Stellar nucleosynthesis is the creation (nucleosynthesis) of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. 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 Burbidge, 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.
Nucleosynthesis is the process that creates new atomic nuclei from pre-existing nucleons. The first nuclei were formed a few minutes after the Big Bang, through the process called Big Bang nucleosynthesis. After about 20 minutes, the universe had cooled to a point at which these processes ended, so only the fastest and simplest reactions occurred, leaving our universe containing about 75% hydrogen, 24% helium by mass. The rest is traces of other elements such as lithium and the hydrogen isotope deuterium. The universe still has approximately the same composition.
A chemical element is a species of atom having the same number of protons in their atomic nuclei. For example, the atomic number of oxygen is 8, so the element oxygen consists of all atoms which have 8 protons.
Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles. The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in atomic "binding energy" between the atomic nuclei before and after the reaction. Fusion is the process that powers active or "main sequence" stars, or other high magnitude stars.
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 (red giant 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.
Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. The table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star.
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 Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars or dwarf stars. These are the most numerous true stars in the universe, and include the Earth's Sun.
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around 5,000 K or lower. The appearance of the red giant is from yellow-orange to red, including the spectral types K and M, but also class S stars and most carbon stars.
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 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. 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.
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 formation in the universe. Over time an initial, relatively smooth distribution of matter will collapse to form pockets of higher density, typically creating a hierarchy of condensed structures such as clusters of galaxies, stellar groups, stars and planets.
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 process. As the neon-burning process ends, the core of the star contracts and heats until it reaches the ignition temperature for oxygen burning. Oxygen burning reactions are similar to those of carbon burning; however, they must occur at higher temperatures and densities due to the larger Coulomb barrier of oxygen. Oxygen in the core ignites in the temperature range of (1.5–2.6)×109 K and in the density range of (2.6–6.7)×109g/cm3. The principal reactions are given below, where the branching ratios assume that the deuteron channel is open (at high temperatures):
The mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. It is approximately equal to the atomic mass of the atom expressed in atomic mass units. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. Hence, the difference between the mass number and the atomic number Z gives the number of neutrons (N) in a given nucleus: N = A - Z.
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 isotopes of the chemical elements in the solar system. 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 (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 as a source of heat and light.
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.
The Sun, or Sol, is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, and its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Roughly three quarters of the Sun's mass consists of hydrogen (~73%); the rest is mostly helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron.
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 stellar 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 occur at the high temperatures believed to exist in stellar interiors.
Sir Arthur Stanley Eddington 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 luminosity of stars, or the radiation generated by accretion onto a compact object, is named in his honour.
Francis William Aston FRS was an English 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 for his enunciation of the whole number rule. He was a fellow of the Royal Society and Fellow of Trinity College, Cambridge.
Hydrogen is the chemical element with the symbol H and atomic number 1. With a standard atomic weight of 1.008, hydrogen is the lightest element in the periodic table. Hydrogen is the most abundant chemical substance in the Universe, constituting roughly 75% of all baryonic mass. Non-remnant stars are mainly composed of hydrogen in the plasma state. The most common isotope of hydrogen, termed protium, has one proton and no neutrons.
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. 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. 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.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. :
Hans Albrecht Bethe was a German-American nuclear physicist who made important contributions to astrophysics, quantum electrodynamics and solid-state physics, and won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis.
The proton–proton chain reaction is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. It dominates in stars with masses less than or equal to that of the Sun, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun.
The CNO cycle is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain reaction. Unlike the latter, the CNO cycle is a catalytic cycle. It is dominant in stars that are more than 1.3 times as massive as the Sun.
Hoyle's theory was expanded to other processes, beginning with the publication of a 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 by neutron capture. Significant improvements were made by Alastair G. W. 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.
The most important reactions in stellar nucleosynthesis:
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 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 dominant energy production process is the proton–proton 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 deuterium nucleus (one proton plus one neutron) along with an ejected positron and neutrino. 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 each complete fusion cycle, the proton–proton chain reaction releases about 26.2
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. 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 energy transfer become 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 10% of its energy from the CNO cycle.During a complete CNO cycle, 25.0
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 4×106 K , making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately 16×106 K, but thereafter it increases more rapidly in efficiency as the temperature rises, than does the proton-proton reaction. 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 about 15.7×106 K. As a main sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.
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 helium core and the star moves to the horizontal branch where it burns helium in its core. More massive stars ignite helium in their cores without a flash and execute a blue loop before reaching the asymptotic giant branch. Despite the name, stars on a blue loop from the red giant branch are typically not blue in color, 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 supergiants. After helium is exhausted in the core of a star, it will continue in a shell around the carbon-oxygen core.
In all cases, helium is fused to carbon via the triple-alpha process. 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.
The reaction rate per volume between species A and B, having number densities nA,B is given by:
where 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 , where is the de Broglie wavelength. Thus semi-classically the cross section is proportional to .
However, since the reaction involves quantum tunneling, there is an exponential damping at low energies that depends on Gamow factor EG, giving:
where S(E) depends on the details of the nuclear interaction.
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.
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, at E0, where:
The exponent can then be approximated around E0 as:
And the reaction rate is approximated as:
Values of S(E0) are typically 10−3-103 in units of 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. diproton) half-life 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 14
, has S(E0) ~ S(0) = 3.5 keV b, while the limiting reaction in the proton-proton chain reaction, the creation of deuterium from two protons, has a much lower S(E0) ~ S(0) = 4*10−22 keV 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.
