White dwarf

White dwarf

Overview

A white dwarf, also called a degenerate dwarf, is a small star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

 composed mostly of electron-degenerate matter. They are very dense
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

; a white dwarf's mass is comparable to that of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and its volume is comparable to that of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

. Its faint luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

 comes from the emission
Thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation....

 of stored thermal energy
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

. In January 2009, the Research Consortium on Nearby Stars
Research Consortium on Nearby Stars
The Research Consortium on Nearby Stars is an international group of astronomers founded in 1994 to investigate the stars nearest to the Solar System - those within 10 parsecs...

 project counted eight white dwarfs among the hundred star systems nearest the Sun.
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Encyclopedia

A white dwarf, also called a degenerate dwarf, is a small star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

 composed mostly of electron-degenerate matter. They are very dense
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

; a white dwarf's mass is comparable to that of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and its volume is comparable to that of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

. Its faint luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

 comes from the emission
Thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation....

 of stored thermal energy
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

. In January 2009, the Research Consortium on Nearby Stars
Research Consortium on Nearby Stars
The Research Consortium on Nearby Stars is an international group of astronomers founded in 1994 to investigate the stars nearest to the Solar System - those within 10 parsecs...

 project counted eight white dwarfs among the hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910 by Henry Norris Russell
Henry Norris Russell
Henry Norris Russell was an American astronomer who, along with Ejnar Hertzsprung, developed the Hertzsprung–Russell diagram . In 1923, working with Frederick Saunders, he developed Russell–Saunders coupling which is also known as LS coupling.-Biography:Russell was born in 1877 in Oyster Bay, New...

, Edward Charles Pickering
Edward Charles Pickering
Edward Charles Pickering was an American astronomer and physicist, brother of William Henry Pickering.Along with Carl Vogel, Pickering discovered the first spectroscopic binary stars. He wrote Elements of Physical Manipulations .Pickering attended Boston Latin School, and received his B.S. from...

, and Williamina Fleming
Williamina Fleming
-External links:* * * * from the Astronomical Society of the Pacific- Obituaries :*...

;, p. 1 the name white dwarf was coined by Willem Luyten in 1922.

White dwarfs are thought to be the final evolutionary state
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...

 of all stars whose mass is not high enough to become a neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

—over 97% of the stars in our galaxy
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

., §1. After the hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

fusing
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

 lifetime of a main-sequence star of low or medium mass ends, it will expand to a red giant
Red giant
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower...

 which fuses helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 to carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 and oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 in its core by the triple-alpha process
Triple-alpha process
The triple alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei are transformed into carbon.Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores...

. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

, around 1 billion K, an inert mass of carbon and oxygen will build up at its center. After shedding its outer layers to form a planetary nebula
Planetary nebula
A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...

, it will leave behind this core, which forms the remnant white dwarf. Usually, therefore, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is above 8 solar masses but below 10.5 solar masses,the core temperature suffices to fuse carbon but not neon
Neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...

, in which case an oxygen-neon–magnesium
Magnesium
Magnesium is a chemical element with the symbol Mg, atomic number 12, and common oxidation number +2. It is an alkaline earth metal and the eighth most abundant element in the Earth's crust and ninth in the known universe as a whole...

 white dwarf may be formed. Also, some helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 white dwarfs appear to have been formed by mass loss in binary systems.

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported by the heat generated by fusion against gravitational collapse
Gravitational collapse
Gravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...

. It is supported only by electron degeneracy pressure
Electron degeneracy pressure
Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time. The resulting emergent repulsive force is...

, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...

—approximately 1.4 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

es—beyond which it cannot be supported by electron degeneracy pressure. A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

 via a process known as carbon detonation
Carbon detonation
Carbon detonation is the violent re-ignition of thermonuclear fusion in a dead star, which produces a Type Ia supernova. A white dwarf undergoes carbon detonation only if it has a normal binary companion which is close enough to the dwarf star to dump sufficient amounts of matter onto the dwarf,...

. (SN 1006
SN 1006
SN 1006 was a supernova, widely seen on Earth beginning in the year 1006 AD; Earth was about 7,200 light-years away from the supernova. It was the brightest apparent magnitude stellar event in recorded history reaching an estimated -7.5 visual magnitude...

 is thought to be a famous example.)

A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature
Color temperature
Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, and other fields. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of...

, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf
Black dwarf
A black dwarf is a hypothetical stellar remnant, created when a white dwarf becomes sufficiently cool to no longer emit significant heat or light...

. However, since no white dwarf can be older than the age of the Universe
Age of the universe
The age of the universe is the time elapsed since the Big Bang posited by the most widely accepted scientific model of cosmology. The best current estimate of the age of the universe is 13.75 ± 0.13 billion years within the Lambda-CDM concordance model...

 (approximately 13.7 billion years), even the oldest white dwarfs still radiate at temperatures of a few thousand kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

s, and no black dwarfs are thought to exist yet.

Discovery


The first white dwarf discovered was in the triple star system of 40 Eridani
40 Eridani
40 Eridani is a triple star system less than 16.5 light years away from Earth. It is in the constellation Eridanus. The primary star of the system, 40 Eridani A, is easily visible to the naked eye...

, which contains the relatively bright main sequence
Main sequence
The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

 star 40 Eridani A, orbited at a distance by the closer binary system
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

 of the white dwarf 40 Eridani B and the main sequence
Main sequence
The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

 red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

 40 Eridani C. The pair 40 Eridani B/C was discovered by Friedrich Wilhelm Herschel on January 31, 1783;, p. 73 it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve
Otto Wilhelm von Struve
Otto Wilhelm von Struve was a Russian astronomer. In Russian, his name is normally given as Otto Vasil'evich Struve...

 in 1851. In 1910, Henry Norris Russell
Henry Norris Russell
Henry Norris Russell was an American astronomer who, along with Ejnar Hertzsprung, developed the Hertzsprung–Russell diagram . In 1923, working with Frederick Saunders, he developed Russell–Saunders coupling which is also known as LS coupling.-Biography:Russell was born in 1877 in Oyster Bay, New...

