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

Collective neutrino flavor conversions in core-collapse supernovae (SNe) begin with instabilities, initially triggered when the dominant $\nu_e$ outflow concurs with a small antineutrino flux of opposite lepton number, with $\overline{\nu}_e$ dominating over $\overline{\nu}_\mu$. 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 $\overline{\nu}_e$ over $\overline{\nu}_\mu$ along some direction. Therefore, post-processing SN simulations cannot consistently capture later fast instabilities because the early slow ones have already altered the conditions.