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[[Image:Sirius A and B Hubble photo.jpg|thumb|right|Image of [[Sirius|Sirius A and Sirius B]] taken by the [[Hubble Space Telescope]]. Sirius B, which is a white dwarf, can be seen as a faint dot to the lower left of the much brighter Sirius A.]]

A '''white dwarf''', also called a '''degenerate dwarf''', is a small [[star]] composed mostly of [[Degenerate matter#Electron degeneracy|electron-degenerate matter]].  Because a white dwarf's mass is comparable to that of the [[Sun]] and its volume is comparable to that of the [[Earth]], it is very [[density|dense]].  Its faint [[luminosity]] comes from the [[Thermal radiation|emission]] of stored [[heat|thermal energy]].<ref name="osln" />  White dwarfs comprise roughly 6% of all known stars in the [[Local Interstellar Cloud|solar neighborhood]].<ref>[http://www.chara.gsu.edu/RECONS/TOP100.posted.htm The One Hundred Nearest Star Systems], Todd J. Henry, RECONS, April 11, 2007.  Accessed on line May 4, 2007.</ref>  The unusual faintness of white dwarfs was first recognized in 1910 by [[Henry Norris Russell]], [[Edward Charles Pickering]], and [[Williamina Fleming]];<ref name="schatzman" /><sup>, p.&nbsp;1</sup> the name ''white dwarf'' was coined by [[Willem Luyten]] in 1922.<ref name="holberg" />

White dwarfs are thought to be the final [[stellar evolution|evolutionary state]] of all stars whose mass is not too high—over 97% of the stars in [[Milky way|our galaxy]].<ref name="cosmochronology" /><sup>, §1.</sup>   After the [[hydrogen]]-[[nuclear fusion|fusing]] lifetime of a [[main-sequence star]] of low or medium mass ends, it will expand to a [[red giant]] which fuses [[helium]] to [[carbon]] and [[oxygen]] in its core by the [[triple-alpha process]].  If a red giant has insufficient mass to generate the core temperatures required to fuse [[carbon]], an inert mass of carbon and oxygen will build up at its center.  After shedding its outer layers to form a [[planetary nebula]], it will leave behind this core, which forms the remnant white dwarf.<ref name="rln">[http://spiff.rit.edu/classes/phys230/lectures/planneb/planneb.html Late stages of evolution for low-mass stars], Michael Richmond, lecture notes, Physics 230, [[Rochester Institute of Technology]].  Accessed on line May 3, 2007.</ref>  Usually, therefore, white dwarfs are composed of carbon and oxygen.  It is also possible that core temperatures suffice to fuse carbon but not [[neon]], in which case an oxygen-[[neon]]-[[magnesium]] white dwarf may be formed.<ref name="oxne">[http://adsabs.harvard.edu/abs/2005ASPC..334..165W On Possible Oxygen/Neon White Dwarfs: H1504+65 and the White Dwarf Donors in Ultracompact X-ray Binaries], K. Werner, N. J. Hammer, T. Nagel, T. Rauch, and S. Dreizler, pp. 165 ff. in ''14th European Workshop on White Dwarfs; Proceedings of a meeting held at Kiel, July 19–23, 2004'', edited by D. Koester and S. Moehler, San Francisco: Astronomical Society of the Pacific, 2005.</ref>  Also, some [[helium]] white dwarfs<ref name="apj606_L147">[http://adsabs.harvard.edu/abs/2004ApJ...606L.147L A Helium White Dwarf of Extremely Low Mass], James Liebert, P. Bergeron, Daniel Eisenstein, H.C. Harris, S.J. Kleinman, Atsuko Nitta, and Jurek Krzesinski, ''The Astrophysical Journal'' '''606''', #2 (May 2004), pp. L147&ndash;L149.  Accessed on line March 5, 2007.</ref><ref name="he2">[http://spaceflightnow.com/news/n0704/17whitedwarf Cosmic weight loss: The lowest mass white dwarf], press release, [[Harvard-Smithsonian Center for Astrophysics]], April 17, 2007.</ref> appear to have been formed by mass loss in binary systems.

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported against [[gravitational collapse]] by the heat generated by fusion.  It is supported only by [[electron degeneracy pressure]], causing it to be extremely dense.  The physics of degeneracy yields a maximum mass for a nonrotating white dwarf, the [[Chandrasekhar limit]]&mdash;approximately 1.4 [[solar mass]]es&mdash;beyond which it cannot be supported by degeneracy pressure.  A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a [[Type Ia supernova]] via a process known as [[carbon detonation]].<ref name="osln">[http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL22.pdf Extreme Stars: White Dwarfs & Neutron Stars], Jennifer Johnson, lecture notes, Astronomy 162, [[Ohio State University]].  Accessed on line May 3, 2007.</ref><ref name="rln" /> ([[SN 1006]] is thought to be a famous example.)

A white dwarf is very hot when it is formed but since it has no source of energy, it will gradually radiate away its energy and cool down.  This means that its radiation, which initially has a high [[color temperature]], will lessen and redden with time.  Over a very long time, a white dwarf will cool to temperatures at which it will no longer be visible, and become a cold ''[[black dwarf]]''.<ref name="rln" />  However, since no white dwarf can be older than the [[Age of the universe|age of the Universe]] (approximately 13.7 billion years),<ref name="aou">[http://arxiv.org/abs/astro-ph/0603449v2 Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology], D. N. Spergel, R. Bean, O. Doré, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, arXiv:astro-ph/0603449v2, February 27, 2007.</ref> even the oldest white dwarfs still radiate at temperatures of a few thousand [[kelvin]]s, and no black dwarfs are thought to exist yet.<ref name="osln" /><ref name="cosmochronology">[http://adsabs.harvard.edu/abs/2001PASP..113..409F The Potential of White Dwarf Cosmochronology], G. Fontaine, P. Brassard, and P. Bergeron, ''Publications of the Astronomical Society of the Pacific'' '''113''', #782 (April 2001), pp. 409&ndash;435.</ref>

==Discovery==

The first white dwarf discovered was in the [[triple star system]] of [[40 Eridani]], which contains the relatively bright [[main sequence]] star [[40 Eridani A]], orbited at a distance by the closer [[binary 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 [[Friedrich Wilhelm Herschel]] on January 31, 1783;<ref>[http://links.jstor.org/sici?sici=0261-0523(1785)75%3C40%3ACODSBW%3E2.0.CO%3B2-P Catalogue of Double Stars], William Herschel, ''Philosophical Transactions of the Royal Society of London'' '''75''' (1785), pp. 40&ndash;126</ref><sup>, p.&nbsp;73</sup> it was again observed by [[Friedrich Georg Wilhelm Struve]] in 1825 and by [[Otto Wilhelm von Struve]] in 1851.<ref>[http://adsabs.harvard.edu/abs/1926BAN.....3..128V  The orbit and the masses of 40 Eridani BC], W. H. van den Bos, ''Bulletin of the Astronomical Institutes of the Netherlands'' '''3''', #98 (July 8, 1926), pp. 128&ndash;132.</ref><ref>[http://adsabs.harvard.edu/abs/1974AJ.....79..819H Astrometric study of four visual binaries], W. D. Heintz, ''Astronomical Journal'' '''79''', #7 (July 1974), pp. 819&ndash;825.</ref>  In 1910, it was discovered by [[Henry Norris Russell]], [[Edward Charles Pickering]] and [[Williamina Paton Stevens Fleming|Williamina Fleming]] that despite being a dim star, 40 Eridani B was of [[stellar classification|spectral type]] A, or white.<ref name="holberg">[http://adsabs.harvard.edu/abs/2005AAS...20720501H How Degenerate Stars Came to be Known as White Dwarfs], J. B. Holberg, ''Bulletin of the American Astronomical Society'' '''37''' (December 2005),  p. 1503.</ref>  In 1939, Russell looked back on the discovery:<ref name="schatzman">''White Dwarfs'', E. Schatzman, Amsterdam: North-Holland, 1958.</ref><sup>, p.&nbsp;1</sup>

<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&mdash;including comparison stars&mdash;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&mdash;it led to the discovery that all the stars of very faint absolute magnitude were of spectral class M.  In conversation on this subject (as I recall it), I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B.  Characteristically, he sent a note to the Observatory office and before long the answer came (I think from Mrs Fleming) that the spectrum of this star was A.  I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called "possible" values of the surface brightness and density.  I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: "It is just these exceptions that lead to an advance in our knowledge", and so the white dwarfs entered the realm of study!</blockquote>

