White dwarf

Source: Wikipedia, the free encyclopedia.
"Degenerate dwarf" redirects here. Not to be confused with
Degenerate star
.
For other uses, see White dwarf (disambiguation).

Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius A.

A white dwarf is a

Willem Luyten
in 1922.

White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star or black hole. This includes over 97% of the stars in the Milky Way.[4]: §1  After the hydrogen-fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant during which it fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon (around 1 billion K), an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, which is the remnant white dwarf.[5] Usually, white dwarfs are composed of carbon and oxygen (CO white dwarf). If the mass of the progenitor is between 7 and 9 solar masses (M☉), the core temperature will be sufficient to fuse carbon but not neon, in which case an oxygen–neon–magnesium (ONeMg or ONe) white dwarf may form.[6] Stars of very low mass will be unable to fuse helium; hence, a helium white dwarf[7][8] may form 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. As a result, it cannot support itself by the heat generated by fusion against gravitational collapse, but is supported only by electron degeneracy pressure, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit — approximately 1.44 times M☉ — 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 via a process known as carbon detonation;[1][5] SN 1006 is thought to be a famous example.

A white dwarf is very hot when it forms, but because it has no source of energy, it will gradually cool as it radiates its energy away. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool and its material will begin to crystallize, starting with the core. The star's low temperature means it will no longer emit significant heat or light, and it will become a cold black dwarf.[5] Because the length of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the known universe (approximately 13.8 billion years),[9] it is thought that no black dwarfs yet exist.[1][4] The oldest known white dwarfs still radiate at temperatures of a few thousand kelvins, which establishes an observational limit on the maximum possible age of the universe.[10]

Discovery

See also: List of white dwarfs

The first white dwarf discovered was in the

Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white.[12] In 1939, Russell looked back on the discovery:[3]
: 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.[13]

The white dwarf companion of Sirius, Sirius B, 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 (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:[14]

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;[14] C.A.F. Peters computed an orbit for it in 1851.[15] It was not until 31 January 1862 that Alvan Graham Clark observed a previously unseen star close to Sirius, later identified as the predicted companion.[15] Walter Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.[16]

In 1917,

Arthur Stanley Eddington.[12][22] Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939.[3]: 3  Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known,[23] and by 1999, over 2,000 were known.[24] Since then the Sloan Digital Sky Survey has found over 9,000 white dwarfs, mostly new.[25]

Composition and structure

Although white dwarfs are known with estimated masses as low as 0.17 M☉

compact stars such as neutron stars, quark stars (hypothetical),[29] and black holes
.

White dwarfs were found to be extremely dense soon after their discovery. If a star is in a

spectrum. If the star's distance is known, its absolute luminosity can also be estimated. From the absolute luminosity and distance, the star's surface area and its radius can be calculated. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that due to their relatively high temperature and relatively low absolute luminosity, Sirius B and 40 Eridani B must be very dense. When Ernst Öpik 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's, which was so high that he called it "impossible".[32] As Arthur Eddington put it later, in 1927:[33]
: 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, the light from Sirius B should be gravitationally redshifted.[22] This was confirmed when Adams measured this redshift in 1925.[34]

Material Density in kg/m3 Notes
Supermassive black hole c. 1,000[35] Critical density of a black hole of around 108 solar masses.
Water (fresh) 1,000 At STP
Osmium 22,610 Near room temperature
The core of the Sun c. 150,000
White dwarf 1 × 109[1]
Atomic nuclei
 2.3 × 1017[36] Does not depend strongly on size of nucleus
Neutron star core 8.4 × 1016 – 1 × 1018
Small black hole 2 × 1030[37] Critical density of an Earth-mass black hole.

