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The radioactive nuclei $^{\textbf{26}}\mathrm{Al}$ and $^{\textbf{60}}\mathrm{Fe}$ in the Cosmos and in the solar system

Published online by Cambridge University Press:  09 December 2021

R. Diehl
Max Planck Institut für extraterrestrische Physik, D-85748 Garching, Germany
M. Lugaro
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary ELTE Eötvös Loránd University, Institute of Physics, Budapest 1117, Pázmány Péter sétány 1/A, Hungary School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia
A. Heger
School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), Clayton, VIC 3800, Australia Center of Excellence for Astrophysics in Three Dimensions (ASTRO-3D), Australia Joint Institute for Nuclear Astrophysics, 1 Cyclotron Laboratory, NSCL, Michigan State University, East Lansing, MI 48824, USA
A. Sieverding
School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
X. Tang
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, P.R. China
K. A. Li
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, P.R. China
E. T. Li
College of Physics and Optoelectronic Engineering, ShenZhen University, Shenzhen, P.R. China
C. L. Doherty
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia
M. G. H. Krause
Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK
A. Wallner
Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, 01328 Dresden, Germany Research School of Physics, Australian National University, Canberra, ACT 2601, Australia
N. Prantzos
Institut d’Astrophysique, Paris, France
H. E. Brinkman
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary Graduate School of Physics, University of Szeged, Dom ter 9, Szeged 6720, Hungary
J. W. den Hartogh
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary
B. Wehmeyer
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK
A. Yagüe López
Konkoly Observatory, Eötvös Loránd Research Network (ELKH), H-1121 Budapest, Konkoly Thege M. út 15-17, Hungary
M. M. M. Pleintinger
Max Planck Institut für extraterrestrische Physik, D-85748 Garching, Germany
P. Banerjee
Discipline of Physics, Indian Institute of Technology Palakkad, Kerala 678557, India
W. Wang
School for Physics and Technology, Wuhan University, Wuhan 430072, P.R. China WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan 430072, P.R. China
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The cosmic evolution of the chemical elements from the Big Bang to the present time is driven by nuclear fusion reactions inside stars and stellar explosions. A cycle of matter recurrently re-processes metal-enriched stellar ejecta into the next generation of stars. The study of cosmic nucleosynthesis and this matter cycle requires the understanding of the physics of nuclear reactions, of the conditions at which the nuclear reactions are activated inside the stars and stellar explosions, of the stellar ejection mechanisms through winds and explosions, and of the transport of the ejecta towards the next cycle, from hot plasma to cold, star-forming gas. Due to the long timescales of stellar evolution, and because of the infrequent occurrence of stellar explosions, observational studies are challenging, as they have biases in time and space as well as different sensitivities related to the various astronomical methods. Here, we describe in detail the astrophysical and nuclear-physical processes involved in creating two radioactive isotopes useful in such studies, $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ . Due to their radioactive lifetime of the order of a million years, these isotopes are suitable to characterise simultaneously the processes of nuclear fusion reactions and of interstellar transport. We describe and discuss the nuclear reactions involved in the production and destruction of $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ , the key characteristics of the stellar sites of their nucleosynthesis and their interstellar journey after ejection from the nucleosynthesis sites. This allows us to connect the theoretical astrophysical aspects to the variety of astronomical messengers presented here, from stardust and cosmic-ray composition measurements, through observation of $\gamma$ rays produced by radioactivity, to material deposited in deep-sea ocean crusts and to the inferred composition of the first solids that have formed in the Solar System. We show that considering measurements of the isotopic ratio of $^{26}\mathrm{Al}$ to $^{60}\mathrm{Fe}$ eliminate some of the unknowns when interpreting astronomical results, and discuss the lessons learned from these two isotopes on cosmic chemical evolution. This review paper has emerged from an ISSI-BJ Team project in 2017–2019, bringing together nuclear physicists, astronomers, and astrophysicists in this inter-disciplinary discussion.

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© The Author(s), 2021.Published by Cambridge University Press on behalf of the Astronomical Society of Australia

1. Introduction

Understanding the cosmic evolution of the composition of matter from the Big Bang until the present time requires tracing the ensemble of atomic nuclei through their nuclear transformations on their journey across space and time. These transformations are called ‘nucleosynthesis’: nuclear reactions that rearrange how protons and neutrons are grouped into the different isotopes of the chemical elements. In nature, nuclear reactions may occur through collisions or disintegration of nuclei in hot and energetic environments, such as the Big Bang, stellar explosions, the hot interiors of stars, and the interstellar space where they involve accelerated cosmic-ray particles. Rearrangements of nucleons through nuclear reactions therefore drive the change of elemental and isotopic composition in the Universe from the almost pure H and He made in the Big Bang to the current rich variety of elements, including C to U, that also enables biological life. This process is called ‘chemical evolution’.Footnote a In this review, we will disentangle the processes involved by picking specific nuclei as examples, and tracing their origins and cosmic journey to us.

The relative abundances of different isotopes in a given material are the result of the nucleosynthetic episodes that such an ensemble of nucleons and isotopes has experienced along its cosmic trajectory. First, we have to understand the nucleosynthesis processes themselves, within stars and stellar explosions, that modify the nuclear composition; the nuclear reactions here mostly occur in low-probability tails at energies of tens of keV, which in many cases is far from what we can study by experiments in terrestrial laboratories, so that often sophisticated extrapolations are required. Beyond these nuclear reactions and their sites, we have to understand how nuclei are transported in and out of stellar nucleosynthesis sites and towards the next generation of stellar nucleosynthesis sites throughout the Galaxy. A key ingredient is the path through the interstellar matter towards newly forming stars, after nuclei have been ejected from the interior of a star by a stellar wind or a stellar explosion.

It is possible to measure interstellar isotopes and their relative abundances directly, by suitably capturing cosmic matter and then determining its isotopic composition, e.g., using mass spectrometry. In fact, cosmic matter rains down onto Earth continuously in modest but significant quantity—the discovery of live radioactive $^{60}\mathrm{Fe}$ isotopes in Pacific ocean crusts (Knie et al. Reference Knie, Korschinek, Faestermann, Dorfi, Rugel and Wallner2004) and in galactic cosmic rays (Binns et al. Reference Binns2016) have demonstrated this. It is a major challenge for astronomical instrumentation, however, to determine abundances of cosmic nuclei for regions that are not accessible through material transport or spacecraft probes, i.e., in different parts of our current and past Universe. For example, in starlight spectra only some isotopic signatures may be recognised, and only when measuring at extremely high spectral resolution.

Astronomical abundance measurements are subject to biases, in particular, because atomic nuclei appear in different phases, such as plasma, neutral or partially-ionized atoms, or molecules. Therefore, observational signals differ from each other. For example, an elemental species may be accelerated as cosmic rays or condensed into dust, depending on how a meteoric inclusion, such as a pre-solar dust grain, had been formed, or how an ion mixture may generate an observable spectral line in the atmosphere of a star, characteristically absorbing the starlight originating from the interiors of stars. Observations of cosmic isotopes are rather direct if radioactive isotopes can be seen via their radioactive-decay signatures outside stars, i.e., without biases and distortions from absorption. This is possible when characteristic $\gamma$ -ray lines are measured from such radioactive decay. The detection of characteristic $^{26}\mathrm{Al}$ decay $\gamma$ rays (Mahoney et al. Reference Mahoney, Ling, Jacobson and Lingenfelter1982) was the first direct proof that nucleosynthesis must be ongoing within the current Galaxy, because this isotope has a characteristic decay half-life of $0.72\,$ Myr, much shorter than the age of the Galaxy, more than 10 Gyr. $^{26}\mathrm{Al}$ , and, similarly, $^{60}\mathrm{Fe}$ (with a half-life of 2.62 Myr), both probe recent nucleosynthesis and ejecta transport. They have been measured in $\gamma$ rays from interstellar space, have been found in terrestrial deposits, and have even been inferred to exist in specific abundance in the first solids that formed in the Solar System 4.6 Gyr ago. These two isotopes exemplify a new approach to cosmic chemical evolution studies, which involves a wide community, from nuclear physicists through Solar System scientists, astrophysical theorists, and astronomers working on a broad range of topics. As a result, there is a significant diversity of scientific publications addressing these two isotopes, with discussions increasing in intensity over the past two decades (Figure 1). This review focuses on discussion of these two specific isotopes, in relation to the nuclear and astrophysical processes involved in the cycle of matter that drives cosmic chemical evolution.

Figure 1. Scientific publications per year, addressing $^{26}\mathrm{Al}$ (above) and $^{60}\mathrm{Fe}$ (below). A total of $>$ 2 000 refereed papers with $>$ 25 000 citations and $>$ 300 000 reads (for $^{26}\mathrm{Al}$ ) represent the size of the community involved in these topics. (Data and plots from NASA ADS).

In this paper, we assemble and combine the different views on this theme from a working group on ‘Radioactive Nuclei in the Cosmos and in the Solar System’ that met at ISSI-BeijingFootnote b in 2018 and 2019. The team included astronomers, theorists in various aspects of astrophysics and nuclear physics, as well as nuclear physics experimentalists. The members of the working group covered a variety of different expertises and interests and we chose to exploit this diversity to describe the journey of cosmic isotopes from a nuclear astrophysics perspective using the two isotopes $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ as examples. We describe the properties of these nuclei and their reactions with other nuclei, the astrophysical processes involved in their production, and how observations of their abundance ratio can be exploited to learn about which nuclear transformations happen inside stars and their explosions.

The main goal of this paper is to pose the scientific questions in all their detail, not to provide ultimate consensus nor answers. We aim to illuminate the approximations and biases in our way of arguing and learning, as this is important for all theory, observations, and experiment. Ideally, we wish to identify critical observations, experiments, and simulations that can help to validate or falsify these approximations, towards a better understanding of the physical processes involved in transforming the initial H and He during cosmic evolution into the material mix that characterises our current, life-hosting Universe.

In Sections 2, we focus on the case of $^{26}\mathrm{Al}$ and carry this discussion from nuclear properties and reaction physics through cosmic nucleosynthesis sites to interstellar transport and creation of astronomical messengers. Sections 3 discusses the case of $^{60}\mathrm{Fe}$ and what is different from the case of $^{26}\mathrm{Al}$ in relation to each of those processes for $^{60}\mathrm{Fe}$ . Sections 4 shows how investigation of the abundance ratio of these two isotopes allows to eliminate some of the unknowns in astrophysical modelling and interpretation. Our conclusions (Sections 5) summarise the nuclear physics, astrophysics, astronomical, and methodological issues, and the lessons learned as well as the open questions from the study of $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ in the context of cosmic chemical evolution.

2. The cosmic trajectory of $^{\textbf{26}}\textbf{Al}$

2.1. Nuclear properties, creation and destruction reactions

2.1.1. Nuclear properties of $^{26}\mathrm{Al}$

Figure 2 shows the $^{26}\mathrm{Al}$ isotope within its neighbouring nuclides, with $^{27}\mathrm{Al}$ as the only stable isotope of Al. The ground state of $^{26}\mathrm{Al}$ ( $^{26}\mathrm{Al}^g$ ) (see Figure 3) has a spin and parity of $5^+$ and a $\beta^+$ -decay half-life of 0.717 Myr. It decays into the first excited state of $^{26}\mathrm{Mg}$ ( $1\,809$ keV; $2^+$ ), which then undergoes $\gamma$ -decay to the ground state of $^{26}\mathrm{Mg}$ producing the characteristic $\gamma$ ray at 1 808.63 keV. The first excited state of $^{26}\mathrm{Al}$ at 228 keV ( $^{26}\mathrm{Al}^m$ ) is an isomeric state with a spin and parity of $0^+$ . It is directly connected to the $^{26}\mathrm{Al}^g$ state via the highly-suppressed M5 $\gamma$ -decay with a half-life of 80 500 yr according to shell model calculations (Coc, Porquet, & Nowacki Reference Coc, Porquet and Nowacki2000; Banerjee et al. Reference Banerjee, Misch, Ghorui and Sun2018. $^{26}\mathrm{Al}^m$ decays with a half-life of just 6.346 s almost exclusively to the ground state of $^{26}\mathrm{Mg}$ via super-allowed $\beta^+$ -decay(Audi et al. Reference Audi, Kondev, Wang, Huang and Naimi2017), with a branching ratio of 100.0000 $^{+0}_{-0.0015}$ (Finlay et al. Reference Finlay2012).

Figure 2. The table of isotopes in the neighbourhood of ${}^{26}\mathrm{Al}$ . Each isotope is identified by its usual letters and the total number of nucleons, with stable isotopes and black and unstable isotopes in colored boxes. The second line for unstable isoptopes indicates the lifetime. The third line lists spin and parity of the nucleus ground state. The primary decay channel is indicated in the bottom left. The stable elements have their abundance fractions on Earth in the last row. (extracted from Karlsruher Nuklidkarte, original by the JRC of the EU)

In cosmic nucleosynthesis, the correct treatment of $^{26}\mathrm{Al}^m$ and $^{26}\mathrm{Al}^g$ in reaction network calculations is crucial (Runkle, Champagne, & Engel Reference Runkle, Champagne and Engel2001; Gupta & Meyer Reference Gupta and Meyer2001). When ${}^{26}\mathrm{Al}$ is produced by a nuclear reaction, it is produced in an excited state, which rapidly decays to the isomeric and/or ground states by a series of $\gamma$ -ray cascades. At low temperatures ( $T\lesssim$ 0.15 GK), communication between $^{26}\mathrm{Al}^m$ and $^{26}\mathrm{Al}^g$ can be ignored due to the negligibly-low internal transition rates. Therefore, $^{26}\mathrm{Al}^m$ and $^{26}\mathrm{Al}^g$ can be treated as two distinct species with their separate production and destruction reaction rates (Iliadis et al. Reference Iliadis, Champagne, Chieffi and Limongi2011).

At higher temperatures ( $T\gtrsim$ 0.4 GK), instead, higher excited states of $^{26}\mathrm{Al}$ can be populated on very short timescales by photo-excitation of $^{26}\mathrm{Al}^g$ and $^{26}\mathrm{Al}^m$ resulting in thermal equilibrium where the abundance ratio of the states are simply given by the Boltzmann distribution. In this case, it is sufficient to have just one species of $^{26}\mathrm{Al}$ in reaction network calculations defined by its thermal equilibrium ( $^{26}\mathrm{Al}^t$ ), with suitable reaction rates that take into account the contributions from all the excited states that are populated according to the Boltzmann distribution (Iliadis et al. Reference Iliadis, Champagne, Chieffi and Limongi2011).

The situation becomes complicated at intermediate temperatures (0.15 GK $\lesssim$ T $\lesssim$ 0.40 GK). Although, $^{26}\mathrm{Al}^g$ and $^{26}\mathrm{Al}^m$ can still communicate with each other via the higher excited states, the timescale required to achieve thermal equilibrium becomes comparable or even longer than the timescale for $\beta^+$ -decay for $^{26}\mathrm{Al}^m$ (as well as $\beta^+$ -decay of higher excited states). Thus, neither the assumption of thermal equilibrium nor treating $^{26}\mathrm{Al}^g$ and $^{26}\mathrm{Al}^m$ as two separate species are viable options (Banerjee et al. Reference Banerjee, Misch, Ghorui and Sun2018; Misch et al. Reference Misch, Ghorui, Banerjee, Sun and Mumpower2021). In this case, it becomes necessary to treat at least the lowest four excited states as separate species in the reaction network, along with their mutual internal transition rates, in order to calculate the abundance of $^{26}\mathrm{Al}$ accurately (Iliadis et al. Reference Iliadis, Champagne, Chieffi and Limongi2011). However, as will be discussed below, it turns out that the production of $^{26}\mathrm{Al}$ in stars happen mostly either in the low or the high temperature regime, and the problematic intermediate temperature regime is rarely encountered.

2.1.2. Production and destruction of $^{26}\mathrm{Al}$

$^{26}\mathrm{Al}$ is expected to be primarily produced in the hydrostatic burning stages of stars through p-capture reactions on 25Mg. These occur in massive stars during core hydrogen burning, hydrostatic/explosive carbon/neon shell burning, and in the hydrogen-burning shell, in some cases located at the base of convective envelope, of asymptotic giant branch (AGB) stars. Explosive oxygen/neon shell burning probably also contributes to the production of this isotope. All these sites are be described in more detail in Section 2.2. The typical temperatures of the H-burning core in massive stars and the H-burning shell of AGB stars are $T=0.04-0.09$ GK. In these environments, ${}^{26}\mathrm{Al}$ is produced by $^{25}\mathrm{Mg(p},\gamma)^{26}\mathrm{Al}^{g,m}$ acting on the initial abundance of ${}^{25}{\rm Mg}$ within the MgAl cycle shown in Figure 4. ${}^{25}{\rm Mg}$ can also be produced by the $^{24}\mathrm{Mg(p},\gamma)^{25}\mathrm{Al}(\beta^+)^{25}\mathrm{Mg}$ reaction chain at the temperature above 0.08GK. At such low temperatures, there is no communication between $^{26}\mathrm{Al}^{g}$ and $^{26}\mathrm{Al}^{m}$ . $^{26}\mathrm{Al}^{g}$ may be destroyed by $^{26}\mathrm{Al}^{g}(p,\gamma)^{27}\mathrm{Si}$ and by the $\beta^+$ -decay.

Figure 3. The nuclear level and decay scheme of $^{26}\mathrm{Al}$ (simplified). $\gamma$ rays are listed as they arise from decay of $^{26}\mathrm{Al}$ , including annihilation of the positrons from $\beta^+$ -decay.

Hydrostatic C/Ne shell burning occurs at a temperature around 1.2 GK. Here, $^{26}\mathrm{Al}$ is produced by the $^{24}\mathrm{Mg(n},\gamma)^{25}\mathrm{Mg(p},\gamma)^{26}\mathrm{Al}^{t}$ reaction chain. The detailed flow chart is shown in Figure 5. At the temperature of C/Ne shell burning, $^{26}\mathrm{Al}$ reaches thermal equilibrium and can be treated at a single species, $^{26}\mathrm{Al}^{t}$ (see above). Destruction of $^{26}\mathrm{Al}$ mostly occurs through neutron capture reactions. The main neutron sources are the 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ and ${}^{12}$ C( ${}^{12}$ C,n) ${}^{23}\mathrm{Mg}$ reactions. ${}^{26}\mathrm{Al}^{t}$ is also destroyed by the $\beta^+$ -decay process in C/Ne shell burning. The explosive C/Ne shell burning may raise the temperature up to 2.3 GK and then quickly cool down to 0.1 GK within a time scale of 10 s. The detailed flow chart in these conditions is shown in Figure 6. ${}^{26}\mathrm{Al}$ is produced by the same process as during hydrostatic C/Ne shell burning, except that the ${}^{23}$ Na( $\alpha$ ,p) ${}^{26}\mathrm{Mg}$ reaction competes with ${}^{23}\mathrm{Na}(p,\gamma){}^{24}\mathrm{Mg}$ and the $^{25}\mathrm{Mg}(\alpha,n)^{28}\mathrm{Si}$ reaction competes with ${}^{25}\mathrm{Mg(p},\gamma)^{26}\mathrm{Al}^t$ . These two $\alpha$ -induced reactions bypass the the production of ${}^{26}\mathrm{Al}^t$ . ${}^{26}\mathrm{Al}^t$ is primarily destroyed by ${}^{26}\mathrm{Al}^t(n,p)^{26}\mathrm{Mg}$ instead of $\beta^+$ -decay.

