An Etymological Dictionary of Astronomy and Astrophysics
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To become dark or darker. → darkening.

Verb of → dark.

The act or process of becoming dark or darker. → limb darkening.

Verbal noun of of → darken.

The darkening, or brightening, of a region on a star due to localized decrease, or increase, in the → effective gravity. Gravity darkening is explained by the → von Zeipel theorem, whereby on stellar surface the → radiative flux is proportional to the effective gravity. This means that in → rotating stars regions close to the pole are brighter (and have higher temperature) than regions close to the equator. Gravity darkening occurs also in corotating → binary systems, where the → tidal force leads to both gravity darkening and gravity brightening. The effects are often seen in binary star → light curves. See also → gravity darkening exponent. Recent theoretical work (Espinosa Lara & Rieutord, 2011, A&A 533, A43) has shown that gravity darkening is not well represented by the von Zeipel theorem. This is supported by new interferometric observations of some rapidly rotating stars indicating that the von Zeipel theorem seems to overestimate the temperature difference between the poles and equator.

→ gravity; → darkening

According to the → von Zeipel theorem, the emergent flux, F, of total radiation at any point over the surface of a rotationally or tidally distorted star in → hydrostatic equilibrium varies proportionally to the local gravity acceleration: F ∝ g_eff^α, where g_eff is the → effective gravity and α is the gravity darkening coefficient. See also the → gravity darkening exponent.

→ gravity; → darkening; → coefficient.

The exponent appearing in the power law that describes the → effective temperature of a → rotating star as a function of the → effective gravity, as deduced from the → von Zeipel theorem or law. Generalizing this law, the effective temperature is usually expressed as T_eff∝ g_eff^β, where β is the gravity darkening exponent with a value of 0.25. It has, however, been shown that the relation between the effective temperature and gravity is not exactly a power law. Moreover, the value of β = 0.25 is appropriate only in the limit of slow rotators and is smaller for fast rotating stars (Espinosa Lara & Rieutord, 2011, A&A 533, A43).

→ gravity; → darkening; → exponent.

An apparent decrease in brightness of the Sun near its edge as compared to its brightness toward the center. Limb darkening is readily apparent in photographs of the Sun. The reason is that when we look toward the disk's center we look into deeper and hence hotter layers along the line of sight. Toward the limb, we get radiation from higher and hence cooler and less bright layers of the → photosphere. Limb darkening has been detected in the case of several other stars. A similar phenomenon occurs in → eclipsing binaries where the effect of limb darkening on one or both components manifests itself in the shape of the system's → light curve.

→ limb; → darkening.