signals affected by the RSF conversion and the MSW effect, we use the time evolution of the density profile including the shock propagation in the stellar interior used in [@kk08]. The progenitor model is a 15 $M_\odot$ presupernova of [@ww95]. The core collapse and shock propagation are calculated taking account of general relativity and assuming spherical symmetry. The neutrino transport is not taken into account by assuming adiabatic explosion. Details of the hydrodynamical simulation are written in [@kk08].

The snapshots of the density profile of the SN at $t = 0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9$, and 10 s are shown in Fig. 1. A very wide range of the density from $10^{10}$ ${\rm g cm^{-3}}$ to 1 ${\rm g cm^{-3}}$ is shown. Therefore, we take account of the shock propagation effect on the RSF conversion which will occur in a high density region. On the other hand, this model assumes adiabatic explosion as mentioned above. The evolution of electron fraction is not considered. In this study, we assume that the electron fraction is constant in the innermost hot-bubble and wind region where the mass coordinate is smaller than 1.43 $M_\odot$. We consider two cases 