The spectral type of 40 Eridani B was officially described in 1914 by [[Walter Sydney Adams|Walter Adams]].<ref>[http://adsabs.harvard.edu/abs/1914PASP...26..198A An A-Type Star of Very Low Luminosity], Walter S. Adams, ''Publications of the Astronomical Society of the Pacific'' '''26''', #155 (October 1914), p. 198.</ref>

The companion of [[Sirius]], [[Sirius|Sirius B]], was next to be discovered.  During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. [[Friedrich Wilhelm Bessel|Friedrich Bessel]] used just such precise measurements to determine that the stars Sirius (α Canis Majoris) and [[Procyon]] (α Canis Minoris) were changing their positions.  In 1844 he predicted that both stars had unseen companions:<ref name="fwbessel">[http://adsabs.harvard.edu/abs/1844MNRAS...6..136. On the Variations of the Proper Motions of ''Procyon'' and ''Sirius''], F. W. Bessel, communicated by J. F. W. Herschel, ''Monthly Notices of the Royal Astronomical Society'' '''6''' (December 1844), pp. 136&ndash;141.</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 Heinrich Friedrich Peters|C. H. F. Peters]] computed an orbit for it in 1851.<ref name="flammarion">[http://adsabs.harvard.edu/abs/1877AReg...15..186F The Companion of Sirius], Camille Flammarion, ''The Astronomical Register'' '''15''', #176 (August 1877), pp. 186&ndash;189.</ref>  It was not until January 31, 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 B to be similar to that of Sirius.<ref>[http://adsabs.harvard.edu/abs/1915PASP...27..236A The Spectrum of the Companion of Sirius], W. S. Adams, ''Publications of the Astronomical Society of the Pacific'' '''27''', #161 (December 1915), pp. 236&ndash;237.</ref>    

In 1917, [[Adriaan Van Maanen]] discovered [[Van Maanen's Star]], an isolated white dwarf.<ref>[http://adsabs.harvard.edu/abs/1917PASP...29..258V Two Faint Stars with Large Proper Motion], A. van Maanen, ''Publications of the Astronomical Society of the Pacific'' '''29''', #172 (December 1917), pp. 258&ndash;259.</ref>   These three white dwarfs, the first discovered, are the so-called ''classical white dwarfs''.<ref name="schatzman" /><sup>, p.&nbsp;2</sup>  Eventually, many faint white stars were found which had high [[proper motion]], indicating that they could be suspected to be low-luminosity stars close to the Earth, and hence white dwarfs.  [[Willem Luyten]] appears to have been the first to use the term ''white dwarf'' when he examined this class of stars in 1922;<ref name="holberg" /><ref>[http://adsabs.harvard.edu/abs/1922PASP...34..156L The Mean Parallax of Early-Type Stars of Determined Proper Motion and Apparent Magnitude], Willem J. Luyten, ''Publications of the Astronomical Society of the Pacific'' '''34''', #199 (June 1922), pp. 156&ndash;160.</ref><ref>[http://adsabs.harvard.edu/abs/1922PASP...34...54L Note on Some Faint Early Type Stars with Large Proper Motions], Willem J. Luyten, ''Publications of the Astronomical Society of the Pacific'' '''34''', #197 (February 1922), pp. 54&ndash;55.</ref><ref>[http://adsabs.harvard.edu/abs/1922PASP...34..132L Additional Note on Faint Early-Type Stars with Large Proper-Motions], Willem J. Luyten, ''Publications of the Astronomical Society of the Pacific'' '''34''', #198 (April 1922), p. 132.</ref><ref>[http://articles.adsabs.harvard.edu/cgi-bin/nph-journal_query?volume=34&plate_select=NO&page=356&journal=PASP. Third Note on Faint Early Type Stars with Large Proper Motion], Willem J. Luyten, ''Publications of the Astronomical Society of the Pacific'' '''34''', #202 (December 1922),  pp. 356&ndash;357.</ref>  the term was later popularized by [[Arthur Stanley Eddington]].<ref name="holberg" /><ref name="eddington" />  Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s.  18 white dwarfs had been discovered by 1939.<ref name="schatzman" /><sup>, p.&nbsp;3</sup>  Luyten and others continued to search for white dwarfs in the 1940s.  By 1950, over a hundred were known,<ref>[http://adsabs.harvard.edu/abs/1950AJ.....55...86L The search for white dwarfs], W. J. Luyten, ''Astronomical Journal'' '''55''', #1183 (April 1950), pp. 86&ndash;89.</ref> and by 1999, over 2,000 were known.<ref name="villanovar4">[http://adsabs.harvard.edu/abs/1999ApJS..121....1M A Catalog of Spectroscopically Identified White Dwarfs], George P. McCook and Edward M. Sion, ''The Astrophysical Journal Supplement Series'' '''121''', #1 (March 1999), pp. 1&ndash;130.</ref>  Since then the [[Sloan Digital Sky Survey]] has found over 9,000 white dwarfs, mostly new.<ref name="sdssr4">[http://adsabs.harvard.edu/abs/2006ApJS..167...40E A Catalog of Spectroscopically Confirmed White Dwarfs from the Sloan Digital Sky Survey Data Release 4], Daniel J. Eisenstein, James Liebert, Hugh C. Harris, S. J. Kleinman, Atsuko Nitta, Nicole Silvestri, Scott A. Anderson, J. C. Barentine, Howard J. Brewington, J. Brinkmann, Michael Harvanek, Jurek Krzesiński, Eric H. Neilsen, Jr., Dan Long, Donald P. Schneider, and Stephanie A. Snedden, ''The Astrophysical Journal Supplement Series'' '''167''', #1 (November 2006), pp. 40&ndash;58.</ref>

==Composition and structure==
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Although white dwarfs are known with estimated masses as low as 0.17<ref>[http://adsabs.harvard.edu/abs/2007ApJ...660.1451K The Lowest Mass White Dwarf], Mukremin Kulic, Carlos Allende Prieto, Warren R. Brown, and D. Koester, ''The Astrophysical Journal'' '''660''', #2 (May 2007), pp. 1451&ndash;1461.</ref> and as high as 1.33<ref name="sdsswd">[http://adsabs.harvard.edu/abs/2007MNRAS.375.1315K White dwarf mass distribution in the SDSS], S. O. Kepler, S. J. Kleinman, A. Nitta, D. Koester, B. G. Castanheira, O. Giovannini, A. F. M. Costa, and L. Althaus, ''Monthly Notices of the Royal Astronomical Society'' ''375'', #4 (March 2007), pp. 1315&ndash;1324.</ref> solar masses, the mass distribution is strongly peaked at 0.6 solar mass, and the majority lie between 0.5 to 0.7 solar mass.<ref name="sdsswd" />  The estimated radii of observed white dwarfs, however, are typically between 0.008 and 0.02 times the [[solar radius|radius of the Sun]];<ref>[http://adsabs.harvard.edu/abs/1979ApJ...228..240S Masses and radii of white-dwarf stars. III - Results for 110 hydrogen-rich and 28 helium-rich stars], H. L. Shipman, ''The Astrophysical Journal'' '''228''' (February 15, 1979), pp. 240&ndash;256.</ref> this is comparable to the Earth's radius of approximately 0.009 solar radius.  A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically a million times smaller than the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, 1,000,000 times greater than the average density of the Sun, or approximately 10<sup>6</sup> [[gram]]s (1 [[tonne]]) per [[cubic centimeter]].<ref name="osln" />  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, [[black hole]]s and, hypothetically, [[quark star]]s.<ref>''[http://epubl.luth.se/1402-1757/2005/25/LTU-LIC-0525-SE.pdf Exotic Phases of Matter in Compact Stars]'', Fredrik Sandin, licentiate thesis, Luleå University of Technology, May 8, 2005.</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 B and 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit.  This was done for Sirius B by 1910,<ref>''Preliminary General Catalogue'', L. Boss, Washington, D.C.: Carnegie Institution, 1910.</ref> yielding a mass estimate of 0.94 [[solar mass]].  (A more modern estimate is 1.00 solar mass.)<ref name="apj_630">[http://adsabs.harvard.edu/abs/w2005ApJ...630L..69L The Age and Progenitor Mass of Sirius B], James Liebert, Patrick A. Young, David Arnett, J. B. Holberg, and Kurtis A. Williams, ''The Astrophysical Journal'' '''630''', #1 (September 2005) pp. L69&ndash;L72.</ref>  Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its [[effective temperature|effective surface temperature]], and hence from its [[spectrum]].   If the star's distance is known, its overall luminosity can also be estimated.  Comparison of the two figures yields the star's radius.  Reasoning of this sort led to the realization, puzzling to astronomers at the time, that Sirius B and 40 Eridani B must be very dense.  For example, when [[Ernst Öpik]] estimated the density of a number of visual binary stars in 1916, he found that 40 Eridani B had a density of over 25,000 times the [[Sun]]'s, which was so high that he called it "impossible".<ref>[http://adsabs.harvard.edu/abs/1916ApJ....44..292O The Densities of Visual Binary Stars], E. Öpik, ''The Astrophysical Journal'' '''44''' (December 1916), pp. 292&ndash;302.</ref>  As [[Arthur Stanley Eddington]] put it later in 1927:<ref>''Stars and Atoms'', A. S. Eddington, Oxford: Clarendon Press, 1927.</ref><sup>, p.&nbsp;50</sup>

