# White dwarf

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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 pinprick of light to the lower left of the much brighter Sirius A.

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A white dwarf, also called a degenerate dwarf, is a stellar remnant composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun, and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored thermal energy.[1] The nearest known white dwarf is Sirius B, 8.6 light years away, the smaller component of the Sirius binary star. There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun.[2] The unusual faintness of white dwarfs was first recognized in 1910 by Henry Norris Russell, Edward Charles Pickering, and Williamina Fleming;[3], p. 1 the name white dwarf was coined by Willem Luyten in 1922.[4]

White dwarfs are thought to be the final evolutionary state of all stars whose mass is not high enough to become a neutron star (including our Sun)—over 97% of the stars in the Milky Way.[5], §1. After the hydrogenfusing lifetime of a main-sequence star of low or medium mass ends, it will expand to a red giant which 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 shedding its outer layers to form a planetary nebula, it will leave behind this core, which forms the remnant white dwarf.[6] Usually, therefore, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is between 8 and 10.5 solar masses (Template:Solar mass), the core temperature is sufficient to fuse carbon but not neon, in which case an oxygen-neon–magnesium white dwarf may be formed.[7] Also, some helium white dwarfs[8][9] 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. It 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 1.4 Template:Solar mass—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][6] (SN 1006 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. 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 to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf.[6] However, 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 universe (approximately 13.8 billion years),[10] and since no white dwarf can be older than the age of the universe, it is thought that no black dwarfs yet exist.[1][5] The oldest white dwarfs still radiate at temperatures of a few thousand kelvins.

## Discovery

The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the relatively bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C. The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783;[11], p. 73 it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve in 1851.[12][13] In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white.[4] In 1939, Russell looked back on the discovery:[3], 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.[14]

The 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:[15]

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;[15] C. A. F. Peters computed an orbit for it in 1851.[16] 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.[16] Walter Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.[17]

In 1917, Adriaan van Maanen discovered Van Maanen's Star, an isolated white dwarf.[18] These three white dwarfs, the first discovered, are the so-called classical white dwarfs.[3], p. 2 Eventually, many faint white stars were found which had high proper motion, 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;[4][19][20][21][22] the term was later popularized by Arthur Stanley Eddington.[4][23] 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], p. 3 Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known,[24] and by 1999, over 2,000 were known.[25] Since then the Sloan Digital Sky Survey has found over 9,000 white dwarfs, mostly new.[26]

## Composition and structure

Template:Star nav Although white dwarfs are known with estimated masses as low as 0.17[27] and as high as 1.33 Template:Solar mass,[28] the mass distribution is strongly peaked at 0.6 Template:Solar mass, and the majority lie between 0.5 to 0.7 Template:Solar mass.[28] The estimated radii of observed white dwarfs, however, are typically between 0.008 and 0.02 times the radius of the Sun;[29] 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 g/cm3, or 1 tonne per cubic centimetre.[1] A typical white dwarf star has a density of between 10 7 and 1011 kg per cubic meter. A normal-sized matchbox containing white dwarf material would have a mass of some 250 tonnes. White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars, black holes and, hypothetically, quark stars.[30]

White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary 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,[31] yielding a mass estimate of 0.94 Template:Solar mass. (A more modern estimate is 1.00 Template:Solar mass.)[32] Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and hence from its spectrum. 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 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".[33] As Arthur Stanley Eddington put it later in 1927:[34], 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, the light from Sirius B should be gravitationally redshifted.[23] This was confirmed when Adams measured this redshift in 1925.[35]

