View source for Eddington luminosity

{{short description|Maximum luminosity of a body in hydrostatic equilibrium}}
The '''Eddington luminosity''', also referred to as the '''Eddington limit''', is the maximum [[luminosity]] a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called [[hydrostatic equilibrium]]. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven [[stellar wind]] from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are driven mostly by the less intense [[absorption line|line absorption]]{{Definition needed|What does it mean for a stellar wind to be "driven by line absorption"?|date=May 2024}}.<ref>{{cite journal |bibcode=2008AIPC..990..250V |title=Continuum driven winds from super-Eddington stars. A tale of two limits |author=A. J. van Marle |author2=S. P. Owocki |author3=N. J. Shaviv  |date=2008 |journal=AIP Conference Proceedings |volume=990 |pages=250–253 |doi=10.1063/1.2905555|arxiv = 0708.4207 |s2cid=118364586 }}</ref> The Eddington limit is invoked to explain the observed luminosities of accreting [[black hole]]s such as [[quasar]]s.

Originally, Sir [[Arthur Eddington]] took only the [[electron scattering]] into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also takes into account other radiation processes such as [[Bremsstrahlung|bound–free and free–free radiation]] interaction.

==Derivation==
The Eddington limit is obtained by setting the outward [[radiation pressure]] equal to the inward gravitational force. Both forces decrease by [[inverse-square law]]s, so once equality is reached, the hydrodynamic flow is the same throughout the star.

From [[Euler equations (fluid dynamics)|Euler's equation]] in [[hydrostatic equilibrium]], the mean acceleration is zero,

<math display="block">
\frac{d u}{d t}  = - \frac{\nabla p}{\rho} - \nabla \Phi = 0 
</math>

where <math>u</math> is the velocity, <math>p</math> is the pressure, <math>\rho</math> is the density, and <math>\Phi</math> is the [[gravitational potential]]. If the pressure is dominated by radiation pressure associated with an irradiance <math>F_{\rm rad}</math>,

<math display="block">
-\frac{\nabla p}{\rho} = \frac{\kappa}{c} F_{\rm rad}\,.
</math>

Here <math>\kappa</math> is the [[Opacity (optics)|opacity]] of the stellar material, defined as the fraction of radiation energy [[flux]] absorbed by the medium per unit density and unit length. For [[Hydrogen ion|ionized hydrogen]], <math>\kappa=\sigma_{\rm T}/m_{\rm p} </math>, where <math>\sigma_{\rm T}</math> is the [[Thomson scattering]] cross-section for the [[electron]] and <math>m_{\rm p}</math> is the mass of a [[proton]]. Note that <math>F_{\rm rad}=d^2E/dAdt</math> is defined as the energy flux over a surface, which can be expressed with the momentum flux using <math>E=pc</math> for radiation. Therefore, the rate of momentum transfer from the radiation to the gaseous medium per unit density is <math>\kappa F_{\rm rad}/c</math>, which explains the right-hand side of the above equation.

The luminosity of a source bounded by a surface <math>S</math> may be expressed with these relations as

<math display="block"> 
L = \int_S F_{\rm rad} \cdot dS = \int_S \frac{c}{\kappa} \nabla \Phi \cdot dS\,. 
</math>

Now assuming that the opacity is a constant, it can be brought outside the integral. Using [[Divergence theorem|Gauss's theorem]] and [[Poisson's equation]] gives

<math display="block"> 
L = \frac{c}{\kappa} \int_S \nabla \Phi \cdot dS = \frac{c}{\kappa} \int_V \nabla^2 \Phi \, dV = \frac{4 \pi G  c}{\kappa} \int_V \rho \, dV  = \frac{4 \pi G M  c}{\kappa}  
</math>

where <math>M</math> is the mass of the central object. This result is called the Eddington luminosity.<ref>Rybicki, G. B.; Lightman, A. P. ''Radiative Processes in Astrophysics''. New York: J. Wiley & Sons 1979.</ref> For pure ionized hydrogen,

<math display="block">\begin{align}L_{\rm Edd}&=\frac{4\pi G M m_{\rm p} c} {\sigma_{\rm T}}\\
&\cong 1.26\times10^{31}\left(\frac{M}{M_\bigodot}\right){\rm W}
= 1.26\times10^{38}\left(\frac{M}{M_\bigodot}\right){\rm erg/s}
= 3.2\times10^4\left(\frac{M}{M_\bigodot}\right) L_\bigodot 
\end{align}
</math>

where <math>M_\bigodot</math> is the mass of the Sun and <math>L_\bigodot</math> is the luminosity of the Sun.