<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 3,000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox."  What reply can one make to such a message?  The reply which most of us made in 1914 was&mdash;"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 B should be [[gravitational redshift|gravitationally redshifted]].<ref name="eddington">[http://adsabs.harvard.edu/abs/1924MNRAS..84..308E On the relation between the masses and luminosities of the stars], A. S. Eddington, ''Monthly Notices of the Royal Astronomical Society'' '''84''' (March 1924), pp. 308&ndash;332.</ref>  This was confirmed when Adams measured this redshift in 1925.<ref>[http://adsabs.harvard.edu/abs/1925PNAS...11..382A The Relativity Displacement of the Spectral Lines in the Companion of Sirius], Walter S. Adams, ''Proceedings of the National Academy of Sciences of the United States of America'' '''11''', #7 (July 1925), pp. 382&ndash;387.</ref>

Such densities are possible because white dwarf material is not composed of [[atom]]s bound 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 to each other than [[atomic orbital|electron orbital]]s&mdash;the regions occupied by electrons bound to an atom&mdash;would normally allow.<ref name="eddington" />   Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present.<ref name="fowler">[http://adsabs.harvard.edu/abs/1926MNRAS..87..114F On Dense Matter], R. H. Fowler, ''Monthly Notices of the Royal Astronomical Society'' '''87''' (1926), pp. 114&ndash;122.</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 which satisfy the Pauli exclusion principle.<ref>[http://links.jstor.org/sici?sici=0080-4630%2819800610%29371%3A1744%3C8%3ATDOTQM%3E2.0.CO%3B2-K The Development of the Quantum Mechanical Electron Theory of Metals: 1900-28], Lillian H. Hoddeson and G. Baym, ''Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences'' '''371''', #1744 (June 10, 1980), pp. 8&ndash;23.</ref>  At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ''[[ground state|ground]]'', state; some of them had to occupy higher-energy states, forming a band of lowest-available energy states, the ''[[Fermi sea]]''.   This state of the electrons, called ''[[degenerate matter|degenerate]]'', meant that a white dwarf could cool to zero temperature and still possess high energy.  Another way of deriving this result is by use of the [[uncertainty principle]]: the high density of electrons in a white dwarf means that their positions are relatively localized, creating a corresponding uncertainty in their momenta.  This means that some electrons must have high momentum and hence high kinetic energy.<ref name="fowler" /><ref name="scibits" />

Compression of a white dwarf will increase the number of electrons in a given volume.  Applying either the Pauli exclusion principle or the uncertainty principle, we can see that this will increase the kinetic energy of the electrons, causing pressure.<ref name="fowler" /><ref>[http://www.astro.cornell.edu/~rbean/a211/211_notes_lec_12.pdf Lecture 12 - Degeneracy pressure], Rachel Bean, lecture notes, Astronomy 211, [[Cornell University]].  Accessed on line September 21, 2007.</ref>  This ''[[electron degeneracy pressure]]'' is what supports a white dwarf against [[gravitational collapse]].  It depends only on density and not on temperature.  Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is so much greater than that of a low-mass white dwarf that [[#Mass-radius relationship and mass limit|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 is another consequence of being supported by electron degeneracy pressure. These masses were first published in 1929 by [[Wilhelm Anderson]]<ref>&Uuml;ber die Grenzdichte der Materie und der Energie, [[Wilhelm Anderson]], ''Zeitschrift f&uuml;r Physik'' '''56''', #11&ndash;12 (November 1929), pp. 851&ndash;856.</ref> and in 1930 by [[Edmund C. Stoner]].<ref name="stoner">The Equilibrium of Dense Stars, Edmund C. Stoner, ''Philosophical Magazine'' (7th series) '''9''' (1930), pp. 944&ndash;963.</ref>  The modern 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">[http://adsabs.harvard.edu/abs/1931ApJ....74...81C The Maximum Mass of Ideal White Dwarfs], S. Chandrasekhar, ''The Astrophysical Journal'' '''74''', #1 (July 1931), pp. 81&ndash;82.</ref>  For a nonrotating white dwarf, it is equal to approximately 5.7/''μ''<sub>e</sub><sup>2</sup> solar masses, where ''μ''<sub>e</sub> is the average molecular weight per electron of the star.<ref name="chandra2">[http://adsabs.harvard.edu/abs/1935MNRAS..95..207C The Highly Collapsed Configurations of a Stellar Mass (second paper)], S. Chandrasekhar, ''Monthly Notices of the Royal Astronomical Society'', '''95''' (1935), pp. 207&ndash;225.</ref><sup>, eq. (63)</sup>  As the carbon-12 and oxygen-16 which predominantly compose a carbon-oxygen white dwarf both have [[atomic number]] equal to half their [[atomic weight]], one should take ''μ''<sub>e</sub> equal to 2 for such a star,<ref name="scibits" /> leading to the commonly quoted value of 1.4 solar masses.  (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,<ref name="stoner" /><sup>, p.&nbsp;955</sup> so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, ''μ''<sub>e</sub>, equal to 2.5, giving a limit of 0.91 solar mass.)  Together with [[William Alfred Fowler]], Chandrasekhar received the [[Nobel Prize in Physics|Nobel prize]] for this and other work in 1983.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1983/ The Nobel Prize in Physics 1983], [[Nobel Foundation]].  Accessed on line May 4, 2007.</ref>  The limiting mass is now called the ''[[Chandrasekhar limit]]''. 

If a white dwarf were to exceed the Chandrasekhar limit, and [[nuclear reaction]]s did not take place, the pressure exerted by [[electron]]s would no longer be able to balance the [[gravity|force of gravity]], and it would collapse into a denser object such as a [[neutron star]].<ref name="collapse">[http://www.arxiv.org/abs/astro-ph/9701225v1 The Possible White Dwarf-Neutron Star Connection], R. Canal and J. Gutierrez, arXiv:astro-ph/9701225v1, January 29, 1997.</ref>  However, carbon-oxygen white dwarfs accreting mass from a neighboring star undergo a runaway nuclear fusion reaction, which leads to a [[Type Ia supernova]] explosion in which the white dwarf is destroyed, just before reaching the limiting mass.<ref name="sniamodels">[http://adsabs.harvard.edu/abs/2000ARA&A..38..191H Type IA Supernova Explosion Models], Wolfgang Hillebrandt and Jens C. Niemeyer, ''Annual Review of Astronomy and Astrophysics'' '''38''' (2000), pp. 191&ndash;230.</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]]-[[nuclear fusion|fusing]] [[red dwarf]]s, whose cores are supported in part by thermal pressure,<ref>[http://adsabs.harvard.edu/abs/2000ARA&A..38..337C Theory of Low-Mass Stars and Substellar Objects], Gilles Chabrier and Isabelle Baraffe, ''Annual Review of Astronomy and Astrophysics'' '''38''' (2000), pp. 337&ndash;377.</ref> or the even lower-temperature [[brown dwarf]]s.<ref>[http://www.astro.uiuc.edu/~kaler/sow/hrd.html The Hertzsprung-Russell (HR) diagram], Jim Kaler, online article.  Accessed on line May 5, 2007.</ref>

===Mass-radius relationship and mass limit===

It is simple to derive a rough relationship between the mass and radii of white dwarfs using an energy minimization argument.  The energy of the white dwarf can be approximated by taking it to be the sum of its gravitational [[potential energy]] and [[kinetic energy]].  The gravitational potential energy of a unit mass piece of white dwarf, ''E''<sub>g</sub>, will be on the order of −''GM''/''R'', where ''G'' is the [[gravitational constant]], ''M'' is the mass of the white dwarf, and ''R'' is its radius.  The kinetic energy of the unit mass, ''E''<sub>k</sub>, will primarily come from the motion of electrons, so it will be approximately ''N'' ''p''<sup>2</sup>/2''m'', where ''p'' is the average electron momentum, ''m'' is the electron mass, and ''N'' is the number of electrons per unit mass.  Since the electrons are [[degenerate matter|degenerate]], we can estimate ''p'' to be on the order of the uncertainty in momentum, Δ''p'', given by the [[uncertainty principle]], which says that Δ''p'' Δ''x'' is on the order of the reduced [[Planck constant]], ''ħ''.  Δ''x'' will be on the order of the average distance between electrons, which will be approximately ''n''<sup>−1/3</sup>, i.e., the reciprocal of the cube root of the number density, ''n'', of electrons per unit volume.  Since there are ''N'' ''M'' electrons in the white dwarf and its volume is on the order of ''R''<sup>3</sup>, ''n'' will be on the order of ''N'' ''M'' / ''R''<sup>3</sup>.<ref name="scibits">[http://www.sciencebits.com/StellarEquipartition Estimating Stellar Parameters from Energy Equipartition], ScienceBits.  Accessed on line May 9, 2007.</ref>

