--- title: White dwarf summary: The exposed core of a dead Sun-like star, about as massive as the Sun but the size of Earth, held up by the quantum pressure of its electrons and cooling for billions of years. science_status: [observed, model, sim] categories: [White dwarfs, Stellar remnants, Compact objects] aliases: [White dwarfs, Degenerate dwarf, WD, WDR, DA white dwarf, DB white dwarf, DC white dwarf, DO white dwarf, DQ white dwarf, DZ white dwarf, Polluted white dwarf, Magnetic white dwarf] infobox: type: white_dwarf image: File:Sirius_A_and_B_Hubble.jpg image_caption: "Observation: Sirius A and its white dwarf companion Sirius B (lower left), Hubble Space Telescope" spectral_classes: [DA (hydrogen), DB (neutral helium), DO (ionised helium), DC (no lines), DQ (carbon), DZ (metals)] temperature_index: "number after the letters = 50,400 / Teff (e.g. DA2 is about 25,000 K)" teff_k: "about 4,000 (oldest) to over 100,000 (newborn)" mass_msun: "typically about 0.6; about 0.15 to 1.35" radius_rearth: "about 0.3 (heaviest) to about 2 (lightest); about 1.35 at 0.6 solar masses" radius_km: "about 8,600 at 0.6 solar masses; about 2,100 for the heaviest known" mean_density_kg_m3: 4e8 surface_gravity_log_g_cgs: "about 8 (range about 7 to 9.5)" maximum_mass_msun: "about 1.4 (Chandrasekhar limit, 1.44 in the classic calculation)" cooling_age_gyr: "0 to about 10 for the oldest in the Galactic disk" progenitor_mass_msun: "about 0.85 to about 8 (upper end uncertain)" core_composition: "carbon and oxygen (most); helium (lowest masses, from binaries); oxygen and neon (highest masses)" magnetic_field_mg: "none detected to about 1,000 (1 billion gauss)" metal_pollution: "at least 27 percent, possibly about half, of young white dwarfs accreting rocky debris" companions: "common; Sirius B, Procyon B, 40 Eridani B are companions of brighter stars" known_count: "about 359,000 high-confidence candidates in Gaia EDR3; about 1,100 within 40 pc" nearest_known: "Sirius B, 2.64 pc (8.6 light years)" sim: entity: stellar_class.white_dwarf code: WDR refs: - id: chandrasekhar1931 type: article-journal author: [{family: Chandrasekhar, given: S.}] title: "The Maximum Mass of Ideal White Dwarfs" container-title: The Astrophysical Journal issued: 1931 volume: 74 page: "81" DOI: 10.1086/143324 - id: fontaine2001 type: article-journal author: [{family: Fontaine, given: G.}, {family: Brassard, given: P.}, {family: Bergeron, given: P.}] title: "The Potential of White Dwarf Cosmochronology" container-title: Publications of the Astronomical Society of the Pacific issued: 2001 volume: 113 page: "409-435" DOI: 10.1086/319535 - id: cummings2018 type: article-journal author: [{family: Cummings, given: Jeffrey D.}, {family: Kalirai, given: Jason S.}, {family: Tremblay, given: P.-E.}, {family: Ramirez-Ruiz, given: Enrico}, {family: Choi, given: Jieun}] title: "The White Dwarf Initial-Final Mass Relation for Progenitor Stars from 0.85 to 7.5 solar masses" container-title: The Astrophysical Journal issued: 2018 volume: 866 page: "21" DOI: 10.3847/1538-4357/aadfd6 - id: kalirai2008 type: article-journal author: [{family: Kalirai, given: Jasonjot S.}, {literal: "et al."}] title: "The Initial-Final Mass Relation: Direct Constraints at the Low-Mass End" container-title: The Astrophysical Journal issued: 2008 volume: 676 page: "594-609" DOI: 10.1086/527028 - id: bond2017 type: article-journal author: [{family: Bond, given: Howard E.}, {literal: "et al."}] title: "The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry" container-title: The Astrophysical Journal issued: 2017 volume: 840 page: "70" DOI: 10.3847/1538-4357/aa6af8 - id: bond2015 type: article-journal author: [{family: Bond, given: Howard E.}, {literal: "et al."}] title: "Hubble Space Telescope Astrometry of the Procyon System" container-title: The Astrophysical Journal issued: 2015 volume: 813 page: "106" DOI: 10.1088/0004-637X/813/2/106 - id: bond2017b type: article-journal author: [{family: Bond, given: Howard E.}, {literal: "et al."}] title: "Astrophysical Implications of a New Dynamical Mass for the Nearby White Dwarf 40 Eridani B" container-title: The Astrophysical Journal issued: 2017 volume: 848 page: "16" DOI: 10.3847/1538-4357/aa8a63 - id: caiazzo2021 type: article-journal author: [{family: Caiazzo, given: Ilaria}, {literal: "et al."}] title: "A highly magnetized and rapidly rotating white dwarf as small as the Moon" container-title: Nature issued: 2021 volume: 595 page: "39-42" DOI: 10.1038/s41586-021-03615-y - id: mestel1952 type: article-journal author: [{family: Mestel, given: L.