Stellar nucleosynthesis

Stellar nucleosynthesis is the process by which the natural abundances of the chemical elements within stars change due to nuclear fusion reactions in the cores and their overlying mantles. Stars are said to evolve (age) with changes in the abundances of the elements within. Core fusion increases the atomic weight of elements and reduces the number of particles, which would lead to a pressure loss except that gravitation leads to contraction, an increase of temperature, and a balance of forces.^[1] A star loses most of its mass when it is ejected late in the star's stellar lifetimes, thereby increasing the abundance of elements heavier than helium in the interstellar medium. The term supernova nucleosynthesis is used to describe the creation of elements during the evolution and explosion of a presupernova star, as Fred Hoyle advocated presciently in 1954.^[2] A stimulus to the development of the theory of nucleosynthesis was the discovery of variations in the abundances of elements found in the universe. Those abundances, when plotted on a graph as a function of atomic number of the element, have a jagged sawtooth shape that varies by factors of tens of millions. This suggested a natural process other than random. Such a graph of the abundances can be seen at History of nucleosynthesis theory article. Of the several processes of nucleosynthesis, stellar nucleosynthesis is the dominating contributor to elemental abundances in the universe.

A second stimulus to understanding the processes of stellar nucleosynthesis occurred during the 20th century, when it was realized that the energy released from nuclear fusion reactions accounted for the longevity of the Sun as a source of heat and light.^[3] The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides it energy and the synthesis of new nuclei is a byproduct of that fusion process. This became clear during the decade prior to World War II. The fusion-produced nuclei are restricted to those only slightly heavier than the fusing nuclei; thus they do not contribute heavily to the natural abundances of the elements. Nonetheless, this insight raised the plausibility of explaining all of the natural abundances of elements in this way. The prime energy producer in our Sun is the fusion of hydrogen to form helium, which occurs at a solar-core temperature of 14 million kelvin.

History

In 1920 Arthur Eddington proposed that stars obtained their energy from nuclear fusion of hydrogen to form helium and raised the possibility that the heavier elements are produced in stars.

In 1920, Arthur Eddington, on the basis of the precise measurements of atomic masses by F.W. Aston and a preliminary suggestion by Jean Perrin, proposed that stars obtained their energy from nuclear fusion of hydrogen to form helium and raised the possibility that the heavier elements are produced in stars.^[4][5][6] This was a preliminary step toward the idea of nucleosynthesis. 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.^[7] He defined 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. A clear physical description of the proton–proton chain and of the CNO cycle appears in a 1968 textbook.^[8] Bethe's two papers 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.^[9] 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.^[10] This is the dominant work in stellar nucleosynthesis.^[11] 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, Hoyle's theory was expanded to other processes, beginning with the publication of a celebrated review paper in 1957 by Burbidge, Burbidge, Fowler and Hoyle (commonly referred to as the B²FH paper).^[12] 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 picture for the origin of primary nuclei 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^[13] (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^[14] and of the R-process,^[15] as well as of the burning of silicon into the abundant alpha-particle nuclei and iron-group elements,^[16] and discovered radiogenic chronologies^[17] for determining the age of the elements. The entire research field expanded rapidly in the 1970s.

Key reactions

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

A version of the periodic table indicating the origins – including stellar nucleosynthesis – of the elements. All elements above 103 (lawrencium) are also manmade and are not included.

The most important reactions in stellar nucleosynthesis:

• Hydrogen fusion:
  • Deuterium fusion
  • The proton–proton chain
  • The carbon–nitrogen–oxygen cycle
• Helium fusion:
  • The triple-alpha process
  • The alpha process
• Fusion 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 fusion

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 fusion (nuclear fusion of four protons to form a helium-4 nucleus^[18]) is the dominant process that generates energy in the cores of main-sequence stars. It is also called "hydrogen burning", which should not be confused with the chemical combustion of hydrogen in an oxidizing atmosphere. There are two predominant processes by which stellar hydrogen fusion occurs: proton-proton chain and the carbon-nitrogen-oxygen (CNO) cycle. Ninety percent of all stars, with the exception of white dwarfs, are fusing hydrogen by these two processes.

