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Kramers opacity law

(opacity's relation to density and temperature)

Kramers opacity law relates a material's opacity to its density and temperature. It applies to high temperatures, e.g., in stars, and applies to bound-free (photoionization) and free-free (bremsstrahlung) absorption of visible light and other electromagnetic radiation. It states, that for a material:

Opacity ∝ ρ T-3.5

Since opacity is already defined as the value relating density to the rate of reduction of intensity, within the regime of Kramers opacity law, the actual reduction, and values such as the optical depth depend upon the density squared.

Equations have been developed to provide the constant of proportionality for each of the three above types of absorption, which may be summed. Among the elements of these equations are mass fractions, the density, and a Gaunt factor, a wavelength-dependent estimate of some quantum-mechanical contributions to the opacity. Gaunt factors are incorporated in tractable models of both bound-free and free-free opacity. An additional factor, a guillotine factor is also used in modeling bound-free opacity, to account for the difference in opacity between ionized and neutral atoms: in certain temperature ranges, the degree of ionization (and thus the guillotine factor) vary a lot by temperature and the name Guillotine suggests the relatively sharp cutoff.

Kramers law is a different law, also used in astrophysics, that describes the spectrum of bremsstrahlung X-ray radiation.

(Pedantic note: the English-language possessive form of the last name Kramers is Kramers's or Kramers', but not Kramer's, which is often used for his laws. For the present, I use Kramers, in the same sense as Heisenberg uncertainty principle or Einstein tensor.)

Further reading:'_opacity_law