Monte Carlo Study of Supernova Neutrino Spectra Formation

The neutrino flux and spectra formation in a supernova core is studied by using a Monte Carlo code. The dominant opacity contribution for ν μ is elastic scattering on nucleons ν μ N → N ν μ , where ν μ always stands for either ν μ or ν τ . In addition, we switch on or off a variety of processes that allow for the exchange of energy or the creation and destruction of neutrino pairs, notably nucleon bremsstrahlung NN → NN ν μ μ , the pair annihilation processes e + e - → ν μ μ and ν e e → ν μ μ , recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons ν μ e ± → e ± ν μ , and elastic scattering on electron neutrinos and antineutrinos ν μ ν e → ν e ν μ and ν μ e → e ν μ . The least important processes are neutrino-neutrino scattering and e + e - annihilation. The formation of the spectra and fluxes of ν μ is dominated by the nucleonic processes, i.e., bremsstrahlung and elastic scattering with recoil, but also ν e e annihilation and ν μ e ± scattering contribute significantly. When all processes are included, the spectral shape of the emitted neutrino flux is always "pinched," i.e., the width of the spectrum is smaller than that of a thermal spectrum with the same average energy. In all of our cases we find that the average μ energy exceeds the average e energy by only a small amount, 10% being a typical number. Weak-magnetism effects cause the opacity of ν μ to differ slightly from that of μ , translating into differences of the luminosities and average energies of a few percent. Depending on the density, temperature, and composition profile, the flavor-dependent luminosities L ν e , L e , and L ν μ can mutually differ from each other by up to a factor of 2 in either direction.