Neutrino emission from a hot, dense, plane-parallel atmosphere in hydrostatic equilibrium. I

The plane-parallel, semiinfinite static neutrino atmosphere problem is solved. The atmosphere is assumed to consist of free nucleons, electrons, positrons, and photons, with electron neutrinos and antineutrinos the only means by which energy and lepton number may be transported. The atmosphere is assumed to be in hydrostatic equilibrium with a constant surface gravitational acceleration. The transport equations for neutrinos and antineutrinos and the three constraint equations which completely determine the structure of the atmosphere are solved simultaneously. It is found that in general the spectra are well approximated by Fermi distributions at high energies where opacities are large, but deviate significantly from Fermi distributions at lower energies. High values of energy flux and low values of lepton number flux produce atmospheres dominated by relativistic particles. High values of lepton number flux cause large neutrino chemical potential gradients, so that energy is carried inward by antineutrinos while neutrinos carry energy outward.