View source for White dwarf

{{short description|Type of stellar remnant composed mostly of electron-degenerate matter}}
{{hatnote group|
{{redirect-distinguish|Degenerate dwarf|Degenerate star}}
{{Duplicated citations|reason=[[User:Polygnotus/DuplicateReferences|DuplicateReferences]] detected:<br>
* https://arxiv.org/abs/astro-ph/0212469 (refs: 11, 130)<br>
* https://doi.org/10.1086%2F122654 (refs: 18, 157)<br>
* https://doi.org/10.1086%2F313186 (refs: 25, 74)<br>
* https://doi.org/10.1111%2Fj.1365-2966.2006.11388.x (refs: 28, 103)<br>
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{{Use dmy dates|date=December 2020}}
[[File:Sirius A and B Hubble photo.editted.PNG|thumb|Image of [[Sirius]]&nbsp;A and Sirius&nbsp;B taken by the [[Hubble Space Telescope]]. Sirius&nbsp;B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius&nbsp;A.]]

A '''white dwarf''' is a [[Compact star|stellar core remnant]] composed mostly of [[electron-degenerate matter]]. A white dwarf is very [[density|dense]]: its mass is comparable to the [[Sun]]'s and its volume [[Earth]]'s. No [[nuclear fusion]] takes place in a white dwarf; what light it radiates is from its residual [[heat]].<ref name="osln" /> The nearest known white dwarf is [[Sirius B]], at 8.6&nbsp;light years, the smaller component of the Sirius [[binary star]]. There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun.<ref>
{{cite web
 |last=Henry |first=T.J.  |author-link=Todd J. Henry
 |date=1 January 2009
 |title=The one hundred nearest star systems
 |publisher=[[Research Consortium on Nearby Stars]]
 |url=http://www.astro.gsu.edu/RECONS/TOP100.posted.htm
 |access-date=21 July 2010  |url-status=live
 |archive-url=https://web.archive.org/web/20071112173559/http://www.chara.gsu.edu/RECONS/TOP100.posted.htm
 |archive-date=12 November 2007
}}
</ref> The unusual faintness of white dwarfs was first recognized in 1910.<ref name="schatzman"/>{{rp|page=1}} The name ''white dwarf'' was coined by [[Willem Jacob Luyten]] in 1922.

White dwarfs are thought to be the final [[stellar evolution|evolutionary state]] of stars whose [[mass]] is not high enough to become a [[neutron star]] or [[black hole]]. This includes over 97% of the stars in the [[Milky Way]].<ref name="cosmochronology"/>{{rp|§1}} After the [[hydrogen]]-[[stellar nucleosynthesis|fusing]] period of a [[main sequence|main-sequence star]] of [[Stellar mass|low or intermediate mass]] ends, such a star will expand to a [[red giant]] and fuse [[helium]] to [[carbon]] and [[oxygen]] in its core by the [[triple-alpha process]]. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon (around {{val|e=9|u=K}}), an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a [[planetary nebula]], it will leave behind a core, which is the remnant white dwarf.<ref name="rln">
{{cite web
 |last=Richmond  |first=M.
 |title=Late stages of evolution for low-mass stars
 |series=Lecture notes, Physics&nbsp;230
 |publisher=[[Rochester Institute of Technology]]
 |url=http://spiff.rit.edu/classes/phys230/lectures/planneb/planneb.html
 |access-date=3 May 2007  |url-status=live
 |archive-url=https://web.archive.org/web/20170904224040/http://spiff.rit.edu/classes/phys230/lectures/planneb/planneb.html
 |archive-date=4 September 2017
}}
</ref> Usually, white dwarfs are composed of carbon and oxygen ('''CO white dwarf'''). If the mass of the progenitor is between 7 and 9&nbsp;[[solar mass]]es ({{solar mass|link=y}}), the core temperature will be sufficient to fuse carbon but not [[neon]], in which case an oxygen–neon–[[magnesium]] ('''ONeMg''' or '''ONe''') white dwarf may form.<ref name="oxne">
{{cite conference
 |last1=Werner   |first1=K.     |last2=Hammer |first2=N.J.
 |last3=Nagel    |first3=T.     |last4=Rauch  |first4=T.
 |last5=Dreizler |first5=S.
 |year=2005
 |title=On possible oxygen / neon white dwarfs: H1504+65 and the white dwarf donors in ultracompact X-ray binaries
 |conference=14th European Workshop on White Dwarfs
 |volume=334  |page=165
 |arxiv=astro-ph/0410690
 |bibcode=2005ASPC..334..165W
}}
</ref> Stars of very low mass will be unable to fuse helium; hence, a helium white dwarf<ref name="apj606_L147">
{{cite journal
 |last1=Liebert    |first1=James  |last2=Bergeron |first2=P.
 |last3=Eisenstein |first3=D.     |last4=Harris   |first4=H. C.
 |last5=Kleinman   |first5=S. J.  |last6=Nitta    |first6=A.
 |last7=Krzesinski |first7=J.
 |year=2004
 |title=A helium white dwarf of extremely low mass
 |journal=[[The Astrophysical Journal]]
 |volume=606  |issue=2  |pages=L147
 |arxiv=astro-ph/0404291  |bibcode=2004ApJ...606L.147L
 |s2cid=118894713   |doi=10.1086/421462 
}}
</ref><ref name="he2">
{{cite press release
 |date=17 April 2007
 |title=Cosmic weight loss: The lowest mass white dwarf
 |publisher=[[Harvard-Smithsonian Center for Astrophysics]]
 |url=http://spaceflightnow.com/news/n0704/17whitedwarf
 |access-date=20 April 2007  |url-status=live
 |archive-url=https://web.archive.org/web/20070422034650/http://spaceflightnow.com/news/n0704/17whitedwarf/
 |archive-date=22 April 2007
}}
</ref> may form by mass loss in an [[interacting binary star]] system.<ref>{{cite journal
 | title=Evolution of Helium White Dwarfs of Low and Intermediate Masses
 | last1=Althaus | first1=L. G. | last2=Benvenuto | first2=O. G.
 | journal=The Astrophysical Journal
 | volume=477 | issue=1 | pages=313–334 | date=March 1997
 | doi=10.1086/303686 | bibcode=1997ApJ...477..313A }}</ref>

Because the material in a white dwarf no longer undergoes fusion reactions, it lacks a heat source to support it against [[gravitational collapse]]. Instead, it is supported only by [[electron degeneracy pressure]], causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the [[Chandrasekhar limit]]{{Mdash}}  approximately 1.44&nbsp;times {{solar mass|link=y}}{{Mdash}} beyond which electron degeneracy pressure cannot support it. A carbon–oxygen white dwarf which approaches this limit, typically by mass transfer from a companion star, may explode as a [[Type Ia supernova]] via a process known as [[carbon detonation]];<ref name=osln>
{{cite web
 |last=Johnson  |first=J.
 |year=2007
 |title=Extreme stars: White dwarfs & neutron stars
 |type=Lecture notes |series=Astronomy&nbsp;162
 |publisher=[[Ohio State University]]
 |url=http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL22.html
 |access-date=17 October 2011  |url-status=live
 |archive-url=https://web.archive.org/web/20120331194342/http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL22.html
 |archive-date=31 March 2012
}}
</ref><ref name="rln"/> [[SN 1006]] is a likely example.

A white dwarf, very hot when it forms, gradually cools as it radiates its energy. This radiation, which initially has a high [[color temperature]], lessens and reddens over time. Eventually a white dwarf will cool enough that its material will begin to crystallize, starting with the core. No longer emitting significant heat or light, and it will become a cold [[black dwarf]].<ref name="rln" /> Inasmuch as the length of time it takes for a white dwarf to reach this end state has been calculated to be longer than the current age of the known universe (approximately 13.8&nbsp;billion years),<ref name=aou>
{{cite journal
 |last1=Spergel  |first1=D.N.     |last2=Bean     |first2=R.
 |last3=Doré     |first3=O.       |last4=Nolta    |first4=M.R.
 |last5=Bennett  |first5=C.L.     |last6=Dunkley  |first6=J.
 |last7=Hinshaw  |first7=G.       |last8=Jarosik  |first8=N.
 |last9=Komatsu  |first9=E.       |last10=Page    |first10=L.
 |last11=Peiris  |first11=H.V.    |last12=Verde   |first12=L.
 |last13=Halpern |first13=M.      |last14=Hill    |first14=R.S.
 |last15=Kogut   |first15=A.      |last16=Limon   |first16=M.
 |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
}}
</ref> it is thought that no black dwarfs exist.<ref name="osln" /><ref name="cosmochronology">
{{cite journal
 |last1=Fontaine |first1=G.
 |last2=Brassard |first2=P.
 |last3=Bergeron |first3=P.
 |year=2001
 |title=The potential of white dwarf cosmochronology
 |journal=[[Publications of the Astronomical Society of the Pacific]]
 |volume=113  |issue=782  |pages=409–435
 |bibcode=2001PASP..113..409F
 |doi=10.1086/319535  |doi-access=free
}}
</ref> The oldest known white dwarfs still radiate at temperatures of a few thousand [[kelvin]]s, which establishes an observational limit on the maximum possible [[age of the universe]].<ref name="2003ApJ...591..288H">§3, {{cite journal |author1=Heger, A. |author2=Fryer, C.L. |author3=Woosley, S.E. |author4=Langer, N. |author5=Hartmann, D.H. |title=How massive single stars end their life |journal=Astrophysical Journal |year=2003 |volume=591 |issue=1 |pages=288–300 |bibcode=2003ApJ...591..288H  |doi=10.1086/375341 |arxiv=astro-ph/0212469|s2cid=59065632 }}</ref>

