Limb Darkening of the Sun
darkening describes the diminishing of intensity in the image of a star
moving from the center of the image to the edge or limb of the
The amount of the limb darkening varies strongly with wavelength. In the blue light, the decrease in brightness towards the limb is more than in the red. Therefore, the limb is dominated by the red portion of the light.
For the sun (at a mean wavelength of 550 nm), the limb darkening is well expressed (Cox, A. N.: Allen's Astrophysical Quantities, Springer, 2000) by the expression:
I/I0 = a0 + a1 cos i + a2 cos2 i (0° <= i <= 90°)
a0 = 0.3, a1 = 0.93, a2 = -0.23Limb darkening occurs as the result of two effects:
A more simple model (applet at left) is "Model 1":
I/I0 = 0.3 + 0.7 cos i (0° <= i <= 90°)
or "Model 2" (applet at left):
I/I0 = 0.4 + 0.6 sqrt[1-(r/R)2] (0 <= r <= R)
- The density of the star diminishes as the distance from the center increases.
- The temperature of the star diminishes as the distance from the center increases.
The length of the blue arrow represents the thickness of absorbing gas from which a certain fraction of photons can escape.
High-temperature photons emitted at A will just barely escape from the star, as will the low temperature photons emitted at B.