, Edward Charles Pickering
Edward Charles Pickering
Edward Charles Pickering was an American astronomer and physicist, brother of William Henry Pickering.Along with Carl Vogel, Pickering discovered the first spectroscopic binary stars. He wrote Elements of Physical Manipulations .Pickering attended Boston Latin School, and received his B.S. from...

 and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type
Stellar classification
In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...

 A, or white. In 1939, Russell looked back on the discovery:, p. 1

I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars—including comparison stars—which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, and I discussed. This piece of apparently routine work proved very fruitful—it led to the discovery that all the stars of very faint absolute magnitude were of spectral class M. In conversation on this subject (as I recall it), I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B. Characteristically, he sent a note to the Observatory office and before long the answer came (I think from Mrs Fleming) that the spectrum of this star was A. I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: "It is just these exceptions that lead to an advance in our knowledge", and so the white dwarfs entered the realm of study!


The spectral type of 40 Eridani B was officially described in 1914 by Walter Adams
Walter Sydney Adams
Walter Sydney Adams was an American astronomer.-Life and work:He was born in Antioch, Syria to missionary parents, and was brought to the U.S. in 1885 He graduated from Dartmouth College in 1898, then continued his education in Germany...

.

The companion of Sirius
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...

, Sirius B
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...

, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius (α Canis Majoris) and Procyon
Procyon
Procyon is the brightest star in the constellation Canis Minor. To the naked eye, it appears to be a single star, the seventh brightest in the night sky with a visual apparent magnitude of 0.34...

 (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:

If we were to regard Sirius and Procyon as double stars, the change of their motions would not surprise us; we should acknowledge them as necessary, and have only to investigate their amount by observation. But light is no real property of mass. The existence of numberless visible stars can prove nothing against the existence of numberless invisible ones.


Bessel roughly estimated the period of the companion of Sirius to be about half a century; C. A. F. Peters
Christian August Friedrich Peters
Christian August Friedrich Peters was a German astronomer. He was the father of astronomer Carl Friedrich Wilhelm Peters.He was born in Hamburg and died in Kiel....

 computed an orbit for it in 1851. It was not until January 31, 1862 that Alvan Graham Clark
Alvan Graham Clark
Alvan Graham Clark , born in Fall River, Massachusetts, was an American astronomer and telescope-maker. He was the son of Alvan Clark, founder of Alvan Clark & Sons....

 observed a previously unseen star close to Sirius, later identified as the predicted companion. Walter Adams
Walter Sydney Adams
Walter Sydney Adams was an American astronomer.-Life and work:He was born in Antioch, Syria to missionary parents, and was brought to the U.S. in 1885 He graduated from Dartmouth College in 1898, then continued his education in Germany...

 announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.

In 1917, Adriaan Van Maanen
Adriaan Van Maanen
Adriaan van Maanen was a Dutch–American astronomer.Van Maanen, born into a well-to-do family in Friesland, studied astronomy at the University of Utrecht and worked briefly at the University of Groningen...

 discovered Van Maanen's Star
Van Maanen's star
Van Maanen's star is a white dwarf star. Out of the white dwarfs known, it is the third closest to the Sun, after Sirius B and Procyon B, in that order, and the closest known solitary white dwarf...

, an isolated white dwarf. These three white dwarfs, the first discovered, are the so-called classical white dwarfs., p. 2 Eventually, many faint white stars were found which had high proper motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...

, indicating that they could be suspected to be low-luminosity stars close to the Earth, and hence white dwarfs. Willem Luyten appears to have been the first to use the term white dwarf when he examined this class of stars in 1922; the term was later popularized by Arthur Stanley Eddington
Arthur Stanley Eddington
Sir Arthur Stanley Eddington, OM, FRS was a British astrophysicist of the early 20th century. He was also a philosopher of science and a popularizer of science...

. Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939., p. 3 Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known, and by 1999, over 2,000 were known. Since then the Sloan Digital Sky Survey
Sloan Digital Sky Survey
The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after the Alfred P...

 has found over 9,000 white dwarfs, mostly new.

Composition and structure



Although white dwarfs are known with estimated masses as low as 0.17 and as high as 1.33 solar masses, the mass distribution is strongly peaked at 0.6 solar mass, and the majority lie between 0.5 to 0.7 solar mass. The estimated radii of observed white dwarfs, however, are typically between 0.008 and 0.02 times the radius of the Sun; this is comparable to the Earth's radius of approximately 0.009 solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically a million times smaller than the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, 1,000,000 times greater than the average density of the Sun, or approximately 106 gram
Gram
The gram is a metric system unit of mass....

s (1 tonne
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

) per cubic centimeter. White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact star
Compact star
In astronomy, the term compact star is used to refer collectively to white dwarfs, neutron stars, other exotic dense stars, and black holes. These objects are all small for their mass...

s such as neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s, black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s and, hypothetically, quark star
Quark star
A quark star or strange star is a hypothetical type of exotic star composed of quark matter, or strange matter. These are ultra-dense phases of degenerate matter theorized to form inside particularly massive neutron stars....

s.
Material Density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 in kg/m3
Notes
Water (fresh) 1,000 At STP
Standard conditions for temperature and pressure
Standard condition for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data...

Osmium
Osmium
Osmium is a chemical element with the symbol Os and atomic number 76. Osmium is a hard, brittle, blue-gray or blue-blacktransition metal in the platinum family, and is the densest natural element. Osmium is twice as dense as lead. The density of osmium is , slightly greater than that of iridium,...

 
22,610 Near room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...

The core of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 
~150,000
White dwarf star
Atomic nuclei  Does not depend strongly on size of nucleus
Neutron star core
Black hole Critical density of an Earth-mass black hole


White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

 system, as is the case for Sirius B and 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius B by 1910, yielding a mass estimate of 0.94 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

. (A more modern estimate is 1.00 solar mass.) Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its effective surface temperature
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...

