GALACTIC CHEMICAL EVOLUTION AND SOLAR s-PROCESS ABUNDANCES: DEPENDENCE ON THE ¹³C-POCKET STRUCTURE

The general structure of the GCE model adopted in this work is the same described by Travaglio et al. (2004). The GCE model follows the composition of stars, stellar remnants, interstellar matter (atomic and molecular gas), and their mutual interaction, in the three main zones of the Galaxy, halo, thick disk, and thin disk. We concentrate on the chemical evolution inside the solar annulus, located 8.5 kpc from the Galactic center. The thin disk is divided into independent concentric annuli, and we neglect any dependence on Galactocentric radius.

The chemical evolution is regulated by the star formation rate (SFR), initial mass function (IMF), and nucleosynthesis yields from different stellar mass ranges and populations. The SFR has been determined self-consistently as the result of aggregation, which are interacting and interchanging processes of the interstellar gas that may occur spontaneously or stimulated by the presence of other stars. The stellar contributions from different mass ranges or from single and binary stars are treated separately: we distinguish between single low- and intermediate-mass stars ending their life as a He or C–O white dwarf (0.8 M_☉ ⩽ M < 8 M_☉), single massive stars exploding as Type II supernovae (SNeII, 8 M_☉ ⩽ M ⩽ 100 M_☉), and binary stars that give rise to Type Ia supernova (SNIa) events. SFR and IMF are the same as adopted by Travaglio et al. (2004).

In Figure 1 (top panel), the SFR rate in the three Galactic zones is displayed versus [Fe/H]. Galactic halo and thick disk are assumed to form on a relatively short timescale: after only <0.5 Gyr the metallicity increases up to [Fe/H] ∼−1.5 (halo phase), to reach [Fe/H] ∼−1.0 faster than in 2 Gyr. The thin-disk phase in our GCE model starts after ∼1 Gyr, at [Fe/H] ∼−1.5. The corresponding [O/Fe] versus [Fe/H] is shown in Figure 1 (bottom panel), together with an updated compilation of observational data (see caption). Because oxygen is mainly synthesized by short-lived SNeII, and under the hypothesis that Fe is mostly produced by long-lived SNeIa (∼one-third by SNeII and ∼two-thirds by SNeIa), the presence of a knee in the trend of [O/Fe] versus [Fe/H] indicates the delayed contribution to iron by SNeIa.

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We refer to Travaglio et al. (2004 and references therein) for more details on the adopted GCE model.

The GCE is computed as function of time up to the present epoch (t_Today = 13.8 Gyr, updated by WMAP; Spergel et al. 2003; Bennett et al. 2013). Given that the solar system formation occurred 4.6 Gyr ago, the Galactic time corresponding to the birth of the solar system is t_☉ = 9.2 Gyr, about 0.7 Gyr later than found by Travaglio et al. (2004). This temporal shift has been achieved by slightly reducing the Fe contribution by SNeIa.

Solar abundances have been updated according to Lodders et al. (2009), while Travaglio et al. (2004) adopted solar values by Anders & Grevesse (1989).

Stellar yields by Rauscher et al. (2002) and Travaglio et al. (2004a) are used for SNeII and SNeIa, respectively. A detailed description of the AGB yields adopted in this work is given in Section 2.2.

We have considered a set of five AGB models with low initial mass (M = 1.3, 1.4, 1.5, 2, and 3 M_☉, representing the AGB mass range 1.3 ⩽M/M_☉ < 4; hereafter LMS) and two AGB models with intermediate initial mass (M = 5 and 7 M_☉, among 4 ⩽M/M_☉ < 8; hereafter IMS).

The s-process AGB yields have been obtained with a post-process nucleosynthesis method (Gallino et al. 1998) based on input data (like temperature and density during TPs, the mass of the H shell and He intershell, the overlapping factor, and the residual mass of the envelope) of full evolutionary FRANEC models by Straniero et al. (2003) for LMS and Straniero et al. (2000) for IMS. For details on AGB models, we refer to Bisterzo et al. (2010). Here we briefly review the basic information useful to this work.

