white dwarf#Stars with low to medium mass

{{See also|List of white dwarfs}}

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.

{{cite journal

|last=Herschel |first=W. |author-link=William Herschel

|year=1785

|title=Catalogue of Double Stars

|journal=Philosophical Transactions of the Royal Society of London

|volume=75 |pages=40–126

|bibcode=1785RSPT...75...40H |jstor=106749

|doi=10.1098/rstl.1785.0006 |doi-access=free |s2cid=186209747

}}

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.

{{cite conference

|last=Holberg |first=J. B.

|year=2005

|title=How degenerate stars came to be known as 'white dwarfs'

|volume=207 |page=1503

|conference=American Astronomical Society meeting 207

|bibcode=2005AAS...20720501H

}}

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.

{{cite book | author = Evry L. Schatzman | date = 1958 | title = White Dwarfs | publisher = North-Holland Publishing Company | isbn = 978-0-598-58212-6 | url = https://books.google.com/books?id=PrixAAAAIAAJ}}{{rp|page=1}}

The spectral type of 40 Eridani B was officially described in 1914 by Walter Adams.

{{cite journal

|last=Adams |first=W.S. |author-link=Walter Sydney Adams

|year=1914

|title=An A-type star of very low luminosity

|journal=Publications of the Astronomical Society of the Pacific

|volume=26 |issue= 155 |page=198

|bibcode=1914PASP...26..198A

|doi= 10.1086/122337 |doi-access=free

}}

The white dwarf companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius (α Canis Majoris) and Procyon (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions.

{{cite journal

|last1=Bessel |first1=F.W. |author-link=Friedrich Wilhelm Bessel

|year=1844

|title=On the variations of the proper motions of Procyon and Sirius

|journal=Monthly Notices of the Royal Astronomical Society

|volume=6 |issue=11 |pages=136–141

|bibcode=1844MNRAS...6R.136B

|doi=10.1093/mnras/6.11.136a |doi-access=free

}}

Bessel roughly estimated the period of the companion of Sirius to be about half a century; C.A.F. Peters computed an orbit for it in 1851.

{{cite journal

|last=Flammarion |first=Camille

|title=The companion of Sirius

|year=1877

|volume=15 |page=186

|journal=Astronomical Register

|bibcode=1877AReg...15..186F

}}

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

{{cite journal

|last=Adams |first=W.S. |author-link=Walter Sydney Adams

|year=1915

|title=The spectrum of the companion of Sirius

|journal=Publications of the Astronomical Society of the Pacific

|volume=27 |issue=161 |page=236

|bibcode=1915PASP...27..236A

|doi= 10.1086/122440 |doi-access=free

}}

In 1917, Adriaan van Maanen discovered van Maanen's Star, an isolated white dwarf.

{{cite journal

|last=van Maanen |first=A. |author-link=Adriaan van Maanen

|year=1917

|title=Two faint stars with large proper motion

|journal=Publications of the Astronomical Society of the Pacific

|volume=29 |issue=172 |page=258

|bibcode=1917PASP...29..258V

|doi=10.1086/122654 |doi-access=free

}}

These three white dwarfs, the first discovered, are the so-called classical white dwarfs.{{rp|page=2}} Eventually, many faint white stars that had high proper motion were found, 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;

{{cite journal

|last=Luyten |first=W.J. |author-link=Willem Luyten

|year=1922

|title=The mean parallax of early-type stars of determined proper motion and apparent magnitude

|journal=Publications of the Astronomical Society of the Pacific

|volume=34 |issue=199 |page=156

|bibcode=1922PASP...34..156L

|doi= 10.1086/123176 |doi-access=free

}}

{{cite journal

|last=Luyten |first=W.J. |author-link=Willem Luyten

|year=1922

|title=Note on some faint early-type stars with large proper motions

|journal=Publications of the Astronomical Society of the Pacific

|volume=34 |issue=197 |page=54

|bibcode=1922PASP...34...54L

|doi= 10.1086/123146 |doi-access=free

}}

{{cite journal

|last=Luyten |first=W.J. |author-link=Willem Luyten

|year=1922

|title=Additional note on faint early-type stars with large proper motions

|journal=Publications of the Astronomical Society of the Pacific

|volume=34 |issue=198 |page=132

|bibcode=1922PASP...34..132L

|doi= 10.1086/123168 |doi-access=free

}}

{{cite journal

|last=Aitken |first=R.G.

|year=1922

|title=Comet c 1922 (Baade)

|journal=Publications of the Astronomical Society of the Pacific

|volume=34 |issue= 202 |page=353

|bibcode=1922PASP...34..353A

|doi= 10.1086/123244 |doi-access=free

}}

the term was later popularized by Arthur Eddington. Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939.{{rp|page=3}} Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known,

{{cite journal

|last1=Luyten |first1=W.J. |author-link=Willem Luyten

|year=1950

|title=The search for white dwarfs

|journal=The Astronomical Journal

|volume=55 |page=86

|bibcode=1950AJ.....55...86L

|doi= 10.1086/106358 |doi-access=free

}}

and by 1999, over 2000 were known.

{{cite journal

|last1=McCook |first1=George P.

|last2=Sion |first2=Edward M.

|year=1999

|title=A catalog of spectroscopically identified white dwarfs

|journal=The Astrophysical Journal Supplement Series

|volume=121 |issue= 1 |pages=1–130

|bibcode=1999ApJS..121....1M

|doi=10.1086/313186 |doi-access=free

}}

Since then the Sloan Digital Sky Survey has found over 9000 white dwarfs, mostly new.

{{cite journal

|last1=Eisenstein |first1=Daniel J. |last2=Liebert |first2=James

|last3=Harris |first3=Hugh C. |last4=Kleinman |first4=S. J.

|last5=Nitta |first5=Atsuko |last6=Silvestri |first6=Nicole

|last7=Anderson |first7=Scott A. |last8=Barentine |first8=J. C.

|last9=Brewington |first9=Howard J. |last10=Brinkmann |first10=J.

|last11=Harvanek |first11=Michael |last12=Krzesiński |first12=Jurek

|last13=Neilsen |first13=Eric H. Jr.

|last14=Long |first14=Dan |last15=Schneider |first15=Donald P.

|last16=Snedden |first16=Stephanie A. |author16-link=Stephanie Snedden

|display-authors=6

|year=2006

|title=A catalog of spectroscopically confirmed white dwarfs from the Sloan Digital Sky Survey, data release 4

|journal=The Astrophysical Journal Supplement Series

|volume=167 |issue=1 |pages=40–58

|s2cid=13829139 |bibcode=2006ApJS..167...40E

|arxiv=astro-ph/0606700 |doi= 10.1086/507110

}}

{{star nav}}

Although white dwarfs are known with estimated masses as low as {{solar mass|0.17}}

{{cite journal

|last1=Kilic |first1=M. |last2=Allende Prieto |first2=C.

|last3=Brown |first3=Warren R. |last4=Koester |first4=D.

|year=2007

|title=The lowest mass white dwarf

|journal=The Astrophysical Journal

|volume=660 |issue=2 |pages=1451–1461

|arxiv= astro-ph/0611498

|bibcode=2007ApJ...660.1451K

|doi= 10.1086/514327

|s2cid=18587748

}}

and as high as {{solar mass|1.33}},

{{cite journal

|last1=Kepler |first1=S.O. |author1-link=Kepler de Souza Oliveira

|last2=Kleinman |first2=S.J. |last3=Nitta |first3=A.

|last4=Koester |first4=D. |last5=Castanheira |first5=B.G.

|last6=Giovannini |first6=O. |last7=Costa |first7=A.F.M.

|last8=Althaus |first8=L.

|year=2007

|title=White dwarf mass distribution in the SDSS

|journal=Monthly Notices of the Royal Astronomical Society

|volume=375 |issue=4 |pages=1315–1324

|arxiv= astro-ph/0612277 |bibcode=2007MNRAS.375.1315K

|doi=10.1111/j.1365-2966.2006.11388.x |doi-access=free |s2cid=10892288

}}

the mass distribution is strongly peaked at {{solar mass|0.6}}, and the majority lie between {{solar mass|0.5 and 0.7}}. The estimated radii of observed white dwarfs are typically 0.8–2% the radius of the Sun;

{{cite journal

|last=Shipman |first=H.L.

|year=1979

|title=Masses and radii of white-dwarf stars. III – Results for 110 hydrogen-rich and 28 helium-rich stars

|journal=The Astrophysical Journal

|volume=228 |page=240

|bibcode=1979ApJ...228..240S

|doi=10.1086/156841

}}

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 a million times smaller than the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, {{val|1000000}} times greater than the average density of the Sun, or approximately {{val|e=6|ul=g/cm3}}, or 1 tonne per cubic centimetre. A typical white dwarf has a density of between 10⁴ and {{val|e=7|u=g/cm3}}. 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.{{cite book|first=Andreas |last=Schmitt |title= Dense Matter in Compact Stars: A Pedagogical Introduction |series=Lecture Notes in Physics |year=2010 |volume=811 |publisher=Springer |pages=4,143 |doi=10.1007/978-3-642-12866-0 |isbn=978-3-642-12866-0 |arxiv=1001.3294}}

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 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,

{{cite book

|last=Boss |first=L.

|year=1910

|title=Preliminary General Catalogue of 6188 stars for the epoch 1900

|publisher=Carnegie Institution of Washington

|bibcode=1910pgcs.book.....B |lccn=10009645

|url=https://archive.org/details/preliminarygene00obsegoog

|via=Archive.org

}}

yielding a mass estimate of {{solar mass|0.94}}, which compares well with a more modern estimate of {{solar mass|1.00}}.

{{cite journal

|last1=Liebert |first1=James |last2=Young |first2=P. A.

|last3=Arnett |first3=D. |last4=Holberg |first4=J. B.

|last5=Williams |first5=K. A.

|date=2005

|title=The age and progenitor mass of Sirius B

|journal=The Astrophysical Journal

|volume=630 |issue=1 |page=L69

|arxiv= astro-ph/0507523 |bibcode=2005ApJ...630L..69L

|doi= 10.1086/462419 |s2cid=8792889

}} Since hotter bodies radiate more energy than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and that from its spectrum. If the star's distance is known, its absolute luminosity can also be estimated. From the absolute luminosity and distance, the star's surface area and its radius can be calculated. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that due to their relatively high temperature and relatively low absolute luminosity, Sirius B and 40 Eridani B must be very dense. When Ernst Öpik estimated the density of a number of visual binary stars in 1916, he found that 40 Eridani B had a density of over {{val|25000}} times that of the Sun, which was so high that he called it "impossible".

{{cite journal

|last1=Öpik |first1=E.

|date=1916

|title=The densities of visual binary stars

|journal=The Astrophysical Journal

|volume=44 |page=292

|bibcode=1916ApJ....44..292O

|doi= 10.1086/142296 |doi-access=free

}}

As Arthur Eddington put it later, in 1927:

{{cite book

|last=Eddington |first=A.S. |author-link=Arthur Stanley Eddington

|date=1927

|title=Stars and Atoms

|url=https://archive.org/details/in.ernet.dli.2015.173636 |publisher=Clarendon Press

|lccn=27015694

}}

{{rp|page=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 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."

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.

{{cite journal

|last1=Eddington |first1=A. S.

|date=1924

|title=On the relation between the masses and luminosities of the stars

|journal=Monthly Notices of the Royal Astronomical Society

|volume=84 |issue=5

|pages=308–333

|bibcode=1924MNRAS..84..308E

|doi=10.1093/mnras/84.5.308

|doi-access=free

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

{{cite journal

|last1=Adams |first1=W. S.

|date=1925

|title=The Relativity Displacement of the Spectral Lines in the Companion of Sirius

|journal=Proceedings of the National Academy of Sciences

|volume=11 |issue=7 |pages=382–387

|bibcode=1925PNAS...11..382A

|doi= 10.1073/pnas.11.7.382

|pmid=16587023

|pmc=1086032|doi-access=free

}}

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.

{{cite journal

|last1=Fowler |first1=R. H.

|date=1926

|title=On dense matter

|journal=Monthly Notices of the Royal Astronomical Society

|volume=87 |issue=2

|pages=114–122

|bibcode=1926MNRAS..87..114F

|doi=10.1093/mnras/87.2.114

|doi-access=free

}} 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.