In an explosive proton-rich environment such as within a nova, the peak temperature may reach about 0.3 GK. Here, $^{26}\mathrm{Al}$ is produced by two sequences of reactions: $^{24}\mathrm{Mg(p},\gamma)$ $^{25}\mathrm{Al}(\beta^+)^{25}\mathrm{Mg(p},\gamma)^{26}\mathrm{Al}^{g,m}$ , and $^{24}\mathrm{Mg(p},\gamma)$ $^{25}\mathrm{Al}(p,\gamma)^{26}\mathrm{Si}(\beta^+)^{26}\mathrm{Al}^{g,m}$ , which favours the production of $^{26}\mathrm{Al}^{m}$ , therefore bypassing the observable $^{26}\mathrm{Al}^{g}$ .

$^{26}\mathrm{Al}$ can also be directly produced in the core-collapse supernova $\nu$ process via $^{26}\mathrm{Mg}(\nu_e,e^-)$ (Woosley et al. Reference Woosley, Hartmann, Hoffman and Haxton1990), when the high-energy ( ${\sim}10\ \mathrm{MeV}$ ) neutrinos emitted during the collapse and cooling of a massive star interact with nuclei in the mantle that is processed by the explosion shock at the same time. Neutrino-nucleus reactions that lead to proton emission also increase the production of $^{26}\mathrm{Al}$ via the reactions discussed above. The contribution of the $\nu$ process to the total supernova yield is expected to be at the 10% level (Sieverding et al. Reference Sieverding, Martnez-Pinedo, Langanke, Heger, Kubono, Kajino, Nishimura, Isobe, Nagataki, Shima and Takeda2017; Timmes et al. Reference Timmes, Woosley, Hartmann, Hoffman, Weaver and Matteucci1995b); we caution that this value is subject to uncertainties in the neutrino physics and the details of the supernova explosion mechanism.

2.1.3. Uncertainties in the relevant reaction rates

The uncertainties of the rates of main production reactions 25Mg(p, $\gamma)^{26}\mathrm{Al}^{g}$ and 25Mg(p, $\gamma)^{26}\mathrm{Al}^{m}$ are around 10% at $T_9$ >0.15; at lower temperatures, the uncertainties are even larger than 30% (Iliadis et al. Reference Iliadis, Longland, Champagne, Coc and Fitzgerald2010). Since there is little communication between $^{26}\mathrm{Al}^g$ and $^{26}\mathrm{Al}^m$ at $T_9$ <0.15, these two reactions need to be determined individually. Two critical resonance strengths, at centre-of-mass energies $E_{c.m.}=92$ and 198 keV, have been measured using the LUNA underground facility with its accelerator (Strieder et al. Reference Strieder2012). However, due to the lack of statistical precision of the measurement and of decay transition information, the branching ratio of the ground state transition still holds a rather large uncertainty, in spite of some progress from a recent measurement with Gammasphere at Argonne National Laboratory (ANL) (Kankainen et al. Reference Kankainen2021). Prospects to re-study this resonance with better statics are offered by the new JUNA facility in China, also extending the measurements down to the resonance at 58 keV with a more intense beam (Liu et al. Reference Liu2016). Note that at such low energies, screening needs to be taken into account, in order to obtain the actual reaction rate in stellar environments (Strieder et al. Reference Strieder2012).

Figure 4. The Na-Mg-Al cycle encompasses production and destruction reactions, and describes $^{26}\mathrm{Al}$ in stellar environments.

Figure 5. Integrated reaction flow for the hydrostatic C/Ne shell burning calculated with the NUCNET nuclear network code. The thickness of the arrows correspond to the intensities of the flows; red and black arrows show $\beta$ interactions and nuclear reactions, respectively. Here $^{26}\mathrm{Al}$ is at its thermal equilibrium. Only a fraction of the flows of Na, Mg, Al and Si are displayed. The neutron source reactions, such as 12C+12C and 22Ne( $\alpha$ , n), are not shown.

The effect of variations of other thermonuclear reaction rates on the ${}^{26}\mathrm{Al}$ production in massive stars was investigated in detail by Iliadis et al. (Reference Iliadis, Champagne, Chieffi and Limongi2011), who performed nucleosynthesis post-processing calculations for each site by adopting temperature and density time profiles from astrophysical models, and then applying reaction rates from the STARLIB compilation (Sallaska et al. Reference Sallaska, Iliadis, Champange, Goriely, Starrfield and Timmes2013). The effect of $^{26}\mathrm{Al}^m$ has also explicitly been taken into account. These authors identified the following four reactions: $^{26}\mathrm{Al}^{t}(n,p)^{26}$ Mg, $^{25}\mathrm{Mg}(\alpha,n)^{28}\mathrm{Si}$ , $^{24}\mathrm{Mg(n},\gamma)^{25}\mathrm{Mg}$ and $^{23}\mathrm{Na}(\alpha,p)^{26}\mathrm{Mg}$ to significantly affect the $^{26}\mathrm{Al}$ production yield in massive stars. For a status review of these reaction rates see Iliadis et al. (Reference Iliadis, Champagne, Chieffi and Limongi2011), who estimate a typical reaction-rate uncertainty of a factor two.

Recently, four direct measurements of $^{23}\mathrm{Na}(\alpha,p)^{26}\mathrm{Mg}$ have been performed (Almaraz-Calderon et al. Reference Almaraz-Calderon2014; Howard et al. Reference Howard, Munch, Fynbo, Kirsebom, Laursen, Diget and Hubbard2015; Tomlinson et al. Reference Tomlinson2015; Avila et al. Reference Avila2016). The reaction rate in the key temperature region, around 1.4 GK, was found to be consistent within 30% with that predicted by the statistical model (Rauscher & Thielemann Reference Rauscher and Thielemann2000, NON-SMOKER). This level of precision in the $^{23}\mathrm{Na}(\alpha,p)^{26}\mathrm{Mg}$ reaction rate should allow useful comparisons between observed and simulated astrophysical $^{26}\mathrm{Al}$ production.

The determination of the $^{26}\mathrm{Al}^{t}(n,p)^{26}\mathrm{Mg}$ reaction rate actually requires the independent measurements of two reactions: $^{26}\mathrm{Al}^{g}(n,p)^{26}\mathrm{Mg}$ and $^{26}\mathrm{Al}^{m}(n,p)^{26}$ Mg. Two direct measurements of $^{26}\mathrm{Al}^{g}(n,p)^{26}\mathrm{Mg}$ have been published up to now, using $^{26}\mathrm{Al}^g$ targets (Trautvetter et al. Reference Trautvetter1986; Koehler et al. Reference Koehler, Kavanagh, Vogelaar, Gledenov and Popov1997). Their results differ by a factor of 2, calling for more experimental work. The preliminary result of a new measurement of $^{26}\mathrm{Al}(n,p)^{26}\mathrm{Mg}$ performed by the n $\_$ TOF collaboration is a promising advance (Tagliente et al. Reference Tagliente2019). Production of a $^{26}\mathrm{Al}^m$ target is not feasible due to the short lifetime of $^{26}\mathrm{Al}^m$ . So, indirect measurement methods appear promising, such as the Trojan Horse Method (Tribble et al. Reference Tribble, Bertulani, Cognata, Mukhamedzhanov and Spitaleri2014).

On top of the main reactions discussed above, the ${}^{12}$ C+ ${}^{12}$ C fusion reaction drives C/Ne burning and therefore the production of ${}^{26}{\rm Al}$ there. Herein, 12C(12C, $\alpha)^{20}\mathrm{Ne}$ and 12C(12C, $p)^{23}\mathrm{Ne}$ are two major reaction channels. Measurements of these have been performed at energies above $E_{c.m.} = 2.1\ \mathrm{MeV}$ , and three different extrapolation methods have been used to estimate the reaction cross section at lower energies (Beck, Mukhamedzhanov, & Tang Reference Beck, Mukhamedzhanov and Tang2020). Comparing to the standard rate CF88 from Caughlan & Fowler (Reference Caughlan and Fowler1988), the indirect measurement using the Trojan Horse Method suggests an enhancement of the reaction rate due to a number of potential resonances in the unmeasured energy range (Tumino et al. Reference Tumino2018), while the phenomenological ‘hindrance model’ suggests a greatly suppressed and lower rate (Jiang et al. Reference Jiang2018). Normalizing the rates to the CF88 standard rate, the Trojan Horse Method rate and the hindrance rate are 1.8 and 0.3 at $T_9=1.2\ \mathrm{GK}$ , respectively. However, differences are reduced to less than 20% at $T=2.0$ GK. A systematic study of the carbon isotope system suggests that the reaction rate is at most a factor of 2 different from the standard rate, and that the hindrance model is not a valid model for the carbon isotope system (Zhang et al. Reference Zhang2020; Li et al. Reference Li, Fang, Bucher, Li, Ru and Tang2020). Direct measurements are planned in both underground and ground-level labs to reduce the uncertainty.

Figure 6. Same as Figure 5 but for C/Ne explosive burning.

The 12C(12C, $n)^{23}\mathrm{Mg}$ reaction is an important neutron source for C burning, and has been measured first at energies above $E_{c.m.} = 3\ \mathrm{MeV}$ ; with a recent experiment, measured energies are now extending down to the Gamow window. At typical carbon shell burning temperatures, $T = 1.1-1.3\ \mathrm{GK}$ , the uncertainty is less than 40%, and reduced to 20% at $T = 1.9-2.1\ \mathrm{GK}$ , which is relevant for explosive C burning (Bucher et al. Reference Bucher2015).

The $^{22}\mathrm{Ne}(\alpha,n)^{25}\mathrm{Mg}$ reaction is another important neutron source. It has been measured directly down to $E_{cm} = 0.57\ \mathrm{MeV}$ with an experimental sensitivity of 10−11b (Jaeger et al. Reference Jaeger, Kunz, Mayer, Hammer, Staudt, Kratz and Pfeiffer2001). For a typical C shell burning temperature $T = 1.2\ \mathrm{GK}$ , the important energies span from 0.84 to 1.86 MeV, and these are fully covered by the experimental measurements. Therefore, the uncertainty is less than $\pm$ 6% for both hydrostatic and explosive C burning. At the temperatures of the He shell burning, the uncertainty would be as large as 70%; while this is not relevant for the production of ${}^{26}{\rm Al}$ (Iliadis et al. Reference Iliadis, Longland, Champagne, Coc and Fitzgerald2010), it is very crucial for the production of ${}^{60}{\rm Fe}$ . During He burning, the $^{22}\mathrm{Ne}(\alpha,\gamma$ ) rate also affects the amount of $^{22}\mathrm{Ne}$ available for the production of neutrons. A number of indirect measurements have obtained important information on the nuclear structure of 26Mg. However, evaluations of the reaction rates following the collection of new nuclear data presently show differences of up to a factor of 500, resulting in considerable uncertainty in the resulting nucleosynthesis. Detailed discussions can be found in the recent compilations (Longland, Iliadis, & Karakas Reference Longland, Iliadis and Karakas2012a; Adsley et al. Reference Adsley2021). Direct measurements of 22Ne+ $\alpha$ in an underground laboratory are urgently needed to achieve accurate rates for astrophysical applications.

Finally, the cross section for $^{26}\mathrm{Mg}(\nu_e,e^-)^{26}\mathrm{Al}$ is dominated by the transition to the isobaric analog state of the $^{26}\mathrm{Mg}$ ground state at $228.3\,\mathrm{keV}$ and further contributions from a number of Gamow-Teller (GT) transitions at low energies. Zegers et al. (Reference Zegers2006) have used charge exchange reactions to determine the GT strength distribution of 26Mg. Sieverding et al. (Reference Sieverding, Martnez-Pinedo, Huther, Langanke and Heger2018b) have calculated the cross section based on these experimental results with forbidden transitions at higher energies. Figure 7 shows a comparison between the theoretical cross section based on the ‘Random Phase Approximation’ and the values using the experimentally determined strength at low energies. The particle emission branching has been calculated with a statistical model code (Loens Reference Loens2010; Rauscher et al. Reference Rauscher, Thielemann, Görres and Wiescher2000). While the theoretical model captures the total cross section quite well, the values for transition to the ${}^{26}{\rm Mg}$ ground state are substantially underestimated in the calculations.

Figure 7. Cross section for the reaction $^{26}\mathrm{Mg}(\nu_e,e^-)$ comparing results based entirely on theoretical calculations (red lines) and results based on the experimentally measured Gamow-Teller strength distribution (blue lines). The experimentally determined distribution increases the strength at low energies and gives a larger cross section for the transitions to the $^{26}\mathrm{Al}$ ground state.

2.2. Cosmic nucleosynthesis environments

Here we address stellar nucleosynthesis, as we know it from models and theoretical considerations, in greater detail first for stars that are not massive enough to end in a core collapse, then for the different nucleosynthesis regions within massive stars and their core-collapse supernovae; and finally, we comment on other explosive sites such as novae and high-energy reactions in interstellar matter.

2.2.1. Low- and intermediate-mass stars

Low and intermediate mass stars (of initial masses $\approx\ 0.8{-}8\ {\rm M}_{\odot}$ ) become AGB stars after undergoing core H and He burning. An AGB star consists of a CO core, H and He burning shells surrounded by a large and extended H-rich convective envelope. These two shells undergo alternate phases of stable H burning and repeated He flashes (thermal pulses) with associated convective regions. Mixing events (called ‘third dredge ups’) can occur after thermal pulses, whereby the base of the convective envelope penetrates inwards, dredging up material processed by nuclear reactions from these deeper shell burning regions into the envelope. Mass is lost through a stellar wind and progressively strips the envelope releasing the nucleosynthetic products into the interstellar environment (see Karakas & Lattanzio Reference Karakas and Lattanzio2014 for a recent review of AGB stars.).

The production of $^{26}\mathrm{Al}$ Footnote c within AGB stars has been the focus of considerable study (e.g., Norgaard Reference Norgaard1980; Forestini, Arnould, & Paulus Reference Forestini, Arnould and Paulus1991; Mowlavi & Meynet Reference Mowlavi and Meynet2000; Karakas & Lattanzio Reference Karakas and Lattanzio2003; Siess & Arnould Reference Siess and Arnould2008; Lugaro & Karakas Reference Lugaro and Karakas2008; Ventura, Carini, & D’Antona Reference Ventura, Carini and D’Antona2011). Here we do not attempt a review of the extensive literature, but briefly summarize the relevant nucleosynthesis, model uncertainties, stellar yields, and the overall galactic contribution.

The main site of $^{26}\mathrm{Al}$ production in low-mass AGB stars is within the H-burning shell. Even in the lowest mass AGB stars, temperatures are such ( ${\geq}$ 40 MK), that the MgAl chain can occur and the $^{26}\mathrm{Al}$ is produced via the 25Mg(p, $\gamma)^{26}\mathrm{Al}$ reaction. The H burning ashes are subsequently engulfed in the thermal pulse convective zone, with some $^{26}\mathrm{Al}$ surviving and later enriching the surface via the third dredge up. In AGB stars of masses ${\geq}$ 2– $3\ {{\rm M}_{\odot}}$ (depending on metallicity) the temperature within the thermal pulse is high enough ( ${>}$ 300 MK) to activate the 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ reaction. The neutrons produced from this reaction efficiently destroy the $^{26}\mathrm{Al}$ (via the $^{26}\mathrm{Al}$ (n,p) $^{26}\mathrm{Mg}$ and $^{26}\mathrm{Al}$ (n, $\alpha)^{23}$ Na channels), leaving small amounts to be later dredged to the surface.

In more massive AGB stars another process is able to produce $^{26}\mathrm{Al}$ : the hot bottom burning. This hot bottom burning takes place when the base of the convective envelope reaches high enough temperatures for nuclear burning ( ${\sim}$ 50–140 MK). Due to the lower density at the base of the convective envelope than in the H burning shell, higher temperatures are required here to activate the Mg-Al chain of nuclear reactions. The occurrence of hot bottom burning is a function of initial stellar mass and metallicity, with higher mass and/or lower metallicity models reaching higher temperatures. The lower mass limits for hot bottom burning (as well as its peak temperatures) also depend on stellar models, in particular on the treatment of convection (e.g.Ventura & D’Antona Reference Ventura and D’Antona2005). Values from representative models of the Monash group (Karakas Reference Karakas2010) are ${\sim}5\ {{\rm M}_{\odot}}$ at metallicity $Z=0.02$ , decreasing to ${\sim}3.5\ {{\rm M}_{\odot}}$ at $Z=0.0001$ . Typically, there is larger production of $^{26}\mathrm{Al}$ by hot bottom burning when temperatures at the base of the envelope are higher and the AGB phase is longer. The duration of the AGB phase is set by the mass loss rate, which is a major uncertainty in the predicted $^{26}\mathrm{Al}$ yields (Mowlavi & Meynet Reference Mowlavi and Meynet2000; Siess & Arnould Reference Siess and Arnould2008; Höfner & Olofsson Reference Höfner and Olofsson2018).

As the temperature at the base of the convective envelope increases two other reactions become important. First, at $\sim$ 80 MK, $^{24}\mathrm{Mg}$ is efficiently destroyed via $^{24}\mathrm{Mg}(p,\gamma)^{25}\mathrm{Al}(\beta^{+})^{25}\mathrm{Mg}$ leading to more seed $^{25}\mathrm{Mg}$ for $^{26}\mathrm{Al}$ production, Second, at above 100 MK, the $^{26}\mathrm{Al}$ itself is destroyed via $^{26}\mathrm{Al}(p,\gamma)^{27}\mathrm{Si}(\beta^{+})^{27}\mathrm{Al}$ . This last reaction has the largest nuclear reaction rates uncertainty within the Mg-Al chain, variations of this rate within current uncertainties greatly modify the AGB stellar $^{26}\mathrm{Al}$ yield (Izzard et al. Reference Izzard, Lugaro, Karakas, Iliadis and van Raai2007; van Raai et al. Reference van Raai, Lugaro, Karakas and Iliadis2008).

