 Solution

Below about $10^4\mathrm{K}$, neutral hydrogen electronic excitation becomes inefficient because the lowest relevant excitation energies greatly exceed the typical particle thermal energy. Primordial gas therefore needs molecular hydrogen cooling through rotational and vibrational transitions; HD can cool still colder gas where it is sufficiently abundant. Without molecules or metals, cooling can stall near the atomic threshold.

In enriched gas, metal-line cooling from low-energy fine-structure transitions, notably singly ionized carbon and neutral oxygen, remains effective below that threshold. At higher densities, molecular rotational lines such as CO and energy transfer from gas to dust followed by dust infrared emission are important. Cold-gas cooling is primarily molecular, fine-structure, or dust-mediated, according to composition and density. Molecule formation, dissociating radiation and the Cosmic microwave background temperature floor constrain how far cooling proceeds.