The maximum possible luminosity of a source in hydrostatic equilibrium is the Eddington luminosity. If the luminosity exceeds the Eddington limit, then the radiation pressure drives an outflow.

The mass of the proton appears because, in the typical environment for the outer layers of a star, the radiation pressure acts on electrons, which are driven away from the center. Because protons are negligibly pressured by the analog of Thomson scattering, due to their larger mass, the result is to create a slight charge separation and therefore a radially directed [[electric field]], acting to lift the positive charges, which, under the conditions in stellar atmospheres, typically are free protons. When the outward electric field is sufficient to levitate the protons against gravity, both electrons and protons are expelled together.

===Different limits for different materials===
The derivation above for the outward light pressure assumes a [[hydrogen]] [[Plasma (physics)|plasma]]. In other circumstances the pressure balance can be different from what it is for hydrogen.

In an evolved star with a pure [[helium]] atmosphere, the electric field would have to lift a helium nucleus (an [[alpha particle]]), with nearly 4&nbsp;times the mass of a proton, while the radiation pressure would act on 2&nbsp;free electrons. Thus twice the usual Eddington luminosity would be needed to drive off an atmosphere of pure helium.

At very high temperatures, as in the environment of a [[black hole]] or [[neutron star]], high-energy photons can interact with nuclei, or even with other photons, to create an electron–[[positron]] plasma. In that situation the combined mass of the positive–negative charge carrier pair is approximately 918&nbsp;times smaller (half of the proton-to-electron mass ratio), while the radiation pressure on the positrons doubles the effective upward force per unit mass, so the limiting luminosity needed is reduced by a factor of ≈&nbsp;918×2.

The exact value of the Eddington luminosity depends on the chemical composition of the gas layer and the spectral energy distribution of the emission. A gas with [[Abundance of the chemical elements#Universe|cosmological abundances]] of hydrogen and helium is much more transparent than gas with [[Abundances of the elements (data page)#Sun and solar system|solar abundance ratios]]. [[Spectroscopy|Atomic line]] transitions can greatly increase the effects of radiation pressure, and line-driven winds exist in some bright stars (e.g., [[Wolf–Rayet star|Wolf–Rayet]] and [[O-type star]]s).

==Super-Eddington luminosities==

The role of the Eddington limit in today's research lies in explaining the very high mass loss rates seen in, for example, the series of outbursts of [[Eta Carinae|η&nbsp;Carinae]] in 1840–1860.<ref>{{cite journal |first1=N. |last1=Smith |first2=S.P. |last2=Owocki |year=2006 |title=On the role of continuum driven eruptions in the evolution of very massive stars and population&nbsp;III stars |journal=[[Astrophysical Journal]] |volume=645 |issue=1 |pages=L45–L48 |doi=10.1086/506523 |arxiv = astro-ph/0606174 |s2cid=15424181 |bibcode=2006ApJ...645L..45S }}</ref> The regular, line-driven stellar winds can only explain a mass loss rate of around {{10^|−4}}~{{10^|−3}} solar masses per year, whereas losses of up to {{nobr|{{small|{{sfrac| 1 | 2 }}}} solar mass}} per year are needed to understand the η&nbsp;Carinae outbursts. This can be done with the help of the super-Eddington winds driven by broad-spectrum radiation.

[[Gamma-ray burst]]s, [[nova]]e and [[supernova]]e are examples of systems exceeding their Eddington luminosity by a large factor for very short times, resulting in short and highly intensive mass loss rates. Some [[X-ray binaries]] and [[active galactic nucleus|active galaxies]] are able to maintain luminosities close to the Eddington limit for very long times. For accretion-powered sources such as accreting [[neutron star]]s or [[cataclysmic variable]]s (accreting [[white dwarf]]s), the limit may act to reduce or cut off the accretion flow, imposing an Eddington limit on accretion corresponding to that on luminosity. Super-Eddington accretion onto stellar-mass black holes is one possible model for [[ultraluminous X-ray source]]s (ULXSs).<ref>{{cite journal |last1=Bachetti |first1=Matteo |last2=Heida |first2=Marianne |last3=Maccarone |first3=Thomas |last4=Huppenkothen |first4=Daniela |last5=Israel |first5=Gian Luca |last6=Barret |first6=Didier |last7=Brightman |first7=Murray |last8=Brumback |first8=McKinley |last9=Earnshaw |first9=Hannah P. |last10=Forster |first10=Karl |last11=Fürst |first11=Felix |last12=Grefenstette |first12=Brian W. |last13=Harrison |first13=Fiona A. |last14=Jaodand |first14=Amruta D. |last15=Madsen |first15=Kristin K. |display-authors=6 |date=2022-10-01 |df=dmy-all |title=Orbital decay in {{nobr|M82 X-2}} |journal=[[The Astrophysical Journal]] |volume=937 |issue=2 |page=125 |doi=10.3847/1538-4357/ac8d67 |doi-access=free |issn=0004-637X |hdl=2299/25784 |hdl-access=free |arxiv=2112.00339 |bibcode=2022ApJ...937..125B }}</ref><ref>{{cite press release |title=NASA study helps explain limit-breaking ultra-luminous X-ray sources |date=6 April 2023 |publisher=[[NASA]] / [[Jet Propulsion Laboratory]] (JPL) |url=https://www.jpl.nasa.gov/news/nasa-study-helps-explain-limit-breaking-ultra-luminous-x-ray-sources |access-date=2023-04-18 |lang=en-US}}</ref>

