Editing Brown dwarf (section)

== Theory ==
{{more citations needed section|date=July 2020}}
{{Star nav}}
The standard mechanism for [[stellar evolution|star birth]] is through the gravitational collapse of a cold interstellar cloud of gas and dust. As the cloud contracts, it heats due to the [[Kelvin–Helmholtz mechanism]]. Early in the process the contracting gas quickly radiates away much of the energy, allowing the collapse to continue. Eventually, the central region becomes sufficiently dense to trap radiation. Consequently, the central temperature and density of the collapsed cloud increase dramatically with time, slowing the contraction, until the conditions are hot and dense enough for thermonuclear reactions to occur in the core of the [[protostar]]. For a typical star, gas and radiation pressure generated by the [[thermonuclear fusion]] reactions within its core will support it against any further gravitational contraction. [[Hydrostatic equilibrium]] is reached, and the star will spend most of its lifetime fusing hydrogen into helium as a main-sequence star.

If, however, the initial<ref name=Forbes_Loeb_2019/> mass of the protostar is less than about {{Solar mass|0.08}},<ref>{{cite journal | title=The theory of brown dwarfs and extrasolar giant planets | last1=Burrows | first1=Adam | last2=Hubbard | first2=W. B. | last3=Lunine | first3=J. I. | last4=Liebert | first4=James | journal=Reviews of Modern Physics | volume=73 | issue=3 | pages=719–765 | date=July 2001 | doi=10.1103/RevModPhys.73.719 | arxiv=astro-ph/0103383 | bibcode=2001RvMP...73..719B | s2cid=204927572 | quote=Hence the HBMM at solar metallicity and Y<sub>α</sub> = 50.25 is 0.07 – 0.074 {{solar mass}}, ... while the HBMM at zero metallicity is 0.092 {{solar mass}} }}</ref> normal hydrogen [[thermonuclear fusion]] reactions will not ignite in the core. Gravitational contraction does not heat the small [[protostar]] very effectively, and before the temperature in the core can increase enough to trigger fusion, the density reaches the point where electrons become closely packed enough to create quantum [[electron degeneracy pressure]]. According to the brown dwarf interior models, typical conditions in the core for density, temperature and pressure are expected to be the following:
* <math>10\,\mathrm{g/cm^3} \,\lesssim\, \rho_c \,\lesssim\, 10^3\,\mathrm{{g}/{cm^{3}}} </math>
* <math>T_c \lesssim 3 \times 10^6\,\mathrm{K} </math>
* <math>P_c \sim 10^5\,\mathrm{Mbar}.</math>
<!-- [[File:tdwarf_art.jpg|thumb|left|alt=A picture of a Brown Dwarf|An artist's impression of a brown dwarf and its moon]] -->
This means that the protostar is not massive or dense enough ever to reach the conditions needed to sustain hydrogen fusion. The infalling matter is prevented, by electron degeneracy pressure, from reaching the densities and pressures needed.

Further gravitational contraction is prevented and the result is a brown dwarf that simply cools off by radiating away its internal thermal energy. Note that, in principle, it is possible for a brown dwarf to slowly accrete mass above the [[hydrogen burning limit]] without initiating hydrogen fusion. This could happen via mass transfer in a binary brown dwarf system.<ref name=Forbes_Loeb_2019/>

=== High-mass brown dwarfs versus low-mass stars ===
[[Lithium]] is generally present in brown dwarfs and not in low-mass stars. Stars, which reach the high temperature necessary for fusing hydrogen, rapidly deplete their lithium. Fusion of [[lithium-7]] and a [[proton]] occurs, producing two [[helium-4]] nuclei. The temperature necessary for this reaction is just below that necessary for hydrogen fusion. Convection in low-mass stars ensures that lithium in the whole volume of the star is eventually depleted. Therefore, the presence of the lithium spectral line in a candidate brown dwarf is a strong indicator that it is indeed a substellar object.

==== Lithium test ====
Brown dwarfs can be divided into two groups, those with enough mass fuse lithium and those with smaller mass. This is known as the '''lithium test'''.<ref>{{Cite journal |last1=Martín |first1=E L |last2=Lodieu |first2=N |last3=del Burgo |first3=C |date=2022-02-21 |title=New constraints on the minimum mass for thermonuclear lithium burning in brown dwarfs |journal=Monthly Notices of the Royal Astronomical Society |volume=510 |issue=2 |pages=2841–2850 |doi=10.1093/mnras/stab2969 |doi-access=free |issn=0035-8711}}</ref>

Heavier stars, like the Sun, can also retain lithium in their outer layers, which never get hot enough to fuse lithium, and whose convective layer does not mix with the core where the lithium would be rapidly depleted. Those larger stars are easily distinguishable from brown dwarfs by their size and luminosity.

