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We study how the influence of the shock wave appears in neutrino oscillationsand the neutrino spectrum using density profile of adiabatic explosion model ofa core-collapse supernova which is calculated in an implicit Lagrangian codefor general relativistic spherical hydrodynamics. We calculate expected eventrates of neutrino detection at SK and SNO for various theta_{13} values andboth normal and inverted hierarchies. The predicted event rates of bar{nu}_eand nu_e depend on the mixing angle theta_{13} for the inverted and normalhierarchies, respectively, and the influence of the shock appears for about 2 -8 s when sin^2 2 theta_{13} is larger than 10^{-3}. These neutrino signals forthe shock propagation is decreased by < 30 % for bar{nu}_e in inverted (SK) orby < 15 % for nu_e in normal hierarchy (SNO) compared with the case withoutshock. The obtained ratio of the total event for high-energy neutrinos (20 MeV< E_{nu} < 60 MeV) to low-energy neutrinos (5 MeV < E_{nu} < 20 MeV) isconsistent with the previous studies in schematic semi-analytic or otherhydrodynamic models of the shock propagation. The time dependence of thecalculated ratio of the event rates of high-energy to low-energy neutrinos is avery useful observable which is sensitive to theta_{13} and hierarchies.Namely, time-dependent ratio shows clearer signal of the shock propagation thatexhibits remarkable decrease by at most factor \sim 2 for bar{nu}_e in inverted(SK), whereas it exhibits smaller change by \sim 10 % for nu_e in normalhierarchy (SNO). Observing time-dependent high-energy to low-energy ratio ofthe neutrino events thus would provide a piece of very useful information toconstrain theta_{13} and mass hierarchy, and eventually help understanding thepropagation how the shock wave propagates inside the star.

Neutrino oscillation and expected event rate of supernova neutrinos in adiabatic explosion model