White dwarf

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. 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. This star was far out of the normal pattern when Russell first created his now famous luminosity (brightness) versus spectral type (color) diagram. Publicly Russell suggested that the spectral type may not be correct. However the spectral type of 40 Eridani B was independently confirmed in 1914 by Walter Adams. In 1939, Russell looked back on the discovery and noted that Pickering had suggested that such exceptions lead to breakthroughs and in this case it led to the discovery of white dwarfs. Bessel roughly estimated the period of the companion of Sirius to be about half a century; 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. In 1917, Adriaan van Maanen discovered van Maanen's Star, an isolated white dwarf. These three white dwarfs, the first discovered, are the so-called classical white dwarfs. he used the term dwarf; the term was later popularized by Arthur Eddington as white dwarf. and by 1999, over 2000 were known. Since then the Sloan Digital Sky Survey has found over 9000 white dwarfs, mostly new. Theory development The extreme density of white dwarf stars was initially a theoretical puzzle. If a star is in a binary system, as is the case for Sirius B or 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 (which compares well with a more modern estimate of ). Since hotter bodies radiate more energy than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and star's spectrum gives its temperature. 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 visual binary stars in 1916, he found that 40 Eridani B had a density of over  times that of the Sun, which was so high that he called it "impossible". As Eddington put it in 1927: 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 3000 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." 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 than normally allowed by electron orbitals limited by normal matter. Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient. 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 that satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons cannot all occupy the lowest-energy, or ground, state; some of them would have 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. and in 1930 by Edmund C. Stoner. This value was corrected by considering hydrostatic equilibrium for the density profile, and the presently known value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs". For a non-rotating white dwarf, it is equal to approximately , where is the average molecular weight per electron of the star. As the carbon-12 and oxygen-16 that predominantly compose a carbon–oxygen white dwarf both have atomic numbers equal to half their atomic weight, one should take equal to 2 for such a star, leading to the commonly quoted value of . (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements, The limiting mass is now called the Chandrasekhar limit. == Occurrence ==

Galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs. There are currently thought to be eight white dwarfs among the one hundred star systems nearest the Sun. The nearest and brightest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. The population of white dwarf stars is expected to grow. Existing stars with masses from about include over 97% of the stars in the Milky Way and these stars will evolve into white dwarfs. == Composition and structure ==

