Earth matter effects in detection of supernova neutrinos

We calculated the matter effect, including both the Earth and supernova, on the detection of neutrinos from type II supernovae at the proposed Daya Bay reactor neutrino experiment. It is found that apart from the dependence on the flip probability $P_H$ inside the supernova and the mass hierarchy of neutrinos, the amount of the Earth matter effect depends on the direction of the incoming supernova neutrinos, and reaches the biggest value when the incident angle of neutrinos is around 93°. In the reaction channel ${\overline{\nu }}_e+p\to e^{+}+n$ the Earth matter effect can be as big as about 12%. For other detection processes the amount of the Earth matter effect is a few per cent.

Figure 1

Illustration of the path of the SN neutrinos reaching the detector in the Earth. $D$ is the location of the detector, $\theta$ is the incident angle of neutrinos, and $O$ is the center of the Earth.

Figure 2

The event number of the reaction ${\overline{\nu }}_e+p\to e^{+}+n$ as a function of the incident angle of the SN neutrino. The solid curve corresponds to $P_H=0$, 1 (normal hierarchy) and $P_H=1$ (inverted hierarchy). The dashed curve corresponds to $P_H=0$ (inverted hierarchy).

Figure 3

The total event number of neutrino-electron elastic scattering via charged and neutral currents ${\nu }_{\alpha }({\overline{\nu }}_{\alpha })+e^{-}\to {\nu }_{\alpha }({\overline{\nu }}_{\alpha })+e^{-}$ as a function of the incident angle of the SN neutrinos. The solid curve corresponds to $P_H=1$ (normal and inverted hierarchies), the dashed curve corresponds to $P_H=0$ (normal hierarchy), and the dotted curve corresponds to $P_H=0$ (inverted hierarchy), respectively.

Figure 4

The total event number of the reactions of neutrinos with ${}^{12}C$ as a function of the incident angle of the SN neutrinos. The solid curve corresponds to $P_H=1$ (normal and inverted hierarchies), the dashed curve corresponds to $P_H=0$ (normal hierarchy), and the dotted curve corresponds to $P_H=0$ (inverted hierarchy), respectively.

Figure 5

The flux of the SN ${\overline{\nu }}_e$ at the detector multiplied by ${10}^{-8}$. The solid curve represents the cases where supernova and Earth matter effects are included for $\theta =180°$, $P_H=0$, 1 (normal hierarchy) or $P_H=0$ (inverted hierarchy). The dashed curve represents the case where supernova and Earth matter effects are included for $\theta =180°$, $P_H=0$ (inverted hierarchy) or the case where the supernova matter effect is included but the Earth matter effect is not for $P_H=0$ (inverted hierarchy). The dotted curve represents the cases where the supernova matter effect is included but the Earth matter effect is not for $P_H=0$, 1 (normal hierarchy) or $P_H=1$ (inverted hierarchy). The dot-dashed (dot-dot-dashed) curve represents the flux given by Eq. (6) (Eq. (12)) where the neutrinos do not oscillate at all (oscillate as in vacuum).