{{cite journal

|last1=Hoddeson |first1=L. H.

|last2=Baym |first2=G.

|date=1980

|title=The Development of the Quantum Mechanical Electron Theory of Metals: 1900–28

|journal=Proceedings of the Royal Society of London

|volume=371 |issue=1744 |pages=8–23

|doi=10.1098/rspa.1980.0051

|jstor=2990270

|bibcode = 1980RSPSA.371....8H |s2cid=120476662

}} 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.

{{cite web

|title=Estimating Stellar Parameters from Energy Equipartition

|url=http://www.sciencebits.com/StellarEquipartition

|website=ScienceBits

|author=Nir Shaviv

|access-date=9 May 2007

|archive-url=https://web.archive.org/web/20120522041201/http://www.sciencebits.com/StellarEquipartition

|archive-date=22 May 2012

|url-status=live

}}

Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.

{{cite web

|last1=Bean |first1=R. |author-link1=Rachel Bean

|title=Lecture 12 – Degeneracy pressure

|url=http://www.astro.cornell.edu/~rbean/a211/211_notes_lec_12.pdf

|series=Lecture notes, Astronomy 211

|publisher=Cornell University

|access-date=21 September 2007

|archive-url=https://web.archive.org/web/20070925204454/http://www.astro.cornell.edu/~rbean/a211/211_notes_lec_12.pdf

|archive-date=2007-09-25

}} This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.

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

{{cite journal

|last1=Anderson |first1=W. |author-link=Wilhelm Anderson

|date=1929

|title=Über die Grenzdichte der Materie und der Energie

|journal=Zeitschrift für Physik |language=de

|volume=56 |issue=11–12 |pages=851–856

|bibcode=1929ZPhy...56..851A

|doi=10.1007/BF01340146

|s2cid=122576829

}} and in 1930 by Edmund C. Stoner.

{{cite journal

|last1=Stoner |first1=C.

|date=1930

|title=The Equilibrium of Dense Stars

|journal=Philosophical Magazine

|volume=9 |issue=60

|page=944

|bibcode=1930LEDPM...9..944S

}} 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".

{{cite journal

|last1=Chandrasekhar |first1=S.

|date=1931

|title=The Maximum Mass of Ideal White Dwarfs

|journal=The Astrophysical Journal

|volume=74 |page=81

|bibcode=1931ApJ....74...81C

|doi= 10.1086/143324

|doi-access=free

}} For a non-rotating white dwarf, it is equal to approximately {{math|{{solar mass|5.7}} / μ_e²}}, where {{math|μ_e}} is the average molecular weight per electron of the star.

{{cite journal

|last1=Chandrasekhar |first1=S.

|date=1935

|title=The highly collapsed configurations of a stellar mass (Second paper)

|volume=95 |issue=3

|pages=207–225

|journal=Monthly Notices of the Royal Astronomical Society

|bibcode=1935MNRAS..95..207C

|doi=10.1093/mnras/95.3.207

|doi-access=free

}}{{rp|eqn.(63)}} 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 {{math|μ_e}} equal to 2 for such a star, leading to the commonly quoted value of {{solar mass|1.4}}. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,{{rp|page=955}} so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, {{math|μ_e}}, equal to 2.5, giving a limit of {{solar mass|0.91}}.) Together with William Alfred Fowler, Chandrasekhar received the Nobel Prize for this and other work in 1983.

{{cite web

|title=The Nobel Prize in Physics 1983

|url=http://nobelprize.org/nobel_prizes/physics/laureates/1983/

|publisher=The Nobel Foundation

|access-date=4 May 2007

|archive-url=https://web.archive.org/web/20070506154131/http://nobelprize.org/nobel_prizes/physics/laureates/1983/

|archive-date=6 May 2007

|url-status=live

}} The limiting mass is now called the Chandrasekhar limit.

{{cite journal

|doi=10.1088/1361-6552/acdbb0

|last=Low

|first=Andrew M.

|title=The Chandrasekhar limit: a simplified approach

|journal=Physics Education

|year=2023

|volume=58

|issue=4

|page=045008|bibcode=2023PhyEd..58d5008L

|doi-access=free

}}

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 and, in the absence of nuclear reactions, would begin to collapse.

{{cite journal

|last1=Lieb

|first1=E. H.

|last2=Yau

|first2=H.-T.

|date=1987

|title=A rigorous examination of the Chandrasekhar theory of stellar collapse

|journal=The Astrophysical Journal

|volume=323

|issue=1

|pages=140–144

|bibcode=1987ApJ...323..140L

|doi=10.1086/165813

|url=https://dash.harvard.edu/handle/1/32706795

|access-date=20 March 2020

}}

{{cite journal

|last1=Mazzali |first1=P. A.

|last2=Röpke |first2=F. K.

|last3=Benetti |first3=S.

|last4=Hillebrandt |first4=W.

|date=2007

|title=A Common Explosion Mechanism for Type Ia Supernovae

|journal=Science

|volume=315 |issue=5813 |pages=825–828

|arxiv=astro-ph/0702351

|bibcode=2007Sci...315..825M

|doi=10.1126/science.1136259

|pmid=17289993

}} However, 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.

{{cite book

|last=Wheeler |first=J. C.

|date=2000

|title=Cosmic Catastrophes: Supernovae, Gamma-Ray Bursts, and Adventures in Hyperspace

|url=https://books.google.com/books?id=s3SFQgAACAAJ

|page=96

|publisher=Cambridge University Press

|isbn=978-0-521-65195-0

}} 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.

{{cite book

|last1=Canal |first1=R.

|last2=Gutierrez |first2=J.

|date=1997

|chapter=The Possible White Dwarf-Neutron Star Connection

|title=White Dwarfs

|arxiv=astro-ph/9701225

|doi=10.1007/978-94-011-5542-7_7

|volume=214

|pages=49–55

|series=Astrophysics and Space Science Library

|isbn=978-94-010-6334-0

|bibcode=1997ASSL..214...49C

|s2cid=9288287

}}

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.

{{cite journal

|last1=Piro |first1=A. L.

|last2=Thompson |first2=T. A.

|last3=Kochanek |first3=C. S.

|year=2014

|title=Reconciling 56Ni production in Type Ia supernovae with double degenerate scenarios

|journal=Monthly Notices of the Royal Astronomical Society

|volume=438 |issue=4 |pages=3456

|arxiv=1308.0334

|bibcode=2014MNRAS.438.3456P

|doi=10.1093/mnras/stt2451

|doi-access=free

|s2cid=27316605

}} 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.

{{cite journal

|last1=Chen |first1=W.-C.

|last2=Li |first2=X.-D.

|year=2009

|title=On the Progenitors of Super-Chandrasekhar Mass Type Ia Supernovae

|journal=The Astrophysical Journal

|volume=702 |issue=1|pages=686–691

|arxiv=0907.0057

|bibcode=2009ApJ...702..686C

|doi=10.1088/0004-637X/702/1/686

|s2cid=14301164

}}

{{cite journal

|last1=Howell |first1=D. A.

|last2=Sullivan |first2=M.

|last3=Conley |first3=A. J.

|last4=Carlberg |first4=R. G.

|date=2007

|title=Predicted and Observed Evolution in the Mean Properties of Type Ia Supernovae with Redshift

|journal=Astrophysical Journal Letters

|volume=667 |issue=1 |pages=L37–L40

|arxiv=astro-ph/0701912

|bibcode=2007ApJ...667L..37H

|doi=10.1086/522030

|s2cid=16667595

}}{{cite journal|title=Standardization of type Ia supernovae |first1=Rodrigo C. V. |last1=Coelho |first2=Maurício O. |last2=Calvão |first3=Ribamar R. R. |last3=Reis |first4=Beatriz B. |last4=Siffert |arxiv=1411.3596 |journal=European Journal of Physics |volume=36 |year=2015 |issue=1 |page=015007 |doi=10.1088/0143-0807/36/1/015007|bibcode=2015EJPh...36a5007C }}

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,

{{cite journal

|last1=Chabrier |first1=G.

|last2=Baraffe |first2=I.

|date=2000

|title=Theory of low-Mass stars and substellar objects

|journal=Annual Review of Astronomy and Astrophysics

|volume=38 |pages=337–377

|arxiv= astro-ph/0006383

|bibcode=2000ARA&A..38..337C

|doi= 10.1146/annurev.astro.38.1.337

|s2cid=59325115

}} or the even lower-temperature brown dwarfs.

{{cite web

|last=Kaler

|first=J.

|title=The Hertzsprung-Russell (HR) diagram

|url=http://stars.astro.illinois.edu/sow/hrd.html

|access-date=5 May 2007

|archive-url=https://web.archive.org/web/20090831174414/http://stars.astro.illinois.edu/sow/hrd.html

|archive-date=31 August 2009

|url-status=live

}}

{{See also|Chandrasekhar's white dwarf equation|Neutron star#Gravity and equation of state}}

The relationship between the mass and radius of white dwarfs can be estimated using the nonrelativistic Fermi gas equation of state, which gives{{cite book

|last1=Kawaler |first1=S. D.

|chapter=White Dwarf Stars

|editor1-last=Kawaler |editor1-first=S. D.

|editor2-last=Novikov |editor2-first=I.

|editor3-last=Srinivasan |editor3-first=G.

|date=1997

|title=Stellar remnants

|publisher=1997

|isbn=978-3-540-61520-0

}}{{rp|25}}

$$\backslash frac\{R\}\{R\_\backslash odot\}\; \backslash approx\; 0.012\backslash left\; (\; \backslash frac\{M\}\{M\_\backslash odot\}\backslash right\; )^\{-1/3\}\; \backslash left\; (\backslash frac\{\backslash mu\_e\}\{2\}\backslash right)^\{-5/3\},$$

where {{mvar|R}} is the radius, {{mvar|M}} is the mass of the white dwarf, and the subscript $\backslash odot$ indicates relative to the Sun. The chemical potential, $\backslash mu\_e$ 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.{{Cite journal |last1=Bédard |first1=A. |last2=Bergeron |first2=P. |last3=Fontaine |first3=G. |date=October 2017 |title=Measurements of Physical Parameters of White Dwarfs: A Test of the Mass–Radius Relation |journal=The Astrophysical Journal |language=en |volume=848 |issue=1 |pages=11 |doi=10.3847/1538-4357/aa8bb6 |doi-access=free |arxiv=1709.02324 |bibcode=2017ApJ...848...11B |issn=0004-637X}}

Since this analysis uses the non-relativistic formula {{math|1= p² / 2m}} for the kinetic energy, it is non-relativistic. When the electron velocity in a white dwarf is close to the speed of light, the kinetic energy formula approaches {{math|1=pc}} where {{math|c}} 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:

$$M\_\{\backslash rm\; limit\}\; \backslash approx\; 1.46\backslash left\; (\backslash frac\{\backslash mu\_e\}\{2\}\backslash right)^\{-2\}$$

The observation of many white dwarf stars implies that either they started with masses similar to the Sun or something dramatic happened to reduce their mass.

File:ChandrasekharLimitGraph.svg

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state that 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, the radius is inversely proportional to the cube root of the mass.{{rp|eqn.(80)}} Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass. This is the limiting value of the mass – called the Chandrasekhar limit – at which the white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium. The average molecular weight per electron, {{math|μ_e}}, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.

{{cite web

|title=Basic symbols

|url=http://vizier.u-strasbg.fr/doc/catstd-3.2.htx

|work=Standards for Astronomical Catalogues, Version 2.0

|access-date=12 January 2007

|publisher=VizieR

|archive-url=https://web.archive.org/web/20170508162629/http://vizier.u-strasbg.fr/doc/catstd-3.2.htx

|archive-date=8 May 2017

|url-status=live

}}

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.

{{cite web

|last1=Tohline

|first1=J. E.

|author-link=Joel E. Tohline

|url=http://www.phys.lsu.edu/astro/H_Book.current/H_Book.html

|title=The Structure, Stability, and Dynamics of Self-Gravitating Systems

|access-date=30 May 2007

|archive-url=https://web.archive.org/web/20100627133917/http://www.phys.lsu.edu/astro/H_Book.current/H_Book.html

|archive-date=27 June 2010

|url-status=live

}} 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,

{{cite journal

|last1=Hoyle |first1=F.

|date=1947

|title=Stars, Distribution and Motions of, Note on equilibrium configurations for rotating white dwarfs

|volume=107 |issue=2

|pages=231–236

|journal=Monthly Notices of the Royal Astronomical Society

|bibcode=1947MNRAS.107..231H

|doi=10.1093/mnras/107.2.231

|doi-access=free

}} 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.

