Effects of neutrino oscillation on supernova neutrino: inverted mass hierarchy

We study the effects of neutrino oscillation on supernova neutrino in the case of the inverted mass hierarchy ($m_3\ll m_1<m_2$) as well as the normal mass hierarchy ($m_1<m_2\ll m_3$). Numerical analysis using a realistic supernova and presupernova model allows us to discuss quantitatively a possibility to probe neutrino oscillation parameters. We show that information about the mass hierarchy can be obtained if ${\theta }_{13}$ is rather large (${\sin }^{2}2{\theta }_{13}>{10}^{-3}$) and that ${\theta }_{13}$ can be well probed by SuperKamiokande if the neutrino mass hierarchy is the inverted case. Errors due to the uncertainty of the original neutrino spectra and the Earth effect are also discussed.