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 designed to be useful for models that try to do a single calculation covering all wavelengths rather than treating each wavelength individually, and given the complexity of the effect of a gas on a spectrum, to make such models tractable. It is:
1 1 ∞ Iν ——— = — ∫ —— dν <κ> I 0 κν
A model stellar atmosphere using this short cut is called a gray atmosphere.