Although white dwarfs are known with estimated masses as low as and as high as , the mass distribution is strongly peaked at , and the majority lie between . this is comparable to the Earth's radius of approximately 0.9% solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically one millionth of the Sun's; the average density of matter in a white dwarf must therefore be, very roughly,  times greater than the average density of the Sun, or approximately , or 1 tonne per cubic centimetre. A typical white dwarf has a density of between 104 and . White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars and the hypothetical quark stars. Core types A typical white dwarf star, a CO white dwarf, is 99% carbon and oxygen by mass, with the remainder being a thin layer of He and H. Main sequence stars close to the upper mass limit of are thought to fuse carbon into neon, forming O-Ne white dwarf stars. Very light stars, below never fuse He into carbon and oxygen so they form He-core white dwarfs. If a carbon-oxygen white dwarf accreted enough matter to reach the Chandrasekhar limit of about 1.44 solar masses (for a non-rotating star), it would no longer be able to support the bulk of its mass through electron degeneracy pressure The current view is that this limit is not normally attained; increasing temperature and density inside the core ignite carbon fusion as the star approaches the limit (to within about 1%) before collapse is initiated. In contrast, for a core primarily composed of oxygen, neon and magnesium, the collapsing white dwarf will typically form a neutron star. In this case, only a fraction of the star's mass will be ejected during the collapse. If a white dwarf star accumulates sufficient material from a stellar companion to raise its core temperature enough to ignite carbon fusion, it will undergo runaway nuclear fusion, completely disrupting it. There are three avenues by which this detonation is theorised to happen: stable accretion of material from a companion, the collision of two white dwarfs, or accretion that causes ignition in a shell that then ignites the core. The dominant mechanism by which Type Ia supernovae are produced remains unclear. Despite this uncertainty in how Type Ia supernovae are produced, Type Ia supernovae have very uniform properties and are useful standard candles over intergalactic distances. Some calibrations are required to compensate for the gradual change in properties or different frequencies of abnormal luminosity supernovae at high redshift, and for small variations in brightness identified by light curve shape or spectrum. Mass–radius relationship The relationship between the mass and radius of white dwarfs can be estimated using the nonrelativistic Fermi gas equation of state, which gives \frac{R}{R_\odot} \approx 0.012\left ( \frac{M}{M_\odot}\right )^{-1/3} \left (\frac{\mu_e}{2}\right)^{-5/3}, where is the radius, is the mass of the white dwarf, and the subscript \odot indicates the Sun; therefore {R} / {R_\odot} is the radius in units of solar radius and {M} / {M_\odot} is the mass in units of solar mass. The chemical potential, \mu_e is a thermodynamic property giving the change in energy as one electron is added or removed; it relates to the composition of the star. Numerical treatment of more complete models have been tested against observational data with good agreement. Since this analysis uses the non-relativistic formula 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 where is the speed of light, and it can be shown that the Fermi gas model has no stable equilibrium in the ultrarelativistic limit. In particular, this analysis yields the maximum mass of a white dwarf, which is: 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. If the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle 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 will be dynamically stable. 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. The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously. Radiation and cooling 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, or the even lower-temperature brown dwarfs. 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. White dwarf luminosity varies over 7 orders of magnitude, from over 100 times that of the Sun to under that of the Sun. Hot white dwarfs, with surface temperatures in excess of , 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. White dwarfs also radiate neutrinos through the Urca process. This process has more effect on hotter and younger white dwarfs. Because neutrinos can pass easily through stellar plasma, they can drain energy directly from the dwarf's interior; this mechanism is the dominant contribution to cooling for approximately the first 20 million years of a white dwarf's existence. An outer shell of non-degenerate matter sits on top of the degenerate core. The outermost layers, which are cooler than the interior, 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. White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. Most observed white dwarfs have relatively high surface temperatures, between 8000 K and . This trend stops at extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below , and one of the coolest so far observed, WD J2147–4035, has a surface temperature of approximately 3050 K. The reason for this is that the Universe's age is finite; there has not been enough time for white dwarfs to cool 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 our galactic disk found in this way is 8 billion years. The crystal structure is thought to be a body-centered cubic lattice. In 1995 it was suggested that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory, and in 2004, observations were made that suggested approximately 90% of the mass of BPM 37093 had crystallized. Other work gives a crystallized mass fraction of between 32% and 82%. 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. Another possible mechanism that was suggested to explain this cooling anomaly in some types of white dwarfs 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. Chemical fractionation between the ionic species in the plasma mixture can release a similar or even greater amount of energy. This energy release was first confirmed in 2019 after the identification of a pile up in the cooling sequence of more than white dwarfs observed with the Gaia satellite. Low-mass helium white dwarfs (mass ), 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 for hundreds of millions of years. In addition, they remain in a bloated proto-white dwarf stage for up to 2 Gyr before they reach the cooling track. Atmosphere and spectra system Although most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy typically shows that their emitted light comes from an atmosphere that is observed to be either hydrogen or helium dominated. The dominant element is usually at least 1000 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. This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope that 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 of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately of the star's total mass. 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 that 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 by the effective temperature. For example, a white dwarf with only  He  lines in its spectrum and an effective temperature of could be given the classification of "DB3", or, if warranted by the precision of the temperature measurement, "DB3.5". Likewise, a white dwarf with a polarized magnetic field, an effective temperature of , and a spectrum dominated by  He  lines that also had hydrogen features could be given the classification of DBAP3. The symbols "?" and ":" may also be used if the correct classification is uncertain. 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 to , the spectrum will be classified DO, dominated by singly ionized helium. From to , the spectrum will be DB, showing neutral helium lines, and below about , the spectrum will be featureless and classified DC. While theoretical work suggests that some types of white dwarfs may have stellar corona, searches at X-ray and radio wavelengths, where coronae are most easily detected, have been unsuccessful. A few white dwarfs have been observed to have inhomogeneous atmosphere with one side dominated by hydrogen and the other side dominated by helium. Metal-rich white dwarfs 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. The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky planetesimals. 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. This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted. In the 1960s, it was proposed that white dwarfs might have magnetic fields due to conservation of total surface magnetic flux that existed in its progenitor star phase. 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. The first magnetic white dwarf to be discovered was GJ 742 (also known as ), which was identified by James Kemp, John Swedlund, John Landstreet and Roger Angel in 1970 to host a magnetic field by its emission of circularly polarized light. It is thought to have a surface field of approximately 300 million gauss (30 kT). Many of the presently known magnetic 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. White dwarf magnetic fields may also be measured without spectral lines, using the techniques of broadband circular polarimetry, or maybe through measurement of their frequencies of radio emission via the electron cyclotron maser. The magnetic fields in a white dwarf may allow for the existence of a new type of chemical bond, perpendicular paramagnetic bonding, in addition to ionic and covalent bonds, though detecting molecules bonded in this way is expected to be difficult. 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. A second white dwarf pulsar was discovered in 2023. == Variability ==

