Inastrophysics,stellar nucleosynthesis is thecreation ofchemical elements bynuclear fusion reactions withinstars. Stellar nucleosynthesis has occurred since theoriginal creation ofhydrogen,helium andlithium during theBig Bang. As apredictive theory, it yields accurate estimates of theobserved abundances of the elements. It explains why the observed abundances of elements change over time and why some elements and theirisotopes are much more abundant than others. The theory was initially proposed byFred Hoyle in 1946,[1] who later refined it in 1954.[2] Further advances were made, especially to nucleosynthesis byneutron capture of the elements heavier thaniron, byMargaret andGeoffrey Burbidge,William Alfred Fowler andFred Hoyle in their famous 1957B2FH paper,[3] 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 byburning hydrogen (main sequence star), thenhelium (horizontal branch star), and progressively burninghigher 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 viastellar wind, forming aplanetary nebula, while a higher–mass star will eject mass via a sudden catastrophic event called asupernova. The termsupernova nucleosynthesis is used to describe the creation of elements during the explosion of a massive star orwhite dwarf.
The advanced sequence of burning fuels is driven bygravitational collapse and its associated heating, resulting in the subsequent burning ofcarbon,oxygen andsilicon. However, most of the nucleosynthesis in the mass rangeA = 28–56 (from silicon to nickel) is actually caused by the upper layers of the starcollapsing onto the core, creating a compressionalshock wave 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, calledexplosive nucleosynthesis orsupernova nucleosynthesis, is the final epoch of stellar nucleosynthesis.
A stimulus to the development of the theory of nucleosynthesis was the discovery of variations in theabundances of elements found in the universe. The need for a physical description was already inspired by the relative abundances of the chemical elements in theSolar 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 (seehistory of nucleosynthesis theory).[4] 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 theenergy released from nuclear fusion reactions accounted for the longevity of theSun as a source of heat and light.[5]
In 1920,Arthur Eddington, on the basis of the precise measurements of atomic masses byF.W. Aston and a preliminary suggestion byJean Perrin, proposed that stars obtained their energy fromnuclear fusion ofhydrogen to formhelium and raised the possibility that the heavier elements are produced in stars.[6][7][8] This was a preliminary step toward the idea of stellar nucleosynthesis. In 1928George Gamow derived what is now called theGamow factor, aquantum-mechanical formula yielding the probability for two contiguous nuclei to overcome the electrostaticCoulomb barrier between them and approach each other closely enough to undergo nuclear reaction due to thestrong nuclear force which is effective only at very short distances.[9]: 410 In the following decade the Gamow factor was used byRobert d'Escourt Atkinson andFritz Houtermans and later byEdward 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 a 1939 paper entitled "Energy Production in Stars",Hans Bethe analyzed the different possibilities for reactions by which hydrogen is fused into helium.[10] He defined two processes that he believed to be the sources of energy in stars. The first one, theproton–proton chain reaction, is the dominant energy source in stars with masses up to about the mass of the Sun. The second process, thecarbon–nitrogen–oxygen cycle, which was also considered byCarl Friedrich von Weizsäcker in 1938, is more important in more massive main-sequence stars.[11]: 167 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.[12]: 365 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 intoiron.[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.[2][13]
Hoyle's theory was extended to other processes, beginning with the publication of the 1957 review paper "Synthesis of the Elements in Stars" byMargaret Burbidge,Geoffrey Burbidge,William Alfred Fowler andFred Hoyle, more commonly referred to as theB2FH paper.[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. Significant improvements were made byAlastair G. W. Cameron and byDonald D. Clayton. In 1957 Cameron presented his own independent approach to nucleosynthesis,[14] 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 thes-process in 1961[15] and of ther-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.
The most important reactions in stellar nucleosynthesis:
Hydrogen fusion (nuclear fusion of four protons to form ahelium-4 nucleus[20]) is the dominant process that generates energy in the cores ofmain-sequence stars. It is also called "hydrogen burning", which should not be confused with thechemicalcombustion of hydrogen in anoxidizing 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 ofwhite dwarfs, are fusing hydrogen by these two processes.[21]: 245
In the cores of lower-mass main-sequence stars such as theSun, the dominant energy production process is theproton–proton chain reaction. This creates a helium-4 nucleus through a sequence of reactions that begin with the fusion of two protons to form adeuterium nucleus (one proton plus one neutron) along with an ejected positron and neutrino.[22] In each complete fusion cycle, the proton–proton chain reaction releases about 26.2 MeV.[22] Proton-proton chain with a dependence of approximately T4, meaning the reaction cycle is highly sensitive 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,[23] theenergy flux toward the surface is sufficiently low and energy transfer from the core region remains byradiative heat transfer, rather than byconvective heat transfer.[24] 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 theCNO cycle, which is acatalytic 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.[22] 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 throughneutrino emission.[22] CNO cycle is highly sensitive to temperature, with rates proportional to the 16th to 20th power of the temperature; a 10% increase in temperature would result in a 350% increase 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.[25] This results in such an intense outward energy flux thatconvective energy transfer becomes more important than doesradiative transfer. As a result, the core region becomes aconvection zone, which stirs the hydrogen fusion region and keeps it well mixed with the surrounding proton-rich region.[26] 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.[25] The Sun produces on the order of 1% of its energy from the CNO cycle.[27][a][28]: 357 [29][b]
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 about4×106 K,[30] making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately1.6×107 K, but thereafter it increases more rapidly in efficiency as the temperature rises, than does the proton–proton reaction.[31] Above approximately1.7×107 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 theSun.[32] The Sun itself has a core temperature of about1.57×107 K.[33]: 5 As a main-sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.[25]
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 thered 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 ahelium flash from adegenerate helium core, and the star moves to thehorizontal branch where it burns helium in its core. More massive stars ignite helium in their core without a flash and execute ablue loop before reaching theasymptotic giant branch. Such a star initially moves away from the AGB toward bluer colours, then loops back again to what is called theHayashi track. An important consequence of blue loops is that they give rise to classicalCepheid variables, of central importance in determining distances in theMilky Way and to nearby galaxies.[34]: 250 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 largelycarbon andoxygen. The most massive stars become supergiants when they leave the main sequence and quickly start helium fusion as they becomered supergiants. After the helium is exhausted in the core of a star, helium fusion will continue in a shell around the carbon–oxygen core.[20][24]
In all cases, helium is fused to carbon via the triple-alpha process, i.e., three helium nuclei are transformed into carbon via8Be.[35]: 30 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.[36]: 398
The reaction rate density between speciesA andB, having number densitiesnA,B, is given by:wherekr is thereaction rate constant of each single elementary binary reaction composing thenuclear fusion process;whereσ(v) is the cross-section at relative velocityv, and averaging is performed over all velocities.
Semi-classically, the cross section is proportional to, where is thede Broglie wavelength. Thus semi-classically the cross section is proportional to.
However, since the reaction involvesquantum tunneling, there is an exponential damping at low energies that depends onGamow factorEG, given by anArrhenius-type equation:Here astrophysicalS-factorS(E) depends on the details of the nuclear interaction, and has the dimension of an energy multiplied by across section.
One then integrates over all energies to get the total reaction rate, using theMaxwell–Boltzmann distribution and the relation:wherek = 86,17 μeV/K, is thereduced mass. The integrand equals
Since this integration off(E, constantT) has an exponential damping at high energies of the form and at low energies from the Gamow factor, the integral almost vanishes everywhere except around the peak at E0, calledGamow peak.[37]: 185 There:
Thus:
and
The exponent can then be approximated aroundE0 as:
And the reaction rate is approximated as:[38]
Values ofS(E0) are typically10−3 – 103keV·b, but are damped by a huge factor when involving abeta decay, due to the relation between the intermediate bound state (e.g.diproton)half-life and the beta decay half-life, as in theproton–proton chain reaction. Note that typical core temperatures inmain-sequence stars (the Sun) givekT of the order of 1 keV:[39].[40]: ch. 3
Thus, the limiting reaction in theCNO cycle, proton capture by14
7N, hasS(E0) ~S(0) = 3.5 keV·b, while the limiting reaction in theproton–proton chain reaction, the creation ofdeuterium from two protons, has a much lowerS(E0) ~S(0) = 4×10−22 keV·b.[41][42] Incidentally, since the former reaction has a much higher Gamow factor, and due to the relativeabundance 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.[43]
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