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) ∝ geff (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 (Teff (θ) ∝ geff (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.
See also: Named for Edvard Hugo von Zeipel, Swedish astronomer (1873-1959), who published
his work in 1924 (MNRAS 84, 665); → theorem.