In the cores of lower-mass main-sequence stars such as the Sun, the dominant energy production process is the proton–proton 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 deuterium nucleus (one proton plus one neutron) along with an ejected positron and neutrino.^[19] In each complete fusion cycle, the proton–proton chain reaction releases about 26.2 MeV.^[19] The proton–proton chain reaction cycle is relatively insensitive to temperature; a 10% rise of temperature would increase energy production by this method by 46%, hence, this hydrogen fusion process can occur in up to a third of the star's radius and occupy half the star's mass. For stars above 35% of the Sun's mass,^[20] the energy flux toward the surface is sufficiently low and energy transfer from the core region remains by radiative heat transfer, rather than by convective heat transfer.^[21] As a result, there is little mixing of fresh hydrogen into the core or fusion products outward.

In higher-mass stars, the dominant energy production process is the CNO cycle, which is a catalytic cycle that uses nuclei of carbon, nitrogen and oxygen as intermediaries and in the end produces a helium nucleus as with the proton-proton chain.^[19] During a complete CNO cycle, 25.0 MeV of energy is released. The difference in energy production of this cycle, compared to the proton–proton chain reaction, is accounted for by the energy lost through neutrino emission.^[19] The CNO cycle is very temperature sensitive, a 10% rise of temperature would produce a 350% rise in energy production. About 90% of the CNO cycle energy generation occurs within the inner 15% of the star's mass, hence it is strongly concentrated at the core.^[22] This results in such an intense outward energy flux that convective energy transfer become more important than does radiative transfer. As a result, the core region becomes a convection zone, which stirs the hydrogen fusion region and keeps it well mixed with the surrounding proton-rich region.^[23] 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.^[22] Our Sun produces 10% of its energy from the CNO cycle.

The type of hydrogen fusion process that dominates in a star is determined by the temperature dependency differences between the two reactions. The proton–proton chain reaction starts at temperatures about 7006400000000000000♠4×10⁶ K,^[24] making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately 7007160000000000000♠16×10⁶ K, but thereafter it increases more rapidly in efficiency as the temperature rises, than does the proton-proton reaction.^[25] Above approximately 7007170000000000000♠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.^[26] The Sun itself has a core temperature of about 7007157000000000000♠15.7×10⁶ K. As a main sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.^[22]

Helium fusion

Main sequence stars accumulate helium in their cores as a result of hydrogen fusion, but the core does not become hot enough to initiate helium fusion. Helium fusion first begins when a star leaves the red giant branch after accumulating sufficient helium in its core to ignite it. In stars around the mass of the sun, this begins at the tip of the red giant branch with a helium flash from a degenerate helium core and the star moves to the horizontal branch where it burns helium in its core. More massive stars ignite helium in their cores without a flash and execute a blue loop before reaching the asymptotic giant branch. Despite the name, stars on a blue loop from the red giant branch are typically yellow giants, possibly Cepheid variables. They fuse helium until the core is largely carbon and oxygen. The most massive stars become supergiants when they leave the main sequence and quickly start helium fusion as they become red supergiants. After helium is exhausted in the core of a star, it will continue in a shell around the carbon-oxygen core.^[18][21]

In all cases, helium is fused to carbon via the triple-alpha process. This can then form oxygen, neon, and heavier elements via the alpha process. In this way, the alpha process preferentially produces elements with even numbers of protons by the capture of helium nuclei. Elements with odd numbers of protons are formed by other fusion pathways.

References

Further reading

• 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]. 
• G. Wallerstein; I. Iben Jr.; P. Parker; A.M. Boesgaard; G.M. Hale; A. E. Champagne; et al. (1997). "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. 
• 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. 
• Clayton, Donald D. (2003). Handbook of Isotopes in the Cosmos. Cambridge: Cambridge University Press. ISBN 0-521-82381-1. 

External links

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

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