, and hence from its spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

. If the star's distance is known, its overall luminosity can also be estimated. Comparison of the two figures yields the star's radius. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that Sirius B and 40 Eridani B must be very dense. For example, when Ernst Öpik
Ernst Öpik
Ernst Julius Öpik was a noted Estonian astronomer and astrophysicist who spent the second half of his career at the Armagh Observatory in Northern Ireland.-Education:...

 estimated the density of a number of visual binary stars in 1916, he found that 40 Eridani B had a density of over 25,000 times the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

's, which was so high that he called it "impossible". As Arthur Stanley Eddington
Arthur Stanley Eddington
Sir Arthur Stanley Eddington, OM, FRS was a British astrophysicist of the early 20th century. He was also a philosopher of science and a popularizer of science...

 put it later in 1927:, p. 50
We learn about the stars by receiving and interpreting the messages which their light brings to us. The message of the Companion of Sirius when it was decoded ran: "I am composed of material 3,000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox." What reply can one make to such a message? The reply which most of us made in 1914 was—"Shut up. Don't talk nonsense."


As Eddington pointed out in 1924, densities of this order implied that, according to the theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, the light from Sirius B should be gravitationally redshifted
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...

. This was confirmed when Adams measured this redshift in 1925.

Such densities are possible because white dwarf material is not composed of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s bound by chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

s, but rather consists of a plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

 of unbound nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 and electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s. There is therefore no obstacle to placing nuclei closer to each other than electron orbitals
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

—the regions occupied by electrons bound to an atom—would normally allow. Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present. This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Since electrons obey the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...

, no two electrons can occupy the same state, and they must obey Fermi-Dirac statistics
Fermi-Dirac statistics
Fermi–Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli Exclusion Principle...

, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ground
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

, state; some of them had to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

, meant that a white dwarf could cool to zero temperature and still possess high energy. Another way of deriving this result is by use of the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

: the high density of electrons in a white dwarf means that their positions are relatively localized, creating a corresponding uncertainty in their momenta. This means that some electrons must have high momentum and hence high kinetic energy.

Compression of a white dwarf will increase the number of electrons in a given volume. Applying either the Pauli exclusion principle or the uncertainty principle, we can see that this will increase the kinetic energy of the electrons, causing pressure. This electron degeneracy pressure
Electron degeneracy pressure
Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time. The resulting emergent repulsive force is...

is what supports a white dwarf against gravitational collapse
Gravitational collapse
Gravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...

. It depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is so much greater than that of a low-mass white dwarf that the radius of a white dwarf decreases as its mass increases.

The existence of a limiting mass that no white dwarf can exceed is another consequence of being supported by electron degeneracy pressure. These masses were first published in 1929 by Wilhelm Anderson
Wilhelm Anderson
Wilhelm Robert Karl Anderson was a German-Estonian astrophysicist who studied the physical structure of the stars.- Life :...

 and in 1930 by Edmund C. Stoner. The modern value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar, FRS ) was an Indian origin American astrophysicist who, with William A. Fowler, won the 1983 Nobel Prize for Physics for key discoveries that led to the currently accepted theory on the later evolutionary stages of massive stars...

 in his paper "The Maximum Mass of Ideal White Dwarfs". For a nonrotating white dwarf, it is equal to approximately 5.7/μe2 solar masses, where μe is the average molecular weight per electron of the star., eq. (63) As the carbon-12 and oxygen-16 which predominantly compose a carbon-oxygen white dwarf both have atomic number
Atomic number
In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...

 equal to half their atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

, one should take μe equal to 2 for such a star, leading to the commonly quoted value of 1.4 solar masses. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,, p. 955 so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, μe, equal to 2.5, giving a limit of 0.91 solar mass.) Together with William Alfred Fowler
William Alfred Fowler
William Alfred "Willy" Fowler was an American astrophysicist and winner of the Nobel Prize for Physics in 1983. He should not be confused with the British astronomer Alfred Fowler....

, Chandrasekhar received the Nobel prize
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...

 for this and other work in 1983. The limiting mass is now called the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...

.

If a white dwarf were to exceed the Chandrasekhar limit, and nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

s did not take place, the pressure exerted by electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s would no longer be able to balance the force of gravity, and it would collapse into a denser object such as a neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

. However, carbon-oxygen white dwarfs accreting mass from a neighboring star undergo a runaway nuclear fusion reaction, which leads to a Type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

 explosion in which the white dwarf is destroyed, just before reaching the limiting mass.

New research indicates that many white dwarfs—at least in certain types of galaxies—may not approach that limit by way of accretion. In a paper published in the journal Nature in February 2010, astronomers Marat Gilfanov and Akos Bogdan, both of the Max Planck Institute for Astrophysics
Max Planck Institute for Astrophysics
The Max Planck Institute for Astrophysics is a Max Planck Institute, located in Garching, near Munich, Bavaria, Germany. It was founded as Max Planck Institute for Physics and Astrophysics in 1958 and split up into the Max Planck Institute for Astrophysics and the Max Planck Institute for Physics...

 in Garching, Germany, postulated that at least some of the white dwarfs that become supernovae attain the necessary mass not by accretion but by colliding with one another. Gilfanov and Bogdan said that in elliptical galaxies such collisions are the major source of supernovae. Their hypothesis is based on the fact that the x-rays produced by the white dwarfs' accretion of matter—measured using NASA's Chandra X-Ray Observatory
Chandra X-ray Observatory
The Chandra X-ray Observatory is a satellite launched on STS-93 by NASA on July 23, 1999. It was named in honor of Indian-American physicist Subrahmanyan Chandrasekhar who is known for determining the maximum mass for white dwarfs. "Chandra" also means "moon" or "luminous" in Sanskrit.Chandra...