== Discovery ==
{{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 star|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.<ref>
{{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
}}
</ref> In 1910, [[Henry Norris Russell]], [[Edward Charles Pickering]] and [[Williamina Fleming]] discovered that, despite being a dim star, 40&nbsp;Eridani&nbsp;B was of [[stellar classification|spectral type]]&nbsp;A, or white.<ref name=holberg>
{{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&nbsp;207
 |bibcode=2005AAS...20720501H
}}
</ref> In 1939, Russell looked back on the discovery:<ref name="schatzman">
{{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}}</ref>{{rp|page=1}}
<blockquote>I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars – including comparison stars – which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, and I discussed. This piece of apparently routine work proved very fruitful – it led to the discovery that all the stars of very faint absolute magnitude were of spectral class&nbsp;M. In conversation on this subject (as I recall it), I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40&nbsp;Eridani&nbsp;B. Characteristically, he sent a note to the Observatory office and before long the answer came (I think from Mrs.&nbsp;Fleming) that the spectrum of this star was A. I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: "It is just these exceptions that lead to an advance in our knowledge", and so the white dwarfs entered the realm of study!</blockquote>

The spectral type of 40 Eridani B was officially described in 1914 by [[Walter Sydney Adams|Walter Adams]].<ref>
{{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
}}
</ref>

The white dwarf companion of Sirius, Sirius&nbsp;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 Wilhelm Bessel|Friedrich Bessel]] used position measurements to determine that the stars Sirius (α&nbsp;Canis Majoris) and [[Procyon]] (α&nbsp;Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:<ref name="fwbessel">
{{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
}}
</ref>

<blockquote>If we were to regard ''Sirius'' and ''Procyon'' as double stars, the change of their motions would not surprise us; we should acknowledge them as necessary, and have only to investigate their amount by observation. But light is no real property of mass. The existence of numberless visible stars can prove nothing against the existence of numberless invisible ones.</blockquote>

Bessel roughly estimated the period of the companion of Sirius to be about half a century;<ref name=fwbessel/> [[Christian August Friedrich Peters|C.A.F. Peters]] computed an orbit for it in 1851.<ref name=flammarion>
{{cite journal
 |last=Flammarion |first=Camille
 |title=The companion of Sirius
 |year=1877
 |volume=15 |page=186
 |journal=[[Astronomical Register]]
 |bibcode=1877AReg...15..186F
}}
</ref> It was not until 31&nbsp;January 1862 that [[Alvan Graham Clark]] observed a previously unseen star close to Sirius, later identified as the predicted companion.<ref name=flammarion/> [[Walter Sydney Adams|Walter Adams]] announced in 1915 that he had found the spectrum of Sirius&nbsp;B to be similar to that of Sirius.<ref>
{{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
}}
</ref>

In 1917, [[Adriaan van Maanen]] discovered [[van Maanen's Star]], an isolated white dwarf.<ref>
{{cite journal
 |last=van&nbsp;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
}}
</ref> These three white dwarfs, the first discovered, are the so-called ''classical white dwarfs''.<ref name=schatzman/>{{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;<ref name="holberg"/><ref>
{{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
}}
</ref><ref>
{{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
}}</ref><ref>
{{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
}}
</ref><ref>
{{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
}}
</ref> the term was later popularized by [[Arthur Eddington]].<ref name=holberg/><ref name=eddington/> Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18&nbsp;white dwarfs had been discovered by 1939.<ref name=schatzman/>{{rp|page=3}} Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known,<ref>
{{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
}}
</ref> and by 1999, over 2000 were known.<ref name=villanovar4>
{{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
}}
</ref> Since then the [[Sloan Digital Sky Survey]] has found over 9000&nbsp;white dwarfs, mostly new.<ref name=sdssr4>
{{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&nbsp;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
}}
</ref>

== Composition and structure ==
{{star nav}}
Although white dwarfs are known with estimated masses as low as 0.17&nbsp;{{solar mass}}<ref>
{{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
}}
</ref> and as high as 1.33&nbsp;{{solar mass}},<ref name="sdsswd">
{{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
}}
</ref> the mass distribution is strongly peaked at 0.6&nbsp;{{solar mass}}, and the majority lie between 0.5 and 0.7&nbsp;{{solar mass}}.<ref name=sdsswd/> The estimated radii of observed white dwarfs are typically 0.8–2% the [[solar radius|radius of the Sun]];<ref>
{{cite journal
 |last=Shipman |first=H.L.
 |year=1979
 |title=Masses and radii of white-dwarf stars. III – Results for 110&nbsp;hydrogen-rich and 28&nbsp;helium-rich stars
 |journal=[[The Astrophysical Journal]]
 |volume=228  |page=240
 |bibcode=1979ApJ...228..240S
 |doi=10.1086/156841
}}
</ref> 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}}&nbsp;times greater than the average density of the Sun, or approximately {{val|e=6|ul=g/cm3}}, or 1&nbsp;[[tonne]] per cubic centimetre.<ref name=osln/> A typical white dwarf has a density of between 10<sup>4</sup> 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 star]]s such as [[neutron star]]s and the hypothetical [[quark star]]s.<ref name="Saumon2022"/><ref>{{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}}</ref>

White dwarfs were found to be extremely dense soon after their discovery. If a star is in a [[binary star|binary]] system, as is the case for Sirius&nbsp;B or 40&nbsp;Eridani&nbsp;B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius&nbsp;B by 1910,<ref>
{{cite book
 |last=Boss |first=L.
 |year=1910
 |title=Preliminary General Catalogue of 6188&nbsp;stars for the epoch&nbsp;1900
 |publisher=[[Carnegie Institution of Washington]]
 |bibcode=1910pgcs.book.....B  |lccn=10009645
 |url=https://archive.org/details/preliminarygene00obsegoog
 |via=Archive.org
}}
</ref> yielding a mass estimate of {{solar mass|0.94}}, which compares well with a more modern estimate of {{solar mass|1.00}}.<ref name=apj_630>
{{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&nbsp;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
 }}</ref> Since hotter bodies radiate more energy than colder ones, a star's surface brightness can be estimated from its [[effective temperature|effective surface temperature]], and that from its [[stellar spectrum|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&nbsp;B and 40&nbsp;Eridani&nbsp;B must be very dense. When [[Ernst Öpik]] estimated the density of a number of visual binary stars in 1916, he found that 40&nbsp;Eridani&nbsp;B had a density of over {{val|25000}}&nbsp;times that of the [[Sun]], which was so high that he called it "impossible".<ref>
{{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
}}
</ref> As [[Arthur Eddington]] put it later, in 1927:<ref>
{{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
}}
</ref>{{rp|page=50}}
<blockquote>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&nbsp;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."</blockquote>

As Eddington pointed out in 1924, densities of this order implied that, according to the theory of [[general relativity]], the light from Sirius&nbsp;B should be [[gravitational redshift|gravitationally redshifted]].<ref name="eddington">{{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
}}</ref> This was confirmed when Adams measured this redshift in 1925.<ref>
{{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
 }}</ref>

{| class="wikitable"  style="width:50%; text-align:left; float:left; margin-right:1em;"
|-
! Material !! [[Density]] [{{val|u=kg/m3}}] !! Notes
|-
| Supermassive black hole || {{circa}} 1000<ref name="CMS1999">{{cite journal|last1=Celotti |first1=A. |last2=Miller |first2=J.C. |last3=Sciama |first3=D.W. |title= Astrophysical evidence for the existence of black holes |date=1999|pages=A3–A21|issue=12A |journal=Class. Quantum Grav. |volume=16 |arxiv=astro-ph/9912186 |doi = 10.1088/0264-9381/16/12A/301 |bibcode=1999CQGra..16A...3C |s2cid=17677758 }}</ref> || Critical density of a black hole of around 10<sup>8</sup> solar masses.
|-
| Water (liquid) || 1000 || At [[Standard temperature and pressure|STP]]
|-
| [[Osmium]] || {{val|22610}} || Near [[room temperature]]
|-
| The core of the Sun || {{circa}} {{val|150000}} ||
|-
| White dwarf || {{val|1|e=9}}<ref name="osln" /> ||
|-
| [[Atomic nuclei]] || {{val|2.3|e=17}}<ref>
 {{cite web
  |last=Nave
  |first=C. R.
  |url=http://hyperphysics.phy-astr.gsu.edu/HBASE/Nuclear/nucuni.html
  |title=Nuclear Size and Density
  |work=[[HyperPhysics]]
  |publisher=[[Georgia State University]]
  |access-date=26 June 2009
  |archive-url=https://web.archive.org/web/20090706034134/http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nucuni.html
  |archive-date=6 July 2009
  |url-status=live
 }}</ref> || Does not depend strongly on size of nucleus
|-
| Neutron star core || {{val|8.4|e=16}} – {{val|1|e=18}} ||
|-
| Small black hole || {{val|2|e=30}}<ref name=adams1997>
 {{cite book
  |first1=Steve |last1=Adams
  |date=1997
  |title=Relativity: an introduction to space-time physics
  |place=London; Bristol
  |page=240
  |publisher=[[CRC Press]]
  |isbn=978-0-7484-0621-0
  |bibcode=1997rist.book.....A
 }}</ref> || Critical density of an Earth-mass black hole.
|}
Such densities are possible because white dwarf material is not composed of [[atom]]s joined by [[chemical bond]]s, but rather consists of a [[plasma (physics)|plasma]] of unbound [[atomic nucleus|nuclei]] and [[electron]]s. There is therefore no obstacle to placing nuclei closer than normally allowed by [[atomic orbital|electron orbitals]] limited by normal matter.<ref name="eddington" /> Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient.<ref name="fowler">
{{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
 }}</ref> 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 [[quantum state|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.<ref>
{{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
}}</ref> At zero temperature, therefore, electrons cannot all occupy the lowest-energy, or ''[[ground state|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 matter|degenerate]]'', meant that a white dwarf could cool to zero temperature and still possess high energy.<ref name="fowler" /><ref name="scibits">
{{cite web
 |title=Estimating Stellar Parameters from Energy Equipartition
 |url=http://www.sciencebits.com/StellarEquipartition
 |website=ScienceBits
 |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
}}</ref>

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.<ref name="fowler" /><ref>
{{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
}}</ref> 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.<ref name="osln" />

