RSF conversion. The resonance densities of two RSF conversions depend on $1/|1-2Y_e|$, so that the resonance densities will drastically change in accordance with the change in $Y_e$. Furthermore, the relation between mass eigenstates and flavor eigenstates will change at $Y_e = 0.5$. Therefore, we expect that new neutrino signals will be detected in a SN explosion in our Galaxy, if neutrinos are Majorana particles and have finite magnetic moment ($\sim 10^{-12} \mu_B$), and the SN has strong magnetic field. Although there are many studies on the RSF conversion (e.g., [@as03a; @as03b; @as03c; @af03]), this type of the RSF conversion effect on SN neutrino signal has not been studied very well.

In this study, we investigate detailed dependence of RSF conversion effects of SN neutrinos on the electron fraction in SN ejecta. In particular, we pay attention to the difference of RSF conversion at the electron fraction below and above 0.5. We will discuss the time variation of a SN neutrino signal along the evolutionary change in $Y_e$ and the dependence on neutrino oscillation parameters, i.e., mass hierarchy and the mixing angle $\theta_{13}$.

We organize this article as follows. In Sec. II, the SN explosion model adopted in this study is 