Detailed calculations are presented for the radiative cooling of a hot (10^4 K ≤ T ≤ 10^6 K) interstellar gas. Below 10^6 K such a gas is not in ionization equilibrium because it is cooling faster than it is recombining. The gas is more ionized at a particular temperature and emits harder radiation than a gas in equilibrium at the same temperature. Optical forbidden lines, particularly the [0 II], [0 III] lines, are much stronger than the hydrogen Balmer lines. Hydrogen lines, if observable, would show a Balmer decrement not very different from that of a radiatively excited nebula. Results are presented in three cases: the first two have initial conditions determined when a 40- or 100-eV photon burst suddenly ionizes the gas, corresponding to a "fossil Stromgren sphere" suddenly formed by an ultraviolet or soft X-ray supernova burst. In the third case the gas is cooling from steady-state ionic abundances at 10^6 K (e.g., a supernova shell that has reached the late radiative-cooling stage).
Kafatos, M. (1973) Time-Dependent Radiative Cooling of a Hot Low-Density Cosmic Gas, Astrophysical Journal, 182:433-447. doi: 10.1086/152151