Axial Symmetry Breaking in Self-Induced Flavor Conversionof Supernova Neutrino Fluxes

Neutrino-neutrino refraction causes self-induced flavor conversion in dense neutrino fluxes. For the first time, we include the azimuth angle of neutrino propagation as an explicit variable and find a new generic multi-azimuth-angle instability which, for simple spectra, occurs in the normal neutrino mass hierarchy. Matter suppression of this instability in supernovae requires larger densities than the traditional bimodal case. The new instability shows explicitly that solutions of the equations for collective flavor oscillations need not inherit the symmetries of initial or boundary conditions. This change of paradigm requires reconsideration of numerous results in this field.

Figure 1

Growth rate $\kappa$ for blackbody-like zenith distribution, single energy $\pm {\omega }_0$, and $ϵ=1/2$. Black line: All cases for $\overline{\lambda }=\lambda +ϵ\mu =0$ (no matter effect). Other lines: Indicated unstable cases for $\overline{\lambda }=300|{\omega }_0|$.

Figure 2

Region where $\kappa r>1$ for IH (blue) and NH (red), depending on radius $r$ and multiangle matter potential $\lambda$ for our simplified SN model. Thick black line: SN density profile. Thin dashed lines: Contours of constant electron density, where $Y_e$ is the electron abundance per baryon. (The IH case corresponds to Fig. 4 of Ref. 18, except for the simplified spectrum used here.)