An Etymological Dictionary of Astronomy and Astrophysics
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A → rotating star cannot simultaneously achieve → hydrostatic equilibrium and → rigid body rotation. The paradox can be solved if → baroclinic flows (essentially a → differential rotation and a → meridional circulation) are included. For a broader view of the subject see: M. Rieutord, 2006, in Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars, ed. M. Rieutord & B. Dubrulle, EAS Publ., 21, 275, arXiv:astro-ph/0608431.

→ von Zeipel theorem; → paradox.

A theorem that establishes a relation between the → radiative flux at some → colatitude on the surface of a → rotating star and the local → effective gravity (which is a function of the → angular velocity and colatitude). For a rotating star in which → centrifugal forces are not negligible, the → equipotentials where gravity, centrifugal force, and pressure are balanced will no longer be spheres. The theorem states that the radiative flux is proportional to the local effective gravity at the considered colatitude, F(θ) ∝ g_eff (θ)^α, where α is the → gravity darkening coefficient. As a consequence, the stellar surface will not be uniformly bright, because there is a much larger flux and a higher → effective temperature at the pole than at the equator (T_eff (θ) ∝ g_eff (θ)^β, where β is the → gravity darkening exponent. In → massive stars this latitudinal dependence of the temperature leads to asymmetric → mass loss and also to enhanced average → mass loss rates. Also called → gravity darkening. See also → von Zeipel paradox; → meridional circulation; → baroclinic instability; → Eddington-Sweet time scale.

Named for Edvard Hugo von Zeipel, Swedish astronomer (1873-1959), who published his work in 1924 (MNRAS 84, 665); → theorem.

Same as the → von Zeipel theorem.

→ von Zeipel theorem; → law.