WHEN DO SUPERNOVA NEUTRINOS OF DIFFERENT FLAVORS HAVE SIMILAR LUMINOSITIES BUT DIFFERENT SPECTRA

Muon and tau neutrinos (nu(x)) interact with protoneutron star matter only via neutral currents and exchange energy with the stellar gas predominantly by neutrino-electron scattering and neutrino-pair processes. In contrast, electron neutrinos and antineutrinos (nu(e) and ($) over bar nu(e)) are frequently absorbed and produced in charged-current mediated reactions with nucleons. Therefore the emergent nu(e) and ($) over bar nu(e) originate fr om layers with lower temperatures further out in the star and are emitted with much lower characteristic spectral temperatures. In addition, a major contribution to the nu(e) and ($) over bar nu(e) opacities is due to absorptions, while the opacity of nu(x) is strongly dominated by scattering reactions with nucleons and nuclei in which the nu(x) energy is (essentially) conserved. Therefore the nu(x) distribution is nearly isotropic when nu(x) decouple energetically and their outward diffusion is slowed down. In a generalized form to include this effect, the Stefan-Boltzmann Radiation Law can account for both the facts that nu(e) (($) over bar nu(e)) and nu(x) emerge from the star with similar luminosities but with very different characteristic spectral temperatures. Simple analytical expressions to estimate the effect are given. If, as recently argued, even at densities significantly below nuclear matter density neutral-current scatterings were associated with considerable energy transfer between neutrino and target particle, one might expect spectral temperatures of nu(x) much closer to those of nu(e) and ($) over bar nu(e). This is of relevance for the detection of neutrino signals from supernovae.