Such densities are possible because white dwarf material is not composed of

Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.[38][40]

Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure 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 much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.[1]

The existence of a limiting mass that no white dwarf can exceed without collapsing to a neutron star is another consequence of being supported by electron degeneracy pressure. Such limiting masses were calculated for cases of an idealized, constant density star in 1929 by

atomic weight, one should take μe equal to 2 for such a star,[40] leading to the commonly quoted value of 1.4 M☉. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,[43]: 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 M☉.) Together with William Alfred Fowler, Chandrasekhar received the Nobel Prize for this and other work in 1983.[46] The limiting mass is now called the Chandrasekhar limit
.

If a white dwarf were to exceed the Chandrasekhar limit, and nuclear reactions did not take place, the pressure exerted by electrons would no longer be able to balance the force of gravity, and it would collapse into a denser object called a neutron star.[47] Carbon–oxygen white dwarfs accreting mass from a neighboring star undergo a runaway nuclear fusion reaction, which leads to a Type Ia supernova explosion in which the white dwarf may be destroyed, before it reaches the limiting mass.[48]

New research indicates that many white dwarfs – at least in certain types of galaxies – may not approach that limit by way of accretion. It has been postulated that at least some of the white dwarfs that become supernovae attain the necessary mass by colliding with one another. It may be that in

standard candles in determining distances.[49]

White dwarfs have low

hydrogen-fusing red dwarfs, whose cores are supported in part by thermal pressure,[50] or the even lower-temperature brown dwarfs.[51]

Mass–radius relationship

See also: Chandrasekhar's white dwarf equation and Neutron star § Gravity and equation of state

The relationship between the mass and radius of low-mass white dwarfs can be estimated using the nonrelativistic Fermi gas equation of state, which gives[40]

where R is the radius, M is the total mass of the star, N is the number of electrons per unit mass (dependent only on composition), me is the electron mass, is the

reduced Planck constant, and G is the gravitational constant
.

Since this analysis uses the non-relativistic formula T = p2 / 2m for the kinetic energy, it is non-relativistic. When the electron velocity in a white dwarf is close to the speed of light, the kinetic energy formula approaches T = pc where c is the speed of light, and it can be shown that there is no stable equilibrium in the ultrarelativistic limit. In particular, this analysis yields the maximum mass of a white dwarf, which is[40]

Radius–mass relations for a model white dwarf. Mlimit is denoted as MCh

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute 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.[45]: eqn.(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 – 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 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.[45][52]

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

dynamically stable.[55]

Rotating white dwarfs and the estimates of their diameter in terms of the angular velocity of rotation has been treated in the rigorous mathematical literature.[56] The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously.[57]

Radiation and cooling

The degenerate matter that makes up the bulk of a white dwarf has a very low

thermal conductivity. As a result, the interior of the white dwarf maintains an almost uniform temperature as it cools down, starting at approximately 108 K shortly after the formation of the white dwarf and reaching less than 106 K for the coolest known white dwarfs.[58] An outer shell of non-degenerate matter sits on top of the degenerate core. The outermost layers, which have temperatures below 105 K, radiate roughly as a black body
. A white dwarf remains visible for a long time, as its tenuous outer atmosphere slowly radiates the thermal content of the degenerate interior.

The visible radiation emitted by white dwarfs varies over a wide color range, from the whitish-blue color of an O, B or A-type main sequence star to the yellow-orange of a late K or early M-type star.

extreme ultraviolet observations.[62]

White dwarfs also radiate neutrinos through the Urca process.[63] This process has more effect on hotter and younger white dwarfs.

A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.

As was explained by Leon Mestel in 1952, unless the white dwarf accretes matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished.[64][65]: §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.[5] 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. The rate of cooling has been estimated for a carbon white dwarf of 0.59 M☉ with a hydrogen atmosphere. After initially taking approximately 1.5 billion years to cool to a surface temperature of 7,140 K, 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.[66]: Table 2 

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K.

