Technically Speaking: Stellar Opacity
and Optical Depth

Astronomers often like to use a measure of the opacity that is called the optical depth. Imagine light of some original intensity I(0) passing through an atmosphere. After some distance, the intensity will be denoted by I and will be related to the original intensity by

I = I(0) e-x

where e = 2.718 ... is the transcendental number associated with natural logarithms and exponential functions. The optical depth is defined to be the power x in this equation.

Although this may seem an abstract way to measure opacity, it often turns out that it simplifies more complex discussions. Roughly, an atmosphere is very opaque for optical depths greater than about 1 and clouds with optical depth much less than 1 are termed optically thin and those with optical depth much greater than 1 are termed optically thick.

Opacity

We are familiar with the absorption of light by an atmosphere. For example, in a fog we can see only a short distance relative to the distance we can see on a clear day. Because the efficiency of an atmosphere at absorbing light is so important, we define a quantity called the opacity to specify how "opaque" an atmosphere is. If we can see large distances the opacity is small and if we can see only a short distance the opacity is large.

A Qualitative Definition
Opacity has a technical definition related to the definition of optical depth given in the adjacent box. However, for our discussion it will be sufficient to consider opacity qualitatively as a measure of how well an atmosphere absorbs light.

Radiation Transport
Generally, understanding the properties of a star's atmosphere is a difficult problem in radiative transport, a discipline that seeks to describe how electromagnetic radiation moves through an atmosphere. This is a complex mathematical problem that requires extensive analysis and large-scale computer simulations for its solution.