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]]<ref>
{{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
 }}</ref> and in 1930 by [[Edmund C. Stoner]].<ref name="stoner">{{cite journal
 |last1=Stoner |first1=C.
 |date=1930
 |title=The Equilibrium of Dense Stars
 |journal=[[Philosophical Magazine]]
 |volume=9 |page=944
}}</ref> 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".<ref name="chandra4">
{{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
}}</ref> For a non-rotating white dwarf, it is equal to approximately {{math|5.7 {{solar mass}} / ''μ''<sub>e</sub><sup>2</sup>}}, where {{math|''μ''<sub>e</sub>}} is the average molecular weight per electron of the star.<ref name="chandra2">
{{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
}}</ref>{{rp|eqn.(63)}} As the carbon-12 and oxygen-16 that predominantly compose a carbon–oxygen white dwarf both have [[atomic number]]s equal to half their [[atomic weight]], one should take {{math|''μ''<sub>e</sub>}} equal to 2 for such a star,<ref name="scibits" /> leading to the commonly quoted value of 1.4&nbsp;{{solar mass}}. (Near the beginning of the 20th&nbsp;century, there was reason to believe that stars were composed chiefly of heavy elements,<ref name="stoner" />{{rp|page=955}} so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, {{math|''μ''<sub>e</sub>}}, equal to 2.5, giving a limit of 0.91&nbsp;{{solar mass}}.) Together with [[William Alfred Fowler]], Chandrasekhar received the [[Nobel Prize in Physics|Nobel Prize]] for this and other work in 1983.<ref>
{{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
}}</ref> The limiting mass is now called the ''[[Chandrasekhar limit]]''.<ref>
{{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
 }}</ref>

If a carbon-oxygen white dwarf accreted enough matter to reach the [[Chandrasekhar limit]] of about 1.44 [[solar mass]]es (for a non-rotating star), it would no longer be able to support the bulk of its mass through electron degeneracy pressure<ref name=collapse/> and, in the absence of nuclear reactions, would begin to collapse.<ref name="Chandrasekhar">{{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
 }}</ref><ref name="Mazzali2007">
{{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 (journal)|Science]]
 |volume=315 |issue=5813 |pages=825–828
 |arxiv=astro-ph/0702351
 |bibcode=2007Sci...315..825M
 |doi=10.1126/science.1136259
 |pmid=17289993
 }}</ref>  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.<ref name="Mazzali2007"/><ref>
{{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
 }}</ref> 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.<ref name="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
}}</ref> 

If a white dwarf star accumulates sufficient material from a stellar companion to raise its core temperature enough to [[Carbon detonation|ignite]] [[Carbon burning process|carbon fusion]], it will undergo [[Thermal runaway|runaway]] nuclear fusion, completely disrupting it. There are three avenues by which this detonation is theorised to happen: stable [[accretion (astrophysics)|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.<ref name="Piro2014">
{{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
 }}</ref> Despite this uncertainty in how type Ia supernovae are produced, type Ia supernovae have very uniform properties and are useful [[Cosmic distance ladder|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.<ref name="chen">
{{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
 }}</ref><ref>
{{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
 }}</ref><ref>{{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 }}</ref>

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 fusion|hydrogen-fusing]]<!-- it is THIS place where a hyphen must stay, oh typographers from hell --> [[red dwarf]]s, whose cores are supported in part by thermal pressure,<ref>
{{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
}}</ref> or the even lower-temperature [[brown dwarf]]s.<ref>
{{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
}}</ref>

=== Mass–radius relationship ===
{{See also|Chandrasekhar's white dwarf equation|Neutron star#Gravity and equation of state}}
The relationship between the mass and radius of low-mass white dwarfs can be estimated using the nonrelativistic [[Fermi gas]] equation of state, which gives<ref name="scibits" />

{{block indent|<math> R \approx \frac{N^{5/3} \hbar^2}{2m_\text{e} GM^{1/3}},</math>}}

where {{mvar|R}} is the radius, {{mvar|M}} is the total mass of the star, {{mvar|N}} is the number of electrons per unit mass (dependent only on composition), {{math|''m''<sub>e</sub>}} is the [[electron mass]], <math>\hbar</math> is the [[reduced Planck constant]], and {{mvar|G}} is the [[gravitational constant]].

Since this analysis uses the non-relativistic formula {{math|1=''T'' = ''p''<sup>2</sup> / 2''m''}} 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=''T'' = ''pc''}} where {{math|''c''}} is the speed of light, and it can be shown that there is no stable equilibrium in the [[ultrarelativistic limit]]. In particular, this analysis yields the maximum mass of a white dwarf, which is<ref name="scibits" />

{{block indent|<math>M_{\rm limit} \approx N^2 \left(\frac{\hbar c}{G}\right)^{3/2}.</math>}}

[[File:ChandrasekharLimitGraph.svg|thumb|upright=1.2|right|Radius–mass relations for a model white dwarf. {{math|''M''<sub>limit</sub>}} is denoted as M<sub>Ch</sub>]]

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.<ref name="chandra2" />{{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''<sub>e</sub>}}, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.<ref name="chandra2" /><ref name="stds">
{{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
}}</ref>

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]].<ref> {{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
}}</ref> 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,<ref>
{{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
}}</ref> 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 [[dynamics (mechanics)|dynamically]] stable.<ref>
{{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
}}</ref>

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.<ref>{{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 }}</ref> The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously.<ref>{{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 }}</ref>

=== Radiation and cooling ===
The degenerate matter that makes up the bulk of a white dwarf has a very low [[opacity (optics)|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 10<sup>8</sup>&nbsp;K shortly after the formation of the white dwarf and reaching less than 10<sup>6</sup>&nbsp;K for the coolest known white dwarfs.<ref name="Saumon2022">{{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 }}</ref> 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.<ref name="Saumon2022"/>

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-type star|late]] K- or early M-type star.<ref name="sionspectra">
{{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
}}</ref> White dwarf effective surface temperatures extend from over {{val|150000}}&nbsp;K<ref name="villanovar4" /> to barely under 4000&nbsp;K.<ref name="cool">{{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}}</ref><ref name="wden">
{{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
}}</ref> 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.<ref name="wden" /> 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-ray]]s. This enables the composition and structure of their atmospheres to be studied by soft [[X-ray astronomy|X-ray]] and [[UV astronomy|extreme ultraviolet observations]].<ref>
{{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
}}</ref>

White dwarfs also radiate [[neutrino]]s through the [[Urca process]].<ref>{{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 }}</ref> 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.<ref name="Saumon2022"/>

[[File:Size IK Peg.png|left|upright=1.2|thumb|A comparison between the white dwarf [[IK Pegasi]] B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of {{val|35500|u=K}}.]]
As was explained by [[Leon Mestel]] in 1952, unless the white dwarf [[accretion (astrophysics)|accretes]] matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished.<ref>
{{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
}}</ref><ref>
{{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
}}</ref>{{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.<ref name="rln" /> 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 [[Sources and sinks|energy sink]] other than radiation, it follows that its cooling slows with time. The rate of cooling has been estimated for a [[carbon]] white dwarf of 0.59 {{solar mass}} with a [[hydrogen]] atmosphere. After initially taking approximately 1.5&nbsp;billion years to cool to a surface temperature of 7140&nbsp;K, cooling approximately 500 more kelvins to 6590&nbsp;K takes around 0.3&nbsp;billion years, but the next two steps of around 500&nbsp;kelvins (to 6030&nbsp;K and 5550&nbsp;K) take first 0.4 and then 1.1&nbsp;billion years.<ref>
{{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
}}</ref>{{rp|Table&nbsp;2}}

Most observed white dwarfs have relatively high surface temperatures, between 8000&nbsp;K and {{val|40000|u=K}}.<ref name="sdssr4" /><ref>
{{cite journal
 |title=A Catalogue of Spectroscopically Identified White Dwarfs
 |last1=McCook |first1=G. P.
 |last2=Sion |first2=E. M.
 |journal=The Astrophysical Journal Supplement Series
 |volume=121
 |issue=1
 |pages=1–130
 |doi=10.1086/313186
 |bibcode=1999ApJS..121....1M|year=1999 |doi-access=free
}}</ref> 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.<ref name="disklf">
{{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
}}</ref> This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below {{val|4000|u=K}},<ref>
{{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
}}</ref> and one of the coolest so far observed, [[WD J2147–4035]], has a surface temperature of approximately 3050&nbsp;K.<ref name="Elms2022">{{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}}</ref> The reason for this is that the Universe's age is finite;<ref>
{{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
}}</ref><ref>
{{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
}}</ref> 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&nbsp;billion years.<ref name="disklf" /> 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.<ref name="osln" /> At very low temperatures (<4000 K) white dwarfs with hydrogen in their atmosphere will be affected by [[Collision-induced absorption and emission|collision induced absoption]] (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. Hence these white dwarfs are called [[IR-faint white dwarfs]]. White dwarfs with hydrogen-poor atmospheres, such as WD J2147–4035, are less affected by CIA and therefore have a yellow to orange color.<ref name="Bergeron2022">{{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}}</ref><ref name="Elms2022" />

[[File:Gaia hrd wds2.png|thumb|The white dwarf cooling sequence seen by ESA's [[Gaia (spacecraft)|Gaia mission]]]]
White dwarf core material is a completely [[Ionization|ionized]] [[plasma (physics)|plasma]] – a mixture of [[atomic nucleus|nuclei]] and [[electron]]s – 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.<ref>{{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 }}</ref> The crystal structure is thought to be a [[body-centered cubic]] lattice.<ref name="cosmochronology" /><ref>
{{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
}}</ref> In 1995 it was suggested that [[asteroseismology|asteroseismological]] observations of [[#Variability|pulsating white dwarfs]] yielded a potential test of the crystallization theory,<ref>
{{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
}}</ref> and in 2004, observations were made that suggested approximately 90% of the mass of [[BPM 37093]] had crystallized.<ref>{{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 }}</ref><ref name="lucy">{{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}}</ref><ref>
{{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
}}</ref> Other work gives a crystallized mass fraction of between 32% and 82%.<ref name="Brassard">
{{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
}}</ref> 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.<ref>{{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 }}</ref> Another possible mechanism that was suggested to explain the seeming delay in the cooling of some types of white dwarves is a solid–liquid distillation process: the crystals formed in the core are buoyant and float up, thereby displacing heavier liquid downward, thus causing a net release of gravitational energy.<ref>{{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}}</ref> Chemical [[fractionation]] between the ionic species in the plasma mixture can release a similar or even greater amount of energy.<ref>{{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 }}</ref><ref>{{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 }}</ref><ref>{{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 }}</ref> 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.<ref>
{{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
}}</ref> 

