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Stars with initial masses between about 0.8 and 10 M dominate the stellar population in our Milky Way Galaxy. This mass interval spans a huge range in stellar lifetimes, from the longest lived low-mass stars, that have existed for as long as our Galaxy (≈ 1.2 × 1010 years) to the most massive of this range, whose lives are over in the blink of a cosmic eye (≲ 20 million years). These stars are numerous because of the shape of the initial mass function which peaks at ≈ 1 M. Their importance is underlined by that fact that they experience a diversity of rich nucleosynthesis, making them crucial contributors to the chemical evolution of elements in our Universe (e.g., Travaglio et al. 2001a; Romano et al. 2010; Kobayashi, Karakas, & Umeda 2011b). When these stars evolve they lose mass through strong stellar outflows or winds and it has been estimated that they have produced nearly 90% of the dust injected into the interstellar medium (ISM) of our Galaxy, with massive stars accounting for the rest (Sloan et al. 2008). Furthermore, galaxies dominated by intermediate-age stellar populations have a significant fraction of their starlight emitted by low- and intermediate-mass stars, especially when they evolve off the main sequence to the giant branches (Mouhcine & Lançon 2002; Maraston 2005; Maraston et al. 2006; Tonini et al. 2009; Melbourne et al. 2012).

For low- and intermediate-mass stars the most important nucleosynthesis occurs when the stars reach the giant branches. It is during the ascent of the red giant branch (RGB) that the first dredge-up occurs. This changes the surface composition by mixing to the surface material from the interior that has been exposed to partial hydrogen (H) burning. It is also on the upper part of the RGB where extra mixing processes occur in the envelopes of low-mass giants. These are processes not included in traditional calculations which assume convection is the only mixing mechanism present. Such processes may include meridional circulation, shear mixing, and various hydrodynamic and magnetic mixing processes. Empirically we know that something occurs that results in further products of H-burning nucleosynthesis becoming visible at the surface.

The more massive stars in our selected mass range will also experience a second dredge-up, which occurs following core helium (He) exhaustion as the star begins its ascent of the giant branch for the second time, now called the asymptotic giant branch, or AGB. It is on the AGB where we expect the largest changes to the surface composition. These are driven by a complex interplay of nucleosynthesis and mixing. The nucleosynthesis is driven by thermal instabilities in the He-burning shell, known as shell flashes or thermal pulses. The products of this burning, mostly carbon, may be mixed to the stellar surface by recurrent convective mixing episodes. These mixing episodes can occur after each thermal pulse and are known as third dredge-up events.

Thermal pulses are responsible for a large variety of stellar spectral types. Stars begin their lives with an atmosphere that is oxygen rich, in the sense that the ratio of the number of carbon to oxygen atoms n(C) / n(O) is less than unity. Recurring third dredge-up on the AGB can add enough carbon to the envelope that the star becomes carbon rich with n(C) / n(O) ≥ 1, hence becoming a ‘carbon star’ (or C star). There are many different types of C stars including both intrinsic, meaning that they result from internal evolution (as described above, e.g., C(N) stars) or extrinsic, where it is mass transfer from a close binary C star that produces n(C) / n(O) ≥ 1 in a star that is not sufficiently evolved to have thermal pulses itself (e.g., CH stars and dwarf C stars; Wallerstein & Knapp 1998). It is also the third dredge-up that mixes to the surface the heavy elements such as barium and lead that are produced by the slow neutron capture process (the s-process). This can result in S-stars, barium stars, and technetium-rich stars (Wallerstein & Knapp 1998). Strong stellar winds then expel this enriched material into the ISM, where it can contribute to the next generation of star formation.

Intermediate-mass AGB stars may also experience hot bottom burning (HBB), where the bottom of the convective envelope penetrates into the top of the H-burning shell. Proton-capture nucleosynthesis occurs at the base of the mixed envelope (Blöcker & Schoenberner 1991; Lattanzio 1992; Boothroyd, Sackmann, & Wasserburg 1995). Third dredge-up operates alongside HBB and this can lead to some interesting results, such as substantial production of primary nitrogen, together with other hydrogen-burning products including sodium and aluminium.