Galactic disk found in this way is 8 billion years.[68] A white dwarf will eventually, in many trillions of years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. No black dwarfs are thought to exist yet.[1]

The white dwarf cooling sequence seen by ESA's Gaia mission

White dwarf core material is a completely ionized plasma – a mixture of

body-centered cubic lattice.[4][74] In 1995 it was suggested that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,[75] and in 2004, observations were made that suggested approximately 90% of the mass of BPM 37093 had crystallized.[76][77][78] Other work gives a crystallized mass fraction of between 32% and 82%.[79] As a white dwarf core undergoes crystallization into a solid phase, latent heat is released which provides a source of thermal energy that delays its cooling.[80] Another possible mechanism that was suggested to explain the seeming delay in the cooling of some types of white dwarves is a solid-liquid distillation process: the crystals formed in the core are buoyant and float up, thereby displacing heavier liquid downward, thus causing a net release of gravitational energy.[81] Chemical fractionation between the ionic species in the plasma mixture can release a similar or even greater amount of energy.[82][83][84] This energy release was first confirmed in 2019 after the identification of a pile up in the cooling sequence of more than 15,000 white dwarfs observed with the Gaia satellite.[85]

Low-mass helium white dwarfs (mass < 0.20 M☉), often referred to as "extremely low-mass white dwarfs, ELM WDs" are formed in binary systems. As a result of their hydrogen-rich envelopes, residual hydrogen burning via the CNO cycle may keep these white dwarfs hot on a long timescale. In addition, they remain in a bloated proto-white dwarf stage for up to 2 Gyr before they reach the cooling track.[86]

Atmosphere and spectra

Artist's impression of the WD J0914+1914 system.[87]

Although most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy typically shows that their emitted light comes from an atmosphere which is observed to be either hydrogen or helium dominated. The dominant element is usually at least 1,000 times more abundant than all other elements. As explained by Schatzman in the 1940s, the high surface gravity is thought to cause this purity by gravitationally separating the atmosphere so that heavy elements are below and the lighter above.[88][89]: §§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 phase and may also contain material accreted from the interstellar medium. The envelope is believed to consist of a helium-rich layer with mass no more than 1⁄100 of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1⁄10,000 of the star's total mass.[61][90]: §§4–5 

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore at almost the same temperature (

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.[61]

White dwarf spectral types[24]
Primary and secondary features
A H lines present
B He I lines
C Continuous spectrum; no lines
O He II lines, accompanied by He I or H lines
Z Metal 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,[59][91] and various classification schemes have been proposed and used since then.[92][93] 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 adjacent table), and a temperature index number, computed by dividing 50,400 K by the effective temperature
. For example:

  • A white dwarf with only He I 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, an effective temperature of 17,000 K, and a spectrum dominated by He I lines which also had hydrogen features could be given the classification of DBAP3.

The symbols "?" and ":" may also be used if the correct classification is uncertain.[24][59]

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs.[61] The next class in number is of DBs, approximately 16%.[94] The hot, above 15,000 K, DQ class (roughly 0.1%) have carbon-dominated atmospheres.[95] 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. 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.[90]: §2.4 [61]

H2) has been detected in spectra of the atmospheres of some white dwarfs.[96]

Metal-rich white dwarfs

Elements discovered in the atmosphere of white dwarfs colder than 25,000 K.

Around 25–33% of white dwarfs have metal lines in their spectra, which is notable because any heavy elements in a white dwarf should sink into the star's interior in just a small fraction of the star's lifetime.[97] The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky planetesimals.[97] The bulk composition of the accreted object can be measured from the strengths of the metal lines. For example, a 2015 study of the white dwarf Ton 345 concluded that its metal abundances were consistent with those of a differentiated, rocky planet whose mantle had been eroded by the host star's wind during its asymptotic giant branch phase.[98]

Magnetic field

Magnetic fields in white dwarfs with a strength at the surface of c. 1 million

circularly polarized light.[103] It is thought to have a surface field of approximately 300 million gauss (30 kT).[89]
: §8 

Since 1970, magnetic fields have been discovered in well over 200 white dwarfs, ranging from 2×103 to 109 gauss (0.2 T to 100 kT).[104] The large number of presently known magnetic white dwarfs is due to the fact that most white dwarfs are identified by low-resolution spectroscopy, which is able to reveal the presence of a magnetic field of 1 megagauss or more. Thus the basic identification process also sometimes results in discovery of magnetic fields.[105] It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).[106][107]

