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 overlying mantles of stars. Stars are said to evolve (age) with changes in the abundances of the elements within. Core fusion increases the atomic weight of its gaseous elements, causing pressure loss and contraction accompanied by increase of temperature. Stars lose most of their mass when it is ejected late in their 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. One stimulus to the development of the theory of nucleosynthesis was the 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 a random distribution. Such a graph of the abundances can be seen at History of nucleosynthesis theory. Stellar nucleosynthesis is the dominating contributor to several processes that also occur under the collective term nucleosynthesis.

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. The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides that energy and synthesizes new nuclei as a byproduct of that fusion process. This became clear during the decade prior to World War II. The fusion product 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 the 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. 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. 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 p-p chain and of the CNO cycle appears in a 1968 textbook. 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. 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. This is the dominant work in stellar nucleosynthesis. 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). 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 (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 and of the R-process, as well as of the burning of silicon into the abundant alpha-particle nuclei and iron-group elements, and discovered radiogenic chronologies 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 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. (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. 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, the energy flux toward the surface is sufficiently low that the core region remains a radiative zone, rather than becoming convective. In each complete fusion cycle, the p-p chain reaction releases about 26.2 MeV.

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. 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. 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. 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. 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.

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, 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. 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. 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. As a main sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.

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.

External links

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