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26 - Cosmological Radiative Transfer

from Part Four - Ions and Photons in the Cosmos

Published online by Cambridge University Press:  17 December 2025

Christopher W. Churchill
Affiliation:
New Mexico State University
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Summary

Astronomers collect light, nothing more. The formalism of radiative transfer is a macroscopic treatment of microscopic interplay between light and matter; it employs macroscopic variables that parameterize microscopic interactions. In this chapter we describe the radiation and photon field and define the fundamental macroscopic quantity – the specific intensity. The geometry of radiative transfer is key as it involves an origin and an observer defined line-of-sight perspective. The observed solid angle is expressed for a cosmologically distant observer, from which flux vectors and the observed flux are derived. The equation of radiative transfer is introduced, including the macroscopic parameters known as the emission and extinction coefficients and the optical depth and mean free path. The solution for pure absorption is given including illustrations of the anatomy of an absorption line in terms of optical depth. The details hidden within a beam-averaged astronomical absorption spectrum are described, followed by a treatment of partial covering, from which the covering factor is derived. Finally, a formal definition of column density is provided.

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