{{cite journal

|last1=Ostriker |first1=J. P.

|last2=Bodenheimer |first2=P.

|date=1968

|title=Rapidly Rotating Stars. II. Massive White Dwarfs

|journal=The Astrophysical Journal

|volume=151 |page=1089

|bibcode=1968ApJ...151.1089O

|doi= 10.1086/149507

|doi-access=free

}}

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.{{cite journal |bibcode=1994CMaPh.166..417C |title=On diameters of uniformly rotating stars |last1=Chanillo |first1=Sagun |last2=Li |first2=Yan Yan |journal=Communications in Mathematical Physics |year=1994 |volume=166 |issue=2 |page=417 |doi=10.1007/BF02112323 |s2cid=8372549 |url=http://projecteuclid.org/euclid.cmp/1104271617 }} The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously.{{cite journal |bibcode=2012JDE...253..553C |title=A remark on the geometry of uniformly rotating stars |last1=Chanillo |first1=Sagun |last2=Weiss |first2=Georg S. |journal=Journal of Differential Equations |year=2012 |volume=253 |issue=2 |page=553 |doi=10.1016/j.jde.2012.04.011 |arxiv=1109.3046 |s2cid=144301 }}

The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, because any absorption of a photon requires that an electron must transition to a higher empty state, which may not be possible as the energy of the photon may not be a match for the possible quantum states available to that electron, hence radiative heat transfer within a white dwarf is low; it does, however, have a high thermal conductivity. As a result, the interior of the white dwarf maintains an almost uniform temperature as it cools down, starting at approximately 10⁸ K shortly after the formation of the white dwarf and reaching less than 10⁶ K for the coolest known white dwarfs.{{cite journal |last1=Saumon |first1=Didier |last2=Blouin |first2=Simon |last3=Tremblay |first3=Pier-Emmanuel |title=Current challenges in the physics of white dwarf stars |journal=Physics Reports |date=November 2022 |volume=988 |pages=1–63 |doi=10.1016/j.physrep.2022.09.001|arxiv=2209.02846 |bibcode=2022PhR...988....1S |s2cid=252111027 }} 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.

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.

{{cite journal

|last1=Sion |first1=E. M.

|last2=Greenstein |first2=J. L.

|last3=Landstreet |first3=J. D.

|last4=Liebert |first4=James

|last5=Shipman |first5=H. L.

|last6=Wegner |first6=G. A.

|date=1983

|title=A proposed new white dwarf spectral classification system

|journal=The Astrophysical Journal

|volume=269 |page=253

|bibcode=1983ApJ...269..253S

|doi= 10.1086/161036

|doi-access=free

}} White dwarf effective surface temperatures extend from over {{val|150000}} K to barely under 4000 K.{{cite journal |last1=Hambly |first1=N. C. |last2=Smartt |first2=S. J. |last3=Hodgkin |first3=S. T. |date=1997 |title=WD 0346+246: A Very Low Luminosity, Cool Degenerate in Taurus |journal=The Astrophysical Journal |volume=489 |issue=2 |pages=L157 |bibcode=1997ApJ...489L.157H |doi=10.1086/316797 |doi-access=free}}

{{cite encyclopedia

|last1=Fontaine |first1=G.

|last2=Wesemael |first2=F.

|title=White dwarfs

|editor1-last=Murdin |editor1-first=P.

|date=2001

|encyclopedia=Encyclopedia of Astronomy and Astrophysics

|publisher=IOP Publishing/Nature Publishing Group

|isbn=978-0-333-75088-9

}} In accordance with the Stefan–Boltzmann law, luminosity increases with increasing surface temperature (proportional to T{{sup|4}}); this surface temperature range corresponds to a luminosity from over 100 times that of the Sun to under {{frac|1|{{val|10000}}}} that of the Sun. Hot white dwarfs, with surface temperatures in excess of {{val|30000|u=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.

{{cite journal

|last1=Heise |first1=J.

|date=1985

|title=X-ray emission from isolated hot white dwarfs

|journal=Space Science Reviews

|volume=40 |issue=1–2

|pages=79–90

|bibcode=1985SSRv...40...79H

|doi= 10.1007/BF00212870

|s2cid=120431159

}}

White dwarfs also radiate neutrinos through the Urca process.{{cite journal |bibcode=2005MNRAS.356..131L |title=A two-stream formalism for the convective Urca process |journal=Monthly Notices of the Royal Astronomical Society |volume=356 |issue=1 |pages=131–144 |last1=Lesaffre |first1=P. |last2=Podsiadlowski |first2=Ph. |last3=Tout |first3=C. A. |year=2005 |arxiv=astro-ph/0411016 |doi=10.1111/j.1365-2966.2004.08428.x |doi-access=free |s2cid=15797437 }} 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.

File:Size IK Peg.png B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of {{val|35500|u=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.

{{cite journal

|last1=Mestel |first1=L.

|date=1952

|title=On the theory of white dwarf stars. I. The energy sources of white dwarfs

|journal=Monthly Notices of the Royal Astronomical Society

|volume=112 |issue=6

|pages=583–597

|bibcode=1952MNRAS.112..583M

|doi=10.1093/mnras/112.6.583

|doi-access=free

}}

{{cite conference

|last1=Kawaler |first1=S. D.

|date=1998

|title=White Dwarf Stars and the Hubble Deep Field

|conference=The Hubble Deep Field: Proceedings of the Space Telescope Science Institute Symposium

|page=252

|arxiv=astro-ph/9802217

|bibcode=1998hdf..symp..252K

|isbn=978-0-521-63097-9

}}{{rp|§2.1}} White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. As a white dwarf cools, its surface temperature decreases, the radiation that it emits reddens, and its luminosity decreases. Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time. The rate of cooling has been estimated for a carbon white dwarf of {{solar mass|0.59}} with a hydrogen atmosphere. After initially taking approximately 1.5 billion years to cool to a surface temperature of 7140 K, cooling approximately 500 more kelvins to 6590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6030 K and 5550 K) take first 0.4 and then 1.1 billion years.

{{cite journal

|last1=Bergeron |first1=P.

|last2=Ruiz |first2=M. T.

|last3=Leggett |first3=S. K.

|date=1997

|title=The Chemical Evolution of Cool White Dwarfs and the Age of the Local Galactic Disk

|journal=The Astrophysical Journal Supplement Series

|volume=108 |issue=1

|pages=339–387

|bibcode=1997ApJS..108..339B

|doi= 10.1086/312955

|doi-access=free

}}{{rp|Table 2}}

Most observed white dwarfs have relatively high surface temperatures, between 8000 K and {{val|40000|u=K}}. A white dwarf, though, spends more of its lifetime at cooler temperatures than at hotter temperatures, so we should expect that there are more cool white dwarfs than hot white dwarfs. Once we adjust for the selection effect that hotter, more luminous white dwarfs are easier to observe, we do find that decreasing the temperature range examined results in finding more white dwarfs.

{{cite journal

|last1=Leggett |first1=S. K.

|last2=Ruiz |first2=M. T.

|last3=Bergeron |first3=P.

|date=1998

|title=The Cool White Dwarf Luminosity Function and the Age of the Galactic Disk

|journal=The Astrophysical Journal

|volume=497 |issue=1

|pages=294–302

|bibcode=1998ApJ...497..294L

|doi= 10.1086/305463

|doi-access=free

}} This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below {{val|4000|u=K}},

{{cite journal

|last1=Gates |first1=E.

|last2=Gyuk |first2=G.

|last3=Harris |first3=H. C.

|last4=Subbarao |first4=M.

|last5=Anderson |first5=S.

|last6=Kleinman |first6=S. J.

|last7=Liebert |first7=James

|last8=Brewington |first8=H.

|last9=Brinkmann |first9=J. | display-authors = 6

|date=2004

|title=Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey

|journal=The Astrophysical Journal

|volume=612 |issue=2 |pages=L129

|arxiv= astro-ph/0405566

|bibcode=2004ApJ...612L.129G

|doi= 10.1086/424568

|s2cid=7570539

}} and one of the coolest so far observed, WD J2147–4035, has a surface temperature of approximately 3050 K.{{cite journal |last1=Elms |first1=Abbigail K. |last2=Tremblay |first2=Pier-Emmanuel |last3=Gänsicke |first3=Boris T. |last4=Koester |first4=Detlev |last5=Hollands |first5=Mark A. |last6=Gentile Fusillo |first6=Nicola Pietro |last7=Cunningham |first7=Tim |last8=Apps |first8=Kevin |date=2022-12-01 |title=Spectral analysis of ultra-cool white dwarfs polluted by planetary debris |journal=Monthly Notices of the Royal Astronomical Society |volume=517 |issue=3 |pages=4557–4574 |arxiv=2206.05258 |bibcode=2022MNRAS.517.4557E |doi=10.1093/mnras/stac2908 |issn=0035-8711 |doi-access=free}} The reason for this is that the Universe's age is finite;

{{cite journal

|last1=Winget |first1=D. E.

|last2=Hansen |first2=C. J.

|last3=Liebert |first3=James

|last4=Van Horn |first4=H. M.

|last5=Fontaine |first5=G.

|last6=Nather |first6=R. E.

|last7=Kepler |first7=S. O.

|last8=Lamb |first8=D. Q.

|date=1987

|title=An independent method for determining the age of the universe

|journal=The Astrophysical Journal

|volume=315 |pages=L77

|bibcode=1987ApJ...315L..77W

|doi=10.1086/184864

|hdl=10183/108730

|doi-access=free

|hdl-access=free

}}

{{cite book

|last1=Trefil |first1=J. S.

|date=2004

|title=The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe

|publisher=Dover Publications

|isbn=978-0-486-43813-9

}} 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. A white dwarf will eventually, in many trillions of years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. No black dwarfs are thought to exist yet.

At very low temperatures (<4000 K) white dwarfs with hydrogen in their atmosphere will be affected by collision induced absorption (CIA) of hydrogen molecules colliding with helium atoms. This affects the optical red and infrared brightness of white dwarfs with a hydrogen or mixed hydrogen-helium atmosphere. This makes old white dwarfs with this kind of atmosphere bluer than the main cooling sequence. White dwarfs with hydrogen-poor atmospheres, such as WD J2147–4035, are less affected by CIA and therefore have a yellow to orange color.{{cite journal |last1=Bergeron |first1=P. |last2=Kilic |first2=Mukremin |last3=Blouin |first3=Simon |last4=Bédard |first4=A. |last5=Leggett |first5=S. K. |last6=Brown |first6=Warren R. |date=2022-07-01 |title=On the Nature of Ultracool White Dwarfs: Not so Cool after All |journal=The Astrophysical Journal |volume=934 |issue=1 |pages=36 |arxiv=2206.03174 |bibcode=2022ApJ...934...36B |doi=10.3847/1538-4357/ac76c7 |issn=0004-637X |doi-access=free}}

File:Gaia hrd wds2.png. The axes are absolute magnitude in the G-band vs. a color index G-band magnitude minus RP (Gaia red photometer) magnitude]]

White dwarf core material is a completely ionized plasma – a mixture of nuclei and electrons – that is initially in a fluid state. It was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize into a solid state, starting at its center.{{cite journal |last1=van Horn |first1=H. M. |title=Crystallization of White Dwarfs |journal=The Astrophysical Journal |date=January 1968 |volume=151 |page=227 |doi=10.1086/149432|bibcode=1968ApJ...151..227V }} The crystal structure is thought to be a body-centered cubic lattice.

