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 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 which allow for the exchange of energy or the creation and destruction of neutrino pairs, notably nucleon bremsstrahlung NN → NNνμν̄μ, the pair annihilation processes e e → νμν̄μ and νeν̄e → νμν̄μ, recoil in elastic nucleon scattering, elastic scattering on electrons νμe ± → eνμ and elastic scattering on electron neutrinos and anti-neutrinos νμνe → νeνμ and νμν̄e → ν̄eνμ. The least important processes are neutrino-neutrino scattering and ee annihilation. The formation of the spectra and fluxes is dominated by the nucleonic processes, i.e. bremsstrahlung and elastic scattering with recoil, but also νeν̄e annihilation and νμe ± scattering contribute on a significant level. When all processes are included, the spectral shape of the emitted neutrino flux is always “pinched” and can be represented by a nominal Fermi-Dirac function with an effective degeneracy parameter in the range 1–2, depending on the details of the background model. In all of our cases we find that the average νμ and ν̄μ energy exceeds the average ν̄e energy by only a small amount, 10% being a typical number. Depending on the density, temperature, and composition profile, the flavor-dependent luminosities Lνe , Lν̄e , and Lνμ can mutually differ from each other by up to a factor of two in either direction. Subject headings: diffusion — neutrinos — supernovae: general