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 ${\bar{\nu }}_e$ dominating over ${\bar{\nu }}_{\mu }$. 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 $20\mathrm{m}\mathrm{s}$ of collapse, i.e., local spectral excesses of ${\bar{\nu }}_e$ over ${\bar{\nu }}_{\mu }$ along some direction. Therefore, post-processing SN simulations cannot consistently capture later fast instabilities because the early slow ones have already altered the conditions.