As described in Section 1, the total mass of the pocket and the ¹³C and ¹⁴N profiles inside the pocket itself are not well established, owing to the lack of a definite description of the physical mechanisms that allow the diffusion of a few protons into the He intershell. In our LMS models, the amount of ¹³C and ¹⁴N in the ¹³C pocket are artificially introduced. The ¹³C and ¹⁴N abundances are treated as free parameters kept constant pulse by pulse. We adopt a specific shape and size of the ¹³C pocket called case ST (see Section 3), which was used to reproduce the solar main component of the s process as the average of two AGB models with initial mass M = 1.5 and 3.0 M_☉ and half solar metallicity (see Arlandini et al. 1999).

To interpret the spectroscopic s-process spread observed in C- and s-rich stars at a given metallicity, LMS models are computed for a large range of ¹³C pockets, obtained by multiplying or dividing the ¹³C (and ¹⁴N) abundances of case ST by different factors and leaving the mass of the pocket constant. The case ST × 2 corresponds to an upper limit, because further proton ingestion leads to the formation of ¹⁴N at expenses of ¹³C. The minimum ¹³C pocket that significantly affects the s distribution depends on the initial iron content of the star, given that the number of neutrons available per iron seeds increases with decreasing metallicity. As a minimum ¹³C pocket, we assume case ST × 0.1 at disk metallicities and case ST × 0.03 in the halo (see discussion by Bisterzo et al. 2010, 2011).

LMS models of M = 1.3, 1.4, 1.5, and 2 M_☉ have been computed by following the interpolation formulae given by Straniero et al. (2003) for −1.0 ⩽ [Fe/H] ⩽ 0.0 and then further extrapolating the stellar parameters from [Fe/H] = +0.2 down to [Fe/H] = −3.6 as described by Bisterzo et al. (2010). Note that for M = 1.3 M_☉ models, the conditions for the activation of the TDU episodes are never reached for metallicities higher than [Fe/H] ∼−0.6 (Straniero et al. 2003), and we compute 1.3 M_☉ yields starting from [Fe/H] = −0.6 down to −3.6.

Starting from Domínguez et al. (1999; see also Boothroyd & Sackmann 1988), it was shown that, for a given initial mass, the core mass increases with decreasing metallicity and AGB models with M ≳ 3 M_☉ and [Fe/H] ∼−1.3 are not far from the transition zone between LMS and IMS stars. As discussed by Bisterzo et al. (2010), we have assumed that AGB stars with M = 3 M_☉ should behave as IMS for [Fe/H] ≲ −1.6. Thus, our 3 M_☉ models have been have been computed by extrapolating the stellar parameters from 3 M_☉ models by Straniero et al. (2003) in the metallicity interval between −1.6 ⩽ [Fe/H] ⩽ +0.2.

We recall that low metallicity IMS stars may be affected by an extremely efficient dredge-up called hot TDU (Herwig 2004; Lau et al. 2009), which may influence the structure of the star and its evolution. Because nucleosynthesis models that include hot TDU are still subject of study, we have computed IMS yields only for [Fe/H] ⩾−1.6 (Bisterzo et al. 2010).

IMS models are based on full evolutionary AGB models by Straniero et al. (2000). Their 5.0 M_☉ models at [Fe/H] = 0 and −1.3 show comparable characteristics, e.g., temperature during TPs, TDU, and He-intershell masses. Thus, we have assumed that the structure of 5.0 M_☉ models from [Fe/H] = +0.2 down to [Fe/H] = −1.6 are barely distinguishable from solar. Solar 5 and 7 M_☉ models described by Straniero et al. (2000) have comparable He-intershell mass and temperature at the bottom of the TPs, while the TDU mass is a factor of ∼6 lower in 7 M_☉ model. Starting from these stellar characteristics, we have extrapolated the 7.0 M_☉ models in the metallicity range between −1.6 ⩽ [Fe/H] ⩽ +0.2.

The treatment of mass loss in IMS models is largely uncertain (see, e.g., Ventura & D'Antona 2005b), and the number of TPs with TDU experienced by IMS stars may vary by a factor of three or more, affecting the structure and nucleosynthesis of the star itself. With the efficient mass loss adopted in our IMS models, AGB with M = 5 and 7 M_☉ experience 24 TPs followed by TDU (Bisterzo et al. 2010).

