Atomic and molecular cooling thresholds for galaxy formation ($T_{\mathrm{atomic}}\sim 10^4\mathrm{K},T_{\mathrm{molecular}}\sim 10^2\text{–}10^3\mathrm{K}$)

Primordial atomic line cooling becomes effective near the temperature where electronic excitations are accessible, of order ten thousand kelvin. Molecular hydrogen has lower-energy transitions and can cool colder gas if it forms and survives. The corresponding virial temperature thresholds translate into epoch-dependent halo mass thresholds. Radiation, molecular chemistry, metal-line cooling and gas density qualify a single universal minimum galaxy mass.