Progress on nuclear reaction rates affecting the stellar production of ²⁶Al

The observation of cosmic radioisotopes relies on radioactive decay occurring outside the radioisotope stellar production sites, therefore, they are not distorted from absorption of photons by gas, which occur within the high density stellar matter. Hence, such astronomical data from radioactive decay convey direct information about nuclear reactions within cosmic sites that is otherwise hidden from direct observation (with the exception of neutrinos, which are, however, not observable from distant sites). Commonly available astronomical abundance data from atomic-line spectroscopy are also interpreted in terms of cosmic nucleosynthesis; this is, however, quite indirect information, in particular because the density and ionization state of atoms at the surface of stars is controlled not only by nuclear reactions but also by atomic processes that strongly affect the abundances. Therefore, the characteristic γ-ray lines measured from radioactive decay provide more direct astronomical data. The detection of the characteristic γ rays from ²⁶Al decay is the first direct, convincing proof that nucleosynthesis is going on within the current Galaxy ³⁰ , because ²⁶Al has a characteristic decay time of a million years, much shorter than the age of the Galaxy of more than 10 billion years. Therefore, ²⁶Al γ rays can be used to study recent nucleosynthesis sources and the transport of ejected material into the interstellar medium.

Direct observations of ²⁶Al decay in interstellar space through its characteristic γ-rays with energy 1808.65 keV had been motivated by theorists [12], and was first achieved by the HEAO-C satellite in 1978/1979 observing the central regions of our Milky Way Galaxy [13]. The NASA Compton Gamma-Ray Observatory (1991–2000) with the COMPTEL instrument provided a sky image of the ²⁶Al γ-ray line, which showed a structured ²⁶Al emission, extended along the plane of the Galaxy [14–16] (figure 2). This image was obtained from measurements taken over years 1991–2000 throughout the sky. It uses a maximum-entropy regularization together with the likelihood of the image's projected data fitting the measurement, and varies the image iteratively until a best image is found to fit the measured events. Such forward convolution analysis is required, as the direct inversion of measured data is not possible; the signal of the ²⁶Al sky is translated into the data space of measured events by the instrument response function, which includes Compton scattering (as a probabilistic process), and is singular (hence cannot be inverted). The high instrumental background needs careful modelling, and Poissonian statistics must be properly included, hence the maximum-likelihood method is used (see [17, 18] for details on COMPTEL data analysis). The reliability of such γ-ray imaging has been consolidated in many studies (see, e.g. [19]). The ²⁶Al γ-ray image and the structures it showed was found to be in broad agreement with earlier expectations of ²⁶Al being produced throughout the Galaxy mostly from massive stars and their CCSNe since young stars are typically located on the plane of the Galaxy, and these young stars are preferentially massive.

Zoom In Zoom Out Reset image size

In 2002, the continuing INTEGRAL mission of the European Space Agency (ESA) started, with its high-resolution γ-ray spectrometer SPI, deepening the astronomical harvests of ²⁶Al emission (figure 3). Note that the COMPTEL scintillation detectors had an instrumental resolution of ∼200 keV, compared to ∼3 keV for the SPI Ge detectors. This led to deeper, Galaxy-wide investigations of ²⁶Al [20], as recently reviewed [21]. Furthermore, INTEGRAL allowed to spatially resolve specific and well-constrained massive star groups (OB associations), and therefore to test our understanding of massive star groups and how they shape the star-forming interstellar medium (see [22] for a review of astrophysical issues and lessons). Important herein are the Cygnus, the Orion [23] and the Scorpius–Centaurus [24] stellar groups. Altogether, astronomical ²⁶Al observations have led to both the tracing of the path of nucleosynthesis ejecta after they leave their sources and eventually end up in next generation stars, and the investigation of the cosmic production sites, i.e. stars and supernovae. For the latter objective, it is essential to have the best-possible knowledge of the physics of the stellar sites and of the nuclear reactions involving ²⁶Al, as discussed here.

Zoom In Zoom Out Reset image size

Ice cores, deep-sea sediments, and deep-sea FeMn crust material are favourable locations to search for live radionuclides on Earth produced by nearby (in time and space) stellar nucleosynthetic events. These materials have very low growth rates, of the order of mm to cm per thousands to millions of years, and therefore they can provide time-resolved information over time scales of million years. However, because the number of radioactive atoms to be counted is tiny (e.g. ²⁶Al is typically 12 to 16 orders-of-magnitude lower in abundance than the stable terrestrial ²⁷Al), only accelerator mass spectrometry (AMS) [3] has so far reached the sensitivity required for such studies. AMS directly counts the radionuclide of interest one by one by means of a particle detector after the sample material is dissolved and the radionuclide of interest is chemically separated from the bulk material. Thanks to this methodology it has been possible to detect on Earth ⁶⁰Fe from one or several nearby CCSNe that occurred roughly 2–8 Myr ago [26–28], where ⁶⁰Fe is another radioisotope with a half-life T_1/2 = 2.62 Myr produced by massive stars and their supernovae, also observable via γ-ray satellites [29].

Detection of ⁶⁰Fe of stellar origin is possible because its terrestrial production is negligible. In contrast, ²⁶Al is produced not only in stars but also in the terrestrial atmosphere through cosmic-ray induced nuclear spallation reactions on abundant stable isotopes, such as ²⁷Al(p, p–n), ²⁶Mg(p, n), ²⁸Si(p, ³He), and ²⁴Mg(³He, p). Furthermore, production inside the terrestrial archives themselves and influx of interplanetary dust grains may add spurious amounts of cosmic-ray produced ²⁶Al. Stellar ²⁶Al may be of the order of only a few percent, up to roughly 10%, relative to its terrestrial component [3]. Therefore, to identify a stellar ²⁶Al signal above the terrestrial background requires an extremely sensitive and efficient detection technique. Feige et al [3] searched for presence of stellar ²⁶Al in an extensive set of deep-sea sediment samples that covered a time-period between 1.7 and 3.2 Myr ago and found an exponential decline of ²⁶Al with the age of the samples that can be explained by radioactive decay of terrestrial ²⁶Al. This indicates no significant ²⁶Al above the terrestrial signal. Nevertheless, owing to the large number of samples analyzed, these data allowed the deduction of an upper limit for the stellar ²⁶Al.

This upper limit is crucial when taken together with the previously derived stellar ⁶⁰Fe, as the live ²⁶Al and ⁶⁰Fe radioisotopes found on Earth originated from nucleosynthesis in massive stars and, in particular, constrain models of the nearby CCSN that occurred 2 Myr ago. These are the same sources that dominate both the current abundances of live ²⁶Al and ⁶⁰Fe in the Galaxy and their extinct abundances in the early Solar System—since massive stars are present in star-forming regions (sections 1.1 and 1.3). Therefore, comparison between three different types of constraints can provide us with significant information on both massive star nucleosynthesis and the environment of the formation of the the Sun. The Earth samples produced a lower limit ⁶⁰Fe/²⁶Al between 0.1 and 0.33, which is close to the value obtained from Galaxy-wide gamma-ray spectrometry with INTEGRAL of 0.2–0.4 [29]. However, it is well above the ⁶⁰Fe/²⁶Al ratio derived for the early Solar System of 0.002. This calls for a different origin of ²⁶Al in the early Solar System, relative to the current live ²⁶Al in the Galaxy and in Earth archives. The problem is further compounded by theoretical CCSN yields, which currently overproduce ⁶⁰Fe relative to ²⁶Al, even compared to the spectroscopic γ-ray observations [30–32].

Analysis of the isotopic composition of Mg in Ca–Al-rich inclusions (CAIs) from primitive meteorites, the oldest solid objects to have formed within the Solar System, demonstrates that ²⁶Al was present in the early Solar System with ²⁶Al/²⁷Al ≃ 5 × 10⁻⁵. The isochrone method with which this is achieved is explained using figure 4, which presents the first observational evidence of the presence of ²⁶Al. Several different minerals were analysed within the same sample (of same color in the plot), and for each of these minerals the ratios ²⁷Al/²⁴Mg and ²⁶Mg/²⁴Mg were measured and plotted against each other as in the figure. ²⁷Al is the only stable isotope of Al, and ²⁴Mg the most abundant stable isotope of Mg. Therefore, the ²⁷Al/²⁴Mg ratio is a good measure of how much total Al and Mg are present inside each mineral ³¹ . Because ²⁶Mg is the daughter nucleus of ²⁶Al, the ²⁶Mg/²⁴Mg ratio can trace the potential initial presence of ²⁶Al: i.e. ²⁶Mg/²⁴Mg = ²⁶Mg^⋆/²⁴Mg + ²⁶Mg^initial/²⁴Mg, where ²⁶Mg^⋆ is the radiogenic abundance from the decay of ²⁶Al, and ²⁶Mg^initial its initial abundance in the material from which the mineral comes from, which is a constant. The discovery of the presence of ²⁶Al is based on the fact that the ²⁶Mg/²⁴Mg ratios measured in different types of Mg-rich (i.e. low Al/Mg) and Al-rich (i.e. high Al.Mg) show a linear correlation with Al/Mg. The only way to explain such linear correlation is that the excess of ²⁶Mg was initially due to an excess of ²⁶Al. The slope of the line provide us with the initial ²⁶Al/²⁷Al ratio, given that the first term in the equation above can be written as ²⁶Al/²⁷Al × ²⁷Al/²⁴Mg (figure 4).

Zoom In Zoom Out Reset image size

The presence of ²⁶Al in the early Solar System was actually predicted in the 1950s before its discovery, because an early heating source was needed to melt the interiors of the first planetesimals that formed within the first Myr [36]. This heat was driven by the γ-ray photons generated when ²⁶Al decays to ²⁶Mg inside a rocky body, the same photons that are observed via the INTEGRAL satellite when ²⁶Al decays in the interstellar medium (figure 3). One of the consequences of such heat is that the ice inside those planetesimals that formed beyond the ice line (initially made of roughly 50% ice) melted and the water was lost. The timescale of this water loss was shorter than the accretion timescale of planetesimals into terrestrial planets. As sketched in figure 5 from [37], if ²⁶Al is present in planetesimals, water-poor planets, such as the Earth, which is only a few percent water, result and are known to be habitable world. If ²⁶Al is not present in significant quantity, instead, water-rich, ocean planets are predicted, which are potentially more difficult to harbour life. Therefore, the presence of ²⁶Al in star-forming regions can strongly affect the habitability of the planetary systems formed in such regions. Understanding the production of ²⁶Al in stars is therefore crucial to understand the water context of extrasolar terrestrial planets. However, the origin of ²⁶Al in the early Solar System is still unclear and strongly debated with several separate stellar origin scenarios proposed ³² , each of which have different probabilities to occur in star-forming regions [6].

