Model-independent approach to the reconstruction of multiflavor supernova neutrino energy spectra

The model-independent reconstruction of the energy spectra of ${\overline{\nu }}_e$, ${\nu }_e$, and ${\nu }_x$ (i.e., ${\nu }_{\mu }$, ${\nu }_{\tau }$, and their antiparticles) from the future observation of a galactic core-collapse supernova (SN) is of crucial importance to understand the microscopic physics of SN explosions. To this end, we propose a practically useful method to combine the multichannel detection of SN neutrinos in a large liquid-scintillator detector (e.g., JUNO), namely, the inverse beta decay ${\overline{\nu }}_e+p\to e^{+}+n$, the elastic neutrino-proton scattering $\nu +p\to \nu +p$ and the elastic neutrino-electron scattering $\nu +e^{-}\to \nu +e^{-}$, and reconstruct the energy spectra of ${\overline{\nu }}_e$, ${\nu }_e$, and ${\nu }_x$ by making the best use of the observational data in those three channels. In addition, the neutrino energy spectra from the numerical simulations of the delayed neutrino-driven SN explosions are implemented to demonstrate the robustness of our method. Taking the ordinary matter effects into account, we also show how to extract the initial neutrino energy spectra in the presence of neutrino flavor conversions.

Figure 1

The neutrino event spectra at a JUNO-like LS detector for a galactic SN at the distance of 10 kpc, where the first row refers to the IBD (left panel) and $p\mathrm{ES}$ (right panel) channels while the second row to the $e\mathrm{ES}$ channel. In the latter case, the event numbers are shown in both linear and logarithmic scales in the left and right panel, respectively.

Figure 2

The response matrix for the LS detector, which has been implemented in the combined analysis. Three rows correspond to the IBD (upper), $p\mathrm{ES}$ (middle), and $e\mathrm{ES}$ (lower) channels, respectively, while three columns correspond to the ${\nu }_e$ (left), ${\overline{\nu }}_e$ (middle), and $4{\nu }_x$ (right) spectra. The finite energy resolution of $3\%/\sqrt{E_{\mathrm{o}}/(\mathrm{MeV})}$ and the quenching effects in the LS detector have been taken into account, and the energy threshold $E_{\mathrm{o}}^{\mathrm{th}}=0.2\mathrm{MeV}$ has been assumed.

Figure 3

The unfolded neutrino spectra from the combined analysis, where the upper, middle, and lower rows correspond to the SN distances at 10, 1, and 0.2 kpc, respectively. The right column shows the whole neutrino spectra, while the left column focuses on the high-energy parts.

Figure 4

The unfolded neutrino spectra from the combined analysis for different flavor neutrinos, where the SN distance is 1 kpc and the energy threshold $E_{\mathrm{o}}^{\mathrm{th}}$ is 0.2 MeV for blue points and 0.01 MeV for orange points.

Figure 5

The bias distributions for ${\overline{\nu }}_e$, ${\nu }_e$, and ${\nu }_x$ from top to bottom, respectively, for the SN at 1 kpc, where high (green), medium (blue), and low (orange) values of regularization parameter are applied during the unfolding procedure. The solid lines are for the mean bias and the shade areas are due to standard deviations of the mean bias, which are explained in the text.

Figure 6

The bias distributions of the reconstructed neutrino spectra for the SN at 1 kpc. In the unfolding process, the response matrix has been built with the flat neutrino spectra (left column), or with the neutrino spectra from each numerical model (right column). The dashed horizontal lines are shown for the best precision of the corresponding reconstructed spectra in Fig. 3.

Figure 7

The convolution of the response matrices in Fig. 2 with the flavor conversion matrix in Eq. (10) in the case of normal neutrino mass ordering (left panel) or that in Eq. (11) in the case of inverted neutrino mass ordering (right panel).

Figure 8

The initial SN neutrino spectra reconstructed via the combined analysis, where neutrino flavor conversions are taken into account in the case of the normal mass ordering (left panel) or the inverted mass ordering (right panel).