{{cite journal

|last1=Barrat |first1=J. L.

|last2=Hansen |first2=J. P.

|last3=Mochkovitch |first3=R.

|date=1988

|title=Crystallization of carbon-oxygen mixtures in white dwarfs

|journal=Astronomy and Astrophysics

|volume=199 |issue=1–2

|pages=L15

|bibcode=1988A&A...199L..15B

}} In 1995 it was suggested that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,

{{cite journal

|last1=Winget |first1=D. E.

|date=1995

|title=The Status of White Dwarf Asteroseismology and a Glimpse of the Road Ahead

|volume=4 |issue=2

|page=129

|journal=Baltic Astronomy

|bibcode=1995BaltA...4..129W

|doi=10.1515/astro-1995-0209|doi-access=free

}} and in 2004, observations were made that suggested approximately 90% of the mass of BPM 37093 had crystallized.{{cite journal |last1=Metcalfe |first1=T. S. |last2=Montgomery |first2=M. H. |last3=Kanaan |first3=A. |title=Testing White Dwarf Crystallization Theory with Asteroseismology of the Massive Pulsating DA Star BPM 37093 |journal=The Astrophysical Journal |date=20 April 2004 |volume=605 |issue=2 |pages=L133–L136 |doi=10.1086/420884|arxiv=astro-ph/0402046 |bibcode=2004ApJ...605L.133M |s2cid=119378552 }}{{cite news |url=http://news.bbc.co.uk/2/hi/science/nature/3492919.stm |title=Diamond star thrills astronomers |archive-url=https://web.archive.org/web/20070205114340/http://news.bbc.co.uk/2/hi/science/nature/3492919.stm |archive-date=5 February 2007 |first=David |last=Whitehouse |work=BBC News |date=16 February 2004 |access-date=6 January 2007}}

{{cite journal

|last1=Kanaan |first1=A.

|last2=Nitta |first2=A.

|last3=Winget |first3=D. E.

|last4=Kepler |first4=S. O.

|last5=Montgomery |first5=M. H.

|last6=Metcalfe |first6=T. S.

|last7=Oliveira |first7=H.

|last8=Fraga |first8=L.

|last9=Da Costa |first9=A. F. M.| display-authors = 6

|date=2005

|title=Whole Earth Telescope observations of BPM 37093: A seismological test of crystallization theory in white dwarfs

|journal=Astronomy and Astrophysics

|volume=432 |issue=1

|pages=219–224

|arxiv=astro-ph/0411199

|bibcode= 2005A&A...432..219K

|doi=10.1051/0004-6361:20041125

|s2cid=7297628

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

{{cite journal

|last1=Brassard |first1=P.

|last2=Fontaine |first2=G.

|date=2005

|title=Asteroseismology of the Crystallized ZZ Ceti Star BPM 37093: A Different View

|journal=The Astrophysical Journal

|volume=622 |issue=1

|pages=572–576

|bibcode=2005ApJ...622..572B

|doi= 10.1086/428116

|doi-access=free

}}

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.{{cite journal |first1=B. M. S. |last1=Hansen |first2=James |last2=Liebert |title=Cool White Dwarfs |journal=Annual Review of Astronomy and Astrophysics |volume=41 |page=465 |year=2003|doi=10.1146/annurev.astro.41.081401.155117 |bibcode=2003ARA&A..41..465H }} 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.{{cite journal |last1=Antoine |first1=Bédard |last2=Simon |first2=Blouin |last3=Sihao |first3=Cheng |date=2024 |title=Buoyant crystals halt the cooling of white dwarf stars |url=https://www.nature.com/articles/s41586-024-07102-y.epdf |journal=Nature |language=en |volume=627 |issue=8003 |pages=286–288 |doi= 10.1038/s41586-024-07102-y|pmid=38448597 |arxiv=2409.04419 |bibcode=2024Natur.627..286B |issn=1476-4687}} Chemical fractionation between the ionic species in the plasma mixture can release a similar or even greater amount of energy.{{cite journal |last1=Althaus |first1=L. G. |last2=García-Berro |first2=E. |last3=Isern |first3=J. |last4=Córsico |first4=A. H. |last5=Miller Bertolami |first5=M. M. |title=New phase diagrams for dense carbon-oxygen mixtures and white dwarf evolution |journal=Astronomy & Astrophysics |date=January 2012 |volume=537 |pages=A33 |doi=10.1051/0004-6361/201117902|arxiv=1110.5665 |bibcode=2012A&A...537A..33A |s2cid=119279832 }}{{cite journal |last1=Blouin |first1=Simon |last2=Daligault |first2=Jérôme |last3=Saumon |first3=Didier |title=22 Ne Phase Separation as a Solution to the Ultramassive White Dwarf Cooling Anomaly |journal=The Astrophysical Journal Letters |date=1 April 2021 |volume=911 |issue=1 |pages=L5 |doi=10.3847/2041-8213/abf14b|arxiv=2103.12892 |bibcode=2021ApJ...911L...5B |s2cid=232335433 |doi-access=free }}{{cite journal |last1=Blouin |first1=Simon |last2=Daligault |first2=Jérôme |last3=Saumon |first3=Didier |last4=Bédard |first4=Antoine |last5=Brassard |first5=Pierre |title=Toward precision cosmochronology: A new C/O phase diagram for white dwarfs |journal=Astronomy & Astrophysics |date=August 2020 |volume=640 |pages=L11 |doi=10.1051/0004-6361/202038879|arxiv=2007.13669 |bibcode=2020A&A...640L..11B |s2cid=220793255 }} This energy release was first confirmed in 2019 after the identification of a pile up in the cooling sequence of more than {{val|15000}} white dwarfs observed with the Gaia satellite.

{{cite journal

|last1=Tremblay |first1=P.-E.

|last2=Fontaine |first2=G.

|last3=Fusillo |first3=N. P. G.

|last4=Dunlap |first4=B. H.

|last5=Gänsicke |first5=B. T.

|last6=Hollands |first6=M. H.

|last7=Hermes |first7=J. J.

|last8=Marsh |first8=T. R.

|last9=Cukanovaite |first9=E.

|last10=Cunningham |first10=T.

|display-authors=6

|date=2019

|title=Core crystallization and pile-up in the cooling sequence of evolving white dwarfs

|journal=Nature

|volume=565 |issue=7738 |pages=202–205

|bibcode=2019Natur.565..202T

|doi=10.1038/s41586-018-0791-x

|pmid=30626942

|url=http://wrap.warwick.ac.uk/112800/7/WRAP-core-crystallization-pile-up-cooling-sequence-evolving-white-dwarfs-Tremblay-2019.pdf

|arxiv=1908.00370

|s2cid=58004893

|access-date=23 July 2019

|archive-url=https://web.archive.org/web/20190723202013/http://wrap.warwick.ac.uk/112800/7/WRAP-core-crystallization-pile-up-cooling-sequence-evolving-white-dwarfs-Tremblay-2019.pdf

|archive-date=23 July 2019

|url-status=live

}}

Low-mass helium white dwarfs (mass {{solar mass|< 0.20}}), 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.{{cite journal|last1=Chen |first1=J. |display-authors=etal |year=2021 |title=Slowly cooling white dwarfs in M13 from stable hydrogen burning |journal=Nature Astronomy |volume=5 |number=11 |pages=1170–1177 |doi=10.1038/s41550-021-01445-6 |arxiv=2109.02306|bibcode=2021NatAs...5.1170C }} In addition, they remain in a bloated proto-white dwarf stage for up to 2 Gyr before they reach the cooling track.{{cite journal |first1=A. G. |last1=Istrate |first2=T. M. |last2=Tauris |first3=N. |last3=Langer |first4=J. |last4=Antoniadis |year=2014 |title=The timescale of low-mass proto-helium white dwarf evolution |journal=Astronomy and Astrophysics|volume=571 |page=L3 |bibcode=2014A&A...571L...3I |arxiv=1410.5471 |doi=10.1051/0004-6361/201424681 |s2cid=55152203 }}

File:Artist’s impression of the WDJ0914+1914 system.tif system{{cite web |title=First Giant Planet around White Dwarf Found – ESO observations indicate the Neptune-like exoplanet is evaporating |url=https://www.eso.org/public/news/eso1919/ |website=www.eso.org |access-date=4 December 2019 |language=en |archive-url=https://web.archive.org/web/20191204214723/https://www.eso.org/public/news/eso1919/ |archive-date=4 December 2019 |url-status=live}}]]

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.

{{cite journal

|last1=Schatzman |first1=E.

|date=1945

|title=Théorie du débit d'énergie des naines blanches

|volume=8 |page=143

|journal=Annales d'Astrophysique

|bibcode=1945AnAp....8..143S

}}

{{cite journal

|last1=Koester |first1=D.

|last2=Chanmugam |first2=G.

|date=1990

|title=Physics of white dwarf stars

|journal=Reports on Progress in Physics

|volume=53 |issue=7 |pages=837–915

|bibcode=1990RPPh...53..837K

|doi= 10.1088/0034-4885/53/7/001

|s2cid=122582479

}}{{rp|§§5–6}} 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 {{frac|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 {{frac|1|{{val|10000}}}} of the star's total mass.{{rp|§§4–5}}

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore at almost the same temperature (isothermal), and it is also hot: a white dwarf with surface temperature between {{val|8000|u=K}} and {{val|16000|u=K}} will have a core temperature between approximately {{val|5000000|u=K}} and {{val|20000000|u=K}}. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941,

{{cite journal

|last1=Kuiper |first1=G. P.

|date=1941

|title=List of Known White Dwarfs

|journal=Publications of the Astronomical Society of the Pacific

|volume=53 |issue=314

|page=248

|bibcode=1941PASP...53..248K

|doi= 10.1086/125335

|doi-access=free

}} and various classification schemes have been proposed and used since then.

{{cite journal

|last1=Luyten |first1=W. J.

|date=1952

|title=The Spectra and Luminosities of White Dwarfs

|journal=The Astrophysical Journal

|volume=116 |page=283

|bibcode=1952ApJ...116..283L

|doi= 10.1086/145612

}}

{{cite book

|last1=Greenstein |first1=J. L.

|date=1960

|title=Stellar atmospheres

|url=https://archive.org/details/stellaratmospher0000gree |url-access=registration

|publisher=University of Chicago Press

|bibcode=1960stat.book.....G

|lccn=61-9138

}} 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 {{val|50400|u=K}} by the effective temperature. For example, a white dwarf with only He I lines in its spectrum and an effective temperature of {{val|15000|u=K}} 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 {{val|17000|u=K}}, and a spectrum dominated by He I 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.

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs. The next class in number is of DBs, approximately 16%. The hot, above {{val|15000|u=K}}, DQ class (roughly 0.1%) have carbon-dominated atmospheres.

{{cite journal

|last1=Dufour |first1=P.

|last2=Liebert |first2=James

|last3=Fontaine |first3=G.

|last4=Behara |first4=N.

|date=2007

|title=White dwarf stars with carbon atmospheres

|journal=Nature

|volume=450 |issue=7169 |pages=522–4|pmid=18033290

|bibcode=2007Natur.450..522D

|doi=10.1038/nature06318

|arxiv = 0711.3227 |s2cid=4398697

}} 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 {{val|100000|u=K}} to {{val|45000|u=K}}, the spectrum will be classified DO, dominated by singly ionized helium. From {{val|30000|u=K}} to {{val|12000|u=K}}, the spectrum will be DB, showing neutral helium lines, and below about {{val|12000|u=K}}, the spectrum will be featureless and classified DC.{{rp|§2.4}}

Molecular hydrogen (H₂) has been detected in spectra of the atmospheres of some white dwarfs.{{cite journal |bibcode=2013ApJ...766L..18X |title=Discovery of Molecular Hydrogen in White Dwarf Atmospheres |last1=Xu |first1=S. |last2=Jura |first2=M. |last3=Koester |first3=D. |last4=Klein |first4=B. |last5=Zuckerman |first5=B. |journal=The Astrophysical Journal |year=2013 |volume=766 |issue=2 |pages=L18 |doi=10.1088/2041-8205/766/2/L18 |arxiv=1302.6619 |s2cid=119248244 }} 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.{{cite journal |last1=Weisskopf |first1=Martin C. |last2=Wu |first2=Kinwah |last3=Trimble |first3=Virginia |last4=O’Dell |first4=Stephen L. |last5=Elsner |first5=Ronald F. |last6=Zavlin |first6=Vyacheslav E. |last7=Kouveliotou |first7=Chryssa |date=2007-03-10 |title=A Chandra Search for Coronal X-Rays from the Cool White Dwarf GD 356 |url=https://iopscience.iop.org/article/10.1086/510776 |journal=The Astrophysical Journal |language=en |volume=657 |issue=2 |pages=1026–1036 |doi=10.1086/510776 |issn=0004-637X|arxiv=astro-ph/0609585 |bibcode=2007ApJ...657.1026W }}{{cite journal|last1=Route|first1=Matthew|title=The Decline and Fall of ROME. V. A Preliminary Search for Star-disrupted Planet Interactions and Coronal Activity at 5 GHz among White Dwarfs within 25 pc|journal=The Astrophysical Journal|date=20 December 2024|volume=977|issue=1|page=261|doi=10.3847/1538-4357/ad9567|arxiv=2411.13718|doi-access=free |bibcode=2024ApJ...977..261R }}