Conversely, brown dwarfs at the high end of their mass range can be hot enough to deplete their lithium when they are young. Dwarfs of mass greater than {{Jupiter mass|65}} can burn their lithium by the time they are half a billion years old.<ref>{{cite journal |last1=Kulkarni |first1=Shrinivas R. |author-link=Shrinivas Kulkarni |title=Brown Dwarfs: A Possible Missing Link Between Stars and Planets |journal=Science |date=30 May 1997 |volume=276 |issue=5317 |pages=1350–1354 |doi=10.1126/science.276.5317.1350 |bibcode=1997Sci...276.1350K }}</ref>

==== Atmospheric methane ====
Unlike stars, older brown dwarfs are sometimes cool enough that, over very long periods of time, their atmospheres can gather observable quantities of [[methane]], which cannot form in hotter objects. Dwarfs confirmed in this fashion include [[Gliese 229]]B.

==== Iron, silicate and sulfide clouds ====
Main-sequence stars cool, but eventually reach a minimum [[bolometric luminosity]] that they can sustain through steady fusion. This luminosity varies from star to star, but is generally at least 0.01% that of the Sun.{{citation needed|reason=as in talk page|date=April 2013}} Brown dwarfs cool and darken steadily over their lifetimes; sufficiently old brown dwarfs will be too faint to be detectable.
[[File:Brown dwarf clouds.png|thumb|300x300px|Cloud models for the early T-type brown dwarfs [[SIMP J013656.5+093347|SIMP J0136+09]] and [[2MASS J21392676+0220226|2MASS J2139+02]] (left two panels) and the late T-type brown dwarf 2M0050–3322.]]
Clouds are used to explain the weakening of the [[Iron(I) hydride|iron hydride]] (FeH) spectral line in late L-dwarfs. [[Iron]] clouds deplete FeH in the upper atmosphere, and the cloud layer blocks the view to lower layers still containing FeH. The later strengthening of this chemical compound at cooler temperatures of mid- to late T-dwarfs is explained by disturbed clouds that allows a telescope to look into the deeper layers of the atmosphere that still contains FeH.<ref>{{cite journal |last1=Burgasser |first1=Adam J. |last2=Marley |first2=Mark S. |last3=Ackerman |first3=Andrew S. |last4=Saumon |first4=Didier |last5=Lodders |first5=Katharina |last6=Dahn |first6=Conard C. |last7=Harris |first7=Hugh C. |last8=Kirkpatrick |first8=J. Davy |date=2002-06-01 |title=Evidence of Cloud Disruption in the L/T Dwarf Transition |journal=The Astrophysical Journal |volume=571 |issue=2 |pages=L151–L154 |doi=10.1086/341343 |arxiv=astro-ph/0205051 |bibcode=2002ApJ...571L.151B |issn=0004-637X|doi-access=free }}</ref> Young L/T-dwarfs (L2-T4) show high [[Variable star|variability]], which could be explained with clouds, hot spots, magnetically driven [[aurora]]e or [[Thermochemistry|thermochemical]] instabilities.<ref>{{cite journal |last1=Vos |first1=Johanna M. |last2=Faherty |first2=Jacqueline K. |last3=Gagné |first3=Jonathan |last4=Marley |first4=Mark |last5=Metchev |first5=Stanimir |last6=Gizis |first6=John |last7=Rice |first7=Emily L. |last8=Cruz |first8=Kelle |date=2022-01-01 |title=Let the Great World Spin: Revealing the Stormy, Turbulent Nature of Young Giant Exoplanet Analogs with the Spitzer Space Telescope |journal=The Astrophysical Journal |volume=924 |issue=2 |pages=68 |doi=10.3847/1538-4357/ac4502 |arxiv=2201.04711 |bibcode=2022ApJ...924...68V |issn=0004-637X|doi-access=free }}</ref> The clouds of these brown dwarfs are explained as either iron clouds with varying thickness or a lower thick iron cloud layer and an upper [[silicate]] cloud layer. This upper silicate cloud layer can consist out of [[quartz]], [[enstatite]], [[corundum]] and/or [[Forsterite|fosterite]].