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. The first variable white dwarf found was HL Tau 76; in 1965 and 1966, and was observed 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 pulsations. GW Vir stars are not, strictly speaking, white dwarfs, but are stars that 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. 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. == Formation ==

After the hydrogen-fusing period of a main-sequence star of low or intermediate mass ends, such a star will expand onto the red giant branch, and eventually to the asymptotic giant branch with an outer hydrogen shell fusing to helium and an expanding helium shell that fuses to create a carbon and oxygen core by the triple-alpha process. Alternate fusing of the helium shell and hydrogen shells creates thermal pulses; these pulses combine with convective currents to create dust grains that are driven outward by radiation pressure creating strong stellar winds. The ejected mass forms a planetary nebula leaving behind a core, which is the remnant white dwarf. A white dwarf radiates light from residual heat, not from nuclear fusion. It is thought that, over a lifespan that considerably exceeds the age of the universe ( 13.8 billion years), 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. 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 believed to be mostly the product of mass loss in binary systems. Proposals to explain those helium white dwarfs that are not part of binary systems include mass loss due to a large exoplanetary companion, stars being stripped of material by companions exploding as supernovae, and various types of stellar mergers. Stars with low to medium mass If the mass of a main-sequence star is between , White dwarfs with a mass greater than are termed ultramassive white dwarfs. When formed in single-star systems, these are expected to have an oxygen-neon core. However, a significant fraction (~20%) of ultramassive white dwarfs are formed through white dwarf mergers. In this case the result is a carbon-oxygen ultramassive white dwarf. 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 collapse and it will explode in a core-collapse supernova that will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star. Some main-sequence stars, of perhaps , 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. Although a few white dwarfs have been identified that 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 that appear to be only explicable by the accretion of material onto an oxygen–neon–magnesium white dwarf. Type Iax supernova Type Iax supernovae, that involve helium accretion by a white dwarf, have been proposed to be a channel for transformation of this type of stellar remnant. 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, but produces an asymmetric explosion that kicks the star, often known as a zombie star, to the high speeds of a 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. These iron-core white dwarfs would be smaller than the carbon–oxygen kind of similar mass and would cool and crystallize faster than those. == Fate ==

Once formed, a white dwarf is stable and will usually continue to cool almost indefinitely. 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. The lifetime of a white dwarf is thought to be on the order of the hypothetical lifetime of the proton, known to be at least 1034–1035 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 non-degenerate lump of matter, and finally disappears completely in a total time around 1038 years. == Debris disks and planets ==