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of the lightest isotope of hydrogen during the early phases of the Universe. Primordial nucleosynthesis is believed by most cosmologists to have taken place in the interval from roughly 10 seconds to 20 minutes after the Big Bang, and is calculated to be responsible for the formation of most of the universe's helium as the isotope helium-4 (4He), along with small amounts of the hydrogen isotope deuterium, the helium isotope helium-3 (3He), and a very small amount of the lithium isotope lithium-7 (7Li). In addition to these stable nuclei, two unstable or radioactive isotopes were also produced: the heavy hydrogen isotope tritium ; and the beryllium isotope beryllium-7 (7Be); but these unstable isotopes later decayed into 3He and 7Li, as above.
The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei are transformed into carbon.
The carbon-burning process or carbon fusion is a set of nuclear fusion reactions that take place in the cores of massive stars (at least 8 at birth) that combines carbon into other elements. It requires high temperatures (> 5×108 K or 50 keV) and densities (> 3×109 kg/m3).
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 fuels that power them for their long lives in the main sequence on the Hertzsprung–Russell diagram. It follows the previous stages of hydrogen, helium, carbon, neon and oxygen burning processes.
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 during their red giant phase. A much rarer runaway helium fusion process can also occur on the surface of accreting white dwarf stars.
Stellar structure models describe the internal structure of a star in detail and make predictions about the luminosity, the color and the future evolution of the star. Different classes and ages of stars have different internal structures, reflecting their elemental makeup and energy transport mechanisms.
A convection zone, convective zone or convective region of a star is a layer which is unstable to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation and conduction.
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 processes called helium burning, carbon burning, oxygen burning, and silicon burning, in which the ashes of one nuclear fuel become, after compressional heating, the fuel for the subsequent burning stage. During hydrostatic burning these fuels synthesize overwhelmingly the alpha-nucleus products. A rapid final explosive burning is caused by the sudden temperature spike owing to passage of the radially moving shock wave that was launched by the gravitational collapse of the core. W. D. Arnett and his Rice University colleagues demonstrated that the final shock burning would synthesize the non-alpha-nucleus isotopes more effectively than hydrostatic burning was able to do, suggesting that the expected shock-wave nucleosynthesis is an essential component of supernova nucleosynthesis. Together, shock-wave nucleosynthesis and hydrostatic-burning processes create most of the isotopes of the elements carbon, oxygen, and elements with Z = 10–28. As a result of the ejection of the newly synthesized isotopes of the chemical elements by supernova explosions their abundances steadily increased within interstellar gas. That increase became evident to astronomers from the initial abundances in newly born stars exceeding those in earlier-born stars.
The core of the Sun is considered to extend from the center to about 0.2 to 0.25 of solar radius. It is the hottest part of the Sun and of the Solar System. It has a density of 150 g/cm3 at the center, and a temperature of 15 million kelvins. The core is made of hot, dense plasma, at a pressure estimated at 265 billion bar at the center. Due to fusion, the composition of the solar plasma drops from 68–70% hydrogen by mass at the outer core, to 33% hydrogen at the core/Sun center.
Nuclear astrophysics is an interdisciplinary branch of physics involving close collaboration among researchers in various subfields of nuclear physics and astrophysics: notably stellar modeling; measurement and theoretical estimation of nuclear reaction rates; physical cosmology and cosmochemistry; gamma ray, optical and X-ray astronomy; and extending our knowledge about nuclear lifetimes and masses. In general terms, nuclear astrophysics aims to understand the origin of the chemical elements and the energy generation in stars.
The B2FH paper, named after the initials of the authors of the paper, Margaret Burbidge, Geoffrey Burbidge, William A. Fowler, and Fred Hoyle, is a landmark paper on the origin of the chemical elements published in Reviews of Modern Physics in 1957. The title of that paper is "Synthesis of the Elements in Stars", but as that paper grew in influence, it came to be referred to only as "B2FH". The B2FH paper spread stellar nucleosynthesis theory widely in the scientific community, especially among astronomers who saw everyday relevance to their quest, at a time when it was appreciated by only a handful of experts in nuclear physics. But it did not create the theory of stellar nucleosynthesis as much as bring it vividly to life.
Beryllium-8 (8Be) is an unstable radionuclide with 4 neutrons and 4 protons. It is an unbound resonance and nominally an isotope of beryllium. It decays into two alpha particles with a half-life on the order of 10−16 seconds; this has important ramifications in stellar nucleosynthesis as it creates a bottleneck in the creation of heavier chemical elements. The properties of 8Be have also led to speculation on the fine tuning of the Universe, and theoretical investigations on cosmological evolution had 8Be been stable.
The turnoff point for a star refers to the point on the Hertzsprung-Russell diagram where it leaves the main sequence after the exhaustion of its main fuel. It is often referred to as the main sequence turnoff.
A stellar core is the extremely hot, dense region at the center of a star. For an ordinary main sequence star, the core region is the volume where the temperature and pressure conditions allow for energy production through thermonuclear fusion of hydrogen into helium. This energy in turn counterbalances the mass of the star pressing inward; a process that self-maintains the conditions in thermal and hydrostatic equilibrium. The minimum temperature required for stellar hydrogen fusion exceeds 107 K (10 MK), while the density at the core of the Sun is over 100 g/cm3. The core is surrounded by the stellar envelope, which transports energy from the core to the stellar atmosphere where it is radiated away into space.