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Stellar nucleosynthesis is the creation (nucleosynthesis) of
chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
s by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
,
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
and
lithium Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid ...
during the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from t ...
. As a predictive theory, it yields accurate estimates of the observed abundances of the elements. It explains why the observed abundances of elements change over time and why some elements and their isotopes are much more abundant than others. The theory was initially proposed by Fred Hoyle in 1946, who later refined it in 1954. Further advances were made, especially to nucleosynthesis by neutron capture of the elements heavier than iron, by Margaret and Geoffrey Burbidge, William Alfred Fowler and Hoyle in their famous 1957 B2FH paper, which became one of the most heavily cited papers in astrophysics history. Stars evolve because of changes in their composition (the abundance of their constituent elements) over their lifespans, first by burning hydrogen (
main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Her ...
star), then
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
( horizontal branch star), and progressively burning higher elements. However, this does not by itself significantly alter the abundances of elements in the universe as the elements are contained within the star. 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. The term supernova nucleosynthesis is used to describe the creation of elements during the explosion of a massive star or white dwarf. The advanced sequence of burning fuels is driven by
gravitational collapse Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formatio ...
and its associated heating, resulting in the subsequent burning of
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon makes ...
,
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as we ...
and
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...
. However, most of the nucleosynthesis in the mass range (from silicon to nickel) is actually caused by the upper layers of the star collapsing onto the core, creating a compressional
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
rebounding outward. The shock front briefly raises temperatures by roughly 50%, thereby causing furious burning for about a second. This final burning in massive stars, called ''explosive nucleosynthesis'' or supernova nucleosynthesis, is the final epoch of stellar nucleosynthesis. 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 the chemical elements in the solar system. Those abundances, when plotted on a graph as a function of the atomic number of the element, have a jagged sawtooth shape that varies by factors of tens of millions (see
history of nucleosynthesis theory Nucleosynthesis is the process that creates new atomic nuclei from pre-existing nucleons (protons and neutrons) and nuclei. According to current theories, the first nuclei were formed a few minutes after the Big Bang, through nuclear reactions in ...
). 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 In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
released from nuclear fusion reactions accounted for the longevity of the Sun as a source of heat and light.


History

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 Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
to form
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
and raised the possibility that the heavier elements are produced in stars. This was a preliminary step toward the idea of stellar nucleosynthesis. In 1928 George Gamow derived what is now called the Gamow factor, a
quantum-mechanical Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
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 The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called t ...
which is effective only at very short distances. In the following decade the Gamow factor was used by Atkinson and Houtermans and later by Edward Teller and Gamow himself to derive the rate at which nuclear reactions would occur at the high temperatures believed to exist in stellar interiors. In 1939, in a Nobel lecture 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 more important in more massive main-sequence 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. 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 thermodynamically into
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
. 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. Hoyle's theory was extended to other processes, beginning with the publication of the 1957 review paper "Synthesis of the Elements in Stars" by
Burbidge Burbidge is a surname. Notable people with the surname include: * Frederick William Thomas Burbidge (1847–1905), English explorer and botanist * Geoffrey Burbidge (1925–2010), English astronomy professor * George Burbidge (1847–1908), Canadi ...
,
Burbidge Burbidge is a surname. Notable people with the surname include: * Frederick William Thomas Burbidge (1847–1905), English explorer and botanist * Geoffrey Burbidge (1925–2010), English astronomy professor * George Burbidge (1847–1908), Canadi ...
, Fowler and Hoyle, more 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 by neutron capture. Significant improvements were made by Alastair G. W. Cameron and by
Donald D. Clayton Donald Delbert Clayton (born March 18, 1935) is an American astrophysicist whose most visible achievement was the prediction from nucleosynthesis theory that supernovae are intensely radioactive. That earned Clayton the NASA Exceptional Scientifi ...
. In 1957 Cameron presented his own independent approach to nucleosynthesis, informed by Hoyle's example, and introduced computers into time-dependent calculations of evolution of nuclear systems. Clayton calculated the first time-dependent models of the ''s''-process in 1961 and of the ''r''-process in 1965, as well as of the burning of silicon into the abundant alpha-particle nuclei and iron-group elements in 1968, and discovered radiogenic chronologies for determining the age of the elements.


Key reactions

The most important reactions in stellar nucleosynthesis: *
Hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
fusion: ** Deuterium fusion ** The proton–proton chain ** The carbon–nitrogen–oxygen cycle *
Helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
fusion: ** The triple-alpha process ** The alpha process * Fusion of heavier elements: ** Lithium burning: a process found most commonly in
brown dwarf Brown dwarfs (also called failed stars) are substellar objects that are not massive enough to sustain nuclear fusion of ordinary hydrogen (hydrogen-1, 1H) into helium in their cores, unlike a main sequence, main-sequence star. Instead, they have ...
s ** Carbon-burning process ** Neon-burning process ** Oxygen-burning process ** Silicon-burning process * Production of elements heavier than
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
: **
Neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
capture: *** The r-process *** The s-process ** Proton capture: *** The rp-process *** The p-process ** Photodisintegration


Hydrogen fusion

Hydrogen fusion (nuclear fusion of four protons to form a helium-4 nucleus) 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 A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wit ...
combustion of hydrogen in an
oxidizing Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...
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 A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes ...
, 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 reactions that begin with the fusion of two protons to form a
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
nucleus (one proton plus one neutron) along with an ejected positron and neutrino. In each complete fusion cycle, the proton–proton chain reaction releases about 26.2 MeV. 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, 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. 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. 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 A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
emission. 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. This results in such an intense outward energy flux that convective energy transfer becomes 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. 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. Our Sun produces on the order of 1% 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 , making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately , but thereafter it increases more rapidly in efficiency as the temperature rises, than does the proton–proton reaction. Above approximately , 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 about . As a main-sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.