For accreting [[black hole]]s, not all the energy released by accretion has to appear as outgoing luminosity, since energy can be lost through the [[event horizon]], down the hole. Such sources effectively may not conserve energy. Then the accretion efficiency, or the fraction of energy actually radiated of that theoretically available from the gravitational energy release of accreting material, enters in an essential way.

== Other factors ==
The Eddington limit is not a strict limit on the luminosity of a stellar object. The limit does not consider several potentially important factors, and super-Eddington objects have been observed that do not seem to have the predicted high mass-loss rate. Other factors that might affect the maximum luminosity of a star include:

*'''Porosity'''. A problem with steady winds driven by broad-spectrum radiation is that both the radiative flux and gravitational acceleration scale with ''r''<sup>−2</sup>. The ratio between these factors is constant, and in a super-Eddington star, the whole envelope would become gravitationally unbound at the same time. This is not observed. A possible solution is introducing an atmospheric porosity, where we imagine the stellar atmosphere to consist of denser regions surrounded by regions of lower-density gas. This would reduce the coupling between radiation and matter, and the full force of the radiation field would be seen only in the more homogeneous outer, lower-density layers of the atmosphere.
*'''Turbulence'''. A possible destabilizing factor might be the turbulent pressure arising when energy in the [[convection zone]]s builds up a field of supersonic turbulence. The importance of turbulence is being debated, however.<ref>{{cite journal |bibcode=2003ApJ...589..960S |title=Turbulent pressure in the envelopes of yellow hypergiants and luminous blue variables |author=R. B. Stothers |date=2003 |journal=Astrophysical Journal |volume=589 |issue=2 |pages=960–967 |doi=10.1086/374713|doi-access=free }}</ref>
*'''Photon bubbles'''. Another factor that might explain some stable super-Eddington objects is the [[photon bubble]] effect. Photon bubbles would develop spontaneously in radiation-dominated atmospheres when the radiation pressure exceeds the gas pressure. We can imagine a region in the stellar atmosphere with a density lower than the surroundings, but with a higher radiation pressure. Such a region would rise through the atmosphere, with radiation diffusing in from the sides, leading to an even higher radiation pressure. This effect could transport radiation more efficiently than a homogeneous atmosphere, increasing the allowed total radiation rate. [[Accretion disc]]s may exhibit luminosities as high as 10–100 times the Eddington limit without experiencing instabilities.<ref>{{cite journal |bibcode=1992ApJ...388..561A |title=Photon bubbles: Overstability in a magnetized atmosphere |author= J. Arons |date=1992 |journal=Astrophysical Journal |volume=388 |pages=561–578 |doi=10.1086/171174}}</ref>

==Humphreys–Davidson limit==
[[File:Lbvstar.png|thumb|right|350px|upright=1.2| The upper [[H–R diagram]] with the empirical Humphreys-Davidson limit marked (green line). Stars are observed above the limit only during brief outbursts.]]

Observations of massive stars show a clear upper limit to their luminosity, termed the Humphreys–Davidson limit after the researchers who first wrote about it.<ref>
{{cite journal
 |last1 = Humphreys |first1 = R.M.  |author1-link = Roberta M. Humphreys
 |last2 = Davidson  |first2 = K.
 |year = 1979
 |title = Studies of luminous stars in nearby galaxies. III - Comments on the evolution of the most massive stars in the Milky Way and the Large Magellanic Cloud
 |journal = [[The Astrophysical Journal]]
 |volume = 232 |page = 409
 |doi = 10.1086/157301 |issn = 0004-637X
 |bibcode = 1979ApJ...232..409H |lang = en
}}
</ref>
Only highly unstable objects are found, temporarily, at higher luminosities.  Efforts to reconcile this with the theoretical Eddington limit have been largely unsuccessful.<ref name=glatzel>
{{cite journal
 |last1 = Glatzel    |first1 = W.
 |last2 = Kiriakidis |first2 = M.
 |date = 15 July 1993
 |title = Stability of massive stars and the Humphreys–Davidson limit
 |journal = [[Monthly Notices of the Royal Astronomical Society]]
 |volume = 263  |issue = 2  |pages = 375–384
 |doi = 10.1093/mnras/263.2.375  |doi-access = free
 |bibcode = 1993MNRAS.263..375G
 |url = https://academic.oup.com/mnras/article-pdf/263/2/375/18539248/mnras263-0375.pdf
}}
</ref>