IMS AGB stars play a minor role in the Galactic enrichment of s-process isotopes, with the exception of a few neutron-rich isotopes as ⁸⁶Kr, ⁸⁷Rb, and ⁹⁶Zr (Travaglio et al. 2004). Indeed, the mass of the He intershell is about a factor of 10 lower in IMS than in LMS. Thus, the overall amount of material dredged into the envelope of IMS decreases by at least one order of magnitude with respect to LMS (Straniero et al. 2000). Moreover, IMS experience hot bottom burning during the interpulse phase: the bottom of the convective envelope reaches the top of the H-burning shell and the temperature at the base is large enough (T ≳ 4 × 10⁷ K) to activate the CN cycle, thus converting ¹²C to ¹⁴N (see, e.g., Karakas & Lattanzio 2003; Ventura & D'Antona 2005a). Hot bottom burning may even inhibit the formation of the ¹³C pocket in IMS of low metallicity (Goriely & Siess 2004; Herwig 2004). As a consequence, the ¹³C(α, n)¹⁶O neutron source is expected to have a small or even negligible effect on neutron capture isotopes heavier than A ∼ 90. On the basis of these considerations, new AGB IMS yields have been computed with a negligible ¹³C pocket. The introduction of a small ¹³C pocket (M(¹³C) = 10⁻⁷M_☉), as assumed in the old IMS models adopted by Travaglio et al. (2004), has negligible effects on solar s-process predictions (see Section 2.3).

On the other hand, a higher temperature is reached at the bottom of the TPs of IMS (T ∼ 3.5 × 10⁸ K), so that the ²²Ne(α, n)²⁵Mg reaction is efficiently activated. Because of the high peak neutron density (N_n ∼ 10¹² n cm⁻³), ⁸⁶Kr, ⁸⁷Rb, and ⁹⁶Zr are strongly overproduced, owing to the branchings at ⁸⁵Kr, ⁸⁶Rb, and ⁹⁵Zr. The observational evidence of the strong activation of the ²²Ne(α, n)²⁵Mg reaction (associated to IMS) is the excess of Rb with respect to Zr (see, e.g., Lambert et al. 1995; Tomkin & Lambert 1999; Abia et al. 2001, and most recently Yong et al. 2008; García-Hernández et al. 2009, 2013; D'Orazi et al. 2013). The high [Rb/Zr] observed in some OH/IR AGB stars seems to be incompatible with IMS predictions. Karakas et al. (2012) proposed that delayed superwinds may increase the number of TPs and thus the [Rb/Fe] and [Rb/Zr] predictions. A complementary possibility to solve the mismatch between observed and predicted [Rb/Zr] in OH/IR AGB stars has been suggested by García-Hernández et al. (2009) and van Raai et al. (2012), who discussed how model atmospheres of luminous pulsating AGB stars may be incomplete⁸ and [Rb/Fe] may be overestimated.

Given the present uncertainties, our 5 and 7 M_☉ models may experience a larger number of TPs under the hypothesis of a less efficient mass loss. However, the resulting effect on solar s-process predictions is marginal (with the exception of the neutron-rich isotopes ⁸⁶Kr, ⁸⁷Rb, and ⁹⁶Zr; see Section 2.3), because the solar s contribution from LMS stars dominates over IMS.

In IMS with initial mass of M ∼ 6–8 M_☉, the temperature at the base of the convective envelope further increases (T ≳ 1 × 10⁸ K), leading to a greater degree of proton-capture nucleosynthesis that efficiently activates CNO, NeNa, and MgAl cycles as well. These more massive AGB stars, ending as Ne–O core white dwarfs or possibly less massive neutron stars, are called super-AGB stars (SAGB). The mass and metallicity limits of SAGB depend on models, and the treatment of core carbon ignition and burning and the efficiency of the TDU are very uncertain (e.g., Siess 2010; Ventura et al. 2013). At present, SAGB yields have not been included in our GCE calculations because no information about heavy s-process elements is available in literature (Karakas et al. 2012; Doherty et al. 2014).