Zoom In Zoom Out Reset image size

For example, Cameron and Truran [39] were the first to propose a simultaneous enrichment plus triggered collapse scenario, in which a nearby CCSN ejects freshly synthesised material into a dense molecular cloud core thereby triggering its collapse to form the solar nebula (see e.g. [40–42]). Alternate mechanisms for the injection of ²⁶Al-rich material from a CCSN have been proposed, including, for example, pollution of the already formed disk [43–45]. Other scenarios postulate that the gas that later collapsed to form the protosolar molecular cloud was pre-enriched in ²⁶Al by an earlier generation of massive stars either within the star-forming region or the galactic interstellar medium itself [46–51]. The winds of stars of mass > 30 M_⊙ could also produce enough ²⁶Al to be a candidate source [52, 53]. Brinkman et al [54] showed that lower mass stars could also achieve high yields if they are part of a binary system (section 2.2.1). Another possible origin is an AGB star [55], however, this source seems unlikely because these stars cannot produce the required ²⁶Al abundance without also overproducing several radionuclides heavier than iron [35]. Furthermore, low-mass stars formed in the same molecular cloud as the Sun take a long time to reach the AGB phase (∼1 Gyr), by which time the molecular cloud is since long dispersed. Finally, that a molecular cloud would be visited by an AGB star formed elsewhere has been shown observationally to be very unlikely [56].

In summary, investigation of the production of ²⁶Al by nuclear reactions in massive stars, and its ejection from massive stars, both during the wind phases and the following CCSN explosion, is relevant to understand the evolution and properties of planetesimals and planets both within solar and extrasolar systems.

Stardust grains are recovered from meteorites and carry the pure signature of the nucleosynthesis that occurred in their parent stars, therefore, they are effectively tiny specks of stars [57, 58]. Evidence that ²⁶Al was incorporated into stardust grains that formed around stars and supernovae is inferred from the Mg composition of the grains, and in particular from the excess in the daughter nucleus ²⁶Mg, relative to the other stable Mg isotopes. Most of the grains originated from AGB stars, with some (a few percent) of grains also showing the signature of an origin from CCSNe and novae. Therefore, even if AGB stars and novae are not the major producers or ²⁶Al in the Galaxy, relative to massive stars, it is necessary to investigate their ²⁶Al production to interpret the presence of ²⁶Al in stardust grains, at the time of their formation.

Many recovered and analysed stardust minerals are rich in Al and poor in Mg, so that the signature of ²⁶Al is evident and measurable. These include silicon carbide (SiC) and graphite, which are carbon (C)-rich grains that form in a gas when C > O, and corundum (Al₂O₃) and hibonite (CaAl₁₂O₁₉), which are oxygen (O)-rich grains that form when C < O. If there are only just traces of Mg originally in the grains, then the full initial abundance of ²⁶Al at the time of the grain formation can be recovered as the whole abundance of ²⁶Mg. In other words, the abundance of ²⁶Al is derived directly from the abundance of ²⁶Mg because Mg is not a main component of the material: the Mg abundance is orders-of-magnitude smaller than that of Al in, e.g. aluminium oxides and silicon carbide grains (see, e.g. figure 2 of [59]), therefore, stable ²⁶Mg is an orders-of-magnitude less significant contributor to the atoms at mass 26. ³³ Groopman et al [60] significantly improved the derivation of the initial ²⁶Al abundance by using the isochrone method for stardust grains as done for Solar System materials (section 1.3). This method produces more accurate results, generally showing higher ratios than previously estimated due to a better estimate of contamination.

Overall, C-rich stardust grains believed to have originated from CCSNe show very high abundances of ²⁶Al, with inferred ²⁶Al/²⁷Al ratios in the range 0.1–1, higher than standard theoretical predictions in the C > O regions of the ejecta. These ratios can be used to constrain the nucleosynthesis models, and they require an extra production mechanism for ²⁶Al to be at work in the C-rich regions of CCSNe beyond those described in section 2.2.2. This mechanism may be related to ingestion of hydrogen into the He-burning shell and the subsequent explosive nucleosynthesis [62]. The grains that are known to have originated in AGB stars show somewhat lower ²⁶Al abundances than grains from CCSNe, with ²⁶Al/²⁷Al ratios in the range 10⁻³ to 10⁻². Also these grains can be used to constrain AGB nucleosynthesis models [7, 63, 64]. For example, oxide grains belonging to a specific group (Group 2) show strong depletion in ¹⁸O/¹⁶O and have also relatively high ²⁶Al/²⁷Al ratios. Both features are a product of efficient hydrogen burning, possibly connected to hot bottom burning (HBB) in massive AGB stars [7] or extra-mixing in low-mass AGB stars [65] (see section 2.1). Finally, some grains have been potentially interpreted as nova condensates and their relatively high ²⁶Al/²⁷Al ratios, up to 0.3–0.5, have been used as one of the main indications of such signature origin [66, 67] (see section 2.3 for more details).

The evolution of the average abundance of a radioactive nucleus such as ²⁶Al in the galactic interstellar medium is generally controlled by the establishment of a steady-state equilibrium between its ejection by stellar sources and its radioactive decay. When such equilibrium is established, the number of ²⁶Al nuclei N₂₆ no longer changes with time t: ${{\rm{d}}{N}}_{26}/{\rm{d}}{t}=0$. The ${{\rm{d}}{N}}_{26}/{\rm{d}}{t}=0$ rate is made of two terms: one is a positive production term given by the stellar production rate per unit time, defined as dP₂₆/dt; the other is a negative destruction term, wrought by the decay and equal to N₂₆ × λ₂₆ = N₂₆/τ₂₆, where λ₂₆ is the decay rate of ²⁶Al, and τ₂₆ its mean lifetime. If the total abundance change is zero, then the two terms are equal and the equilibrium abundance N₂₆ is equal to (dP₂₆/dt)τ₂₆. This formula, together with the stellar production rates predicted for the main stellar producers of ²⁶Al in the Galaxy (see section 2), enables us to quickly compare the predicted ²⁶Al abundance in the Galaxy to that inferred from γ-ray observations, which represents the sum of the contribution of all nearby young stellar populations currently ejecting this radioisotope.

However, this simple steady-state formula is not enough to interpret the data accurately. Theoretical models must also account for the star formation rate of the Milky Way today; the initial mass function, in order to model stellar populations; and the fact that stellar yields may vary with stellar mass and metallicity, as well as potentially their binary status. Furthermore, stellar enrichment within the interstellar medium is not continuous but represented by events discrete in time and space, therefore, it cannot be accurately described by a continuous dP₂₆/dt production rate. Local enhancements or reductions in the ²⁶Al abundance due to spatial and temporal inhomogeneities must also be considered in numerical simulations [68, 69]. This is a challenging task because the evolution of ²⁶Al depends both on the time interval between the formation of the progenitor star that led to the enrichment event, a parameter that is currently poorly constrained, as well as their spatial distribution. Comparing 3D hydrodynamic simulated distributions of ²⁶Al to the observed 1.8 MeV emission line flux maps of figure 2 [70, 71] has provided constraints on the Galaxy-wide distribution of ²⁶Al, and showed that our observer position may be highly biased by the local environment and the stars that populated it. Furthermore, dedicated models [72, 73] are needed when considering specific star-forming regions and the 'super-bubbles' generated by the energy from massive stars within them.

Interpreting the abundances of ²⁶Al derived from meteoritic data also requires the use of chemical evolution models, in this case specifically because the initial ²⁶Al abundance in the mineral can be measured only relative to that of the stable ²⁷Al. For the early Solar System, while the abundance of ²⁶Al reflects the local star formation rate at the time of the formation of the Sun, the abundance of the stable isotope ²⁷Al encodes the complete past enrichment history of the Galaxy and can only be predicted using galaxy models that properly integrate the galactic star formation history with stellar yields [74–77]. These predictions are, however, affected by many uncertainties such as the total stellar mass formed prior to the formation of the Solar System, the amount of stable ²⁷Al locked in stellar remnants (white dwarfs, black holes, neutron stars), and large-scale outflows that remove some of the ²⁷Al content from the Galaxy [76, 77].

All the uncertainties described above can be significantly reduced by considering the ⁶⁰Fe/²⁶Al ratio, since ⁶⁰Fe is a radioisotope with a similar half-life (2.62 Myr) and, like ²⁶Al, can be measured via γ-rays and meteoritic analysis, and is also produced mostly by massive stars. Therefore, its ratio relative to ²⁶Al solves some of the problems listed above, i.e. a chemical evolution simulation that follows the complete history of the Galaxy is not necessary to give us a direct insight into the stellar sources of these radioisotope. The steady-state equilibrium number ratio of the two radioisotope is N₆₀/N₂₆ = (dP₆₀/dP₂₆)(τ₆₀/τ₂₆), and the number ratio of the two radioisotope derived from the flux (F) ratio observed via γ-rays is N₆₀/N₂₆ = (F₆₀/F₂₆)(τ₆₀/τ₂₆) ³⁴ . Therefore, the ⁶⁰Fe/²⁶Al production ratio in massive stars (by number) can be directly compared to the observed flux ratio [29]. The result is that current models overproduce ⁶⁰Fe relative to ²⁶Al compared to the spectroscopic γ-ray observations by a factor of 3–10 [30–32], and there are inconsistencies not only between models and observations, but also between observations of different types (see end of section 1.2). Moreover, in reality, local inhomogeneities can also affect the ⁶⁰Fe/²⁶Al ratio, even if these two radioisotope came from exactly the same sources, since they decay with different half-lives. Considering temporal heterogeneities within a statistical framework results in an increase of roughly 10% in the ⁶⁰Fe/²⁶Al ratio relative to that calculated using the basic steady-state formula [78], but even larger fluctuations are found in more sophisticated models of the interstellar medium [51] and of giant molecular clouds [79].

Finally, we stress that the fundamental input for any numerical predictions of the evolution of ²⁶Al in the Galaxy—whether associated with chemical evolution models, interstellar medium simulations, or single-source enrichment models are the adopted stellar yields discussed below and e.g. in [9, 80–83]. In fact, the quantitative predictive capabilities of even the most sophisticated simulations are still limited by the large uncertainties affecting nucleosynthesis and stellar evolution calculations. In the following section, we describe in more detail the production of ²⁶Al in different types of astronomical objects, from low to high mass stars and binary interaction objects, and the associated uncertainties. Lower mass stars during their AGB phase (section 2.1) are specifically relevant to understand the origin of ²⁶Al in the majority of meteoritic stardust grains. Massive stars and their CCSNe (section 2.2) are the dominant producers of ²⁶Al in the Galaxy and in star-forming regions, which are relevant for the early Solar System. Novae are also relevant as potential contributors to galactic ²⁶Al, as well as sources of rare stardust grains; they will be discussed in section 2.3.

