 Local thermodynamic equilibrium

Local thermodynamic equilibrium assumes matter populations follow thermal distributions at the local temperature: excitation follows the Boltzmann distribution and ionization the Saha equation. It permits a temperature gradient; it does not require the radiation field itself to be a blackbody.

For true absorption and its inverse thermal emission, $j_{\nu }^{\mathrm{abs}}/{\alpha }_{\nu }^{\mathrm{abs}}=B_{\nu }(T)$, the Planck function. The total source function need not equal $B_{\nu }$ when scattering contributes. Distinguishing matter equilibrium from radiation equilibrium is essential near a star's escaping surface.^[ref]