Resource Letter: Synthesis of the elements in stars

Human curiosity, our need to ask questions and to wonder about our world, is the driving force behind every major discovery. One of the most important questions asked over the centuries is “Where do we come from?” Looking into the constituents of the human body, and of everything that makes up our planet, one finds the known chemical elements. Therefore, the question, “Where do we come from?” becomes “What is the origin of the chemical elements?”

This is one of the questions that the field of nuclear astrophysics is trying to address. Nuclear astrophysics is a multi-disciplinary field that includes observations done by astronomers, stellar models created by astrophysicists, and experiments and theory by nuclear physicists.

Modern nuclear astrophysics is also part of the era of multi-messenger astronomy, in which information is combined from different observables coming from the same stellar source. Such observables include electromagnetic radiation in many different wavelengths, neutrinos, and gravitational waves, as well as the study of solar-system samples and stardust grains. The latter term refers to grains of material, typically embedded in meteorites, which carry signatures of astrophysical events before the formation of the solar system.

State-of-the-art astrophysical models attempt to explain the available observables by creating a realistic description of stellar interiors, as well as the nuclear reactions that take place in them. This nuclear input typically comes from experiments at nuclear accelerator laboratories, which provide access to the exact isotopes that drive these stellar processes, even if they cannot be found naturally on Earth. Finally, when experiments cannot access the relevant nuclear properties, nuclear theory is essential for predicting the missing properties of the relevant exotic isotopes.

It is therefore clear that all subfields in nuclear astrophysics are linked together. It is impossible to make significant progress in the field without close collaboration. Observations, modeling, and nuclear input are all interconnected and guide each other to make new discoveries. Research addressing these questions is published in a wide variety of journals since this is a multidisciplinary field. Nuclear physics experimental and theoretical work is often published in Physical Review Letters, Physical Review C, Nuclear Physics A, Physics Letters B, and Journal of Physics G. Work that is focused more on the astrophysics side usually appears in the Astrophysical Journal, Astronomy & Astrophysics, Physical Review D, and Monthly Notices of the Royal Astronomical Society. High impact results can appear in Nature or Science. Many of the papers appear on the arXiv after submission or publication and this way can be accessed freely. However, it is important to note that papers appearing on the arXiv did not always go through the peer-review process.

The field of nuclear astrophysics was born during the first half of the 20th century. The question regarding the energy production in our Sun and other stars was an open question for a long time, but only through the discoveries in nuclear physics were we able to create a more accurate picture. All the discoveries and understanding at the time were collected in a publication by Margaret Burbidge, Geoffrey Burbidge, William Fowler, and Fred Hoyle, in 1957, known as B2FH from the authors' initials.¹ It is interesting to note that the author list consisted of an astronomer, an astrophysicist, a nuclear experimentalist, and a theorist, reflecting the diversity required in the field from its inception. B2FH put together a comprehensive picture of nucleosynthesis that explained the production of every isotope, and that picture is largely still accurate today. It should be noted that around the same time a second publication, by Alastair Cameron, gave roughly the same description of nucleosynthesis.² A more modern description of the full field can be found in textbooks, such as Refs. 3 and 4.

• 1.

  “ Synthesis of the elements in stars,” E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle, Rev. Mod. Phys. 29, 547 (1957) https://doi.org/10.1103/RevModPhys.29.547

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  . Provides the first comprehensive description of nucleosynthesis in stars. (I)

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  “ Nuclear reactions in stars and nucleogenesis,” A. G. W. Cameron, Publ. Astron. Soc. Pac. 69 201 (1957) https://doi.org/10.1086/127051

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  . Published at the same time as B2FH, this paper also provides a description of nucleosynthesis in stars. (I)

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  Cauldrons in the Cosmos: Nuclear Astrophysics, C. E. Rolfs and W. S. Rodney ( The University of Chicago Press, Chicago, 1988).

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  Nuclear Physics of Stars, C. Iliadis ( Wiley-VCH, Second Edition, 2015). The most recent textbook on nuclear astrophysics provides more astrophysics background and more calculations compared to the previous textbook. (I)

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Today, there are 118 known elements. 90 of them are naturally found in the Solar System and 28 are “artificial,” meaning that they are made in the laboratory. New heavier elements are still being discovered today, and they are called “superheavy” elements. This is an active field of research, which searches for the limits of nuclear stability and existence. A nice overview of recent discoveries with a complete reference list, a historic perspective, and outlook can be found in Ref. 5.