<ref>{{cite journal |last1=Vos |first1=Johanna M. |last2=Burningham |first2=Ben |last3=Faherty |first3=Jacqueline K. |last4=Alejandro |first4=Sherelyn |last5=Gonzales |first5=Eileen |last6=Calamari |first6=Emily |last7=Bardalez Gagliuffi |first7=Daniella |last8=Visscher |first8=Channon |last9=Tan |first9=Xianyu |last10=Morley |first10=Caroline V. |last11=Marley |first11=Mark |last12=Gemma |first12=Marina E. |last13=Whiteford |first13=Niall |last14=Gaarn |first14=Josefine |last15=Park |first15=Grace |date=2023-02-01 |title=Patchy Forsterite Clouds in the Atmospheres of Two Highly Variable Exoplanet Analogs |journal=The Astrophysical Journal |volume=944 |issue=2 |pages=138 |doi=10.3847/1538-4357/acab58 |arxiv=2212.07399 |bibcode=2023ApJ...944..138V |issn=0004-637X|doi-access=free }}</ref><ref>{{cite journal |last1=Manjavacas |first1=Elena |last2=Karalidi |first2=Theodora |last3=Vos |first3=Johanna M. |last4=Biller |first4=Beth A. |last5=Lew |first5=Ben W. P. |date=2021-11-01 |title=Revealing the Vertical Cloud Structure of a Young Low-mass Brown Dwarf, an Analog to the β-Pictoris b Directly Imaged Exoplanet, through Keck I/MOSFIRE Spectrophotometric Variability |journal=The Astronomical Journal |volume=162 |issue=5 |pages=179 |doi=10.3847/1538-3881/ac174c |arxiv=2107.12368 |bibcode=2021AJ....162..179M |issn=0004-6256|doi-access=free }}</ref> It is however not clear if silicate clouds are always necessary for young objects.<ref>{{cite journal |last1=Tremblin |first1=P. |last2=Chabrier |first2=G. |last3=Baraffe |first3=I. |last4=Liu |first4=Michael. C. |last5=Magnier |first5=E. A. |last6=Lagage |first6=P. -O. |last7=Alves de Oliveira |first7=C. |last8=Burgasser |first8=A. J. |last9=Amundsen |first9=D. S. |last10=Drummond |first10=B. |date=2017-11-01 |title=Cloudless Atmospheres for Young Low-gravity Substellar Objects |journal=The Astrophysical Journal |volume=850 |issue=1 |pages=46 |doi=10.3847/1538-4357/aa9214 |arxiv=1710.02640 |bibcode=2017ApJ...850...46T |issn=0004-637X|doi-access=free }}</ref> Silicate absorption can be directly observed in the [[Infrared astronomy|mid-infrared]] at 8 to 12 μm. Observations with [[Spitzer Space Telescope#Instruments|Spitzer IRS]] have shown that silicate absorption is common, but not ubiquitous, for L2-L8 dwarfs.<ref>{{cite journal |last1=Suárez |first1=Genaro |last2=Metchev |first2=Stanimir |date=2022-07-01 |title=Ultracool dwarfs observed with the Spitzer infrared spectrograph - II. Emergence and sedimentation of silicate clouds in L dwarfs, and analysis of the full M5-T9 field dwarf spectroscopic sample |journal=Monthly Notices of the Royal Astronomical Society |volume=513 |issue=4 |pages=5701–5726 |doi=10.1093/mnras/stac1205 |doi-access=free |issn=0035-8711|arxiv=2205.00168 |bibcode=2022MNRAS.513.5701S }}</ref> Additionally, [[Mid-Infrared Instrument|MIRI]] has observed silicate absorption in the planetary-mass companion [[VHS J1256–1257|VHS 1256b]].<ref>{{cite journal |last1=Miles |first1=Brittany E. |last2=Biller |first2=Beth A. |last3=Patapis |first3=Polychronis |last4=Worthen |first4=Kadin |last5=Rickman |first5=Emily |last6=Hoch |first6=Kielan K. W. |last7=Skemer |first7=Andrew |last8=Perrin |first8=Marshall D. |last9=Whiteford |first9=Niall |last10=Chen |first10=Christine H. |last11=Sargent |first11=B. |last12=Mukherjee |first12=Sagnick |last13=Morley |first13=Caroline V. |last14=Moran |first14=Sarah E. |last15=Bonnefoy |first15=Mickael |date=2023-03-01 |title=The JWST Early-release Science Program for Direct Observations of Exoplanetary Systems II: A 1 to 20 μm Spectrum of the Planetary-mass Companion VHS 1256-1257 b |journal=The Astrophysical Journal |volume=946 |issue=1 |pages=L6 |doi=10.3847/2041-8213/acb04a |arxiv=2209.00620 |bibcode=2023ApJ...946L...6M |issn=0004-637X|doi-access=free }}</ref>

