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

We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum by using the density profile of the adiabatic explosion model of a core-collapse supernova, which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We calculate expected event rates of neutrino detection at Super-Kamiokande (SK) and Sudbury Neutrino Observatory (SNO) for various theta(13) values and both normal and inverted hierarchies. The predicted event rates of (nu) over bar (e) and nu(e) depend on the mixing angle theta(13) for the inverted and normal mass hierarchies, respectively, and the influence of the shock wave appears for about 2-8 s when sin(2)2 theta(13) is larger than 10(-3). These neutrino signals for the shock-wave propagation is decreased by less than or similar to 30% for (nu) over bar (e) in inverted hierarchy (SK) or by less than or similar to 15% for nu(e) in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos (20 MeV <= E-v <= 60 MeV) to low-energy neutrinos (5 MeV less than or similar to E <= 20 MeV) is consistent with the previous studies in schematic semianalytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy neutrinos to the event rates of low-energy neutrinos is a very useful observable which is sensitive to theta(13) and mass hierarchies. Namely, the time-dependent ratio shows a clearer signal of the shock-wave propagation that exhibits a remarkable decrease by at most a factor of similar to 2 for (nu) over bar (e) in inverted hierarchy (SK), whereas it exhibits a smaller change by similar to 10% for nu(e) in normal hierarchy (SNO). Observing the time-dependent high-energy to low-energy ratio of the neutrino events thus would provide a piece of very useful information to constrain theta(13) and mass hierarchy and eventually help understand how the shock wave propagates inside the star.