Solving for the kinetic energy per unit mass, ''E''<sub>k</sub>, we find that
::<math>E_k \approx \frac{N (\Delta p)^2}{2m} \approx \frac{N \hbar^2 n^{2/3}}{2m} \approx \frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.</math>
The white dwarf will be at equilibrium when its total energy, ''E''<sub>g</sub> + ''E''<sub>k</sub>, is minimized.  At this point, the kinetic and gravitational potential energies should be comparable, so we may derive a rough mass-radius relationship by equating their magnitudes:
::<math>|E_g|\approx\frac{GM}{R} = E_k\approx\frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.</math>
Solving this for the radius, ''R'', gives<ref name="scibits" />
::<math> R \approx \frac{N^{5/3} \hbar^2}{2m GM^{1/3}}.</math>
Dropping ''N'', which depends only on the composition of the white dwarf, and the universal constants leaves us with a relationship between mass and radius:
::<math>R \sim \frac{1}{M^{1/3}}, \,</math>
i.e., the radius of a white dwarf is inversely proportional to the cube root of its mass.

Since this analysis uses the non-relativistic formula ''p''<sup>2</sup>/2''m'' for the kinetic energy, it is non-relativistic.  If we wish to analyze the situation where the electron velocity in a white dwarf is close to the [[speed of light]], ''c'', we should replace ''p''<sup>2</sup>/2''m'' by the extreme relativistic approximation ''p'' ''c'' for the kinetic energy.  With this substitution, we find
::<math>E_{k\ {\rm relativistic}} \approx \frac{M^{1/3} N^{4/3} \hbar c}{R}.</math>
If we equate this to the magnitude of ''E''<sub>g</sub>, we find that ''R'' drops out and the mass, ''M'', is forced to be<ref name="scibits" />
::<math>M_{\rm limit} \approx N^2 \left(\frac{\hbar c}{G}\right)^{3/2}.</math>

[[Image:WhiteDwarf mass-radius.jpg|thumb|350px|right|Radius-mass relations for a model white dwarf.]]
To interpret this result, observe that as we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase.  As this velocity approaches ''c'', the extreme relativistic analysis becomes more exact, meaning that the mass ''M'' of the white dwarf must approach ''M''<sub>limit</sub>.  Therefore, no white dwarf can be heavier than the limiting mass ''M''<sub>limit</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]] which describes the relationship between density and pressure in the white dwarf material.  If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the [[hydrostatic equation]] together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium.  In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass.<ref name="chandra2" /><sup>, eq. (80)</sup>  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&mdash;called the ''[[Chandrasekhar limit]]''&mdash;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, ''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">[http://vizier.u-strasbg.fr/doc/catstd-3.2.htx ''Standards for Astronomical Catalogues, Version 2.0''], section 3.2.2.  Accessed on line January 12, 2007.</ref>

These computations all assume that the white dwarf is nonrotating.  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>[http://www.phys.lsu.edu/astro/H_Book.current/H_Book.shtml ''The Structure, Stability, and Dynamics of Self-Gravitating Systems''], Joel E. Tohline, online book.  Accessed on line May 30, 2007.</ref>  For a uniformly rotating white dwarf, the limiting mass increases only slightly.  However, if the star is allowed to rotate nonuniformly, and [[viscosity]] is neglected, then, as was pointed out by [[Fred Hoyle]] in 1947,<ref>[http://adsabs.harvard.edu/abs/1947MNRAS.107..231H Note on equilibrium configurations for rotating white dwarfs], F. Hoyle, ''Monthly Notices of the Royal Astronomical Society'' '''107''' (1947), pp. 231&ndash;236.</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, however, will be [[dynamics (mechanics)|dynamically]] stable.<ref>[http://adsabs.harvard.edu/abs/1968ApJ...151.1089O Rapidly Rotating Stars. II. Massive White Dwarfs], Jeremiah P. Ostriker and Peter Bodenheimer, ''The Astrophysical Journal'' '''151''' (March 1968), pp. 1089&ndash;1098.</ref>

===Radiation and cooling===
The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type [[main sequence]] star to the red of a M-type [[red dwarf]].<ref name="sionspectra">[http://adsabs.harvard.edu/abs/1983ApJ...269..253S A proposed new white dwarf spectral classification system], E. M. Sion, J. L. Greenstein, J. D. Landstreet, J. Liebert, H. L. Shipman, and G. A. Wegner, ''The Astrophysical Journal'' '''269''', #1 (June 1, 1983), pp. 253&ndash;257.</ref>  White dwarf [[effective temperature|effective surface temperature]]s extend from over 150,000 K<ref name="villanovar4" /> to under 4,000 K.<ref name="cool" /><ref name="wden">White dwarfs, Gilles Fontaine and Fran&ccedil;ois Wesemael, in ''Encyclopedia of Astronomy and Astrophysics'', edited by Paul Murdin, Bristol and Philadelphia: Institute of Physics Publishing and London, New York and Tokyo: Nature Publishing Group, 2001.  ISBN 0333750888.</ref>  In accordance with the [[Stefan-Boltzmann law]], luminosity increases with increasing surface temperature; this surface temperature range corresponds to a luminosity from over 100 times the Sun's to under 1/10,000th that of the Sun's.<ref name="wden" />  Hot white dwarfs, with surface temperatures in excess of 30,000 K, have been observed to be sources of soft (i.e., lower-energy) [[X-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>[http://adsabs.harvard.edu/abs/1985SSRv...40...79H X-ray emission from isolated hot white dwarfs], J. Heise, ''Space Science Reviews'' '''40''' (February 1985), pp. 79&ndash;90.</ref>