'''Iron rain''' as part of atmospheric convection processes is possible only in brown dwarfs, and not in small stars. The spectroscopy research into iron rain is still ongoing, but not all brown dwarfs will always have this atmospheric anomaly. In 2013, a heterogeneous iron-containing atmosphere was imaged around the B component in the nearby Luhman 16 system.<ref>{{cite journal |last1=Biller |first1=Beth A. |last2=Crossfield |first2=Ian J. M. |last3=Mancini |first3=Luigi |last4=Ciceri |first4=Simona |last5=Southworth |first5=John |last6=Kopytova |first6=Taisiya G. |last7=Bonnefoy |first7=Mickaël |last8=Deacon |first8=Niall R. |last9=Schlieder |first9=Joshua E. |last10=Buenzli |first10=Esther |last11=Brandner |first11=Wolfgang |last12=Allard |first12=France |last13=Homeier |first13=Derek |last14=Freytag |first14=Bernd |last15=Bailer-Jones |first15=Coryn A. L. |last16=Greiner |first16=Jochen |last17=Henning |first17=Thomas |last18=Goldman |first18=Bertrand |title=Weather on the Nearest Brown Dwarfs: Resolved Simultaneous Multi-Wavelength Variability Monitoring of WISE J104915.57–531906.1AB |journal=[[The Astrophysical Journal Letters]] |date=6 November 2013 |volume=778| issue=1 |pages=L10 |doi=10.1088/2041-8205/778/1/l10 |arxiv=1310.5144 |bibcode=2013ApJ...778L..10B |s2cid=56107487 }}</ref>

For late T-type brown dwarfs only a few variable searches were carried out. Thin cloud layers are predicted to form in late T-dwarfs from [[chromium]] and [[potassium chloride]], as well as several [[sulfide]]s. These sulfides are [[Manganese(II) sulfide|manganese sulfide]], [[sodium sulfide]] and [[zinc sulfide]].<ref>{{cite journal |last1=Morley |first1=Caroline V. |last2=Fortney |first2=Jonathan J. |last3=Marley |first3=Mark S. |last4=Visscher |first4=Channon |last5=Saumon |first5=Didier |last6=Leggett |first6=S. K. |date=2012-09-01 |title=Neglected Clouds in T and Y Dwarf Atmospheres |url=https://ui.adsabs.harvard.edu/abs/2012ApJ...756..172M |journal=The Astrophysical Journal |volume=756 |issue=2 |pages=172 |doi=10.1088/0004-637X/756/2/172 |issn=0004-637X|arxiv=1206.4313 |bibcode=2012ApJ...756..172M |s2cid=118398946 }}</ref> The variable T7 dwarf [[2M0050–3322]] is explained to have a top layer of potassium chloride clouds, a mid layer of sodium sulfide clouds and a lower layer of manganese sulfide clouds. Patchy clouds of the top two cloud layers could explain why the methane and water vapor bands are variable.<ref>{{cite journal |last1=Manjavacas |first1=Elena |last2=Karalidi |first2=Theodora |last3=Tan |first3=Xianyu |last4=Vos |first4=Johanna M. |last5=Lew |first5=Ben W. P. |last6=Biller |first6=Beth A. |last7=Oliveros-Gómez |first7=Natalia |date=2022-08-01 |title=Top-of-the-atmosphere and Vertical Cloud Structure of a Fast-rotating Late T Dwarf |journal=The Astronomical Journal |volume=164 |issue=2 |pages=65 |doi=10.3847/1538-3881/ac7953 |arxiv=2206.07566 |bibcode=2022AJ....164...65M |issn=0004-6256|doi-access=free }}</ref>

At the lowest temperatures of the Y-dwarf [[WISE 0855−0714|WISE 0855-0714]] patchy cloud layers of sulfide and [[Ice|water ice]] clouds could cover 50% of the surface.<ref>{{cite journal |last1=Faherty |first1=Jacqueline K. |last2=Tinney |first2=C. G. |last3=Skemer |first3=Andrew |last4=Monson |first4=Andrew J. |date=2014-09-01 |title=Indications of Water Clouds in the Coldest Known Brown Dwarf |url=https://ui.adsabs.harvard.edu/abs/2014ApJ...793L..16F |journal=The Astrophysical Journal |volume=793 |issue=1 |pages=L16 |doi=10.1088/2041-8205/793/1/L16 |issn=0004-637X|arxiv=1408.4671 |bibcode=2014ApJ...793L..16F |hdl=1959.4/unsworks_36908 |s2cid=119246100 }}</ref>

=== Low-mass brown dwarfs versus high-mass planets ===
[[File:Brown Dwarf HD 29587 B.png|thumb|right|An artistic concept of the brown dwarf around the star [[HD 29587]], a companion known as [[HD 29587 b]], estimated to be about 55 Jupiter masses]]

Like stars, brown dwarfs form independently, but, unlike stars, they lack sufficient mass to "ignite" hydrogen fusion. Like all stars, they can occur singly or in close proximity to other stars. Some orbit stars and can, like planets, have eccentric orbits.

