Gravity darkening, also referred to as gravity brightening, is an

astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies ...

phenomenon A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried W ...

where the poles of a

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

are brighter than the equator, due to rapid rotation and oblate shape. When a star is oblate, it has a larger radius at its equator than it does at its poles. As a result, the poles have a higher surface gravity, and thus higher temperature and pressure is needed to maintain

hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...

. Thus, the poles are "gravity brightened", and the equator "gravity darkened". The star becomes oblate (and hence gravity darkening occurs) because the centrifugal force resulting from rotation creates additional outward pressure on the star. The

centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...

is expressed mathematically as :

F_\text = m \Omega^2 \rho,

where

m

is mass (in this case of a small volume element of the star),

\Omega

is the

angular 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 ...

, and

\rho

is the radial distance from the axis of rotation. In the case of a star, the value of

\rho

is largest at the equator and smallest at the poles. This means that equatorial regions of a star have a greater centrifugal force than the pole. The centrifugal force pushes mass away from the axis of rotation, resulting in less overall pressure on the gas in the equatorial regions of the star. This causes the gas in this region to become less dense, and cooler.

Von Zeipel's theorem In astrophysics, the von Zeipel theorem states that the radiative flux 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. The theorem is: : ...

states that the radiation from a star is proportional to the local effective gravity, that is to the gravity reduced by any centrifugal force at that location on the star's surface. Then 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 ...

is proportional to the fourth root of the effective gravity.

References

{{DEFAULTSORT:Gravity Darkening Stellar phenomena