Role of Matter Inhomogeneity on Fast Flavor Conversion of Supernova Neutrinos

Abstract

We study how a spatially varying matter potential $\lambda$, arising from neutrino-electron forward scattering, affects the onset, evolution, and nonlinear outcome of fast neutrino flavor conversions (FFCs) triggered by the presence of zero crossings in the angular distribution of the neutrino electron lepton number (ELN). We find that increasing the spatial variation rate of $\lambda$ can strongly influence FFC dynamics and even stabilize systems that are otherwise unstable. Using stability analysis based solely on initial conditions, we identify for the first time a critical variation rate above which no FFC occurs even if the flavor instability exists. Below this critical rate, a substantial $\lambda$ variation delays the onset of FFCs and quickly generates small-scale, incoherent features in the nonlinear regime, which leads to a similar coarse-grained outcome that eliminates the ELN crossing as in the homogeneous case. Our findings emphasize the need to consider matter inhomogeneity in improved supernova models accounting for FFCs, and we propose simple analytical ways to incorporate this effect.