The H–D limit for cool [[Supergiant|supergiants]] is placed at around 320,000 {{Solar luminosity}}.<ref name=Davies-Beasor-2020>
{{Cite journal
 |last1 = Davies |first1 = Ben
 |last2 = Beasor |first2 = Emma R.
 |date = 2020-03-21
 |title = The 'red supergiant problem': The upper luminosity boundary of type&nbsp;II supernova progenitors
 |journal = [[Monthly Notices of the Royal Astronomical Society]]
 |volume = 493  |issue = 1  |pages = 468–476
 |doi = 10.1093/mnras/staa174  |doi-access = free
 |arxiv = 2001.06020  |bibcode = 2020MNRAS.493..468D
 |issn = 0035-8711  |lang = en
 |url = https://academic.oup.com/mnras/article/493/1/468/5709941
}}
</ref>

{{clear}}

{| class="wikitable sortable"
|+ Most luminous known K- and M-type supergiants
! Name
! Luminosity<br />({{Solar luminosity}})
!Effective temperature<br />([[Kelvin|K]])
! [[Spectral type]]
!class=unsortable|Notes
!class=unsortable|References
|-
|NGC1313-310
|513,000
|3,780
|K5-M0
|
|<ref name=":1">{{Cite journal |last1=Wit |first1=S. de |last2=Bonanos |first2=A. Z. |last3=Antoniadis |first3=K. |last4=Zapartas |first4=E. |last5=Ruiz |first5=A. |last6=Britavskiy |first6=N. |last7=Christodoulou |first7=E. |last8=De |first8=K. |last9=Maravelias |first9=G. |last10=Munoz-Sanchez |first10=G. |last11=Tsopela |first11=A. |date=2024-09-01 |title=Investigating episodic mass loss in evolved massive stars - II. Physical properties of red supergiants at subsolar metallicity |url=https://www.aanda.org/articles/aa/full_html/2024/09/aa49607-24/aa49607-24.html |journal=Astronomy & Astrophysics |language=en |volume=689 |pages=A46 |doi=10.1051/0004-6361/202449607 |arxiv=2402.12442 |bibcode=2024A&A...689A..46D |issn=0004-6361}}</ref>
|-
|NGC253-222
|501,000
|3,750
|M0-M2
|Uncertain extinction and thus uncertain luminosity.
|<ref name=":1" />
|-
| LGGS J013339.28+303118.8
| 479,000
|3,837
| M1Ia
|
| <ref name=Drout-Massey-Meynet-2012/>
|-
| [[Stephenson 2 DFK 49]]
| 390,000
|4,000
| K4
|Another paper estimate a much lower luminosity ({{solar luminosity|245,000}})<ref name=davies2007>{{Cite journal |last1=Davies |first1=Ben |last2=Figer |first2=Don F. |last3=Kudritzki |first3=Rolf-Peter |last4=MacKenty |first4=John |last5=Najarro |first5=Francisco |last6=Herrero |first6=Artemio |date=2007-12-01 |title=A Massive Cluster of Red Supergiants at the Base of the Scutum-Crux Arm |url=https://ui.adsabs.harvard.edu/abs/2007ApJ...671..781D |journal=The Astrophysical Journal |volume=671 |issue=1 |pages=781–801 |doi=10.1086/522224 |arxiv=0708.0821 |bibcode=2007ApJ...671..781D |issn=0004-637X}}</ref>
| <ref name=Humphreys-Helmel-etal-2020>
 {{Cite journal
 |last1 = Humphreys |first1 = Roberta M.    |last2 = Helmel |first2 = Greta
 |last3 = Jones     |first3 = Terry J.      |last4 = Gordon |first4 = Michael S.
 |date = 2020-09-02
 |title = Exploring the mass-loss histories of the red supergiants
 |journal = [[The Astronomical Journal]]
 |volume = 160  |issue = 3  |page = 145
 |issn = 1538-3881  |arxiv = 2008.01108
 |doi = 10.3847/1538-3881/abab15  |doi-access = free
|bibcode = 2020AJ....160..145H }}
</ref>
|-
| HD 269551 A
|389,000
|3,800
|K/M
|
| <ref name=Massey-Neugent-etal-2023>
{{Cite journal
 |last1=Massey  |first1=Philip    |last2=Neugent |first2=Kathryn F.
 |last3=Ekström |first3=Sylvia    |last4=Georgy  |first4=Cyril
 |last5=Meynet  |first5=Georges
 |date=2023-01-01
 |title=The time-averaged mass-loss rates of red supergiants as revealed by their luminosity functions in M31 and M33
 |journal = [[The Astrophysical Journal]]
 |volume = 942  |issue = 2  |page = 69
 |arxiv=2211.14147  |issn=0004-637X
 |doi=10.3847/1538-4357/aca665 |doi-access=free
|bibcode=2023ApJ...942...69M }}
</ref>
|-
|NGC7793-34
|380,000
|3,840
|M0-M2
|
|<ref name=":1" />
|-
| LGGS J013418.56+303808.6
