Neutrino Energy Loss from the Plasma Process at all Temperatures and Densities

TL;DR

An analytic approximation to the dispersion equations for photons and plasmons is developed that is correct to order $\ensuremath{\alpha}$ in the classical, degenerate, and relativistic limits for all momenta $k$ and is correct at small $ k$ for all temperatures and electron densities.

Abstract

We present a unified approach which is accurate at all temperatures and densities for calculating the energy loss from a stellar plasma due to the plasma process, the decay of photons and plasmons into neutrino pairs. To allow efficient numerical calculations, an analytic approximation to the dispersion equations for photons and plasmons is developed. It is correct to order $α$ in the classical, degenerate, and relativistic limits for all momenta $k$ and is correct at small $k$ for all temperatures and electron densities. Within the same approximations, concise expressions are derived for the transverse, longitudinal, and axial vector components of the neutrino emissivity.