Neutrinos from SN 1987A, Earth matter effects, and the large mixing angle solution of the solar neutrino problem

We study the properties of the oscillation effects in the matter of the Earth on antineutrino fluxes from supernovae. We show that these effects can provide an explanation of the difference in the energy spectra of the events detected by Kamiokande-2 and IMB detectors from SN 1987A as well as the absence of high-energy events with $E\gtrsim 40$ MeV. This explanation requires the neutrino oscillation parameters $\Delta m^2$ and ${\sin }^{2}2\theta$ to be in the region of the large mixing angle solution of the solar neutrino problem and the normal mass hierarchy if $|U_{e3\mathrm{}}{|}^2\gtrsim {10}^{-3}.$ The hierarchy can be inverted if $|U_{e3\mathrm{}}{|}^2\ll {10}^{-3}.$ The solution of the solar neutrino problem based on ${\nu }_e$ conversion to a pure sterile state is disfavored by SN 1987A data.