Material Density in kg/m3 Notes
Water (fresh) 1,000 At STP
Osmium 22,610 Near room temperature
The core of the Sun ~150,000
White dwarf star 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
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 atoms joined by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer to each other than electron orbitals—the regions occupied by electrons bound to an atom—would normally allow.[23] Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present.[38] This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle.[39] At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ground, 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, 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, we can see that this will increase the kinetic energy of the electrons, increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. 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 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 is another consequence of being supported by electron degeneracy pressure. These masses were first published in 1929 by Wilhelm Anderson[42] and in 1930 by Edmund C. Stoner.[43] The modern value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs".[44] For a non-rotating white dwarf, it is equal to approximately 5.7/μe2 Template:Solar mass, where μe is the average molecular weight per electron of the star.[45], eq. (63) As the carbon-12 and oxygen-16 which predominantly compose a carbon-oxygen white dwarf both have atomic number equal to half their atomic weight, one should take μe equal to 2 for such a star,[40] leading to the commonly quoted value of 1.4 Template:Solar mass. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,[43], 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 Template:Solar mass.) 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] However, 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 is destroyed, just before reaching 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 elliptical galaxies such collisions are the major source of supernovae. This hypothesis is based on the fact that less X-rays than expected are produced by the white dwarfs' accretion of matter. 30 to 50 times more X-rays would be expected to be produced by an amount of matter falling onto a population of accreting white dwarfs sufficient to produce supernovae at the observed rate. It has been concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion onto 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 candles in determining distances across the universe.[49]

White dwarfs have low luminosity 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, such as the 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 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 and kinetic energy. The gravitational potential energy of a unit mass piece of white dwarf, Eg, will be on the order of GM ∕ R, where Template:Mvar is the gravitational constant, M is the mass of the white dwarf, and Template:Mvar is its radius. The kinetic energy of the unit mass, Ek, will primarily come from the motion of electrons, so it will be approximately Np2 ∕ 2m, where Template:Mvar is the average electron momentum, Template:Mvar is the electron mass, and Template:Mvar is the number of electrons per unit mass. Since the electrons are degenerate, we can estimate Template:Mvar to be on the order of the uncertainty in momentum, Δp, given by the uncertainty principle, which says that Δp Δx is on the order of the reduced Planck constant, 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, Template:Mvar, of electrons per unit volume. Since there are NM electrons in the white dwarf and its volume is on the order of R3, Template:Mvar will be on the order of NM ∕ R3.[40]

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

${\displaystyle E_{k}\approx {\frac {N(\Delta p)^{2}}{2m}}\approx {\frac {N\hbar ^{2}n^{2/3}}{2m}}\approx {\frac {M^{2/3}N^{5/3}\hbar ^{2}}{2mR^{2}}}.}$

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:

${\displaystyle |E_{g}|\approx {\frac {GM}{R}}=E_{k}\approx {\frac {M^{2/3}N^{5/3}\hbar ^{2}}{2mR^{2}}}.}$

Solving this for the radius, Template:Mvar, gives[40]

${\displaystyle R\approx {\frac {N^{5/3}\hbar ^{2}}{2mGM^{1/3}}}.}$

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

${\displaystyle R\sim M^{-1/3}}$

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, Template:Mvar, we should replace p2 ∕ 2m by the extreme relativistic approximation pc for the kinetic energy. With this substitution, we find

${\displaystyle E_{k\ {\rm {relativistic}}}\approx {\frac {M^{1/3}N^{4/3}\hbar c}{R}}.}$

If we equate this to the magnitude of Eg, we find that Template:Mvar drops out and the mass, Template:Mvar, is forced to be[40]

${\displaystyle M_{\rm {limit}}\approx N^{2}\left({\frac {\hbar c}{G}}\right)^{3/2}.}$
Radius–mass relations for a model white dwarf. Mlimit is denoted as MCh

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 Template:Mvar, the extreme relativistic analysis becomes more exact, meaning that the mass Template:Mvar of the white dwarf must approach Mlimit. Therefore, no white dwarf can be heavier than the limiting mass Mlimit, or 1.4 Template:Solar mass.

