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_μN → Nν_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 → NNν_μμ, the pair annihilation processes e⁺e^- → ν_μμ and ν_ee → ν_μμ, recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons ν_μe^± → e^±ν_μ, and elastic scattering on electron neutrinos and antineutrinos ν_μν_e → ν_eν_μ and ν_μe → _eν_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_ee annihilation and ν_μe^± 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_νe, L_e, and L_νμ can mutually differ from each other by up to a factor of 2 in either direction.