# Von Zeipel theorem

In astrophysics, the von Zeipel theorem states that the radiative flux $F$ in a uniformly rotating star is proportional to the local effective gravity $g_\textrm{eff}$. Specifically,

$F=-\frac{L(P)}{4\pi G M_{*}(P)}g_\textrm{eff}$

where the luminosity $L$ and mass $M_{*}$ are evaluated on a surface of constant pressure $P$. The effective temperature $T_\textrm{eff}$ can then be found at a given colatitude $\theta$ from the local effective gravity

$T_{\textrm{eff}}(\theta)\sim g_{\textrm{eff}}^{1/4}(\theta)$.[1][2]

The theorem is named after Swedish astronomer Edvard Hugo von Zeipel.

## References

1. ^ von Zeipel, Edvard Hugo (1924). "The radiative equilibrium of a rotating system of gaseous masses". Monthly Notices of the Royal Astronomical Society 84: 665–719. Bibcode:1924MNRAS..84..665V.
2. ^ Maeder, André (1999). "Stellar evolution with rotation IV: von Zeipel's theorem and anistropic losses of mass and angular momentum". Astronomy and Astrophysics 347: 185–193. Bibcode:1999A&A...347..185M.