| 363,000
|3,837
|
|
| <ref name=Drout-Massey-Meynet-2012>
{{cite journal
 |last1=Drout  |first1=Maria R.
 |last2=Massey |first2=Philip
 |last3=Meynet |first3=Georges
 |date=2012-04-18
 |title=The yellow and red supergiants of M33
 |journal = [[The Astrophysical Journal]]
 |volume=750 |issue=2 |page = 97
 |issn=0004-637X |arxiv=1203.0247
 |doi=10.1088/0004-637x/750/2/97 |doi-access=free
 |bibcode=2012ApJ...750...97D
 }}
</ref>
|-
| LGGS J004428.12+415502.9
| 339,000
|–
| K2I
|
|<ref name=McDonald-Davies-Beasor-2022>
{{cite journal
 |last1 = McDonald  |first1 = Sarah L.E.
 |last2 = Davies    |first2 = Ben
 |last3 = Beasor    |first3 = Emma R.
 |date = 2022-01-08
 |title = Red supergiants in M31: the Humphreys–Davidson limit at high metallicity
 |journal = [[Monthly Notices of the Royal Astronomical Society]]
 |volume = 510  |issue = 3  |pages = 3132–3144
 |doi = 10.1093/mnras/stab3453  |doi-access = free
 |lang = en
 |issn = 0035-8711 |arxiv = 2111.13716
 |url = https://academic.oup.com/mnras/article/510/3/3132/6445032
}}
</ref>
|-
|NGC247-154
|332,000
|3,570
|M2-M4
|
|<ref name=":1" />
|-
| [[AH Scorpii]]
| 331,000
|3,682
| M5Ia
|
| <ref>
{{cite journal
 |last1 = Arroyo-Torres |first1 = B.         |last2 = Wittkowski  |first2 = M.
 |last3 = Marcaide      |first3 = J.M.       |last4 = Hauschildt  |first4 = P.H.
 |date = June 2013
 |title = The atmospheric structure and fundamental parameters of the red supergiants AH&nbsp;Scorpii, UY&nbsp;Scuti, and KW&nbsp;Sagittarii
 |journal = [[Astronomy & Astrophysics]]
 |volume = 554 |page = A76
 |arxiv = 1305.6179  |issn = 0004-6361
 |doi = 10.1051/0004-6361/201220920 |doi-access = free
 |bibcode = 2013A&A...554A..76A }}
</ref>
|-
|WLM 02
|331,000
|4,660
|K2-3I
|
|<ref>{{Cite journal |url=https://academic.oup.com/mnras/article/505/3/4422/6294474 |access-date=2024-09-12 |journal=Monthly Notices of the Royal Astronomical Society |doi=10.1093/mnras/stab1611|doi-access=free |title=The temperatures of red supergiants in low-metallicity environments |date=2021 |last1=González-Torà |first1=Gemma |last2=Davies |first2=Ben |last3=Kudritzki |first3=Rolf-Peter |last4=Plez |first4=Bertrand |volume=505 |issue=3 |pages=4422–4443 |arxiv=2106.01807 }}</ref>
|-
| SMC 18592
| 309,000<ref name="Davies-Crowther-Beasor-2018">
{{Cite journal |last1=Davies |first1=Ben |last2=Crowther |first2=Paul A. |last3=Beasor |first3=Emma R. |date=2018-08-01 |title=The luminosities of cool supergiants in the Magellanic Clouds, and the Humphreys-Davidson limit revisited |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=478 |issue=3 |pages=3138–3148 |arxiv=1804.06417 |bibcode=2018MNRAS.478.3138D |doi=10.1093/mnras/sty1302 |doi-access=free |issn=0035-8711}}
</ref> - 355,000<ref name="Massey-Neugent-etal-2023" />
|4,050<ref name="Massey-Neugent-etal-2023" />
| K5–M0Ia
|
|
|-
| LGGS J004539.99+415404.1
| 309,000
|–
| M3I
|
| <ref name=McDonald-Davies-Beasor-2022/>
|-
| LGGS J013350.62+303230.3
| 309,000
|3,800
|
|
| <ref name=Massey-Neugent-etal-2023/>
|-
| HV 888
| 302,000
|3,442<ref>{{Cite journal |last1=Ren |first1=Yi |last2=Jiang |first2=Bi-Wei |date=2020-07-01 |title=On the Granulation and Irregular Variation of Red Supergiants |journal=The Astrophysical Journal |volume=898 |issue=1 |pages=24 |doi=10.3847/1538-4357/ab9c17 |doi-access=free |arxiv=2006.06605 |bibcode=2020ApJ...898...24R |issn=0004-637X}}</ref>–3,500<ref>{{Cite journal |last1=Groenewegen |first1=M. A. T. |last2=Sloan |first2=G. C. |date=2018-01-01 |title=Luminosities and mass-loss rates of Local Group AGB stars and red supergiants |url=https://ui.adsabs.harvard.edu/abs/2018A&A...609A.114G |journal=Astronomy and Astrophysics |volume=609 |pages=A114 |doi=10.1051/0004-6361/201731089 |arxiv=1711.07803 |bibcode=2018A&A...609A.114G |issn=0004-6361}}</ref><ref>{{Cite journal |last1=Kamath |first1=D. |last2=Wood |first2=P. R. |last3=Van Winckel |first3=H. |date=2015-12-01 |title=Optically visible post-AGB stars, post-RGB stars and young stellar objects in the Large Magellanic Cloud |journal=Monthly Notices of the Royal Astronomical Society |volume=454 |issue=2 |pages=1468–1502 |doi=10.1093/mnras/stv1202 |doi-access=free |arxiv=1508.00670 |bibcode=2015MNRAS.454.1468K |issn=0035-8711}}</ref>
