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 θ13 values and both normal and inverted hierarchies. The predicted event rates of ν̄e and νe depend on the mixing angle θ13 for the inverted and normal mass hierarchies, respectively, and the influence of the shock wave appears for about 2-8 s when ^sin-22θ13 is larger than 10 ^-3. These neutrino signals for the shock-wave propagation is decreased by 30% for ν̄e in inverted hierarchy (SK) or by 15% for νe in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos (20MeV Eν60MeV) to low-energy neutrinos (5MeV Eν20MeV) 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 θ13 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 ∼2 for ν̄e in inverted hierarchy (SK), whereas it exhibits a smaller change by ∼10% for νe 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 θ13 and mass hierarchy and eventually help understand how the shock wave propagates inside the star.