Gravity darkening is the variation of surface brightness and effective temperature with effective gravity over a rotating or tidally distorted star. Lower equatorial gravity generally corresponds to cooler equatorial regions. The radiative gravity-darkening law applies to the idealized uniformly rotating, radiatively transporting, composition-uniform case; its exponent is not universal for every stellar envelope.
In uniformly rotating stellar hydrostatic equilibrium, composition-uniform thermodynamic quantities are functions of the total potential. Radiative conductivity gives , with . On one surface, is constant, so the outward flux is . The Stefan–Boltzmann law therefore gives . This is a surface-flux law: the material temperature constant on an interior equipotential is not the latitude-dependent emergent effective temperature.
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Gravity darkening is a phenomenon in astrophysics that describes how the brightness of a star varies across its surface due to the effects of gravity. This effect is most pronounced in rotating stars, where the centrifugal force caused by rotation causes the star to become oblate, meaning it is flattened at the poles and bulging at the equator. In such stars, the gravitational field strength is not uniform across the surface; it is stronger at the poles and weaker at the equator.