Editing White dwarf (section)

=== 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 {{solar mass|0.59}} 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 name="villanovar4" /> 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 absorption]] (CIA) of hydrogen molecules colliding with helium atoms. This affects the optical red and infrared brightness of white dwarfs with a hydrogen or mixed hydrogen-helium atmosphere. This makes old white dwarfs with this kind of atmosphere bluer than the main cooling sequence. White dwarfs with hydrogen-poor atmospheres, such as WD J2147–4035, are less affected by CIA and therefore have a yellow to orange color.<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]].  The axes are [[absolute magnitude]] in the [[Photometric system|G-band]] vs. a [[color index]] G-band magnitude minus RP ([[Gaia (spacecraft)|Gaia]] red photometer) magnitude]]
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 this [[White dwarf cooling anomaly|cooling anomaly]] in some types of white dwarfs is a solid–liquid distillation process: the crystals formed in the core are buoyant and float up, thereby displacing heavier liquid downward, thus causing a net release of gravitational energy.<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>