= Radiative gravity-darkening law
{title2=$F_n\propto g,\ T_e\propto g^{1/4}$}
= von Zeipel theorem
{c}
{synonym}
In <uniformly rotating stellar hydrostatic equilibrium>, composition-uniform thermodynamic quantities are functions of the total potential. <Radiative conductivity> gives $\mathbf F=f(\phi)\nabla\phi$, with $f=-\chi\,dT/d\phi$. On one surface, $f$ is constant, so the outward flux is $F_n=f g$. The <Stefan–Boltzmann law> therefore gives $T_e\propto g^{1/4}$. 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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