Nuclear synthesis in stars

With the exception of hydrogen, helium, and a small number of other light elements, the chemical elements found on Earth and throughout the universe were all formed in various stages of nuclear fusion within stellar interiors. Although these processes cannot be observed directly, models for element synthesis and the dissemination of that material to interstellar space help explain the relative amounts of elements observed in the Sun and other stars.

Overview

Nuclear synthesis is the process by which stars convert light elements, such as hydrogen and helium, into heavier elements, such as carbon, oxygen, magnesium, silicon, iron, and the rest of the stable elements found on Earth and throughout the cosmos. The process of nuclear synthesis requires conditions of high temperature and high density to proceed. Only under such extremes can positively charged nuclei, which must interact to form heavier species, overcome the enormous Coulomb repulsion that dominates under usual conditions. As a result, the dominant sites of nuclear synthesis in the present universe are in the cores of stars. Even at a temperature of fifteen million kelvins and a tremendous density of 150,000 kilograms per cubic meter (typical of the environment at the center of the Sun), only rarely will an individual collision between nuclei successfully penetrate the Coulomb barrier and allow the nuclei to approach within the critical distance (10^-15 meters, or one fermi, which is on the order of their radii) where the attractive strong nuclear force mediates their interaction. Outer layers of stars do not participate in the synthesis of the elements but are of great importance for the transport of energy generated by the nucleosynthesis processes taking place inside the core.

The first major nuclear reaction in stars is the conversion of four single protons to a helium four nucleus consisting of two protons and two neutrons (uncharged particles of roughly the same mass as a proton). This reaction requires several stages to complete. First, two protons must fuse to form a nucleus of deuterium (also known as “heavy hydrogen” or hydrogen 2) consisting of one proton and one neutron. To maintain charge balance, a positively charged particle known as a positron, having the exact mass of an electron, is emitted along with an uncharged weakly interacting particle called a neutrino. The deuterium nucleus fuses with another free proton to form a helium 3 nucleus with two protons and a neutron. In the process, a high-energy gamma-ray photon is emitted. Another group of protons must repeat the entire sequence to form a second helium 3 nucleus. The final stage of the reaction occurs when two helium 3 nuclei interact to form a single nucleus of helium 4, consisting of two protons and two neutrons. Two free protons are generated in this final step. A careful count of the particles involved indicates that the net reaction has converted four free protons to a single helium nucleus. The amount of energy released in each net conversion is exceedingly small; thus, many such reactions must occur within stars to produce enough energy to keep the temperature high enough to maintain the gas pressure required to hold up their massive outer layers against gravitational collapse.

A star like the Sun originally has a sufficient supply of hydrogen to continue the synthesis of helium in its core for about ten billion years. Subsequently, the lack of readily available fuel in the core of the star forces it to change its internal structure to find additional energy sources. The predominantly helium core is too low a temperature to initiate helium fusion, so it can only contract, releasing gravitational potential energy and growing hotter. This raises the temperature of the hydrogen immediately outside the core to the point that hydrogen fusion can occur in a shell around the core. The outer layers expand and cool, and the star swells to become a red giant. Meanwhile, the helium core continues to contract, and its temperature continues to rise. When the temperature reaches 100 million kelvins, the core begins to fuse helium into carbon.

Helium fusion is known as the triple-alpha process. The name derives from the interaction of three nuclei of helium 4, also known as alpha particles. Once again, a multistage reaction must occur. Two alpha particles fuse to form a nucleus of beryllium 8, which has four protons and four neutrons. In the process, a gamma-ray photon is emitted. The beryllium 8 nucleus is unstable and will decay into alpha particles within 3 10^-16 seconds. If, however, during this brief period, the beryllium 8 nucleus captures another alpha particle, the result is the formation of a stable carbon 12 nucleus, again with the emission of a gamma-ray photon.

