In 1920 Arthur Eddington was the first one to suggest that stars obtained their energy from nuclear fusion of hydrogen to form helium.

In 1920, Arthur Eddington, on the basis of the precise measurements of atoms by F.W. Aston, was the first to suggest that stars obtained their energy from nuclear fusion of hydrogen to form helium. In 1928, George Gamow derived what is now called the Gamow factor, a quantum-mechanical formula that gave the probability of bringing two nuclei sufficiently close for the strong nuclear force to overcome the Coulomb barrier. The Gamow factor was used in the decade that followed by Atkinson and Houtermans and later by Gamow himself and Edward Teller to derive the rate at which nuclear reactions would proceed at the high temperatures believed to exist in stellar interiors.

 

In 1939, in a paper entitled "Energy Production in Stars", Hans Bethe analyzed the different possibilities for reactions by which hydrogen is fused into helium.^[2] He selected two processes that he believed to be the sources of energy in stars. The first one, the proton–proton chain reaction, is the dominant energy source in stars with masses up to about the mass of the Sun. The second process, the carbon-nitrogen-oxygen cycle, which was also considered by Carl Friedrich von Weizsäcker in 1938, is most important in more massive stars. These works concerned the energy generation capable of keeping stars hot. They did not address the creation of heavier nuclei, however. That theory was begun by Fred Hoyle in 1946 with his argument that a collection of very hot nuclei would assemble into iron.^[3] Hoyle followed that in 1954 with a large paper describing how advanced fusion stages within stars would synthesize elements between carbon and iron in mass.^[4] This is the dominant work in stellar nucleosynthesis.^[5] It provided the roadmap to how the most abundant elements on earth had been synthesized from initial hydrogen and helium, making clear how those abundant elements increased their galactic abundances as the galaxy aged.

 

Quickly, many important omissions in Hoyle's theory were corrected, beginning with the publication of a celebrated review paper in 1957 by Burbidge, Burbidge, Fowler and Hoyle (commonly referred to as the B²FH paper).^[6] This review paper collected and refined earlier research into a heavily cited picture that gave promise of accounting for the observed relative abundances of the elements; but it did not itself enlarge Hoyle's 1954 work as much as many assumed, except in the understanding of nucleosynthesis of those elements heavier than iron. Significant improvements were made by Alastair GW Cameron and by Donald D. Clayton. Cameron presented his own independent approach^[7] (following Hoyle's approach for the most part) of nucleosynthesis. He introduced computers into time-dependent calculations of evolution of nuclear systems. Clayton calculated the first time-dependent models of the S-process^[8] and of the R-process,^[9] of the burning of silicon into iron-group elements,^[10] and discovered radiogenic chronologies^[11] for determining the age of the elements. The entire research field expanded rapidly in the 1970s.

 

Cross section of a red giant showing nucleosynthesis and elements formed.

The most important reactions in stellar nucleosynthesis:

• Hydrogen fusing:
  • Deuterium burning
  • The proton-proton chain
  • The carbon-nitrogen-oxygen cycle
• Helium burning:
  • The triple-alpha process
  • The alpha process
• Burning of heavier elements:
  • Lithium burning: a process found most commonly in brown dwarfs
  • Carbon burning process
  • Neon burning process
  • Oxygen burning process
  • Silicon burning process
• Production of elements heavier than iron:
  • Neutron capture:
    • The R-process
    • The S-process
  • Proton capture:
    • The Rp-process
  • Photo-disintegration:
    • The P-process

Hydrogen burning

Main articles: Proton-proton chain reaction, CNO cycle, and Deuterium burning

Illustration of the proton–proton chain reaction sequence

Overview of the CNO-I cycle. The helium nucleus is released at the top-left step.

"Hydrogen burning" is an expression that astronomers sometimes use for the stellar process that results in the nuclear fusion of four protons to form a nucleus of helium-4.^[12] (This should not be confused with the chemical combustion of hydrogen in an oxidizing atmosphere.) There are two predominant processes by which stellar hydrogen burning occurs.

