Von Zeipel theorem

In astrophysics, the von Zeipel theorem states that the radiative flux formula_1 in a uniformly rotating star is proportional to the local effective gravity formula_2. Specifically,
where the luminosity formula_4 and mass formula_5 are evaluated on a surface of constant pressure formula_6. The effective temperature formula_7 can then be found at a given colatitude formula_8 from the local effective gravity:
This relation ignores the effect of convection in the envelope, so it primarily applies to early-type stars. The theorem is named after Swedish astronomer Edvard Hugo von Zeipel.
According to the theory of rotating stars, if the rotational velocity of a star depends only on the radius, it cannot simultaneously be in thermal and hydrostatic equilibrium. This is called the von Zeipel paradox. The paradox is resolved, however, if the rotational velocity also depends on height, or there is a meridional circulation. A similar situation may arise in accretion disks.