Opacity ($\kappa$)

Opacity is an extinction cross-section per unit mass. It controls the photon mean free path and therefore the radiative temperature gradient in an optically thick star.

The Kramers opacity law has $\kappa ={\kappa }_0\rho T^{-7/2}$ for bound-free and free-free absorption under its idealized ionized-gas assumptions.

Electron-scattering opacity is approximately independent of density and temperature in a fully ionized nonrelativistic plasma of fixed composition. For hydrogen mass fraction $X$, ${\kappa }_{\mathrm{es}}\simeq 0.2(1+X)\mathrm{c}{\mathrm{m}}^2{\mathrm{g}}^{-1}$.

Free-free opacity is absorption caused when a photon is absorbed during a Coulomb encounter between an electron and an ion. In the Kramers approximation its Rosseland mean scales approximately as ${\kappa }_{\mathrm{ff}}\propto \rho T^{-7/2}$.