Nuclear Astrophysics & Stellar Reactions

Nuclear astrophysics is an interdisciplinary branch of physics involving close collaboration among researchers in various subfields of nuclear physics and astrophysics with significant emphasis in areas such as stellar modelling measurement and theoretical estimation of nuclear reaction rates, cosmology, cosmochemistry, gamma rays, optical and X-ray astronomy, and extending our knowledge about nuclear lifetime's and masses. In general terms, nuclear astrophysics aims to understand the origin of the chemical elements and the energy generation in stars.

The basic principles of explaining the origin of the elements and the energy generation in stars were laid down in the theory of nucleosynthesis which came together in the late 1950s from the seminal works of Burbidge, Burbidge, Fowler, and Hoyle in a famous paper and independently by Cameron. Fowler is largely credited with initiating the collaboration between astronomers, astrophysicists, and experimental nuclear physicists which is what we now know as nuclear astrophysics, winning the Nobel Prize for this in 1983.

The theory of stellar nucleosynthesis reproduces the chemical abundances observed in the Solar System and galaxy, which from hydrogen to uranium, show an extremely varied distribution spanning twelve orders of magnitude (one trillion). While impressive, these data were used to formulate the theory, and a scientific theory must be predictive in order to have any merit. The theory of stellar nucleosynthesis has been well-tested by observation and experiment since the theory was first formulated.

Although the foundations of the science are bona fide, there are still many remaining open questions. A few of the long-standing issues are heliumfusion, he astrophysical site of the r-process, anomalous lithium abundances in Population III stars, and the explosion mechanism in core-collapse supernovae.

A stimulus to the development of the theory of nucleosynthesis was the discovery of variations in the abundances of elements found in the universe. The need for a physical description was already inspired by the relative abundances of isotopes of the chemical elements in the solar system. 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 that is not random. 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.

Notable Points:

The most important reactions in stellar nucleosynthesis is the Helium fusion: The triple-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
• The P-process : Photodisintegration

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 not blue in color, but are rather yellow giants, possibly Cepheid variable. 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.

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.

Nuclear Reactions in Stars 

The most basic property of stars is that their radiant energy must derive from internal sources. Given the great length of time that stars endure (some 10 billion years in the case of the Sun), it can be shown that neither chemical nor gravitational effects could possibly yield the required energies. Instead, the cause must be nuclear events wherein lighter nuclei are fused to create heavier nuclei, an inevitable by-product being energy.

In the interior of a star, the particles move rapidly in every direction because of the high temperatures present. Every so often a proton moves close enough to a nucleus to be captured, and a nuclear reaction takes place. Only protons of extremely high energy (many times the average energy in a star such as the Sun) are capable of producing nuclear events of this kind. A minimum temperature required for fusion is roughly 10 million K. Since the energies of protons are proportional to temperature, the rate of energy production rises steeply as temperature increases.

For the Sun and other normal main-sequence stars, the source of energy lies in the conversion of hydrogen to helium. The nuclear reaction thought to occur in the Sun is called the proton-proton cycle. In this fusion reaction, two protons (¹H) collide to form a deuteron (a nucleus of deuterium, ²H), with the liberation of a positron (the electron’s positively charged antimatter counterpart, denoted e⁺). Also emitted is a neutral particle of very small mass called a neutrino, ν. While the helium “ash” remains in the core where it was produced, the neutrino escapes from the solar interior within seconds. The positron encounters an ordinary negatively charged electron, and the two annihilate each other, with much energy being released. This annihilation energy amounts to 1.02 megaelectron volts (MeV), which accords well with Einstein’s equation E = mc² (where m is the mass of the two particles, c the velocity of light, and E the liberated energy).

Next, a proton collides with the deuteron to form the nucleus of a light helium atom of atomic weight 3, ³He. A “hard” X-ray (one of the higher energy) or gamma-ray (γ) photon also is emitted. The most likely event to follow in the chain is a collision of this ³He nucleus with a normal ⁴He nucleus to form the nucleus of a beryllium atom of weight 7, ⁷Be, with the emission of another gamma-ray photon. The ⁷Be nucleus in turn captures a proton to form a boron nucleus of atomic weight 8, ⁸B, with the liberation of yet another gamma ray.

The ⁸B nucleus, however, is very unstable. It decays almost immediately into beryllium of atomic weight 8, ⁸Be, with the emission of another positron and a neutrino. The nucleus itself thereafter decays into two helium nuclei, ⁴He. These nuclear events can be represented by the following equations:

In the course of these reactions, four protons are consumed to form one helium nucleus, while two electrons perish.

The mass of four hydrogen atoms is 4 × 1.00797, or 4.03188, atomic mass units; that of a helium atom is 4.0026. Hence, 0.02928 atomic mass unit, or 0.7 percent of the original mass, has disappeared. Some of this has been carried away by the elusive neutrinos, but most of it has been converted to radiant energy. In order to keep shining at its present rate, a typical star (e.g., the Sun) needs to convert 674 million tons of hydrogen to 670 million tons of helium every second. According to the formula E = mc², more than four million tons of matter literally disappear into radiation each second.