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state 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.[45], 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—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 centrifugal pseudo-force arising from working in a rotating frame.[53] For a uniformly rotating white dwarf, the limiting mass increases only slightly. However, if the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in 1947,[54] 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 stable.[55]

### Radiation and cooling

The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, 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. 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 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.[56]

The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type main sequence star to the red of an M-type red dwarf.[57] White dwarf effective surface temperatures extend from over 150,000 K[25] to barely under 4,000 K.[58][59] 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 1/10,000 that of the Sun's.[59] 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-rays. This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations.[60]

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.[61][62], §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.[6] 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, have estimated the rate of cooling for a carbon white dwarf of 0.59 Template:Solar mass with a hydrogen atmosphere. After initially cooling 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.[63], Table 2.

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K.[26][64] 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.[65] This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K,[66] and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K.[58] The reason for this is that, as the Universe's age is finite,[67][68] 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.[65] A white dwarf will eventually, in many trillion years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. However, no black dwarfs are thought to exist yet.[1]

Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star.[69] The crystal structure is thought to be a body-centered cubic lattice.[5][70] In 1995 it was pointed out that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,[71] 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 had crystallized.[69][72][73] Other work gives a crystallized mass fraction of between 32% and 82%.[74] As a white dwarf core undergoes crystallization into a solid phase, latent heat is released which provides a source of thermal energy that delays the gradual cooling of the star.[75]

Low-mass helium white dwarfs (with a mass < 0.20 Msun, often referreed 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.[76]

### Atmosphere and spectra

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-dominated 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 on the bottom and lighter ones on top.[77][78], §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 stars total mass.[59][79], §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 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.[59]

White dwarf spectral types[25]
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,[57][80] and various classification schemes have been proposed and used since then.[81][82] 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. 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.[25][57]

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs.[59] The next class in number is of DBs (approximately 16%).[83] A small fraction (roughly 0.1%) have carbon-dominated atmospheres, the hot (above 15,000 K) DQ class.[84] 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.[79],§ 2.4.[59]

#### Molecular hydrogen in white dwarf atmospheres

{{#invoke:main|main}} In 2013 S. Xu, M. Jura, D. Koster, B. Klein, and B. Zuckerman published a scientific paper in Astrophysical Journal Letters announcing the discovery of H2 in white dwarf stellar atmospheres [85]

### Magnetic field

Magnetic fields in white dwarfs with a strength at the surface of ~1 million gauss (100 teslas) 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.[86] This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted.[87], pp. 39–43 In the 1960s, it was proposed that white dwarfs might have magnetic fields because of conservation of total surface magnetic flux 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.[78], §8;[88], p. 484 The first magnetic white dwarf to be observed was GJ 742, which was detected to have a magnetic field in 1970 by its emission of circularly polarized light.[89] It is thought to have a surface field of approximately 300 million gauss (30 kT).[78], §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).[90][91]

#### Chemical bonds

The magnetic fields in a white dwarf star may allow for the existence of a new type of chemical bond, perpendicular paramagnetic bonding, in addition to ionic and covalent bonds, resulting in what has been initially described as "magnetized matter" in research published in 2012.[92]

## Variability

 DAV (GCVS: ZZA) DA spectral type, having only hydrogen 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 Types of pulsating white dwarf[93][94], §1.1, 1.2.

Early calculations suggested that there might be white dwarfs whose luminosity varied with a period of around 10 seconds, but searches in the 1960s failed to observe this.[78], § 7.1.1;[95] The first variable white dwarf found was HL Tau 76; in 1965 and 1966, Arlo U. Landolt observed it to vary with a period of approximately 12.5 minutes.[96] 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 pulsations.[78], § 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;[78], pp. 891, 895 DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;[59], p. 3525 and GW Vir stars (sometimes subdivided into DOV and PNNV stars), with atmospheres dominated by helium, carbon, and oxygen.[94],§1.1, 1.2;[97],§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 and the white dwarf region. They may be called pre-white dwarfs.[94], § 1.1;[98] 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.[99]

## 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 Template:Solar mass.[5][100] 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, it will never become hot enough to fuse helium at its core. It is thought that, over a lifespan that considerably exceeds the age (~13.8 billion years)[10] 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 nuclei.[101] Owing to the very long 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[6][8][9][102][103][104] or mass loss due to a large planetary companion.[105][106]