[[Image:Size IK Peg.png|left|320px|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 35,500&nbsp;K.]]
As was explained by [[Leon Mestel]] in 1952, unless the white dwarf [[accretion (astrophysics)|accrete]]s matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished.<ref>[http://adsabs.harvard.edu/abs/1952MNRAS.112..583M On the theory of white dwarf stars. I. The energy sources of white dwarfs], L. Mestel, ''Monthly Notices of the Royal Astronomical Society'' '''112''' (1952), pp. 583–597.</ref><ref>[http://adsabs.harvard.edu/abs/1998hdf..symp..252K White Dwarf Stars and the Hubble Deep Field], S. D. Kawaler, pp. 252–271 in ''The Hubble Deep Field: Proceedings of the Space Telescope Science Institute Symposium, held in Baltimore, Maryland, May 6-9, 1997'', edited by Mario Livio, S. Michael Fall, and Piero Madau, Space Telescope Science Institute symposium series, 11, New York: Cambridge University Press, 1998, ISBN 0521630975.</ref><sup>,&nbsp;§2.1.</sup>  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 which it emits reddens, and its luminosity decreases.  Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time.   Bergeron, Ruiz, and Leggett, for example, estimate that after a [[carbon]] white dwarf of 0.59 solar mass with a [[hydrogen]] atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1.5 billion years, cooling approximately 500 more kelvins to 6,590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6,030 K and 5,550 K) take first 0.4 and then 1.1 billion years.<ref>[http://adsabs.harvard.edu/abs/1997ApJS..108..339B The Chemical Evolution of Cool White Dwarfs and the Age of the Local Galactic Disk], P. Bergeron, Maria Teresa Ruiz, and S. K. Leggett, ''The Astrophysical Journal Supplement Series'' '''108''', #1 (January 1997), pp. 339&ndash;387.</ref><sup>, Table 2.</sup>  Although white dwarf material is initially [[plasma (physics)|plasma]]&mdash;a fluid composed of [[atomic nucleus|nuclei]] and [[electron]]s&mdash;it was theoretically predicted in the 1960s that at a late stage of cooling, it should [[crystallize]], starting at the center of the star.<ref name="metcalfe1">[http://adsabs.harvard.edu/abs/2004ApJ...605L.133M Testing White Dwarf Crystallization Theory with Asteroseismology of the Massive Pulsating DA Star BPM 37093], T. S. Metcalfe, M. H. Montgomery, and A. Kanaan, ''The Astrophysical Journal'' '''605''', #2 (April 2004), pp. L133&ndash;L136.</ref>  The crystal structure is thought to be a [[body-centered cubic]] lattice.<ref name="cosmochronology" /><ref>[http://adsabs.harvard.edu/abs/1988A&A...199L..15B Crystallization of carbon-oxygen mixtures in white dwarfs], J. L. Barrat, J. P. Hansen, and R. Mochkovitch, ''Astronomy and Astrophysics'' '''199''', #1&ndash;2 (June 1988), pp. L15&ndash;L18.</ref> In 1995 it was pointed out that [[asteroseismology|asteroseismological]] observations of [[#Variability|pulsating white dwarf]]s yielded a potential test of the crystallization theory,<ref>[http://adsabs.harvard.edu/abs/1995BaltA...4..129W The Status of White Dwarf Asteroseismology and a Glimpse of the Road Ahead], D. E. Winget, ''Baltic Astronomy'' '''4''' (1995), pp. 129&ndash;136.</ref>  and in 2004, Travis Metcalfe and a team of researchers at the [[Harvard-Smithsonian Center for Astrophysics]] estimated, on the basis of such observations, that approximately 90% of the mass of [[BPM 37093]] had crystallized.<ref name="metcalfe1" /><ref name="lucy">[http://news.bbc.co.uk/2/hi/science/nature/3492919.stm Diamond star thrills astronomers], David Whitehouse, BBC News, February 16, 2004.  Accessed on line January 6, 2007.</ref><ref>[http://cfa-www.harvard.edu/press/pr0407.html Press release], Harvard-Smithsonian Center for Astrophysics, 2004.</ref><ref>[http://arxiv.org/abs/astro-ph/0411199v1 Whole Earth Telescope observations of BPM 37093: a seismological test of crystallization theory in white dwarfs], A. Kanaan, A. Nitta, D. E. Winget, S. O. Kepler, M. H. Montgomery, T. S. Metcalfe, et al., arXiv:astro-ph/0411199v1, November 8, 2004.</ref>    Other work gives a crystallized mass fraction of between 32% and 82%.<ref name="Brassard">[http://adsabs.harvard.edu/abs/2005ApJ...622..572B Asteroseismology of the Crystallized ZZ Ceti Star BPM 37093: A Different View], P. Brassard and G. Fontaine, ''The Astrophysical Journal'' '''622''', #1 (March 2005), pp. 572&ndash;576.</ref>

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K.<ref name="sdssr4" /><ref name="villanovavizier">[http://cdsweb.u-strasbg.fr/cgi-bin/Cat?III/235A III/235A: A Catalogue of Spectroscopically Identified White Dwarfs], G.P. McCook and E.M. Sion, on line at the [[Centre de Données astronomiques de Strasbourg]].  Accessed on line May 9, 2007.</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">[http://adsabs.harvard.edu/abs/1998ApJ...497..294L The Cool White Dwarf Luminosity Function and the Age of the Galactic Disk], S. K. Leggett, Maria Teresa Ruiz, and P. Bergeron, ''The Astrophysical Journal'' '''497''' (April 1998), pp. 294&ndash;302.</ref>  This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K,<ref>[http://adsabs.harvard.edu/abs/2004ApJ...612L.129G Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey], Evalyn Gates, Geza Gyuk, Hugh C. Harris, Mark Subbarao, Scott Anderson, S. J. Kleinman, James Liebert, Howard Brewington, J. Brinkmann, Michael Harvanek, Jurek Krzesinski, Don Q. Lamb, Dan Long, Eric H. Neilsen, Jr., Peter R. Newman, Atsuko Nitta, and Stephanie A. Snedden, ''The Astrophysical Journal'' '''612''', #2 (September 2004), pp. L129&ndash;L132.</ref> and one of the coolest so far observed, [[WD 0346+246]], has a surface temperature of approximately 3,900 K.<ref name="cool">[http://adsabs.harvard.edu/abs/1997ApJ...489L.157H WD 0346+246: A Very Low Luminosity, Cool Degenerate in Taurus], N. C. Hambly, S. J. Smartt, and S. Hodgkin, ''The Astrophysical Journal'' '''489''' (November 1997), pp. L157&ndash;L160.</ref>  The reason for this is that, as the Universe's age is finite,<ref>''The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe'', James S. Trefil, Mineola, New York: Dover Publications, 2004.  ISBN 0486438139.</ref> there has not been time for white dwarfs to cool down below this temperature.  The [[white dwarf luminosity function]] can therefore be used to find the time when stars started to form in a region; an estimate for the age of the [[Galactic disk]] found in this way is 8 billion years.<ref name="disklf" />

A white dwarf will eventually cool and become a non-radiating ''[[black dwarf]]'' in approximate thermal equilibrium with its surroundings and with the [[cosmic background radiation]].  However, no black dwarfs are thought to exist yet.<ref name="osln" />

===Atmosphere and spectra===
Although most white dwarfs are thought to be composed of carbon and oxygen, [[spectroscopy]] typically shows that their emitted light comes from an atmosphere which is observed to be either [[hydrogen]]-dominated or [[helium]]-dominated.  The dominant element is usually at least 1,000 times more abundant than all other elements.  As explained by [[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 on the bottom and lighter ones on top.<ref>[http://adsabs.harvard.edu/abs/1945AnAp....8..143S Théorie du débit d'énergie des naines blanches], Evry Schatzman, ''Annales d'Astrophysique'' '''8''' (January 1945), pp. 143&ndash;209.</ref><ref name="physrev">[http://adsabs.harvard.edu/abs/1990RPPh...53..837K Physics of white dwarf stars], D. Koester and G. Chanmugam, ''Reports on Progress in Physics'' '''53''' (1990), pp. 837&ndash;915.</ref><sup>, §5&ndash;6</sup>  This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope which is a residue of the star's envelope in the [[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 1/100th of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/10,000th of the stars total mass.<ref name="wden" /><ref name="kawaler">White Dwarf Stars, Steven D. Kawaler, in ''Stellar remnants'', S. D. Kawaler, I. Novikov, and G. Srinivasan, edited by Georges Meynet and Daniel Schaerer, Berlin: Springer, 1997.  Lecture notes for Saas-Fee advanced course number 25.  ISBN 3540615202.</ref><sup>, §4&ndash;5.</sup>

Although thin, these outer layers determine the thermal evolution of the white dwarf.  The degenerate [[electron]]s in the bulk of a white dwarf conduct heat well.  Most of a white dwarf's mass is therefore almost [[isothermal]], and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K.  The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.<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; no He I or metal lines
|-
| B
| He I lines; no H or metal lines
|-
| C
| Continuous spectrum; no lines
|-
| O
| He II lines, accompanied by He I or H lines
|-
| Z
| Metal lines; no H or He I lines
|-
| Q
| Carbon lines present
|-
| X
| Unclear or unclassifiable spectrum
|-
! 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 classify white dwarf spectra appears to have been by [[G. P. Kuiper]] in 1941,<ref name="sionspectra" /><ref>[http://adsabs.harvard.edu/abs/1941PASP...53..248K List of Known White Dwarfs], Gerard P. Kuiper, ''Publications of the Astronomical Society of the Pacific'' '''53''', #314 (August 1941), pp. 248&ndash;252.</ref> and various classification schemes have been proposed and used since then.<ref>[http://adsabs.harvard.edu/abs/1952ApJ...116..283L The Spectra and Luminosities of White Dwarfs], Willem J. Luyten, ''Astrophysical Journal'' '''116''' (September 1952), pp. 283&ndash;290.</ref><ref>[http://adsabs.harvard.edu/abs/1960stat.conf.....G Stellar atmospheres], Jesse Leonard Greenstein, in ''Stars and Stellar Systems'', vol. 6, ''Stellar Atmospheres'', edited by J. L. Greenstein, Chicago: University of Chicago Press, 1960.</ref>  The system currently in use was introduced by Edward M. Sion and his coauthors in 1983 and has been subsequently revised several times.  It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the table to the right), and a temperature index number, computed by dividing 50,400 K by the [[effective temperature]].  For example: 
* A white dwarf with only [[Spectroscopic notation|He I]] lines in its spectrum and an effective temperature of 15,000 K could be given the classification of DB3, or, if warranted by the precision of the temperature measurement, DB3.5.
* A white dwarf with a polarized [[magnetic field]], an effective temperature of 17,000 K, and a spectrum dominated by [[Spectroscopic notation|He I]] lines which also had [[hydrogen]] features could be given the classification of DBAP3.
The symbols ? and : may also be used if the correct classification is uncertain.<ref name="villanovar4" /><ref name="sionspectra" />  

