Supernova nucleosynthesis is a theory of the nucleosynthesis of the chemical elements in supernova explosions, advanced as the nucleosynthesis of elements from carbon to nickel in massive stars by Fred Hoyle in 1954. In 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 (A = 2Z) products. A rapid final explosive burning is caused by the sudden heating 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 (Z = 6), oxygen (Z = 8), and elements with Z = 10–28 (from neon to nickel). 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 of earlier-born stars.
Elements heavier than nickel are comparatively rare owing to the decline with atomic weight of their nuclear binding energies per nucleon, but they too are created in part within supernovae. Of greatest interest historically has been their synthesis by rapid capture of neutrons during the r-process, reflecting the common belief that supernova cores are likely to provide the necessary conditions. But see the r-process below for a recently discovered alternative. The r-process isotopes are roughly a 100,000 times less abundant than the primary chemical elements fused in supernova shells above. Furthermore, other nucleosynthesis processes in supernovae are thought to also be responsible for some nucleosynthesis of other heavy elements, notably, the proton capture process known as the rp-process, the slow capture of neutrons (s-process) in the Helium-burning shells and in the carbon-burning shells of massive stars, and a photodisintegration process known as the γ-process (gamma-process). The latter synthesizes the lightest, most neutron-poor, isotopes of the elements heavier than iron from preexisting heavier isotopes.
The theory was first proposed by Hoyle in 1954, in which he predicted the existence of the excited state in the 12C nucleus that enables the triple-alpha process to burn resonantly, enabling it to heat the helium cores of stars while synthesizing massive quantities of carbon and oxygen; and he introduced the sequels of carbon-burning synthesizing Ne, Mg and Na and of oxygen-burning synthesizing Si, Al and S. He also predicted that the collapse of the cores of massive stars was "inevitable" owing to their increasing rate of energy loss by neutrinos.
Thirteen years after the B2FH paper, W. D. Arnett and colleagues demonstrated that the final burning in the passing shock wave launched by collapse of the core could synthesize non-alpha-particle isotopes more effectively than hydrostatic burning could, suggesting that explosive nucleosynthesis is an essential component of supernova nucleosynthesis. A shock wave rebounded from matter collapsing onto the dense core, if strong enough to lead to mass ejection of the mantle of supernovae, would also be strong enough to provide the sudden heating needed for explosive thermonuclear burning within the mantle. It is seeing how that shock wave can reach the mantle that became the theoretical difficulty. Supernova observations assured that it must occur.
Hoyle's 1954 theory fell into obscurity for decades after the more-famous B2FH paper was published in 1957 and did not include Hoyle's original description of nucleosynthesis in massive stars. Donald D. Clayton has attributed the obscurity to Hoyle's 1954 paper describing its key equation only in words, and a lack of careful review by Hoyle of the B2FH draft by coauthors who had themselves not studied Hoyle's paper.
A supernova is a violent explosion of a star that occurs under two principal scenarios. The first is that a white dwarf star, which is the remnant of a low-mass star that has exhausted its nuclear fuel, undergoes a thermonuclear explosion after its mass is increased beyond its Chandrasekhar limit by accreting nuclear-fuel mass from a more diffuse companion star (usually a red giant) with which it is in binary orbit. The second, and about threefold more common, scenario occurs when a massive star (12–35 times more massive than the sun), usually a supergiant at the critical time, reaches nickel-56 in its nuclear fusion (or burning) processes. Without the thermal support from fusion, the core of the pre-supernova massive star collapses owing to the strong gravitational pull. The energy transfer from the core collapse causes the supernova display. The nickel-56 isotope has one of the largest binding energies per nucleon of all isotopes, and is therefore the last isotope whose synthesis during core silicon burning releases energy by nuclear fusion, exothermically. The binding energy per nucleon declines for atomic weights heavier than A = 56, ending fusion's history of supplying thermal energy to the star. Dozens of research papers have been published in the attempt to describe the hydrodynamics of how a small one percent the shock-wave energy at the core, which is about 1053 ergs, is transmitted to the overlying mantle in the face of continuing infall onto the core. That uncertainty remains in the full description of core-collapse supernovae.
Nuclear fusion reactions that produce elements heavier than iron absorb nuclear energy and are said to be endothermic reactions. When such reactions dominate, the internal temperature that supports the star's outer layers drops. Because the outer envelope is no longer sufficiently supported by the radiation pressure, the star's gravity pulls its mantle rapidly inward. As the star collapses, this mantle collides violently with the growing incompressible stellar core, which has a density almost as great as an atomic nucleus, producing a shockwave that rebounds outward through the unfused material of the outer shell. The increase of temperature by the passage of that shockwave is sufficient to induce fusion in that material, often called explosive nucleosynthesis. The energy deposited by the shockwave leads to the star's explosion, dispersing fusing material from the star into interstellar space.
