The Thomson optical depth (τT or just τ) is optical depth due to Thomson scattering and is of interest when the latter is the primary type of scattering, e.g., when electromagnetic radiation (EMR) passes through a medium in which it is likely to pass close to electrons, such as within an ionized medium. It is often cited/used in cosmology. Determining the Thomson optical depth is of interest in studying distant EMR such as the cosmic microwave background (CMB), that passed over a long distance through reionized media, since the opaqueness due to Thomson scattering tends to cover up interesting detail in the primordial CMB such as its deviations and polarization. The term Thomson thick refers to material with considerable Thomson optical depth.
Similarly, the terms Compton optical depth, and Compton thick are used for Compton scattering, which is a subject of study regarding X-rays from active galactic nuclei. Resulting spectral features are used to determine whether such scattering is occurring, and to work out what sort of EMR produced the observed results.
The Thomson optical depth and dispersion measure (DM) (used in radio astronomy regarding pulsar signals and fast radio bursts) are both measures of electron column density: the DM is scaled to match it and the Thomson optical depth is this column density multiplied by the Thomson-scattering cross section of an electron.