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Rosseland mean opacity

(Rosseland mean)
(a useful weighted average of opacities at all the wavelengths)

The Rosseland mean opacity (or simply Rosseland mean) is a weighted average (across frequency) of the opacity of a material, e.g., gas or plasma through which electromagnetic radiation is passing. It is a simplification allowing models to carry out a single calculation covering all wavelengths rather than varying the calculation by wavelength. Given the complexity of the effect of a gas on a spectrum, it makes such models far more tractable. It is:

 1    1  ∞ Iν
——— = — ∫   —— dν
<κ>   I 0   κν


The calculation averages (with weighting) the mean free path of photons, i.e., the reciprocal of opacity, taking the reciprocal of the result as the Rosseland mean. The Rosseland mean depends upon the function of intensity over frequency, and for a substance at thermodynamic equilibrium (or local thermodynamic equilibrium), the intensity of black-body radiation of the temperature is often used, i.e., the Planck function. A model stellar atmosphere using this short cut is called a gray atmosphere.

Further reading:

Referenced by pages:
gray atmosphere
mean molecular weight (μ)
opacity (κ)
optical depth (τ)
equation of radiative transfer (RTE)