# Kelvin–Helmholtz mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to drop, and the star or planet shrinks as a result. This compression, in turn, heats the core of the star/planet. This mechanism is evident on Jupiter and Saturn and on brown dwarfs whose central temperatures are not high enough to undergo nuclear fusion. It is estimated that Jupiter radiates more energy through this mechanism than it receives from the Sun, but Saturn might not. The latter process causes Jupiter to shrink at a rate of two centimetres each year.[1]

The mechanism was originally proposed by Kelvin and Helmholtz in the late nineteenth century to explain the source of energy of the Sun. By the mid-nineteenth century, conservation of energy had been accepted, and one consequence of this law of physics is that the Sun must have some energy source to continue to shine. Because nuclear reactions were unknown, the main candidate for the source of solar energy was gravitational contraction.

However, it soon was recognized by Sir Arthur Eddington and others that the total amount of energy available through this mechanism only allowed the Sun to shine for millions of years rather than the billions of years that the geological and biological evidence suggested for the age of the Earth. (Kelvin himself had argued that the Earth was millions, not billions, of years old.) The true source of the Sun's energy remained uncertain until the 1930s, when it was shown by Hans Bethe to be nuclear fusion.

## Power generated by a Kelvin–Helmholtz contraction[2]

It was theorised that the gravitational potential energy from the contraction of the Sun could be its source of power. To calculate the total amount of energy that would be released by the Sun in such a mechanism (assuming uniform density), it was approximated to a perfect sphere made up of concentric shells. The gravitational potential energy could then be found as the integral over all the shells from the centre to its outer radius.

Gravitational potential energy from Newtonian mechanics is defined as:

${\displaystyle U=-{\frac {Gm_{1}m_{2}}{r}},}$

where G is the gravitational constant, and the two masses in this case are that of the thin shells of width dr, and the contained mass within radius r as one integrates between zero and the radius of the total sphere. This gives:

${\displaystyle U=-G\int _{0}^{R}{\frac {m(r)4\pi r^{2}\rho }{r}}\,dr,}$

where R is the outer radius of the sphere, and m(r) is the mass contained within the radius r. Changing m(r) into a product of volume and density to satisfy the integral,

${\displaystyle U=-G\int _{0}^{R}{\frac {4\pi r^{3}\rho 4\pi r^{2}\rho }{3r}}\,dr=-{\frac {16}{15}}G\pi ^{2}\rho ^{2}R^{5}.}$

Recasting in terms of the mass of the sphere gives the total gravitational potential energy as

${\displaystyle U=-{\frac {3GM^{2}}{5R}}.}$

While uniform density is not correct, one can get a rough order of magnitude estimate of the expected age of our star by inserting known values for the mass and radius of the Sun, and then dividing by the known luminosity of the Sun (note that this will involve another approximation, as the power output of the Sun has not always been constant):

${\displaystyle {\frac {U_{\text{r}}}{L_{\odot }}}\approx {\frac {1.1\times 10^{41}~{\text{J}}}{3.9\times 10^{26}~{\text{W}}}}\approx 8\,900\,000~{\text{years}},}$

where ${\displaystyle L_{\odot }}$ is the luminosity of the Sun. While giving enough power for considerably longer than many other physical methods, such as chemical energy, this value was clearly still not long enough due to geological and biological evidence that the Earth was billions of years old. It was eventually discovered that thermonuclear energy was responsible for the power output and long lifetimes of stars.[3]

## References

1. ^ Patrick G. J. Irwin (2003). Giant Planets of Our Solar System: Atmospheres, Composition, and Structure. Springer. ISBN 3-540-00681-8.
2. ^ BW Carroll & DA Ostlie (2007). An Introduction to Modern Astrophysics (2nd Ed.). Pearson Addison Wesley. pp. 296–298. ISBN 0-8053-0402-9. Archived from the original on 2015-12-22.
3. ^ R. Pogge (2006-01-15). "The Kelvin-Helmholtz Mechanism". Lecture 12: As Long as the Sun Shines. Ohio State University. Retrieved 2009-11-05.
Blitzar

Blitzars are a hypothetical type of astronomical object in which a spinning pulsar rapidly collapses into a black hole. They are proposed as an explanation for fast radio bursts (FRBs). The idea was proposed in 2013 by Heino Falcke and Luciano Rezzolla.

Bright giant

The luminosity class II in the Yerkes spectral classification is given to bright giants. These are stars which straddle the boundary between ordinary giants and supergiants, based on the appearance of their spectra.

CN star

A CN star is a star with strong cyanogen bands in its spectrum. Cyanogen is a simple molecule of one carbon atom and one nitrogen atom, with absorption bands around 388.9 and 421.6 nm. This group of stars was first noticed by Nancy G. Roman who called them 4150 stars.

Gravitational compression

Gravitational compression is a phenomenon in which gravity, acting on the mass of an object, compresses it, reducing its size and increases the object's density.

At the center of a planet or star, gravitational compression produces heat by the Kelvin–Helmholtz mechanism. This is the mechanism that explains how Jupiter continues to radiate heat produced by its gravitational compression.The most common reference to gravitational compression is stellar evolution. The Sun and other main-sequence stars are produced by the initial gravitational collapse of a molecular cloud. Assuming the mass of the material is large enough, gravitational compression reduces the size of the core, increasing its temperature until hydrogen fusion can begin. This hydrogen-to-helium fusion reaction releases energy that balances the inward gravitational pressure and the star becomes stable for millions of years. No further gravitational compression occurs until the hydrogen is nearly used up, reducing the thermal pressure of the fusion reaction. At the end of the Sun's life, gravitational compression will turn it into a white dwarf.At the other end of the scale are massive stars. These stars burn their fuel very quickly, ending their lives as supernovae, after which further gravitational compression will produce either a neutron star or a black hole from the remnants.