Figure 8 shows the $^{26}\mathrm{Al}$ yields for a range of metallicites ( $Z = 0.02-0.0001$ ) as a function of initial mass from the Monash set of models of Karakas (Reference Karakas2010) and Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio and Siess2014a); Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio, Siess and Campbell2014b). The relative efficiency of the two different modes of production are evident: in the lower mass models, where $^{26}\mathrm{Al}$ is enhanced only by the third dredge-ups of the H-shell ashes, show a low yield of $\approx 10^{-8}\,{-}\,3\ \times\ 10^{-7}\ {{\rm M}_{\odot}}$ . The more massive AGB stars that undergo hot bottom burning, instead, have substantially higher yield of $\approx 10^{-6}\,{-}\,10^{-4}\ {{\rm M}_{\odot}}$ .

Metallicity also has an impact to the AGB $^{26}\mathrm{Al}$ yield, in particular for intermediate-mass AGB stars. The larger yields at $Z=0.004$ and 0.008, when compared to $Z=0.02$ , are primarily due to their higher temperatures and longer AGB phases. At the lowest metallicity ( $Z=0.0001$ ) the seed $^{25}\mathrm{Mg}$ nuclei are not present in sufficient amounts to further increase the $^{26}\mathrm{Al}$ yield even with a higher temperature and similar duration of the AGB phase. This is the case even thought the majority of the initial envelope $^{24}\mathrm{Mg}$ has been transmuted to 25Mg, and the intershell $^{25}\mathrm{Mg}$ is efficiently dredged-up via the third dredge-ups. The decreasing trend in $^{26}\mathrm{Al}$ yield for the most massive metal-poor models is due to their shorter AGB phase, less third dredge-up and higher hot-bottom burning temperatures, which activate the destruction channel $^{26}\mathrm{Al}(p,\gamma)^{27}\mathrm{Si}$ .

The contribution from AGB stars to the galactic inventory of $^{26}\mathrm{Al}$ has been estimated at between $0.1{-}0.4\ {{\rm M}_{\odot}}$ (e.g., Mowlavi & Meynet Reference Mowlavi and Meynet2000). More recently Siess & Arnould (Reference Siess and Arnould2008) also included super-AGB starsFootnote d yields in this contribution, and also their impact seems to be rather modest. Even when factoring in the considerable uncertainties impacting the yields, AGB stars are expected to be of only minor importance to the Galactic $^{26}\mathrm{Al}$ budget at solar metallicity. However, Siess & Arnould (Reference Siess and Arnould2008) noted that at lower metallicity, around that of the Magellanic clouds ( $Z = 0.004{-}0.008$ ), the contribution of AGB and super-AGB stars may have been far more significant.

Figure 8. AGB star yields of $^{26}\mathrm{Al}$ for the range of metallicities ( $Z = 0.02-$ 0.0001) as a function of initial mass. Results taken from Karakas (Reference Karakas2010) and Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio and Siess2014a); Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio, Siess and Campbell2014b)

2.2.2. Massive Stars and their core-collapse supernovae

Massive stars are defined as stars with main-sequence masses of more than 8– $10\,\mathrm{M}_\odot$ . They are characterized by relatively high ratios of temperature over density ( $T/\rho$ ) throughout their evolution. Due to this, such stars tend to be more luminous. Unlike lower-mass stars, they avoid electron degeneracy in the core during most of their evolution. Therefore, core contraction leads to a smooth increase of the temperature. This causes the ignition of all stable nuclear burning phases, from H, He, C, Ne, and O burning up to the burning of Si both in the core and in shells surrounding it. The final Fe core is bound to collapse, while Si burning continues in a shell and keeps on increasing the mass of the core. During this complex sequence of core and shell burning phases, many of the elements in the Universe are made. A substantial fraction of those newly-made nuclei are removed from the star and injected into the interstellar medium by the core-collapse supernova explosion, leaving behind a neutron star or a black hole. The collapse of the core is accompanied by the emission of a large number of neutrinos. The energy spectrum of these neutrinos reflects the high temperature environment from which they originate, with mean energies of 10– $20\,\mathrm{MeV}$ . The fact that these neutrinos could be observed in Supernova 1987A is a splendid confirmation of our understanding of the the lives and deaths of massive stars (Burrows & Lattimer Reference Burrows and Lattimer1987; Arnett Reference Arnett1987).

The mechanism that ultimately turns the collapse of a stellar core into a supernova explosion is an active field of research. In our current understanding, a combination of neutrino heating and turbulent fluid motion are crucial components for successful explosions (see Janka Reference Janka2012; Burrows & Vartanyan Reference Burrows and Vartanyan2021, for reviews of the status of core-collapse modeling). Due to the multi-dimensional nature and multi-physics complexity of this problem, simulations of such explosions from first principles are still in their infancy (Müller Reference Müller2016). Parametric models, however, have proven to be able to explain many properties of supernovae, although they need to be fine-tuned accordingly (Burrows & Vartanyan Reference Burrows and Vartanyan2021).

The supernova explosion expels most of the stellar material that had been enriched in metals by the hydrostatic burning and the explosion shock itself. Before the explosion, strong winds already take away some of the outer envelopes of these massive stars, especially in the luminous blue variable and Wolf-Rayet phases of evolution (as will be discussed in detail see below). This ejected material also contains a range of radioactive isotopes, including some with lifetimes long enough to be observable long after the explosion has faded, such as $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ . In this section we describe the various ways in which $^{26}\mathrm{Al}$ is made in massive stars and the ensuing supernova explosion.

The production of $^{26}\mathrm{Al}$ always operates through the 25Mg(p, $\gamma)^{26}\mathrm{Al}$ reaction, which is active during different epochs of the stellar evolution. We can distinguish four main phases that contribute to the production of $^{26}\mathrm{Al}$ during massive star evolution and the supernova explosion (Limongi & Chieffi Reference Limongi and Chieffi2006b).

  1. 1. In H core and shell burning $^{26}\mathrm{Al}$ is produced from the $^{25}\mathrm{Mg}$ that is present due to the initial metallicity.

  2. 2. During convective C/Ne shell burning $^{26}\mathrm{Al}$ is produced from the $^{25}\mathrm{Mg}$ that results from the Mg-Al cycle with protons provided by the C fusion reactions.

  3. 3. The supernova explosion shock initiates explosive C/Ne burning and $^{26}\mathrm{Al}$ is efficiently produced in the region of suitable peak temperature around $2.3\,\mathrm{GK}$ . As we will show, this is the dominant contribution for stars in the mass range 10–30 $\mathrm{M}_\odot$ .

  4. 4. Neutrino interactions during the explosion can also affect the abundance of ${}^{26}{\rm Al}$ .

Figure 9 shows the profile of the $^{26}\mathrm{Al}$ mass fraction for a $15\,\mathrm{M}_\odot$ stellar model, calculated with the KEPLER hydrodynamics code in spherical symmetry. The pre-supernova as well as the post-explosion abundance profiles are shown, and the production mechanisms indicated. We now discuss in detail each of the four main mechanisms listed above.

H core and shell burning: The production in the convective core H burning during the main sequence mostly depends on the size of the convective core and the initial amount of 25Mg. $^{26}\mathrm{Al}$ in the region that undergoes core He burning is destroyed due to neutron-capture reactions, but some of it may survive in the layers outside of the burning region. The $^{26}\mathrm{Al}$ produced during H core burning is also threatened by the lifetime of the star. Since the post-main-sequence, i.e., post-H-burning, evolution of a star can take more than 0.1 Myr, due to the exponential radioactive decay most of this early made $^{26}\mathrm{Al}$ decays before it can be ejected by a supernova explosion. In H-shell burning, $^{26}\mathrm{Al}$ is also produced and it is more likely to survive until it is ejected. In cases in which the H-burning contribution is important for the final $^{26}\mathrm{Al}$ yield, this component is sensitive to H burning conditions and in particular to the treatment of convection.

Another way for $^{26}\mathrm{Al}$ from H burning to contribute to the ejecta is mass loss. For single stars, mass is lost via stellar winds driven by radiation pressure (Cassinelli Reference Cassinelli1979; Vink Reference Vink2011). Thus, it is stronger for more luminous, more massive stars. Stellar mass loss has been a subject of study for a long time (Lamers et al. 1999; Vink Reference Vink2011), but the details of the implementation in models still gives rise to significant uncertainties (Farrell et al. Reference Farrell, Groh, Meynet and Eldridge2020). The H-burning contribution to $^{26}\mathrm{Al}$ is most-important for massive stars with initial mass ${>}30\,\mathrm{M}_\odot$ for which stellar winds are strong enough to remove material from the H burning regions below the H envelope (Limongi & Chieffi Reference Limongi and Chieffi2006b).

Figure 9. Mass fraction profiles of $^{26}\mathrm{Al}$ indicating regions of different production mechanisms.

Stellar rotation may significantly increase mass loss and the mixing efficiency (Groh et al. Reference Groh2019; Ekström et al. Reference Ekström2012), which has significant impact on the ${}^{26}{\rm Al}$ yields. Stellar-evolution models that include a description of rotation have been developed for decades (see Maeder & Meynet Reference Maeder and Meynet2000; Heger, Langer, & Woosley Reference Heger, Langer and Woosley2000, for extensive reviews). However, the effects are still not well-understood. A major challenge is to model the transport of angular momentum within stars (Aerts, Mathis, & Rogers Reference Aerts, Mathis and Rogers2019). This determines how fast the internal regions of the star rotate at different radii and different latitudes. Friction from laminar and turbulent flows between layers of different velocity transports angular momentum, and Coriolis forces add complexity. It is, therefore, far from straightforward to determine how much rotation-induced mixing happens in different regions of a star. This affects transport of heat and of material, and thus where and how nuclear burning may occur.

Figure 10. ${}^{26}{\rm Al}$ yields from three stellar evolution codes with different implementations of stellar rotation. Shown are contributions from winds of solar metallicity stars (Ekström et al. Reference Ekström2012; Limongi & Chieffi Reference Limongi and Chieffi2018; Brinkman et al. Reference Brinkman, den Hartogh, Doherty, Pignatari and Lugaro2021), and supernova yields (Limongi & Chieffi Reference Limongi and Chieffi2018). Initial rotation rates of 0 (non-rotating), 150, and 300 km s−1 are considered, as indicated in the legend. Yields are in units of ${{\rm M}_{\odot}}$ . Based on Figure 4b of Brinkman et al. (Reference Brinkman, den Hartogh, Doherty, Pignatari and Lugaro2021).

A wealth of information has become available on internal rotation rates of low-mass stars (Aerts et al. Reference Aerts, Mathis and Rogers2019), thanks to asteroseismology studies, e.g., with data from the Kepler and TESS spacecrafts (Borucki et al. Reference Borucki2010; Ricker et al. Reference Ricker2015). These internal rotation rates can help us to investigate the stellar interiors directly. This led, for example, to the insight that rotation has a negligible effect on the ‘slow’ neutron-capture process nucleosynthesis in low-mass AGB stars (den Hartogh et al. Reference den Hartogh, Hirschi, Lugaro, Doherty, Battino, Herwig, Pignatari and Eggenberger2019). Information on the internal rotation rates of massive stars is more sparse, while there is information available on the rotation rates of black holes and neutron stars, which are the final phases of massive star evolution.Recently, Belczynski et al. (Reference Belczynski2020) investigated how to match the LIGO/Virgo-derived compact-star merger rates, and their black hole masses and spins.This was attributed by these authors to the effect of magnetic fields via the Tayler-Spruit dynamo (Spruit Reference Spruit2002) or similar processes (e.g. Fuller, Piro, & Jermyn Reference Fuller, Piro and Jermyn2019). None of the current published massive star yields include this effect so far, which means that the currently available yields from rotating massive stars may likely overestimate the effects of rotation.

Recent nucleosynthesis models including stellar rotation allow us to get estimates of the impact of rotational mixing on the stellar yields. Figure 10 illustrates several characteristic cases. Rotation generally is found to increase $^{26}\mathrm{Al}$ yields, due to the fact that the H-burning convective core is more extended and therefore more ${}^{25}{\rm Mg}$ is burnt into ${}^{26}{\rm Al}$ , which is also mixed up more efficiently due to rotation, and due to the fact that these stars experience more mass loss than their non-rotating counterparts. For the lowest-mass models, 13 and 15 ${{\rm M}_{\odot}}$ , Limongi & Chieffi (Reference Limongi and Chieffi2018) find a large increase in the yields of rotating models, which is due to a significant increase in the mass-loss. This large increase is however not found in the other two studies. For the higher mass-end, $30\ \mathrm{M}_{\odot}$ and up, the mass-loss is less affected by stellar rotation, and the yields only increase slightly, compared to the non-rotating models. This is the same for all three studies. The supernova yields for the lowest-mass stars, shown in Figure 10, are another factor of 10–100 higher than the rotating single-star yields from the same set. Supernova yields for higher masses are zero in the scenario discussed by Limongi & Chieffi (Reference Limongi and Chieffi2018), because stars with an initial mass higher than $25\,\mathrm{M}_{\odot}$ are assumed to collapse completely into black holes, and therefore do not eject $^{26}\mathrm{Al}$ in their supernova. In Section 4.2, we will also consider this comparisons in the light of population synthesis for both $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ (Figures 40 and 39).

The presence of a binary companion may also have a significant impact on the ${}^{26}{\rm Al}$ yields from massive stars, because binary interactions can affect the mass loss. As shown by Sana et al. (Reference Sana2012), massive stars are rarely single stars: most, if not all, are found in binary or even multiple systems. If close enough, the stars within such a system can interact and the gravitational pull between the stars affects the mass loss, known as Roche lobe overflow. In turn the mass loss affects the internal structure and thus further evolution of the star. Figure 11 shows how binarity may affect $^{26}\mathrm{Al}$ yields across the stellar-mass range (Brinkman et al. Reference Brinkman, Doherty, Pols, Li, Côté and Lugaro2019).When the binary interaction takes place during the main sequence or shortly after, but before helium is ignited in the core, the impact on the amount of the ejected ${}^{26}{\rm Al}$ can be significant, and mostly prominent at the lower mass-end of massive stars (10– $35\,\mathrm{M}_{\odot}$ ). Single stars in this mass range lose only a small fraction of their whole H envelope, leaving a significant amount of ${}^{26}{\rm Al}$ locked inside. However, when part of a binary system, much more of the envelope can be stripped off because of mass transfer, which exposes the deeper layers of the star, those that were once part of the H-burning core, and now are the regions where most of the ${}^{26}{\rm Al}$ is located (Brinkman et al. Reference Brinkman, Doherty, Pols, Li, Côté and Lugaro2019). For more massive stars ( $M_{*}\geq35\,\mathrm{M}_{\odot}$ ), instead, mass loss through the stellar winds is strong even for single stars: these are the Wolf-Rayet stars observed to expose their He, C, N, or O-rich regions to the surface. These stars lose their H envelope and reveal deeper layers during their main-sequence evolution or shortly after even without having a companion, and the impact of binarity is found to be insignificant, especially for initial masses of $50\,\mathrm{M}_{\odot}$ and higher.

Figure 11. Yields of ${}^{26}{\rm Al}$ for various single star studies, as well as the effective binary yields defined as the average increase of the yield from a single star to the primary star of a binary system, when considering a range of periods (see Brinkman et al. Reference Brinkman, Doherty, Pols, Li, Côté and Lugaro2019, for details).

However, there are still many uncertainties concerning mass loss in general, and even more so in the combination of binary evolution and mass transfer, as orbital separations change in response to stellar evolution, and different phases of mass transfer may occur (Podsiadlowski et al. Reference Podsiadlowski, Langer, Poelarends, Rappaport, Heger and Pfahl2004; Sana et al. Reference Sana2012). For wide binaries, little may change with respect to single-star evolution; but for close binaries, the impact on stellar evolution may be large (Sana et al. Reference Sana2012). Moreover, the coupling of binary evolution and mass transfer with rotation and its effect on the core-collapse explosive yields have not been explored yet.

Convective C/Ne shell burning: The production of $^{26}\mathrm{Al}$ in this region in the pre-supernova stage can be substantial, as shown in Figure 9 where the mass fraction can reach values up to above $10^{-4}$ . The production of $^{26}\mathrm{Al}$ in C/Ne burning requires the existence of a convective shell that burns C at a sufficiently high temperature. Convection is necessary for the supply of fresh 25Mg, to which the C-burning reactions provide the protons. At the same time, convection moves $^{26}\mathrm{Al}$ out of the hottest burning regions, where it is destroyed quickly. However, the $^{26}\mathrm{Al}$ produced in this process does not contribute to the final yield because it is later destroyed by the high temperatures induced by the explosion shock (Figure 9). Different models for the same mass range, however, may obtain almost no $^{26}\mathrm{Al}$ produced during convective C-burning, while the production later during explosive burning still may lead to very similar overall $^{26}\mathrm{Al}$ yields. In principle, this depends on the explosion dynamics and in particular on the explosion energy. The peak temperature, however, only scales very weakly with the explosion energy, and therefore, even very weak explosions with energies of the order of $10^{50}$ ergs produce enough $^{26}\mathrm{Al}$ to dominate over the contribution from C/Ne shell burning to the total yield.

Explosive contributions: For the explosive contribution of core-collapse supernovae two main quantities affect the $^{26}\mathrm{Al}$ production. First, as a pre-requisite, the amount of produced $^{26}\mathrm{Al}$ scales with the $^{24}\mathrm{Mg}$ mass fraction in the C/Ne layer, because the production proceeds through $^{24}\mathrm{Mg}(n,\gamma)^{25}\mathrm{Mg}(p,\gamma)^{26}\mathrm{Al}$ . This depends on the conditions of C core and shell burning during the hydrostatic evolution of the star and the C-burning reaction rates, as discussed above (Section 2.1). Second, the optimal peak temperature for $^{26}\mathrm{Al}$ production is in a narrow range between $2.1$ and $2.5\,\mathrm{GK}$ . This depends on the reaction rates of 25Mg(p, $\gamma)^{26}\mathrm{Al}$ , on the neutron capture reaction on $^{26}\mathrm{Al}$ , and on the neutron sources. If the temperature is above the optimal value, i.e., at smaller radii, charged particle reactions efficiently destroy the produced $^{26}\mathrm{Al}$ . If the temperature is too low, overcoming the Coulomb barrier in $^{25}\mathrm{Mg}(p,\gamma)^{26}\mathrm{Al}$ is harder, reducing the production. Figure 12 shows the $^{26}\mathrm{Al}$ mass fraction profile as a function of the peak temperature reached at a given radius. Across the mass range of progenitor models, between 13 and $30\,\mathrm{M}_\odot$ , the highest $^{26}\mathrm{Al}$ mass fraction is reached for the same peak temperature. The maximum mass fraction, i.e., the height of the peak in Figure 12, depends mostly on the local mass fraction of $^{24}\mathrm{Mg}$ (which is required to produce $^{25}\mathrm{Mg}$ by neutron captures during the explosion). Since the peak temperature at a given radius depends on the explosion energy, different explosion energies move the peak to different densities. This also changes the value of the maximum $^{26}\mathrm{Al}$ mass fraction. Since charged-particle induced nuclear reactions are highly temperature-dependent, the peak temperature is the most important quantity. Density and seed abundance enter linearly, the range of peak $^{26}\mathrm{Al}$ mass fraction is relatively narrow, within a factor two. The site of the explosive production of $^{26}\mathrm{Al}$ is relatively far away from the stellar core, and therefore not very sensitive to the dynamics of the explosion mechanism itself. The explosion energy, however, depends on the supernova engine, and thus affects the position of the peak mass fraction. The amount of matter exposed to the critical optimal conditions can also change by asymmetries of the explosion. While Figure 12 shows that the mechanism is always qualitatively similar, the actual yield significantly depends on the mass of material that is contained in the region that reaches this temperature. This varies much more between models, and gives rise to the non-monotonic dependence of the $^{26}\mathrm{Al}$ yields on the progenitor mass shown in Figure 12. The optimal temperature is largely determined by the nuclear reaction rates and thus independent of the progenitor model (Figure 12).