The highly magnetized white dwarf in the binary system AR Scorpii was identified in 2016 as the first pulsar in which the compact object is a white dwarf instead of a neutron star.[108]

Chemical bonds

The magnetic fields in a white dwarf may allow for the existence of a new type of

ionic and covalent bonds, resulting in what has been initially described as "magnetized matter" in research published in 2012.[109]

Variability

Main article: Pulsating white dwarf
See also: Cataclysmic variables
Types of pulsating white dwarf[110][111]: §§1.1, 1.2 
DAV (
GCVS
: ZZA)		 DA
absorption lines
in its spectrum
DBV (GCVS: ZZB) DB spectral type, having only helium absorption lines in its spectrum
GW Vir (GCVS: ZZO) Atmosphere mostly C, He and O; may be divided into DOV and PNNV stars

Early calculations suggested that there might be white dwarfs whose luminosity

GW Vir stars, sometimes subdivided into DOV and PNNV stars, with atmospheres dominated by helium, carbon, and oxygen.[111][114] 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 and the white dwarf region. They may be called pre-white dwarfs.[111][115] 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 evidence about the interiors of white dwarfs.[116]

Formation

White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about 0.07 to 10 M☉.[4][117] The composition of the white dwarf produced will depend on the initial mass of the star. Current galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs.[118]

Stars with very low mass

If the mass of a main-sequence star is lower than approximately half a solar mass, it will never become hot enough to fuse helium in its core.[citation needed] It is thought that, over a lifespan that considerably exceeds the age of the universe (c. 13.8 billion years),[9] such a star will eventually burn all its hydrogen, for a while becoming a blue dwarf, and end its evolution as a helium white dwarf composed chiefly of helium-4 nuclei.[119] Due to the very long time this process takes, it is not thought to be the origin of the observed helium white dwarfs. Rather, they are thought to be the product of mass loss in binary systems[5][7][8][120][121][122] or mass loss due to a large planetary companion.[123][124]

Stars with low to medium mass

If the mass of a main-sequence star is between 0.5 and 8 M☉[citation needed] like the Sun, its core will become sufficiently hot to fuse helium into carbon and oxygen via the triple-alpha process, but it will never become sufficiently hot to fuse carbon into neon. 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. It will then expel most of its outer material, creating a planetary nebula, 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.[120][125][126]

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, initially supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will

compact star.[117][127] Some main-sequence stars, of perhaps 8 to 10 M☉, although sufficiently massive to fuse carbon to neon and magnesium, may be insufficiently massive to fuse neon. Such a star may leave a remnant white dwarf composed chiefly of oxygen, neon, and magnesium, 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.[128][129] Although a few white dwarfs have been identified which may be of this type, most evidence for the existence of such comes from the novae called ONeMg or neon novae. The spectra of these novae 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.[6][130][131]

Type Iax supernova

hypervelocity star. The matter processed in the failed detonation is re-accreted by the white dwarf with the heaviest elements such as iron falling to its core where it accumulates.[132] These iron-core white dwarfs would be smaller than the carbon–oxygen kind of similar mass and would cool and crystallize faster than those.[133]

Fate

Artist's concept of white dwarf aging
Internal structures of white dwarfs. To the left is a newly formed white dwarf, in the center is a cooling and crystallizing white dwarf, and the right is a black dwarf.