### Stars with low to medium mass

If the mass of a main-sequence star is between approximately 0.5 to 8 Template:Solar mass, 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.[102][107][108]

### 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, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will collapse and it will explode in a core-collapse supernova which will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star.[100][109] Some main-sequence stars, of perhaps 8 to 10 Template:Solar mass, 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[110][111] 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 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.[7][112][113]

### Type Ia supernovae

Type Ia supernovae, that involve one or two previous white dwarfs, have been proposed to be a channel for transformation of this type of stellar remmant. In this scenario, the carbon detonation produced in a Type Ia supernova is too weak to destroy the white dwarf, expelling just a small part of its mass as ejecta and producing an asymmetric explosion that kicks the star at high speeds as a Hypervelocity star. The matter processed in the failed detonation is re-accreted back by the white dwarf with the heaviest elements such as iron falling to its core and accumulating there.[114]

These iron-core white dwarfs would be smaller than their carbon-oxygen kind of similar mass and would cool and crystallize faster than them.[115]

## Fate

Artist’s impression of debris around a white dwarf star.[116]

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. Assuming that the Universe continues to expand, it is thought that in 1019 to 1020 years, the galaxies will evaporate as their stars escape into intergalactic space.[117], §IIIA. White dwarfs should generally survive this, although an occasional collision between white dwarfs may produce a new fusing star or a super-Chandrasekhar mass white dwarf which will explode in a Type Ia supernova.[117], §IIIC, IV. The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the proton, known to be at least 1032 years. Some simple grand unified theories predict a proton lifetime 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 processes involving a virtual black hole; 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.[117], §IV.

## Debris disks and planets

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

A white dwarf's stellar and planetary system 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 of the central star of the Helix Nebula 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.[118][119] Similarly, observations made in 2004 indicated the presence of a dust cloud around the young white dwarf G29-38 (estimated to have formed from its AGB progenitor about 500 million years ago), which may have been created by tidal disruption of a comet passing close to the white dwarf.[120] Some estimations based on the metal content of the atmospheres of the white dwarfs consider that at least a 15% of them may be orbited by planets and/or asteroids, or at least their debris.[121] Another suggested idea is that white dwarfs could be orbited by the stripped cores of rocky planets, that would have survived the red giant phase of their star but losing their outer layers and, given those planetary remnants would likely be made of metals, to attempt to detect them looking for the signatures of their interaction with the white dwarf's magnetic field.[122]

There is a planet in the white dwarf–pulsar binary system PSR B1620-26.

There are two circumbinary planets around the white dwarf–red dwarf binary NN Serpentis.

## Habitability

It has been proposed that white dwarfs with surface temperatures of less than 10,000 Kelvin could harbor a habitable zone at a distance between ~0.005 to 0.02 AU that would last 3 billion years. The goal is to search for transits of hypothetical Earth-like planets that could have migrated inward and/or formed there. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong eclipses.[123] Newer research, however, 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 unhabitable by triggering a greenhouse effect.[124] Another suggested constraint to this idea is the origin of those planets. Leaving aside in-situ formation on an 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 spiraling towards its core, 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.[125]

## Binary stars and novae

If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including novae and Type Ia supernovae. It may also be a super-soft x-ray source if it is able to take material from its companion fast enough to sustain fusion on its surface.[126] 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.[127][128]

### Type Ia supernovae

{{#invoke:main|main}} The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1.4 Template:Solar mass. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly.)[129] 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 in the white dwarf or its collapse into a neutron star.[47]

Accretion provides the currently favored mechanism, the single-degenerate model, for Type Ia supernovae. In this model, a carbonoxygen white dwarf accretes material from a companion star,[48], p. 14. increasing its mass and compressing its core. It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit.[48] 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 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.[1][48][130] 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], 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.[131]

### Cataclysmic variables

{{#invoke:main|main}} 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 hydrogen fusion. 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. Astronomers have also observed dwarf novae, 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 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.[1][48][132][133] Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.[133]

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### General

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### Physics

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