}] title: "On the Theory of White Dwarf Stars: I. The Energy Sources of White Dwarfs" container-title: Monthly Notices of the Royal Astronomical Society issued: 1952 volume: 112 page: "583-597" DOI: 10.1093/mnras/112.6.583 - id: winget1987 type: article-journal author: [{family: Winget, given: D. E.}, {literal: "et al."}] title: "An independent method for determining the age of the universe" container-title: The Astrophysical Journal issued: 1987 volume: 315 page: "L77" DOI: 10.1086/184864 - id: tremblay2019 type: article-journal author: [{family: Tremblay, given: Pier-Emmanuel}, {literal: "et al."}] title: "Core crystallization and pile-up in the cooling sequence of evolving white dwarfs" container-title: Nature issued: 2019 volume: 565 page: "202-205" DOI: 10.1038/s41586-018-0791-x - id: sion1983 type: article-journal author: [{family: Sion, given: E. M.}, {family: Greenstein, given: J. L.}, {family: Landstreet, given: J. D.}, {family: Liebert, given: J.}, {family: Shipman, given: H. L.}, {family: Wegner, given: G. A.}] title: "A proposed new white dwarf spectral classification system" container-title: The Astrophysical Journal issued: 1983 volume: 269 page: "253" DOI: 10.1086/161036 - id: koester2014 type: article-journal author: [{family: Koester, given: D.}, {family: Gänsicke, given: B. T.}, {family: Farihi, given: J.}] title: "The frequency of planetary debris around young white dwarfs" container-title: Astronomy & Astrophysics issued: 2014 volume: 566 page: "A34" DOI: 10.1051/0004-6361/201423691 - id: vanderburg2015 type: article-journal author: [{family: Vanderburg, given: Andrew}, {literal: "et al."}] title: "A disintegrating minor planet transiting a white dwarf" container-title: Nature issued: 2015 volume: 526 page: "546-549" DOI: 10.1038/nature15527 - id: vanderburg2020 type: article-journal author: [{family: Vanderburg, given: Andrew}, {literal: "et al."}] title: "A giant planet candidate transiting a white dwarf" container-title: Nature issued: 2020 volume: 585 page: "363-367" DOI: 10.1038/s41586-020-2713-y - id: hillebrandt2000 type: article-journal author: [{family: Hillebrandt, given: Wolfgang}, {family: Niemeyer, given: Jens C.}] title: "Type Ia Supernova Explosion Models" container-title: Annual Review of Astronomy and Astrophysics issued: 2000 volume: 38 page: "191-230" DOI: 10.1146/annurev.astro.38.1.191 - id: riess1998 type: article-journal author: [{family: Riess, given: Adam G.}, {literal: "et al."}] title: "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant" container-title: The Astronomical Journal issued: 1998 volume: 116 page: "1009-1038" DOI: 10.1086/300499 - id: gentilefusillo2021 type: article-journal author: [{family: Gentile Fusillo, given: N. P.}, {literal: "et al."}] title: "A catalogue of white dwarfs in Gaia EDR3" container-title: Monthly Notices of the Royal Astronomical Society issued: 2021 volume: 508 page: "3877-3896" DOI: 10.1093/mnras/stab2672 - id: obrien2024 type: article-journal author: [{family: O'Brien, given: Mairi W.}, {literal: "et al."}] title: "The 40 pc sample of white dwarfs from Gaia" container-title: Monthly Notices of the Royal Astronomical Society issued: 2024 volume: 527 page: "8687-8705" DOI: 10.1093/mnras/stad3773 images_wanted: - file: File:Sirius_A_and_B_Hubble.jpg subject: "Hubble image of Sirius A, heavily overexposed, with the faint dot of Sirius B at lower left" source: esa-hubble page_url: "https://esahubble.org/images/heic0516a/" image_url: "https://cdn.esahubble.org/archives/images/large/heic0516a.jpg" credit: "NASA, ESA, H. Bond (STScI), and M. Barstow (University of Leicester)" licence: "CC BY 4.0" - file: File:White_dwarf_mass_radius_diagram.svg subject: "Diagram: white dwarf radius against mass, falling towards zero near 1.4 solar masses, with Sirius B, Procyon B, 40 Eridani B and ZTF J1901+1458 marked; Earth's and the Moon's radii as reference lines" source: other note: "to be drawn (diagram); values in the page's Notable white dwarfs table" --- A **white dwarf** is what remains when a star like the Sun has burned its fuel and shed its outer layers: a bare stellar core, typically about 60 per cent as massive as the Sun but only the size of Earth. Nothing inside it burns. It is held up by the quantum-mechanical pressure of electrons packed as tightly as nature allows, and it shines only with stored heat, fading for billions of years. More than 95 per cent of the stars in the Galaxy, the Sun among them, will end this way :cite[fontaine2001]. The nearest, Sirius B, is 8.6 light years away :cite[bond2017]. ::figure{src="File:Sirius_A_and_B_Hubble.jpg" size=wide alt="A brilliant white star with diffraction spikes fills the frame; a tiny faint dot sits to its lower left." caption="Observation: Sirius A, the brightest star in the night sky, overexposed, with its white dwarf companion Sirius B as the faint dot at lower left. Sirius B has about the Sun's mass packed into a ball smaller than Earth. Credit: NASA, ESA, H. Bond (STScI), and M. Barstow (University of Leicester)."