A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf. Assuming that the

grand unified theories predict a proton lifetime between 1030 and 1036 years. If these theories are not valid, the proton might still decay by complicated nuclear reactions or through quantum gravitational processes involving virtual black holes; 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 decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely.[134]
: §IV 

A white dwarf can also be cannibalized or evaporated by a companion star, causing the white dwarf to lose so much mass that it becomes a

planetary mass object. The resultant object, orbiting the former companion, now host star, could be a helium planet or diamond planet.[135][136]

Debris disks and planets

Artist's impression of debris around a white dwarf[137]
Comet falling into white dwarf (artist's impression)[138]

A white dwarf's

stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. There are several indications that a white dwarf has a remnant planetary system.[citation needed
]

The most common observable evidence of a remnant planetary system is pollution of the spectrum of a white dwarf with

Kuiper Belt objects, the lithium is thought to come from accreted crust material and the beryllium is thought to come from exomoons.[143]

A less common observable evidence is infrared excess due to a flat and optically thick debris disk, which is found in around 1–4% of white dwarfs.

Poynting–Robertson drag, which is stronger for less massive white dwarfs. The Poynting–Robertson drag will also cause the dust to orbit closer and closer towards the white dwarf, until it will eventually sublimate and the disk will disappear. A debris disk will have a lifetime of around a few million years for white dwarfs hotter than 10,000 K. Colder white dwarfs can have disk-lifetimes of a few 10 million years, which is enough time to tidally disrupt a second rocky body and forming a second disk around a white dwarf, such as the two rings around LSPM J0207+3331.[148]

The least common observable evidence of planetary systems are detected major or minor planets. Only a handful of giant planets and a handful of minor planets are known around white dwarfs.

Roche radius of the white dwarf.[161] The mechanism behind the pollution of white dwarfs in binaries was also explored as these systems are more likely to lack a major planet, but this idea cannot explain the presence of dust around single white dwarfs.[162] While old white dwarfs show evidence of dust accretion, white dwarfs older than ~1 billion years or >7000 K with dusty infrared excess were not detected[163] until the discovery of LSPM J0207+3331 in 2018, which has a cooling age of ~3 billion years. The white dwarf shows two dusty components that are being explained with two rings with different temperatures.[141]

Planets around white dwarfs
System name host star minor planet? Number of planets Mass planet (MJ) semi-major axis (au or R☉) discovery method discovery year Note Reference
PSR B1620-26 white dwarf+pulsar 1 2.5±1 23 au pulsar timing 1993 [164]
NN Serpentis PCEB: white dwarf+red dwarf 2 c: 6.91±0.54

d: 2.28±0.38

c: 5.38±0.20 au

d: 3.39±0.10 au

eclipse timing variation 2010 PCEB is surrounded by a dusty disk,[165] might be only one planet[166] [167]
WD 0806-661 single 1 1.5-8 2500 au direct imaging 2011 WD 0806-661 B can be interpreted as either a sub-brown dwarf or an exoplanet. [168][169]
WD J0914+1914 single 1 15-16 R☉ detection of accreted planet material via spectroscopy 2019 likely ice giant [170]
WD 1856+534 single 1 >0.84[171] 4 R☉ transiting 2020 the white dwarf co-moves with G 229-20 A/B [172][173][174]
MOA-2010-BLG-477L single 1 1.5+1.8
−0.3 		1-5 au microlensing 2012/2021 a Jupiter-analogue [175]
WD 1145+017 single minor planet 1 1.16 R☉[176] transiting 2015 [177]
SDSS J1228+1040 single minor planet 1 0.73 R☉ variable Calcium absorption line 2019 orbits within the debris disk of the white dwarf [178]
WD 0145+234 single minor planet 1 1.2 R☉[179] tidal disruption event 2019 [180]
ZTF J0139+5245 single minor planet 1 0.36 au transiting 2020 highly eccentric orbit (e>0.97)[149] [181][182]
ZTF J0328-1219 single minor planet 2 b: 2.11 R☉

c: 2.28 R☉

transiting 2021 discovery paper also describes candidates around 4 other white dwarfs [183][184]

The metal-rich white dwarf WD 1145+017 is the first white dwarf observed with a disintegrating minor planet which transits the star.[185][177] The disintegration of the planetesimal generates a debris cloud which passes in front of the star every 4.5 hours, causing a 5-minute-long fade in the star's optical brightness.[177] The depth of the transit is highly variable.[177]

The giant planet

hydrogen line as well as other lines in the spectrum of the white dwarf revealed the presence of the giant planet.[170]

The white dwarf

NEOWISE data. The brightening is not seen before 2018. It is interpreted as the tidal disruption of an exoasteroid, the first time such an event has been observed.[180]

WD 1856+534 is the first and only transiting major planet around a white dwarf (as of 2022).

