Discovered by
Karl Schwarzschild
Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.
Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-r ...
,
[Karl Schwarzschild, Gesammelte Werke: Collected Works,]
Page 14, the Schwarzschild criterion is a criterion in
astrophysics where a stellar medium is stable
against convection when the rate of change in temperature (T) by altitude (Z) satisfies
:
where
is
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
and
is the
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity ...
at constant pressure.
If a gas is unstable against convection then if an element is displaced upwards its buoyancy will cause it to keep rising or, if it is displaced downwards, it is denser than its surroundings and will continue to sink. Therefore, the Schwarzschild criterion dictates whether an element of a star will rise or sink if displaced by random fluctuations within the star or if the forces the element experiences will return it to its original position.
For the Schwarzschild criterion to hold the displaced element must have a
bulk velocity which is highly
subsonic. If this is the case then the time over which the pressures surrounding the element changes is much longer than the time it takes for a sound wave to travel through the element and smooth out pressure differences between the element and its surroundings. If this were not the case the element would not hold together as it traveled through the star.
In order to keep rising or sinking in the star the displaced element must not be able to become the same density as the gas surrounding it. In other words, it must respond
adiabatically to its surroundings. In order for this to be true it must move fast enough for there to be insufficient time for the element to exchange heat with its surroundings.
[Karl Schwarzschild, Gesammelte Werke: Collected Works,]
Page 106,
See also
*
Archimedes' principle
Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' ...
*
Brunt–Väisälä frequency
In atmospheric dynamics, oceanography, asteroseismology and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is a measure of the stability of a fluid to vertical displacements such as those caused by convection. More precisely ...
*
Convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conve ...
References
Astrophysics
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