For planets and moons, equilibrium is reached when the compression is balanced by a pressure gradient. This is due to gravity. This pressure gradient is in the opposite direction due to the strength of the material, at which point gravitational compression ceases.

Infrared dark cloud

An infrared dark cloud (IRDC) is a cold, dense region of a giant molecular cloud. They can be seen in silhouette against the bright diffuse mid-infrared emission from the galactic plane.

Internal heating

Internal heat is the heat source from the interior of celestial objects, such as stars, brown dwarfs, planets, moons, dwarf planets, and (in the early history of the Solar System) even asteroids such as Vesta, resulting from contraction caused by gravity (the Kelvin–Helmholtz mechanism), nuclear fusion, tidal heating, core solidification (heat of fusion released as molten core material solidifies), and radioactive decay. The amount of internal heating depends on mass; the more massive the object, the more internal heat it has; also, for a given density, the more massive the object, the greater the ratio of mass to surface area, and thus the greater the retention of internal heat. The internal heating keeps celestial objects warm and active.

Iron star

In astronomy, an iron star is a hypothetical type of compact star that could occur in the universe in the extremely far future, after perhaps 101500 years.

The premise behind iron stars states that cold fusion occurring via quantum tunnelling would cause the light nuclei in ordinary matter to fuse into iron-56 nuclei. Fission and alpha-particle emission would then make heavy nuclei decay into iron, converting stellar-mass objects to cold spheres of iron. The formation of these stars is only a possibility if protons do not decay. Though the surface of a neutron star may be iron, according to some predictions, it is distinct from an iron star.

Unrelatedly, the term is also used for blue supergiants which have a forest of forbidden FeII lines in their spectra. They are potentially quiescent hot luminous blue variables. Eta Carinae has been described as a prototypical example.

A lead star is a low-metallicity star with an overabundance of lead and bismuth as compared to other products of the S-process.

List of hottest stars

This is a list of hottest stars so far discovered (excluding degenerate stars), arranged by decreasing temperature. The stars with temperatures higher than 60,000 K are included.

OB star

OB stars are hot, massive stars of spectral types O or early-type B that form in loosely organized groups called OB associations. They are short lived, and thus do not move very far from where they formed within their life. During their lifetime, they will emit much ultraviolet radiation. This radiation rapidly ionizes the surrounding interstellar gas of the giant molecular cloud, forming an H II region or Strömgren sphere.

In lists of spectra the "spectrum of OB" refers to "unknown, but belonging to an OB association so thus of early type".

Photometric-standard star

Photometric-standard stars are a series of stars that have had their light output in various passbands of photometric system measured very carefully. Other objects can be observed using CCD cameras or photoelectric photometers connected to a telescope, and the flux, or amount of light received, can be compared to a photometric-standard star to determine the exact brightness, or stellar magnitude, of the object.A current set of photometric-standard stars for UBVRI photometry is that published by Arlo U. Landolt in 1992 in the Astronomical Journal, vol. 104, no. 1, p. 340-371.

Protostar

A protostar is a very young star that is still gathering mass from its parent molecular cloud. The protostellar phase is the earliest one in the process of stellar evolution. For a low mass star (i.e. that of the Sun or lower), it lasts about 500,000 years The phase begins when a molecular cloud fragment first collapses under the force of self-gravity and an opaque, pressure supported core forms inside the collapsing fragment. It ends when the infalling gas is depleted, leaving a pre-main-sequence star, which contracts to later become a main sequence star at the onset of Hydrogen fusion.

Q star

A Q-Star, also known as a grey hole, is a hypothetical type of a compact, heavy neutron star with an exotic state of matter. The Q stands for a conserved particle number. A Q-Star may be mistaken for a stellar black hole.

Starfield (astronomy)

A starfield refers to a set of stars visible in an arbitrarily-sized field of view, usually in the context of some region of interest within the celestial sphere. For example: the starfield surrounding the stars Betelgeuse and Rigel could be defined as encompassing some or all of the Orion constellation.

Stellar-wind bubble

A stellar-wind bubble is a cavity light years across filled with hot gas blown into the interstellar medium by the high-velocity (several thousand km/s) stellar wind from a single massive star of type O or B. Weaker stellar winds also blow bubble structures, which are also called astrospheres. The heliosphere blown by the solar wind, within which all the major planets of the Solar System are embedded, is a small example of a stellar-wind bubble.

Stellar-wind bubbles have a two-shock structure. The freely-expanding stellar wind hits an inner termination shock, where its kinetic energy is thermalized, producing 106 K, X-ray emitting plasma. The hot, high-pressure, shocked wind expands, driving a shock into the surrounding interstellar gas. If the surrounding gas is dense enough (number densities ${\displaystyle n>0.1{\mbox{ cm}}^{-3}}$ or so), the swept-up gas radiatively cools far faster than the hot interior, forming a thin, relatively dense shell around the hot, shocked wind.

Stellar atmosphere

The stellar atmosphere is the outer region of the volume of a star, lying above the stellar core, radiation zone and convection zone.

Supernova impostor

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Yellow giant

A yellow giant is a luminous giant star of low or intermediate mass (roughly 0.5–11 solar masses (M)) in a late phase of its stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature as low as 5,200-7500 K. The appearance of the yellow giant is from white to yellow, including the spectral types F and G. About 10.6 percent of all giant stars are yellow giants.

Young stellar object

Young stellar object (YSO) denotes a star in its early stage of evolution. This class consists of two groups of objects: protostars and pre-main-sequence stars.

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