Intermittent Turbulence, Fast Flavor Conversion, and Observable Supernova Probes

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 $\hat{I}´\ddot{I}/⟨\ddot{I}⟩=0.4$, $\bar{\hat{I}}»/\hat{I}¼=1$, and hence $\hat{I}{º}_0=0.16$, the representative $N=2$, $r=2$ cascade gives $\ddot{I}{ƒ}_{\mathrm{int}}^2=1.124$ and an intermittent conversion fraction $1-P_{\mathrm{base}}\simeq 0.455$. The older weaker normalization $\hat{I}{º}_0=0.05$ gives $1-P_{\mathrm{base}}\simeq 0.324$. The corresponding Mori-like heating ratios are $Q_{\mathrm{int}}/Q_{\mathrm{hom}}=1.060$ 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.