—are no more than 1/30th to 1/50th of what would be expected to be produced by an amount of matter falling into a white dwarf sufficient to produce enough mass to cause the star to go supernova. In other words, at least in some circumstances, accretion simply does not add enough matter to cause a white dwarf to approach the Chandrasekhar limit, and the two astronomers concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion to white dwarfs. The significance of this finding is that there could be two types of supernovae, which could mean that the Chandrasekhar limit might not always apply in determining when a white dwarf goes supernova, given that two colliding white dwarfs could have a range of masses. This in turn would confuse efforts to use exploding white dwarfs as standard measurements in determining the nature of the universe.

White dwarfs have low luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

 and therefore occupy a strip at the bottom of the Hertzsprung-Russell diagram, a graph of stellar luminosity versus color (or temperature). They should not be confused with low-luminosity objects at the low-mass end of the main sequence
Main sequence
The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

, such as the hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

fusing
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

 red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

s, whose cores are supported in part by thermal pressure, or the even lower-temperature brown dwarf
Brown dwarf
Brown dwarfs are sub-stellar objects which are too low in mass to sustain hydrogen-1 fusion reactions in their cores, which is characteristic of stars on the main sequence. Brown dwarfs have fully convective surfaces and interiors, with no chemical differentiation by depth...

s.

Mass-radius relationship and mass limit


It is simple to derive a rough relationship between the mass and radii of white dwarfs using an energy minimization argument. The energy of the white dwarf can be approximated by taking it to be the sum of its gravitational potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

 and kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

. The gravitational potential energy of a unit mass piece of white dwarf, Eg, will be on the order of −GM/R, where G is the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

, M is the mass of the white dwarf, and R is its radius. The kinetic energy of the unit mass, Ek, will primarily come from the motion of electrons, so it will be approximately N p2/2m, where p is the average electron momentum, m is the electron mass, and N is the number of electrons per unit mass. Since the electrons are degenerate
Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

, we can estimate p to be on the order of the uncertainty in momentum, Δp, given by the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

, which says that Δp Δx is on the order of the reduced Planck constant
Planck constant
The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

, ħ. Δx will be on the order of the average distance between electrons, which will be approximately n−1/3, i.e., the reciprocal of the cube root of the number density, n, of electrons per unit volume. Since there are N M electrons in the white dwarf and its volume is on the order of R3, n will be on the order of N M / R3.

Solving for the kinetic energy per unit mass, Ek, we find that

The white dwarf will be at equilibrium when its total energy, Eg + Ek, is minimized. At this point, the kinetic and gravitational potential energies should be comparable, so we may derive a rough mass-radius relationship by equating their magnitudes:

Solving this for the radius, R, gives

Dropping N, which depends only on the composition of the white dwarf, and the universal constants leaves us with a relationship between mass and radius:

i.e., the radius of a white dwarf is inversely proportional to the cube root of its mass.

Since this analysis uses the non-relativistic formula p2/2m for the kinetic energy, it is non-relativistic. If we wish to analyze the situation where the electron velocity in a white dwarf is close to the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, c, we should replace p2/2m by the extreme relativistic approximation p c for the kinetic energy. With this substitution, we find

If we equate this to the magnitude of Eg, we find that R drops out and the mass, M, is forced to be



To interpret this result, observe that as we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase. As this velocity approaches c, the extreme relativistic analysis becomes more exact, meaning that the mass M of the white dwarf must approach Mlimit. Therefore, no white dwarf can be heavier than the limiting mass Mlimit, or 1.4 Solar masses.

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...

 which describes the relationship between density and pressure in the white dwarf material. If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass., eq. (80) Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass. This is the limiting value of the mass—called the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...

—at which the white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas
Fermi gas
A Fermi gas is an ensemble of a large number of fermions. Fermions, named after Enrico Fermi, are particles that obey Fermi–Dirac statistics. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density,...

 in hydrostatic equilibrium. The average molecular weight per electron, μe, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.

These computations all assume that the white dwarf is non-rotating. If the white dwarf is rotating, the equation of hydrostatic equilibrium must be modified to take into account the centrifugal pseudo-force arising from working in a rotating frame. For a uniformly rotating white dwarf, the limiting mass increases only slightly. However, if the star is allowed to rotate nonuniformly, and viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 is neglected, then, as was pointed out by Fred Hoyle
Fred Hoyle
Sir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...

 in 1947, there is no limit to the mass for which it is possible for a model white dwarf to be in static equilibrium. Not all of these model stars, however, will be dynamically
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...

 stable.

Radiation and cooling


The degenerate matter that makes up the bulk of a white dwarf has a very low opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...

, because any absorption of a photon requires an electron transition to a higher empty state, which may not be available given the energy of the photon; it also has a high thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

. As a result, the interior of the white dwarf maintains a constant temperature, approximately 107 K. However, an outer shell of non-degenerate matter cools from approximately 107 K to 104 K. This matter radiates roughly as a black body
Black body
A black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...

 to determine the visible color of the white dwarf. A white dwarf remains visible for a long time, because it radiates as a roughly 104 K body, while its interior is at 107 K.

The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type main sequence
Main sequence
The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

 star to the red of a M-type red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

. White dwarf effective surface temperatures
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...

 extend from over 150,000 K to barely under 4,000 K. In accordance with the Stefan-Boltzmann law, luminosity increases with increasing surface temperature; this surface temperature range corresponds to a luminosity from over 100 times the Sun's to under 1/10,000th that of the Sun's. Hot white dwarfs, with surface temperatures in excess of 30,000 K, have been observed to be sources of soft (i.e., lower-energy) X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s. This enables the composition and structure of their atmospheres to be studied by soft X-ray
X-ray astronomy
X-ray astronomy is an observational branch of astronomy which deals with the study of X-ray observation and detection from astronomical objects. X-radiation is absorbed by the Earth's atmosphere, so instruments to detect X-rays must be taken to high altitude by balloons, sounding rockets, and...

 and extreme ultraviolet observations
UV astronomy
Ultraviolet astronomy is generally used to refer to observations of electromagnetic radiation at ultraviolet wavelengths between approximately 10 and 320 nanometres; shorter wavelengths—higher energy photons—are studied by X-ray astronomy and gamma ray astronomy...