| M4Ia
|
| <ref name="Davies-Crowther-Beasor-2018" />
|-
| [[RW Cephei]]
| 300,000
|4,400
| K2Ia-0
|A K-type yellow hypergiant.
| <ref>
{{cite journal
 |last1 = Jones     |first1 = Terry Jay
 |last2 = Shenoy    |first2 = Dinesh
 |last3 = Humphreys |first3 = Roberta
 |date = 2023-05-11
 |title = The recent mass-loss history of the hypergiant RW&nbsp;Cep
 |journal = [[Research Notes of the American Astronomical Society]]
 |volume = 7  |issue = 5  |page = 92
 |issn = 2515-5172
 |doi = 10.3847/2515-5172/acd37f  |doi-access = free
|bibcode = 2023RNAAS...7...92J
 }}
</ref>
|-
| LGGS J013358.54+303419.9
| 295,000
|4,050
|
|
| <ref name=Massey-Neugent-etal-2023/>
|-
| [[GCIRS 7]]
| 295,000
|3,600<ref>{{Cite journal |last1=Paumard |first1=T. |last2=Pfuhl |first2=O. |last3=Martins |first3=F. |last4=Kervella |first4=P. |last5=Ott |first5=T. |last6=Pott |first6=J. -U. |last7=Le Bouquin |first7=J. B. |last8=Breitfelder |first8=J. |last9=Gillessen |first9=S. |last10=Perrin |first10=G. |last11=Burtscher |first11=L. |last12=Haubois |first12=X. |last13=Brandner |first13=W. |date=2014-08-01 |title=GCIRS 7, a pulsating M1 supergiant at the Galactic centre . Physical properties and age |url=https://ui.adsabs.harvard.edu/abs/2014A&A...568A..85P |journal=Astronomy and Astrophysics |volume=568 |pages=A85 |doi=10.1051/0004-6361/201423991 |arxiv=1406.5320 |bibcode=2014A&A...568A..85P |issn=0004-6361}}</ref>
| M1I
|
| <ref>
{{cite journal
 |last1=Guerço   |first1=Rafael         |last2=Smith     |first2=Verne V.
 |last3=Cunha    |first3=Katia          |last4=Ekström   |first4=Sylvia
 |last5=Abia     |first5=Carlos         |last6=Plez      |first6=Bertrand
 |last7=Meynet   |first7=Georges        |last8=Ramirez   |first8=Solange V.
 |last9=Prantzos |first9=Nikos          |last10=Sellgren |first10=Kris
 |last11=Hayes   |first11=Cristian R.   |last12=Majewski |first12=Steven R.
 |date=2022-09-13
 |title=Evidence of deep mixing in IRS&nbsp;7, a cool massive supergiant member of the Galactic nuclear star cluster
 |journal = [[Monthly Notices of the Royal Astronomical Society]]
 |volume=516  |issue=2  |pages=2801–2811
 |doi=10.1093/mnras/stac2393
 |doi-access=free |issn=0035-8711  |arxiv=2208.10529  |lang=en
 |url=https://academic.oup.com/mnras/article/516/2/2801/6675813
}}
</ref>
|-
| SP77 21-12
| 295,000
|4,050
| K5-M3
|
| <ref name=Massey-Neugent-etal-2023/>
|-
| [[EV Carinae]]
| 288,000
|3,574<ref>{{Cite journal |last1=van Loon |first1=J. Th. |last2=Cioni |first2=M. -R. L. |last3=Zijlstra |first3=A. A. |last4=Loup |first4=C. |date=2005-07-01 |title=An empirical formula for the mass-loss rates of dust-enshrouded red supergiants and oxygen-rich Asymptotic Giant Branch stars |url=https://ui.adsabs.harvard.edu/abs/2005A&A...438..273V |journal=Astronomy and Astrophysics |volume=438 |issue=1 |pages=273–289 |doi=10.1051/0004-6361:20042555 |arxiv=astro-ph/0504379 |bibcode=2005A&A...438..273V |issn=0004-6361}}</ref>
| M4.5Ia
|
| <ref name=Davies-Beasor-2020/>
|-
| HV 12463
| 288,000
|3,550
| M
| Probably not a LMC member.
| <ref name=Massey-Neugent-etal-2023/>
|-
| LGGS J003951.33+405303.7
| 288,000
|–
|
|
| <ref name=McDonald-Davies-Beasor-2022/>
|-
| LGGS J013352.96+303816.0
| 282,000
|3,900
|
|
| <ref name="Massey-Neugent-etal-2023" />
|-
|[[RSGC1]]-F13