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres.  They make up the majority (approximately three-quarters) of all observed white dwarfs.<ref name="wden" />  A small fraction (roughly 0.1%) have carbon-dominated atmospheres, the hot (above 15,000 K) DQ class.<ref>[http://adsabs.harvard.edu/abs/2007Natur.450..522D White dwarf stars with carbon atmospheres], Patrick Dufour, James Liebert, G. Fontaine, and N. Behara, ''Nature'' '''450''', #7169 (November 2007), pp. 522–524, {{bibcode|2007Natur.450..522D}}, {{doi|10.1038/nature06318}}</ref>  The classifiable remainder (DB, DC, DO, DZ, and cool DQ) have helium-dominated atmospheres.    Assuming that carbon and metals are not present, which spectral classification is seen depends on the [[effective temperature]].  Between approximately 100,000 K to 45,000 K, the spectrum will be classified DO, dominated by singly ionized helium.  From 30,000 K to 12,000 K, the spectrum will be DB, showing neutral helium lines, and below about 12,000 K, the spectrum will be featureless and classified DC.<ref name="kawaler" /><sup>,§ 2.4</sup><ref name="wden" />  The reason for the absence of white dwarfs with helium-dominated atmospheres and effective temperatures between 30,000 K and 45,000 K, called the ''DB gap'', is not clear.  It is suspected to be due to competing atmospheric evolutionary processes, such as gravitational separation and convective mixing.<ref name="wden" />

===Magnetic field===
[[Magnetic field]]s in white dwarfs with a strength at the surface of ~1 million [[Gauss (unit)|gauss]] (100 [[tesla (unit)|tesla]]s) 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>[http://adsabs.harvard.edu/abs/1947Natur.159..658B The magnetic field of massive rotating bodies], P. M. S. Blackett, ''Nature'' '''159''', #4046 (May 17, 1947), pp. 658&ndash;666.</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>[http://links.jstor.org/sici?sici=0080-4606%28197511%2921%3C1%3APMSBBB%3E2.0.CO%3B2-W Patrick Maynard Stuart Blackett, Baron Blackett, of Chelsea, 18 November 1897-13 July 1974], Bernard Lovell, 
''Biographical Memoirs of Fellows of the Royal Society'' '''21''' (November 1975), pp. 1&ndash;115.</ref><sup>, pp.&nbsp;39&ndash;43</sup>  In the 1960s, it was proposed that white dwarfs might have magnetic fields because of conservation of total surface [[magnetic flux]] during the evolution of a non-degenerate star to a white dwarf.  A surface magnetic field of ~100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of ~100·100<sup>2</sup>=1 million gauss (100 T) once the star's radius had shrunk by a factor of 100.<ref name="physrev" /><sup>, §8;</sup><ref>[http://adsabs.harvard.edu/abs/1969Ap&SS...4..464G Coherent Mechanisms of Radio Emission and Magnetic Models of Pulsars], V. L. Ginzburg, V. V. Zheleznyakov, and V. V. Zaitsev, ''Astrophysics and Space Science'' '''4''' (1969), pp. 464&ndash;504.</ref><sup>, p.&nbsp;484</sup>  The first magnetic white dwarf to be observed was [[GJ 742]], which was detected to have a magnetic field in 1970 by its emission of [[circularly polarized]] light.<ref>[http://adsabs.harvard.edu/abs/1970ApJ...161L..77K Discovery of Circularly Polarized Light from a White Dwarf], James C. Kemp, John B. Swedlund, J. D. Landstreet, and  J. R. P. Angel, ''The Astrophysical Journal'' '''161''' (August 1970), pp. L77&ndash;L79.</ref>  It is thought to have a surface field of approximately 300 million gauss (30 kT).<ref name="physrev" /><sup>, §8</sup>  Since then magnetic fields have been discovered in well over 100 white dwarfs, ranging from 2×10<sup>3</sup> to 10<sup>9</sup> gauss (0.2 T to 100 kT).  Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).<ref>[http://adsabs.harvard.edu/abs/2007A&A...462.1097J The fraction of DA white dwarfs with kilo-Gauss magnetic fields], S. Jordan, R. Aznar Cuadrado, R. Napiwotzki, H. M. Schmid, and S. K. Solanki, ''Astronomy and Astrophysics'' '''462''', #3 (February 11, 2007), pp. 1097&ndash;1101.</ref><ref>[http://adsabs.harvard.edu/cgi-bin/bib_query?2003AJ....125..348L The True Incidence of Magnetism Among Field White Dwarfs], James Liebert, P. Bergeron, and J. B. Holberg, ''Astronomical Journal'' '''125''', #1 (January 2003), pp. 348&ndash;353.</ref>

==Variability==
{| class="wikitable" style="float: right"
|-
| '''DAV''' ([[General Catalog of Variable Stars|GCVS]]: ''ZZA'') || DA [[White_dwarf#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; <br /> may be divided into '''DOV''' and '''PNNV''' stars
|-
| colspan=2 align=center | ''Types of pulsating white dwarf''<ref>[http://cdsweb.u-strasbg.fr/afoev/var/ezz.htx ZZ Ceti variables], Association Fran&ccedil;aise des Observateurs d'Etoiles Variables, web page at the Centre de
Données astronomiques de Strasbourg.  Accessed on line June 6, 2007.</ref><ref name="quirion" /><sup>, §1.1, 1.2.</sup>
|}

{{Main|Pulsating white dwarf}}
:''See also: [[#Cataclysmic variables|Cataclysmic variables]]''