LAWD 37 are suspected to have giant exoplanets due to anomaly in the Hipparcos-Gaia proper motion. For GD 140 it is suspected to be a planet several times more massive than Jupiter and for LAWD 37 it is suspected to be a planet less massive than Jupiter.[186][187] Additionally, WD 0141-675 was suspected to have a super-Jupiter with an orbital period of 33.65 days based on Gaia astrometry. This is remarkable because WD 0141-675 is polluted with metals and metal polluted white dwarfs have long be suspected to host giant planets that disturb the orbits of minor planets, causing the pollution.[188] Both GD 140 and WD 0141 will be observed with JWST in cycle 2 with the aim to detect infrared excess caused by the planets.[189] However, the planet candidate at WD 0141-675 was found to be a false positive caused by a software error.[190]

A JWST survey of four metal polluted white dwarfs found two directly imaged exoplanet candidates with masses of 1-7 MJ. One orbits around WD 1202−232 (LP 852-7) and the other around WD 2105−82 (LAWD 83). If confirmed they would be the first directly imaged planets that likely formed from circumstellar disk material, representing a new population of directly imaged giant planets that are more similar to solar system giants in age and probably also in their atmosphere. Confirmation will be possible via the common proper motion method with JWST.[191]

In 2024 it was discovered that the white dwarf in the

PHL 5038AB system is polluted with calcium from rocky material. The white dwarf is orbited by a brown dwarf, which was discovered in 2009. This is seen as perhaps the first case of linking white dwarf pollution with the presence of a substellar object. It is thought that the orbits of planetesimals are being disrupted by the brown dwarf, causing the pollution of the white dwarf.[192]

Habitability

It has been proposed that white dwarfs with surface temperatures of less than 10,000 Kelvins could harbor a

transits of hypothetical Earth-like planets that could have migrated inward or formed there. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong eclipses.[193] Newer research casts some doubts on this idea, given that the close orbits of those hypothetical planets around their parent stars would subject them to strong tidal forces that could render them uninhabitable by triggering a greenhouse effect.[194] Another suggested constraint to this idea is the origin of those planets. Leaving aside formation from the accretion disk surrounding the white dwarf, there are two ways a planet could end in a close orbit around stars of this kind: by surviving being engulfed by the star during its red giant phase, and then spiralling inward, or inward migration after the white dwarf has formed. The former case is implausible for low-mass bodies, as they are unlikely to survive being absorbed by their stars. In the latter case, the planets would have to expel so much orbital energy as heat, through tidal interactions with the white dwarf, that they would likely end as uninhabitable embers.[195]

Binary stars and novae

The merger process of two co-orbiting white dwarfs produces gravitational waves

If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including

super-soft x-ray source if it is able to take material from its companion fast enough to sustain fusion on its surface.[196] On the other hand, phenomena in binary systems such as tidal interaction and star–disc interaction, moderated by magnetic fields or not, act on the rotation of accreting white dwarfs. In fact, the (securely known) fastest-spinning white dwarfs are members of binary systems (the fastest one being the white dwarf in CTCV J2056-3014).[197] A close binary system of two white dwarfs can radiate energy in the form of gravitational waves, causing their mutual orbit to steadily shrink until the stars merge.[198][199]

Type Ia supernovae

Main article: Type Ia supernova

The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1.4 M☉. This limit may increase if the white dwarf is rotating rapidly and nonuniformly.

binary systems 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 in the white dwarf or its collapse into a neutron star.[47]