Stars with initial mass in the range 1–8 M_⊙ end their lives as AGB stars. Their structure consists of a degenerate carbon–oxygen core, above which sit a helium-burning shell and a hydrogen-burning shell separated by an He-rich region called the 'intershell'. Surrounding this central region of the star is an extended, hydrogen-rich, convective envelope. The configuration of thin helium and hydrogen burning shells is unstable, leading to periodic runaway helium-burning episodes, known as thermal pulses. During these thermal pulses, convection mixes the ashes of helium-burning in the intershell region. As a thermal pulse subsides, the star undergoes a structural readjustment that allows the convective envelope to deepen, penetrating the intershell and dragging freshly synthesised material to the surface. This is known as the third dredge-up and it may happen after each thermal pulse. Depending on the strength of the stellar winds (which strip mass from the surface) and the mass of the envelope, an AGB star may undergo a few to many tens of such thermal pulses before the entire envelope is removed and the star transitions to the post-AGB phase. For detailed reviews of AGB stars and their evolution, we refer the reader to Herwig [84] and Karakas and Lattanzio [85].

The production of ²⁶Al in AGB stars has been studied by many authors [35, 63, 86, 87]. Both the hydrogen-burning and the helium-burning shells are relevant to synthesis of ²⁶Al. In the latter, the initial abundances of the two heavy magnesium isotopes, ²⁵Mg and ²⁶Mg, are enhanced via α-captures onto ²²Ne, and then dredged-up into the stellar envelope. Directly at the base of the envelope, or in the radiative region just below it, depending on the initial stellar mass, shell hydrogen burning converts ²⁵Mg into ²⁶Al via proton captures as part of the Mg–Al chain shown in figure 6.

Zoom In Zoom Out Reset image size

Above initial masses around 4 M_⊙, the exact value depending on the metallicity and the choice of the convective model, the base of the stellar convective envelope is deep enough that it lies within the upper regions of the hydrogen-burning shell. Convection therefore cycles material from the entire envelope of the star through the hydrogen burning shell, in a process referred to as HBB. The combined action of the third dredge-up adding freshly synthesised ²⁵Mg to the envelope, and the HBB processing this material via the Mg–Al chain makes massive AGB stars substantial producers of ²⁶Al [87, 88]. This is in agreement with the high ²⁶Al/²⁷Al ratios in Group 2 oxide grains, and make massive AGB stars that experience HBB a candidate source of these grains [7], together with the Cool Bottom Process in low-mass stars are discussed below. The effect of reaction rate uncertainties on HBB in massive AGB stars has been carefully examined by Izzard et al (2007) [89], who concluded that uncertainties in the ²⁵Mg(p, γ)²⁶Al and ²⁶Al(p, γ)²⁷Si rates lead to an uncertainty in the ²⁶Al yields from a factor of few at solar metallicity to up to two orders-of-magnitude at lower metallicities. The so-called super-AGB stars also evolve to the AGB but experience carbon burning in the core after the helium-burning has taken place. This results in ONe- rather than CO-rich cores ³⁵ . The initial masses of these stars are in the range 8–10 M_⊙, depending on metallicity. In these super-AGB stars the base of the convective envelopes is very hot (up to 100 MK) and therefore HBB is very efficient leading to significant production of ²⁶Al. Nevertheless, the overall super-AGB contribution to the estimated galactic content of roughly 2.8 M_⊙ does not exceed 0.3 M_⊙, i.e. 10% of the total [90].

In canonical low-mass AGB models, where only convective mixing is taken into account, the hydrogen-burning shell is separated from the convective envelope by a radiative 'buffer' region where no mixing occurs. Therefore, the ²⁶Al produced by H burning in the top layers of the H-burning ashes ³⁶ is ingested inside the thermal pulse, where it can be destroyed by neutron-captures with neutrons generated by the ²²Ne(α, n)²⁵Mg reaction. What is left is then carried to the stellar surface via the third dredge-up. By this mechanism, the surfaces of low-mass AGB stars are predicted to have ²⁶Al/²⁷Al of the order of a few 10⁻³, in qualitative agreement with those observed in the SiC grains that originated in these stars [63].

The main stellar model uncertainties associated with AGB stars that impact the production of ²⁶Al are the efficiency of the third dredge-up, the choice of mass-loss rate, and the convective mixing model. The efficiency of the third dredge-up is affected by the method employed to find the convective boundary, e.g. [91]. More efficient third dredge-up in massive AGB stars, for example, carries more ²⁵Mg from the intershell into the envelope, which is then processed into ²⁶Al via HBB. The mass-loss rate influences the duration of the AGB phase, with stronger mass loss leading to fewer thermal pulses and less nucleosynthesis [92]. The choice of the convective model affects the temperature structure of the stellar envelope and therefore the temperature at which HBB can take place. More efficient convection leads to higher HBB temperatures, favouring ²⁶Al production [93, 94]. It can also lead to higher stellar luminosities, which may accelerate mass loss [93].

Another main uncertainty is related to the possible occurrence of non-convective mixing in AGB stars with initial mass below 2–3 M_⊙. This mixing may allow the crossing of the radiative buffer region and carry ashes from the hydrogen-burning shell into the convective envelope during the periods in-between thermal pulses (refereed to as interpulse periods) and boost the production of ²⁶Al. Wasserburg et al [95] first suggested a non-convective mixing process, which they called Cool Bottom Process (CBP, in contrast to HBB in the most massive stars) as an explanation for some CNO isotope anomalies observed in low-mass AGB stars and stardust grains of AGB origin. In the CBP model, it is assumed that material is carried from the lower edge of the convective envelope down to the innermost layers of the hydrogen shell where it experiences proton-capture reactions and then returns it to the convective zone.

The work of [96] showed that the surface of AGB stars with mass ≤2 M_⊙ and close to solar metallicity can be enriched in ²⁶Al up to ²⁶Al/²⁷Al = 0.1. However, they did not provide any hypothesis on the physical mechanism driving the mixing, and treated the depth and the mixing rates as free parameters.

Furthermore, to reach ²⁶Al/²⁷Al = 0.1 in the stellar envelope the CBP model of the quoted authors must push the carried materials down to the deepest layers of the H-shell, where the temperature is greater than 5.5 × 10⁷ K, before returning to the stellar envelope. The so-induced circulation of hot (still burning) matter can strongly affect the stellar energy balance, with relevant luminosity feedback.

In the last two decades many studies have been carried out on non-convective mixing phenomena of low-mass red giants and numerous hypotheses have been formulated on their cause: from stellar rotation [97], to thermohaline mixing [98], and gravity waves [99], stellar magnetic fields [100], and their combined effect [101, 102]. In the case of ²⁶Al the problem remains that to synthesize this radioisotope in significant amounts via extra-mixing, material must experience relatively high temperatures, and most of the proposed mixing models listed above do not predict ²⁶Al production. For example, the average molecular weight inversion due to the ³He(³He, pp)⁴He reaction, which triggers the thermohaline mixing, occurs in the H shell where the temperature is ∼3.5 × 10⁷ K, too low to efficiently activate the ²⁵Mg(p, γ)²⁶Al reaction [64, 103]. Only the extra-mixing induced by the effects of the stellar magnetic field proposed in [104] is currently able to produce the ²⁶Al/²⁷Al ratios of up to a few 10⁻¹ measured in oxide stardust grains of Group 2, also showing strong deficits in ¹⁸O, an isotope efficiently destroyed by H burning [105].

Magnetic-induced mixing in very low-mass (≤1.5 M_⊙) AGB stars can predict high ²⁶Al/²⁷Al because it operates via small bubbles of magnetized material, which rise from the H-burning shell to the base of the convective envelope [65], instead of moving material from top to bottom as in the classic CBP model. With state-of-the-art methods, the magnetic extra-mixing predictions of the Al isotopic ratios in low-mass AGB stars do not appear to be significantly affected by reaction rate uncertainties. For example, when using the rates by [106] and [107] for the (p, γ) captures on ²⁵Mg and ²⁶Al^g, respectively, instead of those reported by [108] the changes in the resulting ²⁶Al/²⁷Al isotopic ratio is smaller than the variations due to the stellar model parameters (such as the stellar mass, the mass loss, and the mixing depth). However, the magnetically induced extra-mixing is relatively fast and the transported material has no time to be affected by proton captures along the path from above the H-burning shell to the envelope (as instead it might happen in the classic CBP). Therefore, any change induced by the mixing in the stellar surface composition reflects the abundances in the H-burning shell. As a consequence any uncertainty or change in the nuclear physics input that affects the ²⁶Al/²⁷Al distribution in the shell will also affect the one in the stellar envelope (see the brief analysis by [109]).

From the map of the γ-ray observations from the ²⁶Al decay (see, e.g. figure 2), it is clear that most ²⁶Al is confined to the galactic plane and to some specific clumps (see, e.g. figure 16 of [110] and [111–113]). These clumps coincide with known groups of massive stars (i.e, with initial mass > 10 M_⊙ ³⁷ ), usually referred to as 'OB associations', due to the fact that these massive stars are blue/blue-white stars with surface temperatures roughly above 20 000 K belonging to the spectroscopic O and B classes [114, 115]. The ²⁶Al γ-ray map therefore indicates that most of the ²⁶Al in our Galaxy is produced by massive stars [19, 116, 117]. Theoretical models in fact predict that massive stars eject large abundances of ²⁶Al, both through stellar winds and CCSN explosions. Like in most of other stellar sources, ²⁶Al is mainly made via the ²⁵Mg(p, γ)²⁶Al reaction, while there are two main destruction channels: proton and neutron capture reactions, depending on the burning phase. Here, we focus first in section 2.2.1 on the winds from both single massive stars and massive stars that have a companion in a close binary system. We also discuss very massive stars (VMS), i.e. with masses above 100 M_⊙ [118]. Second, in section 2.2.2 we discuss in detail the contribution to ²⁶Al coming from the CCSN explosive ejecta.

Overall, for stars of masses below roughly 40 M_⊙, the contribution of the explosive ejecta is typically dominant relative to that of the winds. For example, when looking at table 3 of Limongi and Chieffi [119], both contributions to ²⁶Al, from the hydrostatic and explosive phases (see section 2.2.2), are ejected during the explosion. In stars of higher masses, instead the winds are stronger (see section 2.2.1) and therefore their contribution to the total amount ejected increases to become similar to that ejected during the explosion. Neutrino processes are not usually included in the CCSN models, but can contribute a relatively minor component of ²⁶Al, as we present at the end of section 2.2.2. It should be kept in mind that, as discussed in detail below, these different contributions are strongly model-dependent. Stellar rotation and binarity, mixing in the hydrostatic and explosive phases of the stellar evolution, CCSN properties, such as the mass of the remnant and the energy of the explosion, as well as the choice of the reaction rates can all affect the different contributions to the total ²⁶Al yield from massive stars of different masses.