The short lifetime of those AGB stars that experience HBB (τ ≲ 100Myr) has implicated them as potential polluters of Galactic globular clusters (GCs), which show abundance trends consistent with hot H burning (Gratton, Sneden, & Carretta 2004; Gratton, Carretta, & Bragaglia 2012; Prantzos, Charbonnel, & Iliadis 2007). The ability of detailed models to match the observed abundance trend depends on highly uncertain assumptions about the treatment of convection and mass loss in stellar models (e.g., Fenner et al. 2004; Karakas et al. 2006a; Ventura & D’Antona 2009).

Not so long ago there was a belief that if you were interested in the chemical evolution of the Galaxy, or indeed the Universe, then all you needed was yields from core-collapse supernovae (SNe), and perhaps Type I supernovae (e.g., Timmes, Woosley, & Weaver 1995). But with an increased understanding of the breadth and depth of nucleosynthesis in AGB stars has come clear evidence that the picture is simply incomplete without them. It has been shown by Kobayashi et al. (2011b) that AGB models are essential to reproduce the solar system abundances of carbon, nitrogen, and the neutron-rich isotopes of oxygen and neon. Similarly, Renda et al. (2004) and Kobayashi et al. (2011a) showed the importance of AGB stars for fluorine. Fenner et al. (2004) performed a similar study for magnesium, highlighting the contribution from intermediate-mass AGB stars of low metallicity to the chemical evolution of 25Mg and 26Mg. The importance of AGB stars to understanding the composition anomalies seen in globular clusters is just another reason why they are of such interest to contemporary astrophysics.

1.1. Definitions and overview of evolution

We will here be concerned with stars with masses between about 0.8 and 10 M. Stars more massive than this proceed through all nuclear burning phases and end their lives as core-collapse supernovae. While these massive stars are relatively rare they inject considerable energy and nucleosynthesis products into the galaxy per event. For this reason they are extremely important when considering the evolution of galaxies. Their remnants are either neutron stars or black holes (for the evolution and nucleosynthesis of massive stars we refer the reader to Langer 2012; Nomoto, Kobayashi, & Tominaga 2013).

Stars that will become AGB stars begin their journey with core H and He burning (and possibly C burning on the ‘super-AGB’; see below), before they lose their outer envelopes to a stellar wind during the AGB phase of stellar evolution. It is convenient to define mass ranges according to the evolutionary behaviour the stars will experience. The exact numerical values will, of course, depend on the star’s composition and possibly other effects (such as rotation, which we ignore for now).

The definitions we will use are given below and shown in Figure 1 for solar metallicity. A reduction in the global stellar metallicity will shift the borders introduced here to a lower mass (e.g., core C burning will ignite at about 7 M at Z = 10-4 instead of about 8 M at Z = Z ≈ 0.014). We introduce some new nomenclature in this diagram, while maintaining the definitions of ‘low’ and ‘intermediate’ mass as given in the existing literature.

Figure 1

Figure 1. Schematic showing how stellar mass determines the main nuclear burning phases at solar metallicity, as well as the fate of the final remnant. This defines the different mass intervals we will deal with in this paper. Note that the borders are often not well determined theoretically, depending on details such as mass loss and the implementation of mixing, for example. This is particularly true for the borders around the region of the electron-capture supernovae. Likewise, all numbers are rough estimates, and depend on composition in addition to details of the modelling process.

1.1.1. The lowest mass stars

We define the ‘lowest mass stars’ as those that burn H in their core but take part in no further (significant) nuclear burning processes.

1.1.2. The low-mass stars

We have defined ‘low-mass stars’ to be those with initial masses between about 0.8 and 2 M which experience He ignition under degenerate conditions, known as the core He flash (Demarque & Mengel 1971; Despain 1981; Deupree 1984; Dearborn, Lattanzio, & Eggleton 2006; Mocák et al. 2009). Stars more massive than this succeed in igniting He gently. These low-mass stars will experience core He burning and then all but the least massive of these will go on to the AGB (without an appreciable second dredge-up), ending their lives as C-O white dwarfs (WDs, see Figure 1).

1.1.3. The intermediate-mass stars

We then enter the domain of ‘intermediate-mass stars’, a name well known in the literature. Here we have broken this mass range into three distinct sub-classes, based on C ignition and their final fate. We will only use these new names when the sub-divisions are important, otherwise we simply call them ‘intermediate-mass stars’.