} ## What holds a white dwarf up In an ordinary star, the pressure of hot gas balances gravity, and fusion keeps the gas hot. A white dwarf has no fusion, so something else must hold it up. That something is **electron degeneracy pressure**. The Pauli exclusion principle forbids two electrons from sharing the same quantum state, so when matter is squeezed hard enough, electrons are forced into states of ever higher momentum. They push back whether the star is hot or cold, which is why a white dwarf can cool for billions of years without shrinking. The numbers are extreme. Procyon B, a white dwarf of 0.592 solar masses, has a radius of 0.0123 solar radii, about 8,600 km, or 1.35 times Earth's :cite[bond2015]. Its mean density is about $4 \times 10^{8}$ kg/m³, roughly 400 kg in every cubic centimetre, and its surface gravity is about $10^6$ m/s², a hundred thousand times Earth's. Astronomers write this as $\log g \approx 8$, the logarithm of the gravity in centimetres per second squared. ### Heavier is smaller For slowly moving electrons, degeneracy pressure grows with density as $P \propto \rho^{5/3}$. Balancing that against gravity gives a surprising result: $$ R \propto M^{-1/3}, $$ so a heavier white dwarf is a smaller one. Add mass and the star shrinks, the electrons are squeezed faster, and as their speeds approach the speed of light the pressure law softens towards $P \propto \rho^{4/3}$. At that point no radius can balance gravity, and there is a maximum mass. Subrahmanyan Chandrasekhar calculated it in 1931 :cite[chandrasekhar1931]; for matter made of carbon and oxygen it is about 1.44 solar masses in the classic calculation. Real white dwarfs become unstable a little below that, and one that grows close to the limit by gaining mass can ignite its carbon and explode :cite[hillebrandt2000]. The measured stars follow the curve. Sirius B has 1.018 ± 0.011 solar masses and is a little smaller than Earth :cite[bond2017]. The heaviest known white dwarf, ZTF J1901+1458, is thought to be close to the limit, with a radius of about 2,100 km, only slightly larger than the Moon's :cite[caiazzo2021]. ## How white dwarfs form A star of up to about eight times the Sun's mass ends its life as a red giant and then an asymptotic giant branch star, puffing its outer layers into space as a glowing planetary nebula. The core left behind, made of carbon and oxygen ash from helium burning, is the white dwarf. The very lightest white dwarfs, below about half a solar mass, have helium cores; they cannot have formed from single stars in the age of the Universe and are made when a companion strips a red giant early. The heaviest can have cores of oxygen and neon. The **initial-final mass relation** links a star's birth mass to the white dwarf it leaves. Measured from white dwarfs in star clusters of known age, it shows that stars from 0.85 to 7.5 solar masses shed between a third and five sixths of their mass on the way :cite[cummings2018]. The Sun will leave a white dwarf of a little over half its present mass. ## Cooling, crystals and cosmic clocks A white dwarf is born at over 100,000 K and simply cools. Leon Mestel showed in 1952 that its luminosity falls roughly as $L \propto t^{-7/5}$ :cite[mestel1952]: it dims quickly at first, then more and more slowly. Because the physics is so simple, a white dwarf's temperature and mass give its **cooling age**, and the coolest white dwarfs in a population date the population itself. The faintest white dwarfs in the Galactic disk showed in 1987 that the disk is about 9 billion years old :cite[winget1987] :cite[fontaine2001]. As it cools, the carbon and oxygen in the core freeze into a crystal lattice, releasing latent heat that slows the cooling for a while. Gaia's precise measurements of thousands of nearby white dwarfs revealed the resulting pile-up in the colour-brightness diagram in 2019, the first direct evidence that white dwarf cores crystallise :cite[tremblay2019]. ## Spectral classes White dwarf spectral types begin with D, for degenerate, followed by a letter for the strongest features in the spectrum and a number for the temperature :cite[sion1983]: | Class | Spectrum shows | What it means | |---|---|---| | DA | hydrogen lines | a thin hydrogen skin over the star; the most common class | | DB | neutral helium lines | a helium surface, about 12,000 to 30,000 K | | DO | ionised helium lines | a very hot helium surface | | DC | no lines | too cool for lines to form | | DQ | carbon features | carbon dredged up from the core | | DZ | metal lines | calcium, magnesium or iron, accreted from outside | The number is $50{,}400/T_\mathrm{eff}$, rounded: Sirius B, at about 25,000 K, is a DA2. Letters combine for mixed spectra, and an H or P marks a magnetic star. Gravity at a white dwarf's surface is so strong that heavy elements sink out of sight within days to millions of years. Any metals seen must have arrived recently. ## Polluted white dwarfs and the ghosts of planets Between a quarter and a half of young white dwarfs are accreting rocky material right now :cite[koester2014]. The source is the remnant of a planetary system: asteroids or comets nudged onto orbits that take them close to the star, where tides shred them into a disk of dust that rains onto the surface. The metals in the star's atmosphere then give the bulk composition of rocks from another planetary system, measured element by element. The process has been caught in the act. WD 1145+017 shows dimming events every 4.5 hours from a disintegrating body and its trailing dust :cite[vanderburg2015], and in 2020 a giant planet candidate was found transiting the white dwarf WD 1856+534 every 1.4 days :cite[vanderburg2020]. ## Magnetism, mergers and explosions Some white dwarfs carry fields of millions to hundreds of millions of gauss. ZTF J1901+1458 has a surface field of 600 to 900 million gauss and spins once every 6.94 minutes; its extreme mass, field and spin suggest it formed when two white dwarfs merged :cite[caiazzo2021]. A white dwarf that gains mass from a companion, or merges with another, can approach the Chandrasekhar limit and ignite carbon in a runaway that destroys it completely: a **Type Ia supernova** :cite[hillebrandt2000]. Because these explosions have similar peak brightness, they serve as distance markers across the Universe; in 1998 they revealed that the expansion of the Universe is accelerating :cite[riess1998]. ## How we know Sirius B was the first white dwarf found, from the wobble it gives Sirius A: Friedrich Bessel predicted an unseen companion in 1844, and Alvan Clark saw it in 1862. Its mass is still measured the same way. Hubble's astrometry of the 50.1-year orbit gives 1.018 ± 0.011 solar masses, and its cooling age is about 126 million years :cite[bond2017]. Procyon B and 40 Eridani B are weighed the same way :cite[bond2015] :cite[bond2017b]. Gaia has turned white dwarfs from a few hundred curiosities into a mapped population: its third data release yields about 359,000 high-confidence candidates :cite[gentilefusillo2021], and a volume-complete census within 40 parsecs of the Sun contains about 1,100 :cite[obrien2024]. ## Notable white dwarfs | Name | Class | Mass (solar masses) | Distance | Note | |---|---|---|---|---| | Sirius B | DA2 | 1.018 ± 0.011 | 2.64 pc (8.6 ly) | nearest white dwarf; cooling age about 126 Myr :cite[bond2017] | | Procyon B | DQZ | 0.592 ± 0.006 | 3.5 pc (11.5 ly) | radius 0.0123 solar radii :cite[bond2015] | | 40 Eridani B | DA | 0.573 ± 0.018 | 5.0 pc (16 ly) | in a triple system; cooling age about 122 Myr :cite[bond2017b] | | Van Maanen's Star | DZ | | 4.3 pc (14 ly) | nearest white dwarf with no companion :cite[obrien2024] | | ZTF J1901+1458 | magnetic | about 1.33 to 1.36 | | heaviest known; radius about 2,100 km :cite[caiazzo2021] | | WD 1145+017 | polluted | | | disintegrating planetesimal in orbit :cite[vanderburg2015] | | WD 1856+534 | cool, old | | | giant planet candidate in a 1.4-day orbit :cite[vanderburg2020] | :::callout{type=sim title="In Pax Abyssi"} White dwarfs are one of the star classes on the galaxy map, and the catalogue carries the nearby ones as their own entries: Sirius B, Procyon B and 40 Eridani B beside their bright partners. When the simulation creates a white dwarf it gives it a spectral class (DA, DB, DC, DO, DQ or DZ) and a temperature tier, can flag it as magnetic, polluted or pulsating, and sets its radius from its mass with Nauenberg's analytic fit to the Chandrasekhar relation. A generated star's white dwarf takes its mass from the measured initial-final mass relation :cite[kalirai2008]. No white dwarf is yet a flyable stop. ::: ## See also - [[Neutron star]] - [[Black hole]] - [[Red giant]] - [[Yellow dwarf]] - [[Stellar classification]] - [[Star catalogue]] - [[Habitable zone]]