The multiple stages required for hydrogen and helium fusion and the relative infrequency of successful fusion events at temperatures typical of the cores of stars are responsible for moderating the consumption of nuclear fuel and the energy output of stars. If this moderation were not the case, the lifetimes of stars would be insufficient for the formation of planetary systems and the evolution of life as it is known on Earth.

Once stars manage to build up carbon nuclei in their cores, the way is theoretically clear for stars to build up additional elements with relatively simple single-stage interactions. Alpha particle capture by carbon nuclei produces oxygen nuclei. The fusion of two carbon nuclei could form a magnesium nucleus, but it is more likely to produce a neon nucleus plus a helium nucleus. A great assortment of nuclear species can form, and with them, the variety of available pathways for further fusion increases rapidly. However, one additional requirement must be met. As nuclei with a greater number of positively charged protons are formed, the collisions required to fuse such nuclei must become increasingly energetic to overcome the proportionately larger Coulomb repulsion. Carbon 12, for example, which has six protons and six neutrons in its nucleus, does not fuse until a temperature of 600 million kelvins is achieved at the center of a star. Silicon 28 (with fourteen protons and fourteen neutrons in its nucleus) does not fuse until a temperature of three billion kelvins is attained.

Stars like the Sun never reach core temperatures high enough for significant carbon fusions, although small amounts of oxygen can form via alpha particle captures by carbon. Thus, the Sun will end its life with a slowly contracting carbon-oxygen core, while its outer layers are ejected eventually to form a planetary nebula, a low-density shell of gas illuminated by the now-exposed high-temperature core. The core, which at this point is an extremely small, high-density sphere known as a white dwarf, will cool slowly and fade over many billions of years to become a black dwarf.

Elements heavier than carbon are formed by stars with a higher mass than the Sun. Stars with masses greater than four solar masses but less than eight solar masses proceed through their evolution in much the same manner as lower-mass stars, only faster. The greater pressure exerted by the more massive overlying layers increases the temperature and, hence, the rates of nuclear reactions in the core; thus, such stars burn their available fuel more quickly than one-solar-mass stars. A five-solar-mass star, for example, will form a carbon-oxygen core within 200 million years. In these intermediate-mass stars, ignition of carbon may take place explosively, and the star may blow itself apart in a carbon-detonation supernova explosion; however, it is more likely that the star will have lost so much mass through strong stellar winds that its core will never reach carbon-detonation temperature.

In stars more massive than about eight solar masses, the core temperature rises quickly enough to allow further nuclear burning. Although the details are uncertain because of the complexity and variety of available nuclear-burning pathways, the general pattern is clear. As high-mass stars burn heavier and heavier elements, each new nuclear species first ignites in the core and then in a shell surrounding the core once it has exhausted that nuclear fuel. Within eight million years, a twenty-five-solar-mass star builds up layer upon layer of heavy elements—eventually, an inert iron core forms at the center of this star. Iron fifty-six nuclei can fuse into heavier nuclei only with energy input, so it is stable against further fusion. Instead, the iron core contracts rapidly in a vain attempt to liberate enough gravitational potential energy to hold up the star's outer layers. Quickly, the core reaches temperatures at which the iron nuclei spontaneously disintegrate into individual alpha particles, which drains the core of energy. The star’s outer layers collapse onto the high-temperature core, resulting in a spectacular core-collapse supernova explosion.

Alternative pathways for the formation of heavy elements exist other than those caused by the fusion of alpha particles with nuclei, such as carbon, magnesium, and silicon, or the fusion of these nuclei with themselves. During the evolution of stars, a fraction of all the usual fusion reactions produces free neutrons. These neutrons are captured subsequently by other nuclei, producing elements (or isotopes of elements) not synthesized by the usual charged nuclei process. A nucleus that captures an additional neutron is often unstable and will spontaneously beta decay after a time into an element with an additional proton. To maintain charge balance, the nucleus gives up an electron. The process of neutron capture and subsequent beta decay is known as the s-process (“s” for “slow” because of the relatively slow production rate of free neutrons in stellar interiors). Because the neutron is an uncharged particle, it need not overcome the repulsion of the positively charged nuclei to interact; thus, the s-process can proceed at relatively low temperatures. In the highly energetic environment of a supernova, many free neutrons are available. A nucleus may accept many free neutrons before it has time to beta decay. This phenomenon, known as the r-process (“r” for “rapid” because of the rapid addition of neutrons before the decay of the nucleus), accounts for the formation of elements heavier than iron. Eventually, a nucleus saturated with neutrons will decay via the emission of alpha particles or electrons into other nuclear species.