After a star completes the oxygen burning process, its core is composed primarily of silicon and sulfur. If it has sufficiently high mass, it further contracts until its core reaches temperatures in the range of 2.7–3.5 billion Kelvin (keV). At these temperatures, silicon and other isotopes suffer photoejection of nucleons by energetic thermal photons (γ) ejecting especially alpha particles (4He). 230–300  The nuclear process of silicon burning differs from earlier fusion stages of nucleosynthesis in that it entails a balance between alpha-particle captures and their inverse photo ejection which establishes abundances of all alpha-particle elements in the following sequence in which each alpha particle capture shown is opposed by its inverse reaction, namely, photo ejection of an alpha particle by the abundant thermal photons:
28Si + 4He ↔ 32S + γ; 32S + 4He ↔ 36Ar + γ; 36Ar + 4He ↔ 40Ca + γ; 40Ca + 4He ↔ 44Ti + γ; 44Ti + 4He ↔ 48Cr + γ; 48Cr + 4He ↔ 52Fe + γ; 52Fe + 4He ↔ 56Ni + γ; 56Ni + 4He ↔ 60Zn + γ.
The alpha-particle nuclei 44Ti and those more massive in the final five reactions listed are all radioactive, but they decay after their ejection in supernova explosions into abundant isotopes of Ca, Ti, Cr, Fe and Ni. This post-supernova radioactivity became of great importance for the emergence of gamma-ray-line astronomy.
In these physical circumstances of rapid opposing reactions, namely alpha-particle capture and photo ejection of alpha particles, the abundances are not determined by alpha-particle-capture cross sections; rather they are determined by the values that the abundances must assume in order to balance the speeds of the rapid opposing-reaction currents. Each abundance takes on a stationary value that achieves that balance. This picture is called nuclear quasiequilibrium. Many computer calculations, for example, using the numerical rates of each reaction and of their reverse reactions have demonstrated that quasiequilibrium is not exact but does characterize well the computed abundances. Thus the quasiequilibrium picture presents a comprehensible picture of what actually happens. It also fills in an uncertainty in Hoyle's 1954 theory. The quasiequilibrium buildup shuts off after 56Ni because the alpha-particle captures become slower whereas the photo ejections from heavier nuclei become faster. Non-alpha-particle nuclei also participate, using a host of reactions similar to 36Ar + neutron ↔ 37Ar + photon and its inverse which set the stationary abundances of the non-alpha-particle isotopes, where the free densities of protons and neutrons are also established by the quasiequilibrium. However, the abundance of free neutrons is also proportional to the excess of neutrons over protons in the composition of the massive star; therefore the abundance of 37Ar, using it as an example, is greater in ejecta from recent massive stars than it was from those in early stars of only H and He; therefore 37Cl, to which 37Ar decays after the nucleosynthesis, is called a "secondary isotope". The silicon burning in the star progresses through a temporal sequence of such nuclear quasiequilibria in which the abundance of 28Si slowly declines and that of 56Ni slowly increases. This amounts to a nuclear abundance change 2 28Si >> 56Ni, which may be thought of as silicon burning into nickel in the nuclear sense. In interest of economy the photodisintegration rearrangement and the nuclear quasiequilibrium that it achieves is referred to as silicon burning. The entire silicon-burning sequence lasts about one day in the core of a contracting massive star and stops after 56Ni has become the dominant abundance. The final explosive burning caused when the supernova shock passes through the silicon-burning shell lasts only seconds, but its roughly 50% increase in the temperature causes furious nuclear burning, which becomes the major contributor to nucleosynthesis in the mass range 28–60. The star can no longer release energy via nuclear fusion because a nucleus with 56 nucleons has the lowest mass per nucleon of all the elements in the sequence. The next step up in the alpha-particle chain would be 60Zn, which has slightly more mass per nucleon and thus is less thermodynamically favorable. 56Ni (which has 28 protons) has a half-life of 6.02 days and decays via β+ decay to 56Co (27 protons), which in turn has a half-life of 77.3 days as it decays to 56Fe (26 protons). However, only minutes are available for the 56Ni to decay within the core of a massive star. This establishes 56Ni as the most abundant of the radioactive nuclei created in this way. Its radioactivity energizes the late supernova light curve and creates the pathbreaking opportunity for gamma-ray-line astronomy. See SN 1987A light curve for the aftermath of that opportunity. Clayton and Meyer have recently generalized this process still further by what they have named the secondary supernova machine, attributing the increasing radioactivity that energizes late supernova displays to the storage of increasing Coulomb energy within the quasiequilibrium nuclei called out above as the quasiequilibria shift from primarily 28Si to primarily 56Ni. The visible displays are powered by the decay of that excess Coulomb energy.
During this phase of the core contraction, the potential energy of gravitational compression heats the interior to roughly three billion degrees K, which briefly maintains pressure support and opposes rapid core contraction. However, since no additional heat energy can be generated via new fusion reactions, the final unopposed contraction rapidly accelerates into a collapse lasting only a few seconds. The central portion of the star is now crushed into either a neutron star or, if the star is massive enough, a black hole. The outer layers of the star are blown off in an explosion triggered by the outward moving supernova shock, known as a Type II supernova whose displays last days to months. The escaping portion of the supernova core may initially contain a large density of free neutrons, which may synthesize, in about one second while inside the star, roughly half of the elements in the universe that are heavier than iron via a rapid neutron-capture mechanism known as the r-process. See below.
