Von Zeipel theorem

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

.^[1][2]

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."

References