.


As was explained by Leon Mestel
Leon Mestel
Leon Mestel is a British astronomer and astrophysicist and Emeritus Professor at the University of Sussex. His research interests are in the areas of star formation and structure, especially stellar magnetism and astrophysical magnetohydrodynamics. He has won both the Eddington Medal and the Gold...

 in 1952, unless the white dwarf accretes
Accretion (astrophysics)
In astrophysics, the term accretion is used for at least two distinct processes.The first and most common is the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disc. Accretion discs are common around smaller stars or stellar remnants...

 matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished., §2.1. White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. As a white dwarf cools, its surface temperature decreases, the radiation which it emits reddens, and its luminosity decreases. Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time. Pierre Bergeron, Maria Tereza Ruiz, and Sandy Leggett, for example, estimate that after a carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 white dwarf of 0.59 solar mass with a hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1.5 billion years, cooling approximately 500 more kelvins to 6,590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6,030 K and 5,550 K) take first 0.4 and then 1.1 billion years., Table 2. Although white dwarf material is initially plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

—a fluid composed of nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 and electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star. The crystal structure is thought to be a body-centered cubic lattice. In 1995 it was pointed out that asteroseismological
Asteroseismology
Asteroseismology also known as stellar seismology is the science that studies the internal structure of pulsating stars by the interpretation of their frequency spectra. Different oscillation modes penetrate to different depths inside the star...

 observations of pulsating white dwarfs yielded a potential test of the crystallization theory, and in 2004, Antonio Kanaan, Travis Metcalfe and a team of researchers with the Whole Earth Telescope estimated, on the basis of such observations, that approximately 90% of the mass of BPM 37093
BPM 37093
BPM 37093 is a variable white dwarf star of the DAV, or ZZ Ceti, type, with a hydrogen atmosphere and an unusually high mass of approximately 1.1 times the Sun's. It is about 50 light-years from Earth, in the constellation Centaurus, and vibrates; these pulsations cause its luminosity to vary...

 had crystallized. Other work gives a crystallized mass fraction of between 32% and 82%.

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K. A white dwarf, though, spends more of its lifetime at cooler temperatures than at hotter temperatures, so we should expect that there are more cool white dwarfs than hot white dwarfs. Once we adjust for the selection effect that hotter, more luminous white dwarfs are easier to observe, we do find that decreasing the temperature range examined results in finding more white dwarfs. This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K, and one of the coolest so far observed, WD 0346+246
WD 0346+246
WD 0346+246 is a white dwarf star. It was discovered in 1997 when examination of photographs taken for a survey of brown dwarfs in the Pleiades revealed a faint star with high proper motion. It is one of the coolest white dwarfs known, with an effective temperature estimated to be approximately...

, has a surface temperature of approximately 3,900 K. The reason for this is that, as the Universe's age is finite, there has not been time for white dwarfs to cool down below this temperature. The white dwarf luminosity function can therefore be used to find the time when stars started to form in a region; an estimate for the age of the Galactic disk found in this way is 8 billion years.

A white dwarf will eventually, in many trillion years, cool and become a non-radiating black dwarf
Black dwarf
A black dwarf is a hypothetical stellar remnant, created when a white dwarf becomes sufficiently cool to no longer emit significant heat or light...

in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. However, no black dwarfs are thought to exist yet.

Atmosphere and spectra


Although most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 typically shows that their emitted light comes from an atmosphere which is observed to be either hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

-dominated or helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

-dominated. The dominant element is usually at least 1,000 times more abundant than all other elements. As explained by Schatzman
Évry Schatzman
Evry Léon Schatzman was a French astrophysicist.His father, Benjamin Schatzman, was a dentist born in Tulcea, Romania and emigrated at a young age with his family in Palestine. Schatzman began his studies at the École Normale Supérieure in November 1939...

 in the 1940s, the high surface gravity
Surface gravity
The surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in...

 is thought to cause this purity by gravitationally separating the atmosphere so that heavy elements are on the bottom and lighter ones on top., §5–6 This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope which is a residue of the star's envelope in the AGB
Asymptotic Giant Branch
The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their lives....

 phase and may also contain material accreted from the interstellar medium
Interstellar medium
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space...

. The envelope is believed to consist of a helium-rich layer with mass no more than 1/100th of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/10,000th of the stars total mass., §4–5.

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore almost isothermal, and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.
White dwarf spectral types
Primary and secondary features
A H lines present; no He I or metal lines
B He I lines; no H or metal lines
C Continuous spectrum; no lines
O He II lines, accompanied by He I or H lines
Z Metal lines; no H or He I lines
Q Carbon lines present
X Unclear or unclassifiable spectrum
Secondary features only
P Magnetic white dwarf with detectable polarization
H Magnetic white dwarf without detectable polarization
E Emission lines present
V Variable

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941, and various classification schemes have been proposed and used since then. The system currently in use was introduced by Edward M. Sion, Jesse L. Greenstein and their coauthors in 1983 and has been subsequently revised several times. It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the table to the right), and a temperature index number, computed by dividing 50,400 K by the effective temperature
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...

. For example:
  • A white dwarf with only He I
    Spectroscopic notation
    Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and molecular orbitals.-Ionization states:Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by the element's symbol followed by a Roman numeral...

     lines in its spectrum and an effective temperature of 15,000 K could be given the classification of DB3, or, if warranted by the precision of the temperature measurement, DB3.5.
  • A white dwarf with a polarized magnetic field
    Magnetic field
    A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

    , an effective temperature of 17,000 K, and a spectrum dominated by He I
    Spectroscopic notation
    Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and molecular orbitals.-Ionization states:Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by the element's symbol followed by a Roman numeral...

     lines which also had hydrogen
    Hydrogen
    Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

     features could be given the classification of DBAP3.