Stars with initial masses less than about eight times the sun never develop a core large enough to collapse and they eventually lose their atmospheres to become white dwarfs, stable cooling spheres of carbon supported by the pressure of degenerate electrons. Nucleosynthesis within those lighter stars is therefore limited to nuclides that were fused in material located above the final white dwarf. This limits their modest yields returned to interstellar gas to carbon-13 and nitrogen-14, and to isotopes heavier than iron by slow capture of neutrons (the s-process). A significant minority of white dwarfs will nonetheless explode, however, because they formed in a binary orbit with a giant companion star that loses mass to the stronger gravitational field of the white dwarf, which then grows past its Chandrasekhar limit and explodes as a Type Ia supernova, synthesizing about a solar mass of radioactive 56Ni isotopes. Its radioactive decay to iron keeps Type Ia optically very bright for weeks and creates more than half of all iron in the universe. Virtually all of the remainder of stellar nucleosynthesis occurs, however, in more frequent stars that are massive enough to end as Type II supernovae. In the presupernova massive star this includes helium burning, carbon burning, oxygen burning and silicon burning. Much of that yield may never leave the star but instead disappears into its collapsed core. The yield that is ejected is substantially fused in last-second explosive burning caused by the shock wave launched by core collapse. Prior to core collapse, fusion of elements between silicon and iron occurs only in the largest of stars, and then in limited amounts. Thus the nucleosynthesis of the abundant primary elements defined as those that could be synthesized in stars of initially only hydrogen and helium (left by the Big Bang), is substantially limited to core-collapse supernova nucleosynthesis.
During supernova nucleosynthesis, the r-process creates very neutron-rich heavy isotopes, which decay after the event to the first stable isotope, thereby creating the neutron-rich stable isotopes of all heavy elements. This neutron capture process occurs in high neutron density with high temperature conditions. In the r-process, any heavy nuclei are bombarded with a large neutron flux to form highly unstable neutron rich nuclei which very rapidly undergo beta decay to form more stable nuclei with higher atomic number and the same atomic mass. The neutron density is extremely high, about 1022-24 neutrons per cubic centimeter. First calculation of an evolving r-process, showing the evolution of calculated results with time, also suggested that the r-process abundances are a superposition of differing neutron fluences. Small fluence produces the first r-process abundance peak near atomic weight A = 130 but no actinides, whereas large fluence produces the actinides uranium and thorium but no longer contains the A = 130 abundance peak. These processes occur in a fraction of a second to a few seconds, depending on details. Hundreds of subsequent papers published have utilized this time-dependent approach. Interestingly, the only modern nearby supernova, 1987A, has not revealed r-process enrichments. Modern thinking is that the r-process yield may be ejected from some supernovae but swallowed up in others as part of the residual neutron star or black hole.
Entirely new astronomical data about the r-process was discovered in 2017 when the LIGO and Virgo gravitational-wave observatories discovered a merger of two neutron stars that had previously been orbiting one another That can happen when both massive stars in orbit with one another become core-collapse supernovae, leaving neutron-star remnants. Everyone could "hear" the replay of the increasing orbital frequency as the orbit became smaller and faster owing to energy loss by gravitational waves. The localization on the sky of the source of those gravitational waves radiated by that orbital collapse and merger of the two neutron stars, creating a black hole, but with significant spun off mass of highly neutronized matter, enabled several teams to discover and study the remaining optical counterpart of the merger, finding spectroscopic evidence of r-process material thrown off by the merging neutron stars. The bulk of this material seems to consist of two types: hot blue masses of highly radioactive r-process matter of lower-mass-range heavy nuclei (A < 140) and cooler red masses of higher mass-number r-process nuclei (A > 140) rich in lanthanides (such as uranium, thorium, californium etc.). When released from the huge internal pressure of the neutron star, these neutralized ejecta expand and radiate detected optical light for about a week. Such duration of luminosity would not be possible without heating by internal radioactive decay, which is provided by r-process nuclei near their waiting points. Two distinct mass regions (A < 140 and A > 140) for the r-process yields have been known since the first time dependent calculations of the r-process. Because of these spectroscopic features it has been argued that r-process nucleosynthesis in the Milky Way may have been primarily ejecta from neutron-star mergers rather than from supernovae. These results offer a new possibility for clarifying six decades of uncertainty over the site of origin of r-process nuclei. Confirming relevance of this discovery by gravitational-wave astronomy to the r-process is the radiogenic power from radioactive decay of r-process nuclei that maintains the visibility of these spun off r-process fragments. Otherwise they would dim quickly. Unquestionably this discovery raised support for such mergers being the main sources of the r-process nuclei rather than core-collapse supernovae; but that debate continues.
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