MSW effect in supernova-shock propagation

It is pointed out that shock wave propagation has influences on the supernova neutrino oscillation by changing density profile and neutrino survival probability (MSW effect). Using an implicit Lagrangian code for general relativistic spherical hydrodynamics, we succeeded in calculating propagation of shock waves which are generated by adiabatic collapse of iron cores and pass into the stellar envelopes. We apply our model to the neutrino oscillation and calculate neutrino energy spectra of three light-neutrino families. We examined how the influence of the shock wave appear in the neutrino spectra, and found that the influences of the shock wave in the neutrino spectra move from low-energy side to high-energy side according to the shock propagation.