This theory provides a good understanding of solar energy generation, although for decades it suffered from one potential problem. The neutrino flux from the Sun was measured by different experimenters, and only one-third of the flux of electron neutrinos predicted by the theory was detected. (Neutrinos come in three types, each associated with a charged lepton: electron neutrino, muon neutrino, and tau neutrino.) Over that time, however, the consensus grew that the solar neutrino problem and its solution lay not with the astrophysical model of the Sun but with the physical nature of neutrinos themselves. In the late 1990s and the early 21st century, scientists discovered that neutrinos oscillate (change types) between electron neutrinos, the state in which they were created in the Sun, and muon or tau neutrinos, states that are more difficult to detect when they reach Earth.
The main source of energy in hotter stars is the carbon cycle (also called the CNO cycle for carbon, nitrogen, and oxygen), in which hydrogen is transformed into helium, with carbon serving as a catalyst. The reactions proceed as follows: first, a carbon nucleus, ¹²C, captures a proton (hydrogen nucleus), ¹H, to form a nucleus of nitrogen, ¹³N, a gamma-ray photon being emitted in the process; thus, ¹²C + ¹H → ¹³N + γ. The light ¹³N nucleus is unstable, however. It emits a positron, e⁺, which encounters an ordinary electron, e⁻, and the two annihilate one another. A neutrino also is released, and the resulting ¹³C nucleus is stable. Eventually the ¹³C nucleus captures another proton, forms ¹⁴N, and emits another gamma-ray photon. In symbols the reaction is represented by the equations¹³N → ¹³C + e⁺ + ν; then ¹³C + ¹H → ¹⁴N + γ. Ordinary nitrogen, ¹⁴N, is stable, but when it captures a proton to form a nucleus of light oxygen-15, ¹⁵O, the resulting nucleus is unstable against beta decay. It therefore emits a positron and a neutrino, a sequence of events expressed by the equations ¹⁴N + ¹H → ¹⁵O + γ; then ¹⁵O → ¹⁵N + e⁺ + ν.
Again, the positron meets an electron, and the two annihilate each other while the neutrino escapes. Eventually the ¹⁵N nucleus encounters a fast-moving proton, ¹H, and captures it, but the formation of an ordinary ¹⁶O nucleus by this process occurs only rarely. The most likely effect of this proton capture is a breakdown of ¹⁵N and a return to the ¹²C nucleus—that is,¹⁵N + ¹H → ¹²C + ⁴He + γ. Thus, the original ¹²C nucleus reappears, and the four protons that have been added permit the formation of a helium nucleus. The same amount of mass has disappeared, though a different fraction of it may have been carried off by the neutrinos.
Only the hottest stars that lie on the main sequence shine with energy produced by the carbon cycle. The faint red dwarfs use the proton-proton cycle exclusively, whereas stars such as the Sun shine mostly by the proton-proton reaction but derive some contribution from the carbon cycle as well.
The aforementioned mathematical relationships permit the problem of stellar structure to be addressed notwithstanding the complexity of the problem. An early assumption that stars have a uniform chemical composition throughout their interiors simplified the calculations considerably, but it had to be abandoned when studies in stellar evolution proved that the compositions of stars change with age. Computations need to be carried out by a step-by-step process known as numerical integration. They must take into account that the density and pressure of a star vanish at the surface, whereas these quantities and the temperature remain finite at the core.
Resulting models of a star’s interior, including the relation between mass, luminosity, and radius, are determined largely by the mode of energy transport. In the Sun and the fainter main-sequence stars, energy is transported throughout the outer layers by convective currents, whereas in the deep interior, energy is transported by radiation. Among the hotter stars of the main sequence, the reverse appears to be true. The deep interiors of the stars that derive their energy primarily from the carbon cycle are in convective equilibrium, whereas in the outer parts the energy is carried by radiation. The observed masses, luminosities, and radii of most main-sequence stars can be reproduced with reasonable and uniform chemical composition.
Chemically homogeneous models of giant and supergiant stars cannot be constructed. If a yellow giant such as Capella is assumed to be built like a main-sequence star, its central temperature turns out to be so low that no known nuclear process can possibly supply the observed energy output. Progress has been made only by assuming that these stars were once main-sequence objects that, in the course of their development, exhausted the hydrogen in their deep interiors. Inert cores consequently formed, composed mainly of the helium ash left from the hydrogen-fusion process. Since no helium nuclear reactions are known to occur at the few tens of millions of kelvins likely to prevail in these interiors, no thermonuclear energy could be released from such depleted cores. Instead, energy is assumed to be generated in a thin shell surrounding the inert core where some fuel remains, and it is presumably produced by the carbon cycle. Such models are called shell-source models. As a star uses up increasing amounts of its hydrogen supply, its core grows in mass while the outer envelope of the star continues to expand. These shell-source models explain the observed luminosities, masses, and radii of giants and supergiants.

