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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, helium and lithium 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 the ...
. 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 Margaret is a female first name, derived via French () and Latin () from grc, μαργαρίτης () meaning "pearl". The Greek is borrowed from Persian. Margaret has been an English name since the 11th century, and remained popular througho ...
and
Geoffrey Burbidge Geoffrey Ronald Burbidge FRS (24 September 1925 – 26 January 2010) was an English astronomy professor and theoretical astrophysicist, most recently at the University of California, San Diego. He was married to astrophysicist Margaret Burbi ...
,
William Alfred Fowler William Alfred Fowler ( ) was an American nuclear physicist, later astrophysicist, who, with Subrahmanyan Chandrasekhar, won the 1983 Nobel Prize in Physics. He is known for his theoretical and experimental research into nuclear reactions with ...
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 H ...
star), then helium ( 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 A planetary nebula (PN, plural PNe) is a type of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from red giant stars late in their lives. The term "planetary nebula" is a misnomer because they are unrelated ...
, while a higher–mass star will eject mass via a sudden catastrophic event called a supernova. The term
supernova nucleosynthesis Supernova nucleosynthesis is the nucleosynthesis of chemical elements in supernova explosions. In sufficiently massive stars, the nucleosynthesis by fusion of lighter elements into heavier ones occurs during sequential hydrostatic burning proce ...
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 and its associated heating, resulting in the subsequent burning of carbon, oxygen and silicon. 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 med ...
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 Supernova nucleosynthesis is the nucleosynthesis of chemical elements in supernova explosions. In sufficiently massive stars, the nucleosynthesis by fusion of lighter elements into heavier ones occurs during sequential hydrostatic burning proce ...
, 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). 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 The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
as a source of heat and light.


History

In 1920,
Arthur Eddington Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumi ...
, on the basis of the precise measurements of atomic masses by
F.W. Aston Francis William Aston FRS (1 September 1877 – 20 November 1945) was a British chemist and physicist who won the 1922 Nobel Prize in Chemistry for his discovery, by means of his mass spectrograph, of isotopes in many non-radioactive elements ...
and a preliminary suggestion by
Jean Perrin Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids ( sedimentation equilibrium), verified Albert Einstein’s explanation of this ...
, 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 stellar nucleosynthesis. In 1928
George Gamow George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...
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, qu ...
formula yielding the probability for two contiguous nuclei to overcome the electrostatic
Coulomb barrier The Coulomb barrier, named after Coulomb's law, which is in turn named after physicist Charles-Augustin de Coulomb, is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a ...
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 the ...
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 Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care fo ...
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 The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfre ...
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 Carl Friedrich Freiherr von Weizsäcker (; 28 June 1912 – 28 April 2007) was a German physicist and philosopher. He was the longest-living member of the team which performed nuclear research in Germany during the Second World War, under W ...
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. 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, 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. 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 fusion: **
Deuterium fusion Deuterium fusion, also called deuterium burning, is a nuclear fusion reaction that occurs in stars and some substellar objects, in which a deuterium nucleus and a proton combine to form a helium-3 nucleus. It occurs as the second stage of the prot ...
** The proton–proton chain ** The carbon–nitrogen–oxygen cycle * Helium fusion: ** The triple-alpha process ** The
alpha process The alpha process, also known as the alpha ladder, is one of two classes of nuclear fusion reactions by which stars convert helium into heavier elements, the other being the triple-alpha process. The triple-alpha process consumes only helium, an ...
* Fusion of heavier elements: **
Lithium burning Lithium burning is a nucleosynthetic process in which lithium is depleted in a star. Lithium is generally present in brown dwarfs and not in older low-mass stars. Stars, which by definition must achieve the high temperature (2.5 × 106 K) necess ...
: 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 ( 1H) into helium in their cores, unlike a main-sequence star. Instead, they have a mass between the most ma ...
s ** Carbon-burning process **
Neon-burning process The neon-burning process is a set of nuclear fusion reactions that take place in evolved massive stars with at least 8 Solar masses. Neon burning requires high temperatures and densities (around 1.2×109 K or 100 keV and 4×109 kg/m3). At suc ...
**
Oxygen-burning process The oxygen-burning process is a set of nuclear fusion reactions that take place in massive stars that have used up the lighter elements in their cores. Oxygen-burning is preceded by the neon-burning process and succeeded by the silicon-burning pro ...
**
Silicon-burning process In astrophysics, silicon burning is a very brief sequence of nuclear fusion reactions that occur in massive stars with a minimum of about 8–11 solar masses. Silicon burning is the final stage of fusion for massive stars that have run out of the f ...
* Production of elements heavier than iron: ** Neutron capture: *** The r-process *** The s-process ** Proton capture: *** The
rp-process The rp-process (rapid proton capture process) consists of consecutive proton captures onto seed nuclei to produce heavier elements. It is a nucleosynthesis process and, along with the ''s''-process and the ''r''-process, may be responsible fo ...
*** The p-process **
Photodisintegration Photodisintegration (also called phototransmutation, or a photonuclear reaction) is a nuclear process in which an atomic nucleus absorbs a high-energy gamma ray, enters an excited state, and immediately decays by emitting a subatomic particle. The ...


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 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, are fusing hydrogen by these two processes. In the cores of lower-mass main-sequence stars such as the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
, 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 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 Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, rather than by
convective heat transfer Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes o ...
. 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 The CNO cycle (for carbon–nitrogen–oxygen; sometimes called Bethe–Weizsäcker cycle after Hans Albrecht Bethe and Carl Friedrich von Weizsäcker) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, ...
, which is a
catalytic cycle In chemistry, a catalytic cycle is a multistep reaction mechanism that involves a catalyst. The catalytic cycle is the main method for describing the role of catalysts in biochemistry, organometallic chemistry, bioinorganic chemistry, materials ...
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 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 Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convect ...
energy transfer becomes more important than does
radiative transfer Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative trans ...
. As a result, the core region becomes a
convection zone A convection zone, convective zone or convective region of a star is a layer which is unstable due to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation ...
, 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 is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
. 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 The red-giant branch (RGB), sometimes called the first giant branch, is the portion of the giant branch before helium ignition occurs in the course of stellar evolution. It is a stage that follows the main sequence for low- to intermediate-mass sta ...
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 A helium flash is a very brief thermal runaway nuclear fusion of large quantities of helium into carbon through the triple-alpha process in the core of low mass stars (between 0.8 solar masses () and 2.0 ) during their red giant phase (the Sun is ...
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 core without a flash and execute a
blue loop In the field of stellar evolution, a blue loop is a stage in the life of an evolved star where it changes from a cool star to a hotter one before cooling again. The name derives from the shape of the evolutionary track on a Hertzsprung–Russell ...
before reaching the
asymptotic giant branch The asymptotic giant branch (AGB) is a region of the Hertzsprung–Russell diagram populated by evolved cool luminous stars. This is a period of stellar evolution undertaken by all low- to intermediate-mass stars (about 0.5 to 8 solar masses) late ...
. Such a star initially moves away from the AGB toward bluer colours, then loops back again to what is called the
Hayashi track The Hayashi track is a luminosity–temperature relationship obeyed by infant stars of less than in the pre-main-sequence phase (PMS phase) of stellar evolution. It is named after Japanese astrophysicist Chushiro Hayashi. On the Hertzsprung–R ...
. An important consequence of blue loops is that they give rise to classical
Cepheid variable A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. A strong direct relationship between a Cepheid varia ...
s, of central importance in determining distances in the Milky Way 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 and oxygen. The most massive stars become supergiants when they leave the main sequence and quickly start helium fusion as they become
red supergiant Red supergiants (RSGs) are stars with a supergiant luminosity class ( Yerkes class I) of spectral type K or M. They are the largest stars in the universe in terms of volume, although they are not the most massive or luminous. Betelgeuse and Anta ...
s. 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 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 In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
: ::\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 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 ato ...
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 The CNO cycle (for carbon–nitrogen–oxygen; sometimes called Bethe–Weizsäcker cycle after Hans Albrecht Bethe and Carl Friedrich von Weizsäcker) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, ...
, 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 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 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)
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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's Cosmicopia {{Portal bar, Physics, Chemistry, Astronomy, Outer space, Solar System, Science Nucleosynthesis Nuclear physics Nucleosynthesis, Stellar Astrophysics Concepts in astronomy