### source function

**(S)**
(measure indicating the effect of a material on EMR passing through)

A **source function** (often indicated as **S**) is a measure of the
effect of a material (e.g., gas or plasma) on electromagnetic radiation
(EMR, e.g., visible light) passing through, specifically the rate
(per distance) that EMR is contributed (emission coefficient)
divided by the ratio removed (also per distance, the
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 may be written in terms of a source function:

1 d
- ——— —— I_{λ} = I_{λ}-S_{λ}
κ_{λ}ρ ds

- λ - wavelength.
- κ
_{λ} - absorption coefficient at wavelength λ.
- s - position along the beam, i.e., ds is for distance traveled.
- 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.

(*physics,EMR,measure*)
**Further reading:**

https://en.wikipedia.org/wiki/Source_function

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