The depletion of hydrogen fuel is appreciable even for a dwarf, middle-aged star such as the Sun. The Sun seems to have been shining at its present rate for about the last 20 percent of its current age of five billion years. For its observed luminosity to be maintained, the Sun’s central temperature must have increased considerably since the formation of the solar system, largely as a consequence of the depletion of the hydrogen in its interior along with an accompanying increase in molecular weight and temperature. During the past five billion years, the Sun probably brightened by about half a magnitude; in early Precambrian time (about two billion years ago), the solar luminosity must have been some 20 percent less than it is today.

Bibliography: 

1. Hoyle, F. (1946). "The synthesis of the elements from hydrogen". Monthly Notices of the Royal Astronomical Society. 106 (5): 343–383. Bibcode:1946MNRAS.106..343H. doi:10.1093/mnras/106.5.343.
2. ^ a b Hoyle, F. (1954). "On Nuclear Reactions Occurring in Very Hot STARS. I. The Synthesis of Elements from Carbon to Nickel". The Astrophysical Journal Supplement Series. 1: 121. Bibcode:1954ApJS....1..121H. doi:10.1086/190005.
3. ^ a b Burbidge, E. M.; Burbidge, G. R.; Fowler, W.A.; Hoyle, F. (1957). "Synthesis of the Elements in Stars" (PDF). Reviews of Modern Physics. 29 (4): 547–650. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547.
4. ^ Suess, H. E.; Urey, H. C. (1956). "Abundances of the Elements". Reviews of Modern Physics. 28 (1): 53–74. Bibcode:1956RvMP...28...53S. doi:10.1103/RevModPhys.28.53.
5. ^ a b Clayton, D. D. (1968). Principles of Stellar Evolution and Nucleosynthesis. University of Chicago Press.
6. ^ Eddington, A. S. (1920). "The internal constitution of the stars". The Observatory. 43: 341–358. Bibcode:1920Obs....43..341E.
7. ^ Eddington, A. S (1920). "The Internal Constitution of the Stars". Nature. 106 (2653): 14. Bibcode:1920Natur.106...14E. doi:10.1038/106014a0.
8. ^ Selle, D. (October 2012). "Why the Stars Shine" (PDF). Guidestar. Houston Astronomical Society. pp. 6–8. Archived(PDF) from the original on 2013-12-03.
9. ^ Bethe, H. A. (1939). "Energy Production in Stars". Physical Review. 55 (5): 434–456. doi:10.1103/PhysRev.55.434.
10. ^ Clayton, D. D. (2007). "HISTORY OF SCIENCE: Hoyle's Equation". Science. 318(5858): 1876–1877. doi:10.1126/science.1151167.
11. ^ Cameron, A. G. W. (1957). Stellar Evolution, Nuclear Astrophysics, and Nucleogenesis (PDF) (Report). Atomic Energy of Canada. Report CRL-41.
12. ^ Clayton, D. D.; Fowler, W. A.; Hull, T. E.; Zimmerman, B. A. (1961). "Neutron capture chains in heavy element synthesis". Annals of Physics. 12 (3): 331–408. doi:10.1016/0003-4916(61)90067-7.
13. ^ Seeger, P. A.; Fowler, W. A.; Clayton, D. D. (1965). "Nucleosynthesis of Heavy Elements by Neutron Capture". The Astrophysical Journal Supplement Series. 11: 121–126. Bibcode:1965ApJS...11..121S. doi:10.1086/190111.
14. ^ Bodansky, D.; Clayton, D. D.; Fowler, W. A. (1968). "Nucleosynthesis During Silicon Burning". Physical Review Letters. 20 (4): 161–164. Bibcode:1968PhRvL..20..161B. doi:10.1103/PhysRevLett.20.161.
15. ^ Bodansky, D.; Clayton, D. D.; Fowler, W. A. (1968). "Nuclear Quasi-Equilibrium during Silicon Burning". The Astrophysical Journal Supplement Series. 16: 299. Bibcode:1968ApJS...16..299B. doi:10.1086/190176.
16. ^ Clayton, D. D. (1964). "Cosmoradiogenic Chronologies of Nucleosynthesis". The Astrophysical Journal. 139: 637. doi:10.1086/147791.
17. ^ a b Jones, Lauren V. (2009), Stars and galaxies, Greenwood guides to the universe, ABC-CLIO, pp. 65–67, ISBN 0-313-34075-7
18. ^ a b c d Böhm-Vitense, Erika (1992), Introduction to Stellar Astrophysics, 3, Cambridge University Press, pp. 93–100, ISBN 0-521-34871-4
19. ^ 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.
20. ^ 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
21. ^ 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
22. ^ Karttunen, Hannu; Oja, Heikki (2007), Fundamental astronomy (5th ed.), Springer, p. 247, ISBN 3-540-34143-9
23. ^ 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
24. ^ Salaris, Maurizio; Cassisi, Santi (2005), Evolution of stars and stellar populations, John Wiley and Sons, pp. 119–123, ISBN 0-470-09220-3

^ 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: