stellar nucleosynthesis


  • [22] 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.

  • Clayton calculated the first time-dependent models of the s-process in 1961[15] and of the r-process in 1965,[16] as well as of the burning of silicon into the abundant alpha-particle
    nuclei and iron-group elements in 1968,[17][18] and discovered radiogenic chronologies[19] for determining the age of the elements.

  • [1] Hoyle followed that in 1954 with a paper describing how advanced fusion stages within massive stars would synthesize the elements from carbon to iron in mass.

  • [21]: 245  In the cores of lower-mass main-sequence stars such as the Sun, the dominant energy production process is the proton–proton chain reaction.

  • Stars evolve because of changes in their composition (the abundance of their constituent elements) over their lifespans, first by burning hydrogen (main sequence star), then
    helium (horizontal branch star), and progressively burning higher elements.

  • 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 type of hydrogen fusion process that dominates in a star is determined by the temperature dependency differences between the two reactions.

  • [39][40] Incidentally, since the former reaction has a much higher Gamow factor, and due to the relative abundance of elements in typical stars, the two reaction rates are
    equal at a temperature value that is within the core temperature ranges of main-sequence stars.

  • 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.

  • [25] Helium fusion[edit] Main articles: Triple-alpha process and Alpha process 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.

  • [3] 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 by neutron capture.

  • Key reactions The most important reactions in stellar nucleosynthesis: • Hydrogen fusion: o Deuterium fusion o The proton–proton chain o The carbon–nitrogen–oxygen cycle •
    Helium fusion: o The triple-alpha process o The alpha process • Fusion of heavier elements: o Lithium burning: a process found most commonly in brown dwarfs o Carbon-burning process o Neon-burning process o Oxygen-burning process o Silicon-burning
    process • Production of elements heavier than iron: o Neutron capture:  The r-process  The s-process o Proton capture:  The rp-process  The p-process o Photodisintegration Hydrogen fusion[edit] Main articles: Proton–proton chain reaction,
    CNO cycle, and Deuterium fusion Proton–proton chain reaction CNO-I cycle The helium nucleus is released at the top-left step.

  • [10] 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.

  • 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.

  • The need for a physical description was already inspired by the relative abundances of the chemical elements in the solar system.

  • The proton–proton chain reaction starts at temperatures about ,[30] making it the dominant fusion mechanism in smaller stars.

  • Since this integration has an exponential damping at high energies of the form and at low energies from the Gamow factor, the integral almost vanished everywhere except around
    the peak, called Gamow peak,[36]: 185  at E0, where: Thus: The exponent can then be approximated around E0 as: And the reaction rate is approximated as:[37] Values of S(E0) are typically keV·b, but are damped by a huge factor when involving
    a beta decay, due to the relation between the intermediate bound state (e.g.

  • The second process, the carbon–nitrogen–oxygen cycle, which was also considered by Carl Friedrich von Weizsäcker in 1938, is more important in more massive main-sequence stars.

  • Hydrogen fusion (nuclear fusion of four protons to form a helium-4 nucleus[20]) is the dominant process that generates energy in the cores of main-sequence stars.

  • In 1928 George Gamow derived what is now called the Gamow factor, a quantum-mechanical formula yielding the probability for two contiguous nuclei to overcome the electrostatic
    Coulomb barrier between them and approach each other closely enough to undergo nuclear reaction due to the strong nuclear force which is effective only at very short distances.

  • This temperature is achieved in the cores of main-sequence stars with at least 1.3 times the mass of the Sun.

  • One then integrates over all energies to get the total reaction rate, using the Maxwell–Boltzmann distribution and the relation: where is the reduced mass.

  • 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.

  • For stars above 35% of the Sun’s mass,[23] 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.

  • However, most of the nucleosynthesis in the mass range A = 28–56 (from silicon to nickel) is actually caused by the upper layers of the star collapsing onto the core, creating
    a compressional shock wave rebounding outward.

  • [33]: 5  As a main-sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.

  • In this way, the alpha process preferentially produces elements with even numbers of protons by the capture of helium nuclei.

  • However, since the reaction involves quantum tunneling, there is an exponential damping at low energies that depends on Gamow factor EG, giving an Arrhenius equation: where
    S(E) depends on the details of the nuclear interaction, and has the dimension of an energy multiplied for a cross section.

  • [24] As a result, there is little mixing of fresh hydrogen into the core or fusion products outward.

  • Later in its life, a low-mass star will slowly eject its atmosphere via stellar wind, forming a planetary nebula, while a higher–mass star will eject mass via a sudden catastrophic
    event called a supernova.

  • It explains why the observed abundances of elements change over time and why some elements and their isotopes are much more abundant than others.


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