Editing Brown dwarf (section)

== Binary brown dwarfs ==

=== Brown dwarf–brown dwarf binaries ===
[[File:Hubble Space Telescope - Brown Dwarf Binaries.gif|thumb|Multi-epoch images of brown dwarf binaries taken with the [[Hubble Space Telescope]]. The binary Luhman 16 AB (left) is closer to the Solar System than the other examples shown here.]]
Brown dwarfs binaries of type M, L, and T are less common with a lower mass of the primary.<ref>{{cite web |title=Are the Coolest Brown Dwarfs Loners? |url=https://www.noirlab.edu/public/announcements/geminiann16003/ |access-date=2023-04-16 |website=www.noirlab.edu }}</ref> L-dwarfs have a binary fraction of about {{Val|24|6|2}}% and the binary fraction for late T, early Y-dwarfs (T5-Y0) is about {{val|8|6|u=%}}.<ref name=":11">{{cite journal |last1=Fontanive |first1=Clémence |last2=Biller |first2=Beth |last3=Bonavita |first3=Mariangela |last4=Allers |first4=Katelyn |date=2018-09-01 |title=Constraining the multiplicity statistics of the coolest brown dwarfs: binary fraction continues to decrease with spectral type |journal=Monthly Notices of the Royal Astronomical Society |volume=479 |issue=2 |pages=2702–2727 |doi=10.1093/mnras/sty1682 |doi-access=free |arxiv=1806.08737 |bibcode=2018MNRAS.479.2702F |issn=0035-8711}}</ref>

Brown dwarf binaries have a higher companion-to-host ratio <math>q=M_B/M_A</math> for lower mass binaries. Binaries with a [[Red dwarf|M-type star]] as a primary have for example a broad distribution of ''q'' with a preference of ''q''&nbsp;≥&nbsp;0.4. Brown dwarfs on the other hand show a strong preference for ''q''&nbsp;≥&nbsp;0.7. The separation is decreasing with mass: M-type stars have a separation peaking at 3–30 [[astronomical unit]]s (au), M-L-type brown dwarfs have a projected separation peaking at 5–8 au and T5–Y0 objects have a projected separation that follows a [[Log-normal distribution|lognormal distribution]] with a peak separation of about 2.9&nbsp;au.<ref name=":11" />

An example is the closest brown dwarf binary Luhman 16 AB with a primary L7.5 dwarf and a separation of 3.5&nbsp;au and ''q''&nbsp;=&nbsp;0.85. The separation is on the lower end of the expected separation for M-L-type brown dwarfs, but the mass ratio is typical.

It is not known if the same trend continues with Y-dwarfs, because their sample size is so small. The Y+Y dwarf binaries should have a high mass ratio q and a low separation, reaching scales of less than one au.<ref>{{cite journal |last1=Opitz |first1=Daniela |last2=Tinney |first2=C. G. |last3=Faherty |first3=Jacqueline |last4=Sweet |first4=Sarah |last5=Gelino |first5=Christopher R. |last6=Kirkpatrick |first6=J. Davy |date=2016-02-24 |title=Searching for Binary Y dwarfs with the Gemini Multi-Conjugate Adaptive Optics System (GeMS) |journal=The Astrophysical Journal |volume=819 |issue=1 |pages=17 |doi=10.3847/0004-637X/819/1/17 |arxiv=1601.05508 |bibcode=2016ApJ...819...17O |s2cid=3208550 |issn=1538-4357 |doi-access=free }}</ref> In 2023, the Y+Y dwarf [[WISE J0336−0143|WISE J0336-0143]] was confirmed as a binary with [[James Webb Space Telescope|JWST]], with a mass ratio of q=0.62±0.05 and a separation of 0.97 astronomical units. The researchers point out that the sample size of low-mass binary brown dwarfs is too small to determine if WISE J0336-0143 is a typical representative of low-mass binaries or a peculiar system.<ref name=":14">{{cite journal |last1=Calissendorff |first1=Per |last2=De Furio |first2=Matthew |last3=Meyer |first3=Michael |last4=Albert |first4=Loïc |last5=Aganze |first5=Christian |last6=Ali-Dib |first6=Mohamad |last7=Gagliuffi |first7=Daniella C. Bardalez |last8=Baron |first8=Frederique |last9=Beichman |first9=Charles A. |last10=Burgasser |first10=Adam J. |last11=Cushing |first11=Michael C. |last12=Faherty |first12=Jacqueline Kelly |last13=Fontanive |first13=Clémence |last14=Gelino |first14=Christopher R. |last15=Gizis |first15=John E. |date=2023-03-29 |title=JWST/NIRCam Discovery of the First Y+Y Brown Dwarf Binary: WISE J033605.05–014350.4 |journal=The Astrophysical Journal Letters |volume=947 |issue=2 |pages=L30 |doi=10.3847/2041-8213/acc86d |arxiv=2303.16923 |bibcode=2023ApJ...947L..30C |s2cid=257833714 |doi-access=free }}</ref>

