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Eddington limit

The Eddington limit, or Eddington luminosity was first worked out by Arthur Eddington. It is a natural limit to the normal luminosity of stars. The state of balance is a hydrostatic equilibrium. When a star exceeds the Eddington limit, it loses mass with a very intense radiation-driven stellar wind from its outer layers.

Eddington's models treated a star as a sphere of gas held up against gravity by internal thermal pressure. Eddington showed that radiation pressure was necessary to prevent collapse of the sphere.[1]

Most massive stars have luminosities far below the Eddington luminosity, so their winds are mostly driven by the less intense line absorption.[2] The Eddington limit explains the observed luminosity of accreting black holes such as quasars.

Super-Eddington luminosities

Eddington limit explains the very high mass loss rates seen in the outbursts of η Carinae in 1840–1860.[3] The regular stellar winds can only stand for a mass loss rate of about 10−4–10−3 solar masses per year. Mass loss rates of up to 0.5 solar masses per year are needed to understand the η Carinae outbursts. This can be done with the help of the super-Eddington broad spectrum radiation driven winds.

Gamma-ray bursts, novae and supernovae 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 galaxies are able to maintain luminosities close to the Eddington limit for very long times. For accretion powered sources such as accreting neutron stars or cataclysmic variables (accreting white dwarfs), the limit may act to reduce or cut off the accretion flow. Super-Eddington accretion onto stellar-mass black holes is one possible model for ultraluminous X-ray sources (ULXs).

For accreting black holes, all the energy released by accretion does not have to appear as outgoing luminosity, since energy can be lost through the event horizon, down the hole. Effectively, such sources may not conserve energy.

Most luminous known K- and M-type supergiants
Name Luminosity
(L☉) 		Effective temperature
(K) 		Spectral type Notes References
LGGS J013312.26+310053.3 575,000 4,055 [4]
LGGS J004520.67+414717.3 562,000 – M1I Likely not a member of the Andromeda Galaxy, should be treated with caution in regards to the H–D limit.[5] [5]
LGGS J013339.28+303118.8 479,000 3,837 M1Ia [4]
Stephenson 2 DFK 49 390,000 4,000 K4 Another paper estimate a much lower luminosity (245,000 L☉)[6] [7]
HD 269551 A 389,000 3,800 K/M [8]
WOH S170 380,000 3,750 M Large Magellanic Cloud membership uncertain. [8]
RSGC1-F02 363,000 3660 M2 [9]
LGGS J013418.56+303808.6 363,000 3,837 [4]
LGGS J004428.12+415502.9 339,000 – K2I [5]
AH Scorpii 331,000 3,682 M5Ia [10]
SMC 18592 309,000[11] - 355,000[8] 4,050[8] K5–M0Ia
LGGS J004539.99+415404.1 309,000 – M3I [5]
LGGS J013350.62+303230.3 309,000 3,800 [8]
HV 888 302,000 3,442[12]–3,500[13][14] M4Ia [11]
RW Cephei 300,000 4,400 K2Ia-0 [15]
LGGS J013358.54+303419.9 295,000 4,050 [8]
GCIRS 7 295,000 3,600[16] M1I [17]
SP77 21-12 295,000 4,050 K5-M3 [8]
EV Carinae 288,000 3,574[18] M4.5Ia [19]
HV 12463 288,000 3,550 M Probably not a LMC member. [8]
LGGS J003951.33+405303.7 288,000 – [5]
LGGS J013352.96+303816.0 282,000 3,900 [8]
RSGC1-F13 282,000 3,590 [9]
WOH G64 282,000 3,400 M5I Likely the largest known star. [20]
Westerlund 1 W26 275,000 3,782 M0.5-M6Ia [21]
LGGS J004731.12+422749.1 275,000 – [5]
VY Canis Majoris 270,000 3,490 M3–M4.5 [22]
Mu Cephei 269,000+111,000
−40,000 		3750 M2 Ia [23]
LGGS J004428.48+415130.9 269,000 M1I [5]
RSGC1-F01 263,000 3,450 M5 [9]
LGGS J013241.94+302047.5 257,000 3,950 [8]
LMC 145013 251,000[11] - 339,000[8] 3,950[8] M2.5Ia–Ib
LMC 25320 251,000 3,800 M [8]

Eddington Limit Media

  • The upper H–R diagram with the empirical Humphreys-Davidson limit marked (green line). Stars are observed above the limit only during brief outbursts.