About 1400 AGB models with initial masses of M = 1.4, 1.5, and 2 M_☉ have been computed in the metallicity range between [Fe/H] = −3.6 up to +0.2, for a range of ¹³C pockets and a total of 28 metallicities. About 300 AGB models with initial masses of M = 1.3 M_☉ have been computed between [Fe/H] = −3.6 up to −0.6, for a range of ¹³C pockets and a total of 20 metallicities. Note that the s-process abundances in the interstellar medium at the epoch of the solar system formation are essentially derived from previous AGB generations starting from [Fe/H] ≳−1.6 (see Travaglio et al. 2004; Serminato et al. 2009). Thus, AGB models with a more refined grid of 20 metallicities have been computed between [Fe/H] = −1.6 and 0.⁹

Similarly, about three hundred 3 M_☉ models have been run between [Fe/H] = −1.6 up to +0.2, for a range of ¹³C pockets and a total of 20 metallicities. Forty M = 5 and 7 M_☉ models with a negligible ¹³C pocket have been calculated between [Fe/H] = −1.6 up to +0.2, for 20 metallicities in total.

Linear interpolations/extrapolations over the whole mass AGB range (1.3 ⩽ M/M_☉ < 8, with mass steps of 0.1 M_☉) have been carried out for AGB yields not explicitly calculated. With respect to Travaglio et al. (2004), we have introduced new AGB models of initial masses 1.3, 1.4, and 2 M_☉.

All AGB yields have been computed with an updated neutron capture network according to the online database KADoNiS¹⁰ and more recent measurements: ^{92, 94, 96}Zr (Tagliente et al. 2010, 2011a, 2011b), ^{186, 187, 188}Os (Mosconi et al. 2010), and the p-only ¹⁸⁰W (Marganiec et al. 2010), as well as ⁴¹K and ⁴⁵Sc (Heil et al. 2009), ^{24, 25, 26}Mg (Massimi et al. 2012), ⁶³Ni (Lederer et al. 2013), and ^{64, 70}Zn (Reifarth et al. 2012), among light isotopes that marginally affect the s-process contribution. Note that we employed Mutti et al. (2005) for ^{80, 82, 83, 84, 86}Kr, Patronis et al. (2004) for ^{136, 137}Cs, Reifarth et al. (2003) for ^{148, 149}Pm, and Best et al. (2001) for ^{152, 154}Eu.

Furthermore, AGB initial abundances are scaled to the updated solar values by Lodders et al. (2009).

The s-process GCE predictions at the epoch of the solar system formation are displayed in Figure 2 as percentages of the abundances by Lodders et al. (2009). The s-only isotopes are represented by solid circles. Different symbols have been used for ⁹⁶Zr (big asterisk), ¹⁸⁰Ta (empty circle), which also receives contributions from the p process and from neutrino–nucleus interactions in massive stars, and ¹⁸⁷Os (empty triangle), which is affected by the long-lived decay of ¹⁸⁷Re (4.1 × 10¹⁰ yr). We distinguish ²⁰⁸Pb, which is produced at ∼50% by LMS of low metallicity, with a big filled square.

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In the framework of GCE, we have considered a weighted average among the various ¹³C-pocket strengths (see Section 1). Observations of s-process rich stars at disk metallicity (see, e.g., Käppeler et al. 2011, their Figure 12) suggest that most of them lie in the range between case ST × 1.5 down to ST/1.5. Very few stars can be interpreted by case ST × 2. Actually, for ¹³C pockets below case ST/6 the s enhancement becomes negligible. We exclude case ST × 2 from the average of the ¹³C pockets, and we give a weight of ∼25% to case ST × 1.3. The unbranched s-only ¹⁵⁰Sm can be taken as reference isotope for the whole s-process distribution, because its solar abundance is well defined (5% uncertainty as a rare earth element, "REE") and the neutron capture cross section is given at 1%.

A complete list of s-process percentages of all isotopes and elements from Kr to Bi is given in Table 1, where updated GCE results are compared with previous GCE predictions by Travaglio et al. (2004). The theoretical s-process predictions by Travaglio et al. (2004) were normalized to solar abundances by Anders & Grevesse (1989). The s percentages of LMS, IMS, and the total s contribution (LMS + IMS) are reported for GCE results by Travaglio et al. (2004; Columns 3, 4, and 5) and this work (Columns 6, 7, and 8). Values in column 8 correspond to those displayed in Figure 2. In comparison to GCE results, we list in Column 2 the main s process contributions by Bisterzo et al. (2011), obtained as in Arlandini et al. (1999) by averaging between AGB models of M = 1.5 and 3 M_☉ and half solar metallicity.