1.1.4. The lower intermediate mass stars

These stars are not sufficiently massive to ignite the C in their core, which is now composed primarily of C and O following He burning. We say the star is of ‘lower intermediate mass’, being about 2 − 7 M. These stars will proceed to the AGB following core He exhaustion, and the more massive of them will experience the second dredge-up as they begin their ascent of the AGB. They will end their lives as C-O white dwarfs.

1.1.5. The middle intermediate mass stars

At slightly higher masses we find C ignites (off centre) under degenerate conditions. We have defined these stars as ‘middle intermediate-mass stars’. These stars go on to experience thermal pulses on what is called the ‘super-AGB’; they are distinguished from genuine massive stars by the fact that they do not experience further nuclear burning in their cores. Super-AGB stars were first studied by Icko Iben and collaborators (e.g., Ritossa, Garcia-Berro, & Iben 1996), and their final fate depends on the competition between mass loss and core growth. If they lose their envelope before the core reaches the Chandrasekhar mass, as is the usual case, then the result is an O-Ne white dwarf.

1.1.6. The massive intermediate mass stars

If, on the other hand, the core grows to exceed the Chandrasekhar mass then these stars may end their lives as electron-capture supernovae. Stars in this very narrow mass range (perhaps less than 0.5 M) we shall call ‘massive intermediate-mass stars’.

It is still unclear what fraction of super-AGB stars explode as electron-capture supernovae, the details being dependent on uncertain input physics and implementation choices (Poelarends et al. 2008). The existence of massive white dwarfs (Gänsicke et al. 2010), with masses above the C-O core limit of ≈ 1.1 M lends some support to the scenario that at least some fraction evade exploding as supernovae. The super-AGB stars that do explode as electron-capture supernovae have been proposed as a potential site for the formation of heavy elements via the rapid neutron capture process (the r-process; Wanajo et al. 2009; Wanajo, Janka, & Müller 2011). A review of this field is therefore particularly timely as we are only now becoming aware of the nucleosynthesis outcomes of super-AGB stars and their progeny (Siess 2010; Doherty et al. 2014a, 2014b).

1.1.7. The massive stars

Stars with masses greater than about 10 M we call ‘massive stars’ and these will proceed through Ne/O burning and beyond, and end their lives as iron core collapse supernovae. Note that there is a rich variety of outcomes possible, depending on the way one models mixing and other processes, and we do not show all of the different sub-cases here. We have tried to maintain the existing definitions in the literature, while adding some divisions that we think are useful. We also reserve the use of the word ‘massive’ for those stars that end their lives as supernovae, being either ‘massive intermediate stars’ in the case of electron-capture supernovae, or the traditional ‘massive stars’ for the case of iron core-collapse supernovae.

1.2. Stellar yield calculations

Stellar yields are an essential ingredient of chemical evolution models. Prior to 2001, the only stellar yields available for low- and intermediate-mass stars were for synthetic AGB evolution models or from a combination of detailed and synthetic models (van den Hoek & Groenewegen 1997; Forestini & Charbonnel 1997; Marigo 2001; Izzard et al. 2004).

Synthetic AGB models are generally calculated by constructing fitting formulae to the results of detailed models, rather than by solving the equations of stellar evolution. This approach was originally motivated by the linear core-mass versus luminosity relation noted by Paczyński (1970). It was soon realised that many other important descriptors and properties of AGB evolution could be similarly parameterised, saving the huge effort that goes into a fully consistent solution of the equations of stellar evolution, with all of the important input physics that is required (opacities, equations of state, thermonuclear reaction rates, convective mixing, etc.). These models can be used to examine rapidly the effect of variations in some stellar physics or model inputs. One must remember of course that there is no feedback on the structure. Any change that would alter the stellar structure such that the parameterised relations also change is not going to be included in the results. Nevertheless, even within this limitation there are many uses for synthetic models. Further, we are now starting to see the next generation of synthetic codes. These sophisticated codes are more like hybrids, combining parameterised evolution with detailed envelope integrations. An example is the Colibri code of Marigo et al. (2013).

With the growth of cluster computing it is now common to have access to thousands of CPU nodes. It is possible for stellar models of many different masses and compositions to be calculated in detail on modern computer clusters. In this way we can obtain results from detailed models in reasonable times. The first stellar yields from detailed AGB models were published by Ventura et al. (2001) and Herwig (2004b) but for limited ranges of masses and/or metallicities. The first stellar yields for a large range of masses, and metallicities from detailed AGB models were published by Karakas & Lattanzio (2007), with an update by Karakas (2010. In Section 5 we provide an updated list of the latest AGB stellar yields that are available in the literature.