References

  1. ↑ Eddington A.S. 1926. The internal constitution of stars. Cambridge University Press. ISBN 0-521-33708-9
  2. ↑ van Marle A.J; Owocki S.P. & Shaviv N.J. 2008 (2008). "Continuum driven winds from super-Eddington stars. A tale of two limits". AIP Conference Proceedings. 990: 250–253. arXiv:0708.4207. Bibcode:2008AIPC..990..250V. doi:10.1063/1.2905555. S2CID 118364586.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  3. ↑ Smith N. & Owocki S.P. 2006 (2006). "On the role of continuum driven eruptions in the evolution of very massive stars and population III stars". Astrophysical Journal. 645 (1): L45–L48. arXiv:astro-ph/0606174. Bibcode:2006ApJ...645L..45S. doi:10.1086/506523. S2CID 15424181.
  4. ↑ 4.0 4.1 4.2 Drout, Maria R.; Massey, Philip; Meynet, Georges (2012-04-18). "The yellow and red supergiants of M33". The Astrophysical Journal. 750 (2): 97. arXiv:1203.0247. Bibcode:2012ApJ...750...97D. doi:10.1088/0004-637x/750/2/97. ISSN 0004-637X.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 McDonald, Sarah L.E.; Davies, Ben; Beasor, Emma R. (2022-01-08). "Red supergiants in M31: the Humphreys–Davidson limit at high metallicity". Monthly Notices of the Royal Astronomical Society. 510 (3): 3132–3144. arXiv:2111.13716. doi:10.1093/mnras/stab3453. ISSN 0035-8711.
  6. ↑ Davies, Ben; Figer, Don F.; Kudritzki, Rolf-Peter; MacKenty, John; Najarro, Francisco; Herrero, Artemio (2007-12-01). "A Massive Cluster of Red Supergiants at the Base of the Scutum-Crux Arm". The Astrophysical Journal. 671 (1): 781–801. arXiv:0708.0821. Bibcode:2007ApJ...671..781D. doi:10.1086/522224. ISSN 0004-637X.
  7. ↑ Humphreys, Roberta M.; Helmel, Greta; Jones, Terry J.; Gordon, Michael S. (2020-09-02). "Exploring the mass-loss histories of the red supergiants". The Astronomical Journal. 160 (3): 145. arXiv:2008.01108. Bibcode:2020AJ....160..145H. doi:10.3847/1538-3881/abab15. ISSN 1538-3881.
  8. ↑ 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 8.10 8.11 8.12 Massey, Philip; Neugent, Kathryn F.; Ekström, Sylvia; Georgy, Cyril; Meynet, Georges (2023-01-01). "The time-averaged mass-loss rates of red supergiants as revealed by their luminosity functions in M31 and M33". The Astrophysical Journal. 942 (2): 69. arXiv:2211.14147. Bibcode:2023ApJ...942...69M. doi:10.3847/1538-4357/aca665. ISSN 0004-637X.
  9. ↑ 9.0 9.1 9.2 Decin, Leen; Richards, Anita M. S.; Marchant, Pablo; Sana, Hugues (January 2024). "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". Astronomy & Astrophysics. 681: A17. arXiv:2303.09385. Bibcode:2024A&A...681A..17D. doi:10.1051/0004-6361/202244635. ISSN 0004-6361.
  10. ↑ Arroyo-Torres, B.; Wittkowski, M.; Marcaide, J.M.; Hauschildt, P.H. (June 2013). "The atmospheric structure and fundamental parameters of the red supergiants AH Scorpii, UY Scuti, and KW Sagittarii". Astronomy & Astrophysics. 554: A76. arXiv:1305.6179. Bibcode:2013A&A...554A..76A. doi:10.1051/0004-6361/201220920. ISSN 0004-6361.
  11. ↑ 11.0 11.1 11.2 Davies, Ben; Crowther, Paul A.; Beasor, Emma R. (2018-08-01). "The luminosities of cool supergiants in the Magellanic Clouds, and the Humphreys-Davidson limit revisited". Monthly Notices of the Royal Astronomical Society. 478 (3): 3138–3148. arXiv:1804.06417. Bibcode:2018MNRAS.478.3138D. doi:10.1093/mnras/sty1302. ISSN 0035-8711.
  12. ↑ Ren, Yi; Jiang, Bi-Wei (2020-07-01). "On the Granulation and Irregular Variation of Red Supergiants". The Astrophysical Journal. 898 (1): 24. arXiv:2006.06605. Bibcode:2020ApJ...898...24R. doi:10.3847/1538-4357/ab9c17. ISSN 0004-637X.
