Interplay of neutrino flavor, spin and collective oscillations in supernovae

We present an analysis of a neutrino flux evolution in an extreme astrophysical environment peculiar to supernovae accounting for effects of an arbitrarily moving media and strong magnetic field. For neutrinos propagating inside a supernova the resonances in the flavour and spin-flavour oscillations engendered by the neutrino magnetic moment interaction with a magnetic field and weak interactions with the transversally moving matter are accounted for. In addition, we also account for the effect of the collective neutrino oscillations and discuss possible spectral splits of the final neutrino fluxes that can arise due to spin and spin-flavour oscillations in this case