Figure 12. Mass fraction of $^{26}\mathrm{Al}$ for mass shells from a range of core-collapse supernova models. Results are shown for a whole series of models with initial masses between 13 and $30\,\mathrm{M}_\odot$ (as indicated in the legend). The temperature that leads to the largest $^{26}\mathrm{Al}$ mass fractions is very similar in all the models.

Neutrino interactions: $^{26}\mathrm{Al}$ yields are also coupled directly to the neutrino emission from core collapse by the $\nu$ process, as mentioned in Section 2.1.2. The neutrinos that are copiously emitted from the cooling proto-neutron star during a supernova explosions are sufficiently energetic and numerous to induce nuclear reactions in the outer layers of the star. Such reactions on the most abundant species have been found to be responsible for, or at least contribute, to the solar abundances of a handful of rare isotopes, including, 7Li, 11B, 19F, 138La, and 180Ta. The $\nu$ process also leaves traces in the supernova yields of long-lived radioactive isotopes, such as 10Be, 92Nb, and 98Tc and contributes to the explosive yield of $^{26}\mathrm{Al}$ . This occurs in a direct and an indirect way. A direct production channel exists through $^{26}\mathrm{Mg}(\nu_e,e^-)$ . Indirectly, neutral-current inelastic neutrino scattering can lead to nuclear excitations that decay by proton emission, i.e., reactions such as 20Ne $(\nu_x,\nu_x' p)$ , where $\nu_x$ includes all neutrino flavours. This provides another source of protons for $^{25}\mathrm{Mg}(p,\gamma)^{26}\mathrm{Al}$ to occur, and enhances production of $^{26}\mathrm{Al}$ outside of the optimal temperature region. With re-evaluated neutrino-nucleus cross sections, a study of 1D explosions for progenitors in the mass range 13–30 $\mathrm{M}_\odot$ has confirmed an early finding (Timmes et al. Reference Timmes, Woosley, Hartmann, Hoffman, Weaver and Matteucci1995b) that the $\nu$ process increases the $^{26}\mathrm{Al}$ yields by up to $40\,\%$ . Previous studies, however, had assumed relatively large energies for the supernova neutrinos that are not supported by current simulation results. The contribution of the $\nu$ process to $^{26}\mathrm{Al}$ is significantly reduced when such lower neutrino energies are adopted. For neutrino spectra with temperature $T_{\nu_e}=2.8\,\mathrm{MeV}$ for $\nu_e$ and $T_{\nu_x}=4\,\mathrm{MeV}$ for all other flavours, the increase of the $^{26}\mathrm{Al}$ yield due to neutrinos is reduced to at most $10\,\%$ (Figure 13).

Figure 13. $^{26}\mathrm{Al}$ supernova yields from massive star progenitors in the range of 13–30 $\mathrm{M}_\odot$ showing the also the contribution of the $\nu$ process and its dependence on the neutrino spectra (Sieverding et al. Reference Sieverding, Martnez-Pinedo, Huther, Langanke and Heger2018b). The progenitor models and explosion trajectories have been calculated with the KEPLER hydrodynamics code.

There are still large uncertainties in the prediction of the neutrino emission from a supernova explosion. During the early phases of vigorous accretion, the neutrino spectra can be much more energetic, increasing the contribution of the $\nu$ process (Sieverding et al. Reference Sieverding, Martnez Pinedo, Langanke, Harris and Hix2018a). Neutrino flavour oscillations add additional uncertainty. The production of $^{26}\mathrm{Al}$ occurs mostly at densities below the critical density for neutrino flavour transformations due to the MSW resonance.Footnote e Due to collective non-linear effects, however, neutrino flavour transformations may occur below the region relevant for the production of $^{26}\mathrm{Al}$ . This could lead to a significant increase of the $\nu_e$ spectral temperature. Tentative calculations indicate that the $^{26}\mathrm{Al}$ yield may be increased by up to a factor 2, if a complete spectral swap between $\nu_e$ and the heavy flavour neutrinos takes place below the O/Ne layer (Sieverding, Müller, & Qian Reference Sieverding, Müller and Qian2020).

2.2.3. Other explosive events: Thermonuclear supernovae, Novae, X-ray bursts, and kilonovae

Other cosmic environments are also plausible candidate to host the nuclear reactions that produce $^{26}\mathrm{Al}$ . Extremely hot plasma temperatures are likely when matter falls onto compact objects: the gravitational energy released by a proton that falls onto a neutron star is 2 GeV. Therefore, nuclear reactions are expected on the surfaces of neutron stars and in the accretion disks that accompany newly forming black holes. However, significant cosmic contributions to $^{26}\mathrm{Al}$ from these objects are unlikely for two reasons: (i) these events are so energetic that nuclei are decomposed into nucleons and $\alpha$ particles, and the $^{26}\mathrm{Al}$ abundance in such conditions will be low; and (ii) there is hardly significant material ejected from such compact regions.

One example of an exception, i.e., where significant material is ejected, is the recent observational confirmation of a kilonova (Abbott et al. Reference Abbott2017). Here, the formation of a compact object after collision of two neutron stars has evidently led to brightening of the object from freshly-produced radioactivity, and the spectra of the kilonova light can be interpreted as a hint at overabundance in nuclei heavier than Fe (Smartt et al. Reference Smartt2017). If consolidated (in view of the significant uncertainties due to atomic-line unknowns and explosion asymmetries), this represents a potential signature of ‘rapid’ neutron capture (r-process) nucleosynthesis. An ejected amount of such material in the range $10^{-4}$ up to $10^{-2}\ {{\rm M}_{\odot}}$ has been inferred (Abbott et al. Reference Abbott2019). However, being predominantly a result of neutron reactions, this ejected material is not expected to hold any significant amounts of $^{26}\mathrm{Al}$ . Similarly, nuclear reactions that occur on the surfaces of neutron stars in binary systems are unlikely to contribute any significant cosmic $^{26}\mathrm{Al}$ . Such reactions have been observed in the form of Type-I X-ray bursts (Bildsten Reference Bildsten, Holt and Zhang2000; Galloway et al. Reference Galloway, Muno, Hartman, Psaltis and Chakrabarty2008). These are thermonuclear runaway explosions after accretion of critical amounts of H and He on neutron star surfaces. Even He ashes may ignite and create super-bursts. The rapid proton capture (rp) process during an explosive hydrogen burst will process surface material up the isotope sequence out to Sm, and hence also include $^{26}\mathrm{Al}$ production. Characteristic afterglows have been observed, that are powered from the various radioactive by-products, likely including $^{26}\mathrm{Al}$ (Woosley et al. Reference Woosley2004).

Another hot and dense nuclear-reaction site is the thermonuclear runaway in a white dwarf star after ignition of carbon fusion. This is believed to produce a supernova of type Ia. Herein, temperatures of several GK and high densities of order 108−10 g cm−3 allow for the full range of nuclear reactions reaching nuclear statistical equilibrium (Seitenzahl & Townsley Reference Seitenzahl and Townsley2017). From such an equilibrium, one expects that the main products will be iron-group isotopes and elements, i.e., products near the maximum of nuclear binding energy, which is reached for 56Ni. $^{26}\mathrm{Al}$ will also be produced herein. But the reaction paths are driven to tighter-bound nuclei under these circumstances. The results from models show relatively low $^{26}\mathrm{Al}$ yields of ${\sim}10^{-8}\ {{\rm M}_{\odot}}$ (Iwamoto et al. Reference Iwamoto, Brachwitz, Nomoto, Kishimoto, Umeda, Hix and Thielemann1999; Nomoto & Leung Reference Nomoto and Leung2018). Therefore, we consider supernovae of Type Ia to be rather unimportant contributors to cosmic $^{26}\mathrm{Al}$ .

Novae are also potential contributors of ${}^{26}{\rm Al}$ in the Galaxy, as mentioned in Section 2.1.2. Herein, hot hydrogen burning reactions can lead to significant $^{26}\mathrm{Al}$ production (Jose & Hernanz Reference Jose and Hernanz1998), with $^{26}\mathrm{Al}$ mass fractions around $10^{-3}$ for the more-massive O-Ne white dwarfs. A major uncertainty in nova modelling is how the observationally inferred large ejected masses would be generated; this appears to ask for some currently unknown source of energy to make nova explosions more violent. A total contribution from novae to Galactic $^{26}\mathrm{Al}$ of 0.1– $0.4\,{{\rm M}_{\odot}}$ have been estimated from self-consistent models (Jose & Hernanz Reference Jose and Hernanz1998). Higher values may possibly occur under favourable circumstances, with up to ${\sim}10^{-6}\ {{\rm M}_{\odot}}$ for an individual nova (Starrfield et al. Reference Starrfield, Truran, Politano, Sparks, Nofar and Shaviv1993).

2.2.4. Interstellar spallation reactions

Cosmic-ray nuclei are characterised as relativistic particles by definition; therefore, when they collide with interstellar matter, the energies in the colliding-system coordinates exceed the threshold for nuclear reactions. Since H is the most abundant nucleus in cosmic gas, nuclear fusion reactions between heavier nuclei are very rare. The most common reactions occurring with cosmic rays are fragmentations, or ‘spallation’ reactions, whereby the heavier nucleus is fragmented, or split up, into lighter daughter nuclei. Because the abundances of nuclei heavier than iron in cosmic rays is negligible, such spallation is a significant production channel only for cosmic nuclei lighter than iron. Therefore, spallation is among the candidate source processes for interstellar $^{26}\mathrm{Al}$ (Ramaty, Kozlovsky, & Lingenfelter Reference Ramaty, Kozlovsky and Lingenfelter1979), but also in the early Solar System, via solar accelerated particles, as well as in the Earth’s atmosphere at all times. The cross section for production of $^{26}\mathrm{Al}$ from cosmic-ray neutrons, as an example, is about 150 mbarn, at its maximum of a collision energy of about 30 MeV, as shown in Figure 14 (Reedy Reference Reedy2013). This figure also indicates which energy range of cosmic rays may contribute to interstellar spallation reactions contributing to $^{26}\mathrm{Al}$ . An estimate may be obtained from the known origins of Be and B from cosmic ray spallation of interstellar C, N, and O nuclei. The solar abundance of CNO, a 10−2 fraction by mass, and of Be+B, 10−9, imply an efficiency of 10−7 for spallation of CNO mass over the 10 Gy of the Galaxy’s age. Considering that present $^{26}\mathrm{Al}$ would have been produced only during its recent radioactive lifetime of 1 My and from even less-abundant heavier nuclei, its production from spallation would be ${\sim}10^{-3}\ {{\rm M}_{\odot}}$ . This is well below of yields of stars and supernovae as discussed above; spallation is not a significant source of Galactic $^{26}\mathrm{Al}$ , even though its effect is observed in the abundance of $^{26}\mathrm{Al}$ in cosmic rays (Section 2.4.2).

Figure 14. Cross sections for spallation reactions of cosmic rays (adapted from Reedy Reference Reedy2013). Reactions are indicated in the legend, and include $^{26}\mathrm{Al}$ production from neutron reactions.

2.3. From the stellar nucleosynthesis sources into galactic medium and stellar systems

2.3.1. Modelling the evolution of ${}^{26}{\rm Al}$ abundance in the galactic interstellar matter

Stars process the material out of which they were formed and return both the processed and unprocessed portions of their composition back to the interstellar medium when they die—except for the stellar mass that is buried in a compact remnant star or black hole. The processed and unprocessed material can then again be converted into stars. This procedure creates a cycle where matter is processed by multiple generations of stars. Overall, this gradually increases the fraction of processed gas in relation to unprocessed gas. Newly-formed nuclei are then enriched in the interstellar medium, as cosmic time proceeds. Since the processed matter mostly consists of metals, the metallicity of the simulation volume increases with time. Studies of galactic chemical evolution investigate how the abundances of isotopes in stars and the interstellar medium evolve due to this cycle over the history of a galaxy.

Analytical descriptions of chemical evolution have been presented (Tinsley Reference Tinsley1974; Tinsley & Larson Reference Tinsley and Larson1978; Clayton Reference Clayton1985; Pagel Reference Pagel1997; Matteucci et al. Reference Matteucci, Franco, Francois and Treyer1989; Timmes, Woosley, & Weaver Reference Timmes, Woosley and Weaver1995a; Chiappini, Matteucci, & Gratton Reference Chiappini, Matteucci and Gratton1997; Prantzos Reference Prantzos1999; Chiappini Reference Chiappini2001), implementing assumptions about interstellar and source processes of various types in the descriptions of entire galaxies or different regions, such as the solar neighbourhood. Numerical chemcial-evolution models handle a given simulation volume with given resolution, and assume specific phases of interstellar matter and specific stellar objects (single and multiples) with their lifetimes for stellar and binary evolution. The consumption and re-ejection of matter from star formation and from nucleosynthesis ejecta, respectively, are evaluated as a function of time, to model the compositional changes in interstellar matter. For every time interval, assumptions are made on how interstellar matter is converted into stars, and how nucleosynthesis sources feed back the enriched ejecta. Current, sophisticated numerical models implement complex assumptions for the details of the modelling (e.g. Côté et al. Reference Côté, Lugaro, Reifarth, Pignatari, Világos, Yagüe and Gibson2019a). An example is considering the evolution of the rate at which stars are formed, either intrinsically via star formation efficiencies which regulate the rate at which gas is converted into stars, or empirically, following known cosmic star formation rates. Other examples include the various galactic inflows and outflows, and delay times varied and adapted to a diversity of source types, from Type Ia supernovae to binary mergers.

While a general growth with cosmic time holds for the overall metallicity, this does not necessarily apply to radioactive isotopes. Consider a simple case: a one dimensional simulation volume converts matter and assumes stellar lifetimes in such a way that this results in constant time interval $\delta$ between stellar deaths of the same type, which eject a constant amount of $y_{\text{prod}}$ of a certain radioactive species. Then, the amount $y_{\text{obs}}$ of that species observed inside the volume ranges from $y_{\text{obs}}=y_{\text{mem}}$ to $y_{\text{obs}}=y_{\text{mem}} \mathrm{e}^{- \delta / \tau}$ , with $\tau$ being the mean radioactive lifetime of the isotope, and $y_{\text{mem}}$ being a memory term with values that range from $y_{\text{mem}} = y_{\text{prod}}$ if $\tau \ll \delta$ to $y_{\text{mem}} = y_{\text{prod}} \times \tau/\delta$ if $\tau \gg \delta$ . If the memory term is large enough, a steady-state behaviour emerges, even in the case of a stochastic distribution for the $\delta$ values (Tsujimoto, Yokoyama, & Bekki Reference Tsujimoto, Yokoyama and Bekki2017; Côté, Yagüe, Világos & Lugaro Reference Côté, Yagüe, Világos and Lugaro2019b).

Therefore, the abundance evolution of $^{26}\mathrm{Al}$ cannot be easily traced using 1D Galactic chemical-evolution models that impose instantaneous mixing (therefore recycling) of the interstellar matter, since this homogeneization approximation becomes less accurate the shorter the radioactive lifetime. In fact, if $\tau < \delta$ , temporal heterogeneities become the dominant effect to determine the distribution of the abundance of ${}^{26}{\rm Al}$ in the interstellar medium, and spatial heterogeneities contribute also because a fraction of the radioactive nuclei decays as it travels interstellar distances. The effect of these hetereogeneities has been explored both at the scale of the Galaxy (Fujimoto, Krumholz, & Tachibana Reference Fujimoto, Krumholz and Tachibana2018) and of Giant Molecular Clouds (Vasileiadis, Nordlund, & Bizzarro Reference Vasileiadis, Nordlund and Bizzarro2013).

Even when considering integrated, global effects, to compare to ${}^{26}{\rm Al}$ data from steady diffuse $\gamma$ -ray emission from the bulk of ejecta, the 1D homogeneization approximation is inherently insufficient. For modelling any observed emission, assumptions about the formation of its morphologies have to be made. This has been modelled using different approaches, for example by Pleintinger et al. (Reference Pleintinger, Siegert, Diehl, Fujimoto, Greiner, Krause and Krumholz2019), Pleintinger (Reference Pleintinger2020), and Fujimoto et al. (Reference Fujimoto, Krumholz and Inutsuka2020a). The specific case of star forming regions with their bubbles and superbubbles needs another more dedicated approach, as detailed below.

2.3.2. $^{26}\mathrm{Al}$ and the role of superbubbles

Short-lived massive stars shape their environment in star-forming regions via the mechanical and radiation energy they eject during their life, from main sequence and Wolf-Rayet winds to their core-collapse supernova. This displaces the ambient interstellar medium and creates a low-density region around the star, a bubble. If several bubbles overlap, which is rather the norm, as massive stars usually form in groups, a superbubble forms. At the time of the supernova explosion, the ejecta typically move into a superbubble with a diameter of the order of 100 pc (e.g., Krause et al. Reference Krause, Fierlinger, Diehl, Burkert, Voss and Ziegler2013) As outlined in Section 2.2, $^{26}\mathrm{Al}$ is ejected from massive stars, and therefore, represents a tracer of their mass ejections.

Ejecta leave the sources in the form of hot, fast gas. Cooling quickly as they expand, dust may form and condense some significant fraction of $^{26}\mathrm{Al}$ . Sluder et al. (Reference Sluder, Milosavljević and Montgomery2018) predict a dust mass of ${\approx}0.5\ {{\rm M}_{\odot}}$ for the core-collapse supernova SN1987A before the reverse shock would have passed through the ejecta. This is compatible with dust mass estimates from infrared-emission measurements with Herschel (Matsuura et al. Reference Matsuura2011) and Alma (Cigan et al. Reference Cigan2019). Dust components of various temperatures are present, but the main component is at ${\approx}20$ K (Matsuura et al. Reference Matsuura2019). Much of this dust is, however, believed to be destroyed again later, by sputtering, once the reverse shock has fully traversed through and thermalised the ejecta. This happens on a timescale of ${\approx}10^3$ yr, and even earlier in higher density environments (Nath, Laskar, & Shull Reference Nath, Laskar and Shull2008). In agreement with this expectation, observations of core-collapse supernova remnants show dust only in young supernova remnants and not in older ones, and central dust only for remnants with ages ${\lesssim}10^3$ yr (Chawner et al. Reference Chawner2020), although some dust must survive, since we find stardust from core-collapse supernovae inside meteorites (Section 2.4.4). Massive-star winds develop a similar reverse shock, which, however, now travels outwards in the observer’s frame (Weaver et al. Reference Weaver, McCray, Castor, Shapiro and Moore1977). At late times, and in a realistic environments, shock heating of the ejecta can take place at distances ${\gtrsim}10\ \mathrm{pc}$ from the ejecting star (Krause et al. Reference Krause, Fierlinger, Diehl, Burkert, Voss and Ziegler2013).

