If we take a look at a very small wavelength interval of the spectrum of a star - a single spectral line - limb darkening is quite different again. For this example I chose the Hα line, a spectral line of the hydrogen atom and a prominent line in many stellar spectra. In the lower panel of the figure you can see how the line, which is in absorption here, looks like. Its rest wavelength (in vacuum) is at 656.46 nm, which corresponds to a red color in the visible wavelength range. This is why, if we look at the Sun through a telescope with an Hα filter, the solar disk is red.
The continuum left and right to the line is normalized to one. This way it is easy to see that the center of the line is more than 40 % less bright than the continuum. What I show here are not observations but I use theoretical models of spectra - a computational calculation of how the spectrum of a certain star should look like. I used PHOENIX spectra of a Sun-like star, which are pretty close to what we observe in nature. Actually, I think it is really amazing that people can calculate a star in a computer.
What I'd like to show in this diagram is that if you go in small wavelengths steps from one side of the line to the other, the limb darkening changes a lot. The color code now is from the left side of the line (blue) to the right side of the line (red); each point of the line corresponds to the line with the same color in the upper panel. You can see that the violet/blue and the red lines, which are coming from outside the spectral line, show the limb darkening we saw in previous posts for the visual wavelength regime (large interval). Now if you go inside the line you see that the limb darkening dramatically decreases, meaning that the brightness on the limb goes up. It goes even further up then in the case of infra-red wavelengths. At the bottom of the Hα line the limb darkening is very weak; in the Hα core the solar disk looks much more uniformly bright than we see it with the eye.
This behavior is true for many spectral lines but not for all. Depending on where the spectral line is created in the atmosphere of the star, the spectral line might even get darker to the limb. The point is: Different parts of a spectral line can have very different limb 'darkening'. And what we usually see as limb darkening is the continuum case, which is the average over a large interval of the spectrum (and over many spectral lines).
