Optical depth in astrophysics refers to a specific level of transparency.
respectively, can vary widely depending on the absorptivity of the astrophysical environment.
is able to show the relationship between these two quantities and can lead to a greater understanding of the structure inside a star.
Optical depth is a measure of the extinction coefficient or absorptivity up to a specific 'depth' of a star's makeup.
These can generally be calculated from other equations if a fair amount of information is known about the chemical makeup of the star.
From the definition, it is also clear that large optical depths correspond to higher rate of obscuration.
Optical depth can therefore be thought of as the opacity of a medium.
In most astrophysical problems, this is exceptionally difficult to solve since solving the corresponding equations requires the incident radiation as well as the radiation leaving the star.
is the wavelength of the incident light before being absorbed or scattered.
[2] The Beer–Lambert law is only appropriate when the absorption occurs at a specific wavelength,
For a gray atmosphere, for instance, it is most appropriate to use the Eddington Approximation.
is simply a constant that depends on the physical distance from the outside of a star.
Since it is difficult to define where the interior of a star ends and the photosphere begins, astrophysicists usually rely on the Eddington Approximation to derive the formal definition of
Devised by Sir Arthur Eddington the approximation takes into account the fact that H− produces a "gray" absorption in the atmosphere of a star, that is, it is independent of any specific wavelength and absorbs along the entire electromagnetic spectrum.
is the effective temperature at that depth and
This illustrates not only that the observable temperature and actual temperature at a certain physical depth of a star vary, but that the optical depth plays a crucial role in understanding the stellar structure.
It also serves to demonstrate that the depth of the photosphere of a star is highly dependent upon the absorptivity of its environment.
is about 2/3, which corresponds to a state where a photon would experience, in general, less than 1 scattering before leaving the star.
The above equation can be rewritten in terms of