Massive stars are usually formed in OB associations or clusters together with other stars (e.g., Zinnecker & Yorke Reference Zinnecker and Yorke2007). For the path of $^{26}\mathrm{Al}$ through the interstellar medium, we need to consider two distinct phases of star cluster evolution: the ‘embedded’ and the ‘exposed’ phases (see Krause et al. Reference Krause2020, for a recent review). In the embedded phase, the winds and eventual explosions occur in a dense, filamentary gas, so that mixing is strong, and much of the $^{26}\mathrm{Al}$ may diffuse into cold, star-forming gas. $^{26}\mathrm{Al}$ transport simulated by Vasileiadis et al. (Reference Vasileiadis, Nordlund and Bizzarro2013) finds for model times applicable to embedded star-forming regions isotopic ratios of $10^{-6} <\, ^{26}\mathrm{Al}/^{27}\mathrm{Al}\, < 10^{-4}$ . This is compatible with meteoritic results for the early Solar System, where ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ${\simeq}5 \times 10^{-5}$ (see Section 2.4.3).

However we caution that the study of Vasileiadis et al. (Reference Vasileiadis, Nordlund and Bizzarro2013) used periodic boundary conditions, which prevents a clearing of the dense gas on a larger scale, that would otherwise happen via formation of a superbubble. Therefore, the results of Vasileiadis et al. (Reference Vasileiadis, Nordlund and Bizzarro2013) may not apply beyond the embedded phase. The embedded phase lasts for at most a few Myr, in clouds where massive stars are formed (e.g., Krause et al. Reference Krause2020). The feedback processes as a whole in processing gas of a giant molecular cloud typically encompass several tens of Myr. For most of the time that a massive star group ejects ${}^{26}{\rm Al}$ , the group is exposed, rather than embedded. This means, a superbubble has formed and the dense gas has mostly been dislocated into the supershell of compressed material forming the outer edge of the superbubble.

In Figure 15 we show a 3D simulation of the evolution of a superbubble (see also Krause et al. Reference Krause2018), based on parameters for the nearby Sco-Cen massive-star region that are estimated from a variety of astronomical data. After ejection, $^{26}\mathrm{Al}$ spreads quickly throughout the superbubble. Wind and shock velocities are of the order of 1 000 km s−1. The ejecta therefore traverse the entire superbubble, which can have a diameter of typically $\approx$ 100–1 000 pc (Krause et al. Reference Krause2015), in less than about 1 Myr which is the $^{26}\mathrm{Al}$ decay time. The simulation also shows local $^{26}\mathrm{Al}$ -density variations within the superbubble of the order of a factor ten, due to gas which may be sloshing back and forth within the superbubble (Krause & Diehl Reference Krause and Diehl2014), and due to supernova explosions (snapshot at 14.9 Myr in Figure 15, pink, shell-like feature).

Figure 15. The Sco-Cen superbubble from different astronomical constraints: This Hi image is taken in the 21 cm hyperfine-structure line from atomic hydrogen, integrated over the velocity range –20…0 km s−1 of HI generally approaching the observer. It shows the Scorpius-Centaurus supershell extending above and below the Galactic disk in the background. Yellow boxes show upper limits to the distances of the respective HI features, from Nai absorption against background stars. An orange circle represents the region of significant $^{26}\mathrm{Al}$ $\gamma$ -ray emission as observed. Adapted from Krause et al. (Reference Krause2018).

The diffusion of ejecta from bubbles and superbubbles into dense star-forming gas and the incorporation into newly formed stellar systems has been modelled on the Galactic scale by Fujimoto et al. (Reference Fujimoto, Krumholz and Tachibana2018). They find 56% of $^{26}\mathrm{Al}$ diffusing into molecular gas, and the isotopic ratio $^{26}\mathrm{Al}/^{27}\mathrm{Al}$ predicted for newly formed stellar systems falls between $10^{-5}$ and $10^{-4}$ . This would make the Sun a rather typical star regarding its $^{26}\mathrm{Al}$ abundance, whereas the predicted $^{60}\mathrm{Fe}$ is orders of magnitude higher than observed in the early solar system (this also is found in the study of Vasileiadis et al. Reference Vasileiadis, Nordlund and Bizzarro2013, and other studies that are based on typical core-collapse supernova yields). It should be noted that in the study of Fujimoto et al. (Reference Fujimoto, Krumholz and Tachibana2018) they apply scaling factorsFootnote f to massive-star yields, and they also adopt for simplicity a zero delay time for the collapse of the presolar cloud, while delay may have a considerable effect due to interstellar mixing.

Gamma-ray observations of the $^{26}\mathrm{Al}$ decay in its 1 809 keV line (see Section 2.4.5) support this picture of emission and transport of $^{26}\mathrm{Al}$ via bubbles and superbubbles in three ways: first, $^{26}\mathrm{Al}$ has been directly detected (with a significance of $6\sigma$ ) towards the Scorpius-Centaurus superbubble (Krause et al. Reference Krause2018). Figure 15 illustrates this: the HI image from the GASS HI survey (velocity channels from $-20$ to 0 $\mathrm{km\ s}^{-1}$ have been summed) shows the nearby Scorpius-Centaurus supershell walls above and below the bright HI ridge of the Galactic disk in the background; the nearby distance of the cavity is confirmed by upper limits that have been estimated by association of the Hi features in position and velocity with Nai absorption against background stars with distances known from Hipparcos or Gaia paralaxes, and these upper limits in pc are given in yellow boxes in the figure; the $\gamma$ -ray emission from $^{26}\mathrm{Al}$ is overlaid as an orange circle. Second, bulk Doppler shifts of the Galactic $^{26}\mathrm{Al}$ emission are observed to be different from cold-gas velocities by about 200 $\mathrm{km\ s}^{-1}$ (Kretschmer et al. Reference Kretschmer, Diehl, Krause, Burkert, Fierlinger, Gerhard, Greiner and Wang2013); this would be consistent with expectations for an outflow from the spiral arms into large inter-arm superbubbles (Krause et al. Reference Krause2015). Third, the Galactic $^{26}\mathrm{Al}$ scale height is larger than for the dense gas components, again suggesting an association with hot, tenuous superbubble gas (Pleintinger et al. Reference Pleintinger, Siegert, Diehl, Fujimoto, Greiner, Krause and Krumholz2019). The dynamics of hot gas sloshing-around within the bubble produces spatial variations in X-ray luminosity and spectra, as observed, e.g., in the Orion-Eridanus superbubble (Krause et al. Reference Krause, Diehl, Böhringer, Freyberg and Lubos2014).

A large part of $^{26}\mathrm{Al}$ may leave the Galactic disc and may trace metal loss into the halo. The omnidirectional growth of superbubbles changes as bubbles reach the disk-halo interface above the Galactic disk, roughly at a scale height of gas of order 50–100 pc (e.g., Baumgartner & Breitschwerdt Reference Baumgartner and Breitschwerdt2013), which is a small extent for superbubbles. When superbubbles reach this diameter, the shells are accelerated into the Galactic halo. Instabilities then destroy the shells, and the $^{26}\mathrm{Al}$ -enriched hot gas can stream at high velocity into the halo. Due to large differences in gas densities between spiral arms and interarm regions, details of the diffusion of $^{26}\mathrm{Al}$ into the halo depend on the properties of the spiral arms (Fujimoto et al. Reference Fujimoto, Krumholz and Inutsuka2020a): If the self-gravity of the disc stars is the dominant force of the system, one formes so called material arms, where the gas assembles at the centre of the spiral arm. Stars then form in the centres of the spiral arms and are surrounded by dense gas. This impedes the expansion of superbubbles and would hence lead to little diffusion of $^{26}\mathrm{Al}$ out of the Galactic disc. For density-wave-type arms, which could arise from gravitational interaction of the disc with the bar, or interaction with infalling galaxies such as the Sagittarius dwarf galaxy, one expects the massive stars to be offset from dense gas in the spiral arms. Superbubbles can then expand comparatively easily beyond the scale height of the disc with a significant loss of $^{26}\mathrm{Al}$ to the Galactic halo. 3D hydrodynamics simulations with externally-imposed spiral arms (Rodgers-Lee et al. Reference Rodgers-Lee, Krause, Dale and Diehl2019) model the latter situation and show that $^{26}\mathrm{Al}$ extends up to several kpc into the halo. Synthetic maps from this work show diffuse, clumpy structure, similar to what is observed (Figure 17). This component of $^{26}\mathrm{Al}$ may trace a disk outflow through chimneys, that may leak a significant fraction of the Galactic $^{26}\mathrm{Al}$ production into the halo (Krause et al. Reference Krause, Rodgers-Lee, Dale, Diehl and Kobayashi2021).

Figure 16. 3D hydrodynamics simulation of a superbubble. Time increases from top to bottom and is indicated in the individual panels. Left: sightline-averaged gas density. Right: sightline-averaged $^{26}\mathrm{Al}$ density. Adapted from Krause et al. (Reference Krause2018).

Figure 17. Synthetic map for 1.8 MeV emission from radioactive decay of $^{26}\mathrm{Al}$ . The map has been obtained from a whole-disc, 3D hydrodynamic simulation, with superbubbles concentrated towards spiral arms. The resolution is $4^\circ$ , as it is for the observed COMPTEL map. Adapted from Rodgers-Lee et al. (Reference Rodgers-Lee, Krause, Dale and Diehl2019)

2.3.3. The present solar system within the local bubble

The Solar System is currently embedded into an interstellar environment that had been shaped by supernovae and winds from massive stars creating a network of filaments, shells, and superbubbles (e.g., Lallement et al. Reference Lallement2018, Krause & Hardcastle (Reference Krause and Hardcastle2021) for a recent review). Different interstellar environments may have existed during the past several million years, and, certainly, at the time of solar system formation 4.5 Gy ago.

The nearest star-forming regions relevant for shaping the local interstellar environment are the Scorpius-Centaurus groups (distance about 140 pc), the Perseus-Taurus complex with Perseus OB2 (300 pc), the Orion OB1 subgroups (about 400 pc), and the Cygnus complex (with several associations at 700–1 500 pc and the massive OB2 cluster at about 1400 pc) (see Pleintinger Reference Pleintinger2020; Kounkel & Covey Reference Kounkel and Covey2019, for a literature summary). It had been thought that the nearby star forming activity was related to the Gould Belt structure (Pöppel Reference Pöppel, Montmerle and André2001) that had been attributed to a local distortion of the Galaxy by an infalling high-velocity cloud (Olano Reference Olano1982). This interpretation of a causal connection and common origin of all these nearby star groups may have been an overinterpretation, and has been put in doubt recently (Alves et al. Reference Alves2020).

At least for the last 3 Myr and possibly for more than 10 Myr (Fuchs et al. Reference Fuchs, Breitschwerdt, de Avillez and Dettbarn2009), the Solar System has been located inside the Local Superbubble, a cavity with a density of ${\sim}$ 0.005 H atoms cm−3 ( $10^{-26}\mathrm{g}\cdot\mathrm{cm}^{-3}$ ). This cavity extends for ${\sim}$ 60–100 pc around the Sun within the galactic plane, and forms an open structure perpendicular to the plane, a galactic ‘chimney’ (Slavin Reference Slavin2017).

The Solar System as a whole is moving relative to its also-moving dynamic surroundings: a velocity of sometimes exceeding $25\ \mathrm{km}\cdot\mathrm{s}^{-1}$ relative to the local structures within the Local Superbubble is observed. In addition to Earth and the Solar System experiencing such varying-density environments, the Solar System with Earth and Moon may have been exposed also to transient waves of supernova ejecta in its cosmic history. A simple estimate using the average supernova rate of our Galaxy suggests that supernova explosions might occur on average at a rate of every few million years within a distance of $\leq$ 150 pc, which is considered the maximum distance from where supernova ejecta can directly penetrate into the Solar System. Such changing environments may also modulate the flux of interstellar dust and galactic cosmic rays at Earth (Lallement et al. Reference Lallement, Bertaux and Quémerais2014).

Interstellar dust grains can penetrate deep into the Solar System: Space-born satellites such as STARDUST and ACE have been observing dust and particles near Earth with characteristics of origins outside the Solar System. In contrast to interstellar-gas ions, only dust grains with larger diameters above a size of 0.2 $\mu$ m will overcome the ram pressure of the solar wind and not be deflected away by the interplanetary magnetic field. Thus there will be a significant mass filter on these dust grains as they approach Earth orbit.

In this way, some fraction of the $^{26}\mathrm{Al}$ that condensed into dust particles may penetrate deep into the Solar System. By using these larger dust grains as vehicles, interstellar $^{26}\mathrm{Al}$ may accumulate on Earth in archives such as deep-sea sediments and ferromanganese (FeMn) crusts and nodules. These archives grow slowly over time, and thus include interstellar particles collected over time-periods up to millions of years, while also including time information imprinted on the sedimentation from magnetic-field changes, and radio-isotopes produced by cosmic-ray in the atmosphere. Therefore, a search for traces from interstellar material in solar-system deposits was suggested (Ellis, Fields, & Schramm Reference Ellis, Fields and Schramm1996). These nuclides could be present as geological radioisotope anomalies, ‘live’, i.e., before they decay into stable nuclides (Feige et al. Reference Feige, Wallner, Winkler, Merchel, Fifield, Korschinek, Rugel and Breitschwerdt2012; Feige et al. Reference Feige2013). Note that highly-energetic cosmic ray particles also reach the Solar System and Earth, and are detected by satellite-born instruments. But deposits from these cosmic rays in deep-sea layers are many orders of magnitudes less abundant (Korschinek & Kutschera Reference Korschinek and Kutschera2015).

In summary, the direct detection of live radionuclides such as $^{26}\mathrm{Al}$ on Earth is an important tool in the studies of nucleosynthesis in massive stars, and of interstellar medium dust formation and its transport through interstellar space and into the Solar System (Fields et al. Reference Fields2019). Such a detection also holds information on the local interstellar environment and its history, i.e. within a distance of order ${\sim}$ 150 pc, and for a time window of order of a few life-times of the radionuclide (e.g., a few Myr for $^{26}\mathrm{Al}$ ); this must be taken into account when interpreting signals from such deposits.

2.4. Measurements of cosmic ${}^{\textbf{26}}\textbf{Al}$

Measuring cosmic radioactive isotopes is (and has always been) inherently ‘multi-messenger astronomy’. In fact, cosmic radioactive isotopes may be measured either in the laboratory in the form of solid materials, or astronomically via remote sensing. For each of these types of measurement the available approaches are more or less direct. First, we begin our description with the materials that can be analysed in laboratories. These are either samples of terrestrial materials found in sediments, ocean crusts, and meteorites, or samples acquired through space technology from the Moon, comets, cosmic dust, as well as cosmic-ray particles. Such materials experienced a journey from their cosmic production site to where we can recover it and biases due to its transport and deposition need to be considered. Only indirect conclusions can be drawn as radioactive isotopes may have decayed already, and the mix of parent/daughter products may have a complex composition and re-processing history, such as for example in the case of early Solar System materials. Second, we describe the astronomical methods. Direct isotope information is obtained from characteristic $\gamma$ -ray lines that accompany radioactive decay. Less direct, still valuable astronomical measurements are possible from atomic and molecular lines, where the isotopic information must be decoded from auxilliary information.

2.4.1. Interstellar dust collected on earth

The radioactive lifetime of ${\sim}$ 1 Myr defines the detectability of the presence of $^{26}\mathrm{Al}$ in the interstellar medium before it decays. If condensed into interstellar dust, a fraction of it may enter the Solar System, and may eventually become incorporated into terrestrial archives. Ice cores, deep-sea sediments and deep-sea FeMn crust material grow over time-periods of hundreds of thousand years to tens of million years, and thus provide a proper data archive with time resolved material samples. In particular, deep-sea sediments with growth rates of less than cm kyr−1 and FeMn crusts with very low growth rates of only mm Myr−1 provide time-resolved information over time scales of million years; such archives cover a full time period during which most of $^{26}\mathrm{Al}$ would have decayed.

An enhanced concentration of $^{26}\mathrm{Al}$ in such archives may thus be a signature of an enhanced interstellar influx of $^{26}\mathrm{Al}$ . However, $^{26}\mathrm{Al}$ is also naturally produced near Earth in the terrestrial atmosphere through cosmic-ray induced nuclear reactions. Minor additional $^{26}\mathrm{Al}$ contributions in these archives are in-situ production within the archives. Influx of interplanetary dust grains, which also contain spurious amounts of cosmic-ray produced spallogenic $^{26}\mathrm{Al}$ , provide a minor background to a search of $^{26}\mathrm{Al}$ of stellar nucleosynthesis origin. Any interstellar $^{26}\mathrm{Al}$ influx must therefore be detected on top of this naturally existing and approximately constant Solar System $^{26}\mathrm{Al}$ production. Simple estimates suggest that a reasonable interstellar influx could be of order a few percent and up to 10% relative to the terrestrial production (Feige et al. Reference Feige2013; Feige et al. Reference Feige2018). For example, using measured $^{60}\mathrm{Fe}$ data as a proxy for $^{26}\mathrm{Al}$ influx from the interstellar gas (see Section 3.4), deposition rates into terrestrial archives of only between a few to some 50 $^{26}\mathrm{Al}$ atoms per cm $^2$ and per yr are estimated (Feige et al. Reference Feige2018), corresponding to $^{26}\mathrm{Al}$ concentrations of some 1 000 atoms per gram in deep-sea sediment. Consequently, detection of $^{26}\mathrm{Al}$ from interstellar gas requires an extremely sensitive and efficient detection technique in order to identify a signal above the terrestrial background.

So far, only accelerator mass spectrometry has the required sensitivity for such studies. In this approach, one directly counts the radionuclide of interest one by one by means of a particle detector. The sample material needs to be pre-processed, i.e., dissolved so that the radionuclide of interest will be chemically separated from the bulk material. An accelerated ion beam of the Al separated in this way from the sample includes $^{26}\mathrm{Al}$ together with stable terrestrial $^{27}\mathrm{Al}$ (typically 12–16 orders of magnitude higher in abundance). In this ion beam, the $^{26}\mathrm{Al}$ ions will be filtered out with electrostatic and magnetic deflectors removing unwanted background, and eventually the $^{26}\mathrm{Al}$ nuclei can be identified essentially background-free with an energy-sensitive particle detector. Detection efficiencies for $^{26}\mathrm{Al}$ are typically of order one atom out of 10 000.

Recently, Feige et al. (Reference Feige2018) searched for presence of interstellar $^{26}\mathrm{Al}$ in an extensive set of deep-sea sediment samples that covered a time-period between 1.7 and 3.2 Myr (Figure 18). No significant $^{26}\mathrm{Al}$ above the terrestrial signal was found. The data show an exponential decline of $^{26}\mathrm{Al}$ with the age of the samples that can be explained by radioactive decay of terrigenic $^{26}\mathrm{Al}$ . Nevertheless, owing to the large number of samples analyzed, these data allowed to deduce an upper limit for the influx of interstellar $^{26}\mathrm{Al}$ (see Section 4.3). A much more favourable situation exists for measuring the radioisotope $^{60}\mathrm{Fe}$ from interstellar deposits in Earth, because terrestrial production is negligible for this isotope (see Section 3.4).

Figure 18. The $^{26}\mathrm{Al}$ search in terrestrial archives did not reveal a signal. The top graph shows $^{26}\mathrm{Al}$ counts versus age of the layer within the sample, with the grey band illustrating what would be expected from extrapolating the surface $^{26}\mathrm{Al}$ abundance due to radioactive decay. The lower-left graph shows the $^{60}\mathrm{Fe}$ signal discussed in Sections 3.4, and the lower-right graph indicates how a ratio of 0.02 for $^{60}\mathrm{Fe}/^{26}\mathrm{Al}$ would translate into an $^{26}\mathrm{Al}$ signal versus the actual data, as a decay-corrected version of the upper graph. (From Feige et al. Reference Feige2018).

2.4.2. Cosmic rays near Earth

Along with dust grains, ‘galactic cosmic rays’ provide a sample of matter from outside the Solar system. Despite almost a century of active research, the physics of cosmic rays (concerning their sources, acceleration and propagation in the Galaxy) is not yet thoroughly understood. In particular, key questions herein are related to the timescales of various processes, such as acceleration in one event or in a series of events, and their confinement in the Galaxy. Radionuclides unstable to $\beta^{\pm}$ decay or e-capture, and with laboratory lifetimes close to the ${\sim}$ Myr timescales of interest for galactic cosmic rays, provide important probes of the aforementioned processes (Mewaldt et al. Reference Mewaldt2001).

Despite more than a century of intense observational and theoretical investigation, the origin of cosmic rays is still unclear. Several steps are involved between the production of the Galactic cosmic-ray nuclides in stellar interiors and their detection near Earth:

  1. 1. stellar nucleosynthesis,

  2. 2. ejection by stellar winds and explosions,

  3. 3. elemental fractionation,

  4. 4. acceleration of these ‘primary’ nuclides, by shocks due to supernovae and winds of massive stars,

  5. 5. propagation through the interstellar medium of the Galaxy, where those nuclides are fragmented (‘spallated’ by collisions with the ambient gas), giving rise to ‘secondary’ nuclei;

  6. 6. modulation at the heliospheric boundary, and

  7. 7. detection of cosmic rays near Earth.

In particular, cosmic-ray transport through interstellar space within the Galaxy has been studied with models of varying sophistication, which account for a large number of astrophysical observables (see the comprehensive review of Strong, Moskalenko, & Ptuskin Reference Strong, Moskalenko and Ptuskin2007, and references therein). To describe the composition data, less sophisticated models are sufficient, like e.g. the ‘leaky-box’ model, where cosmic rays are assumed to fill homogeneously a cylindrical box - the Galactic disk - and their intensity in the interstellar medium is assumed to be in a steady state equilibrium between several production and destruction processes. The former involve acceleration in cosmic-ray sources and production ‘in-flight’ trough fragmentation of heavier nuclides, while the latter include either physical losses from the ‘leaky box’ (escape from the Galaxy) or losses in energy space (ionization) and in particle space (fragmentation, radioactive decay or pion production in the case of proton-proton collisions). Most of the physical parameters describing these processes are well known, although some spallation cross sections still suffer from considerable uncertainties.

The many intricacies of cosmic-ray transport are encoded in a simple parameter, the ‘escape length’ $\Lambda_{\rm esc}$ (in g cm−2): it represents the average column density traversed by nuclei of Galactic cosmic rays before escaping the Galactic leaky box. The abundance ratio of a secondary to a primary nuclide depends essentially on the escape parameter $\Lambda_{\rm esc}$ . Observations of LiBeB/CNO and ScTiV/Fe in arriving Galactic cosmic rays, interpreted in this framework, suggest a mean escape length $\Lambda_{\rm esc} {\sim}$ 7 g cm−2. In fact, the observed secondary/primary ratios display some energy dependence, which translates into an energy dependent $\Lambda_{\rm esc}(E)$ , going through a maximum at $E\sim$ 1 GeV nucleon-1 and decreasing both at higher and lower energies. The observed energy dependence of $\Lambda_{\rm esc}(E)$ can be interpreted in the framework of more sophisticated transport models and provides valuable insight into the physics of transport (role of turbulent diffusion, convection by a Galactic wind, re-acceleration, etc.); those same models can be used to infer the injection spectra of cosmic rays at the source (see Strong et al. Reference Strong, Moskalenko and Ptuskin2007). Once the key parameters of the leaky-box model are adjusted to reproduce the key secondary/primary ratios, the same formalism may be used in order to evaluate the secondary fractions (produced by fragmentation in-flight) of all Galactic cosmic-ray nuclides. Those fractions depend critically on the relevant spallation cross sections, which are well known in most cases. Fractions close to 1 imply an almost purely secondary nature while fractions close to 0 characterize primary nuclides (like, e.g. 12C, 16O, 24Mg, $^{56}\mathrm{Fe}$ etc.). Contrary to the latter, the former are very sensitive to the adopted $\Lambda_{\rm esc}$ (Wiedenbeck et al. Reference Wiedenbeck2007).

$^{26}\mathrm{Al}$ has been measured with the CRIS instrument on the ACE satellite (Yanasak et al. Reference Yanasak2001) (Figure 19). This $^{26}\mathrm{Al}$ is plausibly ‘secondary’, i.e., it has been produced from heavier cosmic-ray nuclei through spallation reactions. Therefore, it is not of stellar origin, and cosmic-ray $^{26}\mathrm{Al}$ measurements are not diagnostic towards $^{26}\mathrm{Al}$ sources beyond such interstellar spallation. This is different for $^{60}\mathrm{Fe}$ , as discussed in Section 3.4.

Figure 19. Measurements of $^{26}\mathrm{Al}$ with the CRIS instrument on the ACE satellite, in different energy ranges of the observed cosmic ray particles (adapted from Yanasak et al. Reference Yanasak2001). The y axis shows CRIS counts, the x axis the calculated mass in AMU units. Note that this $^{26}\mathrm{Al}$ is most probably the result of interstellar spallations from heavier cosmic-ray nuclei, hence ‘secondary’, and not of stellar nucleosynthesis, while contributing to observed abundances.

2.4.3. Early solar system materials

One of the most interesting events in the Universe in relation to measuring the ${}^{26}{\rm Al}$ isotope is the birth of our own Solar System. It was predicted in the 1950s that $^{26}\mathrm{Al}$ should have been part of the newborn Solar System as a heating source (Urey Reference Urey1955), and in 1970s, Lee et al. (Reference Lee, Papanastassiou and Wasserburg1977) discovered that a relatively large abundance of ${}^{26}{\rm Al}$ was in fact present when the Sun formed. Since such primordial ${}^{26}{\rm Al}$ is now decayed, its original abundance 4.6 Gyr ago can only be inferred indirectly, from excesses in its daughter isotope ${}^{26}{\rm Mg}$ , and particularly from the correlation of such excess in the form of ${}^{26}{\rm Mg}$ / ${}^{24}{\rm Mg}$ versus Al/Mg ratios of the analysed samples. The ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratio present at the time of the formation of a given sample can be derived through the slope of the linear isochrone that can be constructed by connecting data points obtained from inclusions of different chemical composition (i.e., different Al/Mg) with their varying ${}^{26}{\rm Mg}$ excess (see Figure 20).

Calcium-aluminium-rich inclusions (CAIs) are believed to be the oldest solids to have formed in the early Solar System that have been recovered so far from meteorites. The ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratio derived from such CAIs is $(5.23 \pm 0.13) \times 10^{-5}$ (Jacobsen et al. 2008). This is more than one order of magnitude higher than the ratio expected to be present in the interstellar medium at the time of the formation of the Sun (see, e.g., Huss et al. Reference Huss, Meyer, Srinivasan, Goswami and Sahijpal2009; Côté et al. Reference Côté, Lugaro, Reifarth, Pignatari, Világos, Yagüe and Gibson2019a, and Figure 25). An explanation for this requires investigation of the temporal and spatial heterogeneity of the interstellar medium (see Section 2.3.3) and/or invoking extra local stellar sources of ${}^{26}{\rm Al}$ beyond those that contribute this isotope to the galactic interstellar medium. Such extra sources should have contributed close in time and space to the formation of the Sun.

Figure 20. Radiogenic ${}^{26}{\rm Mg}$ excess ( $\delta$ ${}^{26}{\rm Mg}$ , represented as deviations in parts per 1 000 from a terrestrial standard) versus the ${}^{27}{\rm Al}$ / ${}^{24}{\rm Mg}$ ratio in CAIs from the Allende CV3 carbonaceous chondrite. Red squares are from Jacobsen et al. (2008) and the blue diamonds from Bizzarro et al. (Reference Bizzarro, Baker and Haack2004). The lines represent the isochrones derived from fitting the data points. The slope of the lines represent the initial ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratio at the time of the formation of the CAIs, and the intercept at ${}^{27}{\rm Al}$ / ${}^{24}{\rm Mg}$ , the initial ${}^{26}{\rm Mg}$ / ${}^{24}{\rm Mg}$ ratio. (From Jacobsen et al. 2008, by permission).

2.4.4. Stardust in meteorites

Stardust grains found in meteorites formed around stars and supernovae carry the undiluted signature of the nucleosynthesis occurring in or near these cosmic sites via their isotopic abundances, as measured in the laboratory (Lugaro Reference Lugaro2005; Zinner Reference Zinner and Davis2014). Many types of stardust grains have been recovered so far, both carbon and oxygen rich. Both these classes include types of minerals that are rich in Al, in particular silicon carbide (SiC) and graphite in the case of C-rich grains, and corundum $\mathrm{Al}_2\mathrm{O}_3$ in the case of O-rich grains. These grains are also poor in Mg, which allow us to identify the measured abundance of ${}^{26}{\rm Mg}$ as the initial abundance of ${}^{26}{\rm Al}$ at the time of their formation in stellar outflows. In this simple, traditional approach the derivation of the initial ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ for stardust grains is not based on an isochrone, as for Solar System materials (Sec. 2.4.3), but on abundance of ${}^{26}{\rm Mg}$ . This is approximately correct because Mg is not a main component of neither SiC, graphite, corundum ( $\mathrm{Al}_3\mathrm{O}_2$ ), nor hibonite ( $\mathrm{CaAl}_{12}\mathrm{O}_{19}$ ) grains. Mg is, however, a main component of spinel ( $\mathrm{MgAl}_2\mathrm{O}_4$ ). Therefore, for this type of stardust grains the initial abundance of ${}^{26}{\rm Al}$ needs to be disentangled from the initial abundance of ${}^{26}{\rm Mg}$ . Stochiometric spinel contains two atoms of Al per each atom of Mg, which corresponds roughly to 25 times higher than in the average Solar System material. In single stardust spinel grains, however, this proportion may vary and such variation needs to be taken into account when attempting to derive the initial ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratio. A more recent study by Groopman et al. (Reference Groopman2015), applyed the isochrone method also to stardust grains and demonstrated that the ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ abundance ratios for stardust derived from such analysis result in more accurate measurements, and generally higher ratios than previously estimated (see Figure 21).

Figure 21. Ranges of ${}^{12}{\rm C}$ / ${}^{13}$ and ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratios in presolar low-density graphite (LD) and $\mathrm{Si}_{3}\mathrm{N}_{4}$ grains from supernovae, and SiC grains of different populations: M (mainstream) grains from AGB stars, X grains from supernovae, and AB grains of unclear origin. (From Groopman et al. Reference Groopman2015, by permission).

Overall, the C-rich grains believed to originate from core-collapse supernovae show very high abundances of ${}^{26}{\rm Al}$ , with inferred ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratios in the range 0.1–1 (see Figure 20, grey and light and blue symbols), higher than theoretical predictions. They apparently require some extra production mechanism for ${}^{26}{\rm Al}$ at work in core-collapse supernovae beyond those described in Section 2.2.2; possibly, this is related to ingestion of H into the He-burning shell and subsequent explosive nucleosynthesis (Pignatari et al. Reference Pignatari2013). The grains that originated in AGB stars show somewhat lower ${}^{26}{\rm Al}$ abundances (see Figure 20), green symbols), with ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ in the range $10^{-3}$ $10^{-2}$ . These numbers can also be used for comparison and constraints to the nucleosynthesis models and the nuclear reactions involved in the production of ${}^{26}{\rm Al}$ in AGB stars of low mass, which become C-rich and are the origin of most of the SiC grains (van Raai et al. Reference van Raai, Lugaro, Karakas and Iliadis2008). The AGB stardust most rich in ${}^{26}{\rm Al}$ is represented by O-rich grains belonging to the specific Group II. These grains show strong depletion in ${}^{18}{\rm O}$ / ${}^{16}{\rm O}$ and have relatively high ${}^{26}{\rm Al}$ / ${}^{27}{\rm Al}$ ratios (up to 0.1). These features are both a product of efficient H burning, attributed to some kind of extra mixing in low-mass AGB stars (Palmerini et al. Reference Palmerini, La Cognata, Cristallo and Busso2011), and recently also connected to hot-bottom burning in massive AGB stars (see Section 2.2.1 and Lugaro et al. Reference Lugaro2017).

Figure 22. The $^{26}\mathrm{Al}$ sky as imaged with data from the COMPTEL telescope on NASA’s Compton Gamma-Ray Observatory. This image (Plüschke et al. Reference Plüschke2001) was obtained from measurements taken 1991–2000, and using a maximum-entropy regularization together with likelihood to iteratively fit a best image to the measured photons.

2.4.5. Gamma rays from interstellar $^{26}\mathrm{Al}$

The direct observation of $^{26}\mathrm{Al}$ decay in interstellar space through its characteristic gamma rays with energy 1808.65 keV was advertised as an exciting possibility of $\gamma$ -ray astronomy in its early years (Lingenfelter & Ramaty Reference Lingenfelter and Ramaty1978). The HEAO-C satellite then obtained sufficiently-sensitive measurements from galactic $\gamma$ -rays in 1978/1979, which were published in 1982 as a first and convincing detection of $^{26}\mathrm{Al}$ decay in interstellar space and therefore a proof of currently-ongoing nucleosynthesis in our Galaxy (Mahoney et al. Reference Mahoney, Ling, Jacobson and Lingenfelter1982).

The HEAO-C finding was confirmed by balloon-borne observations in the 1980s (e.g. Ballmoos, Diehl, & Schoenfelder Reference Ballmoos, Diehl and Schoenfelder1986); but the sparse signals and poor sensitivity and spatial resolution could only reveal 1.8 MeV emission from the general direction towards the galactic centre. The observed emission location prompted speculations throughout that decade about the origin of the emission, attributed to various sources: novae (Clayton & Leising Reference Clayton and Leising1987), AGB stars (Bazan et al. Reference Bazan, Brown, Clayton and Truran1993), WR stars (Prantzos & Casse Reference Prantzos and Casse1986) supernovae (Woosley & Pinto Reference Woosley, Pinto, Gehrels and Share1988) and even a supermassive star in the Galactic centre (Hillebrandt, Thielemann, & Langer Reference Hillebrandt, Thielemann and Langer1987). Uncertainties in the yields—and even the frequencies—of all those sources made it difficult to conclude. It was thus suggested that the spatial profile of the gamma-ray emission as function of galactic longitude could reveal the underlying $^{26}\mathrm{Al}$ sources, being more peaked towards the galactic centre in some cases (where an old stellar population, such as novae or low mass AGB stars would dominate) than in others (where a young population, such as massive stars and their core-collapse supernova would dominate). Prantzos (Reference Prantzos, Durouchoux and Prantzos1991) suggested that the smoking gun for the case of massive stars would be the observation of enhanced $\gamma$ -ray emission from the directions tangent to the spiral arms of the Galaxy, where most massive stars form and die.

The exciting prospect to measure radioactive decays from recently-synthesised cosmic nuclei gave a new impetus to observational $\gamma$ -ray astronomy. The NASA Compton Gamma-Ray Observatory was agreed upon as a flagship mission. Even though its high-resolution spectrometer (GRSE) instrument had been abandoned in the late planning phase due to technical and financial problems, the Compton Gamma-Ray Observatory mission from 1991 until 2000 collected valuable data that provided the first all-sky survey in $\gamma$ -rays, including lines from cosmic radioactivity. The Imaging Compton Telescope (COMPTEL, one of four instruments aboard this observatory) sky survey provided a sky image in the $^{26}\mathrm{Al}$ $\gamma$ -ray line (see Figure 22), which showed structured $^{26}\mathrm{Al}$ emission, extended along the plane of the Galaxy (Plüschke et al. Reference Plüschke2001; Prantzos & Diehl Reference Prantzos and Diehl1996; Diehl et al. Reference Diehl1995), in broad agreement with earlier expectations of $^{26}\mathrm{Al}$ being produced throughout the Galaxy and mostly from massive stars and their supernovae. We caution here that this argument is based on massive stars showing up in clusters, while AGB stars and novae evolve on longer time scale and thus can move away from their birth sites before ejecting $^{26}\mathrm{Al}$ ; but this may not hold for the higher-mass end of AGB stars (evolving within ${\sim}$ 3 10 $^7$ yr) and high-luminosity novae, so that their $^{26}\mathrm{Al}$ contribution would be degenerate with that of massive stars beyond $8\ \mathrm{M}_{\odot}$ and their core-collapse supernovae.

While the COMPTEL detectors lacked the spectral resolution required for line identification and spectroscopic studies (with ${\sim}200\ \mathrm{keV}$ instrumental resolution, compared to ${\sim}3\ \mathrm{keV}$ for Ge detectors, at the energy of the $^{26}\mathrm{Al}$ line), a 1995 balloon experiment also carrying high-resolution Ge detectors provided an indication that the $^{26}\mathrm{Al}$ line was significantly broadened to 6.4 keV (Naya et al. Reference Naya, Barthelmy, Bartlett, Gehrels, Leventhal, Parsons, Teegarden and Tueller1996). This implied kinematic Doppler broadening of astrophysical origin of 540 km s−1. Considering the $1.04 \times 10^6$ y mean life of $^{26}\mathrm{Al}$ , such a large line width would naively translate into kpc-sized cavities around $^{26}\mathrm{Al}$ sources, or alternatively major fractions of $^{26}\mathrm{Al}$ should be condensed on grains so that they travel ballistically and are not decelerated by cavity shells (Chen et al. Reference Chen, Winkler, Courvoisier and Durouchoux1997; Sturner & Naya Reference Sturner and Naya1999).

