Emissivity

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The emissivity of a material (usually written <math>\epsilon</math>) is the ratio of energy radiated by the material to energy radiated by a black body at the same temperature. It is a measure of a material's ability to absorb and radiate energy. A true black body would have an <math>\epsilon=1</math> while any real object would have <math>\epsilon<1</math>.

This emissivity depends on factors such as temperature, emission angle, and wavelength. However, a typical engineering assumption is to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the grey body assumption. When dealing with non-black surfaces, the deviations from ideal black body behavior are determined by both the geometrical structure and the chemical composition, and follow Kirchhoff's law of thermal radiation: emissivity equals absorptivity (for an object in thermal equilibrium), so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.

[edit] Astrophysical Greybody

The monochromatic flux density radiated by a greybody at frequency <math>\nu</math> through solid angle <math>d\Omega</math> is given by <math>F_{\nu} = B_{\nu}(T) Q_{\nu} d\Omega </math> where <math>B_{\nu}</math> is the Plank function for a blackbody at temperature T and emissivity <math>Q_{\nu}</math>.

For a uniform medium of optical depth <math>\tau_{\nu}</math> radiative transfer means that the radiation will be reduced by a factor <math>e^{-\tau}</math> giving . The optical depth is often approximated by the ratio of the emitting frequency to the frequency where τ=1 all raised to an exponent β. For cold dust clouds in the interstellar medium β is approximately two. Therefore Q becomes,