The variations between GCE results by Travaglio et al. (2004) and those computed in this work (see Table 1) are partly due to the updated nuclear reaction network and new solar abundances.

The solar abundance distribution is essentially based on CI carbonaceous chondrite measurements in terrestrial laboratories with increasingly accurate experimental methods. Among the exceptions are volatile elements such as CNO, which are evaluated from photospheric determinations, or noble gases such as Ne, evaluated from solar corona winds. Kr and Xe solar abundances are derived theoretically from neutron-capture element systematics (Palme & Beer 1993; Reifarth et al. 2002). Since 1989, C, N, and O abundances have been steadily revised downward thanks to progress in atmospheric models (see, e.g., Asplund 2005), partially affecting the isotopic mass fraction of heavier isotopes.¹¹ Moreover, the photospheric abundances observed today are different from those existing at the beginning of the solar system (4.6 Gyr ago), because of the element settling from the solar photosphere into the Sund 's interior. Lodders et al. (2009) found that original protosolar values of elements heavier than He (Z) were ∼13% larger than observed today (whereas He increases by about ∼15%).

In Figure 3, we show updated GCE results normalized to solar abundances by Lodders et al. (2009; black symbols) and Anders & Grevesse (1989; gray symbols; as made by Travaglio et al. 2004). Noteworthy solar abundance variations¹² (>10%) are CNO (∼−30%), P (∼−20%), S (−25%), Cl (+37%), Kr (+24%), Nb (+13%), I (+22%), Xe (+16%), and Hg (+35%).

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Additional differences between the GCE results shown in Table 1 are derived from experimental cross section measurements and theoretical nuclear improvements provided in the last decade.

New GCE calculations include the recent theoretical evaluation of the ²²Ne(α, n)²⁵Mg rate by Longland et al. (2012), which is based on the direct experimental measurement by Jaeger et al. (2001). At AGB temperatures (T₈ ∼ 2.5–3.5), the ²²Ne(α, n)²⁵Mg rate by Longland et al. (2012) is very close to the value by Jaeger et al. (2001), and it is about a factor of two lower than the rate we used so far: the lowest limit by Käppeler et al. (1994).¹³ The ²²Ne(α, n)²⁵Mg neutron source produces variations of the s isotopes close to the branching points: updated GCE calculations have reduced the s contribution to few light isotopes, ⁸⁶Kr, ^{85, 87}Rb, and ⁹⁶Zr (and the s-only ⁹⁶Mo), with a complementary increase of ^{86, 87}Sr, owing to the branches at ⁸⁵Kr, ⁸⁶Rb, and ⁹⁵Zr. Minor effects (<10%) are seen for heavier isotopes (see Bisterzo et al. 2013; Figure 1, bottom panel). A discussion of the major branching points of the s process and the effect of the new ²²Ne(α, n)²⁵Mg rate will be given in S. Bisterzo et al. (in preparation).

The total s production of ⁹⁶Zr obtained in 2004 (∼80%) was particularly large. Updated GCE results predict that about half of solar ⁹⁶Zr comes from AGB stars (∼3% from IMS and ∼36% from LMS; see Table 1). Travaglio et al. (2011) estimated an additional non-negligible p-process contribution to ⁹⁶Zr by SNeIa (up to 30%).

However, we remind that ⁹⁶Zr is strongly sensitive to the ⁹⁵Zr(n, γ)⁹⁶Zr rate, which is largely uncertain when being evaluated only theoretically. In this regard, we adopt a rate roughly half the value recommended by Bao et al. (2000), close to that by Toukan & Käppeler (1990), and in agreement with Zr isotopic measurements in presolar SiC grains (Lugaro et al. 2003). Recently, Lugaro et al. (2014) provide a lower estimation of the ⁹⁵Zr(n, γ)⁹⁶Zr rate: at kT ∼ 23 keV, their value is roughly three times lower than that by Bao et al. (2000) and about half of that by Toukan & Käppeler (1990). This results in a decreased GCE s contribution to solar ⁹⁶Zr by ∼10%.

