resonances are adiabatic, the mixed state of $\nu_2$ and $\bar{\nu}_2$ does not change the mass eigenstate throughout the spectra. The $\nu_2$ ($\bar{\nu}_2$) corresponds to 70 % of $\nu_{\mu,\tau}$ ($\bar{\nu}_{\mu,\tau}$) in vacuum.

Finally, we show the case of the inverted mass hierarchy and $Y_e = 0.51$ in the inner region. Figure 7 shows the conversion probabilities from $\bar{\nu}_e$ \[7(a)\] and $\nu_{\mu,\tau}$ \[7(b)\]. The conversion between $\bar{\nu}_e$ and $\nu_{\mu,\tau}$ occurs at RSF-H resonance in this case. This is similar to the first case. Almost all $\bar{\nu}_e$ convert to $\nu_{\mu,\tau}$ at the RSF-H. The $\bar{\nu}_e$ corresponds to $\nu_3$ at the high density limit and there is no resonance after the RSF-H resonance. On the other hand, $\nu_{\mu,\tau}$ changes flavors three times. The $\nu_{\mu,\tau}$ is a mixed state of $\bar{\nu}_1$ and $\bar{\nu}_3$ at high density limit. About a half of $\nu_{\mu,\tau}$, corresponding to $\bar{\nu}_3$, converts to $\bar{\nu}_e$ at RSF-H resonance. The mass eigenstate $\bar{\nu}_3$ changes the flavors at MSW-H resonance. It appears as the mixed state of $\bar{\nu}_{\mu,\tau}$ and a small fraction of $\bar{\nu}_e$ in vacuum. The mass eigenstate $\bar{\nu}_1$ converts to $\nu_1$ at RSF-X resonance, so that it appears as 70 % of $\nu_e$ and 30 % of $\nu_{\mu,\tau}$ in vacuum.

Neutrino signal