The symbols ? and : may also be used if the correct classification is uncertain.

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs. The next class in number is of DBs (approximately 16%). A small fraction (roughly 0.1%) have carbon-dominated atmospheres, the hot (above 15,000 K) DQ class. Those classified as DB, DC, DO, DZ, and cool DQ have helium-dominated atmospheres. Assuming that carbon and metals are not present, which spectral classification is seen depends on the effective temperature
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...

. Between approximately 100,000 K to 45,000 K, the spectrum will be classified DO, dominated by singly ionized helium. From 30,000 K to 12,000 K, the spectrum will be DB, showing neutral helium lines, and below about 12,000 K, the spectrum will be featureless and classified DC.,§ 2.4.

Magnetic field


Magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s in white dwarfs with a strength at the surface of ~1 million gauss
Gauss (unit)
The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B , named after the German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter; it equals 1 tesla...

 (100 teslas
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

) were predicted by P. M. S. Blackett in 1947 as a consequence of a physical law he had proposed which stated that an uncharged, rotating body should generate a magnetic field proportional to its angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. This putative law, sometimes called the Blackett effect
Blackett effect
The Blackett effect, also called gravitational magnetism, is the hypothetical generation of a magnetic field by an uncharged, rotating body. This effect has never been observed.-History:...

, was never generally accepted, and by the 1950s even Blackett felt it had been refuted., pp. 39–43 In the 1960s, it was proposed that white dwarfs might have magnetic fields because of conservation of total surface magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

 during the evolution of a non-degenerate star to a white dwarf. A surface magnetic field of ~100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of ~100·1002=1 million gauss (100 T) once the star's radius had shrunk by a factor of 100., §8;, p. 484 The first magnetic white dwarf to be observed was GJ 742
GJ 742
GJ 742 is a white dwarf star located about 43 light years from Earth in the constellation Draco. With a magnitude of about 13 it is visible only through a large telescope.-Properties:...

, which was detected to have a magnetic field in 1970 by its emission of circularly polarized light. It is thought to have a surface field of approximately 300 million gauss (30 kT)., §8 Since then magnetic fields have been discovered in well over 100 white dwarfs, ranging from 2×103 to 109 gauss (0.2 T to 100 kT). Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).

Variability


DAV (GCVS: ZZA) DA spectral type, having only hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 absorption lines in its spectrum
DBV (GCVS: ZZB) DB spectral type, having only helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 absorption lines in its spectrum
GW Vir (GCVS: ZZO) Atmosphere mostly C, He and O;
may be divided into DOV and PNNV stars
Types of pulsating white dwarf, §1.1, 1.2.


Early calculations suggested that there might be white dwarfs whose luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

 varied
Variable star
A star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth...

 with a period of around 10 seconds, but searches in the 1960s failed to observe this., § 7.1.1; The first variable white dwarf found was HL Tau 76
HL Tau 76
HL Tau 76 is a variable white dwarf star of the DAV type. It was observed by G. Haro and W. J. Luyten in 1961, and was the first variable white dwarf discovered when, in 1968, Arlo U. Landolt found that it varied in brightness with a period of approximately 749.5 seconds, or 12.5 minutes...

; in 1965 and 1966, Arlo U. Landolt
Arlo U. Landolt
Arlo U. Landolt is an American astronomer. Landolt has worked principally in photometry and has published a number of widely used lists of standard stars. In 1995, he received the George van Biesbroeck Prize from the American Astronomical Society...

 observed it to vary with a period of approximately 12.5 minutes. The reason for this period being longer than predicted is that the variability of HL Tau 76, like that of the other pulsating variable white dwarfs known, arises from non-radial gravity wave
Gravity wave
In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....

 pulsations., § 7. Known types of pulsating white dwarf include the DAV, or ZZ Ceti, stars, including HL Tau 76, with hydrogen-dominated atmospheres and the spectral type DA;, pp. 891, 895 DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;, p. 3525 and GW Vir stars (sometimes subdivided into DOV and PNNV stars), with atmospheres dominated by helium, carbon, and oxygen.,§1.1, 1.2;,§1. GW Vir stars are not, strictly speaking, white dwarfs, but are stars which are in a position on the Hertzsprung-Russell diagram between the asymptotic giant branch
Asymptotic Giant Branch
The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their lives....

 and the white dwarf region. They may be called pre-white dwarfs., § 1.1; These variables all exhibit small (1%–30%) variations in light output, arising from a superposition of vibrational modes with periods of hundreds to thousands of seconds. Observation of these variations gives asteroseismological
Asteroseismology
Asteroseismology also known as stellar seismology is the science that studies the internal structure of pulsating stars by the interpretation of their frequency spectra. Different oscillation modes penetrate to different depths inside the star...

 evidence about the interiors of white dwarfs.

Formation


White dwarfs are thought to represent the end point of stellar evolution
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...

 for main-sequence stars with masses from about 0.07 to 10 solar masses. The composition of the white dwarf produced will differ depending on the initial mass of the star.

Stars with very low mass


If the mass of a main-sequence star is lower than approximately half a solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

, it will never become hot enough to fuse helium at its core. It is thought that, over a lifespan exceeding the age (~13.7 billion years) of the Universe, such a star will eventually burn all its hydrogen and end its evolution as a helium white dwarf composed chiefly of helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...

 nuclei. Owing to the time this process takes, it is not thought to be the origin of observed helium white dwarfs. Rather, they are thought to be the product of mass loss in binary systems or mass loss due to a large planetary companion.

Stars with low to medium mass


If the mass of a main-sequence star is between approximately 0.5 and 8 solar masses, its core will become sufficiently hot to fuse helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 into carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 and oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 via the triple-alpha process
Triple-alpha process
The triple alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei are transformed into carbon.Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores...

, but it will never become sufficiently hot to fuse carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 into neon
Neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...