==== Size and fuel-burning ambiguities ====
Brown dwarfs are all roughly the same radius as Jupiter. At the high end of their mass range ({{Jupiter mass|60–90}}), the volume of a brown dwarf is governed primarily by [[degenerate matter|electron-degeneracy]] pressure,<ref>{{cite journal |title=Planetesimals to Brown Dwarfs: What is a Planet? |date=2006-08-20 |pages=193–216 |first1=Gibor |last1=Basri |last2=Brown |first2=Michael E. |author-link2=Michael E. Brown |volume=34 |issue=2006 |doi=10.1146/annurev.earth.34.031405.125058 |journal=[[Annual Review of Earth and Planetary Sciences]] |arxiv=astro-ph/0608417 |bibcode=2006AREPS..34..193B|s2cid=119338327 }}</ref> as it is in white dwarfs; at the low end of the range ({{Jupiter mass|10}}), their volume is governed primarily by [[Coulomb barrier|Coulomb pressure]], as it is in planets. The net result is that the radii of brown dwarfs vary by only 10–15% over the range of possible masses. Moreover, the mass–radius relationship shows no change from about one Saturn mass to the onset of hydrogen burning ({{val|0.080|0.008|u=M_Solar}}), suggesting that from this perspective brown dwarfs are simply high-mass Jovian planets.<ref name="ChenKipping">{{cite journal |last1=Chen |first1=Jingjing |last2=Kipping |first2=David |date=2016 |title=Probabilistic Forecasting of the Masses and Radii of Other Worlds |journal=The Astrophysical Journal |volume=834 |issue=1 |page=17 |arxiv=1603.08614 |doi=10.3847/1538-4357/834/1/17 |s2cid=119114880 |doi-access=free |bibcode=2017ApJ...834...17C }}</ref> This can make distinguishing them from planets difficult.

In addition, many brown dwarfs undergo no fusion; even those at the high end of the mass range (over {{Jupiter mass|60}}) cool quickly enough that after 10&nbsp;million years they no longer undergo [[deuterium burning|fusion]].

==== Heat spectrum ====
X-ray and infrared spectra are telltale signs of brown dwarfs. Some emit [[X-ray]]s; and all "warm" dwarfs continue to glow tellingly in the red and [[infrared]] spectra until they cool to planet-like temperatures (under {{val|1000|u=K}}).

[[Gas giant]]s have some of the characteristics of brown dwarfs. Like the Sun, [[Jupiter]] and [[Saturn]] are both made primarily of hydrogen and helium. Saturn is nearly as large as Jupiter, despite having only 30% the mass. Three of the giant planets in the Solar System (Jupiter, Saturn, and [[Neptune]]<!-- Uranus emits only barely more heat than it receives from the Sun, per source -->) emit much more (up to about twice) heat than they receive from the Sun.<ref>{{cite web |url=http://astronomy.nmsu.edu/tharriso/ast105/UranusandNeptune.html |title=The Jovian Planets: Uranus, and Neptune |access-date=2013-03-15 |archive-url=https://web.archive.org/web/20120118184803/http://astronomy.nmsu.edu/tharriso/ast105/UranusandNeptune.html |archive-date=2012-01-18 |url-status=dead }}</ref><ref>{{cite web |url=http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/planets.html |title=Cool Cosmos – Planets and Moons |access-date=2019-02-11 |archive-date=2019-02-21 |archive-url=https://web.archive.org/web/20190221171452/http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/planets.html |url-status=dead }}</ref> All four giant planets have their own "planetary" systems, in the form of extensive moon systems.

==== Current IAU standard ====
Currently, the [[International Astronomical Union]] considers an object above {{Jupiter mass|13}} (the limiting mass for thermonuclear fusion of deuterium) to be a brown dwarf, whereas an object under that mass (and orbiting a star or stellar remnant) is considered a planet. The minimum mass required to trigger sustained hydrogen burning (about {{Jupiter mass|80}}) forms the upper limit of the definition.<ref>{{cite web |title=Working Group on Extrasolar Planets: Definition of a "Planet" |website=IAU position statement |date=2003-02-28 |url=http://home.dtm.ciw.edu/users/boss/definition.html |access-date=2014-04-28 |archive-url=https://web.archive.org/web/20141216075559/http://home.dtm.ciw.edu/users/boss/definition.html |archive-date=2014-12-16 |url-status=dead }}</ref>

It is also debated whether brown dwarfs would be better defined by their formation process rather than by theoretical mass limits based on nuclear fusion reactions.<ref name="PT-June2008">{{cite journal |last=Burgasser |first=Adam J. |date=June 2008 |title=Brown dwarfs: Failed stars, super Jupiters |url=http://astro.berkeley.edu/~gmarcy/astro160/papers/brown_dwarfs_failed_stars.pdf |url-status=dead |journal=[[Physics Today]] |location=Cambridge, MA |publisher=Massachusetts Institute of Technology |volume=61 |issue=6 |pages=70–71 |bibcode=2008PhT....61f..70B |doi=10.1063/1.2947658 |archive-url=https://web.archive.org/web/20130508182012/http://astro.berkeley.edu/~gmarcy/astro160/papers/brown_dwarfs_failed_stars.pdf |archive-date=May 8, 2013 |access-date=March 31, 2022 |via=American Institute of Physics}}</ref> Under this interpretation brown dwarfs are those objects that represent the lowest-mass products of the [[star formation]] process, while planets are objects formed in an [[accretion disk]] surrounding a star. The coolest free-floating objects discovered, such as [[WISE 0855]], as well as the lowest-mass young objects known, like [[PSO J318.5−22]], are thought to have masses below {{Jupiter mass|13}}, and as a result are sometimes referred to as [[planetary-mass object]]s due to the ambiguity of whether they should be regarded as [[rogue planets]] or brown dwarfs. There are planetary-mass objects known to orbit brown dwarfs, such as [[2M1207b]], [[2MASS J044144b]] and [[CFHTWIR-Oph 98 b|Oph 98 B]].

