Suppression of Fast Flavor Conversion by Red Turbulence in Supernovae

Abstract

Fast flavor conversions (FFCs) in supernovae, driven by neutrino-neutrino refraction, can catastrophically equilibrate flavors and potentially affect the neutrino-driven explosion. We present a pivotal insight: matter density fluctuations characterized by red spectra ($ν<0$), naturally arising in stratified supernova environments, can suppress such instabilities by inducing accelerated decoherence. By deriving exact analytical solutions for two-flavor evolution in red turbulent matter-where correlations grow as $t^{|ν|}$-we uncover a novel acceleration of coherence loss. This dynamical decoherence mechanism raises an effective energy barrier against the collective growth of flavor instabilities. Translating our master-equation results into an effective damping rate for FFC linear analysis, we find that realistic red turbulence ($ν\sim -1$, fluctuation strength $ξ_ν\sim 0.1$) can elevate the FFC threshold by a factor of $\sim 3-5$, potentially stabilizing regions that would otherwise undergo explosion-killing flavor equilibration (or vice versa). Our work provides the first analytical criterion for FFC suppression in turbulent media and identifies red turbulence as a critical, physics-grounded ingredient missing from current supernova models.

Figures (1)

• Figure 1: Electron neutrino survival probability $P_{ee}(x)$ for turbulence with different spectral indices $\nu$, demonstrating the effect of temporal correlations on decoherence. White noise ($\nu=0$, blue solid line) produces the strongest decoherence, reaching the lowest asymptotic value. Red noise with $\nu=-0.5$ (orange dashed), $\nu=-1.0$ (green dash-dot), and $\nu=-2.0$ (red dotted) shows progressively weaker decoherence as $\nu$ decreases, with higher asymptotic survival probabilities. This indicates that long-range temporal correlations (red spectra) preserve flavor coherence more effectively than uncorrelated (white) fluctuations, despite having identical integrated turbulence strength $\xi=0.1$. The small-scale regularization $\epsilon=0.01$ (we introduce a physical cutoff $\epsilon \sim \tau_{\text{diss}}$ at the dissipation scale, modifying the kernel to $K(t) \propto t^{-\nu} \exp(-\epsilon/t)$. For $\nu<0$, this regularization ensures mathematical consistency while having negligible effect on physical results) ensures convergence of all memory integrals.