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

Abstract

Collective neutrino flavor conversions in core-collapse supernovae (SNe) begin with instabilities, initially triggered when the dominant $ν_e$ outflow concurs with a small antineutrino flux of 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.

Figures (7)

• Figure 1: Double-crossed spectrum from our SN model at $62\,\mathrm{ms}$ post bounce, $r = 100\,\mathrm{km}$, and an angle to the radial direction of $\cos\theta = 0.6$ (asterisk in Fig. \ref{['fig:flipped']}). Spectra reconstructed from discretized energy bins using a Gamma fit, as in Ref. Tamborra:2012ac. The total (i.e. energy-integrated) DLN is positive; the positive contribution is highlighted with blue shade. A local excess in an energy interval of flipped neutrinos, with the opposite DLN (red shade), forms a spectral crossing and can cause an instability. Dotted line for DLN energy distribution.
• Figure 2: Fraction of flipped $\overline{\nu}_e$ color-coded as a function of radius and direction at different times. Regions exhibiting a $\overline{\nu}$ or $\nu$ crossing are indicated by colored lines, using a threshold of 5% for the flipped fraction. The shock wave radius is shown (dashed white line) and the $\overline{\nu}_e$ sphere (dotted white), defined as the radius where the $\overline{\nu}_e$ number flux equals one-quarter of the density. The number-changing reactions for $\overline{\nu}_\mu$ freeze out much deeper inside. The asterisk marks the location for the energy distribution shown in Fig. \ref{['fig:crossing']}.
• Figure 3: Number of e-folds induced by the growth of slow instabilities as a function of neutrino location and direction. The panel layout and the positions of neutrinospheres and shock waves are the same as in Fig. \ref{['fig:crossing']}.
• Figure S1: Fraction of flipped $\overline{\nu}_e$ as a function of radius and direction. Same as Fig. \ref{['fig:flipped']} of the main text, now for all available time snapshots.
• Figure S3: Typical wavelength of unstable modes, estimated as $k^{-1}\sim (\mu \epsilon)^{-1}$Fiorillo:2024pnsFiorillo:2025ankFiorillo:2025zio. The progressively darkening color corresponds to increasing time.