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. The most common observable evidence of a remnant planetary system is pollution of the spectrum of a white dwarf with metal absorption lines. 27–50% of white dwarfs show a spectrum polluted with metals, but these heavy elements settle out in the atmosphere of white dwarfs colder than . The most widely accepted hypothesis is that this pollution comes from tidally disrupted rocky bodies. The white dwarf van Maanen 2 shows iron, calcium and magnesium in its atmosphere, but van Maanen misclassified it as the faintest F-type star based on the calcium H- and K-lines. The nitrogen in white dwarfs is thought to come from nitrogen-ice of extrasolar Kuiper Belt objects, the lithium is thought to come from accreted crust material and the beryllium is thought to come from exomoons. and later confirmed as a debris disk. 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. Some estimations based on the metal content of the atmospheres of the white dwarfs consider that at least 15% of them may be orbited by planets or asteroids, or at least their debris. 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. Other suggested ideas of how white dwarfs are polluted with dust involve the scattering of asteroids by planets or via planet-planet scattering. Liberation of exomoons from their host planet could cause white dwarf pollution with dust. Either the liberation could cause asteroids to be scattered towards the white dwarf or the exomoon could be scattered into the Roche radius of the white dwarf. 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. 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 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. Another possible way to detect planetary systems around white dwarfs is through their radio emissions. In 2004 and 2005, A. J. Willes and K. Wu hypothesized that when an exoplanet travels through the magnetosphere of a white dwarf, it may generate auroral radio emissions from the magnetic poles of the white dwarf, similar to how Io stimulates radio emissions from Jupiter; a search for such radio emission from nine white dwarfs by researchers using the Arecibo radio telescope did not find any so far. Similarly, observations made in 2004 indicated the presence of a dust cloud around the young (estimated to have formed from its AGB progenitor about 500 million years ago) white dwarf G29-38, which may have been created by tidal disruption of a comet passing close to the white dwarf. The metal-rich white dwarf WD 1145+017 is the first white dwarf observed with a disintegrating minor planet that transits the star. The disintegration of the planetesimal generates a debris cloud that passes in front of the star every 4.5 hours, causing a 5-minute-long fade in the star's optical brightness. The white dwarf WD 0145+234 shows brightening in the mid-infrared, seen in NEOWISE data. The brightening, not seen before 2018, may be due to the tidal disruption of an exoasteroid, the first time such an event has been observed. WD 1856+534 is the first transiting major planet to be observed orbiting a white dwarf, and remains the only such example as of 2023. MOA-2010-BLG-477L, a white dwarf discovered thanks to a microlensing event, is also known to have a giant planet. 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 been suspected to host giant planets that disturb the orbits of minor planets, causing the pollution. 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. The planet candidate at WD 0141-675 was found to be a false positive caused by a software error. == Habitability ==

A search has been proposed for transits of hypothetical Earth-like planets around white dwarfs with surface temperatures of less than . Such stars that could harbor a habitable zone at a distance of  0.005 to 0.02 AU that would last upwards of 3 billion years. This is so close that any habitable planets would be tidally locked. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong eclipses. 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. 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. == Binary stars and novae ==

s 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. 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). Type Ia supernovae The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~ . This limit may increase if the white dwarf is rotating rapidly and nonuniformly. White dwarfs in 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. It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit. 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. The single-degenerate model was the favored mechanism for Type Ia supernovae, but now, because of observations, the double-degenerate model is thought to be the more likely scenario. Predicted rates of white dwarf-white dwarf mergers are comparable to the rate of Type Ia supernovae and would explain the lack of hydrogen in the spectra of Type Ia supernovae. The main mechanism for Type Ia supernovae remains an open question. In the single-degenerate scenario, the accretion rate onto the white dwarf needs to be within a narrow range dependent on its mass so that the hydrogen burning on the surface of the white dwarf is stable. If the accretion rate is too low, novae on the surface of the white dwarf will blow away accreted material. If it is too high, the white dwarf will expand and the white dwarf and companion star will be in a common envelope. This stops the growth of the white dwarf thus preventing it from reaching the Chandrasekhar limit and exploding. Tycho's Supernova of 1572 was also a type Ia supernova, and its remnant has been detected. WD 0810–353, a white dwarf 11 parsecs away from the Sun, is possibly a hypervelocity runaway ejected from a Type Ia supernova, though this has been disputed. Post-common envelope binary A post-common envelope binary (PCEB) is a binary consisting of a white dwarf or hot subdwarf 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 then evolve into one of several dramatic outcomes: a high-field magnetic white dwarf, a white dwarf pulsar, a double-degenerate binary, or even a Type Ia supernova. Because a PCEB may evolve at some point into a cataclysmic variable, some of them are also called pre-cataclysmic variables. Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources. White dwarfs can also exist as binaries or multiple star systems that only consist of white dwarfs. An example of a resolved triple white dwarf system is WD J1953−1019, discovered with Gaia DR2 data. One interesting field is the study of remnant planetary systems around white dwarfs. It is expected that planets orbiting several AU from a star will survive the star's post-main-sequence transformation into a white dwarf. Moreover, white dwarfs, being much smaller and correspondingly less luminous than their progenitors, are less likely to outshine any bodies in orbit around them. This makes white dwarfs advantageous targets for direct-imaging searches for exoplanets and brown dwarfs. The first brown dwarf to be detected by direct imaging was the companion to the white dwarf GD 165 A, discovered in 1988. More recently, the white dwarf WD 0806−661 was found to have a cold companion body of substellar mass, variously described as a brown dwarf or an exoplanet. == Nearest white dwarfs ==