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Tolman–Oppenheimer–Volkoff limit

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The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of cold, non-rotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars. Stars more massive than the TOV limit collapse into a black hole. The original calculation in 1939, which neglected complications such as nuclear forces between neutrons, placed this limit at approximately 0.7 solar masses (M☉). Later, more refined analyses have resulted in larger values.

Theoretical work in 1996 placed the limit at approximately 1.5 to 3.0 M☉,[1] corresponding to an original stellar mass of 15 to 20 M☉; additional work in the same year gave a more precise range of 2.2 to 2.9 M☉.[2]

Data from GW170817, the first gravitational wave observation attributed to merging neutron stars (thought to have collapsed into a black hole[3] within a few seconds after merging[4]) placed the limit in the range of 2.01 to 2.17 M☉.[5]

In the case of a rigidly spinning neutron star, meaning that different levels in the interior of the star all rotate at the same rate, the mass limit is thought to increase by up to 18–20%.[4][5]

History

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The idea that there should be an absolute upper limit for the mass of a cold (as distinct from thermal pressure supported) self-gravitating body dates back to the 1932 work of Lev Landau, based on the Pauli exclusion principle. Pauli's principle shows that the fermionic particles in sufficiently compressed matter would be forced into energy states so high that their rest mass contribution would become negligible when compared with the relativistic kinetic contribution (RKC). RKC is determined just by the relevant quantum wavelength λ, which would be of the order of the mean interparticle separation. In terms of Planck units, with the reduced Planck constant ħ, the speed of light c, and the gravitational constant G all set equal to one, there will be a corresponding pressure given roughly by

.

At the upper mass limit, that pressure will equal the pressure needed to resist gravity. The pressure to resist gravity for a body of mass M will be given according to the virial theorem roughly by

,

where ρ is the density. This will be given by ρ = ⁠m/λ3⁠, where m is the relevant mass per particle. It can be seen that the wavelength cancels out so that one obtains an approximate mass limit formula of the very simple form

.

In this relationship, m can be taken to be given roughly by the proton mass. This even applies in the white dwarf case (that of the Chandrasekhar limit) for which the fermionic particles providing the pressure are electrons. This is because the mass density is provided by the nuclei in which the neutrons are at most about as numerous as the protons. Likewise the protons, for charge neutrality, must be exactly as numerous as the electrons outside.

In the case of neutron stars this limit was first worked out by J. Robert Oppenheimer and George Volkoff in 1939, using the work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutrons in a neutron star formed a degenerate cold Fermi gas. They thereby obtained a limiting mass of approximately 0.7 solar masses,[6][7] which was less than the Chandrasekhar limit for white dwarfs.

Oppenheimer and Volkoff's paper notes that "the effect of repulsive forces, i.e., of raising the pressure for a given density above the value given by the Fermi equation of state ... could tend to prevent the collapse."[7] And indeed, the most massive neutron star detected so far, PSR J0952–0607, is estimated to be much heavier than Oppenheimer and Volkoff's TOV limit at 2.35±0.17 M☉.[8][9] More realistic models neutron stars including baryon strong force repulsion predict a neutron star mass limit of 2.2 to 2.9 M☉.[10][11] The uncertainty in the value reflects the fact that the equations of state for extremely dense matter are not well known.

Applications

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In a star less massive than the limit, the gravitational compression is balanced by short-range repulsive neutron–neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse.[12]: 74  If its mass is above the limit, the star will collapse to some denser form. It could form a black hole, or change composition and be supported in some other way (for example, by quark degeneracy pressure if it becomes a quark star). Because the properties of hypothetical, more exotic forms of degenerate matter are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.

A black hole formed by the collapse of an individual star must have mass exceeding the Tolman–Oppenheimer–Volkoff limit. Theory predicts that because of mass loss during stellar evolution, a black hole formed from an isolated star of solar metallicity can have a mass of no more than approximately 10 solar masses.[13]:Fig. 16 Observationally, because of their large mass, relative faintness, and X-ray spectra, a number of massive objects in X-ray binaries are thought to be stellar black holes. These black hole candidates are estimated to have masses between 3 and 20 solar masses.[14][15] LIGO has detected black hole mergers involving black holes in the 7.5–50 solar mass range; it is possible – although unlikely – that these black holes were themselves the result of previous mergers.