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.<ref>{{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 }}</ref> In addition, they remain in a bloated proto-white dwarf stage for up to 2&nbsp;Gyr before they reach the cooling track.<ref>{{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 }}</ref>

=== Atmosphere and spectra ===
[[File:Artist’s impression of the WDJ0914+1914 system.tif|thumb|Artist's impression of the [[WD J0914+1914]] system.<ref>{{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}}</ref>]]

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&nbsp;times more abundant than all other elements. As explained by [[Evry Schatzman|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.<ref>
{{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
}}</ref><ref name="physrev">
{{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
}}</ref>{{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 [[asymptotic giant branch|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.<ref name="wden" /><ref name="kawaler">
{{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
}}</ref>{{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.<ref name="wden" />

{| class="wikitable" style="float: right"
|+ White dwarf spectral types<ref name="villanovar4" />
|-
! colspan="2" | Primary and secondary features
|-
| A
| H lines present
|-
| B
| He I lines
|-
| C
| Continuous spectrum; no lines
|-
| O
| He II lines, accompanied by He I or H lines
|-
| Z
| Metal lines
|-
| Q
| Carbon lines present
|-
| X
| Unclear or unclassifiable spectrum
|-
! colspan="2" | Secondary features only
|-
| P
| Magnetic white dwarf with detectable polarization
|-
| H
| Magnetic white dwarf without detectable polarization
|-
| E
| Emission lines present
|-
| V
| Variable
|}
The first attempt to [[Stellar classification#White dwarf classifications|classify white dwarf spectra]] appears to have been by [[G. P. Kuiper]] in 1941,<ref name="sionspectra" /><ref>
{{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
}}</ref> and various classification schemes have been proposed and used since then.<ref>
{{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
}}</ref><ref>
{{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
}}</ref> 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 [[Spectroscopic notation|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 [[Spectroscopic notation|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.<ref name="villanovar4" /><ref name="sionspectra" />

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs.<ref name="wden" /> The next class in number is of DBs, approximately 16%.<ref>
{{cite journal
 |last1=Kepler |first1=S. O.
 |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.
 |title=White dwarf mass distribution in the SDSS
 |date=2007
 |journal=Monthly Notices of the Royal Astronomical Society
 |volume=375 |issue=4 |pages=1315–1324
 |bibcode=2007MNRAS.375.1315K
 |doi=10.1111/j.1365-2966.2006.11388.x
 |doi-access=free
 |arxiv = astro-ph/0612277 |s2cid=10892288
}}</ref> The hot, above {{val|15000|u=K}}, DQ class (roughly 0.1%) have carbon-dominated atmospheres.<ref>
{{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
}}</ref> 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.<ref name="kawaler"/>{{rp|§2.4}}<ref name="wden" />

[[Molecules in stars|Molecular]] hydrogen ([[Molecular hydrogen|H<sub>2</sub>]]) has been detected in spectra of the atmospheres of some white dwarfs.<ref name="dwarf">{{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 }}</ref> 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.<ref name=Weisskopf2007>{{Cite journal |last=Weisskopf |first=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}}</ref><ref name=Route2024>{{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 }}</ref>

==== Metal-rich white dwarfs ====
[[File:Periodic Table White Dwarfs.png|thumb|Elements discovered in the atmosphere of white dwarfs colder than {{val|25000|u=K}}.]]
Around 25–33% of white dwarfs have metal lines in their spectra, which is notable because any heavy elements in a white dwarf should sink into the star's interior in just a small fraction of the star's lifetime.<ref name=":0">{{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 }}</ref> The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky [[planetesimal]]s.<ref name=":0" /> 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 [[Planetary differentiation|differentiated]], rocky planet whose mantle had been eroded by the host star's wind during its [[asymptotic giant branch]] phase.<ref>{{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 }}</ref>

=== Magnetic field ===
Magnetic fields in white dwarfs with a strength at the surface of {{circa}} 1&nbsp;million [[Gauss (unit)|gauss]] (100&nbsp;[[tesla (unit)|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]].<ref>
{{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
}}</ref> This putative law, sometimes called the ''[[Blackett effect]]'', was never generally accepted, and by the 1950s even Blackett felt it had been refuted.<ref>
{{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
}}</ref>{{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.<ref>
{{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
}}</ref> A surface magnetic field of {{circa}} 100&nbsp;gauss (0.01&nbsp;T) in the progenitor star would thus become a surface magnetic field of {{circa}} 100&nbsp;×&nbsp;100<sup>2</sup>&nbsp;= 1&nbsp;million gauss (100&nbsp;T) once the star's radius had shrunk by a factor of 100.<ref name="physrev" />{{rp|§8}}<ref>
{{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
}}</ref>{{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.<ref>
{{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
}}
</ref> It is thought to have a surface field of approximately 300&nbsp;million gauss (30&nbsp;kT).<ref name="physrev" />{{rp|§8}}

Since 1970, magnetic fields have been discovered in well over 200&nbsp;white dwarfs, ranging from {{val|2|e=3}} to {{val|e=9}}&nbsp;gauss (0.2&nbsp;T to 100&nbsp;kT).<ref>
{{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
}}
</ref> 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&nbsp;megagauss or more. Thus the basic identification process also sometimes results in discovery of magnetic fields.<ref>
{{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
}}
</ref> White dwarf magnetic fields may also be measured without spectral lines, using the techniques of broadband circular [[Polarimetry|polarimetry]], or maybe through measurement of their frequencies of radio emission via the [[Solar_radio_emission#Electron-cyclotron_maser_emission|electron cyclotron maser]].<ref name=Route2024/>  It has been estimated that at least 10% of white dwarfs have fields in excess of 1&nbsp;million gauss (100&nbsp;T).<ref>
{{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
}}
</ref><ref>
{{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
}}</ref> The magnetic fields in a white dwarf may allow for the existence of a new type of [[chemical bond]], [[perpendicular paramagnetic bond]]ing, in addition to [[ionic bond|ionic]] and [[covalent bond]]s, though detecting molecules bonded in this way is expected to be difficult.<ref>
{{cite news
 |first=Zeeya  |last=Merali
 |date=19 July 2012
 |title=Stars draw atoms closer together
 |department=Nature News & Comment
 |journal=[[Nature (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
}}
</ref>

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.<ref>
{{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
}}
</ref> A second white dwarf pulsar was discovered in 2023.<ref>{{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 }}</ref>

== Variability ==
{{Main|Pulsating white dwarf}}
{{See also|#Cataclysmic variables|l1=Cataclysmic variables}}

{| class="wikitable" style="float: right"
|+ Types of pulsating white dwarf<ref>
 {{cite web
  |title=ZZ Ceti variables
  |publisher=Association Française des Observateurs d'Etoiles Variables
  |website=Centre deDonnées astronomiques de Strasbourg
  |url=http://cdsweb.u-strasbg.fr/afoev/var/ezz.htx
  |access-date=6 June 2007
  |archive-url=https://web.archive.org/web/20070205132930/http://cdsweb.u-strasbg.fr/afoev/var/ezz.htx
  |archive-date=5 February 2007
 }}
</ref><ref name="quirion" />{{rp|§§1.1, 1.2}}
|-
| '''DAV''' ([[General Catalog of Variable Stars|GCVS]]: ''ZZA'') || DA [[#Atmosphere and spectra|spectral type]], having only hydrogen [[absorption line]]s in its spectrum
|-
| '''DBV''' (GCVS: ''ZZB'') || DB spectral type, having only [[helium]] absorption lines in its spectrum
|-
| '''GW Vir''' (GCVS: ''ZZO'') || Atmosphere mostly C, He and O; may be divided into '''DOV''' and '''PNNV''' stars
|}

Early calculations suggested that there might be white dwarfs whose luminosity [[variable star|varied]] with a period of around 10 seconds, but searches in the 1960s failed to observe this.<ref name="physrev" />{{rp|§7.1.1}}<ref>
{{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
}}</ref> 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&nbsp;minutes.<ref>
{{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
}}</ref> 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.<ref name="physrev" />{{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;<ref name="physrev" />{{rp|891, 895}} ''DBV'', or ''V777&nbsp;Her'', stars, with helium-dominated atmospheres and the spectral type DB;<ref name="wden" />{{rp|3525}} and ''[[GW Vir stars]]'', sometimes subdivided into ''DOV'' and ''PNNV'' stars, with atmospheres dominated by helium, carbon, and oxygen.<ref name="quirion">
{{cite journal
 |last1=Quirion |first1=P.-O.
 |last2=Fontaine |first2=G.
 |last3=Brassard |first3=P.
 |date=2007
 |title=Mapping the Instability Domains of GW&nbsp;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
}}</ref><ref>
{{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&nbsp;1159 star HE&nbsp;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
}}</ref> 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''.<ref name="quirion" /><ref>
{{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
}}</ref> 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 [[asteroseismology|asteroseismological]] evidence about the interiors of white dwarfs.<ref>
{{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
}}</ref>

== Formation ==
White dwarfs are thought to represent the end point of [[stellar evolution]] for main-sequence stars with masses from about 0.07 to 10&nbsp;{{solar mass}}.<ref name="cosmochronology" /><ref name="evo">
{{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
}}</ref> 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.<ref>{{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 }}</ref>

=== Stars with very low mass ===
If the mass of a main-sequence star is lower than approximately half a [[solar mass]], it will never become hot enough to ignite and fuse helium in its core.<ref name=Brown2011>{{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 }}</ref> It is thought that, over a lifespan that considerably exceeds the age of the universe ({{circa}} 13.8&nbsp;billion years),<ref name="aou" /> such a star will eventually burn all its hydrogen, for a while becoming a [[Blue dwarf (red-dwarf stage)|blue dwarf]], and end its evolution as a helium white dwarf composed chiefly of [[helium-4]] nuclei.<ref>
{{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
}}</ref> 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.<ref name="rln" /><ref name="apj606_L147" /><ref name="he2" /><ref name="sj">{{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}}</ref><ref>
{{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
}}</ref><ref>{{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
}}</ref> 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.<ref>
{{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
}}</ref><ref>
{{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
}}</ref>

