We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum using density profile of 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 SK and SNO for various theta_{13} values and both normal and inverted hierarchies. The predicted event rates of bar{nu}_e and nu_e depend on the mixing angle theta_{13} for the inverted and normal hierarchies, 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 for the shock propagation is decreased by < 30 % for bar{nu}_e in inverted (SK) or by < 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_{nu} < 60 MeV) to low-energy neutrinos (5 MeV < E_{nu} < 20 MeV) is consistent with the previous studies in schematic semi-analytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy to low-energy neutrinos is a very useful observable which is sensitive to theta_{13} and hierarchies. Namely, time-dependent ratio shows clearer signal of the shock propagation that exhibits 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 normal hierarchy (SNO). Observing 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 understanding the propagation how the shock wave propagates inside the star.
About twenty events of supernova neutrinos were detected from SN1987A [1,2]. Some neutrino features such as neutrino temperatures and the energy carried out by neutrinos that had been obtained from the data of SN1987A were consistent with theoretical expectation [3][4][5][6]. However, the detected number of the neutrino events was still too small to find out more details about other flavors of the supernova neutrinos and the explosion mechanism.
Although, we have not yet obtained neutrino events from the second core-collapse supernova which is the rare event of the century, detection of next supernova neutrinos is highly desirable to obtain important information on the neutrinos and the explosion mechanism.
The expected information from the supernova neutrino observations is classified into two categories of implication for neutrino physics and for supernova physics.
Large-volume underground detectors are now operating to detect various neutrino events.
For example, Super-Kamiokande (SK), which is at the Kamioka mine in Japan, is a water Cherenkov detector, filled with 50,000 ton pure water (32,000 ton fiducial volume for the burst mode and 22,500 ton for the other modes) [7]. KamLAND is a liquid scintillator detector with 1,000 ton active volume [8]. Sudbury Neutrino Observatory (SNO) has operated as a heavy water Cherenkov detector, filled with 1,000 ton fiducial volume [9]. Now, a new generation experiment, SNO+, is planned to be constructed [10]. We achieved remarkable development of the neutrino physics, especially about neutrino oscillation from the solar, atmospheric and reactor neutrino experiments with these detectors. In addition, the supernova neutrinos are thought to be fascinating targets of these detectors. If one supernova explodes at the Galactic center, thousands of neutrino events will be observed in Super-Kamiokande [11]. Furthermore, megaton-size neutrino detectors will detect ×10 5 supernova neutrino events in the future [12][13][14][15][16]. The neutrinos are released directly from the core, in which the extreme physical condition of very high density is realized. Therefore, the supernova neutrinos would become the probe of such an environment.
Neutrino flavor change by the neutrino oscillations relates to neutrino oscillation parameters, i.e., the mixing angles, mass hierarchy, and CP violation phase. Most of neutrino oscillation parameters have been determined by the various neutrino experiments [17][18][19].
However, the mixing angle θ 13 is not precisely constrained, and only the upper bound is known from reactor experiments (e.g., [20]). In addition, the neutrino mass hierarchy, i.e., the sign of ∆m 2 13 ≡ m 2 3 -m 2 1 , and the CP violation phase remain unknown. However, among many studies about implication on these unknown neutrino parameters from future supernova neutrinos [21][22][23][24][25][26][27][28][29], there are several proposed possibilities that the detection of the neutrinos from the next Galactic supernova would constrain the neutrino oscillation parameters and identify the mass hierarchy more precisely [26][27][28][29].
Most of the supernova neutrinos are released for about 10 seconds after the core bounce, and interact with electrons when the neutrinos propagate through stellar matter. Therefore, Mikheyev-Smirnov-Wolfstein (MSW) effect is to be taken into account in the neutrino oscillations of the supernova neutrinos. The MSW effect on the supernova neutrino signal has been investigated previously in literatures (e.g., [21,[30][31][32]). For example, the initial progenitor mass dependence of the early neutrino burst taking account of the MSW effect was studied in [33], and the Earth matter effects of the supernova neutrinos were identified in [34][35][36][37]. Moreover, neutrino spin-flavor conversion in supernova has been studied considering numerically in [38][39][40] and analytically in [41,42].
Recently, the effect of the shock wave on MSW effect of neutrino oscillations in supernova was studied [22,43]. This effect appears as a decrease of the average energy of ν e in the case of normal mass hierarchy (or νe in the case of inverted mass hierarchy) [44,45]. Since the shock wave passes through H-resonance region, whose typical resonance density is ∼ 10 3 g/cm 3 in a few seconds after core bounce, the adiabaticity of the resonance changes.
The time dependence of the neutrino events monitors the density profile of the supernova [26-28, 45, 46]. Therefore, using MSW effects embedded in the supernova neutrinos, we are able to find the density profile of the supernova. However, in many previous studies the influences of the shock wave on the neutrino events were discussed schematically using simplified and parameterized shock-wave profiles [27].
There are many supernova simulations taking account of various explosion mechanisms.
However, there are a few studies in which the neutrino oscillations were calculated by using simulation results because almo
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