A few white dwarves have been observed to have inhomogeneous atmosphere with one side dominated by hydrogen and the other side dominated by helium.{{Cite journal |last1=Moss |first1=Adam |last2=Kilic |first2=Mukremin |last3=Bergeron |first3=Pierre |last4=Jewett |first4=Gracyn |last5=Brown |first5=Warren R. |date=2025-04-01 |title=The Emerging Class of Double-faced White Dwarfs |journal=The Astrophysical Journal |volume=983 |issue=1 |pages=14 |doi=10.3847/1538-4357/adbd3a |doi-access=free |issn=0004-637X|arxiv=2501.05649 }}

File:Periodic Table White Dwarfs.png

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.{{cite journal |title=Extrasolar Cosmochemistry |journal=Annual Review of Earth and Planetary Sciences |date=2014-01-01|pages=45–67 |volume=42 |issue=1 |doi=10.1146/annurev-earth-060313-054740 |first1=M. |last1=Jura |first2=E.D. |last2=Young |bibcode=2014AREPS..42...45J|doi-access=free }} The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky planetesimals. The bulk composition of the accreted object can be measured from the strengths of the metal lines. For example, a 2015 study of the white dwarf Ton 345 concluded that its metal abundances were consistent with those of a differentiated, rocky planet whose mantle had been eroded by the host star's wind during its asymptotic giant branch phase.{{cite journal |title=The composition of a disrupted extrasolar planetesimal at SDSS J0845+2257 (Ton 345) |journal = Monthly Notices of the Royal Astronomical Society |date=2015-08-11|pages=3237–3248 |volume=451 |issue=3 |doi=10.1093/mnras/stv1201 |language=en |first1=D.J. |last1=Wilson |first2=B.T. |last2=Gänsicke |first3=D. |last3=Koester |first4=O. |last4=Toloza |first5=A. F. |last5=Pala |first6=E. |last6=Breedt |first7=S.G. |last7=Parsons |doi-access = free |arxiv=1505.07466 |bibcode=2015MNRAS.451.3237W|s2cid=54049842 }}

Magnetic fields in white dwarfs with a strength at the surface of {{circa}} 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.

{{cite journal

|last1=Blackett |first1=P. M. S.

|date=1947

|title=The Magnetic Field of Massive Rotating Bodies

|journal=Nature

|volume=159 |issue=4046 |pages=658–66

|bibcode=1947Natur.159..658B

|doi= 10.1038/159658a0

|pmid=20239729

|s2cid=4133416

}} This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted.

{{cite journal

|last1=Lovell |first1=B.

|date=1975

|title=Patrick Maynard Stuart Blackett, Baron Blackett, of Chelsea. 18 November 1897 – 13 July 1974

|journal=Biographical Memoirs of Fellows of the Royal Society

|volume=21 |pages=1–115

|doi=10.1098/rsbm.1975.0001

|jstor=769678

|s2cid=74674634

}}{{rp|page=39–43}} 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.

{{cite journal

|last1=Landstreet |first1=John D.

|date=1967

|title=Synchrotron radiation of neutrinos and its astrophysical significance

|journal=Physical Review

|volume=153 |issue=5 |pages=1372–1377

|bibcode=1967PhRv..153.1372L

|doi= 10.1103/PhysRev.153.1372

}} A surface magnetic field of {{circa}} 100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of {{circa}} 100 × 100² = 1 million gauss (100 T) once the star's radius had shrunk by a factor of 100.{{rp|§8}}

{{cite journal

|last1=Ginzburg |first1=V. L.

|last2=Zheleznyakov |first2=V. V.

|last3=Zaitsev |first3=V. V.

|date=1969

|title=Coherent mechanisms of radio emission and magnetic models of pulsars

|journal=Astrophysics and Space Science

|volume=4 |issue=4 |pages=464–504

|bibcode=1969Ap&SS...4..464G

|doi= 10.1007/BF00651351

|s2cid=119003761

}}{{rp|page=484}} The first magnetic white dwarf to be discovered was GJ 742 (also known as {{nowrap|GRW +70 8247}}), 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.

{{cite journal

|last1=Kemp |first1=J.C. |last2=Swedlund |first2=J.B.

|last3=Landstreet |first3=J.D. |last4=Angel |first4=J.R.P.

|date=1970

|title=Discovery of circularly polarized light from a white dwarf

|journal=The Astrophysical Journal

|volume=161 |page=L77

|bibcode=1970ApJ...161L..77K

|doi=10.1086/180574 |doi-access=free

}}

It is thought to have a surface field of approximately 300 million gauss (30 kT).{{rp|§8}}

Since 1970, magnetic fields have been discovered in well over 200 white dwarfs, ranging from {{val|2|e=3}} to {{val|e=9}} gauss (0.2 T to 100 kT).

{{cite journal

|last1=Ferrario |first1=Lilia

|last2=de Martino |first2=Domtilla

|last3=Gaensicke |first3=Boris

|date=2015

|title=Magnetic white dwarfs

|journal=Space Science Reviews

|volume=191 |issue=1–4 |pages=111–169

|bibcode=2015SSRv..191..111F

|doi= 10.1007/s11214-015-0152-0 |arxiv=1504.08072|s2cid=119057870

}}

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.

{{cite journal

|last1=Kepler |first1=S.O.

|last2=Pelisoli |first2=I.

|last3=Jordan |first3=S.

|last4=Kleinman |first4=S.J.

|last5=Koester |first5=D.

|last6=Kuelebi |first6=B.

|last7=Pecanha |first7=V.

|last8=Castanhiera |first8=B.G.

|last9=Nitta |first9=A.

|last10=Costa |first10=J.E.S.

|last11=Winget |first11=D.E.

|last12=Kanaan |first12=A.

|last13=Fraga |first13=L.

|date=2013

|title=Magnetic white dwarf stars in the Sloan Digital Sky Survey

|journal=Monthly Notices of the Royal Astronomical Society

|volume=429 |issue=4 |pages=2934–2944

|bibcode=2013MNRAS.429.2934K

|doi= 10.1093/mnras/sts522

|doi-access=free

|arxiv=1211.5709|s2cid=53316287

}}

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. It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).

{{cite journal

|last1=Landstreet |first1=J.D.

|last2=Bagnulo |first2=S.

|last3=Valyavin |first3=G.G.

|last4=Fossati |first4=L.

|last5=Jordan |first5=S.

|last6=Monin |first6=D.

|last7=Wade |first7=G.A.

|date=2012

|title=On the incidence of weak magnetic fields in DA white dwarfs

|journal=Astronomy and Astrophysics

|volume=545 |issue=A30 |pages=9pp

|bibcode=2012A&A...545A..30L |doi=10.1051/0004-6361/201219829

|arxiv=1208.3650|s2cid=55153825

}}

{{cite journal

|last1=Liebert |first1=James

|last2=Bergeron |first2=P.

|last3=Holberg |first3=J. B.

|title=The True Incidence of Magnetism Among Field White Dwarfs

|date=2003

|journal=The Astronomical Journal

|volume=125 |issue=1 |pages=348–353

|arxiv=astro-ph/0210319 |bibcode=2003AJ....125..348L

|doi=10.1086/345573 |s2cid=9005227

}} 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.

{{cite news

|first=Zeeya |last=Merali

|date=19 July 2012

|title=Stars draw atoms closer together

|department=Nature News & Comment

|journal=Nature

|doi=10.1038/nature.2012.11045 |doi-access=free

|url=http://www.nature.com/news/stars-draw-atoms-closer-together-1.11045

|access-date=21 July 2012 |url-status=live

|archive-url=https://web.archive.org/web/20120720200709/http://www.nature.com/news/stars-draw-atoms-closer-together-1.11045

|archive-date=20 July 2012

}}

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.

{{cite journal

|last1=Buckley |first1=D.A.H. |last2=Meintjes |first2=P.J.

|last3=Potter |first3=S.B. |last4=Marsh |first4=T.R.

|last5=Gänsicke |first5=B.T.

|date=2017-01-23

|title=Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii |language=en

|journal=Nature Astronomy

|volume=1 |issue=2 |page=0029

|doi=10.1038/s41550-016-0029 |s2cid=15683792

|arxiv=1612.03185 |bibcode=2017NatAs...1E..29B

}}

A second white dwarf pulsar was discovered in 2023.{{cite journal|first1=Ingrid |last1=Pelisoli |display-authors=etal |title=A 5.3-min-period pulsing white dwarf in a binary detected from radio to X-rays |journal=Nature Astronomy |volume=7 |pages=931–942 |year=2023 |issue=8 |doi=10.1038/s41550-023-01995-x |arxiv=2306.09272|bibcode=2023NatAs...7..931P }}

{{Main|Pulsating white dwarf}}

{{Seealso|Cataclysmic variables}}

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.{{rp|§7.1.1}}

{{cite journal

|last1=Lawrence |first1=G. M.

|last2=Ostriker |first2=J. P.

|last3=Hesser |first3=J. E.

|date=1967

|title=Ultrashort-Period Stellar Oscillations. I. Results from White Dwarfs, Old Novae, Central Stars of Planetary Nebulae, 3c 273, and Scorpius XR-1

|journal=The Astrophysical Journal

|volume=148 |pages=L161

|bibcode=1967ApJ...148L.161L

|doi= 10.1086/180037

}} 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.

{{cite journal

|last1=Landolt |first1=A. U.

|date=1968

|title=A New Short-Period Blue Variable

|journal=The Astrophysical Journal

|volume=153 |page=151

|bibcode=1968ApJ...153..151L

|doi= 10.1086/149645 |doi-access=free

}} 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.{{rp|§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;{{rp|891, 895}} DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;{{rp|3525}} and GW Vir stars, sometimes subdivided into DOV and PNNV stars, with atmospheres dominated by helium, carbon, and oxygen.

{{cite journal

|last1=Quirion |first1=P.-O.

|last2=Fontaine |first2=G.

|last3=Brassard |first3=P.

|date=2007

|title=Mapping the Instability Domains of GW Vir Stars in the Effective Temperature–Surface Gravity Diagram

|journal=The Astrophysical Journal Supplement Series

|volume=171 |issue=1

|pages=219–248

|bibcode=2007ApJS..171..219Q

|doi= 10.1086/513870

|doi-access=free

}}

{{cite journal

|last1=Nagel |first1=T.

|last2=Werner |first2=K.

|date=2004

|title=Detection of non-radial g-mode pulsations in the newly discovered PG 1159 star HE 1429-1209

|journal=Astronomy and Astrophysics

|volume=426 |issue=2 |pages=L45

|arxiv= astro-ph/0409243

|doi= 10.1051/0004-6361:200400079

|bibcode=2004A&A...426L..45N

|s2cid=9481357

}} 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.

{{cite journal

|last1=O'Brien |first1=M. S.

|date=2000

|title=The Extent and Cause of the Pre–White Dwarf Instability Strip

|journal=The Astrophysical Journal

|volume=532 |issue=2 |pages=1078–1088

|arxiv= astro-ph/9910495

|bibcode=2000ApJ...532.1078O

|doi= 10.1086/308613

|s2cid=115958740

}} 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.

{{cite journal

|last1=Winget |first1=D. E.

|title=Asteroseismology of white dwarf stars

|date=1998

|journal=Journal of Physics: Condensed Matter

|volume=10 |issue=49 |pages=11247–11261

|bibcode= 1998JPCM...1011247W

|doi=10.1088/0953-8984/10/49/014

|s2cid=250749380

}}

White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about {{solar mass|0.07 to 10}}.

{{cite journal

|last1=Heger |first1=A.

|last2=Fryer |first2=C. L.

|last3=Woosley |first3=S. E.

|last4=Langer |first4=N.

|last5=Hartmann |first5=D. H.

|date=2003

|title=How Massive Single Stars End Their Life

|journal=The Astrophysical Journal

|volume=591 |issue=1

|pages=288–300

|arxiv= astro-ph/0212469

|bibcode=2003ApJ...591..288H

|doi= 10.1086/375341

|s2cid=59065632

}} The composition of the white dwarf produced will depend on the initial mass of the star. Current galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs.{{cite journal |doi=10.1088/1742-6596/172/1/012004 |title=The galactic population of white dwarfs |journal=Journal of Physics |series=Conference Series |volume=172 |page=012004 |year=2009 |last1=Napiwotzki |first1=Ralf |issue=1 |bibcode=2009JPhCS.172a2004N |arxiv=0903.2159|s2cid=17521113 }}

If the mass of a main-sequence star is lower than approximately half a solar mass, it will never become hot enough to ignite and fuse helium in its core.{{cite journal |first1=J. M. |last1=Brown |first2=M. |last2=Kilic |first3=W. R. |last3=Brown |first4=S. J. |last4=Kenyon |date=2011 |title=The binary fraction of low-mass white dwarfs |journal=The Astrophysical Journal |volume=730 |number=67 |page=67 |doi=10.1088/0004-637X/730/2/67|arxiv=1101.5169 |bibcode=2011ApJ...730...67B }} It is thought that, over a lifespan that considerably exceeds the age of the universe ({{circa}} 13.8 billion years),

{{cite journal

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|last3=Doré |first3=O. |last4=Nolta |first4=M.R.