=== Stars with low to medium mass ===
If the mass of a main-sequence star is between 0.5 and 8&nbsp;{{solar mass}},<ref name=Brown2011/><ref name=Woolsey2002/> 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.<ref name="sj" /><ref name="vd1">{{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}}</ref><ref name="vd2">{{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}}</ref>

=== Stars with medium to high mass ===
If a star is massive enough, its core will eventually become sufficiently hot to fuse carbon to neon, and then to fuse neon to iron. Such a star will not become a white dwarf, because the mass of its central, non-fusing core, initially supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will [[gravitational collapse|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]].<ref name="evo" /><ref>
{{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
}}</ref> Some main-sequence stars, of perhaps 8 to 10&nbsp;{{solar mass}}, although sufficiently massive to [[Carbon-burning process|fuse carbon to neon and magnesium]], may be insufficiently massive to [[Neon-burning process|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]].<ref>
{{cite journal
 |title=Evolution of 8–10&nbsp;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
}}</ref><ref name=Woolsey2002>
{{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
}}</ref> 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 [[nova]]e 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.<ref name="oxne" /><ref>
{{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
}}</ref><ref>
{{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
}}</ref>

=== Type Iax supernova ===
[[Type Ia supernova#Type Iax|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.<ref name="ironcore">
{{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
}}</ref> These ''iron-core'' white dwarfs would be smaller than the carbon–oxygen kind of similar mass and would cool and crystallize faster than those.<ref name="ironcore2">
{{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
}}</ref>

== Fate ==
[[File:White Dwarf Ages.ogv|thumb|Artist's concept of white dwarf aging]]
[[File:Whitedwarfsevolution.png|thumb|Internal structures of white dwarfs. To the left is a newly formed white dwarf, in the center is a cooling and crystallizing white dwarf, and the right is a black dwarf.]]
A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf. Assuming that the [[universe]] continues to expand, it is thought that in 10<sup>19</sup> to 10<sup>20</sup> years, the [[galaxy|galaxies]] will evaporate as their [[star]]s escape into intergalactic space.<ref name="fate">{{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 }}</ref>{{rp|§IIIA}} White dwarfs should generally survive galactic dispersion, although an occasional collision between white dwarfs may produce a new [[nuclear fusion|fusing]] star or a super-Chandrasekhar mass white dwarf that will explode in a [[Type Ia supernova]].<ref name="fate" />{{rp|§§IIIC, IV}} The subsequent lifetime of white dwarfs is thought to be on the order of the hypothetical lifetime of the [[proton]], known to be at least 10<sup>34</sup>–10<sup>35</sup> years. Some [[grand unified theory|grand unified theories]] predict a [[proton decay|proton lifetime]] between 10<sup>30</sup> and 10<sup>36</sup> years. If these theories are not valid, the proton might still decay by complicated nuclear reactions or through [[quantum gravity|quantum gravitational]] processes involving [[virtual black hole]]s; in these cases, the lifetime is estimated to be no more than 10<sup>200</sup> years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely.<ref name="fate" />{{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 [[Carbon planet|diamond planet]].<ref name=2007ApJ...669.1279S>{{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 }}</ref><ref>{{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}}</ref><ref name=TIME-2011-08-26>{{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)|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}}</ref>

== Debris disks and planets ==
{{see also|List of exoplanets and planetary debris around white dwarfs}}
[[File:Artist’s impression of debris around a white dwarf star.jpg|thumb|Artist's impression of debris around a white dwarf<ref>{{cite news |title=Hubble finds dead stars "polluted" with planetary debris |url=http://www.spacetelescope.org/images/heic1309a/ |access-date=10 May 2013 |newspaper=ESA/Hubble Press Release|archive-url=https://web.archive.org/web/20130609084315/http://www.spacetelescope.org/images/heic1309a/ |archive-date=9 June 2013 |url-status=live}}</ref>]]
[[File:Comet falling into white dwarf.jpg|left|thumb|Comet falling into white dwarf (artist's impression)<ref>{{cite web|title=Comet falling into white dwarf (artist's impression)|url=https://www.spacetelescope.org/images/heic1703a/|website=www.spacetelescope.org|access-date=14 February 2017|archive-url=https://web.archive.org/web/20170215024452/https://www.spacetelescope.org/images/heic1703a/|archive-date=15 February 2017|url-status=live}}</ref>]]
A white dwarf's [[stellar system|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 [[Metallicity|metal]] absorption lines. 27–50% of white dwarfs show a spectrum polluted with metals,<ref>{{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}}</ref> 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 [[Tidal force|tidally disrupted]] rocky bodies.<ref>{{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}}</ref><ref name=":2" /> The first observation of a metal-polluted white dwarf was by van Maanen<ref>{{cite journal |last=van Maanen |first=A. |date=1917-12-01 |title=Two Faint Stars with Large Proper Motion |bibcode=1917PASP...29..258V |journal=Publications of the Astronomical Society of the Pacific |volume=29 |issue=172 |page=258 |doi=10.1086/122654 |s2cid=250734202 |issn=0004-6280|doi-access=free }}</ref> in 1917 at the [[Mount Wilson Observatory]] and is now recognized as the first evidence of [[exoplanet]]s in astronomy.<ref name="Klein 61">{{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 }}</ref> The white dwarf [[van Maanen 2]] shows iron, [[calcium]] and magnesium in its atmosphere,<ref>{{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}}</ref> but van Maanen misclassified it as the faintest [[F-type star]] based on the calcium [[Fraunhofer lines|H- and K-lines]].<ref>{{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}}</ref> 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 (geology)|crust]] material and the beryllium is thought to come from [[exomoon]]s.<ref name="Klein 61"/>

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.<ref name=":2" /> The first white dwarf with infrared excess was discovered by Zuckerman and Becklin in 1987 in the near-infrared around [[G 29-38|Giclas 29-38]]<ref>{{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}}</ref> and later confirmed as a debris disk.<ref name=":3" /> 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]].<ref>{{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 }}</ref>