|282,000<ref name=":0" /> - 290,000<ref name="Humphreys-Helmel-etal-2020" />
|3,590 - 4,200
|M3 - K2
|
|<ref name=":0">{{Cite journal |last1=Decin |first1=Leen |last2=Richards |first2=Anita M. S. |last3=Marchant |first3=Pablo |last4=Sana |first4=Hugues |date=January 2024 |title=ALMA detection of CO rotational line emission in red supergiant stars of the massive young star cluster RSGC1 -- Determination of a new mass-loss rate prescription for red supergiants |journal=Astronomy & Astrophysics |volume=681 |pages=A17 |arxiv=2303.09385 |bibcode=2024A&A...681A..17D |doi=10.1051/0004-6361/202244635 |issn=0004-6361}}</ref><ref name="Humphreys-Helmel-etal-2020" />
|-
| LGGS J004731.12+422749.1
| 275,000
|–
|
|
| <ref name=McDonald-Davies-Beasor-2022/>
|-
| [[VY Canis Majoris]]
| 270,000
|3,490
| M3–M4.5
|
| <ref>
{{cite journal
 |last1 = Wittkowski    |first1 = M.        |last2 = Hauschildt |first2 = P.H.
 |last3 = Arroyo-Torres |first3 = B.        |last4 = Marcaide   |first4 = J.M.
 |date = April 2012
 |title = Fundamental properties and atmospheric structure of the red supergiant VY&nbsp;Canis Majoris based on VLTI/AMBER spectro-interferometry
 |journal = [[Astronomy & Astrophysics]]
 |volume = 540 |page = L12
 |arxiv = 1203.5194  |issn = 0004-6361
 |doi = 10.1051/0004-6361/201219126  |doi-access = free
 |bibcode = 2012A&A...540L..12W }}
</ref>
|-
| [[Mu Cephei]]
| {{val|269,000|111000|40000|fmt=commas}}
| 3,750
| M2 Ia
|
| <ref>
{{Cite journal
 |last1=Davies
 |first1=Ben
 |last2=Beasor 
 |first2=Emma R.
 |date=March 2020
 |title=The 'red supergiant problem': the upper luminosity boundary of Type II supernova progenitors
 |bibcode=2020MNRAS.493..468D
 |journal=[[MNRAS]]
 |language=en
 |volume=493
 |issue=1
 |pages=468–476
 |doi=10.1093/mnras/staa174
 |doi-access=free
 |arxiv=2001.06020 
 |s2cid=210714093 }}
</ref>
|-
| LGGS J004428.48+415130.9
| 269,000
|
| M1I
|
| <ref name=McDonald-Davies-Beasor-2022/>
|-
|[[RSGC1-F01]]
|263,000<ref name=":0" /> - 335,000<ref name="Humphreys-Helmel-etal-2020" />
|3,450
|M5
|
|<ref name=":0" />
|-
|NGC247-155
|263,000
|3,510
|M2-M4
|Uncertain extinction and thus uncertain luminosity.
|<ref name=":1" />
|-
| LGGS J013241.94+302047.5
| 257,000
|3,950
|
|
| <ref name=Massey-Neugent-etal-2023/>
|-
|NGC300-125
|257,000
|3,350
|M2-M4
|
|<ref name=":1" />
|-
|[[Westerlund 1 W26]]
|256,000 - 312,000
|3,720 - 4,000
|M0.5-M6Ia
|
|<ref>
{{cite thesis |last=Arévalo |first=Aura |title=The red supergiants in the supermassive stellar cluster Westerlund&nbsp;1 |date=2019-01-22 |degree=Mestrado em Astronomia |publisher=[[Universidade de São Paulo]] |url=http://www.teses.usp.br/teses/disponiveis/14/14131/tde-12092018-161841/ |place=São Paulo, Brazil |doi=10.11606/d.14.2019.tde-12092018-161841 |doi-access=free |lang=en}}
</ref>
|-
|[[HD 143183]]
|254,000
|3,605
|M3
|
|<ref name=healy/>
|-
| LMC 145013
| 251,000<ref name="Davies-Crowther-Beasor-2018" /> - 339,000<ref name="Massey-Neugent-etal-2023" />
|3,950<ref name="Massey-Neugent-etal-2023" />
| M2.5Ia–Ib
|
|
|-
| LMC 25320
| 251,000
|3,800
| M
|
| <ref name=Massey-Neugent-etal-2023/>
|-
|[[V354 Cephei]]
|250,000
|3,615
|M1Ia-M3.5Ib
|
|<ref name=healy>{{Cite journal |last1=Healy |first1=Sarah |last2=Horiuchi |first2=Shunsaku |last3=Colomer Molla |first3=Marta |last4=Milisavljevic |first4=Dan |last5=Tseng |first5=Jeff |last6=Bergin |first6=Faith |last7=Weil |first7=Kathryn |last8=Tanaka |first8=Masaomi |last9=Otero |first9=Sebastián |date=2024-04-01 |title=Red supergiant candidates for multimessenger monitoring of the next Galactic supernova |bibcode=2024MNRAS.529.3630H |journal=Monthly Notices of the Royal Astronomical Society |volume=529 |issue=4 |pages=3630–3650 |doi=10.1093/mnras/stae738 |doi-access=free |issn=0035-8711|arxiv=2307.08785 }}</ref>
|}