In Figure 2 and in what follows we show stellar evolutionary sequences that were computed using the Mount Stromlo/Monash Stellar Structure code. This code has undergone various revisions and updates over the past decades (e.g., Lattanzio 1986, 1989, 1991; Frost & Lattanzio 1996b; Karakas & Lattanzio 2007; Campbell & Lattanzio 2008; Karakas, Campbell, & Stancliffe 2010; Karakas, García-Hernández, & Lugaro 2012). We will highlight particular improvements that affect the nucleosynthesis in Section 3. We note that the stellar evolutionary sequences described here are calculated using a reduced nuclear network that includes only H, He, C, N, and O. The wealth of data on abundances from stars necessitates the inclusion of more nuclear species. Most of these are involved in reactions that produce negligible energy (e.g., the higher order H burning Ne-Na and Mg-Al reactions; Arnould, Goriely, & Jorissen 1999). For this reason, a post-processing nucleosynthesis code is usually sufficient, provided there is no feedback on the structure from the reactions not included in the evolutionary calculations. This is indeed usually the case.

Figure 2

Figure 2. A Hertzsprung-Russell (HR) diagram showing the evolutionary tracks for masses of 1, 2, 3, and 6 M with a global metallicity of Z = 0.02. The evolutionary tracks show the evolution from the ZAMS through to the start of thermally-pulsing AGB. The thermally-pulsing phase has been removed for clarity. The location of the tip of the RGB is indicated by the asterisk.

We take the results from our evolutionary calculations and use them as input for our post-processing nucleosynthesis code Monsoon (Cannon 1993; Frost et al. 1998a) in order to calculate the abundances of many elements and isotopes (for a selection of recent papers we refer the interested reader to Campbell & Lattanzio 2008; Lugaro et al. 2012; Kamath, Karakas, & Wood 2012; Karakas et al. 2012; Shingles & Karakas 2013; Doherty et al. 2014a). In Monsoon we require initial abundances (usually scaled solar) along with nuclear reaction rates and β-decay lifetimes, and include time-dependent convection using an advective algorithm. We couple the nuclear burning with convective mixing in relevant regions of the star. It is important to remember that the results presented here depend on the input physics and numerical procedure, with different codes sometimes finding different results. For example, the inclusion of core overshoot during the main sequence and core He-burning will lower the upper mass limit for a C-O core AGB star from ≈ 8 M to ≈ 6 M (e.g., Bertelli et al. 1986a, 1986b; Lattanzio et al. 1991; Bressan et al. 1993; Fagotto et al. 1994).

The most recent reviews of AGB evolution and nucleosynthesis include Busso, Gallino, & Wasserburg (1999), with a focus on nucleosynthesis and the operation of the s-process, and Herwig (2005), who reviewed the evolution and nucleosynthesis of AGB stars in general, including a discussion of multi-dimensional hydrodynamical simulations relevant to AGB star evolution. Since 2005 there have been many advances, including insights into AGB mass loss provided by the Spitzer and Herschel Space Observatories, new theoretical models of AGB stars covering a wide range of masses and compositions, and the publication of stellar yields from detailed AGB star models. In this review we focus on theoretical models of low- and intermediate-mass stars and in particular on recent progress in calculating AGB yields. Not only are yields needed for chemical evolution modelling but they are also needed to interpret the wealth of observational data coming from current surveys such as SkyMapper (Keller et al. 2007) and SEGUE (Yanny et al. 2009), which are geared toward discovering metal-poor stars in the Galactic halo. Future surveys and instruments (e.g., the GAIA-ESO survey, HERMES on the AAT, APOGEE, LAMOST) will also require accurate stellar yields from stars in all mass ranges in order to disentangle the Galactic substructure revealed through chemical tagging (Freeman & Bland-Hawthorn 2002).

Finally we note that, as we will discuss in Section 2.2.4, there is compelling evidence for some form of mixing on the RGB that is needed to explain the abundances seen at the tip of the RGB. The standard models simply fail in this regard. While the number of isotopes affected is reasonably small (e.g., 3He, 7Li, 13C) it is essential to include the effect of this mixing in order to properly model the chemical evolution of those few isotopes. Usually, a set of stellar yields is calculated based on standard models, which we know are wrong because they fail to match the observed abundances along the RGB.

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