The 13-Jupiter-mass cutoff is a rule of thumb rather than a quantity with precise physical significance. Larger objects will burn most of their deuterium and smaller ones will burn only a little, and the 13{{Non breaking hyphen}}Jupiter-mass value is somewhere in between.<ref name=bodenheimer2013>{{cite journal |last1=Bodenheimer |first1=Peter |last2=D'Angelo |first2=Gennaro |last3=Lissauer |first3=Jack J. |author-link3=Jack J. Lissauer |last4=Fortney |first4=Jonathan J. |last5=Saumon |first5=Didier |title=Deuterium Burning in Massive Giant Planets and Low-mass Brown Dwarfs Formed by Core-nucleated Accretion |journal=The Astrophysical Journal |date=2013 |volume=770 |issue=2 |pages=120 (13 pp.) |doi=10.1088/0004-637X/770/2/120 |arxiv=1305.0980 |bibcode=2013ApJ...770..120B|s2cid=118553341 }}</ref> The amount of deuterium burnt also depends to some extent on the composition of the object, specifically on the amount of [[helium]] and [[deuterium]] present and on the fraction of heavier elements, which determines the atmospheric opacity and thus the radiative cooling rate.<ref name=Spiegel2011>{{cite journal |last1=Spiegel |first1=David S. |last2=Burrows |first2=Adam |last3=Milson |first3=John A. |title=The Deuterium-Burning Mass Limit for Brown Dwarfs and Giant Planets |journal=The Astrophysical Journal |volume=727 |issue=1 |page=57 |date=2011 |doi=10.1088/0004-637X/727/1/57 |arxiv=1008.5150 |bibcode=2011ApJ...727...57S|s2cid=118513110 }}</ref>

As of 2011 the [[Extrasolar Planets Encyclopaedia]] included objects up to 25 Jupiter masses, saying, "The fact that there is no special feature around {{Jupiter mass|13|jup=y}} in the observed mass spectrum reinforces the choice to forget this mass limit".<ref>{{cite journal |last1=Schneider |first1=Jean |last2=Dedieu |first2=Cyril |last3=Le Sidaner |first3=Pierre |last4=Savalle |first4=Renaud |last5=Zolotukhin |first5=Ivan |title=Defining and cataloging exoplanets: The exoplanet.eu database |date=2011 |volume=532 |issue=79 |journal=[[Astronomy & Astrophysics]] |arxiv=1106.0586 |doi=10.1051/0004-6361/201116713 |pages=A79 |bibcode=2011A&A...532A..79S |s2cid=55994657 }}</ref> As of 2016, this limit was increased to 60 Jupiter masses,<ref>{{cite book |last=Schneider |first=Jean |arxiv=1604.00917 |chapter=Exoplanets versus brown dwarfs: the CoRoT view and the future |title=The CoRoT Legacy Book |date=July 2016 |page=157 |doi=10.1051/978-2-7598-1876-1.c038 |isbn=978-2-7598-1876-1|s2cid=118434022 }}</ref> based on a study of mass–density relationships.<ref>{{cite journal |arxiv=1506.05097 |last1=Hatzes |first1=Artie P. |author-link1=Artie P. Hatzes |last2=Rauer |first2=Heike |author-link2=Heike Rauer |title=A Definition for Giant Planets Based on the Mass-Density Relationship |year=2015 |doi=10.1088/2041-8205/810/2/L25 |volume=810 |issue=2 |journal=The Astrophysical Journal |page=L25 |bibcode=2015ApJ...810L..25H |s2cid= 119111221 }}</ref>