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" /><sup>, § 7.1.1;</sup><ref>[http://adsabs.harvard.edu/abs/1967ApJ...148L.161L Ultrashort-Period Stellar Oscillations. I. Results from White Dwarfs, Old Novae, Central Stars of Planetary Nebulae, 3C 273, and Scorpius XR-1], George M. Lawrence, Jeremiah P. Ostriker, and James E. Hesser, ''The Astrophysical Journal'' '''148''', #3 (June 1967), pp. L161&ndash;L163.</ref>  The first variable white dwarf found was [[HL Tau 76]]; in 1965 and 1966, [[Arlo U. Landolt]] observed it to vary with a period of approximately 12.5 minutes.<ref>[http://adsabs.harvard.edu/abs/1968ApJ...153..151L A New Short-Period Blue Variable], Arlo U. Landolt, ''The Astrophysical Journal'' '''153''', #1 (July 1968), pp. 151&ndash;164.</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" /><sup>, § 7.</sup>  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" /><sup>, pp.&nbsp;891, 895</sup> ''DBV'', or ''V777 Her'', stars, with helium-dominated atmospheres and the spectral type DB;<ref name="wden">White dwarfs, Gilles Fontaine and Fran&ccedil;ois Wesemael, in ''Encyclopedia of Astronomy and Astrophysics'', ed. Paul Murdin, Bristol and Philadelphia: Institute of Physics Publishing and London, New York and Tokyo: Nature Publishing Group, 2001.  ISBN 0333750888.</ref><sup>, p.&nbsp;3525</sup> and ''GW Vir'' stars (sometimes subdivided into ''DOV'' and ''PNNV'' stars), with atmospheres dominated by helium, carbon, and oxygen.<ref name="quirion">[http://adsabs.harvard.edu/abs/2007ApJS..171..219Q Mapping the Instability Domains of GW Vir Stars in the Effective Temperature-Surface Gravity Diagram], P.-O. Quirion, G. Fontaine, and P. Brassard, ''The Astrophysical Journal Supplement Series'' '''171''', #1 (July 2007), pp. 219&ndash;248.</ref><sup>,§1.1,&nbsp;1.2;</sup><ref>[http://adsabs.harvard.edu/abs/2004A%26A...426L..45N Detection of non-radial g-mode pulsations in the newly discovered PG 1159 star HE 1429-1209], T. Nagel and K. Werner, ''Astronomy and Astrophysics'' '''426''' (2004), pp. L45&ndash;L48.</ref><sup>,§1.</sup>  GW Vir stars are not, strictly speaking, white dwarfs, but are stars which are in a position on the [[Hertzsprung-Russell diagram]] between the [[asymptotic giant branch]] and the white dwarf region.   They may be called ''pre-white dwarfs''.<ref name="quirion" /><sup>, § 1.1;</sup><ref>[http://adsabs.harvard.edu/abs/2000ApJ...532.1078O The Extent and Cause of the Pre-White Dwarf Instability Strip], M. S. O'Brien, ''The Astrophysical Journal'' '''532''', #2 (April 2000), pp. 1078&ndash;1088.</ref>  These variables all exhibit small (1%&ndash;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>[http://dx.doi.org/10.1088/0953-8984/10/49/014 Asteroseismology of white dwarf stars], D. E. Winget, ''Journal of Physics: Condensed Matter'' '''10''', #49 (December 14, 1998), pp. 11247&ndash;11261.  DOI 10.1088/0953-8984/10/49/014.</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 solar masses.<ref name="cosmochronology" /><ref name="evo">[http://adsabs.harvard.edu/abs/2003ApJ...591..288H How Massive Single Stars End Their Life], A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, ''The Astrophysical Journal'' '''591''', #1 (2003), pp. 288&ndash;300.</ref>  The composition of the white dwarf produced will differ depending on the initial mass of the star.
===Stars with very low mass===
If the mass of a main-sequence star is lower than approximately half a [[solar mass]], it will never become hot enough to fuse helium at its core.  It is thought that, over a lifespan exceeding the age (~13.7 billion years)<ref name="aou" /> of the Universe, such a star will eventually burn all its hydrogen and end its evolution as a helium white dwarf composed chiefly of [[helium-4]] nuclei.<ref>[http://adsabs.harvard.edu/abs/1997ApJ...482..420L The End of the Main Sequence], Gregory Laughlin, Peter Bodenheimer,  and Fred C. Adams, ''Astrophysical Journal'' '''482''', #1 (June 10, 1997), pp. 420&ndash;432.</ref>  Owing to the time this process takes, it is not thought to be the origin of observed helium white dwarfs.  Rather, they are thought to be the product of mass loss in binary systems <ref name="rln" /><ref name="apj606_L147" /><ref name="he2" /><ref name="sj">[http://www.arm.ac.uk/~csj/astnow.html Stars Beyond Maturity], Simon Jeffery, online article.  Accessed on line May 3, 2007.</ref><ref>[http://adsabs.harvard.edu/abs/2001AN....322..405S Helium core white dwarf evolution&mdash;including white dwarf companions to neutron stars], M. J. Sarna, E. Ergma, and J. Gerskevits, ''Astronomische Nachrichten'' '''322''', #5/6 (December 2001), pp. 405&ndash;410.</ref><ref>[http://adsabs.harvard.edu/abs/2005MNRAS.362..891B The formation of helium white dwarfs in close binary systems - II], O. G. Benvenuto, M. A. De Vito, ''Monthly Notices of the Royal Astronomical Society'' '''362''', #3 (September 2005), pp. 891&ndash;905.</ref> or mass loss due to a large planetary companion.<ref>[http://adsabs.harvard.edu/abs/1998A%26A...335L..85N Formation of undermassive single white dwarfs and the influence of planets on late stellar evolution], G. Nelemans and T. M. Tauris, ''Astronomy and Astrophysics'' '''335''' (July 1998), pp. L85–L88.</ref><ref>{{cite news| url=http://space.newscientist.com/article/mg19726394.900-planet-diet-helps-white-dwarfs-stay-young-and-trim.html| title= Planet diet helps white dwarfs stay young and trim| date= 18 January 2008| publisher= NewScientist.com news service}}</ref>

===Stars with low to medium mass===
If the mass of a main-sequence star is between approximately 0.5 and 8 solar masses, its core will become sufficiently hot to fuse [[helium]] into [[carbon]] and [[oxygen]] via the [[triple-alpha process]], but it will never become sufficiently hot to fuse [[carbon]] into [[neon]].  Near the end of the period in which it undergoes fusion reactions, such a star will have a carbon-oxygen core which does not undergo fusion reactions, surrounded by an inner helium-burning shell and an outer hydrogen-burning shell.  On the Hertzsprung-Russell diagram, it will be found on the [[asymptotic giant branch]].  It will then expel most of its outer material, creating a [[planetary nebula]], until only the carbon-oxygen core is left.  This process is responsible for the carbon-oxygen white dwarfs which form the vast majority of observed white dwarfs.<ref name="sj" /><ref name="vd1">[http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_lowmass.html the evolution of low-mass stars], Vik Dhillon, lecture notes, Physics 213, University of Sheffield.  Accessed on line May 3, 2007.</ref><ref name="vd2">[http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_highmass.html the evolution of high-mass stars], Vik Dhillon, lecture notes, Physics 213, University of Sheffield.  Accessed on line May 3, 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, 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]] which will leave behind a remnant [[neutron star]], [[black hole]], or possibly a more exotic form of [[compact star]].<ref name="evo" /><ref>[http://adsabs.harvard.edu/abs/2005JPhG...31S.651S Strange quark matter in stars: a general overview], J&uuml;rgen Schaffner-Bielich, ''Journal of Physics G: Nuclear and Particle Physics'' '''31''', #6 (2005), pp. S651&ndash;S657; also [http://arxiv.org/abs/astro-ph/0412215v1 arXiv:astro-ph/0412215v1].</ref>  Some main-sequence stars, of perhaps 8 to 10 [[solar mass]]es, 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>[http://adsabs.harvard.edu/abs/1984ApJ...277..791N Evolution of 8&ndash;10 solar mass stars toward electron capture supernovae. I - Formation of electron-degenerate O + Ne + Mg cores], Ken'ichi Nomoto, ''The Astrophysical Journal'' '''277''' (February 15, 1984), pp. 791&ndash;805.</ref><ref>[http://adsabs.harvard.edu/abs/2002RvMP...74.1015W The evolution and explosion of massive stars], S. E. Woosley, A. Heger, and T. A. Weaver, ''Reviews of Modern Physics'' '''74''', #4 (October 2002), pp. 1015&ndash;1071.</ref>  Although some isolated white dwarfs have been identified which may be of this type, most evidence for the existence of such stars comes from the novae called ''ONeMg'' or ''neon'' novae.  The spectra of these [[nova]]e exhibit abundances of neon, magnesium, and other intermediate-mass elements which appear to be only explicable by the accretion of material onto an oxygen-neon-magnesium white dwarf.<ref name="oxne" /><ref>[http://adsabs.harvard.edu/abs/2004A&A...421.1169W Chandra and FUSE spectroscopy of the hot bare stellar core H 1504+65], K. Werner, T. Rauch, M. A. Barstow, and J. W. Kruk, ''Astronomy and Astrophysics'' '''421''' (2004), pp. 1169&ndash;1183.</ref><ref>[http://adsabs.harvard.edu/abs/1994ApJ...425..797L On the interpretation and implications of nova abundances: an abundance of riches or an overabundance of enrichments], Mario Livio and James W. Truran, ''The Astrophysical Journal'' '''425''', #2 (April 1994), pp. 797&ndash;801.</ref>

==Fate==
A white dwarf is stable once formed and will continue to cool almost indefinitely; eventually, it will become a black white dwarf, also called a [[black dwarf]].  Assuming that the [[Universe]] continues to expand, it is thought that in 10<sup>19</sup> to 10<sup>20</sup> [[year]]s, the [[galaxy|galaxies]] will evaporate as their [[star]]s escape into intergalactic space.<ref name="fate">[http://adsabs.harvard.edu/abs/1997RvMP...69..337A A dying universe: the long-term fate and evolution of astrophysical objects], Fred C. Adams and Gregory Laughlin, ''Reviews of Modern Physics'' '''69''', #2 (April 1997), pp. 337&ndash;372.</ref><sup>,&nbsp;§IIIA.</sup>  White dwarfs should generally survive this, although an occasional collision between white dwarfs may produce a new [[nuclear fusion|fusing]] star or a super-Chandrasekhar mass white dwarf which will explode in a [[type Ia supernova]].<ref name="fate" /><sup>,&nbsp;§IIIC,&nbsp;IV.</sup>  The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the [[proton]], known to be at least 10<sup>32</sup> years.  Some simple [[grand unified theory|grand unified theories]] predict a [[proton decay|proton lifetime]] of no more than 10<sup>49</sup> years.  If these theories are not valid, the proton may decay by more complicated nuclear processes, or by [[quantum gravity|quantum gravitational]] processes involving a [[virtual black hole]]; 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 [[atomic nucleus|nuclei]] decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely.<ref name="fate" /><sup>,&nbsp;§IV.</sup>

==Stellar system==
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.  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>[http://news.bbc.co.uk/1/hi/sci/tech/6357765.stm Comet clash kicks up dusty haze], BBC News, February 13, 2007.  Accessed on line September 20, 2007.</ref><ref>[http://adsabs.harvard.edu/abs/2007ApJ...657L..41S A Debris Disk around the Central Star of the Helix Nebula?], K. Y. L. Su, Y.-H. Chu, G. H. Rieke, P. J. Huggins, R. Gruendl, R. Napiwotzki, T. Rauch, W. B. Latter, and K. Volk, ''The Astrophysical Journal'' '''657''', #1 (March 2007), pp. L41&ndash;L45.</ref>  Similarly, observations made in 2004 indicated the presence of a dust cloud around the young white dwarf star [[G29-38]] (estimated to have formed from its [[asymptotic giant branch|AGB]] progenitor about 500 million years ago), which may have been created by tidal disruption of a comet passing close to the white dwarf.<ref>[http://adsabs.harvard.edu/abs/2005ApJ...635L.161R The Dust Cloud around the White Dwarf G29-38], William T. Reach, Marc J. Kuchner, Ted von Hippel, Adam Burrows, Fergal Mullally, Mukremin Kilic, and D. E. Winget, ''The Astrophysical Journal'' '''635''', #2 (December 2005), pp. L161&ndash;L164.</ref>   If a white dwarf is in a [[binary star|binary system with a stellar companion]], a variety of phenomena may occur, including [[nova]]e and [[Type Ia supernova]]e. 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.

