The hydrostatic equilibrium equation

What information can we use to determine the interior structure of the stars? All we see is a faint dot of light from which we have to deduce everything. We saw in Volume 2 that the light we receive from main sequence stars comes from a surface layer which has a thickness of the order of 100 to 1000 km, while the radii of main sequence stars are of the order of 105 to 107 km. Any light emitted in the interior of the stars is absorbed and re-emitted in the star, very often before it gets close enough to the surface to escape without being absorbed again. For the sun it actually takes a photon 107 years to get from the interior to the surface, even though for a radius of 700 000 km a photon would need only 2.5 seconds to get out in a straight line. There is only one kind of radiation that can pass straight through the stars – these are the neutrinos whose absorption cross-sections are so small that the chances of being absorbed on the way out are essentially zero. Of course, the same property makes it very difficult to observe them because they hardly interact with any material on Earth either. We shall return to this problem later. Except for neutrinos we have no radiation telling us directly about the stellar interior. We have, however, a few basic observations which can inform us indirectly about stellar structure.

For most stars, we observe that neither their brightness nor their color changes measurably in centuries. This basic observation tells us essentially everything about the stellar interior.