The [[Exoplanet Data Explorer]] includes objects up to 24 Jupiter masses with the advisory: "The 13 Jupiter-mass distinction by the IAU Working Group is physically unmotivated for planets with rocky cores, and observationally problematic due to the [[Minimum mass|sin i ambiguity]]."<ref name="eod">{{cite journal |arxiv=1012.5676 |title=The Exoplanet Orbit Database |date=2010 |bibcode=2011PASP..123..412W |doi=10.1086/659427 |volume=123 |issue=902 |journal=[[Publications of the Astronomical Society of the Pacific]] |pages=412–422 |last1=Wright |first1=Jason T. |last2=Fakhouri |first2=Onsi |last3=Marcy |first3=Geoffrey W. |author-link3=Geoffrey Marcy |last4=Han |first4=Eunkyu |last5=Feng |first5=Y. Katherina |last6=Johnson |first6=John Asher |author-link6=John Johnson (astronomer) |last7=Howard |first7=Andrew W. |last8=Fischer |first8=Debra A. |author-link8=Debra Fischer |last9=Valenti |first9=Jeff A. |last10=Anderson |first10=Jay |last11=Piskunov |first11=Nikolai |s2cid=51769219 }}</ref> The [[NASA Exoplanet Archive]] includes objects with a mass (or minimum mass) equal to or less than 30 Jupiter masses.<ref>[http://exoplanetarchive.ipac.caltech.edu/docs/exoplanet_criteria.html Exoplanet Criteria for Inclusion in the Archive], NASA Exoplanet Archive</ref>

==== Sub-brown dwarf <span class="anchor" id="Sub-brown dwarf"></span> ====
{{Main|Sub-brown dwarf}}
[[File:Sol Cha-110913-773444 Jupiter.jpg|thumb|A size comparison between the [[Sun]], a young sub-brown dwarf, and [[Jupiter]]. As the sub-brown dwarf ages, it will gradually cool and shrink.]]

Objects below {{Jupiter mass|13}}, called '''sub-brown dwarfs''' or '''planetary-mass brown dwarfs''', form in the same manner as [[star]]s and brown dwarfs (i.e. through the collapse of a [[nebula|gas cloud]]) but have a [[Planetary-mass object|mass below the limiting mass for thermonuclear fusion]] of [[deuterium]].<ref>[http://www.dtm.ciw.edu/boss/definition.html Working Group on Extrasolar Planets – Definition of a "Planet"] {{webarchive|url=https://web.archive.org/web/20120702204018/http://www.dtm.ciw.edu/boss/definition.html |date=2012-07-02 }} Position statement on the definition of a "planet" (IAU)</ref>

Some researchers call them free-floating planets,<ref name="Delorme2012">{{cite journal |last1=Delorme |first1=Philippe |first2=Jonathan |last2=Gagné |first3=Lison |last3=Malo |first4=Céline |last4=Reylé |first5=Étienne |last5=Artigau |first6=Loïc |last6=Albert |first7=Thierry |last7=Forveille |first8=Xavier |last8=Delfosse |first9=France |last9=Allard |first10=Derek |last10=Homeier |title=CFBDSIR2149-0403: a 4–7 Jupiter-mass free-floating planet in the young moving group AB Doradus? |journal=Astronomy & Astrophysics |date=December 2012 |arxiv=1210.0305 |doi=10.1051/0004-6361/201219984 |bibcode=2012A&A...548A..26D |volume=548 |page=A26|s2cid=50935950 }}</ref> whereas others call them planetary-mass brown dwarfs.<ref name="Luhman20140421">{{cite journal |title=Discovery of a ~250 K Brown Dwarf at 2 pc from the Sun |journal=[[The Astrophysical Journal Letters]] |first=Kevin L. |last=Luhman |author-link=Kevin Luhman |volume=786 |issue=2 |page=L18 |date=21 April 2014 |doi=10.1088/2041-8205/786/2/L18 |arxiv=1404.6501 |bibcode=2014ApJ...786L..18L|s2cid=119102654 }}</ref>