By a combination of charged-particle fusion reactions and neutron captures via the s- and r-processes, the stable elements in the periodic table are formed. It is important to note that a single star does not build up all the elements that are presently observed in its outer atmosphere. Indeed, several generations of stars must have been born, lived, and died for the elements found in the Sun to have been formed. The elements that are created in previous generations of stars are dispersed and eventually mixed into the interstellar medium, the material between the stars from which future generations of stars ultimately form. Thus, the nuclear synthesis of elements is an ongoing process.

Methods of Study

Models of nuclear synthesis in stars are derived from a comparison of the observed abundances of the elements in stars, the Earth, the Moon, meteorites, and other solar-system objects against sophisticated computer models for the synthesis of the elements. Direct confirmation of the nuclear processes is not available because the outer layers of stars prevent observation of the composition of stellar cores, where the products of element synthesis reside during a star’s lifetime. Further complications are introduced because the elemental abundances in relatively recently formed stars, such as the Sun, are the net result of nuclear synthesis products formed in many previous generations of stars with a wide range of stellar masses. Thus, comparisons of observation with synthesis models necessarily involve assumptions about the initial mass distribution of stars that formed in the Milky Way galaxy, the evolution of stars, the mass loss from the outer atmospheres of stars during their lifetimes, the nature of supernovae, mixing of elements in the interstellar medium, as well as subsequent processes, such as the effects of the impact of cosmic rays (high-energy charged particles) on nuclei in the interstellar medium. A self-consistent picture can be drawn in which the observations of elemental abundances agree with the model predictions reasonably well.

The most readily available test for nuclear synthesis models and all their associated assumptions comes from a detailed inspection of the elements detected in the spectrum of light from the Sun. To a first approximation, the shape of the solar spectrum resembles that of the Planck curve of blackbody radiation—that is, the distribution of energy coming from a body in thermodynamic equilibrium. Superimposed upon this continuous spectrum is a multitude of dark lines that form when light is absorbed selectively by elements present in the solar photosphere. Patterns and strengths of absorption lines observed in terrestrial laboratories and calculated from detailed models of atomic-energy levels can then be compared to observed patterns and strengths of absorption lines found in the solar spectrum. In this way, a description of the relative abundances of elements in the Sun’s photosphere can be constructed. Since it is assumed the Sun was initially well-mixed, the photospheric abundances should be representative of the Sun’s original composition.

Other bright stars near the Sun have nearly the same relative abundances of elements in their atmospheres because they formed at a similar epoch out of interstellar gas with much the same chemical composition. Some of these stars are hotter than the Sun; most are cooler. Patterns and strengths of absorption lines caused by the elements are affected greatly by the temperature of the stellar surface, providing a convenient check on models for line formation under different conditions. Stars that are much older than the Sun and its neighbors also play an important role in the comparison of models for nuclear synthesis in stars. Stars have been identified in the outer halo of the Milky Way galaxy that must have formed at early times. From the spectra of these old stars, astronomers obtain a picture of the production of elements at a time before nuclear syntheses from numerous generations of stars enriched the interstellar medium with heavier nuclei.

