Limb Darkening of the Sun





Limb 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 image.

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 = -0.23

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)

limb darkening sun star



Limb darkening occurs as the result of two effects:
- 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.

Limb
                    darkening Sun

 

Web Links

Limb Darkening (Wikipedia)

Stellar Atmospheres: Limb Darkening

Limb Darkening


Updated: 20.10.2023