Limb darkening

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Limb darkening is an optical phenomenon observed in stars, including the Sun, where the center part of the stellar disk appears brighter than the edge or limb. This effect is a result of the temperature gradient in the star's atmosphere and the angle at which light is emitted from different parts of the star.

Explanation

Limb darkening occurs because the light we see from the center of the star comes from deeper, hotter layers, while the light from the edge or limb comes from higher, cooler layers. As a result, the intensity of light decreases from the center to the edge of the stellar disk.

Mathematical Description

The intensity of light, \( I(\mu) \), observed at an angle \( \mu \) (where \( \mu = \cos \theta \) and \( \theta \) is the angle between the line of sight and the normal to the stellar surface) can be described by the following limb darkening law:

\[ I(\mu) = I(1) \left[ 1 - u \left( 1 - \mu \right) \right] \]

where \( I(1) \) is the intensity at the center of the disk and \( u \) is the limb darkening coefficient, which depends on the wavelength of the light and the properties of the star's atmosphere.

Applications

Limb darkening is an important factor in various fields of astronomy and astrophysics. It is crucial for accurate measurements of stellar diameters, the analysis of eclipsing binary stars, and the interpretation of transit light curves in the search for exoplanets.

Observations

The phenomenon of limb darkening can be observed in the Sun using solar telescopes. It is also detected in other stars through high-resolution imaging and spectroscopic techniques.

Related Concepts

• Stellar atmosphere
• Radiative transfer
• Photosphere
• Solar limb

See Also

• Star
• Sun
• Astrophysics
• Eclipsing binary
• Exoplanet