Detecting supernovae neutrino with Earth matter effect

We study Earth matter effect in oscillations of supernovae neutrinos. We show that detecting Earth matter effect gives an independent measurement of spectra of supernovae neutrinos, i.e., the flavor difference of the spectra of supernovae neutrinos. We study the effect of energy resolution and angular resolution of a final electron or positron on detecting the signal of Earth matter effect. We show that varying the widths of energy bins in analysis can change the signal strength of Earth matter effect and the statistical fluctuation. A reasonable choice of energy bins can both suppress the statistical fluctuation and make a good signal strength relative to the statistical fluctuation. Neutrino detectors with good energy resolution and good angular resolution are therefore preferred so that there is more freedom to vary energy bins and to optimize the signal of Earth matter effect in analyzing events of supernovae neutrinos.