### Sobolev approximation

(tractable model used in specific kinds of spectral line analysis)

The **Sobolev approximation** is a means of approximating the solution
to the radiative transfer equation under specific challenging
conditions, i.e., in gas with a very high **velocity gradient**. In
astrophysics, it is used in the analysis of spectral lines, i.e.,
to model the environment that produces observed lines.
The Sobolev approximation assumes local variation in the
velocity gradient are negligible as compared to variations over
longer lengths. The **Sobolev length** is a calculated distance
below which gradations are presumed ignorable.

(*mathematics,model,spectrography,radiative transfer*)
**Further reading:**

http://dictionary.obspm.fr/?showAll=1&formSearchTextfield=Sobolev+approximation

https://ui.adsabs.harvard.edu/abs/1985ApJ...293..258H/abstract

http://www.ifa.hawaii.edu/users/kud/teaching_12/wind_4.pdf

https://arxiv.org/abs/2009.06322

**Referenced by page:**

line shape function

Index