Observations of the orbit of binary systems containing brown dwarfs can be used to measure the mass of the brown dwarf. In the case of [[2MASSW J0746425+2000321]], the secondary weighs 6% of the solar mass. This measurement is called a dynamical mass.<ref>{{cite press release |first=Hervé |last=Bouy |url=https://www.eso.org/public/news/eso0420/ |title=Weighing Ultra-Cool Stars – Large Ground-Based Telescopes and Hubble Team-Up to Perform First Direct Brown Dwarf Mass Measurement |publisher=European Southern Observatory |access-date=2019-12-11 }}</ref><ref>{{cite journal |last1=Bouy |first1=Hervé |last2=Duchêne |first2=Gaspard |last3=Köhler |first3=Rainer |last4=Brandner |first4=Wolfgang |last5=Bouvier |first5=Jérôme |last6=Martín |first6=Eduardo L. |last7=Ghez |first7=Andrea Mia |last8=Delfosse |first8=Xavier |last9=Forveille |first9=Thierry |last10=Allard |first10=France |last11=Baraffe |first11=Isabelle |first12=Gibor |last12=Basri |first13=Laird M. |last13=Close |first14=Caer E. |last14=McCabe |date=2004-08-01 |title=First determination of the dynamical mass of a binary L dwarf |journal=Astronomy & Astrophysics |volume=423 |issue=1 |pages=341–352 |arxiv=astro-ph/0405111 |doi=10.1051/0004-6361:20040551 |issn=0004-6361 |bibcode=2004A&A...423..341B |s2cid=3149721 }}</ref> The brown dwarf system closest to the Solar System is the binary Luhman 16. It was attempted to search for planets around this system with a similar method, but none were found.<ref>{{cite journal |last1=Bedin |first1=Luigi R. |last2=Pourbaix |first2=Dimitri |last3=Apai |first3=Dániel |last4=Burgasser |first4=Adam J. |last5=Buenzli |first5=Esther |last6=Boffin |first6=Henri M. J. |last7=Libralato |first7=Mattia |date=2017-09-01 |title=Hubble Space Telescope astrometry of the closest brown dwarf binary system – I. Overview and improved orbit |url=https://academic.oup.com/mnras/article/470/1/1140/3896221 |journal=Monthly Notices of the Royal Astronomical Society |volume=470 |issue=1 |pages=1140–1155 |arxiv=1706.00657 |doi=10.1093/mnras/stx1177 |doi-access=free |issn=0035-8711 |hdl=10150/625503 |s2cid=119385778 }}</ref>

=== Unusual brown dwarf binaries ===
[[File:SDSS J1416+1348 legacy dr10.jpg|thumb|The wide brown dwarf binary [[SDSS J141624.08+134826.7|SDSS J1416+1348]]]]
The wide binary system [[2M1101AB]] was the first binary with a separation greater than {{Val|20|ul=AU}}. The discovery of the system gave definitive insights to the formation of brown dwarfs. It was previously thought that wide binary brown dwarfs are not formed or at least are disrupted at ages of 1–10 [[Myr]]. The existence of this system is also inconsistent with the ejection hypothesis.<ref>{{cite journal |last=Luhman |first=Kevin L. |date=2004-10-10 |title=The First Discovery of a Wide Binary Brown Dwarf |journal=The Astrophysical Journal |volume=614 |issue=1 |pages=398–403 |arxiv=astro-ph/0407344 |doi=10.1086/423666 |issn=0004-637X |bibcode=2004ApJ...614..398L |s2cid=11733526 }}</ref> The ejection hypothesis was a proposed hypothesis in which brown dwarfs form in a multiple system, but are ejected before they gain enough mass to burn hydrogen.<ref>{{cite journal |last1=Reipurth|first1=Bo|last2=Clarke|first2=Cathie|date=June 2003|title=Brown Dwarfs as Ejected Stellar Embryos: Observational Perspectives|journal=IAUS|volume=211|pages=13–22|issn=1743-9221|bibcode=2003IAUS..211...13R|arxiv=astro-ph/0209005|doi=10.1017/s0074180900210188|s2cid=16822178 }}</ref>