Although we often talk about the synthesis of the elements in stars, the question should really be about the synthesis of “isotopes” in stars. Isotopes are variations of an element, having the same number of protons but different numbers of neutrons. Different isotopes of the same element are typically synthesized in different astrophysical processes and even different stellar environments. Therefore, it is important to switch our discussion from the synthesis of the elements to the synthesis of the different isotopes, the so-called “nucleosynthesis.”

In the same way that in chemistry all elements are plotted together in the periodic table of the elements, in nuclear physics, and in nuclear astrophysics, all isotopes are presented on the chart of nuclei, shown in Fig. 1. This chart displays the number of protons on the y axis and the number of neutrons on the x axis, therefore each element occupies a single row. Many versions of this chart exist and are color-coded for various nuclear properties like the half-life of each isotope or its decay mode. An interactive version can be found on the National Nuclear Data Center website (https://www.nndc.bnl.gov). In Fig. 1 version, the gray scale represents the half-life of each isotope, with lighter colors corresponding to shorter half-lives and the black boxes corresponding to stable isotopes. The colored lines on top show the rough paths of the various astrophysical processes discussed in this Resource Letter.

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  “ The limits of nuclear mass and charge,” W. Nazarewicz, Nat. Phys. 14, 537 (2018) https://doi.org/10.1038/s41567-018-0163-3

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Soon after the Big Bang, within roughly a second, protons and neutrons start to form, followed a few minutes later by the formation of the first nuclei. Only hydrogen, helium, and traces of lithium were produced during the Big Bang because the universe cooled too fast for other nuclear reactions to take place to form heavier elements. Therefore, all other elements must be made in stars. There are still open questions regarding the involved nuclear reactions and the relevant conditions of Big Bang nucleosynthesis. A recent review of the field can be found in Ref. 6.

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  “ Big bang nucleosynthesis: Present status,” R. Cyburt et al, Rev. Mod. Phys. 88 015004 (2016) https://doi.org/10.1103/RevModPhys.88.015004

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Before diving into the details of the various nucleosynthesis processes, it is important to have a general understanding of the birth, life, and death of stars. This background is critical since stellar evolution is closely linked to the various nuclear reactions responsible for energy production and nucleosynthesis. Nuclear reactions taking place at the center of a star release enough energy to balance the star's gravitational collapse. Different nuclear reactions play this role at the various stages of stellar evolution and under different conditions. An introduction to this field can be found in Ref. 4 and also in Refs. 7 and 8 and many other textbooks.

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  Galactic Astronomy, J. Binney and M. Merrifield ( Princeton U. P., Princeton, NJ, 1998). Example textbook with a description of stellar evolution, which is essential to understand nuclear astrophysics processes in stars. (E)

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  “ The life and times of an intermediate mass star—In isolation/in a close binary,” I. Iben Jr., Q. J. R. Astron. Soc. 26, 1 (1985)

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  . Example textbook with a description of stellar evolution, which is essential to understand nuclear astrophysics processes in stars. (E)

At the beginning of its life, a star consists mainly of hydrogen. As it contracts due to gravitational forces, the temperature in its center starts to increase, which enables the fusion of hydrogen nuclei (protons) to begin. There are different reaction sequences that can make this happen depending on the conditions and exact composition of the star. The result is the conversion of four hydrogen nuclei into one helium nucleus and the release of energy. This energy release is what balances the star from further collapse and continues until the hydrogen fuel at the center runs out or is insufficient to stop the core from collapsing. The main reaction sequences are:

• •

  The pp chain: starting from a pure hydrogen environment, nuclear reaction sequences “burn” that hydrogen producing helium. The pp chain dominates for lighter stars, up to about the mass of our Sun.

• •

  The CNO cycle: for stars that are already enriched in some carbon, nitrogen, and oxygen from previous generations of stellar evolution and nucleosynthesis, these three elements can serve as catalysts and help convert hydrogen to helium. There are multiple CNO cycles that can be found in the literature. A historic review of the CNO cycle can be found in Ref. 9.