2.2.1. Massive star winds in single and binary systems

The ²⁶Al that is expelled from a massive star by winds is produced by hydrogen burning both in the core and, later, in a shell via proton-captures on ²⁵Mg. This ²⁶Al can be ejected by stellar winds when layers that once belonged to the H-burning core are exposed at the surface (in the case of Wolf–Rayet (WR) stars) or in the non-WR regime if some mixing mechanism allows the ²⁶Al produced in H-burning regions to diffuse into the stellar envelope up to the surface. Convection, rotational mixing in the radiative zones of the star and mass losses are key processes that may enrich the surface in ²⁶Al. For all massive stars, after the main sequence, the convective envelope penetrates into the layers where ²⁶Al has been produced and transports this radioisotope to the stellar surface. The strong winds following the main sequence expel these layers from the stars, carrying the ²⁶Al into the surrounding interstellar medium (ISM). For WR stars, the stellar winds already start during hydrogen burning and are so strong that the entire hydrogen-rich envelope is removed, all the way down to the top of the layer processed by the CNO-cycle (also known as the helium core), and this eventually includes the hydrogen-burning shell. The deeper layers exposed this way contain more ²⁶Al, leading to increased wind yields for these stars. After core hydrogen burning, ²⁶Al is quickly destroyed in the core during helium-burning by neutron capture reactions, specifically the (n, p) and (n, α) channels. However, because the convective helium-burning core is smaller than the original convective hydrogen-burning core, enough ²⁶Al survives to be expelled from the star into the ISM.

At solar metallicity, Z = 0.014, all single massive stars above 30 M_⊙ experience phases of strong mass loss during their lifetimes. The amount of ²⁶Al ejected by the winds of massive stars, considering the currently recommended mass loss rate prescriptions (see [120] for the hot phase, [121, 122] for the cool phase, and [123] or [124] for the WR phase), depends in a sensitive way on the initial metallicity. At very low metallicity the amount of ²⁶Al ejected is much smaller than at solar metallicity because the winds are expected to be much weaker, and therefore the mass loss is smaller. Figure 7 shows the ²⁶Al yields ejected by the stellar winds as a function of initial stellar mass for models of solar metallicity predicted by various studies reported in the literature for non-rotating, solar metallicity stars. The highest yields are for stars with initial masses >30–40 M_⊙. These stars become the so-called WR stars mentioned before, as they lose their entire hydrogen-rich envelope, exposing their helium cores. During the phase where layers that belonged to the core H-burning phase (which are enriched in helium and nitrogen) are exposed at the surface, large amounts of ²⁶Al are expelled into the ISM by these stars. Massive stars with masses between 10 and 30 M_⊙ instead do not lose enough mass to expose the layers that have been processed by CNO burning.

Zoom In Zoom Out Reset image size

Interestingly, most massive stars are found in binary systems (see e.g. [131]) and are close enough to each other to interact. Sana et al (2012) [132] found that more than 50% of all O-type stars (stars with initial masses from 15 M_⊙ and higher) will interact with their companion during their lifetimes. More than 25% of these stars will interact with their companion even before the end of the main sequence [133]. These interactions influence both the evolution of the stars, and the ²⁶Al yields [125, 134]. The process resulting from binary interaction that mostly influences the yields is the mass-transfer between the two stars due to Roche lobe overflow. The evolution of the primary (i.e. the initially heavier star of the binary) can be strongly affected by this, as compared to their single-star counterparts. For example, the time at which mass loss starts and the amount of mass lost by the star can be influenced by binary interaction. The main effect of the mass-transfer is that more mass is lost from the primary stars, uncovering the layers rich in ²⁶Al that otherwise would not be uncovered if the star was evolving in isolation (for more details see [125]). The ²⁶Al injected into the ISM by binary systems is a combination of the ²⁶Al present in the layers stripped by mass-transfer and expelled, and the ²⁶Al present in the deeper layers of the star that are driven off by the stellar winds (see figures 10 and 11 of [125]). The effect of binary interactions can be seen in figure 7 by comparing the red and the blue lines. The yields of the primary stars increase strongly below 30–40 M_⊙, up to a factor of 100 for the least massive stars (10–15_⊙). Above 30–40 M_⊙, the binary interactions do not increase the yields of the stars anymore, as the winds are already very efficient in ejecting ²⁶Al.

Aside from massive star binaries and Wolf–Rayet stars, VMSs can also contribute significantly to the ²⁶Al enrichment of the ISM. The opinion widely held until 2010 was that the most massive stars in the Universe are of an order of 100–150 M_⊙. More recent studies, however, have found evidence for the existence of VMSs of higher masses [135–137]). These stars are thought to dominate the mechanical energy input and ionising radiation [138, 139] of star-forming regions such as the Tarantula nebula. Moreover, the mass-loss rates of VMSs have been shown theoretically [140] and observationally [136] to be larger than previously assumed via mass-loss rates of Vink et al 2001 [122]. The discovered upturn in mass loss for the most massive stars occurs at a transition point where optically thin O-star winds transform to becoming optically thick [140, 141]. Recent population synthesis models [142] including stellar evolution models for VMSs [129, 143] with the new higher mass-loss rates [140] need to be constructed to predict the likely dominant contribution of VMSs to the galactic ²⁶Al emission budget. We expect such contributions to be high because VMSs are nearly homogeneous stars: their convective core during the main sequence phase extends over more than 90% of the total mass of the star. This means that almost all ²⁵Mg initially present in the star can be converted into ²⁶Al via proton captures and the reservoir of matter enriched in newly produced ²⁶Al may correspond to almost the whole star. Furthermore, VMSs are very luminous and are expected to have strong radiation-driven winds. These two factors lead us to predict large amounts of ²⁶Al to be ejected from these stars. For example, the non-rotating 500 M_⊙ model by [129] shown in figure 7 loses about 450 M_⊙ during the main sequence, leading to an ²⁶Al yield of 7.6 × 10⁻³ M_⊙. This is a factor 100 more ²⁶Al than for a 60 M_⊙ star computed with the same code. Of course, these stars are very rare, however, their yields are so large that even a few events can have a strong impact on the galactic ²⁶Al budget.

The main uncertainties that affect the production of ²⁶Al in massive stars are of two types: those involving the nuclear reaction rates, in particular the ²⁵Mg(p, γ)²⁶Al rate and its branching ratio to the ground state of ²⁶Al, and the ²⁶Al(p, γ)²⁷Si rate; and those involving the physics input of the stellar models, including: the size of the convective core, the mass-loss rates, either induced by radiative line driven winds or by mass loss due to mass-transfer episodes in close binaries, and the mixing processes in the radiative zones of the stars, such as turbulence induced mixing due to rotation. An increase either in either the size of the convective core, the mass-loss rates, or the mixing in radiative zones, would lead to an increase of the ²⁶Al yields. See e.g. the discussion in Palacios et al [80].

2.2.2. CCSN from massive stars, hydrostatic and explosive nucleosynthesis

Several studies have been dedicated to the production of ²⁶Al in massive stars including their following CCSN explosions [9, 75, 81, 144]. On the one hand, it is expected and shown by theoretical stellar simulations that the H-burning and C-burning ashes are ²⁶Al-rich, as compared to the rest of the ejecta because these regions are rich in the protons needed to produce ²⁶Al (protons are produced during C-burning via the ¹²C(¹²C, p)²³Na reaction). On the other hand, during He-burning there are no protons available to efficiently produce ²⁶Al, and if there is any ²⁶Al already present here, it is typically destroyed by neutron captures, with neutrons produced by the ¹³C(α, n)¹⁶O and ²²Ne(α, n)²⁵Mg reactions. In more advanced stages like explosive O-burning and Si-burning, neither ²⁵Mg or ²⁶Al are efficiently produced [75].

While these general guidelines are derived from the nuclear astrophysics properties leading to the nucleosynthesis of ²⁶Al, stellar models show significant variations due to intrinsic properties and simulation parameters. In figure 8 we show the ²⁶Al mass fraction profile as function of mass coordinate for a M = 15 M_⊙ star and a M = 20 M_⊙ star model after the explosion [145], together with the profile of other major isotopes indicative of the stellar structure, and of ²⁵Mg, the seed nucleus for the production of ²⁶Al. Moving from the outer mass coordinate towards the center of the star, the first ²⁶Al peak is observed in the H-burning layers for both models, this derives from destruction of most of the initial ²⁵Mg via proton capture. Just below the H-burning layers, in the upper part of the H-poor, He-rich shell there is a significant amount of ²⁶Al left from the burning that happened before the CCSN. For the 15 M_⊙ model, for example, the peak is around a mass fraction of 2 × 10⁻⁵. This peak is due to either direct mixing of ²⁶Al from the H-burning region just above, or to mixing of ¹⁴N, which provides protons via the ¹⁴N(n, p) ¹⁴C reaction, using the neutrons produced by ¹³C(α, n)¹⁶O. In the 20 M_⊙ model this peak abundance is much more restricted in mass than in the 15 M_⊙ model. At the bottom of the He shell, instead, ²⁶Al is completely destroyed by the neutron captures triggered during the CCSN explosion in this region of the stars (the so-called 'neutron burst', or n-process, [146–148]). Further differences between the 15 and the 20 M_⊙ models are seen in the C-burning ashes. While the ²⁶Al abundances before the explosion are comparable in the two cases (with a mass fraction of the order of few 10⁻⁶), the 20 M_⊙ model shows a much stronger explosive production than the 15 M_⊙ model, visible at a mass coordinate roughly 3.6 M_⊙, and comparable to the abundance made by H-burning.

Zoom In Zoom Out Reset image size

Alternative nucleosynthesis conditions from those described above may also be present and provide a significant contribution to the amount of ²⁶Al ejected by a CCSN, for instance, these can be related to convective-reactive events during the hydrostatic evolution of the progenitor star. The work of [62] showed that a significant amount of ²⁶Al can be also produced in the explosive He-burning ejecta, following the ingestion of H in the convective He-shell [149, 150].