Abundances of elements formed in stars also can be obtained from chemical analysis of ancient rocks and meteorites found on the surface of Earth and the Moon. An inspection of such material provides a snapshot of the composition of the gas and dust from which the solar system formed about 4.5 billion years ago. Sophisticated laboratory equipment, such as particle accelerators and mass spectrometers, can be used to obtain very precise estimates of the relative abundances of the elements found in these rocks. Though such studies provide important clues, the interpretation is complicated by the chemical differentiation and segregation that must have occurred due to past geologic activity on Earth and Moon. Samples of material obtained from the asteroid belt between Mars and Jupiter and samples from the surfaces of comets will be extremely important, as the asteroids and comets presumably have not suffered changes as significant as those that have occurred on Earth and Moon.

Context

Modern understanding of the formation of elements in the stars began with speculations for the source of energy required to sustain stars over their long lifetimes. Early ideas, which envisioned the Sun powered by gravitational potential energy liberated during a slow contraction, failed when it was demonstrated that the Earth was billions, rather than millions, of years old. In the early 1900s, it was realized that the extreme conditions of temperature and density at the centers of stars might be sufficient to set loose the energy that was locked away in the nuclei.

Physicists and astronomers in the 1920s and 1930s (such as Henry Norris Russell and Stanley Sir Arthur Eddington) outlined the basic processes by which the transformation of hydrogen nuclei into helium nuclei could lead to the energy generation required to power stars. A significant impetus for these ideas came from the use of the newly developed quantum mechanics, in particular by George Gamow, which demonstrated that a small fraction of the collisions between hydrogen nuclei in the core of the Sun could penetrate the repulsive Coulomb barrier. Further advances came in the 1950s when a concerted attack on the problem of the formation of the elements was undertaken by the physicists Ernst Opik, Edwin Salpeter, Fred Hoyle, and others. Detailed data for the relative abundances of elements found in the Sun and on Earth available in the mid-1950s prompted an outline of the neutron capture processes jointly by Margaret and Geoffrey Burbidge, William A. Fowler, and Fred Hoyle, and independently by Alistair Cameron.

Dramatic confirmation of the theoretical ideas for nuclear burning in the late stages of stellar evolution came with the supernova event of February 1987 (Supernova 1987A), when a twenty-solar-mass star in the nearby Large Magellanic Cloud galaxy exploded (about 160,000 light-years away). Supernova 1987A was the first nearby supernova to go off in modern times, and observations by astronomers from all over the world made it possible, for the first time, to obtain detailed spectra of the processed material as it emerged from this explosion. In the future, details of stellar evolution and the roles that stars of different masses play in creating the elements should become clearer. Studies of the oldest stars known, stars with substantially lower abundances of the heavy elements than are found in the Sun, will illuminate the nature of the first generation of objects that formed in the galaxy following the Big Bang.

Bibliography

Arnett, David. Supernovae and Nucleosynthesis. Princeton, N.J.: Princeton University Press, 1996.

Beatty, J. Kelly, Carolyn Collins Petersen, and Andrew Chaikin, eds. The New Solar System. 4th ed. Cambridge, Mass.: Sky, 1999.

Chaisson, Eric. Cosmic Dawn: The Origins of Matter and Life. Boston: Little, Brown, 1981.

Chaisson, Eric, and Steve McMillan. Astronomy Today. 9th ed. Addison-Wesley, 2018.

Clayton, Donald. Handbook of Isotopes in the Cosmos: Hydrogen to Gallium. Cambridge University Press, 2003.

Ekström, Sylvia. "Massive Star Modeling and Nucleosynthesis." Frontiers in Astronomy and Space Sciences, vol. 8, 21 Apr. 2021, doi.org/10.3389/fspas.2021.617765.

Freedman, Roger A., and William J. Kaufmann III. Universe: Stars and Galaxies. 6th ed. W. H. Freeman, 2019.

Pagel, Bernard. Nucleosynthesis and Chemical Evolution of Galaxies. 2nd ed. Cambridge University Press, 2009.

Schneider, Stephen E., and Thomas T. Arny. ISE Pathways to Astronomy. 6th ed. McGraw-Hill, 2020.