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|last7=Hinshaw |first7=G. |last8=Jarosik |first8=N.

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|last17=Meyer |first17=S.S. |last18=Odegard |first18=N.

|last19=Tucker |first19=G.S. |last20=Weiland |first20=J.L.

|last21=Wollack |first21=E. |last22=Wright |first22=E.L.

|display-authors=6

|year=2007

|title=Wilkinson Microwave Anisotropy Probe (WMAP) three year results: Implications for cosmology

|journal=The Astrophysical Journal Supplement Series

|volume=170 |issue=2 |pages=377–408

|arxiv=astro-ph/0603449 |bibcode=2007ApJS..170..377S

|doi=10.1086/513700 |s2cid=1386346

}}

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.

{{cite journal

|last1=Laughlin |first1=G.

|last2=Bodenheimer |first2=P.

|last3=Adams |first3=Fred C.

|date=1997

|title=The End of the Main Sequence

|journal=The Astrophysical Journal

|volume=482 |issue=1

|pages=420–432

|bibcode=1997ApJ...482..420L

|doi=10.1086/304125

|doi-access=free

}} Due to the very long time this process takes, it is not thought to be the origin of the observed helium white dwarfs. Rather, they are thought to be mostly the product of mass loss in binary systems.{{cite web |url=http://star.arm.ac.uk/~csj/pus/astnow/astnow.html |title=Stars Beyond Maturity |archive-url=https://web.archive.org/web/20150404004046/http://star.arm.ac.uk/~csj/pus/astnow/astnow.html |archive-date=4 April 2015 |author=Jeffery, Simon |access-date=3 May 2007}}

{{cite journal

|last1=Sarna |first1=M. J.

|last2=Ergma |first2=E.

|last3=Gerškevitš |first3=J.

|journal=Astronomische Nachrichten

|date=2001

|title=Helium core white dwarf evolution – including white dwarf companions to neutron stars

|volume=322 |issue=5–6 |pages=405–410

|bibcode=2001AN....322..405S

|doi= 10.1002/1521-3994(200112)322:5/6<405::AID-ASNA405>3.0.CO;2-6

}}

{{cite journal

|last1=Benvenuto |first1=O. G.

|last2=De Vito |first2=M. A.

|date=2005

|title=The formation of helium white dwarfs in close binary systems – II

|journal=Monthly Notices of the Royal Astronomical Society

|volume=362 |issue=3 |pages=891–905

|bibcode=2005MNRAS.362..891B

|doi= 10.1111/j.1365-2966.2005.09315.x |doi-access=free

}} Proposals to explain those helium white dwarfs that are not part of binary systems include mass loss due to a large planetary companion, stars being stripped of material by companions exploding as supernovae, and various types of stellar mergers.

{{cite journal

|last1=Nelemans |first1=G.

|last2=Tauris |first2=T. M.

|title=Formation of undermassive single white dwarfs and the influence of planets on late stellar evolution

|date=1998

|journal=Astronomy and Astrophysics

|volume=335 |pages=L85

|arxiv= astro-ph/9806011

|bibcode=1998A&A...335L..85N

}}

{{cite journal

|first1=Xianfei |last1=Zhang

|first2=Philip D. |last2=Hall

|first3=C. Simon |last3=Jeffery

|first4=Shaolan |last4=Bi

|year=2018

|title=Evolution models of helium white dwarf–main-sequence star merger remnants: the mass distribution of single low-mass white dwarfs

|journal=Monthly Notices of the Royal Astronomical Society

|volume=474

|pages=427–432

|doi=10.1093/mnras/stx2747

|doi-access=free

|arxiv=1711.03285

}}

If the mass of a main-sequence star is between {{solar mass|0.5 and 8}}, 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 that 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 that form the vast majority of observed white dwarfs.{{cite web |url=http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_lowmass.html |title=The evolution of low-mass stars |archive-url=https://web.archive.org/web/20121107125754/http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_lowmass.html |archive-date=7 November 2012 |author=Dhillon, Vik |series=lecture notes, Physics 213 |publisher=University of Sheffield |access-date=3 May 2007}}{{cite web |url=http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_highmass.html |title=The evolution of high-mass stars |archive-url=https://web.archive.org/web/20121107125747/http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_highmass.html |archive-date=7 November 2012 |author=Dhillon, Vik |series=lecture notes, Physics 213 |publisher=University of Sheffield |access-date=3 May 2007}}

White dwarfs with a mass greater than {{val|1.05|u=Solar mass}} 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.{{cite journal

| title=Forever young white dwarfs: When stellar ageing stops

| last1=Camisassa | first1=María E. | last2=Althaus | first2=Leandro G.

| last3=Torres | first3=Santiago | last4=Córsico | first4=Alejandro H.

| last5=Rebassa-Mansergas | first5=Alberto | last6=Tremblay | first6=Pier-Emmanuel

| last7=Cheng | first7=Sihao | last8=Raddi | first8=Roberto

| display-authors=1 | journal=Astronomy & Astrophysics

| volume=649 | at=id. L7 | date=May 2021

| doi=10.1051/0004-6361/202140720 | arxiv=2008.03028

| bibcode=2021A&A...649L...7C }}

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.

{{cite journal

|bibcode=2005JPhG...31S.651S

|arxiv=astro-ph/0412215

|doi= 10.1088/0954-3899/31/6/004

|title=Strange quark matter in stars: A general overview

|date=2005

|last1=Schaffner-Bielich |first1=Jürgen

|journal=Journal of Physics G: Nuclear and Particle Physics

|volume=31 |issue=6 |pages=S651–S657

|s2cid=118886040

}} Some main-sequence stars, of perhaps {{solar mass|8 to 10}}, 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.

{{cite journal

|title=Evolution of 8–10 solar mass stars toward electron capture supernovae. I – Formation of electron-degenerate O + NE + MG cores

|date=1984

|last1=Nomoto |first1=K.

|journal=The Astrophysical Journal

|volume=277 |page=791

|bibcode=1984ApJ...277..791N

|doi= 10.1086/161749 |doi-access=free

}}

{{cite journal

|bibcode=2002RvMP...74.1015W

|doi= 10.1103/RevModPhys.74.1015

|title=The evolution and explosion of massive stars

|date=2002

|last1=Woosley |first1=S. E.

|last2=Heger |first2=A.

|last3= Weaver

|first3= T. A.

|journal=Reviews of Modern Physics

|volume=74 |issue=4 |pages=1015–1071

}} 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.

{{cite journal

|bibcode=2004A&A...421.1169W

|arxiv= astro-ph/0404325

|doi= 10.1051/0004-6361:20047154

|title=Chandra and FUSE spectroscopy of the hot bare stellar core H?1504+65

|date=2004

|last1=Werner |first1=K.

|last2=Rauch |first2=T.

|last3=Barstow |first3=M. A.

|last4=Kruk |first4=J. W.

|journal=Astronomy and Astrophysics

|volume=421 |issue=3 |pages=1169–1183

|s2cid= 2983893

}}

{{cite journal

|bibcode=1994ApJ...425..797L

|doi= 10.1086/174024

|title=On the interpretation and implications of nova abundances: An abundance of riches or an overabundance of enrichments

|date=1994

|last1=Livio |first1=Mario

|last2=Truran |first2=James W.

|journal=The Astrophysical Journal

|volume=425 |page=797

|doi-access=free

}}

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.

{{cite journal

|bibcode=2012ApJ...761L..23J

|doi=10.1088/2041-8205/761/2/L23

|title=Failed-detonation Supernovae: Subluminous Low-velocity Ia Supernovae and their Kicked Remnant White Dwarfs with Iron-rich Cores

|date=2012

|last1=Jordan |first1=George C. IV.

|last2=Perets |first2=Hagai B.

|last3=Fisher |first3=Robert T.

|last4=van Rossum |first4=Daniel R.

|journal=The Astrophysical Journal Letters

|volume=761 |issue=2

|pages=L23

|arxiv = 1208.5069 |s2cid=119203015

}} These iron-core white dwarfs would be smaller than the carbon–oxygen kind of similar mass and would cool and crystallize faster than those.

{{cite journal

|bibcode=2000MNRAS.312..531P

|doi=10.1046/j.1365-8711.2000.03236.x

|title=The evolution of iron-core white dwarfs

|date=2000

|last1=Panei |first1=J. A.

|last2=Althaus |first2=L. G.

|last3=Benvenuto |first3=O. G.

|journal=Monthly Notices of the Royal Astronomical Society

|volume=312 |issue=3

|pages=531–539

|doi-access=free

|arxiv = astro-ph/9911371 |s2cid=17854858

}}

File:White Dwarf Ages.ogv

File:Whitedwarfsevolution.png

Once formed, a white dwarf is stable and will usually continue to cool almost indefinitely, eventually to become 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.{{cite journal |last1=Adams |first1=Fred C. |last2=Laughlin |first2=Gregory |date=1997 |title=A dying universe: The long-term fate and evolution of astrophysical objects |journal=Reviews of Modern Physics |volume=69 |issue=2 |pages=337–372 |arxiv=astro-ph/9701131 |bibcode=1997RvMP...69..337A |doi=10.1103/RevModPhys.69.337|s2cid=12173790 }}{{rp|§IIIA}} White dwarfs should generally survive galactic dispersion, although an occasional collision between white dwarfs may produce a new fusing star (eg. an extreme helium star){{cite journal | title=The origin and pulsations of extreme helium stars | last=Jeffery | first=C. Simon | journal=Precision Asteroseismology, Proceedings of the International Astronomical Union | series=IAU Symposium | volume=301 | pages=297–304 | date=February 2014 | doi=10.1017/S1743921313014488 | arxiv=1311.1635 | bibcode=2014IAUS..301..297J }} or a super-Chandrasekhar mass white dwarf that will explode in a Type Ia supernova.{{rp|§§IIIC, IV}}

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. Some grand unified theories predict a proton lifetime between 10³⁰ and 10³⁶ years. If these theories are not valid, the proton might still decay by complicated nuclear reactions or through quantum gravitational processes involving virtual black holes; in these cases, the lifetime is estimated to be no more than 10²⁰⁰ years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses enough mass to become a non-degenerate lump of matter, and finally disappears completely.{{rp|§IV}}

A white dwarf can also be cannibalized or evaporated by a companion star, causing the white dwarf to lose so much mass that it becomes a planetary mass object. The resultant object, orbiting the former companion, now host star, could be a helium planet or diamond planet.{{cite journal |title=Mass-Radius Relationships for Solid Exoplanets |last1=Seager |first1=S. |last2=Kuchner |first2=M. |last3=Hier-Majumder |first3=C. |last4=Militzer |first4= B. |journal=The Astrophysical Journal |volume=669 |issue=2 |pages=1279–1297 |publication-date=November 2007 |doi=10.1086/521346 |arxiv=0707.2895 |bibcode=2007ApJ...669.1279S |date=19 July 2007|s2cid=8369390 }}{{cite journal |doi=10.1126/science.1208890 |title=Transformation of a Star into a Planet in a Millisecond Pulsar Binary |year=2011 |last1=Bailes |first1=M. |journal=Science |volume=333 |number=6050 |pages=1717–1720 |pmid=21868629 |arxiv=1108.5201 |bibcode=2011Sci...333.1717B |display-authors=etal}}{{cite magazine |last=Lemonick |first= Michael |date=26 August 2011 |title=Scientists Discover a Diamond as Big as a Planet |url=http://www.time.com/time/health/article/0,8599,2090471,00.html |magazine=Time Magazine |archive-url=https://web.archive.org/web/20130824010717/http://www.time.com/time/health/article/0,8599,2090471,00.html |archive-date=24 August 2013 |access-date=18 June 2015}}

