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.

Fr.: coefficient de l'assombrissement gravitationnel

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.

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).