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The term limb darkening refers to reduced light seen at the outer edge of the image of some observed astronomical bodies, a phenomenon evident in images of the Sun. Such an outer edge is referred to as the body's limb. Such a brightness-reduction at the edges of an observed glowing body can be (and is presumed to be) caused by an outer layer that is not entirely opaque, which for stars and the Sun, is termed its atmosphere. Analysis of the amounts of reduction across the face of the observed body yield clues to its atmosphere's thickness, makeup, and layering.
The phenomenon is due to the body's somewhat-indistinct outer surface: some of the light that we see is from below the surface, passing through layers that filtering out some of the light from below. At middle of the body's image, light from 1 km within the body has been filtered some amount on its way out, but near the edge of the image, light from 1 km within travels through and angle through the outer km and a greater percentage of the light is blocked. Similarly, we find the Sun not as bright near sunrise or sunset when the sunlight passes through Earth atmosphere at an angle, and viewing Earth from the Moon, city lights will show more when that part of Earth is directly facing the Moon than when they are near the horizon.
Limb darkening of other stars can be deduced through the light curves of transiting planets: the star's brightness is reduced a bit less when the blocked light is from the limb.