  13. ↑ Groenewegen, M. A. T.; Sloan, G. C. (2018-01-01). "Luminosities and mass-loss rates of Local Group AGB stars and red supergiants". Astronomy and Astrophysics. 609: A114. arXiv:1711.07803. Bibcode:2018A&A...609A.114G. doi:10.1051/0004-6361/201731089. ISSN 0004-6361.
  14. ↑ Kamath, D.; Wood, P. R.; Van Winckel, H. (2015-12-01). "Optically visible post-AGB stars, post-RGB stars and young stellar objects in the Large Magellanic Cloud". Monthly Notices of the Royal Astronomical Society. 454 (2): 1468–1502. arXiv:1508.00670. Bibcode:2015MNRAS.454.1468K. doi:10.1093/mnras/stv1202. ISSN 0035-8711.
  15. ↑ Jones, Terry Jay; Shenoy, Dinesh; Humphreys, Roberta (2023-05-11). "The recent mass-loss history of the hypergiant RW Cep". Research Notes of the American Astronomical Society. 7 (5): 92. Bibcode:2023RNAAS...7...92J. doi:10.3847/2515-5172/acd37f. ISSN 2515-5172.
  16. ↑ Paumard, T.; Pfuhl, O.; Martins, F.; Kervella, P.; Ott, T.; Pott, J. -U.; Le Bouquin, J. B.; Breitfelder, J.; Gillessen, S.; Perrin, G.; Burtscher, L.; Haubois, X.; Brandner, W. (2014-08-01). "GCIRS 7, a pulsating M1 supergiant at the Galactic centre . Physical properties and age". Astronomy and Astrophysics. 568: A85. arXiv:1406.5320. Bibcode:2014A&A...568A..85P. doi:10.1051/0004-6361/201423991. ISSN 0004-6361.
  17. ↑ Guerço, Rafael; Smith, Verne V.; Cunha, Katia; Ekström, Sylvia; Abia, Carlos; Plez, Bertrand; Meynet, Georges; Ramirez, Solange V.; Prantzos, Nikos; Sellgren, Kris; Hayes, Cristian R.; Majewski, Steven R. (2022-09-13). "Evidence of deep mixing in IRS 7, a cool massive supergiant member of the Galactic nuclear star cluster". Monthly Notices of the Royal Astronomical Society. 516 (2): 2801–2811. arXiv:2208.10529. doi:10.1093/mnras/stac2393. ISSN 0035-8711.
  18. ↑ van Loon, J. Th.; Cioni, M. -R. L.; Zijlstra, A. A.; Loup, C. (2005-07-01). "An empirical formula for the mass-loss rates of dust-enshrouded red supergiants and oxygen-rich Asymptotic Giant Branch stars". Astronomy and Astrophysics. 438 (1): 273–289. arXiv:astro-ph/0504379. Bibcode:2005A&A...438..273V. doi:10.1051/0004-6361:20042555. ISSN 0004-6361.
  19. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Davies-Beasor-2020.
  20. ↑ Ohnaka, K.; Driebe, T.; Hofmann, K.-H.; Weigelt, G.; Wittkowski, M. (2008-06-01). "Spatially resolved dusty torus toward the red supergiant WOH G64 in the Large Magellanic Cloud". Astronomy & Astrophysics. 484 (2): 371–379. arXiv:0803.3823. Bibcode:2008A&A...484..371O. doi:10.1051/0004-6361:200809469. ISSN 0004-6361.
  21. ↑ Arévalo, Aura (2019-01-22). The red supergiants in the supermassive stellar cluster Westerlund 1. São Paulo, Brazil: Universidade de São Paulo. doi:10.11606/d.14.2019.tde-12092018-161841 . http://www.teses.usp.br/teses/disponiveis/14/14131/tde-12092018-161841/. 
  22. ↑ Wittkowski, M.; Hauschildt, P.H.; Arroyo-Torres, B.; Marcaide, J.M. (April 2012). "Fundamental properties and atmospheric structure of the red supergiant VY Canis Majoris based on VLTI/AMBER spectro-interferometry". Astronomy & Astrophysics. 540: L12. arXiv:1203.5194. Bibcode:2012A&A...540L..12W. doi:10.1051/0004-6361/201219126. ISSN 0004-6361.
  23. ↑ Davies, Ben; Beasor, Emma R. (March 2020). "The 'red supergiant problem': the upper luminosity boundary of Type II supernova progenitors". MNRAS. 493 (1): 468–476. arXiv:2001.06020. Bibcode:2020MNRAS.493..468D. doi:10.1093/mnras/staa174. S2CID 210714093.
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