Moreover, ⁹⁶Zr depends on the number of TPs experienced by the adopted AGB models. Our LMS models with M = 1.5, 2, and 3 M_☉ experience several TPs with TDU, from 20 to 35 TPs depending on the mass and metallicity (Bisterzo et al. 2010, their Table 2), reaching temperatures high enough to partly activate the ²²Ne(α, n)²⁵Mg neutron source and to open the branch at ⁹⁶Zr. A stronger mass loss would partly reduce the s contribution to ⁹⁶Zr from LMS AGB stars.

On the other hand, our M = 5 and 7 M_☉ models experience 24 TPs. Given the large uncertainty affecting the treatment of mass loss in IMS (Section 2.2), the number of TPs may increase by a factor of three or more (in particular for M = 7 M_☉ models), leading to a greater overall amount of material dredged up. Owing to the dominant s contribution from LMS stars over IMS, the general effect on solar GCE prediction would be negligible even by increasing the mass of the TDU in both M = 5 and 7 M_☉ models several times. Exceptions are ⁸⁶Kr, ⁸⁷Rb, and ⁹⁶Zr, which receive a non-negligible contribution from IMS stars: by increasing the TDU mass of IMS by a factor of six, the solar prediction to ⁹⁶Zr increases from ∼40% up to ∼60%; similar variations affect ⁸⁶Kr (∼+20%), and larger effects are show by ⁸⁷Rb (from ∼30% up to ∼70%).

As discussed in Section 2.2, new IMS yields are computed with a negligible ¹³C pocket; instead, Travaglio et al. (2004) assumed that a ¹³C pocket with M(¹³C) = 10⁻⁷M_☉ could form in IMS, yielding an increase of ∼10% to solar ⁹⁶Zr, ∼3% to ⁸⁶Kr, and ∼6% to ⁸⁷Rb. Solar GCE predictions of isotopes with A > 100 show marginal variations, because the ¹³C-pocket contribution from IMS is almost negligible (up to a few percent) when compared with that of LMS.

New neutron capture cross-section measurements further modify the s-process distribution. Travaglio et al. (2004) adopted the compilation by Bao et al. (2000), while we refer to KADoNiS (as well as few additional measurements listed above). Important variations come from the new ¹³⁹La(n, γ)¹⁴⁰La rate by Winckler et al. (2006), the ¹⁸⁰Ta^m(n, γ)¹⁸¹Ta rate by Wisshak et al. (2004; including the revised stellar enhancement factor, SEF, by KADoNiS), and the improved treatment of the branch at ¹⁷⁶Lu, which modifies the ¹⁷⁶Lu/¹⁷⁶Hf ratio (Heil et al. 2008). The solar s contribution to La, often used as a reference element to disentangle between s- and r-process enrichment in the atmosphere of peculiar stars, increases by ∼+10% (from 63% to 76%, see Table 1). The solar s production of ¹⁸⁰Ta^m increases from ∼50% to ∼80%, substantially reducing the contribution expected from the p process.

Discrepancies of ∼10% for ¹⁵⁴Gd and ¹⁶⁰Dy and ∼20% for ¹⁹²Pt (see Section 2.4) suggest that large uncertainties affect the neutron capture cross sections at stellar energy (e.g., SEF evaluation) for isotopes with A > 150. Note that ¹⁶⁰Dy may receive a small contribution from the p process (Travaglio et al. 2011). Despite all Pb isotopes having well-determined neutron capture cross sections (see KADoNiS), the contribution to the s-only ²⁰⁴Pb is affected by the branch at ²⁰⁴Tl, which produces variations of ∼10%.

Finally, as recalled above, the new GCE predictions adopt an extended range of AGB yields, including M = 1.3, 1.4, and 2 M_☉ models. In Travaglio et al. (2004), only M = 1.5 and 3 M_☉ models among LMS were used for GCE calculations.

AGB stars with initial mass of M = 1.3 and 1.4 M_☉ experience 5 and 10 TPs followed by TDU, respectively (Bisterzo et al. 2010). This results in an additional s-process contribution of about 5% and 10% at the epoch of the solar system, without modifying the s distribution. Note that for metallicities higher than [Fe/H] ∼−0.6, M = 1.3 M_☉ models do not contribute to the chemical evolution of the Galaxy because the conditions for the activation of the TDU episodes are never reached in our models (see Straniero et al. 2003).