 

In the cores of lower mass main sequence stars such as the Sun, the dominant process is the proton-proton chain reaction (pp-chain reaction). This creates a helium-4 nucleus through a sequence of chain reactions that begin with the fusion of two protons to form a nucleus of deuterium.^[13] The subsequent process of deuterium burning will consume any pre-existing deuterium found at the core. The pp-chain reaction cycle is relatively insensitive to temperature, so this hydrogen burning process can occur in up to a third of the star's radius and occupy half the star's mass. As a result, for stars above 35% of the Sun's mass,^[14] the energy flux toward the surface is sufficiently low that the core region remains a radiative zone, rather than becoming convective.^[15] In each complete fusion cycle, the p-p chain reaction releases about 26.2 MeV.^[13]

 

In higher mass stars, the dominant process is the CNO cycle, which is a catalytic cycle that uses nuclei of carbon, nitrogen and oxygen as intermediaries to produce a helium nucleus.^[13] During a complete CNO cycle, 25.0 MeV of energy is released. The difference in energy compared to the p-p chain reaction is accounted for by the energy lost through neutrino emission.^[13] The CNO cycle is very temperature sensitive, so it is strongly concentrated at the core. About 90% of the CNO cycle energy generation occurs within the inner 15% of the star's mass.^[16] This results in an intense outward energy flux that can not be sustained by radiative transfer. As a result, the core region becomes a convection zone, which stirs the hydrogen burning region and keeps it well mixed with the surrounding proton-rich region.^[17] This core convection occurs in stars where the CNO cycle contributes more than 20% of the total energy. As the star ages and the core temperature increases, the region occupied by the convection zone slowly shrinks from 20% of the mass down to the inner 8% of the mass.^[16]

 

The type of hydrogen burning process that dominates inside a star is determined by the temperature dependency differences between the two reactions. The pp-chain reaction starts at temperatures around 4×10⁶ K,^[18] making it the dominant mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately 15×10⁶ K, but thereafter it increases more rapidly in efficiency than the pp-chain reaction as the temperature grows.^[19] Above approximately 17×10⁶ K, the CNO cycle becomes the dominant source of energy. This temperature is achieved in the cores of main sequence stars with at least 1.3 times the mass of the Sun.^[20] The Sun itself has a core temperature of around 15.7×10⁶ K and only 0.8% of the energy being produced in the Sun comes from the CNO cycle.^[21] As a main sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.^[16]

 

Once a star with about 0.5–10 times the mass of the Sun has consumed nearly all the hydrogen at its core, it begins to evolve up the red giant branch. Hydrogen burning occurs in a shell surrounding an inert helium core until the steadily increasing core temperature exceeds 1×10⁸ K. At that point helium burning begins with a thermal runaway process called the helium flash with hydrogen burning continuing in a thin shell surrounding the now active helium core.^[15]

 

 