Some of the reactions included in the pp chain and the CNO cycle are still under study by modern facilities, in particular ones that are installed in underground laboratories as described later in this Resource Letter. A review of the reactions involved in the pp chain and the CNO cycle can be found in Ref. 10.

Once the stellar core runs out of hydrogen fuel, it is left with predominantly helium. However, the temperature is not high enough for nuclear reactions with helium to take place. At this point, there is nothing opposing the gravitational collapse of the star and the pressure of the outer layers causes the core to contract and heat up until helium reactions become possible in the core and hydrogen burns in a shell outside of the core. The fusion of two helium-4 nuclei results in beryllium-8, which is unbound and breaks back into two helium-4 nuclei. The fusion of one helium-4 and one proton is also not possible since the resulting lithium-5 is also unbound.

The way for helium burning to proceed is through an extremely rare reaction called the “triple alpha” reaction where three helium-4 nuclei fuse together to form carbon-12. The probability for such a reaction is of course very small, and in 1953, Fred Hoyle famously predicted that there must be a resonance that enables this reaction to proceed faster. This so-called “Hoyle state” was soon after discovered experimentally. A review of the Hoyle state can be found in Ref. 11.

The created carbon-12 can capture a helium-4 nucleus and create oxygen-16 which is written as ¹²C(α,γ)¹⁶O. This is a very slow reaction and is considered the “Holy grail” for the field since it influences almost all stellar nucleosynthesis into heavier elements as well as the evolution of the star itself. A detailed collection of the nuclear physics around the ¹²C(α,γ)¹⁶O reaction can be found in Ref. 12.

Massive stars continue their evolution with additional burning phases in the sequence: carbon, neon, oxygen, and silicon. Each reaction chain is typically more complex than the previous stages, resulting in complicated reaction networks with a large number of nuclear reactions to be addressed. The final product following silicon burning is an iron core at the center of the massive star. The elements around iron are the most bound isotopes on the nuclear chart. As a result, nuclear reactions in this region do not release energy to help balance the star's gravitational pressure. On the contrary, they absorb energy, which results in the collapse of the star and potentially its explosion as a core-collapse supernova or its collapse as a black hole depending on the mass of the star.

The network of nuclear reactions during the last burning stages of the star is often dominated by reactions in equilibrium, meaning that one reaction is balanced by its reverse one, or multiple reactions are balanced by each other (reaction cycles). As a result, only a small number of reactions are critical for our understanding of these stages, typically the reactions entering or escaping the reaction cycles. These burning cycles have been known for a long time and are nicely described in the textbook by Iliadis.⁴ 

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  “ The Hoyle state in ¹²C”, M. Freer and H. O. U., Fynbo, Prog. Part. Nucl. Phys. 78, 1 (2014) https://doi.org/10.1016/j.ppnp.2014.06.001

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  “ The ¹²C(α,γ)¹⁶O reaction and its implications for stellar helium burning,” R. J. deBoer et al, Rev. Mod. Phys. 89 035007 (2017) https://doi.org/10.1103/RevModPhys.89.035007

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  . An overview of the ¹²C alpha-capture reaction including its astrophysical importance, theoretical description, and the plethora of experimental efforts. (I)

The fusion of lighter elements to form heavier ones ends around iron. At this point, the Coulomb barrier for the nuclei becomes so high that it is not energetically possible to continue building heavier elements through charged particle induced reactions. As a result, the main way to produce the heavy elements is through neutron-capture reactions. Two main processes were proposed for this purpose: the slow (s) neutron-capture process and the rapid (r) process. As their names imply, the s process takes place in environments with relatively few available neutrons, while the r process is an explosive process with extreme neutron densities. One additional process, the p process, was introduced to explain the production of roughly 30 neutron-deficient isotopes, which could not be reached via neutron captures. The p process (or γ process as is often called) involves photodisintegration reactions on pre-existing seed nuclei.

An r process review that focuses on the nuclear physics input was published recently in Ref. 13.

A review of the s process can be found in Refs. 14 and 15. The most recent review of the p/γ process was published in Ref. 16.

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  “ r-process nucleosynthesis: Connecting rare-isotope beam facilities with the cosmos,” C. Horowitz et al, J. Phys. G 46, 083001 (2019) https://doi.org/10.1088/1361-6471/ab0849

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  “ The s process: Nuclear physics, stellar models, and observations,” F. Kappeler, R. Gallino, S. Bisterzo, and W. Aoki, Rev. Mod. Phys. 83, 57 (2011)

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  “ Neutron Reactions in Astrophysics”, R. Reifarth, C. Lederer, and F. Kappeler, J. Phys. G: Nucl. Part. Phys. 41, 053101 (2014) https://doi.org/10.1088/0954-3899/41/5/053101

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  “ Constraining the astrophysical origin of the p-nuclei through nuclear physics and meteoritic data,” T. Rauscher, N. Dauphas, I. Dillmann, C. Froelich, Zs. Fülop, and Gy. Gyürky, Rep. Progr. Phys. 76, 066201 (2013) https://doi.org/10.1088/0034-4885/76/6/066201

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  . Review of the astrophysical p process including observables such as solar system abundances and meteoritic data. (I)

One of the biggest questions around r-process nucleosynthesis has been “where does the r process take place?” For many decades core-collapse supernovae were considered the dominant candidate, and more recently, neutron-star mergers were introduced as a possible alternative.¹⁷ However, both scenarios had successes and difficulties in reproducing the observed data and no clear candidate could be selected. Things changed in 2017 with the discovery of the first neutron-star merger event (GW170817) though gravitational-wave and electromagnetic observations.^18,19 The gravitational-wave observation enabled the identification of the event, while the accompanying electromagnetic spectra carried signatures of r-process nucleosynthesis (the so-called kilonova). This was the first solid evidence for a possible r-process site. Still, the puzzle is not yet solved, and it remains to be seen if neutron-star mergers are the only source of r-process material, or if there are contributions from other sites, and if yes how much. To answer these questions, it is now more important than ever to have accurate nuclear input in r-process calculations so that we can accurately describe the various astrophysical environments.

Additional constraints for the r-process conditions can also be provided by studying long-lived radioisotopes in meteorites. The ratio of ¹²⁹I/²⁴⁷Cm was shown to be sensitive not only to the site of the r process but also to different areas of the same site that exhibit different conditions.²⁰ This is because the two radioisotopes have a similar half-life (⁠ $≈$ 15 million years) but because of their different atomic numbers their relative abundances strongly depend on the physical conditions of the r-process nucleosyntheis.²⁰ With the kilonova signatures and the radioisotope ratios, we now have more observational constraints than ever before, and the hunt for a solid description of r-process nucleosynthesis continues.

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  “ Origin of the heaviest elements: The rapid neutron capture process,” J. J. Cowan, C. Sneden, J. E. Lawler, A. Aprahamian, M. Wiescher, K. Langanke, and G. Martínez-Pinedo, F. K. Thielemann, Rev. Mod. Phys. 93, 015002 (2021) https://doi.org/10.1103/RevModPhys.93.015002

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  “ ¹²⁹I and ²⁴⁷Cm in meteorites constrain the last astrophysical source of solar r-process elements”, B. Côté, M. Eichler, A. Y. López, N. Vassh, M. R. Mumpower, B. Világos, B. Soós, A. Arcones, T. M. Sprouse, R. Surman, M. Pignatari, M. K. Peto, B. Wehmeyer, T. Rauscher, and M. Lugaro, Science 371, 945 (2021) https://doi.org/10.1126/science.aba1111

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  . Paper that describes the use of the ¹²⁹I/²⁴⁷Cm to provide constraints to the astrophysical conditions of the r process. (I)

The s, r, and p processes explained the majority of the astronomical observations for more than five decades. Recently, however, modern telescopes gave rise to abundance patterns that cannot be explained by these three processes alone and new scenarios had to be proposed. Some of the new observations that lead to these new developments can be found in Refs. 21 and 22.

With the exception of isotopic measurements in stardust grains, in general observations provide information only on elemental abundances. It is therefore unclear whether the discrepant observations should be resolved with neutron-rich or proton-rich astrophysical processes. On the proton-rich side, neutrino interactions during a core-collapse supernova can convert some of the existing protons into neutrons, which in turn induce (n,p) reactions on existing nuclei. These, together with proton-capture reactions can produce some of the proton-rich isotopes through the so-called νp process. Frohlich et al.²³ corresponds to the article that introduced the νp process.

On the neutron-rich side three processes were introduced, all proceeding in conditions somewhere between the s and r processes. The three processes are the “weak r process,” the “i process,” and the “n process.” The processes involve similar groups of neutron-rich nuclei, not very far from stability (as shown in Fig. 1), however, their produced abundance patterns are different and can therefore be differentiated. Modern research focuses on understanding these processes and estimating their possible contributions to the element abundances in the universe. These processes exhibit significant open questions both on the astrophysics side (like what the conditions and site for each of the processes are) and from the unclear physics side (in particular, neutron-capture reactions).

• 21.

  “ The diverse origins of neutron-capture elements in the metal-poor star HD 94028: Possible detection of products of i-process nucleosynthesis,” Roederer et al, Astroph. J. 821, 37 (2016) https://doi.org/10.3847/0004-637X/821/1/37

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  . Article that discusses the observational signatures of the i process and the astrophysical models that describe it. (A)

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  “ Molybdenum and Zirconium isotopes from a supernova neutron burst,” B. S. Meyer et al, Astrophysical J. 540, L52 (2000)

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  “ Neutrino-induced nucleosynthesis of A>64 nuclei: The νp Process,” C. Frohlich et al, Phys. Rev. Lett. 96, 142502 (2006) https://doi.org/10.1103/PhysRevLett.96.142502

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  “ Sensitivity studies for the weak r process: Neutron capture rates,” R. Surman et al, AIP Adv. 4, 041008 (2014) https://doi.org/10.1063/1.4867191

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  “ The impact of (n,γ) reaction rate uncertainties of unstable isotopes on the i-process nucleosynthesis of the elements from Ba to W,” P. Denissenkov et al, Mon. Not. R. Astronomical Soc. 488, 4258 (2019) https://doi.org/10.1093/mnras/stz1921

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  . Article that discusses the neutron-capture reactions that drive the astrophysical i process. (I)

Each of the astrophysical scenarios discussed in the earlier sections involves a distinct set of nuclei and interactions between them. When modeling each process and comparing it to the available observations, it is critical to use the most accurate nuclear properties and reaction rates. These define not only the synthesis of heavier elements but also the amount of energy released/absorbed, the produced/captured particles, and in general the whole evolution of the astrophysical environment all the way to a possible explosion. As such, a large effort is dedicated to identifying the nuclear properties that impact each astrophysical process, measuring them directly if possible, and if not, providing experimental constraints and theoretical predictions.

The process of identifying and implementing accurate nuclear input in astrophysical models is complex. Since the communities working on these two aspects are different, it is critical to create connections and collaborations. This happens through publications, of course, but also through dedicated conferences and workshops discussing specific aspects of stellar nucleosynthesis, collaboration meetings, or simply direct one-on-one contacts. From the point of view of the experimental work, two points are the most critical: (1) When preparing a new proposal either for funding or for performing an experiment at a large facility, it is important to work closely with modelers to identify the most important nuclear properties to be measured so that the submitted proposal (and later the experiment) is well justified. (2) After the experiment and data analysis are completed, the new scientific result needs to be entered back into the astrophysical model to explore its impact. Once again, having direct collaboration with modelers makes this process more streamlined and the results more impactful for the whole community.

Depending on whether the participating nuclei in a stellar process are stable or radioactive, there are different facilities and experimental techniques that need to be used. In this section, the nuclear input is divided into nuclear reaction experiments with stable and with radioactive beams. The measurements often focus on the relevant nuclear reaction rates, but other nuclear properties, like masses, decay properties, and level schemes, are also crucial and need to be measured.

Nuclear reaction is the process in which a nucleus interacts with another nucleus or a subatomic particle. After this interaction occurs, the reaction products can be the same as the initial reactants, but they can also be very different. The two reactants can fuse into a single compound nucleus, typically produced at a highly excited state, which deexcites by emitting γ rays and light particles (neutrons, protons, alphas) or even through fission. The two reactants can also interact through other reaction mechanisms that do not require their full fusion. Details about the various types of nuclear reactions can be found in standard nuclear physics textbooks. For nuclear astrophysics, the most common reaction type is the fusion of a nucleus with a proton, neutron or alpha-particle and the emission of γ-rays and/or light particles.

