astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...

, the von Zeipel theorem states that the

radiative flux Radiative flux, also known as radiative flux density or radiation flux (or sometimes power flux density), is the amount of Power (physics), power radiated through a given area, in the form of photons or other elementary particles, typically measure ...

F

in a uniformly rotating star is proportional to the local effective gravity

g_\text

. The theorem is named after Swedish astronomer

Edvard Hugo von Zeipel Edvard Hugo von Zeipel (8 February 1873 – 8 June 1959) was a Swedish astronomer, with the specialist fields of study of celestial mechanics, astrophotography, and theoretical astrophysics. He worked at the Stockholm Observatory from 1897 to 1900, ...

. The theorem is: :

F = -\frac g_\text,

where the luminosity

L

and mass

M_*

are evaluated on a surface of constant pressure

P

. The

effective temperature The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...

T_\text

can then be found at a given

colatitude In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non- ...

\theta

from the local effective gravity: :

T_\text(\theta) \sim g_\text^(\theta).

This relation ignores the effect of convection in the envelope, so it primarily applies to

early-type star In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the ...

s. According to the theory of rotating stars, if the

rotational velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an objec ...

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 disk An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other fo ...

References

{{astronomy-stub Stellar astronomy Equations of astronomy