Chemical potential effects on neutrino diffusion in supernovae

Abstract

Typically collapsing supernova hydrodynamic computations assume LTE neutrino transport andimpose photon-like behavior, i.e., fix the neutrino chemical potentials at zero. The validity of the latter condition is investigated in the diffusion approximation to transport. A coupled system of diffusion equations for energy and lepton number is solved in a collapsing supernova ambience. The results indicate a substantial growth in the neutrino chemical potential for densities above 1012 gm cm−3. The rate of energy transport is affected significantly by the concomitant increases in Fermi integrals and gradients in chemical potential counter to those of temperature. It is found that the extent of neutrino particle/antiparticle interaction also affects energy diffusion rates. Thus the photon-like condition on neutrino transport may misrepresent supernova energetics substantially. An extension of the usual Sn transport to include lepton characteristics is deemed necessary for a definitive answer to the neutrino transport supernova question.