The traditional way of measuring nuclear reactions is to have an accelerator facility produce a stable beam, often protons or alpha particles, which is then impinged on a thin foil, the so-called “target.” The main consideration other than the reaction participants is the beam energy. It is important that the selected energy corresponds to the temperature of the stellar environment. This astrophysically relevant energy range is the so-called “Gamow window.” Despite the six decades that the field of nuclear astrophysics has been active, and the numerous experiments measuring relevant nuclear reactions, there are still several reactions that are out of reach. Modern accelerator facilities strive to provide higher beam intensities to increase the number of reactions. Often, however, the reaction products are very few and they are hidden under large amounts of background radiation, either from the natural room-background or from interactions of cosmic rays with the detector material. For this reason, the highest sensitivity in stellar reaction experiments is achieved at underground laboratories. In underground laboratories, the cosmic rays that hit the Earth's surface are greatly attenuated. This causes the relevant background in nuclear detectors to be reduced by several orders of magnitude. As such, reaction measurements that are not possible on the Earth's surface become possible when going underground.

A description of stable beam experimental techniques and facilities can be found in the Iliadis textbook.⁴ For more details on underground facilities, a recent review article on the pioneering underground facility “LUNA” can be found in Ref. 26.

• 26.

  “ LUNA: Status and prospects,” Prog. Part. Nucl. Phys. 98 55 (2018). Review of underground experiments for nuclear astrophysics with a focus on the LUNA facility in Italy. (I)

Several of the astrophysical processes mentioned earlier are driven by nuclei that are unstable. The properties and interactions of these exotic nuclei are critical input in astrophysical models. These isotopes can be produced at so-called “radioactive ion beam facilities” or “rare isotope facilities.” Such facilities always start with a stable isotope that can be found naturally on Earth. They accelerate this isotope to high velocities and through a nuclear reaction they produce a range of new isotopes, many of which are radioactive. Powerful filters can separate out the unwanted isotopes, using electric and magnetic fields, and in this way create a secondary beam of particles that consist mainly of the radioactive isotope of interest. This beam is then sent to the experimental station to either measure the properties of the particular isotope (mass, half-life, decay properties, etc.) or study the nuclear reactions induced by this isotope at astrophysical energies.

A topical review of radioactive beam facilities, as well as experimental techniques for measuring relevant nuclear properties, was published in Ref. 13. Although the review focuses on r process applications, the majority of the experimental facilities and techniques apply to all astrophysical processes that involve radioactive nuclei.

Often the nuclei that drive certain astrophysical processes are not available for experiments, or even if they are, the properties of interest cannot be measured. It is therefore of paramount importance to have reliable theoretical models that can predict nuclear properties and nuclear reactions entering astrophysical models. Depending on the property, the type of reaction, and even the mass region, different theoretical models exist, with varying degrees or reliability. This is because nuclei are complex many-body systems and with current computing power it is not possible to describe them all without making approximations. Only the lightest nuclei can be described from first principles. Therefore, nuclear theory and nuclear experiment go hand-in-hand, with theoretical models using experimental constraints where available and experiments targeting measurements that will help improve the theoretical models.

A discussion of nuclear theory is also included in the Iliadis textbook⁴ and for more details the reader can look at the textbook by Nunes and Thomson.²⁴ 

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The field of nuclear astrophysics is currently moving forward at a fast pace. New astronomical observations, and especially multi-messenger observations, provide new insight into the inner workings of stars that needs to be explained. The higher than ever computer power and the era of machine-learning techniques offer new possibilities in modeling stellar environments and nuclei with the highest possible accuracy. Finally, advances in experimental technology allow for the study of nuclei and nuclear reactions never before possible. The next generation of nuclear facilities, either underground or on the Earth's surface, offer stable beams or radioactive beams with higher power than ever. At the same time, new detector technologies and new experimental techniques allow the study of nuclei and their reactions in new ways that help tackle major unanswered questions in the field. With such advances on all fronts of nuclear astrophysics, and with communities that collaborate closely, the future of the field is bright.