More recently the wide binary [[W2150AB]] was discovered. It has a similar mass ratio and [[Gravitational binding energy|binding energy]] as 2M1101AB, but a greater age and is located in a different region of the galaxy. While 2M1101AB is in a closely crowded region, the binary W2150AB is in a sparsely-separated field. It must have survived any dynamical interactions in its natal [[star cluster]]. The binary belongs also to a few L+T binaries that can be easily resolved by ground-based observatories. The other two are [[SDSS J1416+1348|SDSS J1416+13AB]] and Luhman 16.<ref>{{cite journal |last1=Faherty |first1=Jacqueline K. |last2=Goodman |first2=Sam |last3=Caselden |first3=Dan |last4=Colin |first4=Guillaume |last5=Kuchner |first5=Marc J. |last6=Meisner |first6=Aaron M. |last7=Gagné |first7=Jonathan |last8=Schneider |first8=Adam C. |last9=Gonzales |first9=Eileen C. |last10=Bardalez Gagliuffi |first10=Daniella C. |last11=Logsdon |first11=Sarah E. |title=WISE2150-7520AB: A very low mass, wide co-moving brown dwarf system discovered through the citizen science project Backyard Worlds: Planet 9 |journal=The Astrophysical Journal |volume=889 |issue=2 |pages=176 |arxiv=1911.04600 |doi=10.3847/1538-4357/ab5303 |year=2020 |bibcode=2020ApJ...889..176F |s2cid=207863267 |doi-access=free }}</ref>

There are other interesting binary systems such as the [[eclipsing binary]] brown dwarf system [[2MASS J05352184–0546085]].<ref name="Stassun2006"/> Photometric studies of this system have revealed that the less massive brown dwarf in the system is hotter than its higher-mass companion.<ref name=":1" />

=== Brown dwarfs around stars ===
{{Main|Brown-dwarf desert}}
Brown dwarfs and massive planets in a close orbit (less than 5 au) around stars are rare and this is sometimes described as the brown dwarf desert. Less than 1% of stars with the mass of the sun have a brown dwarf within 3–5 au.<ref>{{cite journal |last1=Grether |first1=Daniel |last2=Lineweaver |first2=Charles H. |date=2006-04-01 |title=How Dry is the Brown Dwarf Desert? Quantifying the Relative Number of Planets, Brown Dwarfs, and Stellar Companions around Nearby Sun-like Stars |url=https://ui.adsabs.harvard.edu/abs/2006ApJ...640.1051G |journal=The Astrophysical Journal |volume=640 |issue=2 |pages=1051–1062 |doi=10.1086/500161 |arxiv=astro-ph/0412356 |bibcode=2006ApJ...640.1051G |s2cid=8563521 |issn=0004-637X}}</ref>

An example for a star–brown dwarf binary is the first discovered T-dwarf [[Gliese 229|Gliese 229 B]], which orbits around the main-sequence star Gliese 229 A, a red dwarf. Brown dwarfs orbiting [[subgiant]]s are also known, such as [[TOI-1994b]] which orbits its star every 4.03 days.<ref>{{cite journal |last1=Page |first1=Emma |last2=Pepper |first2=Joshua |last3=Kane |first3=Stephen |last4=Zhou |first4=George |last5=Addison |first5=Brett |last6=Wright |first6=Duncan |last7=Wittenmyer |first7=Robert |last8=Johnson |first8=Marshall |last9=Evans |first9=Philip |last10=Collins |first10=Karen |last11=Hellier |first11=Coel |last12=Jensen |first12=Eric |last13=Stassun |first13=Keivan |last14=Rodriguez |first14=Joseph |date=2022-06-01 |title=TOI-1994b: An Eccentric Brown Dwarf Transiting a Subgiant |journal=American Astronomical Society Meeting Abstracts |url=https://ui.adsabs.harvard.edu/abs/2022AAS...24030521P |volume=54 |issue=6 |pages=305.21|bibcode=2022AAS...24030521P }}</ref>

