Matter Effects on Neutrino Oscillations in Different Supernova Models

In recent years, with the development of simulations about supernova explosion, we have a better understanding about the density profiles and the shock waves in supernovae than before. There might be a reverse shock wave, another sudden change of density except the forward shock wave, or even no shock wave, emerging in the supernova. Instead of using the expression of the crossing probability at the high resonance, P_H, we have studied the matter effects on neutrino oscillations in different supernova models. In detail, we have calculated the survival probability of ν_e (P_s) and the conversion probability of ν_x (P_c) in the Schrödinger equation within a simplified two-flavor framework for a certain case, in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova. Our calculations was based on the data of density in three different supernova models obtained from simulations. In our work, we do not steepen the density gradient around the border of the shock wave, which differs to what was done in most of the other simulations. It is found that the mass and the density distribution of the supernova do make a difference on the behavior of P_s and P_c. With the results of P_s and P_c, we can estimate the number of ν_e (and ν_x) remained in the beam after they go through the matter in the supernova.