Accretion provides the currently favored mechanism called the single-degenerate model for

thermonuclear flame consumes much of the white dwarf in a few seconds, causing a Type Ia supernova explosion that obliterates the star.[1][48][201] 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.[48]
: 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 high rate by the same process. Once the accretion stops, the star gradually slows until the spin is no longer enough to prevent the explosion.[202]

The historical bright

WD 0810-353.[205]

Post-common envelope binary

Main article: Post common envelope binary

A post-common envelope binary (PCEB) is a binary consisting of a white dwarf and a closely tidally-locked red dwarf (in other cases this might be a brown dwarf instead of a red dwarf). These binaries form when the red dwarf is engulfed in the red giant phase. As the red dwarf orbits inside the common envelope, it is slowed down in the denser environment. This slowed orbital speed is compensated with a decrease of the orbital distance between the red dwarf and the core of the red giant. The red dwarf spirals inwards towards the core and might merge with the core. If this does not happen and instead the common envelope is ejected, then the binary ends up in a close orbit, consisting of a white dwarf and a red dwarf. This type of binary is called a post-common envelope binary. The evolution of the PCEB continues as the two dwarf stars orbit closer and closer due to magnetic braking and by releasing gravitational waves. The binary might evolve at some point into a cataclysmic variable, and therefore post-common envelope binaries are sometimes called pre-cataclysmic variables.

Cataclysmic variables

Main article: Cataclysmic variable star

Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by

cataclysmic variables. As well as novae and dwarf novae, several other classes of these variables are known, including polars and intermediate polars, both of which feature highly magnetic white dwarfs.[1][48][206][207] Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.[207]

Other non-pre-supernova binaries

Other non-pre-supernova binaries include binaries that consist of a

Gaia DR2 data. One interesting field is the study of remnant planetary systems around white dwarfs. While stars are bright and often outshine the exoplanets and brown dwarfs that orbit them, the white dwarfs are faint. This allows astronomers to study these brown dwarfs or exoplanets in more detail. The sub-brown dwarf around the white dwarf WD 0806−661
is one such example.

Nearest

White Dwarfs within 25 Light Years[208]
Identifier WD Number Distance (
ly
) 		Type Absolute
magnitude 		Mass
(M☉) 		Luminosity
(L☉) 		Age (
Gyr
) 		Objects in system
Sirius B 0642–166 8.66 DA 11.18 0.98 0.0295 0.10 2
Procyon B 0736+053 11.46 DQZ 13.20 0.63 0.00049 1.37 2
Van Maanen 2 0046+051 14.07 DZ 14.09 0.68 0.00017 3.30 1
LP 145-141
 1142–645 15.12 DQ 12.77 0.61 0.00054 1.29 1
40 Eridani B 0413-077 16.39 DA 11.27 0.59 0.0141 0.12 3
Stein 2051 B 0426+588 17.99 DC 13.43 0.69 0.00030 2.02 2
G 240-72 1748+708 20.26 DQ 15.23 0.81 0.000085 5.69 1
Gliese 223.2
 0552–041 21.01 DZ 15.29 0.82 0.000062 7.89 1
Gliese 3991 B[209]
 1708+437 24.23 D?? >15 0.5 <0.000086 >6 2

Gallery

  • Illustration of rocky debris around a white dwarf [210]
    Illustration of rocky debris around a white dwarf
    [210]
  • Cocoon of a new white dwarf in the centre of NGC 2440
    Cocoon of a new white dwarf in the centre of NGC 2440
  • Artist's impression of an evolving white dwarf and millisecond pulsar binary system [211]
    Artist's impression of an evolving white dwarf and millisecond pulsar binary system
    [211]
  • Illustration of an ultracool dwarf with a companion white dwarf [212]
    Illustration of an
    ultracool dwarf with a companion white dwarf
    [212]

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External links and further reading

Wikimedia Commons has media related to White dwarfs.

General

Physics

Variability

  • Winget, D.E. (1998). "Asteroseismology of white dwarf stars". Journal of Physics: Condensed Matter. 10 (49): 11247–11261.
    S2CID 250749380
    .

Magnetic field

Frequency

Observational

Images

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