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 nu(mu) is elastic scattering on nucleons nu(mu)N --> Nnu(mu), where nu(mu) always stands for either nu(mu) or nu(tau). 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 --> NNnu(mu)(nu) over bar (mu), the pair annihilation processes e(+)e(-) --> nu(mu)(nu) over bar (mu) and nu(e)(nu) over bar (e) --> nu(mu)(nu) over bar (mu), recoil and weak magnetism in elastic nucleon scattering, elastic scattering on electrons nu(mu)e(+/-)-->e(+/-)nu(mu), and elastic scattering on electron neutrinos and antineutrinos nu(mu)nu(e) --> nu(e)nu(mu) and nu(mu)(nu) over bar (e) --> (nu) over bar (e)nu(mu). The least important processes are neutrino-neutrino scattering and e(+)e(-) annihilation. The formation of the spectra and fluxes of nu(mu) is dominated by the nucleonic processes, i.e., bremsstrahlung and elastic scattering with recoil, but also nu(e)(nu) over bar (e) annihilation and nu(mu)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 (nu) over bar (mu) energy exceeds the average (nu) over bar (e) energy by only a small amount, 10% being a typical number. Weak-magnetism effects cause the opacity of nu(mu) to differ slightly from that of (nu) over bar (mu), 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 Lnu(e), L (nu) over bar (e), and L-numu can mutually differ from each other by up to a factor of 2 in either direction.