There is also disagreement if some low-mass brown dwarfs should be considered planets. The [[NASA Exoplanet Archive|NASA Exoplanet archive]] includes brown dwarfs with a minimum mass less or equal to 30 Jupiter masses as planets as long as there are other criteria fulfilled (e.g. orbiting a star).<ref>{{cite web |title=Exoplanet Criteria for Inclusion in the Exoplanet Archive |url=https://exoplanetarchive.ipac.caltech.edu/docs/exoplanet_criteria.html |access-date=2023-04-16 |website=exoplanetarchive.ipac.caltech.edu}}</ref> The Working Group on Extrasolar Planets (WGESP) of the [[International Astronomical Union|IAU]] on the other hand only considers planets with a mass below 13 Jupiter masses.<ref>{{cite web |title=Working Group on Extrasolar Planets |url=https://w.astro.berkeley.edu/~basri/defineplanet/IAU-WGExSP.htm |access-date=2023-04-16 |website=w.astro.berkeley.edu}}</ref>

=== White dwarf–brown dwarf binaries ===
[[File:LSPM J0241+2553AB.jpg|thumb|[[LSPM J0241+2553AB]], a wide white dwarf(A)–brown dwarf(B) binary.]]
Brown dwarfs around [[white dwarf]]s are quite rare. [[GD 165|GD 165 B]], the prototype of the L dwarfs, is one such system.<ref>{{cite journal |last1=Farihi |first1=Jay |last2=Christopher |first2=Micol|date=October 2004 |title=A Possible Brown Dwarf Companion to the White Dwarf GD 1400 |journal=The Astronomical Journal |volume=128 |issue=4 |pages=1868 |arxiv=astro-ph/0407036 |doi=10.1086/423919 |issn=1538-3881 |bibcode=2004AJ....128.1868F |s2cid=119530628 }}</ref> Such systems can be useful in determining the age of the system and the mass of the brown dwarf. Other white dwarf-brown dwarf binaries are [[COCONUTS-1|COCONUTS-1 AB]] (7&nbsp;billion years old),<ref name=":3" /> and [[LSPM J0055+5948|LSPM J0055+5948 AB]] (10&nbsp;billion years old),<ref name=":12">{{cite journal |last1=Meisner |first1=Aaron M. |last2=Faherty |first2=Jacqueline K. |last3=Kirkpatrick |first3=J. Davy |last4=Schneider |first4=Adam C. |last5=Caselden |first5=Dan |last6=Gagné |first6=Jonathan |last7=Kuchner |first7=Marc J. |last8=Burgasser |first8=Adam J. |last9=Casewell |first9=Sarah L. |last10=Debes |first10=John H. |last11=Artigau |first11=Étienne |last12=Bardalez Gagliuffi |first12=Daniella C. |last13=Logsdon |first13=Sarah E. |last14=Kiman |first14=Rocio |last15=Allers |first15=Katelyn |date=2020-08-01 |title=Spitzer Follow-up of Extremely Cold Brown Dwarfs Discovered by the Backyard Worlds: Planet 9 Citizen Science Project |journal=The Astrophysical Journal |volume=899 |issue=2 |pages=123 |doi=10.3847/1538-4357/aba633 |arxiv=2008.06396 |bibcode=2020ApJ...899..123M |s2cid=221135837 |issn=0004-637X |doi-access=free }}</ref> [[SDSS J22255+0016|SDSS J22255+0016 AB]] (2&nbsp;billion years old)<ref name=":13">{{cite journal |last1=French |first1=Jenni R. |last2=Casewell |first2=Sarah L. |last3=Dupuy |first3=Trent J. |last4=Debes |first4=John H. |last5=Manjavacas |first5=Elena |last6=Martin |first6=Emily C. |last7=Xu |first7=Siyi |date=2023-03-01 |title=Discovery of a resolved white dwarf–brown dwarf binary with a small projected separation: SDSS J222551.65+001637.7AB |journal=Monthly Notices of the Royal Astronomical Society |volume=519 |issue=4 |pages=5008–5016 |doi=10.1093/mnras/stac3807 |doi-access=free |arxiv=2301.02101 |bibcode=2023MNRAS.519.5008F |issn=0035-8711}}</ref> [[WD 0806−661|WD 0806−661 AB]] (1.5–2.7&nbsp;billion years old).<ref>{{cite journal |last1=Leggett |first1=S. K. |last2=Tremblin |first2=P. |last3=Esplin |first3=T. L. |last4=Luhman |first4=K. L. |last5=Morley |first5=Caroline V. |date=2017-06-01 |title=The Y-type Brown Dwarfs: Estimates of Mass and Age from New Astrometry, Homogenized Photometry, and Near-infrared Spectroscopy |journal=The Astrophysical Journal |volume=842 |issue=2 |pages=118 |doi=10.3847/1538-4357/aa6fb5 |arxiv=1704.03573 |bibcode=2017ApJ...842..118L |s2cid=119249195 |issn=0004-637X |doi-access=free }}</ref>