==See also==
* [[Hayashi limit]]
* [[List of most massive stars]]
* [[M82 X-1]]
* [[M82 X-2]]

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



== Further reading ==
{{refbegin|25em|small=yes}}
* {{cite book
 |first1 = Juhan   |last1 = Frank
 |first2 = Andrew  |last2 = King
 |first3 = Derek   |last3 = Raine
 |year = 2002
 |title = Accretion Power in Astrophysics   |edition = 3rd
 |publisher = Cambridge University Press
 |isbn=0-521-62957-8
}}

* {{cite journal
 |first1 = John A. |last1 = Regan        |first2 = Turlough P. |last2 = Downes
 |first3 = Marta   |last3 = Volonteri    |first4 = Ricarda   |last4 = Beckmann
 |first5 = Alessandro |last5 = Lupi      |first6 = Maxime    |last6 = Trebitsch
 |first7 = Yohan   |last7 = Dubois
 |year = 2019
 |title = Super-Eddington accretion and feedback from the first massive seed black holes
 |journal = [[Monthly Notices of the Royal Astronomical Society]]
 |volume = 486  |issue = 3  |pages = 3892–3906
 |arxiv = 1811.04953
 |doi = 10.1093/mnras/stz1045
 |doi-access = free |bibcode = 2019MNRAS.486.3892R
}}

{{refend}}

==External links==
* [http://www.sciencebits.com/SurpassingEddington Surpassing the Eddington Limit].

{{Star}}

[[Category:Concepts in astrophysics]]
[[Category:Stellar astronomy]]