Finally, neutrinos from the collapsing stellar core leading to the ν-process [151, 152] also affect the production of ²⁶Al in two ways: directly via the ²⁶Mg (ν_e , e⁻) reaction, and indirectly by providing additional protons for the ²⁵Mg (p, γ) reaction, mostly from ²⁰Ne $({\nu }_{x},{\nu }_{x}^{\prime} p)$ and spallation from other abundant nuclei. The cross sections for the neutrino-induced reactions are very well constrained [153], in particular, the Gamow–Teller strength for ²⁶Mg (ν_e , e⁻) has been determined by charge-exchange reactions [154]. The contribution of this process to ²⁶Al, however, is very sensitive to the rather uncertain neutrino-energy spectrum. Depending on the neutrino energies, the ν process may lead to an increase of the ²⁶Al yields by 10%–40% [75, 153].

Classical novae are the stellar explosions that take place in stellar binary systems, consisting of a compact, white dwarf star and a low-mass companion, typically a K or M main sequence star, although observations increasingly reveal more evolved companions. Novae exhibit a sudden rise in optical brightness, with peak luminosity reaching 10⁴–10⁵ solar luminosity. During the explosion, roughly 10⁻⁵–10⁻³ M_⊙ of material is ejected into the interstellar medium, at a speed of several 10³ km s⁻¹. Novae are expected to recur with typical periodicity between 1 and 100 year (recurrent novae) and 10⁴–10⁵ year (classical novae).

The main nuclear reactions involved in the production and destruction of ²⁶Al in novae, and their associated uncertainties, have been discussed in several papers (e.g. [155, 156]) and are illustrated in figure 6). The synthesis of ²⁶Al in novae requires the presence of some seed nuclei, such as ^24,25Mg, or to some extent, ²³Na, and ^20,22Ne. Since novae do not achieve high enough temperatures to power CNO-breakout, ²⁶Al production requires an underlying ONe white dwarf (rather than a CO white dwarf) and some mixing to occur at the interface between the outer layer of the core and the envelope. The main nuclear reaction path leading to ²⁶Al is ²⁴Mg(p, γ)²⁵Al(β⁺)²⁵Mg(p, γ)^26gAl, whereas destruction is dominated by the ^26gAl(p, γ)²⁷Si reaction. The current main source of nuclear uncertainty comes from the rate of the ²⁵Al(p, γ)²⁶Si reaction: because ²⁶Si only decays to the isomeric state of ²⁶Al this reaction determines the fraction of the nuclear path that proceeds through the isomeric ²⁶ⁱAl state, via the decay of ²⁶Si thus by-passing ^26gAl synthesis.

Already before the discovery of ²⁶Al in the interstellar medium by the HEAO-3 satellite through the detection of the 1809 keV γ-ray line [157, 158], Ward [159] suggested that ²⁶Al could be produced efficiently in astrophysical environments such as classical nova outbursts, characterized by a rapid rise to maximum temperatures around T_peak ∼ (2–3) × 10⁸ K, followed by a relatively fast decline. One-zone, explosive H-burning nucleosynthesis studies corroborated this idea (see, e.g. [160, 161]), and concluded that while classical novae might produce sufficient amounts of ²⁶Al to reproduce some of the observed isotopic anomalies found in meteorites, they would not represent major galactic factories of ²⁶Al. These calculations, however, assumed solar composition (or CNO-only enhanced) envelopes. With the advent of models of nova explosions on ONeMg white dwarf stars [162], one-zone nova nucleosynthesis models predicted large amounts of radioisotope (such as ²²Na and ²⁶Al) in their ejecta [163, 164], suggesting that these novae might represent significant, though still not dominant, sources of the Galactic ²⁶Al.

The following 1D hydrodynamic simulations [165, 166] stressed the crucial role played by convection in carrying a fraction of the fresh ²⁶Al synthesized at the base of envelope to the outer, cooler layers where destruction through proton captures could be prevented. Still, the composition adopted for the underlying ONeMg white dwarfs adopted in these models was too crude as it was based on calculations of hydrostatic C-burning nucleosynthesis by Arnett and Truran [167] with mass fraction ratios X(¹⁶O):X(²⁰Ne):X(²⁴Mg) of 1.5:2.5:1. Stellar evolution models of intermediate-mass stars [168, 169] revealed that ONe white dwarfs are instead made basically of ¹⁶O and ²⁰Ne, with above ratios of 10:6:1. The dramatic reduction in the ²⁴Mg seeds resulted in a significant decrease in the contribution of novae to the galactic ²⁶Al predicted by the first 1D hydrodynamic simulations from accretion to ejection for a realistic composition of the underlying white dwarf, and with updated nuclear reaction rates [170, 171].

Since the late 1990s, all hydrodynamic 1D nova simulations systematically resulted in some ²⁶Al production. This includes the most recent 12321 nova models [172], which include the effect of the inverse energy cascade that characterizes turbulent convection in nova outbursts on the time-dependent amount of mass dredged-up from the outer white dwarf layers, and a time-dependent convective velocity profile throughout the envelope, as computed by 3D simulations [173–175]. While these state-of-the-art models yield more massive envelopes than those previously reported, and result in more violent outbursts characterized by higher peak temperatures and greater ejected masses, their ²⁶Al yields are similar to previous estimates for ONe novae (see [172] for details).

A crude estimate of the contribution of novae to the amount of ²⁶Al present in our Galaxy can be obtained from [163, 170]:

$$\begin{eqnarray}&&M{(}^{26}\mathrm{Al})\sim \tau {(}^{26}\mathrm{Al})\,f(\mathrm{ONe})\,{M}_{\mathrm{ejec}}\,X{(}^{26}\mathrm{Al})\,{R}_{\mathrm{nova}},\end{eqnarray} \tag{ 1 }$$

where M_ejec is the mean ejected mass during a nova outburst, X(²⁶Al) is the mean mass fraction of ²⁶Al in the ejecta, f(ONe) is the fraction of ONe novae (typically, 1/3; see Livio and Truran 1994), R_nova is the nova rate ($\sim {50}_{-23}^{+31}$ year⁻¹ [176]), and τ(²⁶Al) is the mean lifetime of ^26gAl (1 Myr). From these estimates, and adopting a relatively favorable ONe nova model (e.g. M_ejec(²⁶Al) ∼ 2 × 10⁻⁸ M_⊙ [171]), we obtain an upper limit to the contribution of novae to the Galactic ²⁶Al content of ≤ 0.34 M_⊙. This corresponds to about 12% of the Galactic ²⁶Al (∼2.8 ± 0.8 M_⊙ [177]) and is in qualitative agreement with the analysis of COMPTEL/CGRO 1.809 MeV ²⁶Al emission map [177, 178], which favors younger progenitors (i.e. WR stars and CCSN, as discussed in section 2.2). However, it is worth noting that this estimate is affected by large uncertainties, since the mean ejected mass per nova outburst and the variation of the nova rate since the formation of our Galaxy are not well constrained.

The rate of the ²⁶Al production reaction is dominated by resonant proton captures to levels above the proton threshold at 6306.33(6) keV [181] in ²⁶Al. Direct proton captures to bound states in ²⁶Al and the contribution from the subthreshold (3⁺) resonance at ${E}_{{\rm{res}}}=-24.86(10)$ keV are negligible compared to the resonant captures at temperatures above ≈0.006 GK [182]. Therefore, we focus here on the resonant proton captures. Table 1 summarises the available data on the excitation energies, spins and parities as well as the resonance energies and strengths for the relevant states in ²⁶Al. The ground state spin and parity of ²⁵Mg is 5/2⁺, and therefore ℓ = 0 proton captures populate states with J^π = 2⁺ or 3⁺ in ²⁶Al, ℓ = 1 proton captures states with J^π = 1⁻, ..., 4⁻, and ℓ = 2 states with J^π = 0⁺, ..., 5⁺. All states, except the J^π = (7) state at 6695 keV, can be populated via ℓ = 0 − 2 proton captures, however, many of the spin-parity assignments are still tentative (see table 1) and further studies are needed.

Table 1. Excitation energies (E_x ) together with the spins and parities (J^π ) for the excited states above the proton separation energy (S_p = 6306.33(6) keV [181]) in ²⁶Al. The excitation energies, spins and parities are from from [1] unless stated otherwise. The resonance energies have been recomputed from the excitation energies include a correction for atomic binding of ΔB_e = − 1.14 keV. The resonance energies (E_res), and experimentally determined resonance strengths ω γ for the relevant states are given. The resonance strengths are the total resonance strengths—the f₀ factors are the branching of the resonance to the ground state of ²⁶Al. The f₀ has been recomputed [183] from the listed values in the ENSDF repository including the full cascade to the ground state and the isomer. Only states up to E_x = 6800 keV are listed.

Ex (keV)	Jπ	Eres (keV)	ω γ (eV)	fa
6280.33(9)	(3+)	–24.85(11)	${\theta }_{p}^{2}=0.0127{(26)}^{0}$	0.770(3)
6343.46(8)	4+ [184]	38.29(10)	4.9(21) × 10−22 b [184]	0.79(5)
6363.99(8)	3+	58.81(10)	2.9(5) × 10−13 [185]	0.81(5)
6398.64(21)	2− [186]	93.46(22)	3.5(4) × 10−10 [187, 188]	0.67(4) [188, 189]
6414.46(10)	(0 to 2+)	109.28(12)	2.3(1) × 10−11 c [190]	0.0042(6) d
6436.44(11)	(3 to 5+)	131.26(13)	≤ 2.5 × 10−10 [187]	0.727(3)
6495.94(7)	(3 to 5+)	190.76(9)	5.2(36) × 10−7 e	0.75(2) [187]
6550.68(7)	(4+, 5−)	245.50(9)	55.0(63) × 10−7 [179]	0.80(1)
6598.32(16)	(5+)	293.14(17)	45.0(52) × 10−6 [179]	0.71(1)
6610.40(6)	(3−)	305.22(8)	2.8(3) × 10−2 f	0.878(10) g
6680.45(7)	(2+)	375.27(9)	6.0(6) × 10−2 [191]	0.67(1)
6724.25(7)	(4−)	419.07(9)	7.4(2) × 10−2 [191]	0.96(1)
6783.79(5)	(2−)	478.61(8)	7.3(11) × 10−2 [179]	0.56(1)
6789.30(4)	(3−)	484.12(7)	60.0(77) × 10−3 [179]	0.90(1)

^a Spectroscopic factor C² S = 0.022 from Endt and Rolfs [192], single-particle proton width calculated from the parameters given by Iliadis [193]. An uncertainty on the spectroscopic factor of 20% has been assumed. ^b Expectation and variance of the resonance strength using ω γ = 4.5 × 10⁻²² and a factor 1.5 uncertainty in [184]. ^c Expectation and variance of the resonance strength using ω γ = 2.1 × 10⁻¹¹ and a factor 1.5 uncertainty in [184]. ^d This resonance is given as f₀ = 0.71 in [182] citing then yet-to-be-published paper by Endt, de Wit and Alderliesten which is presumably [194]. The decay branches listed in [194] give f₀ = 0.0041(7). The listed γ-ray branches in the ENSDF database give f₀ = 0.0042(6). We adopt f₀ = 0.0042(6). This resonance is rather weak for both radiative capture to the ground state and isomeric state and the astrophysical impact of this reassignment is negligible. ^e Weighted average with additional estimate of systematic uncertainty of ω γ = 9.0(6) × 10⁻⁷ [187] and ω γ_g = 1.1(2) × 10⁻⁷ and f₀ = 0.74(1) [191]. ^f Weighted average 3.07(13) × 10⁻² [195] and ω γ = 2.1(2) × 10⁻² and f₀ = 0.87(1) [191]. ^g f₀ = 0.91(1) using ENSDF values.