The ESA INTEGRAL space observatory with its Ge-detector based spectrometer SPI, launched in 2002, provided a wealth of high-quality spectroscopic data accumulated over its more than 15-year long mission. The sensitivity of current $\gamma$ -ray surveys penetrates to intensities as low as $10^{-5}\ \mathrm{ph\ cm}^{-1}\mathrm{s}^{-1}$ or below, with typical exposure times of at least a month, and correspondingly longer for deeper exposures. This allowed higher precision Galaxy-wide study of $^{26}\mathrm{Al}$ (Diehl et al. Reference Diehl2006), aided by the spectral information from the $^{26}\mathrm{Al}$ line, which now is resolved with a width of ${\sim}$ 3 keV (Figure 23). These deep observations also provide a solid foundation for the detailed test of our understanding of the activity of massive stars within specific and well-constrained massive star groups (see Krause et al. Reference Krause, Rodgers-Lee, Dale, Diehl and Kobayashi2021, for a review of astrophysical issues and lessons), with specific results for the Orion (Voss et al. Reference Voss, Diehl, Vink and Hartmann2010) and Scorpius-Centaurus (Krause et al. Reference Krause2018) stellar groups.

Figure 23. The $^{26}\mathrm{Al}$ line as seen with INTEGRAL high-resolution spectrometer SPI and 13 years of measurements integrated (Siegert Reference Siegert2017).

It is not straightforward to interpret measurements of $\gamma$ -ray line emission. As Figure 22 shows, the inherent blurring of the measurement by the response function of the $\gamma$ -ray telescopes, and their inherently-high background, require sophisticated deconvolution and fitting methods to obtain the astrophysical result. Bayesian methods need to be applied, and simple methods of subtracting background and inverting data with the instrument response matrix are not feasible. Comparisons to predictions can be made in different ways. One may consider the $^{26}\mathrm{Al}$ amount in the Galaxy and compare measurements with theoretical predictions; this has been done up to the early 2000s (see Diehl et al. Reference Diehl2006, and discussions therein). For example, the total mass of $^{26}\mathrm{Al}$ within the Galaxy can be estimated from observations, and compared to theoretical estimates. Observational estimates are based on the measured flux of $\gamma$ -ray photons, but the $^{26}\mathrm{Al}$ mass depends on the assumed distance to the $^{26}\mathrm{Al}$ that produced those photons upon decay (see Pleintinger et al. Reference Pleintinger, Siegert, Diehl, Fujimoto, Greiner, Krause and Krumholz2019, for a discussion of such bias). We believe now that observations constrain this to fall between 1.7 and $3.5\ {{\rm M}_{\odot}}$ , with a best current estimate of $2\ {{\rm M}_{\odot}}$ (Pleintinger Reference Pleintinger2020). Similarly, theoretical estimates based on predicted, theoretical $^{26}\mathrm{Al}$ yield for a given type of nucleosynthetic source also depend on extrapolation to the galactic mass, i.e., on how many sources of such type have contributed to the current $^{26}\mathrm{Al}$ mass in the galactic interstellar medium. For example, Wolf-Rayet winds have been estimated to contribute ( $0.9\pm 0.5)\ {{\rm M}_{\odot}}$ of $^{26}\mathrm{Al}$ per Myr (Meynet et al. Reference Meynet, Arnould, Prantzos and Paulus1997), the number later updated to 0.6– $1.4\ {{\rm M}_{\odot}}$ per Myr (Palacios et al. Reference Palacios, Meynet, Vuissoz, Knödlseder, Schaerer, Cerviño and Mowlavi2005). For massive stars altogether (winds plus supernova), Limongi & Chieffi (Reference Limongi and Chieffi2006b) provided a thorough discussion of uncertainties, and give a best estimate of $2.0\ {{\rm M}_{\odot}}$ of $^{26}\mathrm{Al}$ for the Galaxy as a whole.Footnote g

We may use the $\gamma$ -ray measurement to represent the $^{26}\mathrm{Al}$ content in the current Galaxy, and translate this into an isotopic ratio for $^{26}\mathrm{Al}/^{27}\mathrm{Al}$ , which has been discussed above for stardust grains and for the early Solar System. If we assume a total interstellar gas mass of $4.95\times10^9\ {{\rm M}_{\odot}}$ (Robin et al. Reference Robin, Reylé, Derrière and Picaud2003) and an abundance of $^{27}\mathrm{Al}$ taken from solar abundances of 6.4 (Lodders Reference Lodders2010), and obtain a value of 6 $\times$ 10−6 for $^{26}\mathrm{Al}/^{27}\mathrm{Al}$ . If the interstellar medium abundance of $^{27}\mathrm{Al}$ scales linearly with time, 4.6 Gy before present, this ratio would have been roughly 3 times higher, but still roughly a factor of two lower than the canonical early Solar System value obtained from CAI inclusions in meteorites of $5 \times 10^{-5}$ (Jacobsen et al. 2008), as shown in Figure 25. It should be noted that this is a conservative upper limit estimate as there is no evidence that metal abundances grew with time in the past 5 Gyr, but rather there is a large spread at each age (see, e.g. Casagrande et al. Reference Casagrande, Schönrich, Asplund, Cassisi, Ramrez, Meléndez, Bensby and Feltzing2011).

Figure 24. The $^{26}\mathrm{Al}$ line as seen towards different directions (in Galactic longitude) with INTEGRAL’s high-resolution spectrometer SPI. This demonstrates kinematic line shifts from the Doppler effect, due to large-scale Galactic rotation (Kretschmer et al. Reference Kretschmer, Diehl, Krause, Burkert, Fierlinger, Gerhard, Greiner and Wang2013).

As theoretical predictions have become more sophisticated in predicting directly the expected observational signatures (Fujimoto et al. Reference Fujimoto, Krumholz and Tachibana2018; Rodgers-Lee et al. Reference Rodgers-Lee, Krause, Dale and Diehl2019), more accurate comparisons can be made. However, biases in both the observations and the theoretical predictions require great care in drawing astrophysical conclusions (Pleintinger et al. Reference Pleintinger, Siegert, Diehl, Fujimoto, Greiner, Krause and Krumholz2019). In particular, theoretical predictions often need to make assumptions about our Galaxy and its morphology. These are particularly critical for the vicinity of the solar position, as nearby sources would appear as bright emission that may dominate the signal (Fujimoto et al. Reference Fujimoto, Krumholz and Inutsuka2020a).

Kinematic constraints could be obtained from the $^{26}\mathrm{Al}$ line width and centroid (Kretschmer et al. Reference Kretschmer, Diehl, Krause, Burkert, Fierlinger, Gerhard, Greiner and Wang2013) and have added an important new aspect to the trace of nucleosynthesis by radioactivities. Kinematics of nucleosynthesis ejecta are reflected in these observables from high resolution spectroscopy through the Doppler effect (Figure 24); velocities down to tens of km s−1 are accessible. Their analysis within multi-messenger studies using the stellar census and information on atomic and molecular lines from radio data, as well as hot plasma from X-ray emission (Voss et al. Reference Voss, Diehl, Hartmann, Cerviño, Vink, Meynet, Limongi and Chieffi2009; Voss et al. Reference Voss, Diehl, Vink and Hartmann2010; Krause et al. Reference Krause, Fierlinger, Diehl, Burkert, Voss and Ziegler2013; Krause et al. Reference Krause, Diehl, Böhringer, Freyberg and Lubos2014), have taught us that the ejection of new nuclei and their feeding into next-generation stars apparently is a much more complex process than the instantaneous recycling approximation assumed in most 1D chemical evolution models (see Section 2.3.1). Thanks to observational constraints such as the $\gamma$ -ray line measurements of $^{26}\mathrm{Al}$ , ejection and transport of new nuclei can now be studied in more detail. These $^{26}\mathrm{Al}$ observations and their analyses have led to an $^{26}\mathrm{Al}$ ‘astronomy’ within studies of stellar feedback and massive-star nucleosynthesis (e.g., Krause et al. Reference Krause, Rodgers-Lee, Dale, Diehl and Kobayashi2021).

Figure 25. The $^{26}\mathrm{Al}/^{27}\mathrm{Al}$ ratio measured from $\gamma$ rays in the current Galaxy, extrapolated to the early Solar System (hatched area), as compared to measurements from the first solids that formed in the Solar System (Sections 2.4.3) and in stardust grains (Sections 2.4.4). (From a presentation by Roland Diehl at the 2013 Gordon conference).

In summary, the lessons learned from the $^{26}\mathrm{Al}$ $\gamma$ -ray observations can be summarised as follows:

  1. $^{26}\mathrm{Al}$ is abundantly present throughout our Galaxy, both in the inner galactic regions as well as through outer spiral arm regions.

  2. The sources of $^{26}\mathrm{Al}$ cluster in specific regions. This is not compatible with $^{26}\mathrm{Al}$ ejections from classical novae, because the few times 10 $^7$ individual sources expected from the galactic nova rate and spatial distribution would make a smooth and centrally-bright appearance of the $^{26}\mathrm{Al}$ $\gamma$ -ray sky. Also intermediate- and low-mass AGB stars are not favoured sources, from the same smoothness reasoning.

  3. The accumulated current mass of $^{26}\mathrm{Al}$ in the Galaxy is estimated between about 1.7 and 3 ${{\rm M}_{\odot}}$ . This estimate depends on the spatial distribution of sources assumed throughout the Galaxy because the source distance determines the $\gamma$ -ray brightness, with a 30% uncertainty arising from this assumption. As discussed by Pleintinger et al. (Reference Pleintinger, Siegert, Diehl, Fujimoto, Greiner, Krause and Krumholz2019), nearby sources are also important in such estimate.

  4. The galactic $^{26}\mathrm{Al}$ mass can be used to estimate the rates of core-collapse supernovae and star formation, when relying on $^{26}\mathrm{Al}$ yields from theoretical models. Diehl et al. (Reference Diehl2006) discussed this in detail. Adopting an origin from massive stars alone, they derived a core-collapse supernova rate of 1.9 $\,{\pm}\,$ 1.1 per century. This is in agreement with other supernova rate estimates, most of which rely on data either from the solar vicinity or from other galaxies assumed to be similar to the Milky Way galaxy. Therefore, despite the large (systematic) uncertainty quoted above, this measurement is significant, because it is based on $^{26}\mathrm{Al}$ $\gamma$ rays as a more penetrating tracer, measured from the entire Galaxy. The systematic errors are related to nuclear astrophysics and specifically the stellar yields, rather than to occultations and their corrections. Accounting for better understandings about nearby source regions and their contributions to the measured $\gamma$ -ray flux, this estimate has been updated to a supernova rate of 1.3 $\,{\pm}\,$ 0.6 events per century (Diehl et al. Reference Diehl2018b). This has been converted to a star formation rate in our Galaxy of 2– $5\ {{\rm M}_{\odot}}\ \mathrm{yr}^{-1}$ (Diehl et al. Reference Diehl2006; Rodgers-Lee et al. Reference Rodgers-Lee, Krause, Dale and Diehl2019), when adopting an initial-mass distribution of stars and a mass limit for core-collapses to occur. Note that the probability of massive-star explosions versus direct collapse, and as function of initial mass, has been much discussed in the recent years (O’Connor & Ott Reference O’Connor and Ott2011, see also Sections 2.2 and 4.2).

  5. Several individual regions within the Galaxy have been identified as sources of $^{26}\mathrm{Al}$ . These are: Cygnus (Knödlseder et al. Reference Knödlseder, Cerviño, Le Duigou, Meynet, Schaerer and von Ballmoos2002; Martin, Knödlseder, & Meynet Reference Martin, Knödlseder and Meynet2008; Martin et al. Reference Martin, Knödlseder, Diehl and Meynet2009), Carina (Voss et al. Reference Voss, Martin, Diehl, Vink, Hartmann and Preibisch2012; Knoedlseder et al. Reference Knoedlseder, Bennett, Bloemen, Diehl, Hermsen, Oberlack, Ryan and Schoenfelder1996), Orion (Voss et al. Reference Voss, Diehl, Vink and Hartmann2010; Diehl et al. Reference Diehl, Kretschmer, Plüschke, Cerviño, Hartmann, van der Hucht, Herrero and Esteban2003), Scorpius-Centaurus (Krause et al. Reference Krause2018; Diehl et al. Reference Diehl2010), and Perseus (Pleintinger Reference Pleintinger2020). Their observations provide more stringent constraints on massive-star models because in these regions the stellar population is known to much better precision, often even allowing for age constraints. Multi-wavelength tests of $^{26}\mathrm{Al}$ origins have been made, using $^{26}\mathrm{Al}$ $\gamma$ rays to understand nucleosynthesis yields, interstellar cavity sizes as seen in HI data for kinetic energy ejections, stellar census seen in optical for the stellar population scaling, and interstellar electron abundance estimated from pulsar dispersion measures characterising the ionization power of the massive star population (see Voss et al. Reference Voss, Diehl, Hartmann, Cerviño, Vink, Meynet, Limongi and Chieffi2009, for more detail on the population synthesis method).

  6. The high apparent velocity seen for bulk motion of decaying $^{26}\mathrm{Al}$ (Kretschmer et al. Reference Kretschmer, Diehl, Krause, Burkert, Fierlinger, Gerhard, Greiner and Wang2013) shows that $^{26}\mathrm{Al}$ velocities remain higher than the velocities within typical interstellar gas for 10 $^6$ years, and have a bias in the direction of Galactic rotation. This has been interpreted as $^{26}\mathrm{Al}$ decay occurring preferentially within large cavities (superbubbles; see Section 2.3.2 and Figure 26), which are elongated away from sources into the direction of large-scale Galactic rotation. Krause et al. (Reference Krause2015) have discussed that wind-blown superbubbles around massive-star groups plausibly extend further in forward directions away from spiral arms (that host the sources), and such superbubbles can extend up to kpc (see also Rodgers-Lee et al. Reference Rodgers-Lee, Krause, Dale and Diehl2019; Krause et al. Reference Krause, Rodgers-Lee, Dale, Diehl and Kobayashi2021).

    Figure 26. The line-of-sight velocity shifts seen in the $^{26}\mathrm{Al}$ line versus Galactic longitude, compared to measurements for molecular gas, and a model assuming $^{26}\mathrm{Al}$ blown into inter-arm cavities at the leading side of spiral arms (Kretschmer et al. Reference Kretschmer, Diehl, Krause, Burkert, Fierlinger, Gerhard, Greiner and Wang2013; Krause et al. Reference Krause2015).

The main open issues in $\gamma$ -ray measurements of $^{26}\mathrm{Al}$ are:

  1. Imaging resolution of measurements is currently inadequate to locate source regions such as massive-star groups to adequate precision. This also constrains the measurements of the latitude extent of $\gamma$ -ray emission from $^{26}\mathrm{Al}$ .

  2. Sensitivities of current instruments are too low to measure $^{26}\mathrm{Al}$ in regions of the galactic halo (and the superbubbles extending there), or in regions where contributions from lower-mass stars and/or novae may dominate $^{26}\mathrm{Al}$ locally, as well as in external nearby galaxies such as the LMC or M31.

  3. Methods to compare measured data to model predictions are indirect. It is desirable to have models predict measured data; rather, currently we are restricted to deconvolve the measured data under some assumptions about the $^{26}\mathrm{Al}$ sources, and define comparisons of models to data in parameters that are subject to systematics from how models were constructed as well as how data have been deconvolved (see Pleintinger Reference Pleintinger2020).

2.4.6. Other electromagnetic radiation

Supernova remnants can be studied through X-ray spectroscopy. The hot plasma with temperatures around 10 $^7$ K produces highly-ionized atoms, such that metals like Si, Mn, Fe have as few electrons as H and He (Vink Reference Vink2012). These measurements have shown enhancements in metals that are signposts of recently-enriched gas in these objects, as expected. It is not as straightforward as in $\gamma$ rays to interpret these data in terms of absolute abundances of new nuclei, however, because the degree of ionisation is difficult to assess in such a dynamic, hot, and tenuous plasma. Nevertheless, metal ratios and unusual enrichments have been determined (Yamaguchi & Koyama Reference Yamaguchi and Koyama2010), which provide a diagnostic of supernova nucleosynthesis. $^{26}\mathrm{Al}$ , however, is inaccessible to X-ray spectroscopy, being a rather light nucleus.

A few years ago, advances in sub-mm spectroscopy have been reported with the first instruments for the ALMA sub-mm observatory, and corresponding advances in laboratory studies to identify lines for molecules including radioactive species. Rotational lines of 26AlF could be measured from a point nova-like source called CK Vul (Kaminski et al. 2018), which represents a breakthrough, as spatial resolution allows to pinpoint a source directly. However, it is also clear that molecule production such as in this case will only occur under very special conditions. While this bias makes it difficult to derive conclusions on $^{26}\mathrm{Al}$ sources generally, learning about special sources will be a very fruitful complement of $^{26}\mathrm{Al}$ observations in $\gamma$ rays, stardust, and cosmic rays, especially for molecule-rich environments such as AGB stars and even proto-planetary discs.

3. The cosmic trajectory of $^{\textbf{60}}\textbf{Fe}$

3.1. Nuclear properties, creation and destruction reactions

3.1.1. Nuclear properties of $^{60}\mathrm{Fe}$

$^{60}\mathrm{Fe}$ is a neutron rich isotope with 8 excess neutrons. The nuclide chart is shown in Figure 27 illustrates the nuclides that may be involved in the production or destruction of $^{60}\mathrm{Fe}$ . $^{60}\mathrm{Fe}$ is unstable with a relatively long half-life of 2.62 Myr. This terrestrial half-life is well determined, with two recent experiments (Wallner et al. Reference Wallner2015b; Ostdiek et al. Reference Ostdiek2017) confirming the half-life of 2.62 Myr presented by Rugel et al. (Reference Rugel2009), and, initially surprising, 75% longer than the previous standard value (Kutschera et al. Reference Kutschera1984). The decay and level scheme is shown in Figure 28. The ground state of ${}^{60}\mathrm{Fe}$ has spin and parity of 0+. Its long lifetime is due to the higher multipole $\beta$ decay transitions to the 2 $^+$ state of ${}^{60}$ Co ( $E_x=58.59\ \mathrm{keV}$ ). This state rapidly decays to the ground state through an internal transition mostly, with a $\gamma$ transition fraction of 2%. ${}^{60}$ Co is an unstable nucleus with a half-life of 5.2714 yr. It decays to ${}^{60}$ Ni dominantly by emitting two characteristic gamma rays with energies of 1.173 and 1.333 MeV, respectively.

