Basic Equations for Radiative Transfer

Abstract

A light-ray (a bundle of photons) travels through and interacts with gaseous materials, via emission, absorption, and scattering. The intensity of a light-ray obeys a linear integro-differential equation, the so-called radiative transfer equation, which is just the Boltzmann equation for photons. The distribution of gas particles is microscopically described by the Boltzmann equation in the phase space, while macroscopic quantities of fluids obey hydrodynamical equations, which are moment equations of the Boltzmann equation. Similarly, the propagation of photons is described by the radiative transfer equation, whereas moment quantities of radiation fields obey the moment equations of the radiative transfer equation. In this chapter, we first derive the fundamental equation for photon transfer and show its formal solutions in the Newtonian regime. We also derive moment equations with closure relations.