The first studies on excited states above the proton threshold in ²⁶Al were carried out via ²⁵Mg(³He,d) reactions with the Tandem Van de Graaff accelerator at the University of Pennsylvania in late 1970s [196]. Several states were discovered and angular momenta assigned for the proton transfers based on the angular distribution of the cross sections and distorted-wave Born approximation analysis. Champagne et al did a thorough investigation of the ²⁵Mg(³He,d) reaction at the Wright Nuclear Structure Laboratory MP Tandem Van de Graaff accelerator in early 1980s [197, 198]. States at 6343 and 6400 keV were assigned as 3⁺, the latter only tentatively. Proton widths and resonance strengths were deduced for many of the states by scaling from the determined proton width for the 374 keV resonance. The ²⁵Mg(³He,d) reaction was revisited at the Princeton AVF cyclotron, and it was found that the 6343 keV state is actually the 6364 keV (3⁺) state and the 6400 keV is a J = 2 state at 6398 keV [199]. The state reported at 6343 keV in [197] was observed using the ²⁷Al(³He,α)²⁶Al but had been misassigned as a ²⁵Mg+p resonance. It was not populated in the ²⁵Mg(³He,d) reaction in [199], suggesting that the 6343 keV state is not a strong single-proton state and therefore does not play a crucial role in the overall reaction rate. The proton width for the 374 keV resonance was re-determined, using the γ-ray branching ratio together with previous data, in [199], and found to be significantly lower, Γ_p = 0.82(20) eV [199], than the previously determined value Γ_p = 460(129) eV [198]. The calculated resonance strength for the 92 keV resonance (ω γ ≤ 2.7 × 10⁻¹³ eV [199]) is significantly lower than the recently measured value, suggesting that the proton width might have been underestimated for the 374 keV resonance in [199]. Indeed, the resonance strength for the 92 keV resonance was revised to 8.5 × 10⁻¹¹ eV in [200]. This is already much closer to the recently measured value ω γ = 2.9(6) × 10⁻¹⁰ [187].

The doublet of states at 6343 and 6364 keV was confirmed in [201], where J^π = 2⁻ was proposed for the 6399 keV state. A spin of (1⁺, 2) for the 6399 keV state has been adopted in the latest Nuclear Data Sheet [1] instead of the previous suggestions of 3⁺ [197, 198] and 2⁻ [199, 201]. More recently, angular distribution data, measured with the Gammasphere detector array for the two most intense γ-ray transitions from the 6399 keV state, support a J^π = 2⁻ assignment for this state [186].

The resonance widths and strengths for the ²⁵Mg(p, γ)²⁶Al reaction have been studied directly using a low-energy proton beam and ²⁵Mg target, for example in [202–205]. In addition, spectroscopic factors for proton-unbound levels in ²⁶Al and their influence on stellar reaction rates have been investigated, e.g. in [206]. For low-energy resonances, the strength is almost entirely determined by the proton width Γ_p : $\omega \gamma =\omega \tfrac{{{\rm{\Gamma }}}_{p}{{\rm{\Gamma }}}_{\gamma }}{{\rm{\Gamma }}}\approx \omega {{\rm{\Gamma }}}_{p}$, when Γ_p ≪ Γ_γ . The proton width depends on the spectroscopic factor, C² S, and the single-particle width Γ_s.p. as Γ_p = C² SΓ_s.p.. For a nlj proton-transfer, single-particle widths scale with the center-of-mass-energy as shown in figure 2 of [184]. Spectroscopic factors can be obtained from measurements [196, 200, 206], or from shell model calculations. For example, the strength for the 58 keV resonance has been recently extracted based on spectroscopic factors determined in the ²⁵Mg(⁷Li, ⁶He)²⁶Al reaction at the Q3D magnetic spectrometer of the HI-13 tandem accelerator [185].

Direct underground measurements of several resonances have been reported by the LUNA collaboration. The rate has also been recently measured underground at JUNA [207] and these data are being analysed. Limata et al [195] measured the strength for the 304 keV resonance from the emitted γ-rays and found it to be 30.7 ± 1.7 meV, in good agreement with earlier work, with the exception of the AMS work of Arazi et al [191]. Limata et al also performed an AMS study and could not reproduce the result of Arazi et al [191] but instead agreed with their own γ-ray based value. They, therefore, neglected the Arazi et al [191] value in their recommended strength of 30.8 ± 1.3 meV, which averaged their result with that of the NACRE compilation [208]. This result was then used as a reference strength for a study of the resonances at 92, 130 and 189.6 keV by Strieder et al [187]. Only an upper limit could be determined for the 130 keV resonance and it is not expected to contribute to the astrophysical rate.

Endt et al [182] studied the astrophysical aspects of the ²⁵Mg(p, γ)²⁶Al reaction and made thorough compilations of the excited states in ²⁶Al [209]. Iliadis et al [184] then reinvestigated the previous literature data in 1996, and reported a new suggested rate for the reaction. In particular resonances at E_r = 58 and 92 keV were found to dominate the reaction rate in the temperature region 0.02–0.15 GK [184] relevant for hydrogen burning in stars. At 0.1–1.5 GK, the resonances at 190, 304, 374, and 418 keV, start to dominate the reaction rate as shown in [191].

We have recalculated the reaction rates using the RatesMC code. The resonance energy correction results in an effective increase in the resonance energies of 1.14 keV compared to the existing literature values based on ${E}_{{\rm{res}}}={E}_{{x}}-{S}_{p}$. For resonances with only upper limits for the resonance strengths, the reduced widths are estimated by randomly sampling from a Porter–Thomas distribution using the experimental upper limit as an hard cutoff value. This is not entirely statistically accurate since the experimental upper limits should be quoted to some confidence level with an associated probability density function used to derive the upper limit at that confidence level [210] (though these data are frequently lacking in the published studies). However, the effect of this is small (see [210–212] for more details). The corresponding contribution plots for the resonances are shown in figures 9 and 10. The 93- and 305 keV resonances dominate over the astrophysically relevant temperature range and both resonances have been measured directly by LUNA. The 59 keV resonance strength has thus far remained inaccessible for direct measurements. The corresponding re-evaluated reaction rates to the ground state and isomeric state of ²⁶Al are given in tables 8 and 9. In addition to the proton-capture rate, the de-excitations from the populated states in ²⁶Al to the ground and isomeric states of ²⁶Al need to be taken into account. The rates are typically multiplied by the corresponding ground state branching fraction f₀, see, e.g. [184]. Thermal excitation between the states, discussed in section 4, complicates the situation.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As recently evident in the study of Lotay et al, there remains some uncertainty and occassional inconsistencies in the ground state branching fractions (f₀) for each resonance. For example, the f₀ value of the E_r = 95 keV resonance was revised from f₀ = 0.52 ± 0.02(stat. ) ± 0.06 (syst.) [186] to f₀ = 0.76(10) [189]. Similarly, on the basis of the γ-ray branching information stored in the ENSDF database, the f₀ value for the astrophysically unimportant E_r = 109 keV resonance has values ranging from f₀ = 0.0041(7) to f₀ = 0.71 depending on the source. New, independent measurements of these ground state branching fractions are advisable in order to validate the existing results.

Proton capture on ²⁶Al provides the main destruction mechanism for ²⁶Al in several stellar sites such as classical novae, convective core hydrogen burning in massive stars, and hydrogen burning in intermediate-mass AGB stars. The uncertainties in the ²⁶Al(p, γ)²⁷Si reaction rate at the temperatures present in these environments can result in large variations in the ²⁶Al abundance. For example, sensitivity studies show that this uncertainty leads to variations of up to two orders-of-magnitude in AGB calculations [89]. The situation is further complicated by the existence of the 228 keV isomeric state in ²⁶Al, which must be treated separately from the ground state at temperatures below 0.4 GK, as discussed above [216]. Thus, the ²⁶Al^g(p, γ)²⁷Si and ²⁶Al^m(p, γ)²⁷Si reaction rates must be determined independently to understand the destruction of ²⁶Al in the stellar sites described above. Due to the impact of these reaction rates on the abundance of galactic ²⁶Al, there have been a wide variety of direct and indirect measurements aimed at determining these rates.

For ²⁶Al^g (p, γ)²⁷Si resonances at E_r > 190 keV, which have less of an influence on the destruction of ²⁶Al, the strengths are well constrained by previous direct measurements [217, 218]. The resonance around E_r = 184–190 keV is an important resonance but there is some disagreement in its resonance energy. The most recent direct measurement of ²⁶Al^g(p, γ)²⁷Si was completed in inverse kinematics at TRIUMF using the DRAGON recoil separator with an intense ²⁶Al ion beam (∼2.5 × 10^{9 26}Al s⁻¹). This study determined the energy and strength of the resonance that dominates the rate in classical novae to be E_r = 184 ± 1 keV and ω γ = 35 ± 7 μeV, respectively [219], resulting in an increase of 20% in ²⁶Al^g production in nova models when compared with the previous unpublished values [217]. The properties of this resonance are consistent with a p-wave assignment for this resonance J^π = (7 − 13)/2⁻ based on the spectroscopic factor from a ²⁶Al(³He, d)²⁷Si measurement by Vogelaar et al [220]. A subsequent γ-ray spectroscopy study of ²⁷Si gave a J^π = 11/2⁺ assignment to a state at E_x = 7651.9(6) keV [221, 222] based on comparison with the E_x = 7948 keV state in the mirror nucleus, ²⁷Al, corresponding to an ℓ_p = 0 resonance at E_r = 188.6(4) keV. A later ²⁶Al(d, p)²⁷Al study clarified the spin and parity of the mirror state in ²⁷Al as J^π = 11/2⁻ [214]. There is now a consensus that the resonance between E_r = 184 − 190 keV has a J^π = 11/2⁻, ℓ_p = 1 assignment. The energy of this resonance remains a matter of some disagreement and there is not, at present, any way of resolving this discrepancy. To account for this we have computed the resonance energy with an inflated uncertainty following the procedure set out in [223].