Oppenheimer and Volkoff discounted the influence of heat, stating in reference to work by Landau (1932), 'even [at] 107 degrees... the pressure is determined essentially by the density only and not by the temperature'[7] – yet it has been estimated[16] that temperatures can reach up to approximately >109 K during formation of a neutron star, mergers and binary accretion. Another source of heat and therefore collapse-resisting pressure in neutron stars is 'viscous friction in the presence of differential rotation.'[16]

Oppenheimer and Volkoff's calculation of the mass limit of neutron stars also neglected to consider the rotation of neutron stars, however we now know that neutron stars are capable of spinning at much faster rates than were known in Oppenheimer and Volkoff's time. The fastest-spinning neutron star known is PSR J1748-2446ad, rotating at a rate of 716 times per second[17][18] or 43,000 revolutions per minute, giving a linear (tangential) speed at the surface on the order of 0.24c (i.e., nearly a quarter the speed of light). Star rotation interferes with convective heat loss during supernova collapse, so rotating stars are more likely to collapse directly to form a black hole [19]: 1044 

List of least massive black holes

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See also: Stellar black hole
Content here is transcluded from List of least massive black holes.


Name Mass
(M☉) 		Distance
(ly) 		Companion class Mass determination method Notes Refs.
V723 Monocerotis 3.04±0.06 1,500 K0III Spectroscopic radial velocity measurements of companion. The companion star was identified in 2022 to actually be a warm subgiant [20] [20][21]
2MASS J05215658+4359220 3.3+2.8
−0.7		 10,000 K-type (?) giant Spectroscopic radial velocity measurements of noninteracting companion. In Milky Way outskirts. Recent Hubble ultraviolet data has suggested the companion to this object is actually a warm subgiant, and ruling out smaller compact companions such as a white dwarf.[22] [22][23][24][25]
GW190425's remnant 3.4+0.3
−0.1		 518,600,000 N/A Gravitational wave data of neutron star merger from LIGO and Virgo interferometers. 97% chance of prompt collapse into a black hole immediately after merger. Alternative study suggests collapse 2.5 hours later. [23][26][27][28]
NGC 3201-1 4.36±0.41 15,600 (see Notes) Spectroscopic radial velocity measurements of noninteracting companion. In globular cluster NGC 3201. Companion is 0.8M☉ main sequence turn-off. [23][29]
GRO J1719-24/
GRS 1716−249		 ≥4.9 8,500 K0-5 V Near-infrared photometry of companion and Eddington flux. LMXB system. [23][30]
4U 1543-47 5.0+2.5
−2.3		 30,000 ± 3,500 A2 (V)? Spectroscopic radial velocity measurements of companion. SXT system. [23][31]
XTE J1650-500 ≥5.1 8,500 ± 2,300 K4V Orbital resonance modeling from QPOs Transient binary X-ray source [32][33]
GRO J1655-40 5.31±0.07 <5,500 F6IV Precision X-ray timing observations from RossiXTE. LMXB system. [34][35]
GX 339-4 5.9±3.6 26,000 N/A [23]


List of objects in mass gap

[edit]

This list contains objects that may be neutron stars, black holes, quark stars, or other exotic objects. This list is distinct from the list of least massive black holes due to the undetermined nature of these objects, largely because of indeterminate mass, or other poor observation data.

Name Mass
(M☉) 		Distance
(ly) 		Companion class Mass determination method Notes Refs.
GW170817's remnant 2.74+0.04
−0.01		 144,000,000 N/A Gravitational wave data of neutron star merger from LIGO and Virgo interferometers. In NGC 4993. Possibly collapsed into a black hole 5–10 seconds after merger. [36]
SS 433 3.0–30.0 18,000 ± 700 A7Ib First discovered microquasar system. Confirmed to have a magnetic field, which is atypical for a black hole; however, it could be the field of the accretion disk, not of the compact object. [37][38][39]
LB-1 2.0–70.0 approx. 7,000 Be star/stripped helium star Initially thought to be first black hole in pair-instability mass gap. [40][41]
Cygnus X-3 2.0–5.0 24,100 ± 3,600 WN4-6 Near-infrared spectroscopy and atmosphere model fitting of companion. Microquasar system. Major differences between the spectrum of Cyg X-3 and typical accreting BH can be explained by properties of its companion star. [42][43]
LS I +61 303 1.0–4.0 7,000 B0Ve Spectroscopic radial velocity measurements of companion. Microquasar system. It has a spectrum typical for black holes, however it emits HE and VHE gamma rays similar to neutron stars LS_2883 and HESS J0632+057, as well as mysterious object LS 5039. [44][45]
LS 5039 3.7+1.3
−1.0		 8,200 ± 300 O(f)N6.5V Intermediate-dispersion spectroscopy and atmosphere model fitting of companion. Microquasar system. Only lowest possible mass allows it not to be a black hole. [46]
GRO J0422+32/V518 Persei 3.97+0.95
−1.87		 8,500 M4.5V Photometric light curve modelling. SXT system. Only mass close to lowest possible allows it not to be a black hole. [23][47]