1. ^ Donald D. Clayton, Principles of stellar Evolution and Nucleosynthesis. McGraw-Hill, New York (1968); reissued by University of Chicago Press (1983)
2. ^ Energy Production in Stars by Hans Bethe
3. ^ F. Hoyle (1946). "The synthesis of the elements from hydrogen". Monthly Notices of the Royal Astronomical Society 106: 343–383. Bibcode:1946MNRAS.106..343H.
4. ^ F. Hoyle, Synthesis of the elements between carbon and nickel, Astrophys. J. Suppl., 1, 121 (1954)
5. ^ D. D. Clayton, Hoyle's equation, Science, 318, 1876–77 (2007)
6. ^ E. M. Burbidge, G. R. Burbidge, W. A. Fowler, F. Hoyle (1957). "Synthesis of the Elements in Stars". Reviews of Modern Physics 29 (4): 547–650. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547.
7. ^ A. G. W. Cameron, Stellar Evolution, Nuclear astrophysics and nucleogenesis, Chalk River (Canada) Report CRL-41 (1957)
8. ^ Donald D. Clayton, W. A. Fowler, T. E. Hull, and B. A. Zimmerman, "Neutron capture chains in heavy element synthesis", Ann. Phys., 12, 331–408, (1961)
9. ^ Seeger, P. A., W. A. Fowler, and Donald D. Clayton, "Nucleosynthesis of heavy elements by neutron capture", Astrophys. J. Suppl, XI, 121–66, (1965)
10. ^ Bodansky, D., Donald D. Clayton, and W. A. Fowler, "Nucleosynthesis during silicon burning", Phys. Rev. Letters, 20, 161–64, (1968); Bodansky, D., Donald D. Clayton, and W. A. Fowler, Nuclear quasi-equilibrium during silicon burning, Astrophys. J. Suppl. No. 148, 16, 299–371, (1968)
11. ^ Donald D. Clayton, "Cosmoradiogenic chronologies of nucleosynthesis", Astrophys. J., 139, 637–63, (1964)
12. ^ Jones, Lauren V. (2009), Stars and galaxies, Greenwood guides to the universe, ABC-CLIO, pp. 65–67, ISBN 0-313-34075-7
13. ^ ^{a b c d} Böhm-Vitense, Erika (1992), Introduction to Stellar Astrophysics 3, Cambridge University Press, pp. 93–100, ISBN 0-521-34871-4
14. ^ Reiners, A.; Basri, G. (March 2009). "On the magnetic topology of partially and fully convective stars". Astronomy and Astrophysics 496 (3): 787–790. arXiv:0901.1659. Bibcode:2009A&A...496..787R. doi:10.1051/0004-6361:200811450. Cite uses deprecated parameters (help)
15. ^ ^{a b} de Loore, Camiel W. H.; Doom, C. (1992), Structure and evolution of single and binary stars, Astrophysics and space science library 179, Springer, pp. 200–214, ISBN 0-7923-1768-8
16. ^ ^{a b c} Jeffrey, C. Simon (2010), "Stellar structure and evolution: an introduction", in Goswami, A.; Reddy, B. E., Principles and Perspectives in Cosmochemistry, Springer, pp. 64–66, ISBN 3-642-10368-5
17. ^ Karttunen, Hannu; Oja, Heikki (2007), Fundamental astronomy (5th ed.), Springer, p. 247, ISBN 3-540-34143-9
18. ^ Reid, I. Neill; Hawley, Suzanne L. (2005), New light on dark stars: red dwarfs, low-mass stars, brown dwarfs, Springer-Praxis books in astrophysics and astronomy (2nd ed.), Springer, p. 108, ISBN 3-540-25124-3
19. ^ Salaris, Maurizio; Cassisi, Santi (2005), Evolution of stars and stellar populations, John Wiley and Sons, pp. 119–123, ISBN 0-470-09220-3
20. ^ Schuler, S. C.; King, J. R.; The, L.-S. (2009), "Stellar Nucleosynthesis in the Hyades Open Cluster", The Astrophysical Journal 701 (1): 837–849, arXiv:0906.4812, Bibcode:2009ApJ...701..837S, doi:10.1088/0004-637X/701/1/837
21. ^ Goupil, M. J.; Lebreton, Y.; Marques, J. P.; Samadi, R.; Baudin, F. (January 2011), "Open issues in probing interiors of solar-like oscillating main sequence stars 1. From the Sun to nearly suns", Journal of Physics: Conference Series 271 (1): 012031, arXiv:1102.0247, Bibcode:2011JPhCS.271a2031G, doi:10.1088/1742-6596/271/1/012031 Cite uses deprecated parameters (help)

• Bethe, H. A. (1939). "Energy Production in Stars". Physical Review 55 (1): 103. Bibcode:1939PhRv...55..103B. doi:10.1103/PhysRev.55.103.
• Bethe, H. A. (1939). "Energy Production in Stars". Physical Review 55 (5): 434–456. Bibcode:1939PhRv...55..434B. doi:10.1103/PhysRev.55.434.
• Hoyle, F. (1954). "On Nuclear Reactions occurring in very hot stars: Synthesis of elements from carbon to nickel". Astrophys. J. 1 (Supplement 1): 121–146. Bibcode:1954ApJS....1..121H. doi:10.1086/190005.
• Clayton, Donald D. (1968). Principles of Stellar Evolution and Nucleosynthesis. New York: McGraw-Hill.
• Ray (2004). "Stars as thermonuclear reactors: Their fuels and ashes". arXiv:astro-ph/0405568 [astro-ph].
• Wallerstein, G.; I. Iben Jr.; P. Parker; A.M. Boesgaard; G.M. Hale; A. E. Champagne; C.A. Barnes; F. Käppeler; V.V. Smith; R.D. Hoffman; F.X. Timmes; C. Sneden; R.N. Boyd; B.S. Meyer; D.L. Lambert (1999). "Synthesis of the elements in stars: forty years of progress" (pdf). Reviews of Modern Physics 69 (4): 995–1084. Bibcode:1997RvMP...69..995W. doi:10.1103/RevModPhys.69.995. Retrieved 2006-08-04. Cite uses deprecated parameters (help)
• Woosley, S. E.; A. Heger; T. A. Weaver (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. Cite uses deprecated parameters (help)
• Clayton, Donald D. (2003). Handbook of Isotopes in the Cosmos. Cambridge: Cambridge University Press. ISBN 0-521-82381-1.

• How the Sun Shines by John N. Bahcall
• Nucleosynthesis in NASA's Cosmicopia

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