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.<ref name=":4">{{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 }}</ref><ref name="Mullally2024"/> {{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=<div align="center">([[:File:NASA-ExoplanetOrbitingWhiteDwarfStarWD1856+534.webm|NASA; video; 2:10]])</div> |width2=250 |footer= }}Infrared spectroscopic observations made by NASA's [[Spitzer Space Telescope]] of the central star of the [[Helix Nebula]] suggest the presence of a dust cloud, which may be caused by cometary collisions. It is possible that infalling material from this may cause X-ray emission from the central star.<ref>{{cite news |url=http://news.bbc.co.uk/1/hi/sci/tech/6357765.stm |title=Comet clash kicks up dusty haze |archive-url=https://web.archive.org/web/20070216010400/http://news.bbc.co.uk/1/hi/sci/tech/6357765.stm |archive-date=16 February 2007 |work=BBC News |date=13 February 2007 |access-date=20 September 2007}}</ref><ref>
{{cite journal
 |bibcode=2007ApJ...657L..41S
 |arxiv= astro-ph/0702296
 |doi= 10.1086/513018
 |title=A Debris Disk around the Central Star of the Helix Nebula?
 |date=2007
 |last1=Su |first1=K. Y. L.
 |last2=Chu |first2=Y.-H.
 |last3=Rieke |first3=G. H.
 |last4=Huggins |first4=P. J.
 |last5=Gruendl |first5=R.
 |last6=Napiwotzki |first6=R.
 |last7=Rauch |first7=T.
 |last8=Latter |first8=W. B.
 |last9=Volk |first9=K.
 |journal=The Astrophysical Journal
 |volume=657 |issue= 1
 |pages=L41
 |s2cid= 15244406
}}</ref> Similarly, observations made in 2004 indicated the presence of a dust cloud around the young (estimated to have formed from its AGB progenitor about 500&nbsp;million years ago) white dwarf [[G29-38]], which may have been created by tidal disruption of a [[comet]] passing close to the white dwarf.<ref name=":3">
{{cite journal
 |bibcode=2005ApJ...635L.161R
 |arxiv= astro-ph/0511358
 |doi= 10.1086/499561
 |title=The Dust Cloud around the White Dwarf G29-38
 |date=2005
 |last1=Reach |first1=William T.
 |last2=Kuchner |first2=Marc J.
 |last3=Von Hippel |first3=Ted
 |last4=Burrows |first4=Adam
 |last5=Mullally |first5=Fergal
 |last6=Kilic |first6=Mukremin
 |last7=Winget |first7=D. E.
 |journal=The Astrophysical Journal
 |volume=635 |issue=2 |page=L161
 |s2cid= 119462589
}}</ref> Some estimations based on the metal content of the atmospheres of the white dwarfs consider that at least 15% of them may be orbited by planets or [[asteroid]]s, or at least their debris.<ref>{{cite journal |author1=Sion, Edward M. |author2=Holberg, J.B. |author3=Oswalt, Terry D. |author4=McCook, George P. |author5=Wasatonic, Richard |title=The White Dwarfs Within 20&nbsp;Parsecs of the Sun: Kinematics and Statistics |date=2009 |journal=The Astronomical Journal |volume=138 |number=6 |pages=1681–1689 |bibcode=2009AJ....138.1681S |doi=10.1088/0004-6256/138/6/1681 |arxiv=0910.1288|s2cid=119284418 }}</ref> Another suggested idea is that white dwarfs could be orbited by the stripped cores of [[rocky planet]]s, that would have survived the red giant phase of their star but losing their outer layers and, given those planetary remnants would likely be made of [[metal]]s, to attempt to detect them looking for the signatures of their interaction with the white dwarf's [[magnetic field]].<ref>{{cite journal |author1=Li, Jianke |author2=Ferrario, Lilia |author3=Wickramasinghe, Dayal |title=Planets around White Dwarfs |year=1998 |journal=Astrophysical Journal Letters |volume=503 |page=L151 |number=1 |id=p. L51 |bibcode=1998ApJ...503L.151L |doi=10.1086/311546 |doi-access=free}}</ref> Other suggested ideas of how white dwarfs are polluted with dust involve the scattering of asteroids by planets<ref>{{cite journal |last1=Debes |first1=John H. |last2=Walsh|first2=Kevin J. |last3=Stark |first3=Christopher |date=24 February 2012 |journal=The Astrophysical Journal |language=en |volume=747 |issue=2 |page=148 |arxiv=1201.0756 |doi=10.1088/0004-637X/747/2/148 |issn=0004-637X |title=The Link Between Planetary Systems, Dusty White Dwarfs, and Metal-Polluted White Dwarfs|bibcode=2012ApJ...747..148D |s2cid=118688656 }}</ref><ref>{{cite journal |last1=Veras |first1=Dimitri |last2=Gänsicke |first2=Boris T. |date=2015-02-21|title=Detectable close-in planets around white dwarfs through late unpacking|journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=447 |issue=2 |pages=1049–1058 |arxiv=1411.6012 |doi=10.1093/mnras/stu2475 |doi-access=free |issn=0035-8711 |bibcode=2015MNRAS.447.1049V|s2cid=119279872 }}</ref><ref>{{cite journal |last1=Frewen |first1=S. F. N. |last2=Hansen |first2=B. M. S. |date=2014-04-11|title=Eccentric planets and stellar evolution as a cause of polluted white dwarfs |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=439 |issue=3 |pages=2442–2458 |arxiv=1401.5470 |doi=10.1093/mnras/stu097 |doi-access=free |issn=0035-8711 |bibcode=2014MNRAS.439.2442F|s2cid=119257046 }}</ref> or via planet-planet scattering.<ref>{{cite journal |last1=Bonsor |first1=Amy |last2=Gänsicke |first2=Boris T. |last3=Veras |first3=Dimitri |last4=Villaver |first4=Eva|last5=Mustill |first5=Alexander J. |date=2018-05-21|title=Unstable low-mass planetary systems as drivers of white dwarf pollution |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=476 |issue=3 |pages=3939–3955 |arxiv=1711.02940 |doi=10.1093/mnras/sty446 |doi-access=free |issn=0035-8711 |bibcode=2018MNRAS.476.3939M|s2cid=4809366 }}</ref> Liberation of [[exomoon]]s from their host planet could cause white dwarf pollution with dust. Either the liberation could cause asteroids to be scattered towards the white dwarf or the exomoon could be scattered into the [[Roche radius]] of the white dwarf.<ref>{{cite journal |last1=Gänsicke |first1=Boris T. |last2=Holman |first2=Matthew J. |last3=Veras |first3=Dimitri |last4=Payne |first4=Matthew J. |date=2016-03-21|title=Liberating exomoons in white dwarf planetary systems|journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=457 |issue=1 |pages=217–231 |arxiv=1603.09344 |doi=10.1093/mnras/stv2966 |doi-access=free |issn=0035-8711 |bibcode=2016MNRAS.457..217P|s2cid=56091285 }}</ref> The mechanism behind the pollution of white dwarfs in binaries was also explored as these systems are more likely to lack a major planet, but this idea cannot explain the presence of dust around single white dwarfs.<ref>{{cite journal |last1=Rebassa-Mansergas |first1=Alberto |last2=Xu (许偲艺) |first2=Siyi |last3=Veras |first3=Dimitri |date=2018-01-21|title=The critical binary star separation for a planetary system origin of white dwarf pollution |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=473 |issue=3 |pages=2871–2880 |arxiv=1708.05391 |doi=10.1093/mnras/stx2141 |doi-access=free |issn=0035-8711 |bibcode=2018MNRAS.473.2871V|s2cid=55764122 }}</ref> While old white dwarfs show evidence of dust accretion, white dwarfs older than ~1 billion years or >7000 K with dusty infrared excess were not detected<ref>{{cite journal |last1=Becklin |first1=E. E. |last2=Zuckerman |first2=B. |last3=Farihi |first3=J. |date=10 February 2008 |title=Spitzer IRAC Observations of White Dwarfs. I. Warm Dust at Metal-Rich Degenerates |journal=The Astrophysical Journal |language=en |volume=674 |issue=1 |pages=431–446 |arxiv=0710.0907 |doi=10.1086/521715 |issn=0004-637X |bibcode=2008ApJ...674..431F|s2cid=17813180 }}</ref> until the discovery of LSPM J0207+3331 in 2018, which has a cooling age of ~3 billion years. The white dwarf shows two dusty components that are being explained with two rings with different temperatures.<ref name=":2">{{cite journal |last1=Debes |first1=John H. |last2=Thévenot |first2=Melina |last3=Kuchner |first3=Marc J. |last4=Burgasser |first4=Adam J. |last5=Schneider |first5=Adam C. |last6=Meisner |first6=Aaron M. |last7=Gagné |first7=Jonathan |last8=Faherty |first8=Jacqueline K.|author8-link=Jackie Faherty |last9=Rees |first9=Jon M. |date=2019-02-19|title=A 3 Gyr White Dwarf with Warm Dust Discovered via the Backyard Worlds: Planet 9 Citizen Science Project |journal=The Astrophysical Journal |volume=872 |issue=2|page=L25 |arxiv=1902.07073 |doi=10.3847/2041-8213/ab0426 |issn=2041-8213 |bibcode=2019ApJ...872L..25D|s2cid=119359995 |doi-access=free }}</ref>

Another possible way to detect planetary systems around white dwarfs is through their radio emissions.  In 2004 and 2005, A. J. Willes and K. Wu hypothesized that when an exoplanet travels through the [[magnetosphere]] of a white dwarf, it may generate auroral radio emissions from the magnetic poles of the white dwarf, similar to how [[Io_(moon)|Io]] stimulates [[Magnetosphere_of_Jupiter|radio emissions from Jupiter]].  However, a search for such radio emission from nine white dwarfs by researchers using the [[Arecibo_Observatory|Arecibo radio telescope]] did not find any so far.<ref name=Route2024/>

The metal-rich white dwarf [[WD 1145+017]] is the first white dwarf observed with a disintegrating minor planet that transits the star.<ref>{{cite web |title = Zombie Star Caught Feasting on Asteroids |url=http://news.nationalgeographic.com/2015/10/151021-zombie-dead-star-eats-asteroid-astronomy/ |website=National Geographic News |access-date=2015-10-22|first=Michael D. |last=Lemonick |date=2015-10-21 |archive-url=https://web.archive.org/web/20151024081958/http://news.nationalgeographic.com/2015/10/151021-zombie-dead-star-eats-asteroid-astronomy/ |archive-date=24 October 2015 |url-status=dead}}</ref><ref name=":1">{{cite journal |title=A disintegrating minor planet transiting a white dwarf |journal=Nature |date=2015-10-22|pages=546–549 |volume=526 |issue=7574 |doi=10.1038/nature15527 |language = en |first1=Andrew |last1=Vanderburg |first2=John Asher |last2=Johnson |first3=Saul |last3=Rappaport |first4=Allyson |last4=Bieryla |first5=Jonathan |last5=Irwin |first6=John Arban |last6=Lewis |first7=David |last7=Kipping |first8=Warren R. |last8=Brown |first9=Patrick |last9=Dufour |arxiv=1510.06387 |bibcode=2015Natur.526..546V |pmid=26490620|s2cid=4451207 }}</ref> The disintegration of the planetesimal generates a debris cloud that passes in front of the star every 4.5&nbsp;hours, causing a 5-minute-long fade in the star's optical brightness.<ref name=":1" /> The depth of the transit is highly variable.<ref name=":1" />

The giant planet [[WD J0914+1914]]b is being [[Photoevaporation|evaporated]] by the strong ultraviolet radiation of the hot white dwarf. Part of the evaporated material is being accreted in a gaseous disk around the white dwarf. The weak [[H-alpha|hydrogen line]] as well as other lines in the spectrum of the white dwarf revealed the presence of the giant planet.<ref name="Gänsicke">{{cite web |last1=Gänsicke |first1=Boris T. |last2=Schreiber |first2=Matthias R. |last3=Toloza |first3=Odette |last4=Gentile Fusillo |first4=Nicola P. |last5=Koester |first5=Detlev |last6=Manser |first6=Christopher J. |title=Accretion of a giant planet onto a white dwarf |url=https://www.eso.org/public/archives/releases/sciencepapers/eso1919/eso1919a.pdf |url-status=live |archive-url=https://web.archive.org/web/20191204215002/https://www.eso.org/public/archives/releases/sciencepapers/eso1919/eso1919a.pdf |archive-date=4 December 2019 |access-date=2019-12-11 |website=ESO}}</ref>

The white dwarf [[WD 0145+234]] shows brightening in the mid-infrared, seen in [[NEOWISE]] data. The brightening, not seen before 2018, may be due to the [[Roche limit|tidal disruption]] of an [[exoasteroid]], the first time such an event has been observed.<ref name=":5">{{cite journal |last1=Wang |first1=Ting-Gui |last2=Jiang |first2=Ning |last3=Ge |first3=Jian |last4=Cutri |first4=Roc M. |last5=Jiang |first5=Peng |last6=Sheng |first6=Zhengfeng |last7=Zhou |first7=Hongyan |last8=Bauer |first8=James |last9=Mainzer |first9=Amy |last10=Wright |first10=Edward L. |date=November 2019 |title=An On-going Mid-infrared Outburst in the White Dwarf 0145+234: Catching in Action of Tidal Disruption of an Exoasteroid? |arxiv=1910.04314 |journal=Astrophysical Journal Letters |volume=886 |number=1 |page=L5 |doi=10.3847/2041-8213/ab53ed |doi-access=free |bibcode=2019ApJ...886L...5W }}</ref>

