A model-independent approach to the reconstruction of multi-flavor 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 multi-channel 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.