While the measurement of Ruiz et al [219] significantly reduced the uncertainty in ²⁶Al^g (p, γ)²⁷Si for nova nucleosynthesis, lower energy resonances dominate this reaction rate at the lower temperatures found in AGB and massive stars. At these lower energies, direct measurements become unfeasible with currently available ²⁶Al beam intensities and indirect measurements are required. Specifically, the 127 keV resonance in ²⁷Si is thought to dominate the reaction rate in these environments as it is the only known ℓ_p = 0 proton-capture resonance in this energy regime [224]. This and other resonances have been studied indirectly in a variety of measurements including transfer and γ-ray transition studies (e.g. [220, 221, 225, 226]). More recently, there have been multiple studies in inverse kinematics with unstable ²⁶Al beams including two measurements of resonances in the mirror ²⁷Al nucleus in inverse kinematics via the ²⁶Al(d, p)²⁷Al reaction [107, 214] and a measurement of states in ²⁷Si via ²⁶Al(d, n)²⁷Si [227]. In these studies, spectroscopic factors of states in ²⁷Al and ²⁷Si were measured to determine the resonance strengths of those states. The values of the strength of the 127 keV resonance obtained via the mirror studies [107, 214] are in agreement with each other, but a factor of four higher than the previously accepted value [220]. However, there are worrying discrepancies for this resonance between the resonance information reported in [107] (C² S = 0.0102(21) and $\omega \gamma ={2.6}_{-0.9}^{+0.7}\times {10}^{-8}$ eV) and [228] (C² S = 0.0093(7) and ω γ = 5.7(4) × 10⁻⁸ eV), i.e. a lower spectroscopic factor is calculated to result in a larger partial width and resonance strength. Based on this, some of the discrepancies between these experimental results are likely due to the theoretical treatment of the experimental data. Revisiting the original experimental studies and treating them with consistent experimental methods may help to resolve these discrepancies and will provide better constraints on ²⁶Al destruction by proton capture. As an example, the later study of [228] notes that the results of [214] has a technical fault in the number of nodes for the computation of the transfer amplitudes. Notwithstanding these concerns, the 127 keV resonance dominates the reaction rate at relevant temperatures for ²⁶Al nucleosynthesis in massive and AGB stars. While the ²⁶Al(d, n)²⁷Si measurement only yielded an upper limit on the spectroscopic factor of this state, the results were consistent with these mirror studies [227]. Clearly, a direct measurement of this resonance strength—one which obviates some of the theoretical inconsistencies of the transfer data is a high priority for future studies once more intense ²⁶Al beams become available.

As discussed above, at temperatures below around 0.4 GK, the isomer and ground state must be treated as separate nuclei and thus the ²⁶Al^m (p, γ)²⁷Si reaction rate should be determined independently from proton capture on the ground state. However, previous determinations of this reaction rate were typically scaled from the ²⁶Al^g (p, γ)²⁷Si rate, despite the large spin difference between the ground (5⁺) and isomeric (0⁺) states, as little experimental data for proton capture on the isomer was available [229]. A direct measurement of the strength of the E_r = 447 keV resonance in ²⁶Al^m (p, γ)²⁷Si is currently the only direct resonance information for this reaction [230]. A measurement of the ²⁷Al(³He, t)²⁷Si*(p)²⁶Al^g,m and ²⁸Si(³He, α)²⁷Si*(p)²⁶Al^g,m reactions was performed at the Wright Nuclear Structure Laboratory to indirectly determine the ²⁶Al^m (p, γ)²⁷Si reaction rate based on experimental information [231]. While this study was only able to put a lower limit on the reaction rate, as proton decays from states in ²⁷Si at energies of E_r ≥ 445 keV could be measured, this study confirmed that different resonances in ²⁷Si dominate the two rates. A similar study of the ²⁷Al(³He, t)²⁷Si*(p)²⁶Al reaction using the same Enge Split-Pole spectrograph, now installed at the John D Fox Accelerator laboratory at Florida State University, was recently performed detecting proton decays down to E_r ≃ 300 keV in order to further improve the reaction rate determination [232].

Alongside these charge-exchange reaction studies, a complementary investigation of the γ-decaying properties of ²⁶Al^m + p resonant states was performed at Argonne National Laboratory [222, 233, 234]. In that work [222, 233, 234], a ¹²C(¹⁶O, n) fusion-evaporation reaction was used to populate excited states in ²⁷Si, located above the ²⁶Al^m + p emission energy of 7691.3(1) keV [235], and the resulting γ decays were recorded with the Gammasphere detector array [236, 237]. γ decays were observed from all resonant states with energies E_r ≤ 500 keV and spin assignments were obtained from angular distribution measurements. Furthermore, by examining the mirror nucleus ²⁷Al over a suitable energy range, it was possible to propose parity assignments for key resonances. In [222, 233, 234], it was concluded that a J^π = 5/2⁺ state at E_r = 146.3(3) keV is likely to dominate the astrophysical ²⁶Al^m(p, γ) reaction for low stellar temperatures, while a proposed J^π = 3/2⁻ state at E_r = 378.3(30) keV governs the rate for temperature, T > 0.15 GK. However, it should be noted that due to the very high excitation energies of ²⁶Al^m + p resonant states, the accurate matching of mirror states is extremely challenging. In particular, it is very difficult to know how mirror shifts are affected when both the ²⁷Si and ²⁷Al systems become particular unbound, which is the case for a number of the proposed analog pairs.

More recently, a measurement of the ²⁶Al^m (d, p)²⁷Al reaction in inverse kinematics was performed using an isomeric ²⁶Al beam produced at the ATLAS facility at Argonne National Laboratory [215]. Similar to the studies of Pain et al [107] and Margerin et al [214], this measurement aimed to determine spectroscopic factors of states in ²⁶Al(d, p)²⁷Al reactions that are mirrors of the ²⁶Al^m + p resonances in ²⁷Si. Using this mirror symmetry, an upper limit of the reaction rate was determined, which is dominated by resonances at E_r = 146 and 378 keV over astrophysically relevant temperatures. The ²⁶Al^m (p, γ)²⁷Si reaction rate determined here is smaller than that for the ground state by an order of magnitude or more at T₉ ≤ 0.3 GK, implying that destruction via the isomer is not significant in most stellar sites. However, further study of resonances in ²⁷Si both directly and indirectly is still warranted.

We have recomputed the ²⁶Al(p, γ)²⁷Si reaction rates (i.e. for the ground and metastable states) using the RatesMC code [211] and the information in tables 2 and 3. The corresponding contribution plots for the resonances are shown in figures 11 and 12. Resonances for which there is no measured proton width or resonance strength have been treated by assuming that the reduced proton widths are drawn from a Porter–Thomas distribution with mean θ² = 0.0045 with a factor of 3 variation on that mean value. This factor variation is based on the observed scatter in the mean of the Porter–Thomas distribution determined from experimental results of proton capture and scattering reactions. For more details about this assumption including the data upon which this assumption is based, see the discussion in section 5.2.1 of [210] and the experimentally determined spread in the reduced widths reported in figure 4 and section IV.B of [212]. Experimental upper limits are used to truncate the distribution where appropriate. There are a number of different sources for the resonance information for the two reactions which have been discussed in the text above. The sources for different spectroscopic information used in the calculations of the rates are given in tables 2 and 3. Of particular note in the present evaluation is the increased uncertainty in the resonance energy of the E_r = 188 keV resonance due to the disagreement between the resonances energies determined with DRAGON and γ-ray spectroscopy, and the probable need for a reconsideration of the various ²⁶Al(d, p)²⁷Al mirror studies to try to account for systematic differences between experiments before a full re-evaluation of the ²⁶Al^m (p, γ)²⁷Si reaction with realistic uncertainties.

For the ²⁶Al^m (p, γ)²⁷Si reaction rate, the rate has been recalculated only using known level information. While this information is somewhat lacking in the region of interest, the recent direct measurement of the 447 keV resonance strength, which dominates the reaction rate from 0.3 to 2.5 GK [230], now allows for a more accurate reaction rate determination. Nevertheless, some caution is required in the interpretation of the ²⁶Al^m (p, γ)²⁷Si reaction rate since many of the known states in ²⁷Si have spins and parities identified from fusion-evaporation reactions [221]; these reactions introduce a large amount of angular momentum and low-spin states may readily be missed in these experiments. Studies of low-spin states are therefore encouraged, especially indirect measurements of the 218 keV resonance, which is likely to dominate the reaction rate at temperatures below 0.3 GK. Comparison with the mirror nucleus, ²⁷Al, which has been rather well studied may help to rule out the existence of additional states.

The sensitivity study by Iliadis et al [241] has shown that the ²⁶Al(n, p)²⁶Mg and ²⁶Al(n, α)²³Na reactions are of importance for the determination of ²⁶Al abundances produced during hydrostatic C-shell and explosive Ne/C-shell burning phases in massive stars. These reactions involve excited states in ²⁷Al within about 500 keV above the ²⁶Al + n threshold (S_n = 13057.91 (12) keV) where the level density ρ is extremely high ($\rho \equiv {\rm{d}}{N}({E}_{x})/{{\rm{d}}{E}}_{x}\gt 80$ MeV⁻¹ [242]). These states decay by proton or α-particle emission because of the lower ²⁶Mg + p and ²³Na + α thresholds (S_p = 8271 keV, S_α = 10092 keV).

At present, only few experimental data on both reactions are available. The first measurement of the ²⁶Al(n, p₁) ³⁸ reaction was performed by Trautvetter and Käppeler using a quasi-Maxwellian neutron spectrum at around kT = 31 keV [243]. This was followed by a more comprehensive study in 1984 [244] using neutron spectra around various energies (40 meV, 31 keV, 71 keV, and 310 keV), including also the ²⁶Al(n, p₀) channel, which is 3-100 times weaker than (n, p₁), and providing an upper limit on the ²⁶Al(n, p₂) channel at 40 meV. Roughly 10 years later, Koehler et al [245] determined ²⁶Al(n, p₁) and ²⁶Al(n, α₀) cross sections using the neutron time-of-flight technique at the Los Alamos Neutron Science Center (LANSCE). The ²⁶Al(n, p₁) cross section was found to be in disagreement with the earlier data [244] in the limited neutron energy range of overlap (at around 30 keV), leading to a higher stellar reaction rate by a factor of about two. Roughly 15 years ago, De Smet et al reported a measurement of ²⁶Al(n, α₀₊₁) reaction cross sections using the GELINA neutron time-of-flight facility at the Geel Joint Research Centre of the European Commission [246]. The GELINA measurements overlapped in the lower neutron regime with the the LANSCE experimental study (the maximum neutron energy for the (n, α₀) study was 10 keV [245]) and also data at higher neutron energies were obtained. De Smet et al identified several new resonances for the ²⁶Al(n,α) reaction. Both, Koehler et al and De Smet et al, provided resonance strengths for a resonance at around 6 keV neutron energy, however, their results disagree by a factor of 1.8. This leads to a large discrepancy of the astrophysical reaction rates deduced from these data.