[[WD 1856+534]] is the first transiting major planet to be observed orbiting a white dwarf, and remains the only such example as of 2023.<ref name="Vanderburg2020">{{cite journal
  |title      = A giant planet candidate transiting a white dwarf
  |display-authors = etal
  |first1     = Andrew  |last1 = Vanderburg
  |first2     = Saul A. |last2 = Rappaport
  |first3     = Siyi |last3 = Xu
  |first4     = Ian J. M. |last4 = Crossfield
  |first5     = Juliette C. |last5 = Becker
  |first6     = Bruce |last6 = Gary
  |date       = September 2020
  |journal    = Nature
  |volume     = 585
  |issue = 7825
  |pages      = 363–367
  |doi        = 10.1038/s41586-020-2713-y
  |pmid = 32939071
 |arxiv      = 2009.07282
  |bibcode    = 2020Natur.585..363V
 }}</ref><ref>{{cite journal
 |first=David
 |last=Kipping
 |title=The giant nature of WD 1856 b implies that transiting rocky planets are rare around white dwarfs
 |journal=Monthly Notices of the Royal Astronomical Society
 |volume=527
 |number=2
 |date=January 2024
 |pages=3532–3541
 |doi=10.1093/mnras/stad3431|doi-access=free
 |arxiv=2310.15219
 }}</ref> [[MOA-2010-BLG-477L]], a white dwarf discovered thanks to a [[microlensing event]], is also known to have a giant planet.<ref name=Blackman2021>{{cite journal
 |arxiv=2110.07934
 |year=2021
 |title=A Jovian analogue orbiting a white dwarf star
 |doi=10.1038/s41586-021-03869-6
 |last1=Blackman |first1=J. W.
 |last2=Beaulieu |first2=J. P.
 |last3=Bennett |first3=D. P.
 |last4=Danielski |first4=C.
 |last5=Alard |first5=C.
 |last6=Cole |first6=A. A.
 |last7=Vandorou |first7=A.
 |last8=Ranc |first8=C.
 |last9=Terry |first9=S. K.
 |last10=Bhattacharya |first10=A.
 |last11=Bond |first11=I.
 |last12=Bachelet |first12=E.
 |last13=Veras |first13=D.
 |last14=Koshimoto |first14=N.
 |last15=Batista |first15=V.
 |last16=Marquette |first16=J. B.
 |journal=Nature |volume=598 |issue=7880 |pages=272–275 |pmid=34646001
 |bibcode=2021Natur.598..272B
 }}</ref><ref name="Mullally2024"/>

[[GD 140]] and [[LP 145-141|LAWD 37]] are suspected to have giant exoplanets due to anomaly in the [[Hipparcos]]-Gaia proper motion. For GD 140 it is suspected to be a planet several times more massive than Jupiter and for LAWD 37 it is suspected to be a planet less massive than Jupiter.<ref>{{cite journal |last1=Kervella |first1=Pierre |last2=Arenou |first2=Frédéric |last3=Mignard |first3=François |last4=Thévenin |first4=Frédéric |date=2019-03-01 |title=Stellar and substellar companions of nearby stars from Gaia DR2. Binarity from proper motion anomaly |url=https://ui.adsabs.harvard.edu/abs/2019A&A...623A..72K |journal=Astronomy and Astrophysics |volume=623 |pages=A72 |doi=10.1051/0004-6361/201834371 |arxiv=1811.08902 |bibcode=2019A&A...623A..72K |s2cid=119491061 |issn=0004-6361}}</ref><ref>{{cite journal |last1=Kervella |first1=Pierre |last2=Arenou |first2=Frédéric |last3=Thévenin |first3=Frédéric |date=2022-01-01 |title=Stellar and substellar companions from Gaia EDR3. Proper-motion anomaly and resolved common proper-motion pairs |url=https://ui.adsabs.harvard.edu/abs/2022A&A...657A...7K |journal=Astronomy and Astrophysics |volume=657 |pages=A7 |doi=10.1051/0004-6361/202142146 |arxiv=2109.10912 |bibcode=2022A&A...657A...7K |s2cid=237605138 |issn=0004-6361}}</ref> Additionally, WD 0141-675 was suspected to have a super-Jupiter with an orbital period of 33.65 days based on Gaia astrometry. This is remarkable because WD 0141-675 is polluted with metals and metal polluted white dwarfs have long be suspected to host giant planets that disturb the orbits of minor planets, causing the pollution.<ref name="GaiaDR3">{{cite journal |last1=Gaia Collaboration |last2=Arenou |first2=F. |last3=Babusiaux |first3=C. |last4=Barstow |first4=M. A. |last5=Faigler |first5=S. |last6=Jorissen |first6=A. |last7=Kervella |first7=P. |last8=Mazeh |first8=T. |last9=Mowlavi |first9=N. |last10=Panuzzo |first10=P. |last11=Sahlmann |first11=J. |last12=Shahaf |first12=S. |last13=Sozzetti |first13=A. |last14=Bauchet |first14=N. |last15=Damerdji |first15=Y. |date=2023 |title=''Gaia'' Data Release 3 |journal=Astronomy & Astrophysics |volume=674 |pages=A34 |doi=10.1051/0004-6361/202243782 |arxiv=2206.05595 |s2cid=249626026 }}</ref> Both GD 140 and WD 0141 will be observed with [[James Webb Space Telescope|JWST]] in cycle 2 with the aim to detect infrared excess caused by the planets.<ref>{{cite web |title=CYCLE 2 GO |url=https://www.stsci.edu/home/jwst/science-execution/approved-programs/general-observers/cycle-2-go |access-date=2023-05-15 |website=STScI.edu |language=en}}</ref> However, the planet candidate at WD 0141-675 was found to be a false positive caused by a software error.<ref>{{cite web |url=https://www.cosmos.esa.int/web/gaia/dr3-known-issues |title=Gaia DR3 known issues |date=5 May 2023 |publisher=[[ESA]] |access-date=8 August 2023 |quote=During validation of epoch astrometry for Gaia DR4, an error was discovered, that had already had an impact on the Gaia DR3 non-single star results. [...] We can conclude that the solutions for [...] WD 0141-675 [...] are false-positives as far as Gaia non-single star processing is concerned.}}</ref>

A JWST survey of four metal polluted white dwarfs found two [[List of directly imaged exoplanets|directly imaged exoplanet]] candidates with masses of 1–7&nbsp;{{Jupiter mass}}. One orbits around [[WD 1202−232]] (LP  852-7) and the other around [[WD 2105−82]] (LAWD 83). If confirmed they would be the first directly imaged planets that likely formed from circumstellar disk material, representing a new population of directly imaged giant planets that are more similar to [[Giant planet|solar system giants]] in age and probably also in their atmosphere. Confirmation will be possible via the common [[proper motion]] method with JWST.<ref name="Mullally2024">{{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 }}</ref>

In 2024 it was discovered that the white dwarf in the [[PHL 5038AB]] system is polluted with calcium from rocky material. The white dwarf is orbited by a [[brown dwarf]], which was discovered in 2009. This is seen as perhaps the first case of linking white dwarf pollution with the presence of a [[substellar object]]. It is thought that the orbits of [[Planetesimal|planetesimals]] are being disrupted by the brown dwarf, causing the pollution of the white dwarf.<ref>{{cite journal |last1=Casewell |first1=S. L. |last2=Debes |first2=J. |last3=Dupuy |first3=T. J. |last4=Dufour |first4=P. |last5=Bonsor |first5=A. |last6=Rebassa-Mansergas |first6=A. |last7=Murillo-Ojeda |first7=R. |last8=French |first8=J. R. |last9=Xu |first9=Siyi (许偲艺) |last10=Martin |first10=E. |last11=Manjavacas |first11=E. |date=8 Apr 2024 |title=PHL 5038AB: Is the brown dwarf causing pollution of its white dwarf host star? |journal=MNRAS |volume=530 |issue=3 |pages=3302–3309 |doi=10.1093/mnras/stae974 |doi-access=free |arxiv=2404.05488}}</ref>

== Habitability ==
It has been proposed that white dwarfs with surface temperatures of less than {{val|10000|u=K}} could harbor a [[habitable zone]] at a distance of {{circa}}&nbsp;0.005 to 0.02&nbsp;[[Astronomical unit|AU]] that would last upwards of 3&nbsp;billion years.<!-- see page 2 of the paper--> This is so close that any habitable planets would be [[tidally locked]]. The goal is to search for [[transit (astronomy)|transits]] of hypothetical Earth-like planets that could have migrated inward or formed there. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong [[eclipse]]s.<ref>
{{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
}}</ref> 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 force]]s that could render them uninhabitable by triggering a [[greenhouse effect]].<ref>
{{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
}}</ref> 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.<ref>
{{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
}}</ref>

== Binary stars and novae ==
[[File:White dwarfs circling each other and then colliding.gif|right|thumb|The merger process of two co-orbiting white dwarfs produces [[gravitational wave]]s]]
If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including [[nova]]e 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.<ref name=di_stefano_et_al1997>
{{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
}}</ref> 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).<ref>{{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}}</ref> A close binary system of two white dwarfs can lose angular momentum and radiate energy in the form of [[gravitational wave]]s, causing their mutual orbit to steadily shrink until the stars merge.<ref name=hscfa20101116>
{{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
}}</ref><ref name=hscfa20110713>
{{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
}}</ref>

=== Type Ia supernovae ===
{{Main|Type Ia supernova}}
The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~&nbsp;1.4&nbsp;{{solar mass}}. This limit may increase if the white dwarf is rotating rapidly and nonuniformly.<ref>
{{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
}}</ref> White dwarfs in [[binary (astronomy)|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 [[nuclear fusion|fusion]] in the white dwarf or its collapse into a neutron star.<ref name="collapse" />

There are two models that might explain the progenitor systems of [[Type Ia supernova|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.<ref name="sniamodels">
{{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
}}</ref>{{rp|14}} It is believed that [[compression (physical)|compressional]] heating of the core leads to [[carbon detonation|ignition]] of [[carbon burning process|carbon fusion]] as the mass approaches the Chandrasekhar limit.<ref name="sniamodels" /> 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 [[thermal runaway|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.<ref name="osln" /><ref name="sniamodels" /><ref>
{{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
}}</ref> In another possible mechanism for Type&nbsp;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.<ref name="sniamodels" />{{rp|14}} In both cases, the white dwarfs are not expected to survive the Type Ia supernova.<ref name=":6">{{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 }}</ref>

