= Compton cooling by the cosmic microwave background
{title2=$t_C\propto(1+z)^{-4}/x_e$}
Hot electrons can transfer energy to <Cosmic microwave background> photons through <Compton scattering>. For a fixed electron fraction $x_e$ and electron temperature well above the radiation temperature, the <optically thin gas cooling time> scales approximately as $(1+z)^{-4}/x_e$. Its volume loss scales with electron density, not with $n_H^2$, because the radiation density is independent of local gas density. The process tends toward the radiation temperature; it heats rather than cools electrons colder than that radiation.
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