===Type Ia supernovae===
[[Image:Main tycho remnant full.jpg|right|thumb|150px|Composite image of [[SN 1572]] or [[Tycho Brahe|Tycho]]'s Nova, the remnant of a Type Ia supernova.]]

{{Main|Type Ia supernova}}
The mass of an isolated, nonrotating white dwarf cannot exceed the [[Chandrasekhar limit]] of ~1.4 solar masses. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly.)<ref>[http://adsabs.harvard.edu/abs/2004A&A...419..623Y Presupernova Evolution of Accreting White Dwarfs with Rotation], S.-C. Yoon and N. Langer, ''Astronomy and Astrophysics'' '''419''', #2 (May 2004), pp. 623&ndash;644.  Accessed on line May 30, 2007.</ref>  White dwarfs in [[binary (astronomy)|binary]] systems, however, can accrete material from a companion star, increasing both their mass and their density.  As their mass approaches the Chandrasekhar limit, this could theoretically lead to either the explosive ignition of [[nuclear fusion|fusion]] in the white dwarf or its collapse into a [[neutron star]].<ref name="collapse" />

Accretion provides the currently favored mechanism, the ''single-degenerate model'', for [[type Ia supernovae]].  In this model, a [[carbon]]-[[oxygen]] white dwarf accretes material from a companion star,<ref name="sniamodels" /><sup>, p.&nbsp;14.</sup> increasing its mass and compressing its core.  It is believed that [[physical compression|compression]]al 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>[http://adsabs.harvard.edu/abs/2006A&A...453..229B Theoretical light curves for deflagration models of type Ia supernova], S. I. Blinnikov, F. K. Röpke, E. I. Sorokina, M. Gieseler, M. Reinecke, C. Travaglio, W. Hillebrandt, and M. Stritzinger, ''Astronomy and Astrophysics'' '''453''', #1 (July 2006), pp.229&ndash;240.</ref>  In another possible mechanism for type Ia supernovae, the ''double-degenerate model'', two carbon-oxygen white dwarfs in a binary system merge, creating an object with mass greater than the Chandrasekhar limit in which carbon fusion is then ignited.<ref name="sniamodels" /><sup>, p.&nbsp;14.</sup>

===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]]. Since the white dwarf's core remains intact, these surface explosions can be repeated as long as accretion continues.  This weaker kind of repetitive cataclysmic phenomenon is called a (classical) [[nova]].  Astronomers have also observed [[dwarf nova]]e, which have smaller, more frequent luminosity peaks than classical novae.  These are thought to be caused by the release of [[gravitational potential energy]] when part of the [[accretion disc]] collapses onto the star, rather than by fusion.  In general, binary systems with a white dwarf accreting matter from a stellar companion are called [[cataclysmic variable]]s.  As well as novae and dwarf novae, several other classes of these variables are known.<ref name="osln" /><ref name="sniamodels" /><ref name="nasa1">[http://imagine.gsfc.nasa.gov/docs/science/know_l2/cataclysmic_variables.html Imagine the Universe! Cataclysmic Variables], fact sheet at NASA Goddard.  Accessed on line May 4, 2007.</ref><ref name="nasa2">[http://heasarc.gsfc.nasa.gov/docs/objects/cvs/cvstext.html Introduction to Cataclysmic Variables (CVs)], fact sheet at NASA Goddard. Accessed on line May 4, 2007.</ref>  Both fusion- and accretion-powered cataclysmic variables have been observed to be [[X-ray]] sources.<ref name="nasa2" />

== See also ==
{{portal|Space|Earth-moon.jpg}}
* [[Planetary nebula]]
* [[PG 1159 star]]
* [[Pulsating white dwarf]]
* [[Stellar classification]]
* [[Timeline of white dwarfs, neutron stars, and supernovae]]
* [[Degenerate matter]]
* [[Black dwarf]]
* [[Supernova]]
* [[Red dwarf]]
* [[Brown dwarf]]
* [[Robust Associations of Massive Baryonic Objects (RAMBOs)]]
* [[Neutron star]]

==References==
{{reflist|colwidth=35em}}

==External links and further reading==
{{Wiktionary}}
===General===
* White Dwarf Stars, Steven D. Kawaler, in ''Stellar remnants'', S. D. Kawaler, I. Novikov, and G. Srinivasan, edited by Georges Meynet and Daniel Schaerer, Berlin: Springer, 1997.  Lecture notes for Saas-Fee advanced course number 25.  ISBN 3540615202.
===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 0471873179.
* [http://adsabs.harvard.edu/abs/1990RPPh...53..837K Physics of white dwarf stars], D. Koester and G. Chanmugam, ''Reports on Progress in Physics'' '''53''' (1990), pp.&nbsp;837&ndash;915.
*[http://www.davegentile.com/thesis/white_dwarfs.html ''White dwarf stars and the Chandrasekhar limit''], Dave Gentile, Master's thesis, [[DePaul University]], 1995.
*[http://www.sciencebits.com/StellarEquipartition Estimating Stellar Parameters from Energy Equipartition], sciencebits.com.  Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments.
===Variability===
*[http://dx.doi.org/10.1088/0953-8984/10/49/014 Asteroseismology of white dwarf stars], D. E. Winget, ''Journal of Physics: Condensed Matter'' '''10''', #49 (December 14, 1998), pp.&nbsp;11247&ndash;11261, {{doi|10.1088/0953-8984/10/49/014}}.

===Magnetic field===
*[http://adsabs.harvard.edu/abs/2000PASP..112..873W Magnetism in Isolated and Binary White Dwarfs], D. T. Wickramasinghe and Lilia Ferrario, ''Publications of the Astronomical Society of the Pacific'' '''112''', #773 (July 2000), pp.&nbsp;873&ndash;924.
===Frequency===
*[http://www.sciencemag.org/cgi/content/full/292/5525/2211a?ck=nck White Dwarfs and Dark Matter], B. K. Gibson and C. Flynn, ''Science'' '''292''', #5525 (June 22, 2001), p.&nbsp;2211, {{doi|10.1126/science.292.5525.2211a}}, PMID 11423620.

===Observational===
* [http://adsabs.harvard.edu/abs/1998ApJ...494..759P Testing the White Dwarf Mass-Radius Relation with HIPPARCOS], J. L. Provencal, H. L. Shipman, Erik Hog, P. Thejll, ''The Astrophysical Journal'' '''494''' (February 20, 1998), pp.&nbsp;759&ndash;767.
* [http://adsabs.harvard.edu/abs/2004ApJ...612L.129G Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey], Evalyn Gates, Geza Gyuk, Hugh C. Harris, Mark Subbarao, Scott Anderson, S. J. Kleinman, James Liebert, Howard Brewington, J. Brinkmann, Michael Harvanek, Jurek Krzesinski, Don Q. Lamb, Dan Long, Eric H. Neilsen, Jr., Peter R. Newman, Atsuko Nitta, and Stephanie A. Snedden, ''The Astrophysical Journal'' '''612''', #2 (September 2004), pp.&nbsp;L129&ndash;L132.
* [http://www.astronomy.villanova.edu/WDCatalog/index.html Villanova University White Dwarf Catalogue WD], G. P. McCook and E. M. Sion.
* [http://adsabs.harvard.edu/abs/2007Natur.450..522D White dwarf stars with carbon atmospheres], P. Dufour, James Liebert, G. Fontaine, and N. Behara, ''Nature'' '''450''' (November 22, 2007), pp.&nbsp;522–524, {{doi|10.1038/nature06318}}, {{arXiv|0711.3227}}.

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