See also

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Notes

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References

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  1. ^ Bombaci, I. (1996). "The Maximum Mass of a Neutron Star". Astronomy and Astrophysics. 305: 871–877. Bibcode:1996A&A...305..871B.
  2. ^ Kalogera, V; Baym, G (11 August 1996). "The Maximum Mass of a Neutron Star". The Astrophysical Journal. 470: L61–L64. arXiv:astro-ph/9608059v1. Bibcode:1996ApJ...470L..61K. doi:10.1086/310296. S2CID 119085893.
  3. ^ Pooley, D.; Kumar, P.; Wheeler, J. C.; Grossan, B. (2018-05-31). "GW170817 Most Likely Made a Black Hole". The Astrophysical Journal. 859 (2): L23. arXiv:1712.03240. Bibcode:2018ApJ...859L..23P. doi:10.3847/2041-8213/aac3d6. S2CID 53379493.
  4. ^ a b Cho, A. (16 February 2018). "A weight limit emerges for neutron stars". Science. 359 (6377): 724–725. Bibcode:2018Sci...359..724C. doi:10.1126/science.359.6377.724. PMID 29449468.
  5. ^ a b Rezzolla, L.; Most, E. R.; Weih, L. R. (2018-01-09). "Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars". Astrophysical Journal. 852 (2): L25. arXiv:1711.00314. Bibcode:2018ApJ...852L..25R. doi:10.3847/2041-8213/aaa401. S2CID 119359694.
  6. ^ Tolman, R. C. (1939). "Static Solutions of Einstein's Field Equations for Spheres of Fluid". Physical Review. 55 (4): 364–373. Bibcode:1939PhRv...55..364T. doi:10.1103/PhysRev.55.364.
  7. ^ a b c Oppenheimer, J. R.; Volkoff, G. M. (1939). "On Massive Neutron Cores". Physical Review. 55 (4): 374–381. Bibcode:1939PhRv...55..374O. doi:10.1103/PhysRev.55.374.
  8. ^ Romani, Roger W.; Kandel, D.; Filippenko, Alexei V.; Brink, Thomas G.; Zheng, WeiKang (2022-08-01). "PSR J0952−0607: The Fastest and Heaviest Known Galactic Neutron Star". The Astrophysical Journal Letters. 934 (2): L17. arXiv:2207.05124. Bibcode:2022ApJ...934L..17R. doi:10.3847/2041-8213/ac8007. ISSN 2041-8205.
  9. ^ "The heaviest neutron star on record is 2.35 times the mass of the sun". 2022-07-22. Retrieved 2024-01-04.
  10. ^ Siegel, Ethan. "The Surprising Reason Why Neutron Stars Don't All Collapse To Form Black Holes". Forbes. Retrieved 2024-01-04.
  11. ^ Burkert, V. D.; Elouadrhiri, L.; Girod, F. X. (2019-05-05). "The pressure distribution inside the proton". Nature. 557 (7705): 396–399. doi:10.1038/s41586-018-0060-z. ISSN 1476-4687. PMID 29769668. S2CID 21724781.
  12. ^ Illari, Phyllis (2019). "Mechanisms, Models and Laws in Understanding Supernovae". Journal for General Philosophy of Science. 50 (1): 63–84. doi:10.1007/s10838-018-9435-y. ISSN 0925-4560.
  13. ^ Woosley, S. E.; Heger, A.; Weaver, T. A. (2002). "The Evolution and Explosion of Massive Stars". Reviews of Modern Physics. 74 (4): 1015–1071. Bibcode:2002RvMP...74.1015W. doi:10.1103/RevModPhys.74.1015. S2CID 55932331.
  14. ^ McClintock, J. E.; Remillard, R. A. (2003). "Black Hole Binaries". arXiv:astro-ph/0306213.
  15. ^ Casares, J. (2006). "Observational Evidence for Stellar-Mass Black Holes". Proceedings of the International Astronomical Union. 2: 3. arXiv:astro-ph/0612312. doi:10.1017/S1743921307004590. S2CID 119474341.
  16. ^ a b Kaminker, A. D.; Kaurov, A. A.; Potekhin, A. Y.; Yakovlev, D. G. (2014-08-21). "Thermal emission of neutron stars with internal heaters". Monthly Notices of the Royal Astronomical Society. 442 (4): 3484–3494. arXiv:1406.0723. doi:10.1093/mnras/stu1102. ISSN 1365-2966.
