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In an optically thin plasma, one convention defines the radiative cooling power per volume by $\mathcal{C}=n_e{n}_H{\Lambda }_{eH}(T)$, where $n_H$ counts hydrogen nuclei. A convention $\mathcal{C}=n_H^2{\Lambda }_{HH}$ instead has ${\Lambda }_{HH}=(n_e/n_H){\Lambda }_{eH}$. Thus the tabulated functions differ even for the same gas. With total particle density $n$, a monatomic-gas radiative gas cooling time is $3n{k}_{B}T/(2\mathcal{C})$ when heating is negligible.^[ref]

gas heats when compression, shocks or absorbed radiation increase its internal energy. Important sources include accretion shocks, stellar winds, supernovae, photoionization, photoelectric emission from interstellar dust, cosmic rays and energy deposited by active galactic nuclei. photoionization heating uses the photoelectron energy above the ionization threshold; compression contributes mechanical work rather than photon absorption.

For specific internal energy $u$, an idealized thermal balance isHere $\mathcal{H},\mathcal{C}$ are powers per volume and $Z$ describes abundances. The electron-hydrogen normalization of the cooling function must be specified: some conventions instead factor out $n_H^2$. For a monatomic gas with total particle density $n$,when heating is negligible. Compare this with the dynamical time: rapid cooling permits loss of pressure support, whereas long cooling times allow a hot atmosphere to persist.

collisional excitation followed by spontaneous emission cools partially ionized gas; radiative recombination also produces continuum cooling. metal lines enhance cooling over substantial intermediate-temperature ranges, while thermal bremsstrahlung gives a roughly $\Lambda \propto T^{1/2}$ high-temperature tail. Atomic hydrogen cooling becomes inefficient below roughly $10^4\mathrm{K}$, where molecular line cooling and interstellar dust can be important. inverse Compton scattering cools hot electrons against a colder radiation field. A tabulated cooling curve assumes a composition and ionization model; photoionization or nonequilibrium ionization can change it.^[ref]

X-ray line ratios and continuum shape constrain temperature and ionization, while the emission measure constrains $\int n_e{n}_{H}dV$. Turning that into a density and radiative gas cooling time also requires a geometry; unresolved clumping, foreground absorption and multiphase gas are important controls.