source function

In the study of radiative transfer (RT), the source function (S) is a measure of the effect of a material on EMR passing through, specifically the rate that EMR is contributed divided by the rate at which EMR is removed. The measure applies to opaque or translucent material such as a gas or plasma, the rates are the fractions of EMR (such as visible light) added or removed per unit distance, which are termed its emission coefficient and its absorption coefficient. The resulting source function has the same units as intensity, and the intensity of a beam of light tends to change toward and approach the source function, virtually matching it if the beam passes through sufficient distance with a constant source function. It has considerable variation by wavelength, and is often specified for a specific wavelength. An equation of radiative transfer (RTE) may be written in terms of a source function:

   1   d
- ——— —— Iλ = Iλ-Sλ
  κλρ ds

• λ - wavelength.
• κ_λ - absorption coefficient at wavelength λ.
• s - position along the beam, i.e., ds is the differential of distance traversed.
• I_λ - intensity at wavelength λ.
• S_λ - source function at wavelength λ.
• ρ - density.

The Eddington-Barbier relation relates the source function to the flux leaving a star, indicating it matches the source function at a vertical optical depth of 2/3, which is a basis for defining a photosphere as beginning at that depth.