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.<ref name=":7">{{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 }}</ref> However, the main mechanism for Type Ia supernovae remains an open question.<ref>{{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 }}</ref> 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.<ref name=":7" /> 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.<ref name=":6" /> 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]].<ref name=":6" />

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.<ref name="hernandez2012">
{{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
}}</ref> [[Tycho's Supernova]] of 1572 was also a type&nbsp;Ia supernova, and its remnant has been detected.<ref name="Krause2008">{{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 }}</ref> [[WD 0810–353]], a white dwarf 11 parsecs away from the Sun, is possibly a [[hypervelocity star|hypervelocity runaway]] ejected from a Type Ia supernova, though this has been disputed.<ref name="dlFM2022">
{{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
}}</ref><ref>{{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 }}</ref>

=== Post-common envelope binary ===
{{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).<ref>{{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 }}</ref> 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 (astronomy)|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.<ref>{{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 }}</ref><ref>{{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 }}</ref> Because a PCEB may evolve at some point into a [[cataclysmic variable]], some of them are also called pre-cataclysmic variables.<ref>{{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 }}</ref><ref name="GaiaDR3"/>

=== Cataclysmic variables ===
{{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 [[Nuclear fusion|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 nova]]e, 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 variable]]s. As well as novae and dwarf novae, several other classes of these variables are known, including [[Polar (star)|polars]] and [[intermediate polar]]s, both of which feature highly magnetic white dwarfs.<ref name="osln" /><ref name="sniamodels" /><ref name="nasa1">{{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}}</ref><ref name="nasa2">{{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}}</ref> Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.<ref name="nasa2" />

=== Other multiple-star systems ===
Other binaries include those that consist of a [[Main-sequence star|main sequence star]] (or giant) and a white dwarf. The binary Sirius AB is an example pair of this type.<ref>{{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}}</ref> 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.<ref>{{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 }}</ref> One interesting field is the study of [[#Debris disks and planets|remnant planetary systems]] around white dwarfs. It is expected that planets orbiting several [[Astronomical unit|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 [[exoplanet]]s and [[brown dwarf]]s. The first brown dwarf to be detected by direct imaging was the companion to the white dwarf [[GD 165|GD 165 A]], discovered in 1988.<ref>{{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}}</ref> 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<ref>{{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 }}</ref><ref>{{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 }}</ref> or an exoplanet.<ref>{{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}}</ref>

== Nearest ==
{| class="wikitable" style="text-align: center;"
|+ White dwarfs within 25 light years<ref>
 {{cite journal
  | last1=Giammichele, N.
  | last2=Bergeron, P.
  | last3=Dufour, P.
  | title=Know Your Neighborhood: A Detailed Model Atmosphere Analysis of Nearby White Dwarfs
  | journal=The Astrophysical Journal Supplement
  | volume=199 | issue=2 | id=29 | page=35
  | date=April 2012
  | doi=10.1088/0067-0049/199/2/29
  | bibcode=2012ApJS..199...29G
  |arxiv = 1202.5581 | s2cid=118304737
 }}</ref>
! class="unsortable" | Identifier
! WD Number
! Distance<br />{{bracket|[[Light year|ly]]}}
! Type
! [[Absolute magnitude|Absolute<br />magnitude]]
! Mass<br />{{bracket|{{solar mass|link=yes}}}}
! Luminosity<br />{{bracket|{{Solar luminosity|link=yes}}}}
! Age<br />{{bracket|[[Gigaannum|Gyr]]}}
! Objects in system
|-
|style="text-align: left;"| [[Sirius]] B
| 0642–166
| 8.66
| DA
| 11.18
| 0.98
| {{val|0.0295}}
| 0.10
| 2
|-
|style="text-align: left;"| [[Procyon]] B
| 0736+053
| 11.46
| DQZ
| 13.20
| 0.63
| {{val|0.00049}}
| 1.37
| 2
|-
|style="text-align: left;"| [[Van Maanen 2]]
| 0046+051
| 14.07
| DZ
| 14.09
| 0.68
| {{val|0.00017}}
| 3.30
| 1
|-
|style="text-align: left;"| [[LP 145-141]]
| 1142–645
| 15.12
| DQ
| 12.77
| 0.61
| {{val|0.00054}}
| 1.29
| 1
|-
|style="text-align: left;"| [[40 Eridani]] B
| 0413-077
| 16.39
| DA
| 11.27
| 0.59
| {{val|0.0141}}
| 0.12
| 3
|-
|style="text-align: left;"| [[Stein 2051]] B
| 0426+588
| 17.99
| DC
| 13.43
| 0.69
| {{val|0.00030}}
| 2.02
| 2
|-
|style="text-align: left;"| [[G 240-72]]
| 1748+708
| 20.26
| DQ
| 15.23
| 0.81
| {{val|0.000085}}
| 5.69
| 1
|-
|style="text-align: left;"| [[Gliese 223.2]]
| 0552–041
| 21.01
| DZ
| 15.29
| 0.82
| {{val|0.000062}}
| 7.89
| 1
|-
|style="text-align: left;"| [[Gliese 3991]] B<ref>
 {{cite journal
  | bibcode=1999A&A...344..897D
  | title=New neighbours. I. 13 new companions to nearby M dwarfs
  | display-authors=1
  | last1=Delfosse | first1=Xavier | last2=Forveille | first2=Thierry
  | last3=Beuzit | first3=Jean-Luc | last4=Udry | first4=Stéphane
  | last5=Mayor | first5=Michel | last6=Perrier | first6=Christian
  | journal=Astronomy and Astrophysics
  | volume=344 | pages=897–910 | date=April 1999
  | arxiv=astro-ph/9812008
 }}</ref>
| 1708+437
| 24.23
| D??
| >&nbsp;15
| 0.5
| <&nbsp;{{val|0.000086}}
| >&nbsp;6
| 2
|}

== See also ==
{{colbegin}}
* {{annotated link|Black dwarf}}
* {{annotated link|Brown dwarf}}
* {{annotated link|Chandrasekhar's white dwarf equation}}
* {{annotated link|Degenerate matter}}
* {{annotated link|List of white dwarfs}}
* {{annotated link|Neutron star}}
* {{annotated link|PG 1159 star}}
* {{annotated link|Planetary nebula}}
* {{annotated link|Robust associations of massive baryonic objects}}
* {{annotated link|Stellar classification}}
* {{annotated link|Timeline of white dwarfs, neutron stars, and supernovae}}
{{colend}}

== References ==
{{reflist|25em}}

== External links and further reading ==
{{Commons category}}

; General :
* {{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
}}
; Physics :
* ''Black holes, white dwarfs, and neutron stars: the physics of compact objects'', Stuart L. Shapiro and Saul A. Teukolsky, New York: Wiley, 1983. {{ISBN|0-471-87317-9}}.
* {{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.

; Variability :
* {{cite journal
 |doi=10.1088/0953-8984/10/49/014
 |bibcode= 1998JPCM...1011247W
 |title=Asteroseismology of white dwarf stars
 |date=1998
 |last1=Winget |first1=D.E.
 |journal=Journal of Physics: Condensed Matter
 |volume=10 |issue=49 |pages=11247–11261 |s2cid= 250749380
}}

; Magnetic field :
* {{cite journal
 |bibcode=2000PASP..112..873W
 |doi= 10.1086/316593
 |title=Magnetism in Isolated and Binary White Dwarfs
 |date=2000
 |last1=Wickramasinghe |first1=D. T.
 |last2=Ferrario |first2=Lilia
 |journal=Publications of the Astronomical Society of the Pacific
 |volume=112 |issue=773 |pages=873–924 |doi-access=free
}}

; Frequency :
* {{cite journal
 |doi=10.1126/science.292.5525.2211a |pmid=11423620
 |title=White Dwarfs and Dark Matter
 |date=2001
 |last1=Gibson |first1=B. K.
 |journal=Science
 |volume=292 |issue=5525 |pages=2211a
 |last2=Flynn |first2=C|arxiv=astro-ph/0104255|s2cid=14080941
}}

; Observational :
* {{cite journal
 |bibcode=1998ApJ...494..759P
 |doi= 10.1086/305238
 |title=Testing the White Dwarf Mass-Radius Relation with Hipparcos
 |date=1998
 |last1=Provencal |first1=J. L.
 |last2=Shipman |first2=H. L.
 |last3=Hog |first3=Erik
 |last4=Thejll |first4=P.
 |journal=The Astrophysical Journal
 |volume=494 |issue=2 |pages=759–767 |doi-access=free
}}
* {{cite journal
 |bibcode=2004ApJ...612L.129G
 |arxiv= astro-ph/0405566
 |doi= 10.1086/424568
 |title=Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey
 |date=2004
 |last1=Gates |first1=Evalyn
 |last2=Gyuk |first2=Geza
 |last3=Harris |first3=Hugh C.
 |last4=Subbarao |first4=Mark
 |last5=Anderson |first5=Scott
 |last6=Kleinman |first6=S. J.
 |last7=Liebert |first7=James
 |last8=Brewington |first8=Howard
 |last9=Brinkmann |first9=J.
 |last10= Harvanek |first10= Michael
 |last11= Krzesinski |first11= Jurek
 |last12= Lamb |first12= Don Q.
 |last13= Long |first13= Dan
 |last14= Neilsen, Jr. |first14= Eric H.
 |last15= Newman |first15= Peter R.
 |last16= Nitta |first16= Atsuko
 |last17= Snedden |first17= Stephanie A.
 |journal=The Astrophysical Journal
 |volume=612 |issue=2 |pages=L129 |s2cid= 7570539
 |display-authors= 8
}}
* {{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 }}
* {{cite journal
 |bibcode=2007Natur.450..522D
 |doi=10.1038/nature06318
 |arxiv=0711.3227
 |title=White dwarf stars with carbon atmospheres
 |date=2007
 |last1=Dufour |first1=P.
 |last2=Liebert |first2=James
 |last3=Fontaine |first3=G.
 |last4=Behara |first4=N.
 |journal=Nature
 |volume=450 |issue=7169 |pages=522–4|pmid=18033290|s2cid=4398697
}}

; Images :
* [https://apod.nasa.gov/apod/white_dwarfs.html White dwarf images] at [[Astronomy Picture of the Day]]

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