=== Role of other physical properties in the mass estimate ===
While spectroscopic features can help to distinguish between [[Red dwarf|low-mass stars]] and brown dwarfs, it is often necessary to estimate the mass to come to a conclusion. The theory behind the mass estimate is that brown dwarfs with a similar mass form in a similar way and are hot when they form. Some have spectral types that are similar to low-mass stars, such as [[2M1101AB]]. As they cool down the brown dwarfs should retain a range of [[Luminosity|luminosities]] depending on the mass.<ref>{{cite journal |last1=Saumon |first1=Didier |last2=Marley |first2=Mark S. |date=December 2008 |title=The Evolution of L and T Dwarfs in Color-Magnitude Diagrams |journal=Astrophysical Journal |volume=689 |issue=2 |pages=1327–1344 |doi=10.1086/592734 |arxiv=0808.2611 |bibcode=2008ApJ...689.1327S |s2cid=15981010 |issn=0004-637X }}</ref><!-- See Figure 2 for example --> Without the age and luminosity, a mass estimate is difficult; for example, an L-type brown dwarf could be an old brown dwarf with a high mass (possibly a low-mass star) or a young brown dwarf with a very low mass. For Y dwarfs this is less of a problem, as they remain low-mass objects near the [[sub-brown dwarf]] limit, even for relatively high age estimates.<ref name=":2">{{cite journal |last1=Marocco |first1=Federico |last2=Kirkpatrick |first2=J. Davy |last3=Meisner |first3=Aaron M. |last4=Caselden |first4=Dan |last5=Eisenhardt |first5=Peter R. M. |last6=Cushing |first6=Michael C. |last7=Faherty |first7=Jacqueline K. |last8=Gelino |first8=Christopher R. |last9=Wright |first9=Edward L. |year=2020 |title=Improved infrared photometry and a preliminary parallax measurement for the extremely cold brown dwarf CWISEP J144606.62-231717.8 |journal=The Astrophysical Journal |volume=888 |issue=2 |pages=L19 |arxiv=1912.07692 |bibcode=2020ApJ...888L..19M |doi=10.3847/2041-8213/ab6201 |s2cid=209386563 |doi-access=free}}</ref> For L and T dwarfs it is still useful to have an accurate age estimate. The luminosity is here the less concerning property, as this can be estimated from the [[spectral energy distribution]].<ref>{{cite journal |last1=Filippazzo |first1=Joseph C. |last2=Rice |first2=Emily L. |last3=Faherty |first3=Jacqueline K.|author3-link=Jackie Faherty |last4=Cruz |first4=Kelle L. |last5=Van Gordon |first5=Mollie M. |last6=Looper |first6=Dagny L. |date=September 2015 |title=Fundamental Parameters and Spectral Energy Distributions of Young and Field Age Objects with Masses Spanning the Stellar to Planetary Regime |journal=Astrophysical Journal |volume=810 |issue=2 |pages=158 |doi=10.1088/0004-637X/810/2/158 |arxiv=1508.01767 |bibcode=2015ApJ...810..158F |s2cid=89611607 |issn=0004-637X }}</ref> The age estimate can be done in two ways. Either the brown dwarf is young and still has spectral features that are associated with youth, or the brown dwarf co-moves with a star or stellar group ([[star cluster]] or [[Stellar association|association]]), where age estimates are easier to obtain. A very young brown dwarf that was further studied with this method is [[2M1207]] and the companion [[2M1207b]]. Based on the location, [[proper motion]] and spectral signature, this object was determined to belong to the ~8-million-year-old [[TW Hydrae association]], and the mass of the secondary was determined to be 8 ± 2 {{Jupiter mass|link=true}}, below the [[deuterium]] burning limit.<ref>{{cite journal |last1=Mohanty |first1=Subhanjoy |last2=Jayawardhana |first2=Ray |last3=Huélamo |first3=Nuria |last4=Mamajek |first4=Eric |date=March 2007 |title=The Planetary Mass Companion 2MASS 1207-3932B: Temperature, Mass, and Evidence for an Edge-on Disk |journal=Astrophysical Journal |volume=657 |issue=2 |pages=1064–1091 |doi=10.1086/510877 |arxiv=astro-ph/0610550 |bibcode=2007ApJ...657.1064M |s2cid=17326111 |issn=0004-637X }}</ref> An example of a very old age obtained by the co-movement method is the brown dwarf + [[white dwarf]] binary COCONUTS-1, with the white dwarf estimated to be {{Val|7.3|2.8|1.6}} [[billion years]] old. In this case the mass was not estimated with the derived age, but the co-movement provided an accurate distance estimate, using [[Gaia (spacecraft)|Gaia]] [[parallax]]. Using this measurement the authors estimated the radius, which was then used to estimate the mass for the brown dwarf as {{Val|15.4|0.9|0.8}} {{Jupiter mass}}.<ref name=":3">{{cite journal |last1=Zhang |first1=Zhoujian |last2=Liu |first2=Michael C. |last3=Hermes |first3=James J. <!-- https://www.bu.edu/cas/ar/2018/7/ a.k.a. "Jota Jota" (https://jjhermes.es), full name James Joseph Hermes Jr. https://repositories.lib.utexas.edu/bitstream/handle/2152/21608/HERMES-DISSERTATION-2013.pdf -->|last4=Magnier |first4=Eugene A. |last5=Marley |first5=Mark S. |last6=Tremblay |first6=Pier-Emmanuel |last7=Tucker |first7=Michael A. |last8=Do |first8=Aaron |last9=Payne |first9=Anna V. |last10=Shappee |first10=Benjamin J. |date=February 2020 |title=COol Companions ON Ultrawide orbiTS (COCONUTS). I. A High-Gravity T4 Benchmark around an Old White Dwarf and A Re-Examination of the Surface-Gravity Dependence of the L/T Transition |journal=The Astrophysical Journal |volume=891 |issue=2 |page=171 |doi=10.3847/1538-4357/ab765c |arxiv=2002.05723 |bibcode=2020ApJ...891..171Z |s2cid=211126544 |doi-access=free }}</ref>