Systems with close, [[Tidal locking|tidally locked]] brown dwarfs orbiting around white dwarfs belong to the [[post common envelope binary|post common envelope binaries]] or PCEBs. Only eight confirmed PCEBs containing a white dwarf with a brown dwarf companion are known, including [[WD 0137−349|WD 0137-349]] AB. In the past history of these close white dwarf–brown dwarf binaries, the brown dwarf is engulfed by the star in the [[Red giant|red giant phase]]. Brown dwarfs with a mass lower than 20 [[Jupiter mass]]es would [[Photoevaporation|evaporate]] during the engulfment.<ref>{{cite press release |first1=Pierre |last1=Maxted |first2=Ralf |last2=Napiwotzki |first3=Paul |last3=Dobbie |first4=Matt |last4=Burleigh |url=https://www.eso.org/public/news/eso0628/ |title=A Sub-Stellar Jonah – Brown Dwarf Survives Being Swallowed |publisher=European Southern Observatory |access-date=2019-12-11 }}</ref><ref>{{cite journal |last1=Casewell |first1=Sarah L. |last2=Braker |first2=Ian P. |last3=Parsons |first3=Steven G. |last4=Hermes |first4=James J. |last5=Burleigh |first5=Matthew R. |last6=Belardi |first6=Claudia |last7=Chaushev |first7=Alexander |last8=Finch |first8=Nicolle L. |last9=Roy |first9=Mervyn |last10=Littlefair |first10=Stuart P. |last11=Goad |first11=Mike |last12=Dennihy |first12=Erik |date=31 January 2018 |title=The first sub-70 min non-interacting WD–BD system: EPIC212235321 |journal=Monthly Notices of the Royal Astronomical Society |volume=476 |issue=1 |pages=1405–1411 |doi=10.1093/mnras/sty245 |doi-access=free |issn=0035-8711 |bibcode=2018MNRAS.476.1405C |arxiv=1801.07773 |s2cid=55776991 }}</ref> The dearth of brown dwarfs orbiting close to white dwarfs can be compared with similar observations of brown dwarfs around main-sequence stars, described as the [[brown-dwarf desert]].<ref>{{cite journal |last1=Longstaff |first1=Emma S. |last2=Casewell |first2=Sarah L. |last3=Wynn |first3=Graham A. |last4=Maxted |first4=Pierre F. L. |last5=Helling |first5=Christiane |date=2017-10-21 |title=Emission lines in the atmosphere of the irradiated brown dwarf WD0137−349B |url=https://academic.oup.com/mnras/article/471/2/1728/3974054 |journal=Monthly Notices of the Royal Astronomical Society |volume=471 |issue=2 |pages=1728–1736 |arxiv=1707.05793 |doi=10.1093/mnras/stx1786 |doi-access=free |issn=0035-8711 |bibcode=2017MNRAS.471.1728L |s2cid=29792989 }}</ref><ref>{{cite journal |last1=Grether |first1=Daniel |last2=Lineweaver |first2=Charles H. |date=April 2006 |title=How Dry is the Brown Dwarf Desert? Quantifying the Relative Number of Planets, Brown Dwarfs, and Stellar Companions around Nearby Sun-like Stars |journal=The Astrophysical Journal |volume=640 |issue=2 |pages=1051–1062 |doi=10.1086/500161 |arxiv=astro-ph/0412356 |bibcode=2006ApJ...640.1051G |issn=0004-637X |doi-access=free }}</ref> The PCEB might evolve into a [[cataclysmic variable star]] (CV*) with the brown dwarf as the donor.