Flavor stability analysis of dense supernova neutrinos with flavor-dependent angular distributions

TL;DR

This paper investigates how flavor-dependent angular distributions of supernova neutrinos influence flavor stability, revealing a novel multi-angle instability that affects flavor conversions at smaller radii, with implications for supernova neutrino modeling.

Contribution

It extends previous supernova neutrino models by analyzing flavor-dependent angular distributions and identifying a new multi-angle instability affecting flavor conversions.

Findings

Enhanced flavor instability for spectra crossing in angular space

Shift of flavor conversion onset to smaller radii

Stability analysis explains flavor dynamics qualitatively and quantitatively

Abstract

Numerical simulations of the supernova (SN) neutrino self-induced flavor conversions, associated with the neutrino-neutrino interactions in the deepest stellar regions, have been typically carried out assuming the "bulb-model". In this approximation, neutrinos are taken to be emitted half-isotropically by a common neutrinosphere. In the recent Ref. \cite{Mirizzi:2011tu} we have removed this assumption by introducing flavor-dependent angular distributions for SN neutrinos, as suggested by core-collapse simulations. We have found that in this case a novel multi-angle instability in the self-induced flavor transitions can arise. In this work we perform an extensive study of this effect, carrying out a linearized flavor stability analysis for different SN neutrino energy fluxes and angular distributions, in both normal and inverted neutrino mass hierarchy. We confirm that spectra of different nu species which cross in angular space (where F_{\nu_e}=F_{\nu_x} and F_{\bar\nu_e}=F_{\bar\nu_x}) present a significant enhancement of the flavor instability, and a shift of the onset of the flavor conversions at smaller radii with respect to the case of an isotropic neutrino emission. We also illustrate how a qualitative (and sometimes quantitative) understanding of the dynamics of these systems follows from a stability analysis.