  17. ^ Hessels, Jason W. T.; Ransom, Scott M.; Stairs, Ingrid H.; Freire, Paulo C. C.; Kaspi, Victoria M.; Camilo, Fernando (2006-03-31). "A Radio Pulsar Spinning at 716 Hz". Science. 311 (5769): 1901–1904. arXiv:astro-ph/0601337. Bibcode:2006Sci...311.1901H. doi:10.1126/science.1123430. ISSN 0036-8075. PMID 16410486.
  18. ^ "SkyandTelescope.com – News from Sky & Telescope – Spinning Pulsar Smashes Record". 2007-12-29. Archived from the original on 2007-12-29. Retrieved 2024-01-05.
  19. ^ Fryer, Chris L.; Heger, Alexander (Oct 2000). "Core-Collapse Simulations of Rotating Stars". The Astrophysical Journal. 541 (2): 1033–1050. arXiv:astro-ph/9907433. Bibcode:2000ApJ...541.1033F. doi:10.1086/309446. ISSN 0004-637X.
  20. ^ a b El-Badry, Kareem; Seeburger, Rhys; Jayasinghe, Tharindu; Rix, Hans-Walter; Almada, Silvia; Conroy, Charlie; Price-Whelan, Adrian M; Burdge, Kevin (2022-04-14). "Unicorns and giraffes in the binary zoo: stripped giants with subgiant companions". Monthly Notices of the Royal Astronomical Society. 512 (4): 5620–5641. arXiv:2203.06348. doi:10.1093/mnras/stac815. ISSN 0035-8711.
  21. ^ Jayasinghe, T.; Stanek, K. Z.; Thompson, Todd A.; Kochanek, C. S.; Rowan, D. M.; Vallely, P. J.; Strassmeier, K. G.; Weber, M.; Hinkle, J. T.; Hambsch, F-J; Martin, D. V.; Prieto, J. L.; Pessi, T.; Huber, D.; Auchettl, K.; Lopez, L. A.; Ilyin, I.; Badenes, C.; Howard, A. W.; Isaacson, H.; Murphy, S. J. (2021). "A unicorn in monoceros: The 3 M⊙ dark companion to the bright, nearby red giant V723 Mon is a non-interacting, mass-gap black hole candidate". Monthly Notices of the Royal Astronomical Society. 504 (2): 2577–2602. arXiv:2101.02212. Bibcode:2021MNRAS.504.2577J. doi:10.1093/mnras/stab907.
  22. ^ a b Bianchi, Luciana; Hutchings, John; Bohlin, Ralph; Thilker, David; Berti, Emanuele (2024). "Revealing the elusive companion of the red giant binary 2MASSJ05215658+4359220 from UV HST and Astrosat-UVIT data". arXiv:2409.06906. doi:10.3847/1538-4357/ad712f (inactive 1 November 2024). {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: DOI inactive as of November 2024 (link)
  23. ^ a b c d e f g Elavsky, F; Geller, A. "Masses in the Stellar Graveyard". Northwestern University.
  24. ^ Thompson, T. A.; Kochanek, C. S.; Stanek, K. Z.; et al. (2019). "A noninteracting low-mass black hole–giant star binary system". Science. 366 (6465): 637–640. arXiv:1806.02751. Bibcode:2019Sci...366..637T. doi:10.1126/science.aau4005. PMID 31672898. S2CID 207815062.
  25. ^ Kumar, V. (2019-11-03). "Astronomers Spot A New Class Of Low-Mass Black Holes". RankRed. Retrieved 2019-11-05.
  26. ^ Abbott, B. P.; et al. (2020). "GW190425: Observation of a Compact Binary Coalescence with Total Mass ~ 3.4 M ⊙". The Astrophysical Journal. 892 (1): L3. arXiv:2001.01761. Bibcode:2020ApJ...892L...3A. doi:10.3847/2041-8213/ab75f5. S2CID 210023687.
  27. ^ Foley, Ryan J.; Coulter, David A.; Kilpatrick, Charles D.; Piro, Anthony L.; Ramirez-Ruiz, Enrico; Schwab, Josiah (2020). "Updated parameter estimates for GW190425 using astrophysical arguments and implications for the electromagnetic counterpart". Monthly Notices of the Royal Astronomical Society. 494 (1): 190–198. arXiv:2002.00956. Bibcode:2020MNRAS.494..190F. doi:10.1093/mnras/staa725.