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 Degeneracy, degenerate, or degeneration may refer to: Arts and entertainment * ''Degenerate'' (album), a 2010 album by the British band Trigger the Bloodshed * Degenerate art, a term adopted in the 1920s by the Nazi Party in Germany to descr ...
helium core, and the star moves to the horizontal branch where it burns helium in its core. More massive stars ignite helium in their core without a flash and execute a blue loop before reaching the asymptotic giant branch. Such a star initially moves away from the AGB toward bluer colours, then loops back again to what is called the Hayashi track. An important consequence of blue loops is that they give rise to classical Cepheid variables, of central importance in determining distances in the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked ey ...
and to nearby galaxies. Despite the name, stars on a blue loop from the red giant branch are typically not blue in colour but are rather yellow giants, possibly Cepheid variables. They fuse helium until the core is largely
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon makes ...
and
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as we ...
. The most massive stars become supergiants when they leave the main sequence and quickly start helium fusion as they become red supergiants. After the helium is exhausted in the core of a star, helium fusion will continue in a shell around the carbon–oxygen core. In all cases, helium is fused to carbon via the triple-alpha process, i.e., three helium nuclei are transformed into carbon via 8Be. 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.


Reaction rate

The reaction rate density between species ''A'' and ''B'', having number densities ''n''''A'',''B'', is given by: ::r = n_A \, n_B \, k where k is the
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the ...
of each single elementary binary reaction composing the nuclear fusion process: ::k = \langle \sigma(v)\,v \rangle here, σ(''v'') is the cross-section at relative velocity ''v'', and averaging is performed over all velocities. Semi-classically, the cross section is proportional to \pi\,\lambda^2, where \lambda = h/p is the de Broglie wavelength. Thus semi-classically the cross section is proportional to \frac. However, since the reaction involves quantum tunneling, there is an exponential damping at low energies that depends on Gamow factor ''E''G, giving an Arrhenius equation: ::\sigma(E) = \frac e^ where ''S''(''E'') depends on the details of the nuclear interaction, and has the dimension of an energy multiplied for a cross section. One then integrates over all energies to get the total reaction rate, using the
Maxwell–Boltzmann distribution In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and use ...
and the relation: ::\frac = n_A n_B \int_0^\frac \, e^ 2\sqrt e^ \,\sqrtdE where m_\text = \frac is the reduced mass. Since this integration has an exponential damping at high energies of the form \sim e^ and at low energies from the Gamow factor, the integral almost vanished everywhere except around the peak, called Gamow peak, at ''E''0, where: ::\frac \left( -\sqrt - \frac\right) \, = \, 0 Thus: ::E_0 = \left(\frackT \sqrt\right)^\frac The exponent can then be approximated around ''E''0 as: ::e^ \approx e^ \exp\left(-\frac\right) And the reaction rate is approximated as: ::\frac \approx n_A \, n_B \, \frac\, \sqrt \frac e^ Values of ''S''(''E''0) are typically , but are damped by a huge factor when involving a
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For e ...
, due to the relation between the intermediate bound state (e.g. diproton)
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
and the beta decay half-life, as in the proton–proton chain reaction. Note that typical core temperatures in main-sequence stars give ''kT'' of the order of keV. Thus, the limiting reaction in the CNO cycle, proton capture by , has ''S''(''E''0) ~ ''S''(0) = 3.5keV·b, while the limiting reaction in the proton–proton chain reaction, the creation of
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
from two protons, has a much lower ''S''(''E''0) ~ ''S''(0) = 4×10−22keV·b. Incidentally, since the former reaction has a much higher Gamow factor, and due to the relative
abundance of elements The abundance of the chemical elements is a measure of the occurrence of the chemical elements relative to all other elements in a given environment. Abundance is measured in one of three ways: by the mass-fraction (the same as weight fraction); ...
in typical stars, the two reaction rates are equal at a temperature value that is within the core temperature ranges of main-sequence stars.Goupil, M., Belkacem, K., Neiner, C., Lignières, F., & Green, J. J., eds., ''Studying Stellar Rotation and Convection: Theoretical Background and Seismic Diagnostics'' (Berlin/Heidelberg: Springer, 2013)
p. 211


References


Notes


Citations


Further reading

* * * * * * * *


External links


"How the Sun Shines"
by John N. Bahcall (Nobel prize site, accessed 6 January 2020)
Nucleosynthesis
in
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeedi ...
's Cosmicopia {{Portal bar, Physics, Chemistry, Astronomy, Outer space, Solar System, Science Nucleosynthesis Nuclear physics Nucleosynthesis, Stellar Astrophysics Concepts in astronomy