<ref>{{cite journal |last1=Rappaport |first1=Saul A. |last2=Vanderburg |first2=Andrew |last3=Nelson |first3=Lorne |last4=Gary |first4=Bruce L. |last5=Kaye |first5=Thomas G. |last6=Kalomeni |first6=Belinda |last7=Howell |first7=Steve B. |last8=Thorstensen |first8=John R. |last9=Lachapelle |first9=François-René |last10=Lundy |first10=Matthew |last11=St-Antoine |first11=Jonathan |date=2017-10-11 |title=WD 1202-024: the shortest-period pre-cataclysmic variable |url=https://academic.oup.com/mnras/article/471/1/948/3892367 |journal=Monthly Notices of the Royal Astronomical Society |volume=471 |issue=1 |pages=948–961 |arxiv=1705.05863 |doi=10.1093/mnras/stx1611 |doi-access=free |issn=0035-8711 |bibcode=2017MNRAS.471..948R |s2cid=119349942 }}</ref> Simulations have shown that highly evolved CV* are mostly associated with substellar donors (up to 80%).<ref name=":15">{{cite journal |last1=Neustroev |first1=Vitaly V. |last2=Mäntynen |first2=Iikka |date=2023-08-01 |title=A brown dwarf donor and an optically thin accretion disc with a complex stream impact region in the period-bouncer candidate BW Sculptoris |journal=Monthly Notices of the Royal Astronomical Society |volume=523 |issue=4 |pages=6114–6137 |doi=10.1093/mnras/stad1730 |arxiv=2212.03264 |bibcode=2023MNRAS.523.6114N |issn=0035-8711|doi-access=free }}</ref> A type of CV*, called [[WZ Sagittae|WZ Sge]]-type [[dwarf nova]] often show donors with a mass near the borderline of low-mass stars and brown dwarfs.<ref>{{cite journal |last=Kato |first=Taichi |date=2015-12-01 |title=WZ Sge-type dwarf novae |journal=Publications of the Astronomical Society of Japan |volume=67 |issue=6 |pages=108 |doi=10.1093/pasj/psv077 |arxiv=1507.07659 |bibcode=2015PASJ...67..108K |issn=0004-6264|doi-access=free }}</ref> The binary [[BW Sculptoris]] is such a dwarf nova with a brown dwarf donor. This brown dwarf likely formed when a donor star lost enough mass to become a brown dwarf. The mass loss comes with a loss of the orbital period until it reaches a minimum of 70–80 minutes at which the period increases again. This gives this evolutionary stage the name [[period bouncer]].<ref name=":15" /> There could also exist brown dwarfs that merged with white dwarfs. The nova [[CK Vulpeculae]] might be a result of such a white dwarf–brown dwarf merger.<ref>{{cite web |first1=Nicolás |last1=Lira |first2=Charles E. |last2=Blue |first3=Calum |last3=Turner |first4=Masaaki |last4=Hiramatsu |url=https://www.almaobservatory.org/en/press-release/when-is-a-nova-not-a-nova-when-a-white-dwarf-and-a-brown-dwarf-collide/ |title=When Is a Nova Not a 'Nova'? When a White Dwarf and a Brown Dwarf Collide |website=ALMA Observatory |url-status=dead |archive-url=https://web.archive.org/web/20191022055806/https://www.almaobservatory.org/en/press-release/when-is-a-nova-not-a-nova-when-a-white-dwarf-and-a-brown-dwarf-collide/ |archive-date=2019-10-22 |access-date=2019-11-12 }}</ref><ref>{{cite journal |last1=Eyres |first1=Stewart P. S. |last2=Evans |first2=Aneurin |last3=Zijlstra |first3=Albert |last4=Avison |first4=Adam |last5=Gehrz |first5=Robert D. |last6=Hajduk |first6=Marcin|author7-link=Sumner Starrfield |last7=Starrfield |first7=Sumner |last8=Mohamed |first8=Shazrene |last9=Woodward |first9=Charles E. |last10=Wagner |first10=R. Mark |date=2018-12-21 |title=ALMA reveals the aftermath of a white dwarf–brown dwarf merger in CK Vulpeculae |url=https://academic.oup.com/mnras/article/481/4/4931/5107360 |journal=Monthly Notices of the Royal Astronomical Society |volume=481 |issue=4 |pages=4931–4939 |arxiv=1809.05849 |doi=10.1093/mnras/sty2554 |doi-access=free |bibcode=2018MNRAS.481.4931E |s2cid=119462149 |issn=0035-8711 }}</ref>