Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 55 / 1 / ii / ii

In the intermediate-temperature interval, atomic line cooling is generally efficient. Collisional excitation of hydrogen and helium followed by photon emission removes thermal energy; collisional ionization and subsequent recombination also contribute. As the gas becomes more ionized, different transitions enter and leave the cooling budget.

For enriched gas, metal-line cooling is often dominant over substantial parts of this interval, because heavy ions provide many ultraviolet and optical transitions. The cooling curve consequently has pronounced peaks rather than one smooth universal power law. Hydrogen/helium atomic processes and metal lines provide the main cooling channels here. Their relative strengths depend on metallicity, ionization state, density and the incident radiation field; these temperature bands describe typical gas, not composition-independent boundaries.

In sufficiently hot ionized gas, electrons radiate when accelerated in ion Coulomb fields: thermal bremsstrahlung is the main continuum cooling process. In the optically thin nonrelativistic limit its emission rate scales approximately asFor hot metal-poor gas this is the principal high-temperature channel. Metal ions still give important metal-line cooling near $10^6\mathrm{K}$, and in enriched gas can remain important up to several million kelvin; one should not infer that crossing $10^6\mathrm{K}$ instantly eliminates all lines. At sufficiently high temperatures most ions are stripped and free-free emission dominates. Inverse Compton cooling can also matter for ionized, diffuse gas in a strong radiation field, especially the high-redshift Cosmic microwave background. The high-temperature asymptote is bremsstrahlung cooling, with metal-line and Compton qualifications where appropriate.