Limb darkening

Given a cloud of gaseous stuff, we can describe absorption and emission of radiation in terms of a quantity called the mean free path. The mean free path is the distance a single photon in the cloud can expect to travel before it is absorbed. It turns out that when we look at something like the sun, what we actually see is a distance of one mean free path below the 'surface' (note that the surface isn't actually very well defined - the sun has less and less dense material further away from its center, all the way out to the orbit of Jupiter or so).

The interesting thing about this is that because of the spherical nature of the sun, in which the temperature decreases as radius increases, one mean free path below the surface in the center of the sun's disk is a lot brighter than one mean free path below the surface at the edge, since the edge is cooler. And since the color of radiation is related to the temperature of the radiating surface, the edges of the sun appear darker and redder than the center. This is true of other stars, too, and the phenomenon is called limb darkening, as the edge of the star is called its limb.