The addition of M = 2 M_☉ yields in GCE computations provides an increase of about 10% of the predicted solar ²⁰⁸Pb, and smaller variations to isotopes with A ≲ 140 (lower than 5%), with the exception of solar ⁹⁶Zr (which is 10% lower). AGB stars with M = 1.5 and 2 M_☉ predict comparable s-process abundances because both models reach similar temperatures during convective TPs and the larger overall amount of material dredged up by the 2 M_☉ model (which experiences about six more TDUs than the 1.5 M_☉ model) is diluted with a more extended envelope (Bisterzo et al. 2010). Thus, in both 1.5 and 2 M_☉ models the marginal activation of the ²²Ne(α, n)²⁵Mg produces a smaller s process contribution to the first s peak (including ⁹⁶Zr) than in 3 M_☉ models, while on average ²⁰⁸Pb is favored, being that the ¹³C(α, n)¹⁶O reaction is the main source of neutrons. Instead, AGB stars with an initial mass of M = 3 M_☉ and [Fe/H] ∼−1 reach higher temperatures at the bottom of the TPs (T₈ = 3.5), feeding more efficiently the first and second s peaks than ²⁰⁸Pb. As a consequence, linear interpolations between M = 1.5 and 3 M_☉ yield, as previously made by Travaglio et al. (2004), induced up to 10% differences in ⁹⁶Zr and ²⁰⁸Pb solar predictions.

Updated GCE calculations plausibly interpret within the nuclear and solar uncertainties all s-only isotopes with A  > 130.

The understanding of the origin of light s-process isotopes with A ⩽ 130 remains enigmatic: we confirm the missing ∼25% predicted solar s contribution to isotopes from ⁸⁶Sr to ¹³⁰Xe (including the s-only ⁹⁶Mo, ¹⁰⁰Ru, ¹⁰⁴Pd, ¹¹⁰Cd, ¹¹⁶Sn, ^{122, 123, 124}Te, and ^{128, 130}Xe) first found by Travaglio et al. (2004). Few of them may receive an additional small contribution from the p process (e.g., 2% to ⁹⁶Mo, 5% to ¹¹⁰Cd, 3% to ¹²²Te, and 6% to ¹²⁸Xe; Travaglio et al. 2011).

In Section 3, we explore the effect of the ¹³C-pocket uncertainty in LMS on GCE predictions at the epoch of the solar system formation.

The solar s-only ¹⁹²Pt predicted by the GCE model is about 20% lower than measured in the solar system. So far, we considered this value plausible within the known uncertainties: the KADoNiS recommended ¹⁹²Pt(n, γ)¹⁹³Pt rate has 20% of uncertainty (590 ± 120 mbarn at 30 keV; Bao et al. 2000), the neutron capture cross sections of ¹⁹¹Os and ¹⁹²Ir are evaluated theoretically at 22%, and the solar Pt abundance is known with 8% of uncertainty (Lodders et al. 2009).

Recently, Koehler & Guber (2013) measured the neutron capture cross sections of Pt isotopes with much improved accuracy and used their experimental results to provide a new theoretical estimation of the ¹⁹²Ir(n, γ) rate. The new Maxwellian-Averaged Cross Sections (MACS) of ¹⁹²Pt(n, γ)¹⁹³Pt (483 ± 20 mbarn at 30 keV; 4% uncertainty) is ∼20% lower than that recommended by KADoNiS, suggesting an increased ¹⁹²Pt prediction (∼90%), which in better agreement with the solar value. On the other hand, the theoretical ¹⁹²Ir(n, γ) rate estimated by Koehler & Guber (2013) is much larger (about +50%) than that by KADoNiS (2080 ± 450 mbarn at 30 keV), reducing again the s contribution to ¹⁹²Pt.

The new GCE prediction of solar ¹⁹²Pt obtained by including neutron capture rates of Pt isotopes and ¹⁹²Ir by Koehler & Guber (2013) is ∼78%. This value may increase up to ∼85% by considering the uncertainty of the theoretical ¹⁹²Ir(n, γ) rate (±22%) and up to 93% by adopting a 2σ uncertainty.

More detailed analyses on ¹⁹²Ir MACS would help to improve the understanding of this branching point and to provide a more accurate solar ¹⁹²Pt estimation (e.g., Rauscher 2012).