  28. ^ Paul Sutter last updated (2022-09-16). "Strange quark star may have formed from a lucky cosmic merger". Space.com. Archived from the original on 2023-03-23. Retrieved 2023-03-30.
  29. ^ Giesers, B; et al. (2018). "A detached stellar-mass black hole candidate in the globular cluster NGC 3201". Monthly Notices of the Royal Astronomical Society: Letters. 475 (1): L15–L19. arXiv:1801.05642. Bibcode:2018MNRAS.475L..15G. doi:10.1093/mnrasl/slx203. S2CID 35600251.
  30. ^ Chaty, S.; Mirabel, I. F.; Goldoni, P.; Mereghetti, S.; Duc, P.-A.; Martí, J.; Mignani, R. P. (2002). "Near-infrared observations of Galactic black hole candidates". Monthly Notices of the Royal Astronomical Society. 331 (4): 1065–1071. arXiv:astro-ph/0112329. Bibcode:2002MNRAS.331.1065C. doi:10.1046/j.1365-8711.2002.05267.x. S2CID 15529877.
  31. ^ Orosz, Jerome A.; Jain, Raj K.; Bailyn, Charles D.; McClintock, Jeffrey E.; Remillard, Ronald A. (2002). "Orbital Parameters for the Soft X-Ray Transient 4U 1543-47: Evidence for a Black Hole". The Astrophysical Journal. 499 (1): 375–384. arXiv:astro-ph/9712018. Bibcode:1998ApJ...499..375O. doi:10.1086/305620. S2CID 16991861.
  32. ^ Slany, P.; Stuchlik, Z. (1 October 2008). "Mass estimate of the XTE J1650-500 black hole from the Extended Orbital Resonance Model for high-frequency QPOs". Astronomy & Astrophysics. 492 (2): 319–322. arXiv:0810.0237. Bibcode:2008A&A...492..319S. doi:10.1051/0004-6361:200810334. S2CID 5526948.
  33. ^ Determination of Black Hole Masses in Galactic Black Hole Binaries Using Scaling of Spectral and Variability Characteristics Shaposhnikov, Nickolai; Titarchuk, Lev; The Astrophysical Journal, Volume 699, Issue 1, pp. 453-468 (2009) doi:10.1088/0004-637X/699/1/453 Pdf
  34. ^ Motta, S. E.; Belloni, T. M.; Stella, L.; Muñoz-Darias, T.; Fender, R. (2014). "Precise mass and spin measurements for a stellar-mass black hole through X-ray timing: The case of GRO J1655-40". Monthly Notices of the Royal Astronomical Society. 437 (3): 2554. arXiv:1309.3652. Bibcode:2014MNRAS.437.2554M. doi:10.1093/mnras/stt2068.
  35. ^ Foellmi, C.; Depagne, E.; Dall, T.H.; Mirabel, I.F (12 June 2006). "On the distance of GRO J1655-40". Astronomy & Astrophysics. 457 (1): 249–255. arXiv:astro-ph/0606269. Bibcode:2006A&A...457..249F. doi:10.1051/0004-6361:20054686. S2CID 119395985.
  36. ^ van Putten, Maurice H P M; Della Valle, Massimo (January 2019). "Observational evidence for extended emission to GW 170817". Monthly Notices of the Royal Astronomical Society: Letters. 482 (1): L46–L49. arXiv:1806.02165. Bibcode:2019MNRAS.482L..46V. doi:10.1093/mnrasl/sly166. we report on a possible detection of extended emission (EE) in gravitational radiation during GRB170817A: a descending chirp with characteristic time-scale τs = 3.01±0.2 s in a (H1,L1)-spectrogram up to 700 Hz with Gaussian equivalent level of confidence greater than 3.3 σ based on causality alone following edge detection applied to (H1,L1)-spectrograms merged by frequency coincidences. Additional confidence derives from the strength of this EE. The observed frequencies below 1 kHz indicate a hypermassive magnetar rather than a black hole, spinning down by magnetic winds and interactions with dynamical mass ejecta.