Additional data on states above the neutron separation threshold and resonance strengths were obtained by Skelton et al [247], who performed an experiment using the time-reverse ²⁶Mg(p, n)²⁶Al and ²³Na(α, n)²⁶Al reactions, thereby accessing information on the (n, p₀) and (n, α₀) channels. The (n, p₁) channel is thought to be astrophysically dominant, but it is not accessible in time-reversed experiments.

Recently, there have been new direct measurements of ²⁶Al(n, p) ²⁶Mg and ²⁶Al(n, α) ²³Na reactions at the new high neutron flux beamline EAR-2 at n_TOF CERN, and at the GELINA facility [248, 249]. Both reaction cross sections were measured up to about 150 keV neutron energy, extending the previously available experimental range for energy dependent data. Resonance strengths of several resonances were provided for the first time. Astrophysical reaction rates, including all relevant branches could be deduced from the data up to about 0.6 GK stellar temperature. Resonance strengths obtained for the ²⁶Al(n, α) ²³Na reaction in [249] agree well with previous data by De Smet et al [246], leading to a good agreement of astrophysical reaction rates at low stellar temperatures. For the ²⁶Al(n, p) ²⁶Mg channel astrophysical reaction rates are higher in the energy region of overlap compared to Trautvetter et al [244], however compatible within 2 standard deviations. Resonance strengths for both reactions are lower than results by Koehler et al [245].

A summary of experimental resonance strengths for ²⁶Al + n resonances is listed in table 4 (note that these data refer to reactions on the experimentally accessible ground state of ²⁶Al).

Indirect studies have also been undertaken to determine the properties of ²⁷Al states above the ²⁶Al^g + n and the ²⁶Al^m + n thresholds, e.g. excitation energy, spin/parity, branching ratio. ²⁷Al states have been populated using proton inelastic scattering at the Tandem-ALTO (Orsay, France) and MLL (Munich, Germany) facilities. Protons were detected using the Enge Split-Pole [250] and Q3D [251] high-resolution magnetic spectrometers as the main detection system, respectively. Energies of more than 30 new ²⁷Al states have been determined above the neutron threshold up to an excitation energy of 13.8 MeV [250]. Proton inelastic scattering has a very unselective reaction mechanism that is well adapted to populate all excited states [252–254], however, on its own, it does not easily allow to identify low orbital momentum neutron capture resonances. Based on the energy of populated ²⁷Al states, the first four lowest energy resonances observed by De Smet et al [246] were populated [250]. Proton and α-particle branching ratios have also been determined for these states by coupling a DSSSD (Double-sided Silicon Stripped Detector) array to the Enge Split-Pole spectrometer [251].

At present, the main remaining challenge is to extend our present knowledge of the properties (energy and strength) of the dominating resonances up to about 500 keV above the ²⁶Al + n threshold. In the alternative approach of indirect measurements it may be interesting to complete the branching ratio measurement by the study of the ²⁶Al(d, p)²⁷Al reaction. This could be used to determine the neutron width, hence providing an indirect determination of the resonance strength. The interest of such transfer reaction is to have the same selectivity as the neutron capture reactions. Such measurements have been reported [107, 214], however, they only cover excitation energies lower than 12 MeV in ²⁷Al. Extending these studies to higher energies would be interesting, though challenging due to the increasing background, the low proton energies, and the limited ²⁶Al beam intensity.

Understanding the ²⁵Al(p, γ)²⁶Si astrophysical reaction rate is especially important in higher-temperature environments such as novae, where this reaction becomes faster than the ²⁵Al β decay (7.2 s). If the proton-capture rate on ²⁵Al is faster than β decay, ²⁶Si will be produced, which in turn decays to the ²⁶Al isomer. The isomer subsequently decays (t_1/2 = 6.3 s) to the ground state of ²⁶Mg, and production of the long-lived ²⁶Al ground state is bypassed (figure 6).

As radioactive beams of ²⁵Al are not currently available at sufficient intensities to directly measure the reaction cross section, estimates of the astrophysical reaction rate have generally been based upon knowledge of the nuclear structure of ²⁶Si. Of relevance to the rate are nuclear levels near the proton threshold at S_p = 5513.8(5) keV in ²⁶Si [255]. Especially important is identifying 2⁺ or 3⁺ levels near the threshold that could provide s-wave resonances for the ²⁵Al(p, γ)²⁶Si reaction. Shell model calculations and comparisons with the ²⁶Mg mirror nucleus indicate that levels of interest may include two 4⁺ states, a 1⁺ state, a 3⁺ state, and a 0⁺ state in the rough excitation energy range E_x = 5400–6200 keV [184, 256, 257].

Some of the first studies searching for relevant ²⁶Si states utilized measurements of the ²⁸Si(p, t)²⁶Si [258] and ²⁹Si(³He,⁶He)²⁶Si reactions [259]. Energies for astrophysically-important levels were extracted from extrapolations of lower-lying level energies previously measured with high precision using γ rays [260]. The energies of several levels near threshold were determined with greater precision, and triton angular distributions from the ²⁸Si(p, t)²⁶Si reaction provided sensitivity to the angular momentum transfers. In 2004, Parpottas et al [261] studied the ²⁴Mg(³He, n)²⁶Si reaction and largely confirmed the excitation energies extracted previously [258, 259]. More interestingly, however, Parpottas et al [261] deduced, from comparisons with statistical model calculations, that the previously-observed level at ∼5916 keV was actually the important 3⁺ level providing an s-wave resonance in the ²⁵Al(p, γ)²⁶Si reaction. This hypothesis was later deemed to be consistent with the angular distribution measured in the ²⁸Si(p, t)²⁶Si reaction [262].

As this 3⁺ resonance dominates the ²⁵Al(p, γ)²⁶Si astrophysical reaction rate, the next most important factor, after its energy, to be determined is its resonance strength. Since the proton width is expected to be much larger than the γ width [184], the resonance strength can be determined once the γ width is known. Early estimates simply assumed the width was the same as the mirror ²⁶Mg level (i.e. Γ_γ = 33 ± 14 meV) where the uncertainty comes from the uncertain ²⁶Mg lifetime and does not account for uncertainties in isospin symmetry [184, 262]. This lifetime was recently remeasured by [263] resulting in Γ_γ = 33 ± 5 meV for the mirror level. Other estimates have come from combining the proton width estimated from a ²⁵Al(d, n)²⁶Si proton-transfer measurement [264] with subsequent determinations of the γ to proton branching ratios, Γ_γ /Γ_p , to extract Γ_γ = 39 ± 21 meV [265], Γ_γ = 59 ± 29 meV [257], and Γ_γ = 71 ± 32 meV [266].

The second most important resonance contribution arises from the 1⁺ state at ∼5675 keV [255]. The resonance is expected to dominate at lower nova temperatures (T < 0.2 GK). The existence of this state was first identified by Caggiano et al [259], and was later verified in ²⁴Mg(³He, n)²⁶Si studies detecting neutrons [261] and γ rays [267–269]. The strength of this resonance is determined by its proton width and estimates currently rely on shell model calculations [256] as only upper limits have been obtained for the strength of the mirror level in ²⁵Mg(d, p)²⁶Mg studies [270].

An additional open question has been recently highlighted by studies of the ²⁴Mg(³He, n γ)²⁶Si reaction [268, 269, 271]. Population of a new level at 5890 keV has been observed and conclusively identified as a 0⁺ state [269]. This seemingly presents an open issue since the 5949 keV level had previously been assigned as 0⁺ by Parpottas et al [261], and shell model calculations indicate that there should only be one 0⁺ state in this energy range [241, 256, 257]. Various authors have speculated that the 5949 keV may in fact be the expected 4⁺ level [255, 257], but this would be at odds with the cross section comparison made by Parpottas et al [261].

Zoom In Zoom Out Reset image size

Recommended resonance values are displayed in table 5 and our newly calculated rate in figure 13. Considering the current state of our knowledge, it appears that the astrophysical ²⁵Al(p, γ)²⁶Si reaction rate is uncertain by roughly a factor of 3 at nova temperatures, primarily due to the uncertain Γ_γ of the J^π = 3⁺ resonance. Perhaps this could be improved by directly measuring the lifetime of the ²⁶Si 3⁺ level. Measurements of the neutron spectroscopic factor of the ²⁶Mg J^π = 1⁺ mirror state would also be useful to constrain the contribution of this state to the reaction rate. A repetition of the ²⁵Mg(d, p)²⁶Mg reaction study [270] at higher energies may be useful to improve the direct to compound nuclear component of the cross section.

Zoom In Zoom Out Reset image size

This discussion of the reaction rate uncertainties assumes that we have a good understanding of the ²⁶Si level structure. There are a number of open questions, however, that stretch our ability to make this claim. For instance if the 5928/5890 keV states are indeed a 3⁺/0⁺ doublet, why was the 5928 keV state populated so strongly in the ²⁸Si(p, t)²⁶Si reaction [258], while the 0⁺ state was populated so weakly? One would expect natural parity states to be populated much more strongly. Note that in [258], the 5928 keV state was labeled as 5916 keV as a result of the uncertain calibration of lower-lying levels [273], and it would be worthwhile to revisit the data from that measurement in light of the more precise energy measurements currently available. Another question is why is the 5890 keV 0⁺ state so readily observable in the ²⁴Mg(³He, n γ)²⁶Si studies [266, 268, 269, 271], but no neutrons were observed populating the state in the ²⁴Mg(³He, n)²⁶Si measurement [261], which seemingly had the resolution to observe it? Finally, the question as to whether we are seeing too many 0⁺ levels and the assertion in [263] of a missing 1⁻ level clearly strains our ability to claim complete knowledge of the relevant ²⁶Si level structure.

The sensitivity study by Iliadis et al [241] identified a number of other reactions that, while not direct producing or destroying ²⁶Al, do affect its final abundance in massive stars. The most influential are the ²⁵Mg(α, n)²⁸Si, the ²³Na(α, p)²⁶Mg, and the neutron capture reactions ²⁴Mg(n, γ)²⁵Mg and ²⁵Mg(n, γ)²⁶Mg. We discuss these reactions separately in the sections below.

3.5.1.  ²⁵Mg(α, n)²⁸Si

3.5.2.  ²³Na(α, p)²⁶Mg

3.5.3.  ²⁴Mg(n, γ)²⁵Mg and ²⁵Mg(n, γ)²⁶Mg