{{see also|List of exoplanets and planetary debris around white dwarfs}}

File:Artist’s impression of debris around a white dwarf star.jpg

File:Comet falling into white dwarf.jpg

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,{{cite journal |last1=Koester |first1=D. |last2=Gänsicke |first2=B. T. |last3=Farihi |first3=J. |date=2014-06-01 |title=The frequency of planetary debris around young white dwarfs |bibcode=2014A&A...566A..34K |journal=Astronomy and Astrophysics |volume=566 |pages=A34 |doi=10.1051/0004-6361/201423691 |arxiv=1404.2617 |s2cid=119268896 |issn=0004-6361}} but these heavy elements settle out in the atmosphere of white dwarfs colder than {{val|20000|u=K}}. The most widely accepted hypothesis is that this pollution comes from tidally disrupted rocky bodies.{{cite journal |last=Jura |first=M. |date=2008-05-01 |title=Pollution of Single White Dwarfs by Accretion of Many Small Asteroids |bibcode=2008AJ....135.1785J |journal=The Astronomical Journal |volume=135 |issue=5 |pages=1785–1792 |doi=10.1088/0004-6256/135/5/1785 |arxiv=0802.4075 |s2cid=16571761 |issn=0004-6256}} The first observation of a metal-polluted white dwarf was by van Maanen in 1917 at the Mount Wilson Observatory and is now recognized as the first evidence of exoplanets in astronomy.{{cite journal |last1=Klein |first1=Beth L. |last2=Doyle |first2=Alexandra E. |last3=Zuckerman |first3=B. |last4=Dufour |first4=P. |last5=Blouin |first5=Simon |last6=Melis |first6=Carl |last7=Weinberger |first7=Alycia J. |last8=Young |first8=Edward D. |date=2021-06-01 |title=Discovery of Beryllium in White Dwarfs Polluted by Planetesimal Accretion |bibcode=2021ApJ...914...61K |journal=The Astrophysical Journal |volume=914 |issue=1 |page=61 |doi=10.3847/1538-4357/abe40b |arxiv=2102.01834 |s2cid=231786441 |issn=0004-637X |doi-access=free }} The white dwarf van Maanen 2 shows iron, calcium and magnesium in its atmosphere,{{cite conference |conference=19Th European Workshop on White Dwarfs |last=Zuckerman |first=B. |date=2015-06-01 |title=Recognition of the First Observational Evidence of an Extrasolar Planetary System |bibcode=2015ASPC..493..291Z |volume=493 |page=291}} but van Maanen misclassified it as the faintest F-type star based on the calcium H- and K-lines.{{cite journal |last=Farihi |first=J. |date=2016-04-01 |title=Circumstellar debris and pollution at white dwarf stars |bibcode=2016NewAR..71....9F |journal=New Astronomy Reviews |volume=71 |pages=9–34 |doi=10.1016/j.newar.2016.03.001 |arxiv=1604.03092 |s2cid=118486264 |issn=1387-6473}} 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.

A less common observable evidence is infrared excess due to a flat and optically thick debris disk, which is found in around 1%–4% of white dwarfs. The first white dwarf with infrared excess was discovered by Zuckerman and Becklin in 1987 in the near-infrared around Giclas 29-38{{cite journal |last1=Zuckerman |first1=B. |last2=Becklin |first2=E. E. |date=1987-11-01 |title=Excess infrared radiation from a white dwarf—an orbiting brown dwarf? |bibcode=1987Natur.330..138Z |journal=Nature |volume=330 |issue=6144 |pages=138–140 |doi=10.1038/330138a0 |s2cid=4357883 |issn=0028-0836}} and later confirmed as a debris disk. White dwarfs hotter than {{val|27000|u=K}} sublimate all the dust formed by tidally disrupting a rocky body, preventing the formation of a debris disk. In colder white dwarfs, a rocky body might be tidally disrupted near the Roche radius and forced into a circular orbit by the Poynting–Robertson drag, which is stronger for less massive white dwarfs. The Poynting–Robertson drag will also cause the dust to orbit closer and closer towards the white dwarf, until it will eventually sublimate and the disk will disappear. A debris disk will have a lifetime of around a few million years for white dwarfs hotter than {{val|10000|u=K}}. Colder white dwarfs can have disk-lifetimes of a few 10 million years, which is enough time to tidally disrupt a second rocky body and forming a second disk around a white dwarf, such as the two rings around LSPM J0207+3331.{{cite journal |last1=Steckloff |first1=Jordan K. |last2=Debes |first2=John |last3=Steele |first3=Amy |last4=Johnson |first4=Brandon |last5=Adams |first5=Elisabeth R. |last6=Jacobson |first6=Seth A. |last7=Springmann |first7=Alessondra |date=2021-06-01 |title=How Sublimation Delays the Onset of Dusty Debris Disk Formation around White Dwarf Stars |bibcode=2021ApJ...913L..31S |journal=The Astrophysical Journal |volume=913 |issue=2 |pages=L31 |doi=10.3847/2041-8213/abfd39 |pmid=35003618 |pmc=8740607 |arxiv=2104.14035 |issn=0004-637X |doi-access=free }}

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.{{cite book |last=Veras |first=Dimitri |bibcode=2021orel.bookE...1V |arxiv=2106.06550 |chapter=Planetary Systems Around White Dwarfs |title=Oxford Research Encyclopedia of Planetary Science |doi=10.1093/acrefore/9780190647926.013.238 |publisher=Oxford University Press |date=2021-10-01|isbn=978-0-19-064792-6 }}{{cite journal |last1=Mullally |first1=Susan E. |last2=Debes |first2=John |last3=Cracraft |first3=Misty |last4=Mullally |first4=Fergal |last5=Poulsen |first5=Sabrina |last6=Albert |first6=Loic |last7=Thibault |first7=Katherine |last8=Reach |first8=William T. |last9=Hermes |first9=J. J. |last10=Barclay |first10=Thomas |last11=Kilic |first11=Mukremin |last12=Quintana |first12=Elisa V. |date=24 Jan 2024 |title=JWST Directly Images Giant Planet Candidates Around Two Metal-Polluted White Dwarf Stars |journal=The Astrophysical Journal Letters |volume=962 |issue=2 |pages=L32 |doi=10.3847/2041-8213/ad2348 |doi-access=free |arxiv=2401.13153|bibcode=2024ApJ...962L..32M }} {{multiple image |header=Exoplanet orbits WD 1856+534 |align=right |direction=vertical |width= |image1=Artist’s impression of WD 1856b (noirlab2023a).jpg |caption1= |width1=250 |image2=NASA-ExoplanetOrbitingWhiteDwarfStarWD1856+534.webm |caption2=

A search has been proposed for transits of hypothetical Earth-like planets around white dwarfs with surface temperatures of less than {{val|10000|u=K}}. Such stars that could harbor a habitable zone at a distance of {{circa}} 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.

{{cite journal

|bibcode=2011ApJ...731L..31A

|arxiv= 1103.2791

|doi= 10.1088/2041-8205/731/2/L31

|title=Transit Surveys for Earths in the Habitable Zones of White Dwarfs

|date=2011

|last1=Agol |first1=Eric

|journal=The Astrophysical Journal Letters

|volume=635 |issue=2 |pages=L31

|s2cid= 118739494

}}

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.

{{cite journal

|bibcode=2013AsBio..13..279B

|arxiv= 1211.6467

|doi= 10.1089/ast.2012.0867

|title=Habitable Planets Around White and Brown Dwarfs: The Perils of a Cooling Primary

|date=2011

|last1=Barnes |first1=Rory |last2=Heller |first2=René

|journal=Astrobiology

|volume=13 |issue=3 |pages=279–291

|pmid=23537137 |pmc=3612282

}} 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.

{{cite journal

|bibcode=2013MNRAS.432..500N

|arxiv=1211.1013

|doi=10.1093/mnras/stt569

|title=On the orbits of low-mass companions to white dwarfs and the fates of the known exoplanets

|date=2013

|last1=Nordhaus |first1=J. |last2=Spiegel |first2=D.S.

|journal=Monthly Notices of the Royal Astronomical Society

|volume=432 |issue=1 |pages=500–505

|doi-access=free

|s2cid=119227364

}}

File:White dwarfs circling each other and then colliding.gifs]]

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.

{{cite book

|author1=Di Stefano, R.

|author2=Nelson, L. A.

|author3=Lee, W.

|author4=Wood, T. H.

|author5=Rappaport, S.

|title=Thermonuclear Supernovae

|contribution=Luminous Supersoft X-ray Sources as Type Ia Progenitors

|volume=486

|pages=148–149 |issue=486

|series=NATO Science Series C: Mathematical and physical sciences

|editor=P. Ruiz-Lapuente |editor2=R. Canal |editor3=J. Isern

|publisher=Springer

|date=1997

|isbn=978-0-7923-4359-2

|bibcode=1997ASIC..486..147D

|doi=10.1007/978-94-011-5710-0_10

|url=https://cds.cern.ch/record/305422

}} 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).{{cite journal |bibcode=2020ApJ...898L..40L|arxiv= 2007.13932|doi= 10.3847/2041-8213/aba618|title=CTCV J2056-3014: An X-Ray-faint Intermediate Polar Harboring an Extremely Fast-spinning White Dwarf|date=2020|last1=Lopes de Oliveira |first1=R.|last2=Bruch |first2=A.|last3=Rodrigues |first3=C. V.|last4=de Oliveira |first4=A. S.|last5=Mukai |first5=K.|journal=The Astrophysical Journal Letters|volume=898 |issue=2 |pages=L40

|s2cid= 220831174|doi-access= free}} A close binary system of two white dwarfs can lose angular momentum and radiate energy in the form of gravitational waves, causing their mutual orbit to steadily shrink until the stars merge.

{{cite news

|author1 = Aguilar, David A.

|author2 = Pulliam, Christine

|title = Astronomers Discover Merging Star Systems that Might Explode

|date = 16 November 2010

|publisher = Harvard-Smithsonian Center for Astrophysics

|url = http://www.cfa.harvard.edu/news/2010/pr201024.html

|access-date = 16 February 2011

|archive-url = https://web.archive.org/web/20110409095557/http://www.cfa.harvard.edu/news/2010/pr201024.html

|archive-date = 9 April 2011

|url-status = live

}}

{{cite news

|author = Aguilar, David A.

|author2 = Pulliam, Christine

|title = Evolved Stars Locked in Fatalistic Dance

|date = 13 July 2011

|publisher = Harvard-Smithsonian Center for Astrophysics

|url = http://www.cfa.harvard.edu/news/2011/pr201119.html

|access-date = 17 July 2011

|archive-url = https://web.archive.org/web/20110715224123/http://www.cfa.harvard.edu/news/2011/pr201119.html

|archive-date = 15 July 2011

|url-status = live

}}

{{Main|Type Ia supernova}}

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

{{cite journal

|bibcode=2004A&A...419..623Y

|arxiv= astro-ph/0402287

|doi= 10.1051/0004-6361:20035822

|title=Presupernova evolution of accreting white dwarfs with rotation

|date=2004

|last1=Yoon |first1=S.-C.

|last2=Langer |first2=N.

|journal=Astronomy and Astrophysics

|volume=419 |issue=2 |pages=623–644

|s2cid= 2963085

}} 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.

There are two models that might explain the progenitor systems of Type Ia supernovae: the single-degenerate model and the double-degenerate model. In the single-degenerate model, a carbon–oxygen white dwarf accretes mass and compresses its core by pulling mass from a companion non-degenerate star.

{{cite journal

|title=Type IA supernova explosion models

|last1=Hillebrandt |first1=W.

|last2=Niemeyer |first2=J. C.

|date=2000

|journal=Annual Review of Astronomy and Astrophysics

|volume=38 |pages=191–230

|arxiv= astro-ph/0006305

|bibcode=2000ARA&A..38..191H

|doi= 10.1146/annurev.astro.38.1.191

}}{{rp|14}} It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit. Because the white dwarf is supported against gravity by quantum degeneracy pressure instead of by thermal pressure, adding heat to the star's interior increases its temperature but not its pressure, so the white dwarf does not expand and cool in response. Rather, the increased temperature accelerates the rate of the fusion reaction, in a runaway 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.