. Near the end of the period in which it undergoes fusion reactions, such a star will have a carbon-oxygen core which does not undergo fusion reactions, surrounded by an inner helium-burning shell and an outer hydrogen-burning shell. On the Hertzsprung-Russell diagram, it will be found on the asymptotic giant branch
Asymptotic Giant Branch
The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their lives....

. It will then expel most of its outer material, creating a planetary nebula
Planetary nebula
A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...

, until only the carbon-oxygen core is left. This process is responsible for the carbon-oxygen white dwarfs which form the vast majority of observed white dwarfs.

Stars with medium to high mass


If a star is massive enough, its core will eventually become sufficiently hot to fuse carbon to neon, and then to fuse neon to iron. Such a star will not become a white dwarf, because the mass of its central, non-fusing core, supported by electron degeneracy pressure
Electron degeneracy pressure
Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time. The resulting emergent repulsive force is...

, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will collapse
Gravitational collapse
Gravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...

 and it will explode in a core-collapse supernova which will leave behind a remnant neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

, black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, or possibly a more exotic form of compact star
Compact star
In astronomy, the term compact star is used to refer collectively to white dwarfs, neutron stars, other exotic dense stars, and black holes. These objects are all small for their mass...

. Some main-sequence stars, of perhaps 8 to 10 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

es, although sufficiently massive to fuse carbon to neon and magnesium
Carbon burning process
The carbon-burning process or carbon fusion is a set of nuclear fusion reactions that take place in massive stars that have used up the lighter elements in their cores...

, may be insufficiently massive to fuse neon
Neon burning process
The neon-burning process is a set of nuclear fusion reactions that take place in massive stars . Neon burning requires high temperatures and densities ....

. Such a star may leave a remnant white dwarf composed chiefly of oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

, neon
Neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...

, and magnesium
Magnesium
Magnesium is a chemical element with the symbol Mg, atomic number 12, and common oxidation number +2. It is an alkaline earth metal and the eighth most abundant element in the Earth's crust and ninth in the known universe as a whole...

, provided that its core does not collapse, and provided that fusion does not proceed so violently as to blow apart the star in a supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...

. Although some isolated white dwarfs have been identified which may be of this type, most evidence for the existence of such stars comes from the novae called ONeMg or neon novae. The spectra of these nova
Nova
A nova is a cataclysmic nuclear explosion in a star caused by the accretion of hydrogen on to the surface of a white dwarf star, which ignites and starts nuclear fusion in a runaway manner...

e exhibit abundances of neon, magnesium, and other intermediate-mass elements which appear to be only explicable by the accretion of material onto an oxygen-neon-magnesium white dwarf.

Fate


A white dwarf is stable once formed and will continue to cool almost indefinitely; eventually, it will become a black white dwarf, also called a black dwarf
Black dwarf
A black dwarf is a hypothetical stellar remnant, created when a white dwarf becomes sufficiently cool to no longer emit significant heat or light...

. Assuming that the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

 continues to expand, it is thought that in 1019 to 1020 years, the galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

 will evaporate as their star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s escape into intergalactic space., §IIIA. White dwarfs should generally survive this, although an occasional collision between white dwarfs may produce a new fusing
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

 star or a super-Chandrasekhar mass white dwarf which will explode in a Type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

., §IIIC, IV. The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

, known to be at least 1032 years. Some simple grand unified theories predict a proton lifetime
Proton decay
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...

 of no more than 1049 years. If these theories are not valid, the proton may decay by more complicated nuclear processes, or by quantum gravitational
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 processes involving a virtual black hole
Virtual black hole
In quantum gravity, a virtual black hole is a black hole that exists temporarily as a result of a quantum fluctuation of spacetime. It is an example of quantum foam and is the gravitational analog of the virtual electron-positron pairs found in quantum electrodynamics...

; in these cases, the lifetime is estimated to be no more than 10200 years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely., §IV.

Stellar system



A white dwarf's stellar and planetary system
Planetary system
A planetary system consists of the various non-stellar objects orbiting a star such as planets, dwarf planets , asteroids, meteoroids, comets, and cosmic dust...

 is inherited from its progenitor star and may interact with the white dwarf in various ways. Infrared spectroscopic observations made by NASA's Spitzer Space Telescope
Spitzer Space Telescope
The Spitzer Space Telescope , formerly the Space Infrared Telescope Facility is an infrared space observatory launched in 2003...

 of the central star of the Helix Nebula
Helix Nebula
The Helix Nebula is a large planetary nebula located in the constellation Aquarius. Discovered by Karl Ludwig Harding, probably before 1824, this object is one of the closest to the Earth of all the bright planetary nebulae. The estimated distance is about 215 parsecs or 700 light-years...

 suggest the presence of a dust cloud, which may be caused by cometary collisions. It is possible that infalling material from this may cause X-ray emission from the central star. Similarly, observations made in 2004 indicated the presence of a dust cloud around the young white dwarf star G29-38
G29-38
Giclas 29-38 is a variable white dwarf star of the DAV, or ZZ Ceti,whose variability is due to large-amplitude, non-radial pulsations, known as gravity waves. It was first reported to be variable by Shulov and Kopatskaya in 1974...

 (estimated to have formed from its AGB
Asymptotic Giant Branch
The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their lives....

 progenitor about 500 million years ago), which may have been created by tidal disruption of a comet passing close to the white dwarf.

If a white dwarf is in a binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

 system and is accreting matter from its companion, a variety of phenomena may occur, including nova
Nova
A nova is a cataclysmic nuclear explosion in a star caused by the accretion of hydrogen on to the surface of a white dwarf star, which ignites and starts nuclear fusion in a runaway manner...

e and Type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

e. It may also be a super-soft x-ray source
Super-soft x-ray source
A super soft X-ray source is an astronomical source of very low energy X-rays. Soft X-rays have energies in the 0.09 to 2.5 keV range, whereas hard X-rays are in the 1-20 keV range. SSXSs are in most cases only detected below 0.5 keV, so that within our own galaxy they are usually hidden by...

 if it is able to take material from its companion fast enough to sustain fusion on its surface. A close binary system of two white dwarfs can radiate energy in the form of gravitational wave
Gravitational wave
In physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...

s, causing their mutual orbit to steadily shrink until the stars merge.

