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Photoionization changes the ion population, often removing bound-state coolants at temperatures where collisional equilibrium would retain them. It can therefore suppress primordial line-cooling peaks. It also supplies photoionization heating. The net loss is cooling minus heating and depends on radiation spectrum, intensity, shielding and gas density. A universal density-independent function of temperature alone is not generally sufficient for irradiated gas.

For a monatomic ideal gas, write the thermal energy density as $u=3n{k}_{B}T/2$. At low optical depth, radiative loss uses an astrophysical cooling function, often written $\mathcal{C}=n_e{n}_H\Lambda (T,Z)$, while $\mathcal{H}$ contains heating. At fixed density the net radiative gas cooling time is approximately $u/(\mathcal{C}-\mathcal{H})$ when the denominator is positive; a cooling flow closer to constant pressure must include enthalpy and compressional work. Comparing this time with the free-fall time of a uniform sphere determines whether pressure can be lost during gravitational contraction.

Hot ionized gas cools by bremsstrahlung and recombination; collisional excitation followed by photon escape supplies atomic and metal-line cooling at lower temperatures. molecular line cooling through rotational or vibrational lines and dust thermal emission become important in cold dense gas. Abundances, ionization state, density-dependent collisional de-excitation, and photon trapping all change the cooling function. Optically thick gas requires radiative transfer, not a simple local density-squared loss law.

Heating comes from photoionization, grain photoelectric heating driven by ultraviolet light, cosmic rays, shocks, turbulent dissipation and compression. photoionization heating deposits the photon energy above the ionization threshold as electron kinetic energy. A thermal equilibrium satisfies $\mathcal{H}=\mathcal{C}$; its stability depends on how the net loss changes under the relevant pressure or density constraint, not merely on equality. Different stable balances permit a multiphase interstellar medium. Spectral-line ratios constrain temperature and ionization, but interpreting them requires density diagnostics, interstellar extinction corrections and a radiation-field model.

For an optically thin low-density gas in collisional ionization equilibrium, the astrophysical cooling function collects losses per pair of hydrogen nuclei into $\mathcal{C}=n_H^2\Lambda (T)$. Its units are $\mathrm{erg}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$; the time unit is missing from the printed guide to the vertical-axis labels. For the primordial atomic cooling curve, only hydrogen and helium provide bound-state coolants.

Near $10^4\mathrm{K}$, collisional excitation of hydrogen becomes effective and subsequent photon emission removes thermal energy. The excitation rate is exponentially suppressed below the atomic energy threshold. Atomic line cooling and collisional ionization generate a strong hydrogen feature around a few $10^4\mathrm{K}$; helium excitation and ionization produce further structure around $10^5\mathrm{K}$. Radiative recombination also contributes. Once the gas is highly ionized, these bound-state losses weaken. At $T\gtrsim 10^6$–$10^7\mathrm{K}$, thermal bremsstrahlung dominates, with approximately $\Lambda \propto T^{1/2}$ apart from slowly varying factors. The figure is an original qualitative sketch anchored to the two supplied values, not an atomic-rate calculation.

Increasing galactic metallicity adds many ionic transitions, producing metal-line cooling and substantially enhancing cooling, particularly in the $10^5$–$10^7\mathrm{K}$ range. Metals also provide low-energy fine-structure transitions below $10^4\mathrm{K}$. The change is not a uniform vertical shift: the positions and strengths of features depend on the elemental abundances and ionization state.

Photoionization removes bound electrons even where collisions alone would leave atoms neutral, often suppressing the hydrogen and helium line peaks and changing the metal-ion population. It also adds photoionization heating. The net thermal loss is then $\mathcal{C}-\mathcal{H}$, with possible heating-cooling equilibrium near $10^4\mathrm{K}$. A single density-independent $\Lambda (T)$ no longer describes every irradiated cloud: the answer also depends on radiation intensity, spectrum, shielding and density. The illustrative photoionized curve denotes altered cooling alone, not the net loss including heating.

Below $10^4\mathrm{K}$, primordial gas can use molecular line cooling, especially rotational and vibrational transitions of molecular hydrogen and, in suitable chemical conditions, hydrogen deuteride. Molecule formation and protection against photodissociation are essential. Enriched gas can additionally use metal-line cooling, other molecular species and dust thermal emission, with gas-dust energy exchange important at high density. At high cosmological redshift, residual free electrons can transfer energy to the cosmic microwave background through Compton cooling by the cosmic microwave background if the gas is hotter than the radiation. Expansion can also cool gas adiabatically, but neither that process nor Compton cooling by the cosmic microwave background is an $n_H^2$ atomic loss law. The atomic threshold is a cooling-channel limitation, not a universal minimum gas temperature.

Absorption of an ionizing photon leaves energy in a photoelectron above the binding energy. Thermalization supplies heat to the gas. Photoionization heating competes with the astrophysical cooling function, can establish thermal equilibrium, and can raise the pressure enough to inhibit baryon accretion into shallow dark-matter haloes.