Photoionization-recombination thermal balance

When the number of photoionizations equals the number of recombinations, and only those processes exchange thermal energy, equilibrium requires $⟨h\nu -h{\nu }_0{⟩}_{\mathrm{abs}}=⟨E_{\mathrm{rec}}(T)⟩$. Photon absorption and electron capture have their own spectral weights. The density cancels from this event balance, but the actual equilibrium temperature requires the two energy averages.^[ref]