Schwarzschild Criterion
Encyclopedia
Discovered by Karl Schwarzschild
, the Schwarzschild Criterion is a criterion in astrophysics
where a stellar medium is stable against convection
where
Where
is gravity and 
is the 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
Karl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished...
, the Schwarzschild Criterion is a criterion in astrophysics
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...
where a stellar medium is stable against convection
Lapse rate
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...
where
Where
is gravity and is the heat capacityHeat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
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
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
. 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.