Kramers' opacity law describes the opacity of a medium in terms of the ambient density and temperature, assuming that the opacity is dominated by bound-free absorption (the absorption of light during ionization of a bound electron) or free-free absorption (the absorption of light when scattering a free ion, also called bremsstrahlung).[1] It is often used to model radiative transfer, particularly in stellar atmospheres.[2] The relation is named after the Dutch physicist Hendrik Kramers, who first derived the form in 1923.[3]
The general functional form of the opacity law is
\bar{\kappa}\propto\rhoT-7/2,
where
\bar{\kappa}
\rho
T
The specific forms for bound-free and free-free are
Bound-free:
\bar{\kappa}bf=4.34 x 1025
| gbf | |
| t |
Z(1+X)
| \rho | \left( | |
| \rmg/cm3 |
| T | |
| \rmK |
\right)-7/2{\rmcm2g-1
\bar{\kappa}ff=3.68 x 1022gff(1-Z)(1+X)
| \rho | \left( | |
| \rmg/cm3 |
| T | |
| \rmK |
\right)-7/2{\rmcm2g-1
\bar{\kappa}es=0.2(1+X){\rmcm2g-1
Here,
gbf
gff
t
Z
X