  37. ^ Cherepashchuk, Anatol (2002). "Observational Manifestations of Precession of Accretion Disk in the SS 433 Binary System". Space Science Reviews. 102 (1): 23–35. Bibcode:2002SSRv..102...23C. doi:10.1023/A:1021356630889. S2CID 115604949.
  38. ^ Abeysekara, A. U.; Albert, A.; Alfaro, R.; Alvarez, C.; Álvarez, J. D.; Arceo, R.; Arteaga-Velázquez, J. C.; Avila Rojas, D.; Ayala Solares, H. A.; Belmont-Moreno, E.; Benzvi, S. Y.; Brisbois, C.; Caballero-Mora, K. S.; Capistrán, T.; Carramiñana, A.; Casanova, S.; Castillo, M.; Cotti, U.; Cotzomi, J.; Coutiño De León, S.; De León, C.; de la Fuente, E.; Díaz-Vélez, J. C.; Dichiara, S.; Dingus, B. L.; Duvernois, M. A.; Ellsworth, R. W.; Engel, K.; Espinoza, C.; et al. (2018). "Very-high-energy particle acceleration powered by the jets of the microquasar SS 433". Nature. 562 (7725): 82–85. arXiv:1810.01892. Bibcode:2018Natur.562...82A. doi:10.1038/s41586-018-0565-5. PMID 30283106. S2CID 52918329.
  39. ^ Staff Writers (2018-10-04). "Scientists discover new nursery for superpowered photons". Space Daily.
  40. ^ Liu, Jifeng; et al. (27 November 2019). "A wide star–black-hole binary system from radial-velocity measurements". Nature. 575 (7784): 618–621. arXiv:1911.11989. Bibcode:2019Natur.575..618L. doi:10.1038/s41586-019-1766-2. PMID 31776491. S2CID 208310287.
  41. ^ Irrgang, A.; Geier, S.; Kreuzer, S.; Pelisoli, I.; Heber, U. (January 2020). "A stripped helium star in the potential black hole binary LB-1". Astronomy and Astrophysics (Letter to the Editor). 633: L5. arXiv:1912.08338. Bibcode:2020A&A...633L...5I. doi:10.1051/0004-6361/201937343.
  42. ^ Koljonen, K. I. I.; MacCarone, T. J. (2017). "Gemini/GNIRS infrared spectroscopy of the Wolf-Rayet stellar wind in Cygnus X-3". Monthly Notices of the Royal Astronomical Society. 472 (2): 2181. arXiv:1708.04050. Bibcode:2017MNRAS.472.2181K. doi:10.1093/mnras/stx2106. S2CID 54028568.
  43. ^ Zdziarski, A. A.; Mikolajewska, J.; Belczynski, K. (2013). "Cyg X-3: A low-mass black hole or a neutron star". Monthly Notices of the Royal Astronomical Society. 429: L104–L108. arXiv:1208.5455. Bibcode:2013MNRAS.429L.104Z. doi:10.1093/mnrasl/sls035. S2CID 119185839.
  44. ^ Massi, M; Migliari, S; Chernyakova, M (2017). "The black hole candidate LS I +61°0303". Monthly Notices of the Royal Astronomical Society. 468 (3): 3689. arXiv:1704.01335. Bibcode:2017MNRAS.468.3689M. doi:10.1093/mnras/stx778. S2CID 118894005.
  45. ^ Albert, J; et al. (2006). "Variable Very-High-Energy Gamma-Ray Emission from the Microquasar LS I +61 303". Science. 312 (5781): 1771–3. arXiv:astro-ph/0605549. Bibcode:2006Sci...312.1771A. doi:10.1126/science.1128177. PMID 16709745. S2CID 20981239.
  46. ^ Casares, J; Ribo, M; Ribas, I; Paredes, J. M; Marti, J; Herrero, A (2005). "A possible black hole in the γ-ray microquasar LS 5039". Monthly Notices of the Royal Astronomical Society. 364 (3): 899–908. arXiv:astro-ph/0507549. Bibcode:2005MNRAS.364..899C. doi:10.1111/j.1365-2966.2005.09617.x. S2CID 8393701.
  47. ^ Gelino, D. M.; Harrison, T. E. (2003). "GRO J0422+32: The Lowest Mass Black Hole?". The Astrophysical Journal. 599 (2): 1254–1259. arXiv:astro-ph/0308490. Bibcode:2003ApJ...599.1254G. doi:10.1086/379311. S2CID 17785067.
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