Figure 27. The table of isotopes in the neighbourhood of ${}^{60}\mathrm{Fe}$ . (see Figure 2 for legend details on the information per isotope, and original reference).

Figure 28. The decay of ${}^{60}\mathrm{Fe}$ with its level scheme. Red arrows indicate $\beta$ decay, blue lines $\gamma$ transitions, and the black arrow marks an internal transition.

Figure 29. Integrated reaction flow chart for the $^{60}\mathrm{Fe}$ nucleosynthesis in the C/Ne shell burning calculated with the 1-zone code NUCNET. As in Figure 5, the thickness of the arrows correspond to the intensities of the flows; red and black arrows show $\beta$ interactions and nuclear reactions, respectively.

3.1.2. Production and destruction of $^{60}\mathrm{Fe}$

Differently from ${}^{26}{\rm Al}$ , which is made mostly via proton captures, $^{60}\mathrm{Fe}$ is produced by a series neutron captures from the stable iron isotopes (see Figure 27). The reaction flow chart for $^{60}\mathrm{Fe}$ nucleosynthesis in two example environments is shown in Figures 29 and 30. $^{60}\mathrm{Fe}$ is produced through $^{58}\mathrm{Fe}(n,\gamma)^{59}\mathrm{Fe}(n,\gamma)^{60}\mathrm{Fe}$ , and destroyed by $^{60}\mathrm{Fe}(p,n)^{60}$ Co and ${}^{60}\mathrm{Fe}(n,\gamma){}^{61}\mathrm{Fe}$ . The branching point at $^{59}\mathrm{Fe}$ is crucial for the production of $^{60}\mathrm{Fe}$ . The rates of these neutron captures have to be within a suitable range to produce enough $^{59}\mathrm{Fe}$ and $^{60}\mathrm{Fe}$ before $^{59}\mathrm{Fe}$ is destroyed by $\beta$ decay or (p,n) reaction, but does not destroy $^{60}\mathrm{Fe}$ significantly through further neutron captures. Estimates of suitable neutron densities fall in the vicinity of $10^{10-11}$ cm−3. These neutron captures are expected to occur mainly in the He and C shells, and possibly also during explosive burning, within massive stars. At the C/Ne shell burning temperature ( $>$ 1 GK), the $^{59}\mathrm{Fe}(n,\gamma)^{60}\mathrm{Fe}$ competes with $^{59}\mathrm{Fe}$ $\beta$ -decay. During Ne/C explosive burning, the temperature is even higher, about 2 GK. Then the $^{59}\mathrm{Fe}(p,n)^{59}$ Co reaction becomes faster than the ${}^{59}\mathrm{Fe}$ $\beta$ decay, and dominates the destruction of ${}^{59}\mathrm{Fe}$ ; again, it competes with the $^{59}\mathrm{Fe}(n,\gamma)^{60}\mathrm{Fe}$ reaction. Other than in massive stars, $^{60}\mathrm{Fe}$ may also produced during helium burning in AGB stars (Section 3.2).

Figure 30. Same as Figure 29 but for Ne/C explosive burning.

${}^{60}\mathrm{Fe}$ is primarily destroyed by the ${}^{60}\mathrm{Fe}(n,\gamma){}^{61}\mathrm{Fe}$ reaction in hydrostatic shell-burning environments, and also by the ${}^{60}\mathrm{Fe}(p,n){}^{60}$ Co reaction during explosive burning. Besides these destructive reactions, ${}^{60}\mathrm{Fe}$ can also undergo $\beta$ -decay within these production sites, due to an enhanced rate at T $\,{>}\,$ 2 GK, as compared to terrestrial conditions.

3.1.3. Reaction rate uncertainties related to $^{60}\mathrm{Fe}$

The temperature dependency of $\beta$ -decay rate of ${}^{59}{\rm Fe}$ has been studied using both theoretical modelling and experimental data. At $T_9=1.2$ , a typical carbon shell burning temperature, the stellar decay rate of ${}^{59}{\rm Fe}$ is two orders of magnitude faster than terrestrial rate. The rate estimate based on large-scale shell-model calculation with KB3 interaction (Langanke & Martinez-Pinedo Reference Langanke and Martinez-Pinedo2001) (LMP) has been widely used in stellar-evolution codes. A recent study based on a new shell model calculation (Li et al. Reference Li, Lam, Qi, Tang and Zhang2016) finds decay rates are about 3 times higher than LMP, at C-shell burning conditions. This calculation also finds that the transition ${}^{59}{\rm Fe}$ ( $5/2^-$ , 472 keV) $\rightarrow$ ${}^{59}{\rm Co}$ ( $7/2^-$ g.s.) plays an important role in the ${}^{59}{\rm Fe}$ $\beta$ -decay. This calls for a better determination of this transition by experiment. A charge exchange experiment could determine the weak interaction strength, helping the estimate for stellar $\beta$ -decay (Cole et al. Reference Cole2012). The ${}^{59}{\rm Co}$ (n,p) ${}^{59}{\rm Fe}$ reaction was studied to determine the weak-interaction Gamow-Teller strengths B(GT) for the allowed transitions from the ${}^{59}{\rm Co}$ ground state to ${}^{59}{\rm Fe}$ . Limited by the poor energy resolution of the neutron beam, the uncertainties of B(GT) came out quite large, ${\sim}$ 40%) (Alford et al. Reference Alford1993). The ${}^{59}{\rm Fe}$ (571 keV) state had been assigned a spin/parity of $3/2^-$ from a (n,p) experiment, while a $\gamma$ multiplicity measurement (Deacon et al. Reference Deacon2007) prefers a 5/2 $^-$ assignment of this state; then this state could also decay via an allowed transition to the ${}^{59}{\rm Co}$ ground state, and contribute to the stellar $\beta$ decay of ${}^{59}{\rm Fe}$ . A high-resolution measurement of the ${}^{59}{\rm Fe}$ (t, ${}^{3}{\rm He}$ ) ${}^{59}{\rm Co}$ reaction, performed at NSCL (Gao et al. Reference Gao2021), found the stellar decay rate to be 3.5(1.1) times faster than the LMP rate, confirming previous shell model calculations (Li et al. Reference Li, Lam, Qi, Tang and Zhang2016), and the contribution of 571keV could be neglected (although its $J^{\pi}$ was still not confirmed). Stellar-evolution calculations show that the ${}^{60}{\rm Fe}$ production of an $18\ {{\rm M}_{\odot}}$ star is decreased by 40% when using the new rate (Gao et al. Reference Gao2021).

Also the effective decay rate of $^{60}\mathrm{Fe}$ in stellar environments is affected by the thermal population of excited states. Due to the lower level density in a even-even nucleus, only the first excited state of $^{60}\mathrm{Fe}$ (2 $^+$ , 824keV) is expected to be notably populated at a temperature of $T\,{\leq}\,$ 2 GK. From currently-accepted shell model calculations (Langanke & Martinez-Pinedo Reference Langanke and Martinez-Pinedo2001), a half-life of 3.14 yr is suggested at 1.3 GK. However, a different earlier approach, based on a single particle approximation (Fuller, Fowler, & Newman Reference Fuller, Fowler and Newman1982), had suggested a much shorter half-life of 0.14 yr. Such a difference has significant impact on the $^{60}\mathrm{Fe}$ yield from massive stars.

The temperatures in explosive burning are higher than that in carbon shell burning, and $\beta$ -decay rates such as of ${}^{59}{\rm Fe}$ and ${}^{60}{\rm Fe}$ would be even faster. However, the ${}^{59}{\rm Fe}$ (p,n) ${}^{59}{\rm Co}$ reaction supersedes the ${}^{59}{\rm Fe}$ $\beta$ -decay at $T_9>2$ , and the uncertainty in $\beta$ -decay only plays a minor role for the ${}^{60}{\rm Fe}$ yields (Figure 30).

In the He burning shell, instead, the temperature never exceeds $T>0.4\,\mathrm{GK}$ , and the ${}^{59}{\rm Fe}$ and ${}^{60}{\rm Fe}$ $\beta$ -decay rates remain at the terrestrial values.

The ${}^{59}{\rm Fe}$ (n, $\gamma$ ) ${}^{60}{\rm Fe}$ reaction is crucial to the production of ${}^{60}{\rm Fe}$ . A direct measurement of this reaction rate is challenged by the short half-life of ${}^{59}{\rm Fe}$ . Experimental results obtained from a Coulomb dissociation experiment of ${}^{60}{\rm Fe}$ (Uberseder et al. Reference Uberseder2009) found a rate is roughly 20% higher than the value estimated from statistical theory as reported in the REACLIB database (Cyburt et al. Reference Cyburt2010). However, the conversion herein of the reverse reaction rates is model dependent, with an uncertainty of about 40%. Clearly, a better experiment for measuring ${}^{59}{\rm Fe}$ (n, $\gamma$ ) ${}^{60}{\rm Fe}$ is needed.

The surrogate ratio method has been proposed as a practicable way to study the neutron capture rate of unstable nuclei (Escher et al. Reference Escher, Burke, Dietrich, Scielzo, Thompson and Younes2012). In such an experiment, one can measure the ${}^{56,58}{\rm Fe}$ (2n, $\gamma$ ) ${}^{58,60}{\rm Fe}$ rate to obtain the ratio between ${}^{57}{\rm Fe}$ (n, $\gamma$ ) ${}^{58}{\rm Fe}$ , which is well known, because ${}^{57}{\rm Fe}$ is a stable isotope, and ${}^{59}{\rm Fe}$ (n, $\gamma$ ) ${}^{60}{\rm Fe}$ . This approach has been proven as feasible in determination of the key s-process reaction ${}^{95}{\rm Zr}$ (n, $\gamma$ ) ${}^{96}{\rm Zr}$ (Yan et al. Reference Yan2017), and suggests a precision of 30% or better. Another surrogate approach is through the ${}^{59}{\rm Fe}$ (d,p) ${}^{60}{\rm Fe}$ reaction with inverse kinematics. In a recent benchmark experiment (Ratkiewicz et al. Reference Ratkiewicz2019), such a technique has achieved about 25% precision for the ${}^{95}{\rm Mo}$ (n, $\gamma$ ) ${}^{96}{\rm Mo}$ rate.

The ${}^{60}{\rm Fe}$ destruction reactions include ${}^{60}{\rm Fe}$ (n, $\gamma$ ) ${}^{61}{\rm Fe}$ , ${}^{60}{\rm Fe}$ (p, n) ${}^{60}{\rm Co}$ . The ${}^{60}{\rm Fe}$ (n, $\gamma$ ) ${}^{61}{\rm Fe}$ rate has been measured directly with an uncertainty of ${\sim}$ 30% (Uberseder et al. Reference Uberseder2009). The ${}^{60}{\rm Fe}$ (p, n) ${}^{60}{\rm Co}$ reaction becomes dominant for destruction in explosive burning. This rate is only estimated from statistical models, it needs to be tested within nucleosynthesis models, and possibly followed up by experimental efforts.

We note that not only the reactions relating to ${}^{59,60}{\rm Fe}$ but also the neutron source reactions, discussed in Section 2.1.3, ${}^{22}{\rm Ne}$ ( $\alpha$ ,n) ${}^{25}{\rm Mg}$ , ${}^{12}{\rm C}$ ( ${}^{12}{\rm C}$ ,n) ${}^{23}{\rm Mg}$ , are crucial to the overall ${}^{60}{\rm Fe}$ yields.

Figure 31. Stellar yields of $^{60}\mathrm{Fe}$ for the range of metallicities ( $Z=0.02$ –40.0001) as a function of initial mass. Results taken from Karakas (Reference Karakas2010) and Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio and Siess2014a); Doherty et al. (Reference Doherty, Gil-Pons, Lau, Lattanzio, Siess and Campbell2014b)

3.2. Stellar nucleosynthesis environments

3.2.1. Low- and intermediate-mass stars

In AGB stars the high neutron flux required for $^{60}\mathrm{Fe}$ production can occur within the thermal pulse convective zone, due to the activation of the 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ neutron source. This reaction requires temperatures in excess of 300 MK and occurs in stars of masses ${\geq}2$ $3\,{{\rm M}_{\odot}}$ (Karakas & Lattanzio Reference Karakas and Lattanzio2014). For efficient $^{60}\mathrm{Fe}$ production the neutron density must exceed ${\approx}$ 1011 n cm−3 (Lugaro et al. Reference Lugaro, Doherty, Karakas, Maddison, Liffman, Garca-Hernández, Siess and Lattanzio2012). The $^{60}\mathrm{Fe}$ must then be mixed from the intershell to the surface via third dredge-up, and hence the yield relies on both the amount and efficiency of third dredge up and also the mass loss rate which dictate the number of third dredge up events that may occur. As mentioned in Section 2.2.1 the mass-loss rate of AGB stars is uncertain, in particular for more metal-poor and massive AGB stars (Höfner & Olofsson Reference Höfner and Olofsson2018). In addition, the efficiency (and even the occurrence at all at higher initial masses) of third dredge up is dependent on uncertain physics, in particular the treatment of convective boundaries (Frost & Lattanzio Reference Frost and Lattanzio1996). Due to this, there is no consensus on whether AGB stars of masses ${\geq}5 {{\rm M}_{\odot}}$ undergo efficient third dredge up (e.g. Karakas Reference Karakas2010; Ritter et al. Reference Ritter, Herwig, Jones, Pignatari, Fryer and Hirschi2018), inefficient third dredge up (Cristallo et al. Reference Cristallo, Straniero, Piersanti and Gobrecht2015), or even no third dredge up at all (Ventura et al. Reference Ventura, Carini and D’Antona2011; Siess Reference Siess2010). This constitutes the main uncertainty for $^{60}\mathrm{Fe}$ production within AGB stars. Reaction rate uncertainties associated with the neutron producing reaction 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ (Longland, Iliadis, & Karakas Reference Longland, Iliadis and Karakas2012b), and the neutron capture reactions $^{58}\mathrm{Fe}$ (n, $\gamma)^{59}\mathrm{Fe}$ , and $^{59}\mathrm{Fe}$ (n, $\gamma)^{60}\mathrm{Fe}$ discussed in Section 3.1 can also impact AGB star $^{60}\mathrm{Fe}$ yields.

Figure 31 shows the $^{60}\mathrm{Fe}$ yields for a range of metallicites ( $Z = 0.02{-}0.0001$ ) as a function of initial mass from the Monash set of models (Karakas Reference Karakas2010; Doherty et al. Reference Doherty, Gil-Pons, Lau, Lattanzio and Siess2014a; Doherty et al. Reference Doherty, Gil-Pons, Lau, Lattanzio, Siess and Campbell2014b). Although individual intermediate-mass AGB stars can make a sizeable amount of $^{60}\mathrm{Fe}$ ( ${\approx}10^{-5}{-}10^{-6}\,{{\rm M}_{\odot}}$ ), low and intermediate mass AGB stars make only a very small contribution to the overall galactic inventory of this isotope (Lugaro & Karakas Reference Lugaro and Karakas2008; Lugaro, Ott, & Kereszturi Reference Lugaro, Ott and Kereszturi2018a), as with the case of $^{26}\mathrm{Al}$ . There are two main effects that make the $^{60}\mathrm{Fe}$ dependent not only on the mass, as discussed above, but also on the metallicity. The mass at which $^{60}\mathrm{Fe}$ production becomes significant decreases with decreasing metallicity. This is because there is a metallicity dependence for the activation of the $^{22}\mathrm{Ne}$ source. Stars of lower metallicities attain higher thermal pulse temperatures, and hence more efficient 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ activation, than their more metal-rich counterparts for the same initial mass. The other effect is due to the fact that in AGB stars $^{22}\mathrm{Ne}$ can be of both primary and secondary origin. This nucleus derives from conversion of 14N in the intershell via the reaction chain 14N( $\alpha,\gamma)^{18}$ F( $\beta^+,\nu)^{18}$ O( $\alpha,\gamma)^{22}$ Ne. The secondary component derives from the initial CNO abundance in the star converted into N via H burning via the CNO cyle within the H shell or at the base of the convective envelope during hot-bottom burning. The primary component derives from the extra 12C produced within the thermal pulse and contributing to the CNO abundance in the star. Therefore, due to the primary nature of the $^{22}\mathrm{Ne}$ neutron source, the maximum amount of $^{60}\mathrm{Fe}$ produced within the intershell is limited primarily by the amount of available $^{56,58}\mathrm{Fe}$ seeds, which depends on the initial stellar metallicity. This can be seen comparing the yields of $Z = 0.0001$ models with those of $Z = 0.008$ over the intermediate-mass regime ${\approx}4$ $6 {{\rm M}_{\odot}}$ . In both cases, there is a flat trend for the $^{60}\mathrm{Fe}$ yield over this mass range due to the relatively constant amount of third dredge up material mixed to the stellar surface. Interestingly, within this mass range the total amount of third dredge up enrichment is also similar for these two metallicities, and hence the offset of ${\approx}$ 50–100 in the $^{60}\mathrm{Fe}$ yields is related primarily to initial metallicity, varying by a factor of ${\approx}$ 80.

Another possible source of $^{60}\mathrm{Fe}$ from intermediate-mass stars is via the explosion of super-AGB stars as electron capture supernovae. These supernovae can produce up to ${\sim}10^{-4}\ {{\rm M}_{\odot}}$ of $^{60}\mathrm{Fe}$ per event (Wanajo, Janka, & Müller Reference Wanajo, Janka and Müller2013), however at solar metallicity these objects are expected to be quite rare, making up only ${\sim}5\%$ of all core collapse supernovae (e.g., Poelarends et al. Reference Poelarends, Herwig, Langer and Heger2008; Doherty et al. Reference Doherty, Gil-Pons, Siess, Lattanzio and Lau2015).

3.2.2. Massive stars and their core-collapse supernovae

In massive stars, the neutrons required to to produce ${}^{60}{\rm Fe}$ are provided mainly by the 22Ne( $\alpha$ ,n) $^{25}\mathrm{Mg}$ neutron source activated during convective C and He shell burning phases as well as by the supernova explosion shock (Limongi & Chieffi Reference Limongi and Chieffi2006a; Jones et al. Reference Jones2019). Figure 32 indicates these regions for a $15 \mathrm{M}_\odot$ model (Sieverding et al. Reference Sieverding, Martnez-Pinedo, Langanke, Heger, Kubono, Kajino, Nishimura, Isobe, Nagataki, Shima and Takeda2017). The balance between these contributions is sensitive to stellar mass and the assumptions made in the stellar evolution models, in particular to convection. The bulk of pre-supernova production occurs relatively late, around 100 yr before collapse (Jones et al. Reference Jones2019), and relatively deep, at most at the bottom of the He-shell. This makes is unlikely for any of the material enriched in