Intermittent Turbulence, Fast Flavor Conversion, and Observable Supernova Probes

TL;DR

This paper develops an exact linear benchmark model for fast flavor conversion in supernovae, incorporating intermittent turbulence via a She-Leveque cascade, and analyzes its impact on neutrino flavor conversion and heating.

Contribution

It introduces a novel benchmark using a She-Leveque cascade to model turbulence effects on flavor conversion, enabling analytical solutions and detailed analysis.

Findings

Intermittency significantly affects the flavor conversion fraction.

The model provides analytical expressions for the dispersion relation and time evolution.

Neutrino spectral hierarchy influences the sign of heating corrections.

Abstract

Fast flavor conversion (FFC) in core-collapse supernovae is usually analyzed in homogeneous backgrounds or with smooth stochastic turbulence closures. We construct an exact linear benchmark in which the matter-noise memory kernel is instead generated by a finite She--Leveque log-Poisson cascade. Projecting the marginal FFC channel onto this kernel gives a causal Volterra equation whose non-Markovian memory closes into a finite local system. The resulting Laplace-space resolvent is rational, with one pole pair for each cascade level, so the dispersion relation, characteristic polynomial, and time-domain solution can be checked analytically. We then connect this benchmark to the realization-level toy model and gain-region heating proxy used in the supplementary derivation. For the updated intermittent choice $\delta\rho/\langle\rho\rangle=0.4$, $\bar\lambda/\mu=1$, and hence $\kappa_0=0.16$, the representative $N=2$, $r=2$ cascade gives $\sigma_{\rm int}^2=1.124$ and an intermittent conversion fraction $1-P_{\rm base}\simeq0.455$. The older weaker normalization $\kappa_0=0.05$ gives $1-P_{\rm base}\simeq0.324$. The corresponding Mori-like heating ratios are $Q_{\rm int}/Q_{\rm hom}=1.060$ and $1.041$, whereas the Wang/Fornax-like ratios are $0.855$ and $0.899$. Thus intermittency mainly controls the conversion fraction, while the neutrino spectral hierarchy controls the sign of the heating correction.