Type Ia supernovae



The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...

 of ~1.4 solar masses. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly.) White dwarfs in binary systems, however, can accrete material from a companion star, increasing both their mass and their density. As their mass approaches the Chandrasekhar limit, this could theoretically lead to either the explosive ignition of fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

 in the white dwarf or its collapse into a neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

.

Accretion provides the currently favored mechanism, the single-degenerate model, for Type Ia supernovae. In this model, a carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 white dwarf accretes material from a companion star,, p. 14. increasing its mass and compressing its core. It is believed that compressional heating of the core leads to ignition
Carbon detonation
Carbon detonation is the violent re-ignition of thermonuclear fusion in a dead star, which produces a Type Ia supernova. A white dwarf undergoes carbon detonation only if it has a normal binary companion which is close enough to the dwarf star to dump sufficient amounts of matter onto the dwarf,...

 of carbon fusion
Carbon burning process
The carbon-burning process or carbon fusion is a set of nuclear fusion reactions that take place in massive stars that have used up the lighter elements in their cores...

 as the mass approaches the Chandrasekhar limit. Because the white dwarf is supported against gravity by quantum degeneracy pressure instead of by thermal pressure, adding heat to the star's interior increases its temperature but not its pressure, so the white dwarf does not expand and cool in response. Rather, the increased temperature accelerates the rate of the fusion reaction, in a runaway
Thermal runaway
Thermal runaway refers to a situation where an increase in temperature changes the conditions in a way that causes a further increase in temperature, often leading to a destructive result...

 process that feeds on itself. The thermonuclear flame consumes much of the white dwarf in a few seconds, causing a Type Ia supernova explosion that obliterates the star. In another possible mechanism for Type Ia supernovae, the double-degenerate model, two carbon-oxygen white dwarfs in a binary system merge, creating an object with mass greater than the Chandrasekhar limit in which carbon fusion is then ignited., p. 14.

Observations have failed to note signs of accretion leading up to Type Ia supernovae, and this is now thought to be because the star is first loaded up to above the Chandrasekhar limit while also being spun up to a very fast rate by the same process. Once the accretion stops the star gradually slows down until the spin is no longer fast enough to prevent the explosion.

Cataclysmic variables



Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by hydrogen fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

. Since the white dwarf's core remains intact, these surface explosions can be repeated as long as accretion continues. This weaker kind of repetitive cataclysmic phenomenon is called a (classical) nova
Nova
A nova is a cataclysmic nuclear explosion in a star caused by the accretion of hydrogen on to the surface of a white dwarf star, which ignites and starts nuclear fusion in a runaway manner...

. Astronomers have also observed dwarf nova
Dwarf nova
A U Geminorum-type variable star, or dwarf nova is a type of cataclysmic variable starhttp://www.sai.msu.su/groups/cluster/gcvs/gcvs/iii/vartype.txt consisting of a close binary star system in which one of the components is a white dwarf, which accretes matter from its companion...

e, which have smaller, more frequent luminosity peaks than classical novae. These are thought to be caused by the release of gravitational potential energy when part of the accretion disc
Accretion disc
An accretion disc is a structure formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of...

 collapses onto the star, rather than by fusion. In general, binary systems with a white dwarf accreting matter from a stellar companion are called cataclysmic variables. As well as novae and dwarf novae, several other classes of these variables are known. Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 sources.

See also


  • Planetary nebula
    Planetary nebula
    A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...

  • PG 1159 star
    PG 1159 star
    A PG 1159 star, often also called a pre-degenerate, is a star with a hydrogen-deficient atmosphere which is in transition between being the central star of a planetary nebula and being a hot white dwarf...

  • Pulsating white dwarf
    Pulsating white dwarf
    A pulsating white dwarf is a white dwarf star whose luminosity varies due to non-radial gravity wave pulsations within itself. Known types of pulsating white dwarfs include DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA, pp. 891, 895; DBV, or V777 Her,...

  • Stellar classification
    Stellar classification
    In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...

  • Timeline of white dwarfs, neutron stars, and supernovae
    Timeline of white dwarfs, neutron stars, and supernovae
    Timeline of white dwarfs, neutron stars, and supernovaeNote that this list is mainly about the development of knowledge, but also about some supernovae taking place. For a separate list of the latter, see the article List of supernovae...

  • Degenerate matter
    Degenerate matter
    Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

  • Black dwarf
    Black dwarf
    A black dwarf is a hypothetical stellar remnant, created when a white dwarf becomes sufficiently cool to no longer emit significant heat or light...

  • Supernova
    Supernova
    A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...

  • Red dwarf
    Red dwarf
    According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

  • Brown dwarf
    Brown dwarf
    Brown dwarfs are sub-stellar objects which are too low in mass to sustain hydrogen-1 fusion reactions in their cores, which is characteristic of stars on the main sequence. Brown dwarfs have fully convective surfaces and interiors, with no chemical differentiation by depth...

  • Robust Associations of Massive Baryonic Objects (RAMBOs)
  • Neutron star
    Neutron star
    A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...


Physics

  • Black holes, white dwarfs, and neutron stars: the physics of compact objects, Stuart L. Shapiro and Saul A. Teukolsky, New York: Wiley, 1983. ISBN 0-471-87317-9.
  • White dwarf stars and the Chandrasekhar limit, Dave Gentile, Master's thesis, DePaul University
    DePaul University
    DePaul University is a private institution of higher education and research in Chicago, Illinois. Founded by the Vincentians in 1898, the university takes its name from the 17th century French priest Saint Vincent de Paul...

    , 1995.
  • Estimating Stellar Parameters from Energy Equipartition, sciencebits.com. Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments.

Observational


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