Instability in the dense supernova neutrino gas with flavor-dependent angular distributions

The usual description of self-induced flavor conversions for neutrinos (ν's) in supernovae is based on the simplified assumption that all the ν's of the different species are emitted "half-isotropically" by a common neutrinosphere, in analogy to a blackbody emission. However, realistic supernova simulations show that νangular distributions at decoupling are far from being half-isotropic and, above all, are flavor-dependent. We show that flavor-dependent angular distributions may lead to crossing points in the angular spectra of different νspecies (where F_{ν_e}=F_{ν_x} and F_{{\barν}_e}=F_{{\barν}_x}) around which a new multi-angle instability can develop. To characterize this effect, we carry out a linearized flavor stability analysis for different SN neutrino angular distributions. We find that this instability can shift the onset of the flavor conversions toward low-radii and produce a smearing of the splitting features found with trivial $ν$ emission models. As a result the spectral differences among ν's of different flavors could be strongly reduced.

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