The current limb darkening implementation seems to work by placing the sprite in front of the star, which increases the brightness in the center:

Compared to photographs, it is noticeably unnatural. Two solutions have been proposed on the Discord:

1. Use the empirical formula as in section 2.4 of this article.
2. Or, more correctly, make the effect dependent on the angle.

CubicApocalypse about the second way:

I'd think angle-based would be relatively easy, using the same view angle/Fresnel effect that basically every game ever uses for pretty much anything
the old HazeColor effect worked the same way, more or less

TTarrants:

Fortunately the limb-darkening laws' coefficients are basically temperature (and metallicity) dependant, so it would be feasible to add them in a nice, "realistic" way in Celestia. M dwarfs having more pronounced limb-darkening than early-type stars, etc.