Source function

The source function is a characteristic of a stellar atmosphere, and describes the ratio of the emission coefficient to the absorption coefficient. It is a measure of how photons in a light beam is removed and replaced by new photons by the material it passes through. It's units is in the cgs-system, $ergs^{-1}cm^{-3}sr^{-1}$. The source function can be written

$S_{\lambda }\equiv {\frac {j_{\lambda }}{\kappa _{\lambda }}}$

where $j_{\lambda }$ is the emission coeffisient, $\kappa _{\lambda }$ is the absorption coeffisient (also known as the opacity (optics)). Putting this into the equation for radiative transfer we get

$-{\frac {1}{\kappa _{\lambda }\rho }}{\frac {dI_{\lambda }}{ds}}=I_{\lambda }-S_{\lambda }$

where s is the distance measured along the path traveled by the beam. The minus sign on the left hand side shows that the intensity decreases as the beam travels, due to the absorption of photons.

See also

• Radiative transfer
• Opacity (optics)

References

• B.W. Carrol, D.A. Ostlie (1996). An Introduction to Modern Astrophysics. Addison-Wesley Publishing Company, Inc. ISBN 0321210301.