Von Zeipel theorem
Encyclopedia
The von Zeipel theorem in astrophysics
states that the radiative flux
,
, in a uniformly rotating star is proportional to the local effective gravity, 
. Specifically,
.
From this we can find the effective temperature
,
, at a given colatitude
,
, from the local effective gravity
.
The von Zeipel law, named for its creator, Swedish astronomer Edvard Hugo von Zeipel, has been used for the better part of a century to predict the difference in surface gravity, brightness and temperature between a rapidly rotating star's poles and its equator. In 2011, using a technique called interferometry University of Michigan
researchers essentially zoomed in to take close-up pictures and measurements of the winter star Regulus. It's the brightest star in the constellation Leonis and if it were spinning just a few percent faster, it would fly apart. The astronomers found that the actual difference in temperature between its equator and poles is much less than the old theory predicts. "Our model fitting of interferometry data shows that while the law correctly describes the trend of surface temperature variation, it deviates quantitively," said Xiao Che, a doctoral student in the Department of Astronomy who is first author of a paper on the findings to be published in Astrophysical Journal on April 20. "It is surprising to me that von Zeipel's law has been adopted in astronomy for such a long time with so little solid observational evidence." It's important to get this number right, says John Monnier, an associate professor in the U-M Department of Astronomy. "In some cases, we found a 5,000-degree Fahrenheit difference between what the theory predicts and what our actual measurements show," Monnier said. "That has a big effect on total luminosity. If we don't take this into account, we get the star's mass and age and total energy output wrong."
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
states that the radiative flux
Radiative flux
Radiative flux, or radiative flux density, is the amount of power radiated through a given area, in the form of photons or other elementary particles, typically measured in W/m2. It is used in astronomy to determine the magnitude and spectral class of a star...
,
, in a uniformly rotating star is proportional to the local effective gravity, . Specifically,.From this we can find the effective temperature
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...
,
, at a given colatitudeColatitude
In spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude.-Astronomical use:The colatitude is useful in astronomy because it refers to the zenith distance of the celestial poles...
,
, from the local effective gravity.The von Zeipel law, named for its creator, Swedish astronomer Edvard Hugo von Zeipel, has been used for the better part of a century to predict the difference in surface gravity, brightness and temperature between a rapidly rotating star's poles and its equator. In 2011, using a technique called interferometry University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
researchers essentially zoomed in to take close-up pictures and measurements of the winter star Regulus. It's the brightest star in the constellation Leonis and if it were spinning just a few percent faster, it would fly apart. The astronomers found that the actual difference in temperature between its equator and poles is much less than the old theory predicts. "Our model fitting of interferometry data shows that while the law correctly describes the trend of surface temperature variation, it deviates quantitively," said Xiao Che, a doctoral student in the Department of Astronomy who is first author of a paper on the findings to be published in Astrophysical Journal on April 20. "It is surprising to me that von Zeipel's law has been adopted in astronomy for such a long time with so little solid observational evidence." It's important to get this number right, says John Monnier, an associate professor in the U-M Department of Astronomy. "In some cases, we found a 5,000-degree Fahrenheit difference between what the theory predicts and what our actual measurements show," Monnier said. "That has a big effect on total luminosity. If we don't take this into account, we get the star's mass and age and total energy output wrong."