{{cite journal

|bibcode=2006A&A...453..229B

|arxiv= astro-ph/0603036

|doi= 10.1051/0004-6361:20054594

|title=Theoretical light curves for deflagration models of type Ia supernova

|date=2006

|last1=Blinnikov |first1=S. I.

|last2=Röpke |first2=F. K.

|last3=Sorokina |first3=E. I.

|last4=Gieseler |first4=M.

|last5=Reinecke |first5=M.

|last6=Travaglio |first6=C.

|last7=Hillebrandt |first7=W.

|last8=Stritzinger |first8=M.

|journal=Astronomy and Astrophysics

|volume=453 |issue= 1

|pages=229–240

|s2cid= 15493284

}} 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.{{rp|14}} In both cases, the white dwarfs are not expected to survive the Type Ia supernova.{{cite journal |last1=Maoz |first1=D. |last2=Mannucci |first2=F. |date=2012-01-18 |title=Type-Ia Supernova Rates and the Progenitor Problem: A Review |url=https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/typeia-supernova-rates-and-the-progenitor-problem-a-review/7E4AB6A714BF2FBE92DEA13AAFDF1E0D |journal=Publications of the Astronomical Society of Australia |language=en |volume=29 |issue=4 |pages=447–465 |doi=10.1071/AS11052 |issn=1448-6083|arxiv=1111.4492 |bibcode=2012PASA...29..447M }}

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.{{cite journal |last1=Wang |first1=Bo |last2=Han |first2=Zhanwen |date=2012-06-01 |title=Progenitors of type Ia supernovae |url=https://www.sciencedirect.com/science/article/pii/S138764731200022X |journal=New Astronomy Reviews |volume=56 |issue=4 |pages=122–141 |doi=10.1016/j.newar.2012.04.001 |issn=1387-6473|arxiv=1204.1155 |bibcode=2012NewAR..56..122W }} However, the main mechanism for Type Ia supernovae remains an open question.{{cite journal |last1=Maoz |first1=Dan |last2=Mannucci |first2=Filippo |last3=Nelemans |first3=Gijs |date=2014-08-18 |title=Observational Clues to the Progenitors of Type Ia Supernovae |url=https://www.annualreviews.org/doi/10.1146/annurev-astro-082812-141031 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=52 |issue=1 |pages=107–170 |doi=10.1146/annurev-astro-082812-141031 |issn=0066-4146|arxiv=1312.0628 |bibcode=2014ARA&A..52..107M }} 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. For the single-degenerate model its companion is expected to survive, but there is no strong evidence of such a star near Type Ia supernovae sites. In the double-degenerate scenario, white dwarfs need to be in very close binaries; otherwise their inspiral time is longer than the age of the universe. It is also likely that instead of a Type Ia supernova, the merger of two white dwarfs will lead to core-collapse. As a white dwarf accretes material quickly, the core can ignite off-center, which leads to gravitational instabilities that could create a neutron star.

The historical bright SN 1006 is thought to have been a Type Ia supernova from a white dwarf, possibly the merger of two white dwarfs.

{{cite journal

|last1=González Hernández |first1=J.I.

|last2=Ruiz-Lapuente |first2=P.

|last3=Tabernero |first3=H. M.

|last4=Montes |first4 =D.

|last5=Canal |first5=R.

|last6=Méndez |first6=J.

|last7=Bedin |first7=L. R.

|title=No surviving evolved companions of the progenitor of SN 1006

|year=2012

|journal=Nature

|volume=489

|issue=7417

|pages=533–536

|pmid=23018963

|arxiv=1210.1948

|bibcode=2012Natur.489..533G

|doi=10.1038/nature11447 |s2cid=4431391

}} Tycho's Supernova of 1572 was also a type Ia supernova, and its remnant has been detected.{{cite journal |last1=Krause |first1=Oliver |display-authors=etal |date=2008 |title=Tycho Brahe's 1572 supernova as a standard type Ia as revealed by its light-echo spectrum |journal=Nature |volume=456 |issue=7222 |pages=617–619 |doi=10.1038/nature07608 |pmid=19052622 |bibcode=2008Natur.456..617K |arxiv=0810.5106|s2cid=4409995 }} 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.

{{cite journal

| last1=de la Fuente Marcos | first1=Raúl | last2=de la Fuente Marcos | first2=Carlos

| title=Deep and fast Solar System flybys: The controversial case of WD 0810-353

| journal=Astronomy & Astrophysics

| url=https://www.aanda.org/component/article?access=doi&doi=10.1051/0004-6361/202245020

| volume= 668| year=2022 | pages=A14 | issn=0004-6361

| doi=10.1051/0004-6361/202245020 | bibcode=2022A&A...668A..14D | arxiv=2210.04863| s2cid=252863734

}}{{cite journal|last1=Landstreet |first1=J. D. |last2=Villaver |first2=E. |last3=Bagnulo |first3=S. |year=2023 |title=Not so fast, not so furious: just magnetic |journal=The Astrophysical Journal |volume=952 |number=2 |page=129 |doi=10.3847/1538-4357/acdac8 |doi-access=free |arxiv=2306.11663|bibcode=2023ApJ...952..129L }}

{{Main|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).{{cite journal|title=A Catalog of Potential Post–Common Envelope Binaries |first1=Matthias U. |last1=Kruckow |first2=Patrick G. |last2=Neunteufel |first3=Rosanne |last3=Di Stefano |first4=Yan |last4=Gao |first5=Chiaki |last5=Kobayashi |journal=The Astrophysical Journal |date=2021 |arxiv=2107.05221 |volume=920 |number=2 |page=86 |doi=10.3847/1538-4357/ac13ac|doi-access=free |bibcode=2021ApJ...920...86K }} 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.{{cite journal|first1=J. |last1=Nordhaus |first2=S. |last2=Wellons |first3=D. S. |last3=Spiegel |first4=B. D. |last4=Metzger |first5=E. G. |last5=Blackman |title=Formation of high-field magnetic white dwarfs from common envelopes |journal=PNAS |volume=108 |number=8 |pages=3135–3140 |doi=10.1073/pnas.1015005108 |year=2011|doi-access=free |pmid=21300910 |pmc=3044383 |arxiv=1010.1529 |bibcode=2011PNAS..108.3135N }}{{cite journal|first1=A. |last1=Rebassa-Mansergas |first2=E. |last2=Solano |first3=F. M. |last3=Jiménez-Esteban |first4=S. |last4=Torres |first5=C. |last5=Rodrigo |first6=A. |last6=Ferrer-Burjachs |first7=L. M. |last7=Calcaferro |first8=L. G. |last8=Althaus |first9=A. H. |last9=Córsico |title=White dwarf–main-sequence binaries from Gaia EDR3: the unresolved 100 pc volume-limited sample |journal=Monthly Notices of the Royal Astronomical Society |volume=506 |number=4 |date=October 2021 |pages=5201–5211 |doi=10.1093/mnras/stab2039|doi-access=free |arxiv=2107.06303 }} Because a PCEB may evolve at some point into a cataclysmic variable, some of them are also called pre-cataclysmic variables.{{cite journal|first1=M. R. |last1=Schreiber |first2=B. T. |last2=Gänsicke |title=The age, life expectancy, and space density of Post Common Envelope Binaries |journal=Astronomy and Astrophysics |volume=406 |pages=305–321 |year=2003 |doi=10.1051/0004-6361:20030801|arxiv=astro-ph/0305531 |bibcode=2003A&A...406..305S }}

{{Main|Cataclysmic variable star}}

Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by hydrogen fusion. These surface explosions can be repeated as long as the white dwarf's core remains intact. 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 the 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 through a release of energy due to 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, including polars and intermediate polars, both of which feature highly magnetic white dwarfs.{{cite web |url=http://imagine.gsfc.nasa.gov/docs/science/know_l2/cataclysmic_variables.html |series=Imagine the Universe! |title=Cataclysmic Variables |archive-url=https://web.archive.org/web/20070709185919/http://imagine.gsfc.nasa.gov/docs/science/know_l2/cataclysmic_variables.html |archive-date=9 July 2007 |department=fact sheet |publisher=NASA Goddard |access-date=4 May 2007}}{{cite web |url=http://heasarc.gsfc.nasa.gov/docs/objects/cvs/cvstext.html |title=Introduction to Cataclysmic Variables (CVs) |archive-url=https://web.archive.org/web/20120206213752/http://heasarc.gsfc.nasa.gov/docs/objects/cvs/cvstext.html |archive-date=6 February 2012 |url-status=live |department=fact sheet |publisher=NASA Goddard |access-date=4 May 2007}} Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.

Other binaries include those that consist of a main sequence star (or giant) and a white dwarf. The binary Sirius AB is an example pair of this type.{{cite book|first1=Andrew |last1=Fraknoi |display-authors=etal |title=Astronomy 2e |publisher=OpenStax |isbn=978-1-951693-50-3 |year=2024 |chapter=18.4 The H–R Diagram |chapter-url=https://openstax.org/books/astronomy-2e/pages/18-4-the-h-r-diagram |page=618}} 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.{{cite journal|first1=M. |last1=Perpinyà-Vallès |first2=A. |last2=Rebassa-Mansergas |first3=B. T. |last3=Gänsicke |first4=S. |last4=Toonen |first5=J. J. |last5=Hermes |first6=N. P. |last6=Gentile Fusillo |first7=P.-E. |last7=Tremblay |title=Discovery of the first resolved triple white dwarf |journal=Monthly Notices of the Royal Astronomical Society |volume=483 |number=1 |date=February 2019 |pages=901–907 |doi=10.1093/mnras/sty3149|doi-access=free |arxiv=1811.07752 }} 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.{{cite journal|first1=Wolfgang |last1=Brandner |first2=Hans |last2=Zinnecker |first3=Taisiya |last3=Kopytova |title=Search for giant planets around seven white dwarfs in the Hyades cluster with the Hubble Space Telescope |journal=Monthly Notices of the Royal Astronomical Society |year=2021 |volume=500 |issue=3 |pages=3920–3925 |doi=10.1093/mnras/staa3422 |doi-access=free |arxiv=2011.03562}} 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{{cite journal | last1=Luhman |first1=K. L. |last2=Burgasser |first2=A. J. |last3=Bochanski |first3=J. J. | year=2011 | title=Discovery of a Candidate for the Coolest Known Brown Dwarf | journal=The Astrophysical Journal Letters |volume=730 |number=1 |pages=L9 |arxiv=1102.5411 |doi=10.1088/2041-8205/730/1/L9 |bibcode=2011ApJ...730L...9L }}{{cite journal |last1=Rodriguez |first1=David R. |last2=Zuckerman |first2=B. |last3=Melis |first3=Carl |last4=Song |first4=Inseok |date=May 2011 |title=The Ultra Cool Brown Dwarf Companion of WD 0806-661B: Age, Mass, and Formation Mechanism |journal=The Astrophysical Journal Letters |volume=732 |number=2 |pages=L29 |doi=10.1088/2041-8205/732/2/L29 |arxiv=1103.3544 |bibcode=2011ApJ...732L..29R }} or an exoplanet.{{cite journal|first1=Dimitri |last1=Veras |first2=N. Wyn |last2=Evans |title=Exoplanets beyond the Solar neighbourhood: Galactic tidal perturbations |journal=Monthly Notices of the Royal Astronomical Society |volume=430 |number=1 |date=21 March 2013 |pages=403–415 |doi=10.1093/mnras/sts647 |doi-access=free |arxiv=1212.4150}}

{{colbegin}}

• {{annotated link|Extreme helium star}}
• {{annotated link|List of white dwarfs}}
• {{annotated link|PG 1159 star}}
• {{annotated link|Robust associations of massive baryonic objects}}
• {{annotated link|Timeline of white dwarfs, neutron stars, and supernovae}}

{{colend}}

{{reflist|25em}}

• {{Cite book |last1=Shapiro |first1=Stuart L. |title=Black Holes, White Dwarfs and Neutron Stars: the physics of compact objects |last2=Teukolsky |first2=Saul A. |date=2004 |publisher=Wiley-VCH Verlag GmbH & Co. KGaA |isbn=978-3-527-41450-5 |series=Physics textbook |location=Weinheim}}

• {{cite web |url=http://www.sciencebits.com/StellarEquipartition |title=Estimating Stellar Parameters from Energy Equipartition |website=sciencebits.com}} — Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments.
• {{cite web |url=http://www.astronomy.villanova.edu/WDCatalog/index.html |publisher=Villanova University |title=White Dwarf Catalogue WD |editor1=McCook, G.P. |editor2=Sion, E.M. |date=9 September 2013 |archive-date=6 July 2024 |archive-url=https://web.archive.org/web/20240706202221/http://www.astronomy.villanova.edu/WDCatalog/index.html |url-status=dead }}
• [https://apod.nasa.gov/apod/white_dwarfs.html White dwarf images] at Astronomy Picture of the Day

{{White dwarf}}

{{Neutron star}}

{{Star}}

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