Abstract
The neutrino flux and spectra formation in a supernova core is studied by using a Monte Carlo code. The dominant opacity contribution for νμ is elastic scattering on nucleons νμN → Nνμ, where νμ always stands for either νμ or ντ. 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 → NNνμμ, the pair annihilation processes e+e- → νμμ and νee → νμμ, recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons νμe± → e±νμ, and elastic scattering on electron neutrinos and antineutrinos νμνe → νeνμ and νμe → eνμ. The least important processes are neutrino-neutrino scattering and e+e- annihilation. The formation of the spectra and fluxes of νμ is dominated by the nucleonic processes, i.e., bremsstrahlung and elastic scattering with recoil, but also νee annihilation and νμe± 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 νμ 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 Lνe, Le, and Lνμ can mutually differ from each other by up to a factor of 2 in either direction.
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